Journal articles on the topic 'Casey Inlier'
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1
Carr, Lidena, Russell Korsch, Wolfgang Preiss, Sandra Menpes, Josef Holzschuh, and Ross Costelloe. "Structural and stratigraphic architecture of Australia's frontier onshore sedimentary basins: the Arckaringa, Officer, Amadeus, and Georgina basins." APPEA Journal 51, no. 2 (2011): 703. http://dx.doi.org/10.1071/aj10083.
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The Onshore Energy Security Program—funded by the Australian Government and conducted by Geoscience Australia—has acquired deep seismic reflection data in conjunction with state and territory geological surveys, across several frontier sedimentary basins to stimulate petroleum exploration in onshore Australia. Here, we present data from two seismic lines collected in SA and NT. Seismic line 08GA-OM1 crossed the Arckaringa and Officer basins in SA and the southern-most Amadeus Basin in NT. Seismic line 09GA-GA1 crossed the northeastern part of the Amadeus Basin and the complete width of the southern Georgina Basin in NT. Structural and sequence stratigraphic interpretations of the seismic lines will be presented here, followed by an assessment of the petroleum potential of the basins. Seismic line 08GA-OM1 also crosses the Neoproterozoic to Devonian eastern Officer Basin. The basin is structurally complex in this area, being dominated by south-directed thrust faults and fault-related folds—providing potential for underthrust petroleum plays. The northern margin of the basin is overthrust to the south by the Mesoproterozoic Musgrave Province. To the north, the Moorilyanna Trough of the Officer Basin is a major depocentre of up to 7,000 m deep. Both seismic lines cross parts of the eastern Amadeus Basin. Seismic line 08GA-OM1 shows that the southern margin of the basin is overthrust to the north by the Musgrave Province with the main movement during the Petermann Orogeny. In the northeast, seismic line 09GA-GA1 crosses two parts of the basin separated by the Paleoproteroozic to Mesoproterozoic Casey Inlier (part of the Arunta Region). The northern margin of the basin is imaged seismically as a southward-verging, thinned-skinned thrust belt, showing considerable structural thickening of the stratigraphic succession. Seismic line 09GA-GA1 was positioned to cross that part of the southern Georgina Basin that was considered previously to be in the oil window. Here, the basin has a complex southern margin, with Neoproterozoic stratigraphy being thrust interleaved with basement rocks of the Arunta Region. The main part of the basin, containing a Neoproterozoic to Devonian succession, is asymmetric, thinning to the north where it overlies the Paleoproterozoic Davenport Province. The well, Phillip–2, drilled adjacent to the seismic line, intersected basement at a depth of 1,489 m, and has been used to map the stratigraphic sequences across the basin.
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Heinz, Jürgen, Wolfgang Fiori, Peter Heusser, and Thomas Ostermann. "Cost Analysis of Integrative Inpatient Treatment Based on DRG Data: The Example of Anthroposophic Medicine." Evidence-Based Complementary and Alternative Medicine 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/748932.
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Background.Much work has been done to evaluate the outcome of integrative inpatient treatment but scarcely the costs. This paper evaluates the costs for inpatient treatment in three anthroposophic hospitals (AHs).Material and Methods.Cost and performance data from a total of 23,180 cases were analyzed and compared to national reference data. Subgroup analysis was performed between the cases with and without anthroposophic medical complex (AMC) treatment.Results.Costs and length of stay in the cases without AMC displayed no relevant differences compared to the national reference data. In contrast the inlier cases with AMC caused an average of € 1,394 more costs. However costs per diem were not higher than those in the national reference data. Hence, the delivery of AMC was associated with a prolonged length of stay. 46.6% of the cases with AMC were high outliers. Only 10.6% of the inlier cases with AMC were discharged before reaching the mean length of stay of each DRG.Discussion.Treatment in an AH is not generally associated with an increased use of resources. However, the provision of AMC leads to a prolonged length of stay and cannot be adequately reimbursed by the current G-DRG system. Due to the heterogeneity of the patient population, an additional payment should be negotiated individually.
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Erguvan, Mustafa, and David MacPhee. "Energy and Exergy Analyses of Tube Banks in Waste Heat Recovery Applications." Energies 11, no. 8 (August 12, 2018): 2094. http://dx.doi.org/10.3390/en11082094.
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In this study, energy and exergy analyses have been investigated numerically for unsteady cross-flow over heated circular cylinders. Numerous simulations were conducted varying the number of inline tubes, inlet velocity, dimensionless pitch ratios and Reynolds number. Heat leakage into the domain is modeled as a source term. Numerical results compare favorably to published data in terms of Nusselt number and pressure drop. It was found that the energy efficiency varies between 72% and 98% for all cases, and viscous dissipation has a very low effect on the energy efficiency for low Reynolds number cases. The exergy efficiency ranges from 40–64%, and the entropy generation due to heat transfer was found to have a significant effect on exergy efficiency. The results suggest that exergy efficiency can be maximized by choosing specific pitch ratios for various Reynolds numbers. The results could be useful in designing more efficient heat recovery systems, especially for low temperature applications.
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Wilson, Reginald A. "Geochemistry and petrogenesis of Ordovician arc-related mafic volcanic rocks in the Popelogan Inlier, northern New Brunswick." Canadian Journal of Earth Sciences 40, no. 9 (September 1, 2003): 1171–89. http://dx.doi.org/10.1139/e03-034.
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The Popelogan Inlier consists mainly of mafic volcanic rocks (lapilli tuffs and massive to amygdaloidal, plagioclase-phyric flows) of the Middle Ordovician Goulette Brook Formation. Pyroclastic rocks include high-MgOCrNi picritic tuffs (type I) containing, in some cases, >20% MgO, and related high-MgO andesitic tuff (type II). High-MgO rocks were generated by 3040% partial melting of an enriched mantle source; type II is descended from type I mainly by fractionation of olivine. Mafic flows comprise basaltic andesites (type III) with low trace-element abundances and strongly fractionated, trace-element-enriched andesites (type IV). Types III and IV represent ~20 and ~10% partial melts, respectively, of a mantle source similar to that of the pyroclastic rocks, based on similar ratios of high field strength elements (HFSE). Unlike types I and II, petrogenesis of mafic flows involved fractionation of plagioclase and possibly amphibole. Volcanic arc signatures include negative Nb and Ti anomalies in all basalt types, along with low abundances of HFSE. Trace-element abundances are inconsistent with prior depletion in the back arc and require involvement of a mantle plume or subcontinental lithosphere. The highly magnesian composition of the picrites demands high melting temperatures and rapid transit through the crust, both of which suggest extension of the arc-bearing plate. Compositionally similar rocks in the South Pacific are associated with unusual tectono-magmatic settings involving ridge subduction, which may have established the necessary extensional environment. It is proposed that subduction of a plume-influenced ridge segment could explain the chemistry of the Goulette Brook volcanic rocks.
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Katina, Stanislav. "Detection of non-affine shape outliers for matched-pair shape data." Tatra Mountains Mathematical Publications 51, no. 1 (November 1, 2012): 83–90. http://dx.doi.org/10.2478/v10127-012-0009-9.
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ABSTRACT Cleft lip/palate (CLP) is a relatively common birth defect so dis- figuring that nowadays it is almost always corrected surgically as early as possible. The postnatal surgical correction does not, however, result in a normally growing upper jaw, but instead, owing to scar tissue, one that grows abnormally. It is important to decide if a clinical treatment group is homogeneous. The example involves data from digitally processed lateral X-ray films of 48 boys who have complete unilateral CLP but no other malformation. 22 landmarks were represented by their Procrustes shape coordinates, principal components of matched- pair differences were examined, and the distribution of the 48 shape changes was studied for outliers in the affine and non-affine subspaces of the full Procrustes shape and form space. To separate outliers from inliers we use bagplots. There are no outliers apparent in the affine subspace. In the non-affine subspaces, we found no outliers in the subspace of bending patterns at large scale but four out- liers in the subspace of local changes at small scale. Almost the same outliers were found by form-space PCA. These latter are associated with possible creases of the corresponding thin-plate splines. In those cases we can use the same spline formalism to relax the outlying form to an inlier by optimal relaxation along the curve d´ecolletage that weighs bending energy against Procrustes distance and stop relaxation on the fence. These maneuvers suggest a possibly novel and interesting fusion of the Procrustes-spline toolkit with outlier detection. They also have practical implications for craniofacial management of CLP follow-up as well as suggestive implications for outlier detection in applied craniometrics and anthropometrics more generally.
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Grossi, Massimo. "On the number of critical points of solutions of semilinear elliptic equations." Electronic Research Archive 29, no. 6 (2021): 4215. http://dx.doi.org/10.3934/era.2021080.
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<p style='text-indent:20px;'>In this survey we discuss old and new results on the number of critical points of solutions of the problem</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE0.1"> \begin{document}$ \begin{equation} \begin{cases} -\Delta u = f(u)&in\ \Omega\\ u = 0&on\ \partial \Omega \end{cases} \;\;\;\;\;\;\;\;(0.1)\end{equation} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ \Omega\subset \mathbb{R}^N $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M2">\begin{document}$ N\ge2 $\end{document}</tex-math></inline-formula> is a smooth bounded domain. Both cases where <inline-formula><tex-math id="M3">\begin{document}$ u $\end{document}</tex-math></inline-formula> is a positive or nodal solution will be considered.</p>
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Li, Xiaoning, Chuanhai Wang, Gang Chen, Qiang Wang, Zunle Hu, Jinning Wu, Shan Wang, and Xing Fang. "Evaluating Efficiency Improvement of Deep-Cut Curb Inlets for Road-Bioretention Stripes." Water 12, no. 12 (November 30, 2020): 3368. http://dx.doi.org/10.3390/w12123368.
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Making a deep cut on the curb inlet has been used in some sponge-city (SPC) projects for road-bioretention stripes to manage stormwater runoff since they were easily implemented in the field. The efficiencies of the deep-cut curb inlets in those projects were unknown for lacking equation to evaluate their efficiencies. Two kinds of retrofit scenarios are commonly used: (1) The curb-cut cases when the deep cut is made only over the width of the curb inlet; (2) the road-curb cut cases when both the curb inlet and a small part of the road surface have a deep cut. An updated two-dimensional flow simulation program, FullSWOF-ZG, was used to determine two important parameters in road curb inlet design: The 100% interception curb inlet lengths (LT) and the curb inlet efficiencies (Eci). Eight-hundred retrofit modeling cases were compared with the no-cut cases to quantify the efficiency improvement of the deep-cut curb inlets. The simulation results show both LT and Eci of the curb-cut cases do not improve much. This case study with limited combinations of longitudinal and cross slopes and inlet lengths demonstrated that Eci of the road-curb cut cases improves to a large extent so that they can be used in the SPC projects and other urban drainage projects to reduce the flooding potentials. A general equation used to design and evaluate the road-curb cut inlets can be developed based on more simulation cases with a wide range of input parameters in a future study.
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Paredes, Jorge Morales, and Félix Humberto Soriano Méndez. "On the Cauchy problems associated to a ZK-KP-type family equations with a transversal fractional dispersion." Discrete & Continuous Dynamical Systems 42, no. 5 (2022): 2257. http://dx.doi.org/10.3934/dcds.2021190.
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<p style='text-indent:20px;'>In this paper we examine the well-posedness and ill-posedeness of the Cauchy problems associated with a family of equations of ZK-KP-type</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{cases} u_{t} = u_{xxx}-\mathscr{H}D_{x}^{\alpha}u_{yy}+uu_{x}, \cr u(0) = \psi \in Z \end{cases} $\end{document} </tex-math> </disp-formula></p><p style='text-indent:20px;'>in anisotropic Sobolev spaces, where <inline-formula><tex-math id="M1">\begin{document}$ 1\le \alpha \le 1 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ \mathscr{H} $\end{document}</tex-math></inline-formula> is the Hilbert transform and <inline-formula><tex-math id="M3">\begin{document}$ D_{x}^{\alpha} $\end{document}</tex-math></inline-formula> is the fractional derivative, both with respect to <inline-formula><tex-math id="M4">\begin{document}$ x $\end{document}</tex-math></inline-formula>.</p>
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Lampunio, Lisa, Yu Duan, Matthew D. Eaton, and Michael J. Bluck. "Mean Flow, Turbulent Structures, and SPOD Analysis of Thermal Mixing in a T-Junction with Variation of the Inlet Flow Profile." Energies 15, no. 22 (November 10, 2022): 8415. http://dx.doi.org/10.3390/en15228415.
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This paper investigates the effects of different inlet flow profiles on thermal mixing within a T-junction using CFD simulations with the IDDES-SST turbulence model. The different combinations of inlet flow profiles are related to different stage in the flow entry region. The effects of the inlet flow profile on the mean and transient flow behaviour are assessed, while a spectral proper orthogonal decomposition and power spectral density analysis are performed to assess the underlying flow structures and the predominant frequency modes. It is found that the vortical structures associated with the horseshoe and hovering vortex systems consist of a single roll-up vortex for cases with uniformly distributed boundary conditions (BCs) at the branch inlet whereas a double roll-up vortex is observed for the other cases. The double roll-up vortex enhances the mixing locally due to the entrainment of fluid from the branch pipe in these vortical structures, which then results in a lower mean temperature distribution. The appearance of the secondary vortex pair and the nested vortices is delayed for cases with uniformly distributed BCs at the branch inlet, which again results in lower thermal mixing and consequently higher values of mean temperature when compared with the other cases. It is also found that the vorticity related to the counter-rotating vortex pair as well as to the second pair of vortices rotating in the opposite direction is higher for cases with uniformly distributed BCs at the branch inlet. Lastly, the combinations of inlet flow profiles lead to different coherent structures, and the dominant frequencies are of a Strouhal number of around 0.7 for uniformly distributed profiles at the branch inlet and in the range 0.4–0.5 for the other cases.
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Li, Xiaoning, Xing Fang, Chuanhai Wang, Gang Chen, Shiwei Zheng, and Yue Yu. "Performance Analysis for Road-Bioretention with Three Types of Curb Inlet Using Numerical Model." Water 13, no. 12 (June 11, 2021): 1643. http://dx.doi.org/10.3390/w13121643.
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The FullSWOF-ZG (Full Shallow Water Overland Flow with infiltration determined by Zones and Grate-inlet submodules) program was used to simulate the road-bioretention (RB) stripe and evaluate the performance of the RB stripe with three types of curb inlet. The program was revised from the open-source FullSWOF-2D program and the validation results indicated FullSWOF-ZG predicts the RB stripe performance accurately. The model cases of 27 RB with different longitude slopes (S0), cross slopes (Sx), and curb inlet lengths (Lci) for the undepressed, composite depressed, and local depressed curb inlets were established in this study. Therefore, 81 cases in total were simulated to explore the curb inlet type and design parameter’s influence on the RB stripe performance. Overall, it was found that the bioretention control efficiency will increase with the S0 decrease, Sx increase, and Lci increase. The composite depressed curb inlet was the most efficient to intercept the road runoff into the bioretention strip, the next best is the local depressed curb inlet, and the undepressed curb inlet was the least efficient. The curb inlet and grate inlet combination in composite depressed curb inlet cases were able to deal with all the road surface runoff for the small longitudinal slope (S0 = 0.1% and 0.3%) to relieve the road local flood inundation.
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Teng, Kaimin, and Xian Wu. "Concentration of bound states for fractional Schrödinger-Poisson system via penalization methods." Communications on Pure & Applied Analysis 21, no. 4 (2022): 1157. http://dx.doi.org/10.3934/cpaa.2022014.
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<p style='text-indent:20px;'>In this paper, we study the following fractional Schrödinger-Poiss-on system</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \begin{cases} \varepsilon^{2s}(-\Delta)^su+V(x)u+\phi u = g(u) & \hbox{in $\mathbb{R}^3$,} \\ \varepsilon^{2t}(-\Delta)^t\phi = u^2,\,\, u>0& \hbox{in $\mathbb{R}^3$,} \end{cases} \end{equation*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ s,t\in(0,1) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ \varepsilon>0 $\end{document}</tex-math></inline-formula> is a small parameter. Under some local assumptions on <inline-formula><tex-math id="M3">\begin{document}$ V(x) $\end{document}</tex-math></inline-formula> and suitable assumptions on the nonlinearity <inline-formula><tex-math id="M4">\begin{document}$ g $\end{document}</tex-math></inline-formula>, we construct a family of positive solutions <inline-formula><tex-math id="M5">\begin{document}$ u_{\varepsilon}\in H_{\varepsilon} $\end{document}</tex-math></inline-formula> which concentrate around the global minima of <inline-formula><tex-math id="M6">\begin{document}$ V(x) $\end{document}</tex-math></inline-formula> as <inline-formula><tex-math id="M7">\begin{document}$ \varepsilon\rightarrow0 $\end{document}</tex-math></inline-formula>.</p>
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FLOWERDEW, M. J., D. M. CHEW, J. S. DALY, and I. L. MILLAR. "Hidden Archaean and Palaeoproterozoic crust in NW Ireland? Evidence from zircon Hf isotopic data from granitoid intrusions." Geological Magazine 146, no. 6 (September 7, 2009): 903–16. http://dx.doi.org/10.1017/s0016756809990227.
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AbstractThe presence of major crystalline basement provinces at depth in NW Ireland is inferred from in situ Hf isotope analysis of zircons from granitoid rocks that cut structurally overlying metasedimentary rocks. Granitoids in two of these units, the Slishwood Division and the Tyrone Central Inlier, contain complex zircons with core and rim structures. In both cases, cores have average ϵHf values that differ from the average ϵHf values of the rims at 470 Ma (the time of granitoid intrusion). The Hf data and similarity in U–Pb age between the inherited cores and detrital zircons from the host metasedimentary rocks suggests local contamination during intrusion rather than transport of the grains from the source region at depth. Rims from the Slishwood Division intrusions have average ϵHf470 values of −7.7, consistent with a derivation from juvenile Palaeoproterozoic crust, such as the Annagh Gneiss Complex or Rhinns Complex of NW Ireland, implying that the deep crust underlying the Slishwood Division is made of similar material. Rims from the Tyrone Central Inlier have extremely negative ϵHf470 values of approximately −39. This isotopic signature requires an Archaean source, suggesting rocks similar to the Lewisian Complex of Scotland, or sediment derived wholly from it, occurs at depth in NW Ireland.
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Ames, F. E., P. A. Barbot, and C. Wang. "Effects of Catalytic and Dry Low NOx Combustor Turbulence on Endwall Heat Transfer Distributions." Journal of Heat Transfer 127, no. 4 (March 30, 2005): 414–24. http://dx.doi.org/10.1115/1.1861923.
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Endwall heat transfer distributions taken in a large-scale low speed linear cascade facility are documented for mock catalytic and dry low NOx (DLN) combustion systems. Inlet turbulence levels range from about 1.0% for the mock catalytic combustor condition to 14% for the mock dry low NOx combustor system. Stanton number contours are presented at both turbulence conditions for Reynolds numbers based on true chord length and exit conditions ranging from 500,000 to 2,000,000. Catalytic combustor endwall heat transfer shows the influence of the complex three-dimensional flow field, while the effects of individual vortex systems are less evident for the mock dry low NOx cases. Turbulence scales have been documented for both cases. Inlet boundary layers are relatively thin for both the mock catalytic and DLN combustor cases. Inlet boundary layer parameters are presented across the inlet passage for the three Reynolds numbers and both the mock catalytic and DLN combustor inlet cases. Both midspan and 95% span pressure contours are included. This research provides a well-documented database taken across a range of Reynolds numbers and turbulence conditions for assessment of endwall heat transfer predictive capabilities.
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Yan, Shusen, and Weilin Yu. "Planar vortices in a bounded domain with a hole." Electronic Research Archive 29, no. 6 (2021): 4229. http://dx.doi.org/10.3934/era.2021081.
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<p style='text-indent:20px;'>In this paper, we consider the inviscid, incompressible planar flows in a bounded domain with a hole and construct stationary classical solutions with single vortex core, which is closed to the hole. This is carried out by constructing solutions to the following semilinear elliptic problem</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1111"> \begin{document}$ \begin{equation} \begin{cases} -\Delta \psi = \lambda(\psi-\frac{\kappa}{4\pi}\ln\lambda)_+^p,\quad &\text{in}\; \Omega,\\ \psi = \rho_\lambda,\quad &\text{on}\; \partial O_0,\\ \psi = 0,\quad &\text{on}\; \partial\Omega_0, \end{cases} \;\;\;\;\;\;\;\;(1)\end{equation} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ p>1 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ \kappa $\end{document}</tex-math></inline-formula> is a positive constant, <inline-formula><tex-math id="M3">\begin{document}$ \rho_\lambda $\end{document}</tex-math></inline-formula> is a constant, depending on <inline-formula><tex-math id="M4">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ \Omega = \Omega_0\setminus \bar{O}_0 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ \Omega_0 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M7">\begin{document}$ O_0 $\end{document}</tex-math></inline-formula> are two planar bounded simply-connected domains. We show that under the assumption <inline-formula><tex-math id="M8">\begin{document}$ (\ln\lambda)^\sigma\leq\rho_\lambda\leq (\ln\lambda)^{1-\sigma} $\end{document}</tex-math></inline-formula> for some <inline-formula><tex-math id="M9">\begin{document}$ \sigma>0 $\end{document}</tex-math></inline-formula> small, (1) has a solution <inline-formula><tex-math id="M10">\begin{document}$ \psi_\lambda $\end{document}</tex-math></inline-formula>, whose vorticity set <inline-formula><tex-math id="M11">\begin{document}$ \{y\in \Omega:\, \psi(y)-\kappa+\rho_\lambda\eta(y)>0\} $\end{document}</tex-math></inline-formula> shrinks to the boundary of the hole as <inline-formula><tex-math id="M12">\begin{document}$ \lambda\to +\infty $\end{document}</tex-math></inline-formula>.</p>
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Filippucci, Roberta, and Marius Ghergu. "Fujita type results for quasilinear parabolic inequalities with nonlocal terms." Discrete & Continuous Dynamical Systems 42, no. 4 (2022): 1817. http://dx.doi.org/10.3934/dcds.2021173.
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<p style='text-indent:20px;'>In this paper we investigate the nonexistence of nonnegative solutions of parabolic inequalities of the form</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{cases} &u_t \pm L_\mathcal A u\geq (K\ast u^p)u^q \quad\mbox{ in } \mathbb R^N \times \mathbb (0,\infty),\, N\geq 1,\\ &u(x,0) = u_0(x)\ge0 \,\, \text{ in } \mathbb R^N,\end{cases} \qquad (P^{\pm}) $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ u_0\in L^1_{loc}({\mathbb R}^N) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ L_{\mathcal{A}} $\end{document}</tex-math></inline-formula> denotes a weakly <inline-formula><tex-math id="M3">\begin{document}$ m $\end{document}</tex-math></inline-formula>-coercive operator, which includes as prototype the <inline-formula><tex-math id="M4">\begin{document}$ m $\end{document}</tex-math></inline-formula>-Laplacian or the generalized mean curvature operator, <inline-formula><tex-math id="M5">\begin{document}$ p,\,q>0 $\end{document}</tex-math></inline-formula>, while <inline-formula><tex-math id="M6">\begin{document}$ K\ast u^p $\end{document}</tex-math></inline-formula> stands for the standard convolution operator between a weight <inline-formula><tex-math id="M7">\begin{document}$ K>0 $\end{document}</tex-math></inline-formula> satisfying suitable conditions at infinity and <inline-formula><tex-math id="M8">\begin{document}$ u^p $\end{document}</tex-math></inline-formula>. For problem <inline-formula><tex-math id="M9">\begin{document}$ (P^-) $\end{document}</tex-math></inline-formula> we obtain a Fujita type exponent while for <inline-formula><tex-math id="M10">\begin{document}$ (P^+) $\end{document}</tex-math></inline-formula> we show that no such critical exponent exists. Our approach relies on nonlinear capacity estimates adapted to the nonlocal setting of our problems. No comparison results or maximum principles are required.</p>
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Wang, Yong Wei, Tao Lu, and Kui Sheng Wang. "Numerical Simulation of Turbulent Flow for Various Inlet Velocities in Tee Junctions with Periodic Porous Media." Advanced Materials Research 424-425 (January 2012): 932–35. http://dx.doi.org/10.4028/www.scientific.net/amr.424-425.932.
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The velocity fields of turbulent flow in Tee junctions have been calculated using large-eddy simulations model for three cases of various inlet velocities with periodic porous media. The ratio of the inlet velocity of the main tube to that of the branch tube were respectively 0.5, 1 and 2 in three cases. In the porous medium region of the Tee junction, the velocity at the center is obvious larger than that at the top or the bottom and the pressure drop heightens rapidly. Comparison of the three cases, the pressure drop, mean velocity, normalized velocity fluctuation and the velocity oscillation versus time are increase as the inlet velocity of the main tube increase.
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Kreuml, Andreas, and Olaf Mordhorst. "Fractional perimeters on the sphere." Discrete & Continuous Dynamical Systems 41, no. 11 (2021): 5439. http://dx.doi.org/10.3934/dcds.2021083.
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<p style='text-indent:20px;'>This note treats several problems for the fractional perimeter or <inline-formula><tex-math id="M1">\begin{document}$ s $\end{document}</tex-math></inline-formula>-perimeter on the sphere. The spherical fractional isoperimetric inequality is established. It turns out that the equality cases are exactly the spherical caps. Furthermore, the convergence of fractional perimeters to the surface area as <inline-formula><tex-math id="M2">\begin{document}$ s \nearrow 1 $\end{document}</tex-math></inline-formula> is proven. It is shown that their limit as <inline-formula><tex-math id="M3">\begin{document}$ s \searrow -\infty $\end{document}</tex-math></inline-formula> can be expressed in terms of the volume.</p>
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Vitillaro, Enzo. "Blow–up for the wave equation with hyperbolic dynamical boundary conditions, interior and boundary nonlinear damping and sources." Discrete & Continuous Dynamical Systems - S 14, no. 12 (2021): 4575. http://dx.doi.org/10.3934/dcdss.2021130.
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<p style='text-indent:20px;'>The aim of this paper is to give global nonexistence and blow–up results for the problem</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{cases} u_{tt}-\Delta u+P(x,u_t) = f(x,u) \qquad &\text{in $(0,\infty)\times\Omega$,}\\ u = 0 &\text{on $(0,\infty)\times \Gamma_0$,}\\ u_{tt}+\partial_\nu u-\Delta_\Gamma u+Q(x,u_t) = g(x,u)\qquad &\text{on $(0,\infty)\times \Gamma_1$,}\\ u(0,x) = u_0(x),\quad u_t(0,x) = u_1(x) & \text{in $\overline{\Omega}$,} \end{cases} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ \Omega $\end{document}</tex-math></inline-formula> is a bounded open <inline-formula><tex-math id="M2">\begin{document}$ C^1 $\end{document}</tex-math></inline-formula> subset of <inline-formula><tex-math id="M3">\begin{document}$ {\mathbb R}^N $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M4">\begin{document}$ N\ge 2 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ \Gamma = \partial\Omega $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M6">\begin{document}$ (\Gamma_0,\Gamma_1) $\end{document}</tex-math></inline-formula> is a partition of <inline-formula><tex-math id="M7">\begin{document}$ \Gamma $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M8">\begin{document}$ \Gamma_1\not = \emptyset $\end{document}</tex-math></inline-formula> being relatively open in <inline-formula><tex-math id="M9">\begin{document}$ \Gamma $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M10">\begin{document}$ \Delta_\Gamma $\end{document}</tex-math></inline-formula> denotes the Laplace–Beltrami operator on <inline-formula><tex-math id="M11">\begin{document}$ \Gamma $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M12">\begin{document}$ \nu $\end{document}</tex-math></inline-formula> is the outward normal to <inline-formula><tex-math id="M13">\begin{document}$ \Omega $\end{document}</tex-math></inline-formula>, and the terms <inline-formula><tex-math id="M14">\begin{document}$ P $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M15">\begin{document}$ Q $\end{document}</tex-math></inline-formula> represent nonlinear damping terms, while <inline-formula><tex-math id="M16">\begin{document}$ f $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M17">\begin{document}$ g $\end{document}</tex-math></inline-formula> are nonlinear source terms. These results complement the analysis of the problem given by the author in two recent papers, dealing with local and global existence, uniqueness and well–posedness.</p>
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Li, Xiaoning, Xing Fang, Yongwei Gong, Junqi Li, Jianlong Wang, Gang Chen, and Ming-Han Li. "Evaluating the Road-Bioretention Strip System from a Hydraulic Perspective—Case Studies." Water 10, no. 12 (December 4, 2018): 1778. http://dx.doi.org/10.3390/w10121778.
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The two-dimensional overland flow simulation program, FullSWOF_2D, was revised to include submodules of determining infiltration by zones (Z) and grate-inlet (G) drainage from a 2D surface to a 1D pipe flow. The updated program, FullSWOF-ZG, was used to evaluate the performance of a road-bioretention strip (RBS) system and explore/understand key parameters of continuous RBS design. The program was validated using eight pervious surfaces under simulated rainfall events and tested with 20 experimental cases of a locally depressed curb inlet. The mean difference of simulated interception efficiencies (36.6%–86.0%) and observed interception efficiencies (34.8%–84.0%) of the curb inlet was 3.5%, which proves the program predicts the curb-inlet interception efficiency accurately. The 20 road-only and 20 RBS modeling cases were designed and modeled using the FullSWOF-ZG program. These case studies have different road lengths, curb inlet lengths, longitudinal slopes, cross slopes, bioretention-overflow inlet heights, and bioretention soil infiltration parameters. Only 34.6%–48.4% of the total runoff volume is intercepted by the RBS’s curb inlet under heavy rainfall (250 mm/h) and the remaining part of the runoff flows downstream along the road, which may cause local inundation and become a safety hazard. The curb inlet becomes the bottleneck of the RBS system that could impede the runoff flowing into the bioretention strip for detention and infiltration to improve the stormwater quality.
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Chen, Xueying, Guanfeng Li, and Sijia Bao. "Symmetry and monotonicity of positive solutions for a class of general pseudo-relativistic systems." Communications on Pure and Applied Analysis 21, no. 5 (2022): 1755. http://dx.doi.org/10.3934/cpaa.2022045.
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<p style='text-indent:20px;'>In this paper, we focus on a class of general pseudo-relativistic systems</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \begin{cases} \begin{aligned} &(-\Delta+m^2)^su(x) = f(u(x), v(x)), \\ &(-\Delta+m^2)^tv(x) = g(u(x), v(x)), \end{aligned} \end{cases} \end{equation*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ m \in (0, +\infty) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ s, t \in (0,1) $\end{document}</tex-math></inline-formula>. Before giving the main results, we first introduce a decay at infinity and a narrow region principle. Then we implement the direct method of moving planes to show the radial symmetry and monotonicity of positive solutions for the above system in both the unit ball and the whole space.</p>
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Ames, Forrest E., Pierre A. Barbot, and Chao Wang. "Effects of Aeroderivative Combustor Turbulence on Endwall Heat Transfer Distributions Acquired in a Linear Vane Cascade." Journal of Turbomachinery 125, no. 2 (April 1, 2003): 210–20. http://dx.doi.org/10.1115/1.1559897.
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Vane endwall heat transfer distributions are documented for a mock aeroderivative combustion system and for a low turbulence condition in a large-scale low speed linear cascade facility. Inlet turbulence levels range from below 0.7% for the low turbulence condition to 14% for the mock combustor system. Stanton number contours are presented at both turbulence conditions for Reynolds numbers based on true chord length and exit conditions ranging from 500,000 to 2,000,000. Low turbulence endwall heat transfer shows the influence of the complex three-dimensional flow field, while the effects of individual vortex systems are less evident for the high turbulence cases. Turbulent scale has been documented for the high turbulence case. Inlet boundary layers are relatively thin for the low turbulence case, while inlet flow approximates a nonequilibrium or high turbulence channel flow for the mock combustor case. Inlet boundary layer parameters are presented across the inlet passage for the three Reynolds numbers and both the low turbulence and mock combustor inlet cases. Both midspan and 95% span pressure contours are included. This research provides a well-documented database taken across a range of Reynolds numbers and turbulence conditions for assessment of endwall heat transfer predictive capabilities.
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Kang, Y. T., Y. Fujita, and T. Kashiwagi. "Combined Heat and Mass Transfer Under Different Inlet Subcooling Modes During NH3-H2O Falling Film Absorption Process." Journal of Energy Resources Technology 123, no. 3 (March 8, 2001): 242–49. http://dx.doi.org/10.1115/1.1377895.
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Experiments were conducted for ammonia-water falling film absorption in a plate heat exchanger with offset strip fins. The objectives of this paper were to analyze combined heat and mass transfer during the ammonia-water absorption process under different inlet subcooling modes, and to obtain heat transfer coefficients (Nusselt number). This paper examined the effects of the inlet subcooling modes, the inlet concentration difference, liquid Reynolds number, and vapor Reynolds number on the heat transfer performance. Inlet liquid concentrations were set at 0, 5, 10, and 15 percent in mass of ammonia, while inlet vapor concentration ranged from 64.7 to 83.6 percent. Experiments were conducted in three ways according to the inlet subcooling conditions, i.e., Case A Tv>Tl, Case B Tv∼Tl, and Case C Tv<Tl. In Case A, there was a rectification process at the top of the test section by the inlet subcooling effect. Water desorption was confirmed in the experiments, which resulted in a lower absorption performance. The heat transfer coefficient increased as the inlet subcooling increased in all cases. The effect of inlet subcooling on heat transfer performance was more significant in Case A than in Cases B and C. The inlet subcooling had more significant effect on the heat transfer performance than the inlet concentration difference. Nusselt number increased as liquid and vapor Reynolds numbers increased. The vapor velocity should be maximized to increase absorption performance in cocurrent ammonia-water absorption process. The parametric analysis provides fundamental understandings of the ammonia-water absorption process, and thus gives a guideline for heat exchanger compactness in ammonia-water absorption systems.
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Liu, W., E. M. Greitzer, and C. S. Tan. "Surface Static Pressures in an Inlet Vortex Flow Field." Journal of Engineering for Gas Turbines and Power 107, no. 2 (April 1, 1985): 387–93. http://dx.doi.org/10.1115/1.3239738.
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An experimental investigation of the three-dimensional flow field associated with an inlet vortex is reported. The specific configuration investigated is an inlet, in proximity to a ground plane, in crosswind. Parametric data are presented to define the regimes of vortex formation in this configuration, as a function of inlet height to diameter ratio and inlet velocity ratio. The detailed static pressure distribution on the inlet is given for two quite different flow regimes, one with a strong inlet vortex and one with no inlet vortex. These new quantitative data are supplemented by flow visualization studies that allow an estimate to be made of the circulation around the inlet vortex. It is argued that the static pressure distributions in both cases can be clearly interpreted using the basic ideas of inlet vortex formation that were previously developed from (qualitative) water tunnel studies.
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Scribben, Angie Rabe, Wing Ng, and Ricardo Burdisso. "Effectiveness of a Serpentine Inlet Duct Flow Control Technique at Design and Off-Design Simulated Flight Conditions." Journal of Turbomachinery 128, no. 2 (March 1, 2004): 332–39. http://dx.doi.org/10.1115/1.2098787.
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An experimental investigation was conducted in a static ground test facility to determine the effectiveness of a serpentine inlet duct active flow control technique for two simulated flight conditions. The experiments used a scaled model of a compact, diffusing, serpentine, engine inlet duct developed by Lockheed Martin with a flow control technique using air injection through microjets at 1% of the inlet mass flow rate. The experimental results, in the form of total pressure measurements at the exit of the inlet, were used to predict the stability of a compression system through a parallel compressor model. The inlet duct was tested at cruise condition and angle of attack flight cases to determine the change in inlet performance due to flow control at different flight conditions. The experiments were run at an inlet throat Mach number of 0.55 and a resulting Reynolds number, based on the hydraulic diameter at the inlet throat, of 1.76*105. For both of the flight conditions tested, the flow control technique was found to reduce inlet distortion at the exit of the inlet by as much as 70% while increasing total pressure recovery by as much as 2%. The inlet total pressure profile was input in a parallel compressor model to predict the changes in stability margin of a compression system due to flow control for design and off-design flight conditions. Without flow control, both cases show a reduction in stability margin of 70%. With the addition of flow control, each case was able to recover a significant portion (up to 55%) of the undistorted stability margin. This flow control technique has improved the operating range of a compression system as compared to the same inlet duct without flow control.
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Behrens, C., and Peggy P. W. Yen. "Esophageal Inlet Patch." Radiology Research and Practice 2011 (2011): 1–3. http://dx.doi.org/10.1155/2011/460890.
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An inlet patch is a congenital anomaly consisting of ectopic gastric mucosa at or just distal to the upper esophageal sphincter. Most inlet patches are largely asymptomatic, but in problematic cases complications related to acid secretion such as esophagitis, ulcer, web and stricture may occur. The diagnosis of inlet patch is strongly suggested on barium swallow where the most common pattern consists of two small indentations on the wall of the esophagus. The diagnosis of inlet patch is confirmed via endoscopy with biopsy. At endoscopy, the lesion appears salmon-coloured and velvety and is easily distinguished from the normal grey-white squamous epithelium of the esophagus. The prominent margins correlate with the radiological findings of indentations and rim-like shadows on barium swallow. Histopathology provides the definitive diagnosis by demonstrating gastric mucosa adjacent to normal esophageal mucosa. No treatment is required for asymptomatic inlet patches. Symptomatic cases are treated with proton pump inhibitors to relieve symptoms related to acid secretion. Strictures and webs are treated with serial dilatation and should be biopsied to rule out malignancy.
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Silva, Edcarlos D., Marcos L. M. Carvalho, and Claudiney Goulart. "Periodic and asymptotically periodic fourth-order Schrödinger equations with critical and subcritical growth." Discrete & Continuous Dynamical Systems 42, no. 3 (2022): 1039. http://dx.doi.org/10.3934/dcds.2021146.
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<p style='text-indent:20px;'>It is established existence of solutions for subcritical and critical nonlinearities considering a fourth-order elliptic problem defined in the whole space <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^N $\end{document}</tex-math></inline-formula>. The work is devoted to study a class of potentials and nonlinearities which can be periodic or asymptotically periodic. Here we consider a general fourth-order elliptic problem where the principal part is given by <inline-formula><tex-math id="M2">\begin{document}$ \alpha \Delta^2 u + \beta \Delta u + V(x)u $\end{document}</tex-math></inline-formula> where <inline-formula><tex-math id="M3">\begin{document}$ \alpha > 0, \beta \in \mathbb{R} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ V: \mathbb{R}^N \rightarrow \mathbb{R} $\end{document}</tex-math></inline-formula> is a continuous potential. Hence our main contribution is to consider general fourth-order elliptic problems taking into account the cases where <inline-formula><tex-math id="M5">\begin{document}$ \beta $\end{document}</tex-math></inline-formula> is negative, zero or positive. In order to do that we employ some fine estimates proving the compactness for the associated energy functional.</p>
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Yomgne, Gael Diebou. "On a nonlinear Laplace equation related to the boundary Yamabe problem in the upper-half space." Communications on Pure & Applied Analysis 21, no. 2 (2022): 517. http://dx.doi.org/10.3934/cpaa.2021186.
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<p style='text-indent:20px;'>We consider in this paper the nonlinear elliptic equation with Neumann boundary condition</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} \begin{cases} \Delta u = a|u|^{m-1}u\, \, \mbox{ in }\, \, \mathbb{R}^{n+1}_{+}\\ \dfrac{\partial u}{\partial t} = b|u|^{\eta-1}u+f\, \, \mbox{ on }\, \, \partial \mathbb{R}^{n+1}_{+}. \end{cases} \end{align*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>For <inline-formula><tex-math id="M1">\begin{document}$ a, b\neq 0 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ m>\frac{n+1}{n-1} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M3">\begin{document}$ (n>1) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M4">\begin{document}$ \eta = \frac{m+1}{2} $\end{document}</tex-math></inline-formula> and small data <inline-formula><tex-math id="M5">\begin{document}$ f\in L^{\frac{nq}{n+1}, \infty}(\partial \mathbb{R}^{n+1}_{+}) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M6">\begin{document}$ q = \frac{(n+1)(m-1)}{m+1} $\end{document}</tex-math></inline-formula> we prove that the problem is solvable. More precisely, we establish existence, uniqueness and continuous dependence of solutions on the boundary data <inline-formula><tex-math id="M7">\begin{document}$ f $\end{document}</tex-math></inline-formula> in the function space <inline-formula><tex-math id="M8">\begin{document}$ \mathbf{X}^{q}_{\infty} $\end{document}</tex-math></inline-formula> where</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE2"> \begin{document}$ \|u\|_{ \mathbf{X}^{q}_{\infty}} = \sup\limits_{t>0}t^{\frac{n+1}{q}-1}\|u(t)\|_{L^{\infty}( \mathbb{R}^{n})}+\|u\|_{L^{\frac{q(m+1)}{2}, \infty}( \mathbb{R}^{n+1}_{+})}+\|\nabla u\|_{L^{q, \infty}( \mathbb{R}^{n+1}_{+})}. $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>As a direct consequence, we obtain the local regularity property <inline-formula><tex-math id="M9">\begin{document}$ C^{1, \nu}_{loc} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M10">\begin{document}$ \nu\in (0, 1) $\end{document}</tex-math></inline-formula> of these solutions as well as energy estimates for certain values of <inline-formula><tex-math id="M11">\begin{document}$ m $\end{document}</tex-math></inline-formula>. Boundary values decaying faster than <inline-formula><tex-math id="M12">\begin{document}$ |x|^{-(m+1)/(m-1)} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M13">\begin{document}$ x\in \mathbb{R}^{n}\setminus\{0\} $\end{document}</tex-math></inline-formula> yield solvability and this decay property is shown to be sharp for positive nonlinearities.</p><p style='text-indent:20px;'>Moreover, we are able to show that solutions inherit qualitative features of the boundary data such as positivity, rotational symmetry with respect to the <inline-formula><tex-math id="M14">\begin{document}$ (n+1) $\end{document}</tex-math></inline-formula>-axis, radial monotonicity in the tangential variable and homogeneity. When <inline-formula><tex-math id="M15">\begin{document}$ a, b>0 $\end{document}</tex-math></inline-formula>, the critical exponent <inline-formula><tex-math id="M16">\begin{document}$ m_c $\end{document}</tex-math></inline-formula> for the existence of positive solutions is identified, <inline-formula><tex-math id="M17">\begin{document}$ m_c = (n+1)/(n-1) $\end{document}</tex-math></inline-formula>.</p>
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Li, Fang, Chen, Gong, Wang, and Li. "Evaluating Curb Inlet Efficiency for Urban Drainage and Road Bioretention Facilities." Water 11, no. 4 (April 23, 2019): 851. http://dx.doi.org/10.3390/w11040851.
Full textAbstract:
An updated two-dimensional flow simulation program, FullSWOF-ZG, which fully (Full) solves shallow water (SW) equations for overland flow (OF) and includes submodules modeling infiltration by zones (Z) and flow interception by grate-inlet (G), was tested with 20 locally depressed curb inlets to validate the inlet efficiency (Eci), and with 80 undepressed curb inlets to validate the inlet lengths (LT) for 100% interception. Previous curb inlet equations were based on certain theoretical approximations and limited experimental data. In this study, 1000 road-curb inlet modeling cases from the combinations of 10 longitudinal slopes (S0, 0.1–1%), 10 cross slopes (Sx, 1.5–6%), and 10 upstream inflows (Qin, 6–24 L/s) were established and modeled to determine LT. The second 1000 modeling cases with the same 10 S0 and 10 Sx and 10 curb inlet lengths (Lci, 0.15–1.5 m) were established to determine Eci. The LT and Eci regression equations were developed as a function of input parameters (S0, Sx, and Qin) and Lci/LT with the multiple linear regression method, respectively. Newly developed regression equations were applied to 10,000 inlet design cases (10 S0, 10 Sx, 10 Qin, and 10 Lci combinations) and comprehensively compared with three equations in previous studies. The 100% intercepted gutter flow (Qg100) equations were derived, and over-prediction of Qg100 from previous methods was strongly correlated to smaller S0. Newly developed equations gave more accurate estimations of LT and Eci over a wide range of input parameters. These equations can be applied to designing urban drainage and road bioretention facilities, since they were developed using a large number of simulation runs with diverse input parameters, but previous methods often overpredict the gutter flow of total interception when the longitudinal slope S0 is small.
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Ming, Sen, Han Yang, and Xiongmei Fan. "Formation of singularities of solutions to the Cauchy problem for semilinear Moore-Gibson-Thompson equations." Communications on Pure and Applied Analysis 21, no. 5 (2022): 1773. http://dx.doi.org/10.3934/cpaa.2022046.
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<p style='text-indent:20px;'>This paper is devoted to investigating formation of singularities for solutions to semilinear Moore-Gibson-Thompson equations with power type nonlinearity <inline-formula><tex-math id="M1">\begin{document}$ |u|^{p} $\end{document}</tex-math></inline-formula>, derivative type nonlinearity <inline-formula><tex-math id="M2">\begin{document}$ |u_{t}|^{p} $\end{document}</tex-math></inline-formula> and combined type nonlinearities <inline-formula><tex-math id="M3">\begin{document}$ |u_{t}|^{p}+|u|^{q} $\end{document}</tex-math></inline-formula> in the case of single equation, combined type nonlinearities <inline-formula><tex-math id="M4">\begin{document}$ |v_{t}|^{p_{1}}+|v|^{q_{1}} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ |u_{t}|^{p_{2}}+|u|^{q_{2}} $\end{document}</tex-math></inline-formula>, combined and power type nonlinearities <inline-formula><tex-math id="M6">\begin{document}$ |v_{t}|^{p_{1}}+|v|^{q_{1}} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M7">\begin{document}$ |u|^{q_{2}} $\end{document}</tex-math></inline-formula>, combined and derivative type nonlinearities <inline-formula><tex-math id="M8">\begin{document}$ |v_{t}|^{p_{1}}+|v|^{q_{1}} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M9">\begin{document}$ |u_{t}|^{p_{2}} $\end{document}</tex-math></inline-formula> in the case of coupled system, respectively. More precisely, blow-up results of solutions to problems in the sub-critical and critical cases are derived by applying test function technique. Moreover, upper bound lifespan estimates of solutions to the coupled systems are investigated. The main new contribution is that lifespan estimates of solutions are associated with the well-known Strauss exponent and Glassey exponent.</p>
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Aloui, Lassaad, and Slim Tayachi. "Local well-posedness for the inhomogeneous nonlinear Schrödinger equation." Discrete & Continuous Dynamical Systems 41, no. 11 (2021): 5409. http://dx.doi.org/10.3934/dcds.2021082.
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<p style='text-indent:20px;'>We consider the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation <inline-formula><tex-math id="M1">\begin{document}$ i\partial_t u +\Delta u = \mu |x|^{-b}|u|^\alpha u,\; u(0)\in H^s({\mathbb R}^N),\; N\geq 1,\; \mu\in {\mathbb C},\; \; b>0 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ \alpha>0. $\end{document}</tex-math></inline-formula> Only partial results are known for the local existence in the subcritical case <inline-formula><tex-math id="M3">\begin{document}$ \alpha<(4-2b)/(N-2s) $\end{document}</tex-math></inline-formula> and much more less in the critical case <inline-formula><tex-math id="M4">\begin{document}$ \alpha = (4-2b)/(N-2s). $\end{document}</tex-math></inline-formula> In this paper, we develop a local well-posedness theory for the both cases. In particular, we establish new results for the continuous dependence and for the unconditional uniqueness. Our approach provides simple proofs and allows us to obtain lower bounds of the blowup rate and of the life span. The Lorentz spaces and the Strichartz estimates play important roles in our argument. In particular this enables us to reach the critical case and to unify results for <inline-formula><tex-math id="M5">\begin{document}$ b = 0 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ b>0. $\end{document}</tex-math></inline-formula></p>
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Lee, Siong, Thomas Choong, Luqman Abdullah, Mus’ab Abdul Razak, and Zhen Ban. "Experimental and CFD Modelling: Impact of the Inlet Slug Flow on the Horizontal Gas–Liquid Separator." Energies 12, no. 1 (December 24, 2018): 41. http://dx.doi.org/10.3390/en12010041.
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For a gas-liquid separator sizing, many engineers have neglected the flow pattern of incoming fluids. The impact of inlet slug flow which impeded onto the separator’s liquid phase will cause a separator fails to perform when sloshing happened in the separator. To date, the study on verifying the impact of inlet slug flow in a separator remains limited. In this paper, the impact of inlet momentum and inlet slug flow on the hydrodynamics in a separator for cases without an inlet device were investigated. The experimental and Computational Fluid Dynamics (CFD) results of cavity formation and sloshing occurrence in the separator in this study were compared. A User Defined Function (UDF) was used to describe the inlet slug flow at the separator inlet. Inlet slug flow occurred at inlet momentum from 200 to 1000 Pa, and sloshing occurred in the separator at 1000 Pa. Both experimental and simulated results showed similar phenomena.
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Chiarello, Felisia Angela, Harold Deivi Contreras, and Luis Miguel Villada. "Nonlocal reaction traffic flow model with on-off ramps." Networks and Heterogeneous Media 17, no. 2 (2022): 203. http://dx.doi.org/10.3934/nhm.2022003.
Full textAbstract:
<p style='text-indent:20px;'>We present a non-local version of a scalar balance law modeling traffic flow with on-ramps and off-ramps. The source term is used to describe the inflow and output flow over the on-ramp and off-ramps respectively. We approximate the problem using an upwind-type numerical scheme and we provide <inline-formula><tex-math id="M1">\begin{document}$ \mathbf{L^{\infty}} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ \mathbf{BV} $\end{document}</tex-math></inline-formula> estimates for the sequence of approximate solutions. Together with a discrete entropy inequality, we also show the well-posedness of the considered class of scalar balance laws. Some numerical simulations illustrate the behaviour of solutions in sample cases.</p>
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Liu, Jiaqi, Yang Hong, Jutao Wang, Chunhua Cai, and Zhiqiang Zhang. "A Thermoelectric MEMS Microwave Power Sensor with Inline Self-Detection Function." Micromachines 13, no. 2 (January 31, 2022): 239. http://dx.doi.org/10.3390/mi13020239.
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In this paper, the design, fabrication and measurement of a thermoelectric MEMS microwave power sensor with the terminal load inline self-detection function is proposed. The structure of the sensor mainly includes a coplanar waveguide, a thermopile, two terminal load resistors and two calibration resistors. In order to realize the inline self-detection function, the load and calibration resistors are designed to form a voltage divider circuit. The fabrication of this sensor is compatible with the GaAs MMIC technology. The on-chip performance is tested by using a microwave experimental platform. The measured reflection loss is less than −10 dB at 0.1–10 GHz. When the bias voltage is not applied, the sensitivity of the sensor is 47.39 μV/mW@5 GHz and 32.58 μV/mW@10 GHz, respectively, and when the bias voltage is applied, the sensitivity is 47.50 μV/mW@5 GHz and 32.73 μV/mW@10 GHz, respectively. The difference between the two cases is less than 0.5% at the same frequency, which indicates that whether or not to apply the bias voltage has little effect on the sensitivity. In addition, when the calibration resistance is increased from 50 to 100 Ω, the current flowing through the load resistance is decreased under the same bias voltage. Therefore, the DC power consumed on the load resistance will be significantly reduced. This makes the measured and theoretical results show better agreement, thus verifying the validity of the design.
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Alhowaity, Sawsan, Ernesto Pérez-Chavela, and Juan Manuel Sánchez-Cerritos. "The curved symmetric $ 2 $– and $ 3 $–center problem on constant negative surfaces." Communications on Pure & Applied Analysis 20, no. 9 (2021): 2941. http://dx.doi.org/10.3934/cpaa.2021090.
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<p style='text-indent:20px;'>We study the motion of the negative curved symmetric two and three center problem on the Poincaré upper semi plane model for a surface of constant negative curvature <inline-formula><tex-math id="M3">\begin{document}$ \kappa $\end{document}</tex-math></inline-formula>, which without loss of generality we assume <inline-formula><tex-math id="M4">\begin{document}$ \kappa = -1 $\end{document}</tex-math></inline-formula>. Using this model, we first derive the equations of motion for the <inline-formula><tex-math id="M5">\begin{document}$ 2 $\end{document}</tex-math></inline-formula>-and <inline-formula><tex-math id="M6">\begin{document}$ 3 $\end{document}</tex-math></inline-formula>-center problems. We prove that for <inline-formula><tex-math id="M7">\begin{document}$ 2 $\end{document}</tex-math></inline-formula>–center problem, there exists a unique equilibrium point and we study the dynamics around it. For the motion restricted to the invariant <inline-formula><tex-math id="M8">\begin{document}$ y $\end{document}</tex-math></inline-formula>–axis, we prove that it is a center, but for the general two center problem it is unstable. For the <inline-formula><tex-math id="M9">\begin{document}$ 3 $\end{document}</tex-math></inline-formula>–center problem, we show the non-existence of equilibrium points. We study two particular integrable cases, first when the motion of the free particle is restricted to the <inline-formula><tex-math id="M10">\begin{document}$ y $\end{document}</tex-math></inline-formula>–axis, and second when all particles are along the same geodesic. We classify the singularities of the problem and introduce a local and a global regularization of all them. We show some numerical simulations for each situation.</p>
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Uy, Robert V., and Christopher E. Brennen. "Experimental Measurements of Rotordynamic Forces Caused by Front Shroud Pump Leakage." Journal of Fluids Engineering 121, no. 3 (September 1, 1999): 633–37. http://dx.doi.org/10.1115/1.2823516.
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Unsteady forces generated by fluid flow through the impeller shroud leakage path of a centrifugal pump were investigated. Different pump shroud geometries were compared, and the effect of leakage path inlet swirl (pump discharge swirl) on the rotordynamic forces was examined for various ratios of fluid throughflow velocity to impeller tip speed. A short axial length leakage path reduced the measured forces, while curvature appeared to increase the destabilizing forces when inlet swirl was present. It was observed that changing the inlet swirl velocity does not appear to significantly affect the measured forces for a given leakage flow coefficient, but any nonzero inlet swirl is destabilizing when compared to cases with no inlet swirl.
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Morgan, Matthew W., and Irving E. Salit. "Human and Canine Blastomycosis: A Common Source Infection." Canadian Journal of Infectious Diseases 7, no. 2 (1996): 147–51. http://dx.doi.org/10.1155/1996/657941.
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In fall 1993 a man and a dog developed blastomycosis after visiting an island off Bayfield Inlet, Georgian Bay, located near Parry Sound, Ontario. The man recovered but the dog died of blastomycosis. It was hypothesized that the common source of exposure was the island since the permanent residences of the two cases were in different cities. One further case of human infection, based on positive serology, and four additional cases of probable canine blastomycosis were identified. All cases had travelled to Bayfield Inlet during summer and early fall 1993. To the authors’ knowledge this is the first Canadian report of a common source of infection of human and canine blastomycosis. This report also provides evidence for a new endemic area of blastomycosis infection.
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Ioannidis, Orestis, Eleftheria Dalampini, Stavros Chatzopoulos, Anastasios Kotronis, George Paraskevas, Athina Konstantara, Nikolaos Papadimitriou, Apostolos Makrantonakis, and Emmanouil Kakoutis. "Acute respiratory failure caused by neglected giant substernal nontoxic goiter." Arquivos Brasileiros de Endocrinologia & Metabologia 55, no. 3 (April 2011): 229–32. http://dx.doi.org/10.1590/s0004-27302011000300009.
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Substernal goiter is usually defined as a goiter in which the thyroid mass has descended the plane of the thoracic inlet or if more than 50% of the thyroid mass is located below the thoracic inlet. Substernal goiters may be asymptomatic or may present with symptoms caused by compression of adjacent organs. Acute respiratory failure is rare in cases of substernal goiter. In cases of symptomatic substernal goiter the treatment is surgical by thyroidectomy. We present a rare case of a giant substernal nontoxic goiter which caused acute respiratory failure which was treated by urgent thyroidectomy through a T-incision.
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Cheng, H. P., C. J. Chen ,, and P. W. Cheng ,. "Computational Fluid Dynamics Performance Estimation of Turbo Booster Vacuum Pump." Journal of Fluids Engineering 125, no. 3 (May 1, 2003): 586–89. http://dx.doi.org/10.1115/1.1566042.
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The CFD performance estimation of turbo booster vacuum pump shows the axial vortex and back flow is evident when the mass flow rate is increased. The pressure is increased from the pump inlet to the outlet for the low mass flow rate cases. But for high mass flow rate cases, the pressure is increased until the region near the end of the rotor then decreased. The calculated inlet pressure, compression ratio, and pumping speed is increased, decreased, and decreased, respectively, when the mass flow rate is increased. The pumping speed is increased when the rotor speed is increased.
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Chelabi, Mohammed Amine, Sergey Dobrotvorskiy, Yevheniia Basova, Borys A. Aleksenko, Milan Edl, Jan Zdebor, and José Machado. "Influence of the Main Geometrical Parameters on the Design and Performance of Mixed Inflow Turbines." Applied Sciences 12, no. 23 (November 28, 2022): 12165. http://dx.doi.org/10.3390/app122312165.
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The blade shape is of great interest to hybrid turbine designers, due to its significant and direct impact on turbine performance. The inlet and outlet diameters of the vane affect the size of the rotor, which is limited because of the small space available in internal combustion engines. The effect of the ratio of the average inlet diameter and the average exducer inlet diameter on the performance of a mixed inlet turbine will be the focus of this study, which consists of two cases included herein for the purpose of illustrating the means of improving rotor performances and controlling the flow mass rate. In the first case, we achieved this by changing the average diameter of the exducer inlet, while, in the second one, we achieved this by changing the average inlet diameter. Additionally, the angles of the inlet and outlet blades were recalculated to preserve the same blade profile and to eliminate the effect of curvilinearity. It was noted that the shape of the blade was very sensitive to changes in the ratio of the investigated diameters, and—in both cases—interesting results were obtained. First, an increase in output work and in total static isentropic efficiency by 2.16% and 2.15%, respectively, was generated, with a saving of 3.52% of the used mass flow and a lighter rotor compared to one that used to take up the same space by using fixed average inlet diameter blades. In the second case, there was an increase in the output work by 3.31%, and in the total static isentropic efficiency by 3.34%, but the rotor became heavier and required an increase in the mass flow used. Since inter-blade flows are very complex, three-dimensional and viscous—featuring various types of secondary and eddy flows—the CFX.15-CFD code was used in all models to solve the averaged Navier–Stokes equations.
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Gholamian, Mojtaba, Gurram Krishna Mohan Rao, and Panitapu Bhramara. "Flow Pattern and Efficiency Changes of Squirrel Cage Fans due to Inlet Diffuser Diameter Changes - Using CFD Method and Experimental Validation." Applied Mechanics and Materials 446-447 (November 2013): 626–30. http://dx.doi.org/10.4028/www.scientific.net/amm.446-447.626.
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Inlet is one the basic elements of squirrel cage fans that has a significant effect on fan performance and efficiency. Recently using the CFD calculation methods with sufficient related tools for finding the flow pattern and related parameters, applying modifications and representing proper solutions, has being increased. In the present case study to study the effect of inlet diffuser diameter on the fan efficiency and flow pattern, using numerical simulations and experimental validations, three different inlet diffuser diameters are used as inlet instead of inlet nozzle. To simulate these cases some geometries with special additional element, proper mesh pattern and size and proper turbulence model was chosen.It is observed performance and efficiency curves of fans with respect to use of inlet nozzle are more flattened with higher magnitude. So fan operation around the best performance point is more stable without significant fluctuation of head pressure and efficiency.
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Valencia, Alvaro. "Pulsating Flow in a Channel With a Backward-Facing Step." Applied Mechanics Reviews 50, no. 11S (November 1, 1997): S232—S236. http://dx.doi.org/10.1115/1.3101841.
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The incompressible laminar flow in a channel with a backward-facing step is studied for steady cases and for pulsating inlet flow conditions. For steady flows, the influrnce of the inlet velocity profile, the height of the step, and the Reynolds number on the reattachment length is investigated. A parabolic entrance profile was used for pulsating flow. It was found with amplitude of oscillation of one by Re = 100 that the primary vortex breakdown through one pulsatile cycle and the wall shear stress in the separation zone varied markedly with pulsating inlet flow.
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Pei, Ji, Xingcheng Gan, Wenjie Wang, Shouqi Yuan, and Yajing Tang. "Multi-Objective Shape Optimization on the Inlet Pipe of a Vertical Inline Pump." Journal of Fluids Engineering 141, no. 6 (April 9, 2019). http://dx.doi.org/10.1115/1.4043056.
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Vertical inline pump is a single-stage single-suction centrifugal pump with a bent pipe before the impeller, which is usually used where installation space is a constraint. In this paper, with three objective functions of efficiencies at 0.5 Qd, 1.0 Qd, and 1.5 Qd, a multi-objective optimization on the inlet pipe of a vertical inline pump was proposed based on genetic algorithm with artificial neural network (ANN). In order to describe the shape of inlet pipe, the fifth-order and third-order Bezier curves were adopted to fit the mid curve and the trend of parameters of cross sections, respectively. Considering the real installation and computation complexity, 11 variables were finally used in this optimization. Latin hypercube sampling (LHS) was adopted to generate 149 sample cases, which were solved by CFD code ANSYS cfx 18.0. The calculation results and design variables were utilized to train ANNs, and these surrogate models were solved for the optimum design using multi-objective genetic algorithm (MOGA). The results showed the following: (1) There was a great agreement between numerical results and experimental results; (2) The ANNs could accurately fit the objective functions and variables. The maximum deviations of efficiencies at 0.5 Qd, 1.0 Qd, and 1.5 Qd, between predicted values and computational values, were 1.94%, 2.35%, and 0.40%; (3) The shape of inlet pipe has great influence on the efficiency at part-load and design conditions while the influence is slight at overload condition; (4) Three optimized cases were selected and the maximum increase of the efficiency at 0.5 Qd, 1.0 Qd, and 1.5 Qd was 4.96%, 2.45, and 0.79%, respectively; and (5) The velocity distributions of outflow in the inlet pipe of the three optimized cases were more uniform than the original one.
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Handayani, Wiwik. "Construction Project Planning and Scheduling: A Case of Inlet Separator Fabrication." Journal of Economics, Finance And Management Studies 04, no. 11 (November 11, 2021). http://dx.doi.org/10.47191/jefms/v4-i11-14.
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Project construction activities must be analyzed from the planning stage to the execution stage so that they can be achieved optimally and achieve the best performance point. Project planning relies on a project scheduling system, of course requiring updates and modifications that show the project conditions in real time. The aims of this paper is propose a project scheduling system that can accommodate projects that have large-scale activities by proposing scheduling and risk analysis using Primavera P6 and Primavera risk analysis. A case study was conducted on the construction of an inlet separator fabrication project in Batam, Indonesia. The proposed method aims to calculate the optimal project completion time through automatic scheduling with primavera software. The method demonstrates practical value for project managers in identifying the shortest project duration and estimating the most optimal time duration for carrying out activities. In addition, using automatic scheduling can provide more complex information including successors and predecessors of activities, critical times, estimates of the overall duration of the project.
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Singh, L., S. N. Singh, and S. S. Sinha. "Inline-Slot Ejector Diffuser for a Warship to Suppress IR Signatures." Warship 2019: Multi-Role Vessels, June 26, 2019. http://dx.doi.org/10.3940/rina.ws.2019.17.
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The infrared (IR) signatures emitted by warships can substantially reduce the survivability chances while operating in the enemy area, as these signatures can be tracked and locked-on by the heat seeking missiles. The primary source for the IR signatures in a warship is the gases emanating from the exhaust of the gas turbine engine. These signatures can be suppressed by installing the passive infrared suppressors such as ejector diffusers, downstream of the turbine exhaust. The prime objective of an ejector diffuser is to reduce the exhaust gases temperature with minimal back pressure. In the present investigation, inline-slot conical ejector diffuser is numerically studied. From the open literature it is found that only step-slot ejector diffuser has been explored and no work on the inline-slot ejector diffuser is reported. Preliminary investigations on the inline-slot ejector diffuser show the performance to be better in terms of mass entrainment and static pressure recovery than the step-slot ejector diffuser, which is commonly used with warship power plants. The focus of the present study is to establish the effect of nozzle exit conditions (i) inlet swirl (S), and (ii) inlet turbulence intensity (TI) on the performance of inline-slot ejector diffuser. In the first part, inlet swirl is varied in the range 0≤S≤0.3 in step of 0.05, and in the second part TI is varied in the range of 1%≤TI≤15% in step of 3%. The performance is evaluated in terms of local and cumulative mass entrainment ratios, non-dimensional temperature distribution, and static pressure recovery. For the first part, it is seen that there is 3% drop in cumulative mass entrainment with the increase in swirl number from 0 to 0.3 and this can be attributed to the drop in potential core region. Higher wall temperatures in the mixing tube are observed for all the configurations with swirl cases. Static pressure recovery increases with the increase in the swirl number. For the second part, the effect of turbulence intensity on the performance of inline slot ejector diffuser is carried out. It is seen that the mass entrainment decreases by ~5% when turbulence intensity is increased from 1% to 15%. No significant effect of turbulence intensity is seen on the temperature distribution and pressure recovery.
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Villalonga, J. F., D. Solari, R. Cuocolo, V. De Lucia, L. Ugga, C. Gragnaniello, J. I. Pailler, et al. "Clinical application of the “sellar barrier’s concept” for predicting intraoperative CSF leak in endoscopic endonasal surgery for pituitary adenomas with a machine learning analysis." Frontiers in Surgery 9 (September 8, 2022). http://dx.doi.org/10.3389/fsurg.2022.934721.
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BackgroundRecently, it was defined that the sellar barrier entity could be identified as a predictor of cerebrospinal fluid (CSF) intraoperative leakage. The aim of this study is to validate the application of the sellar barrier concept for predicting intraoperative CSF leak in endoscopic endonasal surgery for pituitary adenomas with a machine learning approach.MethodsWe conducted a prospective cohort study, from June 2019 to September 2020: data from 155 patients with pituitary subdiaphragmatic adenoma operated through endoscopic approach at the Division of Neurosurgery, Università degli Studi di Napoli “Federico II,” were included. Preoperative magnetic resonance images (MRI) and intraoperative findings were analyzed. After processing patient data, the experiment was conducted as a novelty detection problem, splitting outliers (i.e., patients with intraoperative fistula, n = 11/155) and inliers into separate datasets, the latter further separated into training (n = 115/144) and inlier test (n = 29/144) datasets. The machine learning analysis was performed using different novelty detection algorithms [isolation forest, local outlier factor, one-class support vector machine (oSVM)], whose performance was assessed separately and as an ensemble on the inlier and outlier test sets.ResultsAccording to the type of sellar barrier, patients were classified into two groups, i.e., strong and weak barrier; a third category of mixed barrier was defined when a case was neither weak nor strong. Significant differences between the three datasets were found for Knosp classification score (p = 0.0015), MRI barrier: strong (p = 1.405 × 10−6), MRI barrier: weak (p = 4.487 × 10−8), intraoperative barrier: strong (p = 2.788 × 10−7), and intraoperative barrier: weak (p = 2.191 × 10−10). We recorded 11 cases of intraoperative leakage that occurred in the majority of patients presenting a weak sellar barrier (p = 4.487 × 10−8) at preoperative MRI. Accuracy, sensitivity, and specificity for outlier detection were 0.70, 0.64, and 0.72 for IF; 0.85, 0.45, and 1.00 for LOF; 0.83, 0.64, and 0.90 for oSVM; and 0.83, 0.55, and 0.93 for the ensemble, respectively.ConclusionsThere is a true correlation between the type of sellar barrier at MRI and its in vivo features as observed during endoscopic endonasal surgery. The novelty detection models highlighted differences between patients who developed an intraoperative CSF leak and those who did not.
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Huemer, Florian, Murad Jamalieh, Ferdinand Bammer, and Dirk Hönig. "Inline imaging-ellipsometer for printed electronics." tm - Technisches Messen 83, no. 10 (January 28, 2016). http://dx.doi.org/10.1515/teme-2015-0067.
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AbstractPrinted electronics, e.g. organic photo-voltaic, are usually produced by roll-to-roll printing. For this fast growing market no inline-measurement method for 2D-thickness-distributions after printing exists. In many cases layer-thicknesses are in the sub-μm-range, e.g. 10–300 nm, and ellipsometry is one typical technology for this range, but up to now only in the laboratory, since most ellipsometers are too slow and/or measure only a spot. A new concept, a stroboscopic imaging ellipsometer, enables fast measurement on a line, to acquire the 2D-distribution of thickness, right after printing.
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Zhang, Rong. "Nonexistence of Positive Solutions for high-order Hardy-H$ \acute{e} $non Systems on $ \mathbb{R}^{n} $." Communications on Pure and Applied Analysis, 2022, 0. http://dx.doi.org/10.3934/cpaa.2022078.
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<p style='text-indent:20px;'>In this paper, we study the following high-order Hardy-H<inline-formula><tex-math id="M3">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>non type system:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{cases} \ (-\Delta)^{\frac{\alpha}{2}}u(x) = |x|^{a}v^{p}(x) ,\\ \ (-\Delta)^{\frac{\beta}{2}}v(x) = |x|^{b}u^{q}(x) ,\\ \end{cases} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M4">\begin{document}$ 0<\alpha = s_{1}+2<n $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ 0<\beta = s_{2}+2<n $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M6">\begin{document}$ 0<s_{1},s_{2}<2 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M7">\begin{document}$ a>-s_{1} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M8">\begin{document}$ b>-s_{2} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M9">\begin{document}$ p,q>0 $\end{document}</tex-math></inline-formula>. There are two cases to be considered. The first one is where the domain is the whole space <inline-formula><tex-math id="M10">\begin{document}$ \mathbb{R}^{n} $\end{document}</tex-math></inline-formula>, and the second one is where the domain is bounded. First of all, we consider the above system in the whole space <inline-formula><tex-math id="M11">\begin{document}$ \mathbb{R}^{n} $\end{document}</tex-math></inline-formula>, we show that the above system are equivalent to the integral system:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE2"> \begin{document}$ \begin{cases} \ u(x) = \int_{\mathbb{R}^{n}}\frac{|y|^{a}v^{p}(y)}{|x-y|^{n-\alpha}}dy,\\[1.5mm] \ v(x) = \int_{\mathbb{R}^{n}}\frac{|y|^{b}u^{q}(y)}{|x-y|^{n-\beta}}dy.\\ \end{cases} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>Then by using the method of moving planes in integral forms, we prove that there are no positive solutions for the above integral system. In addition, while in the subcritical case <inline-formula><tex-math id="M12">\begin{document}$ 1<p<\frac{n+\alpha+2a}{n-\alpha} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M13">\begin{document}$ 1<q<\frac{n+\alpha+2b}{n-\alpha} $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M14">\begin{document}$ \alpha = \beta $\end{document}</tex-math></inline-formula> in the above elliptic system, we prove the nonexistence of a positive solution for the above system in <inline-formula><tex-math id="M15">\begin{document}$ \mathbb{R}^{n} $\end{document}</tex-math></inline-formula>. Then, through the <inline-formula><tex-math id="M16">\begin{document}$ Doubling\ Lemma $\end{document}</tex-math></inline-formula> we obtain the singularity estimates of the positive solutions on a bounded domain <inline-formula><tex-math id="M17">\begin{document}$ \Omega $\end{document}</tex-math></inline-formula>.</p>
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Van Anh, Nguyen Thi, and Bui Thi Hai Yen. "On the time-delayed anomalous diffusion equations with nonlocal initial conditions." Communications on Pure and Applied Analysis, 2022, 0. http://dx.doi.org/10.3934/cpaa.2022119.
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<p style='text-indent:20px;'>In this paper, we are interested in the existence of solutions to the anomalous diffusion equations with delay subjected to nonlocal initial condition:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation} \label{01} \begin{cases} \partial _t(k*(u-u_0)) +(- \Delta)^\sigma u = f(t,u,u_\rho) \; {\rm {in }}\ \mathbb R^+\times \Omega,\\ u\bigr |_{\partial \Omega} = 0\; {\rm {in }}\ \mathbb R^+\times \partial \Omega,\\ u(s)+g(u)(s) = \phi(s) \;{\rm {in }}\ \Omega, s\in [-h,0]. \end{cases} \notag \tag{1} \end{equation} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ \Omega $\end{document}</tex-math></inline-formula> is a bounded domain of <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{R}^n $\end{document}</tex-math></inline-formula>, the constant <inline-formula><tex-math id="M3">\begin{document}$ \sigma $\end{document}</tex-math></inline-formula> is in <inline-formula><tex-math id="M4">\begin{document}$ (0,1] $\end{document}</tex-math></inline-formula>. Under appropriate assumptions on <inline-formula><tex-math id="M5">\begin{document}$ k $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ f,g $\end{document}</tex-math></inline-formula>, we obtain the existence of global solutions and decay mild solutions for (1). The tools used include theory of completely positive functions, resolvent operators, the technique of measures of noncompactness and some fixed point arguments in suitable function spaces. Two application examples with respect to the specific cases of the term <inline-formula><tex-math id="M7">\begin{document}$ k $\end{document}</tex-math></inline-formula> in (1) are presented.</p>
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Du, Lele. "Bounds for subcritical best Sobolev constants in W1, p." Communications on Pure & Applied Analysis, 2021, 0. http://dx.doi.org/10.3934/cpaa.2021135.
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<p style='text-indent:20px;'>This paper aims at establishing fine bounds for subcritical best Sobolev constants of the embeddings</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ W_{0}^{1,p}(\Omega)\hookrightarrow L^{q}(\Omega),\quad 1\leq q< \begin{cases} \frac{Np}{N-p},& 1\leq p<N\\ \infty,& p = N \end{cases} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M2">\begin{document}$ N\geq p\geq1 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ \Omega $\end{document}</tex-math></inline-formula> is a bounded smooth domain in <inline-formula><tex-math id="M4">\begin{document}$ \mathbb{R}^{N} $\end{document}</tex-math></inline-formula> or the whole space. The Sobolev limiting case <inline-formula><tex-math id="M5">\begin{document}$ p = N $\end{document}</tex-math></inline-formula> is also covered by means of a limiting procedure.</p>
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Gluesing-Luerssen, Heide, and Hunter Lehmann. "Automorphism groups and isometries for cyclic orbit codes." Advances in Mathematics of Communications, 2021, 0. http://dx.doi.org/10.3934/amc.2021040.
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<p style='text-indent:20px;'>We study orbit codes in the field extension <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_{q^n} $\end{document}</tex-math></inline-formula>. First we show that the automorphism group of a cyclic orbit code is contained in the normalizer of the Singer subgroup if the orbit is generated by a subspace that is not contained in a proper subfield of <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{F}_{q^n} $\end{document}</tex-math></inline-formula>. We then generalize to orbits under the normalizer of the Singer subgroup. In that situation some exceptional cases arise and some open cases remain. Finally we characterize linear isometries between such codes.</p>