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Journal articles on the topic 'Parametr K(t)'

Author: Grafiati

Published: 28 June 2021

Last updated: 2 February 2022

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1

TABUCHI, Toshiaki, Takashi SOEDA, Terushige KAWATA, and Mitsuru SOEDA. "Parameter Estimation of ARMA Process by Taking into Consideration of ^|^part;kx(t)/^|^part;^|^alpha;T^|^middot;^|^epsilon;(t)." Transactions of the Society of Instrument and Control Engineers 24, no. 4 (1988): 357–62. http://dx.doi.org/10.9746/sicetr1965.24.357.

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2

Petzschner, Frederike H., Irene P. Ponce, Martin Blaimer, Peter M. Jakob, and Felix A. Breuer. "Fast MR parameter mapping using k-t principal component analysis." Magnetic Resonance in Medicine 66, no. 3 (March 9, 2011): 706–16. http://dx.doi.org/10.1002/mrm.22826.

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3

Chuan-Hui, N., and S. Xiao-Bao. "Grüneisen parameter of lithium, sodium and potassium at T=298 K." Journal of Physics and Chemistry of Solids 62, no. 7 (July 2001): 1359–61. http://dx.doi.org/10.1016/s0022-3697(01)00007-5.

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4

Deshmukh, Mangesh R., Ganesh M. Bansode, and Pallavi Mahajan. "EVALUATION OF POTATO CULTIVAR FOR GROWTH AND YIELD PARAMETER." World Journal of Biology and Biotechnology 3, no. 1 (April 15, 2018): 203. http://dx.doi.org/10.33865/wjb.003.01.0138.

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The present investigation on evaluation of varietal performance of various potato varieties under Pune Conditions was initiated in Oct 2012. Potato tubers of Kufri Lauvkar, Kufri Badshah, Kufri Pushkar, Kufri Surya, Kufri Khyati, Kufri Ashoka, Kufri Jyoti, Kufri Pukharaj were planted on ridges and furrows. The results revealed that Kufri Surya recorded significantly higher total tuber yield (20.67 t/ha) followed by Kufri Pukharaj (18.45 t/ha). However percent plant emergence and foliage senescence were found non-significant. Whereas results in respect of yield depicted that the variety Kufri Lauvkar produced the lowest tuber yield of 16.23 t/ha. Tuber dry matter (19.69%) was recorded to be the highest in Kufri Surya which was significantly superior in comparison to the remaining varieties. The least incidence of late blight (9.69%) was recorded on Kufri Khyati which was at par with K. Surya (9.74%). The least incidence of early blight (10.29%) was recorded on K. Lauvkar which too was at par with K. Surya. Keeping this in view K. Surya may be recommended as promising variety for Pune region

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5

Mukherjee, Somnath. "Some Studies on K-essence Lagrangian." International Journal of Innovative Research in Physics 2, no. 2 (January 1, 2021): 9–14. http://dx.doi.org/10.15864/ijiip.2202.

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K-essence Lagrangian is studied in the context of an early universe epoch when t → 0. Equation of state parameter ω < −1 as well as deceleration parameter q0 < −1, indicates an accelerated expansion of the universe at an early epoch of time driven by negative pressure generated by dark energy.

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6

Kristoffel, N., and T. Örd. "The Pseudogap and Superconductivity Order Parameter Fluctuations." International Journal of Modern Physics B 12, no. 29n31 (December 20, 1998): 3106–9. http://dx.doi.org/10.1142/s0217979298002155.

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The influence of superconductivity unequilibrium order parameter correlated fluctuations on the normal phase elementary excitations have been investigated. Correspondingly a fluctuating source of pairs appears in the effective Hamiltonian described using the Gaussian free energy functional. A pseudogap (E g ) is found on the Fermi surface decreasing with rising temperature. It is scaled with the parameter α = ∊ F /k B T c . For smaller α-s E g develops more over T c . In non-high-T c systems and overdoped high-T c compounds the pseudogap is suppressed.

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7

Li, Guo, Li Li, and Peng Zhu. "Galloping Control for Iced Conductors Using Tuned Mass Dampers with Fixed Time-Delayed Feedback." Shock and Vibration 2019 (February 27, 2019): 1–9. http://dx.doi.org/10.1155/2019/4823457.

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A tuned mass damper with fixed time-delay feedbacks (TTMD) is first applied to suppress galloping of iced conductors. It is different from general time-delay feedback control, which also connects an added mass to a galloping body and can absorb vibrational energy. The two-degrees-of-freedom model captures the essential mechanical behaviors of iced conductors with TTMD undergoing galloping. The harmonic balance method is then employed to obtain the approximate analytical solutions of the system. Particularly, the expressions of galloping amplitude and angle frequency were obtained. Then the influence regulations of the time-delay parameter T and strength parameter K on galloping control are fully analysed. The results show the added fixed time-delay feedback control can promote the TTMD’s effect, when suitable time-delay parameter T and strength parameter K are chosen. Moreover, the response amplitude and natural frequency change periodically with time-delay parameter T. With strength parameter K increasing, the response amplitude increases or decreases for a fixed value of T and the TTMD’s effect can be enhanced.

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8

Ye, Wen Ming, Xu Teng Hu, Wan Lin Guo, and Ying Dong Song. "Three Dimensional Criterion for Creep Crack Propagation in C(T) Specimen." Applied Mechanics and Materials 853 (September 2016): 142–47. http://dx.doi.org/10.4028/www.scientific.net/amm.853.142.

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Experimental of two kinds of compact tension (CT) specimens’ creep crack propagation are carried out in this paper. Traditional fracture mechanics and three-dimensional fracture theory are compared and the results show that: The K-Tz two-parameter model can eliminate the thickness-effect on the crack growth rates in the relatively low K range, however when K exceed certain values the effect of thickness for crack growth rates still exists; The Ct and Ct-Tz model can describe the thickness-effect of creep crack growth rates in regions of high Ct; When the crack tip stress intensity factor K of the two kinds of thickness (B=5 mm, B=10 mm) specimens equal to 35 and 31 respectively, this material’s creep crack growth control parameter change from K to Ct.

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9

Tseng, Jimmy. "Eisenstein series and an asymptotic for the K-Bessel function." Ramanujan Journal 56, no. 1 (April 8, 2021): 323–45. http://dx.doi.org/10.1007/s11139-020-00358-8.

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AbstractWe produce an estimate for the K-Bessel function $$K_{r + i t}(y)$$ K r + i t ( y ) with positive, real argument y and of large complex order $$r+it$$ r + i t where r is bounded and $$t = y \sin \theta $$ t = y sin θ for a fixed parameter $$0\le \theta \le \pi /2$$ 0 ≤ θ ≤ π / 2 or $$t= y \cosh \mu $$ t = y cosh μ for a fixed parameter $$\mu >0$$ μ > 0 . In particular, we compute the dominant term of the asymptotic expansion of $$K_{r + i t}(y)$$ K r + i t ( y ) as $$y \rightarrow \infty $$ y → ∞ . When t and y are close (or equal), we also give a uniform estimate. As an application of these estimates, we give bounds on the weight-zero (real-analytic) Eisenstein series $$E_0^{(j)}(z, r+it)$$ E 0 ( j ) ( z , r + i t ) for each inequivalent cusp $$\kappa _j$$ κ j when $$1/2 \le r \le 3/2$$ 1 / 2 ≤ r ≤ 3 / 2 .

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10

Ludwig, Donald. "Estimation Techniques for Distributed Parameter Systems (H. T. Banks and K. Kunisch)." SIAM Review 33, no. 3 (September 1991): 486–87. http://dx.doi.org/10.1137/1033115.

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11

Русаков, В. С., В. С. Покатилов, А. С. Сигов, А. А. Белик, and М. Е. Мацнев. "Температурные изменения магнитной структуры мультиферроика BiFe-=SUB=-0.80-=/SUB=-Cr-=SUB=-0.20-=/SUB=-O-=SUB=-3-=/SUB=-." Физика твердого тела 61, no. 6 (2019): 1107. http://dx.doi.org/10.21883/ftt.2019.06.47686.340.

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AbstractThe results of a Mössbauer study of the magnetic structure of multiferroic BiFe_0.80Cr_0.20O_3 in the temperature range of 5–550 K are presented. It is found that a collinear antiferromagnetic structure of the G type is present in BiFe_0.80Cr_0.20O_3 at temperatures below 260 K. Above 260 K, an anharmonic spin wave with a magnetic anisotropy of the easy-axis type with a high value of the anharmonicity parameter m arises. With a further increase in the temperature, the m parameter decreases and tends to zero at T ~ 420 K, at which a harmonic spin wave comes into existence. Above a temperature of about 420 K, the m parameter increases again and the spin wave becomes anharmonic with an easy-plane magnetic anisotropy. At the Néel temperature, T _N = 505 ± 10 K, the sample undergoes a transition from the magnetically ordered to the paramagnetic state. The change in the type of magnetic anisotropy at T ~ 420 K is explained by competing contributions of different signs to the effective magnetic anisotropy constant and their different temperature dependence for the BiFe_0.80Cr_0.20O_3 multiferroic.

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12

Betego´n, C., and J. W. Hancock. "Two-Parameter Characterization of Elastic-Plastic Crack-Tip Fields." Journal of Applied Mechanics 58, no. 1 (March 1, 1991): 104–10. http://dx.doi.org/10.1115/1.2897135.

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Plane-strain elastic-plastic crack-tip fields have been modeled with modified boundary layer formulations based on the first two terms K and T, of the elastic field. These formulations match the appropriate full field solutions. Compressive T stresses reduce the stresses by an amount which is independent of radial distance, corresponding to the introduction of a second term in addition to the dominant plastic singularity. Geometries which maintain J-dominance are characterized by zero or positive T stresses, while geometries with negative T stresses can be described by a two-parameter characterization using J and T into full plasticity.

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13

Dimitrijevic, M. S., and S. Sahal−Bréchot. "Stark broadening parameter tables for In III, Tl III and Pb IV." Serbian Astronomical Journal, no. 158 (1998): 81–91. http://dx.doi.org/10.2298/saj9858081d.

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Using a semiclassical approach, we have calculated electron-, proton-, and ionized helium-impact line widths and shifts for 20 In III multiplets for perturber densities 1014? 1020 cm?3 and 2 Tl III multiplets for perturber densities 1017 ? 1020 cm?3, and temperatures T = 20,000 ? 500,000 K, in both cases. We have calculated as well, electron-, proton-, and He III-impact line widths and shifts for 2 Pb IV multiplets, for perturber densities 1017? 1020 cm?3 and temperatures T = 50,000 ? 1,000,000 K.

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14

Ross, Sheldon M. "THE MEAN WAITING TIME FOR A PATTERN." Probability in the Engineering and Informational Sciences 13, no. 1 (January 1999): 1–9. http://dx.doi.org/10.1017/s0269964899131012.

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Consider a sequence of independent and identically distributed random variables along with a specified set of k-vectors. We present an expression for E [T], the mean time until the last k observed random variables fall within this set. Not only can this expression often be used to obtain bounds on E[T], it also gives rise to an efficient way of approximating E[T] by a simulation. Specific lower and upper bounds for E[T] are also derived. These latter bounds are given in terms of a parameter, and a Markov chain Monte Carlo approach to approximate this parameter by a simulation is indicated. The results of this paper are illustrated by considering the problem of determining the mean time until a sequence of k-valued random variables has a run of size k that encompasses each value.

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15

HAO, ZHIDONG. "THE EXACT SOLUTION OF THE BCS SELF-CONSISTENCY EQUATION AND THE IMPLICATIONS." Modern Physics Letters B 07, no. 22 (September 20, 1993): 1439–47. http://dx.doi.org/10.1142/s021798499300148x.

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The existence of a first order differential equation for the temperature dependence of the energy gap parameter Δk for each k state is pointed out. By using this equation, exact solution for the energy and temperature dependences of Δk is obtained. The energy range over which Δk is appreciable is within a few kBT c around the Fermi surface. Each k state may have its own temperature T c k, above which Δk = 0. In general, these T c k are not necessarily the same for all k states (the superconducting transition temperature T c corresponds to the largest T c k). Limitations of the BCS cutoff approximation are pointed out.

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16

Ceci, S., A. Švarc, B. Zauner, D. M. Manley, and S. Capstick. "Model-independent resonance parameter extraction from the trace of K and T matrices." Physics Letters B 659, no. 1-2 (January 2008): 228–33. http://dx.doi.org/10.1016/j.physletb.2007.11.003.

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17

Li, Chen, Hiroyuki Okamura, and Tadashi Dohi. "Parameter Estimation of $M_{t}/M/1/K$ Queueing Systems With Utilization Data." IEEE Access 7 (2019): 42664–71. http://dx.doi.org/10.1109/access.2019.2906796.

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18

Romero Yanes, José F., Moacir F. L. da Costa, João P. G. Sampaio, Angélica M. Chacón Valero, Filipe X. Feitosa, and Hosiberto B. de Sant'Ana. "Experimental phase behavior and solubility parameter for crude oil + methane [T = 311.15–373.15 K] and crude oil + methane + CO2 mixtures [T = 343.15–383.15 K]." Fuel 288 (March 2021): 119675. http://dx.doi.org/10.1016/j.fuel.2020.119675.

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19

Journal, Baghdad Science. "Study the Characteristic of the Coupling Parameter ( ? ) in Dusty Plasma by Computer modeling." Baghdad Science Journal 7, no. 1 (March 7, 2010): 98–104. http://dx.doi.org/10.21123/bsj.7.1.98-104.

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Computer modeling has been used to investing the Coulomb coupling parameter ?. The effects of the structure parameter K, grain charge Z, plasma density N, temperature dust grain Td, on the Coulomb coupling parameter had been studied. It was seen that the ? was increasing with increasing Z and N, and decrease with increasing K and T. Also the critical value of ? that the phase transfer of the plasma state from liquid to solid was studied.

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20

Kisic, I., I. Bogunovic, Z. Zgorelec, and D. Bilandzija. "Effects of soil erosion by water under different tillage treatments on distribution of soil chemical parameters." Soil and Water Research 13, No. 1 (January 24, 2018): 36–43. http://dx.doi.org/10.17221/25/2017-swr.

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Soil losses by water erosion were studied under six different tillage treatments, which differ in depth and direction of tillage and planting during a twenty-year period (1995–2014) on Stagnosols in central lowland Croatia. Studied tillage treatments were: control plot (bare fallow-BF), ploughing up and down the slope to 30 cm (PUDS), no-tillage (NT), ploughing across the slope to 30 cm (PAS), very deep ploughing across the slope to 50 cm (VDPAS), and subsoiling to 50 cm + ploughing to 30 cm across the slope (SSPAS). The paper presents the following chemical parameters: soil pH, soil organic matter (OM), plant available phosphorus (P-P<sub>2</sub>O<sub>5</sub>), plant available potassium (K-K<sub>2</sub>O), total carbon content (C<sub>tot</sub>), total nitrogen content (N<sub>tot</sub>) and CN ratio of non-eroded soil and soil loss from studied treatments. All soil sediments had significantly higher content of the studied parameters compared to non-eroded soil. The overall respective levels of OM, C<sub>tot</sub>, N<sub>tot</sub>, P-P<sub>2</sub>O<sub>5</sub> and K-K<sub>2</sub>O loss by eroded soil were as follows: 0.86 (NT) − 10.86 (BF) t/ha, 0.10 (SSPAS) – 2.60 (BF) t/ha, 0.015 (SSPAS) – 0.392 (BF) t/ha, 0.012 (NT) − 0.173 (BF) t/ha and 0.017 (SSPAS) − 0.158 (BF) t/ha. No-tillage and treatments with tillage across the slope (PAS, VDPAS, SSPAS) proved to be much more efficient in storing investigated soil nutrients.

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21

Zhang, Xuemei. "Parameter Dependence of Positive Solutions for Second-Order Singular Neumann Boundary Value Problems with Impulsive Effects." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/968792.

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The author considers the Neumann boundary value problem-y′′t+Myt=λωtft,yt, t∈J, t≠tk, -Δy′|t=tk=λIktk,ytk, k=1,2,…,m, y′(0)=y′(1)=0and establishes the dependence results of the solution on the parameterλ, which cover equations without impulsive effects and are compared with some recent results by Nieto and O’Regan.

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22

Razavi, F. S., Y. Rohanizadegan, M. Hajialamdari, M. Reedyk, R. K. Kremer, and B. Mitrović. "The effect of quasiparticle self-energy on Cd2Re2O7 superconductor." Canadian Journal of Physics 93, no. 12 (December 2015): 1646–50. http://dx.doi.org/10.1139/cjp-2015-0173.

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The magnitude and the temperature dependence of the superconducting order parameter Δ(T) of single crystals of Cd2Re2O7 (Tc = 1.02 K) was measured using point-contact spectroscopy. To fit the conductance spectra and to extract the order parameter at different temperatures we generalized the Blonder–Tinkham–Klapwijk theory by including the self-energy of the quasiparticles into the Bogoliubov equations. This modification enabled excellent fits of the conductance spectra. Δ(T) increases steeply below the superconducting transition temperature of 1.02 K and levels off below ∼0.8 K at a value of 0.22(1) meV, ≈40% larger than the BCS value. Our results indicate the presence of a strong electron–phonon interaction and an enhanced quasiparticle damping and may be related to a possible phase transition within the superconducting region at ∼0.8 K.

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23

Sultan, Hummara, Uzma Jan, and S. P. Ahmad. "Bayesian Normal and T-K Approximations for Shape Parameter of Type-I Dagum Distribution." International Journal of Mathematical Sciences and Computing 4, no. 3 (July 8, 2018): 13–22. http://dx.doi.org/10.5815/ijmsc.2018.03.02.

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24

HEALY, PATRICK, and KAROL LYNCH. "TWO FIXED-PARAMETER TRACTABLE ALGORITHMS FOR TESTING UPWARD PLANARITY." International Journal of Foundations of Computer Science 17, no. 05 (October 2006): 1095–114. http://dx.doi.org/10.1142/s0129054106004285.

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In this paper we consider the problem of testing an arbitrary digraph G = (V,E) for upward planarity. In particular we describe two fixed-parameter tractable algorithms for testing the upward planarity of G. The first algorithm that we present can test the upward planarity of G in O(2t · t! · |V|2)-time where t is the number of triconnected components of G. The second algorithm that we present uses a standard technique known as kernelisation and can test the upward planarity of G in O(|V|2 + k4 · (2k)!)-time, where k = |E| - |V|.

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25

Aktaş, Can, Sezgin Aygün, and Pradyumn Kumar Sahoo. "Relationship between magnetic field and anisotropy parameter in gravitation theories." Modern Physics Letters A 33, no. 24 (August 3, 2018): 1850135. http://dx.doi.org/10.1142/s0217732318501353.

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The magnetized strange quark matter (MSQM) solutions are obtained for a Marder type universe using constant deceleration parameter. The exact solutions of field equations are obtained for f(R,[Formula: see text]T) = R + 2f(T) model given by [T. Harko et al., Phys. Rev. D 84, 024020 (2011)] with cosmological term. Also, we have obtained General Relativity (GR) solutions for MSQM distributions. For [Formula: see text], we get the dark energy model, i.e. [Formula: see text], [Formula: see text] and [Formula: see text]. However, for [Formula: see text], we find the cosmological constant [Formula: see text] as negative in f(R,[Formula: see text]T) theory and GR. These results agree with [S. Aygün et al., Astrophys. Space Sci. 361, 380 (2016); C. Aktaş and S. Aygün, Chinese J. Phys. 55, 71 (2017); P. K. Sahoo et al., Mod. Phys. Lett. A 32, 1750105 (2017)] in f(R,[Formula: see text]T) theory. The physical consequences of our obtained models are discussed at the end.

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26

Zubair, M. "Phantom crossing with collisional matter in f(T) gravity." International Journal of Modern Physics D 25, no. 05 (April 2016): 1650057. http://dx.doi.org/10.1142/s0218271816500577.

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We study the late-time cosmological evolution of [Formula: see text] (where [Formula: see text] is the torsion scalar) theories with matter contents consisting of collisional self-interacting matter and radiations. The power law, exponential and logarithmic [Formula: see text] models are considered to explore the evolution of Hubble parameter [Formula: see text], dark energy (DE) equation of state (EoS) [Formula: see text] and effective EoS parameter [Formula: see text]. We show that crossing of phantom divide line can be realized in the presence of collisional matter as compared to the results obtained for the choice of noncollisional matter [K. Bamba, C.-Q. Geng, C.-C. Lee and L.-W. Luo, J. Cosmol. Astropart. Phys. 01 (2011) 021; K. Bamba, C.-Q. Geng and C.-C. Lee, arXiv:1008.4036]. The evolutionary behavior of [Formula: see text] is consistent with the one developed in [P. Wu and H. Yu, Eur. Phys. J. C 71 (2011) 1552] and recent observational data [U. Alam, V. Sahni and A. A. Starobinsky, J. Cosmol. Astropart. Phys. 0406 (2004) 008; S. Nesseris and L. Perivolaropoulos, J. Cosmol. Astropart. Phys. 0701 (2007) 018; P. Wu and H. Yu, Phys. Lett. B 643 (2006) 315; U. Alam, V. Sahni and A. A. Starobinsky, J. Cosmol. Astropart. Phys. 0702 (2007) 011; H. K. Jassal, J. S. Bagla and T. Padmanabhan, Mon. Not. R. Astron. Soc. 405 (2010) 2639].

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27

CARMINATI, CARLO, and GIULIO TIOZZO. "The local Hölder exponent for the dimension of invariant subsets of the circle." Ergodic Theory and Dynamical Systems 37, no. 6 (March 8, 2016): 1825–40. http://dx.doi.org/10.1017/etds.2015.135.

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We consider for each $t$ the set $K(t)$ of points of the circle whose forward orbit for the doubling map does not intersect $(0,t)$, and look at the dimension function $\unicode[STIX]{x1D702}(t):=\text{H.dim}\,K(t)$. We prove that at every bifurcation parameter $t$, the local Hölder exponent of the dimension function equals the value of the function $\unicode[STIX]{x1D702}(t)$ itself. A similar statement holds for general expanding maps of the circle: namely, we consider the topological entropy of the map restricted to the survival set, and obtain bounds on its local Hölder exponent in terms of the value of the function.

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28

TOYOKI, HIROYASU. "PHASE ORDERING SIMULATION OF VECTOR ORDER-PARAMETERS WITHOUT SINGULAR DEFECTS." Modern Physics Letters B 07, no. 06 (March 10, 1993): 397–403. http://dx.doi.org/10.1142/s0217984993000394.

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Cell dynamical study of phase ordering dynamics is presented for vector order-parameter systems without singular defects. The structure factor satisfies the scaling relation; S (k, t) = l (t)2 g(kl(t)), whose tail at kl ≫ 1 is characterized by a single power as g (x) ~ x −χ. The exponent χ is larger than an analytical value χ = d + n where n and d are the dimensionality of order-parameter and space respectively. The characteristic length varies as l (t) ~ t0.5 for n ≥ 4 while the growth for n = 3 is slower than that.

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29

Dinnebier, Robert E., Wayne A. Dollase, Xavier Helluy, Jörg Kümmerlen, Angelika Sebald, Martin U. Schmidt, Silvina Pagola, Peter W. Stephens, and Sander van Smaalen. "Order–disorder phenomena determined by high-resolution powder diffraction: the structures of tetrakis(trimethylsilyl)methane C[Si(CH3)3]4 and tetrakis(trimethylsilyl)silane Si[Si(CH3)3]4." Acta Crystallographica Section B Structural Science 55, no. 6 (December 1, 1999): 1014–29. http://dx.doi.org/10.1107/s0108768199006126.

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The compounds tetrakis(trimethylsilyl)methane C[Si(CH3)3]4 (TC) and tetrakis(trimethylsilyl)silane Si[Si(CH3)3]4 (TSi) have crystal structures with the molecules in a cubic closed-packed (c.c.p.) stacking. At room temperature both structures have space group Fm{\bar 3}m (Z = 4) with a = 13.5218 (1) Å, V = 2472.3 (1) Å3 for TSi, and a = 12.8902 (2) Å, V = 2141.8 (1) Å3 for TC. X-ray scattering data can be described by a molecule with approximately sixfold orientational disorder, ruling out a structure with free rotating molecules. Upon cooling, TSi exhibits a first-order phase transition at T c = 225 K, as is characterized by a jump of the lattice parameter of Δa = 0.182 Å and by an exothermal maximum in differential scanning calorimetry (DSC) with ΔH = 11.7 kJ mol−1 and ΔS = 50.0 J mol−1 K−1. The structure of the low-temperature phase is refined against X-ray powder data measured at 200 K. It has space group P2 13 (Z = 4), a = 13.17158 (6) Å and V = 2285.15 (2) Å3. The molecules are found to be ordered as a result of steric interactions between neighboring molecules, as is shown by analyzing distances between atoms and by calculations of the lattice energy in dependence on the orientations of the molecules. TC has a phase transition at T c1 = 268 K, with Δa 1 = 0.065 Å, ΔH 1 = 3.63 kJ mol−1 and ΔS 1 = 13.0 J mol−1 K−1. A second first-order phase transition occurs at T c2 = 225 K, characterized by Δa 2 = 0.073 Å, ΔH 2 = 6.9 kJ mol−1 and ΔS 2 = 30.0 J mol−1 K−1. The phase transition at higher temperature has not been reported previously. New NMR experiments show a small anomaly in the temperature dependence of the peak positions in NMR to occur at T c2. Rietveld refinements were performed for the low-temperature phase measured at T = 150 K [space group P2 13, lattice parameter a = 12.609 (3) Å], and for the intermediate phase measured at T = 260 K [space group Pa{\bar 3}, lattice parameter a = 12.7876 (1) Å]. The low-temperature phase of TC is formed isostructural to the low-temperature phase of TSi. In the intermediate phase the molecules exhibit a twofold orientational disorder.

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30

El Amrouss, Abdelrachid, and Omar Hammouti. "Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications." Opuscula Mathematica 41, no. 4 (2021): 489–507. http://dx.doi.org/10.7494/opmath.2021.41.4.489.

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Let \(n\in\mathbb{N}^{*}\), and \(N\geq n\) be an integer. We study the spectrum of discrete linear \(2n\)-th order eigenvalue problems \[\begin{cases}\sum_{k=0}^{n}(-1)^{k}\Delta^{2k}u(t-k) = \lambda u(t) ,\quad & t\in[1, N]_{\mathbb{Z}}, \\ \Delta^{i}u(-(n-1))=\Delta^{i}u(N-(n-1)),\quad & i\in[0, 2n-1]_{\mathbb{Z}},\end{cases}\] where \(\lambda\) is a parameter. As an application of this spectrum result, we show the existence of a solution of discrete nonlinear \(2n\)-th order problems by applying the variational methods and critical point theory.

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31

BRASS, PETER, CHRISTIAN KNAUER, HYEON-SUK NA, CHAN-SU SHIN, and ANTOINE VIGNERON. "THE ALIGNED K-CENTER PROBLEM." International Journal of Computational Geometry & Applications 21, no. 02 (April 2011): 157–78. http://dx.doi.org/10.1142/s0218195911003597.

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In this paper we study several instances of the alignedk-center problem where the goal is, given a set of points S in the plane and a parameter k ⩾ 1, to find k disks with centers on a line ℓ such that their union covers S and the maximum radius of the disks is minimized. This problem is a constrained version of the well-known k-center problem in which the centers are constrained to lie in a particular region such as a segment, a line, or a polygon. We first consider the simplest version of the problem where the line ℓ is given in advance; we can solve this problem in time O(n log 2 n). In the case where only the direction of ℓ is fixed, we give an O(n2 log 2 n)-time algorithm. When ℓ is an arbitrary line, we give a randomized algorithm with expected running time O(n4 log 2 n). Then we present (1+ε)-approximation algorithms for these three problems. When we denote T(k, ε) = (k/ε2+(k/ε) log k) log (1/ε), these algorithms run in O(n log k + T(k, ε)) time, O(n log k + T(k, ε)/ε) time, and O(n log k + T(k, ε)/ε2) time, respectively. For k = O(n1/3/ log n), we also give randomized algorithms with expected running times O(n + (k/ε2) log (1/ε)), O(n+(k/ε3) log (1/ε)), and O(n + (k/ε4) log (1/ε)), respectively.

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32

LEBED, A. G. "MAGNETIC TESTS TO REVEAL TRIPLET SUPERCONDUCTIVITY IN (TMTSF)2PF6 AND A POSSIBLE BREAKING OF A TIME REVERSAL SYMMETRY IN Sr2RuO4, LBCO, and YBCO." International Journal of Modern Physics B 16, no. 20n22 (August 30, 2002): 3198. http://dx.doi.org/10.1142/s0217979202013936.

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We propose methods to reveal the existence of a two-component triplet order parameter (which is recently suggested to break a time reversal symmetry in Sr 2 RuO 4) and to test a possible two-component singlet d-wave order parameter in high- T c superconductors (which may also break the time reversal symmetry). We have also determined a spin part (i.e., d(k) = [dx(k) ≠ 0, dy(k) = 0, dz(k) = 0)] of a triplet order parameter1,2 in (TMTSF) 2 PF 6 under pressure by means of an analysis of the experimental H c2 measurements (I. J. Lee et al., Phys. Rev. Lett. 78, 3555 (1997)).

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33

Meliani, M. Hadj, Y. G. Matvienko, and G. Pluvinage. "Two-parameter fracture criterion (K ρ,c -T ef,c ) based on notch fracture mechanics." International Journal of Fracture 167, no. 2 (September 8, 2010): 173–82. http://dx.doi.org/10.1007/s10704-010-9542-1.

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34

Bagarello, Fabio, and Naomichi Hatano. "PT-symmetric graphene under a magnetic field." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2193 (September 2016): 20160365. http://dx.doi.org/10.1098/rspa.2016.0365.

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We propose a P T -symmetrically deformed version of the graphene tight-binding model under a magnetic field. We analyse the structure of the spectra and the eigenvectors of the Hamiltonians around the K and K ′ points, both in the P T -symmetric and P T -broken regions. In particular, we show that the presence of the deformation parameter V produces several interesting consequences, including the asymmetry of the zero-energy states of the Hamiltonians and the breakdown of the completeness of the eigenvector sets. We also discuss the biorthogonality of the eigenvectors, which turns out to be different in the P T -symmetric and P T -broken regions.

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35

Saint-Paul, M., C. Guttin, P. Lejay, O. Leynaud, and P. Monceau. "Elastic properties of the charge density wave system HoTe3." International Journal of Modern Physics B 32, no. 23 (August 29, 2018): 1850249. http://dx.doi.org/10.1142/s0217979218502491.

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We present ultrasonic measurements on the rare earth tritelluride HoTe3 compound. Different anomalies are observed at the upper and lower charge density wave phase transition T[Formula: see text] = 284 K and T[Formula: see text] = 120 K. A striking T2 temperature dependence of the velocities of the longitudinal C[Formula: see text], C[Formula: see text] and shear C[Formula: see text] modes is observed in the ordered phase below the lower CDW phase transition T[Formula: see text]. Such a behavior is related to the temperature dependence of the CDW order parameter.

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36

ZHAO, WENHUA. "DEFORMATIONS AND INVERSION FORMULAS FOR FORMAL AUTOMORPHISMS IN NONCOMMUTATIVE VARIABLES." International Journal of Algebra and Computation 17, no. 02 (March 2007): 261–88. http://dx.doi.org/10.1142/s0218196707003676.

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Let z = (z1, z2,…, zn) be noncommutative free variables and t a formal parameter which commutes with z. Let k be any unital integral domain of any characteristic and Ft(z) = z - Ht(z) with Ht(z) ∈ k[[t]]〈〈z〉〉×n and the order o(Ht(z))≥ 2. Note that Ft(z) can be viewed as a deformation of the formal map F(z):= z - Ht=1(z) when it makes sense (for example, when Ht(z) ∈ k[t]〈〈z〉〉×n). The inverse map Gt(z) of Ft(z) can always be written as Gt(z) = z+Mt(z) with Mt(z) ∈ k[[t]]〈〈z〉〉×n and o(Mt(z)) ≥ 2. In this paper, we first derive the PDEs satisfied by Mt(z) and u(Ft), u(Gt) ∈ k[[t]]〈〈z〉〉 with u(z) ∈ k〈〈z〉〉 in the general case as well as in the special case when Ht(z) = tH(z) for some H(z) ∈ k〈〈z〉〉×n. We also show that the elements above are actually characterized by certain Cauchy problems of these PDEs. Secondly, we apply the derived PDEs to prove a recurrent inversion formula for formal maps in noncommutative variables. Finally, for the case char. k = 0, we derive an expansion inversion formula by the planar binary rooted trees.

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37

Ichise, Masanori, Robert M. Cohen, and Richard E. Carson. "Noninvasive Estimation of Normalized Distribution Volume: Application to the Muscarinic-2 Ligand [18F]FP-TZTP." Journal of Cerebral Blood Flow & Metabolism 28, no. 2 (July 25, 2007): 420–30. http://dx.doi.org/10.1038/sj.jcbfm.9600530.

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Reference tissue methods to estimate neuroreceptor binding are not applicable to [18F]FP-TZTP (a muscarinic-2 cholinergic receptor ligand), because there is no suitable receptor-free reference region. We evaluated a new method to estimate, without using arterial data or a receptor-free reference region, a receptor parameter called the normalized distribution volume, V*T, using a region containing receptors as the input tissue. V*T is defined as VT /K′1 (distribution volume ( VT) normalized by K′1 of the input region). We used a two-parameter multilinear reference tissue model (MRTM2) to generate parametric images of V*T and R1 ( R1 = K1/ K′1) from [18F]FP-TZTP PET data of healthy aged subjects (10 with apolipoprotein E-ε4 alleles (APOE-ε4(+)) and nine without (APOE-ε4(–)). VT and VT were normalized by plasma-free fraction, fP. By one-tissue kinetic analysis (1TKA) with metabolite-corrected plasma data, VT was previously reported as higher in the APOE-ε4(+) group. The noise magnitude of MRTM2 V*T and R1 images were nearly identical to those of 1TKA VT and K1 images. K′1 or fP was not different between the two groups. V*T (mins) (1,659 ± 497) and VT (mL/cm3) (701 ± 99) in APOE-ε4(+) were higher by 38 and 22% than those (1,209 ± 233 and 577 ± 112) in APOE-ε4(–), respectively. The statistical significance for V*T (0.041) was lower than that for VT (0.025), due to the higher intersubject variability of V*T (25%) than that of VT (17%). We conclude that MRTM2 V*T allows detection of group differences in receptor binding without arterial blood or a receptor-free reference region.

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38

Lee, Hyung Yil, and Yun Jae Kim. "Constraint of Semi-Elliptical Surface Cracks in T and L-Joints." Key Engineering Materials 326-328 (December 2006): 939–44. http://dx.doi.org/10.4028/www.scientific.net/kem.326-328.939.

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Critical defects in pressure vessels and pipes are generally found in the form of a semielliptical surface crack, and the analysis of which is consequently an important issue in engineering fracture mechanics. Furthermore, in addition to the traditional single parameter K or J-integral, the second parameter like T-stress should be measured to quantify the constraint effect. In this work, the validity of the line-spring model is investigated by comparing line-spring J-T solutions to the reference 3D finite element J-T solutions. A full 3D-mesh generating program for semi-elliptical surface cracks is employed to provide such reference 3D solutions. Then some structural characteristics of the surface-cracked T and L-joints are studied by mixed mode line-spring finite element. Negative T-stresses observed in T and L-joints indicate the necessity of J-T two parameter approach for analyses of surface-cracked T and L-joints.

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39

Aaserud, Andreas Næs, and David E. Evans. "Realizing the Braided Temperley–Lieb–Jones C*-Tensor Categories as Hilbert C*-Modules." Communications in Mathematical Physics 380, no. 1 (May 23, 2020): 103–30. http://dx.doi.org/10.1007/s00220-020-03729-w.

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Abstract We associate to each Temperley–Lieb–Jones C*-tensor category $${\mathcal {T}}{\mathcal {L}}{\mathcal {J}}(\delta )$$ T L J ( δ ) with parameter $$\delta $$ δ in the discrete range $$\{2\cos (\pi /(k+2)):\,k=1,2,\ldots \}\cup \{2\}$$ { 2 cos ( π / ( k + 2 ) ) : k = 1 , 2 , … } ∪ { 2 } a certain C*-algebra $${\mathcal {B}}$$ B of compact operators. We use the unitary braiding on $${\mathcal {T}}{\mathcal {L}}{\mathcal {J}}(\delta )$$ T L J ( δ ) to equip the category $$\mathrm {Mod}_{{\mathcal {B}}}$$ Mod B of (right) Hilbert $${\mathcal {B}}$$ B -modules with the structure of a braided C*-tensor category. We show that $${\mathcal {T}}{\mathcal {L}}{\mathcal {J}}(\delta )$$ T L J ( δ ) is equivalent, as a braided C*-tensor category, to the full subcategory $$\mathrm {Mod}_{{\mathcal {B}}}^f$$ Mod B f of $$\mathrm {Mod}_{{\mathcal {B}}}$$ Mod B whose objects are those modules which admit a finite orthonormal basis. Finally, we indicate how these considerations generalize to arbitrary finitely generated rigid braided C*-tensor categories.

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40

Morabito, Filippo, and M. Magdalena Rodríguez. "Saddle towers and minimal k-noids in ℍ2 × ℝ." Journal of the Institute of Mathematics of Jussieu 11, no. 2 (June 21, 2011): 333–49. http://dx.doi.org/10.1017/s1474748011000107.

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AbstractGiven k ≥ 2, we construct a (2k − 2)-parameter family of properly embedded minimal surfaces in ℍ2 × ℝ invariant by a vertical translation T, called saddle towers, which have total intrinsic curvature 4π(1 − k), genus zero and 2k vertical Scherk-type ends in the quotient by T. Each of those examples is obtained from the conjugate graph of a Jenkins–Serrin graph over a convex polygonal domain with 2k edges of the same (finite) length. As limits of saddle towers, we obtain properly embedded minimal surfaces, called minimal k-noids, which are symmetric with respect to a horizontal slice (in fact they are vertical bi-graphs) and have total intrinsic curvature 4π(1 − k), genus zero and k vertical planar ends.

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41

AMOSOV, GRIGORI G. "COCYCLE PERTURBATION OF QUASIFREE ALGEBRAIC K-FLOW LEADS TO REQUIRED ASYMPTOTIC DYNAMICS OF ASSOCIATED COMPLETELY POSITIVE SEMIGROUP." Infinite Dimensional Analysis, Quantum Probability and Related Topics 03, no. 02 (June 2000): 237–46. http://dx.doi.org/10.1142/s0219025700000170.

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We study the quasifree algebraic K-flow τ on the hyperfinite factor ℳ with the expanding subfactor [Formula: see text] generated by representations π of the C*-algebra of the canonical anticommutation relations (CAR) [Formula: see text] over separable Hilbert space ℋ. The type of ℳ and [Formula: see text] can be II1 or IIIλ, 0<λ<1, depending on π. The K-flow τ is obtained by the quasifree lifting of one-parameter group ST consisting of shifts in ℋ with the discrete parameter T=Z or the continuous one T=R. We prove that acting on τ by a quasifree inner Markovian cocycle, one can get the required asymptotic behavior of the perturbed group restriction on [Formula: see text].

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42

Tarasov, V. P., V. I. Privalov, Yu A. Buslaev, and U. Eichhoff. "79,81Br and 133Cs Nuclei Quadrupole Interactions and Phase Transitions in Crystalline Caesium Perbromate." Zeitschrift für Naturforschung B 45, no. 7 (July 1, 1990): 1005–9. http://dx.doi.org/10.1515/znb-1990-0716.

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NMR experiments in solid caesium perbromate have recently been performed at magnetic fields of 1.88 T and 7.04 T together with spectral simulations for 79Br, 81Br and 133Cs in solid caesium perbromate. The line shapes are dominated by quadrupole effects. For bromine the quadrupole asymmetry parameter [η] is observed to be zero at all temperatures while the quadrupole coupling constant (CQ) as a function of temperature shows two approximately linear regions on either side of a non-linear region between 200 K and 260 K where an extended orientational phase transition occurs. 133Cs shows an increase of CQ and a decrease of η with increasing temperature. This behaviour may be associated with an anisotropic change of the “a” lattice parameter.

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43

Chaturvedi, Ruchi, Dr R. K. Shrivatav, and Dr Mohd Salim Ahemad. "EFFECT OF CHEMICAL REACTION ON MHD FLOW OF A VISCO-ELASTIC (WALTER'S LIQUID MODEL-B) FLUID THROUGH POROUS MEDIUM WITH HEAT SOURCE." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 8, no. 1 (June 23, 2013): 721–29. http://dx.doi.org/10.24297/ijct.v8i1.6816.

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In this paper we have studied and discussed the problem of unsteady flow of a visco-elastic (walterâ€™s liquid model B) fluid through porous medium in presence of a heat source and a uniform magnetic field with effect of chemical reaction parameter. The effect of chemical reaction parameter g, porous parameter K and magnetic parameter on fluid velocity, temperature and concentration with respect to vertical axis Y and time t are discussed graphically.

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44

Infante, Gennaro, and J. R. L. Webb. "NONLINEAR NON-LOCAL BOUNDARY-VALUE PROBLEMS AND PERTURBED HAMMERSTEIN INTEGRAL EQUATIONS." Proceedings of the Edinburgh Mathematical Society 49, no. 3 (October 2006): 637–56. http://dx.doi.org/10.1017/s0013091505000532.

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AbstractMotivated by some non-local boundary-value problems (BVPs) that arise in heat-flow problems, we establish new results for the existence of non-zero solutions of integral equations of the form$$ u(t)=\gamma(t)\alpha[u]+\int_{G}k(t,s)f(s,u(s))\,\mathrm{d}s, $$where $G$ is a compact set in $\mathbb{R}^{n}$. Here $\alpha[u]$ is a positive functional and $f$ is positive, while $k$ and $\gamma$ may change sign, so positive solutions need not exist. We prove the existence of multiple non-zero solutions of the BVPs under suitable conditions. We show that solutions of the BVPs lose positivity as a parameter decreases. For a certain parameter range not all solutions can be positive, but for one of the boundary conditions we consider we show that there are positive solutions for certain types of nonlinearity. We also prove a uniqueness result.

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45

Parfati, Nani, Jenny Chandra, Tan Kiauw Sia, Doddy de Queljoe, and Thomas Kardjito. "Studi Farmakokinetika Teofilina Setelah Pemberian Oral Dosis Tunggal Tablet Teofilina dan Aminofilina Lepas Kendali pada Subyek Normal." MPI (Media Pharmaceutica Indonesiana) 2, no. 1 (August 29, 2018): 1–8. http://dx.doi.org/10.24123/mpi.v2i1.1295.

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Telah dilakukan penelitian untuk mempelajari farmakokinetika dari teofilina setelahpemberian oral dosis tunggal tablet teofilina dan aminofilina lepas kendali pada subyek normal. Ta–blet teofilina (dosis 300 mg) dan aminofilina (dosis 350 mg) lepas kendali diberikan dalam bentukoral dosis tunggal, pada pria normal (20-30 tahun, 50-75 kg), tidak merokok, dengan fungsi paruparu,hati, ginjal dan jantung normal. Kadar teofilina serum ditentukan dengan metode FlourescencePolarization Immunoassay (FPIA). Parameter farmakokinetika yang diamati meliputi: t maks, Cpmaks, AUC, tetapan laju absorpsi (Ka) dan eliminasi (K) serta t ½ eliminasi. Hasil penelitian menunjukkanbahwa profil kurva kadar teofilina serum terhadap waktu untuk tablet teofilina (AUC=97,56μg/ml jam, Cp maks=5,83 μg/ml, Ka=0,209 jam-1, t maks=4 jam, K=0,080 jam-1, dan t½=8,87 jam)dan aminofilina (AUC=121,93 μg/ml jam, Cp maks=6,70 μg/ml, Ka=0,239 jam-1, t maks=6,8 jam,K=0,061 jam-1, dan t½=11,51 jam) lepas kendali sesuai dengan profil farmakokinetika sediaan lepaskendali pada umumnya.

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46

Wiart, Jaspar, Christiane Lemieux, and Gracia Y. Dong. "On the dependence structure and quality of scrambled (t, m, s)-nets." Monte Carlo Methods and Applications 27, no. 1 (January 10, 2021): 1–26. http://dx.doi.org/10.1515/mcma-2020-2079.

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Abstract In this paper we develop a framework to study the dependence structure of scrambled ( t , m , s ) {(t,m,s)} -nets. It relies on values denoted by C b ⁢ ( 𝒌 ; P n ) {C_{b}({\boldsymbol{k}};P_{n})} , which are related to how many distinct pairs of points from P n {P_{n}} lie in the same elementary 𝒌 {{\boldsymbol{k}}} -interval in base b. These values quantify the equidistribution properties of P n {P_{n}} in a more informative way than the parameter t. They also play a key role in determining if a scrambled set P ~ n {\widetilde{P}_{n}} is negative lower orthant dependent (NLOD). Indeed, this property holds if and only if C b ⁢ ( 𝒌 ; P n ) ≤ 1 {C_{b}({\boldsymbol{k}};P_{n})\leq 1} for all 𝒌 ∈ ℕ s {{\boldsymbol{k}}\in\mathbb{N}^{s}} , which in turn implies that a scrambled digital ( t , m , s ) {(t,m,s)} -net in base b is NLOD if and only if t = 0 {t=0} . Through numerical examples we demonstrate that these C b ⁢ ( 𝒌 ; P n ) {C_{b}({\boldsymbol{k}};P_{n})} values are a powerful tool to compare the quality of different ( t , m , s ) {(t,m,s)} -nets, and to enhance our understanding of how scrambling can improve the quality of deterministic point sets.

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47

Ogi, Hidekazu. "On KMS states for self-dual CCR algebras and Bogoliubov automorphism groups." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 1 (July 1991): 191–97. http://dx.doi.org/10.1017/s0305004100070249.

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AbstractLet be the self-dual CCR algebra over a triplet (K, r, Γ), where K is assumed to be a Hilbert space, and let {τt}t ∈ R be a Bogoliubov automorphism group of induced by a strongly continuous one-parameter unitary group on K. In this paper, we introduce some continuity for linear functionals on and, under this continuity, we study existence, uniqueness, and non-uniqueness of KMS states for .

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48

Guo, Litao, and Chia-Wei Lee. "Reliability Analysis of the Bijective Connection Networks for Components." Mathematics 7, no. 6 (June 14, 2019): 546. http://dx.doi.org/10.3390/math7060546.

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Connectivity is a critical parameter that can measure the reliability of networks. Let Q ⊆ V ( G ) be a vertex set. If G − Q is disconnected and every component of G − Q contains at least k + 1 vertices, then Q is an extra-cut. The number of vertices in the smallest extra-cut is the extraconnectivity κ k ( G ) . Suppose ω ( G ) is the number of components of G and W ⊆ V ( G ) ; if ω ( G − W ) ≥ t , then w is a t-component cut of G. The number of vertices in the least t-component cut is the t-component connectivity c κ t ( G ) of G. The t-component edge connectivity c λ t ( G ) is defined similarly. In this note, we study the BC networks and obtain the t-component (edge) connectivity of bijective connection networks for some t.

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49

CORRADINI, MARIA G., and MICHA PELEG. "Demonstration of the Applicability of the Weibull–Log-Logistic Survival Model to the Isothermal and Nonisothermal Inactivation of Escherichia coli K-12 MG1655†." Journal of Food Protection 67, no. 11 (November 1, 2004): 2617–21. http://dx.doi.org/10.4315/0362-028x-67.11.2617.

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Published isothermal semilogarithmic survival curves of Escherichia coli K-12 MG1655, in the range of 49.8 to 60.6°C, all had noticeable downward concavity. They could be described by the model log S(t) = −b(T)tn, where S(t) = N(t)/N0, N(t) and N0 being the momentary and initial number of organisms, respectively; b(T) is a temperature-dependent rate parameter; and n is a constant found to be about 1.5. The temperature dependence of b(T) could be described by the log-logistic model, b(T) = ln{1 + exp[k(T − Tc)]}, which had an almost perfect fit, with k = 0.88°C−1 and Tc = 60.5°C. The constants, n, k, and Tc were considered the organism's survival parameters in the particular medium. They were incorporated into a rate equation on the assumption that in nonisothermal heating, the momentary inactivation rate is the isothermal rate at the momentary temperature at a time that corresponds to the momentary survival ratio. This model's estimates matched the actual survival curves obtained in the same work under two different nonisothermal heating profiles, lending support to the notion that the Weibull–log-logistic model combination can be used not only to describe isothermal inactivation mathematically, but also to predict survival patterns under nonisothermal conditions.

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50

HIRSCH, MORRIS W. "Fixed points of local actions of nilpotent Lie groups on surfaces." Ergodic Theory and Dynamical Systems 37, no. 4 (January 28, 2016): 1238–52. http://dx.doi.org/10.1017/etds.2015.73.

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Let$G$be a connected nilpotent Lie group with a continuous local action on a real surface$M$, which might be non-compact or have non-empty boundary$\unicode[STIX]{x2202}M$. The action need not be smooth. Let$\unicode[STIX]{x1D711}$be the local flow on$M$induced by the action of some one-parameter subgroup. Assume$K$is a compact set of fixed points of$\unicode[STIX]{x1D711}$and$U$is a neighborhood of$K$containing no other fixed points.Theorem.If the Dold fixed-point index of$\unicode[STIX]{x1D711}_{t}|U$is non-zero for sufficiently small$t>0$,then$\mathsf{Fix}(G)\cap K\neq \varnothing$.

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