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1

Pskhu, A. V., and S. Sh Rekhviashvili. "Retarded Potentials in Fractional Electrodynamics." Moscow University Physics Bulletin 75, no. 4 (July 2020): 316–19. http://dx.doi.org/10.3103/s0027134920040098.

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2

Schiavone, S. E. "Fractional powers of the retarded potential." Applicable Analysis 42, no. 1-4 (December 1991): 145–55. http://dx.doi.org/10.1080/00036819108840038.

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3

Sikora, Beata. "Controllability criteria for time–delay fractional systems with a retarded state." International Journal of Applied Mathematics and Computer Science 26, no. 3 (September 1, 2016): 521–31. http://dx.doi.org/10.1515/amcs-2016-0036.

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Abstract The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U-controllability are established and proved. Numerical examples illustrate the obtained theoretical results.
4

Jiang, Wei, and Zheng Xia Wang. "Image Denoising New Method Based on Fractional Partial Differential Equation." Advanced Materials Research 532-533 (June 2012): 797–802. http://dx.doi.org/10.4028/www.scientific.net/amr.532-533.797.

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Current total variation method excels at denoising and keeping the characteristics of image edges. However, its ability to retain texture details of smoothing region of image is poor. By combining fractional-order differential theory with total variation method, a new image denoising method is proposed. The new method, while effectively inheriting these advantages, uses the fractional-order differential amplitude-frequency and effectively. Simulation results which we have got show that the new method, on the one hand, can better suppress noise, keep the characteristics of image edges, and retain more texture details than integer-order partial differential methods. On the other hand, the method, above mentioned, is more effective and practical on image denoising than results of PSNR.
5

Nguyen, Van Quang, and Suchin Arunsawatwong. "Stability and Stabilization of Retarded Fractional Delay Differential Systems." IFAC Proceedings Volumes 41, no. 2 (2008): 3928–33. http://dx.doi.org/10.3182/20080706-5-kr-1001.00661.

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6

Dhandapani, Prasantha Bharathi, Jayakumar Thippan, Dumitru Baleanu, and Vinoth Sivakumar. "On a novel fuzzy fractional retarded delay epidemic model." AIMS Mathematics 7, no. 6 (2022): 10122–42. http://dx.doi.org/10.3934/math.2022563.

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<abstract><p>The traditional compartmental epidemic models such as SIR, SIRS, SEIR consider mortality rate as a parameter to evaluate the population changes in susceptible, infected, recovered, and exposed. We present a modern model where population changes in mortality are also considered as the parameter. The existing models in epidemiology always construct a system of the closed medium in which they assume that new birth, as well as new death, will not be possible. But in real life, such a concept will not be assumed to not exist. From our wide observation, we find that the changing rate in every population case is notably negligible, That's why we are preferring to calculate them fractionally using FFDE. Using Lofti's fuzzy concept we are picturing the models after that we are estimating their non-integer values using three distinct methodologies LADM-4, DTM-4 for arbitrary fractional-order $ \alpha_i $, and RKM-4. At $ \alpha_{i} = 1, $ comparison of the estimations will be done. In addition to the simulation, works of numerical estimations, the existence of steady states, equilibrium points, and stability analysis are all done.</p></abstract>
7

Tafesse, Simegne, and Nagarajan Sukavanam. "Approximate Controllability of Fractional Order Retarded Semilinear Control Systems." International Journal of Modern Nonlinear Theory and Application 02, no. 03 (2013): 153–60. http://dx.doi.org/10.4236/ijmnta.2013.23020.

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8

Subramanian, Shivaram, and Hanif D. Sherali. "A fractional programming approach for retail category price optimization." Journal of Global Optimization 48, no. 2 (November 21, 2009): 263–77. http://dx.doi.org/10.1007/s10898-009-9491-2.

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9

Kim, Daewook, and Jin-Mun Jeong. "Controllability for Retarded Semilinear Neutral Control Systems of Fractional Order in Hilbert Spaces." Mathematics 9, no. 6 (March 21, 2021): 671. http://dx.doi.org/10.3390/math9060671.

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In this paper, we discuss the approximate controllability for a class of retarded semilinear neutral control systems of fractional order by investigating the relations between the reachable set of the semilinear retarded neutral system of fractional order and that of its corresponding linear system. The research direction used here is to find the conditions for nonlinear terms so that controllability is maintained even in perturbations. Finally, we will show a simple example to which the main result can be applied.
10

Wang, Ying, Jingxiao Jiang, Zhi Cai, and Kaifeng Zhang. "Fractional Prospect Theory-Based Bidding Strategy of Power Retail Company in the Uniform Pricing Electricity Market under Price Uncertainty." Fractal and Fractional 7, no. 3 (February 23, 2023): 210. http://dx.doi.org/10.3390/fractalfract7030210.

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This paper first proposes a fractional prospect theory-based method for modeling the bidding strategy of a power retail company in the uniform pricing electricity market under price uncertainty. Different from the traditional methods which assume that the retail company always bids completely rationally to maximize its individual payoffs, this paper introduces the prospect theory (PT) into the bidding model to reflect the impacts of psychological factors and subjective perceptions. To address the partial uncertainties brought by the continuous probability distribution in the value function, this paper modifies the classical PT into the fractional prospect theory (FPT) and builds up the FPT-based bidding strategy model under 1-segment and 3-segment bidding rules. The simulation results show that the proposed method can effectively model the psychological factors in the bidding strategy of a power retail company in the uniform pricing electricity market under price uncertainty, which can help to further study the competition and equilibrium of the uniform pricing market considering the psychological factors of the participants.
11

Usta, Fuat, and Mehmet Zeki Sarıkaya. "The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities." Demonstratio Mathematica 52, no. 1 (April 12, 2019): 204–12. http://dx.doi.org/10.1515/dema-2019-0017.

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AbstractIn this study we introduced and tested retarded conformable fractional integral inequalities utilizing non-integer order derivatives and integrals. In line with this purpose, we used the Katugampola type conformable fractional calculus which has several practical properties. These inequalities generalize some famous integral inequalities which provide explicit bounds on unknown functions. The results provided here had been implemented to the global existence of solutions to the conformable fractional differential equations with time delay.
12

Rajalakshmi, K., and T. Ramachandramoorthy. "Oxidation of Chalcones by Morpholinium Chlorochromate with Oxalic Acid as Catalyst: Kinetic and Mechanistic Study." Journal of Chemistry 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/240102.

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The kinetics of oxidation of chalcones by morpholinium chlorochromate (MCC) has been studied in 55% acetic acid-water (v/v) medium. The reaction showed unit order dependence each with respect to oxidant and catalyst and fractional order with respect to substrate and H+ion. Increased ionic strength has no effect on the reaction rate. In the case of substituted chalcones, the order with respect to substrate varies depending upon the nature of the substituent present in the ring. In general, the electron withdrawing substituents retard the reaction rate while the electron releasing substituents enhance the rate of the reaction. From the kinetic data obtained, the activation parameters have been calculated and a suitable mechanism has been proposed.
13

Lan, Do, and Vu Nam Phong. "Decay solutions to retarded fractional evolution inclusions with superlinear perturbations." Fixed Point Theory 23, no. 1 (January 2, 2022): 293–310. http://dx.doi.org/10.24193/fpt-ro.2022.1.19.

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14

Garrido-Atienza, María J., and Jianhua Huang. "Retarded Neutral Stochastic Equations Driven by Multiplicative Fractional Brownian Motion." Stochastic Analysis and Applications 32, no. 5 (September 2, 2014): 820–39. http://dx.doi.org/10.1080/07362994.2014.938860.

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15

Bonnet, Catherine, and Jonathan R. Partington. "Analysis of fractional delay systems of retarded and neutral type." Automatica 38, no. 7 (July 2002): 1133–38. http://dx.doi.org/10.1016/s0005-1098(01)00306-5.

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16

Zhang, Xuping, and Yongxiang Li. "Fractional Retarded Evolution Equations with Measure of Noncompactness Subjected to Mixed Nonlocal Plus Local Initial Conditions." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 1 (February 23, 2018): 69–81. http://dx.doi.org/10.1515/ijnsns-2017-0098.

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AbstractWe consider the fractional retarded evolution equations $$^{C}D_{t}^{q}u(t)+Au(t)=f\Big(t,u_t,\int_{0}^{t}w(t,s,u_s)ds\Big),\quad t\in[0,a],$$where $^{C}D_{t}^{q}$, $q\in(0,1]$, is the fractional derivative in the Caputo sense, $-A$ is the infinitesimal generator of a $C_0$-semigroup of uniformly bounded linear operators $T(t)$$(t\geq0)$ on a Banach space $X$ and the nonlinear operators $f$ and $w$ are given functions satisfying some assumptions, subjected to a general mixed nonlocal plus local initial condition of the form $u(t)=g(u)(t)+\phi(t)$, $t\in[-h,0]$. Under more general conditions, the existence of mild solutions and positive mild solutions are obtained by means of fractional calculus and fixed point theory for condensing maps. Moreover, we present an example to illustrate the application of abstract results.
17

Abbas, Saïd, Mouffak Benchohra, and Seenith Sivasundaram. "Coupled Pettis-Hadamard Fractional Differential Systems with Retarded and Advanced Arguments." Journal of Mathematics and Statistics 14, no. 1 (January 1, 2018): 56–63. http://dx.doi.org/10.3844/jmssp.2018.56.63.

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18

Cho, Seong Ho, Jin-Mun Jeong, and Yong Han Kang. "REGULARITY FOR FRACTIONAL ORDER RETARDED NEUTRAL DIFFERENTIAL EQUATIONS IN HILBERT SPACES." Journal of the Korean Mathematical Society 53, no. 5 (September 1, 2016): 1019–36. http://dx.doi.org/10.4134/jkms.j150354.

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19

Zhang, Xuping, Pengyu Chen, and Yongxiang Li. "Fractional Retarded Differential Equations Involving Mixed Nonlocal Plus Local Initial Conditions." Numerical Functional Analysis and Optimization 40, no. 14 (July 9, 2019): 1678–702. http://dx.doi.org/10.1080/01630563.2019.1639728.

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20

Diop, Mamadou A., and María J. Garrido-Atienza. "Retarded evolution systems driven by fractional Brownian motion with Hurst parameter." Nonlinear Analysis: Theory, Methods & Applications 97 (March 2014): 15–29. http://dx.doi.org/10.1016/j.na.2013.11.008.

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21

Zheng, Guoliang, Lili Wan, Tiefeng He, Qingyang Wu, and Xuhui Zhang. "The Propagation Characteristics of Circular Airy Beams with Propagational Fractional-Order Optical Vortices." Photonics 11, no. 1 (January 7, 2024): 64. http://dx.doi.org/10.3390/photonics11010064.

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We investigate the propagation properties of circular Airy beams (CABs) with propagational fractional-order optical vortices (OVs). The superposition of the phase singularity and polarization singularity from a vortex vector beam (VVB) plays a significant role in creating a propagational fractional vortex beam. Propagational fractional vortex beams can be considered as a superposition of left and right circularly polarized vortex beams with different integer topological charges (TCs). We study the propagation characteristics of two kinds of propagational fractional vortex CABs, and the results show that both of the two kinds of beams can stably propagate in free space, and they exhibit an “abruptly auto-focusing” property and “self-healing” property during the propagation. The intensity distribution of the first kind of propagational fractional vortex CAB has an odd number of petals (2m + 1), while the second kind of beam has a crescent-shaped intensity distribution. The influence of turbulence on the beam propagation through atmosphere under different turbulence strengths is also numerically studied in this paper. A fractional vortex CAB with an initial radius r0 = 10 mm can retain its shape after propagating 20 m when the atmospheric refractive-index structure constant CN2=0.2×10−12m−2/3. Our results are expected to broaden the application of CABs.
22

Lapinski, R., N. Perico, A. Remuzzi, F. Sangalli, A. Benigni, and G. Remuzzi. "Angiotensin II modulates glomerular capillary permselectivity in rat isolated perfused kidney." Journal of the American Society of Nephrology 7, no. 5 (May 1996): 653–60. http://dx.doi.org/10.1681/asn.v75653.

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Studies in experimental animals and humans have documented that inhibition of the renin-angiotensin system by angiotensin-converting enzyme inhibitors reduces urinary protein excretion rate and retards the development of renal injury. Here we sought to investigate whether angiotensin II (All) modified the size-selective properties to macromolecules of the glomerular capillary barrier in isolated perfused rat kidney preparation. Compared with basal values, continuous All infusion into the renal artery at the rate of 3 or 8 ng/min, but not at 0.6 ng/min, induced a progressive and significant increase in urinary protein excretion rate. Evaluation of the sieving properties of the glomerular barrier by fractional clearance of polydisperse Ficoll showed that All significantly enhanced the filtration of tracer molecules of radil > or = 34A. All-induced changes in urinary protein excretion rate and in Ficoll fractional clearance were completely prevented by pretreatment with the specific All Type 1 receptor antagonist SR 47436.
23

Lin, Yuanhua, Shanhe Wu, and Wu-Sheng Wang. "A Nonlinear Weakly Singular Retarded Henry-Gronwall Type Integral Inequality and Its Application." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/218507.

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We establish a class of new nonlinear retarded weakly singular integral inequality. Under several practical assumptions, the inequality is solved by adopting novel analysis techniques, and explicit bounds for the unknown functions are given clearly. An application of our result to the fractional differential equations with delay is shown at the end of the paper.
24

Wadhwani, Meena, and Shubha Jain. "Kinetics of Photochemical Oxidation of Glucose by Chloramine-T in Acidic Medium: A Mechanistic Approach." Advanced Materials Research 816-817 (September 2013): 7–12. http://dx.doi.org/10.4028/www.scientific.net/amr.816-817.7.

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A simple, convenient and accurate method for the kinetic study of photochemical oxidation of glucose by chloramine-T in acidic medium is described. The kinetic investigation shows the first order dependence of reaction rate on chloramine-T. With excess concentration of other reactants the reaction rate follows fractional order kinetics with respect to substrate. The reaction is catalyzed by H+ ions as well. A small salt effect and increase in reaction rate with increasing the intensity of light source is also observed. Addition of p-toluene sulphonamide retards the reaction rate. A suitable mechanism in agreement with observed kinetics has been proposed
25

Vanangamudi, G., and S. Srinivasan. "Kinetic Studies on the Oxidation of Someparaandmeta-Substituted Cinnamic Acids by Pyridinium Bromochromate in the Presence of Oxalic Acid (A Co-oxidation Study)." E-Journal of Chemistry 6, no. 3 (2009): 920–27. http://dx.doi.org/10.1155/2009/242743.

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The kinetics of oxidation of cinnamic acids by pyridinium bromochromate (PBC) in the presence of oxalic acid has been studied in acetic acid-water (60:40%) medium. The reaction shows unit order dependence each with respect to oxidant as well as oxalic acid [OX], the order with respect to [H+] and [CA] are fractional. The reaction is acid catalyzed and a low dielectric constant favours the reaction. Increase the ionic strength has no effect on the reaction rate. In the case of substituted cinnamic acids the order with respect to substrate vary depending upon the nature of the substituent present in the ring. In general, the electron withdrawing substituents retard the rate while the electron releasing substituents enhance the rate of reaction. From the kinetic data obtained the activation parameters have been computed and a suitable mechanism has been proposed.
26

Mazhgikhova, M. G. "Dirichlet Problem for a Fractional-Order Ordinary Differential Equation with Retarded Argument." Differential Equations 54, no. 2 (February 2018): 185–92. http://dx.doi.org/10.1134/s0012266118020052.

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27

Arunsawatwong, Suchin, and Quang Van Nguyen. "Design of retarded fractional delay differential systems using the method of inequalities." International Journal of Automation and Computing 6, no. 1 (January 20, 2009): 22–28. http://dx.doi.org/10.1007/s11633-009-0022-x.

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28

Gil-Alana, Luis A., and James E. Payne. "Time series dynamics of US retail gasoline prices: Evidence from fractional integration." Energy Sources, Part B: Economics, Planning, and Policy 12, no. 12 (September 6, 2017): 1066–73. http://dx.doi.org/10.1080/15567249.2017.1360965.

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29

Kapalka, Brian A., Kaan Katircioglu, and Martin L. Puterman. "RETAIL INVENTORY CONTROL WITH LOST SALES, SERVICE CONSTRAINTS, AND FRACTIONAL LEAD TIMES." Production and Operations Management 8, no. 4 (January 5, 2009): 393–408. http://dx.doi.org/10.1111/j.1937-5956.1999.tb00315.x.

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30

Abu Falahah, Ibraheem, Amel Hioual, Mowafaq Omar Al-Qadri, Yazan Alaya AL-Khassawneh, Abdallah Al-Husban, Tareq Hamadneh, and Adel Ouannas. "Synchronization of Fractional Partial Difference Equations via Linear Methods." Axioms 12, no. 8 (July 27, 2023): 728. http://dx.doi.org/10.3390/axioms12080728.

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Discrete fractional models with reaction-diffusion have gained significance in the scientific field in recent years, not only due to the need for numerical simulation but also due to the stated biological processes. In this paper, we investigate the problem of synchronization-control in a fractional discrete nonlinear bacterial culture reaction-diffusion model using the Caputo h-difference operator and a second-order central difference scheme and an L1 finite difference scheme after deriving the discrete fractional version of the well-known Degn–Harrison system and Lengyel–Epstein system. Using appropriate techniques and the direct Lyapunov method, the conditions for full synchronization are determined.Furthermore, this research shows that the L1 finite difference scheme and the second-order central difference scheme may successfully retain the properties of the related continuous system. The conclusions are proven throughout the paper using two major biological models, and numerical simulations are carried out to demonstrate the practical use of the recommended technique.
31

Huang, Tingsheng, Chunyang Wang, and Xuelian Liu. "Depth Image Denoising Algorithm Based on Fractional Calculus." Electronics 11, no. 12 (June 19, 2022): 1910. http://dx.doi.org/10.3390/electronics11121910.

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Depth images are often accompanied by unavoidable and unpredictable noise. Depth image denoising algorithms mainly attempt to fill hole data and optimise edges. In this paper, we study in detail the problem of effectively filtering the data of depth images under noise interference. The classical filtering algorithm tends to blur edge and texture information, whereas the fractional integral operator can retain more edge and texture information. In this paper, the Grünwald–Letnikov-type fractional integral denoising operator is introduced into the depth image denoising process, and the convolution template of this operator is studied and improved upon to build a fractional integral denoising model and algorithm for depth image denoising. Depth images from the Redwood dataset were used to add noise, and the mask constructed by the fractional integral denoising operator was used to denoise the images by convolution. The experimental results show that the fractional integration order with the best denoising effect was −0.4 ≤ ν ≤ −0.3 and that the peak signal-to-noise ratio was improved by +3 to +6 dB. Under the same environment, median filter denoising had −15 to −30 dB distortion. The filtered depth image was converted to a point cloud image, from which the denoising effect was subjectively evaluated. Overall, the results prove that the fractional integral denoising operator can effectively handle noise in depth images while preserving their edge and texture information and thus has an excellent denoising effect.
32

Ruiz-Real, José, Juan Uribe-Toril, Juan Gázquez-Abad, and Jaime de Pablo Valenciano. "Sustainability and Retail: Analysis of Global Research." Sustainability 11, no. 1 (December 20, 2018): 14. http://dx.doi.org/10.3390/su11010014.

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In recent years, the topic of sustainability has gained prominence in many retail sectors. Sustainability is a key element for retailers, who have seen that sustainable development could become an important source of competitive advantage. The purpose of this work is to highlight state of the art sustainability in retailing, for which a bibliometric analysis has been carried out using Web of Science online and Scopus database. Our findings show the most influential countries, journals, authors, and areas of knowledge interested in the topic. By using a fractional counting method to analyze co-occurrence of the author’s keywords, this paper identifies the most frequent terms and seven clusters. This article represents a contribution by identifying the main trends in sustainability and retail research and proposes future research initiatives, such as: analyze under which conditions the sustainability initiatives give better results to retailers; selection of suppliers and supply chain management; evaluate different types of sustainable products; store sustainable management; sustainability actions and retailers image; how to communicate the sustainability actions of retailers; how sustainability actions influence different types of brands; and international and cross-cultural analysis.
33

Bhagwat, V. W., J. Tiwari, A. Choube, and B. Pare. "Kinetics and mechanism of cetyltrimethylammonium bromide catalyzed oxidation of diethylene glycol by chloramine-T in acidic medium." Journal of the Serbian Chemical Society 68, no. 7 (2003): 535–42. http://dx.doi.org/10.2298/jsc0307535b.

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The kinetics and mechanism of the C16TABcatalyzed oxidation of diethylene glycol (2,2?-oxydiethanol) by chloramine-T in acidic medium has been studied. The reaction has a first-order dependence on chloramine-T. With excess concentrations of other reactants, the reaction rate follows fractional order kinetics with respect to [diethylene glycol]. The micellar effect due to cetyltrimethylammonium bromide, a cationic surfactant, has been studied. The reaction is catalyzed by chloride ions as well. The small salt effect and increase in the reaction rate with increasing dielectric constant suggest the involvement of neutral molecules in the rate determining step. Addition of p-toluenesulfonamide retards the reaction rate. On the basis of product analysis, a pertinent mechanism is proposed.
34

Maleki, Mohammad, and Ali Davari. "Fractional retarded differential equations and their numerical solution via a multistep collocation method." Applied Numerical Mathematics 143 (September 2019): 203–22. http://dx.doi.org/10.1016/j.apnum.2019.04.009.

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35

Quintino, Derick David, and Paulo Ferreira. "Diesel prices in Brazil: A dynamic fractional integration analysis." Economics and Business Letters 10, no. 2 (May 31, 2021): 116–25. http://dx.doi.org/10.17811/ebl.10.2.2021.116-125.

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We investigate the behaviour of retail diesel prices in Brazil using fractional integration, with weekly data from January 2010 to April 2020. In this period, we have 3 episodes of relevant economic implications in the country under analysis: i) impeachment of the Brazilian President; ii) the lorry-drivers’ strike; iii) the rise of the global Covid-19 epidemic. We use a sliding windows approach to analyze price dynamics over time. The results suggest that, at the beginning of the sample, prices were non-stationary and non-mean reverting but over the time results changed in the different regions. Results are relevant for market agents and policy-makers, as it can be inferred whether exogenous shocks are temporary, despite taking some time to dissipate completely.
36

Hou, Lijia, Yali Qin, Huan Zheng, Zemin Pan, Jicai Mei, and Yingtian Hu. "Hybrid High-Order and Fractional-Order Total Variation with Nonlocal Regularization for Compressive Sensing Image Reconstruction." Electronics 10, no. 2 (January 12, 2021): 150. http://dx.doi.org/10.3390/electronics10020150.

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Total variation often yields staircase artifacts in the smooth region of the image reconstruction. This paper proposes a hybrid high-order and fractional-order total variation with nonlocal regularization algorithm. The nonlocal means regularization is introduced to describe image structural prior information. By selecting appropriate weights in the fractional-order and high-order total variation coefficients, the proposed algorithm makes the fractional-order and the high-order total variation complement each other on image reconstruction. It can solve the problem of non-smooth in smooth areas when fractional-order total variation can enhance image edges and textures. In addition, it also addresses high-order total variation alleviates the staircase artifact produced by traditional total variation, still smooth the details of the image and the effect is not ideal. Meanwhile, the proposed algorithm suppresses painting-like effects caused by nonlocal means regularization. The Lagrange multiplier method and the alternating direction multipliers method are used to solve the regularization problem. By comparing with several state-of-the-art reconstruction algorithms, the proposed algorithm is more efficient. It does not only yield higher peak-signal-to-noise ratio (PSNR) and structural similarity (SSIM) but also retain abundant details and textures efficiently. When the measurement rate is 0.1, the gains of PSNR and SSIM are up to 1.896 dB and 0.048 dB respectively compared with total variation with nonlocal regularization (TV-NLR).
37

Lolić, Ivana, Petar Sorić, and Marija Logarušić. "A sectoral perspective on the persistence of economic sentiment: mere transitory effect or a long memory process?" Review of Keynesian Economics 11, no. 3 (July 27, 2023): 328–49. http://dx.doi.org/10.4337/roke.2023.03.03.

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Opposing the mainstream view that economic sentiment conveys information of purely short-term relevance, we assess the long memory characteristics of confidence indicators derived from Business and Consumer Surveys (BCS). We utilize a battery of fractional integration tests on five sectoral BCS indicators in 28 European economies. Conforming to social learning theory, we find that the examined confidence indicators in all five sectors exhibit noteworthy persistence. This finding stays intact in various robustness checks: across countries and for different fractional integration test specifications. Nevertheless, post hoc comparisons reveal that confidence in the construction and consumer sectors exhibits considerably more intensive persistence than in the industry, retail trade, and services. Since it is evident that shocks in economic sentiment have long-term or permanent effects, this calls for a revival of Keynesian ideas and the stabilization role of well-thought and timely countercyclical economic policy measures.
38

Dardinier, Thibault, Peter Müller, and Alexander J. Summers. "Fractional resources in unbounded separation logic." Proceedings of the ACM on Programming Languages 6, OOPSLA2 (October 31, 2022): 1066–92. http://dx.doi.org/10.1145/3563326.

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Many separation logics support fractional permissions to distinguish between read and write access to a heap location, for instance, to allow concurrent reads while enforcing exclusive writes. Fractional permissions extend to composite assertions such as (co)inductive predicates and magic wands by allowing those to be multiplied by a fraction. Typical separation logic proofs require that this multiplication has three key properties: it needs to distribute over assertions, it should permit fractions to be factored out from assertions, and two fractions of the same assertion should be combinable into one larger fraction. Existing formal semantics incorporating fractional assertions into a separation logic define multiplication semantically (via models), resulting in a semantics in which distributivity and combinability do not hold for key resource assertions such as magic wands, and fractions cannot be factored out from a separating conjunction. By contrast, existing automatic separation logic verifiers define multiplication syntactically, resulting in a different semantics for which it is unknown whether distributivity and combinability hold for all assertions. In this paper, we present a novel semantics for separation logic assertions that allows states to hold more than a full permission to a heap location during the evaluation of an assertion. By reimposing upper bounds on the permissions held per location at statement boundaries, we retain key properties of separation logic, in particular, the frame rule. Our assertion semantics unifies semantic and syntactic multiplication and thereby reconciles the discrepancy between separation logic theory and tools and enjoys distributivity, factorisability, and combinability. We have formalised our semantics and proved its properties in Isabelle/HOL.
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Forbes, Michael S., Barbara A. Thornhill, Jordan J. Minor, Katherine A. Gordon, Carolina I. Galarreta, and Robert L. Chevalier. "Fight-or-flight: murine unilateral ureteral obstruction causes extensive proximal tubular degeneration, collecting duct dilatation, and minimal fibrosis." American Journal of Physiology-Renal Physiology 303, no. 1 (July 1, 2012): F120—F129. http://dx.doi.org/10.1152/ajprenal.00110.2012.

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Unilateral ureteral obstruction (UUO) is the most widely used animal model of progressive renal disease. Although renal interstitial fibrosis is commonly used as an end point, recent studies reveal that obstructive injury to the glomerulotubular junction leads to the formation of atubular glomeruli. To quantitate the effects of UUO on the remainder of the nephron, renal tubular and interstitial responses were characterized in mice 7 and 14 days after UUO or sham operation under anesthesia. Fractional proximal tubular mass, cell proliferation, and cell death were measured by morphometry. Superoxide formation was identified by nitro blue tetrazolium, and oxidant injury was localized by 4-hydroxynonenol and 8-hydroxydeoxyguanosine. Fractional areas of renal vasculature, interstitial collagen, α-smooth muscle actin, and fibronectin were also measured. After 14 days of UUO, the obstructed kidney loses 19% of parenchymal mass, with a 65% reduction in proximal tubular mass. Superoxide formation is localized to proximal tubules, which undergo oxidant injury, apoptosis, necrosis, and autophagy, with widespread mitochondrial loss, resulting in tubular collapse. In contrast, mitosis and apoptosis increase in dilated collecting ducts, which remain patent through epithelial cell remodeling. Relative vascular volume fraction does not change, and interstitial matrix components do not exceed 15% of total volume fraction of the obstructed kidney. These unique proximal and distal nephron cellular responses reflect differential “fight-or-flight” responses to obstructive injury and provide earlier indexes of renal injury than do interstitial compartment responses. Therapies to prevent or retard progression of renal disease should include targeting proximal tubule injury as well as interstitial fibrosis.
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Min, Liu. "Harnack Inequality and Applications for Stochastic Retarded Differential Equations Driven by Fractional Brownian Motion." Journal of Partial Differential Equations 30, no. 1 (June 2017): 84–94. http://dx.doi.org/10.4208/jpde.v30.n1.7.

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Benchohra, Mouffak, Mokhtar Boumaaza, and Cemil Tunç. "Erd\'elyi-Kober fractional differential inclusions in Banach space with retarded and advanced arguments." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 40, no. 1 (2020): 75. http://dx.doi.org/10.7151/dmdico.1218.

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Kumar, Pradeep, D. N. Pandey, and D. Bahuguna. "Approximations of solutions to a retarded type fractional differential equation with a deviated argument." Journal of Integral Equations and Applications 26, no. 2 (June 2014): 215–42. http://dx.doi.org/10.1216/jie-2014-26-2-215.

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Slama, Abdeldjalil, and Ahmed Boudaoui. "Approximate controllability of retarded impulsive stochastic integro-differential equations driven by fractional Brownian motion." Filomat 33, no. 1 (2019): 289–306. http://dx.doi.org/10.2298/fil1901289s.

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Akbari Moornani, Kamran, and Mohammad Haeri. "On robust stability of LTI fractional-order delay systems of retarded and neutral type." Automatica 46, no. 2 (February 2010): 362–68. http://dx.doi.org/10.1016/j.automatica.2009.11.006.

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45

Mamiya, Ping C., Todd L. Richards, Bradley P. Coe, Evan E. Eichler, and Patricia K. Kuhl. "Brain white matter structure and COMT gene are linked to second-language learning in adults." Proceedings of the National Academy of Sciences 113, no. 26 (June 13, 2016): 7249–54. http://dx.doi.org/10.1073/pnas.1606602113.

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Adult human brains retain the capacity to undergo tissue reorganization during second-language learning. Brain-imaging studies show a relationship between neuroanatomical properties and learning for adults exposed to a second language. However, the role of genetic factors in this relationship has not been investigated. The goal of the current study was twofold: (i) to characterize the relationship between brain white matter fiber-tract properties and second-language immersion using diffusion tensor imaging, and (ii) to determine whether polymorphisms in the catechol-O-methyltransferase (COMT) gene affect the relationship. We recruited incoming Chinese students enrolled in the University of Washington and scanned their brains one time. We measured the diffusion properties of the white matter fiber tracts and correlated them with the number of days each student had been in the immersion program at the time of the brain scan. We found that higher numbers of days in the English immersion program correlated with higher fractional anisotropy and lower radial diffusivity in the right superior longitudinal fasciculus. We show that fractional anisotropy declined once the subjects finished the immersion program. The relationship between brain white matter fiber-tract properties and immersion varied in subjects with different COMT genotypes. Subjects with the Methionine (Met)/Valine (Val) and Val/Val genotypes showed higher fractional anisotropy and lower radial diffusivity during immersion, which reversed immediately after immersion ended, whereas those with the Met/Met genotype did not show these relationships. Statistical modeling revealed that subjects’ grades in the language immersion program were best predicted by fractional anisotropy and COMT genotype.
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Thabaj, K. A., S. A. Chimatadar, and S. T. Nandibewoor. "Oxidation of Tyrosine by Hexacyanoferrate(III) in Aqueous Ethanoic Acid Medium–A Kinetic and Mechanistic Study." Progress in Reaction Kinetics and Mechanism 33, no. 4 (November 2008): 331–48. http://dx.doi.org/10.3184/146867808x372613.

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The kinetics of oxidation of tyrosine by Fe(CN)63- have been studied in 40% AcOH-H2O containing 4.0 mol dm-3 HCl. The oxidation is made possible by varying the difference in redox potential by adding HCl and AcOH to the reaction mixture. The reaction is first order with respect to [Fe(CN)63- and fractional (0.72) order with respect to [tyrosine]. Increasing the acid concentration at constant chloride concentration accelerates the reaction. The order with respect to acid concentration is nearly two and H2Fe(CN)6- is regarded as the active oxidant. The initially formed product, Fe(CN)64- retards the reaction. A suitable mechanism is proposed and the reaction constants of the different steps involved have been evaluated. Activation parameters have also been calculated with respect to the slow step of the mechanism and discussed.
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Sharma, Vandana, K. V. Sharma, and V. W. Bhagwat. "Catalytic Effect of Cetyltrimethylammonium Bromide on the Oxidation of Triethylene glycol by Chloramine-T in Acidic Medium." E-Journal of Chemistry 5, no. 4 (2008): 894–903. http://dx.doi.org/10.1155/2008/402304.

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The kinetics and mechanism of cetyltrimethylammonium bromide catalyzed oxidation of triethylene glycol [2,2'-ethylene diqxybis(ethanol)] by chloramine-T in acidic acid medium have been investigated. The reaction is first order dependence on chloramine-T and fractional order for triethylene glycol with excess concentration of other reactants. The catalytic effect due to cetyletrimethylammonium bromide has been studied. The small salt effect and increase in the reaction rate with increasing dielectric constant suggest the involvement of neutral molecule in the rate-determining step. The addition ofp-toluene sulfonamide retards the reaction rate. The effect of chloride ion on the reaction also studied. The effect of temperature on the reaction has been investigated in the temperature range 313-333K and thermodynamic parameters were calculated from the Arrhenious plot. A tentative mechanism consistent with the experimental results has been proposed.
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Khidasheli, Mirza. "CENTRAL BANK DIGITAL CURRENCY EFFECTS ON FRACTIONAL RESERVE BANKING." Economic Profile 17, no. 1(23) (August 4, 2022): 8–14. http://dx.doi.org/10.52244/ep.2022.23.06.

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An aim of the paper is to explore the outlines of the looming monetary order. For these purposes, we have made a brief retrospective analysis of money genesis. In its inception market had selected gold as a medium of exchange and gold had become a social institution. After WWII the leading force of monetary order changed. The Bretton Woods conference had made a political agreement to endorse the US dollar as a reserve currency. In 1971 the picture had become clearer, and the gold-backed dollar system collapsed as it was predicted earlier. A digital environment has given the reborn of new types of money. The pioneer of digital money was the crypto currency, a decentralized and transparent system to pay and hold the value. As the old saying tells, everything new is well forgotten old one. Since 2021 central Bank of China has launched a digital RMB pilot program. It is easy to grasp that the state tries to substitute the market-developed money (crypto currencies) with the monopolistic system of CBDC. We have found out the effects of CBDC on retail banking and the incapability of CBDC monetary order with fractional reserve banking.
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Xue, H. "Adaptive Cultural Algorithm-Based Cuckoo Search for Time-Dependent Vehicle Routing Problem with Stochastic Customers Using Adaptive Fractional Kalman Speed Prediction." Mathematical Problems in Engineering 2020 (July 24, 2020): 1–18. http://dx.doi.org/10.1155/2020/7258780.

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For the Time-Dependent Vehicle Routing Problem with Stochastic Customers (TDVRPSC), an adaptive Cultural Algorithm-Based Cuckoo Search (CACS) has been proposed in this paper. The convergence of the new algorithm is proved. An adaptive fractional Kalman filter (AFKF) for traffic speed prediction is proposed. An adaptive mechanism for choosing the covariance of state noise is designed. Its mathematical process is proved. Several benchmark instances with different scales are tested, and new solutions are discovered, which are better than the published solutions. The effects of the parameters on the convergence and the results are studied. According to cargo weight of customers to be delivered, the customers can be divided into large, small, and retail customers. The algorithm is tested with fixed demand probability and also different customer types with stochastic demand. The traffic speeds in different business districts in Xiamen at different times are predicted by AFKF. The results show that AFKF has smaller prediction error and better prediction accuracy than fractional Kalman filter and Kalman filter. The effect of different fractional orders on prediction error is compared. The performance of the new algorithm is compared with that of the cultural algorithm and the Cuckoo Search. The result shows that the new algorithm can efficiently and effectively solve DTVRPSC and improve the accuracy of vehicle routing planning of time-varying actual urban traffic road.
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Zimmerman, Sarah L., James Frisbie, David L. Goldstein, Jennifer West, Kevin Rivera, and Carissa M. Krane. "Excretion and conservation of glycerol, and expression of aquaporins and glyceroporins, during cold acclimation in Cope's gray tree frog Hyla chrysoscelis." American Journal of Physiology-Regulatory, Integrative and Comparative Physiology 292, no. 1 (January 2007): R544—R555. http://dx.doi.org/10.1152/ajpregu.00434.2006.

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Cope's gray tree frog Hyla chrysoscelis accumulates glycerol during cold acclimation. We hypothesized that, during this process, gray tree frogs adjust renal filtration and/or reabsorption rates to retain accumulated glycerol. During cold acclimation, plasma concentrations of glycerol rose >200-fold, to 51 mmol/l. Although fractional water reabsorption decreased, glomerular filtration rate (GFR) and, consequently, urine flow were <5% of warm levels, and fractional glycerol reabsorption increased. In contrast, dehydrated frogs increased fractional water reabsorption, decreased GFR, and did not accumulate glycerol. We hypothesized that expression of proteins from the aquaporin (AQP)/glyceroporin (GLP) family was associated with changing patterns of water and glycerol movement. We cloned the cDNA for three such proteins, quantified mRNA expression in nine tissues using real-time quantitative PCR, and functionally characterized them using a Xenopus oocyte expression system. HC-1, an AQP1-like water channel conferring low glycerol permeability, is expressed ubiquitously in warm- and cold-acclimated tissues. HC-2, a water channel most similar to AQP2, is primarily expressed in organs of osmoregulation. HC-3, which is most similar to AQP3, is functionally characterized as a GLP, with low permeability to water but high permeability to glycerol. Aspects of expression levels and functional characteristics varied between cold and warm conditions for each of the three AQPs, suggesting a complex pattern of involvement in osmoregulation related to thermal acclimation.

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