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1
Poláčik, Peter. "On uniqueness of positive entire solutions and other properties of linear parabolic equations." Discrete & Continuous Dynamical Systems - A 12, no. 1 (2005): 13–26. http://dx.doi.org/10.3934/dcds.2005.12.13.
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Ieşan, Dorin, and Ramon Quintanilla. "Qualitative properties in strain gradient thermoelasticity with microtemperatures." Mathematics and Mechanics of Solids 23, no. 2 (2017): 240–58. http://dx.doi.org/10.1177/1081286516680860.
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This paper is devoted to the strain gradient theory of thermoelastic materials whose microelements possess microtemperatures. The work is motivated by an increasing use of materials which possess thermal variation at a microstructure level. In the first part of this paper we deduce the system of basic equations of the linear theory and formulate the boundary-initial-value problem. We establish existence, uniqueness, and continuous dependence results by the means of semigroup theory. Then, we study the one-dimensional problem and establish the analyticity of solutions. Exponential stability and impossibility of localization are consequences of this result. In the case of the anti-plane problem we derive uniqueness and instability results without assuming the positivity of the mechanical energy. Finally, we study equilibrium theory and investigate the effects of a concentrated heat source in an unbounded body.
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Nguyen, Phuoc-Tai, and Hoang-Hung Vo. "Existence, uniqueness and qualitative properties of positive solutions of quasilinear elliptic equations." Journal of Functional Analysis 269, no. 10 (2015): 3120–46. http://dx.doi.org/10.1016/j.jfa.2015.09.003.
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Suárez, Antonio. "Nonnegative solutions for a heterogeneous degenerate competition model." ANZIAM Journal 46, no. 2 (2004): 273–97. http://dx.doi.org/10.1017/s1446181100013845.
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AbstractThis paper deals with the existence, uniqueness and qualitative properties of nonnegative and nontrivial solutions of a spatially heterogeneous Lotka-Volterra competition model with nonlinear diffusion. We give conditions in terms of the coefficients involved in the setting of the problem which assure the existence of nonnegative solutions as well as the uniqueness of a positive solution. In order to obtain these results we employ monotonicity methods, singular spectral theory and a fixed point index.
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Hernández, Eduardo, and Jianhong Wu. "Existence, Uniqueness and Qualitative Properties of Global Solutions of Abstract Differential Equations with State-Dependent Delay." Proceedings of the Edinburgh Mathematical Society 62, no. 3 (2019): 771–88. http://dx.doi.org/10.1017/s001309151800069x.
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AbstractWe study the existence, uniqueness and qualitative properties of global solutions of abstract differential equations with state-dependent delay. Results on the existence of almost periodic-type solutions (including, periodic, almost periodic, asymptotically almost periodic and almost automorphic solutions) are proved. Some examples of partial differential equations with state-dependent delay arising in population dynamics are presented.
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Cabré, Xavier, and Yannick Sire. "Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions." Transactions of the American Mathematical Society 367, no. 2 (2014): 911–41. http://dx.doi.org/10.1090/s0002-9947-2014-05906-0.
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Bhakta, Mousomi, and Debangana Mukherjee. "Nonlocal scalar field equations: Qualitative properties, asymptotic profiles and local uniqueness of solutions." Journal of Differential Equations 266, no. 11 (2019): 6985–7037. http://dx.doi.org/10.1016/j.jde.2018.11.023.
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Berestycki, Henri, and Alessandro Zilio. "Predators–prey models with competition, Part I: Existence, bifurcation and qualitative properties." Communications in Contemporary Mathematics 20, no. 07 (2018): 1850010. http://dx.doi.org/10.1142/s0219199718500104.
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We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their asymptotic properties in time, showing that the solutions have different behavior depending on the choice of the parameters. We also construct heterogeneous stationary solutions and study the limits of strong competition and abundant resources. We then use these information to study some properties such as the existence of solutions that maximize the total population of predators. We prove that in some regimes the optimal solution for the size of the total population contains two or more groups of competing predators.
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Shakhmurov, Veli, and Rishad Shahmurov. "The regularity properties and blow-up of the solutions for improved Boussinesq equations." Electronic Journal of Qualitative Theory of Differential Equations, no. 89 (2021): 1–21. http://dx.doi.org/10.14232/ejqtde.2021.1.89.
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In this paper, we study the Cauchy problem for linear and nonlinear Boussinesq type equations that include the general differential operators. First, by virtue of the Fourier multipliers, embedding theorems in Sobolev and Besov spaces, the existence, uniqueness, and regularity properties of the solution of the Cauchy problem for the corresponding linear equation are established. Here, L p -estimates for a~solution with respect to space variables are obtained uniformly in time depending on the given data functions. Then, the estimates for the solution of linearized equation and perturbation of operators can be used to obtain the existence, uniqueness, regularity properties, and blow-up of solution at the finite time of the Cauchy for nonlinear for same classes of Boussinesq equations. Here, the existence, uniqueness, L p -regularity, and blow-up properties of the solution of the Cauchy problem for Boussinesq equations with differential operators coefficients are handled associated with the growth nature of symbols of these differential operators and their interrelationships. We can obtain the existence, uniqueness, and qualitative properties of different classes of improved Boussinesq equations by choosing the given differential operators, which occur in a wide variety of physical systems.
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Guo, Zongming, Xia Huang, Dong Ye, and Feng Zhou. "Qualitative properties of Hénon type equations with exponential nonlinearity." Nonlinearity 35, no. 1 (2021): 492–512. http://dx.doi.org/10.1088/1361-6544/ac3925.
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Abstract We are interested in the qualitative properties of solutions of the Hénon type equations with exponential nonlinearity. First, we classify the stable at infinity solutions of Δu + |x| α e u = 0 in R N , which gives a complete answer to the problem considered in Wang and Ye (2012 J. Funct. Anal. 262 1705–1727). Secondly, existence and precise asymptotic behaviours of entire radial solutions to Δ2 u = |x| α e u are obtained. Then we classify the stable and stable at infinity radial solutions to Δ2 u = |x| α e u in any dimension.
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González, María del Mar, Mariel Sáez, and Yannick Sire. "Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties." Annali di Matematica Pura ed Applicata (1923 -) 193, no. 6 (2013): 1823–50. http://dx.doi.org/10.1007/s10231-013-0358-2.
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Zhang, Xinguang, Pengtao Xu, Yonghong Wu, and Benchawan Wiwatanapataphee. "The uniqueness and iterative properties of solutions for a general Hadamard-type singular fractional turbulent flow model." Nonlinear Analysis: Modelling and Control 27 (January 25, 2022): 1–17. http://dx.doi.org/10.15388/namc.2022.27.25473.
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In this paper, we consider the iterative properties of positive solutions for a general Hadamard-type singular fractional turbulent flow model involving a nonlinear operator. By developing a double monotone iterative technique we firstly establish the uniqueness of positive solutions for the corresponding model. Then we carry out the iterative analysis for the unique solution including the iterative schemes converging to the unique solution, error estimates, convergence rate and entire asymptotic behavior. In addition, we also give an example to illuminate our results.
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Ben Chrouda, Mohamed. "Uniqueness and Liouville type results for radial solutions of some classes of k -Hessian equations." Electronic Journal of Qualitative Theory of Differential Equations, no. 62 (2022): 1–17. http://dx.doi.org/10.14232/ejqtde.2022.1.62.
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We establish a uniqueness theorem and a Liouville type result for positive radial solutions of some classes of nonlinear autonomous equation with the k -Hessian operator. We also give some interesting qualitative properties of solutions. We provide an approach, based upon a Pohozaev-type identity, that unifies all our results.
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Pei, Minghe, Libo Wang, and Xuezhe Lv. "Existence, uniqueness and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equations." Electronic Journal of Qualitative Theory of Differential Equations, no. 1 (2021): 1–21. http://dx.doi.org/10.14232/ejqtde.2021.1.1.
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Yao, Meiping, Pengzhi Qiao, and Yang Wang. "Some Qualitative Properties of Traveling Wave Fronts of Nonlocal Diffusive Competition-Cooperation Systems of Three Species with Delays." Complexity 2020 (September 18, 2020): 1–19. http://dx.doi.org/10.1155/2020/6909567.
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This paper is concerned with nonlocal diffusion systems of three species with delays. By modified version of Ikehara’s theorem, we prove that the traveling wave fronts of such system decay exponentially at negative infinity, and one component of such solutions also decays exponentially at positive infinity. In order to obtain more information of the asymptotic behavior of such solutions at positive infinity, for the special kernels, we discuss the asymptotic behavior of such solutions of such system without delays, via the stable manifold theorem. In addition, by using the sliding method, the strict monotonicity and uniqueness of traveling wave fronts are also obtained.
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Boulares, Hamid, Abbes Benchaabane, Nuttapol Pakkaranang, Ramsha Shafqat, and Bancha Panyanak. "Qualitative Properties of Positive Solutions of a Kind for Fractional Pantograph Problems using Technique Fixed Point Theory." Fractal and Fractional 6, no. 10 (2022): 593. http://dx.doi.org/10.3390/fractalfract6100593.
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The current paper intends to report the existence and uniqueness of positive solutions for nonlinear pantograph Caputo–Hadamard fractional differential equations. As part of a procedure, we transform the specified pantograph fractional differential equation into an equivalent integral equation. We show that this equation has a positive solution by utilising the Schauder fixed point theorem (SFPT) and the upper and lower solutions method. Another method for proving the existence of a singular positive solution is the Banach fixed point theorem (BFPT). Finally, we provide an example that illustrates and explains our conclusions.
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Guo, Zongming, and Juncheng Wei. "Qualitative properties of entire radial solutions for a biharmonic equation with supercritical nonlinearity." Proceedings of the American Mathematical Society 138, no. 11 (2010): 3957. http://dx.doi.org/10.1090/s0002-9939-10-10374-8.
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Quintanilla, Ramón, and Reinhard Racke. "Qualitative aspects in dual-phase-lag heat conduction." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2079 (2006): 659–74. http://dx.doi.org/10.1098/rspa.2006.1784.
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We investigate the equation of the dual-phase-lag heat conduction proposed by Tzou. To describe this equation, we use the phase lag of the heat flux and the phase lag of the gradient of the temperature. We analyse the basic properties of the solutions of this problem. First, we prove that when both parameters are positive, the problem is well posed and the spatial decay of solutions is controlled by an exponential of the distance. When the phase lag of the gradient of the temperature is bigger than the phase lag of the heat flux, the problem is exponentially stable (which is a natural property to expect for a heat equation) and the spatial behaviour is controlled by an exponential of the square of the distance. Also, a uniqueness result for unbounded solutions is proved in this case.
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Smarrazzo, Flavia. "On a Class of Quasilinear Elliptic Equations with Degenerate Coerciveness and Measure Data." Advanced Nonlinear Studies 18, no. 2 (2018): 361–92. http://dx.doi.org/10.1515/ans-2017-6032.
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AbstractWe study the existence of measure-valued solutions for a class of degenerate elliptic equations with measure data. The notion of solution is natural, since it is obtained by a regularization procedure which also relies on a standard approximation of the datum μ. We provide partial uniqueness results and qualitative properties of the constructed solutions concerning, in particular, the structure of their diffuse part with respect to the harmonic-capacity.
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KHAN, ZAREEN A., and HIJAZ AHMAD. "QUALITATIVE PROPERTIES OF SOLUTIONS OF FRACTIONAL DIFFERENTIAL AND DIFFERENCE EQUATIONS ARISING IN PHYSICAL MODELS." Fractals 29, no. 05 (2021): 2140024. http://dx.doi.org/10.1142/s0218348x21400247.
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Discrete fractional calculus (DFC) is suggested to interpret neural schemes with memory impacts. This study seeks to formulate some discrete fractional nonlinear inequalities with [Formula: see text] fractional sum operators that are used with some conventional and forthright inequalities. Taking into consideration, we recreate the explicit bounds of Gronwall-type inequalities by observing the principle of DFC for unknown functions here. Such inequalities are of new version relative to the current literature findings so far and can be used as a helpful method to evaluate the numerical solutions of discrete fractional differential equations. We show a few uses of the rewarded inequalities to mirror the advantages of our work. Regarding applications, we can apply the acquainted results to discuss boundedness, uniqueness, and continuous dependency on the initial value problem for the solutions of certain underlying worth problems of fractional difference equations. The leading consequences may be proven by the usage of the analysis process and the methodology of the mean value theorem. These variations can be used as an advantageous device in the subjective examination solutions of discrete fractional difference equations.
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Derbazi, Choukri, Qasem M. Al-Mdallal, Fahd Jarad, and Zidane Baitiche. "Some qualitative properties of solutions to a nonlinear fractional differential equation involving two $ \Phi $-Caputo fractional derivatives." AIMS Mathematics 7, no. 6 (2022): 9894–910. http://dx.doi.org/10.3934/math.2022552.
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<abstract><p>The momentous objective of this work is to discuss some qualitative properties of solutions such as the estimate of the solutions, the continuous dependence of the solutions on initial conditions and the existence and uniqueness of extremal solutions to a new class of fractional differential equations involving two fractional derivatives in the sense of Caputo fractional derivative with respect to another function $ \Phi $. Firstly, using the generalized Laplace transform method, we give an explicit formula of the solutions to the aforementioned linear problem which can be regarded as a novelty item. Secondly, by the implementation of the $ \Phi $-fractional Gronwall inequality, we analyze some properties such as estimates and continuous dependence of the solutions on initial conditions. Thirdly, with the help of features of the Mittag-Leffler functions (MLFs), we build a new comparison principle for the corresponding linear equation. This outcome plays a vital role in the forthcoming analysis of this paper especially when we combine it with the monotone iterative technique alongside facet with the method of upper and lower solutions to get the extremal solutions for the analyzed problem. Lastly, we present some examples to support the validity of our main results.</p></abstract>
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Lindstrom, Michael R., and Andrea L. Bertozzi. "Qualitative features of a nonlinear, nonlocal, agent-based PDE model with applications to homelessness." Mathematical Models and Methods in Applied Sciences 30, no. 10 (2020): 1863–91. http://dx.doi.org/10.1142/s0218202520400114.
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In this paper, we develop a continuum model for the movement of agents on a lattice, taking into account location desirability, local and far-range migration, and localized entry and exit rates. Specifically, our motivation is to qualitatively describe the homeless population in Los Angeles. The model takes the form of a fully nonlinear, nonlocal, non-degenerate parabolic partial differential equation. We derive the model and prove useful properties of smooth solutions, including uniqueness and [Formula: see text]-stability under certain hypotheses. We also illustrate numerical solutions to the model and find that a simple model can be qualitatively similar in behavior to observed homeless encampments.
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Bahrouni, Anouar, Hichem Ounaies, and Vicenţiu D. Rădulescu. "Infinitely many solutions for a class of sublinear Schrödinger equations with indefinite potentials." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 3 (2015): 445–65. http://dx.doi.org/10.1017/s0308210513001169.
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In this paper we are concerned with qualitative properties of entire solutions to a Schrödinger equation with sublinear nonlinearity and sign-changing potentials. Our analysis considers three distinct cases and we establish sufficient conditions for the existence of infinitely many solutions.
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Song, Haoyue, and Fanwei Meng. "Some generalizations of delay integral inequalities of Gronwall-Bellman type with power and their applications." Mathematical Foundations of Computing 5, no. 1 (2022): 45. http://dx.doi.org/10.3934/mfc.2021022.
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<p style='text-indent:20px;'>Noting the diverse generalizations of the Gronwall-Bellman inequality, this paper investigates some new delay integral inequalities with power, deriving explicit bound on the solution and providing an example. The inequalities given here can act as powerful tools for studying qualitative properties such as existence, uniqueness, boundedness, stability and asymptotics of solutions of differential and integral equations.</p>
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Hernández-Verón, Miguel Á., and Natalia Romero. "Location, Separation and Approximation of Solutions for Quadratic Matrix Equations." Foundations 2, no. 2 (2022): 457–74. http://dx.doi.org/10.3390/foundations2020030.
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In this work, we focus on analyzing the location and separation of the solutions of the simplest quadratic matrix equation. For this, we use the qualitative properties that we can deduce of the study of the convergence of iterative processes. This study allow us to determine domains of existence and uniqueness of solutions, and therefore to locate and separate the solutions. Another goal is to approximate a solution of the quadratic matrix equation. For this, we consider iterative processes of fixed point type. So, analyzing the convergence of these iterative processes of fixed point type, we locate, separate and approximate solutions of quadratic matrix equations.
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Ferrari, Fausto, and Antonio Vitolo. "Regularity Properties for a Class of Non-uniformly Elliptic Isaacs Operators." Advanced Nonlinear Studies 20, no. 1 (2020): 213–41. http://dx.doi.org/10.1515/ans-2019-2069.
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AbstractWe consider the elliptic differential operator defined as the sum of the minimum and the maximum eigenvalue of the Hessian matrix, which can be viewed as a degenerate elliptic Isaacs operator, in dimension larger than two. Despite of nonlinearity, degeneracy, non-concavity and non-convexity, such an operator generally enjoys the qualitative properties of the Laplace operator, as for instance maximum and comparison principles, ABP and Harnack inequalities, Liouville theorems for subsolutions or supersolutions. Existence and uniqueness for the Dirichlet problem are also proved as well as local and global Hölder estimates for viscosity solutions. All results are discussed for a more general class of weighted partial trace operators.
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GNANN, M. V., H. J. KIM, and H. KNÜPFER. "Travelling wave solutions for a thin-film equation related to the spin-coating process." European Journal of Applied Mathematics 29, no. 3 (2017): 369–92. http://dx.doi.org/10.1017/s0956792517000195.
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We study a problem related to the spin-coating process in which a fluid coats a rotating surface. Our interest lies in the contact-line region for which we propose a simplified travelling wave approximation. We construct solutions to this problem by a shooting method that matches solution branches in the contact-line region and in the interior of the droplet. Furthermore, we prove uniqueness and qualitative properties of the solution connected to the fourth-order nature of the equation, such as a global maximum in the film height close to the contact line, elevated from the average height of the film.
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Ivanov, Tihomir B., and Neli S. Dimitrova. "Qualitative effects of introducing nonlinear birth and death rates for the predator in a predator-prey type model." BIOMATH 6, no. 1 (2017): 1703167. http://dx.doi.org/10.11145/j.biomath.2017.03.167.
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In this paper, we study how introducing nonlinear birth and death rates for the predator might affect the qualitative behavior of a mathematical model, describing predator-prey systems. We base our investigations on a known model, exhibiting anti-predator behavior. We propose a generalization of the latter by introducing generic birth and death rates for the predator and study the dynamics of the resulting system. We establish existence and uniqueness of positive model solutions, their uniform boundedness, existence, local stability and bifurcations of equilibrium points as well as global stability properties of the solutions. Most of the solution properties are demonstrated numerically and graphically by various numerical examples. Based on the obtained results, we show that the model with nonlinear birth and death rates can describe a much more complex behavior of the predator-prey system than the classical model (i.e., with linear rates) does.
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George Maria Selvam, A., and S. Britto Jacob. "STABILITY OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS IN THE FRAME OF ATANGANA-BALEANU OPERATOR." Advances in Mathematics: Scientific Journal 10, no. 5 (2021): 2319–33. http://dx.doi.org/10.37418/amsj.10.5.3.
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Theory of fractional calculus with singular and non-singular kernels is pioneering and has garnered significant interest recently. Fair amount of literature on the qualitative properties of fractional differential and integral equations involving different types of operators is available. This manuscript aims to analyze the stability of a class of nonlinear fractional differential equation in terms of Atangana-Baleanu-Caputo operator. Sufficient conditions for the existence and uniqueness of solutions are obtained by employing classical fixed point theorems and Banach contraction principle. Also adequate conditions for Hyers-Ulam stability are established. To substantiate our analytic results, an example is provided with numerical simulation.
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van Duijn, C. J., L. A. Peletier, and R. J. Schotting. "On the analysis of brine transport in porous media." European Journal of Applied Mathematics 4, no. 3 (1993): 271–302. http://dx.doi.org/10.1017/s0956792500001121.
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An analysis is given of brine transport through a porous medium, which incorporates the effect of volume changes due to variations in the salt concentration. Two specific situations are investigated which lead to self-similarity. We develop the existence and uniqueness theory for the corresponding ordinary differential equations, and give a number of qualitative properties of the solutions. In particular, we present an asymptotic expression for the solution in terms of the relative density difference (ρs−ρf)/ρf. Finally, we show some numerical results. It is found that the volume changes have a noticeable effect on the mass transport only when salt concentrations are large.
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Wang, Pengyan. "Monotonicity of solutions for fractional p-equations with a gradient term." Open Mathematics 20, no. 1 (2022): 465–77. http://dx.doi.org/10.1515/math-2022-0035.
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Abstract In this paper, we consider the following fractional p p -equation with a gradient term: ( − Δ ) p s u ( x ) = f ( x , u ( x ) , ∇ u ( x ) ) . {\left(-\Delta )}_{p}^{s}u\left(x)=f\left(x,u\left(x),\nabla u\left(x)). We first prove the uniqueness and monotonicity of positive solutions in a bounded domain. Then by estimating the singular integrals which define the fractional p p -laplacian along a sequence of approximate maximum points, we obtain monotonicity of positive solutions in the whole space via the sliding method. In order to solve the difficulties caused by the gradient term, we introduce some new techniques which may also be applied to investigate the qualitative properties of solutions for many problems with gradient terms. Our results are extensions of Berestycki and Nirenberg [Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations, J. Geom. Phys. 5 (1988), 237–275] and Wu and Chen [The sliding methods for the fractional p-Laplacian, Adv. Math. 361 (2020), 106933].
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BARTIER, JEAN-PHILIPPE, JEAN DOLBEAULT, REINHARD ILLNER, and MICHAŁ KOWALCZYK. "A QUALITATIVE STUDY OF LINEAR DRIFT-DIFFUSION EQUATIONS WITH TIME-DEPENDENT OR DEGENERATE COEFFICIENTS." Mathematical Models and Methods in Applied Sciences 17, no. 03 (2007): 327–62. http://dx.doi.org/10.1142/s0218202507001942.
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This paper is concerned with entropy methods for linear drift-diffusion equations with explicitly time-dependent or degenerate coefficients. Our goal is to establish a list of various qualitative properties of the solutions. The motivation for this study comes from a model for molecular motors, the so-called Brownian ratchet, and from a nonlinear equation arising in traffic flow models, for which complex long time dynamics occurs. General results are out of the scope of this paper, but we deal with several examples corresponding to most of the expected behaviors of the solutions. We first prove a contraction property for general entropies which is a useful tool for uniqueness and for the convergence to some large time asymptotic solutions which may depend on time. Then we focus on power law and logarithmic relative entropies. When the diffusion term is of the type ∇(|x|α∇·), we prove that the inequality relating the entropy with the entropy production term is a Hardy–Poincaré type inequality, that we establish. Here we assume that α ∈ (0,2] and the limit case α = 2 appears as a threshold for the method. As a consequence, we obtain an exponential decay of the relative entropies. In the case of time-periodic coefficients, we prove the existence of a unique time-periodic solution which attracts all other solutions. The case of a degenerate diffusion coefficient taking the form |x|α with α > 2 is also studied. The Gibbs state exhibits a non-integrable singularity. In this case concentration phenomena may occur, but we conjecture that an additional time-dependence restores the smoothness of the asymptotic solution.
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Sumata, Hiroshi, Frank Kauker, Michael Karcher, and Rüdiger Gerdes. "Covariance of Optimal Parameters of an Arctic Sea Ice–Ocean Model." Monthly Weather Review 147, no. 7 (2019): 2579–602. http://dx.doi.org/10.1175/mwr-d-18-0375.1.
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Abstract The uniqueness of optimal parameter sets of an Arctic sea ice simulation is investigated. A set of parameter optimization experiments is performed using an automatic parameter optimization system, which simultaneously optimizes 15 dynamic and thermodynamic process parameters. The system employs a stochastic approach (genetic algorithm) to find the global minimum of a cost function. The cost function is defined by the model–observation misfit and observational uncertainties of three sea ice properties (concentration, thickness, drift) covering the entire Arctic Ocean over more than two decades. A total of 11 independent optimizations are carried out to examine the uniqueness of the minimum of the cost function and the associated optimal parameter sets. All 11 optimizations asymptotically reduce the value of the cost functions toward an apparent global minimum and provide strikingly similar sea ice fields. The corresponding optimal parameters, however, exhibit a large spread, showing the existence of multiple optimal solutions. The result shows that the utilized sea ice observations, even though covering more than two decades, cannot constrain the process parameters toward a unique solution. A correlation analysis shows that the optimal parameters are interrelated and covariant. A principal component analysis reveals that the first three (six) principal components explain 70% (90%) of the total variance of the optimal parameter sets, indicating a contraction of the parameter space. Analysis of the associated ocean fields exhibits a large spread of these fields over the 11 optimized parameter sets, suggesting an importance of ocean properties to achieve a dynamically consistent view of the coupled sea ice–ocean system.
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Kazakov, A. L., and L. F. Spevak. "Approximate and Exact Solutions to the Singular Nonlinear Heat Equation with a Common Type of Nonlinearity." Bulletin of Irkutsk State University. Series Mathematics 34 (2020): 18–34. http://dx.doi.org/10.26516/1997-7670.2020.34.18.
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The paper deals with the problem of the motion of a heat wave with a specified front for a general nonlinear parabolic heat equation. An unknown function depends on two variables. Along the heat wave front, the coefficient of thermal conductivity and the source function vanish, which leads to a degeneration of the parabolic type of the equation. This circumstance is the mathematical reason for the appearance of the considered solutions, which describe perturbations propagating along the zero background with a finite velocity. Such effects are generally atypical for parabolic equations. Previously, we proved the existence and uniqueness theorem for the problem considered in this paper. Still, it is local and does not allow us to study the properties of the solution beyond the small neighborhood of the heat wave front. To overcome this problem, the article proposes an iterative method for constructing an approximate solution for a given time interval, based on the boundary element approach. Since it is usually not possible to prove strict convergence theorems of approximate methods for nonlinear equations of mathematical physics with a singularity, verification of the calculation results is relevant. One of the traditional ways is to compare them with exact solutions. In this article, we obtain and study an exact solution of the required type, the construction of which is reduced to integrating the Cauchy problem for an ODE. We obtained some qualitative properties, including an interval estimation of the wave amplitude in one particular case. The performed calculations show the effectiveness of the developed computational algorithm, as well as the compliance of the results of calculations with qualitative analysis.
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Sethio, Gabriella, and Salima Hakim. "Visual Metaphors in Set and Properties Design for ‘Setengah Nada Bergeming’ Film Trailer." Journal of Visual Communication Design 6, no. 2 (2022): 61–71. http://dx.doi.org/10.37715/vcd.v6i2.2700.
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In a film production, production design is an important aspect that supports the narrative or story. In production design visual metaphors are often used as concepts for sets and props which have the ability to transform a long text into a shorter visual. Visual metaphor itself is a representation of a place, person, nature, and object that can be a tool to build a narrative as well as describe the nature of a character in a film. The use of visual metaphors can be done by understanding the characters in the film, because each have different characteristics and its own uniqueness. By understanding and using the 3-dimensional aspect of the character as the basis for the design of sets and props, production designers can apply visual metaphors in the design of sets and properties that are suitable for the needs of characters and narratives in films. This paper uses a qualitative approach which elaborates the process of applying visual metaphors into the set and properties design, by using the 3-dimensional character theory as the base for producing the short film trailer entitled Setengah Nada Bergeming. This research finds that by dissecting each element of the 3-dimensional character, production designer can intensify not only how a character is represented and how its contributes in building the entire narrative of the story.
 
 Keyword: visual metaphors, 3-D characters, sets, properties, short film, trailer.
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Sethio, Gabriella, and Salima Hakim. "Visual Metaphors in Set and Properties Design for ‘Setengah Nada Bergeming’ Film Trailer." Journal of Visual Communication Design 6, no. 2 (2022): 1–12. http://dx.doi.org/10.37715/vcd.v6i2.2451.
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In a film production, production design is an important aspect that supports the narrative or story. In production design visual metaphors are often used as concepts for sets and props which have the ability to transform a long text into a shorter visual. Visual metaphor itself is a representation of a place, person, nature, and object that can be a tool to build a narrative as well as describe the nature of a character in a film. The use of visual metaphors can be done by understanding the characters in the film, because each have different characteristics and its own uniqueness. By understanding and using the 3-dimensional aspect of the character as the basis for the design of sets and props, production designers can apply visual metaphors in the design of sets and properties that are suitable for the needs of characters and narratives in films. This paper uses a qualitative approach which elaborates the process of applying visual metaphors into the set and properties design, by using the 3-dimensional character theory as the base for producing the short film trailer entitled Setengah Nada Bergeming. This research finds that by dissecting each element of the 3-dimensional character, production designer can intensify not only how a character is represented and how its contributes in building the entire narrative of the story.
 
 Keyword: visual metaphors, 3-D characters, sets, properties, short film, trailer.
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Chen, Wenxiong, and Leyun Wu. "Liouville Theorems for Fractional Parabolic Equations." Advanced Nonlinear Studies 21, no. 4 (2021): 939–58. http://dx.doi.org/10.1515/ans-2021-2148.
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Abstract In this paper, we establish several Liouville type theorems for entire solutions to fractional parabolic equations. We first obtain the key ingredients needed in the proof of Liouville theorems, such as narrow region principles and maximum principles for antisymmetric functions in unbounded domains, in which we remarkably weaken the usual decay condition u → 0 u\to 0 at infinity to a polynomial growth on 𝑢 by constructing proper auxiliary functions. Then we derive monotonicity for the solutions in a half space R + n × R \mathbb{R}_{+}^{n}\times\mathbb{R} and obtain some new connections between the nonexistence of solutions in a half space R + n × R \mathbb{R}_{+}^{n}\times\mathbb{R} and in the whole space R n - 1 × R \mathbb{R}^{n-1}\times\mathbb{R} and therefore prove the corresponding Liouville type theorems. To overcome the difficulty caused by the nonlocality of the fractional Laplacian, we introduce several new ideas which will become useful tools in investigating qualitative properties of solutions for a variety of nonlocal parabolic problems.
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Salako, Rachidi B., та Wenxian Shen. "Parabolic–elliptic chemotaxis model with space–time-dependent logistic sources on ℝN. I. Persistence and asymptotic spreading". Mathematical Models and Methods in Applied Sciences 28, № 11 (2018): 2237–73. http://dx.doi.org/10.1142/s0218202518400146.
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The current series of three papers is concerned with the asymptotic dynamics in the following parabolic–elliptic chemotaxis system with space- and time-dependent logistic source: [Formula: see text] where [Formula: see text] is a positive integer, [Formula: see text] and [Formula: see text] are positive constants, and the functions [Formula: see text] and [Formula: see text] are positive and bounded. In the first of the series, we investigate the persistence and asymptotic spreading in [Formula: see text]. To this end, under some explicit condition on the parameters, we first show that [Formula: see text] has a unique nonnegative time global classical solution [Formula: see text] with [Formula: see text] for every [Formula: see text] and every nonnegative bounded and uniformly continuous initial function [Formula: see text]. Next we show the pointwise persistence phenomena of the solutions in the sense that, for any solution [Formula: see text] of [Formula: see text] with strictly positive initial function [Formula: see text], there are [Formula: see text] such that [Formula: see text] and show the uniform persistence phenomena of solutions in the sense that there are [Formula: see text] such that for any strictly positive initial function [Formula: see text], there is [Formula: see text] such that [Formula: see text] We then discuss the spreading properties of solutions to [Formula: see text] with compactly supported initial function and prove that there are positive constants [Formula: see text] such that for every [Formula: see text] and every nonnegative initial function [Formula: see text] with nonempty compact support, we have that [Formula: see text] and [Formula: see text] We also discuss the spreading properties of solutions to [Formula: see text] with front-like initial functions. In the second and third of the series, we will study the existence, uniqueness, and stability of strictly positive entire solutions of [Formula: see text] and the existence of transition fronts of [Formula: see text], respectively.
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Prokopska, Aleksandra, and Jacek Abramczyk. "Innovative Building Forms Determined by Orthotropic Properties of Folded Sheets Transformed Into Roof Shells." Journal of the International Association for Shell and Spatial Structures 61, no. 2 (2020): 111–24. http://dx.doi.org/10.20898/j.iass.2020.204.044.
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Qualitative and quantitative characteristics of geometrical and mechanical changes of nominally plane steel sheets folded in one direction, caused by big elastic shape transformations were invented on the basis of the authors' tests, analyzes and computational models of thin-walled folded sheets transformed into shell shapes. Both geometrical and mechanical changes produce significant restrictions in using sheets for shell forms. The deliberate transformations and sheets' characteristics are required to obtain attractive and innovative forms of roof shells and their consistent structures as well as entire buildings. The search for effective solutions related to free forms of buildings and shape transformations of sheets especially in the fields of: shape transformation, effort and stabilization of their walls is necessary due to the high sensitivity of thin-walled open profiles to boundary conditions and loads. A method for shaping such free form buildings that effectively exploit specific orthotropic properties of the transformed sheeting is presented.
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Alturkistani, Raghad, Kavin A, Suresh Devasahayam, et al. "Affordable passive 3D-printed prosthesis for persons with partial hand amputation." Prosthetics and Orthotics International 44, no. 2 (2020): 92–98. http://dx.doi.org/10.1177/0309364620905220.
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Background and Aim: Partial hand amputations are common in developing countries and have a negative impact on patients and their families’ quality of life. The uniqueness of each partial hand amputation, coupled with the relatively high costs of prostheses, makes it challenging to provide suitable prosthetic solutions in developing countries. Current solutions often have long lead times and require a high level of expertise to produce. The aim of this study was to design and develop an affordable patient-specific partial hand prosthesis for developing countries. Technique: The prosthesis was designed for a patient with transmetacarpal amputation (i.e. three amputated fingers and partial palm). The final design was passive, controlled by the contralateral hand, and utilized the advanced flexibility properties of thermoplastic polyurethane in a glove-like design that costs approximately 20 USD to fabricate. Quantitative and qualitative tests were conducted to assess performance of the device after the patient used the final design. A qualitative assessment was performed to gather the patient’s feedback following a series of tests of grasp taxonomy. A quantitative assessment was performed through a grasp and lift test to measure the prosthesis’ maximum load capacity. Discussion: This study showed that the prosthesis enhanced the patient’s manual handling capabilities, mainly in the form of grasp stability. The prosthesis was light weight and could be donned and doffed by the patient independently. Limitations include the need to use the contralateral hand to achieve grasping and low grasp strength. Clinical relevance Persons with partial hand amputation in developing countries lack access to affordable functional prostheses, hindering their ability to participate in the community. 3D-printed prostheses can provide a low-cost solution that is adaptable to different amputation configurations.
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Astafev, Pavel, Aleksey Pavelko, Alexander Lerer, Jakov Reizenkind, Yuvenaliy Noykin, and Larisa Reznichenko. "Microwave-Absorbing Properties of PbMg1/3Nb2/3O3-PbZrO3-PbTiO3-PbGeO3 (PMN-PZT-PG) Solid Solutions on a Microstrip Line in the Microwave Range." Crystals 12, no. 4 (2022): 551. http://dx.doi.org/10.3390/cryst12040551.
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In this paper, a brief review of the current state of research on ferroelectric, ferromagnetic, and multiferroic materials in the microwave range is given, and the main research methods are described. The main areas of application of functional materials in radio electronics are outlined. Multicomponent ferroelectric media based on ferroelectric (PbTiO3), antiferroelectric (PbZrO3), and relaxors (PbMg1/3Nb2/3O3) are considered promising radio-absorbing materials. A method for comparing the electrical parameters of samples using a microstrip line and a network analyzer is described in detail, in which cylindrical samples were placed on a microstrip line. The measurements were carried out in the frequency range 10 MHz–20 GHz. Based on the frequency dependences of the S parameters, the relationships between the resonant frequencies of the samples and their composition were determined. The frequency dependences of the absorption coefficient were calculated for materials of various compositions. For each composition, the effective absorption band was calculated, and a pattern of its distribution over the concentrations of the system components was plotted. For empty areas of the phase diagram, interpolation was performed using the obtained results, which made it possible to obtain a qualitative idea of the radio-absorbing properties of the entire system. It was revealed that the compositions with the greatest variety of different phases had the widest absorption band. The results obtained will help in future research and composition selection for further development of microwave devices such as dielectric resonators, filters, and attenuators.
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Merkulov, Vladislav, and Stanislav Lazarev. "CONTROL AND MONITORING OF FUSION WELDING BY WAY OF EXAMPLE OF MANUFACTURING AIRCRAFT AIR CONDITIONING SYSTEMS ELEMENTS." Bulletin of Bryansk state technical university 2021, no. 9 (2021): 23–28. http://dx.doi.org/10.30987/1999-8775-2021-9-23-28.
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The purpose of the study is estimation of the efficiency of the control systems use for improving the organization of various welding processes and perfectibility of the technological discipline of their implementation. 
 The article opens the concept of "welding production management" as a comprehensive quality and performance management system of the welding process.
 The solution to the problem of reducing the time for optimizing structures was the introduction of a new computer system. It successfully collects data for calculating and analyzing the space of design solutions, for more accurate forecasting of product characteristics based on numerical modeling. The additional module performs the analysis and optimization of the welding process in an interdisciplinary optimization environment. The algorithm sets up strategies for finding the best solution based on the required characteristics and properties of the product. Hybrid and adaptive search methods are used for this purpose.
 The new process eliminates the need to use several segmental systems, while all optimization is now performed in a unified environment.
 The exclusion of the human factor in the selection and installation of the welding mode increases the qualitative and quantitative indicators of the entire technological process, since the preparatory and final time in welding can reach 20% of the entire operation time, and an error in one parameter can lead to a final defect of the whole workpiece.
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Monticelli, Dario D., Kevin R. Payne, and Fabio Punzo. "Poincaré inequalities for Sobolev spaces with matrix-valued weights and applications to degenerate partial differential equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 1 (2018): 61–100. http://dx.doi.org/10.1017/s0308210517000427.
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For bounded domains Ω, we prove that the Lp-norm of a regular function with compact support is controlled by weighted Lp-norms of its gradient, where the weight belongs to a class of symmetric non-negative definite matrix-valued functions. The class of weights is defined by regularity assumptions and structural conditions on the degeneracy set, where the determinant vanishes. In particular, the weight A is assumed to have rank at least 1 when restricted to the normal bundle of the degeneracy set S. This generalization of the classical Poincaré inequality is then applied to develop a robust theory of first-order Lp-based Sobolev spaces with matrix-valued weight A. The Poincaré inequality and these Sobolev spaces are then applied to produce various results on existence, uniqueness and qualitative properties of weak solutions to boundary-value problems for degenerate elliptic, degenerate parabolic and degenerate hyperbolic partial differential equations (PDEs) of second order written in divergence form, where A is calibrated to the matrix of coefficients of the second-order spatial derivatives. The notion of weak solution is variational: the spatial states belong to the matrix-weighted Sobolev spaces with p = 2. For the degenerate elliptic PDEs, the Dirichlet problem is treated by the use of the Poincaré inequality and Lax–Milgram theorem, while the treatment of the Cauchy–Dirichlet problem for the degenerate evolution equations relies only on the Poincaré inequality and the parabolic and hyperbolic counterparts of the Lax–Milgram theorem.
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Шумафов, Магомет Мишаустович. "Second-order stochastic differential equations: stability, dissipativity, periodicity. IV. - A survey." Вестник Адыгейского государственного университета, серия «Естественно-математические и технические науки», no. 2(281) (September 28, 2021): 15–26. http://dx.doi.org/10.53598/2410-3225-2021-2-281-15-26.
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Настоящая статья является продолжением предыдущей статьи и представляет собой четвертую часть работы автора. В работе делается обзор результатов исследований качественных свойств решений стохастических дифференциальных уравнений и систем второго порядка. В первой части был дан краткий обзор результатов работ по стохастической устойчивости решений дифференциальных уравнений и систем второго порядка с использованием аппарата функций Ляпунова. Были приведены некоторые предварительные сведения из теории вероятностей и теории случайных процессов. Во второй части дана конструкция стохастических интегралов Ито и Стратоновича. В третьей части дано понятие стохастического дифференциала, приведена формула Ито дифференцирования сложной функции для стохастических дифференциалов, дано определение стохастического дифференциального уравнения в форме Ито и в форме Стратоновича, сформулирована теорема существования и единственности для решений стохастических дифференциальных уравнений. В настоящей, четвертой, части работы даются вкратце основные сведения из теории устойчивости стохастических дифференциальных уравнений Ито. Приводятся основные определения устойчивости в различных смыслах стохастических дифференциальных систем, формулируются основные общие теоремы об устойчивости в терминах существования функций Ляпунова, являющиеся стохастическими аналогами классических теорем Ляпунова об устойчивости. Дается понятие о стохастических диссипативных системах. Приводится теорема, дающая условия существования периодических и стационарных решений в терминах вспомогательных функций для дифференциальных уравнений со случайной периодической по времени правой частью, представляющей собой периодический или стационарный процесс. This paper is a continuation of the previous papers and presents the fourth part of the author’s work. The paper reviews results concerning qualitative properties of second-order stochastic differential equations and systems. In the first part we gave a short overview on stability of solutions of the second-order stochastic differential equations and systems by Lyapunov functions techniques and introduced some mathematical preliminaries from probability theory and stochastic processes. In the second part the construction of Ito’s and Stratonovich’s stochastic integrals is given. In the third part, analog of the chain rule for stochastic differentials (Ito’s formula) is presented. The stochastic differential equations in the sense of Ito and in the sense of Stratonovich are introduced. The existence and uniqueness theorem for solutions of stochastic differential equations is formulated. In the present fourth part of the work basic facts from the theory of stability of stochastic differential equations are briefly given. The basic definitions of stability in different senses of stochastic differential systems are presented, the basic general theorems on stability are formulated in terms of the existence of Lyapunov functions, which are stochastic analogs of the classical Lyapunov’s theorems on stability. The concept of stochastic dissipative systems is given. A theorem is formulated which gives conditions for existence of periodic and stationary solutions in terms of auxiliary functions for differential equations with a random periodic in time right-hand side, which is a periodic or stationary process.
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Habrel, Mykola, and Mykhailo Habrel. "DIFFERENTIAL URBANISM AS A CONCEPT OF RESTORATION, REORGANIZATION AND DEVELOPMENT OF SUSTAINABILITY OF SPACE UKRAINE." Urban development and spatial planning, no. 81 (August 31, 2022): 70–92. http://dx.doi.org/10.32347/2076-815x.2022.81.70-92.
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The realities of today require changes and development of urban methodology, systematic rethinking of the fundamental categories of urbanism and urban planning. The multiplicity of goals (operational, strategic, tactical, regulatory, long-term planning) of urban planning activities and the probability of tasks (uncertainty and instability of conditions and means) determine the need for multicriteriality of analysis, justification and evaluation of urban planning decisions. The authors elaborated on the categories of differentiation in urbanism. Differential urbanism envisages the return of a significantly higher role to small and medium-sized cities in the space of Ukraine and is aimed at increasing the viability of the country's spatial system, will contribute to the equalization of living conditions for various forms of settlement.
 To build a model of differential urbanism, a model of a five-dimensional urban planning space was used, which includes the dimensions "man - functions - conditions - geometry - time" and covers: 1) consideration of the urbanized system as a whole; 2) based on the fundamental and objective laws of integration (concentration) - differentiation (deconcentration); 3) research and consideration of the specifics of processes in urbanized systems; 4) focus on practical tasks of spatial planning and urban planning; 5) disclosure of relationships between spatial characteristics. The model is presented in the form of a multidimensional matrix (its dimension is determined by the number of elements, and the number of cells corresponds to the number of paired connections) and aims to harmonize spatial characteristics both within the system and with the supersystem. Increasing the sustainability of systems is accompanied by consideration of the entire array of characteristics of space and interactions of all dimensions. The integral criterion for evaluating urbanized systems is defined as advantageous or disadvantageous spatial forms, as well as the properties of space - functionality, energy, uniqueness, dynamism, interconnectedness and unevenness of processes, comfort, efficiency, environmental friendliness, flexibility, reliability, which are combined by us into an integral system viability criterion.
 The characteristics of the spatial system of Ukraine are presented, its features are highlighted, and spatial "shifts" and destruction as a result of the Ukrainian-Russian war are also determined. The requirements, methods, and practical recommendations for reconstruction, reorganization, and increasing the viability of the space of post-war Ukraine based on the provisions of differential urbanism are substantiated. The criteria for evaluating solutions are: the usefulness of the proposal, cost-effectiveness, safety for people and the environment, and the duration of implementation. The need to lay down systemic decisions (strategies for nature protection, formation of the natural framework of the state, selection of regimes of nature protection territories, etc.) was confirmed and the special role of territorial communities was highlighted, which will avoid conflict situations and ensure the development of the state along the path of increasing sustainability.
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Pylypchuk, Oleh, Oleh Strelko, and Yuliia Berdnychenko. "PREFACE." History of science and technology 12, no. 2 (2022): 194–96. http://dx.doi.org/10.32703/2415-7422-2022-12-2-194-196.
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The issue of the journal begins with an article on French sinology. French sinology takes a special place in the history of the sinological studies development. It was France that became the first country where the transformation of missionary sinology, which was common among a limited circle of researchers (mainly in a religious sphere), into the academic scientific discipline, which had already been taught and studied at a professional level in academic institutions, occurred. The Parisian type of sinology used to dominate the entire world for a long time, including such powerful centers of Chinese studies as Germany, Great Britain, the USA, and China itself. In order to form a complete picture of sinology development in France, the authors singled out and analyzed three historical periods covering the entire history of Chinese studies development, starting from its birth and flourishment to the process of stagnation. Modern scientific communication traditionally uses visual narratives, such as comics, for education, presentation of scientific achievements to a mass audience, and as an object of research. In the article by Oksana Hudoshnyk and Oleksandr P. Krupskyi, offers a three-level characterization of the interaction of comic culture and science in a diachronic aspect. Attention is focused not only on the chronological stages of these intersections, the expression of the specifics of the interaction is offered against the background of scientific and public discussions that accompany the comics–science dialogue to this day. Emphasis is placed on the unique phenomenon of the simultaneous concordance of various stages of the dialogue between comics and science, on the prolonged replication of successful inventions into modern experience, and the active testing of known narratives at new levels of a scientific presentation. The next paper assesses the topicality of Vernadsky's concept of the noosphere, coined over almost twenty years starting in the early 20th century. Emphasizing the uniqueness of Vernadsky's concept of the noosphere as the transformation of the biosphere by a man using reason, we concentrate on the assessment of the utopian or realistic nature of his vision of the future of humanity. Based on the philosophical case-studies analysis, it identifies the ideological roots of the noosphere concept, the development of views on the concept in time, the role of reason and scientific thinking, the opinions of its supporters and critics, and Moiseev's related concept of co-evolution. Lectures de Potentia Restitutiva or Of Spring: Explaining the Power of Springing Bodies (1678) is an important book for the history of science. This book is better known for Hooke’s presentation of the law that bears his name. In the article by Isadora Monteiro, seeks to study the Lectures de Potentia Restitutiva once again to better understand Hooke’s thoughts about the rule which bears his name and his conception of gravity, which the author considered a force. Here Hooke’s definitions of body and motion will be presented, as well as his actual objective when he formulated the so-called Hooke’s Law. As we will see, Hooke intended to create a “philosophical scale” to measure the gravitational attraction between bodies. By considering his previous publications, such as An attempt to prove the motion of the Earth from Observations or Micrographia: or some Physiological Descriptions of Minute Bodies, or even unpublished works such as On the inflection of a direct motion into a curve by supervening Attractive principle, it becomes clear that Hooke was already opening a path toward an understanding of gravity before Newton’s Principia (1687) were published. By taking into account the controversy between Isaac Newton and Robert Hooke, we also intend to strengthen the idea that Hooke was an indispensable contributor to the elaboration of a law of universal gravitation. In 1915, the first occupational therapy school was founded by Jane Addams at Hull House (Chicago, USA). In that process, Addams inspired the first generation of occupational therapists, especially Eleanor Clarke Slagle. Thus, in the article by Rodolfo Morrisonseeks to highlight the contribution of Jane Addams to the development of Occupational Therapy through an in-depth bibliographic review, from primary sources. The next article presents the results of a study of the features of biographical and prosopographic materials about famous mathematicians and natural scientists, published in one of the most authoritative journals “Bulletin of Experimental Physics and Elementary Mathematics”, which was published in Kyiv and Odesa during 1886–1917. In fact, the journal was an unofficial periodical printed branch of the Mathematical Department of the Novorossiysk Society of Naturalists. The aim of the next research is to study the policy efforts conducted by the Indonesian government since the beginning of independence in 1945 to present, in advancing science and technology and innovation. A content analysis approach is employed to identify each stipulated regulation in Indonesia in the form of Laws, Government Regulations, Presidential Regulations, Presidential Decrees, and Presidential Instructions. There are 78 regulations in the field of science and technology and innovation that are analyzed. The results of the analysis are described based on the emergence of regulations and institutional implications generated as part of the ecosystem. In the article by Ihor Annienkov, based on the problem-chronological, comparative-historical, historiographical, and source-research methods, as well as the method of actualization, identifies the extent of borrowing foreign design and technological solutions in the Ukrainian Soviet Socialist Republic for projecting electrical machines in the second half of the 1930s, as well as the reasons for the absence of unambiguous information in historiography regarding the existence of this phenomenon in the republic at this chronological stage. The publication provides a general assessment of the quality of scientific support for the processes of creating electrical machines, establishes the ways of fulfilling the scientific-technical borrowings that were studiedand the dynamics of their development, analyzes their role in the growth of the technical level of products of the Ukrainian electrical machine-building branch. In the article by Mykola Ruban and Andrii Fomin, attempts to investigate the historical circumstances of the mastering and development of the industrial production of rolling stock in Ukraine from 1991 to 2021. In the course of the scientific development of the proposed research, materials from mass-circulation newspapers, industry publications of railway transport, as well as technical studies of employees of manufacturing plants were used. The next discusses the conditions and prerequisites for choosing the location of the plant; considers the stage of the establishment (foundation) of the plant; examines the stage of plant construction and equipping it with technological facilities in detail; analyzes the development and establishment of the plant between 1897 and 1914. A brief analysis of locomotive designs produced by the Kharkiv Locomotive Plant from 1897 to 1914 has been made. The article shows the significance of Consultative Congresses of Traction Engineers for the development of railway machinery both at Kharkiv Locomotive Plant and for the entire railway industry. The purpose of next study is to highlight the peculiarities of the development of the Russian aviation industry during the First World War. The focus is on analyzing production programs and matching their quantitative and qualitative parameters to war requirements. Production plans of leading Russian aviation factories as well as qualitative and quantitative parameters of products have been analyzed in the article.
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Zheng, C. G., B. L. Gall, H. W. Gao, A. E. Miller, and R. S. Bryant. "Effects of Polymer Adsorption and Flow Behavior on Two-Phase Flow in Porous Media." SPE Reservoir Evaluation & Engineering 3, no. 03 (2000): 216–23. http://dx.doi.org/10.2118/64270-pa.
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Summary To determine the effect of water-soluble polyacrylamide polymer adsorption and flow behavior on oil recovery, relative permeability and mobility were determined from flow experiments at various polymer concentrations. A selective reduction of the relative permeability to water with respect to the relative permeability to oil was observed for both Berea and reservoir sandstone cores. Adsorbed polymer layer increases water wettability. Relative permeability reduction could be attributed to both wettability change and pore-size restriction due to the adsorbed polymer layer. An empirical model was proposed to correlate the relative permeability reduction and the amount of polymer adsorption. Depletion-layer effect results in a reduced polymer viscosity in porous media with respect to bulk solutions. Modification of the existing shear-rate model allows for accurate prediction of this effect. The integration of the new models in UTCHEM provides a more accurate tool for engineering design of polymer applications. Introduction Water-soluble polyacrylamide polymers have been used to reduce water production in oil wells and for mobility control in injection wells for decades.1 One of the attractive properties of polyacrylamides is their ability to reduce the relative permeability to water more than the relative permeability to oil in porous media. From the published field tests on well treatments by polymer adsorption in the 1970's and 1980's,1,2 only a few jobs were considered to be economically successful. Results could not be interpreted due to the lack of detailed information. At present, the importance of laboratory research and simulation study are emphasized for successful field design. The selective permeability reduction by polymer adsorption was traditionally termed as "permeability reduction" or "residual resistance factor," which is equivalent to the endpoint relative permeability. Previous laboratory results1 indicated that the maximum reduction of the endpoint relative permeability to water caused by polymer adsorption can be as high as a factor of 10, while the reduction of the endpoint relative permeability to oil is less than 2. If crosslinking or swelling agents are applied, the maximum reduction of the relative permeability to water could be more than two orders of magnitude. The mechanisms of this selective reduction have been explored by several researchers.3–5 An understanding of these mechanisms could be obtained from the selective permeability reduction by gels.6 Measurement of the residual resistance alone may provide a qualitative estimation. To model the effect of polymer adsorption, however, a measurement of the relative permeability is necessary, especially when residual saturation and the shape of the relative permeability curves change after polymer adsorption. Modification of the relative permeability by polymer adsorption has been intensively studied recently.3-5,7-10 Ali et al.4 and Barrufet and Ali,5 derived the relative permeability from drainage capillary pressure measured by an ultracentrifuge and showed that the reduction of the relative permeability caused by starch-based polymers is dependent on saturation. The reduction was interpreted as a change in lubrication along the pore walls. Direct measurement of relative permeability after polymer adsorption was also seen in Refs. 3 and 7 through 10. In water-wet porous media, it was found that the residual oil saturation remained almost the same after polymer treatment. At residual oil saturation, the quantity of adsorbed polymer per gram of rock was also found to be almost the same as at 100% water saturation, but the endpoint relative permeability reduction to water was increased in the presence of residual oil. Based on a capillary bundle model, a correlation of the relative permeability curves with polymer-layer thickness was proposed by Zaitoun and Kohler.3 However, the relationship of the polymer-layer thickness with the quantity of adsorbed polymer is still unknown, and further modification of the capillary bundle model may also be needed to model complex pore matrices. On the other hand, as polymer propagates through porous media, polymer solution will be diluted in the propagation front due to dispersion and adsorption, and the dilution could extend to the entire slug if the slug size is too small. So far, few researchers have related the variations of the relative permeability curves as a function of polymer concentration or the quantity of adsorbed polymer. Therefore, one of the objectives in the present study is to measure and correlate relative permeability curves as a function of polymer adsorption. Polymer solution mobility was also studied as a function of polymer concentration. Effective viscosity at low shear rate in porous media is lower than that in bulk solution at the same shear rate. The dependence of the depletion-layer effect on polymer concentration as well as porous media will be examined in this paper. Finally, the numerical models of relative permeability and mobility as a function of polymer concentration developed in this study will be incorporated in UTCHEM. Several cases will be studied to compare incremental oil recovery predicted by these new models with that predicted by previous descriptions of polymer behavior in porous media. A simplified layered reservoir model will be used for comparative simulation runs. Polymer flooding and near-wellbore polymer treatments will also be simulated. Results from these simulations should provide guidelines for future field strategies. Experiment Porous Media. Both strongly water-wet and mildly oil-wet cores were chosen to study the influence of wettability on polymer adsorption, two-phase relative permeability, and polymer solution mobility. The mildly oil-wet medium is a Warden reservoir sandstone core from Santa Fe field, Stephens County, Oklahoma. Two strongly water-wet media are Berea sandstone cores with different permeabilities. Table 1 summarizes the petrophysical properties of these sandstone samples. Fluids. Synthetic brines were prepared to represent reservoir brine (produced water) composition and makeup water (injection water) composition used in the Warden reservoir. Produced water has a total dissolved solid (TDS) of 31,300 ppm which contains 29 g/L NaCl, 0.94 g/L CaCl2, 0.77 g/L MgCl2, 0.11 g/L KCl, and 1.1 g/L NaHCO3, and injection water has a TDS of 1,490 ppm which contains 0.343 g/L CaCl2, 0.252 g/L MgCl2, 0.176 g/L Na2SO4, and 0.72 g/L NaHCO3
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Jain, Rupali S., and M. B. Dhakne. "On Some Qualitative Properties of Mild Solutions of Nonlocal Semilinear Functional Differential Equations." Demonstratio Mathematica 47, no. 4 (2014). http://dx.doi.org/10.2478/dema-2014-0069.
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AbstractIn the present paper, we investigate the qualitative properties such as existence, uniqueness and continuous dependence on initial data of mild solutions of first and second order nonlocal semilinear functional differential equations with delay in Banach spaces. Our analysis is based on semigroup theory and modified version of Banach contraction theorem.
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Ayari, M. Iadh, and Sabri T. M. Thabet. "Qualitative properties and approximate solutions of thermostat fractional dynamics system via a nonsingular kernel operator." Arab Journal of Mathematical Sciences, February 3, 2023. http://dx.doi.org/10.1108/ajms-06-2022-0147.
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PurposeThis paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving a nonsingular kernel operator which is called Atangana-Baleanu-Caputo (ABC) derivative for the first time. The results of the existence and uniqueness of the solution for such a system are investigated with minimum hypotheses by employing Banach and Schauder's fixed point theorems. Furthermore, Ulam-Hyers (UH) stability, Ulam-Hyers-Rassias UHR stability and their generalizations are discussed by using some topics concerning the nonlinear functional analysis. An efficiency of Adomian decomposition method (ADM) is established in order to estimate approximate solutions of our problem and convergence theorem is proved. Finally, four examples are exhibited to illustrate the validity of the theoretical and numerical results.Design/methodology/approachThis paper considered theoretical and numerical methodologies.FindingsThis paper contains the following findings: (1) Thermostat fractional dynamics system is studied under ABC operator. (2) Qualitative properties such as existence, uniqueness and Ulam–Hyers–Rassias stability are established by fixed point theorems and nonlinear analysis topics. (3) Approximate solution of the problem is investigated by Adomain decomposition method. (4) Convergence analysis of ADM is proved. (5) Examples are provided to illustrate theoretical and numerical results. (6) Numerical results are compared with exact solution in tables and figures.Originality/valueThe novelty and contributions of this paper is to use a nonsingular kernel operator for the first time in order to study the qualitative properties and approximate solution of a thermostat dynamics system.
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Boudref, Mohamed-Ahmed, and Ahmed Berboucha. "New inequalities of Gronwall type for the stochastic differential equations." Random Operators and Stochastic Equations 23, no. 3 (2015). http://dx.doi.org/10.1515/rose-2014-0035.
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AbstractIn this paper, we establish some new nonlinear integral inequalities of Gronwall type for Itô integrals. These inequalities generalize some inequalities which can be used in applications as handy tools to study the qualitative as well as quantitative properties of solutions of some stochastic differential equations. We will use this inequalities to show the existence and uniqueness of solutions for nonlinear EDS.