Search

In this paper, by using the concept of changing-periodic time scales and composition theorem of time scales introduced in 2015, we establish a local phase space for functional dynamic equations with infinite delay (FDEID) on an arbitrary time scale with a bounded graininess function μ. Through Krasnoseľskiĭ's fixed point theorem, some sufficient conditions for the existence of local-periodic solutions for FDEID are established for the first time. This research indicates that one can extract a local-periodic solution for dynamic equations on an arbitrary time scale with a bounded graininess function μ through some index function. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some Cauchy problems involving a left-sided Hadamard-type fractional derivative. A theorem on the existence of a unique solution to a nonlinear problem is proved. The main result is obtained using a fixed point theorem due to Banach, as well as the Bielecki norm. A Cauchy formula for the solution of the linear problem is derived. [ABSTRACT FROM AUTHOR]

In this paper we define and study the weak pseudo-BCK algebras as generalizations of weak BCK-algebras, extending some results given by Cı⃖rulis for weak BCK-algebras. We give some characterizations of weak pseudo-BCK algebras and we prove that a weak pseudo-BCK algebra satisfying the right distribution laws is a BCK-algebra. We define the class of commutative weak pseudo-BCK algebras, and we give equivalent definitions and characterization theorems for commutative weak pseudo-BCK algebras. The classes of quasi pseudo-BCK algebras and weak pseudo-BCK(E) algebras are introduced and a characterization theorem for quasi pseudo-BCK algebras is given. We prove that any weak pseudo-BCK(E) algebra is a pseudo-BE algebra and the class of commutative weak pseudo-BCK(E) algebras is equivalent to the class of commutative pseudo-BCK algebras. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and study a new class of problems called partial differential hemivariational inequalities that combines evolution equations and hemivariational inequalities. First, we introduce the concept of strong well-posedness for mixed variational quasi hemivariational inequalities and establish metric characterizations for it. Then we show the existence of solutions and meaningful properties such as measurability and upper semicontinuity for the solution set of the mixed variational quasi hemivariational inequality associated to the partial differential hemivariational inequality. Relying, on these properties we are able to prove the existence of mild solutions for partial differential hemivariational inequalities. Furthermore, we show the compactness of the set of the corresponding mild trajectories. [ABSTRACT FROM AUTHOR]

In this paper, we present the proof of superlensing an arbitrary object using complementary media and we study reflecting complementary media for electromagnetic waves. The analysis is based on the reflecting technique and new results on the compactness, existence, and stability for the Maxwell equations with low regularity data. [ABSTRACT FROM AUTHOR]

The paper is concerned with a priori estimates of positive solutions of quasilinear elliptic systems of equations or inequalities in an open set of Ω ⊂ ℝ N {\Omega\subset\mathbb{R}^{N}} associated to general continuous nonlinearities satisfying a local assumption near zero. As a consequence, in the case Ω = ℝ N {\Omega=\mathbb{R}^{N}} , we obtain nonexistence theorems of positive solutions. No hypotheses on the solutions at infinity are assumed. [ABSTRACT FROM AUTHOR]

In this paper, we concern ourselves with the following Kirchhoff-type equations: { - (a + b ⁢ ∫ ℝ 3 | ∇ ⁡ u | 2 ⁢ 𝑑 x ) ⁢ △ ⁢ u + V ⁢ u = f ⁢ (u) in ⁢ ℝ 3 , u ∈ H 1 ⁢ (ℝ 3) , \left\{\begin{aligned} \displaystyle-\biggl{(}a+b\int_{\mathbb{R}^{3}}\lvert% \nabla u\rvert^{2}\,dx\biggr{)}\triangle u+Vu&\displaystyle=f(u)\quad\text{in % }\mathbb{R}^{3},\\ \displaystyle u&\displaystyle\in H^{1}(\mathbb{R}^{3}),\end{aligned}\right. where a, b and V are positive constants and f has critical growth. We use variational methods to prove the existence of ground state solutions. In particular, we do not use the classical Ambrosetti–Rabinowitz condition. Some recent results are extended. [ABSTRACT FROM AUTHOR]

In this paper, we deal with fractional p-Laplacian equations of the form { (- Δ) p s ⁢ u = λ ⁢ f ⁢ (x , u) , x ∈ Ω , u ⁢ (x) = 0 , x ∈ ℝ N ∖ Ω , \left\{\begin{aligned} \displaystyle(-\Delta)_{p}^{s}u&\displaystyle=\lambda f% (x,u),&&\displaystyle x\in\Omega,\\ \displaystyle u(x)&\displaystyle=0,&&\displaystyle x\in\mathbb{R}^{N}\setminus% \Omega,\end{aligned}\right. where λ ∈ (0 , + ∞) {\lambda\in(0,+\infty)} , 0 < s < 1 < p < + ∞ {0 0 {\delta>0} is small, existence and multiplicity of nontrivial solutions are obtained via variational methods. [ABSTRACT FROM AUTHOR]

Local asymptotic stability analysis is conducted for an initial-boundary-value problem of a Korteweg–de Vries equation posed on a finite interval [ 0 , 2 ⁢ π ⁢ 7 / 3 ] {[0,2\pi\sqrt{7/3}]}. The equation comes with a Dirichlet boundary condition at the left end-point and both the Dirichlet and Neumann homogeneous boundary conditions at the right end-point. It is known that the associated linearized equation around the origin is not asymptotically stable. In this paper, the nonlinear Korteweg–de Vries equation is proved to be locally asymptotically stable around the origin through the center manifold method. In particular, the existence of a two-dimensional local center manifold is presented, which is locally exponentially attractive. Analyzing the Korteweg–de Vries equation restricted on the local center manifold, we obtain a polynomial decay rate of the solution. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following Timoshenko system of thermo-viscoelasticity of type III with frictional damping and delay terms: { ρ 1 ⁢ φ t ⁢ t - K ⁢ (φ x + ψ) x = 0 , (x , t) ∈ (0 , 1) × (0 , ∞) , ρ 2 ⁢ ψ t ⁢ t - b ⁢ ψ x ⁢ x + K ⁢ (φ x + ψ) + β ⁢ θ x = 0 , (x , t) ∈ (0 , 1) × (0 , ∞) , ρ 3 ⁢ θ t ⁢ t - δ ⁢ θ x ⁢ x + γ ⁢ ψ t ⁢ t ⁢ x + ∫ 0 t g ⁢ (t - s) ⁢ θ x ⁢ x ⁢ (s) ⁢ d s + μ 1 ⁢ θ t ⁢ (x , t) + μ 2 ⁢ θ t ⁢ (x , t - τ) = 0 , (x , t) ∈ (0 , 1) × (0 , ∞) , \left\{\begin{aligned} &\displaystyle\rho_{1}\varphi_{tt}-K(\varphi_{x}+\psi)_% {x}=0,&&\displaystyle(x,t)\in(0,1)\times(0,\infty),\\ &\displaystyle\rho_{2}\psi_{tt}-b\psi_{xx}+K(\varphi_{x}+\psi)+\beta\theta_{x}% =0,&&\displaystyle(x,t)\in(0,1)\times(0,\infty),\\ &\displaystyle\rho_{3}\theta_{tt}-\delta\theta_{xx}+\gamma\psi_{ttx}+\int_{0}^% {t}g(t-s)\theta_{xx}(s)\,\mathrm{d}s+\mu_{1}\theta_{t}(x,t)+\mu_{2}\theta_{t}(% x,t-\tau)=0,&&\displaystyle(x,t)\in(0,1)\times(0,\infty),\end{aligned}\right. together with initial datum and boundary conditions of Dirichlet type, where g is a positive non-increasing relaxation function and μ 1 , μ 2 {\mu_{1},\mu_{2}} are positive constants. Under a hypothesis between the weight of the delay term and the weight of the friction damping term, we prove the global existence of solutions by using the Faedo–Galerkin approximations together with some energy estimates. Then, by introducing appropriate Lyapunov functionals, under the imposed constrain on the above two weights, we establish a general energy decay result from which the exponential and polynomial types of decay are only special cases. [ABSTRACT FROM AUTHOR]

Let G be a type 1 connected and simply connected solvable Lie group. The generalized moment map for π in G ^ {\widehat{G}} , the unitary dual of G, sends smooth vectors of the representation space of π to 𝒰 ⁢ (𝔤) * {{\mathcal{U}(\mathfrak{g})}^{*}} , the dual vector space of 𝒰 ⁢ (𝔤) {\mathcal{U}(\mathfrak{g})}. The convex hull of the image of the generalized moment map for π is called its generalized moment set, denoted by J ⁢ (π) {J(\pi)}. We say that G ^ {\widehat{G}} is generalized moment separable when the generalized moment sets differ for any pair of distinct irreducible unitary representations. Our main result in this paper provides a second proof of the generalized moment separability theorem for G. [ABSTRACT FROM AUTHOR]

This paper considers the problem of estimating the permeability in a nonlinear convection-diffusion equation. To overcome the large calculation burden of conventional methods, we apply an adaptive multigrid conjugate gradient method to solve this inverse problem. This new method combines the multigrid multiscale idea with the conjugate gradient method, and adopts the necessary condition that the optimum solution should be the fixed point of the multigrid inversion method. Some numerical results verify that the proposed method both dramatically reduces the required computations and improves the inversion quality. [ABSTRACT FROM AUTHOR]

This paper deals with some inverse problems for the linear elasticity system with origin in elastography: we try to identify the material coefficients from some extra information on (a part of) the boundary. In our main result, we assume that the total variation of the coefficient matrix is a priori bounded. We reformulate the problem as the minimization of a function in an appropriate constraint set. We prove that this extremal problem possesses at least one solution with the help of some regularity results. Two crucial ingredients are a Meyers-like theorem that holds in the context of linear elasticity and a nonlinear interpolation result by Luc Tartar. We also perform some numerical experiments that provide satisfactory results. To this end, we apply the Augmented Lagrangian algorithm, completed with a limited-memory BFGS subalgorithm. Finally, on the basis of these experiments, we illustrate the influence of the starting guess and the errors in the data on the behavior of the iterates. [ABSTRACT FROM AUTHOR]

In this paper we show theoretical convergence of a second-order Adams-Bashforth discontinuous Galerkin method for approximating smooth solutions to scalar nonlinear conservation laws with E-fluxes. A priori error estimates are also derived for a first-order forward Euler discontinuous Galerkin method. Rates are optimal in time and suboptimal in space; they are valid under a CFL condition. [ABSTRACT FROM AUTHOR]

In this paper, we consider a non-linear sequential differential equation with Caputo fractional derivative of Blasius type and we reduce the problem to the equivalent non-linear integral equation. We prove the complete continuity of the non-linear integral operator. The theorem on the existence of a solution of the problem for the Blasius equation of fractional order is also proved. [ABSTRACT FROM AUTHOR]

This paper describes a numerical model and its finite element implementation that used to compute the cavitation effects on nonlinear acoustic fluid and adjacent flexible structure interaction. The system is composed of two sub-systems, namely, the fluid and the flexible flat plate. A fully coupled approach using iterative implicit partitioned scheme was implemented in the present work which can account for the effects associated whit a mutual interaction. This approach included a compressible nonlinear acoustic fluid Eulerian solver and a Lagrangian solver for the flexible structure both in finite element formulation. A novel implementation of acoustic cavitation was made possible with the introduction of a simplified one-fluid cavitation model. The element-by-element PCG (Preconditioned Conjugate Gradient) solver together with diagonal preconditioning is used to solve the large equation system resulting from the finite element discretization of the governing equation of fluid domain. The capability of three different cavitation model, as the cut-off model, Modified Schmidt model and developed model are compared with each other in the evaluation of plate vibration response. Simulation results are presented on a large size shock tube, in which planar shock waves were impacting in “face on” configuration flat plates mounted at tube's end. Results are presented to demonstrate the capability of proposed solver in simulating cavitating nonlinear acoustic fluid. Obtained results show that impact forces caused impinging shock wave and reloading by cavitating region collapse have a considerable effect on the dynamic response of flexible plate. [ABSTRACT FROM AUTHOR]

In this paper, a higher order nonlinear difference equation is considered. By using the critical point theory, we obtain the existence and multiplicity for solutions of difference Dirichlet boundary value problems and give some new results. The proof is based on the variational methods and linking theorem. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new composition theorem for pseudo almost periodic functions under non-Lipschitz conditions. We apply this new composition theorem together with a fixed-point theorem for condensing maps to investigate the existence of p $p$ -mean piecewise pseudo almost periodic mild solutions for a class of impulsive nonautonomous partial functional stochastic evolution equations in Hilbert spaces, and then, the exponential stability of p $p$ -mean piecewise pseudo almost periodic mild solutions is studied. Finally, an example is given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a stochastic two-species competition system with impulsive effects. Some dynamical properties are investigated and sufficient conditions for the stochastic boundedness, stochastic permanence and global attractivity are established. Under some conditions, we conclude that the stochastic model is persistent in mean and extinction. An example is given to illustrate the main result. [ABSTRACT FROM AUTHOR]

Let A be an abelian variety. The abelian Ax–Lindemann theorem shows that the Zariski closure of an algebraic flow in A is a translate of an abelian subvariety of A. The paper discusses some conjectures on the usual topological closure of an algebraic flow in A. The main result is a proof of these conjectures when the algebraic flow is given by an algebraic curve. [ABSTRACT FROM AUTHOR]

Let 𝐅 q \mathbf{F}_{q} be a finite field of q elements. For multiplicative characters χ 1 , … , χ m \chi_{1},\ldots,\chi_{m} of 𝐅 q × \mathbf{F}_{q}^{\times} , we let J ⁢ ( χ 1 , … , χ m ) J(\chi_{1},\ldots,\chi_{m}) denote the Jacobi sum. Nicholas Katz and Zhiyong Zheng showed that for m = 2 m=2 , the normalized Jacobi sum q - 1 / 2 ⁢ J ⁢ ( χ 1 , χ 2 ) q^{-1/2}J(\chi_{1},\chi_{2}) ( χ 1 ⁢ χ 2 \chi_{1}\chi_{2} nontrivial) is asymptotically equidistributed on the unit circle as q → ∞ q\to\infty , when χ 1 \chi_{1} and χ 2 \chi_{2} run through all nontrivial multiplicative characters of 𝐅 q × \mathbf{F}_{q}^{\times}. In this paper, we show a similar property for m ≥ 2 m\geq 2. More generally, we show that the normalized Jacobi sum q - ( m - 1 ) / 2 ⁢ J ⁢ ( χ 1 , … , χ m ) q^{-(m-1)/2}J(\chi_{1},\ldots,\chi_{m}) ( χ 1 ⁢ ⋯ ⁢ χ m \chi_{1}\cdots\chi_{m} nontrivial) is asymptotically equidistributed on the unit circle, when χ 1 , … , χ m \chi_{1},\ldots,\chi_{m} run through arbitrary sets of nontrivial multiplicative characters of 𝐅 q × \mathbf{F}_{q}^{\times} with two of the sets being sufficiently large. The case m = 2 m=2 answers a question of Shparlinski. [ABSTRACT FROM AUTHOR]

A discontinuous Galerkin method on unstructured grids is adapted and implemented for simulation of wave response of subvertical fractured systems in carbonate rocks for numerical solution of direct problems of seismic exploration. The present paper compares seismic responses for several mechanical-mathematical models of a fractured reservoir. The models of collectors differ in the presence and location of media interfaces relative to the collector and also in away of its specification, namely, an explicit selection of fractures with the parameters of the medium in the domain of collector coinciding with the host medium, or differing from it. We indicate the ability to take into account inter-fracture interactions with the use of the model of a fractured layer presented in the paper and study wave processes formed as the result of interaction of seismic pulses with fractured reservoirs. [ABSTRACT FROM AUTHOR]

It is known that a general quintic equation cannot be solved by an ordinary origami construction. Alperin and Lang showed that three simultaneous folds leads to a solution of the general quintic equation. In this paper we improve their result and show that two simultaneous folds are sufficient to solve the general quintic equation. [ABSTRACT FROM AUTHOR]

In this paper we continue to advance the theory regarding the Riesz fractional gradient in the calculus of variations and fractional partial differential equations begun in an earlier work of the same name. In particular, we here establish an L 1 {L^{1}} Hardy inequality, obtain further regularity results for solutions of certain fractional PDE, demonstrate the existence of minimizers for integral functionals of the fractional gradient with non-linear dependence in the field, and also establish the existence of solutions to corresponding Euler–Lagrange equations obtained as conditions of minimality. In addition, we pose a number of open problems, the answers to which would fill in some gaps in the theory as well as to establish connections with more classical areas of study, including interpolation and the theory of Dirichlet forms. [ABSTRACT FROM AUTHOR]

In this paper, we give a remark on the two-phase obstacle-type problem for the p-Laplacian when 1 < p < 2 {1p is close to 2. We prove that the free boundary where the gradient vanishes has locally finite ( n - 1 ) {(n-1)} -Hausdorff measure. [ABSTRACT FROM AUTHOR]

The gauged Witten equation was essentially introduced by Witten in his formulation of the gauged linear σ-model (GLSM), which explains the so-called Landau–Ginzburg/Calabi–Yau correspondence. This is the first paper in a series towards a mathematical construction of GLSM, in which we set up a proper framework for studying the gauged Witten equation and its perturbations. We also prove several analytical properties of solutions and moduli spaces of the perturbed gauged Witten equation. We prove that solutions have nice asymptotic behavior on cylindrical ends of the domain. Under a good perturbation scheme, the energies of solutions are shown to be uniformly bounded by a constant depending only on the topological type. We prove that the linearization of the perturbed gauged Witten equation is Fredholm, and we calculate its Fredholm index. Finally, we define a notion of stable solutions and prove a compactness theorem for the moduli space of solutions over a fixed domain curve. [ABSTRACT FROM AUTHOR]

The paper presents a Monte Carlo algorithm for the study of bidirectional angular characteristics of a scattered polarized radiation based on projection expansion of the density of the corresponding angular distribution over hemispherical harmonics. The results of numerical estimation of two-dimensional angular distributions of the intensity and the polarization degree of the radiation passed through and reflected from optically thick layers of scattering and absorbing substance are presented. [ABSTRACT FROM AUTHOR]

In this paper we provide a simple proof of a Carleman estimate for a second-order elliptic operator P with Lipschitz leading coefficients. We apply such a Carleman estimate to derive a three-sphere inequality for solutions to equation Pu = 0. [ABSTRACT FROM AUTHOR]

Ordinary differential equations (ODEs) are popularly used to model complex dynamic systems by scientists; however, the parameters in ODE models are often unknown and have to be inferred from noisy measurements of the dynamic system. One conventional method is to maximize the likelihood function, but the likelihood function often has many local modes due to the complexity of ODEs, which makes the optimizing algorithm be vulnerable to trap in local modes. In this paper, we solve the global optimization issue of ODE parameters with the help of the Stochastic Approximation Monte Carlo (SAMC) algorithm which is shown to be self-adjusted and escape efficiently from the “local-trapping” problem. Our simulation studies indicate that the SAMC method is a powerful tool to estimate ODE parameters globally. The efficiency of SAMC method is demonstrated by estimating a predator-prey ODEs model from real experimental data. [ABSTRACT FROM AUTHOR]

The ziggurat method is a fast random variable generation method introduced by Marsaglia and Tsang in a series of papers. We discuss how the ziggurat method can be implemented for low-discrepancy sequences, and present algorithms and numerical results when the method is used to generate samples from the normal and gamma distributions. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the (2+1) dimensional sine-Gordon equation analysed earlier [R. Radha and M. Lakshmanan, J. Phys. A Math. Gen. 29, 1551 (1996)] employing the Truncated Painlevé Approach. We then generate the solutions in terms of lower dimensional arbitrary functions of space and time. By suitably harnessing the arbitrary functions present in the closed form of the solution, we have constructed dromion solutions and studied their collisional dynamics. We have also constructed dromion pairs and shown that the dynamics of the dromion pairs can be turned ON or OFF desirably. In addition, we have also shown that the orientation of the dromion pairs can be changed. Apart from the above classes of solutions, we have also generated compactons, rogue waves and lumps and studied their dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of nonlinear impulsive neutral partial functional differential equations with continuous distributed deviating arguments. For this class, we establish sufficient conditions for the H-oscillation of the solutions, using impulsive differential inequalities and an averaging technique with two different boundary conditions. We provide an example to illustrate the main result. [ABSTRACT FROM AUTHOR]

In this paper we apply the multilevel augmentation method to solve an ill-posed integral equation via the iterated Lavrentiev regularization. This method leads to fast solutions of discrete iterated Lavrentiev regularization. The convergence rates of the iterated Lavrentiev regularization are achieved by using a certain parameter choice strategy. Finally, numerical experiments are given to illustrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

In this paper, the iterative reweighted least squares (IRLS) algorithm for sparse signal recovery with partially known support is studied. We establish a theoretical analysis of the IRLS algorithm by incorporating some known part of support information as a prior, and obtain the error estimate and convergence result of this algorithm. Our results show that the error bound depends on the best ( s + k ) {(s+k)} -term approximation and the regularization parameter λ, and convergence result depends only on the regularization parameter λ. Finally, a series of numerical experiments are carried out to demonstrate the effectiveness of the algorithm for sparse signal recovery with partially known support, which shows that an appropriate q ( 0 < q < 1 {0

In this paper, we study local asymptotic stability, global character and periodic nature of solutions of the system of rational difference equations given by ..., n=0, 1,..., where the parameters a, b, c, d, e, f ∊ (0, ∞), and with initial conditions x0, y0 ∊ (0, ∞). Some numerical examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper investigates heat and mass transfer of nanofluid over a stretching sheet with variable thickness. The techniques of similarity transformation and homotopy analysis method are used to find solutions. Velocity, temperature, and concentration fields are examined with the variations of governing parameters. Local Nusselt number and Sherwood number are compared for different values of variable thickness parameter. The results show that there exists a critical value of thickness parameter βc (βc ≈ 0.7) where the Sherwood number achieves its maximum at the critical value βc. For β > βc, the distribution of nanoparticle volume fraction decreases near the surface but exhibits an opposite trend far from the surface. [ABSTRACT FROM AUTHOR]

In this paper, we present a new hybrid algorithm which is a combination of a hybrid Cuckoo search algorithm and Firefly optimization. We focus in this research on a hybrid methodcombining two heuristic optimization techniques, Cuckoo Search (CS) and Firefly Algorithm(FA) for the global optimization. Denoted as CS-FA. The hybrid CS-FA techniqueincorporates concepts from CS and FA and creates individuals in a new generation not only by random walk as found in CS but also by mechanisms of FA. To analyze the benefits of hybridization, we have comparatively evaluated the classical Cuckoo Search and Firefly Algorithms versus the proposed hybridized algorithms (CS-FA). [ABSTRACT FROM AUTHOR]

The paper is devoted to the construction of a probabilistic particlealgorithm. This is related to a nonlinear forward Feynman–Kac-type equation, which represents the solution of a nonconservative semilinear parabolic partial differential equation (PDE).Illustrations of the efficiency of the algorithm are provided by numerical experiments. [ABSTRACT FROM AUTHOR]

Both barrier options and the Heston stochastic volatility model are omnipresent in real-life applications of financial mathematics.In this paper, we apply the Heath–Platen (HP) estimator (as first introduced by Heath and Platen in [12]) to price barrier options in the Heston model setting as an alternative to conventional Monte Carlo methods and PDE based methods.We demonstrate the superior performance of the HP estimator via numerical examples and explain this performance by a detailed look at the underlying theoretical concept of the HP estimator. [ABSTRACT FROM AUTHOR]

The numerical analysis of linear quadratic regulator design problems for parabolic partial differential equations requires solving Riccati equations. In the finite time horizon case, the Riccati differential equation (RDE) arises. The coefficient matrices of the resulting RDE often have a given structure, e.g., sparse, or low-rank. The associated RDE usually is quite stiff, so that implicit schemes should be used in this situation. In this paper, we derive efficient numerical methods for solving RDEs capable of exploiting this structure, which are based on a matrix-valued implementation of the BDF and Rosenbrock methods. We show that these methods are suitable for large-scale problems by working only on approximate low-rank factors of the solutions. We also incorporate step size and order control in our numerical algorithms for solving RDEs. In addition, we show that within a Galerkin projection framework the solutions of the finite-dimensional RDEs converge in the strong operator topology to the solutions of the infinite-dimensional RDEs. Numerical experiments show the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

The paper is focused on study of non-stationary piecewise-linear processes on Poisson point flows with independent identically distributed random variables at support points. An approach to calculate the correlation function of the process on the base of the total probability formula is considered. A general expression for the correlation function of a non-stationary process is obtained. Particular cases are considered. Using the method of direct simulation, it is shown numerically that the correlation function of the process has a point of inflection. [ABSTRACT FROM AUTHOR]

The block inverse iteration and block Newton’s methods proposed by the authors of this paper for computing invariant pairs of regular linear matrix pencils are generalized to the case of regular nonlinear matrix pencils. Numerical properties of the proposed methods are demonstrated with a typical quadratic eigenproblem. [ABSTRACT FROM AUTHOR]

A new combined numerical algorithm for solving inverse problems of epidemiology is described in this paper. The combined algorithm consists of optimization and iterative methods, and determines the parameters specific to a particular population by using the statistical information for a few previous years. The coefficients of the epidemiology model describe particular qualities of the population and the development of the disease. The inverse problem of parameter identification in a mathematical model is reduced to the problem of minimizing an objective function characterizing the square deviation of the statistical data from the experimental data. The combination of statistical and optimization algorithms demonstrates the identification of parameters with an appropriate relative accuracy of 30%. The results can be used by public health organizations to predict the infectious disease epidemic in a given region by comparing the data of simulation with historical data. [ABSTRACT FROM AUTHOR]

In [15], Jean Taylor proved a regularity theorem away from the boundary for Almgren almost minimal sets of dimension 2 in R3. It is quite important for understanding the soap films and the solutions of Plateau's problem away from boundary. In this paper, we will give a regularity result on the boundary for two-dimensional sliding almost minimal sets in R3. [ABSTRACT FROM AUTHOR]

In this paper, the so-called relative∞-capacity is introduced and investigated in a close connection to the viscosity solution of the∞-Laplace equation.We not only show that the relative∞-capacity equals the limit of the p-th root of the relative p-capacity as p → ∞and hence has a simple geometric characterization in terms of the Euclidean distance, but also establish several basic properties for the relative ∞-capacity. Consequently, we apply the relative∞-capacity to the embedding theory of the∞-Sobolev space. More geometrically, we affinize the relative∞-capacity and its fundamental features as much as possible. [ABSTRACT FROM AUTHOR]

For a large class of geometric objects, the passage to categories of quasicoherent sheaves provides an embedding in the 2-category of abelian tensor categories. The notion of weakly Tannakian categories introduced by the author gives a characterization of tensor categories in the image of this embedding. However, this notion requires additional structure to be present, namely a fiber functor. For the case of classical Tannakian categories in characteristic zero, Deligne has found intrinsic properties-expressible entirely within the language of tensor categories-which are necessary and sufficient for the existence of a fiber functor. In this paper we generalize Deligne's result to weakly Tannakian categories in characteristic zero. The class of geometric objects whose tensor categories of quasi-coherent sheaves can be recognized in this manner includes both the gerbes arising in classical Tannaka duality and more classical geometric objects such as projective varieties over a field of characteristic zero. Our proof uses a different perspective on fiber functors, which we formalize through the notion of geometric tensor categories. A second application of this perspective allows us to describe categories of quasi-coherent sheaves on fiber products. [ABSTRACT FROM AUTHOR]

In this paper, we prove that, if Deligne's “petits camarades conjecture” holds, then a Langlands type correspondence holds also for p-adic coefficients on a smooth curve over a finite field. As an application, we prove that any overconvergent F -isocrystal of rank less than or equal to 2 on a smooth curve is ı-mixed. [ABSTRACT FROM AUTHOR]

Recently, the theory of currents and the existence theory for Plateau's problem have been extended to the case of finite-dimensional currents in infinite-dimensional manifolds or even metric spaces; see [5] (and also [7, 39] for the most recent developments). In this paper, in the case when the ambient space is Hilbert, we provide the first partial regularity result, in a dense open set of the support, for n-dimensional integral currents which locally minimize the mass. Our proof follows with minor variants [34], implementing Lipschitz approximation and harmonic approximation without indirect arguments and with estimates which depend only on the dimension n and not on codimension or dimension of the target space. [ABSTRACT FROM AUTHOR]

The goal of this paper is to show that the equivariant Tamagawa number conjecture implies the extended abelian Stark conjecture contained in [12] and [11]. In particular, this gives the first proof of the extended abelian Stark conjecture for the base field Q, since the equivariant Tamagawa number conjecture away from 2 was proved in this context by Burns and Greither in [8] and Flach completed their results at 2 in [13] and [14]. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to observe that a homomorphism of discrete groups f : Γ → G arises as the induced map π0(M) → π0(X) on path components of some closed normal inclusion of topological groups M ⊆ X if and only if the map f can be equipped with a crossed module structure. In that case an essentially unique realization M ⊆ X exists by homotopically discrete topological groups. The results here are topological elaboration and exposition using existing simplicial techniques. [ABSTRACT FROM AUTHOR]