We study continuum and atomistic models for the elastodynamics of crystalline solids at zero temperature. We establish sharp criterion for the regime of validity of the nonlinear elastic wave equations derived from the well-known Cauchy-Born rule.
We prove an L∞ version of the Yan theorem and deduce from it a necessary condition for the absence of free lunches in a model of financial markets, in which asset prices are a continuous Rd valued process and only simple investment strategies are admissible. Our proof is based on a new separation theorem for convex sets of finitely additive measures.
In this work, we consider a Fisher and generalized Fisher equations with variable coefficients. Using truncated Painlevé expansions of these equations, we obtain exact solutions of these equations with a constraint on the coefficients a(t) and b(t).
In this paper, we consider the local and global solution for the nonlinear Schrödinger equation with data in the homogeneous and nonhomogeneous Besov space and the scattering result for small data. The techniques to be used are adapted from the Strichartz type estimate, Kato’s smoothing effect and the maximal function (in time) estimate for the free Schr¨odinger operator.
In this paper, we study the semi-boundless mixed problem for time-fractional telegraph equation. We are able to use the integral transform method (the Fourier sin and cos transforms) to obtain the solution.
When a real-world data set is fitted to a specific type of models, it is often encountered that one or a set of observations have undue influence on the model fitting, which may lead to misleading conclusions. Therefore, it is necessary for data analysts to identify these influential observations and assess their impact on various aspects of model fitting. In this paper, one type of modified Cook’s distances is defined to gauge the influence of one or a set observations on the estimate of the constant coefficient part in partially varyingcoefficient models, and the Cook’s distances are expressed as functions of the corresponding residuals and leverages. Meanwhile, a bootstrap procedure is suggested to derive the reference values for the proposed Cook’s distances. Some simulations are conducted, and a real-world data set is further analyzed to examine the performance of the proposed method. The experimental results are satisfactory.
In this paper, we study mixed elastico-plasticity problems in which part of the boundary is known, while the other part of the boundary is unknown and is a free boundary. Under certain conditions, this problem can be transformed into a Riemann-Hilbert boundary value problem for analytic functions and a mixed boundary value problem for complex equations. Using the theory of generalized analytic functions, the solvability of the problem is discussed.
In this paper, the Dirichlet problem of Stokes approximate of non-homogeneous incompressible Navier-Stokes equations is studied. It is shown that there exist global weak solutions as well as global and unique strong solution for this problem, under the assumption that initial density ρ0(x) is bounded away from 0 and other appropriate assumptions (see Theorem 1 and Theorem 2). The semi-Galerkin method is applied to construct the approximate solutions and a prior estimates are made to elaborate upon the compactness of the approximate solutions.
The purpose of this article is to study the rational evaluation of European options price when the underlying price process is described by a time-change Lévy process. European option pricing formula is obtained under the minimal entropy martingale measure (MEMM) and applied to several examples of particular time-change Lévy processes. It can be seen that the framework in this paper encompasses the Black-Scholes model and almost all of the models proposed in the subordinated market.
The Duffing equation with even-odd asymmetrical nonlinear-restoring force and one external forcing is investigated. The conditions of existence of primary resonance, second-order, third-order subharmonics, morder subharmonics and chaos are given by using the second-averaging method, the Melnikov method and bifurcation theory. Numerical simulations including bifurcation diagram, bifurcation surfaces and phase portraits show the consistence with the theoretical analysis. The numerical results also exhibit new dynamical behaviors including onset of chaos, chaos suddenly disappearing to periodic orbit, cascades of inverse period-doubling bifurcations, period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, symmetrybreaking of periodic orbits, interleaving occurrence of chaotic behaviors and period-one orbit, a great abundance of periodic windows in transient chaotic regions with interior crises and boundary crisis and varied chaotic attractors. Our results show that many dynamical behaviors are strictly departure from the behaviors of the Duffing equation with odd-nonlinear restoring force.
In this paper, we consider the following ODE problem where f ∈ C((0,+∞) × R,R), f(r, s) goes to p(r) and q(r) uniformly in r > 0 as s → 0 and s → +∞, respectively, 0 ≤ p(r) ≤ q(r) ∈ L∞(0,∞). Moreover, for r > 0, f(r, s) is nondecreasing in s ≥ 0. Some existence and non-existence of positive solutions to problem (P) are proved without assuming that p(r) ≡ 0 and q(r) has a limit at infinity. Based on these results, we get the existence of positive solutions for an elliptic problem.
The main result of this study is to obtain, using the localization method in Briand et al. Levi, Fatou and Lebesgue type theorems for the solutions of certain one-dimensional backward stochastic differential equation (BSDEs) with integrable parameters with respect to the terminal condition.