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We study the two-dimensional structural stability of shock waves in a compressible isentropic inviscid elastic material in the sense of the local-in-time existence and uniqueness of discontinuous shock front solutions of the equat...
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We study the two-dimensional structural stability of shock waves in a compressible isentropic inviscid elastic material in the sense of the local-in-time existence and uniqueness of discontinuous shock front solutions of the equations of compressible elastodynamics in two space dimensions. By the energy method based on a symmetrization of the wave equation and giving an a priori estimate without loss of derivatives for solutions of the constant coefficients linearized problem we find a condition sufficient for the uniform stability of rectilinear shock waves. Comparing this condition with that for the uniform stability of shock waves in isentropic gas dynamics, we make the conclusion that the elastic force plays stabilizing role. In particular, we show that, as in isentropic gas dynamics, all compressive shock waves are uniformly stable for convex equations of state. Moreover, for some particular deformations (and general equations of state), by the direct test of the uniform Kreiss-Lopatinski condition we show that the stability condition found by the energy method is not only sufficient but also necessary for uniform stability. As is known, uniform stability implies structural stability of corresponding curved shock waves.
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The correlation between productivity and competition is an oft observed but incompletely understood result. Some suggest that there is a treatment effect of competition on measured productivity, for example, through a reduction of...
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The correlation between productivity and competition is an oft observed but incompletely understood result. Some suggest that there is a treatment effect of competition on measured productivity, for example, through a reduction of managerial slack. Others argue that greater competition makes unproductive establishments exit by reallocating demand to their productive rivals, raising observed average productivity via selection. I study the ready-mix concrete industry and offer three perspectives on this ambivalence. First, using a standard decomposition approach, I look for evidence of greater reallocation of demand to productive plants in more competitive markets. Second, I model the establishment exit decision and construct a semiparametric selection correction to quantify the empirical significance of treatment and selection. Finally, I use a grouped instrumental variable quantile regression to test the distributional predictions of the selection hypothesis. I find no evidence for greater selection or reallocation in more competitive markets; instead, all three results suggest that measured productivity responds directly to competition. Potential channels include specialization and managerial inputs.
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In this article, we discuss, from an economic perspective, two alternative views of restrictions of competition by sports associations. The horizontal approach views such restrictions as an agreement among the participants of a sp...
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In this article, we discuss, from an economic perspective, two alternative views of restrictions of competition by sports associations. The horizontal approach views such restrictions as an agreement among the participants of a sports league with the sports association merely representing an organization executing the horizontal cooperation. In contrast, the vertical approach views the sports association as being a dominant upstream firm enjoying a monopoly position on the market stage for competition organizing services, an important input for the actual product-the sports game. Taking the recent Financial Fair Play (FFP) initiative by UEFA (the Union of European Football Associations) as an example, we demonstrate that the different views lead to different assessments of restrictive effects and, thus, matter for competition policy decisions. The economic story of the potential restrictive effect of FFP on players' and player agents' income may fit more plausibly to the horizontal approach, whereas the potentially anticompetitive foreclosure and deterrence effects of FFP may be economically more soundly reasoned by taking the vertical approach.
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A semilinear reaction–diffusion two-point boundary value problem, whose second-order derivative is multiplied by a small positive parameter ${\varepsilon^2}$ , is considered. It can have multiple solutions. The numerical computat...
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A semilinear reaction–diffusion two-point boundary value problem, whose second-order derivative is multiplied by a small positive parameter ${\varepsilon^2}$ , is considered. It can have multiple solutions. The numerical computation of solutions having interior transition layers is analysed. It is demonstrated that the accurate computation of such solutions is exceptionally difficult. To address this difficulty, we propose an artificial-diffusion stabilization. For both standard and stabilised finite difference methods on suitable Shishkin meshes, we prove existence and investigate the accuracy of computed solutions by constructing discrete sub- and super-solutions. Convergence results are deduced that depend on the relative sizes of ${\varepsilon}$ and N, where N is the number of mesh intervals. Numerical experiments are given in support of these theoretical results. Practical issues in using Newton’s method to compute a discrete solution are discussed.
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A semilinear reaction-diffusion two-point boundary value problem, whose second-order derivative is multiplied by a small positive parameter e{open}_2, is considered. It can have multiple solutions. The numerical computation of sol...
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A semilinear reaction-diffusion two-point boundary value problem, whose second-order derivative is multiplied by a small positive parameter e{open}_2, is considered. It can have multiple solutions. The numerical computation of solutions having interior transition layers is analysed. It is demonstrated that the accurate computation of such solutions is exceptionally difficult. To address this difficulty, we propose an artificial-diffusion stabilization. For both standard and stabilised finite difference methods on suitable Shishkin meshes, we prove existence and investigate the accuracy of computed solutions by constructing discrete sub- and super-solutions. Convergence results are deduced that depend on the relative sizes of e{open} and N, where N is the number of mesh intervals. Numerical experiments are given in support of these theoretical results. Practical issues in using Newton's method to compute a discrete solution are discussed.
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This article is mainly about a low-frequency asymptotic expansion of a unique weak solutions of a semilinear wave equation with a boundary-like antiperiodic condition. Solvability of this problem with weak initial data is also stu...
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This article is mainly about a low-frequency asymptotic expansion of a unique weak solutions of a semilinear wave equation with a boundary-like antiperiodic condition. Solvability of this problem with weak initial data is also studied by applying the Faedo–Galerkin method and using a maximal continuous solution of a nonlinear Volterra integral equation.
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摘要 :We show that the reflexive lattice generated by a double triangle lattice of projections in a finite von Neumann algebra is topologically homeomorphic to the two-dimensional sphere S 2 (plus two distinct points corresponding to ze...
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We show that the reflexive lattice generated by a double triangle lattice of projections in a finite von Neumann algebra is topologically homeomorphic to the two-dimensional sphere S 2 (plus two distinct points corresponding to zero and I). Furthermore, such a reflexive lattice is in general minimally generating for the von Neumann algebra it generates. As an application, we show that if a reflexive lattice ${\mathcal F}$ generates the algebra ${M_n(\mathbb C)}$ of all n × n complex matrices, for some n ≥ 3, then ${\mathcal F\setminus\{0,I\}}$ is connected if and only if it is homeomorphic to S 2.
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We consider the Euler equations on the two-dimensional torus and construct invariant measures for the dynamics of these equations, concentrated on sufficiently regular Sobolev spaces so that strong solutions are also known to exis...
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We consider the Euler equations on the two-dimensional torus and construct invariant measures for the dynamics of these equations, concentrated on sufficiently regular Sobolev spaces so that strong solutions are also known to exist. The proof follows the method of Kuksin (J. Stat. Phys. 115(1/2):469-492) and we obtain in particular that these measures do not have atoms, excluding trivial invariant measures. Then we prove that almost every initial data with respect to the constructed measures give rise to global solutions for which the growth of the Sobolev norms are at most polynomial. To do this, we rely on an argument of Bourgain. Such a combination of Kuksin's and Bourgain's arguments already appear in the work of Sy (J. Math. Pures Appl. 154:108-145). We point out that up to the knowledge of the author, the only general upper-bound for the growth of the Sobolev norm to the 2d Euler equations is double exponential.
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Описан Моп/еШиепа с1оГт\ Ойпояит, яр. п. из Азербайджана (Большой Кавказ, Ллтыагач), наиболее сходный по строению с М. цетсНа/а Вс...
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Описан Моп/еШиепа с1оГт\ Ойпояит, яр. п. из Азербайджана (Большой Кавказ, Ллтыагач), наиболее сходный по строению с М. цетсНа/а ВспПкку, отличаясь индивидуальной формой конечного членика нижнечелюстного щупика, парамер и 8-го уростернита.
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