The existence of positive solutions to second-order Neumann BVPs -u' + Mu = f(t, u), u'(0) = u'(1) = 0 and u' + Mu = f(t, u), u'(0) =u'(1) is proved by a simple application of a Fixed Poin...The existence of positive solutions to second-order Neumann BVPs -u' + Mu = f(t, u), u'(0) = u'(1) = 0 and u' + Mu = f(t, u), u'(0) =u'(1) is proved by a simple application of a Fixed Point Theorem in cones due to Krasnoselskii[1,6].展开更多
This paper is concerned with the global existence and the partial regularity for the weak solution of the Landau-Lifshitz-Maxell system in two dimensions with Neumann boundary conditions.
This paper studies coupled nonlinear diffusion equations with more general nonlinearities, subject to homogeneous Neumann boundary conditions. The necessary and sufficient conditions are obtained for the existence of ...This paper studies coupled nonlinear diffusion equations with more general nonlinearities, subject to homogeneous Neumann boundary conditions. The necessary and sufficient conditions are obtained for the existence of generalized solutions of the system, which extend the known results for nonlinear diffusion systems with more special nonlinearities.展开更多
If a semicircular element and the diagonal subalgebra of a matrix algebra are free in a finite von Neumann algebra （with respect to a normal trace）, then, up to the conjugation by a diagonal unitary element, all ent...If a semicircular element and the diagonal subalgebra of a matrix algebra are free in a finite von Neumann algebra （with respect to a normal trace）, then, up to the conjugation by a diagonal unitary element, all entries of the semicircular element are uniquely determined in the sense of （joint） distribution. Suppose a selfadjoint element is free with the diagonal subalgebra. Then, in the matrix decomposition of the selfa^tjoint element, any two entries cannot be free with each other unless the selfadjoint element is semicircular. We also define a ＂matricial distance＂ between two elements and show that such distance for two free semicircular elements in a finite von Neumann algebra is nonzero and independent of the properties of the von Neumann algebra.展开更多
文摘The existence of positive solutions to second-order Neumann BVPs -u' + Mu = f(t, u), u'(0) = u'(1) = 0 and u' + Mu = f(t, u), u'(0) =u'(1) is proved by a simple application of a Fixed Point Theorem in cones due to Krasnoselskii[1,6].
文摘This paper is concerned with the global existence and the partial regularity for the weak solution of the Landau-Lifshitz-Maxell system in two dimensions with Neumann boundary conditions.
基金the National Natural Science Foundation of China (Nos.10471013 10771024)
文摘This paper studies coupled nonlinear diffusion equations with more general nonlinearities, subject to homogeneous Neumann boundary conditions. The necessary and sufficient conditions are obtained for the existence of generalized solutions of the system, which extend the known results for nonlinear diffusion systems with more special nonlinearities.
文摘If a semicircular element and the diagonal subalgebra of a matrix algebra are free in a finite von Neumann algebra （with respect to a normal trace）, then, up to the conjugation by a diagonal unitary element, all entries of the semicircular element are uniquely determined in the sense of （joint） distribution. Suppose a selfadjoint element is free with the diagonal subalgebra. Then, in the matrix decomposition of the selfa^tjoint element, any two entries cannot be free with each other unless the selfadjoint element is semicircular. We also define a ＂matricial distance＂ between two elements and show that such distance for two free semicircular elements in a finite von Neumann algebra is nonzero and independent of the properties of the von Neumann algebra.
