We consider the permanent function on the faces of the polytope of certain doubly stochastic matrices, whose nonzero entries coincide with those of fully indecomposable square (0, 1)-matrices containing the identity submatrix. We show that a conjecture in K. Pula, S. Z. Song, I. M. Wanless (2011), is true for some cases by determining the minimum permanent on some faces of the polytope of doubly stochastic matrices.
We study the existence of solutions to nonlinear boundary value problems for second order quasilinear ordinary differential equations involving bounded ϕ-Laplacian, subject to integral boundary conditions formulated in terms of Riemann-Stieltjes integrals.
M. Herschend, Y. Liu, H. Nakaoka introduced n-exangulated categories, which are a simultaneous generalization of n-exact categories and (n + 2)-angulated categories. This paper consists of two results on n-exangulated categories: (1) we give an equivalent characterization of axiom (EA2); (2) we provide a new way to construct a closed subfunctor of an n-exangulated category.
Using partial derivatives ∂f/∂z and (partial f/partialbar{z}), we introduce Besov spaces of polyanalytic functions in the open unit disk, as well as in the upper half-plane. We then prove that the dilatations of functions in certain weighted polyanalytic Besov spaces converge to the same functions in norm. When restricted to the open unit disk, we prove that each polyanalytic function of degree q can be approximated in norm by polyanalytic polynomials of degree at most q.
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