We define and study Musielak-Orlicz-Sobolev spaces with zero boundary values on any metric space endowed with a Borel regular measure. We extend many classical results, including completeness, lattice properties and removable sets, to Musielak-Orlicz-Sobolev spaces on metric measure spaces. We give sufficient conditions which guarantee that a Sobolev function can be approximated by Lipschitz continuous functions vanishing outside an open set. These conditions are based on Hardy type inequalities., Takao Ohno, Tetsu Shimomura., and Obsahuje seznam literatury
Geiss, Keller and Oppermann (2013) introduced the notion of n-angulated category, which is a “higher dimensional” analogue of triangulated category, and showed that certain (n-2)-cluster tilting subcategories of triangulated categories give rise to n-angulated categories. We define mutation pairs in n-angulated categories and prove that given such a mutation pair, the corresponding quotient category carries a natural n-angulated structure. This result generalizes a theorem of Iyama-Yoshino (2008) for triangulated categories., Zengqiang Lin., and Obsahuje seznam literatury
Given a sequence of real or complex numbers, we construct a sequence of nested, symmetric matrices. We determine the LU- and QR-factorizations, the determinant and the principal minors for such a matrix. When the sequence is real, positive and strictly increasing, the matrices are strictly positive, inverse M-matrices with symmetric, irreducible, tridiagonal inverses., Jeffrey L. Stuart., and Obsahuje seznam literatury
The aim of this paper is to establish an existence and uniqueness result for a class of the set functional differential equations of neutral type \left\{ {\begin{array}{*{20}c} {D_H X(t) = F(t,X_t ,D_H X_t ),} // {\left. X \right|_{\left[ { - r,0} \right]} = \Psi ,} // \end{array} } \right. where F: [0, b]× C_{0}x L_{0}^{1}\rightarrow K_{c}(E)) is a given function, Kc(E) is the family of all nonempty compact and convex subsets of a separable Banach space E, C0 denotes the space of all continuous set-valued functions X from [−r, 0] into Kc(E), L_{0}^{1} is the space of all integrally bounded set-valued functions X: [−r, 0] → Kc(E), Ψ \in C_{0} and D_{H} is the Hukuhara derivative. The continuous dependence of solutions on initial data and parameters is also studied., Umber Abbas, Vasile Lupulescu, Donald O’Regan, Awais Younus., and Obsahuje seznam literatury
Let u be a holomorphic function and φ a holomorphic self-map of the open unit disk D in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators uCφ from Zygmund type spaces to Bloch type spaces in D in terms of u, φ, their derivatives, and φn, the n-th power of φ. Moreover, we obtain some similar estimates for the essential norms of the operators uCφ, from which sufficient and necessary conditions of compactness of uCφ follows immediately., Xin-Cui Guo, Ze-Hua Zhou., and Obsahuje seznam literatury
Our purpose is to present a number of new facts about the structure of semipositive matrices, involving patterns, spectra and Jordon form, sums and products, and matrix equivalence, etc. Techniques used to obtain the results may be of independent interest. Examples include: any matrix with at least two columns is a sum, and any matrix with at least two rows, a product, of semipositive matrices. Any spectrum of a real matrix with at least 2 elements is the spectrum of a square semipositive matrix, and any real matrix, except for a negative scalar matrix, is similar to a semipositive matrix. M-matrices are generalized to the non-square case and sign patterns that require semipositivity are characterized., Jonathan Dorsey, Tom Gannon, Charles R. Johnson, Morrison Turnansky., and Obsahuje seznam literatury
Generalizing earlier results about the set of idempotents in a Banach algebra, or of self-adjoint idempotents in a C*-algebra, we announce constructions of nice connecting paths in the connected components of the set of elements in a Banach algebra, or of self-adjoint elements in a C*-algebra, that satisfy a given polynomial equation, without multiple roots. In particular, we prove that in the Banach algebra case every such non-central element lies on a complex line, all of whose points satisfy the given equation. We also formulate open questions., Endre Makai Jr., Jaroslav Zemánek., and Obsahuje seznam literatury
Let X be a Banach space of analytic functions on the open unit disk and Γ a subset of linear isometries on X. Sufficient conditions are given for non-supercyclicity of Γ. In particular, we show that the semigroup of linear isometries on the spaces S^{p} (p>1), the little Bloch space, and the group of surjective linear isometries on the big Bloch space are not supercyclic. Also, we observe that the groups of all surjective linear isometries on the Hardy space H^{p} or the Bergman space L_{a}^{p} (1< p< ∞,p\neq 2) are not supercyclic., Abbas Moradi, Karim Hedayatian, Bahram Khani Robati, Mohammad Ansari., and Obsahuje seznam literatury
A maximum matching of a graph G is a matching of G with the largest number of edges. The matching number of a graph G, denoted by {\alpha }'(G), is the number of edges in a maximum matching of G. In 1966, Gallai conjectured that all the longest paths of a connected graph have a common vertex. Although this conjecture has been disproved, finding some nice classes of graphs that support this conjecture is still very meaningful and interesting. In this short note, we prove that Gallai’s conjecture is true for every connected graph G with {\alpha }'(G)\leq 3., Fuyuan Chen., and Obsahuje seznam literatury