We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. Also, we derive some interesting consequences.
In this paper we give some complete characterizations of the primitive of strongly Henstock-Kurzweil integrable functions which are defined on m with values in a Banach space.
Let T : X → X be a continuous selfmap of a compact metrizable space X. We prove the equivalence of the following two statements: (1) The mapping T is a Banach contraction relative to some compatible metric on X. (2) There is a countable point separating family F ⊂ C(X) of non-negative functions f ∈ C(X) such that for every f ∈ F there is g ∈ C(X) with f = g − g ◦ T.
We consider three types of semilinear second order PDEs on a cylindrical domain Ω × (0,∞), where Ω is a bounded domain in RN , N ≥ 2. Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of Ω × (0,∞) is reserved for time t, the third type is an elliptic equation with a singled out unbounded variable t. We discuss the asymptotic behavior, as t → ∞, of solutions which are defined and bounded on Ω × (0,∞).
The purpose of this paper is to establish some common fixed point results for f-nondecreasing mappings which satisfy some nonlinear contractions of rational type in the framework of metric spaces endowed with a partial order. Also, as a consequence, a result of integral type for such class of mappings is obtained. The proved results generalize and extend some of the results of J. Harjani, B. Lopez, K. Sadarangani (2010) and D. S. Jaggi (1977).
We show that asserting the regularity (in the sense of Rund) of a first-order parametric multiple-integral variational problem is equivalent to asserting that the differential of the projection of its Hilbert-Carathéodory form is multisymplectic, and is also equivalent to asserting that Dedecker extremals of the latter $(m+1)$-form are holonomic.
This contribution, which in a brief, succint and almost aphoristic way, critically brings forward to the reader a number of problems of today’s corpus and computational linguistics as well as their unsatisfactory solutions, is trying, at the same time, to do away with a number of myths and simplified opinions in the field. and Příspěvek ve stručné a téměř aforizované podobě připomíná řadu kritizovaných problémů a jejich neuspokojivých řešení v dnešní korpusové a komputační lingvistice a snaží se tak odstranit řadu mýtů a zjednodušujících představ.
Let $W$ be the free monoid over a finite alphabet $A$. We prove that a congruence of $W$ generated by a finite number of pairs $\langle au,u\rangle $, where $a\in A$ and $u\in W$, is always decidable.
We construct a class of special homogeneous Moran sets, called {mk}-quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of {mk}k\geqslant 1, we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of ho- mogeneous Moran sets to assume the minimum value, which expands earlier works., Xiaomei Hu., and Obsahuje seznam literatury