Search results for "wise"
showing 10 items of 369 documents
A pointwise selection principle for metric semigroup valued functions
2008
Abstract Let ∅ ≠ T ⊂ R , ( X , d , + ) be an additive commutative semigroup with metric d satisfying d ( x + z , y + z ) = d ( x , y ) for all x , y , z ∈ X , and X T the set of all functions from T into X . If n ∈ N and f , g ∈ X T , we set ν ( n , f , g , T ) = sup ∑ i = 1 n d ( f ( t i ) + g ( s i ) , g ( t i ) + f ( s i ) ) , where the supremum is taken over all numbers s 1 , … , s n , t 1 , … , t n from T such that s 1 ⩽ t 1 ⩽ s 2 ⩽ t 2 ⩽ ⋯ ⩽ s n ⩽ t n . We prove the following pointwise selection theorem: If a sequence of functions { f j } j ∈ N ⊂ X T is such that the closure in X of the set { f j ( t ) } j ∈ N is compact for each t ∈ T , and lim n → ∞ ( 1 n lim N → ∞ sup j , k ⩾ N , j…
Pointwise k-Pseudo Metric Space
2021
In this paper, the concept of a k-(quasi) pseudo metric is generalized to the L-fuzzy case, called a pointwise k-(quasi) pseudo metric, which is considered to be a map d:J(LX)×J(LX)⟶[0,∞) satisfying some conditions. What is more, it is proved that the category of pointwise k-pseudo metric spaces is isomorphic to the category of symmetric pointwise k-remote neighborhood ball spaces. Besides, some L-topological structures induced by a pointwise k-quasi-pseudo metric are obtained, including an L-quasi neighborhood system, an L-topology, an L-closure operator, an L-interior operator, and a pointwise quasi-uniformity.
Pointwise Hardy inequalities and uniformly fat sets
2008
We prove that it is equivalent for domain in R n \mathbb {R}^n to admit the pointwise p p -Hardy inequality, have uniformly p p -fat complement, or satisfy a uniform inner boundary density condition.
Pointwise Inequalities for Sobolev Functions on Outward Cuspidal Domains
2019
Abstract We show that the 1st-order Sobolev spaces $W^{1,p}(\Omega _\psi ),$$1<p\leq \infty ,$ on cuspidal symmetric domains $\Omega _\psi $ can be characterized via pointwise inequalities. In particular, they coincide with the Hajłasz–Sobolev spaces $M^{1,p}(\Omega _\psi )$.
σ-Continuous and Co-σ-continuous Maps
2009
In this chapter we isolate the topological setting that is suitable for our study. We first present 2.1–2.3 to follow an understandable logical scheme nevertheless the main contribution are presented in 2.4–2.7 and our main tool will be Theorem 2.32. An important concept will be the σ-continuity of a map Φ from a topological space (X, T) into a metric space (Y, g). The σ-continuity property is an extension of continuity suitable to deal with countable decompositions of the domain space X as well as with pointwise cluster points of sequences of functions Φn : X → Y, n = 1,2,… When (X,T) is a subset of a locally convex linear topological space we shall refine our study to deal with σ-slicely …
The Theory of Normed Modules
2020
This chapter is devoted to the study of the so-called normed modules over metric measure spaces. These represent a tool that has been introduced by Gigli in order to build up a differential structure on nonsmooth spaces. In a few words, an \(L^2({{\mathfrak {m}}})\)-normed \(L^\infty ({{\mathfrak {m}}})\)-module is a generalisation of the concept of ‘space of 2-integrable sections of some measurable bundle’; it is an algebraic module over the commutative ring \(L^\infty ({{\mathfrak {m}}})\) that is additionally endowed with a pointwise norm operator. This notion, its basic properties and some of its technical variants constitute the topics of Sect. 3.1.
B1(1)Π state of KCs: high-resolution spectroscopy and description of low-lying energy levels.
2012
The diode laser induced B(1)(1)Π → X(1)Σ(+) fluorescence spectra of the KCs molecule were recorded by Fourier-transform spectrometer with resolution of 0.03 cm(-1). Buffer gas Ar was used to facilitate appearance of rotation relaxation lines in the spectra, thus enlarging the B(1)(1)Π dataset, allowing one to determine the Λ-splitting constants and to reveal numerous local perturbations. A dataset was systematically obtained for B(1)(1)Π vibrational levels ν(') ∈ [0; 5] nonuniformly covering rotational levels with J(') ∈ [7; 233]. For ν(') ∈ [0; 3], the less-perturbed data of f-components were included in the fit. A pointwise potential energy curve (PEC) based on the inverted perturbation a…
On specific stability bounds for linear multiresolution schemes based on piecewise polynomial Lagrange interpolation
2009
Abstract The Deslauriers–Dubuc symmetric interpolation process can be considered as an interpolatory prediction scheme within Harten's framework. In this paper we express the Deslauriers–Dubuc prediction operator as a combination of either second order or first order differences. Through a detailed analysis of certain contractivity properties, we arrive to specific l ∞ -stability bounds for the multiresolution transform. A variety of tests indicate that these l ∞ bounds are closer to numerical estimates than those obtained with other approaches.
A family of higher-order single layer plate models meeting Cz0-requirements for arbitrary laminates
2019
Abstract In the framework of displacement-based equivalent single layer (ESL) plate theories for laminates, this paper presents a generic and automatic method to extend a basis higher-order shear deformation theory (polynomial, trigonometric, hyperbolic…) to a multilayer C z 0 higher-order shear deformation theory. The key idea is to enhance the description of the cross-sectional warping: the odd high-order C z 1 function of the basis model is replaced by one odd and one even high-order function and including the characteristic zig-zag behaviour by means of piecewise linear functions. In order to account for arbitrary lamination schemes, four such piecewise continuous functions are consider…
Analysis of negative-resistance oscillators with piecewise nonlinearity
1977
An iterative method of solution of negative-resistance oscillators with piecewise-analytical characteristics is presented. The method allows the determination of the frequency and the harmonic content of the waveform as a function of the circuit parameters and bias of the nonlinear device. An application of the method, extended to the second order, for a polynomial characteristic limited by two straight lines is also reported. The results are compared with those obtained by numerical integration.