Let Q be a homogeneous function of degree zero that enjoys the vanishing condition on the unit sphere Sn-1(n >= 2). Let TQ be the convolution singular integral operator with kernel Q(x)|x|-n. In this paper, when Q ...
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Let Q be a homogeneous function of degree zero that enjoys the vanishing condition on the unit sphere Sn-1(n >= 2). Let TQ be the convolution singular integral operator with kernel Q(x)|x|-n. In this paper, when Q E L Co ( S n- 1 ), we consider quantitative weighted bounds of composite operators of TQ on rearrangement invariant Banach function spaces. These spaces contain classical Lorentz spaces and Orlicz spaces as special examples. Weighted boundedness of the composite operators on rearrangement invariant quasi-Banach spaces are also given.
For 1 < p < infinity, we show that the Rosenthal X p,w spaces and the Bourgain-Rosenthal-Schechtman R p omega space have the factorization property and the primary factorization property. (c) 2024 The Authors. P...
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For 1 < p < infinity, we show that the Rosenthal X p,w spaces and the Bourgain-Rosenthal-Schechtman R p omega space have the factorization property and the primary factorization property. (c) 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// ***/licenses/by/4.0/).
In this paper, we introduce and study the concept of p-height orthogonality in real normed linear spaces. This orthogonality generalizes the well-known Singer and height orthogonalities. First, we investigate main pro...
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In this paper, we introduce and study the concept of p-height orthogonality in real normed linear spaces. This orthogonality generalizes the well-known Singer and height orthogonalities. First, we investigate main properties of this type of orthogonality. Then, variety of examples are presented to illustrate the relationship between p-height orthogonality and other previously defined (e.g., isosceles, Singer, height and Birkhoff-James) orthogonalities. Also we investigate the existence properties of this new notion of orthogonality. In particular, alpha-existence property is established and some interesting bounds for the values of alpha are obtained. Moreover, some characterizations of inner product spaces are given in terms of p-height orthogonality and its relation with Pythagorean and Birkhoff-James orthogonalities. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data
We investigate here the density of the set of the restrictions from C-C(infinity)(R-d) to C-C(infinity)(Omega) in the Musielak-Orlicz-Sobolev space W-1,W-Phi(Omega). It is a continuation of article [15], where we have...
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We investigate here the density of the set of the restrictions from C-C(infinity)(R-d) to C-C(infinity)(Omega) in the Musielak-Orlicz-Sobolev space W-1,W-Phi(Omega). It is a continuation of article [15], where we have studied density of CC infinity(Rd) in W-k,W-Phi(R-d) for k is an element of N. The main theorem states that for an open subset Omega subset of R-d with its boundary of class C-1, and Musielak-Orlicz function Phi satisfying condition (A1) which is a sort of log-H & ouml;lder continuity and the growth condition Delta 2, the set of restrictions of functions from C-C(infinity)(R-d) to Omega is dense in W-1,W-Phi(Omega). We obtain a corresponding result in variable exponent Sobolev space W-1,W-p(& sdot;)(Omega) under the assumption that the exponent p(x) is essentially bounded on Omega and Phi(x,t)=t(p(x)), t >= 0, x is an element of Omega, satisfies the log-H & ouml;lder condition. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Sociological research increasingly examines the diversity of cultural and religious resources that various community groups contribute to urban spaces and the public sphere. A key focus within this field is the reinte...
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Sociological research increasingly examines the diversity of cultural and religious resources that various community groups contribute to urban spaces and the public sphere. A key focus within this field is the reinterpretation of shared religious and spiritual spaces as part of the tangible and intangible religious cultural heritage. Adopting a spatial perspective, this analysis focuses on the specific case of top-down multi-religious places. Through an exploration of representative examples, this article investigates the different typologies of these places-from complexes that host distinct spaces for different faiths or religions to interfaith chapels and prayer and meditation rooms located in non-religious settings-using the framework of religious cultural heritage. The central conceptual bases of this framework-namely, the historical and memorial value, aesthetic considerations, sacredness and social function-are discussed in terms of their partial and complex association with the qualities of these unconventional spaces. This article suggests that the significance of multi-religious places from the perspective of religious cultural heritage is greater when these places do not serve merely a symbolic function or a purely pragmatic one. This article emphasizes the significance of spatial elements shaped by architectural design and construction choices, which can play a crucial role in integrating multi-religious spaces into the collective memory and foster appreciation for unique forms of sacred beauty.
For any educational programme to be successful, it is essential to have a well-planned and comprehensive syllabus that fosters inclusivity and positive motivation. In my paper, I am going to examine the BA syllabi fro...
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While cable-driven snake robots are promising in exploring confined spaces, their hyper-redundancy makes the collision-free motion planning difficult. In this paper, by combining the prediction lookup and interpolatio...
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While cable-driven snake robots are promising in exploring confined spaces, their hyper-redundancy makes the collision-free motion planning difficult. In this paper, by combining the prediction lookup and interpolation algorithms, we present a new path following method for cable-driven snake robots to high-efficiently slither into complex terrains along a desired path. In our method, we first discretize the desired path into points, and develop the prediction lookup algorithm to efficiently find the points matched with joints of the robot. According to geometric relations between the prediction lookup results and link length of the robot, we develop the interpolation algorithm to reduce the tracking errors caused by the discretization. Finally, simulations and experiments of inspections in two confined spaces including the obstacle array and pipe tank system are performed on our custom-built 25 degree of freedoms(DOFs) cable-driven snake robot. The results demonstrate that the presented method can successfully navigate our snake robot into confined spaces with high computational efficiency and good accuracy, which well verifies effectiveness of our development.
The shearlets are a special case of the wavelets with composite dilation that, among other things, have a basis-like structure and multi-resolution analysis properties. These relatively new representation 'systems...
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The shearlets are a special case of the wavelets with composite dilation that, among other things, have a basis-like structure and multi-resolution analysis properties. These relatively new representation 'systems have encountered wide range of applications, generally surpassing the performance of their ancestors due to their directional sensitivity. Both theories of coorbit spaces and decomposition spaces provide a way of associating some kind of smoothness spaces to shearlets. However, these smoothness spaces are closer to classical Besov type spaces. Here, instead, we define a kind of highly anisotropic inhomogeneous Triebel-Lizorkin spaces and prove that it can be characterized with the so-called "shearlets on the cone" coefficients. We first prove the boundedness of the analysis and synthesis operators with the "traditional" shearlets coefficients. Then, with the development of the smooth Parseval frames of shearlets of Guo and Labate we are able to prove a reproducing identity, which was previously possible only for the L-2 case. We also find some embeddings of the (classical) dyadic spaces into these highly anisotropic spaces, and vice versa, for certain ranges of parameters. In order to keep a concise document we develop our results in the "weightless" case (w = 1) and give hints on how to develop the weighted case. (C) 2012 Elsevier Inc. All rights reserved.
The main object of this paper is to introduce and study some sequence spaces which arise from concept of weighted means, determine their beta-duals and characterize matrix transformations between them. (C) 2002 Elsevi...
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The main object of this paper is to introduce and study some sequence spaces which arise from concept of weighted means, determine their beta-duals and characterize matrix transformations between them. (C) 2002 Elsevier Inc. All rights reserved.
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