THREE KINDS OF DENTABILITIES IN BANACH SPACES AND THEIR APPLICATIONS

In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.

Strategies for multi-step-ahead available parking spaces forecasting based on wavelet transform

A new methodology for multi-step-ahead forecasting was proposed herein which combined the wavelet transform(WT), artificial neural network(ANN) and forecasting strategies based on the changing characteristics of available parking spaces(APS). First, several APS time series were decomposed and reconstituted by the wavelet transform. Then, using an artificial neural network, the following five strategies for multi-step-ahead time series forecasting were used to forecast the reconstructed time series: recursive strategy, direct strategy, multi-input multi-output(MIMO) strategy, DIRMO strategy(a combination of the direct and MIMO strategies), and newly proposed recursive multi-input multi-output(RECMO) strategy which is a combination of the recursive and MIMO strategies. Finally, integrating the predicted results with the reconstructed time series produced the final forecasted available parking spaces. Three findings appear to be consistently supported by the experimental results. First, applying the wavelet transform to multi-step ahead available parking spaces forecasting can effectively improve the forecasting accuracy. Second, the forecasting resulted from the DIRMO and RECMO strategies is more accurate than that of the other strategies. Finally, the RECMO strategy requires less model training time than the DIRMO strategy and consumes the least amount of training time among five forecasting strategies.

General Type-2 Fuzzy Topological Spaces

In this paper, a presented definition of type-2 fuzzy sets and type-2 fuzzy set operation on it was given. The aim of this work was to introduce the concept of general topological spaces were extended in type-2 fuzzy sets with the structural properties such as open sets, closed sets, interior, closure and neighborhoods in topological spaces were extended to general type-2 fuzzy topological spaces and many related theorems are proved.

Construction of Economic Urban Green Spaces with a Case Study of Shijiazhuang City

The accelerating urbanization has brought various problems in environment, land, fund and so on. With the guidance of market economy, economic urban green spaces have become the optimal choice in urban landscaping of China, which can not only improve urban landscapes, ecological environment, satisfy higher spiritual and cultural demands of people, but also create considerable economic benefits, and enhance the coordinated development of economy, society and environment. With Shijiazhuang City as an example, the approaches of constructing economic urban green spaces fit for Shijiazhuang City were analyzed in this study, to provide references for the construction of economic urban green spaces in other cities.

Sobolev Spaces, Schwartz Spaces, and a Definition of the Electromagnetic and Gravitational Coupling

The concept of multiplicity of solutions was developed in [1] which is based on the theory of energy operators in the Schwartz space S-(R) and some subspaces called energy spaces first defined in [2] and [3]. The main idea is to look for solutions of a given linear PDE in those subspaces. Here, this work extends previous developments in S-(Rm)?(m∈Z+) using the theory of Sobolev spaces. Furthermore, we also define the concept of Energy Parallax, which is the inclusion of additional solutions when varying the energy of a predefined system locally by taking into account additional smaller quantities. We show that it is equivalent to take into account solutions in other energy subspaces. To illustrate the theory, one of our examples is based on the variation of Electro Magnetic (EM) energy density within the skin depth of a conductive material, leading to take into account derivatives of EM evanescent waves, particular solutions of the wave equation. The last example is the derivation of the Woodward effect [4] with the variations of the EM energy density under strict assumptions in general relativity. It finally leads to a theoretical definition of an electromagnetic and gravitational (EMG) coupling.

PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES

Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.

Weighted multilinear p-adic Hardy operators and commutators on p-adic Herz-type spaces

In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.

ON F(p,q,s)SPACES

The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and have connections with many other areas of mathematics.In this survey we present some basic properties and recent results on F(p,q,s)spaces.

Identity of Urban Spaces: Assessment and Evaluation

As a major symbol of civilization,the city was built by man for his security and comfort.It is not only a settlement,but also an urban development which has been identified with the spirit that has been breathed into the community.Urban identity which is also known as collective identity,has gained meaning through the content of objective manifestation and the creation of flashbacks,citizens’memories and mental associations.That is what makes urban dwellers become citizens.Although the identity of the city is a result of civic culture,it still has an influence on the process of citizenship and can also be a reason for developing criteria related to the participation and assessment of its inhabitants.According to the view that identity is a set of traits and characteristics that distinguishes the dignity of a person and a society from other individuals and communities,a city becomes characterized and independent by adhering to these criteria.Despite the importance of identity as one of the richest qualitative aspects of urban life that gives meaning and fulfilment to the human quiddity,this complicated and expanded concept has still not been seriously considered,especially in relation to urban spaces.In fact,identity in architecture and urban spaces has recently diminished,since the main focus lies on building spaces for optimized profit and not for high quality living areas.In this research paper,parameters affecting urban identity are evaluated,and strategies and guidelines to promote these parameters are finally presented.

Investigation of Ancient and Large Tree Resources in Green Spaces of Urban Parks: A Case Study of Yunqizhujing Park in Hangzhou, China

Conservation of ancient and large trees in domestic and overseas cities was compared, ancient and large trees were regarded as important cultural relics playing an important role in optimizing urban natural environment and enriching urban humanistic and natural landscapes, and they were also important contents of urban garden works symbolizing urban parks. A case study was carried out Yunqizhujing Park to study conservation of ancient and large trees in park green spaces of Hangzhou City, solutions to current problems were proposed, and constructive suggestions were given for the conservation of ancient and large trees in urban park green spaces.

Common Fixed Point Results for Occasionally Weakly Compatible Maps in G-Symmetric Spaces

The notion of a G-symmetric space is introduced and the common fixed points for some pairs of occasionally weakly compatible maps satisfying some contractive conditions in a G-symmetric space are proved. The results extend and improve some results in literature.

Stable Perturbed Algorithms for a New Class of Generalized Nonlinear Implicit Quasi Variational Inclusions in Banach Spaces

In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its convergence results are established.

On Some <i>I</i>-Convergent Double Sequence Spaces Defined by a Modulus Function

In 2000, Kostyrko, Salat, and Wilczynski introduced and studied the concept of I-convergence of sequences in metric spaces where I is an ideal. The concept of I-convergence has a wide application in the field of Number Theory, trigonometric series, summability theory, probability theory, optimization and approximation theory. In this article we introduce the double sequence spaces and ,for a modulus function f and study some of the properties of these spaces.

The Dual of the Two-Variable Exponent Amalgam Spaces (Lq(),lp())(Ω)

Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (Lq(),lp())(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.

Energy <i>β</i>-Conformal Change and Special Finsler Spaces

The main aim of the present paper is to establish an intrinsic investigation of the energy β-conformal change of the most important special Finsler spaces, namely, Ch-recurrent, Cv-recurrent, C0-recurrent, Sv-recurrent, quasi-C-reducible, semi-C-reducible, C-reducible, P-reducible, C2-like, S3-like, P2-like and h-isotropic, ···, etc. Necessary and sufficient conditions for such special Finsler manifolds to be invariant under an energy β-conformal change are obtained. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.

Near-Vector Spaces Constructed over Zp, for p a Prime

The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Zp for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.

Word Embeddings and Semantic Spaces in Natural Language Processing

One of the critical hurdles, and breakthroughs, in the field of Natural Language Processing (NLP) in the last two decades has been the development of techniques for text representation that solves the so-called curse of dimensionality, a problem which plagues NLP in general given that the feature set for learning starts as a function of the size of the language in question, upwards of hundreds of thousands of terms typically. As such, much of the research and development in NLP in the last two decades has been in finding and optimizing solutions to this problem, to feature selection in NLP effectively. This paper looks at the development of these various techniques, leveraging a variety of statistical methods which rest on linguistic theories that were advanced in the middle of the last century, namely the distributional hypothesis which suggests that words that are found in similar contexts generally have similar meanings. In this survey paper we look at the development of some of the most popular of these techniques from a mathematical as well as data structure perspective, from Latent Semantic Analysis to Vector Space Models to their more modern variants which are typically referred to as word embeddings. In this review of algoriths such as Word2Vec, GloVe, ELMo and BERT, we explore the idea of semantic spaces more generally beyond applicability to NLP.

Some Fixed Point Results of Ciric-Type Contraction Mappings on Ordered <i>G</i>-Partial Metric Spaces

We introduce the concept of generalized quasi-contraction mappings in G-partial metric spaces and prove some fixed point results in ordered G-partial metric spaces. The results generalize and extend some recent results in literature.