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In dynamical systems, Hilbert spaces provide a useful framework for analyzing and solving problems because they are able to handle infinitely dimensional spaces. Many dynamical systems are described by linear operators acting on a Hilbert space. Understanding the spectrum, eigenvalues, and eigenvectors of these operators is crucial. Functional analysis typically involves the use of tensors to represent multilinear mappings between Hilbert spaces, which can result in inequality in tensor Hilbert spaces. In this paper, we study two types of function spaces and use convex and harmonic convex mappings to establish various operator inequalities and their bounds. In the first part of the article, we develop the operator Hermite–Hadamard and upper and lower bounds for weighted discrete Jensen-type inequalities in Hilbert spaces using some relational properties and arithmetic operations from the tensor analysis. Furthermore, we use the Riemann–Liouville fractional integral and develop several new identities which are used in operator Milne-type inequalities to develop several new bounds using different types of generalized mappings, including differentiable, quasi-convex, and convex mappings. Furthermore, some examples and consequences for logarithm and exponential functions are also provided. Furthermore, we provide an interesting example of a physics dynamical model for harmonic mean. Lastly, we develop Hermite–Hadamard inequality in variable exponent function spaces, specifically in mixed norm function space ( l q (·) (L p (·)) ). Moreover, it was developed using classical Lebesgue space ( L p ) space, in which the exponent is constant. This inequality not only refines Jensen and triangular inequality in the norm sense, but we also impose specific conditions on exponent functions to show whether this inequality holds true or not. [ABSTRACT FROM AUTHOR]

We undertake this study with the objective of introducing certain control functions in the contractive condition to prove fixed-point theorems in the framework of complex-valued bipolar metric spaces. The incorporation of control functions broadens the applicability of the contractive condition. This approach yields key results consistent with previous studies. In support of our results, we offer two insightful examples that demonstrate the concepts discussed. Additionally, we present the notion of interpolative contraction in this new and generalized metric space and prove fixed-point theorems for non-self mappings. To demonstrate the application of our approach, we reproduce key findings from several established studies in the field. [ABSTRACT FROM AUTHOR]

The single generalized weighted composition operator D u , ψ n on various spaces of analytic functions has been investigated for decades, i.e., D u , ψ n f = u · (f (n) ∘ ψ) , where f ∈ H (D) . However, the study of the finite sum of generalized weighted composition operators with different orders, i.e., P U , ψ k f = u 0 · f ∘ ψ + u 1 · f ′ ∘ ψ + ⋯ + u k · f (k) ∘ ψ , is far from complete. The boundedness, compactness and essential norm of sums of generalized weighted composition operators from weighted Bergman spaces with doubling weights into Bloch-type spaces are investigated. We show a rigidity property of P U , ψ k . Specifically, the boundedness and compactness of the sum P U , ψ k is equivalent to those of each D u n , ψ n , 0 ≤ n ≤ k. [ABSTRACT FROM AUTHOR]

By using the most generalized gamma function (parametric gamma function, or p-gamma function), we present the most generalized Rabotnov function, called the p-Rabotnov function. Consequently, new fractal–fractional differential and integral operators of a complex variable in an open unit disk are defined and investigated analytically and geometrically. We address some inequalities involving the generalized fractal–fractional integral operator in some spaces of analytic functions. A novel complex fractal–fractional integral transform (CFFIT) is presented. A normalization of the proposed CFFIT is observed in the open unit disk. Examples are illustrated for power series of analytic functions. [ABSTRACT FROM AUTHOR]

A system of fractional differential equations (FDEs) with fractional derivatives of diverse orders is called an incommensurate system of FDEs. In this paper, the well-posedness of the initial value problem for incommensurate systems of FDEs is obtained on the space of continuous functions. Three different methods for this analysis are used and compared. The complexity of such analysis is reduced by new techniques. Strong existence results are obtained by weaker conditions. The uniqueness and the continuous dependency of the solution on initial values are investigated using the Gronwall inequality. [ABSTRACT FROM AUTHOR]

This study looks closely into the analysis of the variation of constants formula given by Φ (t) = S (t) Φ (0) + ∫ 0 t S (t − σ) F (σ , Φ (σ)) d σ , for t ∈ [ 0 , T ] , T > 0 , within the context of modular function spaces L ρ . Additionally, this research explores practical applications of the variation of constants formula in variable exponent Lebesgue spaces L p (·) . Specifically, the study examines these spaces under certain conditions applied to the exponent function p (·) and the functions F as well as the semigroup S (t) , utilizing the symmetry properties of the algebraic semigroup. This investigation sheds light on the intricate interplay between parameters and functions within these mathematical frameworks, offering valuable insights into their behavior and properties in L p (·) . [ABSTRACT FROM AUTHOR]

Let n ∈ N 0 , ψ be an analytic self-map on D and u be an analytic function on D. The single operator D u , ψ n acting on various spaces of analytic functions has been a subject of investigation for many years. It is defined as (D u , ψ n f) (z) = u (z) f (n) (ψ (z)) , f ∈ H (D) . However, the study of the operator P u → , ψ k , which represents a finite sum of these operators with varying orders, remains incomplete. The boundedness, compactness and essential norm of the operator P u → , ψ k on the Bloch space are investigated in this paper, and several characterizations for these properties are provided. [ABSTRACT FROM AUTHOR]

Urban agglomerations are products of urban development, and their regional spaces and functions are more diverse than other cities, which have very high spatial and functional complexity. It is important to clarify the relationships between production–living–ecological (PLE) functions in urban agglomerations to achieve sustainable development. In this study, we took the Middle Reaches of the Yangtze River Urban Agglomerations (MRYRUA) as an example to construct an evaluation index system of regional PLE functions in urban agglomerations. Then, the Pearson correlation model and geographically weighted regression were applied to investigate the relationships between PLE functions and their driving forces. The results showed that the PLE functions in the MRYRUA increased from 2008 to 2018, with the level of the ecological function being higher than the production and living functions. The relationships among PLE functions were dominated by synergies in most cities, though trade-offs had become more evident in the last few years for the whole study area. Trade-offs and synergies among PLE functions were influenced by both natural and socioeconomic factors, with the latter having a stronger effect. Our findings provide a reference for understanding the spatial variations and trade-offs among PLE functions in MRYRUA as well as for balancing the development of PLE functions. [ABSTRACT FROM AUTHOR]

Located in Dali, Yunnan, the Zhaozhou basin is home to many precious architectural heritages, particularly the historical horse caravan architecture. These buildings face the challenge of renewal and transformation. It is of great significance to explore the local population's awareness of the architectural heritage of the horse caravan in order to protect the architectural heritage and facilitate rural revitalization. This study reviews the related research on "space perception", establishes a theoretical framework of space perception under the architectural dimension, and develops hypotheses. The social cluster of typical settlements in the Zhaozhou basin is selected as the research object, and empirical analyses are carried out using SPSS and AMOS software. An analytical framework model of empirical research is constructed to evaluate the space perception of the current social population. The results of the reliability and validity tests of the questionnaire show that the CR is greater than 0.7 and that the AVE is greater than 0.5. The value of the structural equation model fitting index χ2/df is 1.863, which is less than 3. The model test results show that research hypotheses H1–H5 are supported; that is, space perception has a significant positive impact on cognition and local identity, cognition has a significant positive impact on local identity and space function, and place identity has a significant positive impact on space appeal. This study demonstrates the relationship between space perception and the architectural remains of the horse caravan, and it analyzes the human psychological perception behind the material space. The findings support the need for further conservation of the horse caravan architecture. This study further deepens the theory of space perception and its application in the study of vernacular architecture, which can provide a research path for the protection and development of vernacular architectural heritage. [ABSTRACT FROM AUTHOR]

This paper demonstrates that the space of piecewise-smooth bivariate functions can be well-approximated by the space of the functions defined by a set of simple (non-linear) operations on smooth uniform tensor product splines. The examples include bivariate functions with jump discontinuities or normal discontinuities across curves, and even across more involved geometries such as a three-corner discontinuity. The provided data may be uniform or non-uniform, and noisy, and the approximation procedure involves non-linear least-squares minimization. Also included is a basic approximation theorem for functions with jump discontinuity across a smooth curve. [ABSTRACT FROM AUTHOR]

We study the existence and multiplicity of normalized solutions to the fractional logarithmic Schrödinger equation (− Δ) s u + V (ϵ x) u = λ u + u log u 2 in R N , under the mass constraint ∫ R N | u | 2 d x = a. Here, N ≥ 2 , a , ϵ > 0 , λ ∈ R is an unknown parameter, (− Δ) s is the fractional Laplacian and s ∈ (0 , 1) . We introduce a function space where the energy functional associated with the problem is of class C 1 . Then, under some assumptions on the potential V and using the Lusternik–Schnirelmann category, we show that the number of normalized solutions depends on the topology of the set for which the potential V reaches its minimum. [ABSTRACT FROM AUTHOR]

Phase and amplitude modes, also called polariton modes, are emergent phenomena that manifest across diverse physical systems, from condensed matter and particle physics to quantum optics. We study their behavior in an anisotropic Dicke model that includes collective matter interactions. We study the low-lying spectrum in the thermodynamic limit via the Holstein–Primakoff transformation and contrast the results with the semi-classical energy surface obtained via coherent states. We also explore the geometric phase for both boson and spin contours in the parameter space as a function of the phases in the system. We unveil novel phenomena due to the unique critical features provided by the interplay between the anisotropy and matter interactions. We expect our results to serve the observation of phase and amplitude modes in current quantum information platforms. [ABSTRACT FROM AUTHOR]

In response to the increasing building demands in Turkey, particularly in the metropolitan area of Istanbul, followed by other major cities such as Ankara and Izmir, the expansion of construction zones has led to the emergence of tall towers as a pragmatic solution. The design and implementation of tall buildings require newer technologies and interdisciplinary collaboration in aspects such as facade installation, vertical circulation solutions, and fire systems, compared to low-rise buildings. In spite of the proliferation of skyscrapers, there is a noticeable lack of thorough study on space efficiency in Turkey's tall buildings. This article aims to fill this significant gap in the literature. The research method employed in this study focuses on a case study of 54 modern towers constructed in Turkey between 2010 and 2023, ranging in height from 147 to 284 m. Key findings are as follows: (1) residential use, central core, and prismatic forms are the most prevalent architectural preferences; (2) the most preferred structural material and system are concrete and the shear-walled frame system, respectively; (3) average space efficiency and the percentage of core-to-gross-floor area (GFA) were 78% and 19%, respectively, with measurement ranges varying from a minimum of 64% and 9% to a maximum of 86% and 34%. This paper will provide insight for construction stakeholders, especially architects, for sound planning decisions in the development of Turkish tall buildings. [ABSTRACT FROM AUTHOR]

A sample of continuous random functions with auto-regressive structures and possible change-point of the means are considered. We present test statistics for the change-point based on a functional of partial sums. To study their asymptotic behavior, we prove functional limit theorems for polygonal line processes in the space of continuous functions. For some situations, we use a block bootstrap procedure to construct the critical region and provide applications. We also study the finite sample behavior via simulations. Eventually, we apply the statistics to a telecommunications data sample. [ABSTRACT FROM AUTHOR]

This paper considers a nonlinear fractional-order boundary value problem   H D a , g α 1 , β , μ x (t) + f (t , x (t) , H D a , g α 2 , β , μ x (t)) = 0 , for t ∈ [ a , b ] , α 1 ∈ (1 , 2 ] , α 2 ∈ (0 , 1 ] , β ∈ [ 0 , 1 ] with appropriate integral boundary conditions on the Hölder spaces. Here, f is a real-valued function that satisfies the Hölder condition, and   H D a , g α , β , μ represents the tempered-Hilfer fractional derivative of order α > 0 with parameter μ ∈ R + and type β ∈ [ 0 , 1 ] . The corresponding integral problem is introduced in the study of this issue. This paper addresses a fundamental issue in the field, namely the circumstances under which differential and integral problems are equivalent. This approach enables the study of differential problems using integral operators. In order to achieve this, tempered fractional calculus and the equivalence problem of the studied problems are introduced and studied. The selection of an appropriate function space is of fundamental importance. This paper investigates the applicability of these operators on Hölder spaces and provides a comprehensive rationale for this choice. [ABSTRACT FROM AUTHOR]

In this paper, the sampling and reconstruction problems in function subspaces of L p (R n) associated with the multi-dimensional special affine Fourier transform (SAFT) are discussed. First, we give the definition of the multi-dimensional SAFT and study its properties including the Parseval's relation, the canonical convolution theorems and the chirp-modulation periodicity. Then, a kind of function spaces are defined by the canonical convolution in the multi-dimensional SAFT domain, the existence and the properties of the dual basis functions are demonstrated, and the L p -stability of the basis functions is established. Finally, based on the nonuniform samples taken on a dense set, we propose an iterative reconstruction algorithm with exponential convergence to recover the signals in a L p -subspace associated with the multi-dimensional SAFT, and the validity of the algorithm is demonstrated via simulations. [ABSTRACT FROM AUTHOR]

This article primarily investigates the width problem within weighted band-limited function space in a uniform setting. Through an analysis of the properties of s-numbers, we establish a connection between the widths of weighted band-limited function spaces and the s-numbers of infinite-dimensional diagonal operators. Furthermore, employing the discretization method, we estimate the exact asymptotic orders of Kolmogorov n-width and linear n-width in the weighted band-limited function space, which is characterized by the weight ω = ω k = | k | r k ∈ Z 0 . [ABSTRACT FROM AUTHOR]

Lower strict monotonicity points and lower local uniform monotonicity points are considered in the case of Musielak–Orlicz function spaces L Φ endowed with the Mazur–Orlicz F-norm. The findings outlined in this study extend the scope of geometric characteristics observed in F-normed Orlicz spaces, as well as monotonicity properties within specific F-normed lattices. They are suitable for the Orlicz spaces of ordered continuous elements, specifically in relation to the Mazur–Orlicz F-norm. In addition, in this paper presents results that can be used to derive certain monotonicity properties in F-normed Musielak–Orlicz spaces. [ABSTRACT FROM AUTHOR]

In this article, we consider the correction of metric matrices in quasi-Newton methods (QNM) from the perspective of machine learning theory. Based on training information for estimating the matrix of the second derivatives of a function, we formulate a quality functional and minimize it by using gradient machine learning algorithms. We demonstrate that this approach leads us to the well-known ways of updating metric matrices used in QNM. The learning algorithm for finding metric matrices performs minimization along a system of directions, the orthogonality of which determines the convergence rate of the learning process. The degree of learning vectors' orthogonality can be increased both by choosing a QNM and by using additional orthogonalization methods. It has been shown theoretically that the orthogonality degree of learning vectors in the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method is higher than in the Davidon–Fletcher–Powell (DFP) method, which determines the advantage of the BFGS method. In our paper, we discuss some orthogonalization techniques. One of them is to include iterations with orthogonalization or an exact one-dimensional descent. As a result, it is theoretically possible to detect the cumulative effect of reducing the optimization space on quadratic functions. Another way to increase the orthogonality degree of learning vectors at the initial stages of the QNM is a special choice of initial metric matrices. Our computational experiments on problems with a high degree of conditionality have confirmed the stated theoretical assumptions. [ABSTRACT FROM AUTHOR]

In this paper, a short review of the calculus of exact finite-differences of integer order is proposed. The finite-difference operators are called the exact finite-differences of integer orders, if these operators satisfy the same characteristic algebraic relations as standard differential operators of the same order on some function space. In this paper, we prove theorem that this property of the exact finite-differences is satisfies for the space of simple entire functions on the real axis (i.e., functions that can be expanded into power series on the real axis). In addition, new results that describe the exact finite-differences beyond the set of entire functions are proposed. A generalized expression of exact finite-differences for non-entire functions is suggested. As an example, the exact finite-differences of the square root function is considered. The use of exact finite-differences for numerical and computer simulations is not discussed in this paper. Exact finite-differences are considered as an algebraic analog of standard derivatives of integer order. [ABSTRACT FROM AUTHOR]

Territorial spatial planning requires thoughtful consideration of the scientific layout and synergistic control of production, living, and ecological spaces (PLESs). However, research in this field often neglects the human perspective and fails to account for people's demands and behavioral characteristics. This study evaluates the level and spatial characteristics of residents' production, living, and ecological behavioral (PLEB) flow, as well as the spatial pattern of the PLES functions, within the framework of the human–land coupling system. Therefore, to analyze the behavior–space coupling coordination relationship, the coupling coordination model is applied. The results indicate that the overall level of residents' PLEB flow in rural–urban fringe areas is at a lower middle level and the functionality of the PLES is at a medium level, with a spatial distribution pattern of high in the northern and low in the southern areas. Most of the behavior–space matching types are in a state of mismatch between supply and demand. Meanwhile, the PLEB–PLES coupling coordination relationship is generally unbalanced, which is particularly noticeable in the production space. Regardless of whether the behavior–space matching type is a supply deficit or a supply surplus, the mismatch between supply and demand leads to uncoordinated and unreasonable spatial utilization. Overall, the findings of the study provide guidance for future research endeavors about PLESs and suggest embracing a human-centered scientific paradigm. Such a paradigm can promote high-quality, sustainable development of territorial spatial planning while strengthening the capacity and effectiveness of spatial governance and control. [ABSTRACT FROM AUTHOR]

Let X , Y be two Banach spaces and f : X → Y be a standard coarse isometry. In this paper, we first show a sufficient and necessary condition for the coarse left-inverse operator of general Banach spaces to admit a linearly isometric right inverse. Furthermore, by using the well-known simultaneous extension operator, we obtain an asymptotical stability result when Y is a space of continuous functions. In addition, we also prove that every coarse left-inverse operator does admit a linear isometric right inverse without other assumptions when Y is a L p (1 < p < ∞) space, or both X and Y are finite dimensional spaces of the same dimension. Making use of the results mentioned above, we generalize several results of isometric embeddings and give a stability result of coarse isometries between Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we numerically solve the nonlinear time-fractional diffusion equation of distributed order on an unbounded domain with a weak singularity. A fully discrete implicit scheme is developed based on the L1 formula on graded meshes in time and the Galerkin spectral method using the Laguerre function in space. We obtained an α -robust discrete Gronwall inequality and the a priori error estimation of the numerical solution. Then, the existence and uniqueness of the numerical solution are discussed. Next, we present the α -robust stability and convergence of the fully discrete scheme, where the convergence was obtained based on the regularity conditions of the exact solution. A numerical example demonstrates the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

Machine learning (ML) methods are increasingly being applied to analyze biological signals. For example, ML methods have been successfully applied to the human electroencephalogram (EEG) to classify neural signals as pathological or non-pathological and to predict working memory performance in healthy and psychiatric patients. ML approaches can quickly process large volumes of data to reveal patterns that may be missed by humans. This study investigated the accuracy of ML methods at classifying the brain's electrical activity to cognitive events, i.e., event-related brain potentials (ERPs). ERPs are extracted from the ongoing EEG and represent electrical potentials in response to specific events. ERPs were evoked during a visual Go/NoGo task. The Go/NoGo task requires a button press on Go trials and response withholding on NoGo trials. NoGo trials elicit neural activity associated with inhibitory control processes. We compared the accuracy of six ML algorithms at classifying the ERPs associated with each trial type. The raw electrical signals were fed to all ML algorithms to build predictive models. The same raw data were then truncated in length and fitted to multiple dynamic state space models of order n x using a continuous-time subspace-based system identification algorithm. The 4 n x numerator and denominator parameters of the transfer function of the state space model were then used as substitutes for the data. Dimensionality reduction simplifies classification, reduces noise, and may ultimately improve the predictive power of ML models. Our findings revealed that all ML methods correctly classified the electrical signal associated with each trial type with a high degree of accuracy, and accuracy remained high after parameterization was applied. We discuss the models and the usefulness of the parameterization. [ABSTRACT FROM AUTHOR]

In the paper, we develop three new methods for estimating unknown initial temperature in a backward time-fractional diffusion problem, which is transformed to a space-dependent inverse source problem for a new variable in the first method. Then, the initial temperature can be recovered by solving a second-order boundary value problem. The boundary functions and a unique zero element constitute a group symmetry. We derive energetic boundary functions in the symmetry group as the bases to retrieve the source term as an unknown function of space and time. In the second method, the solution bases are energetic boundary functions, and then by collocating the governing equation we obtain the expansion coefficients for retrieving the entire solution and initial temperature. For the first two methods, boundary fluxes are over-specified to retrieve the initial condition. In the third method, we give two boundary conditions and a final time temperature to construct the bases in another symmetry group; the governing equation is collocated to a linear system to obtain the whole solution (initial temperature involved). These three methods are assessed and compared by numerical experiments. [ABSTRACT FROM AUTHOR]

The rationale of this work is to introduce the notion of graphical symmetric spaces and some fixed-point results are proved for H - (ϑ , φ) -contractions in this setting. The idea of graphical symmetric spaces generalizes various spaces equipped with a function which characterizes the distance between two points of the space. Some topological properties of graphical symmetric spaces are discussed. Some fixed-point results for the mappings defined on graphical symmetric spaces are proved. The fixed-point results of this paper generalize and extend several fixed-point results in this new setting. The main results of this paper are applied to obtain the positive solutions of fractional periodic boundary value problems. [ABSTRACT FROM AUTHOR]

In this paper, we study the approximation of continuous functions on a subclass of singular space—the subcartesian space. As is well known, the orbit space of the proper action of a Lie group on a smooth manifold is a subcartesian space. We prove that continuous functions on the orbit space can be approximated by smooth functions. [ABSTRACT FROM AUTHOR]

Nanotechnology has advanced the techniques for elucidating phenomena at the atomic, molecular, and nano-level. As a post nanotechnology concept, nanoarchitectonics has emerged to create functional materials from unit structures. Consider the material function when nanoarchitectonics enables the design of materials whose internal structure is controlled at the nanometer level. Material function is determined by two elements. These are the functional unit that forms the core of the function and the environment (matrix) that surrounds it. This review paper discusses the nanoarchitectonics of confined space, which is a field for controlling functional materials and molecular machines. The first few sections introduce some of the various dynamic functions in confined spaces, considering molecular space, materials space, and biospace. In the latter two sections, examples of research on the behavior of molecular machines, such as molecular motors, in confined spaces are discussed. In particular, surface space and internal nanospace are taken up as typical examples of confined space. What these examples show is that not only the central functional unit, but also the surrounding spatial configuration is necessary for higher functional expression. Nanoarchitectonics will play important roles in the architecture of such a total system. [ABSTRACT FROM AUTHOR]

This is a continuation of our previous study on the shape parameter contained in the shifted surface spline. We insist that the data points be purely scattered without meshes and the domain can be of any shape when conducting function interpolation by shifted surface splines. We also endeavor to make our approach easily accessible for scientists, not only mathematicians. However, the space of interpolated functions is smaller than that used before, leading to sharper function approximation. This function space has particular significance in numerical partial differential equations, especially for equations whose solutions lie in Sobolev space. Although the Fourier transform is deeply involved, scientists without a background in Fourier analysis can easily understand and use our approach. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate a certain sufficiency criterion for uniform convexity, strong starlikeness, and strong convexity of Rabtonov fractional exponential functions. We also study the starlikeness and convexity of order  γ. Moreover, we find conditions so that the Rabotnov functions belong to the class of bounded analytic functions and Hardy spaces. Various consequences of these results are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we present a result on the existence of asymptotically stable solutions of infinite systems (IS) of quadratic Hammerstein integral equations (IEs). Our study will be conducted in the Banach space of functions, which are continuous and bounded on the half-real axis with values in the classical Banach sequence space consisting of real bounded sequences. The main tool used in our investigations is the technique associated with the measures of noncompactness (MNCs) and a fixed point theorem of Darbo type. The applicability of our result is illustrated by a suitable example at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we discuss some extensions of the Maligranda–Orlicz lemma. It deals with the problem of constructing a norm in a subspace of the space of bounded functions, for which it becomes a normed algebra so that the norm introduced is equivalent to the initial norm of the subspace. This is done by satisfying some inequality between these norms. We show in this paper how this inequality is relevant to the study of operator equations in Banach algebras. In fact, we study how to equip a subspace of the space of bounded functions with a norm equivalent to a given one so that it is a normed algebra. We give a general condition for the construction of such norms, which allows us to easily check whether a space with a given norm is an algebra with a pointwise product and the consequences of such a choice for measures of noncompactness in such spaces. We also study quasi-normed spaces. We introduce a general property of measures of noncompactness that allows the study of quadratic operator equations, prove a fixed-point theorem suitable for such problems, and complete the whole with examples and applications. [ABSTRACT FROM AUTHOR]

Inspired by some recent studies of the multiplication operators on holomorphic function spaces of the classical domains such as the open unit disk, the unit ball and the unit polydisk, the purpose of the present paper is to study just the operators that are defined on weighted Zygmund spaces of the first Cartan domain. We obtain some necessary conditions and sufficient conditions for the operators to be bounded and compact. [ABSTRACT FROM AUTHOR]

In this paper, the solution to a spatially colored stochastic heat equation (SHE) is studied. This solution is a random function of time and space. For a fixed point in space, the resulting random function of time has exact, dimension-dependent, global continuity moduli, and laws of the iterated logarithm (LILs). It is obtained that the set of fast points at which LILs fail in this process, and occur infinitely often, is a random fractal, the size of which is evaluated by its Hausdorff dimension. These points of this process are everywhere dense with the power of the continuum almost surely, and their hitting probabilities are determined by the packing dimension dim P (E) of the target set E. [ABSTRACT FROM AUTHOR]

We consider algebras of polynomials and analytic functions that are invariant with respect to semidirect products of groups of bounded operators on Banach spaces with symmetric bases. In particular, we consider algebras of so-called block-symmetric and double-symmetric analytic functions on Banach spaces ℓ p (C n) and the homomorphisms of these algebras. In addition, we describe an algebraic basis in the algebra of double-symmetric polynomials and discuss a structure of the spectrum of the algebra of double-symmetric analytic functions on ℓ p (C n). [ABSTRACT FROM AUTHOR]

New families of direct serendipity and direct mixed finite elements on general planar, strictly convex polygons were recently defined by the authors. The finite elements of index r are H 1 and H (div) conforming, respectively, and approximate optimally to order r + 1 while using the minimal number of degrees of freedom. The shape function space consists of the full set of polynomials defined directly on the element and augmented with a space of supplemental functions. The supplemental functions were constructed as rational functions, which can be difficult to integrate accurately using numerical quadrature rules when the index is high. This can result in a loss of accuracy in certain cases. In this work, we propose alternative ways to construct the supplemental functions on the element as continuous piecewise polynomials. One approach results in supplemental functions that are in H p for any p ≥ 1 . We prove the optimal approximation property for these new finite elements. We also perform numerical tests on them, comparing results for the original supplemental functions and the various alternatives. The new piecewise polynomial supplements can be integrated accurately, and therefore show better robustness with respect to the underlying meshes used. [ABSTRACT FROM AUTHOR]

We introduce a method based on Lipschitz pointwise transformations to define a distance on a Banach function space from its norm. We show how some specific lattice geometric properties (p-convexity, p-concavity, p-regularity) or, equivalently, some types of summability conditions (for example, when the terms of the terms in the sums in the range of the operator are restricted to the interval [ − 1 , 1 ] ) can be studied by adapting the classical analytical techniques of the summability of operators on Banach lattices, which recalls the work of Maurey. We show a technique to prove new integral dominations (equivalently, operator factorizations), which involve non-homogeneous expressions constructed by pointwise composition with Lipschitz maps. As an example, we prove a new family of integral bounds for certain operators on Lorentz spaces. [ABSTRACT FROM AUTHOR]

Fractures function as storage spaces and effective seepage channels for metamorphic rock buried hill reservoirs. Their effectiveness and permeability govern the content and enrichment of oil and gas. Owing to the convoluted distribution patterns of fractures, it is arduous to gauge the effectiveness and permeability of fractures with precision, thus rendering well productivity prediction difficult. This article cites fractured gas reservoirs in a metamorphic rock buried hill as an example. Through comprehensive usage of core and imaging logging data to finely interpret fractures, calculate the fracture parameters that control productivity, including fracture density, fracture width, and fracture porosity. According to the evaluation index of fracture effectiveness, the method of constructing effectiveness index is proposed to quantitatively evaluate the effectiveness. Combined with the study of the law of influence of fracture parameters on reservoir permeability, the permeability index is established to reflect permeability. Productivity coefficients for fractured reservoirs with pollution factors have been established by using well-test interpretation data. To evaluate the well productivity of buried hill reservoirs, a productivity assessment chart is constructed by integrating the fracture effectiveness index, permeability index, and productivity coefficient. This chart enables prompt predictions of the buried hill reservoir's productivity. In order to verify the reliability of the method, a comprehensive comparison is made through conventional, array acoustic logging data and test data. The results show that the method is well applied in the evaluation of metamorphic rock buried hill reservoirs and provides a new idea for the rapid prediction of well productivity. [ABSTRACT FROM AUTHOR]

The present work deals with the acoustic analysis of the Roman theatre of Gubbio, located in Italy, which has already been the subject of architectural studies. Using four specific scenarios, acoustic simulations were carried out to highlight the contributions of different architectural elements to the acoustic response of this open-air theatre. The results were evaluated assuming that unamplified classical music and prose were the main functions of the space, as was the case in the past. The simulated results show that the values of the main acoustic parameters are closer to the optimal ranges borrowed from studies on enclosed theatres, since no criteria are available for Roman theatres. The comparison among different scenarios highlights the poor acoustic response of the existing conditions for a performing arts space. Some suggestions are presented regarding how the outcomes of this research study should be employed. [ABSTRACT FROM AUTHOR]

Vast amounts of monitoring data can be obtained through various optical sensors, and mask detection based on deep learning integrates neural science into a variety of applications in everyday life. However, mask detection poses technical challenges such as small targets, complex scenes, and occlusions, which necessitate high accuracy and robustness in multi-scene target detection networks. Considering that multi-scale features can increase the receptive field and attention mechanism can improve the detection effect of small targets, we propose the YOLO-MSM network based on the multi-scale residual (MSR) block, multi-scale residual cascaded channel-spatial attention (MSR-CCSA) block, enhanced residual CCSA (ER-CCSA) block, and enhanced residual PCSA (ER-PCSA) block. Considering the performance and parameters, we use YOLOv5 as the baseline network. Firstly, for the MSR block, we construct hierarchical residual connections in the residual blocks to extract multi-scale features and obtain finer features. Secondly, to realize the joint attention function of channel and space, both the CCSA block and PCSA block are adopted. In addition, we construct a new dataset named Multi-Scene-Mask, which contains various scenes, crowd densities, and mask types. Experiments on the dataset show that YOLO-MSM achieves an average precision of 97.51%, showing better performance than other detection networks. Compared with the baseline network, the mAP value of YOLO-MSM is increased by 3.46%. Moreover, we propose a module generalization improvement strategy (GIS) by training YOLO-MSM on the dataset augmented with white Gaussian addition noise to improve the generalization ability of the network. The test results verify that GIS can greatly improve the generalization of the network and YOLO-MSM has stronger generalization ability than the baseline. [ABSTRACT FROM AUTHOR]

We prove the modular convexity of the mixed norm L p (ℓ 2) on the Sobolev space W 1 , p (Ω) in a domain Ω ⊂ R n under the sole assumption that the exponent p (x) is bounded away from 1, i.e., we include the case sup x ∈ Ω p (x) = ∞ . In particular, the mixed Sobolev norm is uniformly convex if 1 < inf x ∈ Ω p (x) ≤ sup x ∈ Ω p (x) < ∞ and W 0 1 , p (Ω) is uniformly convex. [ABSTRACT FROM AUTHOR]

The study presented in this paper follows a line of research familiar for Geometric Function Theory, which consists in defining new integral operators and conducting studies for revealing certain geometric properties of those integral operators such as univalence, starlikness, or convexity. The present research focuses on the Bessel function of the first kind and order ν unveiling the conditions for this function to be univalent and further using its univalent form in order to define a new integral operator on the space of holomorphic functions. For particular values of the parameters implicated in the definition of the new integral operator involving the Bessel function of the first kind, the well-known Alexander, Libera, and Bernardi integral operators can be obtained. In the first part of the study, necessary and sufficient conditions are obtained for the Bessel function of the first kind and order ν to be a starlike function or starlike of order α ∈ [ 0 , 1) . The renowned prolific method of differential subordination due to Sanford S. Miller and Petru T. Mocanu is employed in the reasoning. In the second part of the study, the outcome of the first part is applied in order to introduce the new integral operator involving the form of the Bessel function of the first kind, which is starlike. Further investigations disclose the necessary and sufficient conditions for this new integral operator to be starlike or starlike of order 1 2 . [ABSTRACT FROM AUTHOR]

The direction estimation of the coherent source in a uniform circular array is an essential part of the signal processing area of the array, but the traditional uniform circular array algorithm has a low localization accuracy and a poor localization effect on the coherent source. To solve this problem, this paper proposes a two-dimensional direction of arrival (DOA) estimation for the coherent source in broadband. Firstly, the central frequency of the coherent sound source is estimated using the frequency estimation method of the delayed data, and a real-valued beamformer is constructed using the concept of the multiloop phase mode. Then, the cost function in the beam space is obtained. Finally, the cost function is searched in two dimensions to locate the sound source. In this paper, we simulate the DOA of the sound source at different frequencies and signal-to-noise ratios and analyze the resolution of the circular array. The simulation results show that the proposed algorithm can estimate the direction of arrival with high precision and achieve the desired results. [ABSTRACT FROM AUTHOR]

The boundedness of a sum-type operator between weighted-type spaces is characterized and its essential norm is estimated. [ABSTRACT FROM AUTHOR]

This article introduces the concept of near-field (NF) matching as a continuum-mode generalization of port matching in circuit theory suitable for field-theoretic electromagnetic energy transfer scenarios, with a focus on spatio-frequency processes in coupled systems. The concept is rigorously formulated using the full electromagnetic Green's function of a generic receiving surface interacting with arbitrary illumination fields where the Riemannian structure and the electromagnetic boundary condition of the problem are encoded into the tensor structure of a Green's function on a manifold. After a carefully selected combination of proper function spaces for the various field quantities involved, we utilize exact methods to estimate the sizes of various operator quantities using the appropriate function space norms. A field-theoretic measure of power transfer efficiency in generalized NF matching scenarios is introduced, and exact upper bounds on this efficiency are derived using Young's inequality for integral kernel operators. This theoretical study complements and generalizes the largely empirical and problem-specific literature on wireless energy transfer by providing an exact and rigorous mathematical framework that can guide and inform future optimization and design processes. [ABSTRACT FROM AUTHOR]

A parallel high-resolution underwater target detection network is proposed to address the problems of complex underwater scenes and limited target feature extraction capability. First, a high-resolution network (HRNet), a lighter high-resolution human posture estimation network, is used to improve the target feature representation and effectively reduce the semantic information lost in the image during sampling. Then, the attention module (A-CBAM) is improved to capture complex feature distributions by modeling the two-dimensional space in the activation function stage through the introduction of the flexible rectified linear units (FReLU) activation function to achieve pixel-level spatial information modeling capability. Feature enhancement in the spatial and channel dimensions is performed to improve understanding of fuzzy targets and small target objects and to better capture irregular and detailed object layouts. Finally, a receptive field augmentation module (RFAM) is constructed to obtain sufficient semantic information and rich detail information to further enhance the robustness and discrimination of features and improve the detection capability of the model for multi-scale underwater targets. Experimental results show that the method achieves 81.17%, 77.02%, and 82.9% mean average precision (mAP) on three publicly available datasets, specifically underwater robot professional contest (URPC2020, URPC2018) and pattern analysis, statistical modeling, and computational learning visual object classes (PASCAL VOC2007), respectively, demonstrating the effectiveness of the proposed network. [ABSTRACT FROM AUTHOR]

The metrical boundedness and metrical compactness of a new operator from the weighted Bergman-Orlicz spaces to the weighted-type spaces and little weighted-type spaces of analytic functions are characterized. [ABSTRACT FROM AUTHOR]

This paper explores the realm of fractional integral calculus in connection with the one-dimensional Dunkl operator on the space of tempered functions and Lizorkin type space. The primary objective is to construct fractional integral operators within this framework. By establishing the analogous counterparts of well-known operators, including the Riesz fractional integral, Feller fractional integral, and Riemann–Liouville fractional integral operators, we demonstrate their applicability in this setting. Moreover, we show that familiar properties of fractional integrals can be derived from the obtained results, further reinforcing their significance. This investigation sheds light on the utilization of Dunkl operators in fractional calculus and provides valuable insights into the connections between different types of fractional integrals. The findings presented in this paper contribute to the broader field of fractional calculus and advance our understanding of the study of Dunkl operators in this context. [ABSTRACT FROM AUTHOR]

In this paper, we present a constructive description of the function space of all real-valued functions on R (F (R , R)) by presenting a partition of it into 28 distinct blocks and a closed-form formula for the representative function of each of them. Each block contains elements that share common features in terms of the cardinality of their sets of continuity and differentiability. Alongside this classification, we introduce the concept of the Connection, which reveals a special relationship structure between the well-known representatives of four of the blocks: the Cantor function, the Dirichlet function, the Thomae function, and the Weierstrass function. Despite the significance of this field, several perspectives remain unexplored. [ABSTRACT FROM AUTHOR]

The notion of decisive coalitions of voters with different grades of decisiveness is a part of the mathematical framework for many models in social choice theory. More generally, we study aggregation problems in which a subgroup of decision makers have the right to determine the properties of the aggregate. Then, we introduce property spaces and rights to properties and characterize aggregation operators that are consistent with rights to properties. Moreover, we define congruences in property spaces, and we propose a generalization of the Sugeno integral in our framework. [ABSTRACT FROM AUTHOR]