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In order to meet the increasing demand of high-performance control in industrial production, a new sliding mode variable structure control algorithm, Asymptotic Sliding Mode Control (ASMC), is designed in this study to solve the serious chattering problem of sliding mode control. Firstly, a traditional sliding mode exponential approximation law control model and a state space and control function are constructed based on sliding mode control. Secondly, by eliminating the jitter factor, ASMC algorithm is combined with sliding mode control to achieve precise control of permanent magnet synchronous motor (PMSM) and improve its performance. The experimental results indicated that in the simulation experiment, the research system tended to stabilize within 0.2–0.3 seconds, and the system chattering was significantly suppressed. And its output was smoother, the jitter amplitude was significantly reduced by 1/3, and the output torque was more stable. In addition, when the parameter H0 changed to 2H0, the overall speed curve did not change much, with only a slight overshoot. The overshoot was only 2.8%, and the change amplitude was maintained at around 25r/min, indicating that the research system had strong self stability performance. In actual experiments, the current command oscillation of the research system was significantly reduced. The local graph showed that the output fluctuation amplitude of the asymptotic approach law actual control was significantly smaller under no-load disturbance. When the H0 changed towards 2H0, the actual adjustment time was about 0.1 seconds, which was consistent with the simulation experiment. Therefore, the contribution of the research is that the ASMC algorithm can suppress the chattering problem of the system and improve the approaching speed, thus improving the speed regulation quality of the system. This new algorithm has great theoretical and practical significance for improving the performance of PMSM, and is practical in the actual vector control system of PMSM. [ABSTRACT FROM AUTHOR]

Abnormally widened spatial and temporal binding windows (SBW/TBWs; length of space/time whereby stimuli are considered part of the same percept) are observed in schizophrenia. TBW alterations have been associated with altered sense of agency (hereafter referred to as agency), and an associative relationship between embodiment (body ownership) and agency has been proposed. SBWs/TBWs are investigated separately, but no evidence exists of these being separate in mechanism, system or function. The underlying neural substrate of schizophrenia remains unclear. The literature claims either pro-psychotic or anti-psychotic effects of Δ9-Tetrahydrocannabinol (THC) in patients and healthy individuals, but major support for cannabis in the aetiology of schizophrenia is associative, not causal. To clarify if THC is pro- or anti-psychotic, this single-blind, placebo-controlled within-subjects cross-over study tested several hypotheses. 1) Competing hypotheses that a synthetic THC analogue, Nabilone (NAB, 1–2 mg), would alter measures of agency and embodiment in healthy volunteers (n = 32) similarly, or opposite, to that of in patients with schizophrenia. 2) That there would be significant associations between any NAB-induced alterations in individual agency and embodiment measures in the Projected Hand Illusion (PHI). 3) That there is a unitary spatio-temporal binding window (STBW). A large proportion of individuals did not experience the PHI. Multimodal and bi-directional effects of NAB on the PHI were observed. Evidence of a unitary spatio-temporal binding window (STBW) was observed. NAB widened the STBW in some but narrowed it in others as a function of space and delay. No associations were found between agency and embodiment. [ABSTRACT FROM AUTHOR]

We study real interpolation, but instead of interpolating between Banach spaces, we interpolate between general functions taking values in [ 0 , ∞ ]. We show the equivalence of the mean method and the K -method and apply the general theory to interpolation between the norm on a Banach space and the set norm associated with an m-accretive operator on such a space. [ABSTRACT FROM AUTHOR]

In order to explore the influencing factors of spatial and temporal evolution of production-living-ecological space in Beijing Tianjin sandstorm source area, the remote sensing images, natural environment and socio-economic data of Duolun County in Inner Mongolia from 2000 to 2020 were selected, and the spatial auto-correlation model and principal component analysis model were used to analyze the spatial pattern evolution and influencing factors of production-living-ecological space. The results show that: (1) the function of production space decreases slightly, and the degree of spatial agglomeration decreases; (2) The function of living space rose slightly, and its spatial agglomeration degree showed an upward trend; (3) The ecological spatial function showed a slow upward trend, and its spatial agglomeration degree increased; (4) The spatial pattern of production-living-ecological space is characterized by "high in the southwest and low in the northeast"; (5) Precipitation has the greatest impact on the spatial evolution of the production-living-ecological space. The distance from the main residential areas, per capita GDP, the distance from the main roads and the distance from the main waters have strong explanatory power on the spatial evolution of the production-living-ecological space. [ABSTRACT FROM AUTHOR]

We derived exact analytical expressions for the variance, the third central moment, and the skewness of the multiplication gain distribution in uniform avalanche structures. The model assumes Poissonianity and locality of the ionization process and is valid for arbitrary values of the electron and hole ionization coefficients, α and β, respectively, as functions of the space coordinate. Expressions are also provided for the particular case where the ionization coefficients are related by a constant ratio k = β/α. The skewness is found to be always positive and greater than 2, indicating statistically relevant. Finally, the implications for spectral measurements of ionizing radiation are reviewed. [ABSTRACT FROM AUTHOR]

The Strauss point process is a very popular model for describing the random cellular networks, yet several key statistical properties such as intensity, empty space function, and probability generating functional have remained elusive. This article addresses these issues by first leveraging the Poisson saddle point method to approximate the distance‐conditioned intensity for Strauss point processes. Subsequently, the author derives an analytically tractable expression for the distribution of empty space distance based on a conditional thinning mechanism. Additionally, the author establishes an upper bound for the probability generating functional in Strauss point processes, which is crucial for evaluating the Laplace transform of cumulative interference in relevant cellular networks. These findings facilitate the systematic derivation of spatially averaged probability of coverage, and the accuracy of analytic results is validated through simulations. [ABSTRACT FROM AUTHOR]

We identify storage coefficient and hydraulic transmissivity in groundwater flow governed by a linear parabolic equation. Both parameters are assumed to be piecewise constant functions in space. The unknowns are the coefficient values as well as the geometry of the zones where these coefficients are constant. The goal of this work is to improve an adaptive parameterization approach for solving an inverse problem of parameter estimation. We define a posteriori error estimators depending on parameters to refine the computing mesh during the adaptative parametrization algorithm. [ABSTRACT FROM AUTHOR]

In this work, the notion of function of bounded variation in 2-normed spaces was established (Definition 4.2), the set of functions of bounded (2, k)-variation was endowed with a norm (Theorem 4.5), and it was proved that such a set is a Banach space (Theorem 4.6). In addition, the fundamental properties of the functions of bounded (2, k)-variation in the formalism of 2-Hilbert and 2- normed spaces were studied (see Theorems 4.1, 4.3, 4.4). Also, it was shown how to endow a 2-normed space with a function of bounded (2, k)-variation from a classical Hilbert space (Proposition 4.1). A series of examples and counterexamples are presented that enrich the results obtained in this work (4.1 and 4.2) [ABSTRACT FROM AUTHOR]

We study a method for calculating the utility function from a candidate of a demand function that is not differentiable, but is locally Lipschitz. Using this method, we obtain two new necessary and sufficient conditions for a candidate of a demand function to be a demand function. The first concerns the Slutsky matrix, and the second is the existence of a concave solution to a partial differential equation. Moreover, we show that the upper semi-continuous weak order that corresponds to the demand function is unique, and that this weak order is represented by our calculated utility function. We provide applications of these results to econometric theory. First, we show that, under several requirements, if a sequence of demand functions converges to some function with respect to the metric of compact convergence, then the limit is also a demand function. Second, the space of demand functions that have uniform Lipschitz constants on any compact set is compact under the above metric. Third, the mapping from a demand function to the calculated utility function becomes continuous. We also show a similar result on the topology of pointwise convergence. [ABSTRACT FROM AUTHOR]

The length function ℓ q (r , R) is the smallest possible length n of a q-ary linear [ n , n - r ] q R code with codimension (redundancy) r and covering radius R. Let s q (N , ρ) be the smallest size of a ρ -saturating set in the projective space PG (N , q) . There is a one-to-one correspondence between [ n , n - r ] q R codes and (R - 1) -saturating n-sets in PG (r - 1 , q) that implies ℓ q (r , R) = s q (r - 1 , R - 1) . In this work, for R ≥ 3 , new asymptotic upper bounds on ℓ q (t R + 1 , R) are obtained in the following form: ∙ ℓ q (t R + 1 , R) = s q (t R , R - 1) ≤ R ! R R - 2 R · q (r - R) / R · ln q R + o (q (r - R) / R) , r = t R + 1 , t ≥ 1 , q is an arbitrary prime power , q is large enough ; ∙ if additionally R is large enough, then R ! R R - 2 R ∼ 1 e ≈ 0.3679. The new bounds are essentially better than the known ones. For t = 1 , a new construction of (R - 1) -saturating sets in the projective space PG (R , q) , providing sets of small sizes, is proposed. The [ n , n - (R + 1) ] q R codes, obtained by the construction, have minimum distance R + 1 , i.e. they are almost MDS (AMDS) codes. These codes are taken as the starting ones in the lift-constructions (so-called " q m -concatenating constructions") for covering codes to obtain infinite families of codes with growing codimension r = t R + 1 , t ≥ 1 . [ABSTRACT FROM AUTHOR]

In this paper we define, using the Stirling numbers of the second kind, the Gompertz wavelets and show their basic properties. In particular, we prove that the admissibility condition holds for them. We also compute the normalizing factors in the space of the square-integrable functions L2(ℝ) and present an explicit formula for them in terms of the Bernoulli numbers. Then, after implementing the second-order Gompertz wavelets in the Matlab Wavelet Toolbox, we perform numerical experiments demonstrating the practical applicability and effectiveness of the wavelets. [ABSTRACT FROM AUTHOR]

This paper offers a comprehensive analysis of solution representations for ϖ-fractional partial differential equations, specifically focusing on the linear case of the Darboux problem. We exhibit a representation of the solutions for the Darboux problem of ϖ-fractional partial differential equations in the linear case in the space of continuous functions. Through the application of the generalized Gronwall inequality, we establish the Ulam–Hyers–Rassias Mittag–Leffler stability in the space of continuous functions. Three numerical examples are presented to show the effectiveness and the applicability of our results. [ABSTRACT FROM AUTHOR]

In this paper, a convex variational model based on the adaptive total variation (TV) regularization is proposed for image restoration under multiplicative noise. The adaptive weight allows for greater smoothing in the bright region for the suppression of speckles. The model includes a nonconvex data fidelity term and also a quadratic penalty term that enforces the restored image to be close to a reference image deduced from a Gaussian denoiser. It can be viewed as the adaptive TV regularization of the Regularization by Denoising (RED) approach for multiplicative noise removal. We prove that the model admits a unique minimizer in a suitable function space and provide a fast numerical algorithm based on the alternating direction method with multipliers (ADMM) for it. Different Gaussian denoisers, including the patch-based algorithm BM3D and the learning-based algorithm DnCNN, are considered for the model in numerical experiments. It is shown that our model efficiently removes multiplicative noise without introducing artifacts. [ABSTRACT FROM AUTHOR]

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]

Over the past fifty years, the form and function of space habitat modules have remained largely unchanged. While cylindrical modules are relatively simple to transport and deploy, their limited size poses a challenge to their efficiency and usability. In contrast, large space habitat construction projects are costly and present logistical difficulties. The development of polyhedral modules could bridge the gap between these two approaches, allowing for modular, polyhedral units to be assembled and linked together to create larger habitats more efficiently and with less risk. However, identifying the most suitable polyhedron for use in space remains a critical question. Previous research has explored the construction of polyhedral modules, but little rigor has been applied to identifying the most optimal form. This is a crucial issue because the first module to be used will likely set the standard for subsequent modules and any disadvantages present at that time will be perpetuated. Therefore, it is essential to identify the optimal form prior to constructing prototypes. This research paper employs multi-criteria decision analysis and sensitivity analysis to compare various candidate polyhedra across several evaluation metrics, including number of faces, volume to surface area ratio, and joint stress, among several other quantitative and qualitative metrics. The results demonstrate that the Rhombic Dodecahedron is a particularly suitable candidate compared to other forms analyzed. Thus, the Rhombic Dodecahedron should be considered the standard polyhedral form for future research involving the development of polyhedral modules. • Rhombic Dodecahedron identified as optimal polyhedron for space habitat design. • Polyhedral modules surpass cylindrical counterparts in multiple criteria. • Novel multi-criteria analysis method allows cross-metric comparison. [ABSTRACT FROM AUTHOR]

In this paper, we present explicit expressions for conforming finite element function spaces, basis functions, and degrees of freedom on the pentatope (the 4-simplex) and tetrahedral prism elements. More generally, our objective is to construct high-order finite element function spaces that maintain conformity with infinite-dimensional spaces of a carefully chosen de Rham complex in four dimensions. This paper is a natural extension of the companion paper entitled "Conforming finite element function spaces in four dimensions, part I: Foundational principles and the tesseract" by Nigam and Williams (2024). In contrast to Part I, in this paper we focus on two of the most popular elements which do not possess a full tensor-product structure in all four coordinate directions. We note that these elements appear frequently in existing space-time finite element methods. In order to build our finite element spaces, we utilize powerful techniques from the recently developed 'Finite Element Exterior Calculus'. Subsequently, we translate our results into the well-known language of linear algebra (vectors and matrices) in order to facilitate implementation by scientists and engineers. [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]

This study focused on establishing the existence and multiplicity of solutions for gauged nonlinear Schrödinger equations set on the plane with sign-changing potentials. Our findings contribute to the extension of recent advancements in this area of research. Initially, we examined scenarios where the potential function V is lower-bounded and the function space has a compact embedding into Lebesgue spaces. Subsequently, we addressed more complex cases characterized by a sign-changing potential V and a function space that fails to compactly embed into Lebesgue spaces. The proofs of our results are based on the Trudinger-Moser inequality, the application of variational methods, and the utilization of Morse theory. [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]

We introduce a framework based on Rockafellar's perturbation theory to analyze and solve general nonsmooth convex minimization and monotone inclusion problems involving nonlinearly composed functions as well as linear compositions. Such problems have been investigated only from a primal perspective and only for nonlinear compositions of smooth functions in finite-dimensional spaces in the absence of linear compositions. In the context of Banach spaces, the proposed perturbation analysis serves as a foundation for the construction of a dual problem and of a maximally monotone Kuhn–Tucker operator, which is decomposable as the sum of simpler monotone operators. In the Hilbertian setting, this decomposition leads to a block-iterative primal-dual algorithm that fully splits all the components of the problem and appears to be the first proximal splitting algorithm for handling nonlinear composite problems. Various applications are discussed. Funding: The work of L. M. Briceño-Arias was supported by Agencia Nacional de Investigación y Desarrollo-Chile [Grant Fondo Nacional de Desarrollo Científico y Tecnológico 1190871, Grant Centro de Modelamiento Matemático ACE210010, Grant Centro de Modelamiento Matemático FB210005, and basal Funds for Centers of Excellence], and the work of P. L. Combettes was supported by the National Science Foundation [Grant DMS-1818946]. [ABSTRACT FROM AUTHOR]

The main concern of this paper is to study large-time behavior of solutions for an outflow problem to the reduced gravity two and a half layer model in a half space. We establish the existence of stationary solutions and further obtain the large time asymptotic stability of small-amplitude stationary solutions provided that the initial perturbation is sufficiently small. Moreover, we obtain the convergence rate of the solution toward the stationary solution in some weighted Sobolev spaces only for the supersonic case. The proof is based on the basic energy method. A key point for the proof of convergence rates is to capture the positivity of the temporal energy dissipation functional and boundary terms with suitable space weight functions either algebraic or exponential depending on whether or not the incoming far-field velocity satisfy some additional conditions. [ABSTRACT FROM AUTHOR]

The stability, robustness, accuracy, and efficiency of space-time finite element methods crucially depend on the choice of approximation spaces for test and trial functions. This is especially true for high-order, mixed finite element methods which often must satisfy an inf-sup condition in order to ensure stability. With this in mind, the primary objective of this paper and a companion paper is to provide a wide range of explicitly stated, conforming, finite element spaces in four dimensions. In this paper, we construct explicit high-order conforming finite elements on 4-cubes (tesseracts); our construction uses tools from the recently developed 'Finite Element Exterior Calculus'. With a focus on practical implementation, we provide details including Piola-type transformations, and explicit expressions for the volumetric, facet, face, edge, and vertex degrees of freedom. In addition, we establish important theoretical properties, such as the exactness of the finite element sequences, and the unisolvence of the degrees of freedom. [ABSTRACT FROM AUTHOR]

We show that capacity can be computed with locally Lipschitz functions in locally complete and separable metric spaces. Further, we show that if (X,d,\mu) is a locally complete and separable metric measure space, then continuous functions are dense in the Newtonian space N^{1,p}(X). Here the measure \mu is Borel and is finite and positive on all metric balls. In particular, we don't assume properness of X, doubling of \mu or any Poincaré inequalities. These resolve, partially or fully, questions posed by a number of authors, including J. Heinonen, A. Björn and J. Björn. In contrast to much of the past work, our results apply to locally complete spaces X and dispenses with the frequently used regularity assumptions: doubling, properness, Poincaré inequality, Loewner property or quasiconvexity. [ABSTRACT FROM AUTHOR]

In this paper we give a saturated fixed point principle for nonself operators on a large Kasahara space. Our results extend some results given by I.M Olaru and N.A. Secelean in A New Approach of Some Contractive Mappings on Metric Spaces, Mathematics, 2021 9(12). [ABSTRACT FROM AUTHOR]

A subset A of a bitopological space (X, τ1, τ2) is called an (i, j)-ψgs-closed set if (i, j)-ψcl(A) ⊆ U whenever A ⊆ U, U is (i, j)-semi-open in (X, τ1, τ2). In this work, the properties of this set are considered to investigate the concepts of ψgs-functions in bitopological spaces. Specifically, this study establishes some properties and provides characterizations of ψgs-open and ψgs-closed functions, ψgs-continuous functions, and ψgs-irresolute functions in bitopological spaces. [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]

The goal of the paper is to establish quadrature formulas on combinatorial graphs. Three types of quadrature formulas are developed. Quadrature formulas of the first type are obtained through interpolation by variational splines. This set of formulas is exact on spaces of variational splines on graphs. Since bandlimited functions can be obtained as limits of variational splines we obtain quadrature formulas which are approximately exact on spaces of bandlimited functions. Accuracy of this type of quadrature formulas is given in terms of geometry of the set of nodes of splines and in terms of smoothness of functions which is measured by means of the combinatorial Laplace operator. Quadrature formulas of the second type are obtained through point-wise sampling for bandlimited functions and based on existence of certain frames in appropriate subspaces of bandlimited functions. The third type quadrature formulas are based on the average sampling over subgraphs. Our quadrature formulas which are based on sampling are exact on a relevant subspaces of bandlimited functions. The results of the paper have potential applications to problems that arise in data mining. [ABSTRACT FROM AUTHOR]

In this paper, we consider convolution operators, integral operators with weak singularity, Riesz potentials, in particular, those with kernels Ki (x, y) = xi−yi |x−y|n acting in special classes of Banach function spaces X (Ω) and their subspaces Xs (Ω)), and we prove some representation theorems for the functions from Banach-Sobolev spaces. We also prove the boundedness of Riesz potential in additive-invariant spaces. [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 1940, the stability problem of functional equations was arose due to a question of Stanisaw Ulam concerning the stability of group homomorphisms. Significant work was done by Donald H. Hyers about HYERS-ULAM STABILITY and obtained a partial affirmative answer to the question of Ulam in the context of banach spaces in the case of additive mappings. In 1978, T. M. Rassias expanded Hyers's theorem for mappings between Banach spaces by considering an unbounded Cauchy difference subject to a continuity condition upon the mapping. After that, Many Researchers had studied about Hyers-Ulam stability of an additive quadratic type functional equations. In this research article, the Hyers-Ulam stability of an additive quadratic type functional equation was discussed and obtained the generalization of Hyers-Ulam stability of an additive quadratic type functional equation f(x + ay) + af(x - y) = f(x - ay) + af(x + y) for any integer a with a ≠ 1; 0; 1 in 2-Banach space. [ABSTRACT FROM AUTHOR]

The orthogonal polynomials approach with Gegenbauer polynomials is an effective tool for analyzing mixed integral equations (MIEs) due to their orthogonality qualities. This article reviewed recent breakthroughs in the use of Gegenbauer polynomials to solve mixed integral problems. Previous authors studied the problem with a continuous kernel that combined both Volterra (V) and Fredholm (F) components; however, in this paper, we focused on a singular Carleman kernel. The kernel of FI was measured with respect to position in the space L2 [-1,1], while the kernel of VI was considered as a function of time in the space C[0, T], T < 1. The existence of a unique solution was discussed in L2[-1,1] x C[0, T] space. The solution and its error stability were both investigated and commented on. Finally, numerical examples were reviewed, and their estimated errors were assessed using Maple (2022) software. [ABSTRACT FROM AUTHOR]

Our interest in this work is to treat a one-dimensional Porous system with a non-linear damping and a delay in the non-linear internal feedback. We prove the global existence and uniqueness of its solution in suitable function spaces by means of the Faedo-Galerkin procedure combined with the energy method under a suitable relation between the weight of the delayed feedback and the weight of the non-delayed feedback. Also, we give an explicit and general decay rate estimate by applying the well-known multiplier method integrated with some properties of convex functions and for two opposites cases with respect to the speeds of wave propagation. [ABSTRACT FROM AUTHOR]

In this paper we characterize some basic properties of composition operators on the spaces of harmonic Bloch functions. First we provide some equivalent conditions for boundedness and compactness of composition operators. In the sequel we investigate closed range composition operators. These results extends the similar results that were proven for composition operators on the Bloch spaces. [ABSTRACT FROM AUTHOR]

We prove Anderson localization for a class of interactive Fermionic Hamiltonians in a deterministic (including some quasi-periodic) disordered external potential on a one-dimensional lattice. As in our earlier paper on 1-particle Hamiltonians (Chulaevsky, 2014), and in contrast to a recent work (J. Bourgai and I. Kachkovskiy, 2019), the sampling function on the phase space of the dynamical system generating the external potential is not even continuous. As a complement to the parametric analysis of the eigenpairs, we also prove some analogs of the Minami estimate for pairs of eigenvalues in arbitrarily placed intervals, not necessarily nested, or close to/distant from each other [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]

This paper intends to analyze the existing problems of remote sensing data from the perspectives of space remote sensing information data capacity and data types. Then, a framework for rapidly analyzing and processing space remote sensing information is constructed. Then, LSTM is used to realize the fault diagnosis of remote sensing data continuity, discrete sample mixing and strong correlation of sample variation. LSTM conducts a multimodal analysis of remote-control commands, which is applied to modeling. The multi-stage LSTM prediction model is established and integrated efficiently to improve its adaptive ability in complex space environments. In this way, the anomaly recognition of remote sensing information is realized. Experiments show that the algorithm can improve the anomaly detection rate of remote sensing data. Experiments show that the algorithm is feasible. It can provide reliable data interpretation function for space remote sensing information control system. [ABSTRACT FROM AUTHOR]

In the present study, we prove generalizations of Banach, Kannan, Chatterjea, Čirič-Reich-Rus fixed point theorems, as well as of the fixed point theorem for mapping contracting perimeters of triangles. We consider corresponding mappings in semimetric spaces with triangle functions introduced by Bessenyei and Pâles. Such an approach allows us to derive corollaries for various types of semimetric spaces such as metric spaces, ultrametric spaces, and b-metric spaces. The significance of these generalized theorems extends across multiple disciplines, such as optimization, mathematical modeling, and computer science. They may serve to establish stability conditions, demonstrate the existence of optimal solutions, and improve algorithm design. [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]

We extend representation formulas that generalize the similarity principle of solutions to the Vekua equation to certain classes of meta-analytic functions. Also, we solve a generalization of the higher-order Schwarz boundary value problem in the context of meta-analytic functions with boundary conditions that are boundary values in the sense of distributions. [ABSTRACT FROM AUTHOR]

This paper focuses on exploring the existence of solutions for a specific class of FDEs by leveraging fixed point theorem. The equation in question features the Caputo fractional derivative of order 3 < u ˆ ≤ 4 and includes a term Θ (β , Z (β)) alongside boundary conditions. Through the application of a fixed point theorem in appropriate function spaces, we consider nonlocal conditions along with necessary assumptions under which solutions to the given FDE exist. Furthermore, we offer an example to illustrate the results. [ABSTRACT FROM AUTHOR]

For the first time, this paper offers the Bayesian and E‐Bayesian estimation methods using the spacing function (SF) instead of the classical likelihood function. The inverse Lindley distribution, including its parameter and reliability measures, is discussed in this study through the mentioned methods, along with some other classical approaches. Six‐point and six‐interval estimations based on an adaptive Type‐I progressively censored sample are considered. The likelihood and product of spacing methods are used in classical inferential setups. The approximate confidence intervals are discussed using both classical approaches. For various parameters, the Bayesian methodology is studied by taking both likelihood and SFs as observed data sources to derive the posterior distributions. Moreover, the E‐Bayesian estimation method is considered by using the same data sources in the usual Bayesian approach. The Bayes and E‐Bayes credible intervals using both likelihood and SFs are also taken into consideration. Several Monte Carlo experiments are carried out to assess the performance of the acquired estimators, depending on different accuracy criteria and experimental scenarios. Finally, two data sets from the engineering and physics sectors are analyzed to demonstrate the superiority and practicality of the suggested approaches. [ABSTRACT FROM AUTHOR]

This survey shows the way in which the Armenian mathematician Academician M.M. Djrbashian introduced the apparatus of fractional calculus in investigation of weighted classes and spaces of regular functions since his earliest work of 1945 (see [3-4] or Addendum to [22]). The investigations of M.M. Djrbashian in this topic reached their final point by his exhaustive factorization theory for functions meromorphic in the unit disc of the complex plane [11]. The contemporary development of M.M. Djrbashian's ideas can be found in the recent monograph [22]. The survey intends to complete the survey article "Mkhitar Djrbashian and his contribution to fractional calculus" [25], which described the contribution of M.M. Djrbashian mainly from the point of view of basic constructions of the fractional calculus, to the theory of fractional differential equations and integral transforms. [ABSTRACT FROM AUTHOR]

Neglecting small fragments in space debris evolutionary models can lead to a significant underestimation of the collision risk for operational satellites. However, when scaling down to the millimetre range, the debris population grows to over a hundred million objects, making deterministic approaches too computationally expensive. On the contrary, probabilistic models provide a more efficient alternative, which however typically works under some simplifying assumptions on the dynamics, limiting their field of applicability. This work proposes an extension of the density-based collision risk models to any orbital dynamics and impact geometry. The impact rate with a target satellite is derived from a multi-dimensional phase space density function in orbital elements, which discretely varies over both phase space and time. The assumption of a bin-wise constant cloud density allows for the analytical transformation of the six-dimensional distribution in orbital elements into the three-dimensional spatial density function, guaranteeing an efficient and accurate evaluation of the fragments flux. The proposed method is applied to the assessment of the collision risk posed by occurred fragmentation events in different orbital regions on a high-risk target object. The effect on the impact rate of the modelling improvements, compared to previous probabilistic formulations, is discussed. • Density-based model used for the propagation of space debris clouds in different orbital regimes. • Piece-wise analytical method for the estimation of the in-orbit collision probability is derived. • Impact risk posed by occurred fragmentation events on a target spacecraft is assessed. • Density-based models allow the required computational cost to be independent of objects size. [ABSTRACT FROM AUTHOR]