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Shopping malls have replaced traditional public spaces and become an integral part of urban life in many cities. This paper seeks to explore the role of shopping malls as protest sites in Hong Kong during the Anti-Extradition Law Amendment Bill protest movement in 2019. As the protests decentralised and filtered throughout the city, shopping malls became sites of protest and battlegrounds between riot police and protesters. In addition to singing and chanting, organising sit-ins, and exhibiting protest art inside shopping malls, protesters also confronted mall employees as well as disrupted businesses. Based on information gathered through media reports, planning and policy documents, as well as ethnographic observations, this paper aims to examine the role of shopping malls in the urban development of Hong Kong, their function as public spaces during the protest movement, and how the politicisation of shopping malls shaped and sustained the protest movement. This paper contends that the protesters' appropriation of shopping malls not only represented an important first step of reclaiming the right to the city, but also exemplified how such struggle and resistance can be extended beyond traditional protest sites and into different everyday spaces. [ABSTRACT FROM AUTHOR]

In this paper, we propose a stabilized sequential quadratic programming (SQP) method for optimization problems in function spaces. A form of the problem considered in this paper can widely formulate many types of applications, such as obstacle problems, optimal control problems, and so on. Moreover, the proposed method is based on the existing stabilized SQP method and can find a point satisfying the Karush-Kuhn-Tucker (KKT) or asymptotic KKT conditions. One of the remarkable points is that we prove its global convergence to such a point under some assumptions without any constraint qualifications. In addition, we guarantee that an arbitrary accumulation point generated by the proposed method satisfies the KKT conditions under several additional assumptions. Finally, we report some numerical experiments to examine the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

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This paper is concerned with identification of a spatial source function from final time observation in a bi-parabolic equation, where the full source function is assumed to be a product of time dependent and a space dependent function. Due to the ill-posedness of the problem, recently some authors have employed different regularization method and analysed the convergence rates. But, to the best of our knowledge, the quasi-reversibility method is not explored yet, and thus we study that in this paper. As an important implication, the Hölder rates for the apriori and aposteriori error estimates obtained in this paper improve upon the rates obtained in earlier works. Also, in some cases we show that the rates obtained are of optimal order. Further, this work seems to be the first one that has broaden the applicability of the problem by allowing the time dependent component of the source function to change sign. To the best of our knowledge, the earlier known work assumed the fixed sign of the time dependent component by assuming some bounded below condition. [ABSTRACT FROM AUTHOR]

This paper is concerned with the estimation of the partial derivatives of a probability density function of directional data on the d-dimensional torus within the local thresholding framework. The estimators here introduced are built by means of the toroidal needlets, a class of wavelets characterised by excellent concentration properties in both the real and the harmonic domains. In particular, we discuss the convergence rates of the Lp-risks for these estimators, investigating their minimax properties and proving their optimality over a scale of Besov spaces, here taken as nonparametric regularity function spaces. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the iteration of the Laplace transform over certain spaces of generalized functions. As a consequence we prove a new Post-Widder-type inversion formula for this transform over distributions of compact support. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to define a generalized T -transform, is denoted by T n , on function space. This transform can be used to calculate various functionals which are not calculated in the previous paper. We then establish the existence of transform for Fourier-type functionals with some examples in quantum mechanics. Finally, we obtain some relationships for T n -transforms involving the generalized Cameron-Storvick theorem and the recurrence formulas for the T n -transform. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to generalize the measure of non-compactness for the space of continuous functions over the T3½ space. Motivated by the generalized Arzelà-Ascoli theorem for Tichonoff space T via Wallman compactifiaction Wall(T), we constuct a measure of non-compactness for the space Cb(T). We also study some of the properties of this object and give another version of Darbotype theorem, suitable for this particular case. [ABSTRACT FROM AUTHOR]

In this paper, we will study local and global Cauchy problems for the semilinear parabolic equations ∂ t u − Δ u = G (u) with initial data in Herz spaces. These spaces unify and generalize many classical function spaces such as Lebesgue spaces of power weights. Our results cover the results obtained with initial data in Lebesgue spaces. Moreover, the results in Herz spaces are a little different from the results in Lebesgue spaces. [ABSTRACT FROM AUTHOR]

Let Π = { z ∈ C / ℑ z > 0 } , the upper half-plane in the complex plane C . Let H (Π) be the set of all analytic functions on Π and S (Π) be the set of all analytic self-maps on Π. For φ ∈ S (Π) , N ∈ N 0 = N ∪ { 0 } and ψ (N) = (ψ 0 , ψ 1 , ... , ψ N) , where ψ j ∈ H (Π) , j = 0 , 1 , ... , N , define an operator T ψ (N) , φ (f) := ∑ j = 0 N ψ j ⋅ (f (j) ∘ φ) , f ∈ H (Π). In this paper, we characterize the boundedness and compactness of the operator T ψ (N) , φ on the Hardy, weighted-Bergman spaces on Π to weighted-type spaces on Π. [ABSTRACT FROM AUTHOR]

In this paper we study the Riemann–Hilbert problem for variable exponent poly-Smirnov space on a piecewise Lyapunov boundary. At first we introduce the poly-Smirnov function space with variable exponent, we obtain a decomposition of this space and verify the existence of the angular boundary value of function in this space. Then we investigate Dirichlet problem for poly-Smirnov function space. At last we consider Riemann–Hilbert problem for variable exponent poly-Smirnov space on a piecewise Lyapunov boundary. The method is transforming this problem into independent homogeneous Dirichlet problems, and the conditions of solvability as well as the explicit solutions are obtained. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study a new class of function spaces, called N (p , q , s) -type spaces, in the unit ball B of C n . We establish some basic properties of this new function space, together with a characterization via Green's function, and finally, we study the Hadamard gap series in N (p , q , s) -type spaces. This is the first paper in a five part series. The second paper deals with the Carleson measure, while the third paper deals with several different characterizations of N (p , q , s) -type spaces via various norms and some applications to distance problems. Moreover, the fourth paper deals with the atomic decomposition of those functions belonging to N (p , q , s) -type spaces, and finally, the fifth paper deals with the Riemann–Stieltjes operators and multipliers on N (p , q , s) -type spaces. [ABSTRACT FROM AUTHOR]

In the paper, we prove a general universality theorem for the Riemann zeta-function ζ (s) on approximation of a class of analytic functions by generalized shifts ζ (s + ia(τ)). Here a(τ) is a real-valued continuous increasing to +∞ function, uniformly distributed modulo 1 and such that |ζ(σ + ia(τ) + it)|2, for σ > 1/2, has a traditional mean estimate for every t ∈ ℝ. For example, the function tv(τ), v > 0, where t(τ) is the Gram function, satisfies the hypotheses of the proved theorem. For the proof, the method of weak convergence of probabilistic measures in the space of analytic functions is developed. [ABSTRACT FROM AUTHOR]

In this paper, we derive primal and dual second-order necessary and sufficient optimality conditions for a vector optimization problem with equality and inequality constraints where the functions involved are locally Lipschitz. We introduce a weaker notion of second-order Abadie constraint qualification to derive second-order necessary conditions for weak local Pareto minima and strict local Pareto minima of order two in terms of Páles and Zeidan's second-order upper directional derivatives. Dual necessary conditions are derived for both types of minimal solutions in finite-dimensional spaces assuming the functions to be first-order continuously Fréchet differentiable. In the same setting, we derive dual and primal second-order sufficient optimality conditions for strict local Pareto minima of order two in terms of second-order lower directional derivatives. [ABSTRACT FROM AUTHOR]

A Banach space X of analytic function in , the unit disc in , is said to be admissible if it contains the polynomials and convergence in X implies uniform convergence in compact subsets of. If X and Y are two admissible Banach spaces of analytic functions in and g is a holomorphic function in , g is said to be a multiplier from X to Y if g ·f ∈ Y for every f ∈ X. The space of all multipliers from X to Y is denoted M (X, Y), and M (X) will stand for M (X, X). The closed graph theorem shows that if g ∈ M (X, Y) then the multiplication operator Mg, defined by Mg (f) = g · f, is a bounded operator from X into Y. It is known that M (X) ⊂ H∞ and that if g ∈ M (X), then ∥g∥H∞ ≤ ||Mg||. Clearly, this implies that M (X, Y) ⊂ H∞ if Y ⊂ X. If Y ⊄ X, the inclusion M (X, Y) ⊂ H∞ may not be true. In this paper we start presenting a number of conditions on the spaces X and Y which imply that the inclusion M (X, Y) ⊂ H∞ holds. Next, we concentrate our attention on multipliers acting an BMOA and some related spaces, namely, the Qs-spaces (0

Regularity estimates for an integral operator with a symmetric continuous kernel on a convex bounded domain are derived. The covariance of a mean-square continuous random field on the domain is an example of such an operator. The estimates are of the form of Hilbert–Schmidt norms of the integral operator and its square root, composed with fractional powers of an elliptic operator equipped with homogeneous boundary conditions of either Dirichlet or Neumann type. These types of estimates, which couple the regularity of the driving noise with the properties of the differential operator, have important implications for stochastic partial differential equations on bounded domains as well as their numerical approximations. The main tools used to derive the estimates are properties of reproducing kernel Hilbert spaces of functions on bounded domains along with Hilbert–Schmidt embeddings of Sobolev spaces. Both non-homogeneous and homogeneous kernels are considered. In the latter case, results in a general Schatten class norm are also provided. Important examples of homogeneous kernels covered by the results of the paper include the class of Matérn kernels. [ABSTRACT FROM AUTHOR]

This work addresses the relationship between the Italian city-making process following Unification (1861) and the development of military settlements up to the 1920s. The hypothesis presented here is that the building of military settlements and the redevelopment of spaces with new functions, arguably, shaped Italian cities over this period by implementing urban renewal processes and city expansion. Through my analysis, I claim that defence planning had an amenable effect upon the decision-making process of urban planning schemes. In addition, this paper claims that this process has impacted the location of military settlements in ways that boosted the economic and urban images of the city. I do this through a detailed case study of Milan's parade ground. Here, I found that the parade ground dismantling and relocation from the urban centre towards the periphery happened twice, relied on a specific narrative, and was catalysed by two mega-events. I demonstrate that defence planning plays a secondary role in boosting these operations aimed both at replacing military settlements with newly emerging functions and displacing the unwanted functions in the periphery. [ABSTRACT FROM AUTHOR]

In this paper we show that continuous endomorphisms on the space of entire functions with a given order can be expressed as differential operators of infinite order satisfying suitable growth conditions. [ABSTRACT FROM AUTHOR]

In this paper, a recurrent neural network with mixed delays which plays an important role is considered. We are concerned with the existence, uniqueness and global exponential stability of the doubly measure pseudo almost automorphic solutions. First, we establish results that are interesting on the functional space of such functions like composition theorem. Second, by employing the fixed-point theorem and some properties of the measure pseudo almost automorphic functions, some sufficient conditions for the existence, uniqueness and global exponential stability of the doubly measure pseudo almost automorphic solutions have been established. Our results obtained in this paper are new. Finally, two commonly used numerical examples are given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper we study Toeplitz and Cesàro-type operators on holomorphic function spaces on a homogeneous Siegel domain of Type II. We prove several necessary conditions and sufficient conditions for these operators to be continuous or compact, or to belong to suitable Schatten classes. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new properties of (ω , c) -periodic and asymptotically (ω , c) -periodic functions, then we apply them to study the existence and uniqueness of mild solutions of these types to the following semilinear fractional differential equations: (1) { c D t α u (t) = A u (t) + c D t α − 1 f (t , u (t)) , 1 < α < 2 , t ∈ R , u (0) = 0 and (2) { c D t α u (t) = A u (t) + c D t α − 1 f (t , u (t − h)) , 1 < α < 2 , t , h ∈ R + , u (0) = 0 where c D t α (⋅) (1 < α < 2) stands for the Caputo derivative and A is a linear densely defined operator of sectorial type on a complex Banach space X and the function f (t , x) is (ω , c) -periodic or asymptotically (ω , c) -periodic with respect to the first variable. Our results are obtained using the Leray–Schauder alternative theorem, the Banach fixed point principle and the Schauder theorem. Then we illustrate our main results with an application to fractional diffusion-wave equations. [ABSTRACT FROM AUTHOR]

The Minkowski space–time algebra C ℓ 3 , 1 is a powerful tool for studying the theory of electromagnetism and special relativity. In this paper, we intend to establish generalizations of Titchmarsh theorems for certain classes of functions, namely Lipschitz functions in the space L p (R 3 , 1 , C ℓ 3 , 1) for 1 < p ≤ 2. [ABSTRACT FROM AUTHOR]

Quaternionic Fock space is a useful generalization of the Fock space in the complex plane, which plays an important role in quantum mechanics. In view of quaternionic operator theory this topic attains more diversity and complexity. In this paper we first explore the connection between the properties and about the difference of quaternionic weighted composition operators acting on slice regular Fock space with the function theoretic properties of the symbols. It can further imply some topological information on the set of quaternionic weighted composition operators. [ABSTRACT FROM AUTHOR]

In this paper, we prove the boundedness of Hardy operator for monotone functions in grand Lebesgue spaces Lp)(0, 1) (0 < p ≤ 1). In particular, we prove similar results for the Hardy operator in weighted Lebesgue spaces. Also, it is proved that the grand Lebesgue space Lp)(0, 1) is a quasi-Banach function space. Finally, we establish necessary and sufficient conditions for the boundedness of some integral operator in weighted quasi-Banach Lebesgue spaces. [ABSTRACT FROM AUTHOR]

In order to effectively use differential evolution (DE) to solve multi-objective optimisation problems, it is necessary to consider how to ensure the search ability of DE. However, the search ability of DE is affected by related parameters and mutation mode. Based on decomposition, this paper proposed a hybrid differential evolution (HMODE/D) for solving multi-objective optimisation problems. First, when generation satisfies a certain condition, the local optimum is selected using the information of neighbour individual objective values to produce mutation offspring. Then, the heuristic crossover operator is established by using a uniform design method to produce better crossover individuals. Next, an external archive is set for each individual to store the individuals beneficial to the optimisation objective functions. Then, the individual is selected from the external archive to generate mutation offspring. In addition, considering that the performance of DE is determined by parameters, using the relevant information of the objective space function value, the self-adaptive adjustment strategy is adopted for the relevant parameter. Finally, a series of test functions with 5-, 10-, and 15-objectives are performed in the experiments to evaluate the superiority of HMODE/D. The results show that HMODE/D can solve the multi-objective optimisation problem very well. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the concept of the ⊗-product on function space. We then proceed to use this concept to obtain several integration formulas. In addition, we establish various relationships which exist. Also, we establish the relationships among the ⊗-product, the generalized convolution product and the first variation. [ABSTRACT FROM AUTHOR]

This paper examines exponential mean square stability of the split-step theta approximation and the stochastic theta method for the stochastic differential delay equations and stochastic ordinary differential equations (SODEs) under a coupled monotone condition on drift and diffusion coefficients. It is shown that forthe two classes of the theta approximations can preserve the exponential mean square stability when some conditions on the stepsize and drift coefficient are imposed, but for, without the globally Lipschitz continuity, these two classes of theta methods show exponentially mean square stability unconditionally. Moreover, for sufficiently small stepsize, the decay rate as measured by the bound of the Lyapunov exponent can be reproduced arbitrarily accurately. Some results in this paper extend the existing results for linear SODEs to nonlinear stochastic differential equations (SDEs), and also improve our previous results of numerical stability of nonlinear SDEs. [ABSTRACT FROM AUTHOR]

In this paper, we address the random sampling problem for the class of functions in the space of Mellin band-limited functions B T , which are concentrated on a bounded cube. It is established that any Mellin band-limited function can be approximated by an element in a finite-dimensional subspace of B T . Utilizing the notion of covering number and Bernstein's inequality to the sum of independent random variables, we prove that the probabilistic sampling inequality holds for the set of concentrated signals in B T with an overwhelming probability provided the sampling size is large enough. [ABSTRACT FROM AUTHOR]

This paper is devoted to an extension of the bivariate generalized Bernstein-Chlodovsky operators preserving the exponential function exp(2, 2) where exp(α, β) = e−αx−βy, α, β ∈ R+0 and x, y ≥ 0. For these operators, we first examine the weighted approximation properties for continuous functions in the weighted space, and in the latter case, we also obtain the convergence rate for these operators using a weighted modulus of continuity. Then, we investigate the order of approximation regarding local approximation results via Peetre’s K-functional. We introduce the GBS (Generalized Boolean Sum) operators of generalized Bernstein-Chlodovsky operators, and we estimate the degree of approximation in terms of the Lipschitz class of Bögel continuous functions and the mixed modulus of smoothness. Finally, we provide some numerical and graphical examples with different values to demonstrate the rate of convergence of the constructed operators. [ABSTRACT FROM AUTHOR]

The paper presents a novel method for classifying architectural spaces in terms of topological and visual relationships required by the functions of the spaces (where spaces such as bedrooms and bathrooms have less visual and physical relationships due to the privacy, while common spaces such as living rooms have higher visual relationship and physical accessibility) through machine learning (ML). The proposed model was applied to single and two-storey residential plans from the leading architects of the 20th century Among the five different ML models whose performances were evaluated comparatively, the best results were obtained with Cascade Forward Neural Networks (CFNN), and the average model success was calculated as 93%. The features affecting the classification models were examined based on SHAP values and revealed that width, control, 3D visibility and 3D natural daylight luminance were among the most influential. The results of five different ML models indicated that the use of topological and 3D visual relationship features in the automated classification of architectural space function can report very high levels of classification accuracy. The findings show that the classification model can be an important part of developing more efficient and adaptive floor plan design, building management and effective reuse strategies. [ABSTRACT FROM AUTHOR]

There is an increasing understanding of the role of the built environment on children's neighbourhood mobility and play and the importance of this for children's development. This has led to concerns over children's declining neighbourhood mobility and calls to see an increase in children's use of public space. This paper draws on findings from a research study working with 9 and 10 year olds living in inner London, England. The children participated in go-along interviews and a range of other qualitative methods, which explored how they used their neighbourhoods for getting around and play. Findings from the study demonstrate the importance of threshold spaces for children in supporting both their neighbourhood play and their wider neighbourhood travel and mobility. Threshold spaces are defined as a semi-public space that straddle the gap between the private space of the home and the wider public realm. Children's use of threshold spaces was influenced by a reduced movement function in these spaces, restricting vehicles and people passing through, and the presence of signals that it was ok to play, with girls being more sensitive to these features than boys. Threshold spaces were important as a start point for children's wider explorations of their neighbourhoods. [ABSTRACT FROM AUTHOR]

In this paper, we give the nth derivertive criterion for functions belonging to function spaces H K 2 . Furthermore, some sufficient conditions for coefficients of the linear differential equation f (k) + A k − 1 (z) f (k − 1) + ⋯ + A 1 (z) f ′ + A 0 (z) f = A k (z) are found such that all solutions belong to the H K 2 spaces, where A j (z) are analytic functions in D , j = 0 , ... , k. [ABSTRACT FROM AUTHOR]

In this paper we introduce function spaces denoted by L i p k , n (β , α , p) ( 0 < β < 1 , α ≥ 0) as subspaces of L p associated with (k , n) -generalized Fourier transform arising from the Dunkl theory, that we call generalized Dunkl Dini–Lipschitz spaces. Firstly, for 1 < p ≤ 2 , we provide characterizations of these spaces by means modulus of continuity. Moreover, we obtain behaviour estimations related to (k , n) -generalized Fourier transform for 0 < β < 1 and α ≥ 0 , and for α = 0 we obtain an analogue of Titchmarsh's theorem in L p . In the sequel, we introduce the modulus of smoothness related to the (k , n) -generalized Fourier transform for which we derive some of its properties on the Sobolev type space denoted by W p , n l . [ABSTRACT FROM AUTHOR]

In this paper, the boundedness and compactness of embedding from Dirichlet-Morrey spaces Dʎp into tent spaces Ts(µ) are investigated. As an application, we characterize the boundedness of the Volterra integral operator Jg from Dʎp to general function spaces F(2, p(1 - ʎ), s). Meanwhile, the operator Ig and the multiplication operator Mg from Dʎp to F(2, p(1 - ʎ), s) are studied. Furthermore, the essential norm of Jg and Ig from Dʎp to F(2, p(1 - ʎ), s) are also considered. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the 2-local isometries between the vector-valued differentiable function spaces C 0 p (X , E) and C 0 q (Y , E) , where X, Y are open subsets of R and E is a smooth, strictly convex, reflexive and 2-iso-reflexive Banach space (in particular, when 1 ≤ p < ∞ and p ≠ 2 , ℓ p satisfies such conditions). We show that such maps can be written as weighted composition operators. [ABSTRACT FROM AUTHOR]

In this paper, we apply a new approach to a special class of discrete time evolution models and establish a solid mathematical foundation to analyse them. We propose new single and multi-species evolutionary competition models using the evolutionary game theory that require a more advanced mathematical theory to handle effectively. A key feature of this new approach is to consider the discrete models as non-autonomous difference equations. Using the powerful tools and results developed in our recent work [E. D'Aniello and S. Elaydi, The structure of ω-limit sets of asymptotically non-autonomous discrete dynamical systems, Discr. Contin. Dyn. Series B. 2019 (to appear).], we embed the non-autonomous difference equations in an autonomous discrete dynamical systems in a higher dimension space, which is the product space of the phase space and the space of the functions defining the non-autonomous system. Our current approach applies to two scenarios. In the first scenario, we assume that the trait equations are decoupled from the equations of the populations. This requires specialized biological and ecological assumptions which we clearly state. In the second scenario, we do not assume decoupling, but rather we assume that the dynamics of the trait is known, such as approaching a positive stable equilibrium point which may apply to a much broader evolutionary dynamics. [ABSTRACT FROM AUTHOR]

This paper develops a systematic approach to fault diagnostic system design for sensor health monitoring in Lipschitz non-linear systems. The methodology applies to non-linear systems with three or more sensors in which the state is observable through any one of the sensor measurements. Two major issues are addressed in the paper-observer design for the non-linear system to ensure directional growth of residues for failure identification and use of linear matrix inequalities for explicit design of the observer gain. The use of the methodology is demonstrated through an illustrative example. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the estimation of a periodic two-dimensional function f (· , ·) based on observations from its noisy convolution, and convolution kernel g (· , ·) unknown. We derive the minimax lower bounds for the mean squared error assuming that f belongs to certain Besov space and the kernel function g satisfies some smoothness properties. We construct an adaptive hard-thresholding wavelet estimator that is asymptotically near-optimal within a logarithmic factor in a wide range of Besov balls. The proposed estimation algorithm implements a truncation to estimate the wavelet coefficients, in addition to the conventional hard-thresholds. A limited simulations study confirms theoretical claims of the paper. [ABSTRACT FROM AUTHOR]

In this paper, the notions of fully stable well-posedness and fully stable minimum of optimization problems with an extended real-valued objective function in an Asplund space setting are considered, where the objective function undergoes both tilt perturbations and general parameter perturbations. Special cases of the first notion reduce to the stable Hölder minimizers by Zheng and Ng [SIAM J Optim. 2015;25:416–438] and the fully stable Hölder minimizers introduced by Zheng, Zhu and Ng [SIAM J Optim. 2018;28:2601–2624], respectively. By using techniques of variational analysis and generalized differentiation, the results presented in this paper provide insight into necessary or sufficient conditions for tilt-stable minimizers of nonlinear programmes in Asplund spaces and therefore generalize some existing ones in the recent literature. [ABSTRACT FROM AUTHOR]

In this paper, we obtain very natural basic formulas for the modified generalized integral transform (MGIT) on function space. In order to do this, we first introduce an MGIT of functionals on function space. We next establish some basic formulas with respect to the MGIT and the first variation. Finally, we obtain a new version of the Cameron-Storvick theorem via the translation theorem. Some applications are demonstrated as examples which are used in classification of nanoparticles. [ABSTRACT FROM AUTHOR]

This paper addresses the distributed tracking control problem for Lipschitz nonlinear multiagent systems (LNMASs) in the presence of external disturbances and input delay. For this end, a distributed tracking control algorithm is proposed for LNMASs that guarantee each agent can estimate and track a nonlinear target. The suggested algorithm is developed based on a future state predictor and a finite time estimator to cope with the tracking control problem for LNMASs with input delay and external disturbances. Finally, the efficiency of the proposed algorithms is illustrated by simulation results. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to prove the existence result for a class of differential inclusions governed by the difference of two subdifferentials of nonconvex functions in Hilbert spaces. More precisely, by using the Moreau-Yosida regularization, the existence of local solutions for the following differential inclusion u ˙ (t) + ∂ Φ 1 (u (t)) − ∂ Φ 2 (u (t)) ∋ f (t) for almost every t ∈ [ 0 , T 0 ] , u (0) = u 0 is proved, where both functions Φ 1 and Φ 2 are assumed to be primal lower nice uniformly with respect to subgradients. [ABSTRACT FROM AUTHOR]

In this paper, we study the relationship between numerical index of a Banach space E and the numerical index of a class of subspaces of C (Ω , E) , the space of all continuous E-valued functions defined on a compact Hausdorff topological space Ω. The subspaces considered, satisfy an invariance condition and a norm attaining condition proposed by J. Jamison. As a consequence, we prove that the numerical indices of several classes of vector-valued function spaces are less than or equal to the numerical index of the respective range spaces. [ABSTRACT FROM AUTHOR]

In this paper, an extension of the bilateral Laplace transform on infinite-dimensional Banach spaces is introduced. In order to develop the concept of an analytic bilateral Laplace–Feynman transform (BLFT) of functionals on abstract Wiener spaces, we complete the following objectives: we first establish the existence of the analytic BLFT of certain bounded functionals on B. We next extend the operational properties (shifting properties) of the bilateral Laplace transform of functions on Euclidean spaces to the cases of the BLFT of functionals on abstract Wiener spaces. We also provide a convolution product (CP) corresponding to the BLFT and establish a relationship between the BLFT and the CP. We finally provide a representation of an inverse transform of the BLFT. Specifically, we establish a representation of the inverse transform for the BLFT having special parameter via the concept of the analytic Fourier–Feynman transform (FFT). [ABSTRACT FROM AUTHOR]

In this paper a Banach function space (b.f.s. in short) X (Ω) on a n-dimensional bounded domain Ω with Lebesgue measure is considered. The Banach function space X (S) on the (n − 1) -dimensional surface S ⊂ Ω ¯ generated by the norm of the space X (Ω) is defined. The Sobolev function space W X m (Ω) is defined using the norm of the space X (Ω) , as well as the concept of the trace of an arbitrary function from this space on the surface S. Based on this concept, the space of traces W X m (S) is defined and a characterization of this space is given. It was proved that it is boundedly embedded in the space X (S). Particular cases of a functional space X (Ω) can be Lebesgue spaces, Lebesgue spaces with variable summability exponents, Morrey space, Orlicz space, grand Lebesgue spaces and etc. The obtained results allow us to consider boundary value problems for differential equations in b.f.s. W X m (Ω). [ABSTRACT FROM AUTHOR]

The paper is devoted to investigate the existence of solutions of infinite systems of nonlinear quadratic integral equations of Volterra type. We look for solutions of those infinite systems of integral equations which are defined, continuous and bounded on the real half-axis and take real values. In our considerations the basic role will be played by the technique of measures of noncompactness defined in the space of functions defined, continuous and bounded on the real half-axis with values in the sequence space l ∞ consisting of real sequences equipped with the standard supremum norm. We are going to prove an existence result which generalizes all recently obtained results for infinite systems of integral equations. An example illustrating the obtained result will be included. [ABSTRACT FROM AUTHOR]

In practice, the time variable cannot be negative. The square integrable function space L 2 (R +) defined on the half real line R + = (0 , ∞) models the causal signal space. Given a>1, this paper addresses F a -frames in the setting of subspaces of L 2 (R +). We establish the connection between subspace F a -frames and orthogonal projections; characterize all bounded linear operators on L 2 (Z × T a) that transform F a -frames into other F a -frames for a subspace V of L 2 (R +) ; and obtain some sufficient conditions for constructing F a -frames for V from an arbitrarily given one. [ABSTRACT FROM AUTHOR]

Newton's method is usually preferred when solving optimization problems due to its superior convergence properties compared to gradient-based or derivative-free optimization algorithms. However, deriving and computing second-order derivatives needed by Newton's method often is not trivial and, in some cases, not possible. In such cases quasi-Newton algorithms are a great alternative. In this paper, we provide a new derivation of well-known quasi-Newton formulas in an infinite-dimensional Hilbert space setting. It is known that quasi-Newton update formulas are solutions to certain variational problems over the space of symmetric matrices. In this paper, we formulate similar variational problems over the space of bounded symmetric operators in Hilbert spaces. By changing the constraints of the variational problem we obtain updates (for the Hessian and Hessian inverse) not only for the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method but also for Davidon–Fletcher–Powell (DFP), Symmetric Rank One (SR1), and Powell-Symmetric-Broyden (PSB). In addition, for an inverse problem governed by a partial differential equation (PDE), we derive DFP and BFGS "structured" secant formulas that explicitly use the derivative of the regularization and only approximates the second derivative of the misfit term. We show numerical results that demonstrate the desired mesh-independence property and superior performance of the resulting quasi-Newton methods. [ABSTRACT FROM AUTHOR]

Fractal interpolation functions are fixed points of contraction maps on suitable function spaces. In this paper, we introduce the Kantorovich-Bernstein α-fractal operator in the Lebesgue space p(I), 1 ≤ p ≤ ∞. The main aim of this article is to study the convergence of the sequence of Kantorovich-Bernstein fractal functions towards the original functions in p(I) spaces and Lipschitz spaces without affecting the non-linearity of the fractal functions. In the first part of this paper, we introduce a new family of self-referential fractal p(I) functions from a given function in the same space. The existence of a Schauder basis consisting of self-referential functions in p spaces is proven. Further, we derive the fractal analogues of some p(I) approximation results, for example, the fractal version of the classical Müntz-Jackson theorem. The one-sided approximation by the Bernstein α-fractal function is developed. [ABSTRACT FROM AUTHOR]

We prove local in time, uniform in N, estimates for the solutions , Λ, and Γ of a coupled system of Hartree–Fock–Bogoliubov type with interaction potential , with and v a Schwartz function (satisfying additional technical requirements). The initial conditions are general functions in a Sobolev-type space, and the expected correlations in Λ develop dynamically in time. As shown in our previous work, as well as the work of Chong (both in the case), using the conserved quantities of the system of equations, this type of local in time estimates can be extended globally. Also, they can be used to derive Fock space estimates for the approximation of the exact evolution of a Bosonic system by quasi-free states of the form. This will be addressed in detail in future work. [ABSTRACT FROM AUTHOR]