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In the recent surge of papers on ergodic theory within Riesz spaces, this article contributes by introducing enhanced characterizations of ergodicity. Our work extends and strengthens prior results of both the authors and Homann, Kuo, and Watson. Specifically, we show that in a conditional expectation preserving system (E, T, S, e), S can be extended to L1(T) and operates as an isometry on Lp (T) spaces. [ABSTRACT FROM AUTHOR]

The paper investigates uniformly closed subspaces, sublattices, and ideals of finite codimension in Archimedean vector lattices. It is shown that every uniformly closed subspace (or sublattice) of finite codimension may be written as an intersection of uniformly closed subspaces (respectively, sublattices) of codimension one. Every uniformly closed sublattice of codimension n contains a uniformly closed ideal of codimension at most $ 2n $ 2 n. If the vector lattice is uniformly complete then every ideal of finite codimension is uniformly closed. Results of the paper extend (and are motivated by) results of Abramovich Y.A., Lipecki Z. [On ideals and sublattices in linear lattices and F-lattices. Math Proc Cambridge Philos Soc. 1990;108(1):79–87.; On lattices and algebras of simple functions. Comment Math Univ Carolin. 1990;31(4):627–635.], as well as Kakutani's characterization of closed sublattices of $ C(K) $ C (K) spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a large class of (so-called) conditional indicators, on a complete probability space with respect to a sub σ-algebra. A conditional indicator is a positive mapping, which is not necessary linear, but may share common features with the conditional expectation, such as the tower property or the projection property. Several characterizations are formulated. Beyond the definitions, we provide some non trivial examples that are used in finance and may inspire new developments in the theory of operators on Riesz spaces. [ABSTRACT FROM AUTHOR]

In this work, we consider the stochastic Cahn-Hilliard/Allen-Cahn equation with fractional noise, which is fractional in time and white in space. We obtain the existence, uniqueness, and Hölder regularity of the solution. Also, using a weak convergence approach, we prove that the law of solution associated with the above equation with a small perturbation satisfies the large deviation principle in the Hölder norm. [ABSTRACT FROM AUTHOR]

We give an example of an Archimedean Riesz space on which every automorphism is a strictly positive multiple of the identity. [ABSTRACT FROM AUTHOR]

We introduce and study the concept of generating function for natural elements in a Dedekind complete Riesz space equipped with a conditional expectation operator. This allows us to study discrete processes in a free-measure setting. In particular we improve a result obtained by Kuo, Vardy and Watson concerning Poisson approximation. [ABSTRACT FROM AUTHOR]

We give a Hahn-Jordan decomposition in Riesz spaces which generalizes that of [B.A. Watson, An Andô-Douglas type theorem in Riesz spaces with a conditional expectation, Positivity, 13 (2009), 543–558] and a Riesz-Frechet representation theorem for the T-strong dual, where T is a Riesz space conditional expectation operator. The result of Watson was formulated specifically to assist in the proof of the existence of Riesz space conditional expectation operators with given range space, i.e., a result of Andô-Douglas type. This was needed in the study of Markov processes and martingale theory in Riesz spaces. In the current work, our interest is a Riesz-Frechet representation theorem, for which another variant of the Hahn-Jordan decomposition is required. [ABSTRACT FROM AUTHOR]

Relatively uniformly continuous (ruc) semigroups were recently introduced and studied by Kandic, Kramar-Fijavž, and the second-named author, in order to make the theory of one-parameter operator semigroups available in the setting of vector lattices, where no norm is present in general. In this article, we return to the more standard Banach lattice setting – where both ruc semigroups and C0 -semigroups are well-defined concepts – and compare both notions. We show that the ruc semigroups are precisely those positive C0 -semigroups whose orbits are order bounded for small times. We then relate this result to three different topics: (i) equality of the spectral and the growth bound for positive C0 -semigroups; (ii) a uniform order boundedness principle which holds for all operator families between Banach lattices; and (iii) a description of unbounded order convergence in terms of almost everywhere convergence for nets which have an uncountable index set containing a co-final sequence. [ABSTRACT FROM AUTHOR]

This paper extends the well-known Ringrose theory for compact operators to polynomially Riesz operators on Banach spaces. The particular case of an ideal-triangularizable Riesz operator on an order continuous Banach lattice yields that the spectrum of such operator lies on its diagonal, which motivates the systematic study of an abstract diagonal of a regular operator on an order complete vector lattice E. We prove that the class of regular operators for which the diagonal coincides with the atomic diagonal is always a band in , which contains the band of abstract integral operators. If E is also a Banach lattice, then contains positive Riesz and positive AM-compact operators. [ABSTRACT FROM AUTHOR]

It is well known that the bidual of C(X) for a compact space X, supplied with the Arens product, is isometrically isomorphic as a Banach algebra to for some compact space. The space is unique up to homeomorphism. We establish a similar result for realcompact spaces: The order bidual of C(X) for a realcompact space X, when supplied with the Arens product, is isomorphic as an f-algebra to for some realcompact space. The space is unique up to homeomorphism. [ABSTRACT FROM AUTHOR]

It is known that if L is a Dedekind complete Riesz space and (Ω, Σ) is a measurable space, then the partially ordered linear space of all L-valued, finitely additive and order bounded vector measures m on Σ is also a Dedekind complete Riesz space (for the natural operations). In particular, the modulus |m|o of m exists in this space of measures and |m|o is given by a well known formula. Some 20 years ago L. Drewnowski and W. Wnuk asked the question (for L not Dedekind complete) if there is an m for which |m|o exists but, |m|o is not given by the usual formula? We show that such a measure m does indeed exist. [ABSTRACT FROM AUTHOR]

Let L be a truncated Archimedean vector lattice whose truncation is denoted by *. In a recent paper, we proved that there exists a locally compact Hausdorff space X such that L is a lattice isomorphic with a truncated vector lattice of functions in C∞(X) whose truncation is provided by meet with some characteristic function on X. This representation, no matter how interesting it is, has a major drawback, namely, C∞(X) need not be a vector lattice, unless X is extremally disconnected. The main purpose of this paper is to remedy this shortcoming by proving that, indeed, an extremally disconnected locally compact space X can be found such that L can be seen as an order dense vector sublattice of C∞(X) whose truncation is provided, again, by meet with some characteristic function on X. [ABSTRACT FROM AUTHOR]

In this work, we will generalize the moment generating function to Riesz spaces. We will derive some of its properties and use it to prove Chernoff's inequality inn Riesz spaces. [ABSTRACT FROM AUTHOR]

A new class of the Itô integral for Brownian motion is defined and studied in the framework of Riesz spaces. The stochastic process with respect to this stochastic integral is non-adapted and it is a motivitation to construct near-martingales in Riesz spaces. Furthermore, we state Doob–Meyer decomposition theorem for near-submartingales in Riesz spaces. [ABSTRACT FROM AUTHOR]

The current paper develops and analyzes a numerical scheme for the space–time fractional stochastic nonlinear diffusion wave equations. The implicit scheme is based on the matrix transform technique for discretizing the Riesz-space fractional derivative, (3 − α) -order approximation to the Caputo-fractional derivative in time and Taylor's series method to linearize the nonlinear source term, and has been successfully applied to solve a class of nonlinear fractional diffusion wave equation. We prove that the implicit scheme is convergent with β-order in space and (3 − α) order in time, respectively. The optimum error estimates in the temporal-spatial direction and unconditional stability of the implicit scheme have been theoretically investigated. Moreover, several specific numerical experiments confirm the consistency and high efficacy of the provided algorithms, which minimizes the computational costs. [ABSTRACT FROM AUTHOR]

In this paper, we investigate that under which conditions the inverse of an invertible ideal operator becomes an ideal operator. To determine conditions, in the first case, we consider the center of a Riesz space and achieve the solution by using some properties of it. In the second case, we first give an example of an ideal operator which is not order bounded. Then, we research when an ideal operator is order bounded. Thus, we conclude that if an invertible operator is order bounded then being an ideal operator, a band operator, and a disjointness preserving operator are equivalent and the same situation holds for the inverses of these three operators. [ABSTRACT FROM AUTHOR]

We prove in a purely algebraic way that if L is an Archimedean truncated vector lattice then there exists a positive element e in the universal completion Lu of L such that the truncation of L is provided by meet with e. Previous representations of truncated vector lattices by almost-finite extended-real continuous valued functions can be obtained as consequences. [ABSTRACT FROM AUTHOR]

Convergence is a fundamental topic in analysis that is most commonly modeled using topology. However, there are many natural convergences that are not given by any topology; e.g., convergence almost everywhere of a sequence of measurable functions and order convergence of nets in vector lattices. The theory of convergence structures provides a framework for studying more general modes of convergence. It also has one particularly striking feature: it is formalized using the language of filters. This paper develops a general theory of convergence in terms of nets. We show that it is equivalent to the filter-based theory and present some translations between the two areas. In particular, we provide a characterization of pretopological convergence structures in terms of nets. We also use our results to unify certain topics in vector lattices with general convergence theory. [ABSTRACT FROM AUTHOR]

We consider the operator Δ (α , β) − I , where Δ (α , β) is the three term recurrence relation for the Jacobi polynomial R n (α , β) (x) normalized at the point x = 1 and I is the identity operator acting on N . Knowing that for α ≥ β ≥ − 1 2 , these polynomials satisfy a product formula which provides a hypergroup structure on N , we use the tools of harmonic analysis on this hypergroup to solve the space-time fractional diffusion equation { D t σ u (n , t) = − (− Δ (α , β) ) s u (n , t) , t > 0 , n ∈ N , u (n , 0) = f (n). Here, 0 < s , σ ≤ 1 , D t σ is the Caputo time fractional derivative of order σ. The solution is given by f ∗ G σ , s (α , β) (⋅ , t) (n) , G σ , s (α , β) (n , t) being the fundamental solution expressed in terms of Mittag-Leffler function and ∗ is the convolution on the hypergroup N . We prove that, for 0 < s < σ ≤ 1 , G σ , s (α , β) (n , t) is nonnegative and we give some of its properties. Next, we study the one parameter operators associated with this fundamental solution. [ABSTRACT FROM AUTHOR]

In this note we prove that positive multi-valued operators on Riesz spaces which are everywhere defined are always continuous. Further, we prove that the sum of two positive relations having the same null part is itself positive. This result allows us to study the domination problem in the class of positive relations. [ABSTRACT FROM AUTHOR]

In this article, the authors completely answer an open question, presented in Tao et al. [A bridge connecting Lebesgue and Morrey spaces via Riesz norms. Banach J Math Anal. 2021;15(1):20], via showing that the Riesz–Morrey space is truly a new space larger than a particular Lebesgue space with a critical index. Indeed, this Lebesgue space is just the real interpolation space of the Riesz–Morrey space for suitable indices. Moreover, the authors further show that the aforementioned inclusion is also proper, namely, this embedding is sharp in some sense, via constructing two nontrivial spare functions, respectively, on R n and any given cube Q 0 of R n with finite side length. The latter constructed function is inspired by the striking function constructed by Dafni et al. [The space J N p : nontriviality and duality. J Funct Anal. 2018;275:577–603]. All the proofs of these results strongly depend on some exquisite geometrical analysis on cubes of R n . As an application, the relationship between Riesz–Morrey spaces and Lebesgue spaces is completely clarified on all indices. [ABSTRACT FROM AUTHOR]

In this article, the time-space fractional diffusion equation is solved by using the fractional operator in Atangana–Baleanu–Caputo (ABC) sense based on the Mittag-Leffler function involving non-singular and non-local kernels. This study mainly develop the numerical method for time-space linear and non-linear ABC fractional diffusion equation by utilising centred difference approximation with second-order accuracy of Riesz fractional derivative in space and trapezoidal formula for fractional integral approximation for a system of ABC integral equations. Also, we examine the stability and show that the proposed scheme converges at the rate of O (t 2 + h 2) having space mesh size h and time step size t. Numerical simulations are presented based on the presented method. We finished the article with a conclusion. [ABSTRACT FROM AUTHOR]

In the present study, we have used a mean field theory that is also a modified Ginzburg-Landau expansion in the order parameter. Single mode expansion of the order parameter were taken and written in terms of the reciprocal lattice vectors corresponding to the first reflection of the classical phases in such a way that the corresponding contour plot exhibits the required features of the respective phases. 'Wolfram Mathematica 8.0' software was used for calculations and the free energy optimizations. The present theory stabilizes the classical phases in the concentration – temperature phase diagram. And percentage of the stabilized area for the lamellar, hexagonal, and BCC phases, are found to be 35.41%, 42.98%, and 21.61%, respectively. [ABSTRACT FROM AUTHOR]

We provide two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into a convex bornological space using separately two polynomial identities of Kusraeva involving the root mean power and the geometric mean. Furthermore, it is shown that a polynomial on a vector lattice is orthogonally additive whenever it is orthogonally additive on the positive cone. These results improve recent characterizations of bounded orthogonally additive polynomials by G. Buskes and the author. [ABSTRACT FROM AUTHOR]

In this paper we continue our research about links and link topologies on ℓ-groups and Riesz spaces. We show that in a Riesz space E, a link topology τ is a vector topology, if and only if the link consists of all order units in E. We also compare the link topologies with the positive filter topologies on an ℓ-group. In addition, we provide some examples of these constructions. [ABSTRACT FROM AUTHOR]

A nonlinear initial boundary value problem with a time Caputo derivative of fractional-order β ∈ (1 , 2) and a space Riesz derivative of fractional-order α ∈ (1 , 2) is considered. A linearized alternating direction implicit (ADI) scheme for this problem is constructed and analysed. First, we use the classical central difference formula and a new 3 − β -order formula to approximate the second-order derivative and the Caputo derivative in temporal direction, respectively. Meanwhile, the central difference quotient and fractional central difference formula are applied to deal with the spatial discretizations. Then, the proposed ADI scheme is proved unconditionally stable and convergent with the 3 − β -order accuracy in time and the second-order accuracy in space. Furthermore, the effectiveness of the ADI scheme and theoretical findings are illustrated by numerical experiments. [ABSTRACT FROM AUTHOR]

In the present study, we have used a mean field theory that is also a modified Ginzburg-Landau expansion in the order parameter. Single mode expansion of the order parameter were taken and written in terms of the reciprocal lattice vectors corresponding to the first reflection of the classical phases in such a way that the corresponding contour plot exhibits the required features of the respective phases. 'Wolfram Mathematica 8.0' software was used for calculations and the free energy optimizations. The present theory stabilizes the classical phases in the concentration – temperature phase diagram. And percentage of the stabilized area for the lamellar, hexagonal, and BCC phases, are found to be 35.41%, 42.98%, and 21.61%, respectively. [ABSTRACT FROM AUTHOR]

An editorial is presented on commemorating the mathematical legacy of W.A.J. Luxemburg, a distinguished mathematician and former editor of Quaestiones Mathematicae. Topics discussed include Luxemburg's contributions to Riesz spaces theory, non-standard analysis, ordinary differential equations, and entire functions, highlighting his impact on the South African functional analysis community.

Structure and distribution of cells in histological images cause considerable variability among the tissue patterns and make the retrieving and classification as challenging tasks for this type of medical images. In this paper, we propose to extract four local features, namely local energetic information, local structural information, local geometric information, and local patterns to represent the huge texture variability of the histological images in a feature space. For extracting these features, the Riesz transform and Monogenic local binary patterns are used. Riesz transform is an extension of the Hilbert transform for 2-D signals. It provides a monogenic representation for an image where we can capture some local structure information. We used these local features for classification and retrieving purposes. We validated our proposed method on two multiclass archives of histological images, namely Kimiapath24 and Kather datasets. We achieved performance of more than 90% for classification and retrieval in two datasets. [ABSTRACT FROM AUTHOR]

In this paper, a second-order backward difference formula (abbr. BDF2) is used to approximate first-order time partial derivative, the Riesz fractional derivatives are approximated by fourth-order compact operators, a class of new alternating-direction implicit difference scheme (abbr. ADI) is constructed for two-dimensional Riesz space fractional nonlinear reaction–diffusion equation. Stability and convergence of the numerical method are analysed. Numerical experiments demonstrate that the proposed method is effective. [ABSTRACT FROM AUTHOR]

For a positive integer n and a uniformly complete vector lattice E, let denote the n-fold Fremlin vector lattice symmetric tensor product of E. We prove that if there exists a lattice homomorphism φ ∈ E∼ then E is lattice isomorphic to a complemented sublattice of. Moreover, if ker(φ) is a projection band in E then the image of E is also a projection band in. [ABSTRACT FROM AUTHOR]

{10-12} twinning is one of the most important deformation modes in magnesium alloys. It is supposed that with high density of {10-12} twin boundaries, magnesium alloys might show exceptional mechanical properties. In this work, the effects of randomly distributed yttrium (Y) on the {10-12} twinning behaviour in magnesium alloys are investigated. Addition of Y makes it easier to activate {10-11} < 11-23 > dislocations and {10-12} twins, compared with pure Mg. Two types (type I and type II) of bi-crystal were constructed to investigate the Y effects on the migration of {10-12} twin boundaries. For the type I bi-crystals, the tensile stress is parallel to the [0001] lattice vector of the matrix. In this case, Y atoms facilitate the migration of {10-12} twin boundary. For the type II bi-crystals, the tension direction is set as the bisector of the angle between [-1011] and [10-10] lattice vector of the matrix. In this case, owing to the activation of basal slip, {10-12} twin could be consumed by sequential basal stacking faults. In other words, the effect of Y on the migration of {10-12} twin boundaries depends on the loading direction. [ABSTRACT FROM AUTHOR]

We introduce a class of Morrey-type spaces M p , q , Ω λ , which includes the classical Morrey spaces and discuss their properties. We prove a Marcinkiewicz-type interpolation theorem for such spaces. This theorem is then applied to obtaining an analogue of O'Neil's inequality for convolutions and to proving the boundedness in the introduced Morrey-type spaces of the Riesz potential and singular integral operators. [ABSTRACT FROM AUTHOR]

In this research, we consider the alternating direction implicit method for solving the two-dimensional and three-dimensional Riesz space fractional diffusion equations with delay and a nonlinear reaction term. The corresponding theoretical results including stability and convergence are provided. Moreover, the convergence order of the proposed method is improved by using the Richardson extrapolation method. The numerical results are presented to show the robustness and effectiveness of the numerical method. [ABSTRACT FROM AUTHOR]

In this paper, the Riesz-type fractional differential equation is studied. For the equation defined on , its analytical solution is obtained. The existence and uniqueness of the solution are proved when the right-hand side term belongs to Lebesgue space. Furthermore, it is continuous and differentiable provided that the right-hand side term is continuously differentiable and in Sobolev space or the weighted one. For the equation constrained on a bounded domain, we focus on the case with. Mapping property of Riesz derivative operator on bounded domain indicates end-point singularities in the non-weighted space. Based on the observation of null space of the Riesz derivative operator, the well-posed definite problems of the Riesz-type fractional differential equation are proposed. Through a spectral-type method, solutions to those definite problems are obtained along with corresponding regularity analyses in the weighted space. [ABSTRACT FROM AUTHOR]

Pre-Riesz spaces are ordered vector spaces which can be order densely embedded into vector lattices, their so-called vector lattice covers. Given a vector lattice cover Y for a pre-Riesz space X, we address the question how to find vector lattice covers for subspaces of X, such as ideals and bands. We provide conditions such that for a directed ideal I in X its smallest extension ideal in Y is a vector lattice cover. We show a criterion for bands in X and their extension bands in Y as well. Moreover, we state properties of ideals and bands in X which are generated by sets, and of their extensions in Y. [ABSTRACT FROM AUTHOR]

If ℝn is partially ordered by a generating closed cone K, then (ℝn, K) is a pre-Riesz space. We show for a disjointness preserving bijection T on (ℝn, K) that the inverse of T is also disjointness preserving. We prove that for T there is k ∈ 𝒫(b) such that T k is band preserving, where b is the number of bands in (ℝn, K), and 𝒫(b) the set of orders of permutations on b symbols. [ABSTRACT FROM AUTHOR]

In this work, we consider a damped hyperbolic partial differential equation in multiple spatial dimensions with spatial partial derivatives of non-integer order. The equation under investigation is a fractional extension of the well-known sine-Gordon and Klein-Gordon equations from relativistic quantum mechanics. The system has associated an energy functional which is conserved in the undamped regime, and dissipated in the damped case. In this manuscript, we restrict our study to a bounded spatial domain and propose an explicit finite-difference discretization of the problem using fractional centred differences. Together with the scheme, we propose an approximation for the energy functional and show that the energy of the discrete system is conserved/dissipated when the energy of the continuous model is conserved/dissipated. The method guarantees that the energy functionals are positive, in agreement with the continuous counterparts. We show in this work that the method is a uniquely solvable, consistent, stable and convergent technique. [ABSTRACT FROM AUTHOR]

We introduce central generalized Orlicz-Morrey spaces on the unit ball, and study the weighted behavior of spherical means for Riesz potentials of functions in those spaces. We also treat Orlicz-Morrey-Sobolev functions which are monotone in the punctured unit ball in the sense of Lebesgue. [ABSTRACT FROM AUTHOR]

We give elementary and self-contained proofs of the facts that the Lp space with is uniformly convex and its dual space is isometrically isomorphic to . [ABSTRACT FROM AUTHOR]

We consider radially symmetric m-subharmonic functions on the unit ball. We study their convexity and their relation with a solution of the complex Hessian equations. Furthermore, we consider the ordered vector space of radially symmetric m-subharmonic functions which is a Riesz space. [ABSTRACT FROM AUTHOR]

We show that for positive operator B : E → E on Banach lattices, if there exists a positive operator S : E → E such that:1.SB ≤ BS;2.S is quasinilpotent at some x0 > 0; 3.S dominates a non-zero b-AM-compact operator, then B has a non-trivial closed invariant subspace. Also, we prove that for two commuting non-zero positive operators on Banach lattices, if one of them is quasinilpotent at a non-zero positive vector and the other dominates a non-zero b-AM-compact operator, then both of them have a common non-trivial closed invariant ideal. Then we introduce the class of b-AM-compact-friendly operators and show that a non-zero positive b-AM- compact-friendly operator which is quasinilpotent at some x0 > 0 has a non-trivial closed invariant ideal. [ABSTRACT FROM AUTHOR]

In this paper, using the Riesz fractional derivative , we present the Mellin transforms of shifted Airy functions in terms of the Riesz fractional derivatives of Airy functions. We also show some integral addition formulas for the products of Airy functions in terms of the Riesz fractional trigonometric operators. Moreover, the fundamental solution of the Ostrovsky equation is given by the Riesz fractional trigonometric operators. [ABSTRACT FROM AUTHOR]

In this paper, simultaneous identification of damping or anti-damping coefficient and initial value for some Riesz spectral systems is considered. An identification algorithm is proposed based on the fact that the output of the systemhappens to be decomposed into a product of an exponential function and a periodic function. The former contains information of the damping coefficient, while the latter does not. The convergence and error analysis are also developed. Three examples, namely an anti-stablewave equation with boundary anti-damping, the Schrödinger equation with internal antidamping and two connected strings with middle joint anti-damping, are investigated and demonstrated by numerical simulations to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this article we are proposing a strongly stable computationally efficient method in time to numerically solve reaction-diffusion equations with space fractional derivative. The Riesz space fractional derivative is discretized using the second-order fractional centred difference method. Time stepping scheme is based on second-order exponential time differencing Runge-Kutta method. Second-order positivity preserving Padé approximations is used to develop the proposed L-stable method. The computation efficiency of the method is significantly enhanced by using partial fractions splitting technique. The method is shown to be stable and reliable. Solution profiles as well as convergence tables in time are presented for various values of diffusion rates α. [ABSTRACT FROM AUTHOR]

We propose two fourth-order methods in time for one-dimensional space fractional reaction-diffusion equations. The methods are based on fourth-order Exponential Time Differencing Runge-Kutta method. Padé approximations of matrix exponential functions are used to construct an L-stable and an A-stable method. Partial fraction splitting technique is applied to construct more reliable and computationally efficient versions of the methods. Solution profiles as well as convergence rates in time are presented for fractional enzyme kinetics equation and fractional Fisher equation. The L-stable method performs well in the presence of non-smooth mismatched initial-boundary data while the A-stable method is more economical for smooth matched initial-boundary data. [ABSTRACT FROM AUTHOR]

We present a novel Exponential Time Differencing (ETD) scheme for nonlinear Riesz space fractional reaction-diffusion equations. This scheme is based on using a real distinct poles (RDP) discretization for the underlying matrix exponentials. Due to these RDP, the algorithm could be easily implemented in parallel to take advantage of multiple processors for increased computational efficiency. The method is established to be second-order convergent; and proven to be robust for problems involving non-smooth/mismatched initial and boundary conditions and steep solution gradients. We examine the stability of the scheme through its amplification factor and plot the boundaries of the stability regions comparative to other second-order ETD schemes. This numerical scheme combined with fractional central differencing is used for simulating some nonlinear space fractional problems. We demonstrate the superiority of our method over competing second-order ETD schemes, BDF2 scheme, and IMEX schemes. Our experiments show that the proposed scheme is computationally more efficient (in terms of cpu time). Furthermore, we investigate the trade-off between using fractional central differencing and matrix transfer technique in discretization of Riesz fractional derivatives. [ABSTRACT FROM AUTHOR]

Successive differences on a sequence of data help discover some smoothness features of this data. This was one of the main reasons for rewriting the classical interpolation formula in terms of such data differences. The aim of this paper is to mimic them to a sequence of regular samples of a function in a shift-invariant subspace allowing its stable recovery. A suitable expression for the functions in the shift-invariant subspace by an isomorphism with the L2(0,1) space is the key to identify the simple pattern followed by the dual Riesz bases involved in the derived formulas. The paper contains examples illustrating different non-exhaustive situations including also the two-dimensional case. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of isotone cones in Banach spaces. Then, we apply the order monotonic property of the metric projection operator to prove the existence of best approximations for some operators without continuity conditions in partially ordered Banach spaces. [ABSTRACT FROM AUTHOR]