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The magnetohydrodynamic (MHD) flow has been concerned widely for its widespread adoption in the field of astrophysics, electronics and many other industries over the years. The purpose of this article is to introduce the variable and distributed order space fractional models to characterize the MHD flow and heat transfer of heterogeneous viscoelastic fluids in a parallel plates. Based on the central difference approximation of Riesz space fractional derivative, the Crank–Nicolson difference scheme for the governing equations is established, and the effectiveness of the algorithm is verified by two numerical examples. We examine the effects of fractional-order model parameters on the velocity and temperature, our investigation indicates that for the constant fractional model, the larger the fractional order parameter, the smaller the velocity and temperature. The variable space fractional method can be used to describe dynamic behavior with time and space dependence, while the distributed space fractional model can describe various phenomena in which the number of differential orders varies over a certain range, characterizing their complex processes over space, and it is also more suitable for simulating the fluid flow and thermal behavior of complex viscoelastic magnetic fluid. [ABSTRACT FROM AUTHOR]

We present and analyze a local discontinuous Galerkin finite element method to solve the Riesz space distributed-order Sobolev equation. To approximate the distributed-order Riesz space derivative, the Gauss quadrature as the high computational accuracy method is proposed. A multi-term fractional equation is then constructed from the considered equation by approximating the Riesz space derivative. Moreover, stability analysis is provided for a semi-discrete scheme. We provide numerical results to justify the theoretical analysis by solving the ordinary differential equation. We obtain this after implementing the local discontinuous Galerkin scheme on the Riesz space distributed-order Sobolev equation with the Crank–Nicolson scheme as a time marching method and the Laplace transform technique. [ABSTRACT FROM AUTHOR]

In this study, we investigate a high-order accurate conservative finite difference scheme by utilizing a fourth-order fractional central finite difference method for the two-dimensional Riesz space-fractional nonlinear Schrödinger wave equation. The conservation laws of the discrete difference scheme are shown. Meanwhile, the exactness, uniqueness, and prior estimate of the numerical solution are rigorously established. Then, it is proved that the proposed scheme is unconditionally convergent in the discrete L 2 and H γ / 2 norm, where γ is a fractional order. Furthermore, we demonstrate that when the fractional order γ and the spatial grid number J increase, the block-Toeplitz coefficient matrix generated by the spatial discretization becomes ill-conditioned. As a result, we adopt an effective linearized iteration method for the nonlinear system, allowing it to be solved efficiently by the Krylov subspace solver with an appropriate circulant preconditioner, in which the fast Fourier transform is applied to speed up the computational cost at each iterative step. Finally, numerical experiments are presented to validate the theoretical findings and the efficiency of the fast algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a respectively scaled circulant and skew-circulant splitting (RSCSCS) iteration method is employed to solve the Toeplitz-like linear systems arising from time-dependent Riesz space fractional diffusion equations with variable coefficients. The RSCSCS iteration method is shown to be convergent unconditionally by a novel technique, and only requires computational costs of O (N log N) with N denoting the number of interior mesh points in space. In theory, we obtain an upper bound for the convergence factor of the RSCSCS iteration method and discuss the optimal value of its iteration parameter that minimizes the corresponding upper bound. Meanwhile, we also design a fast induced RSCSCS preconditioner to accelerate the convergence rate of the Krylov subspace iteration method likes generalized minimal residual (GMRES) method. Numerical results are presented to show that the efficiencies of our proposed RSCSCS iteration method and the preconditioned GMRES method with the RSCSCS preconditioner. [ABSTRACT FROM AUTHOR]

The article titled "ELECTRONICA" by Will Cordeiro, published in Half Mystic, explores the mesmerizing and transformative power of electronic music. The author describes how the enchanting sounds produced by electronic instruments can manipulate time, matter, and emotions. The fluidity of repetition is revealed through eerie glitches, while the emergence of new sounds disrupts established patterns. The article delves into the intricate nature of electronic music, highlighting its ability to evoke both love and destruction, and emphasizes the hidden depths within the vastness of space. [Extracted from the article]

In this paper, we propose an efficient numerical method for the solution of one and two dimensional Riesz space fractional advection–dispersion equation. To this end, we use the Crank–Nicolson scheme to discretize this equation in temporal direction and prove that the semi-discrete scheme is unconditionally stable. Then, we apply the spectral element method in spatial directions and obtain the fully discrete scheme. We present an error estimate for the fully discrete scheme. The presented numerical results demonstrate the accuracy and efficiency of the proposed method in comparison with other schemes in literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the numerical solution of the Riesz space fractional Sine–Gordon equations. We develop an explicit fourth-order energy-preserving difference scheme for the two-dimensional space fractional Sine–Gordon equation (SGE). The conservation, convergence and boundedness properties of the numerical scheme are rigorously proved. Subsequently, the proposed numerical method is applied to approximate the one-dimensional space fractional SGE. Several numerical experiments are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Approximating Riesz space fractional diffusion equation in time by k -step backward difference formula and in space by spectral Galerkin method, we establish a fully discrete scheme with high order both in time and in space. For k ≤ 5 , we prove the stability of full discretization and obtain the error estimate with order O (τ k + N α 2 − m) , which depends only on the regularity of initial value and right-hand function. Moreover, we extend the proposed method to two dimensional case and derive similar results. Finally, we illustrate the theoretical estimates by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we study the numerical solution of a class of Riesz space fractional telegraph equation. In the spatial direction, the equations are discretized using the fractional central difference scheme, and an equivalent semi-linear form is obtained. Then, a fourth-order exponential Runge–Kutta method is chosen in the temporal direction. Moreover, an efficient method for calculating the matrix exponent and matrix φ -function is proposed by performing a series of matrix transformations on the coefficient matrix in the semi-linear form, improving the efficiency of the matrix functions calculation. Several numerical experiments show that the convergence order of the scheme is O (h 2 + τ 4) , where h is the space step and τ is the time step. The effectiveness of the scheme is also verified. • New numerical methods are proposed for Riesz space-fractional telegraph equations. • The methods convergent of order 2 in space and order 4 in time. • The matrix functions are calculated efficiently by a series of matrix transformations. [ABSTRACT FROM AUTHOR]

In this work, we investigate the active dynamics and ergodicity breaking of a nonequilibrium fractional Langevin equation (FLE) with a power-law memory kernel of the form K (t) ∼ t − (2 − 2 H) , where 1 / 2 < H < 1 represents the Hurst exponent. The system is subjected to two distinct noises: a thermal noise satisfying the fluctuation–dissipation theorem and an active noise characterized by an active Ornstein–Uhlenbeck process with a propulsion memory time τ A. We provide analytic solutions for the underdamped active fractional Langevin equation, performing both analytical and computational investigations of dynamic observables such as velocity autocorrelation, the two-time position correlation, ensemble- and time-averaged mean-squared displacements (MSDs), and ergodicity-breaking parameters. Our results reveal that the interplay between the active noise and long-time viscoelastic memory effect leads to unusual and complex nonequilibrium dynamics in the active FLE systems. Furthermore, the active FLE displays a new type of discrepancy between ensemble- and time-averaged observables. The active component of the system exhibits ultraweak ergodicity breaking where both ensemble- and time-averaged MSDs have the same functional form with unequal amplitudes. However, the combined dynamics of the active and thermal components of the active FLE system are eventually ergodic in the infinite-time limit. Intriguingly, the system has a long-standing ergodicity-breaking state before recovering the ergodicity. This apparent ergodicity-breaking state becomes exceptionally long-lived as H → 1 , making it difficult to observe ergodicity within practical measurement times. Our findings provide insight into related problems, such as the transport dynamics for self-propelled particles in crowded or polymeric media. • First analytic and numerical study for underdamped active fractional Langevin equations. • Active FLEs perform superballistic underdamped dynamics via the viscoelastic feedback. • Activity-induced super- and sub-diffusive dynamics emerge in the overdamped regime. • Time-averaged MSDs are inequivalent with ensemble-averaged MSDs (ergodicity breaking). • Viscoelasticity is critical to duration and degree of the ergodicity breaking state. [ABSTRACT FROM AUTHOR]

Highlights • The existence of invariants for a fractional Klein–Gordon–Zakharov equation is established. • A second-order numerical model is proposed to solve the continuous model. • The model has discrete forms of the invariants which are also conserved. • The existence, uniqueness and boundedness of the numerical solutions are proved. • We prove stability and convergence using a form of the discrete energy method. Abstract Departing from a fractional extension of the well-known one-dimensional Klein–Gordon–Zakharov system, we propose a numerically efficient model to approximate its solutions. The continuous model under investigation considers fractional derivatives of the Riesz type in space, with orders of differentiation in (1, 2]. In analogy with the non-fractional regime, the existence of a positive conserved energy quantity is established in this work. Motivated by this fact, the design of the numerical model focuses on the preservation of the energy. Using fractional-order centered differences to approximate the fractional partial derivatives, we propose a numerical model that preserves a positive discrete form of the energy. The existence and uniqueness of solutions are thoroughly established using fixed-point arguments, and the usual argument with Taylor polynomials is employed to prove the consistency of the numerical model. Some suitable bounds in terms of the energy invariants are found for the solutions of the numerical model. Moreover, using an extension of the energy method for fractional systems, we establish the stability and the convergence properties of the methodology. Finally, we provide some examples to illustrate the accuracy of our numerical implementation, including a numerical study of the convergence rate of the scheme that confirms the validity of the analytical results derived in this work. [ABSTRACT FROM AUTHOR]

Unfolding of a supercell band structure into a primitive Brillouin zone is important for understanding implications of structural distortions, disorder, defects, and solid solutions on materials electronic structure. The necessity of band unfolding is also recognized in the interpretation of angle-resolved photoemission spectroscopy (ARPES) measurements. We describe an extension of the fold2Bloch package by implementing an arbitrary transformation matrix used to establish a relation between the primitive cell and supercell. This development allows us to overcome limitations of supercells constructed exclusively by scaling of primitive cell lattice vectors. It becomes possible to transform between primitive and conventional cells as well as include rotations. The fold2Bloch is publicly available from a GitHub repository as a FORTRAN code. It interfaces with the all-electron full-potential WIEN2k and the pseudopotential VASP density functional theory packages. The fold2Bloch is supplemented by additional pre- and post-processing utilities that aid in generating k points in the supercell (such that they later fall onto a desired path in the primitive Brillouin zone after unfolding) and plotting the unfolded band structure. We selected ▪ as an illustrative example and, for the first time, present its properly unfolded band structure in direct comparison with ARPES measurements. In addition, critical importance of the band unfolding for interpretation of ▪ ARPES data is illustrated and discussed as a perspective. [ABSTRACT FROM AUTHOR]

In this paper, we consider output feedback stabilization for an anti-stable Schrödinger equation with both the internal unknown dynamic and external disturbance. An unknown input type state observer is designed in terms of a new disturbance estimator. Different from the existing results, we never use high gain in the observer design. Hence, the boundedness assumption on the derivative of disturbance, that is usually required by finite-dimensional extended state observer, is no longer required. The anti-stable term is treated by the backstepping transformation which is given by ODE form to make the controller design easier. Although the close-loop system is nonlinear, both the well-posedness and the asymptotic stability are obtained by a linear method in terms of an invertible transformation. The numerical simulations are presented to illustrate that the proposed scheme is very effective. [ABSTRACT FROM AUTHOR]

In this work, we investigate numerically a model governed by a multidimensional nonlinear wave equation with damping and fractional diffusion. The governing partial differential equation considers the presence of Riesz space-fractional derivatives of orders in (1, 2], and homogeneous Dirichlet boundary data are imposed on a closed and bounded spatial domain. The model under investigation possesses an energy function which is preserved in the undamped regime. In the damped case, we establish the property of energy dissipation of the model using arguments from functional analysis. Motivated by these results, we propose an explicit finite-difference discretization of our fractional model based on the use of fractional centered differences. Associated to our discrete model, we also propose discretizations of the energy quantities. We establish that the discrete energy is conserved in the undamped regime, and that it dissipates in the damped scenario. Among the most important numerical features of our scheme, we show that the method has a consistency of second order, that it is stable and that it has a quadratic order of convergence. Some one- and two-dimensional simulations are shown in this work to illustrate the fact that the technique is capable of preserving the discrete energy in the undamped regime. For the sake of convenience, we provide a Matlab implementation of our method for the one-dimensional scenario. [ABSTRACT FROM AUTHOR]

In this work, we investigate a general nonlinear wave equation with Riesz space-fractional derivatives that generalizes various classical hyperbolic models, including the sine-Gordon and the Klein–Gordon equations from relativistic quantum mechanics. A finite-difference discretization of the model is provided using fractional centered differences. The method is a technique that is capable of preserving an energy-like quantity at each iteration. Some computational comparisons against solutions available in the literature are performed in order to assess the capability of the method to preserve the invariant. Our experiments confirm that the technique yields good approximations to the solutions considered. As an application of our scheme, we provide simulations that confirm, for the first time in the literature, the presence of the phenomenon of nonlinear supratransmission in Riesz space-fractional Klein–Gordon equations driven by a harmonic perturbation at the boundary. [ABSTRACT FROM AUTHOR]

In this work, we introduce a spatially discrete model that is a modification of the well-known α -Fermi–Pasta–Ulam chain with damping. The system is perturbed at one end by a harmonic disturbance irradiating at a frequency in the forbidden band-gap of the classical regime, and a nonlocal coupling between the oscillators is considered using discrete Riesz fractional derivatives. We propose fully discrete expressions to approximate an energy functional of the system, and we use them to calculate the total energy of fractional chains over a relatively long period of time [Fract. Diff. Appl. 4 (2004) 153–162]. The approach is thoroughly tested in the case of local couplings against known qualitative results, including simulations of the process of nonlinear recurrence in the traditional chains of anharmonic oscillators. As an application, we provide evidence that the process of supratransmission is present in spatially discrete Fermi–Pasta–Ulam lattices with Riesz fractional derivatives in space. Moreover, we perform numerical experiments for small and large amplitudes of the harmonic disturbance. In either case, we establish the dependency of the critical amplitude at which supratransmission begins as a function of the driving frequency. Our results are in good agreement with the analytic predictions for the classical Fermi–Pasta–Ulam chain. [ABSTRACT FROM AUTHOR]

The paper proposes an identification method for the fractional Hammerstein state space model with colored noise. The traditional identification algorithms of this model suffer from problems such as parameter coupling, unknown intermediate state variables, difficulty in processing noise signal coloring, and low identification accuracy. The proposed method is based on the principle of multiple innovations and involves constructing the partial derivative system of the system output to the system parameters, calculating the sensitivity function for the fractional order, and using historical data with current data to obtain the objective function and its gradient and Hessian matrix. The parameters and fractional orders are then iteratively updated through the Levenberg–Marquardt algorithm. The algorithm's robustness is verified through multiple Monte Carlo experiments under different signal-to-noise ratios on an academic example, and its practicability is demonstrated by applying it to an actual heating system. [ABSTRACT FROM AUTHOR]

In the proposed data-hiding algorithm, a combination of the medical image Metadata and a MAC is embedded into the medical image. Keywords: Algorithms; Emerging Technologies; Engineering; Hospitals; Machine Learning; Vector Quantization EN Algorithms Emerging Technologies Engineering Hospitals Machine Learning Vector Quantization 537 537 1 06/26/23 20230702 NES 230702 2023 JUL 2 (NewsRx) -- By a News Reporter-Staff News Editor at Medical Devices & Surgical Technology Week -- Investigators publish new report on engineering. [Extracted from the article]

In this paper, we propose a split-step Fourier pseudo-spectral method for solving the space fractional coupled nonlinear Schrödinger (CNLS) equations. The space fractional CNLS equations can be split into two subproblems such that one of them is linear. The solution of the nonlinear subproblem is computed exactly. The Riesz space fractional derivative is approximated by a Fourier pseudo-spectral method. The unconditional stability, convergence, discrete charge and multi-symplectic preserving properties for the proposed method are investigated. Then, the proposed method is extended for solving the two-dimensional problem. Finally, some numerical experiments are performed to confirm our theoretical analysis and illustrate the efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we present an accurate numerical method for solving a space-fractional Schrödinger equation in two dimensions. The quantum Riesz–Feller fractional derivative is used to define the fractional derivatives. The weighted average non-standard finite difference method is implemented to study the behavior of the model problem. The stability analysis of the proposed method is given by a recently proposed procedure similar to the standard John von Neumann stability analysis; moreover the truncation error is analyzed. Some numerical test examples are presented with variety values of derivatives of order α , where 1 < α ≤ 2 and of skewness θ . Experimental findings indicate that the proposed method is easy to implement, effective and convenient for solving the proposed model. [ABSTRACT FROM AUTHOR]

This paper deals with the study of the maximum likelihood estimator of the scale parameter for the Riesz distribution. This distribution represents a natural generalization of the Wishart distribution. We give an explicit formula of this estimator and we examine some related asymptotic properties. [ABSTRACT FROM AUTHOR]

In some applications, measurement errors and multiple repeated measurements often lead to a set-based classification task where objects are represented with a set of samples, and the traditional support vector machines (SVMs) do not work in these settings. To deal with this problem, we construct a new classifier called support function machine (SFM) in this work. First, sets in d -dimensional Euclidean space R d are mapped into an infinite-dimensional Banach space C ( S ) (whose elements are functions) via support functions, and then set-based classification in R d is converted into function-based classification in C ( S ). Second, we define the hyperplane via the Riesz representation theorem in Banach space, and discuss the Hausdorff distance of hyperpalnes and maximum margin principle (MMP) in C ( S ). Based on MMP, we construct an optimal problem and discuss some of its properties. Thereafter, we establish an SFM to solve set-based classification. Experiments about water quality evaluation and set-valued data classifications show the superiority of SFM. [ABSTRACT FROM AUTHOR]

In this work, we consider a ( 1 + 1 ) -dimensional Riesz space-fractional damped sine-Gordon equation defined on a bounded spatial interval. Sinusoidal Dirichlet boundary data are imposed at one end of the interval and homogeneous Neumann conditions at the other. The system is initially at rest in the equilibrium position, and is discretized to simulate its complex dynamics. The method employed in this work is a finite-difference discretization of the mathematical model of interest. Our scheme is throughly validated against simulations on the dynamics of the classical and the space-fractional sine-Gordon equations, which are available in the literature. As the main result of this manuscript, we have found numerical evidence on the presence of the phenomenon of nonlinear supratransmission in Riesz space-fractional sine-Gordon systems. Simulations have been conducted in order to predict its occurrence for some values of the fractional order of the spatial derivative, and a wide range of values of the frequency of the sinusoidal perturbation at the boundary. As far as the author knows, this may be one of the first numerical reports on the existence of nonlinear supratransmission in sine-Gordon systems of Riesz space-fractional order. [ABSTRACT FROM AUTHOR]

Keywords: Epidemiology; Health and Medicine; Physics EN Epidemiology Health and Medicine Physics 1677 1677 1 04/17/23 20230421 NES 230421 2023 APR 21 (NewsRx) -- By a News Reporter-Staff News Editor at Health & Medicine Week -- New study results on physics have been published. Keywords for this news article include: Weinan Normal University, Shaanxi, People's Republic of China, Asia, Physics, Epidemiology, Health and Medicine. [Extracted from the article]

Keywords: Tehran; Iran; Engineering; Algorithms; Emerging Technologies; Hospitals; Machine Learning; Vector Quantization EN Tehran Iran Engineering Algorithms Emerging Technologies Hospitals Machine Learning Vector Quantization 680 680 1 03/23/23 20230324 NES 230324 2023 MAR 26 (NewsRx) -- By a News Reporter-Staff News Editor at Medical Devices & Surgical Technology Week -- Research findings on Engineering are discussed in a new report. In the proposed data-hiding algorithm, a combination of the medical image Metadata and a MAC is embedded into the medical image. [Extracted from the article]

The Riesz distributions dealing with positive definite symmetric matrices are usually used to introduce the class of the inverse Riesz distributions. The latter represents the natural extension of the class of the inverse Wishart. In this paper, we first present a sufficient condition allowing the existence of the expectation of the inverse Riesz distribution. Then, we compute it explicitly. For this purpose, we basically use the Cholesky decomposition as well as an important relation satisfied by the first derivative of continuous Riesz distribution’s density. The importance of this first moment consists in the fact that it can be used to estimate the shape parameter through the method of moments. [ABSTRACT FROM AUTHOR]

In this work, the solution of Riesz space fractional partial differential equations of parabolic type is considered. Since fractional-in-space operators have been applied to model anomalous diffusion or dispersion problems in the area of mathematical physics with success, we are motivated in this paper to model the standard Brownian motion with the fractional order operator in the sense of the Riesz derivative. We formulate two viable, efficient and reliable high-order approximation schemes for the Riesz derivative which incorporated both the left- and right-hand sides of the Riemann-Liouville derivatives. The proposed methods are analyzed for both stability and convergence. Finally, the methods are used to explore the dynamic richness of pattern formation in two important fractional reaction-diffusion equations that are still of recurring interest. Experimental results for different values of the fractional parameters are reported. [ABSTRACT FROM AUTHOR]

Recently, it was discovered that the use of fractional derivatives induces the occurrence of multistable states in PWL systems with multiple scrolls. In this paper, we show the emergence of multistable states in a PWL system and study the route of the system to transition from monostable to multistable behavior by reducing the order of the fractional derivative. Using bifurcation diagrams that describe the evolution of the attractor as a consequence of the change in derivative order and basins of attraction, we show that the system has a path to multistability that reveals the mechanism for the occurrence of this behavior. The resulting dynamics shows the coexistence of up to n + 2 attractors, where n is the number of scrolls generated by the integer-order system, which has been confirmed for two different n -multi-scrolls systems. Moreover, the existence and uniqueness of the dynamics is proved by Poincaré sections, which show that the behaviors exist, and coexist, and are not a section of the same solution. • Multistable behavior of n + 2 states compared with the number of presented scrolls in the system. • The n + 2 multistable behavior is obtained in a small region of the integration order variation. • All the different present states are explained using bifurcations diagrams, Poicaré analysis and basins of attraction. • Results are shown and proved for two systems with different number of scrolls. [ABSTRACT FROM AUTHOR]

Abstract: An observable on a quantum structure is any σ-homomorphism of quantum structures from the Borel σ-algebra into the quantum structure. We show that our partial information on an observable known only for all intervals of the form (−∞, t) is sufficient to derive the whole information about the observable defined on quantum structures like σ-MV-algebras, σ-lattice effect algebras, Boolean σ-algebras, monotone σ-complete effect algebras with the Riesz Decomposition Property, the effect algebra of effect operators of a Hilbert space, and systems of functions – effect-tribes. [Copyright &y& Elsevier]

• We investigate a novel non-integer model of the circumscribed self-excited spherical strange attractor. • We consider the Caputo-Fabrizio derivative. • We provide the existence of the solution by the fixed-point theories. • We apply very effective numerical technique. • We demonstrate the numerical simulations. The purpose of this study is to present and examine a novel non-integer model of the circumscribed self-excited spherical strange attractor, which has not been worked yet. To design the fractional-order model, we use the Caputo-Fabrizio derivative. In order to ensure the existence of the solution Picard-Lindel and fixed-point theories are provided. Moreover, the stability of the considered fractional-order model is shown using the Picard iteration and fixed point theory approach. To get the approximate solutions of the proposed fractional model an efficient numerical scheme called the fractional Euler method(FEM) is used. To see the performance of the used method, the behavior of the numerical solutions of the model is examined under various initial conditions(ICs) and fractional orders. Considerable chaotic behaviors of the solutions are obtained which prove the accuracy and reliability of FEM. [ABSTRACT FROM AUTHOR]

Abstract: After reviewing the problematic behavior of some previously suggested finite-interval spatial operators of the symmetric Riesz type, we create a wish list leading toward a new spatial operator suitable to use in the space–time fractional differential equation of anomalous diffusion when the transport of material is strictly restricted to a bounded domain. Based on recent studies of wall effects, we introduce a new definition of the spatial operator and illustrate its favorable characteristics. We provide two numerical methods to solve the modified space–time fractional differential equation and show particular results illustrating compliance to our established list of requirements, most important to the conservation principle and the second law of thermodynamics. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a class of vector-valued wavelet packets of space , which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality properties are characterized by virtue of matrix theory, time–frequency analysis method, and operator theory. Three biorthogonality formulas regarding these wavelet packets are derived. Moreover, it is shown how to gain new Riesz bases of space from these wavelet packets. Relation to some physical theories such as the Higgs field is also discussed. [Copyright &y& Elsevier]

Abstract: A convergence in Riesz spaces is given axiomatically. A Bochner-type integral for Riesz space-valued functions is introduced and some Vitali and Lebesgue dominated convergence theorems are proved. Some properties and examples are investigated. [Copyright &y& Elsevier]

Abstract: Wavelet packets possess excellent characteristics in differentiations of space and spectrum. In this paper, The splitting trick coined by Daubechies is used to construct wavelet packets with an arbitrary dilation matrix A. Different from the classical wavelet packets, instructed by Coifman et al., our method is that we split the wavelet subspaces directly instead of using the low-pass and the high-pass filters associated with the multiresolution analysis. Furthermore, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation matrix not equal to 2I. Finally, we show how to construct various Riesz basis from the wavelet packets. [Copyright &y& Elsevier]

This note addresses the stabilization of a one-dimensional wave equation with control at one end and noncollocated observation at another end. A simple exponentially convergent observer is constructed. The dynamical stabilizing boundary output feedback is designed via the observed state. While the closed-loop system is nondissipative, we show its exponential stability using Riesz basis approach. [ABSTRACT FROM AUTHOR]

Analyzes the close-loop form of a second hyperbolic system with scalar collocated sensor/actuator. Verification of the Riesz basis property of the system for diagonal semigroups; Abstract result of a rank perturbation of discrete-type operators in Hilbert spaces; Validity of spectrum-determined growth condition for generic infinite dimensional systems.

Compactifications of the Chaudhuri-Hockney-Lykken (CHL) string to eight dimensions can be characterized by embeddings of root lattices into the rank 12 momentum lattice ΛM, the so-called Mikhailov lattice. Based on these data, we devise a method to determine the global gauge group structure including all U(1) factors. The key observation is that, while the physical states correspond to vectors in the momentum lattice, the gauge group topology is encoded in its dual. Interpreting a nontrivial π1(G) ≡ Z for the non-Abelian gauge group G as having gauged a Z 1-form symmetry, we also prove that all CHL gauge groups are free of a certain anomaly [1] that would obstruct this gauging. We verify this by explicitly computing Z for all 8D CHL vacua with rank (G) = 10. Since our method applies also to T² compactifications of heterotic strings, we further establish a map that determines any CHL gauge group topology from that of a "parent" heterotic model. [ABSTRACT FROM AUTHOR]

• New fractional-order Lassa fever model is proposed. • Existence and uniqueness of the solution of the model are studied. • Culling strategy mitigates the spread of the disease in rodents population. • Culling strategy only oscillates the number of infected humans. This study formulates a new integer-order ordinary differential equation (ODE) Lassa fever model, through which its corresponding fractional- order differential equation (FODE) is devised via the Caputo fractional-order derivative. The existence and uniqueness of the solution of proposed FODE are studied through the fixed point theory. Using the Mittag-Leffler function, the positivity of the FODE model is determined. As a disease control measure, a culling strategy is applied on the population of rodents. Though this approach reduces the number of infected rodents, it does not completely eradicate the disease in humans. This finding can be relevant in ecological studies since it is practically impossible to cull the whole rodents potentially spreading the Lassa fever virus. [ABSTRACT FROM AUTHOR]

Small displacement methods have been successfully used to calculate the lattice dynamical properties of crystals. It involves displacing atoms by a small amount in order to calculate the induced forces on all atoms in a supercell for the computation of force constants. Even though these methods are widely in use, to our knowledge, there is no systematic discussion of optimal displacement directions from the crystal's symmetry point of view nor a rigorous error analysis of such methods. Based on the group theory and point group symmetry of a crystal, we propose displacement directions, with an equivalent concept of the group of k , deduced directly in the Cartesian coordinates rather than the usual fractional coordinates, that maintain the theoretical maximum for the triple product V spanned by the three displacements to avoid possible severe roundoff errors. The proposed displacement directions are generated from a minimal set of irreducible atomic displacements that keep the required independent force calculations to a minimum. We find the error in the calculated force constants explicitly depends on the inverse of V and inaccuracy of the forces. Test systems such as Si, graphene, and orthorhombic Sb 2 S 3 are used to illustrate the method. Our symmetry-adapted atomic displacement method is shown to be very robust in treating low-symmetry cells with a large 'aspect ratio' due to huge differences in lattice parameters, use of a large vacuum height, or a very oblique unit cell due to unconventional choice of primitive lattice vectors. It is expected that our atomic displacement strategy can be used to address higher-order interatomic interactions to achieve good accuracy and efficiency. [ABSTRACT FROM AUTHOR]

We examine the renormalization of flavor-diagonal vector currents in lattice QCD with the aim of understanding and quantifying the systematic errors from nonperturbative artifacts associated with the use of intermediate momentum-subtraction schemes. Our study uses the highly improved staggered quark action on gluon-field configurations that include nf = 2+1+1 flavors of sea quarks, but our results have applicability to other quark actions. Renormalization schemes that make use of the exact lattice vector Ward-Takahashi identity for the conserved current also have renormalization factors, ZV, for nonconserved vector currents that are free of contamination by nonperturbative condensates. We show this by explicit comparison of two such schemes: that of the vector form factor at zero momentum transfer and the RI-SMOM momentum-subtraction scheme. The two determinations of ZV differ only by discretization effects (for any value of momentum transfer in the RI-SMOM case). The RI'-MOM scheme, although widely used, does not share this property. We show that ZV determined in the standard way in this scheme has O(1%) nonperturbative contamination that limits its accuracy. Instead we define an RI'-MOM ZV from a ratio of local to conserved vector current vertex functions and show that this ZV is a safe one to use in lattice QCD calculations. We also perform a first study of vector current renormalization with the inclusion of quenched QED effects on the lattice using the RI-SMOM scheme. [ABSTRACT FROM AUTHOR]

We study systematic uncertainties in the lattice QCD computation of the hadronic vacuum polarization (HVP) contribution to the muon g-2. We investigate three systematic effects: the finite volume (FV) effect, the cutoff effect, and integration scheme dependence. We evaluate the FV effect at the physical pion mass on two different volumes of (5.4 fm)4 and (10.8 fm)4 using the PACS10 configurations at the same cutoff scale. For the cutoff effect, we compare two types of lattice vector operators, which are local and conserved (point-splitting) currents, by varying the cutoff scale on a larger than (10 fm)4 lattice at the physical point. For the integration scheme dependence, we compare the results between the coordinate- and momentum-space integration schemes at the physical point on a (10.8 fm)4 lattice. Our result for the HVP contribution to the muon g-2 is given by aμhvp = 737 (9) (-18+13)×10-10 in the continuum limit, where the first error is statistical and the second one is systematic. [ABSTRACT FROM AUTHOR]

We present details of a lattice QCD calculation of the Bs → Ds* axial form factor at zero recoil using the highly improved staggered quark (HISQ) formalism on the second-generation MILC gluon ensembles that include up, down, strange and charm quarks in the sea. Using the HISQ action for all valence quarks means that the lattice axial vector current that couples to the W can be renormalized fully nonperturbatively, giving a result free of the perturbative matching errors that previous lattice QCD calculations have had. We calculate correlation functions at three values of the lattice spacing, and multiple b-quark masses, for physical c and s. The functional dependence on the b-quark mass can be determined and compared to heavy quark effective theory expectations, and a result for the form factor obtained at the physical value of the b-quark mass. We find FBs→Ds*(1) = hA1s(1) = 0.9020(96)stat(90)sys. This is in agreement with earlier lattice QCD results, which use NRQCD b quarks, with a total uncertainty reduced by more than a factor of 2. We discuss implications of this result for the B → D* axial form factor at zero recoil and for determinations of Vcb. [ABSTRACT FROM AUTHOR]