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We discuss initial value problems for time evolution equations in one dimensional space which are expressed by the lattice operators and propose some new equations to which complexity of solutions is of polynomial class. Novel type of expressions using shift operators and binary trees are applied for the derivation of solution. [ABSTRACT FROM AUTHOR]

Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment interaction found in most realistic physical models. In this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. The Kraus operators governing the time evolution can be converted into unitary matrices with minimal dilation guaranteed by the Sz.-Nagy theorem. This allows the evolution of the initial state through unitary quantum gates, while using significantly less resource than required by the conventional Stinespring dilation. We demonstrate the algorithm on an amplitude damping channel using the IBM Qiskit quantum simulator and the IBM Q 5 Tenerife quantum device. The proposed algorithm does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models. [ABSTRACT FROM AUTHOR]

For the first time high-order excitations (n>2) have been studied in three multireference couple cluster (MRCC) theories built on the wave operator formalism: (1) the state-universal (SU) method of Jeziorski and Monkhorst (JM) (2) the state-specific Brillouin-Wigner (BW) coupled cluster method, and (3) the state-specific MRCC approach of Mukherjee (Mk). For the H4, P4, BeH2, and H8 models, multireference coupled cluster wave functions, with complete excitations ranging from doubles to hextuples, have been computed with a new arbitrary-order string-based code. Comparison is then made to corresponding single-reference coupled cluster and full configuration interaction (FCI) results. For the ground states the BW and Mk methods are found, in general, to provide more accurate results than the SU approach at all levels of truncation of the cluster operator. The inclusion of connected triple excitations reduces the nonparallelism error in singles and doubles MRCC energies by a factor of 2–10. In the BeH2 and H8 models, the inclusion of all quadruple excitations yields absolute energies within 1 kcal mol-1 of the FCI limit. While the MRCC methods are very effective in multireference regions of the potential energy surfaces, they are outperformed by single-reference CC when one electronic configuration dominates. [ABSTRACT FROM AUTHOR]

In this paper, we establish some Trapezoid type inequalities for generalized fractional integral and related inequalities via exponentially convex functions. A novel and new approach is used to obtain these results for general Riemann Liouville fractional integrals. Various special cases are briefly discussed as applications of the main results. [ABSTRACT FROM AUTHOR]

Taking two and three shared set problems into background, the uniqueness problem of a meromorphic function together with its shift operator have been studied. Our results will improve a number of recent results in the literature. Some examples have been provided in the last section to show that certain conditions used in the paper, is the best possible. [ABSTRACT FROM AUTHOR]

We use the methods of Fourier-Jacobi harmonic analysis to study problems of the approximation of functions in weighted L2 function spaces on the half-axis [0,+∞). We prove analogues of Jackson's direct theorem for the moduli of smoothness of all orders constructed on the basis of Jacobi generalized translations. As a tool for approximation, we use functions with bounded spectrum. [ABSTRACT FROM AUTHOR]

Based on the recent development of sampling and reconstruction results for slowly time-varying single-input single-output channel operators, we derive sampling results in the multiple-input multiple-output setting where all subchannels satisfy an underspread condition, that is, their spreading functions are supported on individual sets of small measure. At the center of our work is the extension of the single-input single-output dual tiling condition to this setting; it characterizes which periodic weighted delta trains can be used to identify a given class of multiple-input multiple-output channel operators satisfying a spreading support constraint. Building on the dual tiling condition, we compute reconstruction formulas for the operator's symbol in closed form and discuss the problem of identifying multiple-input multiple-output operators where only restrictions in size, but not on location and geometry, of the subchannel spreading supports are known. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we extend the concept of absolutely Cesàro boundedness to the fractional case. We construct a weighted shift operator belonging to this class of operators, and we prove that if T is an absolutely Cesàro bounded operator of order α with 0 < α ≤ 1 , then ‖ T n ‖ = o (n α) , generalizing the result obtained for α = 1. Moreover, if α > 1 , then ‖ T n ‖ = O (n). We apply such results to get stability properties for the Cesàro means of bounded operators. [ABSTRACT FROM AUTHOR]

The shift operator matrix (SOM) (from which the exact, composite, grand canonical partition function can be obtained) is used to study a system consisting of simple, nearest-neighbor-interacting particles distributed on a planar M×N lattice. Such an SOM is transformed into the corresponding SOM for a cylindrical lattice of the same dimensions. Utilizing these results, we calculate and compare the physical adsorption isotherms for a M×∞ planar lattice (which has two free edges) and for a cylindrical lattice of the same size (which has no free edges) for several particle–particle interaction potentials and for several values of M. By further modification of the SOM for planar lattices, we show explicitly that the differences between the physical adsorption on these two lattices are reflected in anomalous particle densities along the free edges of the planar lattice. [ABSTRACT FROM AUTHOR]

Reports on the ab initio averaged relativistic effective core potentials (AREP) and spin-orbit (SO) operators for the elements Americium through element 118. Calculation of two sets for certain elements to provide AREP with varying core/valence space definition; Tabulation of the AREP and the SO operators as expansions in Gaussian-type functions.

Racetrack memory is a new technology, which utilizes magnetic domains along a nanoscopic wire in order to obtain extremely high storage density. In racetrack memory, each magnetic domain can store a single bit of information, which can be sensed by a reading port (head). The memory is structured like a tape, which supports a shift operation that moves the domains to be read sequentially by the head. In order to increase the memory’s speed, prior work studied how to minimize the latency of the shift operation, while the no less important reliability of this operation has received only a little attention. In this paper, we design codes, which combat shift errors in racetrack memory, called position errors, namely, shifting the domains is not an error-free operation and the domains may be over shifted or are not shifted, which can be modeled as deletions and sticky insertions. While it is possible to use conventional deletion and insertion-correcting codes, we tackle this problem with the special structure of racetrack memory, where the domains can be read by multiple heads. Each head outputs a noisy version of the stored data and the multiple outputs are combined in order to reconstruct the data. This setup is a special case of the reconstruction problem studied by Levenshtein, however, in our case, the position errors from different heads are correlated. We will show how to take advantage of this special feature of racetrack memories in order to construct codes correcting deletions and sticky insertions. In particular, under this paradigm, we will show that it is possible to correct, with at most a single bit of redundancy, $d$ deletions with $d+1$ heads if the heads are well separated. Similar results are provided for burst of deletions, sticky insertions, and combinations of both deletions and sticky insertions. [ABSTRACT FROM AUTHOR]

We treat synchronization for iterated function systems generated by diffeomorphisms on compact manifolds. Synchronization here means the convergence of orbits starting at different initial conditions when iterated by the same sequence of diffeomorphisms. The iterated function systems admit a description as skew product systems of diffeomorphisms on compact manifolds driven by shift operators. Under open conditions including transitivity and negative fiber Lyapunov exponents, we prove the existence of a unique attracting invariant graph for the skew product system. This explains the occurrence of synchronization. The result extends previous results for iterated function systems by diffeomorphisms on the circle, to arbitrary compact manifolds. [ABSTRACT FROM AUTHOR]

In digital signal processing, a shift-invariant filter can be represented as a polynomial expansion of a shift operation, that is, the $Z$ -transform representation. When extended to graph signal processing (GSP), this would mean that a shift-invariant graph filter can be represented as a polynomial of the shift matrix of the graph. Prior work shows that this holds under the shift-enabled condition that the characteristic and minimum polynomials of the shift matrix are identical. While the shift-enabled condition is often ignored in the literature, this letter shows that this condition is essential for the following reasons. First, we prove that this condition is not just sufficient but also necessary for any shift-invariant filter to be representable by the shift matrix. Moreover, we provide a counterexample showing that given a filter that commutes with a non-shift-enabled graph, it is generally impossible to convert the graph into a shift-enabled graph with a shift matrix still commuting with the original filter. The result provides a deeper understanding of shift-invariant filters when applied in GSP and shows that further investigation of shift-enabled graphs is needed to make them applicable to practical scenarios. [ABSTRACT FROM AUTHOR]

This paper deals with stability and local bifurcations of two-dimensional (2D) spatiotemporal discrete systems. Necessary and sufficient conditions for asymptotic stability of the systems are obtained. They prove to be more accurate than those in the current literature. Some definitions for the bifurcations of 2D spatiotemporal discrete systems are also given, and an illustrative example is provided to explain the new results. [ABSTRACT FROM AUTHOR]

We present a general method of solving the Cauchy problem for a linear parabolic partial differential equation of evolution type with variable coefficients and demonstrate it on the equation with derivatives of orders two, one and zero. The method is based on the Chernoff approximation procedure applied to a specially constructed shift operator. It is proven that approximations converge uniformly to the exact solution. [ABSTRACT FROM AUTHOR]

The equivalence transformations are applied to bring a system of nonlinear input-output (i/o) equations into a nonlinear equivalent of the Popov form, called the strong Popov form, under the assumption that the i/o equations already are in the strong row-reduced form. [ABSTRACT FROM AUTHOR]

In this article Jℱ-class operators are introduced and some basic properties of Jℱ-vectors are given. The Jℱ-class operators include the J-class operators and Jmix-class operators introduced by Costakis and Manoussos in 2008. This class also includes the Jwmix-class and Jerg-class operators defined by Zhang [2012]. Furthermore, for the unilateral weighted backward shifts on a Fréchet sequence space, we establish a criterion under which the shift operators belong to the Jℱ-class. From the criterion it is easy to obtain the existing criteria of hypercyclic backward shifts and of the topological mixing backward shifts. The obtained criterion also reveals the characteristic of Jℱ-class shift operators by the recurrence property. Meanwhile, we obtain infinite topological entropy when the shifts have stronger recurrence property, which generalizes the related results by Brian et al. in 2017. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the gauge transformations of the constrained q-deformed Kadomtsev–Petviashvili (q-KP) hierarchy. Different from the usual case, we have to consider the additional constraints on the Lax operator of the constrained q-deformed KP hierarchy, since the form of the Lax operator must be kept when constructing the gauge transformations. For this reason, the selections of generating functions in elementary gauge transformation operators TD and TI must be very special, which are from the constraints in the Lax operator. At last, we consider the successive applications of n-step of TD and k-step of TI gauge transformations. [ABSTRACT FROM AUTHOR]

In this paper, we characterize disk-cyclic and codisk-cyclic weighted pseudo-shifts on Banach sequence spaces, and consider the bilateral operator weighted shifts on ℓ2(Z,K) as a special case. Moreover, we present a counter-example to show that a result in [Y. X. Liang and Z. H. Zhou], Disk-cyclicity and Codisk-cyclicity of certain shift operators, Operators and Matrices, 9(2015), 831-846] is not correct. [ABSTRACT FROM AUTHOR]

Čučković and Paudyal characterized the lattice of invariant subspaces of the operator T in the Hardy–Hilbert space H 2 ( D ) , where they studied the special case (when p = 2 ) of the space S p ( D ) . We generalize some of their works to the general case when 1 ≤ p < ∞ and determine that M is an invariant subspace of T on H p ( D ) if and only if T z ( M ) is an invariant subspace of M z on S 0 p ( D ) , if and only if T z ( M ) is a closed ideal of S 0 p ( D ) . Furthermore, we provide certain Beurling-type invariant subspaces of M z on S p ( D ) and S 0 p ( D ) . Then, we investigate the boundedness of the operators T g and I g on S p ( D ) . Finally, we investigate the spectrum of multiplication operator M g on S p ( D ) , the isometric multiplication operators and the isometric zero-divisors on S p ( D ) . [ABSTRACT FROM AUTHOR]

While considering nonlinear coherent states with anti-holomorphic coefficients , we identify as first-associated Meixner-Pollaczek polynomials the orthogonal polynomials arising from shift operators which are defined by the sequence . We give a formula defining these polynomials by writing down their generating function. This also leads to construct a Bargmann-type integral transform whose kernel is given in terms of a Humbert's confluent hypergeometric function. [ABSTRACT FROM AUTHOR]

By exploiting a link between Bergman orthogonal polynomials and the Grunsky matrix, probably first observed by Kühnau (Ann Acad Sci Math 10:313-329, 1985), we improve on some recent results on strong asymptotics of Bergman polynomials outside the domain G of orthogonality, and on the entries of the Bergman shift operator. In our proofs, we suggest a new matrix approach involving the Grunsky matrix and use well-established results in the literature relating properties of the Grunsky matrix to the regularity of the boundary of G and the associated conformal maps. For quasiconformal boundaries, this approach allows for new insights for Bergman polynomials. [ABSTRACT FROM AUTHOR]

Estimates of the remainders of certain quadrature formulas are obtained, in particular, of quadrature formulas with nodes that are the zeros of Chebyshev polynomials of the first kind in classes of differentiable functions characterized by a generalized modulus of continuity. [ABSTRACT FROM AUTHOR]

The behavior of irrational rotations on the circle is one of the classical problems in the theory of dynamical systems. In this paper, we consider a weighted shift operator generated by irrational rotation. We give an estimate of the norm of the powers of the mentioned operator and show how it essentially depends on the arithmetic properties of the angle of rotation. The proof is based on some facts of the number theory. [ABSTRACT FROM AUTHOR]

The Sacker–Sell (also called dichotomy or dynamical) spectrumis an important notion in the stability theory of nonautonomous dynamical systems. For instance, when dealing with variational equations on the (nonnegative) half line, the set Σ+determines uniform asymptotic stability or instability of a solution and more general, it is crucial to construct invariant manifolds from the stable hierarchy. Compared to the spectrum associated to dichotomies on the entire line, Σ+has stronger and more flexible perturbation features. In this paper, we study continuity properties of the Sacker–Sell spectrum by means of an operator-theoretical approach. We provide an explicit example that the generally upper-semicontinuous set Σ+can suddenly collapse under perturbation, establish continuity on the class of equations with discrete spectrum and identify system classes having a continuous spectrum. These results for instance allow to vindicate numerical approximation techniques. [ABSTRACT FROM PUBLISHER]

A *-polynomial is a function on a complex Banach space X, which is a sum of so-called (p, q)- polynomials. In turn, for non-negative integers p and q, a (p, q)-polynomial is a function on X, which is the restriction to the diagonal of some mapping, defined on the Cartesian power Xp+q, which is linear with respect to every of its first p arguments and antilinear with respect to every of its other q arguments. The set of all continuous *-polynomials on X form an algebra, which contains the algebra of all continuous polynomials on X as a proper subalgebra. So, completions of this algebra with respect to some natural norms are wider classes of functions than algebras of holomorphic functions. On the other hand, due to the similarity of structures of *-polynomials and polynomials, for the investigation of such completions one can use the technique, developed for the investigation of holomorphic functions on Banach spaces. We investigate the Fr´echet algebra of functions on a complex Banach space, which is the completion of the algebra of all continuous *-polynomials with respect to the countable system of norms, equivalent to norms of the uniform convergence on closed balls of the space. We establish some properties of shift operators (which act as the addition of some fixed element of the underlying space to the argument of a function) on this algebra. In particular, we show that shift operators are well-defined continuous linear operators. Also we prove some estimates for norms of values of shift operators. Using these results, we investigate one special class of functions from the algebra, which is important in the description of the spectrum (the set of all maximal ideals) of the algebra. [ABSTRACT FROM AUTHOR]

We introduce matrix-valued weight functions of arbitrary size, which are analogues of the weight function for the Gegenbauer or ultraspherical polynomials for the parameter $$\nu >0$$ . The LDU-decomposition of the weight is explicitly given in terms of Gegenbauer polynomials. We establish a matrix-valued Pearson equation for these matrix weights leading to explicit shift operators relating the weights for parameters $$\nu $$ and $$\nu +1$$ . The matrix coefficients of the Pearson equation are obtained using a special matrix-valued differential operator in a commutative algebra of symmetric differential operators. The corresponding orthogonal polynomials are the matrix-valued Gegenbauer-type polynomials which are eigenfunctions of the symmetric matrix-valued differential operators. Using the shift operators, we find the squared norm, and we establish a simple Rodrigues formula. The three-term recurrence relation is obtained explicitly using the shift operators as well. We give an explicit nontrivial expression for the matrix entries of the matrix-valued Gegenbauer-type polynomials in terms of scalar-valued Gegenbauer and Racah polynomials using the LDU-decomposition and differential operators. The case $$\nu =1$$ reduces to the case of matrix-valued Chebyshev polynomials previously obtained using group theoretic considerations. [ABSTRACT FROM AUTHOR]

We study a special class of quasi-cyclic codes, obtained from a cyclic code over an extension field of the alphabet field by taking its image on a basis. When the basis is equal to its dual, the dual code admits the same construction. We give some examples of self-dual codes and LCD codes obtained in this way. [ABSTRACT FROM AUTHOR]

Defining a sound shift operator for graph signals, similar to the shift operator in classical signal processing, is a crucial problem in graph signal processing (GSP), since almost all operations, such as filtering, transformation, prediction, are directly related to the graph shift operator. We define a set of energy-preserving shift operators that satisfy many properties similar to their counterparts in classical signal processing, but are different from the shift operators defined in the literature, such as the graph adjacency matrix and Laplacian matrix based shift operators, which modify the energy of a graph signal. We decouple the graph structure represented by eigengraphs and the eigenvalues of the adjacency matrix or the Laplacian matrix. We show that the adjacency matrix of a graph is indeed a linear shift invariant (LSI) graph filter with respect to the defined shift operator. We further define autocorrelation and cross-correlation functions of signals on the graph, enabling us to obtain the solution to the optimal filtering on graphs, i.e., the corresponding Wiener filtering on graphs and the efficient spectra analysis and frequency domain filtering in parallel with those in classical signal processing. This new shift operator based GSP framework enables the signal analysis along a correlation structure defined by a graph shift manifold as opposed to classical signal processing operating on the assumption of the correlation structure with a linear time shift manifold. Several illustrative simulations are presented to validate the performance of the designed optimal LSI filters. [ABSTRACT FROM PUBLISHER]

Through introducing the alternating direction implicit (ADI) technique and the memory-optimized algorithm to the shift operator (SO) finite difference time domain (FDTD) method, the memory-optimized SO-ADI FDTD for nonmagnetized collisional plasma is proposed and the corresponding formulae of the proposed method for programming are deduced. In order to further the computational efficiency, the iteration method rather than Gauss elimination method is employed to solve the equation set in the derivation of the formulae. Complicated transformations and convolutions are avoided in the proposed method compared with the Z transforms (ZT) ADI FDTD method and the piecewise linear JE recursive convolution (PLJERC) ADI FDTD method. The numerical dispersion of the SO-ADI FDTD method with different plasma frequencies and electron collision frequencies is analyzed and the appropriate ratio of grid size to the minimum wavelength is given. The accuracy of the proposed method is validated by the reflection coefficient test on a nonmagnetized collisional plasma sheet. The testing results show that the proposed method is advantageous for improving computational efficiency and saving computer memory. The reflection coefficient of a perfect electric conductor (PEC) sheet covered by multilayer plasma and the RCS of the objects coated by plasma are calculated by the proposed method and the simulation results are analyzed. [ABSTRACT FROM AUTHOR]

In this paper, based on some properties of nabla exponential function êp(t, t0) and shift operators δ± on time scales, by using Krasnoselskii's fixed point theorem in a cone and some mathematical methods, sufficient conditions are established for the existence and nonexistence of positive periodic solutions in shifts δ± for a nabla dynamic system of Nicholson's blowflies on time scales of the following form: ... where t ∈ T, T ⊂ R is a periodic time scale in shifts δ± with period P ∈ [t0, ∞)T and t0 ∈ T is nonnegative and fixed. Finally, two numerical examples are presented to illustrate the feasibility and effectiveness of the results. [ABSTRACT FROM AUTHOR]

In order to analyze the electromagnetic characteristics of plasma more efficiently, a novel FDTD called R-SO-ADI FDTD is proposed. The proposed method which is based on the shift operator technique has clear conceptions and simple formulae, and it saves CPU time and reduces the storage of the field components through combining the reduced formulation technique and the ADI scheme. Calculation results of the RCS of a perfectly conducting cylinder coated by plasma confirm the validity of the proposed method. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to investigate distributionally n-scrambled sets for weighted shift operators. We prove that the unilateral weighted shift operator admits densely invariant distributionally n- ε-scrambled linear manifolds for any ε ∈ (0, 1) and any integer n ⩾ 2, showing that this operator can exhibit maximal distributional n-chaos on a dense invariant linear manifold. Analogous results for the bilateral weighted shift operator are also obtained. [ABSTRACT FROM AUTHOR]

We study the specification property and infinite topological entropy for two specific types of linear operators: translation operators on weighted Lebesgue function spaces and weighted backward shift operators on sequence F -spaces. It is known, from the work of Bartoll, Martínez-Giménez, Murillo-Arcila, and Peris, that for weighted backward shift operators, the existence of a single non-trivial periodic point is sufficient for specification. We show this also holds for translation operators on weighted Lebesgue function spaces. This implies, in particular, that for these operators, the specification property is equivalent to Devaney chaos. We show that these forms of chaos (unsurprisingly) imply infinite topological entropy, but that (surprisingly) the converse does not hold. [ABSTRACT FROM AUTHOR]

Recently, multiple-stacked pancake coils wound with rare-earth barium copper oxide (REBCO) tapes are expected to apply for nuclear magnetic resonance (NMR)/MRI magnets. Since REBCO tapes are very expensive, REBCO magnets should be optimally designed so as to minimize the winding volume. Surely, a highly homogeneous magnetic field is also required for NMR/MRI magnets. To achieve the accurate homogeneity of REBCO magnets, it is necessary to compute the contribution of all REBCO layers one by one, because currents carry over very thin area compared with a whole magnet cross section. However, NMR/MRI magnets generating high-magnetic field usually consist of multiple-stacked REBCO pancake coils, and each pancake coil has >300 turns. To evaluate the field homogeneity contributed by every REBCO layer, therefore, it is necessary to repeatedly compute more than ten thousand times as one magnet shape. In a conventional optimization algorithm, it is necessary to iterate more than one million times for the optimal design of an NMR or MRI magnet. Such an iterative computation is not realistic. Based on the backgrounds, we present a fast computation method using the shift operator of spherical harmonics. In addition, to confirm the validity of the proposed method, it was applied to the shape optimization of 1.5-T MRI magnet. In this paper, the optimization result and computation time are also shown. [ABSTRACT FROM PUBLISHER]

The concept of cyclic tridiagonal pairs is introduced, and explicit examples are given. For a fairly general class of cyclic tridiagonal pairs with cyclicity N , we associate a pair of ‘divided polynomials’. The properties of this pair generalize the ones of tridiagonal pairs of Racah type. The algebra generated by the pair of divided polynomials is identified as a higher-order generalization of the Onsager algebra. It can be viewed as a subalgebra of the q -Onsager algebra for a proper specialization at q the primitive 2 N th root of unity. Orthogonal polynomials beyond the Leonard duality are revisited in light of this framework. In particular, certain second-order Dunkl shift operators provide a realization of the divided polynomials at N = 2 or q = i . [ABSTRACT FROM AUTHOR]

To overcome the limitations of radar cross section characteristic, a method using detection probability as an indicator to evaluate plasma stealth effectiveness is proposed in this paper. Based on shift operator finite-difference time-domain method, the distorted waveform of linear frequency modulation radar echo is obtained when the targets coated with plasma. Then, by making a comparison between outputs of pulse compression with and without plasma, the peak instantaneous signal-to-noise ratio (SNR) loss is calculated. According to the signal detection theory, the relationship between plasma parameters and radar detection probability is built up through the SNR loss, in which the attenuation of radar echo and the mismatch loss of pulse compression are both considered. Finally, effects of plasma parameters including electron density, collision frequency, and radar frequency on the probability of detection have been studied systematically. By adopting detection probability Pd \le 0.1 as a valid criterion, the effective plasma parameters for different radar frequencies are given as a guide when using plasma for stealth application. [ABSTRACT FROM PUBLISHER]

This paper discusses the improvement of the numerical dispersion characteristics of alternating direction implicit (ADI) finite-difference time-domain (FDTD) aimed at acquiring more accurate electromagnetic information of plasma. Through adding the optimization method, which is based on the optimization of spatial derivative to the (2, 4) stencil ADI FDTD, the optimized (2, 4) stencil ADI FDTD is proposed, and its unconditional stability is proved theoretically. The phase velocity error of the optimized (2, 4) stencil ADI FDTD versus propagation angle and grid density is investigated. In addition, the Runge–Kutta auxiliary differential equation (RKADE) scheme for tackling the constitutive relation equation of plasma is deduced, which is without additional storage occupation and computational burden compared with ADE scheme. Its numerical conductivity error is analyzed under different incident frequencies and electron collision frequencies. Through incorporating the RKADE scheme into the optimized (2, 4) stencil ADI FDTD, the optimized (2, 4) stencil RKADE-ADI FDTD is presented. The accuracy and relatively wideband capability of the proposed method is validated by two numerical experiments. [ABSTRACT FROM PUBLISHER]

We establish some properties of the spectrum of the shift operator with nonnegative coefficients on the space of bounded functions on a locally compact commutative group and use them to study the asymptotic properties of linear discrete systems with this operator. [ABSTRACT FROM AUTHOR]

A subshift on a group G is a closed, G -invariant subset of A G , for some finite set A . It is said to be a subshift of finite type (SFT) if it is defined by a finite collection of “forbidden patterns”, to be strongly aperiodic if all point stabilizers are trivial, and weakly aperiodic if all point stabilizers are infinite index in G . We show that groups with at least 2 ends have a strongly aperiodic SFT, and that having such an SFT is a QI invariant for finitely presented groups. We show that a finitely presented torsion free group with no weakly aperiodic SFT must be QI-rigid. The domino problem on G asks whether the SFT specified by a given set of forbidden patterns is empty. We show that decidability of the domino problem is a QI invariant. [ABSTRACT FROM AUTHOR]

This paper is concerned with a higher-dimensional neutral nabla dynamic equation on time scales. Based on the theory of calculus on time scales, we first study some properties of the nabla exponential function êA (t; t0) and shift operators δ±; then by using Krasnoselskii's fixed point theorem and contraction mapping principle as well as the obtained results, sufficient conditions are established for the existence of nonzero periodic solutions in shifts δ± of the equation as the following form: x∇ (t) = A(t)x(t) + f∇ (t, x(t)) + b(t)g(t, x(τ (t))); t ∈ 핋, where A(t) = (aij (t))n x n is a nonsingular matrix with continuous real-valued functions as its elements. Finally, numerical examples are presented to illustrate the applicability of the theoretical results. Index Terms--periodic solution; neutral nabla dynamic equation; shift operator; time scale. [ABSTRACT FROM AUTHOR]

A complex scalar λ is said to be an extended eigenvalue for an operator A on a Hilbert space H if there is a non-zero operator X such that A X = λ X A , and in that case, X is said to be an extended eigenoperator. It is shown that if a bilateral weighted shift has a non-unimodular extended eigenvalue then every extended eigenoperator for A is strictly lower triangular. Also, it is shown that the set of the extended eigenvalues for an injective bilateral weighted shift is either C ∖ D or C ∖ { 0 } or D ‾ ∖ { 0 } , or T , and some examples are constructed in order to show that each of the four shapes does happen. Further, it is shown that the set of the extended eigenvalues for an injective bilateral weighted shift with an even sequence of weights is either C \ { 0 } or T , and that the set of the extended eigenvalues for an invertible bilateral weighted shift is T . Finally, a factorization result is provided for the extended eigenoperators corresponding to a unimodular extended eigenvalue of an injective bilateral weighted shift. [ABSTRACT FROM AUTHOR]

In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coin and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated. [ABSTRACT FROM AUTHOR]

A bounded linear operator T on a Hilbert space is an isometric N-Jordan operator if it can be written as A + Q, where A is an isometry and Q is a nilpotent of order N such that AQ = QA. In this paper, we will show that the only isometric N-Jordan weighted shift operators are isometries. This answers a question recently raised. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the ℓ ∞ -stability of infinite dimensional discrete autonomous systems, whose dynamics is governed by a Laurent polynomial matrix A ( σ , σ − 1 ) in shift operator σ on vector valued sequences. We give necessary and sufficient conditions for the ℓ ∞ -stability of such systems. We also give easy to check tests to conclude or to rule out the ℓ ∞ -stability of such systems. [ABSTRACT FROM AUTHOR]

An estimate of the spectral radius of functional operators generated by operators of multiplication and shift operators in the space of continuous vector functions on the interval is given. It is assumed that shifts have fixed points only at both ends of the interval and belong to one type, i.e., they are either left or right shifts. [ABSTRACT FROM AUTHOR]

We consider the generalized shift operator associated with the Laplace-Bessel differential operator The maximal operator ( B-maximal operator) and the Riesz potential ( B-Riesz potential), associated with the generalized shift operator are investigated. We prove that the B-maximal operator and the B-singular integral operator are bounded from the generalized weighted B-Morrey space to for all , . Furthermore, we prove that the B-Riesz potential , , is bounded from the generalized weighted B-Morrey space to , where , , and . [ABSTRACT FROM AUTHOR]

The Sacker-Sell (also called dichotomy or dynamical) spectrum $$\varSigma $$ is a fundamental concept in the geometric, as well as for a developing bifurcation theory of nonautonomous dynamical systems. In general, it behaves merely upper-semicontinuously and a perturbation theory is therefore delicate. This paper explores an operator-theoretical approach to obtain invariance and continuity conditions for both $$\varSigma $$ and its dynamically relevant subsets. Our criteria allow to avoid nonautonomous bifurcations due to collapsing spectral intervals and justify numerical approximation schemes for $$\varSigma $$ . [ABSTRACT FROM AUTHOR]

In this paper, we discuss a linear operator T defined in Riordan group R by using the upper shift matrix U and lower shift matrix U T , namely for each R ∈ R , T : R ↦ U R U T . Some isomorphic properties of the operator T and the structures of its range sets for different domains are studied. By using the operator T and the properties of Bell subgroup of R , the Riordan type Chu–Vandermonde identities and the Riordan equivalent identities of Format Last Theorem and Beal Conjecture are shown. The applications of the shift operators to the complementary Riordan arrays and to the Riordan involutions and Riordan pseudo-involutions are also presented. [ABSTRACT FROM AUTHOR]

In this paper, some characterizations about orbit invariants, p-scrambled points and scrambled sets are obtained. Applying these results solves a conjecture and two problems given in [X. Fu, Y. You, Nonlinear Anal., 71 (2009), 2141-2152]. [ABSTRACT FROM AUTHOR]