In this paper, a new meshfree approach is proposed for the three-dimensional free vibration analysis of laminated composite elliptical and paraboloidal shells of revolution. The three-dimensional theory of elasticity has been applied to formulations for free vibration analysis of laminated composite elliptical and paraboloidal shells of revolution. The field function is approximated by a new Tchebychev-point

It has been shown that all the known binary Golay complementary sequences of length \(2^m\) can be obtained by a single binary Golay complementary array of dimension m and size \(2\times 2 \times \cdots \times 2\) which can be represented by a Boolean function. However, the construction of new binary Golay complementary sequences of length \(2^m\) or Golay complementary arrays remains an open problem

Let a strongly stable norm ∥⋅∥ on the set Mn of complex n-by-n matrices be given, which means that ∥Ak∥≤∥A∥k for all A∈Mn and all k=1,2,…. Furthermore, let f(x)=∑k=0∞ckxk be a power series with nonnegative coefficients ck≥0 and radius of convergence R>0. If ∥I∥>1, we additionally suppose that c0=f(0)=0. We aim to characterize those A with ∥A∥0 for all k≥1.

We first review a constructive proof of Gabriel's theorem on the representation finiteness of Dynkin quivers for the case of an equioriented quiver of type D. Then, we proceed to the analysis of polystable representations of such a quiver, give a direct proof of the characterisation of its semistable representations, and explain how we may recover a theorem of Abeasis and Koike from this characterisation

Using some concepts and tools from Functional Analysis, we express explicit forms of ‘eigenvectors’ of two Toeplitz operators: An operator of multiplicity one, which appears e.g. in Autoregressive Process, and a banded operator of high multiplicity. Then we investigate the approximate eigenvectors of their associated Toeplitz matrices of large sizes, and after some numerical experiments, the paper

This study is devoted to the evaluation of dynamic impedance of the arch dam foundation embedded in a complex layered half-space. For this purpose, a modified scaled boundary finite element method (SBFEM) is developed for modeling the far field. In order to overcome the limits of scaling requirements of the original SBFEM, a scaled boundary transformation based on a scaling surface is developed, which

Given \(m, n, q\in \mathbb {N}\) such that q is a prime power and \(m\ge 3\), \(a\in \mathbb {F}_q\), we establish a sufficient condition for the existence of a primitive pair \((\alpha , f(\alpha ))\) in \(\mathbb {F}_{q^m}\) such that \(\alpha \) is normal over \(\mathbb {F}_q\) and \(\text {Tr}_{\mathbb {F}_{q^m}/\mathbb {F}_q}(\alpha ^{-1})=a\), where \(f(x)\in \mathbb {F}_{q^m}(x)\) is a rational

An efficient finite element method-boundary element method (FEM-BEM) is proposed for electromagnetic analysis of inhomogeneous objects. The problem domain is discretized and evaluated with FEM, and the BEM introduces a truncated boundary on the surface of the domain utilizing boundary integral equations (BIEs) technique. To guarantee the precision, much dense discretization is usually required when

An innovative generalized Layer-Wise (LW) approach is proposed for the modal analysis of anisotropic doubly-curved shells with an arbitrary shape by employing the Generalized Differential Quadrature (GDQ) method. The geometrical description of shell structures can be traced from both the differential geometry and mapping technique based on a proper definition of the blending functions. The kinematic

An antinorm is a concave nonnegative homogeneous functional on a convex cone. It is shown that if the cone is polyhedral, then every antinorm has a unique continuous extension from the interior of the cone. The main facts of the duality theory in convex analysis, in particular, the Fenchel–Moreau theorem, are generalized to antinorms. However, it is shown that the duality relation for antinorms is

We extend the special affine Fourier transform in the context of quaternion valued functions and study its properties including an uncertainty principle. The same transform is studied on a suitably constructed Boehmian space.

In this paper, we define and classify split quaternion operators. Then, we show that the split quaternion product of a split quaternion operator and a curve, which lies on Lorentzian unit sphere or on hyperbolic unit sphere, parametrizes a ruled surface in the 3-dimensional Minkowski space \(\mathbb {E}_{1}^{3}\) if the vector part of the operator is perpendicular to the position vector of the spherical

In this paper, the fictitious stress method (FSM) as a meshless technique is extended to solve problems with inhomogeneities. The Eshelby's equivalent inclusion theory is coupled with the FSM as a set of particular solutions. There is no domain discretization as analytical solutions for inclusions are employed. The coupling procedure is presented, and the solution is carried out either in a direct

Higher degree forms are homogeneous polynomials of degree d>2, or equivalently symmetric d-linear spaces. This paper is mainly concerned about the algebraic structure of the centres of higher degree forms with applications specifically to direct sum decompositions, namely expressing higher degree forms as sums of forms in disjoint sets of variables. We show that the centre algebra of almost every form

For a positive trace-class operator C and a bounded operator A, we provide an explicit description of the closure of the orbit-closed C-numerical range of A in terms of those operators submajorized by C and the essential numerical range of A. This generalizes and subsumes recent work of Chan, Li and Poon for the k-numerical range, as well as some of our own previous work on the orbit-closed C-numerical

Grouting is a typical HM (hydro-mechanical) coupling process between slurry and rock and widely used in underground engineering to reinforce the strength of fractured rock mass. In present work, based on numerical manifold method (NMM), an NMM-HM grouting model is proposed to investigate slurry flowing and analyze grouting efficiency. In this NMM-HM grouting model, the slurry flows in fractures and

The meshless numerical manifold method (MNMM) inherits two covers of the numerical manifold method. A mathematical cover is composed of nodes' influence domains and a physical cover consists of physical patches, which are produced through cutting mathematical cover by physical boundaries. Because two covers are adopted, MNMM can naturally and uniquely solve both the continuous and discontinuous problems

In this paper, G-majorization inequalities are proven for the gradients of two Gateaux differentiable G-increasing functions defined on a real linear space endowed with the structure of an Eaton triple. Such inequalities can be interpreted as a monotonicity property of certain operators and functionals with respect to a special preorder on the class of all G-increasing functions. The notion of a c-strongly

In this paper, the improved interpolating dimension splitting element-free Galerkin (IIDSEFG) method based on nonsingular weight functions is proposed to solve 3D wave equations. By utilizing the dimension splitting method (DSM), a 3D wave equation is divided into a series of 2D problems. For 2D wave equations, the improved interpolating moving least-squares (IIMLS) method based on nonsingular weight

An improved grain-based numerical manifold method (NMM) is developed to investigate deformation and damage of intact rocks at the meso‑scale. The grain boundaries are embedded into the numerical manifold method using a random Voronoi tessellation technique to approximate the microstructure of rocks at the meso‑scale. To enhance efficiency, an improved contact loop updating algorithm is proposed, which

For n≥2, let Sn∗={(0,n,0),(0,n−1,1),(1,n−1,0),(n,0,0),(n−1,0,1),(n−1,1,0)}. A zero-nonzero pattern A of order n allows Sn∗ if Sn∗⊆i(A), the inertia set of A, and requires Sn∗ if Sn∗=i(A). The study of zero-nonzero patterns allowing Sn∗ was introduced by Berliner et al. [Inertia sets allowed by matrix patterns. Electron J Linear Algebra. 2018;34:343–355]. In this paper, we give characterizations of

We give some examples of EP and non-EP operators to show that the main results of Mohammadzadeh Karizaki et al. [Some results about EP modular operators. Linear Multilinear Algebra. DOI:10.1080/03081087.2020.1844613] are not correct even in the case of Hilbert spaces.

Many techniques in linear algebra make use of properties of inner product spaces and orthogonality. However, when we are working with a finite field such as Fqm, where q is a prime power, we cannot define an inner product space since there is no way to define positivity in the finite fields. We can still define a bilinear form ⟨,⟩:Fqm→Fqm and recover many, but not all, of the techniques and results

All-or-nothing transforms have been defined as bijective mappings on all s-tuples over a specified finite alphabet. These mappings are required to satisfy certain “perfect security” conditions specified using entropies of the probability distribution defined on the input s-tuples. Alternatively, purely combinatorial definitions of AONTs have been given, which involve certain kinds of “unbiased arrays”

In this paper, we study binomials having the form \(x^r(a+x^{3(q-1)})\) over the finite field \(\mathbb {F}_{q^2}\) with \(q=2^m\), and determine all the r’s and coefficients a’s making them permutations. For even m or odd m with \(3\not \mid m\), we prove that the characterization is necessary and sufficient. For the case of odd m and \(3\mid m\), we prove that the corresponding sufficient condition

As an integral representation for holomorphic functions, Cauchy integral formula plays a significant role in the function theory of one complex variable and several complex variables. In this paper, using the idea of several complex analysis we construct the Cauchy kernel in universal Clifford analysis, which has generalized complex differential forms with universal Clifford basic vectors. We establish

The human annulus fibrosus (HAF) is the major component in response to external forces for the intervertebral disk (IVD), which maintains the stability and flexibility of human spine. It can be assumed to be an anisotropic nearly incompressible hyperelastic composite consisting of collagen fibers and matrix in the numerical simulations of biomechanics. However, due to the geometric complexity and material

The bending behaviour of systems of straight elastic beams at different scales is investigated by the well-posed stress-driven nonlocal continuum mechanics. An effective computational methodology, based on nonlocal two-noded finite elements, is developed in order to take accurately into account long-range interactions present in the whole structural domain. The idea consists in partitioning the beam

Efficient and accurate evaluation of free-surface Green's function is the key to hydrodynamic problems solved by boundary element method (BEM). However, so far, there is still no unified numerical method that can accurately approximate all kinds of free-surface Green's functions. In theory, machine learning can be used to approximate any function with high accuracy. In the present study, neural networks

In this paper, the integral Cayley graphs over the nonabelian group V8n=⟨a,b|a2n=b4=1,ba=a−1b−1,b−1a=a−1b⟩ are studied, where n is an odd integer. Character tables of V8n are used to provide a necessary and sufficient condition for the integrality of such Cayley graphs. This is then translated into a simple necessary and sufficient condition for integrality in terms of the associated Boolean algebra

The application of flags to network coding has been introduced recently, see e.g. Liebhold et al. (Des Codes Cryptogr, 86(2):269-284, 2018). It is a variant to random linear network coding and explicit routing solutions for given networks. Here we study lower and upper bounds for the maximum possible cardinality of a corresponding flag code with given parameters.

Semi-bent functions play an important role in symmetric ciphers and sequence designs. So far, there are few studies related to the construction of vectorial semi-bent functions even though lots of work has been done on single-output semi-bent functions. In this paper, three classes of balanced vectorial semi-bent functions are presented with varying cryptographic properties. The classes denoted \({{\mathcal

By adopting the scaling functions of the B-spline wavelet on the interval (BSWI) as interpolation functions, a wavelet-based boundary element method (BEM) model is constructed to compute the band structures of two-dimensional photonic crystals (2D PCs), which are composed of square or triangular lattices with arbitrarily shaped inclusions. The boundary integral equations of both the matrix and inclusion

In this paper, the Fragile Points Method (FPM) has been extended to solve the two-dimensional hyperbolic telegraph equation with specified initial and boundary conditions. Based on a naturally partitioned domain with scattered nodes and the Voronoi Diagram, the discretized FPM equations are derived by a Galerkin weak-form in the spatial domain and a finite difference scheme in the time domain. For

Kirkman triple systems (KTSs) are among the most popular combinatorial designs and their existence has been settled a long time ago. Yet, in comparison with Steiner triple systems, little is known about their automorphism groups. In particular, there is no known congruence class representing the orders of a KTS with a number of automorphisms at least close to the number of points. We partially fill

It is an interesting problem to determine the parameters of BCH codes, due to their wide applications. In this paper, we determine the dimension and the Bose distance of five families of the narrow-sense primitive BCH codes with the following designed distances: (1) \(\delta _{(a,b)}=a\frac{q^m-1}{q-1}+b\frac{q^m-1}{q^2-1}\), where m is even, \(0\le a \le q-1\), \(1\le b \le q-1\), \(1\le a+b \le q-1\)

In this article, we introduce local completely positive k-linear maps between locally C∗-algebras and obtain Stinespring type representation by adopting the notion of ‘invariance’ defined by J. Heo for k-linear maps between C∗-algebras. Also, we supply the minimality condition to make certain that minimal representation is unique up to unitary equivalence. As a consequence, we prove Radon–Nikodým theorem

In this paper, as a generalization of Urquhart's formulas, we present a full description of the sets of inner inverses and (B,C)-inverses over an arbitrary field. In addition, identifying the matrix-vector space with an affine space, we analyse geometrical properties of the main generalized inverse sets. We prove that the set of inner inverses, and the set of (B,C)-inverses, form affine subspaces and

Recently, the authors obtained the Schur multiplier, the non-abelian tensor square and the non-abelian exterior square of d-generator generalized Heisenberg Lie algebras of rank 12d(d−1). Here, we intend to obtain the same results for d-generator generalized Heisenberg Lie algebras of rank t when 12d(d−1)−3≤t≤12d(d−1)−1. Then, as a result, we give similar consequences for a nilpotent Lie algebra L

Stern’s diatomic sequence is a well-studied and simply defined sequence with many fascinating characteristics. The binary signed-digit representation of integers is an alternative representation of integers with much use in efficient computation, coding theory and cryptography. We link these two ideas here, showing that the number of i-bit binary signed-digit representations of an integer n with \(n<2^i\)

A simple \((2,3,v)\) trade is a pair \((T_0,T_1)\) of disjoint sets of \(3\)-subsets (blocks) of a \(v\)-set such that any two elements meet the same number of times in the blocks of \(T_0\) and the blocks of \(T_1\). The size of \(T_0\) equals the size of \(T_1\) and is called the volume of the trade. In this paper, for \(v=4n+2\), we introduce a new partitioning of the set of all 3-subsets of a v-set

In this paper, we address the problem of computing the nearest linearly structured polynomial matrix with prescribed distinct eigenvalues. The problem deals with the computation of the minimal structured perturbation to the coefficient matrices so that the perturbed polynomial matrix has the prescribed eigenvalues and is the nearest to the given polynomial matrix. In recent years, a series of papers

In this note, we study the induced p-norm of circulant matrices A(n,±a,b), acting as operators on the Euclidean space Rn. For circulant matrices whose entries are nonnegative real numbers, in particular for A(n,a,b), we provide an explicit formula for the p-norm, 1≤p≤∞. The calculation for A(n,−a,b) is more complex. The 2-norm is precisely determined. As for the other values of p, two different categories

The classical Ostrowski Theorem gives an estimate for the eigenvalues of a matrix by a union of some disks. In this paper, we present the Ostrowski Theorem on the localization of the spectrum of an operator matrix.

A k-tree is a spanning tree in which every vertex has degree at most k. In this paper, we provide a sufficient condition for the existence of a k-tree in a connected graph with fixed order in terms of the adjacency spectral radius and the signless Laplacian spectral radius, respectively. Also, we give a similar condition for the existence of a perfect matching in a balanced bipartite graph with fixed

Let Ai,P, i=1,…,m, be n by n complex matrices such that each Ai is positive definite. It is shown, among other inequalities, that If 0

In this paper we consider and solve the General Matrix Pencil Completion Problem (GMPCP) under single rank restrictions. These constraints are less limiting than any other restrictions on the GMPCP studied in the past. Thus, the obtained results directly generalize the existing results in the literature on the GMPCP. Finally, as one direct corollary of the main results, we obtain a novel result on

In this paper, we study the problem of decomposing a given tensor into a tensor train such that the tensors at the vertices are orthogonally decomposable. When the tensor train has length two, and the orthogonally decomposable tensors at the two vertices are symmetric, we recover the decomposition by considering random linear combinations of slices. Furthermore, if the tensors at the vertices are symmetric

The second moment of inertia of a continuous axisymmetric object with an arbitrary shape made of a nonhomogeneous material is usually calculated by dividing it into small domains. However, it is a burdensome process to specify the density of the small domains. In this paper, a technique of easily calculating the second moment of inertia of an axisymmetric nonhomogeneous material using boundary integral

In this research, a combination of the numerical manifold method (NMM) and boundary element method (BEM) is presented for solving plane elasticity problems to benefit from the advantages of both methods. For this goal, the domain of the problems is divided into two regions, each region is analyzed separately, and finally, equilibrium and compatibility conditions are controlled in the interface by the

A two-dimensional grouting model considering hydromechanical coupling and fracturing in fractured rock is proposed and implemented in an GPU parallel multiphysics finite element-discrete element software named MultiFracs. The model can simulate the grout flows in existing and induced fractures in the rock media. The fracture network is represented by broken joint elements, which is updated to simulate

Landslide-induced surges, as a complex type of fluid-solid coupling problem, are widespread in mountain regions and cause disastrous consequences. In order to reproduce the entire process of landslide-induced surge, by taking full advantage of material point method (MPM) in simulating large deformation of soil and gravity-driven flow of water, the two-phase double-point material point method (TPDP-MPM)

Numerical simulation for large deformation problems of saturated soil poses an ongoing challenge since it requires the capabilities of modeling large deformations, interactions between solid skeleton and pore water, as well as fluidization behaviors. A hydro-mechanical coupled B-spline material point method is developed to simulate large deformations of saturated soils. Based on Biot's mixture theory

A local gradient smoothing method(LGSM) in the framework of meshless theory is developed for implementing vibration analysis of closed laminate conical, cylindrical shells and annular plates. Based on the theoretical assumptions of the first-order laminated structure, the governing equations and boundary condition equations of the structure elements of revolution are derived and numerically discretized

The two-dimensional shallow water equations (SWEs) are a hyperbolic system of first-order nonlinear partial differential equations which have a characteristic of strong gradient. In this study, a newly-developed numerical model, based on local radial point interpolation method (LRPIM), is adopted to simulate discontinuity in shallow water flows. In order to accurately capture the information of wave

This paper describes a new efficient approach based on the concept of reduced basis for large deformation analysis. The domain problem is discretized using the meshfree particle radial point interpolation method (RPIM), which inherently possesses the Kronecker’s delta property. Meshless numerical integration is evaluated by the Cartesian transformation method (CTM), which enhances the performance of

Functions with low c-differential uniformity were proposed in 2020 and attracted lots of attention, especially the PcN and APcN functions, due to their applications in cryptography. The objective of this paper is to study PcN and APcN functions. As a consequence, we propose two classes of PcN functions and three classes of APcN functions by using the cyclotomic technique and the switching method. In

Total Lagrangian - Smoothed Particle Hydrodynamics (TL-SPH) is a classical algorithm to improve the tensile instability encountered in the conventional Eulerian kernel-based SPH method for solid mechanics. Meanwhile, the gradient correction usually is employed in TL-SPH to enhance the consistency of approximation, which would generate unavoidable time costs. Therefore, a simplified gradient correction

In this paper, to find the numerical solution of the linear systems with the non-Hermitian positive definite matrix, a preconditioned two-sweep shift splitting (PTSS) iteration method is introduced and its convergent conditions are discussed. When the PTSS method is used as a preconditioner, the eigenvalue distribution of the corresponding preconditioned matrix is given. Numerical experiments are reported

A bounded linear operator T on a complex Banach space X is superconvex-cyclic, if for some vector x in the space, C.co(orb(T,x)) is dense. Here, co(orb(T,x)) means the convex hull of {Tnx:n≥0}. In this paper, we give necessary conditions for the superconvex-cyclicity of an operator in terms of the point spectrum of its adjoint. Also, we prove that positive multiples of superconvex-cyclic operators