In this paper the Cayley–Laplace operator \(\Delta _{xu}\) is considered, a rotationally invariant differential operator which can be seen as a generalisation of the classical Laplace operator for functions depending on wedge variables \(X_{ab}\) (the minors of a matrix variable). We will show that the Bessel–Clifford function appears naturally in the framework of two-wedge variables, and explain how

Complex orthogonal designs (CODs) have been used to construct space-time block codes. Its real analog, real orthogonal designs, or equivalently, sum of squares composition formula, have a long history in mathematics. Driven by some practical considerations, Adams et al. (IEEE Trans Info Theory, 57(4):2254–2262, 2011) introduced the definition of balanced complex orthogonal designs (BCODs). The code

A (v, k, t) packing of size b is a system of b subsets (blocks) of a v-element underlying set such that each block has k elements and every t-set is contained in at most one block. P(v, k, t) stands for the maximum possible b. A packing is called abundant if \(b> v\). We give new estimates for P(v, k, t) around the critical range, slightly improving the Johnson bound and asymptotically determine the

A parametrization, given by the Euler angles, of Hermitian matrix generators of even and odd non-degenerate Clifford algebras is constructed by means of the Kronecker product of a parametrized version of Pauli matrices and by the identification of all possible anticommutation sets. The internal parametrization of the matrix generators allows a straightforward interpretation in terms of rotations, and

There is a growing body of literature that recognizes the importance of Smoothed Finite Element Method (S-FEM) in computational fluid dynamics (CFD) fields and, to a lesser extent, in complex turbulent flow problems. This study evaluates the performance of Reynolds-averaged Navier-Stokes (RANS) turbulence models within the S-FEM framework for predicting incompressible turbulent flows. Our assessment

This study proposes an explicit time-integration scheme for the scaled boundary finite element method applied to unbounded domains, leveraging the acceleration unit-impulse response formulation and a block-wise mass lumping strategy to enhance computational efficiency. Additionally, adopting an extrapolation scheme in the calculation of the linearly varying acceleration response and exploiting the

To quantify the influence of moving immersed media on acoustic radiation, this study develops an efficient method for acoustic radiation with arbitrary immersed media interfaces based on the extended finite element method (XFEM) and the Dirichlet-to-Neumann (DtN) boundary condition. The XFEM is employed for efficient and accurate modeling of the acoustic field with boundary shape variations. It requires

This paper conducts the dynamic analysis of fractional poroviscoelastic reinforced subgrade under moving loading. Based on the Biot theory and transversely isotropic (TI) parameter expression of the geogrid reinforced subgrade, the governing equations of the poroelastic reinforced subgrade are established in the wavenumber domain by the double Fourier transform. Considering the viscosity of the soil

Proxy re-encryption (PRE) is a cryptosystem that realizes efficient encrypted data sharing by allowing a third party proxy to transform a ciphertext intended for a delegator (i.e., Alice) to a ciphertext intended for a delegatee (i.e., Bob). Attribute-based proxy re-encrypftion (AB-PRE) generalizes PRE to the attribute-based scenarios, enabling fine-grained access control on ciphertexts. However, the

Sequences with low aperiodic autocorrelation are used in communications and remote sensing for synchronization and ranging. The autocorrelation demerit factor of a sequence is the sum of the squared magnitudes of its autocorrelation values at every nonzero shift when we normalize the sequence to have unit Euclidean length. The merit factor, introduced by Golay, is the reciprocal of the demerit factor

A singular integral equation method is proposed to analyze the complex plane cracks in one-dimensional (1D) orthorhombic quasicrystals. Using the Somigliana formula, the singular integral equations of the curved crack are derived. Based on the general situation of the curved crack, the singular integral equations of the inclined crack and the arc crack are given. Then the analytical solutions for the

In this paper, a novel method is developed to solve the free-field motion of the non-horizontally layered half-space subjected to seismic excitation in the time domain. The total wave motions are decomposed into a known and an unknown wave motion. Making use of the fact that the nodal forces at nodes in half-space resulted from the two motions will be zeros, the scattering problem resulted from the

Quaternion algebra H is an extension of the complex number field, which is a noncommutative associative algebra. In recent years, quaternionic Fourier analysis has interested some mathematicians du...

In this paper, we characterize all N-dimensional hypercomplex numbers having unital Archimedean f-algebra structure. We use matrix representation of hypercomplex numbers to define an order structure on the matrix spectra. We prove that the unique (up to isomorphism) unital Archimedean f-algebra of hypercomplex numbers of dimension \(N \ge 1\) is that with real and simple spectrum. We also show that

Let G be a simple graph on n vertices, and let λ1,λ2,…,λn be the Laplacian eigenvalues of G. The Laplacian Estrada index of G is defined as LEE(G)=∑i=1neλi. Consider a graph G with n≥3 vertices, m ...

Several strategies for solving a nonlinear eigenvalue problem are evaluated. This problem stems from the boundary integral equation solution of propagation in photonic crystal fibers. The origin and specificities of the eigenvalue problem are recalled before considering the solution of this eigenvalue problem. The first strategy, which is the starting point to illustrate the difficulties, is to solve

Smoothed particle hydrodynamics (SPH) has attracted significant attention in recent decades, and exhibits special advantages in modeling complex flows with multiphysics processes and complex phenomena. Its accuracy depends heavily on the distribution of particles, and will generally be lower if the particles are distributed non-uniformly. A high-order SPH scheme is proposed in the present work for

For an odd prime power q, let \(\mathbb {F}_{q^2}=\mathbb {F}_q(\alpha )\), \(\alpha ^2=t\in \mathbb {F}_q\) be the quadratic extension of the finite field \(\mathbb {F}_q\). In this paper, we consider the irreducible polynomials \(F(x)=x^k-c_1x^{k-1}+c_2x^{k-2}-\cdots -c_{2}^qx^2+c_{1}^qx-1\) over \(\mathbb {F}_{q^2}\), where k is an odd integer and the coefficients \(c_i\) are in the form \(c_i=a_i+b_i\alpha

Deep learning techniques, particularly neural networks, have revolutionized computational physics, offering powerful tools for solving complex partial differential equations (PDEs). However, ensuring stability and efficiency remains a challenge, especially in scenarios involving nonlinear and time-dependent equations. This paper introduces novel residual-based architectures, namely the Simple Highway

Pump-jet propulsor excitation transfers to submarine hull along rotor-shaft and duct-stator paths simultaneously. The investigations on the effects of excitation transfer paths on structural vibration and acoustic radiation of submarine are limited. The present work aims to investigate vibro-acoustic characteristics of coupled shaft-submarine hull system utilizing a theoretical wavenumber analysis

A novel hybrid boundary element is developed for polygonal holes in finite anisotropic elastic plates based on two different special fundamental solutions for holes. Since these special fundamental solutions satisfy traction-free condition along the hole's boundary, there is no mesh required on the boundary of polygonal holes. Various types of polygonal holes with rounded corners, such as triangles

The rock-soil mass, subjected to complex and lengthy geological processes, exhibits heterogeneity which induces variations in mechanical properties, thereby affecting the overall stability of slopes. In this paper, a novel numerical model that incorporates the Weibull distribution function into the meshless numerical manifold method based on the strength reduction method (MNMM-SRM) to account for the

In the era of Industry 4.0, the prominence of 3D printing as a pivotal manufacturing technology has greatly expanded, particularly within the domain of additive manufacturing (AM). Among the thriving research applications tailored for integration with AM, topology optimization (TO) has emerged as a resounding success. Given the prerequisite of TO for high-resolution meshing to ensure visual clarity

A three-dimensional hybrid Green function method is proposed to investigate the seakeeping and added resistance performance of ships advancing in waves. As for the method, the whole fluid domain is divided into two subdomains by introducing a regular virtual control surface. In the inner domain, the first order Taylor Expansion Boundary Element Method (TEBEM) based on simple Green function (Rankine

This article presents a numerical formulation based on the Boundary Element Method for the transient dynamic analysis of cracked thick symmetrical composite shells. The integral formulation uses the static fundamental solutions for thick orthotropic symmetric plates and the anisotropic plain elasticity fundamental solution. Domain integrals associated to distributed loads, curvature and inertial terms

The unsaturated zone profoundly affects groundwater (GW) flow induced by pumping and injection due to the capillary forces. However, current radial basis function (RBF) numerical models for GW pumping and injection mostly ignore the unsaturated zone. To bridge this gap, we developed a new three-dimensional weak strong form RBF model in this study, called CCHE3D-GW-RBF. Flow processes were modelled

In this article, we corrected the trilinear formula for triple disjoint matrix multiplication given in the article ‘J. Laderman, V. Pan, X. H. Sha, On practical Algorithms for Accelerated Matrix Mu...

Granite is often encountered in underground engineering, and its mechanical properties and failure behavior directly determine its stability and seepage characteristics. Unlike other rocks, granite is usually considered heterogeneous. Based on the Weibull distribution, this paper proposes a novel modeling method for heterogeneous granite via the combined finite-discrete element method (FDEM), and the

Building from ideas of hypercomplex analysis on the quaternionic unit ball, we introduce Hermitian, Riemannian and Kähler-like structures on the latter. These are built from the so-called regular Möbius transformations. Such geometric structures are shown to be natural generalizations of those from the complex setup. Our structures can be considered as more natural, from the hypercomplex viewpoint

The core and core–EP inverses are two recent generalized inverses that were first introduced and studied for complex matrices, and later for elements of rings with involution. Afterward, weighted v...

Physics-Informed Neural Networks (PINNs) have been extensively used as solvers for partial differential equations (PDEs) and have been widely referenced in the field of physical field simulations. However, compared to traditional numerical methods, PINNs do not demonstrate significant advantages in terms of training accuracy. In addition, electromagnetic field computation involves various governing

The Gray map converts a symbol in \(\mathbb {Z}_4\) to a pair of binary symbols. Therefore, under the Gray map, a linear function from \(\mathbb {Z}_4^n\) to \(\mathbb {Z}_4\) gives rise to a pair of boolean functions from \(\mathbb {F}_2^{2n}\) to \(\mathbb {F}_2\). This paper studies such boolean functions. We state and prove a condition for the nonlinearity of such functions and derive closed-form

Let \({\mathcal {K}}\) be a discrete valued field with finite residue field. In analogy with orthogonality in the Euclidean space \({\mathbb {R}}^n\), there is a well-studied notion of “ultrametric orthogonality” in \({\mathcal {K}}^n\). In this paper, motivated by a question of Erdős in the real case, given integers \(k \ge \ell \ge 2\), we investigate the maximum size of a subset \(S \subseteq {\mathcal

We propose an overlapping algorithm utilizing the -means clustering technique to group scattered data nodes for discretizing elliptic partial differential equations. Unlike conventional kernel-based approximation methods, which select the closest points from the entire region for each center, our algorithm selects only the nearest points within each overlapping cluster. We present computational results

The null-field method (NFM) and the method of auxiliary sources (MAS) have been both used extensively for the numerical solution of boundary-value problems arising in diverse applications involving propagation and scattering of waves. It has been shown that, under certain conditions, the applicability of MAS may be restricted by issues concerning the divergence of the auxiliary currents, manifested

The interface problem is highly challenging due to its non-smoothness, discontinuity, and interface complexity. In this paper, a new and simple Deep Interface Alternation Method (DIAM) is developed to solve elliptic interface problems to avoid dealing with interfaces. It combines the ideas of domain decomposition methods and deep learning methods. Specifically, we first transform the interface problem

We consider the minimum weight of codewords in a quasi-cyclic code and characterize the estimate in its most general setup using their concatenated structure. The new bound we derive generalizes the Jensen and Güneri–Özbudak bounds and it holds for the more general class of multilevel concatenated codes.

Prediction of sound field generated by an infinitely long periodic structure is often required in engineering. One of the examples is the sound field created by vibration of the rail of a slab railway track, of which the radiating and scattering boundaries are periodic in the track direction due to the rail fasteners. To provide a proper computational tool for such problems, we develop the periodic

An iterative three dimensional Boundary Element Method (BEM) is formulated to investigate partial cavitating flows around cylindrical bodies at various angles of attack and validation is pursued through comparison with other numerical models. Also, in this article the effect of angle of attack on two types of head (conical and blunt-head) is investigated. The results show that the effect of angle of

Accurate and efficient calculation of all second-order wave load components in six degrees of freedom (6DoF) remains a challenging task, in particular for structures with sharp edges. Based on Gauss theorem, we have tailor-made an efficient method for direct time-domain solvers utilizing, for instance, boundary element methods. Unlike other methods based on momentum conservation or Gauss theorem that

For the reaction–diffusion equation (RDE) based topology optimization of elastoplastic structure, exactness in volume constraint can be crucial. As a non-traditional numerical method, the recently proposed exact volume constraint requires iterations to determine the precise Lagrangian multiplier. Conversely, conventional inexact volume constraint methods resemble a time-forward scheme, potentially

In this paper, we study properties and constructions of a general family of involutions of finite abelian groups, especially those of finite fields. The involutions we are interested in have the form \(\lambda +g\circ \tau \), where \(\lambda \) and \(\tau \) are endomorphisms of a finite abelian group and g is an arbitrary map on this group. We present some involutions explicitly written as polynomials

In this paper, we propose a novel model for the discrimination of complex three-dimensional connected regions. The modified model is grounded on the Allen–Cahn equation. The modified equation not only maintains the original interface dynamics, but also avoids the unbounded diffusion behavior of the original Allen–Cahn equation. This advantage enables us to accurately populate and extract the complex

Geometric nonlinearities, material nonlinearities, and volume locking are the notable challenges faced in hyperelastic analysis. Traditional methods in this regard are complex and laborious for implementation as they require linearization and formulation of global matrix equations while simultaneously addressing volumetric locking. A mixed node's residual descent method (NRDM) proposed herein can effectively

Locally repairable codes (LRCs) have attracted a lot of attention due to their applications in distributed storage systems. In this paper, we provide new constructions of optimal \((2, \delta )\)-LRCs over \(\mathbb {F}_q\) with flexible parameters. Firstly, employing techniques from finite geometry, we introduce a simple yet useful condition to ensure that a punctured simplex code becomes a \((2,

In this research work, we apply a numerical scheme based on the first-order time integration approach combined with the modifications of the meshless approximation for solving the conservative Allen–Cahn–Navier–Stokes equations. More precisely, we first utilize a first-order time discretization for the Navier–Stokes equations and the time-splitting technique of order one for the dynamics of the phase-field

In this study, the effects of partitioning a square cavity with both vertical and horizontal porous walls on conjugate natural convection heat transfer are investigated numerically using a non-linear Darcy-Brinkman-Forchheimer model. The primary objective is to establish benchmark solutions and a dataset for validating Computational Fluid Dynamics (CFD) simulations. The governing equations, including

An enhanced computational approach is formulated to assess the service performance of active phased array antenna (APAA). For this approach, the discretized system equation of the thermo-mechanical coupling analysis is firstly constructed by the node-based gradient smoothing technique. Then, the stabilization terms are introduced to further improve the computational accuracy and stability, which are

In this paper, we study block-transitive automorphism groups of t-\((k^2,k,\lambda )\) designs. We prove that a block-transitive automorphism group G of a t-\((k^2,k,\lambda )\) design must be point-primitive, and G is either an affine group or an almost simple group. Moreover, the nontrivial t-\((k^2,k,\lambda )\) designs admitting block-transitive automorphism groups of almost simple type with sporadic