The hull of a linear code plays an important role in determining the complexity of algorithms for checking permutation equivalence of two linear codes and computing the automorphism group of a linear code. Regarding the quantum error correction, linear codes with determined hull are used to construct quantum codes. In this paper, we focus on the hull of Simplex codes and punctured Simplex codes. We

Permutation arrays under the Chebyshev metric have been considered for error correction in noisy channels. Let P(n, d) denote the maximum size of any array of permutations on n symbols with pairwise Chebyshev distance d. We give new techniques and improved upper and lower bounds on P(n, d), including a precise formula for P(n, 2).

Cavitation bubbles can be both beneficial and detrimental. One of their beneficial applications is to produce droplets as they oscillate near a confined free surface. In this paper, the oscillation of two spark-generated bubbles beneath a confined free surface and the resultant droplet generation are studied numerically using boundary element method. Three different configurations are considered: (i)

Support vector regression (SVR) with sparrow search algorithm (SSA) is developed as the machine learning (ML) model to predict maximum surface settlement smax caused by tunneling. A novel method for calibrating boundary conditions of analytical solution is proposed, where the maximum surface settlement derived by the analytical method is equal to smax predicted by SSA-SVR method. The elastic analytical

A photovoltaic/thermal (PV/T) system containing a phase change material (PCM) layer located between two parallel air flow channels was numerically studied in the present research. With numerous numerical simulations, the effect of PCM layer thickness (ϕ=5–30 mm) and air mass flow rate (m˙a=0.0123–0.0368 kg/s) on system efficiency were determined. It was found that from the thermal point of view, it

This study explores the prediction of airfoil self-noise through Deep Learning whilst focusing more specifically on the so-called turbulent boundary layer trailing edge (TBL-TE) noise. To this end, a predictive model relying on a Deep Neural Network (DNN) is developed, being then trained using an experimental database of TBL-TE noise signatures previously acquired by NASA. The DNN is favorably benchmarked

Present paper aims to assess the performance and limits of boundary element method for the reliable simulation of ground effect phenomena on hydrodynamic lifting surfaces. Benefitting from the ground effect, especially in extreme ground proximity, suggests a promising concept for lifting bodies. On the other hand, the more pronounced the ground effect, the more complicated flow physics it exhibits

A seminal result of Gerstenhaber gives the maximal dimension of a linear space of nilpotent matrices. It also exhibits the structure of such a space when the maximal dimension is attained. Extensio...

Fast multipole boundary element methods (FMBEM) have been successfully applied to solve ultra-large acoustic problems. In practice, there are still a large number of industrial applications where model sizes are well below a million Degrees of freedom. Thus, it is of practical importance to further improve the solver’s efficiency for such applications. This paper presents a novel formulation of the

In this study, the nonlinear dynamic analysis of functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) beams is examined. The material properties can be estimated by using the modified Halpin-Tsai model and rule of mixture. Based on the third-order shear deformation theory and the von Kármán assumption, the equations of motion is derived and solved by using Jacobi-Ritz method incorporating

In this contribution, an efficient modification of the scaled boundary finite element method for shells is presented to compute accurate results for h-refinement. While previous works on the scaled boundary shell formulation showed inaccurate and unstable results for fine meshes, this modification overcomes such problems by the assumption of a linear force distribution over the thickness. Furthermore

A nonlinear formulation, based on the total Lagrange description of the weighted radial basis collocation method (WRBCM), is proposed for the large deformation analysis of rubber-like materials where the materials are hyperelastic and nearly incompressible. The WRBCM based on the strong form collocation is a genuinely meshfree method that eliminates the need for meshing. As a result, it effectively

We present a numerical scheme using a finite volume method (FVM) to simulate the heat transfer in fluid flowing in a three-dimensional fracture in a rock mass. Heat conduction in the rock mass and heat exchange between the fluid and the rock mass are considered, but fracture deformation is not. This scheme could approximate the thermal energy extraction process from a geothermal system when the fractures

In the present Computational Fluid Dynamic (CFD) simulation, the impact of various shapes of alphabet twisted tape in a shell –tube type of heat exchanger on the pressure drop, temperature, velocity distribution, and heat transfer coefficient was studied numerically. The best shape of the twisted tape was selected by thermo-hydraulic analysis. SIMPLE algorithm and Finite Volume Method (FVM) were then

The numerical manifold method (NMM) is robust and effective in modeling complex fracture problems as it allows the fracture paths to intersect meshes and uses enrichments with Williams expansions to capture the tip singularities. However, mesh cutting and crack-tip enrichment lead to small cut ratios and linear dependence, respectively, for complicated fracture problems. These two situations constantly

This paper studies a question of Bourin on noncommutative Lp spaces. Some inequalities due to Hayajneh et al. [Norm inequalities for positive semidefinite matrices and a question of Bourin II. Int ...

This work introduces fractional d-bar derivatives in the setting of quaternionic analysis, by giving meaning to fractional powers of the quaternionic d-bar derivative. The definition is motivated by starting from nth-order d-bar derivatives for \(n\in {\mathbb {N}}\), and further justified by various natural properties such as composition laws and its action on special functions such as Fueter polynomials

Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in multiple access communication systems in code division. Firstly, this paper studies the Jacobi sums over Galois rings of arbitrary characteristics and completely determines their absolute values. This extends the work by Li et al. (Sci China 56(7):1457–1465, 2013), where the Jacobi

A hybrid version of the strong form meshless Radial Basis Function-Finite Difference (RBF-FD) method is introduced for solving thermo-mechanics. The thermal model is spatially discretised with RBF-FD, where trial functions are polyharmonic splines augmented with polynomials. For time discretisation, the explicit Euler method is employed. An extension of RBF-FD, the hybrid RBF-FD, is introduced for

Deep neural networks (DNNs) for numerical solutions to partial differential equations (PDEs) have exhibited their remarkable merits of meshless methods, dimensionless features, and nonlinear approximation powers. The majority of conventional DNNs are mainly concentrated on the low- or high-dimensional PDE with smooth solutions. In singular problems the DNN does not behave so efficiently as in the smooth

In this paper, closed formulas for the eigenvectors of a particular class of matrices generated by generalized permutation matrices, named generalized circulant matrices, are presented.

We present an efficient and practical numerical method for solving fractional integro-differential equations with a weakly singular kernel in complex two and three-dimensional domains. The reproducing kernel pseudo-spectral method is used to discretize the multidimensional regular and irregular spatial domains, while time discretization is done using a third-order backward differentiation formula.

Structures with holes are prevalent in engineering applications. Analyzing the stress concentration effects caused by holes using the finite element method (FEM) or the boundary element method (BEM) is challenging and time-consuming. Typically, a large number of elements are necessary in the vicinity of holes to achieve accurate results. In this paper, a series of improved hole elements and tube elements

The local-coupling multi-trace and domain decomposition method originally developed to analyze electromagnetic scattering from closed composite objects is extended to solve the scattering from complex multilayer patch objects. Different from the traditional global radiation coupling surface integral equation domain decomposition method and contact-region modeling method (CRM), the local-coupling property

In this work, we provide two applications of the eigenvalues of the unitary Cayley graphs over matrix rings over finite fields. For a ring R, JR denotes the Jacobson radical of R. In 2012, Kiani an...

Automotive coatings often suffer from high-speed stone impact wear damage. Currently, it remains a significant challenge to evaluate the stone-chipping resistance performance of automotive coatings. The main purpose of this work is to develop a computational approach combining a numerical model with a prediction method to achieve this end. The numerical model is developed based on the Computational

The strength of sandstone samples considering different particle sizes is required in many engineering applications. A rock model based on the Voronoi tessellated model is established for studying the failure mechanism of sandstone samples. Uniaxial compression, Brazilian splitting and triaxial compression tests are carried out to evaluate the influence of different crystal sizes on macroscopic parameters

This paper first develops the closed-form solution of a layered halfspace subject to circular ring concentrated loads. The layered halfspace consists of finite layers and a lower halfspace. All the layers in the layered halfspace are homogeneous and transversely isotropic. Integral transform techniques are utilized to derive the solution in cylindrical polar coordinates. Then, the closed-form solution

The Lattice Boltzmann Method (LBM) can be applied to several fluid dynamic problems in the time domain. This numerical method indirectly solves the Navier–Stokes equations in a weakly compressible limit that allows acoustic wave propagation. This work presents a systematic literature review concerning the application of the LBM in acoustics. Applications found in the literature are classified and presented

We introduce, motivate and study \(\varepsilon \)-almost collision-flat universal (ACFU) hash functions \(f:\mathcal X\times \mathcal S\rightarrow \mathcal A\). Their main property is that the number of collisions in any given value is bounded. Each \(\varepsilon \)-ACFU hash function is an \(\varepsilon \)-almost universal (AU) hash function, and every \(\varepsilon \)-almost strongly universal (ASU)

Linear codes of length n over \(\mathbb {Z}_{p^s}\), p prime, called \(\mathbb {Z}_{p^s}\)-additive codes, can be seen as subgroups of \(\mathbb {Z}_{p^s}^n\). A \(\mathbb {Z}_{p^s}\)-linear generalized Hadamard (GH) code is a GH code over \(\mathbb {Z}_p\) which is the image of a \(\mathbb {Z}_{p^s}\)-additive code under a generalized Gray map. It is known that the dimension of the kernel allows to

Various notions of non-malleable secret sharing schemes have been considered. In this paper, we review the existing work on non-malleable secret sharing and suggest a novel game-based definition. We provide a new construction of an unconditionally secure non-malleable threshold scheme with respect to a specified relation. To do so, we introduce a new type of algebraic manipulation detection code and

In the present paper, we give harmonic weight enumerators and Jacobi polynomials for the first-order Reed–Muller codes and the extended Hamming codes. As a corollary, we show the nonexistence of combinatorial 4-designs in these codes.

We consider the function \(x^{-1}\) that inverses a finite field element \(x \in \mathbb {F}_{p^n}\) (p is prime, \(0^{-1} = 0\)) and affine \(\mathbb {F}_{p}\)-subspaces of \(\mathbb {F}_{p^n}\) such that their images are affine subspaces as well. It is proved that the image of an affine subspace L, \(|L |> 2\), is an affine subspace if and only if \(L = s\mathbb {F}_{p^k}\), where \(s\in \mathbb

The process of condensation takes place within the low-pressure stages of the steam turbine when undergoing rapid expansion. The dry supercooled steam turns into very tiny liquid droplets, and the resulting wet steam mixture causes additional losses and maintenance problems. Accurate simulation of steam condensing flows helps to obtain accurate information about the thermodynamics of such flows and

The irreversibility rate analysis on the solar thermal collectors can be used to determine the regions in the geometry with high intensification of the thermal and viscous entropy generation rates (S˙th and S˙fr), thereby improving the geometry. Although the numerical analysis of the hydrothermal characteristics of the solar thermal collector has been widely studied, the entropy generation rate inside

Liu et al. (IEEE Trans Inf Theory 68:3096–3107, 2022) investigated a class of BCH codes \(\mathcal {C}_{(q,q+1,\delta ,1)}\) with \(q=\delta ^m\) a prime power and proved that the set \(\mathcal {B}_{\delta +1}\) of supports of the minimum weight codewords supports a Steiner system \({{\text {S}}}(3,\delta +1,q+1)\). In this paper, we give an equivalent formulation of \(\mathcal {B}_{\delta +1}\) in

In this paper, we solve the bounded rank perturbation problem for matrix pencils without nontrivial homogeneous invariant factors, over arbitrary fields. The solution is based on reducing the probl...

The paper creates two new families of fundamental solutions for the 3D Laplace equation, presented into two parts. For the first part in terms of a planar line as a new coordinate the derived 2D like fundamental solution has a logarithmic singularity, which results in a method of pseudo fundamental solutions. We propose two methods to determine the optimal values of the offset parameter used to locate

One of the popular meshless methods for solving governing equations in applied sciences is a local radial basis function-finite difference (RBF-FD). In this paper, we proposed a new idea for an L- shaped (or like T- and Z-shaped) domain based on the domain decomposition. RBF-FD formulation is used at the interface points to get a better solution, while the classical FD is applied to all sub-regions

This study builds on a recent paper by Lai et al. (2018) in which a novel boundary integral formulation is presented for scalar wave scattering analysis in two-dimensional layered and half-spaces. The seminal paper proposes a hybrid integral representation that combines the Sommerfeld integral and layer potential to efficiently deal with the boundaries of infinite length. In this work, we modify the

The use of phase change materials (PCMs) to store energy in solar systems can be very useful to augment their efficiency. This paper presents a numerical study on the effect of using PCM in a thermal solar panel system. Four tubes containing alumina/water nanofluids (NFs) flow are used in this system, and NFs flow is analyzed. A spiral blade is employed on the tubes. By changing the pitch distance

The oscillating water column (OWC) converter, a prominent and widely adopted device for capturing wave energy, has yet to attain commercialization due to its intricate hydrodynamic behavior. Consequently, numerous laboratory and numerical studies have been carried out on OWC converters. One of the significant parameters in the study and comparison of different converters is their hydrodynamic efficiency

With the widespread use of composites, analysis of their responses under various loadings is of significant importance. In this work, the mechanical behaviors of 2-D orthotropic composites with arbitrary holes are investigated by the numerical manifold method (NMM). Profiting from its unique dual cover systems, namely, the mathematical cover (MC) and the physical cover (PC), the NMM is able to model

In the year 1982, John Chollet conjectured that, for any pair of n×n positive semidefinite matrices A, B, per(A)⋅per(B)≥per(A∘B), where A∘B is the Hadamard product of A and B. This conjecture was p...

Aiming at modeling the reinforcement behavior of geogrid reinforced HIR asphalt pavement structure accurately and efficiently, a mathematical formulation using the Generalized Kelvin Solution (GKS) based method for multi-layer three-dimensional elastic system with the consideration of elastic membrane without thickness is put forward in this thesis to simulate the geogrid reinforcement for HIR pavement

In the event of a fire within a tunnel, the rapid and substantial increase in temperature can prompt swift fractures within the concrete lining. This situation can severely compromise the structural load-bearing capacity and overall safety of the tunnel. The intricate interplay of factors within the tunnel, including temperature, humidity, and pore pressure, necessitates the adoption of a thermo-hydro

A numerical study is done to analyze the effect of fin length on the performance of a building-integrated photovoltaic-phase change material (PV/PCM) unit. The results obtained for cases with different fin lengths (1, 2, 3 and 4 cm) are compared with the findings related to the finless case. The required simulations are conducted by using computational fluid dynamics technique and with the help of

This paper is concerned with the stability of gaps in the essential spectra of self-adjoint relations under non-negative relatively compact perturbation in Hilbert spaces. A stability result about ...