3,980 Results Found

In this research, a groundbreaking framework for the octic B-spline collocation method in n-dimensional spaces is presented. This work is an extension of previous works that involved the creation of B-spline functions in n-dimensional space for the p...

The phase portrait for dynamic systems is a tool used to graphically determine the instantaneous behavior of its trajectories for a set of initial conditions. Classic phase portraits are limited to two dimensions and occasionally snapshots of 3D phas...

The whimsical Las Vegas/Monte Carlo cubic dice are generalized to construct the combinatorial problem of enumerating all n-dimensional hypercube dice and dice of other shapes that exhibit cubic, icosahedral, and higher symmetries. By utilizing powerf...

Chaotic time series have been involved in many fields of production and life, so their prediction has a very important practical value. However, due to the characteristics of chaotic time series, such as internal randomness, nonlinearity, and long-te...

This paper advocates an epistemological turn in the field of digital art history and cultural heritage studies. This epistemological turn is understood as the elaboration of a new (or renewed) epistemic apparatus that allows us to understand and inte...

In this paper, we introduce the notions of the almost anti-periodic discrete process of the N-dimensional vector-valued and $N\times N$ matrix-valued functions. Some basic properties of the almost anti-periodic discrete functions are established. Based...

A time scale is a special measure chain that can unify continuous and discrete spaces, enabling the construction of integrable equations. In this paper, with the Lax operator generated by the displacement operator, N-dimensional lattice integrable sy...

Orthogonal projection a point onto a parametric curve, three classic first order algorithms have been presented by Hartmann (1999), Hoschek, et al. (1993) and Hu, et al. (2000) (hereafter, H-H-H method). In this research, we give a proof of the appro...

The Lenstra-Lenstra-Lovász (LLL) lattice reduction algorithm and many of its variants have been widely used by cryptography, multiple-input-multiple-output (MIMO) communication systems and carrier phase positioning in global navigation satellite syst...

Based on the recent development of two dimensional ℓ₁ major component detection and analysis (ℓ₁ MCDA), we develop a scalable ℓ₁ MCDA in the n-dimensional space to identify the major directions of star-shaped heavy-tailed statistical distributions wi...

The present paper deals with two types of topologies on the set of integers, $\mathbb{Z}$ : a quasi-discrete topology and a topology satisfying the $T_{\frac{1}{2}}$ -separation axiom. Furthermore, for each $n\in \mathbb{N}$ , we develop countably many topologies...

Several previous results valid for one-dimensional nonlinear Fokker-Planck equations are generalized to N-dimensions. A general nonlinear N-dimensional Fokker-Planck equation is derived directly from a master equation, by considering nonlinearitiesin...

The free metaplectic transformation is an N-dimensional linear canonical transformation. This transformation operator is useful, especially for signal processing applications. In this paper, in order to characterize simultaneously local analysis of a...

In this work, we show that an n-dimensional sublattice ${\Lambda }^{\prime }=m\Lambda$ of an n-dimensional lattice $\Lambda$ induces a $G={\mathbb{Z}}_m^n$ tessellation in the flat torus $T_{{\beta }^{\prime }}={\mathbb{R}}^n/{\Lambda }^{\prime }$, where the group G is isomorphic to the lattice partition $\Lambda /{\Lambda }^{\prime }$. As a consequence, we obtain, via this...

A Cop and Drunken Robber (CDR) game is one variation of a famous combinatorial game, called Cops and Robbers, which has been extensively studied and applied in the area of theoretical and computer science as demonstrated by several conferences and pu...

In this work, we present the generalization of some thermodynamic properties of the black body radiation (BBR) towards an n-dimensional Euclidean space. For this case, the Planck function and the Stefan–Boltzmann law have already been given by Landsb...

This paper presents an n-dimensional reduction algorithm for Learning from Demonstration (LfD) for robotic path planning, addressing the complexity of high-dimensional data. The method extends the Douglas–Peucker algorithm by incorporating velo...

The drawbacks of a one-dimensional chaotic map are its straightforward structure, abrupt intervals, and ease of signal prediction. Richer performance and a more complicated structure are required for multidimensional chaotic mapping. To address the s...

The information contained in an n-dimensional (nD) density matrix ρ is parametrized and interpreted in terms of its asymmetry properties through the introduction of a family of components of purity that are invariant with respect to arbitrary rot...

This work considers the Minkowski sum of an N-dimensional ellipsoid and hyperrectangle, a combination that is extremely relevant due to the usage of ellipsoid-adjacent primitives in computer graphics for work such as 3D Gaussian splatting. While para...

We obtain a large number of degree and distance-based topological indices, graph and Laplacian spectra and the corresponding polynomials, entropies and matching polynomials of n-dimensional hypercubes through the use of Hadamard symmetry and recursiv...

The design of neural network architectures is carried out using methods that optimize a particular objective function, in which a point that minimizes the function is sought. In reported works, they only focused on software simulations or commercial...

In the first part of this article, we present a new proof for Korn’s inequality in an n-dimensional context. The results are based on standard tools of real and functional analysis. For the final result, the standard Poincaré inequality...

This study focuses on a novel parameterized Wigner distribution, which is an organic integration of the free metaplectic Wigner distribution and the $\mathbf{K}$-Wigner distribution. We style this as the free metaplectic $\mathbf{K}$-Wigner distribution (FMKWD) and invest...

Because of their locality preservation properties, Space-Filling Curves (SFC) have been widely used in massive point dataset management. However, the completeness, universality, and scalability of current SFC implementations are still not well resolv...

We present recent results on dynamical chiral symmetry breaking in (2 + 1)-dimensional QED with N four-component fermions. The results of the $1/N$ expansion in the leading and next-to-leading orders were found exactly in an arbitrary nonloca...

Nonstandard finite-difference (NSFD) methods, pioneered by R. E. Mickens, offer accurate and efficient solutions to various differential equation models in science and engineering. NSFD methods avoid numerical instabilities for large time steps, whil...

The Lyapunov exponent serves as a measure of the average divergence or convergence between chaotic trajectories from the perspective of Lyapunov exponents (LEs). Chaotic systems with more and larger positive LEs have more complex dynamical behavior a...

We present a high-dimensional quantum key distribution protocol by using N-qudits quantum light states—that is, product states with N photons, each of them in a quantum superposition of dimension d, which provides a high dimension $d^N$ and, accor...

The two-dimensional (2D) Ruddlesden–Popper perovskite exhibits superior chemical stability but suffers from compromised photoelectric properties due to the van der Waals gap. This study presents a novel investigation of surface passivation effe...

Self-powered ultraviolet (UV) photodetectors have attracted considerable attention in recent years because of their vast applications in the military and civil fields. Among them, self-powered UV photodetectors based on p-n heterojunction low-dimensi...

Some existing chaotic maps have the drawbacks of a narrow range of chaotic parameters and discontinuities, which may be inherited by new chaotic systems generated from them as seed maps. We propose a chaotic model that can generate N-dimensional chao...

Bamboo is a natural and renewable building material but its application has been limited due to the low dimensional stability and poor durability against mold. In this study, monomers of hydroxyethyl methacrylate (HEMA) and N-isopropyl acrylamide (NI...

In this paper, we propose a method for the three-dimensional (3D) image visualization of objects under photon-starved conditions using multiple observations and statistical estimation. To visualize 3D objects under these conditions, photon counting i...

A fiber-optic gyroscope (FOG) with lower precision but higher cost advantage is typically selected according to working conditions and engineering budget. Thermal drift is the main factor affecting FOG precision. External thermal calibration methods...

In this work, the optical and electronic characteristics of MoS₂(n,n) and MoSe₂(n,n) nanotubes and 1D van der Waals nanoheterostructures based on them are determined from first principles. It is shown that with an increase in the diameters of MoS₂(n,...

Solvent-free spin crossover (SCO) iron(III) complex, [Fe^III(Him)₂(hapen)]SbF₆ (Him = imidazole, H₂hapen = N,N′-bis(2-hydroxyacetophenylidene)ethylenediamine), is synthesized. The Fe^III ion has an octahedral coordination geometry, with N₂O₂ donor atom...

We prove general stability theorems for n-dimensional quartic-cubic-quadratic-additive type functional equations of the form $\begin{array}{c}\hfill {\displaystyle \sum _{i=1}^{\ell }}{c}_{i}f\left(a_{i1}{x}_1+a_{i2}{x}_2+\cdots +a_{in}{x}_n\right)=0.\end{array}$ by applying the dir...

This paper presents equations for the electron density of the two-dimensional electron gas (2DEG) in AlGaN/GaN heterostructures in three realistic scenarios: (1) AlGaN/GaN heterostructure with surface exposed to ambient with mobile ions, (2) metal ga...

Investigations into the properties of generalized effective temperature are conducted across arbitrary dimensions. Maxwell–Boltzmann distribution is displayed for one, two, and three dimensions, with effective temperatures expressed for each di...

We investigated the ecological requirements in the emergence phase of two congeneric species of Aeshnidae, Aeshna grandis (Linnaeus 1758) and A. juncea (Linnaeus 1758), occurring in syntopy at the southernmost limit of their range. We sampled the exu...

Climate change has been shown to directly influence evapotranspiration, which is one of the crucial watershed processes. The common approach to its calculation is via mathematical equations, such as 1985 Hargreaves-Samani (HS85). It computes referenc...

Using a Poisson approach, we find Laplace transforms of joint occupation times over n disjoint intervals for spectrally negative Lévy processes. They generalize previous results for dimension two.

The research of the fractional Orlicz-Sobolev space and the fractional N-Laplacian operators will give the development of nonlinear elasticity theory, electro rheological fluids, non-Newtonian fluid theory in a porous medium as well as Probability an...

Dispersion-corrected density functional theory (DFT) calculations reveal that the layered electride of dicalcium nitride (Ca₂N) exhibits stronger interlayer binding interactions but lower interlayer friction behavior than that of traditional layered...

In this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The...

The purpose of this paper is to introduce a summary of known results and the definition of the time-like ruled surface with the space-like generating space in the Minkowski space IR₁ⁿ, and to present some characteristic results related with minimali...

In this paper, the generalized Jacobi elliptic functions expansion method with computerized symbolic computation are employed to investigate explicitly analytic solutions of the (N + 1)-dimensional generalized Boussinesq equation. The exact solutions...

We report on 2-dimensional electron gases realized in binary N-polar GaN channels on AlN on sapphire templates grown by metal–organic vapor phase epitaxy. The measured sheet carrier density of $3.8\times {10}^{13}$ cm⁻² is very close to the theo...

In this note, I derive the Chandrasekhar instability of a fluid sphere in (N + 1)-dimensional Schwarzschild–Tangherlini spacetime and take the homogeneous (uniform energy density) solution for illustration. Qualitatively, the effect of a positi...