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This article is a continuation of our research on a one-to-one correspondence between n-dimensional spectral resolutions and n-dimensional observables on lexicographic types of quantum structures which started in Dvurecenskij and Lachman ( https://doi.org/10.1016/j.fss.2021.05.005 ). There we presented the main properties of n-dimensional spectral resolutions and observables, and we studied in depth characteristic points which are crucial for our study. Here we present the main body of our research. We investigate a one-to-one correspondence between n-dimensional observables and n-dimensional spectral resolutions with values in a lexicographic form of quantum structures such as perfect MV-algebras or perfect effect algebras. The multidimensional version of this problem is more complicated than a one-dimensional one because if our algebraic structure is k-perfect for k > 1 , then even for the two-dimensional case of spectral resolutions we have more characteristic points. The results obtained are applied to the existence of an n-dimensional meet joint observable of n one-dimensional observables on a perfect MV-algebra and a sum of n-dimensional observables.

The present paper intensively studies various properties of certain topologies on the set of integers $ {\mathbb Z} $ (resp. $ {\mathbb Z}^n $) which are either homeomorphic or not homeomorphic to the typical Khalimsky line topology (resp. $ n $-dimensional Khalimsky topology). This finding plays a crucial role in addressing some problems which remain open in the field of digital topology.

n-Dimensional fuzzy sets are a type of fuzzy sets where the membership degrees are n-dimensional intervals, i.e., ordered vector of dimension n on [ 0 , 1 ] . A fundamental aspect for aggregation function in types of fuzzy sets is establish the order on the membership valued which be consider. The natural order for n-dimensional intervals is the product order. Nevertheless, in some applications it is necessary to consider admissible orders, i.e., total orders which refines the product order. In this work we introduce three methods for generating admissible orders on n-dimensional fuzzy set. Some results and constructions obtained for the case 1-dimensional are generalized for the case n-dimensional. The concept of (OnmF)-graphs is introduced and a method to determine the best (OnmF)-path with respect to an admissible order was proposed.

Aims/ Objectives: In this paper, we study the existence, nonexistence and multiplicity of positive solutions to the n−dimensional elliptic system systems have been widely studied, but there is relatively little research on n-dimensional elliptic systems. We are very interested in this subject and want to study it. We give new conclusions on the existence, nonexistence and multiplicity of positive solutions for the n-dimensional elliptic system. Study Design: Study on the existence, nonexistence and multiplicity of positive solutions. Place and Duration of Study: School of Applied Science, Beijing Information Science & Technology University, September 2019 to present. Methodology: We prove the existence, nonexistence and multiplicity of positive solutions by the results of fixed point index. Results: We give new conclusions of existence, nonexistence and multiplicity of positive solutionsfor the system. Conclusion: We prove the existence, nonexistence and multiplicity of positive solutions to the n-dimensional elliptic system and give new conclusions.

In this note, we obtain new classification results for static and V‐static manifolds under pinching conditions of two different kinds. Firstly, we prove a classification result in higher dimensions assuming a condition of nonnegative Ricci curvature. This extends some recently obtained gap results on the traceless Ricci tensor. Furthermore, we employ the construction of an Einstein manifold associated to a static manifold in order to obtain a classification result in higher dimensions under a pinching condition on the boundary area.

Analytical solutions of the N-dimensional Schrödinger equation for the newly proposed Varshni-Hulthén potential are obtained within the framework of Nikiforov-Uvarov method by using Greene-Aldrich approximation scheme to the centrifugal barrier. The numerical energy eigenvalues and the corresponding normalized eigenfunctions are obtained in terms of Jacobi polynomials. Special cases of the potential are equally studied and their numerical energy eigenvalues are in agreement with those obtained previously with other methods. However, the behavior of the energy for the ground state and several excited states is illustrated graphically.

We introduce the sum of two n-dimensional observables on a $$\sigma $$ -complete MV-effect algebra and on a lexicographic MV-effect algebra, respectively. The sum is based upon a one-to-one correspondence between n-dimensional observables and n-dimensional spectral resolutions. Therefore, the sum of two observables is defined by their n-dimensional spectral resolutions. In addition, we study also the Olson order between n-dimensional observables using the one-to-one correspondence which enables us to show some semigroup properties of the set of n-dimensional observables with respect to the sum and the Olson order.

The study of the properties of surfaces contributes to the expansion of their use in solving various practical problems, especially if such properties can be generalized to manifolds of n-dimensional space. The most thoroughly studied are the properties of the simplest surfaces, including the properties of a sphere. That is why the simplest surfaces are most often used in practice. Each property not covered in the existing literature expands the indicated possibilities. Therefore, the purpose of this article is to identify the properties of the hypersphere unknown from the literature. Most of the properties of a circle and a sphere have been known since ancient times [1, 4, 5]. The generalized concept of a sphere into multidimensional spaces is based on the general principles of multidimensional geometry [3]. In [4], eleven basic properties of the sphere are listed and analyzed. In works [8, 10] it is shown that a circle can be considered as an isoline, and a sphere as an isosurface when modeling energy fields. In geometric modeling of energy fields with point energy sources, an essential role is played by the distances from the points of the field to the given energy sources [6, 7]. In [9], two schemes are given for determining the parameter t, taking into account the effect of the distance from the points of the field to the point sources of energy on the potentials of the points of the field. In a particular case, if this parameter is determined according to a simplified scheme with f(l)=al2, then the formula for calculating the potential of an arbitrary point of the energy field is a mathematical model of the energy field generated by the number n of point energy sources. The geometric model of the field will be a manifold that can be foliated into a one-parameter set of isospheres [8, 10]. Abstracting from the physical nature of the field, simplifying the equation for calculating the potential of an arbitrary point of the energy field and generalizing it to n-dimensional space, we can formulate the following properties: Property 1. A hypersphere can be considered as a locus of points, the sum of the squared distances from which to n given points is a constant value. Property 2. Arbitrary coefficients ki at distances li affect the parameters of the hypersphere without changing the type of surface.

The fractional matching preclusion number of a graph is the minimum number of edges whose deletion results in the remaining graph that has no fractional perfect matchings. For many networks, their optimal fractional matching preclusion sets are precisely those edges incident with a single vertex. The probability that all failures concentrate around a vertex is often small. To overcome the shortcoming, we consider the concept of conditional fractional matching preclusion, in which isolated vertices are not permitted in fault networks. We establish the conditional fractional matching preclusion numbers and all possible minimum conditional fractional matching preclusion sets for n -dimensional torus networks with n ≥ 3 .

We consider a weakly nonlinear N-dimensional parabolic system whose solutions are subjected to impulsive perturbations upon attainment of a certain fixed subset in the phase space. For broad classes of impulsive perturbations, it is proved that the system generates an impulsive semiflow with the minimal compact uniformly attracting set (uniform attractor) in the phase space. The invariance and stability of the nonimpulsive part of the uniform attractor are established under additional restrictions imposed on impulsive parameters.

In this paper, using the direct method, we study the stability of the following inequality: $$\begin{aligned}&\left\| f\left( \sum ^{n}_{i=1}x_{i}\right) +\sum _{1\le i \prec j\le n}f(x_{i}-x_{j})-n\sum ^{n}_{i=1}f(x_{i})\right\| \le \left\| f\left( \frac{\sum ^{n}_{i=1}x_{i}}{n}\right) \right. \\&\quad \left. +\sum _{1\le i \prec j\le n}f\left( \frac{x_{i}-x_{j}}{n}\right) -\frac{1}{n}\sum ^{n}_{i=1}f(x_{i})\right\| \end{aligned}$$ in Banach spaces, and the stability of the following inequality: $$\begin{aligned}&\left\| f\left( \frac{\sum ^{n}_{i=1}x_{i}}{n}\right) +\sum _{1\le i \prec j\le n}f\left( \frac{x_{i}-x_{j}}{n}\right) -\frac{1}{n}\sum ^{n}_{i=1}f(x_{i})\right\| _{*}\le \left\| f\left( \sum ^{n}_{i=1}x_{i}\right) \right. \\&\quad \left. +\sum _{1\le i \prec j\le n}f(x_{i}-x_{j})-n\sum ^{n}_{i=1}f(x_{i})\right\| _{*}, \end{aligned}$$ in non-Archimedean Banach spaces with n an integer greater than or equal to 2.

In this letter, we derive the CDF (cumulative distribution function) of $k$ th contact distance (CD) and nearest neighbor distance (NND) of the $n$ -dimensional ( $n$ -D) Matern cluster process (MCP). We present a new approach based on relationship between the probability mass function (PMF) and the probability generating function (PGF) of the random variable (RV) denoting the number of points in a ball of arbitrary radius to derive these CDFs. We also validate our analysis via numerical simulations and provide insights using the presented analysis. We also discuss two applications, namely– macro-diversity in cellular networks and caching in D2D networks, to study the impact of clustering on the performance.

Integral-type inequalities and dynamic equations have an important place in time scales. In this paper, we present some innovations of n-dimensional Minkowski’s integral-type inequality on time scales via $\lozenge _{\alpha } $ ◊ α -integral.

An interpolation programme coded in Fortran for irregular N-dimensional cases is presented and freely available. The need for interpolation procedures over irregular meshes or matrixes with interdependent input data dimensions is frequent in geophysical models. Also, these models often embed look-up tables of physics or chemistry modules. Fortran is a fast and powerful language and is highly portable. It is easy to interface models written in Fortran with each other. Our programme does not need any libraries; it is written in standard Fortran and tested with two usual compilers. The programme is fast and competitive compared to current Python libraries. A normalization option parameter is provided when considering different types of units on each dimension. Some tests and examples are provided and available in the code package. Moreover, a geophysical application embedding this interpolation programme is provided and discussed; it consists in determining back trajectories using chemistry-transport or mesoscale meteorological model outputs, respectively, from the widely used CHIMERE and Weather Research and Forecasting (WRF) models.

Submitted; We are interested in the Gevrey properties of the formal power series solution in time of the inhomogeneous semilinear heat equation with a power-law nonlinearity in $1$-dimensional time variable $t\in\mathbb{C}$ and $n$-dimensional spatial variable $x\in\mathbb{C}^n$ and with analytic initial condition and analytic coefficients at the origin $x=0$. We prove in particular that the inhomogeneity of the equation and the formal solution are together $s$-Gevrey for any $s\geq1$. In the opposite case $s

This paper is devoted to the problem of optimization of a function in -dimensional space, which, in general case, is polyextreme and undifferentiated. The new method of deformed stars in n-dimensional space was proposed. It is built on the ideas and principles of the evolutionary paradigm. Method of deformed stars is based on the assumption of using potential solutions groups. There by it allows to increase the rate of the accuracy and the convergence of the achieved result. Populations of potential solutions are used to optimize the multivariable function. In contrast to the classical method of deformed stars, we obtained a method that solves problems in -dimensional space, where the population of solutions consists of 3-, 4-, and 5-point groups. The advantages of the developed method over genetic algorithm, differential evolution and evolutionary strategy as the most typical evolutionary algorithms are shown. Also, experiments were performed to investigate the best configuration of method of deformed stars parameters.

In this work, a new iterative algorithm is presented to solve autonomous n-dimensional fractional nonlinear systems analytically. The suggested scheme is combination of two methods; the Laplace transform and the residual power series. The methodology of this algorithm is presented in details. For the accuracy and effectiveness purposes, two numerical examples are discussed. Finally, the impact of the fractional order acting on these autonomous systems is investigated using graphs and tables.

In this paper, we present the study of the behavior of spherical bubble in N-di-mensions fluid. The fluid is a mixture of vapor and superheated liquid. The math-ematical model is formulated in N-dimensions fluid on the basis of continuity and momentum equations, and solved its analytically. The variable viscosity is taken into an account problem. The obtained results show that the radius of bubble in-creases with the decreasing of the value of N-dimensions. © 2021 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This is an open access article distributed under the CC BY-NC-ND 4.0 terms and conditions.

In this paper, we firstly introduce some new results on overlap functions and n-dimensional overlap functions. On the other hand, in a previous study, Gomez et al. presented some open problems. One of these open problems is “to search the construction of n-dimensional overlapping functions based on bi-dimensional overlapping functions”. To answer this open problem, in this paper, we mainly introduce one construction method of n-dimensional overlap functions based on bivariate overlap functions. We mainly use the conjunction operator ∧ to construct n-dimensional overlap functions based on bivariate overlap functions and study their basic properties.

In this article we study solvable Leibniz algebras with abelian nilradicals. The relation between the dimensions of nilradicals and of the corresponding complemented space to the nilradical is esti...

In this paper, we present the concepts of generalized derivative, directional generalized derivative, subdifferential and conjugate for n-dimensional fuzzy-number-valued functions and discuss the characterizations of generalized derivative and directional generalized derivative by, respectively, using the derivative and directional derivative of crisp functions that are determined by the fuzzy mapping. Furthermore, the relations among generalized derivative, directional generalized derivative, subdifferential and convexity for n-dimensional fuzzy-number-valued functions are investigated. Finally, under two kinds of partial orderings defined on the set of all n-dimensional fuzzy numbers, the duality theorems and saddle point optimality criteria in fuzzy optimization problems with constraints are discussed.

In this review, we discuss new cases of integrable systems on the tangent bundles of finite-dimensional spheres. Such systems appear in the dynamics of multidimensional rigid bodies in nonconservative fields. These problems are described by systems with variable dissipation with zero mean. We found several new cases of integrability of equations of motion in terms of transcendental functions (in the sense of the classification of singularities) that can be expressed as finite combinations of elementary functions.

The purpose of this article is to provide an explicit formula for the bounds of integration of the regular simplex centred at the origin. Furthermore, this article rigorously proves that these inte...

We provide an elementary derivation of the Green function for Poisson’s equation with Neumann boundary data on balls of arbitrary dimension. Surprisingly, until very recently this Green function wa...

With the study of extensive literature on the Laplace transform with one and two variables and its properties, applications are available, but there is no work on n-dimensional Laplace transform. In this research article, we define n-dimensional fractional frequency Laplace transform with shift values. Several theorems are derived with properties of the Laplace transform. The results are numerically analyzed and discussed through MATLAB.

In this paper we are going to investigate a free boundary value problem for the anisotropic N-Laplace operator on a ring domain Ω : = Ω 0 \ Ω ¯ 1 ⊂ 𝕉 N \Omega : = {\Omega _0}\backslash {\bar \Omega _1} \subset {\mathbb{R}^N} , N ≥ 2. Our aim is to show that if the problem admits a solution in a suitable weak sense, then the underlying domain Ω is a Wulff shaped ring. The proof makes use of a maximum principle for an appropriate P-function, in the sense of L.E. Payne and some geometric arguments involving the anisotropic mean curvature of the free boundary.

We study the integrability of an N–dimensional differential Kolmogorov systems of the form x ˙ j = x j ( a j + ∑ k = 1 N a j k x k ) + x j Ψ ( x 1 , … , x N ) , j = 1 , … , N , where a j , and a j k are constants for j , k = 1 , … , N and Ψ ( x 1 , … , x N ) is a homogeneous polynomial of degree n > 2 , with either one additional invariant hyperplane, or with one exponential factor. We also study the integrability of the N–dimensional classical Lotka-Volterra systems (when Ψ ( x 1 , … , x N ) = 0 ). In particular we consider the integrability of the asymmetric May–Leonard systems.

Natural systems displaying optical properties have for long been an inspiration for new classes of optical constructs. Using the same families of materials employed by Nature in combination with their directed assembly allows access to n-dimensions of control to, ultimately, generate optical systems with multiple coexisting functions. This review provides an overview of lab-made optical systems made of protein and polysaccharide-derived materials found in naturally occurring optical systems. Recent advances in optical biomimicry and bioinspired, polyfunctional optical structures are presented, addressing attributes such as sensing, edible devices, biologically activity, and resorbable optical formats.

This paper deals with the global existence for a class of Keller–Segel model with signal-dependent motility and general logistic term under homogeneous Neumann boundary conditions in a higher-dimensional smoothly bounded domain, which can be written as $$\eqalign{& u_t = \Delta (\gamma (v)u) + \rho u-\mu u^l,\quad x\in \Omega ,\;t > 0, \cr & v_t = \Delta v-v + u,\quad x\in \Omega ,\;t > 0.} $$It is shown that whenever ρ ∈ ℝ, μ > 0 and $$l > \max \left\{ {\displaystyle{{n + 2} \over 2},2} \right\},$$then the considered system possesses a global classical solution for all sufficiently smooth initial data. Furthermore, the solution converges to the equilibrium $$\left( {{\left( {\displaystyle{{\rho _ + } \over \mu }} \right)}^{1/(l-1)},{\left( {\displaystyle{{\rho _ + } \over \mu }} \right)}^{1/(l-1)}} \right)$$as t → ∞ under some extra hypotheses, where ρ+ = max{ρ, 0}.

The n-dimensional generalized Hartogs triangles are domains defined by Hpn:={(z1,…,zn)∈Cn:|z1|p1

Eigenvalue behaviours of Schrodinger operator defined on n-dimensional lattice with n + 1 delta potentials are studied. It can be shown that lower threshold eigenvalue and lower threshold resonance...

In this paper we present N-dimensional multiresolution algorithms with and without error control strategies in the point values setting. This work complements the case of cell averages (Ruiz and Trillo, 2017). It can be somehow considered a generalization to N dimensions of several works, see Harten (1993), Harten (1996), Claypoole et al. (2003) [12] , Amat et al. (2002). Apart from presenting the N-dimensional algorithms, we focus mainly on three concerns. Firstly, on deriving the corresponding results proving the stability and giving explicit error bounds. Secondly on explaining in some detail how to carry out the programming, and finally we include some interesting numerical experiments in various dimensions. In particular, we present a different application for each dimension up to N = 5 . They have been chosen to let clear the wide range of possible applications of these algorithms. In 1 D we present an experiment where it is crucial to gain in computational time. In 2 D , we deal with the compression and reconstruction of contour maps representing the topography of a certain terrain such as a seabed. In 3 D , a scalar physical property, namely the salinity, is measured in a three dimensional mesh and then kept to be reconstructed later in time and compared with new measurements. In 4 D , we deal with a temperature field in a cylindrical pipe in a heat exchanger. This field occupies a lot of memory inside a finite elements calculation, and a possibility to deal with this fact is to compress this field or to use the information given by the multiresolution coefficients to save computational time by refining the mesh just in the necessary zones. In 5 D we work with a splitted sinusoidal function, which exemplifies a similar situation to the 2 D contour map, but in a higher dimension.

A dual synchronization scheme combined with compound–compound synchronization is proposed. In usual compound–compound synchronization scheme, synchronization has been achieved for six dynamical systems, while in the presented scheme compound–compound synchronization has been developed in the dual synchronization frame involving twelve dynamical systems. Numerous synchronization schemes such as dual compound, dual combination, compound–compound and compound synchronization may be derived as particular cases of the presented scheme. By employing nonlinear control method and Lyapunov stability criteria, controllers are designed. Illustrations are presented using Genesio-Tesi and Wang chaotic systems. Computational results are presented to show the effectiveness of the proposed methodology. A good agreement has been obtained between analytical methodology and numerical treatment.

In this paper, by using an extension of Mawhin’s continuation theorem and some analysis methods, we study the existence of periodic solutions for the following prescribed mean curvature system $$\frac{d}{{dt}}\varphi \left( {x'} \right) + \nabla W\left( x \right) = p\left( t \right),$$ where x ∊ ℝn, W ∊ C1(ℝn, ℝ), p ∊ C(ℝ, ℝn) is T-periodic and $$\varphi \left( x \right)\frac{x}{{\sqrt {1 + |x{|^2}} }}.$$

In this paper, we adopt a Poisson approach to find Laplace transforms of joint occupation times over n disjoint intervals for pre-exit diffusion processes. Then we generalize previous result for the 2-dimensional case and the 3-dimensional case.

We propose one of possible algorithms for the development of a formal N -multiple power series into a functional N -dimensional regular C -fraction corresponding to this series. In this case, we use the algorithms of development into the corresponding and two-dimensional corresponding fractions for power and double power series.

The discoveries of Herculaneum and Pompeii and the broadened scope of geography in the eighteenth century, and developments in mathematics and physics that began in the nineteenth and continued into the twentieth, renewed studies of ancient works of art led to the creation of opposing factions regarding the “question of perspective”: those who maintained the existence of a single possible perspective, and those who upheld the existence of multiple perspective constructions. To shed light on the debate, this present paper examines some of the factors behind the two positions.

On the unit ball in the n dimensional complex Euclidean space, we introduce a new weighted Bergman space and Toeplitz operators. By Berezin transform and average functions, we estimate the essential norms of the Toeplitz operators.

We consider an elliptic equation driven by a p-Laplacian-like operator, on an n-dimensional Riemannian manifold. The growth condition on the right-hand side of the equation depends on the geometry of the manifold. We produce a nontrivial solution by using a Palais–Smale compactness condition and a mountain pass geometry.

In this paper, a solution to the problem of the motion of a brachistochrone in the ndimensional Euclidean space is firstly presented. The very first formulation of the problem in a two-dimensional case was proposed by J. Bernoulli in 1696. It represented an analytical description of the trajectory for the fastest rolling down under gravitational force only. Thereafter, a number of problems devoted to a brachistochrone were considered with account for gravitational forces, dry and viscous drag forces, and a possible variation in the mass of a moving body. Analytical solution to the formulated problem is presented in details by an example of the body moving along a brachistochrone in three-dimensional Cartesian coordinates. The obtained parametric solution is confirmed by a graphical interpretation of the calculated result. The formulated problem is solved for an ideal case when drag forces are neglected. If dry and viscous friction forces are taken into account, the plane shape of the brachistochrone remains the same,while the analysis of the solution becomes more complicated. When, for example, a side air flow is taken into account, the plane curve is replaced by a three-dimensional brachistochrone.

This paper deals with tensor completion for the solution of multidimensional inverse problems arising in nuclear magnetic resonance (NMR) relaxometry. We study the problem of reconstructing an appr...

In this paper, inspired by the multiplicative generators of overlap functions, we mainly propose the concepts of multiplicative generator pairs of n-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to n. We present the condition under which the pair (g, h) can multiplicatively generate an n-dimensional overlap function Og,h. we focus on the homogeneity and idempotency property on multiplicatively generated n-dimensional overlap functions.

In the present paper we consider the Neumann problem for the $n$-dimensional Helmholtz equation. In particular we deal with the problem of representability of the solutions by means of double layer potentials.