Lipschitz Estimates for Commutators of N-dimensional Fractional Hardy Operators

In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα （R^n） is bounded from L^p（R^n） to L^q（R^n）, where 0 〈 α 〈 1, 1 〈 p, q 〈 ∞ and 1/P - 1/q = （α＋β）/n. Furthermore, the boundedness of Hβ,b on the homogenous Herz space Kq^α,p（R^n） is obtained.

General calculation formulas and recurrence relations of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0

In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.

On Multiplicative Generators of n-Dimensional Overlap Functions

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.

Solutions of Laplace Equation in n-Dimensional Spaces

The solutions of the Laplace equation in n-dimensional space are studied. The angular eigenfunctions have the form of associated Jacob/polynomials. The radial solution of the Helmholtz equation is derived.

Relation Between Dimension and Angular Momentum for Radially Symmetric Potential in N-Dimensional Space

It is proved that when solving SchrSdinger equations for radially symmetric potentials the effect of higher dimensions on the radial wave function is equivalent to the effect of higher angular momenta in lower-dimensional cases. This result is applied to giving solutions for several radially symmetric potentials in N dimensions.

L_p(1≤p≤∞) APPROXIMATION BY AN n-DIMENSIONAL SUBSPACE ON A SET OF n+1 POINTS

Some new characterizations and immediate explicit expressions of best L(1≤p≤∞) approximation and their deviations by an n-dimensional subspace on a set of n+1 points are given.

CANONICAL REPRESENTATIONS AND DEGREE OF FREEDOM FORMULAE OF ORTHOGONAL TENSORS IN N-DIMENSIONAL EUCLIDEAN SPACE

In this paper, with the help of the eigenvalue properties of orthogonal tensors in n-dimensional Euclidean space and the representations of the orthogonal tensors in 2-dimensional space, the canonical representations of orthogonal tensors in n-dimensional Euclidean space are easily gotten. The paper also gives all the constraint relationships among the principal invariants of arbitrarily given orthogonal tensor by use of Cayley-Hamilton theorem; these results make it possible to solve all the eigenvalues of any orthogonal tensor based on a quite reduced equation of m-th order, where m is the integer part ofn \2. Finally, the formulae of the degree of freedom of orthogonal tensors are given.

Sharp Bound for the Generalized m-Linear n-Dimensional Hardy-Littlewood-Polya Operator

In this paper,we calculate the sharp bound for the generalized m-linear n-dimensional Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces.As an application,the sharp bound for the Hardy-Littlewood-Polya operator on power weighted central and noncentral homo-geneous Morrey spaces is obtained.Finally,we also find the sharp bound for the Hausdorff operator on power weighted central and noncentral homogeneous Morrey spaces,which generalizes the previous results.

Characterization for commutators of n-dimensional fractional Hardy operators

In this paper,it was proved that the commutator H_(β,b)generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L^(p1)(R^n)to L^(p2)(R^n)if and only if b is a CMO(R^n)function,where 1/p1-1/p2=β/n,1<p1<∞,0≤β<n.Furthermore, the characterization of H_(β,b)on the homogenous Herz space K_q^(α,p)(R^n)was obtained.

Explicit constants for Hardy’s inequality with power weight on n-dimensional product spaces

In this paper, Hardy operator H on n-dimensional product spaces G = (0, ∞)n and its adjoint operator H* are investigated. We use novel methods to obtain two main results. One is that we characterize the sufficient and necessary conditions for the operators H and H* being bounded from Lp(G, xα) to Lq(G, xβ), and the bounds of the operators H and H* are explicitly worked out. The other is that when 1 < p = q < +∞, norms of the operators H and H* are obtained.

Commutators of n-dimensional rough Hardy operators

In this paper, we study central BMO estimates for commutators of n-dimensional rough Hardy operators. Furthermore, λ-central BMO estimates for commutators on central Morrey spaces are discussed.

A new approach to fuzzy dynamic fault tree analysis using the weakest n-dimensional t-norm arithmetic

Dynamic fault tree analysis is widely used for the reliability analysis of the complex system with dynamic failure characteristics. In many circumstances, the exact value of system reliability is difficult to obtain due to absent or insufficient data for failure probabilities or failure rates of components. The traditional fuzzy operation arithmetic based on extension principle or interval theory may lead to fuzzy accumulations. Moreover, the existing fuzzy dynamic fault tree analysis methods are restricted to the case that all system components follow exponential time-to-failure distributions. To overcome these problems, a new fuzzy dynamic fault tree analysis approach based on the weakest n-dimensional t-norm arithmetic and developed sequential binary decision diagrams method is proposed to evaluate system fuzzy reliability. Compared with the existing approach,the proposed method can effectively reduce fuzzy cumulative and be applicable to any time-tofailure distribution type for system components. Finally, a case study is presented to illustrate the application and advantages of the proposed approach.

Four kinds of raising and lowering operators of n-dimensional hydrogen atom and isotropic harmonic oscillator

The factorization of the radial Schrodinger equation of n-dimensional (n≥2) hydrogen atoms and isotropic harmonic oscillators was investigated and four kinds of raising and lowering operators were derived.The relation between n -dimensional (n≥2) and one-dimensional hydrogen atoms and harmonic oscillators was discussed.

Asymptotic Study to the N-Dimensional Radial Schrdinger Equation for the Quark-Antiquark System

Here an asymptotic study to the N-dimensional radial Schrdinger equation for the quark-antiquark interaction potential employing asymptotic iteration method via an ansatz to the wavefunction is carried out. The complete energy spectra of the consigned system is obtained by computing and adding energy eigenvalues for ground state, for large " r" and for small " r". From this analysis, the mass spectra of heavy quarkonia is derived in three dimensions. Our analytical and numerical results are in good correspondence with other experimental and theoretical studies.

A NOTE ON "THE CAUCHY PROBLEM FOR COUPLED IMBQ EQUATIONS"

In this article, we prove that the Cauchy problem for a N-dimensional system of nonlinear wave equations…… admits a unique global generalized solution in ……and a unique global classical solution in…… the sufficient conditions of the blow up of the solution in finite time are given, and also two examples are given.

m-degree Center-connecting Line of Finite Points Set and Its Properties

In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formula in finite points set. As its application,we extend the Leibniz formula and length of medians formula in n-dimensional simplex to polytope.

Fault diagnosis for t/(t+1)-diagnosable system based on the PMC model

In this paper, a t/(t+1)-diagnosable system is studied, which can locate a set S with |S|≤t+1 containing all faulty units only if the system has at most t faulty units. On the basis of the characterization of the t/(t+1)-diagnosable system, a necessary and sufficient condition is presented to judge whether a system is t/(t+1)-diagnosable. Meanwhile, this paper exposes some new and important properties of the t/(t+1)-diagnosable system to present the t/(t+1)-diagnosability of some networks. Furthermore, the following results for the t/(t+1)-diagnosability of some special networks are obtained: a hypercube network of n -dimensions is (3n-5)/(3n-4)-diagnosable, a star network of n -dimensions is (3n-5)/(3n-4)-diagnosable (n≥5) and a 2D-mesh (3D-mesh) with n 2(n 3) units is 8/9-diagnosable (11/12-diagnosable). This paper shows that in general, the t/(t+1)-diagnosability of a system is not only larger than its t/t -diagnosability , but also its classic diagnosability, specially the t/(t+1)-diagnosability of the hypercube network of n -dimensions is about 3 times as large as its classic t -diagnosability and about 1.5 times as large as its t/t -diagnosability.

Unified Treatment of Screening Coulomb and Anharmonic Oscillator Potentials in Arbitrary Dimensions

A mapping is obtained relating radial screened Coulomb systems with low screening parameters to radial anharmonic oscillators in N-dimensional space. Using the formalism of supersymmetric quantum mechanics, it is shown that exact solutions of these potentials exist when the parameters satisfy certain constraints.

Discreteness Criterion for Subgroups in PU（1,n;C）

In this paper,the authors introduce the discreteness criterion for n-dimensional subgroups in PU(1, n; C).These generalize the well-known discreteness criterion first established by T.Jorgensen.

Irregular but Nonfractal Drums and n-Dimensional Weyl Conjecture

In this paper, we study the asymptotics of the spectrum of the Dirichlet （or Neumann） Laplacian in a bounded open set ΩRn（n≥1） with irregular but nonfractal boundary Ω. We give a partial resolution of the Weyl conjecture, i.e. for the counting function Ni（λ）（i=0: Dirichlet; i=i: Neumann）, we have got a precise estimate of the remainder term Ψi（λ）=φ（λ）-Ni（λ） for large λ, where φ（λ） is the Weyl term. This implies that for the irregular but nonfractal drum Ω, not only the volume |Ω|n is spectral invariant but also the area of boundary |Ω|n-1 might be spectral invariant as well.