Discontinuities of Banana Integrals in Dispersion Relation Representation

We derive the discontinuities of banana integrals using the dispersion relation iteratively,and find a series of identities between the parameterized discontinuities of banana integrals(p-DOBIs).Similar to elliptic integrals,these identities enable the reduction of various p-DOBIs to be a linear combination of some fundamental ones.We present a practical application of p-DOBIs for deriving the Picard–Fuchs operator.Then we establish the expression of generalized dispersion relation,which enables us to obtain the dispersion relation representation of arbitrary banana integrals.Moreover,we propose a hypothesis for generalized dispersion relation and p-DOBIs,which provides a simple way to calculate the discontinuities and transform dispersion relation representation to p-DOBIs.

Legendre-Jacobi’s Elliptic Integrals Shed Light on the Luminosity Distance in Cosmology

This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.

CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS

Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.

THE FRACTIONAL TYPE MARCINKIEWICZ INTEGRALS AND COMMUTATORS ON WEIGHTED HARDY SPACES

This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).

Multiple parametric Marcinkiewicz integrals with mixed homogeneity along surfaces

In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction. The main results essentially improve and extend certain previous results.

Sharp power-type Heronian and Lehmer means inequalities for the complete elliptic integrals

In the article,we prove that the inequalities H_(p)(K(r);E(r))>π/2;L_(q)(K(r);E(r))>π/2 hold for all r 2(0;1)if and only if p≥3=4 and q≥3=4,where Hp(a;b)and Lq(a;b)are respectively the p-th power-type Heronian mean and q-th Lehmer mean of a and b,and K(r)and E(r)are respectively the complete elliptic integrals of the first and second kinds.

The Stability of the Gauss-Laguerre Rule for Cauchy P.V. Integrals on the Half Line

In this paper, the authors give a different and more precise analysis of the stability of the classical Gauss-Laguerre quadrature rule for the Cauchy P.V. integrals on the half line. Moreover, in order to obtain this result they give some new estimates for the distance of the zeros of the Laguerre polynomials that can be useful also in other contests.

Boundedness of singular integrals along surfaces on Lebesgue spaces

In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications of this inequality.

The Calculation of Parameters for DNA Kinetic Structure Based on Monte-Carlo Multiple Integrals

Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA structure statistical mechanical model,and time complexity and precision were analyzed on the calculated results.

Weighted L^p-boundedness of Multilinear Oscillatory Singular Integrals with Calderón-Zygmund Kernel

In this paper, weighted L p-boundedness is obtained for a class of multilinear oscillatory singular integrals with Calderón-Zygmund kernel.

A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES

Let h, be a measurable function defined on R^＋ ×R^＋. Let Ω ∈ L（log L^＋）^υq （S^n1-1 × S^n2-1） （1≤ υq ≤ 2） be homogeneous of degree zero and satisfy certain cancellation conditions. We show that the singular integral Tf（x1,x2）=p.v.∫∫R^n1＋n2 Ω（y′1,y′2）h（｜y1｜,｜y2｜）/｜y1｜^n1｜y2｜^n2 f（x1-y1,x2-y2）dy1dy2maps from Sp,q^α1,α2F（R^n1×R^n2）boundedly to itself for 1 〈 p, q 〈 ∞, α1, α2 ∈R.

Peano Derivatives and Singular Integrals of Arbitrary Order

The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals and Cauchy principal value integrals is established.

On AP-Henstock Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions

In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce the thought of the AP- Henstock integrals of interval-valued functions and fuzzy-number-valued functions which are extensions of [1] and investigate a number of their properties.

On Henstock-Stieltjes Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions

In this paper we introduce the notion of the Henstock-Stieltjes (HS) integrals of interval-valued functions and fuzzy-number-valued functions and discuss some of their properties.

MONOTONICITY,CONVEXITY AND INEQUALITIES INVOLVING THE GENERALIZED ELLIPTIC INTEGRALS

We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.

Functional Integrals and Free Energy in sine-Gordon-Thirring Model with Impurity Coupling

The free energy at low temperature in 1D sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals method. For massive free sine-Gordon-Thirring model, free energy is obtained from perturbation expansion of functional determinant. Moreover, the free energy of massive model is calculated by use of an auxiliary Bose field method.

Functional Integrals and Collective Excitations in Boson-Fermion Model

In this paper, collective excitations in the boson-fermion model are investigated by means of functional integration method. The equations of energy gap and excitation spectrum are derived. Moreover, the Bose energy spectrum of zero wave vector Fermi fields is also calculated.

Functional Integrals and Quantum Fluctuations on Two-Dimensional Noncommutative Space-Time

The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.

Functional Integrals and Excitation Energy in Three-Band Hubbard Model

The normal and anomalous Green＇s functions of antiferromagnetie state in three-band Hubbard model are studied by using functional integrals and temperature Green＇s function method. The equations of energy spectrum are derived. In addition, excitation energy of Fermi fields are calculated under long wave approximation.

Several Fundamental Theorems and Conservative Integrals in Quasicrystal Elasticity Theory

Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.