Three types of integral representations for the cumulative distribution functions of convolutions of Γp(αk,Σk,∆k)–distributions with non–centrality matrices ∆k are given by integration of products of simple complex functions over the p–cube (−π, π]. In particular, the joint distribution of the diagonal elements of a generalized quadratic form XAX ′ with n independentNp(μk,Σ)–distributed columns...

A new mathematical model of time fractional order heat equation and fractional order boundary condition have been constructed in the context of the generalized theory of thermo piezoelasticity. The governing equations have been applied to a semi infinite piezoelectric slab. The Laplace transform technique is used to remove the time-dependent terms in the governing differential equations and the...

Abstract We consider the numerical evaluation of one dimensional projections of general multivariate stable densities introduced by Abdul-Hamid and Nolan (1998). In their approach higher order derivatives of one dimensional densities are used, which seem to be cumbersome in practice. Furthermore there are some difficulties for even dimensions. In order to overcome these difficulties we obtain t...

The Schrödinger equation (Hpsi) (r) = [E+u(E)W(r)]psi(r) with an energy-dependent complex absorbing potential -u(E)W(r), associated with a scattering system, can be reduced for a special choice of u(E) to a harmonic inversion problem of a discrete pseudotime correlation function y(t) = phi(T)U(t)phi. An efficient formula for Green's function matrix elements is also derived. Since the exact prop...

The asymmetric unit of the title compound, [Mn(2)Cl(4)(C(30)H(36)N(6))], contains one-half of the formula unit; a centre of inversion is located at the mid-point of the mol-ecule. The two Mn(2+) ions are bridged by the dual tri-dentate N,N,N',N'-tetra-kis(2-pyridylmeth-yl)hexane-1,6-diamine ligand to form a dinuclear complex. Each Mn atom is five-coordinated in an approximately square-pyramidal...

The asymmetric unit of the title complex, [Ag(2)(C(22)H(30)N(4))(2)](PF(6))(2), consists of one Ag(I) ion, one 1,4-bis-[(3-butyl-imidazolium-1-yl)meth-yl]benzene ligand and one discrete hexa-fluoridophosphate anion. The formula unit is generated by an inversion center. The unique Ag(I) ion is coordinated by two C atoms of two heterocyclic carbene ligands in an essentially linear geometry. In th...

The formula unit of the title mol-ecular complex, 2C(16)H(16)N(2)O(3)·C(16)H(16)N(2)O(2), consists of two (E)-N'-[1-(2-hy-droxy-phen-yl)ethyl-idene]-2-phen-oxy-acetohydrazide mol-ecules and one mol-ecule of 2,2'-(1,1'-azinodiethyl-idyne)diphenol, with the latter located on a crystallographic inversion center. The acetohydrazide mol-ecules are linked into a supermolecular chain along the c axis ...

LetGn,k(K) be the Grassmannian manifold of k-dimensional K-subspaces in K where K = R,C,H is the field of real, complex or quaternionic numbers. For 1 ≤ k ≤ k ≤ n − 1 we define the Radon transform (Rf)(η), η ∈ Gn,k′(K), for functions f(ξ) on Gn,k(K) as an integration over all ξ ⊂ η. When k+ k ≤ n we give an inversion formula in terms of the G̊arding-Gindikin fractional integration and the Cayley...

Migration velocity analysis (MVA) is an approach to solve a partially linearized variant of the waveform inversion problem, i.e. linear in short scales, nonlinear in long scales. The linear inversion part is often approximated by migration in practice, which is only adjoint of linearized Born modeling operator. In this abstract, we derive the gradient formulas for short scales and long scales s...