[en] The behavior at z=1 of the generalized hypergeometric function ₃F₂(a,b,c;e,f;z) is investigated. First the analytic continuation near z=1 is obtained for the general case when s=e+f-a-b-c is not equal to an integer. The corresponding continuation formulas for the special cases when s is equal to an integer are then derived by appropriate limiting processes. When f=c or e=c, the formulas immediately reduce to the well-known continuation formulas of the Gaussian hypergeometric function. (orig.)

[en] The potential theory centres on the standard decomposition and representation theorems for subharmonic functions. In addition, the first and second fundamental theorems of Nevanlinna's theory of meromorphic functions are derived and, after two applications to differential equations, some open problems are discussed. Systematic use is made of L. Schwartz's theory of distributions. (author)

[en] A certain generalization of Hardy's inequality cencerning the fourier coefficients of functions integrable on the circle was discussed. More specifically, we examine a result proved by Ivo Klemes (Klemes, 1993) and his construction sucessively in order to get a bounded function with certain equality-properties, rather than having inequality-properties were examinedthese properties then are used to prove a similar from of Klemes' result but allowing gaps in the spectrum of the function. This new from of Klemes' inequality happens to be a good generalization of McGehee's inequality (Megehee. 1981) which is a generalization of the original Hardy's inequality. (author).

No abstract available

[en] In connection with the formerly type of asymptotic functions the problem of the substitutions of the independent variable with a function of this variable is considered. The proposed substitution type is more general than the one in Sobolev-Schwartz theory of generalized functions. The restrictions for the substitute functions at which the new functions obtained by substitutions would be asymptotic are determined. The sustitute function must be defined and infinitely smooth for all real values of the variable, and the function module has to increase faster than some power of the variable. For each value of the variable at least one function derivative must have a non-zero value. In the proposed scheme symbols like delta(x)²,delta''(x⁵) as well as delta(x³)²,delta''(x⁴)⁵ etc. considered as asymptotic functions are meaningful. However, their functionals over the infinitely smooth test functions with finite support do not lead in general to ordinary but to infinitely large asymptotic numbers

[en] In this study an important result of the characterization for convex functions of complex order is order given and we present a coefficient inequality for convex functions under the regularly univalent conditions

[en] A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Lastly, dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.

[en] The functional integral representation for the generating functional of t-J-V model is obtained. In the case close to half filling this functional integral representation reduces the conventional Hamiltonian of t-J-V model to the Hamiltonian of the system containing holes and spins 1/2 at each lattice size. This effective Hamiltonian coincides with that one obtained one of the authors by different method. This Hamiltonian and its dynamical variables can be used for description of different magnetic phases of t-J-V model. (author). 16 refs

[en] Wavefunction correlations and density matrices for few or many particles are derived from the properties of semiclassical energy Green functions. Universal features of fixed energy (microcanonical) random wavefunction correlation functions appear which reflect the emergence of the canonical ensemble as N → ∞. This arises through a little known asymptotic limit of Bessel functions. Constraints due to symmetries, boundaries and collisions between particles can be included

[en] The behaviour of the inclusive spectrum fsub(ab→c) in the asymptotic region is discussed. On the basis of the Jost-Lehmann-Dyson representation it is shown that inclusive processes are described by some structure functions, depending only on ν, q² (ν=2psub(b)(psub(a)-psub(c)); q²=(psub(a)-psub(c))²) under certain restrictions on the J-L-D spectral functions. As these dynamical characteristics (structure functions) do not depend on the sum(psub(a)+psub(c)), the effective interaction of hadrons ''a'' and ''c'' is as if local