A test statistic based on population quantiles using sample order statistics is suggested. The quantiles of the test statistics are evaluated for generalized exponential distribution. Similar test statistic based on moments of sample order statistic is referred and the proposed test formula is compared with it. Between the pairs of the above models it is established that the test formula propos...

This paper gives a formula for Generalized Exponential sums which depends entirely upon the singularities mod p, similar to the purpose of the Stationary Phase Formula for Igusa Local Zeta Functions. This new formula is then applied to two examples: strongly non-degenerate homogeneous polynomials and general quadratic polynomials. This work was completed as part of the Mount Holyoke Summer Math...

when the relation B−A+C = 1 holds. In this paper a formula is presented which evaluates this series in case when B −A+C is an integer. The formula expresses the infinite series as a linear combination of two Γ-terms with coefficients being finite hypergeometric 3F2 series. Algorithmical problems of summation of infinite hypergeometric series are considered in the light of the generalized formul...

Non-adiabatic transitions are studied in a spin-boson model with multiple scattering points. In order to generalize the Landau–Zener formula, which describes the case of a single scattering point, we define an “effective gap” for a set of scattering points. The generalized formula agrees very well with numerical results of the nonadiabatic dynamics, which we obtained by a direct numerical metho...

In the article, the noted Darboux’s formula of functions with single variable is generalized to that of functions of two independent variables with integral remainder, some important special cases of Darboux’s formula of functions with two variables are obtained, and some estimates of the integral remainders and Darboux’s expansion of the function ln(x + y) are given. These results generalize A...

We introduce a new product formula which combines an orthogonal projection with a complex function of a non-negative operator. Under certain assumptions on the complex function the strong convergence of the product formula is shown. Under more restrictive assumptions even operator-norm convergence is verified. The mentioned formula can be used to describe Zeno dynamics in the situation when the...

The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. The result is applied to prove a conjectural character formula put forward by van der Jeugt et al in the late 80s. We simplify this character formula to cast it into the Kac-Weyl form, and derive from it a closed formula for the dimension...

Recently, two different approaches were put forward to extend the supersymmetry method in random matrix theory from Gaussian ensembles to general rotation invariant ensembles. These approaches are the generalized Hubbard– Stratonovich transformation and the superbosonization formula. Here, we prove the equivalence of both approaches. To this end, we reduce integrals over functions of supersymme...

We introduce generalized operator valued Jost solutions of first order ill-posed differential equations on Hilbert spaces. We then construct an infinite dimensional Evans function for abstract differential equations as a 2– modified Fredholm determinant of the operator obtained by adding the values at zero of the generalized operator valued Jost solutions. Next, we prove a formula that connects...