This article was originally published in Russian in ”Representation Theory, Dynamical Systems, Combinatorial and Algorithmic Methods. Part 2” (A. M. Vershik, ed.), Zapiski Nauchnyh Seminarov POMI 240 (1997), 115–135 (this text in Russian is available via http://www.pdmi.ras.ru/znsl/1997/v240.html). As it was mentioned in the ”Journal-Ref” field this English translation was published in Journal ...

<p style='text-indent:20px;'>In this paper, we establish a new summation formula for Schur processes, called the <i>complete formula</i>. As an application, obtain generating function and asymptotic number of <i>doubled shifted plane partitions</i>, which can be viewed as partitions "shifted at two sides". We prove that order depends only on diagonal width doubled ...

We introduce interpolation analogues of Schur Q-functions — the multiparameter Schur Q-functions. We obtain for them several results: a combinatorial formula, generating functions for one-row and two-rows functions, vanishing and characterization properties, a Pieri-type formula, a Nimmo-type formula (a relation of two Pfaffians), a Giambelli-Schur-type Pfaffian formula, a determinantal formula...

We prove the validity of Schwinger’s quartic nonet mass formula for a general nonet structure with the isoscalar singlet mass being shifted from its “ideal” value. We apply this formula to the problem of the correct qq̄ assignment for the scalar meson nonet. The results favor scalar isoscalar singlet and isoscalar octet masses in the vicinity of 1 GeV and 1.45 GeV, respectively. We explain the f...

In this series we examine the calculation of the 2kth moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper begins the general study of what we call Type II sums which utilize a circle method framework and a convolution of shifted convolution sums to obtain all of the lower order terms in the asy...

We discuss Sekiguchi-type differential operators, their eigenvalues, and a generalization of Andrews-Goulden-Jackson formula. These will be applied to extract explicit formulae involving shifted partitions and hook lengths. 1. Differential operators. The standard Jack symmetric polynomials Pλ(y1, . . . , yn;α) (see Macdoland, Stanley [5, 10]) as well as their shifted counter-parts (replace θ = ...

The objective of this study was to perform a comparative investigation of the capability of various classifiers in discriminating benign from malignant thyroid lesions. Using May Grunvald-Giemsa-stained smears taken by fine needle aspiration (FNA) and a custom image analysis system, 25 nuclear features describing the size, shape and texture of the nuclei were measured in each case. A statistica...

This paper derives asymptotic expansion formulas for option prices and implied volatilities as well as the density of the underlying asset price in multi-dimensional stochastic volatility models. In particular, the integration-byparts formula in Malliavin calculus and the push-down of Malliavin weights are effectively applied. We provide an expansion formula for generalized Wiener functionals a...