Let f = (f1, . . . , fl) : U → Kl, with K = R or C, be a K-analytic mapping defined on an open set U ⊆ Kn, and let Φ be a smooth function on U with compact support. In this paper, we give a description of the possible poles of the local zeta function attached to (f , Φ) in terms of a log-principalization of the ideal If = (f1, . . . , fl). When f is a non-degenerate mapping, we give an explicit...

Following what is basically Kummer’s relatively neglected approach to non-unique factorization, we determine the structure of the irreducible factorizations of an element n in the ring of integers of a number field K. Consequently, we give a combinatorial expression for the number of irreducible factorizations of n in the ring. When K is quadratic, we show in certain cases how quadratic forms c...

In this paper we provide a geometric description of the possible poles of the Igusa local zeta function ZΦ(s, f) associated to an analytic mapping f = (f1, . . . , fl) : U(⊆ K ) → K, and a locally constant function Φ, with support in U , in terms of a log-principalizaton of the K [x]−ideal If = (f1, . . . , fl). Typically our new method provides a much shorter list of possible poles compared wi...

A toroidalization of a dominant morphism $varphi: Xto Y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $X$ and $Y$. We give a proof of toroidalization of locally toroidal morphisms of 3-folds.

The aim of this scientific study was to see the effect of therapeutic interventions on pathological gamblers. 259 subjects were consisted for this study out of these 55 experimental ( treated ) and 55 control ( untreated ) group of pathological gamblers were evaluated at the S.I. Mental and Physical Health Society (SIMPHS), Varanasi, India. All the subjects were matched on the variables of age ...

We compute the cyclicity of open period annuli following generalized Rayleigh-Liénard equation \begin{document}$ \ddot{x}+ax+bx^3-(\lambda_1+\lambda_2 x^2+\lambda_3\dot{x}^2+\lambda_4 x^4+\lambda_5\dot{x}^4+\lambda_6 x^6)\dot{x} = 0 $\end{document} and equivalent planar system $ X_\lambda $, where coefficients perturbation \lambda_j are independent small parameters a, b fixed nonzero constants....

We provide algorithms to count and enumerate representatives of the (right) ideal classes of an Eichler order in a quaternion algebra defined over a number field. We analyze the run time of these algorithms and consider several related problems, including the computation of two-sided ideal classes, isomorphism classes of orders, connecting ideals for orders, and ideal principalization. We concl...