A bstract It is well known that quantum tunneling can be described by instantons in the imaginary-time path integral formalism. However, its description real-time formalism has been elusive. Here we establish a statement characterized general contribution of complex saddle points, which identified using Picard-Lefschetz theory. We demonstrate this explicitly performing Monte Carlo simulations s...

in this paper, the picard method is proposed to solve the bernoulli equation with fuzzy initial condition under generalized h-differentiability. the existence and uniqueness of the solution and convergence of the proposed method are proved in details. finally an example shows the accuracy of this method.

An analogue of the Eisenstein irreducibility criterion is developed for linear differential operators, or, more generally, noncommutative polynomials, and is applied to a few simple examples. Introduction. The question of the irreducibility of an ordinary linear differential operator is of interest in the Picard-Vessiot theory (see Kolchin [1, §22]). Indeed, the operator is irreducible if and o...

Let L2 denote the stable homotopy category of v−1 2 BP -local spectra at the prime three. In [2], it is shown that the Picard group of L2 consisting of isomorphic classes of invertible spectra is isomorphic to either the direct sum of Z and Z/3 or the direct sum of Z and two copies of Z/3. In this paper, we conclude the Picard group is isomorphic to the latter group by showing the existence of ...

S U M M A R Y The stationary Reynolds equation is solved over a rectangular region. The problem is linearized by Picard linearization. The ADI method is used to solve the resulting set of linear equations. A set of parameters is introduced to speed up convergence as well for the Picard linearization as for the ADI method. A comparison is made with Booy-Coleman's method. Results are given for be...

We study nonsingular branched coverings of a homogeneous space X. There is a vector bundle associated with such a covering which was conjectured by O. Debarre to be ample when the Picard number of X is one. We prove this conjecture, which implies Barth-Lefschetz type theorems, for lagrangian grassmannians, and for quadrics up to dimension six. We propose a conjectural extension to homogeneous s...

We classify all smooth projective horospherical varieties with Picard number 1. We prove that the automorphism group of any such variety X acts with at most two orbits and that this group still acts with only two orbits on X blown up at the closed orbit. We characterize all smooth projective two-orbit varieties with Picard number 1 that satisfy this latter property. Mathematics Subject Classifi...

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a carefull analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate th...

This paper discusses the diffusion equation with a damping term as follows ut = div(|Dum|p−2Dum)− u1 |Du|1 , where p > 2,m > 1, and p > p1, q1+p1m > m(p−1) > 1. By the standard Picard iteration method, a sufficient condition is given to the existence of the singular self-similar solutions. Moreover, the paper gives a classification for these singular self-similar solutions. Key–Words: Diffusion...