on the birational geometry of fano 4 folds we study the birational geometry of a fano fourfold x from the point of view of mori dream spaces more precisely we study rational contractions of x here a rational contraction is a rational map f x dashrightarrow y where y is normal and projective which factors as a finite sequence of flips followed by a surjective morphism with connected fibers such f is called elementary if x y 1 where is the picard number we first give a characterization of non movable prime divisors in x when x 6 this is related to the study of birational and divisorial elementary rational contractions of x then we study the rational contractions of fiber type on x which are elementary or more generally quasi elementary the main result is that x 11 if x has an elementary rational contraction of fiber type and x 18 if x has a quasi elementary rational contraction of fiber type

solution of a system of nonlinear equations by adomian decomposition method in this paper the adomian decomposition method is applied to solve a system of nonlinear equations convergence of the method is proved and some examples are presented to illustrate the method

super cubic iterative methods to solve systems of nonlinear equations two super cubic convergence methods to solve systems of nonlinear equations are presented the first method is based on the adomian decomposition method we state and prove a theorem which shows the cubic convergence for this method but numerical examples show super cubic convergence the second method is based on a quadrature formulae to obtain the inverse of jacobian matrix numerical examples show high order convergence for both methods

random walks in random dirichlet environment are transient in dimension d 3 we consider random walks in random dirichlet environment rwde which is a special type of random walks in random environment where the exit probabilities at each site are i i d dirichlet random variables on z d rwde are parameterized by a 2d uplet of positive reals we prove that for all values of the parameters rwde are transient in dimension d ge 3 we also prove that the green function has some finite moments and we characterize the finite moments our result is more general and applies for example to finitely generated symmetric transient cayley graphs in terms of reinforced random walks it implies that directed edge reinforced random walks are transient for d ge 3

random walks in asymmetric random environments we consider random walks on zd with transition ratesp x y given by a random matrix ifp is a small random perturbation of the simple random walk we show that the walk remains diffusive for almost all environmentsp ifd 2 the result also holds for a continuous time markov process with a random drift the corresponding path space measures converge weakly in the scaling limit to the wiener process for almost everyp

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

a note on the local convergence of iterative methods based on adomian decomposition method and 3 node quadrature rule abstract darvishi and barati m t darvishi a barati super cubic iterative methods to solve systems of nonlinear equations appl math comput 2006 10 1016 j amc 2006 11 022 derived a super cubic method from the adomian decomposition method to solve systems of nonlinear equations the authors showed that the method is third order convergent using classical taylor expansion but the numerical experiments conducted by them showed that the method exhibits super cubic convergence in the present work using ostrowski s technique based on point of attraction we show that their method is in fact fourth order convergent we also prove the local convergence of another fourth order method from 3 node quadrature rule using point of attraction

global generation of pluricanonical and adjoint linear series on smooth projective threefolds the purpose of this paper is to show how the cohomological techniques developed by kawamata reid shokurov and others lead to some effective and practical results of reider type on freeness of linear series on smooth complex projective threefolds in recent years there has been a great deal of interest in the geometric properties of pluricanonical and adjoint linear systems on surfaces and higherdimensional varieties among other things one wants to understand as explicitly as possible when the systems in question are base point free or very ample modem work in this area goes back to kodaira kod and bombieri bmb who studied pluricanonical maps of surfaces of general type more recently many of their results have emerged as special cases of a celebrated theorem of reider rdr reider uses vector bundle techniques to show that if b is a nef line bundle on a surface x such that b2 5 then kx b is globally generated unless there exist certain special curves c c x such that b c 1 he also obtains analogous criteria for kx b to be very ample a cohomological approach to these theorems based on miyaoka s vanishing theorem for zariski decompositions was given by sakai sak2

predictor corrector halley method for nonlinear equations abstract in this paper we suggest and analyze a new two step predictor corrector type iterative methods for solving nonlinear equations of the type f x 0 by using the technique of updating the solution this method can be viewed as a predictor corrector iterative halley s method we also consider the convergence analysis of the proposed method to illustrate the efficiency of this new method we give several examples and a comparison with the method of grau and diaz barrero m grau j l diaz barrero an improvement to ostrowski root finding method appl math comput 173 2006 450 456 is given this method can be considered as a refinement and improvement of the halley method

a quenched invariance principle for non elliptic random walk in i i d balanced random environment we consider a random walk on mathbb z d d ge 2 in an i i d balanced random environment that is a random walk for which the probability to jump from x in mathbb z d to nearest neighbor x e is the same as to nearest neighbor x e assuming that the environment is genuinely d dimensional and balanced we show a quenched invariance principle for p almost every environment the diffusively rescaled random walk converges to a brownian motion with deterministic non degenerate diffusion matrix within the i i d setting our result extend both lawler s uniformly elliptic result comm math phys 87 1 pp 81 87 1982 1983 and guo and zeitouni s elliptic result to appear in ptrf 2010 to the general non elliptic case our proof is based on analytic methods and percolation arguments

algorithms for embedded monoids and base point free problems abstract we present algorithms for basic computations with monoids in finitely generated abelian groups such as monoid membership testing and computing an element of the conductor ideal applying them to mori dream spaces we obtain algorithms to test whether a weil divisor class of a given mori dream space is base point free to compute generators of the monoid of base point free cartier divisor classes and to test whether a q factorial mori dream space with known canonical class fulfills fujita s base point free conjecture or not

vector bundles of rank 2 and linear systems on algebraic surfaces let s be a smooth complex algebraic surface and let l be a divisor on s it is well known that the linear system il ksi where ks is the canonical divisor plays an important role in understanding the geometry of s several authors see for example 8 11 studied various properties of this system our paper treats the same subject but the point of view is different from the works mentioned above the philosophy underlying our approach is almost classical points on s more generally effective 0 cycles in special position with respect to il ksi see definition below contain information about the geometry of s this point of view was recently revived in 5 also 10 in fact this paper contains the technique of going from the effective 0 cycle z in special position with respect to il ksi to the geometry of s for the sake of completeness we give a definition and state a theorem which can be found in 5 10

iterative methods improving newton s method by the decomposition method in this paper we present a sequence of iterative methods improving newton s method for solving nonlinear equations the adomian decomposition method is applied to an equivalent coupled system to construct the sequence of the methods whose order of convergence increases as it progresses the orders of convergence are derived analytically and then rederived by applying symbolic computation of maple some numerical illustrations are given

an invariance principle for isotropic diffusions in random environment we investigate in this work the asymptotic behavior of isotropic diffusions in random environment that are small perturbations of brownian motion when the space dimension is three or more we prove an invariance principle as well as transience our methods also apply to questions of homogenization in random media

random walks in random environments random walks in random environments and their diffusion analogues have been a source of surprising phenomena and challenging problems especially in the non reversible situation since they began to be studied in the 1970s we review the model available results and techniques and point out several gaps in the understanding of these processes

new family of iterative methods for nonlinear equations in this paper we suggest and analyze a new family of iterative methods for solving nonlinear equations using the system of coupled equations coupled with decomposition technique several numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations

a third order newton type method to solve systems of nonlinear equations in this paper we present a third order newton type method to solve systems of nonlinear equations in the first we present theoretical preliminaries of the method secondly we solve some systems of nonlinear equations all test problems show the third order convergence of our method

new iterative schemes for nonlinear equations in this paper we suggest and analyze a new iterative method for solving nonlinear equations by using a new decomposition method we also discuss the convergence criteria of these iterative methods several numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations

on new examples of ballistic random walks in random environment in this article we show that random walks in random environment on zd d 3 with transition probabilities which are e perturbations of the simple random walk and such that the expectation of the local drift has size bigger than e with 52 when d 3 3 when d 4 fulfill the condition t introduced by sznitman prob theory related fields 2002 122 509 544 when e is small as a result these walks satisfy a law of large numbers with nondegenerate limiting velocity a central limit theorem and several large deviation controls in particular this provides examples of ballistic random walks in random environment which do not satisfy kalikow s condition in the terminology of sznitman and zerner ann probab 1999 27 1851 1869 an important tool in this work is the effective criterion of sznitman

an invariance principle for a class of non ballistic random walks in random environment we are concerned with random walks on mathbb z d d ge 3 in an i i d random environment with transition probabilities varepsilon close to those of simple random walk we assume that the environment is balanced in one fixed coordinate direction and invariant under reflection in the coordinate hyperplanes the invariance condition was used in baur and bolthausen ann probab 2013 arxiv 1309 3169 as a weaker replacement of isotropy to study exit distributions we obtain precise results on mean sojourn times in large balls and prove a quenched invariance principle showing that for almost all environments the random walk converges under diffusive rescaling to a brownian motion with a deterministic diagonal diffusion matrix our work extends the results of lawler commun math phys 87 81 87 1982 where it is assumed that the environment is balanced in all coordinate directions

new iterative methods for solving nonlinear equation by using homotopy perturbation method in this paper we suggest and analyze a new class of iterative methods for solving nonlinear equations by using the homotopy perturbation method convergence of their method is also considered here we also discuss the efficiency index and computational order of convergence of new methods several numerical examples are given to illustrate the efficiency and performance of these new methods these new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations

an effective criterion for ballistic behavior of random walks in random environment we investigate multi dimensional random walks in random environment specifically we provide an effective criterion which can be checked by inspection of the environment in a finite box and implies a ballistic strong law of large numbers a central limit theorem and several large deviation controls with the help of this criterion we provide an example of a ballistic multi dimensional walk which does not fulfill the criterion introduced by kalikow in 4 the present work complements the results of 9 where a certain condition t was introduced and confirms the interest of this condition

multiscale analysis of exit distributions for random walks in random environments we present a multiscale analysis for the exit measures from large balls in mathbb z d d geq 3 of random walks in certain i i d random environments which are small perturbations of the fixed environment corresponding to simple random walk our main assumption is an isotropy assumption on the law of the environment introduced by bricmont and kupiainen under this assumption we prove that the exit measure of the random walk in a random environment from a large ball approaches the exit measure of a simple random walk from the same ball in the sense that the variational distance between smoothed versions of these measures converges to zero we also prove the transience of the random walk in random environment the analysis is based on propagating estimates on the variational distance between the exit measure of the random walk in random environment and that of simple random walk in addition to estimates on the variational distance between smoothed versions of these quantities

newton like iterative methods for solving system of non linear equations abstract homotopy perturbation method hpm is applied to construct a new family of newton like iterative methods for solving system of non linear equations comparison of the result obtained by the present method with newton raphson method reveals that the accuracy and fast convergence of the new method

iterative methods of order four and five for systems of nonlinear equations the adomian decomposition is used in order to obtain a family of methods to solve systems of nonlinear equations the order of convergence of these methods is proved to be p 2 under the same conditions as the classical newton method also numerical examples will confirm the theoretical results

modified householder iterative method for nonlinear equations abstract in this paper we suggest and analyze a new two step predictor corrector type iterative method for solving nonlinear equations of the type f x 0 this new method includes the two step newton method as a special case we show that this new two step method is a sixth order convergent method several examples are given to illustrate the efficiency of this new method and its comparison with other sixth order methods this method can be considered as a significant improvement of the newton method and its variant forms

a new fourth order newton type method for solution of system of nonlinear equations in this paper we suggest a series of iterative schemes for solution of nonlinear equations we have derived these schemes using adomian decomposition technique developed by adomian in 1980s 22 the methods we suggest have good efficiency and important thing is that these methods are of practical importance the fourth order convergence of the method is proved and few examples are presented to illustrate the methods

random dirichlet environment viewed from the particle in dimension d ge 3 we consider random walks in random dirichlet environment rwde which is a special type of random walks in random environment where the exit probabilities at each site are i i d dirichlet random variables on zd rwde are parameterized by a 2d tuple of positive reals called weights in this paper we characterize for d 3 the weights for which there exists an absolutely continuous invariant probability distribution for the process viewed from the particle we can deduce from this result and from ann inst henri poincare probab stat 47 2011 1 8 a complete description of the ballistic regime for d 3

some iterative methods for solving a system of nonlinear equations in this paper we suggest and analyze two new two step iterative methods for solving the system of nonlinear equations using quadrature formulas we prove that these new methods have cubic convergence several numerical examples are given to illustrate the efficiency and the performance of the new iterative methods these new iterative methods may be viewed as an extension and generalizations of the existing methods for solving the system of nonlinear equations