mesh refinement processes based on the generalized bisection of simplices mesh refinement processes based on the generalized bisection of simplices are discussed and characterized in the context of the general theory of rheinboldt siam j numer anal 17 1980 pp 766 778 then it is proved that such processes allow the construction of sequences of naturally smooth conforming and nested nonuniform meshes in fact it is shown that there exists a generalized mesh refinement operator that for any conforming triangulation delta and for any v subset delta produces a nested smooth conforming triangulation delta containing successors of all elements of v and such that the minimum cell size of delta is bounded from below by half the minimum cell size of delta two conforming mesh refinement algorithms that allow the selective refinement of computational triangulations are explicitly given

an interval newton method we introduce an interval newton method for bounding solutions of systems of nonlinear equations it entails three subalgorithms the first is a gauss seidel type step the second is a real noninterval newton iteration the third solves the linearized equations by elimination we explain why each subalgorithm is desirable and how they fit together to provide solutions in as little as one third or one quarter the time required by krawczyk s method 7 in our implementations

multiple comparison procedures for steady state simulations suppose that there are k 2 different systems i e stochastic processes where each system has an unknown steady state mean performance and unknown asymptotic variance we allow for the asymptotic variances to be unequal and for the distributions of the k systems to be different we consider the problem of running independent single stage simulations to make multiple comparisons of the steady state means of the different systems we derive asymptotically valid as the run lengths of the simulations of the systems tend to infinity simultaneous confidence intervals for each of the following problems all pairwise comparisons of means all contrasts multiple comparisons with a control and multiple comparisons with the best our confidence intervals are based on standardized time series methods and we establish the asymptotic validity of each under the sole assumption that the stochastic processes representing the simulation output of the different systems satisfy a functional central limit theorem although simulation is the context of this paper the results naturally apply to asymptotically stationary time series

an interval arithmetic approach to sensitivity analysis in geometric programming geometric programming has been an important optimization approach in several engineering design areas in this paper we present an approach to sensitivity analysis in geometric programming using interval arithmetic the study of the effect of changes in the problem parameters is important for theoretical as well as for practical reasons to date most of the numerical approaches to sensitivity analysis have characterized the solution in terms of differential changes in the parameters we use interval arithmetic to generate an interval of solution values associated with an interval of parameter values these results indicate a new approach to characterizing solutions to geometric programs in terms of changes in the problem parameters

bounds for lagrange multipliers and optimal points abstract we describe two methods for use in constrained optimization problems one method computes guaranteed bounds on both the lagrange multipliers and on the location of the optimal points the other method bounds the lagrange multipliers only both methods provide bounds for perturbed problems the methods can prove in the presence of rounding the existence or nonexistence of a solution in a given region

using standardized time series to estimate confidence intervals for the difference between two stationary stochastic processes this paper discusses confidence interval estimation for the difference between the means of two independent strictly stationary phi mixing stochastic processes the confidence intervals are based on batched subseries of the two time series and are obtained by using schruben s standardized time series method we compare these intervals with the classical result applied to the batch means and consider different assumptions on the variances and the number of observations the comparison results show that the four new estimators for each case have asymptotic properties that clearly dominate the classical estimator two applications of these intervals are 1 validating stationary discrete event simulation models and 2 comparing two alternative policies or system designs via simulation

preconditioners for the interval gauss seidel method interval newton methods in conjunction with generalized bisection can form the basis of algorithms that find all real roots within a specified box bf x subset bf r n of a system of nonlinear equations f x 0 with mathematical certainty even in finite precision arithmetic in such methods the system f x 0 is transformed into a linear interval system 0 f m bf f bf x bf bar x m if interval arithmetic is then used to bound the solutions of this system the resulting box bf bar x contains all roots of the nonlinear system the interval gauss seidel method is a reasonable way of finding such solution bounds for the overall interval newton bisection algorithm to be efficient the image box bf bar x should be as small as possible to do this the linear interval system is multiplied by a preconditioner matrix y before the interval gauss seidel method is applied in this paper a technique for computing such preconditioner matrices y is described this te

cyclic extensions and the local lifting problem the local oort conjecture states that if is cyclic and k is an algebraically closed eld of characteristic p then all extensions of k t should lift to characteristic zero we prove a critical case of this conjecture in particular we show that the conjecture is always true when vp j j 3 and is true for arbitrarily highly p divisible cyclic groups when a certain condition on the higher ramication ltration is satised

solving polynomial systems using a branch and prune approach this paper presents tt newton a branch and prune algorithm used to find all isolated solutions of a system of polynomial constraints tt newton can be characterized as a global search method which uses intervals for numerical correctness and for pruning the search space early the pruning in tt newton consists of enforcing at each node of the search tree a unique local consistency condition called box consistency which approximates the notion of arc consistency well known in artificial intelligence box consistency is parametrized by an interval extension of the constraint and can be instantiated to produce the hansen sengupta narrowing operator used in interval methods as well as new operators which are more effective when the computation is far from a solution tt newton has been evaluated on a variety of benchmarks from kinematics chemistry combustion economics and mechanics on these benchmarks it outperforms the interval methods we are aware of and compares well with textit state of the art continuation methods limitations of tt newton e g a sensitivity to the size of the initial intervals on some problems are also discussed of particular interest is the mathematical and programming simplicity of the method

a note on the moore test for nonlinear systems the moore test for nonlinear systems is improved in two directions one presents the convergence test theorem under more general conditions another is a second derivative test which reduces by half each edge of the test interval vector in the case of quadratic systems interval techniques are employed in the discussion

inclusion functions and global optimization 11 inclusion functions combined with special subdivision strategies are an effective means of solving the global unconstrained optimization problem although these techniques were determined and numerically tested about ten years ago they are nearly unknown and scarcely used in order to make the role of inclusion functions and subdivision strategies more widespread and transparent we will discuss a related simplified basic algorithm it computes approximations of the global minimum and at the same time bounds the absolute approximation error we will show that the algorithm works and converges under more general assumptions than it has been known hitherto that is only appropriate inclusion functions are expected to exist the number of minimal points finite or infinite is not of importance lipschitz conditions or continuity are not assumed as shown in the appendix the required inclusion functions can be constructed and programmed without difficulty in a natural way using interval analysis

a quadratically convergent krawczyk like algorithm in this paper we introduce a method for computing a solution of a nonlinear system which is similar to that proposed by r krawczyk computing 4 1969 pp 187 201 our method however needs considerably less work per step starting with an interval vector we give a criterion under which the method is convergent to the solution of the system if a solution is contained in the interval vector if the starting vector contains no solution then the method will break down after a finite number of steps

some computable existence uniqueness and convergence tests for nonlinear systems weaker interval arithmetic tests for existence uniqueness and convergence of simplified newton methods than those of moore and qi siam j numer anal 19 1982 pp 845 850 are described numerical results are presented

families of wildly ramified covers of curves in this paper i investigate wildly ramified g galois covers of curves inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i branched at exactly one point over an algebraically closed field k of characteristic p i answer a question of m raynaud by showing that proper families of such covers of a twisted projective line are isotrivial the method is to construct an affine moduli space for covers whose inertia group is of the form inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i there are two other applications of this space in the case that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i the first uses formal patching to compute the dimension of the space of nonisotrivial deformations of in terms of the lower jump of the filtration of higher inertia groups the second gives necessary criteria for good reduction of families of such covers these results will be used in a future paper to prove the existence of such covers with specified ramification data

technical communique injectivity analysis using interval analysis application to structural identifiability this paper presents a new numerical algorithm based on interval analysis able to prove that a differentiable function f email protected r n r n is injective this algorithm also performs a partition of the domain a in subsets a i where for all email protected a i the cardinality of f 1 f x is constant in the context of parameter estimation we show how this algorithm provides an efficient and numerical method to study the structural identifiability of parametric models

interval newton methods and perturbed problems this paper describes a straightforward implementation of a modified newton algorithm which generates the best interval bounding the solution generated using interval newton methods this implementation addresses the issues described by hansen and greenberg for analyzing problems with data perturbations using interval analysis it also indicates a new approach of potentially attractive methods for using interval newton methods while our focus is on perturbed problems sensitivity analysis the results are more generally applicable the major difference in the point of view of perturbed problems versus the general use of interval methods is that in perturbed problems we are focused on the behavior of the function around an optimal solution the more general approach seeks to identify all optimal solutions of the function

new techniques for the analysis of linear interval equations abstract the basic properties of interval matrix multiplication and several well known solution algorithms for linear interval equations are abstracted by the concept of a sublinear map the new concept coupled with a systematic use of ostrowski s comparison operator in a form generalized to interval matrices is used to derive quantitative information about the result of interval gauss elimination andthe limit of various iterative schemes for the solution of linear interval equations moreover optimality results are prove for 1 the use of the midpoint inverse as a preconditioning matrix and 2 gauss seidel iteration with componentwise intersection this extends and improves results by scheu krawczyk and alefeld and herzberger

interval slopes for rational functions and associated centered forms for an arithmetic expression f x involving n rational operations an o n algorithm is given which computes an interval enclosure for the set of slopes f x z where x ranges over an interval x applications to real and complex centered forms are given resulting in improvements over previous results by ratschek siam j numer anal 17 1980 pp 656 662 and petkovic freiburger intervall berichte 83 2 1983 pp 33 50

certification of real inequalities templates and sums of squares we consider the problem of certifying lower bounds for real valued multivariate transcendental functions the functions we are dealing with are nonlinear and involve semialgebraic operations as well as some transcendental functions like cos arctan exp cos arctan exp etc our general framework is to use different approximation methods to relax the original problem into polynomial optimization problems which we solve by sparse sums of squares relaxations in particular we combine the ideas of the maxplus approximations originally introduced in optimal control and of the linear templates originally introduced in static analysis by abstract interpretation the nonlinear templates control the complexity of the semialgebraic relaxations at the price of coarsening the maxplus approximations in that way we arrive at a new template based certified global optimization method which exploits both the precision of sums of squares relaxations and the scalability of abstraction methods we analyze the performance of the method on problems from the global optimization literature as well as medium size inequalities issued from the flyspeck project

chaotic quantum behaved particle swarm optimization algorithm for solving nonlinear system of equations abstract this study proposes a novel chaotic quantum behaved particle swarm optimization algorithm for solving nonlinear system of equations different chaotic maps are introduced to enhance the effectiveness and robustness of the algorithm several benchmark studies are carried out logistic map gives the best results and is utilized in solving nonlinear equation sets nine well known problems are solved with our algorithm and results are compared with quantum behaved particle swarm optimization intelligent tuned harmony search gravitational search algorithm and literature studies comparison results reveal that the proposed algorithm can cope with the highly non linear problems and outperforms many algorithms which exist in the literature

confidence interval estimation using standardized time series observations of a stationary stochastic process can be transformed into a standardized time series this paper presents a lemma giving the asymptotic properties of this standardized series under quite general conditions in particular the conditions are satisfied by stationary discrete event simulations confidence intervals can be constructed using this lemma for illustration we develop two easily computed interval estimators for the process mean when independent replications of the series are available such as in computer simulation experiments these interval estimators may be combined with the classical confidence interval estimator these interval estimators also tend to compensate for simulation initialization bias if the sign of the bias is known in an empirical study using three elementary simulated processes the interval estimators presented here compare favorably with the classical interval estimator in a recent paper goldsman and schruben goldsman d l schruben 1982 asymptotic properties of some confidence interval estimators tech rep 544 school of o r i e cornell university ithaca ny show that the asymptotic properties of the confidence intervals presented in this paper strictly dominate those of classical confidence intervals

global oort groups abstract we study the oort groups for a prime p i e finite groups g such that every g galois branched cover of smooth curves over an algebraically closed field of characteristic p lifts to a g cover of curves in characteristic 0 we prove that all oort groups lie in a particular class of finite groups that we characterize with equality of classes under a conjecture about local liftings we prove this equality unconditionally if the order of g is not divisible by 2 p 2 we also treat the local lifting problem and relate it to the global problem

numerical solutions for systems of qualitative nonlinear algebraic equations by fuzzy logic abstract this paper presents a fuzzy logic approach for determining a numerical solution to a consistent system of algebraic equations f x 0 in which the function f is not explicitly defined and may be underdetermined such systems arise frequently in many engineering design problems where design parameters must be chosen using qualitative information by the designer to meet a set of desired performance constraints the proposed method also can be used for a consistent system of nonlinear equations in which f is explicitly defined and may have fewer independent equations than the number of unknowns however this method is very computationally demanding hence it is not advisable to apply it to problems involving explicit functions that can be solved using other existing numerical methods it is seen that this method works quite well and numerical solutions for such problems can be obtained although it is much slower than newton s method when employed to consistent explicit nonlinear equations

the local lifting problem for dihedral groups let g dp be the dihedral group of order 2p where p is an odd prime let k be an algebraically closed field of characteristic p we show that any action of g on the ring k y can be lifted to an action on r y where r is some complete discrete valuation ring with residue field k and fraction field of characteristic 0

deformations formelles des revetements sauvagement ramifies de courbes algebriques in this paper we study formal moduli for wildly ramified galois covering we prove a local global principle we then focus on the infinitesimal deformations of the z pz covers we explicitly compute a deformation of an automorphism of order p which implies a universal obstruction for p 2 by deforming artin schreier equations we obtain a lower bound on the dimension of the local versal deformation ring at last by comparing the global versal deformation ring to the complete local ring in a point of a moduli space we determine the dimensions of the global and local versal deformation rings

nonlinear equations and optimization abstract interval analysis has led to improved numerical algorithms both for the solution of nonlinear equations and for nonlinear optimization in fact interval analysis has made possible algorithms for solving a problem often predicted to be numerically insoluble the nonlinear global optimization problem in this paper we survey interval methods for solving nonlinear equations and optimization

a cohomological treatise of hkg covers with applications to the nottingham group abstract we characterize harbater katz gabber curves in terms of a family of cohomology classes satisfying a compatibility condition our construction is applied to the description of finite subgroups of the nottingham group

deformation data belyi maps and the local lifting problem we prove existence and nonexistence results for certain differential forms in positive characteristic called good deformation data some of these results are obtained by reduction modulo p of belyi maps as an application we solve the local lifting problem for groups with sylow p subgroup of order p

global optimization to prescribed accuracy abstract programmable methods are outlined for rigorous global optimization to prescribed accuracy with references to enough detail to enable the implementation of the techniques on any computer some directions for future research are indicated

asymptotic properties of some confidence interval estimators for simulation output the classical confidence interval estimator commonly used in simulation is compared with four new estimators based on standardization of a time series presented in a previous paper these new interval estimators are shown to have asymptotic properties that strictly dominate the classical estimator when used with data from independent simulation replications or means of batched observations from a single simulation run two of the new estimators also can be used with a single unbatched replication of a simulation program a situation where the classical estimator is not defined

the oort conjecture on lifting covers of curves we show that the conjecture of oort on lifting covers of curves is true the main ingredients in the proof are a deformation argument in characteristic p and a special case of a very recent result by obus wewers a kind of boundedness result is given as well