some optimal error estimates of biharmonic problem using conforming finite element abstract in this paper the w 2 p error and lp error estimates of conforming finite element methods for biharmonic problem are established via weight function technique where 2 p finally the numerical experiments are provided

endomorphism rings of permutation modules let k be an algebraically closed field of characteristic p and g a finite group then the permutation module kpg of g on the cosets of a sylow p subgroup p is via fitting correspondence strongly related to its endomorphism ring endkg kpg on the other hand each green correspondent in g of a weight module of g occurs as a direct summand of kpg this fact suggests to analyze both structures the permutation module and the associated endomorphism ring towards hints at a proof for alperin s weight conjecture we present a selection of such investigations for different groups and characteristics in particular we focus on the socle and head constituents of the indecomposable direct summands of kpg and of the pims of ee

genetic algorithms with double strings for 0 1 programming problems abstract in this paper genetic algorithms with double strings for 0 1 knapsack problems are first revisited together with some modifications and computational experiments then the genetic algorithms with double strings for 0 1 knapsack problems are extended to deal with more general 0 1 programming problems involving both positive and negative coefficients in the constraints especially new decoding algorithms for double strings using reference solutions both without and with the reference solution updating procedure are proposed so that each of individuals is decoded to the corresponding feasible solution for the general 0 1 programming problems the efficiency and effectiveness of the proposed methods are investigated by comparing them with a branch and bound method with respect to the accuracy of an approximate solution and the processing time through a number of numerical experiments

the number of lifts of a brauer character with a normal vertex in this paper we examine the behavior of lifts of brauer characters in p solvable groups in the main result we show that if ibr g has a normal vertex q and either p is odd or q is abelian then the number of lifts of is at most q q as a corollary we prove that if ibr g has an abelian vertex subgroup q then the number of lifts of in irr g is at most q

error estimates of the lumped mass finite element method for semilinear elliptic problems we are concerned with the semilinear elliptic problems we first investigate the l 2 error estimate for the lumped mass finite element method we then use the cascadic multigrid method to solve the corresponding discrete problem on the basis of the finite element error estimates we prove the optimality of the proposed multigrid method we also report some numerical results to support the theory

an l error estimate for finite element solution of nonlinear elliptic problem with a source term the l error estimate for the finite element solution of nonlinear elliptic problem with a source term is discussed the lumped mass discretization method is used in the discretization and the error estimate o h 2 logh in l norm is obtained

some optimal error estimates for piecewise linear finite element approximations it is shown that the ritz projection onto spaces of piecewise linear finite elements is bounded in the sobolev space wl for 2 p oc this implies that for functions in wf n w2 the error in approximation behaves like 0 h in wp for 2 p oo and like 0 h2 in lp for 2 p oo in all these cases the additional logarithmic factor previously included in error estimates for linear finite elements does not occur

on normal subgroups and simple modules with a given vertex in a p solvable group abstract let n be a normal subgroup of a p solvable group g and let m be a simple fn module where f is an algebraically closed field of characteristic p let q be any p subgroup of g in this paper we count the number of simple fg modules lying over m and having q as a vertex

on fully ramified brauer characters let z be a normal subgroup of a finite group let p 5 be a prime and let ibr z be an irreducible g invariant p brauer character of z suppose that g e for some ibr g then g z is solvable in other words a twisted group algebra over an algebraically closed field of characteristic not 5 with a unique class of simple modules comes from a solvable group

vertices for characters of p solvable groups suppose that g is a finite p solvable group we associate to every irreducible complex character x irr g of g a canonical pair q where q is a p subgroup of g and irr q uniquely determined by x up to g conjugacy this pair behaves as a green vertex and partitions irr g into families of characters using the pair q we give a canonical choice of a certain p radical subgroup r of g and a character irr r associated to x which was predicted by some conjecture of g r robinson

character correspondences and subgroups of operator groups abstract let a and g be finite groups with coprime orders and suppose that a acts on g by automorphisms let g a irr a g irr c g a be the glauberman isaacs correspondence let b a and let irr a g we examine the conjecture that g a is an irreducible constituent of the restriction of g b to c g a and show that it is valid if g is supersolvable then we show when the analog of this conjecture for brauer characters and the uno wolf correspondence holds

brauer characters and the harris knorr correspondence in p solvable groups abstract if b is a p block of a normal subgroup n of a p solvable group g and b is its brauer correspondent in n n l where l is a defect group of b then harris knorr correspondents over b and b contain equal numbers of irreducible brauer characters over height zero brauer characters

an effective genetic algorithm approach to large scale mixed integer programming problems abstract to effectively reduce the search space of gas on large scale mip problems this paper proposed a new variable grouping method based on structure properties of a problem taking the capacity expansion and technology selection problem as a typical example this method groups problem s decision variables over time period and machine line based on this new variable grouping method we developed a variable grouping based genetic algorithm according to problem s structure properties vgga s we tested the performance of vgga s by applying it on the capacity expansion and technology selection problem numerical experiments suggested that vgga s outperforms the standard ga and variable grouping based gas without considering problem s structure properties both on computation time and solution quality although vgga s is proposed based on structure properties of a specific mip problem it is a general optimization algorithm and theoretically applicable to other large scale mip problems

the blocks and weights of finite special linear and unitary groups abstract this paper has two main parts first we give a classification of the l blocks of finite special linear and unitary groups sl n q in the non defining characteristic l 3 second we describe how the l weights of sl n q can be obtained from the l weights of gl n q when l gcd n q and verify the alperin weight conjecture for sl n q under the condition l gcd n q as a step to establish the alperin weight conjecture for all finite groups we prove the inductive blockwise alperin weight condition for any unipotent l block of sl n q if l gcd n q

solving 0 1 knapsack problems based on amoeboid organism algorithm the 0 1 knapsack problem is an open issue in discrete optimization problems which plays an important role in real applications in this paper a new bio inspired model is proposed to solve this problem the proposed method has three main steps first the 0 1 knapsack problem is converted into a directed graph by the network converting algorithm then for the purpose of using the amoeboid organism model the longest path problem is transformed into the shortest path problem finally the shortest path problem can be well handled by the amoeboid organism algorithm numerical examples are given to illustrate the efficiency of the proposed model

a reduction theorem for the alperin weight conjecture the alperin weight conjecture was stated by j alperin in 1986 and constitutes one of the main problems in the representation theory of finite groups in this paper we provide a reduction to simple groups and as an application we prove the conjecture in several cases

a solution to the optimal power flow using genetic algorithm optimal power flow opf is one of the main functions of power generation operation and control it determines the optimal setting of generating units it is therefore of great importance to solve this problem as quickly and accurately as possible this paper presents the solution of the opf using genetic algorithm technique this paper proposes a new methodology for solving opf this methodology is divided into two parts the first part employs the genetic algorithm ga to obtain a feasible solution subject to desired load convergence while the other part employs ga to obtain the optimal solution the main goal of this paper is to verify the viability of using genetic algorithm to solve the opf problem simultaneously composed by the load flow and the economic dispatch problem six buses system are used to highlight the goodness of this solution technique

the strengthened alperin weight conjecture for p solvable groups abstract the alperin weight conjecture is a well known conjecture and it is central to the modern representation theory of finite groups it is known to be true for many types of finite groups but it remains open in particular the conjecture is known to be true for finite p solvable groups in this paper we prove that a very strong form of the conjecture holds for all finite p solvable groups it follows that the strengthening of the alperin weight conjecture that includes galois automorphisms over the p adic numbers holds for all finite p solvable groups this strengthening of the alperin weight conjecture was suggested in an earlier work of navarro on the mckay conjecture the present paper provides the first direct evidence beyond the calculation of individual cases and the case of groups of odd order for this strengthening

iterative methods for variational and complementarity problems in this paper we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems included among such methods are the newton and several successive overrelaxation algorithms for the most part the study is concerned with the family of linear approximation methods these are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches the paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria finally several convergence results are obtained for some nonlinear approximation methods

primitive characters of subgroups ofm groups one of the hardest areas in the character theory of solvable groups continues to be the monomial groups a finite group is said to be an m group or monomial if all of its irreducible characters are monomial that is to say induced from linear characters two are still the main problems on m groups are hall subgroups of m groups monomial under certain oddness hypothesis are normal subgroups of m groups monomial in both cases there is evidence that this could be the case the primitive characters of the subgroups in question are the linear characters this is the best result up to date 4 6 recently some idea appears to be taking form in 14 t okuyama proved that if g is an m group and p is a sylow p subgroup of g then n p p is an m group some time later and more generally i m lsaacs shows that if h is a hall subgroup of an m group then n s h h is also an m group 91 since it is well known that normal hall subgroups of m groups are m groups in this case the strong hypothesis of normality makes the problem immediate perhaps it is not only true that hall subgroups of m groups are m groups but something stronger that hall subgroup normalizers also are in this direction we prove theorem a let g be an m group and let h be a hall subgroup o f g i f c e i r r nc h is primitive then c is linear

schwarz algorithm for the solution of variational inequalities with nonlinear source terms numerical solution of variational inequalities of obstacle type associated with some free boundary problems with nonlinear source terms is considered iterative methods based on the combination of the domain decomposition technique and the newton like approach are proposed for solving discrete obstacle problems arising from the continuous piecewise linear finite element approximation of the problems the calculation processes are easily to be parallelized the convergence and specially the convergent rate of the algorithms are obtained

a multiperiod two echelon multicommodity capacitated plant location problem abstract in this paper we deal with a facility location problem where one desires to establish facilities at two different distribution levels by selecting the time periods our model intends to minimize the total cost for meeting demands for all the products specified over the planning horizon at various customer locations while satisfying the capacity requirements of the production plants and intermediate warehouses we address this problem by means of a formulation as a mixed integer programming problem a lagrangean relaxation is proposed to solve the problem together with a heuristic procedure that constructs feasible solutions of the original problem from the solutions at the lower bounds obtained by the relaxed problems computational tests are provided showing the good performance of this approach for a wide range of problems

fully group graded algebras and a theorem of fong abstract it is proved that any algebra fully graded by a finite group over a complete discrete valuation ring with an algebraically closed residue field of characteristic a prime p is morita equivalent to an embedded graded subalgebra which is a crossed product and an explicit way to get a decomposition of unity with a bounded length is shown when the finite group is p solvable a theorem of fong s type for fully graded algebras is obtained

vertices and normal subgroups in solvable groups abstract for a finite group g and a fixed prime p one can attach to each irreducible brauer character of g a p subgroup q called the vertex of that is unique up to conjugacy in this paper we examine the behavior of the vertices of with respect to normal subgroups when g is assumed to be p solvable for arbitrary finite p solvable groups we develop a correspondence between the set of brauer characters of g with vertex q and the set of brauer characters of a certain subgroup of g with vertex q moreover in the case that g has odd order we extend a result of navarro regarding the behavior with respect to normal subgroups of a correspondence of brauer characters of p degree to a result regarding the behavior with respect to normal subgroups of a correspondence of brauer characters of arbitrary degree

bounds on the number of lifts of a brauer character in a p solvable group abstract the fong swan theorem shows that for a p solvable group g and brauer character ibr p g there is an ordinary character irr g such that 0 where 0 denotes restriction to the p regular elements of g this still holds in the generality of separable groups where ibr p g is replaced by i g for i g let l irr g 0 in this paper we give a lower bound for the size of l in terms of the structure of the normal nucleus of and if g is assumed to be odd and p we give an upper bound for l in terms of the vertex subgroup for

a new genetic algorithm for solving nonconvex nonlinear programming problems abstract in nonlinear programming problems especially nonconvex problems attaining the global optimum is crucial to reach this purpose the current paper represents a new genetic algorithm for solving nonconvex nonlinear programming problems the new method is simpler and more intuitive than the existing models and finds the global optimum of the problem in a reasonable time the proposed technique to attain the global optimum of problem especially in large scale problems instead of increasing the size of population which usually conduces to the curse of dimensionality that is widespread in usual genetic algorithms decomposes the main problem into several sub problems but with lower size of population in each sub problem this decomposition has been formed in such a way that it could envelop the total solution space the proposed genetic algorithm which determines the sufficient sub problems could converge to global optimum of problem to be able to measure the proposed genetic algorithm several problems have been solved in different spectrums herein it has been shown that the proposed technique both in run time and in solution quality is preferred to the usual genetic algorithm in this domain nonlinear continuous programming problems

a real coded genetic algorithm for solving integer and mixed integer optimization problems in this paper a real coded genetic algorithm named mi lxpm is proposed for solving integer and mixed integer constrained optimization problems the proposed algorithm is a suitably modified and extended version of the real coded genetic algorithm lxpm of deep and thakur k deep m thakur a new crossover operator for real coded genetic algorithms applied mathematics and computation 188 2007 895 912 k deep m thakur a new mutation operator for real coded genetic algorithms applied mathematics and computation 193 2007 211 230 the algorithm incorporates a special truncation procedure to handle integer restrictions on decision variables along with a parameter free penalty approach for handling constraints performance of the algorithm is tested on a set of twenty test problems selected from different sources in literature and compared with the performance of an earlier application of genetic algorithm and also with random search based algorithm rst2anu incorporating annealing concept the proposed mi lxpm outperforms both the algorithms in most of the cases which are considered

genetic algorithms and traveling salesman problems abstract a genetic algorithm ga with an asexual reproduction plan through a generalized mutation for an evolutionary operator is developed that can be directly applied to a permutation of n numbers for an approximate global optimal solution of a traveling salesman problem tsp schema analysis of the algorithm shows that a sexual reproduction with the generalized mutation operator preserves the global convergence property of a genetic algorithm thus establishing the fundamental theorem of the ga for the algorithm avoiding an intermediate step of encoding through random keys to preserve crossover or permuting n and using fixing states for legal crossover are the chief benefits of the innovations reported in this paper the algorithm has been applied to a number of natural and artificial problems and the results are encouraging

an effective genetic algorithm approach to multiobjective routing problems morps dynamic programming dp is a mathematical procedure designed primarily to improve the computational efficiency of solving select mathematical programming problems by decomposing them into smaller and hence computationally simpler subproblems in solving multiple objectives dynamic programming problem modp classical approaches reduce the multiple objectives into a single objective of minimizing a weighted sum of objectives the determination of these weights indicate the relative importance of the various objective also if the problem scale increases it becomes difficult to be dealt with even in the case of single objective because of the rapid expansion of the number of states to be considered in this paper we investigated the possibility of using genetic algorithms gas to solve multiobjective routing problems morps this procedure eliminates the need of any user defined weight factor for each objective also the proposed approach is developed to deal with the problems with both single or multiple objectives the simulation results for morps shows that genetic algorithms gas may hopefully be a new approach for such kinds of difficult to solve problems

search space division in gas using phenotypic properties in this article we study a new type of forking ga fga the phenotypic forking ga p fga the fga divides the whole search space into subspaces depending on the convergence status of the population and the solutions obtained so far and is intended to deal with multimodal problems which are difficult to solve using conventional ga we use a multi population scheme which includes one parent population that explores one subspace and one or more child population s exploiting the other subspace the p fga divides the search space using phenotypic properties only and defines a search subspace to be exploited by a child population by a neighborhood hypercube around the current best individual in the phenotypic feature space empirical results on complex function optimization problems show that the p fga performs fairly well compared to a conventional ga two other variants of the p fga the moving window p fga to accelerate the speed of convergence in the child populations and the variable resolution p fga to solve multimodal problems with high precision are also studied in this article

an interactive fuzzy satisficing method for general multiobjective 0 1 programming problems through genetic algorithms with double strings based on a reference solution in this paper focusing on general multiobjective 0 1 programming problems involving positive and negative coefficients we propose an interactive fuzzy satisficing method by extending our previous genetic algorithms with double strings for multiobjective multidimensional 0 1 knapsack problems in the extended genetic algorithms a new decoding algorithm for individuals represented by double strings which maps each individual to a feasible solution is proposed through the introduction of backtracking and individual modification after examining the feasibility and efficiency of the extended genetic algorithms with double strings using a lot of 0 1 programming problems involving positive and negative coefficients an illustrative numerical example demonstrated the feasibility and efficiency of the proposed interactive fuzzy satisficing method