minimizing total weighted completion time in a two machine flow shop scheduling under simple linear deterioration abstract in this paper we address a two machine flow shop scheduling problem under simple linear deterioration by a simple linear deterioration function we mean that the processing time of a job is a simple linear function of its execution start time the objective is to find a sequence that minimizes total weighted completion time optimal schedules are obtained for some special cases for the general case several dominance properties and two lower bounds are derived to speed up the elimination process of a branch and bound algorithm a heuristic algorithm is also proposed to overcome the inefficiency of the branch and bound algorithm computational analysis on randomly generated problems is conducted to evaluate the branch and bound algorithm and heuristic algorithm

on the hyers ulam rassias stability of approximately additive mappings abstract in this paper using an idea from the paper of p gvruta j math anal appl 184 1994 431 436 the results of th m rassias j math anal appl 158 1991 106 113 shall be generalized

on the stability of j homomorphisms abstract the main purpose of this paper is to prove the generalized hyers ulam rassias stability of j homomorphisms between j algebras

vers une decomposition de jordan des blocs des groupes reductifs finis abstract let g be a reductive algebraic group over an algebraic closure of a prime field f p defined over f q with frobenius endomorphism f let g f be the subgroup of rational points let l be a prime number assume that l is different from p if g f is in duality with g f then by a theorem of m broue and j michel m broue j michel blocs et series de lusztig dans un groupe reductif fini j reine angew math 395 1989 56 67 for any l bloc b of g f there exists a unique g f conjugacy class s of l semi simple elements such that some irreducible representation of b is in the rational lusztig s series associated to s if s 1 b is said to be unipotent if g is not connected with identity component g define the unipotent l blocs of g f as the l blocks that cover some unipotent l bloc of g f assuming l is good for g we construct from g f and s some reductive algebraic group g s f defined over f q and a one to one map from the set of l blocks of g f with associated class s onto the set of unipotent l blocks of g s f such that if b corresponds to b then there is a significant height preserving one to one map from the set of irreducible representations irr b onto the set irr b the respective defect groups of b and b are isomorphic the associated brauer categories are equivalent one do not assume that the center of g is connected the class of s may be isolated in g

decomposition numbers of so7 q and sp6 q abstract we complete the l modular decomposition numbers of the unipotent characters in the principal block of the special orthogonal groups so 7 q and the symplectic groups sp 6 q for all prime powers q and all odd primes l different from the defining characteristic

some single machine scheduling problems with general effects of learning and deterioration learning and job deterioration co exist in many realistic scheduling situations this paper introduces a general scheduling model with the effects of learning and deterioration simultaneously which is a significant generalization of some existing models in the literature by the effects of learning and deterioration we mean that job processing times are defined by functions of their start times and positions in the sequence this paper shows that the single machine scheduling problems to minimize the makespan sum of the kth power of completion times total lateness and sum of earliness penalties with a common due date are polynomially solvable under the proposed model it further shows that the problems to minimize the total weighted completion time discounted total weighted completion time maximum lateness maximum tardiness total tardiness and total weighted earliness penalties with a common due date are polynomially solvable under certain conditions

single machine group scheduling problems with deteriorated and learning effect in many realistic situation a job processed later consumes more time than the same job when it is processed earlier this phenomenon is known as deteriorated effect the skills of workers continuously improve when repeating the same or similar tasks this phenomenon is as the learning effect in the literature however most studies considering the deteriorated and learning effect ignore the fact that production efficiency can be increased by grouping various parts and products with similar designs and or production processes this phenomenon is known group technology in the literature in this paper we propose a new group scheduling with deteriorated and learning model where the learning effect not only depends on job position but also depends on the group position the deteriorated effect depends on its starting time of the job we then show that the single machine makespan and the total completion time problems remain polynomial optimal solvable under the proposed model in addition we show the maximum lateness have a polynomial optimal solution under certain agreeable restriction

brauer s height zero conjecture for quasi simple groups abstract we show that brauer s height zero conjecture holds for blocks of finite quasi simple groups this result is used in navarro spath s reduction of this conjecture for general groups to the inductive alperin mckay condition for simple groups

on the inductive alperin mckay and alperin weight conjecture for groups with abelian sylow subgroups abstract we study the inductive alperin mckay conjecture the inductive isaacs navarro refinement and the inductive blockwise alperin weight conjecture for groups of lie type in the generic case of abelian sylow l subgroups we also show that the alternating groups the suzuki groups and the ree groups satisfy the inductive condition necessary for spath s reduction of the blockwise alperin weight conjecture to the case of simple groups

parallel machine scheduling with a deteriorating maintenance activity and total absolute differences penalties in this paper we consider identical parallel machines scheduling problems with a deteriorating maintenance activity in this model each machine has a deteriorating maintenance activity that is delaying the maintenance increases the time required to perform it we need to make a decision on when to schedule the rate modifying activities and the sequence of jobs to minimize some objective function we concentrate on two goals separately namely minimizing the total absolute differences in completion times tadc and the total absolute differences in waiting times tadw we show that the problems remain polynomially solvable under the proposed model

group scheduling with deteriorating jobs to minimize the total weighted number of late jobs abstract deteriorating jobs scheduling has received tremendous attention in the past two decades however the group technology has seldom been discussed with the current emphasis on customer service and meeting the promised delivery dates we consider a single machine scheduling problem of minimizing the total weighted number of late jobs with deteriorating jobs and setup times a branch and bound with several dominance properties and a lower bound is developed to solve this problem optimally computational results show that the proposed algorithm can solve instances up to 1500 jobs in addition statistical tests are conducted to investigate the impact of the parameters

the strong np hardness of the maximum lateness minimization scheduling problem with the processing time based aging effect abstract in this paper we analyse the single machine maximum lateness minimization scheduling problem with the processing time based aging effect where the processing time of each job is described by a non decreasing function dependent on the sum of the normal processing times of preceded jobs the computational complexity of this problem was not determined however we show it is strongly np hard by proving the strong np hardness of the single machine maximum completion time minimization problem with this aging model and job deadlines furthermore we determine the boundary between polynomially solvable and np hard cases

the problem of s m ulam for approximately multiplicative mappings in the present paper we study the problem of s m ulam for approximately multiplicative mappings and we consider new open problems

homomorphisms in c ternary algebras and jb triples abstract in this paper we investigate homomorphisms between c ternary algebras and derivations on c ternary algebras and homomorphisms between j b triples and derivations on j b triples associated with the following apollonius type additive functional equation f z x f z y 1 2 f x y 2 f z x y 4

some single machine and flowshop scheduling problems with a non linear deterioration function the deteriorating job scheduling problems have received increasing attention recently however most researchers assume that the actual job processing time is a linear function of its starting time in fact in some situations the deterioration rate might increase or decrease as time passes for example the temperature of the ingot in the rolling machine might drop at a slower pace as the surface cools down thus the drop of the ingot temperature might have a decreasing rate on the other hand the time to control a fire might go dramatically as time passes and the time to cease a fire might have an increasing rate in this paper we propose a new deteriorating model where the deterioration rate might be increasing or decreasing as time passes under the proposed model we provide the optimal solutions for some single machine problems and some flowshop problems

on the stability of functional equations in banach spaces the paper is devoted to some results on the problem of s m ulam for the stability of functional equations in banach spaces the problem was posed by ulam 60 years ago

formule de mackey pourqgrand soit g un groupe algebrique reductif connexe defini sur une cloture algebrique f du corps fini a p elements f ou p designe un nombre p premier soit f g a g un endomorphisme de frobenius relatif a une f structure sur g ou q est une puissance de p et f designe le sous corps q q de f a q elements on fixe un nombre premier l different de p et on note q une cloture algebrique du corps l adique q si p est un sous groupe l l parabolique de g et si l est un sous groupe de levi f stable de p g lusztig a construit un foncteur r k l a kg f entre les l p f f groupes de grothendieck des categories des q l modules et des q g l l modules respectivement appele foncteur d induction de lusztig ce fonc teur admet un adjoint r kg f a k l appele restriction de lusztig l p la formule de mackey pour l induction de lusztig decrit la composition d un foncteur d induction avec un foncteur de restriction de lusztig plus precisement si q est un autre sous groupe parabolique de g et si m est un sous groupe de levi f stable de q on appelle formule de mackey l egalite suivante

hypersymmetry a z3 graded generalization of supersymmetry we propose a generalization of non commutative geometry and gauge theories based on ternary z3 graded structures in the new algebraic structures we define all products of two entities are left free the only constraining relations being imposed on ternary products these relations reflect the action of the z3 group which may be either trivial i e abc bca cab generalizing the usual commutativity or non trivial i e abc jbca with j e 2 i 3 the usual z2 graded structures such as grassmann lie and clifford algebras are generalized to the z3 graded case certain suggestions concerning the eventual use of these new structures in physics of elementary particles and fields are exposed

quasi isolated blocks and brauer s height zero conjecture this paper has two main results firstly we complete the parametrisation of all p blocks of nite quasi simple groups by nding the so called quasi isolated blocks of exceptional groups of lie type for bad primes this relies on the explicit decomposition of lusztig induction from suitable levi subgroups our second major result is the proof of one direction of brauer s long standing height zero conjecture on blocks of nite groups using the

2 blocks with minimal nonabelian defect groups abstract we study numerical invariants of 2 blocks with minimal nonabelian defect groups these groups were classified by redei see redei 1947 41 if the defect group is also metacyclic then the block invariants are known see sambale 43 in the remaining cases there are only two infinite families of interesting defect groups in all other cases the blocks are nilpotent we prove brauer s k b conjecture and olsson s conjecture for all 2 blocks with minimal nonabelian defect groups for one of the two families we also show that alperin s weight conjecture and dade s conjecture are satisfied this paper is a part of the author s phd thesis

a generalization of the hyers ulam rassias stability of approximately additive mappings abstract in this paper we prove a generalization of the stability of approximately additive mappings in the spirit of hyers ulam and rassias

2 blocks with abelian defect groups we give a classification up to morita equivalence of 2 blocks of quasi simple groups with abelian defect groups as a consequence we show that donovan s conjecture holds for elementary abelian 2 groups and that the entries of the cartan matrices are bounded in terms of the defect for arbitrary abelian 2 groups we also show that a block with defect groups of the form c2m c2m for m 2 has one of two morita equivalence types and hence is morita equivalent to the brauer correspondent block of the normaliser of a defect group this completes the analysis of the morita equivalence types of 2 blocks with abelian defect groups of rank 2 from which we conclude that donovan s conjecture holds for such 2 groups a further application is the completion of the determination of the number of irreducible characters in a block with abelian defect groups of order 16 the proof uses the classification of finite simple groups

equivariance and extendibility in finite reductive groups with connected center we show that several character correspondences for finite reductive groups g are equivariant with respect to group automorphisms under the additional assumption that the linear algebraic group associated to g has connected center the correspondences we consider are the so called jordan decomposition of characters introduced by lusztig and the generalized harish chandra theory of unipotent characters due to broue malle michel in addition we consider a correspondence giving character extensions due to the second author in order to verify the inductive mckay condition from isaacs malle navarro for the non abelian finite simple groups of lie types 3 mathsf d 4 mathsf e 8 mathsf f 4 2 mathsf f 4 and mathsf g 2

minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem abstract this paper considers the following scheduling problem minimize the makespan in a single facility problem where the processing time of a job consists of a fixed and a variable part the variable part depends on the start time of the job the objective is to minimize makespan two optimizing algorithms based on dynamic programming and branch and bound techniques and five heuristic rules have been proposed the heuristic solutions have been compared with the optimal solution for upto 7 jobs to identify the best heuristic the detailed computational results for the branch and bound and the best heuristic rule are then obtained for problems with up to 15 jobs

comment on approximate ternary jordan derivations on banach ternary algebras bavand savadkouhi et al j math phys 50 042303 2009 let a be a banach ternary algebra over c and x a ternary banach a module a c linear mapping d a a x x is called a ternary jordan derivation if d xxx a d x xx x xd x x x xxd x x for all x a bavand savadkouhi et al j math phys 50 042303 2009 investigated ternary jordan derivations on banach ternary algebras associated with the following functional equation f x y z 4 f 3x y 4z 4 f 4x 3z 4 2f x and proved the generalized ulam hyers stability of ternary jordan derivations on banach ternary algebras the mapping f in lemma 2 2 of bavand savadkouhi et al is identically zero and all of the results are trivial in this note we correct the statements of the results and the proofs

isomorphisms between c ternary algebras abstract in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following cauchy jensen additive mappings 0 1 f x y 2 z f x y 2 z f x 2 f z 0 2 f x y 2 z f x y 2 z f y 0 3 2 f x y 2 z f x f y 2 f z these are applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

minimizing the total completion time in single machine scheduling with aging deteriorating effects and deteriorating maintenance activities in a real manufacturing system a machine may need multiple maintenance activities to improve its production efficiency due to the effects of aging or deteriorating this paper considers scheduling with aging or deteriorating effects and deteriorating maintenance activities simultaneously on a single machine we assume that the machine may be subject to several maintenance activities during the planning horizon however due to the restriction of budget of maintenance the upper bound of the maintenance frequency on the machine is assumed to be known in advance moreover we assume that the duration of each maintenance activity depends on the running time of the machine the objective is to find jointly the optimal maintenance frequencies the optimal maintenance positions and the optimal job sequence for minimizing the total completion time we show that all the problems studied are polynomially solvable

the computational complexity analysis of the two processor flowshop problems with position dependent job processing times the two processor flowshop makespan scheduling with piecewise linear position learning aging effects is strongly np hard the two processor flowshop makespan scheduling with common linear position learning aging effects is polynomially solvable the boundary between polynomially solvable and np hard has been is compressed the strong np hardness proof supporting method is described in this paper we analyse the makespan minimization problem in the two processor flowshop environment where the processing time of each job depends on its position in a sequence a position dependent job processing time that is equivalent to the number of previously processed jobs namely if processing times of jobs increase with the number of processed jobs then the aging fatigue deterioration effect is modelled whereas the non increasing dependency describes the learning effect we prove that the considered problem becomes strongly np hard if the processing time of each job is described by a piecewise linear function dependent on its position in a sequence we analyse two types of functions non decreasing aging and non increasing learning furthermore we describe the strong np hardness proof supporting method and elucidate correctness of our other strong np hardness proofs additionally we provide a modification of the johnson s algorithm and prove that it optimally solves the considered problem in the two processor flowshop environment if job processing times are characterized by a common linear non increasing or non decreasing dependency on a job position

lie homomorphisms between lie c algebras and lie derivations on lie c algebras abstract we prove the generalized hyers ulam rassias stability of lie homomorphisms in lie c algebras and of lie derivations on lie c algebras

on special classes of n algebras we define n algebras as linear spaces on which the internal composition law involves n elements m v n v it is known that such algebraic structures are interesting for their applications to problems of modern mathematical physics using the notion of a commutant of two subalgebras of an n algebra we distinguish certain classes of n algebras with reasonable properties semisimple abelian nilpotent solvable we also consider a few examples of n algebras of different types and show their properties

shintani descent for special linear groups abstract in this paper the shintani descent of irreducible characters of finite special linear groups is discussed we parametrize irreducible characters of sl n f q by making use of modified generalized gelfand graev characters shintani descent of irreducible characters of sl n f q m is determined by investigating the shintani descent of generalized gelfand graev characters our results hold for arbitrary p and q

on approximation of approximately linear mappings by linear mappings abstract assume a is a normed linear space b is a banach space and f a b is a mapping approximately linear we solve the following ulam problem give conditions in order for a linear mapping near an approximately linear mapping to exist

approximate ternary jordan derivations on banach ternary algebras let a be a banach ternary algebra over a scalar field r or c and x be a ternary banach a module a linear mapping d a a x x is called a ternary jordan derivation if d xxx a d x xx x xd x x x xxd x x for all x a in this paper we investigate ternary jordan derivations on banach ternary algebras associated with the following functional equation f x y z 4 f 3x y 4z 4 f 4x 3z 4 2f x moreover we prove the generalized ulam hyers stability of ternary jordan derivations on banach ternary algebras

on the inductive blockwise alperin weight condition for classical groups abstract recently there has been substantial progress on the alperin weight conjecture as a step to establish the alperin weight conjecture for all finite groups we prove the inductive blockwise alperin weight condition for simple groups of classical type under some additional assumption

self improving algorithms we investigate ways in which an algorithm can improve its expected performance by fine tuning itself automatically with respect to an unknown input distribution mathcal d we assume here that mathcal d is of product type more precisely suppose that we need to process a sequence i 1 i 2 ldots of inputs i x 1 x 2 ldots x n of some fixed length n where each x i is drawn independently from some arbitrary unknown distribution mathcal d i the goal is to design an algorithm for these inputs so that eventually the expected running time will be optimal for the input distribution mathcal d prod i mathcal d i we give such self improving algorithms for two problems i sorting a sequence of numbers and ii computing the delaunay triangulation of a planar point set both algorithms achieve optimal expected limiting complexity the algorithms begin with a training phase during which they collect information about the input distribution followed by a stationary regime in which the algorithms settle to their optimized incarnations

single machine multiple common due dates scheduling with learning effects in this paper we consider the problem of simultaneous determination of optimal due dates and optimal schedule for the single machine problem with multiple common due dates the penalty for a job is assumed to be a linear function of the due date and the earliness tardiness for the job the objective function is to minimize the total penalty for all jobs we show that with the introduction of learning to job processing times the problem remains polynomially solvable for a given number of multiple common due dates

on unipotent blocks and their ordinary characters there is a great deal of evidence suggesting that block theory for finite reductive groups should lead to an enrichment of the harish chandra theory for those groups see s 5 1 fs2 p2 3 4 h 6 1 10 an e generalized harish chandra theory for e a positive integer is introduced in bmm i a the context is as follows let g be a connected reductive group defined over lfq with associated frobenius endomorphism f let e 1 an integer when l is an f stable levi subgroup of g one denotes by r and re the lusztig functor and its adjoint a unipotent e pair l l is defined by an e split levi subgroup l of g and a unipotent character z d l 1 one writes li z1 l2 j 2 if and only if l1 c l 2 and zl l2 l 1 2 l 4 0 see 3 l the notion of unipotent e cuspidal pairs and the resulting partition of g g v 1 are defined as in the classical case corresponding to e 1 if f is a prime not dividing q and e is the order of q mod f it seems natural in connection with blocks to ask if the partition of the unipotent characters 8 g v l resulting from e theory coincides with f blocks the blocks of g v which are defined by unipotent characters are called unipoteut f blocks we prove

minimizing total completion time in a two machine flow shop with deteriorating jobs this paper considers a two machine flow shop scheduling problem with deteriorating jobs by a deteriorating job we mean that the processing time of a job is an increasing function of its execution start time a simple linear deterioration function is assumed the objective is to find a sequence that minimizes total completion time optimal solutions are obtained for some special cases for the general case several dominance properties and two lower bounds are derived to speed up the elimination process of a branch and bound algorithm a heuristic algorithm is also proposed to overcome the inefficiency of the branch and bound algorithm computational results show that the proposed heuristic algorithm performs effectively and efficiently