q oscillator realizations of the quantum superalgebras slq m n andospq m 2n realizations of the quantum superalgebras corresponding to thea m n b m n c n 1 andd m n series are given in terms of the creation and annihilation operators ofq deformed bose and fermi oscillators

consistency of the disaggregation process in hierarchical planning this paper deals with the planning process of a manufacturing system in which the aggregation of products sharing similar characteristics leads to a hierarchical structure it gives special attention to the consistency of decisions in a two level structure and presents necessary and sufficient conditions for consistency of a disaggregation procedure using a subset of these conditions improves upon the disaggregation procedure proposed by bitran and hax bitran g r a c hax 1981 disaggregation and resource allocation using convex knapsack problems with bounded variables mgmt sci 27 431 441

algorithms for separable nonlinear resource allocation problems we consider a simple resource allocation problem with a single resource constraint the objective function is composed of separable convex performance functions one for each activity likewise the constraint has separable convex resource usage functions one for each activity the objective is to minimize the sum of the performance functions subject to satisfying the resource constraint and nonnegativity constraints this problem extends the well studied problem in which the resource constraint is linear we present several algorithms to solve the problem these algorithms extend approaches developed for the linearly constrained problem they can readily solve large problems and find the optimal solution in a number of iterations that does not exceed the number of variables we provide several examples for illustration purposes present computational results and highlight the similarities and differences among the algorithms

a unified method for a class of convex separable nonlinear knapsack problems abstract in this paper a unified algorithm is proposed for solving a class of convex separable nonlinear knapsack problems which are characterized by positive marginal cost pmc and increasing marginal loss cost ratio imlcr by taking advantage of these two characteristics the proposed algorithm is applicable to the problem with equality or inequality constraints in contrast to the methods based on karush kuhn tucker kkt conditions our approach has linear computation complexity numerical results are reported to demonstrate the efficacy of the proposed algorithm for different problems

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

a realization of generalized deformed oscillators with cyclic symmetry the algebra of generalized deformed oscillators that possess cyclic symmetry is studied the general set of multilinear operator relations is presented which characterizes the multilinear part of the algebra of cyclic extended deformed oscillators the realization scheme of generalized deformed oscillators with cyclic symmetry in terms of those without cyclic symmetry is established it is shown that all generalized deformed oscillators with cyclic symmetry constructed by the scheme are actually equivalent in the viewpoint of mathematics though each generalized deformed oscillator admits its own particular cyclic extended counterpart examples are given to illustrate this peculiar realization scheme

probabilistic solutions for a class of deterministic optimal allocation problems abstract we revisit the general problem of minimizing a separable convex function with both a budget constraint and a set of box constraints this optimization problem arises naturally in many resource allocation problems in engineering economics finance and insurance existing literature tackles this problem by using the traditional kuhn tucker theory which leads to either iterative schemes or yields explicit solutions only under some special classes of convex functions owe to the presence of box constraints this paper presents a novel approach of solving this constrained minimization problem by using the theory of comonotonicity the key step is to apply an integral representation result to express each convex function as the stop loss transform of some suitable random variable by using this approach we can derive and characterize not only the explicit solution but also obtain its geometric meaning and some other qualitative properties

algorithms for the continuous nonlinear resource allocation problem new implementations and numerical studies patriksson 2008 provided a then up to date survey on the continuous separable differentiable and convex resource allocation problem with a single resource constraint since the publication of that paper the interest in the problem has grown several new applications have arisen where the problem at hand constitutes a subproblem and several new algorithms have been developed for its efficient solution this paper therefore serves three purposes first it provides an up to date extension of the survey of the literature of the field complementing the survey in patriksson 2008 with more then 20 books and articles second it contributes improvements of some of these algorithms in particular with an improvement of the pegging that is variable fixing process in the relaxation algorithm and an improved means to evaluate subsolutions third it numerically evaluates several relaxation primal and breakpoint dual algorithms incorporating a variety of pegging strategies as well as a quasi newton method our conclusion is that our modification of the relaxation algorithm performs the best at least for problem sizes up to 30 million variables the practical time complexity for the breakpoint and relaxation algorithms is linear

internal dla and the gaussian free field in previous works we showed that the internal diffusion limited aggregation dla cluster on zd with t particles is almost surely spherical up to a maximal error of o logt if d 2 and o logt if d 3 this paper addresses average error in a certain sense the average deviation of internal dla from its mean shape is of constant order when d 2 and of order r1 d 2 for a radius r cluster in general appropriately normalized the fluctuations taken over time and space scale to a variant of the gaussian free field

q fermionic operators and quantum exceptional algebras using a q deformation of the usual clifford algebra one constructs a realization of the quantum exceptional algebras e6 e7 e8 and f4 in terms of q fermionic operators

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

exceptional lie algebras in terms of fermionic creation annihilation operators from the embedding e8 d4 d4 defining fermionic operators which transform respectively as the vectorial and spinorial representations of d4 the algebra of e8 is constructed in terms of a bilinear in the fermionic operators then by embeddings the adjoint and fundamental representations of the other exceptional algebras are explicitly written

logarithmic fluctuations for internal dla let each of n particles starting at the origin in z 2 perform simple random walk until reaching a site with no other particles lawler bramson and griffeath proved that the resulting random set a n of n occupied sites is with high probability close to a disk br of radius r p n we show that the discrepancy between a n and the disk is at most logarithmic in the radius i e there is an absolute constant c such that with probability 1 br c log r a r 2 br c log r for all suciently large r

realization of exceptional superalgebras in terms of fermion boson creation annihilation operators operators satisfying clifford algebra fermions and weyl algebra bosons are introduced f 4 and g 3 are realized in terms of bilinears of fermions the even part and bilinears of one boson and one fermion the odd part d 2 1 is realized as bilinears the even part and trilinears the odd part of bosons

deformation of lie algebras in a non chevalley basis and embedding of q algebras a deformation scheme for lie algebras in a basis which manifestly exhibits for q 1 the content of a singular subalgebra is presented this scheme allows to build up embedding chains of q algebras which can be physically interesting the case when the rank of the subalgebra is one unit less than the rank of the algebra is studied and explicit constructions of the algebras are given in terms of q bosonic and or q fermionic oscillators

the construction of the q analogues of the harmonic oscillator operators from ordinary oscillator operators the q analogues of boson operators are constructed from ordinary boson operators by an embedding approach accordingly the q deformed quantum algebras su n q can be obtained straightforwardly from corresponding universal enveloping algebras of lie algebra su n

equivalence of deformed fermionic algebras generalized deformations of the fermionic algebra are studied the polynomial representations of these algebras are constructed all the deformation schemes can be realized by the same polynomial basis using the bargmann representation thus proving that all deformed fermionic algebras are isomorphically equivalent to the non deformed fermionic algebra

oil and water a two type internal aggregation model we introduce a two type internal dla model which is an example of a non unary abelian network starting withn oil andn water particles at the origin the particles diuse in z according to the following rule whenever some site x2 z has at least 1 oil and at least 1 water particle present it res by sending 1 oil particle and 1 water particle each to an independent random neighbor x 1 firing continues until every site has at most one type of particles we establish the correct order for several statistics of this model and identify the scaling limit under assumption of existence

q oscillators realization of fq 4 and gq 3 a realization of the quantum superalgebras corresponding to f 4 and g 3 is given in terms of q deformed bosonic and fermionic oscillators

the abelian sandpile and related models abstract the abelian sandpile model is the simplest analytically tractable model of self organized criticality this paper presents a brief review of known results about the model the abelian group structure of the algebra of operators allows an exact calculation of many of its properties in particular when there is a preferred direction one can calculate all the critical exponents characterizing the distribution of avalanche sizes in all dimensions for the undirected case the model is related to q 0 state potts model this enables exact calculation of some exponents in two dimensions and there are some conjectures about others we also discuss a generalization of the model to a network of communicating reactive processors this includes sandpile models with stochastic toppling rules as a special case we also consider a nondashabelian stochastic variant which lies in a different universality class related to directed percolation

formation of an interface by competitive erosion we introduce a graph theoretic model of interface dynamics called competitive erosion each vertex of the graph is occupied by a particle that can be either red or blue new red and blue particles alternately get emitted from their respective bases and perform random walk on encountering a particle of the opposite color they kill it and occupy its position we prove that on the cylinder graph the product of a path and a cycle an interface spontaneously forms between red and blue and is maintained in a predictable position with high probability

deformation of the strange superalgebra p n a deformation uq p n pq n of the extended noncontragredient strange superalgebra of p n denoted by p n is proposed a realization of pq n in terms of q bosons and q fermions is presented then a procedure to build up a set of representations of pq n is briefly discussed as a by product a new realization of suq n is obtained

breakpoint searching algorithms for the continuous quadratic knapsack problem we give several linear time algorithms for the continuous quadratic knapsack problem in addition we report cycling and wrong convergence examples in a number of existing algorithms and give encouraging computational results for large scale problems

disaggregation and resource allocation using convex knapsack problems with bounded variables the allocation of a specific amount of a given resource among competitive alternatives can often be modelled as a knapsack problem this model formulation is extremely efficient because it allows convex cost representation with bounded variables to be solved without great computational efforts practical applications of this problem abound in the fields of operations management finance manpower planning marketing etc in particular knapsack problems emerge in hierarchical planning systems when a first level of decisions need to be further allocated among specific activities which have been previously treated in an aggregate way in this paper we provide a recursive procedure to solve such problems the method differs from classical optimization algorithms of convex programming in that it determines at each iteration the optimal value of at least one variable applications and computational results are presented

sublogarithmic fluctuations for internal dla we consider internal diffusion limited aggregation in dimension larger than or equal to two this is a random cluster growth model where random walks start at the origin of the d dimensional lattice one at a time and stop moving when reaching a site that is not occupied by previous walks it is known that the asymptotic shape of the cluster is a sphere when the dimension is two or more we have shown in a previous paper that the inner resp outer fluctuations of its radius is at most of order log radius resp log2 radius using the same approach we improve the upper bound on the inner fluctuation to log radius when d is larger than or equal to three the inner fluctuation is then used to obtain a similar upper bound on the outer fluctuation