recent trends in ale formulation and its applications in solid mechanics this paper presents a complete derivation and implementation of the arbitrary lagrangian eulerian ale formulation for the simulation of nonlinear static and dynamic problems in solid mechanics the ale equations are presented using a fully coupled implicit approach full expression for the ale virtual work equations and finite element matrices are given the matrix equations are presented in a level of details that facilitates straightforward implementation time integration relations for the dynamic equations are also derived special techniques are presented to adapt the formulation for simulating crack propagation problems several applications in the areas of metal forming metal cutting and crack propagation are solved and presented

minimum cost spanning tree games we consider the problem of cost allocation among users of a minimum cost spanning tree network it is formulated as a cooperative game in characteristic function form referred to as a minimum cost spanning tree m c s t game we show that the core of a m c s t game is never empty in fact a point in the core can be read directly from any minimum cost spanning tree graph associated with the problem for m c s t games with efficient coalition structures we define and construct m c s t games on the components of the structure we show that the core and the nucleolus of the original game are the cartesian products of the cores and the nucleoli respectively of the induced games on the components of the efficient coalition structure

fourier based transmit beampattern design using mimo radar in multiple input multiple output mimo radar settings it is often desirable to transmit power only to a given location or set of locations defined by a beampattern transmit waveform design is a topic that has received much attention recently involving synthesis of both the signal covariance matrix r as well as the actual waveforms current methods involve a two step process of designing r via iterative solutions and then using r to generate waveforms that fulfill practical constraints such as having a constant envelope or drawing from a finite alphabet in this paper a closed form method to design r for a uniform linear array is proposed that utilizes the discrete fourier transform dft coefficients and toeplitz matrices the resulting covariance matrix fulfills the practical constraints such as positive semidefiniteness and the uniform elemental power constraint and provides performance similar to that of iterative methods which require a much greater computation time next a transmit architecture is presented that exploits the orthogonality of frequencies at discrete dft values to transmit a sum of orthogonal signals from each antenna the resulting waveforms provide a lower mean square error than current methods at a much lower computational cost and a simulated detection scenario demonstrates the performance advantages achieved

unconstrained synthesis of covariance matrix for mimo radar transmit beampattern multiple input multiple output mimo radars have many advantages over their phased array counterparts improved spatial resolution better parametric identifiably and greater flexibility to design the transmit beampattern the design of the transmit beampatterns generally requires the waveforms to have arbitrary auto and cross correlation properties the correlation covariance matrix r of the waveforms must be positive semidefinite therefore synthesis of a desired beampattern is usually a constrained optimization problem in this paper to simplify the constrained optimization problem two algorithms are proposed to synthesize the waveform covariance matrix for the desired beampattern in the first proposed algorithm the elements of a square root matrix of the covariance matrix r are parameterized using the coordinates of a hypersphere that implicitly fulfil the constraints this yields an iterative algorithm whose convergence speed can be increased significantly by providing good initial values in the second algorithm the constraints and redundant information in the covariance matrix r are exploited to find a closed form solution the drawback of the second algorithm is that it may yield a pseudocovariance matrix pseudo cm that is not guaranteed to be positive semidefinite however the pseudo cm can be easily converted into a covariance matrix using eigenvalue decomposition and or shrinkage methods moreover a pseudo cm can also be used to provide good initial values for the first algorithm to enable faster convergence

generalized network problems yielding totally balanced games a class of multiperson mathematical optimization problems is considered and is shown to generate cooperative games with nonempty cores the class includes but is not restricted to numerous versions of network flow problems it was shown by owen that for games generated by linear programming optimization problems optimal dual solutions correspond to points in the core we identify a special class of network flow problems for which the converse is true i e every point in the core corresponds to an optimal dual solution

on some balanced totally balanced and submodular delivery games this paper studies a class of delivery problems associated with the chinese postman problem and a corresponding class of delivery games a delivery problem in this class is determined by a connected graph a cost function defined on its edges and a special chosen vertex in that graph which will be referred to as the post office it is assumed that the edges in the graph are owned by different individuals and the delivery game is concerned with the allocation of the traveling costs incurred by the server who starts at the post office and is expected to traverse all edges in the graph before returning to the post office a graph g is called chinese postman submodular or for short cp submodular cp totally balanced cp balanced respectively if for each delivery problem in which g is the underlying graph the associated delivery game is submodular totally balanced balanced respectively for undirected graphs we prove that cp submodular graphs and cp totally balanced graphs are weakly cyclic graphs and conversely an undirected graph is shown to be cp balanced if and only if it is a weakly euler graph for directed graphs cp submodular graphs can be characterized by directed weakly cyclic graphs further it is proven that any strongly connected directed graph is cp balanced for mixed graphs it is shown that a graph is cp submodular if and only if it is a mixed weakly cyclic graph finally we note that undirected directed and mixed weakly cyclic graphs can be recognized in linear time

computing the nucleolus of some combinatorially structured games in this paper we introduce the prenucleolus for a transferable utility game n v where 2 n the prenucleolus is a straightforward generalization of the ordinary prenucleolus where only the coalitions in determine the outcome we impose a combinatorial structure on the collection which enables us to compute the prenucleolus in n 3 time the algorithm can be used for computing the nucleolus of several classes of games among which is the class of minimum cost spanning tree games

cost allocation for a tree network with heterogeneous customers we analyze a cost allocation problem which could naturally arise from a situation wherein a tree networkt n 0 e serving heterogeneous customers has to be constructed the customers located atn require some service from a central supplier located at vertex 0 the customers have heterogeneous preferences for the level or quality of service received from the central supplier we formulate the above cost allocation problem as a cooperative game referred to as anextended tree game the extended tree game is a proper extension of megiddo s 1978 tree game wherein all the customers have identical preferences regarding the level of service received we prove that an extended tree game is convex and we show that its shapley value can be computed in p n time wherep is the number of distinct preference levels we further provide a complete facial description of the core polytope of an extended tree game and demonstrate that even when there are only two classes of customers the number of nonredundant core constraints could be exponential in n nevertheless we are able to construct an p n algorithm to check the core membership of an arbitrary cost allocation which can be used to construct an p n 3 combinatorial algorithm to compute the nucleolus of an extended tree game finally we show that the complements of the facet defining coalitions for the core are all connected in an auxiliary tree graph with node setn

a total ale fe formulation for axisymmetric and torsional problems including viscoplasticity thermodynamic coupling and dynamics this paper first extends a recent assumed enhanced deformation gradient finite ring segment element int j numer methods eng 2001 50 899 918 to arbitary lagrange euler ale computations by setting up the assumed tensor on the computational configuration and second shows an elegant way of incorporating dynamics into real ale computations no splitting into purely lagrange steps and then remeshing steps by introducing material mesh velocities and accelerations and spatial mesh velocities and accelerations copyright 2006 john wiley sons ltd

cost allocation in the chinese postman problem this paper considers a cost allocation problem that arises from a delivery problem associated with the chinese postman problem cpp a delivery problem is described by a connected undirected graph in which each edge belongs to a different player a cost function on the edges of this graph and a fixed vertex which is referred to as the post office assume that the post office is providing some service to the players the nature of this service which can be thought of as mail delivery requires that a server will travel along the edges of the graph and returns to the post office the cost allocation problem is concerned with the cost of providing the service to all players a specific cost allocation rule is introduced and characterized further the class of delivery problems gives rise to a new class of cooperative combinatorial optimization games called delivery games it is shown that the outcome of the allocation rule with respect to a bridge connected euler graph is a core element of the corresponding delivery game

tractable transmit mimo beampattern design under a constant modulus constraint multiple input multiple output mimo radar systems allow each antenna element to transmit a different waveform this waveform diversity can be exploited to enhance the beampattern design in particular effective management of radar radiation power in directions of interest we address the problem of designing a beampattern for mimo radar which in turn is determined by the transmit waveform while unconstrained design is straightforward a key open challenge is enforcing the constant modulus constraint on the radar waveform it is well known that the problem of minimizing deviation of the designed beampattern from an idealized one subject to the constant modulus constraint constitutes a hard nonconvex problem existing methods that address constant modulus invariably lead to a stiff tradeoff between analytical tractability achieved by relaxations and approximations and realistic design that exactly achieves constant modulus but is computationally burdensome a new approach is proposed in our paper which involves solving a sequence of convex equality constrained quadratic programs each of which has a closed form solution and such that constant modulus is achieved at convergence we further prove that the converged solution satisfies the karush kuhn tucker optimality conditions of the aforementioned hard nonconvex problem we evaluate the proposed successive closed forms scf algorithm against the state of the art mimo beampattern design techniques in both narrowband and wideband setups and show that the scf breaks the tradeoff between desirable performance and the associated computation cost

a generalized linear production model a unifying model we introduce a generalized linear production model whose attractive feature being that the resources held by any subset of producerss is not restricted to be the vector sum of the resources held by the members ofs we provide sufficient conditions for the non emptiness of the core of the associated generalized linear production game and show that if the core of the game is not empty then a solution in it can be produced from a dual optimal solution to the associated linear programming problem our generalized linear production model is a proper generalization of the linear production model introduced by owen and it can be used to analyze cooperative games which cannot be studied in the ordinary linear production model framework we use the generalized model to show that the cooperative game induced by a network optimization problem in which players are the nodes of the network has a non empty core we further employ our model to prove the non emptiness of the core of two other classes of cooperative games which were not previously studied in the literature and we also use our generalized model to provide an alternative proof for the non emptiness of the core of the class of minimum cost spanning tree games thus it appears that the generalized linear production model is a unifying model which can be used to explain the non emptiness of the core of cooperative games generated by various seemingly different optimization models

on computing the nucleolus of a balanced connected game the question of fairly allocating costs or cost savings among the participants of a joint enterprise is frequently answered by finding the nucleolus of a related cooperative game in connection with various routing sequencing and scheduling situations connected games often arise their common feature is that all the essential coalitions whose breaking up into subcoalitions is disadvantageous for its members are connected with respect to a fixed order of the players any player between two members of a coalition is also a member of the coalition in the literature several special classes of connected games are discussed that are shown to be balanced in this paper an algorithm is presented that computes the nucleolus of a general n person balanced connected game the input is the array of the explicitly given values of the n n 1 2 connected coalitions the algorithm generates a sequence of at most n n 1 2 payoff vectors starting from a special vertex of the nonempty core and ending in the nucleolus by exploiting the special structure of connected games the initial as well as the subsequent payoff vectors are obtained by evaluating some simple recursive formulas it is shown that the algorithm requires at most o n4 time and o n2 space a 5 person illustrative example is also given

finite alphabet constant envelope waveform design for mimo radar the design of waveforms with specified auto and cross correlation properties has a number of applications in multiple input multiple output mimo radar beampattern design in this work two algorithms are proposed to generate finite alphabet constant envelope ce waveforms with required cross correlation properties the first algorithm proposes a closed form solution to find the finite alphabet ce waveforms to realize the given covariance matrix here gaussian random variables rv s are mapped onto binary phase shift keying bpsk and quadrature phase shift keying qpsk symbols using nonlinear functions and the cross correlation relationship between the gaussian rv s and bpsk qpsk rv s is established this cross correlation relationship is exploited to convert the problem of finding the bpsk qpsk waveforms to realize the covariance matrix corresponding to the given beampattern into finding the gaussian rv s to realize another covariance matrix that can be easily found in the second algorithm by exploiting the results of first algorithm a generalized algorithm to generate bpsk waveforms to approximate the given beampattern is proposed simulation results show that proposed finite alphabet ce waveforms outperform the existing algorithms to approximate the desired beampattern

constant modulus waveform design for mimo radar transmit beampattern a multiple input multiple output radar has great flexibility to design the transmit beampattern via selecting the probing waveform the idea of current transmit beampattern design is to approximate the disired transimit beampattern and minimize the cross correlation sidelobes in this paper under the constant modulus constraint two algorithms are proposed to design the probing waveform directly in the first algorithm the optimization criterion is minimizing the squared error between the designed beampattern and the given beampattern since the objective function is a nonconvex fourth order polynomial and the constant modulus constraint can be regarded as many nonconvex quadratic equality constraints an efficient alternating direction method of multipliers admm algorithm whose convergence speed is very fast is proposed to solve it in the second algorithm the criterion is minimizing the absolute error between the designed beampattern and the given beampattern this nonconvex problem can be formulated as l 1 norm problem which can be solved through a double admm algorithm finally we assess the performance of the two proposed algorithms via numerical results

on the core and nucleolus of minimum cost spanning tree games we develop two efficient procedures for generating cost allocation vectors in the core of a minimum cost spanning tree m c s t game the first procedure requires o n 2 elementary operations to obtain each additional point in the core wheren is the number of users the efficiency of the second procedure which is a natural strengthening of the first procedure stems from the special structure of minimum excess coalitions in the core of an m c s t game this special structure is later used i to ease the computational difficulty in computing the nucleolus of an m c s t game and ii to provide a geometric characterization for the nucleolus of an m c s t game this geometric characterization implies that in an m c s t game the nucleolus is the unique point in the intersection of the core and the kernel we further develop an efficient procedure for generating fair cost allocations which in some instances coincide with the nucleolus finally we show that by employing sterns transfer scheme we can generate a sequence of cost vectors which converges to the nucleolus

totally balanced games and games of flow a class of characteristic function games arising from maximum flow problems is introduced and is shown to coincide with the class of totally balanced games the proof relies on the max flow min cut theorem of ford and fulkerson and on the observation that the class of totally balanced games is the span of the additive games with the minimum operation

on some network flow games we analyze three subclasses of cooperative games arising from network optimization problems in which the resources such as arcs or nodes in the network are controlled by individuals who have conflicting objectives the first subclass of cooperative games is induced by network optimization problems over directed augmented trees we show that for this subclass of games the kernel coincides with the nucleolus and that the nucleolus can be characterized as the unique revenue allocation vector in which every pair of arc owners who are adjacent in the tree are located symmetrically with respect to their bargaining range we further give a linear characterization of the core of this subclass of games which is then used to provide a more explicit representation of the nucleolus and to construct a strongly polynomial algorithm for generating it the second subclass of cooperative games is induced by maximum flow problems in simple undirected networks we provide a useful parametric representation of the core of this subclass of games which is used to characterize the nucleolus and the intersection of the core and the kernel explicitly we show that the intersection of the core and the kernel consists of all revenue allocations in the core which assign equal payoffs to any pair of unseparated arc owners we further demonstrate that among the core vectors the nucleolus is the unique revenue allocation vector in which the smallest allocations are maximized in a lexicographical sense the third cooperative game that we study is the assignment game introduced by shapley and shubik 1972 this game is induced by the assignment problem which can be cast as a network optimization problem we investigate the relationship between the kernel and the core of the assignment game and provide a necessary and sufficient condition for the core to be contained in the kernel we further show that in general the intersection of the kernel and the core is not a convex set we also exhibit that under certain conditions the nucleolus has a simple characterization as the unique vector in the core in which the smallest revenue allocations are maximized in a lexicographical sense finally we consider the horse market example of bohm bawerk 1923 for which it is shown that the core is contained in the kernel and that the nucleolus is the midpoint of the core

constant modulus mimo radar waveform design with minimum peak sidelobe transmit beampattern this paper addresses the problem of minimum peak sidelobe transmit beampattern design for colocated multiple input multiple output radar systems two new methods are proposed to achieve it via designing constant modulus cm waveforms directly one is to maximize the ratio of the minimum mainlobe level to the peak sidelobe level psl without specifying pattern masks and another is to minimize psl under the mainlobe ripple and unspecified waveform modulus constraints the resultant optimization problems are difficult to solve due to the coupled numerator and denominator of the quadratic fractional programming problem formulation in the former and double sided quadratic constraints and unknown waveform modulus in the latter for the former we decouple the numerator and denominator by equivalent transformation and introduction of boundary type auxiliary variables in order that feasible methods are derived to tackle them independently and efficiently for the latter we simplify the coupled double sided quadratic constraints on the same waveform vector into those on different single auxiliary variables to tackle the corresponding nonconvex optimization problem numerical examples show that the proposed algorithms can attain sufficient low peak sidelobe beampattern levels under the cm constraints

traveling salesman games in this paper we discuss the problem of how to divide the total cost of a round trip along several institutes among the institutes visited we introduce two types of cooperative games fixed route traveling salesman games and traveling salesman games as a tool to attack this problem under very mild conditions we prove that fixed route traveling salesman games have non empty cores if the fixed route is a solution of the classical traveling salesman problem core elements provide us with fair cost allocations a traveling salesman game may have an empty core even if the cost matrix satisfies the triangle inequality in this paper we introduce a class of matrices defining ts games with non empty cores

generation of correlated finite alphabet waveforms using gaussian random variables various examples of methods and systems are provided for generation of correlated finite alphabet waveforms using gaussian random variables in e g radar and communication applications in one example a method includes mapping an input signal comprising gaussian random variables rvs onto finite alphabet non constant envelope fance symbols using a predetermined mapping function and transmitting fance waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern the fance waveforms can be based upon the mapping of the gaussian rvs onto the fance symbols in another example a system includes a memory unit that can store a plurality of digital bit streams corresponding to fance symbols and a front end unit that can transmit fance waveforms through a uniform linear array of antenna elements to obtain a corresponding beam pattern the system can include a processing unit that can encode the input signal and or determine the mapping function

linear transmit processing in mimo communications systems we examine and compare the different types of linear transmit processing for multiple input multiple output systems where we assume that the receive filter is independent of the transmit filter contrary to the joint optimization of transmit and receive filters we can identify three filter types similar to receive processing the transmit matched filter the transmit zero forcing filter and the transmit wiener filter we show that the transmit filters are based on similar optimizations as the respective receive filters with an additional constraint for the transmit power moreover the transmit wiener filter has similar convergence properties as the receive wiener filter i e it converges to the matched filter and the zero forcing filter for low and high signal to noise ratio respectively we give closed form solutions for all transmit filters and present the fundamental result that their mean square errors are equal to the errors of the respective receive filters if the information symbols and the additive noise are uncorrelated however our simulations reveal that the bit error ratio results of the transmit filters differ from the results for the respective receive filters