dilations for systems of imprimitivity acting on banach spaces abstract motivated by a general dilation theory for operator valued measures framings and bounded linear maps on operator algebras we consider the dilation theory of the above objects with special structures we show that every operator valued system of imprimitivity has a dilation to a probability spectral system of imprimitivity acting on a banach space this completely generalizes a well known result which states that every frame representation of a countable group on a hilbert space is unitarily equivalent to a subrepresentation of the left regular representation of the group we also prove that isometric group representation induced framings on a banach space can be dilated to unconditional bases with the same structure for a larger banach space this extends several known results on the dilations of frames induced by unitary group representations on hilbert spaces

a duality principle for groups the duality principle for gabor frames states that a gabor sequence obtained by a time frequency lattice is a frame for l2 rd if and only if the associated adjoint gabor sequence is a riesz sequence we prove that this duality principle extends to any dual pairs of projective unitary representations of countable groups we examine the existence problem of dual pairs and establish some connection with classification problems for ii1 factors while in general such a pair may not exist for some groups we show that such a dual pair always exists for every subrepresentation of the left regular unitary representation when g is an abelian infinite countable group or an amenable icc group for free groups with finitely many generators the existence problem of such a dual pair is equivalent to the well known problem about the classification of free group von neumann algebras

multiplicative lidskii s inequalities and optimal perturbations of frames abstract in this paper we study two design problems in frame theory on the one hand given a fixed finite frame f f j j i n for c d we compute those dual frames g of f that are optimal perturbations of the canonical dual frame for f under certain restrictions on the norms of the elements of g on the other hand we compute those v f v f j j i n for invertible operators v which are close to the identity that are optimal perturbations of f that is we compute the optimal perturbations of f among frames g g j j i n that have the same linear relations as f in both cases optimality is measured with respect to submajorization of the eigenvalues of the frame operators hence our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error the key tool for these results is a multiplicative analogue of lidskii s inequality in terms of log majorization and a characterization of the case of equality

runtime analysis of a multi objective evolutionary algorithm for obtaining finite approximations of pareto fronts previous theoretical analyses of evolutionary multi objective optimization emo mostly focus on obtaining approximations of pareto fronts however in practical applications an appropriate value of is critical but sometimes for a multi objective optimization problem mop with unknown attributes difficult to determine in this paper we propose a new definition for the finite representation of the pareto front the adaptive pareto front which can automatically accommodate the pareto front accordingly it is more practical to take the adaptive pareto front or its approximation termed the adaptive pareto front as the goal of an emo algorithm we then perform a runtime analysis of a m 1 multi objective evolutionary algorithm m 1 moea for three mops including a discrete mop with a polynomial pareto front denoted as a polynomial dmop a discrete mop with an exponential pareto front denoted as an exponential dmop and a simple continuous two objective optimization problem sctop by employing an estimator based update strategy in the m 1 moea we show that 1 for the polynomial dmop the whole pareto front can be obtained in the expected polynomial runtime by setting the population size m equal to the number of pareto vectors 2 for the exponential dmop the expected polynomial runtime can be obtained by keeping m increasing in the same order as that of the problem size n and 3 the diversity mechanism guarantees that in the expected polynomial runtime the moea can obtain an adaptive pareto front of sctop for any given precision theoretical studies and numerical comparisons with nsga ii demonstrate the efficiency of the proposed moea and should be viewed as an important step toward understanding the mechanisms of moeas

aliasing and oblique dual pair designs for consistent sampling abstract in this paper we study some aspects of oblique duality between finite sequences of vectors f and g lying in finite dimensional subspaces w and v respectively we compute the possible eigenvalue lists of the frame operators of oblique duals to f lying in v we compute the spectral and geometrical structure of minimizers of convex potentials among oblique duals for f with norm restrictions as an application we show that these optimal duals are the closest to being tight frames and therefore have their spectrum as concentrated as possible among oblique duals with norm restrictions we obtain a complete quantitative analysis of the impact that the relative geometry between the subspaces v and w has in oblique duality we apply this analysis to compute those rigid rotations u for w such that the canonical oblique dual of u f minimize every convex potential we also introduce a notion of aliasing for oblique dual pairs and compute those rigid rotations u for w such that the canonical oblique dual pair associated to u f minimize the aliasing we point out that these two last problems are intrinsic to oblique duality within the context of consistent sampling

phase retrievable operator valued frames and representations of quantum channels abstract we examine some connections among phase retrievable not necessarily self adjoint operator valued frames projective group representation frames and representations of quantum channels we first present some characterizations of phase retrievable frames for general operator systems acting on both finite and infinite dimensional hilbert spaces which generalize the known results for vector valued frames fusion frames and frames of hermitian matrices for an irreducible projective unitary representation of a finite group the image system is automatically phase retrievable and moreover it is a point wisely tight operator valued frames we generalize this notion to more general operator valued frames and prove that point wise tight operator valued frames are exactly the ones that are right equivalent to operator valued tight frames for an operator system that represent a quantum channel we show that phase retrievability of the system is independent of the choices of the representations of the quantum channel

dilations of operator valued measures with bounded p variations and framings on banach spaces abstract the dilations for operator valued measures ovms and bounded linear maps indicate that the dilation theory is in general heavily dependent on the banach space nature of the dilation spaces this naturally led to many questions concerning special type of dilations in particular it is not known whether ultraweakly continuous normal maps can be dilated to ultraweakly continuous homomorphisms we answer this question affirmatively for the case when the domain algebra is an abelian von neumann algebra it is well known that completely bounded hilbert space operator valued measures correspond to the existence of orthogonal projection valued dilations in the sense of naimark and stinespring and ovms with bounded total variations are completely bounded but not the vice versa with the aim of classifying ovms from the dilation point of view we introduce the concept of total p variations for ovms we prove that any completely bounded ovm has finite 2 variation and any ovm with finite p variation can be dilated to a but usually non hilbertian projection valued measure of the same type with the help of framing induced ovms we prove that conventional minimal dilation space of a non trivial framing contains c 0 then does not have bounded p variation

evolutionary algorithms with preference polyhedron for interval multi objective optimization problems multi objective optimization problems mops with interval parameters are ubiquitous in real world applications existing evolutionary optimization methods however aim to obtain a set of well converged and evenly distributed pareto optimal solutions in this paper we presented a novel evolutionary algorithm ea that interacts with a decision maker dm during the optimization process to obtain the most preferred solution the theory of preference polyhedron for the optimization problem with interval parameters was developed first an interactive evolutionary algorithm iea for mops with interval parameters was then proposed based on the theory of preference polyhedron the algorithm periodically provides a set of non dominated solutions to the dm a preference polyhedron is constructed in the objective space by taking the worst solution chosen by the dm as the vertex the solutions with the same rank are sorted based on the polyhedron constructed finally our method was empirically evaluated on several mops with interval parameters where the value functions were used to simulate the dm s responses the numerical results indicated that our method is simpler and more efficient than the a posteriori method

a nonlinear interval number programming method for uncertain optimization problems in this paper a method is suggested to solve the nonlinear interval number programming problem with uncertain coefficients both in nonlinear objective function and nonlinear constraints based on an order relation of interval number the uncertain objective function is transformed into two deterministic objective functions in which the robustness of design is considered through a modified possibility degree the uncertain inequality and equality constraints are changed to deterministic inequality constraints the two objective functions are converted into a single objective problem through the linear combination method and the deterministic inequality constraints are treated with the penalty function method the intergeneration projection genetic algorithm is employed to solve the finally obtained deterministic and non constraint optimization problem two numerical examples are investigated to demonstrate the effectiveness of the present method

random phaseless sampling for causal signals in shift invariant spaces a zero distribution perspective we proved that the phaseless sampling pls in the linear phase modulated shift invariant space sis v e bf i alpha cdot varphi alpha ne 0 is impossible even though the real valued function varphi enjoys the full spark property so does e bf i alpha cdot varphi stated another way the pls in the complex generated siss is essentially different from that in the real generated ones motivated by this we first establish the condition on the complex valued generator phi such that the pls of nonseparable causal nc signals in v phi can be achieved by random sampling the condition is established from the generalized haar condition ghc perspective based on the proposed reconstruction approach it is proved that if the ghc holds then with probability 1 the random sampling density sd 3 is sufficient for the pls of nc signals in the complex generated siss for the real valued case we also prove that if the ghc holds then with probability 1 the random sd 2 is sufficient for the pls of real valued nc signals in the real generated siss for the local reconstruction of highly oscillatory signals such as chirps a great number of deterministic samples are required compared with deterministic sampling the proposed random approach enjoys not only the greater sampling flexibility but the much smaller number of samples to verify our results numerical simulations were conducted to reconstruct highly oscillatory nc signals in the chirp modulated siss

frame representations and parseval duals with applications to gabor frames let x n be a frame for a hilbert space h we investigate the conditions under which there exists a dual frame for x n which is also a parseval or tight frame we show that the existence of a parseval dual is equivalent to the problem whether x n can be dilated to an orthonormal basis under an oblique projection a necessary and sufficient condition for the existence of parseval duals is obtained in terms of the frame excess for a frame g g g induced by a projective unitary representation of a group g it is possible that g g g can have a parseval dual but does not have a parseval dual of the same type the primary aim of this paper is to present a complete characterization for all the projective unitary representations such that every frame g g g with a necessary lower frame bound condition has a parseval dual of the same type as an application of this characterization together with a result about lattice tiling we prove that every gabor frame g g l k again with the same necessary lower frame bound condition has a parseval dual of the same type if and only if the volume of the fundamental domain of l k is less than or equal to 1 2

lazy narrowing strong completeness and eager variable elimination abstract narrowing is an important method for solving unification problems in equational theories that are presented by confluent term rewriting systems because narrowing is a rather complicated operation several authors studied calculi in which narrowing is replaced by more simple inference rules this paper is concerned with one such calculus contrary to what has been stated in the literature we show that the calculus lacks strong completeness so selection functions to cut down the search space are not applicable we prove completeness of the calculus and we establish an interesting connection between its strong completeness and the completeness of basic narrowing we also address the eager variable elimination problem it is known that many redundant derivations can be avoided if the variable elimination rule one of the inference rules of our calculus is given precedence over the other inference rules we prove the completeness of a restricted variant of eager variable elimination in the case of orthogonal term rewriting systems

parseval frames for icc groups abstract we analyze parseval frames generated by the action of an icc group on a hilbert space we parametrize the set of all such parseval frames by operators in the commutant of the corresponding representation we characterize when two such frames are strongly disjoint we prove an undersampling result showing that if the representation has a parseval frame of equal norm vectors of norm 1 n the hilbert space is spanned by an orthonormal basis generated by a subgroup as applications we obtain some sufficient conditions under which a unitary representation admits a parseval frame which is spanned by a riesz sequences generated by a subgroup in particular every subrepresentation of the left regular representation of a free group has this property

convergence of multi objective evolutionary algorithms to a uniformly distributed representation of the pareto front in evolutionary multi objective optimization emo the convergence to the pareto set of a multi objective optimization problem mop and the diversity of the final approximation of the pareto front are two important issues in the existing definitions and analyses of convergence in multi objective evolutionary algorithms moeas convergence with probability is easily obtained because diversity is not considered however diversity cannot be guaranteed by combining the convergence with diversity this paper presents a new definition for the finite representation of a pareto set the b pareto set and a convergence metric for moeas based on a new archive updating strategy the convergence of one such moea to the b pareto sets of mops is proved numerical results show that the obtained b pareto front is uniformly distributed along the pareto front when according to the new definition of convergence the algorithm is convergent

solving the discrete multiple criteria problem using convex cones an interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi concave increasing utility or value function the method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions the maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker responses are used to eliminate alternatives using convex cones based on expressed preferences and then a new set of weights is found that satisfies the indicated preferences the requisite theory and proofs as well as a detailed numerical example are included in addition the results of some computational experiments to test the effectiveness of the method are described

wandering vector multipliers for unitary groups a wandering vector multiplier is a unitary operator which maps the set of wandering vectors for a unitary system into itself a special case of unitary system is a discrete unitary group we prove that for many and perhaps all discrete unitary groups the set of wandering vector multipliers is itself a group we completely characterize the wandering vector multipliers for abelian and icc unitary groups some characterizations of special wandering vector multipliers are obtained for other cases in particular there are simple characterizations for diagonal and permutation wandering vector multipliers similar results remain valid for irrational rotation unitary systems we also obtain some results concerning the wandering vector multipliers for those unitary systems which are the ordered products of two unitary groups there are applications to wavelet systems

symmetric approximation of frames and bases in hilbert spaces we introduce the symmetric approximation of frames by normalized tight frames extending the concept of the symmetric orthogonalization of bases by orthonormal bases in hilbert spaces we prove existence and uniqueness results for the symmetric approximation of frames by normalized tight frames even in the case of the symmetric orthogonalization of bases our techniques and results are new a crucial role is played by whether or not a certain operator related to the initial frame or basis is hilbert schmidt

a fuzzy approach to hierarchical multiobjective programming problems and its application to an industrial pollution control problem in this paper we focus on hierarchical multiobjective programming problems where multiple decision makers in a hierarchical organization have their own multiple objective functions and propose an interactive algorithm based on the dual decomposition method to obtain the satisfactory solution which reflects not only the hierarchical relationships between multiple decision makers but also their own preferences for their objective functions in the proposed algorithm assuming that each of the decision makers has fuzzy goals for his her objective functions corresponding membership functions are elicited from the decision makers in their subjective manner in order to deal with hierarchical multiobjective programming problems a new kind of pareto optimality concept in membership spaces is defined and the concept of decision powers of multiple decision makers in a hierarchical decision structure is introduced the proposed algorithm is applied to the industrial pollution control problem in osaka city in japan in order to show the efficiency of the proposed method

the existence of tight gabor duals for gabor frames and subspace gabor frames abstract let k and l be two full rank lattices in r d we give a complete characterization for all the gabor frames that admit tight dual of the same type the characterization is given in terms of the center valued trace of the von neumann algebra generated by the left regular projective unitary representations associated with the time frequency lattice k l two applications of this characterization were obtained i we are able to prove that every gabor frame has a tight dual if and only if the volume of k l is less than or equal to 1 2 ii we are able to obtain sufficient or necessary conditions for the existence of tight gabor pseudo duals for subspace gabor frames in various cases in particular we prove that every subspace gabor frame has a tight gabor pseudo dual if either the volume v k l 1 2 or v k l 2 moreover if k z d l z d with 1 then a subspace gabor frame g g l k has a tight gabor pseudo dual only when g g l k itself is already tight

increasing selective pressure towards the best compromise in evolutionary multiobjective optimization the extended nosga method most current approaches in the evolutionary multiobjective optimization literature concentrate on adapting an evolutionary algorithm to generate an approximation of the pareto frontier however finding this set does not solve the problem the decision maker still has to choose the best compromise solution out of that set here we introduce a new characterization of the best compromise solution of a multiobjective optimization problem by using a relational system of preferences based on a multicriteria decision aid way of thinking and an outranked based dominance generalization we derive some necessary and sufficient conditions which describe satisfactory approximations to the best compromise such conditions define a lexicographic minimum of a bi objective optimization problem which is a map of the original one the nosga ii method is a nsga ii inspired efficient way of solving the resulting mapped problem

singular value estimates of oblique projections abstract let w and m be two finite dimensional subspaces of a hilbert space h such that h w m and let p w m denote the oblique projection with range w and nullspace m in this article we get the following formula for the singular values of p w m 2 s k p w m 1 min f h x w m 2 where the minimum is taken over the set of all operator pairs f h on h such that r f w r h m and fh p w m and k 1 dim w we also characterize all the pairs where the minimum is attained

frame vector multipliers for finite group representations abstract a frame vector or generator for a group representation of a countable or finite group g on a hilbert space h is a vector h such that g g g is a parseval frame for h frame vector multipliers are the unitary operators on h that map frame vectors to frame vectors based on a characterization of frame vectors with respect to the standard decomposition of a group representation as the direct sums of irreducible subrepresentations with multiplicity we obtain explicit characterizations of frame generator multipliers for two basic cases for finite group representations with the help of these characterizations we obtain some necessary conditions of frame vector multipliers for general frame representations and present several examples to demonstrate how these results can be used to get explicit characterizations for frame vector multipliers

continuous and discrete wavelet transforms this paper is an expository survey of results on integral representations and discrete sum expansions of functions in l 2 bf r in terms of coherent states two types of coherent states are considered weyl heisenberg coherent states which arise from translations and modulations of a single function and affine coherent states called wavelets which arise as translations and dilations of a single function in each case it is shown how to represent any function in l 2 bf r as a sum or integral of these states most of the paper is a survey of literature most notably the work of i daubechies a grossmann and j morlet a few results of the authors are included

approximations for gabor and wavelet frames let be a frame vector under the action of a collection of unitary operators u motivated by the recent work of frank paulsen and tiballi and some application aspects of gabor and wavelet frames we consider the existence and uniqueness of the best approximation by normalized tight frame vectors we prove that for any frame induced by a projective unitary representation for a countable discrete group the best normalized tight frame ntf approximation exists and is unique therefore it applies to gabor frames including gabor frames for subspaces and frames induced by translation groups similar results hold for semi orthogonal wavelet frames

tight frames of compactly supported affine wavelets this paper extends the class of orthonormal bases of compactly supported wavelets recently constructed by daubechies commun pure appl math 41 909 1988 for each integer n 1 a family of wavelet functions having support 0 2n 1 is constructed such that jk x 2j 2 2jx k kj k z is a tight frame of l2 r i e for every f l2 r f c jk jk f jk for some c 0 this family is parametrized by an algebraic subset vn of r4n furthermore for n 2 a proper algebraic subset wn of vn is specified such that all points in vn outside of wn yield orthonormal bases the relationship between these tight frames and the theory of group representations and coherent states is discussed

frames in the bargmann space of entire functions we look at the decomposition of arbitrary f in l2 r in terms of the family of functions cp x w exp iimnab iman i x nb 2 with a b 0 we derive bounds and explicit formulas for the minimal expansion coefficients in the case where ab 2w n n an integer 2 2 transported to the hilbert space f of entire functions introduced by v bargmann these results are expressed as inequalities of the form

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

a fuzzy multiobjective linear programming abstract in this study we focus on an molp problem with fuzzy numbered cost coefficients based on the membership functions the problem is transformed into a multiobjective problem with parametrically interval valued molp problem then by the proposed tolerance analysis of a nondominated set a fuzzy set of the efficient extreme bases can be obtained therefore the fuzzy solutions can be focused to provide complete information for the final decision theoretical developments are provided with numerical illustrations

interactive evolutionary multi objective optimization for quasi concave preference functions we present a new hybrid approach to interactive evolutionary multi objective optimization that uses a partial preference order to act as the fitness function in a customized genetic algorithm we periodically send solutions to the decision maker dm for her evaluation and use the resulting preference information to form preference cones consisting of inferior solutions the cones allow us to implicitly rank solutions that the dm has not considered this technique avoids assuming an exact form for the preference function but does assume that the preference function is quasi concave this paper describes the genetic algorithm and demonstrates its performance on the multi objective knapsack problem

geometric aspects of frame representations of abelian groups hhwe consider frames arising from the action of a unitary representation of a discrete countable abelian group we show that the range of the analysis operator can be determined by computing which characters appear in the representation this allows one to compare the ranges of two such frames which is useful for determining similarity and also for multiplexing schemes our results then partially extend to bessel sequences arising from the action of the group we apply the results to sampling on bandlimited functions and to wavelet and weyl heisenberg frames this yields a sufficient condition for two sampling transforms to have orthogonal ranges and two analysis operators for wavelet and weyl heisenberg frames to have orthogonal ranges the sufficient condition is easy to compute in terms of the periodization of the fourier transform of the frame generators

semantic forgetting in answer set programming the notion of forgetting also known as variable elimination has been investigated extensively in the context of classical logic but less so in nonmonotonic logic programming and nonmonotonic reasoning the few approaches that exist are based on syntactic modifications of a program at hand in this paper we establish a declarative theory of forgetting for disjunctive logic programs under answer set semantics that is fully based on semantic grounds the suitability of this theory is justified by a number of desirable properties in particular one of our results shows that our notion of forgetting can be entirely captured by classical forgetting we present several algorithms for computing a representation of the result of forgetting and provide a characterization of the computational complexity of reasoning from a logic program under forgetting as applications of our approach we present a fairly general framework for resolving conflicts in inconsistent knowledge bases that are represented by disjunctive logic programs and we show how the semantics of inheritance logic programs and update logic programs from the literature can be characterized through forgetting the basic idea of the conflict resolution framework is to weaken the preferences of each agent by forgetting certain knowledge that causes inconsistency in particular we show how to use the notion of forgetting to provide an elegant solution for preference elicitation in disjunctive logic programming

evolutionary algorithms for optimization problems with uncertainties and hybrid indices many optimization problems in real world applications contain both explicit quantitative and implicit qualitative indices that usually contain uncertain information how to effectively incorporate uncertain information in evolutionary algorithms is one of the most important topics in information science in this paper we study optimization problems with both interval parameters in explicit indices and interval uncertainties in implicit indices to incorporate uncertainty in evolutionary algorithms we construct a mathematical uncertain model of the optimization problem considering the uncertainties of interval objectives and then we transform the model into a precise one by employing the method of interval analysis finally we develop an effective and novel evolutionary optimization algorithm to solve the converted problem by combining traditional genetic algorithms and interactive genetic algorithms the proposed algorithm consists of clustering of a large population according to the distribution of the individuals and estimation of the implicit indices of an individual based on the similarity among individuals in our experiments we apply the proposed algorithm to an interior layout problem a typical optimization problem with both interval parameters in the explicit index and interval uncertainty in the implicit index our experimental results confirm the feasibility and efficiency of the proposed algorithm

a needed narrowing strategy the narrowing relation over terms constitutes the basis of the most important operational semantics of languages that integrate functional and logic programming paradigms it also plays an important role in the definition of some algorithms of unification modulo equational theories that are defined by confluent term rewriting systems due to the inefficiency of simple narrowing many refined narrowing strategies have been proposed in the last decade this paper presents a new narrowing strategy that is optimal in several respects for this purpose we propose a notion of a needed narrowing step that for inductively sequential rewrite systems extends the huet and levy notion of a needed reduction step we define a strategy based on this notion that computes only needed narrowing steps our strategy is sound and complete for a large class of rewrite systems is optimal with respect to the cost measure that counts the number of distinct steps of a derivation computes only incomparable and disjoint unifiers and is efficiently implemented by unification

wiener s lemma for twisted convolution and gabor frames as a consequence ca is invertible and bounded on all p zd for 1 p oo simultaneously in this article we study several non commutative generalizations of wiener s lemma and their application to gabor theory the paper is divided into two parts the first part sections 2 and 3 is devoted to abstract harmonic analysis and extends wiener s lemma to twisted convolution the second part section 4 is devoted to the theory of gabor frames specifically to the design of dual windows with good time frequency localization in particular we solve a conjecture of janssen feichtinger and one of us 17 18 9 these two topics appear to be completely disjoint but they are not the solution of the conjectures about gabor frames is an unexpected application of methods from non commutative harmonic analysis to application oriented mathematics it turns out that the connection between twisted convolution and the heisenberg group and the theory of symmetric group algebras are precisely the tools needed to treat the problem motivated by signal analysis to be more concrete we formulate some of our main results first and will deal with the details and the technical background later

a stochastic programming approach to cash management in banking the treasurer of a bank is responsible for the cash management of several banking activities in this work we focus on two of them cash management in automatic teller machines atms and in the compensation of credit card transactions in both cases a decision must be taken according to a future customers demand which is uncertain from historical data we can obtain a discrete probability distribution of this demand which allows the application of stochastic programming techniques we present stochastic programming models for each problem two short term and one mid term models are presented for atms the short term model with fixed costs results in an integer problem which is solved by a fast i e linear running time algorithm the short term model with fixed and staircase costs is solved through its milp equivalent deterministic formulation the mid term model with fixed and staircase costs gives rise to a multi stage stochastic problem which is also solved by its milp deterministic equivalent the model for compensation of credit card transactions results in a closed form solution the optimal solutions of those models are the best decisions to be taken by the bank and provide the basis for a decision support system

on twisted group frames abstract in this paper we study g frames for finite dimensional hilbert spaces where g is a finite group and is a unitary schur multiplier of g we apply the characterizations for tight g frames and central g frames to investigation of g frames that have the maximal spanning property we apply the theory of twisted group frames to obtain a criterion for maximal spanning vectors that generalizes the main result of 16 theorem 1 7 moreover we prove that a projective representation does not admit any maximal spanning vector if it has an at least 2 dimensional subrepresentation that is equivalent to a central projection induced subrepresentation of the regular representation

rational von neumann lattices a rational von neumann lattice is defined as a lattice in phase space with the constants a and b in the x and p directions given by a ratio of integers zeros of harmonic oscillator functions in the kq representation on such lattices are found it is shown that the number of zeros of the kq function determines the number of states by which a set on a von neumann lattice is overcomplete interesting relations between theta functions are derived on the basis of their connection with the harmonic oscillator states in the kq representation

optimal dual frames for erasures for any given frame for the purpose of encoding in a finite dimensional hilbert space we investigate its dual frames that are optimal for erasures for the purpose of decoding we show that in general the canonical dual is not necessarily optimal moreover optimal dual frames are not necessarily unique we present some sufficient conditions under which the canonical dual is the unique optimal dual frame for the erasure problem as an application we get that the canonical dual is the only optimal dual when either the frame is induced by a group representation or the frame is uniform tight

existence of parseval oblique duals of a frame sequence abstract we present a collection of necessary and sufficient conditions for the existence of a parseval oblique dual in an appropriate subspace of a frame sequence this result extends the previous results by han and larson antezana et al and han our proof shows that the problem is closely related with that of extending an operator with norm less than or equal to 1 to an isometry on a subspace

optimal dual frames for communication coding with probabilistic erasures assume that a frame is preselected for encoding in a communication system we investigate the optimal dual frames for signal reconstruction decoding which minimize the maximal error when the probabilistic erasures occur in the transmission process from the perspective of mathematical theory of frames we set up a probability model under which we define the probability optimal po dual frames for a given frame when the frame based coding involves probabilistic erasures we obtain a sufficient and necessary condition under which the canonical dual frame is the unique po dual frame additionally we derive some general sufficient conditions for which the canonical dual frame is either not optimal or it is optimal but not the unique optimal one we present two simulation examples to compare the reconstruction effects when both the po dual frames and the general optimal go dual frames are used for reconstruction