an equilibrium existence theorem bewley 14 theorem l proved an infinite dimensional equilibrium existence theorem which is a significant extension of the classical finite dimensional theorem of arrow and debreu 11 the assumptions on technology and preferences are natural and applicable in a wide variety of cases the proof is based on a limit argument that makes direct use of the existence of equilibrium in the finite dimensional case this paper establishes the existence of equilibrium under assumptions which are essentially the same as those given by bewley with the additional assumption that the preference orderings of consumers are representable by real valued utility functions this approach is related to the welfare approach of negishi 9 and arrow and hahn 2 chap 51 in the finite dimensional case and simplifies the approach originally adopted by bewley 5 in addition to making clear the role played by each of the assumptions in establishing the existence of equilibrium this approach has the merit of constructing directly a certain real valued function that is maximised at an equilibrium a result that provides a powerful tool in the analysis of qualitative properties of an equilibrium a model of resource allocation in continuous time over an infinite horizon that may be viewed as an application of the model that follows is given in 181

on the design of multifilter banks and orthonormal multiwavelet bases several forms of parametric expressions for orthogonal multifilter banks are presented the explicit expressions for a group of orthogonal multifilter banks that generate symmetric antisymmetric scaling functions and orthonormal multiwavelets are obtained based on these parametric expressions for orthogonal multifilter banks orthonormal multiwavelet pairs with good time frequency localization are constructed and examples of optimal multifilter banks are provided

algebraic convergence of schottky groups a discrete faithful representation of the free group on g generators f g into isom h 3 is said to be a schottky group if h 3 d is homeomorphic to a handlebody h g where d is the domain of discontinuity for s action on the sphere at infinity for h 3 schottky space s g the space of all schottky groups is parameterized by the quotient of the teichmuller space f s g of the closed surface of genus g by mod 0 h g where mod 0 h g is the group of isotopy classes of homeomorphisms of s g which extend to homeomorphisms of h g which are homotopic to the identity masur exhibited a domain o h g of discontinuity for mod 0 h g s action on pl s g the space of projective measured laminations on s g so b h g o h g mod 0 h g may be appended to s g as a boundary

embedded image coding using zerotrees of wavelet coefficients the embedded zerotree wavelet algorithm ezw is a simple yet remarkably effective image compression algorithm having the property that the bits in the bit stream are generated in order of importance yielding a fully embedded code the embedded code represents a sequence of binary decisions that distinguish an image from the null image using an embedded coding algorithm an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly also given a bit stream the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream in addition to producing a fully embedded bit stream the ezw consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images yet this performance is achieved with a technique that requires absolutely no training no pre stored tables or codebooks and requires no prior knowledge of the image source the ezw algorithm is based on four key concepts 1 a discrete wavelet transform or hierarchical subband decomposition 2 prediction of the absence of significant information across scales by exploiting the self similarity inherent in images 3 entropy coded successive approximation quantization and 4 universal lossless data compression which is achieved via adaptive arithmetic coding

orthogonal and biorthogonal fir hexagonal filter banks with sixfold symmetry recently hexagonal image processing has attracted attention the hexagonal lattice has several advantages in comparison with the rectangular lattice the conventionally used lattice for image sampling and processing for example a hexagonal lattice needs less sampling points it has better consistent connectivity it has higher symmetry and its structure is plausible to human vision systems the multiresolution analysis method has been used for hexagonal image processing since the hexagonal lattice has high degree of symmetry it is desirable that the hexagonal filter banks designed for multiresolution hexagonal image processing also have high order of symmetry which is pertinent to the symmetry structure of the hexagonal lattice the orthogonal or prefect reconstruction pr hexagonal filter banks that are available in the literature have only threefold symmetry in this paper we investigate the construction of orthogonal and pr finite impulse response fir hexagonal filter banks with sixfold symmetry we obtain block structures of 7 size refinement seven channel two dimensional orthogonal and pr fir hexagonal filter banks with sixfold rotational symmetry radic7 refinement orthogonal and biorthogonal wavelets based on these block structures are constructed in this paper we also consider fir hexagonal filter banks with axial line symmetry and we present a block structure of fir hexagonal filter banks with pseudo sixfold axial symmetry

the application of multiwavelet filterbanks to image processing multiwavelets are a new addition to the body of wavelet theory realizable as matrix valued filterbanks leading to wavelet bases multiwavelets offer simultaneous orthogonality symmetry and short support which is not possible with scalar two channel wavelet systems after reviewing this theory we examine the use of multiwavelets in a filterbank setting for discrete time signal and image processing multiwavelets differ from scalar wavelet systems in requiring two or more input streams to the multiwavelet filterbank we describe two methods repeated row and approximation deapproximation for obtaining such a vector input stream from a one dimensional 1 d signal algorithms for symmetric extension of signals at boundaries are then developed and naturally integrated with approximation based preprocessing we describe an additional algorithm for multiwavelet processing of two dimensional 2 d signals two rows at a time and develop a new family of multiwavelets the constrained pairs that is well suited to this approach this suite of novel techniques is then applied to two basic signal processing problems denoising via wavelet shrinkage and data compression after developing the approach via model problems in one dimension we apply multiwavelet processing to images frequently obtaining performance superior to the comparable scalar wavelet transform

parametrizations of symmetric orthogonal multifilter banks with different filter lengths abstract this paper is devoted to a study of parametrizations of symmetric orthogonal multifilter banks with different filter lengths to construct symmetric orthogonal multifilter banks h g which generate balanced multiwavelets of multiplicity 2 the filter lengths of the rows of h regarded as the scalar filters must be different in this paper complete factorizations of symmetric orthogonal multifilter banks with different filter lengths are obtained based on these factorizations construction of balanced multiwavelets with good approximation and smoothness properties are discussed

a study on orthogonal two direction vector valued wavelets and two direction wavelet packets abstract in this paper the notion of two direction vector valued multiresolution analysis and the two direction orthogonal vector valued wavelets are introduced the definition for two direction orthogonal vector valued wavelet packets is proposed an algorithm for constructing a class of two direction orthogonal vector valued compactly supported wavelets corresponding to the two direction orthogonal vector valued compactly supported scaling functions is proposed by virtue of matrix theory and time frequency analysis method the properties of the two direction vector valued wavelet packets are investigated at last the direct decomposition relation for space l 2 r r is presented

on a resource allocation model with infinite horizon in this paper we treat a resource allocation model defined on an infinite interval we show that the solution of the corresponding problem with finite horizon cannot be extended to a solution of the infinite horizon problem since the resource allocation problem in the unmodified setting does not have a solution on an unbounded interval to change this situation we bring an additional state constraint into the model which contains a weight function the new problem called now the adapted resource allocation problem has an optimal solution which will be identified by means of the duality concept of klotzler

pontryagin type maximum principle for budget constrained infinite horizon optimal control problems with linear dynamics abstract in this paper a class of infinite horizon optimal control problems with an isoperimetrical constraint also interpreted as a budget constraint is considered herein a linear both in the state and in the control dynamic is allowed the problem setting includes a weighted sobolev space as the state space for this class of problems we establish the necessary optimality conditions in form of a pontryagin type maximum principle including a transversality condition the proved theoretical result is applied to a linear quadratic regulator problem

on the existence of an arrow radner equilibrium in the case of complete markets a remark we consider a continuous time pure exchange stochastic economy with a financial sector we first give a proof of the equivalence of arrow radner and arrow debreu equilibria under the assumption that the gains associated to the securities form a local martingale generator we then give a simple proof of existence of an arrow debreu equilibrium in the separable utility case under the assumption that either all agents have finite marginal utility at zero or aggregate endowment is uniformly bounded below

infinite horizon cancer treatment model with isoperimetrical constraint existence of optimal solutions and numerical analysis abstractin this paper a class of infinite horizon optimal control problems with a mixed control state isoperimetrical constraint also interpreted as a budget constraint is considered the underlying dynamics is assumed to be affine linear in control the crucial idea which is followed in this paper is the choice of a weighted sobolev space as the state space for this class of problems we establish an existence result and apply it to a bilinear model of optimal cancer treatment with an isoperimetrical constraint including the overall amount of drugs used during the whole therapy horizon a numerical analysis of this model is provided by means of open source software package ocmat which implements a continuation method for solving discounted infinite horizon optimal control problems

image coding using wavelet transform a scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed this method involves two steps first a wavelet transform used in order to obtain a set of biorthogonal subclasses of images the original image is decomposed at different scales using a pyramidal algorithm architecture the decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image second according to shannon s rate distortion theory the wavelet coefficients are vector quantized using a multiresolution codebook to encode the wavelet coefficients a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed in order to allow the receiver to recognize a picture as quickly as possible at minimum cost a progressive transmission scheme is presented it is shown that the wavelet transform is particularly well adapted to progressive transmission

new image compression techniques using multiwavelets and multiwavelet packets advances in wavelet transforms and quantization methods have produced algorithms capable of surpassing the existing image compression standards like the joint photographic experts group jpeg algorithm for best performance in image compression wavelet transforms require filters that combine a number of desirable properties such as orthogonality and symmetry however the design possibilities for wavelets are limited because they cannot simultaneously possess all of the desirable properties the relatively new field of multiwavelets shows promise in obviating some of the limitations of wavelets multiwavelets offer more design options and are able to combine several desirable transform features the few previously published results of multiwavelet based image compression have mostly fallen short of the performance enjoyed by the current wavelet algorithms this paper presents new multiwavelet transform and quantization methods and introduces multiwavelet packets extensive experimental results demonstrate that our techniques exhibit performance equal to or in several cases superior to the current wavelet filters

enhanced frequency analysis using wavelets an enhanced frequency analysis method is introduced using a phase shift wavelet representation to analyse individual frequency components and to reveal features of a given signal the frequency representation provides details at each time location without the loss caused by local orthogonality between the wavelet basis functions and the given signal which occurs when a normal wavelet decomposition is employed movement of the local orthogonality locations corresponding to the phase shift of the wavelet basis functions are studied and it is shown that these movements are important and can be used to reveal features of the signal in the frequency domain such as continuities smoothness and trends several examples are presented to illustrate the method and an application to a permanent magnet synchronous drive system is provided to demonstrate the approach

one dimensional infinite horizon variational problems arising in continuum mechanics in this paper we study a variational problem for real valued functions defined on an infinite semiaxis of the line to wit given x 2 we seek a minimal solution to the problem minimize the functional given by i left w left cdot right right int limits 0 infty f left w left s right ddot w left s right right ds w in ax left upsilon in w loc 2 1 left 0 infty right left upsilon left 0 right dot upsilon left 0 right x right right p

optimal multifilter banks design related symmetric extension transform and application to image compression the design of optimal multifilter banks and optimum time frequency resolution multiwavelets with different objective functions is discussed the symmetric extension transform related to multifilter banks with symmetric properties is presented it is shown that such a symmetric extension transform is nonexpensive more optimal multifilter banks for image compression are constructed and some of them are used in image compression experiments show that optimal multifilter banks have better performances in image compression than daubechies orthogonal wavelet filters and daubechies least asymmetric wavelet filters and for some images they even have better performances than the scalar 9 7 tap biorthogonal wavelet filters experiments also show that the symmetric extension transform provided in this paper improves the rate distortion performance compared with the periodic extension transform

state constrained optimal control problems with states of low regularity we consider first order optimality conditions for state constrained optimal control problems in particular we study the case where the state equation does not have enough regularity to admit existence of a slater point in function space we overcome this difficulty by a special transformation under a density condition we show existence of lagrange multipliers which have a representation via measures and additional regularity properties

balanced multiwavelets theory and design this article deals with multiwavelets which are a generalization of wavelets in the context of time varying filter banks and with their applications to signal processing and especially compression by their inherent structure multiwavelets are fit for processing multichannel signals this is the main issue in which we are interested first we review material on multiwavelets and their links with multifilter banks and especially time varying filter banks then we have a close look at the problems encountered when using multiwavelets in applications and we propose new solutions for the design of multiwavelets filter banks by introducing the so called balanced multiwavelets

second order necessary conditions for the infinite horizon variational problems we give new proofs of first order and second order necessary conditions for the infinite horizon variational problems in the framework of the continuous time we study the notion of conjugate points and we build new second order necessary conditions we also translate all of our results into the hamiltonian formalism moreover we apply these general results to the special lagrangians in the form e delta i lx dot x

structure of approximate solutions for discrete time control systems arising in economic dynamics in this work we study the structure of approximate solutions of an autonomous discrete time control system with a compact metric space of states x which is a subset of a finite dimensional euclidean space this control system is described by a nonempty closed set x x which determines a class of admissible trajectories programs and by a bounded upper semicontinuous function v r1 which determines an optimality criterion we are interested in turnpike properties of the approximate solutions which are independent of the length of the interval for all sufficiently large intervals usually in economic dynamics the turnpike properties have been studied for systems such that all their good programs converge to a turnpike which was an interior point of in this paper we establish turnpike results for a large class of control systems for which the turnpike is not necessarily an interior point of

optimal control problems with mixed control state constraints noindent we consider control problems governed by semilinear parabolic equations in the presence of pointwise mixed control state constraints we obtain optimality conditions with finitely additive measures as multipliers associated to the mixed constraints we study the regularity of the multipliers for different problems in particular when a monotonicity or a separation condition is satisfied we prove that multipliers are bounded measurable functions

hyperbolic structures on 3 manifolds i deformation of acylindrical manifolds this is the first in a series of papers showing that haken manifolds have hyperbolic structures this first was published the second two have existed only in preprint form and later preprints were never completed this eprint is only an approximation to the published version which is the definitive form for part i and is provided for convenience only all references and quotations should be taken from the published version since the theorem numbering is different and not all corrections have been incorporated into the present version parts ii and iii will be made available as eprints shortly

weighted functional spaces approach in infinite horizon optimal control problems a systematic analysis of hidden opportunities and advantages abstract this paper constitutes the advantages of using the weighted sobolev and weighted lebesgue spaces in optimal control problems defined on an infinite time interval based on numerous examples it demonstrates how the introduction of certain weight or density functions into the problem statement may influence the existence of an optimal solution and the optimality of a chosen candidate the positive effects of the proper relation between the state and the co state functional spaces for the necessary optimality conditions as well as for the development of numerical schemes are discussed this paper is based on over one decade of research in this field and summarizes the main findings concerning the use of weight functions in optimal control problems

orthogonal multiwavelets with optimum time frequency resolution a procedure to design orthogonal multiwavelets with good time frequency resolution is introduced formulas to compute the time durations and the frequency bandwidths of scaling functions and multiwavelets are obtained parameter expressions for the matrix coefficients of the multifilter banks that generate symmetric antisymmetric scaling functions and multiwavelets supported in o n are presented for n 2 6 orthogonal multiwavelets with optimum time frequency resolution are constructed and some optimal multifilter banks are provided

limits of geometrically tame kleinian groups let f be a finitely generated geometrically tame kleinian group with h3 f m when m has a finite volume the hyperbolic structure of m is unique up to homotopy by mostow s rigidity theorem but when m has infinite volume it is meaningful to consider the deformation space of the hyperbolic structure of m let ah m denote the space of faithful representations with discrete image from nl m to psl2 c modulo conjugacy with the topology of algebraic convergence until now only a little is known about ah m when f is of second kind there exists the space of quasi conformal deformation of f denoted by qho m with the quasi conformal or quasi isometric topology there is a canonical continuous injection t qho m ah m we abuse the notation qho m for t qho m the topological type of qho m has been determined by sullivan 21 one method for investigating ah m is to consider limits of sequences in qho m boundary groups in bers 3 and double limits in thurston 24 are such examples for considering limits it is important to determine when a sequence in ah m converges it was shown by thurston 24 and morgan shalen 16 that when m is acylindrical every sequence in ah m has a converging subsequence we gave in ohshika 19 a sufficient condition of convergence for geometrically finite groups in w 2 of this paper we prove a theorem which implies the existence of converging subsequence in all of the above cases the case of boundary groups double limits acylindrical manifolds and the theorem in 19 the statement is as follows

convergence of freely decomposable kleinian groups we consider a compact orientable hyperbolic 3 manifold with a compressible boundary suppose that we are given a sequence of geometrically finite hyperbolic metrics whose conformal boundary structures at infinity diverge to a projective lamination we prove that if this limit projective lamination is doubly incompressible then the sequence has compact closure in the deformation space as a consequence we generalise thurston s double limit theorem and solve his conjecture on convergence of function groups affirmatively

stability of a turnpike phenomenon for approximate solutions of nonautonomous discrete time optimal control systems abstract we study turnpike properties of approximate solutions of nonautonomous discrete time optimal control systems which are determined by sequences of lower semicontinuous objective functions to have these properties means that the approximate solutions of the problems are determined mainly by the objective functions and are essentially independent of the choice of intervals and endpoint conditions except in regions close to the endpoints we show that these turnpike properties are stable under small perturbations of the objective functions

design of prefilters for discrete multiwavelet transforms the pyramid algorithm for computing single wavelet transform coefficients is well known the pyramid algorithm can be implemented by using tree structured multirate filter banks the authors propose a general algorithm to compute multiwavelet transform coefficients by adding proper premultirate filter banks before the vector filter banks that generate multiwavelets the proposed algorithm can be thought of as a discrete vector valued wavelet transform for certain discrete time vector valued signals the proposed algorithm can be also thought of as a discrete multiwavelet transform for discrete time signals the authors then present some numerical experiments to illustrate the performance of the algorithm which indicates that the energy compaction for discrete multiwavelet transforms may be better than the one for conventional discrete wavelet transforms

discounted value representations of temporal preferences this paper examines the proposition that temporal preferences may be represented in terms of discount functions an analytical framework is developed within which preferences are defined over a set of programs or prospects over time necessary and sufficient conditions for generalized discounting discounting as well as exponential discounting are established for a class of program sets over discrete and continuous time

adaptive multiwavelet based watermarking through jpw masking in this paper a multibit multiplicative spread spectrum watermarking using the discrete multiwavelet including unbalanced and balanced multiwavelet transform is presented performance improvement with respect to existing algorithm is obtained by means of a new just perceptual weighting jpw model the new model incorporates various masking effects of human visual perception by taking into account the eye s sensitivity to noise changes depending on spatial frequency luminance and texture of all the image subbands in contrast to conventional jnd threshold model jpw describing minimum perceptual sensitivity weighting to noise changes is fitter for nonadditive watermarking specifically watermarking strength is adaptively adjusted to obtain minimum perceptual distortion by employing the jpw model correspondingly an adaptive optimum decoding is derived using a statistic model based on generalized gaussian distribution ggd for multiwavelet coefficients of the cover image furthermore the impact of multiwavelet characteristics on proposed watermarking scheme is also analyzed finally the experimental results show that proposed jpw model can improve the quality of the watermarked image and give more robustness of the watermark as compared with a variety of state of the art algorithms

on minimal lattice factorizations of symmetric antisymmetric multifilterbanks this paper introduces two minimal lattice structures for symmetric antisymmetric multiwavelets samwts and symmetric antisymmetric multifilterbanks samfbs first by exploring the relation of the symmetric antisymmetric property in multifilterbanks and the linear phase property in traditional scalar filterbanks we show that the implementation and design of an samfb can be converted into that of a four channel scalar linear phase perfect reconstruction filterbank lpprfb then based on the lattice factorization for lpprfbs we propose two fast modular minimal structures for samfbs to demonstrate the effectiveness of the proposed lattice structures several rational or dyadic coefficient samwt design examples are presented along with their application in image coding

existence results and finite horizon approximates for infinite horizon optimization problems the paper deals with infinite horizon optimization problems the existence of optimal solutions is obtained as a consequence of an asymptotic growth condition we also exhibit finite horizon approximates that yield upper and lower bounds for the optimal values and whose optimal solutions converge to the long term optimal trajectories

on a market equilibrium theorem with an infinite number of commodities abstract a direct proof is given of the market equilibrium theorem of gale nikaido and debreu for an infinite dimensional commodity space the theorem is closely related to a recent result of aliprantis and brown but allows for excess demand correspondences rather than excess demand functions

brief paper pseudospectral methods for solving infinite horizon optimal control problems an important aspect of numerically approximating the solution of an infinite horizon optimal control problem is the manner in which the horizon is treated generally an infinite horizon optimal control problem is approximated with a finite horizon problem in such cases regardless of the finite duration of the approximation the final time lies an infinite duration from the actual horizon at t in this paper we describe two new direct pseudospectral methods using legendre gauss lg and legendre gauss radau lgr collocation for solving infinite horizon optimal control problems numerically a smooth strictly monotonic transformation is used to map the infinite time domain t 0 onto a half open interval t 1 1 the resulting problem on the finite interval is transcribed to a nonlinear programming problem using collocation the proposed methods yield approximations to the state and the costate on the entire horizon including approximations at t these pseudospectral methods can be written equivalently in either a differential or an implicit integral form in numerical experiments the discrete solution exhibits exponential convergence as a function of the number of collocation points it is shown that the map f 1 1 0 can be tuned to improve the quality of the discrete approximation

different interpretations of the improper integral objective in an infinite horizon control problem abstract we provide an example of a convex infinite horizon problem with a linear objective functional where the different interpretations of the improper integral 0 f t x t u t d t in either lebesgue or riemann sense lead to different but finite optimal values

a general approach for analysis and application of discrete multiwavelet transforms this paper proposes a general paradigm for the analysis and application of discrete multiwavelet transforms particularly to image compression first we establish the concept of an equivalent scalar wavelet filter bank system in which we present an equivalent and sufficient representation of a multiwavelet system of multiplicity r in terms of a set of r equivalent scalar filter banks this relationship motivates a new measure called the good multifilter properties gmps which define the desirable filter characteristics of the equivalent scalar filters we then relate the notion of gmps directly to the matrix filters as necessary eigenvector properties for the refinement masks of a given multiwavelet system second we propose a generalized efficient and nonredundant framework for multiwavelet initialization by designing appropriate preanalysis and post synthesis multirate filtering techniques finally our simulations verified that both orthogonal and biorthogonal multiwavelets that possess gmps and employ the proposed initialization technique can perform better than the popular scalar wavelets such as daubechies d8 wavelet and the d 9 7 wavelet and some of these multiwavelets achieved this with lower computational complexity

optimal control problems involving optimal economic growth with infinite horizon abstract we examine the existence of optimal solutions for a very general optimal economic growth problem with unbounded planning time horizon a convexity hypothesis about a certain orientor field plays a crucial role in the proof then we conduct sensitivity analysis and determine the relation between optimal pairs and the initial capital accumulation finally we see what happens if the convexity hypothesis we have made no longer exists this leads us to the introduction of the relaxed system and its comparison with the original one

svd based modeling for image texture classification using wavelet transformation this paper introduces a new model for image texture classification based on wavelet transformation and singular value decomposition the probability density function of the singular values of wavelet transformation coefficients of image textures is modeled as an exponential function the model parameter of the exponential function is estimated using maximum likelihood estimation technique truncation of lower singular values is employed to classify textures in the presence of noise kullback leibler distance kld between estimated model parameters of image textures is used as a similarity metric to perform the classification using minimum distance classifier the exponential function permits us to have closed form expressions for the estimate of the model parameter and computation of the kld these closed form expressions reduce the computational complexity of the proposed approach experimental results are presented to demonstrate the effectiveness of this approach on the entire 111 textures from brodatz database the experimental results demonstrate that the proposed approach improves recognition rates using a lower number of parameters on large databases the proposed approach achieves higher recognition rates compared to the traditional subband energy based approach the hybrid imm svm approach and the ggd based approach

a new prefilter design for discrete multiwavelet transforms in conventional wavelet transforms prefiltering is not necessary due to the lowpass property of a scaling function this is no longer true for multiwavelet transforms a few research papers on the design of prefilters have appeared but the existing prefilters are usually not orthogonal which often causes problems in coding moreover the condition on the prefilters was imposed based on the first step discrete multiwavelet decomposition we propose a new prefilter design that combines the ideas of the conventional wavelet transforms and multiwavelet transforms the prefilters are orthogonal but nonmaximally decimated they are derived from a very natural calculation of multiwavelet transform coefficients in this new prefilter design multiple step discrete multiwavelet decomposition is taken into account our numerical examples by taking care of the redundant prefiltering indicate that the energy compaction ratio with the geronimo hardin massopust 1994 2 wavelet transform and our new prefiltering is better than the one with daubechies d sub 4 wavelet transform

an existence result for optimal economic growth problems abstract an existence result for optimal control problems of lagrange type with unbounded time domain is derived very directly from a corresponding result for problems with bounded time domain this subsumes the main existence result of r f baum j optim theory appl 19 1976 89 116 and has the existence results for optimal economic growth problems of s i takekuma j math econom 7 1980 193 208 and m j p magill econometrica 49 1981 679 711 j math anal appl 82 1981 66 74 as simple corollaries in addition a new notion of uniform integrability is used which coincides with the classical notion if the time domain is bounded