sufficient second order optimality conditions for semilinear control problems with pointwise state constraints second order sufficient optimality conditions are established for the optimal control of semilinear elliptic and parabolic equations with pointwise constraints on the control and the state in contrast to former publications on this subject the cone of critical directions is the smallest possible in the sense that the second order sufficient conditions are the closest to the associated necessary ones the theory is developed for elliptic distributed controls in domains up to dimension three moreover problems of elliptic boundary control and parabolic distributed control are discussed in spatial domains of dimension two and one respectively

the calderon problem with partial data in this paper we improve an earlier result by bukhgeim and uhlmann 1 by showing that in dimension n 3 the knowledge of the cauchy data for the schr nodinger equation measured on possibly very small subsets of the boundary determines uniquely the potential we follow the general strategy of 1 but use a richer set of solutions to the dirichlet problem this implies a similar result for the problem of electrical impedance tomography which consists in determining the conductivity of a body by making voltage and current measurements at the boundary

nonequiprobable signaling on the gaussian channel signaling schemes for the gaussian channel based on finite dimensional lattices are considered the signal constellation consists of all lattice points within a region r and the shape of this region determines the average signal power spherical signal constellations minimize average signal power and in the limit as n to infinity the shape gain of the n sphere over the n cube approaches pi e 6 approximately 1 53 db a nonequiprobable signaling scheme is described that approaches this full asymptotic shape gain in any fixed dimension a signal constellation omega is partitioned into t subconstellations omega sub 0 omega sub tau 1 of equal size by scaling a basic region r signal points in the same subconstellation are used equiprobably and a shaping code selects the subconstellation omega sub i with frequency f sub i shaping codes make it possible to achieve any desired fractional bit rate the schemes presented are compared with equiprobable signaling schemes based on voronoi regions of multidimensional lattices for comparable shape gain and constellation expansion ratio the peak to average power ratio of the schemes presented is superior furthermore a simple table lookup is all that is required to address points in the constellations it is also shown that it is possible to integrate coding and nonequiprobable signaling within a common multilevel framework

necessary optimality conditions for control problems and the stone cech compactification this paper deals with optimal control problems of parabolic equations in the presence of pointwise state constraints we consider bounded controls which act in the initial condition of the state equation the state variable is a bounded continuous function on the domain q omega times 0 t but is not continuous on overline q in this case the multiplier associated with state constraints is a regular bounded finitely additive measure on q but not a sigma additive one using some properties of the stone u c ech compactification we prove a decomposition theorem for this measure which allows us to interpret the adjoint equation in a classical sense we obtain new optimality conditions for these kinds of problems and we apply these results to the case of bilateral constraints

probabilistic construction of large constraint length trellis codes for sequential decoding probabilistic algorithms are given for constructing good large constraint length trellis codes for use with sequential decoding that can achieve the channel cutoff rate bound at a bit error rate ber of 10 sup 5 10 sup 6 the algorithms are motivated by the random coding principle that an arbitrary selection of code symbols will produce a good code with high probability one algorithm begins by choosing a relatively small set of codes randomly the error performance of each of these codes is evaluated using sequential decoding and the code with the best performance among the chosen set is retained another algorithm treats the code construction as a combinatorial optimization problem and uses simulated annealing to direct the code search trellis codes for 8 psk and 16 qam constellations with constraint lengths v up to 20 are obtained simulation results with sequential decoding show that these codes reach the channel cutoff rate bound at a ber of 10 sup 5 10 sup 6 and achieve 5 0 6 35 db real coding gains over uncoded systems with the same spectral efficiency and up to 2 0 db real coding gains over 64 state trellis codes using viterbi decoding

optimal control of pdes in a complex space setting application to the schrodinger equation in this paper we discuss optimality conditions for abstract optimization problems over complex spaces we then apply these results to optimal control problems with a semigroup structure as an application we detail the case when the state equation is the schrodinger one with pointwise constraints on the bilinear control we derive first and second order optimality conditions and address in particular the case that the control enters the state equation and cost function linearly

minimax control of parabolic systems with state constraints in this paper we study a minimax control problem for parabolic equations in the presence of pointwise state constraints the terminology minimax here refers to a cost functional defined with a l infty norm the directional derivatives of the l infty norm are elements of l infty therefore the adjoint equation may involve finitely additive measures in place of radon measures to overcome this difficulty we introduce a compactification of stone u c ech type we prove necessary optimality conditions which are new both in the case with no state constraints and in the case with state constraints under some convexity conditions these optimality conditions are also sufficient

stability of the calderon problem for less regular conductivities abstract in these notes we prove log type stability for the calderon problem with conductivities in c 1 e we follow the lines of a recent work by haberman and tataru in which they prove uniqueness for c 1

optimality conditions for some nonqualified problems of distributed control this article determines the necessary and sufficient optimality conditions for some nonqualified problems of optimal control in the case of a distributed control for a system governed by a second order elliptic partial differential equation the authors study both bilateral and unilateral constraints on the state of the system

necessary optimality conditions for infinite dimensional state constrained control problems abstract this paper is concerned with first order necessary optimality conditions for state constrained control problems in separable banach spaces assuming inward pointing conditions on the constraint we give a simple proof of pontryagin maximum principle relying on infinite dimensional neighboring feasible trajectories theorems proved in 20 further we provide sufficient conditions guaranteeing normality of the maximum principle we work in the abstract semigroup setting but nevertheless we apply our results to several concrete models involving controlled pdes pointwise state constraints as positivity of the solutions are allowed

perturbed optimization in banach spaces i a general theory based on a weak directional constraint qualification using a directional form of constraint qualification weaker than robinson s we derive an implicit function theorem for inclusions and use it for first and second order sensitivity analyses of the value function in perturbed constrained optimization we obtain holder and lipschitz properties and under a no gap condition first order expansions for exact and approximate solutions as an application differentiability properties of metric projections in hilbert spaces are obtained using a condition generalizing polyhedricity we also present in the appendix a short proof of a generalization of the convex duality theorem in banach spaces

no gap second order optimality conditions for optimal control problems with a single state constraint and control the paper deals with optimal control problems with only one control variable and one state constraint of arbitrary order we consider the case of finitely many boundary arcs and touch times we obtain a no gap theory of second order conditions allowing to characterize second order quadratic growth

second order analysis for strong solutions in the optimal control of parabolic equations in this paper we provide a second order analysis for strong solutions in the optimal control of parabolic equations we consider the case of box constraints on the control and final integral constraints on the state in contrast to sufficient conditions assuring quadratic growth in the weak sense i e when the cost increases at least quadratically for admissible controls uniformly near to the nominal one see e g 16 26 our main result provides a sufficient condition for quadratic growth of the cost for admissible controls whose associated states are uniformly near to the state of the nominal one as a consequence of our results for qualified problems with a strictly convex and quadratic hamiltonian we prove that both notions of quadratic growth coincide

stability estimates for the calderon problem with partial data this is a follow up of a previous article where we proved local stability estimates for a potential in a schr odinger equation on an open bounded set in dimension n 3 from the dirichlet to neumann map with partial data the region under control was the penumbra delimited by a source of light outside of the convex hull of the open set these local estimates provided stability of log log type corresponding to the uniqueness results in calder on s inverse problem with partial data proved by kenig sj ostrand and uhlmann in this article we prove the corresponding global estimates in all dimensions higher than three the estimates are based on the construction of solutions of the schr odinger equation by complex geometrical optics developed in the anisotropic setting by dos santos ferreira kenig salo and uhlmann to solve the calder on problem in certain admissible geometries

algorithmic construction of trellis codes an algorithmic approach is proposed whereby long convolutional codes of rate r sub c k n can easily be constructed for any chosen signal constellation in signal space these algorithms are iterative and in each step a number of candidate codes are found which locally maximize the distance hamming or euclidean between the codewords the result is not necessarily a free distance optimizing code however since the construction complexity can be chosen optimal codes are quite frequently found the codes ae constructed such that a rapid growth of the column distance is achieved a method of combining two codes into a single code of twice the constraint length is also presented

optimal stability estimate in the inverse boundary value problem for periodic potentials with partial data abstract we consider the inverse boundary value problem for operators of the form q in an infinite domain r r 1 n n 3 with a periodic potential q for dirichlet to neumann data localized on a portion of the boundary of the form 1 r 1 with 1 being the complement either of a flat or spherical portion of we prove that a log type stability estimate holds

a survey of the maximum principles for optimal control problems with state constraints this paper gives a survey of the various forms of pontryagin s maximum principle for optimal control problems with state variable inequality constraints the relations between the different sets of optimality conditions arising in these forms are shown furthermore the application of these maximum principle conditions is demonstrated by solving some illustrative examples

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

calderon inverse problem with partial data on riemann surfaces on a fixed smooth compact riemann surface with boundary m0 g we show that for the schrodinger operator v with potential v c m0 for some 0 the dirichlet to neumann map n measured on an open set m0 determines uniquely the potential v we also discuss briefly the corresponding consequences for potential scattering at 0 frequency on riemann surfaces with asymptotically euclidean or asymptotically hyperbolic ends

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

the upper and lower second order directional derivatives of a sup type function the purpose of this paper is to give a formula for expressing the second order directional derivatives of the sup type functions x sup f x t t t in terms of the first and second derivatives off x t wheret is a compact set in a metric space and we assume thatf f x and 2f x2 are continuous on n t we will give a geometrical meaning of the formula we will moreover give a sufficient condition fors x to be directionally twice differentiable

the calderon problem with partial data in two dimensions we prove for a two dimensional bounded domain that the cauchy data for the schrodinger equation measured on an arbitrary open subset of the boundary determines uniquely the potential this implies for the conductivity equation that if we measure the current fluxes at the boundary on an arbitrary open subset of the boundary produced by voltage potentials supported in the same subset we can determine uniquely the conductivity we use carleman estimates with degenerate weight functions to construct appropriate complex geometrical optics solutions to prove the results

pontryagin s principle for state constrained control problems governed by parabolic equations with unbounded controls this paper deals with optimal control problems governed by semilinear parabolic equations with pointwise state constraints and unbounded controls under some strong stability assumption we obtain necessary optimality conditions in the form of a pontryagin s minimum principle in qualified form a pontryagin s principle in nonqualified form is also proved without any stability condition

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

optimal control of semilinear multistate systems with state constraints this paper deals with state constrained optimal control problems governed by a semilinear multistate equation the authors prove the existence of solutions and derive optimality conditions

a priori error estimates for finite element discretizations of parabolic optimization problems with pointwise state constraints in time in this paper we consider an optimal control problem which is governed by a linear parabolic equation and is subject to state constraints pointwise in time optimal order error estimates are developed for a space time finite element discretization of this problem numerical examples confirm the theoretical results as a by product of our analysis we derive a new regularity result for the optimal control

stability estimates for the radon transform with restricted data and applications in this article we prove a stability estimate going from the radon transform of a function with limited angle distance data to the l p norm of the function itself under some conditions on the support of the function we apply this theorem to obtain stability estimates for an inverse boundary value problem with partial data

stability estimates for the inverse boundary value problem for the biharmonic operator with bounded potentials abstract in this article stability estimates are given for the determination of the zeroth order bounded perturbations of the biharmonic operator when the boundary neumann measurements are made on the whole boundary and on slightly more than half the boundary respectively for the case of measurements on the whole boundary the stability estimates are of ln type and for the case of measurements on slightly more than half of the boundary we derive estimates that are of ln ln type

trellis coded modulation with multidimensional constellations trellis coded modulation schemes using four eight or 16 dimensional constellations have a number of potential advantages over the usual two dimensional schemes a smaller constituent two dimensional constellation easier tolerance to phase ambiguities and a better trade off between complexity and coding gain a number of such schemes are presented and evaluated starting with a variety of multidimensional lattices we show how to select multidimensional constellations how to partition them into subsets how to construct trellis codes using those subsets and how to map hits to constellation points simplifications of the viterbi decoding algorithm are presented we conclude that there are multidimensional trellis coded modulation schemes that perform better for the same complexity than do two dimensional schemes

trellis coding with multidimensional qam signal sets trellis coding using multidimensional quadrature amplitude modulation qam signal sets is investigated finite size 2d signal sets are presented that have minimum average energy are 90 degrees rotationally symmetric and have from 16 to 1024 points the best trellis codes using the finite 16 qam signal set with two four six and eight dimensions are found by computer search the multidimensional multi d signal set is constructed from the 2 d signal set the best moderate complexity trellis codes for infinite lattices with two four six and eight dimensions are also found the minimum free squared euclidean distance and number of nearest neighbors for these codes were used as the selection criteria many of the multi d codes are fully rotationally invariant and give asymptotic coding gains up to 6 0 db from the infinite lattice codes the best codes for transmitting j j 1 4 j 1 3 j 1 2 j 2 3 and j 3 4 b sym j an integer are presented

a mathematical analysis of blowup for thermal reactions the spatially nonhomogeneous case the equations describing the induction period process for a super critical high activation energy thermal explosion in a bounded domain are studied a formal proof based on comparison techniques is used to show that the temperature perturbation becomes unbounded as t to t b leqq infty for values of the frank kamenetski parameter delta greater than the critical value upper and lower bound estimates for t b are found by using specified comparison equations a comparison of these bounds with values of t b obtained from numerical solutions of the basic equations shows that the estimates provide an excellent prediction of the escape time when delta is greater than 2 3 times the critical value for smaller values of delta where heat loss is more significant a better comparison equation is required

optimal control of a parabolic equation with time dependent state constraints in this paper we study the optimal control problem of the heat equation with a cubic nonlinearity by a distributed control over a subset of the domain in the presence of a state constraint the latter is integral over the space and has to be satisfied each time using for the first time the technique of alternative optimality systems in the context of optimal control of partial differential equations we show that both the control and multiplier are continuous in time under some natural geometric hypotheses we can prove that extended polyhedricity holds allowing us to obtain no gap second order optimality conditions that characterize quadratic growth an expansion of the value function and of approximate solutions can be computed for a directional perturbation of the right hand side of the state equation

pontryagin s principle for state constrained boundary control problems of semilinear parabolic equations this paper deals with state constrained optimal control problems governed by semilinear parabolic equations we establish a minimum principle of pontryagin s type to deal with the state constraints we introduce a penalty problem by using ekeland s principle the key tool for the proof is the use of a special kind of spike perturbations distributed in the domain where the controls are defined conditions for normality of optimality conditions are given

new trellis codes based on lattices and cosets a new technique is proposed for constructing trellis codes which provides an alternative to ungerboeck s method of set partitioning the new codes use a signal constellation consisting of points from an n dimensional lattice lambda with an equal number of points from each coset of a sublattice lambda one part of the input stream drives a generalized convolutional code whose outputs are cosets of lambda while the other part selects points from these cosets several of the new codes are better than those previously known

a study of vector quantization for noisy channels several issues related to vector quantization for noisy channels are discussed an algorithm based on simulated annealing is developed for assigning binary codewords to the vector quantizer code vectors it is shown that this algorithm could result in dramatic performance improvements as compared to randomly selected codewords a modification of the simulated annealing algorithm for binary codeword assignment is developed for the case where the bits in the codeword are subjected to unequal error probabilities resulting from unequal levels of error protection an algorithm for the design of an optimal vector quantizer for a noisy channel is briefly discussed and its robustness under channel mismatch conditions is studied numerical results for a stationary first order gauss markov source and a binary symmetric channel are provided it is concluded that the channel optimized vector quantizer design algorithm if used carefully can result in a fairly robust system with no additional delay the case in which the communication channel is nonstationary as in mobile radio channels is studied and some preliminary ideas for quantizer design are presented

stability of the inverse conductivity problem in the plane for less regular conductivities abstract the dirichlet to neumann map or voltage to current map takes dirichlet data u f to the conormal derivatives u at the boundary where u is a solution to the elliptic equation div u 0 on a plane lipchitz domain r2 we consider the inverse conductivity problem that consists of the recovery of in the interior of from the knowledge of we prove stability for this inverse map assuming an isotropic conductivity c1 e we reduce the equation div u 0 to an equivalent system and use the scattering transform this approach relaxes the number of derivatives of required in former works

determining a magnetic schrodinger operator from partial cauchy data in this paper we show in dimension n 3 that knowledge of the cauchy data for the schrodinger equation in the presence of a magnetic potential measured on possibly very small subsets of the boundary determines uniquely the magnetic field and the electric potential we follow the general strategy of 7 using a richer set of solutions to the dirichlet problem that has been used in previous works on this problem

well posedness of the shooting algorithm for state constrained optimal control problems with a single constraint and control this paper deals with the shooting algorithm for optimal control problems with a scalar control and a regular scalar state constraint additional conditions are displayed under which the so called alternative formulation is equivalent to pontryagin s minimum principle the shooting algorithm appears to be well posed invertible jacobian iff i the no gap second order sufficient optimality condition holds and ii when the constraint is of order q geq 3 there is no boundary arc stability and sensitivity results without strict complementarity at touch points are derived using robinson s strong regularity theory under a minimal second order sufficient condition the directional derivatives of the control and state are obtained as solutions of a linear quadratic problem

trellis coded multidimensional phase modulation a 2l dimensional multiple phase shift keyed l mpsk signal set is obtained by forming the cartesian product of l two dimensional mpsk signal sets a systematic approach to partitioning l mpsk signal sets that is based on block coding is used an encoder system approach is developed it incorporates the design of a differential precoder a systematic convolutional encoder and a signal set mapper trellis coded l 4psk l 8psk and l 16psk modulation schemes are found for 1

pontryagin s principle for local solutions of control problems with mixed control state constraints this paper deals with optimal control problems of semilinear parabolic equations with pointwise state constraints and coupled integral state control constraints we obtain necessary optimality conditions in the form of a pontryagin s minimum principle for local solutions in the sense of l p p leq infty

second order necessary optimality conditions for minimizing a sup type function the second derivative of an envelope cannot be expressed only by second derivatives of the constituent functions by taking account of this fact we derive new second order necessary optimality conditions for minimization of a sup type function the conditions involve an extra term besides the second derivative of the lagrange function furthermore we will comment on the relationship between the extra term and a kind of second order directional derivative of the sup type function

construction of trellis codes with a good distance profile systematic feedforward trellis codes for 8 psk and 16 qam modulation are constructed using a nested step by step algorithm which guarantees a good distance profile this makes the codes suitable for use with sequential decoding where a rapidly growing distance profile is needed to reduce the average number of computations in addition to having a good distance profile the new codes achieve asymptotic coding gains of up to 6 53 db a procedure based upon the fano 1963 algorithm fa is used to calculate the free distance of the new codes this procedure is very effective for finding the free distances of long trellis codes because of the computational and storage efficiency of the fa from a comparison of the new systematic feedforward codes with ungerboeck s 1982 1987 systematic feedback codes the authors conjecture that a systematic feedforward code of constraint length 2 spl nu can achieve the same free distance as a systematic feedback code of constraint length spl nu