some existence and regularity results for abstract non autonomous parabolic equations abstract we study existence uniqueness and regularity of the strict classical and strong solutions u c 0 t e of the non autonomous evolution equation u t a t u t t with the initial datum u 0 x in a banach space e under the classical kato tanabe assumptions the domains of the operators a t are not needed to be dense in e we prove necessary and sufficient conditions for existence and holder regularity of the solution and its derivative

conservative arrays multidimensional modulation codes for holographic recording in holographic storage two dimensional arrays of binary data is optically recorded in a medium via an interference process to ensure optimum operation of a holographic recording system it is desirable that the patterns of 1s light and 0s no light in the recorded array satisfy the following modulation constraint in each row and column of the array there are at least t transitions of the type 1 spl rarr 0 or 0 spl rarr 1 for a prescribed integer t a two dimensional array with this property is said to be a conservative array of strength t in general an n dimensional conservative array of strength t is a binary array having at least t transitions in each column extending in any of the n dimensions of the array we present an algorithm for encoding unconstrained binary data into an n dimensional conservative array of strength t the algorithm employs differential coding and error correcting codes using n binary codes one per dimension with minimum hamming distance d spl ges 2t 3 we apply a certain transformation to an arbitrary information array which ensures that the number of transitions in each dimension is determined by the minimum distance of the corresponding code

counterexamples on l_p maximal regularity we establish a transference result for l p maximal regularity for the abstract cauchy problem on banach space from this result we deduce counterexamples to l p maximal regularity 1 p infty in particular we obtain an operator b without any l p maximal regularity although it admits bounded imaginary powers with vert b is vert 1 for all s in mathbb r we also derive an operator which satisfies l p maximal regularity on bounded intervals 0 t but not on the half line mathbb r

the projective geometry of freudenthal s magic square abstract we connect the algebraic geometry and representation theory associated to freudenthal s magic square we give unified geometric descriptions of several classes of orbit closures describing their hyperplane sections and desingularizations and interpreting them in terms of composition algebras in particular we show how a class of invariant quartic polynomials can be viewed as generalizations of the classical discriminant of a cubic polynomial

analyticity of the stokes semigroup in spaces of bounded functions the analyticity of the stokes semigroup with the dirichlet boundary condition is established in spaces of bounded functions when the domain occupied with fluid is bounded or more generally admissible which admits a special estimate for the helmholtz decomposition the proof is based on a blow up argument this is the first proof of the analyticity in spaces of bounded functions which was left open more than thirty years

abstract quasilinear parabolic equations on considere des problemes paraboliques quasi lineaires abstraits p 0 u t a t u t u t f t u t t 0 u o u 0 ou u t est une fonction a valeurs dans un espace de banach x on donne des theoremes d existence locale et d unicite pour des solutions classiques et strictes de p 0

the positive capacity region of two dimensional run length constrained channels a binary sequence satisfies a one dimensional d k constraint if every run of zeros with possible exception of the first and the last runs has length at least d and at most k a binary two dimensional array satisfies a d k constraint if each row and each column satisfies the one dimensional d k constraint few models have been proposed in the literature to handle two dimensional data the diamond model the square model the hexagonal model and the triangular model the constraints in the different directions might be asymmetric and hence many kind of constraints are defined depending on the number of directions in the model for example a two dimensional array in the diamond model satisfies a d1 k1 d2 k 2 constraint if it satisfies the one dimensional d1 k1 constraint horizontally and the one dimensional d 2 k2 constraint vertically in this correspondence the region in which the capacity is zero or positive in the various models is examined asymmetric constraints in the diamond model and symmetric constraints in the other models are considered in particular an almost complete solution for asymmetric constraints in the diamond model is provided

asymptotic constancy for pseudo monotone dynamical systems on function spaces abstract a pseudo monotone dynamical system is a dynamical system which preserves the order relation between initial points and equilibrium points the purpose of this paper is to present some convergence oscillation and order stability criteria for pseudo monotone dynamical systems on function spaces for which each constant function is an equilibrium point some applications to neutral functional differential equations and semilinear parabolic partial differential equations with neumann boundary condition are given

parabolic evolution equations in interpolation and extrapolation spaces on etudie le probleme de cauchy pour des equations d evolution lineaires a t u f t o t t de type parabolique dans un espace de banach x 0 on considere des resultats d existence d unicite et de continuite pour a t u u f t u o t t

holder classes with boundary conditions as interpolation spaces on etudie la caracterisation de certains espaces d interpolation reels entre le domaine d un operateur differentiel elliptique avec des conditions aux limites generales et l espace de banach de fonctions continues dans lequel le domaine est plonge

two dimensional runlength constrained arrays with equal horizontal and vertical constraints a binary array is a d1 k1 d2 k 2 runlength constrained array if the runs of zeros in every row and column have length at least d1 and at most k1 and the runs of ones in every row and column have length at least d2 and at most k2 such arrays arise in the context of digital storage devices writing n m n d1 k1 d2 k2 for the number of d1 k 1 d2 k2 runlength constrained arrays of size mtimesn the capacity c d1 k1 d2 k2 is defined to be limm nrarrinfin 1 mn log2n m n d1 k 1 d2 k2 let d2 be an integer such that d2 ges 1 the paper shows that c 1 d2 delta d2 d2 is positive when delta ges 2 but is zero when delta les 1

partial characterization of the positive capacity region of two dimensional asymmetric run length constrained channels a binary sequence satisfies a one dimensional d k run length constraint if every run of zeros has length at least d and at most k a two dimensional binary pattern is d sub 1 k sub 1 d sub 2 k sub 2 constrained if it satisfies the one dimensional d sub 1 k sub 1 run length constraint horizontally and the one dimensional d sub 2 k sub 2 run length constraint vertically for given d sub 1 k sub 1 d sub 2 and k sub 2 the asymmetric two dimensional capacity is defined as c sub d1 k1 d2 k2 lim sub m n spl rarr spl infin 1 mn log sub 2 n sub m n sup d1 k1 d2 k2 where n sub m n sup d1 k1 d2 k2 denotes the number of d sub 1 k sub 1 d sub 2 k sub 2 constrained m spl times n binary patterns we determine whether the capacity is positive or is zero for many choices of d sub 1 k sub 1 d sub 2 k sub 2

dynamical analysis of distributed parameter tubular reactors this paper is dedicated to the dynamical analysis of tubular reactor models namely plug flow and axial dispersion reactors involving sequential reactions for which the kinetics only depends on the concentrations of the reactants involved in the reaction this analysis is performed by describing these models as infinite dimensional state space systems with bounded observation and control operators it is shown that these systems are exponentially stable and that a the plug flow reactor model is observable when the component concentrations are measured at the reactor output and observable with respect to its physical domain when only the product concentration is measured and it is reachable with respect to its physical domain when it is controlled at the reactor input and b any finite set of dominant modes of the axial dispersion reactor model is observable when either all the component concentrations or only the product concentration are measured and reachable by using appropriate sensors and actuators the dynamical properties of related finite dimensional models are also discussed

trajectory analysis of nonisothermal tubular reactor nonlinear models the existence and uniqueness of the state trajectories temperature and reactant concentration are analyzed for nonisothermal plug flow and axial dispersion tubular reactor models it is mainly shown that these trajectories exist on the whole nonnegative real time axis and the set of all physically feasible state values is invariant under the dynamics equations the main nonlinearity in the model originates from the arrhenius type kinetics term in the model equations the analysis essentially uses lipschitz and dissipativity properties of the nonlinear operator involved in the dynamics and the concept of state trajectory positivity

entropy bounds for constrained two dimensional random fields the maximum entropy and thereby the capacity of two dimensional 2 d fields given by certain constraints on configurations is considered upper and lower bounds are derived a new class of 2 d processes yielding good lower bounds is introduced asymptotically the process achieves capacity for constraints with limited long range effects the processes are general and may also be applied to e g data compression of digital images results are given for the binary hard square model which is a 2 d run length limited model and some other 2 d models with simple constraints

nonlinear analytic semiflows in this paper a local existence and regularity theory is given for nonlinear parabolic initial value problems x t f x t and quasilinear initial value problems x t a x t x t f x t this theory extends the theory of daprato and grisvard of 1979 and shows how various properties like analyticity of solutions can be derived as a direct corollary of the existence theorem

solvability and maximal regularity of parabolic evolution equations with coefficients continuous in time abstract we establish maximal regularity of type lp for a parabolic evolution equation u t a t u t f t with a c 0 t l d a 0 x and construct the corresponding evolution family on the underlying banach space x our proofs are based on the operator sum method and the use of evolution semigroups the results are applied to parabolic partial differential equations with continuous coefficients

ein neuer zusammenhang zwischen einfachen gruppen und einfachen singularitaten we describe a new construction to obtain a simple hypersurface singularity from the corresponding simple complex lie groupg letx be the closed orbit in the projective space attached to the lie algebra mathfrak g ofg consider a regular nilpotent element y 0 in mathfrak g and denote byh y 0 the hyperplane orthogonal toy 0 with respect to the killing form then the hyperplane sectionx h y 0 has exactly one singularity which is simple of desired type by variation of the pointy 0 we obtain a versal deformation the construction generalizes with minor modifications to any characteristicp of the basefield even in bad characteristic we recover at least the positive part of the semiuniversal deformation we prove that forp 2 a simple quasihomogeneous singularity of type a7 resp d8 is adjacent to e7 resp e8 provided its dimension is even furthermore a8 is adjacent to e8 forp 3

geometric descriptions of entangled states by auxiliary varieties the aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry in the context of this paper geometric means each stratum of the hilbert space corresponding to an entangled state is an open subset of an algebraic variety built by classical geometric constructions tangent lines secant lines from the set of separable states in this setting we describe well known classifications of multipartite entanglement such as 2 2 n 1 for n 1 quantum systems and a new description with the 2 3 3 quantum system our results complete the approach of miyake and make stronger connections with recent work of algebraic geometers moreover for the quantum systems detailed in this paper we propose an algorithm based on the classical theory of invariants to decide to which subvariety of the hilbert space a given state belongs

on the capacity of two dimensional run length constrained channels two dimensional binary patterns that satisfy one dimensional d k run length constraints both horizontally and vertically are considered for a given d and k the capacity c sub d k is defined as c sub d k lim sub m n spl rarr spl infin log sub 2 n sub m n sup d k mn where n sub m n sup d k denotes the number of m spl times n rectangular patterns that satisfy the two dimensional d k run length constraint bounds on c sub d k are given and it is proven for every d spl ges 1 and every k d that c sub d k 0 if and only if k d 1 encoding algorithms are also discussed

global solutions of abstract quasilinear parabolic equations abstract local and global existence and uniqueness for strict solutions of abstract quasilinear parabolic equations are studied applications to quasilinear parabolic partial differential equations are also given

maximal space regularity for abstract linear non autonomous parabolic equations the linear non autonomous evolution equation u t a t u t f t t e 0 t with the initial datum u o x in the space c o t e where e is a banach space and a t is a family of infinitesimal generators of bounded analytic semigroups is considered the domains d t are supposed constant in t and possibly not dense in e maximal regularity of the strict and classical solutions i e regularity of u and a u with values in the interpolation spaces d o l co and da b between d o and e is studied a characterization of such spaces in a concrete case is also given 0 1985 academic press inc

lq optimal control of infinite dimensional systems by spectral factorization abstract we consider the standard lq optimal control of an exponentially stabilizable and detectable infinite dimensional semigroup state space system with bounded sensing and control it is reported that the reachable restriction of the lq optimal state feedback operator can be identified 1 by solving a spectral factorization problem delivering a bistable spectral factor with entries in the distributed proper stable transfer function algebra and 2 by obtaining any constant solution of an operator diophantine equation over the properties of the restricted solution feedback operator are discussed it is shown in particular that the lq optimal state feedback operator and its reachable restriction coincide whenever the unreachable state components are unobservable these theoretical results are applied to a simple model of heat diffusion with collocated sensor and actuator leading to an approximation procedure converging exponentially fast to the lq optimal state feedback operator this procedure is based on approximate spectral factorization by symmetric extraction and on simple residue calculus

nonlocal problems for boussinesq equations abstract in this paper the existence and uniqueness of solution of the integral boundary value problem for abstract boussinesq equations are obtained

improvements on lower bounds for the blow up time under local nonlinear neumann conditions abstract this paper studies the heat equation u t u in a bounded domain r n n 2 with positive initial data and a local nonlinear neumann boundary condition the normal derivative u n u q on partial boundary 1 for some q 1 while u n 0 on the other part we investigate the lower bound of the blow up time t of u in several aspects first t is proved to be at least of order q 1 1 as q 1 since the existing upper bound is of order q 1 1 this result is sharp secondly if is convex and 1 denotes the surface area of 1 then t is shown to be at least of order 1 1 n 1 for n 3 and 1 1 ln 1 1 for n 2 as 1 0 while the previous result is 1 for any 1 n 1 finally we generalize the results for convex domains to the domains with only local convexity near 1

the principle of linearized stability for quasilinear parabolic evolution equations on donne des conditions pour la stabilite des points d equilibre des equations paraboliques quasilineaires avec des conditions aux limites non lineaires u a t u u u f t u 7b b t u u 0 u t 0 u 0 t 0 t

pathwise mild solutions for quasilinear stochastic partial differential equations abstract stochastic partial differential equations spdes have become a key modeling tool in applications yet there are many classes of spdes where the existence and regularity theory for solutions is not completely developed here we contribute to this aspect and prove the existence of mild solutions for a broad class of quasilinear cauchy problems including among others cross diffusion systems as a key application our solutions are local in time and are derived via a fixed point argument in suitable function spaces the key idea is to combine in a suitable way the classical theory of deterministic quasilinear parabolic partial differential equations pdes with recent theory of evolution semigroups we also show how to apply our theory to the shigesada kawasaki teramoto skt model furthermore we provide examples of blow up and ill posed operators which can occur after finite time showing that solutions can only be local in time for general quasilinear spdes while they might be global in time for special subclasses of problems

optimal lq feedback regulation of a nonisothermal plug flow reactor model by spectral factorization the linear quadratic lq optimal temperature and reactant concentration regulation problem is studied for a partial differential equation model of a nonisothermal plug flow tubular reactor by using a nonlinear infinite dimensional hilbert state space description first the dynamical properties of the linearized model around a constant temperature equilibrium profile along the reactor are studied it is shown that it is exponentially stable and approximately reachable next the general concept of lq feedback is introduced it turns out that any lq feedback is optimal from the input output viewpoint and stabilizing for the plug flow reactor linearized model a state lq feedback operator is computed via the solution of a matrix riccati differential equation mrde in the space variable thanks to the reachability property the computed lq feedback is actually the optimal one then the latter is applied to the nonlinear model and the resulting closed loop system dynamical performances are analyzed a criterion is given which guarantees that the constant temperature equilibrium profile is an asymptotically stable equilibrium of the closed loop system moreover under the same criterion it is shown that the control law designed previously is optimal along the nonlinear closed loop model with respect to some cost criterion the results are illustrated by some numerical simulations

optimal regularity for a class of singular abstract parabolic equations a general class of singular abstract cauchy problems is considered which naturally arises in applications to certain free boundary problems existence of an associated evolution operator characterizing its solutions is established and is subsequently used to derive optimal regularity results the latter are well known to be important basic tools needed to deal with corresponding nonlinear cauchy problems such as those associated to free boundary problems

singularities of duals of grassmannians abstract let x p n be a smooth irreducible nondegenerate projective variety and let x p n denote its dual variety the locus of bitangent hyperplanes i e hyperplanes tangent to at least two points of x is a component of the singular locus of x in this paper we provide a sufficient condition for this component to be of maximal dimension and show how it can be used to determine which dual varieties of grassmannians are normal that last part may be compared to what has been done for hyperdeterminants by j weyman and a zelevinsky 1996 in 23

the quadrifocal variety abstract multi view geometry is reviewed from an algebraic geometry perspective and multi focal tensors are constructed as equivariant projections of the grassmannian a connection to the principal minor assignment problem is made by considering several flatlander cameras the ideal of the quadrifocal variety is computed up to degree 8 and partially in degree 9 using the representations of gl 3 4 in the polynomial ring on the space of 3 3 3 3 tensors further representation theoretic analysis gives a lower bound for the number of minimal generators

quasilinear evolution equations and parabolic systems it is shown that general quasilinear parabolic systems possess unique maximal classical solutions for sufficiently smooth initial values provided the boundary conditions are time independent moreover it is shown that in the autonomous case these equations generate local semi flows on appropriate sobolev spaces our results apply in particular to the case of prescribed boundary values dirichlet boundary conditions

optimal control design for time varying catalytic reactors a riccati equation based approach the linear quadratic lq optimal control problem is studied for a partial differential equation model of a time varying catalytic reactor first the dynamical properties of the linearised model are studied next an lq control feedback is computed by using the corresponding operator riccati differential equation whose solution can be obtained via a related matrix riccati partial differential equation finally the designed controller is applied to the non linear reactor system and tested numerically

on the abstract cauchy problem of parabolic type in spaces of continuous functions on etudie l existence l unicite et les proprietes de regularite des solutions du probleme de cauchy u t au r f t o t t u o u 0 ou a d a ce e est un operateur lineaire clos dans l espace de banach e

holder regularity in variational parabolic non homogeneous equations abstract we prove optimal holder regularity results for the solutions to second order variational parabolic equations with holder continuous coefficients and non homogeneous boundary data using analytic semigroups methods

bounds on the capacity of constrained two dimensional codes bounds on the capacity of constrained two dimensional 2 d codes are presented the bounds of calkin and wilf see siam j discr math vol 11 no 1 p 54 60 1998 apply to first order symmetric constraints the bounds are generalized in a weaker form to higher order and nonsymmetric constraints results are given for constraints specified by run length limits or a minimum distance between pixels of a given value

maximal regularity for evolution equations by interpolation and extrapolation on considere le probleme aux valeurs initiales pour l equation d evolution abstraite u t b t u t f t 0 t t ou b t est pour tout t le generateur infinitesimal d un semi groupe analytique dans un b espace e on considere le cas ou le domaine d b t de b t ne depend pas de t

linear and nonlinear degenerate differential operators and applications abstract the boundary value and mixed value problems for linear and nonlinear singular degenerate abstract elliptic and parabolic equations are studied the linear problems involve some parameters the uniform l p separability properties of linear problems and the optimal regularity results for nonlinear problems are obtained the equations include linear operators defined in banach spaces in which by choosing the spaces and operators we can obtain numerous classes of problems for singular degenerate differential equations which occur in a wide variety of physical systems

shannon capacity of m ary redundant multitrack runlength limited codes we consider multiamplitude multitrack runlength limited d k constrained channels with and without clock redundancy we calculate the shannon capacities of these channels and present some simple 100 efficient codes to compute capacity a constraint graph equivalent to the usual runlength limited constraint graph is used the introduced graph model has the vertex labeling independent of number of tracks to be written on in parallel which provides computational savings when the number of tracks is large we show that increasing the number of tracks written on in parallel provides significant increase of per track capacity for the more restrictive clocking constraint case i e when k d but it does not have much influence on the channel capacity when k spl ges d

lq boundary control of a diffusion convection reaction system in this work the boundary control of a distributed parameter system modelled by linear parabolic partial differential equations pdes with spatially varying coefficients is studied an infinite dimensional state space setting is considered and an exact transformation of the boundary actuation is realised to obtain an evolutionary model the evolutionary model which incorporates the spatially varying coefficients of the underlying set of the pdes is used for subsequent linear quadratic regulator synthesis the formulated linear quadratic state feedback controller is applied to a nonlinear model of the reactor and its performance is studied

curve shortening and the topology of closed geodesics on surfaces we study flat knot types of geodesics on compact surfaces m2 for every flat knot type and any riemannian metric g we introduce a conley index associated with the curve shortening flow on the space of immersed curves on m2 we conclude existence of closed geodesics with prescribed flat knot types provided the associated conley index is nontrivial

instabilities in a two dimensional combustion model with free boundary we prove instability of the planar travelling wave solution in a two dimensional free boundary problem modelling the propagation of near equidiffusional premixed flames in the whole plane we reduce the problem to a fixed boundary fully nonlinear parabolic system the spectrum of the linearized operator contains an interval 0 c c 0 so we cannot construct backward solutions we use an argument about stability of dynamical systems in banach spaces in order to prove pointwise instability of the moving front

on some abstract degenerate problems of parabolic type 2 the nonlinear case on etudie certaines caracteristiques du probleme aux valeurs initiales degenere d m t u t dt l t u t f t t 0 m t u t t 0 w 0 ou m t l t sont des operateurs lineaires clos de y dans x deux espaces de banach et f est continue de 0 0 dans x w 0 x

quadratic control for linear time varying systems an infinite dimensional linear time varying system on the interval infty infty is considered we introduce three quadratic problems the infinite horizon problem and one sided and two sided average cost problems a riccati equation on infty infty is considered first and sufficient conditions for the existence and uniqueness of a bounded solution are given then by dynamic programming the quadratic problems are solved similar problems in the stochastic case are considered

dynamics of a periodically pulsed bio reactor model abstract global attractivity and uniform persistence are established for both single species growth and two species competition in a periodically pulsed bio reactor model in terms of principal eigenvalues of the periodic parabolic eigenvalue problem by appealing to the theories of monotone discrete dynamical systems abstract persistence asymptotically periodic semiflows and perturbation of global attractors

homogeneous projective varieties with degenerate secants the secant variety of a projective variety x in p denoted by sec x is defined to be the closure of the union of lines in p passing through at least two points of x and the secant deficiency of x is defined by 2 dimx 1 dimsec x we list the homogeneous projective varieties x with 0 under the assumption that x arise from irreducible representations of complex simple algebraic groups it turns out that there is no homogeneous non degenerate projective variety x with sec x 6 p and 8 and the e6 variety is the only homogeneous projective variety with largest secant deficiency 8 this gives a negative answer to a problem posed by r lazarsfeld and a van de ven if we restrict ourselves to homogeneous projective varieties introduction the secant variety of a projective variety x in p denoted by sec x is defined to be the closure of the union of lines in p passing through at least two points of x and the secant deficiency of x is defined by 2 dimx 1 dim sec x in 1979 f l zak proved a significant inequality 3 dimx 4 2 dim p for a smooth non degenerate x with secx 6 p which had been conjectured by r hartshorne ht conjecture 4 2 see also fl lv z from the viewpoint of zak s inequality projective varieties x which attain the equality namely severi varieties were studied actively and zak finally found that there are exactly four severi varieties see fr t lv z it turns out that those varieties are all homogeneous and have 1 2 4 8 for the extremal case of odd dimensional x in which 3 dimx 5 2 dim p t fujita f gave a classification for 3 dimensional x and m ohno o recently gave classifications for 5 dimensional x and for 7dimensional x under a certain condition where those x of dimension 3 5 7 have 1 2 3 respectively thus several authors have studied projective varieties x with 0 the purpose of this article is to list the homogeneous projective varieties x with 0 under the assumption that x arise from irreducible representations of complex simple algebraic groups zak already obtained a table of those x in case received by the editors april 9 1996 1991 mathematics subject classification primary 14m17 14n05 17b10 20g05 c 1999 american mathematical society 533 license or copyright restrictions may apply to redistribution see http www ams org journal terms of use

on the closedness of the sum of two closed operators o t t 1 where e g a is the infinitesimal generator of an analytic semigroup in a complex banach space x we find that in general it is false that for every fe lp 0 t x problem 1 has a solution uewi p o t x c lp o t a usually it is necessary to impose some further regularity conditions on f consider for instance the way in which problem 1 is studied in the paper 8 and compare th 3 7 and 3 14 which are applied in w 4 of the same paper to solve problem 1 we find that in general we have only strong solutions while in the hilbert space setting we have strict solutions this corresponds to the fact that in general the operator a b where b u u is only closable while in a hilbert space it is closed this remark suggests that the better result may depend on the nicer geometric properties of a hilbert space with respect to a general banach space and it is natural to ask which conditions should be imposed on the banach space to force the sum of two suitable closed opera tors to be closed the above considerations motivate the manifold aim of the present paper a to find conditions on a banach space x and on closed linear operators a and b acting in x which ensure that a b is closed b to apply the result of a to problem 1 it seems that the convenient property for the banach space x is convexity or otherwise stated the umd condition for information about these equiva lent conditions we refer to 4 in which it is also proved that if x is convex and l p oe then the hilbert transform is continuous from lp r x into lp r x on the other hand it is also known see 2 that if there exists pe 1 oe such that the hilbert transform is continuous from lp r x into itself

degenerate and singular evolution equations in banach space on etudie l equation operateur ba 1 u a 0 u h dans des espaces de banach sous certaines hypotheses permettant d appliquer les resultats obtenus pour le probleme aux valeurs initiales d a 1 t u t dt a 0 t u t h t 0 t t lim t 0 a 1 t u t 0 ou a i t i 0 1 est un bon operateur lineaire clos entre espaces de banach

capacity bounds for the three dimensional 0 1 run length limited channel the capacity c sub 0 1 sup 8 of a three dimensional 0 1 run length constrained channel is shown to satisfy 0 522501741838 spl les c sub 0 1 sup 8 spl les 0 526880847825

the dynamical systems approach to differential equations bulletin new series of the american mathematical society volume 11 number 1 july 1984 the dynamical systems approach to differential equations by morris w hirsch 1 this harmony that human intelligence believes it discovers in nature does it exist apart from that intelligence no without doubt a reality completely independent of the spirit which conceives it sees it or feels it is an impossibility a world so exterior as that even if it existed would be forever inaccessible to us but what we call objective reality is in the last analysis that which is common to several thinking beings and could be common to all this common part we will see can be nothing but the harmony expressed by mathematical laws h poincare la valeur de la science p 9 ignorance of the roots of the subject has its price no one denies that modern formulations are clear elegant and precise it s just that it s impossible to comprehend how any one ever thought of them m spivak a comprehensive introduction to differential geometry introduction the mathematical subject we call dynamical systems was fathered by poin care developed sturdily under birkhoff and has enjoyed a vigorous new growth for the last twenty years as i try to show in chapter i it is interesting to look at this mathematical development as the natural outcome of a much broader theme which is as old as science itself the universe is a sytem which changes in time every mathematician has a particular way of thinking about mathematics but rarely makes it explicit yet such perspectives in any particular field can be of great value to nonexperts who must apply the results of the field or who want to learn them in some fields the points of view of its practitioners cluster around several comparatively clearly defined concepts and insights dynamical systems theory is one of them the basic concepts go back to poincare the main thrust of chapters i and ii is to explain rather discursively some of received by the editors december 14 1983 1980 mathematics subject classification primary 00a25 00a99 01a45 01a55 01a60 34a40 34c35 34d10 34d30 35b05 35b35 35b40 35b50 35b30 35k55 54h20 58f25 58f40 58f12 58f10 58d25 58d07 46a40 46e10 47h07 47h20 92a15 92a17 secondary 06f30 35b65 58f13 35j60 46e05 92 03 90 03 90a16 supported in part by national science foundation and institute for advanced study 1984 american mathematical society 0273 0979 84 1 00 25 per page

global existence and maximal regularity of solutions of gradient systems abstract in this article we use a galerkin method to prove a maximal regularity result for the following abstract gradient system u t g t e u t f t for a e t 0 t u 0 u 0 this abstract result is applied to nonlinear diffusion equations and to nondegenerate quasilinear parabolic equations with nonlocal coefficients

a second order magnus type integrator for quasi linear parabolic problems in this paper we consider an explicit exponential method of classical order two for the time discretisation of quasi linear parabolic problems the numerical scheme is based on a magnus integrator and requires the evaluation of two exponentials per step our convergence analysis includes parabolic partial differential equations under a dirichlet boundary condition and provides error estimates in sobolev spaces in an abstract formulation the initial boundary value problem is written as an initial value problem on a banach space x u t a u t u t 0 t t u 0 given involving the sectorial operator a v d x with domain d c x independent of v v c x under reasonable regularity requirements on the problem we prove the stability of the numerical method and derive error estimates in the norm of certain intermediate spaces between x and d various applications and a numerical experiment illustrate the theoretical results

writing sequences on the plane the problem of arranging two dimensional arrays of data into one dimensional sequences comes up in image processing color quantization and optical and magnetic data recording a good arrangement should enable the one dimensional sequences to be modeled as markov chains or shifts of finite type since this is not possible in general two dimensional data is most commonly scanned by rows columns or diagonals we look into three unusual ways to write a sequence in the plane by penrose tilings by space filling curves and by cylindrical and spiral lattices we show how penrose tilings can be used to record information and how some spiral lattices can be used for quantization of color spaces

global existence for semilinear parabolic systems on etudie des problemes aux valeurs limites et initiales paraboliques semilineaires de la forme u t a t u f t x u du d 2m 1 u dans t 0 b t u 0 sur t 0 u t 0 u 0 sur ou est un domaine de r n

fully nonlinear integrodifferential equations in general banach space on etudie des equations integrodifferentielles non lineaires dans un espace de banach qui peuvent etre considerees comme la version abstraite d equations integrodifferentielles partielles non lineaires on considere un probleme aux valeurs limites et initiales

on the evolution operator for a class of non autonomous abstract parabolic equations abstract we state existence and several properties of the evolution operator relevant to a family a t 0 t t of generators of analytic semigroups in a banach space the assumption that certain interpolation spaces do not depend on t allows us to weaken the usual regularity hypotheses on t a t requiring only continuity in suitable topologies