quantitative thermo acoustic imaging an exact reconstruction formula this paper aims to mathematically advance the field of quantitative thermo acoustic imaging given several electromagnetic data sets we establish for the first time an analytical formula for reconstructing the absorption coefficient from thermal energy measurements since the formula involves derivatives of the given data up to the third order it is unstable in the sense that small measurement noises may cause large errors however in the presence of measurement noise the obtained formula together with a noise regularization technique provides a good initial guess for the true absorption coefficient we finally correct the errors by deriving a reconstruction formula based on the least square solution of an optimal control problem and prove that this optimization step reduces the errors occurring and enhances the resolution

rigorous approximation of stationary measures and convergence to equilibrium for iterated function systems we study the problem of the rigorous computation of the stationary measure and of the rate of convergence to equilibrium of an iterated function system described by a stochastic mixture of two or more dynamical systems that are either all uniformly expanding on the interval either all contracting in the expanding case the associated transfer operators satisfy a lasota yorke inequality we show how to compute a rigorous approximations of the stationary measure in the l 1 norm and an estimate for the rate of convergence the rigorous computation requires a computer aided proof of the contraction of the transfer operators for the maps and we show that this property propagates to the transfer operators of the ifs in the contracting case we perform a rigorous approximation of the stationary measure in the wasserstein kantorovich distance and rate of convergence using the same functional analytic approach we show that a finite computation can produce a realistic computation of all contraction rates for the whole parameter space we conclude with a description of the implementation and numerical experiments

mathematical modeling in photoacoustic imaging of small absorbers this paper is devoted to mathematical modeling in photoacoustic imaging of small absorbers we propose a new method for reconstructing small absorbing regions inside a bounded domain from boundary measurements of the induced acoustic signal we also show the focusing property of the back propagated acoustic signal indeed we provide two different methods for locating a targeted optical absorber from boundary measurements of the induced acoustic signal the first method consists of a multiple signal classification music type algorithm and the second one uses a multifrequency approach we also show results of computational experiments to demonstrate efficiency of the algorithms

ergodic properties of markov maps inr d for domainsi r d bounded or not the notion of a markov map fromi into itself is developed it is shown that under a condition of renyi type and the assumption that the map is markov any probability density tends inl1 norm to a unique invariant measure under the action of the perron frobenius operatorp the smoothness and ergodic properties of that invariant measure are studied the paper generalizes results of lasota and yorke from dimension one to higher dimension

on the uniqueness and stability of an inverse problem in photo acoustic tomography this article deals with the uniqueness and stability of the solution of a problem of optimal control related to the photo acoustic tomography process we prove stability results of the optimal solution with respect to the source and to the observation data and we compute the corresponding derivatives

to recovering the moments from the spherical mean radon transform abstract this article deals with characterizations of a function in terms of its circular mean radon transform we present a new approach the consistency method showing how to describe the class of real valued planar functions f which have the given circular mean radon transform m f over circles centered on the unit circle also expressions are derived for the geometric moments of an unknown function in terms of its circular mean radon transform

the perron frobenius operators invariant measures and representations of the cuntz krieger algebras for a transformation f on a measure space x we show that the perron frobenius operator of f can be written by a representation l2 x of the cuntz krieger algebra oa associated with f when f satisfies some assumption especially when oa is the cuntz algebra on and l2 x in the above is some irreducible representation of on then there is an f invariant measure on x which is absolutely continuous with respect to

randomly chosen chaotic maps can give rise to nearly ordered behavior abstract parrondo s paradox j m r parrondo g p harmer d abbott new paradoxical games based on brownian ratchets phys rev lett 85 2000 5226 5229 see also o e percus j k percus can two wrongs make a right coin tossing games and parrondo s paradox math intelligencer 24 3 2002 68 72 states that two losing gambling games when combined one after the other either deterministically or randomly can result in a winning game that is a losing game followed by a losing game a winning game inspired by this paradox a recent study j almeida d peralta salas m romera can two chaotic systems give rise to order physica d 200 2005 124 132 asked an analogous question in discrete time dynamical system can two chaotic systems give rise to order namely can they be combined into another dynamical system which does not behave chaotically numerical evidence is provided in j almeida d peralta salas m romera can two chaotic systems give rise to order physica d 200 2005 124 132 that two chaotic quadratic maps when composed with each other create a new dynamical system which has a stable period orbit the question of what happens in the case of random composition of maps is posed in j almeida d peralta salas m romera can two chaotic systems give rise to order physica d 200 2005 124 132 but left unanswered in this note we present an example of a dynamical system where at each iteration a map is chosen in a probabilistic manner from a collection of chaotic maps the resulting random map is proved to have an infinite absolutely continuous invariant measure acim with spikes at two points from this we show that the dynamics behaves in a nearly ordered manner when the foregoing maps are applied one after the other deterministically as in o e percus j k percus can two wrongs make a right coin tossing games and parrondo s paradox math intelligencer 24 3 2002 68 72 the resulting composed map has a periodic orbit which is stable

lotz rabiger s nets of markov operators in l 1 spaces abstract the lotz rabiger nets lr nets introduced in rabiger 1993 18 under the name m nets provide an appropriate setting for investigation various mean ergodic theorems in banach spaces in the present paper we prove several convergence theorems for lr nets of markov operators in l 1 spaces which extend theorems 1 and 5 from emel yanov 2004 8 and theorem 1 1 from lasota 1983 11

annealed and quenched limit theorems for random expanding dynamical systems in this paper we investigate annealed and quenched limit theorems for random expanding dynamical systems making use of functional analytic techniques and more probabilistic arguments with martingales we prove annealed versions of a central limit theorem a large deviation principle a local limit theorem and an almost sure invariance principle we also discuss the quenched central limit theorem dynamical borel cantelli lemmas erdos renyi laws and concentration inequalities

on the number of invariant measures for higher dimensional chaotic transformations lets be a bounded region inr n and letp s l i 1 m be a partition ofs into a finite number of closed subsets having piecewisec2 boundaries of finite n 1 dimensional measure let s s be piecewisec2 onp and expanding in the sense that there exists 0 1 such that for anyi 1 2 m dt i 1 wheredt i 1 is the derivative matrix oft i 1 and is the euclidean matrix norm we prove that for some classes of such mappings for example jabtonski transformations or convexity preserving transformations the number of crossing points constitutes a bound for the number of ergodic absolutely continuous invariant measures we give examples showing that in general the simple bound of one dimensional dynamics cannot be generalized to higher dimensions in fact we show that it is possible to construct piecewise expandingc2 transformations on a fixed partition with a finite number of elements but which have an arbitrarily large number of ergodic absolutely continuous invariant measures

approximation for the measures of ergodic transformations of the real line let p varphi l 1 r to l 1 r be the frobenius perron operator corresponding to a nonsingular point transformation of the real liner into itself and let for each natural numbern pn be the discrete analogue ofpf it is shown that under fairly weak restrictions on the equationf pf f has an unique solutionf0 such thatf0 0 a e f0 1 and that this solution can be approximated inl1 r in two different ways 1 by the sequence left 1 mathord left vphantom 1 n right kern nulldelimiterspace n sum limits k 0 n 1 p varphi k f right wheref 0 f 1 and 2 by the sequence s on of simple functions such thatsn pn s on

toward a mathematical holographic principle in work started in 17 and continued in this paper our objective is to study selectors of multivalued functions which have interesting dynamical properties such as possessing absolutely continuous invariant measures we specify the graph of a multivalued function by means of lower and upper boundary maps tau 1 and tau 2 on these boundary maps we define a position dependent random map r p tau 1 tau 2 p 1 p which at each time step moves the point x to tau 1 x with probability p x and to tau 2 x with probability 1 p x under general conditions for each choice of p r p possesses an absolutely continuous invariant measure with invariant density f p let varvec tau be a selector which has invariant density function f one of our objectives is to study conditions under which p x exists such that r p has f as its invariant density function when this is the case the long term statistical dynamical behavior of a selector can be represented by the long term statistical behavior of a random map on the boundaries of g we refer to such a result as a mathematical holographic principle we present examples and study the relationship between the invariant densities attainable by classes of selectors and the random maps based on the boundaries and show that under certain conditions the extreme points of the invariant densities for selectors are achieved by bang bang random maps that is random maps for which p x in 0 1

microwave imaging by elastic deformation in this paper we show that by using microwave measurements at different frequencies and ultrasound localized perturbations to create local changes in the medium it is possible to extend the method developed by ammari et al in siam j appl math 68 2008 pp 1557 1573 to problems of the form nabla cdot a nabla u k 2 qu 0 in omega u varphi on partial omega and to reliably reconstruct both the real valued functions a and q from the internal energies a nabla u 2 and q u 2

absolutely continuous invariant measures for random maps with position dependent probabilities abstract a random map is discrete time dynamical system in which one of a number of transformations is randomly selected and applied at each iteration of the process usually the map k is chosen from a finite collection of maps with constant probability p k in this note we allow the p k s to be functions of position in this case the random map cannot be considered to be a skew product the main result provides a sufficient condition for the existence of an absolutely continuous invariant measure for position dependent random maps on 0 1 geometrical and topological properties of sets of absolutely continuous invariant measures attainable by means of position dependent random maps are studied theoretically and numerically

collapsing of chaos in one dimensional maps in their numerical investigation of the family of one dimensional maps f x d 1 2jxj where 2 diamond et al p diamond et al physica d 86 1999 559 571 have observed the surprising numerical phenomenon that a large fraction of initial conditions chosen at random eventually wind up at 1 a repelling fixed point this is a numerical artifact because the continuous maps are chaotic and almost every true trajectory can be shown to be dense in 1 1 the goal of this paper is to extend and resolve this obvious contradiction we model the numerical simulation with a randomly selected map while they used 27 bit precision in computing f we prove for our model that this numerical artifact persists for an arbitrary high numerical prevision the fraction of initial points eventually winding up at 1 remains bounded away from 0 for every numerical precision 2000 elsevier science b v all rights reserved

a note on invariant measures for markov maps of an interval we present two examples of markov maps which satisfy the expanding condition renyi s condition and do not admit any absolutely continuous invariant measures these examples are counterexamples to the theorem formulated in 1 p 1

sharp estimates for the neumann functions and applications to quantitative photo acoustic imaging in inhomogeneous media we obtain sharp lp and holder estimates for the neumann function of the operator ik on a bounded domain we also obtain quantitative description of its singularity we then apply these estimates to quantitative photo acoustic imaging in inhomogeneous media the problem is to reconstruct the optical absorption coefficient of a diametrically small anomaly from the absorbed energy density

the bms group and generalized gravitational instantons the ordinary bondi metzner sachs bms group b is the best candidate for the fundamental symmetry group of general relativity it has been shown that b admits generalizations to real space times of any signature and also to complex space times it has been suggested that certain continuous unitary irreducible representations irs of b and of its generalizations correspond to gravitational instantons here i make this correspondence more precise and i take this suggestion one step further by arguing that a subclass of irs of b and of its generalizations correspond to generalized gravitational instantons some of these generalized gravitational instantons involve in their definition certain subgroups of the cartesian product group cn cm where cr is the cyclic group of order r with this motivation i give the subgroups of cn cm explicitly

attainable densities for random maps abstract we consider a random map t t where 1 2 k is a collection of maps of an interval and p 1 p 2 p k is a collection of the corresponding position dependent probabilities that is p k x 0 for k 1 2 k and k 1 k p k x 1 at each step the random map t moves the point x to k x with probability p k x for a fixed collection of maps t can have many different invariant probability density functions depending on the choice of the weighting probabilities most of the results in this paper concern random maps where is a family of piecewise linear semi markov maps we investigate properties of the set of invariant probability density functions of t that are attainable by allowing the probabilities in to vary in a certain class of functions we prove that the set of all attainable densities can be determined algorithmically we also study the duality between random maps generated by transformations and random maps constructed from a collection of their inverse branches such representation may be of greater interest in view of new methods of computing entropy w slomczynski j kwapien k yczkowski entropy computing via integration over fractal measures chaos 10 2000 180 188

compactness of eigenvectors for certain families of non negative matrices conditions are given which guarantee that the normalized left eigenvectors of certain classes of non negative matrices of unbounded dimension interpreted as functions of 0 1 form precompact sets in l1 these eigenvectors are uniformly bounded above and in some cases uniformly bounded below

exponential decay of correlations for random lasota yorke maps we consider random piecewise smooth piecewise invertible maps mainly on the interval but also in higher dimensions we assume that on the average and possibly without any stochastic uniformity i the maps expand distances ii do not have too many pieces iii do not have too large a distortion and iv are strongly mixing we assume it no markov property we prove that as in the classical case of the iteration of a fixed piecewise expanding map of the interval we have it exponential decay of random correlations our proof builds on the one given by c liverani for deterministic mixing and piecewise expanding interval maps

perron frobenius operators and representations of the cuntz krieger algebras for infinite matrices abstract in this paper we extend the work of kawamura see k kawamura the perron frobenius operators invariant measures and representations of the cuntz krieger algebras j math phys 46 2005 for cuntz krieger algebras o a for infinite matrices a we generalize the definition of branching systems prove their existence for any given matrix a and show how they induce some very concrete representations of o a we use these representations to describe the perron frobenius operator associated to a nonsingular transformation as an infinite sum and under some hypothesis we find a matrix representation for the operator we finish the paper with a few examples

to local reconstruction from the spherical mean radon transform abstract the article suggests a new approach using the so called consistency method for the inversion of the spherical mean radon transform in 2d with detectors on a line we present a new iterative formula which gives an algorithm to recover an unknown function supported completely on one side of a line l from its spherical means over circles centered on the line l our reconstruction formula has the benefit of being local such an inversion is required in problems of thermo and photo acoustic tomography ultrasound reflection tomography radar imaging and a few other

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

construction of the irreducibles of b 2 2 the ordinary bondi metzner sachs bms group b is the common asymptotic symmetry group of all radiating asymptotically flat lorentzian spacetimes as such b is the best candidate for the universal symmetry group of general relativity however in studying quantum gravity spacetimes with signatures other than the usual lorentzian one and complex spacetimes are frequently considered generalizations of b appropriate to these other signatures have been defined earlier in particular the generalization b 2 2 appropriate to the ultrahyperbolic signature has been described in detail and the study of its irreducible unitary representations irs of b 2 2 has been initiated the infinite little groups have been given explicitly but the finite little groups have only been partially described this study is completed by describing in detail the finite little groups and by giving all the necessary information in order to construct the irs of b 2 2 in all cases

absolutely continuous invariant measures for random non uniformly expanding maps we prove existence of at most denumerable many absolutely continuous invariant probability measures for random one dimensional dynamical systems with asymptotic expansion if the rate of expansion lyapunov exponents is bounded away from zero we obtain finitely many ergodic absolutely continuous invariant probability measures describing the asymptotics of almost every point we also prove a similar result for higher dimensional random non uniformly expanding dynamical systems the results are consequences of the construction of such measures for skew products with essentially arbitrary base dynamics and asymptotic expansion along the fibers in both cases our method deals with either critical o singular points for the random maps

singular perturbations of piecewise monotonic maps of the interval let t 0 1 0 1 be a piecewise monotonic c2 and expanding map in computing an orbit i x0 i 0 we model the roundoff error at each iteration by a singular perturbation i e xn 1 xn w wherew is a random variable taking on discrete values in an interval e e the main result proves that this process admits an absolutely continuous invariant measure which approaches the absolutely continuous measure invariant under the deterministic map t as the precision of computation e 0

asymptotic periodicity of the iterates of markov operators on dit que p l 1 l 1 est un operateur de markov si 1 pf 0 pour f 0 et 2 pf f si f 0 on montre que tout operateur de markov p a une certaine decomposition spectrale si pout tout f l 1 avec f 0 et f 1 p n f 7b f quand n ou 7b f est un sous ensemble fortement compact de l 1

the exact hausdorff dimension for a class of fractal functions in recent years a number of authors an incomplete list is 1 2 3 6 7 9 11 12 131 have considered a class of real functions whose graphs are in general fractal sets in r2 in this paper we give sufficient conditions for the fractal and hausdorff dimensions to be equal for a certain subclass of fractal functions the sets we consider are examples of self affine fractals generated using iterated function systems i f s falconer s has shown that for almost all such sets the fractal and hausdorff dimensions are equal and he gives a formula for the common dimension due originally to moran s these results however give no information about individual fractal functions in this paper we extend moran s original method and show that if certain conditions on the i f s are satisfied then the two dimensions are equal kono 111 and bedford 121 considered special cases of the subclass of fractal functions that we will introduce bedford and urbanski 13 use a nonlinear setting to present conditions for the equality of hausdorff and fractal dimension however their criteria are based on measure theoretic characterizations and the use of the concept of generalized pressure our criterion on the other hand is based on the underlying geometry of the attractor and is easier to verify we will show this on two specific examples which are more general than the self ahine functions presented in 13

computing invariant measures of piecewise convex transformations lets 0 1 0 1 be a piecewise convex transformation satisfying some conditions which guarantee the existence of an absolutely continuous invariant probability measure we prove the convergence of a class of markov finite approximations for computing the invariant measure using a compactness argument forl1 spaces

invariant densities for random maps of the interval on etudie des applications aleatoires de 0 1 qui representent des systemes dynamiques sur le carre 0 1 0 1 on donne des conditions suffisantes pour qu une application aleatoire ait une mesure invariante absolument continue

an inverse initial boundary value problem for the wave equation in the presence of imperfections of small volume we consider for the wave equation the inverse problem of identifying locations and certain properties of the shapes of small conductivity inhomogeneities in a homogeneous background medium from dynamic boundary measurements on part of the boundary and for a finite interval in time using as weights particular background solutions constructed by a geometrical control method we develop an asymptotic method based on appropriate averaging of the partial dynamic boundary measurements our approach is expected to lead to very effective computational identification algorithms

on the representation theory of the bondi metzner sachs group and its variants in three space time dimensions the original bondi metzner sachs bms group b is the common asymptotic symmetry group of all asymptotically flat lorentzian radiating 4 dim space times as such b is the best candidate for the universal symmetry group of general relativity g r in 1973 with this motivation mccarthy classified all relativistic b invariant systems in terms of strongly continuous irreducible unitary representations irs of b here we introduce the analogue b 2 1 of the bms group b in 3 space time dimensions b 2 1 itself admits thirty four analogues both real in all signatures and in complex space times in order to find the irs of both b 2 1 and its analogues we need to extend wigner mackey s theory of induced representations the necessary extension is described and is reduced to the solution of three problems these problems are solved in the case where b 2 1 and its analogues are equipped with the hilbert topology the extended theory is necessary in order to construct the irs of both b and its analogues

spectral decomposition for combinations of markov operators abstract let p p1 1 p2 be the convex combination of two constrictive markov operators if p is constrictive then the spectral representation of p is related to the spectral representations of p1 and p2

approach to equilibrium for locally expanding maps in ℝ k by using a well known technique from classical statistical mechanics of one dimensional lattice spin systems we prove existence of an absolutely continuous invariant asymptotic measure for certain locally expanding mapst of the unit cube in k we generalize herewith in a certain sense the results of lasota and yorke on piecewise expanding maps of the unit interval to higher dimensions we show a kuzmin type theorem for these systems from which exponential approach to equilibrium and strong mixing properties follow