controllability and observability of 2d thermal flow in bulk storage facilities using sensitivity fields abstractto control and observe spatially distributed thermal flow systems the controllable field and observable field around the actuator and sensor are of interest respectively for spatially distributed systems the classical systems theoretical concepts of controllability and observability are in general difficult to apply in this study sensitivity fields were used to analyse the behaviour from input to state and from initial state to output for the analysis of controllability and observability a large scale bulk storage facility with coupled thermal flow of air and agro products was used analysis of this system using the classical systems theory results in controllability and observability results that are dependent on the step size of the spatially discretised system due to matrix multiplications inaccurate results are calculated if the step size is too small our findings indicate that input state and initial state output sensitivity fields provide sufficient information about the contro

a many body rage theorem we prove a generalized version of the rage theorem for n body quantum systems the result states that only bound states of systems with 0 leqslant n leqslant n particles persist in the long time average the limit is formulated by means of an appropriate weak topology for many body systems which was introduced by the second author in a previous work and is based on reduced density matrices this topology is connected to the weak topology of states on the algebras of canonical commutation or anti commutation relations and we give a formulation of our main result in this setting

regional optimal control for a class of semilinear systems with distributed controls abstractthis paper considers a regional optimal control problem for a class of semilinear infinite dimensional systems with distributed controls the existence of an optimal control is proven and then this control is characterised for four cases of admissible controls theoretical results lead to a useful algorithm that we illustrate by simulations of two heat equations

operateurs conjugues et proprietes de propagation we use an algebraic criteria based on local positivity of a commutator which asserts the existence of a direction of propagation for the flowe iht associated to a self adjoint operatorh

regional controllability of distributed parameter systems the purpose of this paper is to show how one can achieve regional controllability for distributed systems first we give a definition and some properties of this new concept then we concentrate on the determination of a control achieving regional controllability with minimum energy a direct method is developed and is illustrated by a hyperbolic system with point control and a parabolic system with zone control we also give an important remark that converts the problem into a constrained optimization one

zero temperature properties of rna secondary structures we analyze different microscopic rna models at zero temperature we discuss both the most simple model which suffers a large degeneracy of the ground state and models in which the degeneracy has been removed in a more or less severe manner we calculate low energy density of states using a coupling perturbing method where the ground state of a modified hamiltonian that repels the original ground state is determined we evaluate scaling exponents starting from measurements of overlaps and energy differences in the case of models without accidental degeneracy of the ground state we are able to clearly establish the existence of a glassy phase with ensuremath theta ensuremath simeq 1 3 87 15 aa 64 60 fr

dispersive charge transfer model with long range quantum interactions abstract we present a method of proving the asymptotic completeness of wave operators associated with the scattering of a quantum particle in a field of classical particles with long range interactions based on some propagation estimates of the type recently developed in the theory of n body systems the approach allows us to treat a class of dispersive systems where the free hamiltonian has the form h 0 p d covering for example the case of the relativistic hamiltonian p c 2 2 1 2

on long range scattering even if special cases are not well understood it pays sometimes to consider a problem at hand in the most general framework thus addressing the existence of wave operators for the most general potentials hormander ho1 has discovered a natural asymptotic evolution for the long range scattering it is determined by a solution s k t of a certain hamilton jacobi equation

universality classes for extreme value statistics the equilibrium low temperature physics of disordered systems is governed by the statistics of extremely low energy states it is thus relevant to discuss the possible universality classes for extreme value statistics we compare the usual probabilistic classification to the results of the replica approach we show in detail for several problems including the random energy model and the decaying burgers turbulence that one class of independent variables corresponds exactly to the so called one step replica symmetry breaking solution in the replica language we argue that this universality class holds if the correlations are sufficiently weak and propose a conjecture on the level of correlations which leads to different universality classes

obituary to a j pritchard on the 12th of august 2007 tony pritchard professor of mathematics at the university of warwick died suddenly at the age of 70 from a heart attack while on holiday with his family on the island of lanzarote both of the authors have had the privilege of working with him for many years we have lost both a colleague and a friend the following notes are dedicated to his memory

a new proof of the propagation theorem for n body quantum systems a new proof of i sigal s and a soffer s propagation theorem is given this theorem describes a large class of operators which are kato smooth with respect to ann body schrodinger operator

extremal properties of random systems we find that the probability distribution for the largest intervals p l exhibits universal properties for different systems including random walk and random cutting models in particular p l has an infinite set of singularities at l 1 k with k 2 3 which become weaker and weaker as k ensuremath rightarrow ensuremath infty additionally p l has an essential singularity at l 0 these properties are also found in many dimensional situations

asymptotic completeness for n body short range quantum systems a new proof we give an alternative geometrical proof of asymptotic completeness for an arbitrary number of quantum particles interacting through shortrange pair potentials it relies on an estimate showing that the intercluster motion concentrates asymptotically on classical trajectories

the n particle scattering problem asymptotic completeness for short range systems on demontre la completude asymptotique pour des systemes de mecanique quantique a courte portee constitues d un nombre arbitraire de particules

propagation of singularities in many body scattering in the presence of bound states abstract in this paper we describe the propagation of singularities of tempered distributional solutions u s of h u 0 where h is a many body hamiltonian h v 0 v a v a and is not a threshold of h under the assumption that the inter particle e g two body interactions v a are real valued polyhomogeneous symbols of order 1 e g coulomb type with the singularity at the origin removed here the term singularity refers to a microlocal description of the lack of decay at infinity thus we prove that the set of singularities of u is a union of maximally extended broken bicharacteristics of h these are curves in the characteristic variety of h which can be quite complicated due to the existence of bound states we use this result to describe the wave front relation of the s matrices we also analyze lagrangian properties of this relation which shows that the relation is not too large in terms of its dimension

freezing transition of the random bond rna model statistical properties of the pairing weights to characterize the pairing specificity of rna secondary structures as a function of temperature we analyze the statistics of the pairing weights as follows for each base i of the sequence of length n we consider the n 1 pairing weights w i j with the other bases j not equal i of the sequence we numerically compute the probability distributions p1 w of the maximal weight w i max max j w i j the probability distribution pi y 2 of the parameter y2 i summation operator j w i 2 j as well as the average values of the moments y k i summation operator j w i k j we find that there are two important temperatures t c t gap the distribution p1 w vanishes at some value w 0 t 1 and accordingly the moments y k i decay exponentially as w 0 t k in k for t t gap the distributions p1 w and pi y2 present the characteristic derrida flyvbjerg singularities at w 1n and y 2 1 n for n 1 2 in particular there exists a temperature dependent exponent mu t that governs the singularities p1 w approximately 1 w mu t 1 and pi y2 approximately 1 y 2 mu t 1 as well as the power law decay of the moments y k i approximately 1k mu t the exponent mu t grows from the value mu t 0 0 up to mu t gap approximately 2 the study of spatial properties indicates that the critical temperature t c where the large scale roughness exponent changes from the low temperature value zeta approximately 0 67 to the high temperature value zeta approximately 0 5 corresponds to the exponent mu t c 1 for t t c there exists frozen pairs of all sizes whereas for t c t t gap there exists frozen pairs but only up to some characteristic length diverging as xi t approximately 1 t c t nu with nu approximately 2 the similarities and differences with the weight statistics in levy sums and in derrida s random energy model are discussed

bilinear optimal control of a kirchhoff plate abstract we consider the problem of optimal control of a kirchhoff plate a bilinear control is used as a force to make the plate close to a desired profile taking into the account a quadratic cost of control we prove the existence of an optimal control and characterize it uniquely through the solution of an optimality system

dependence of rna secondary structure on the energy model we analyze a microscopic rna model which includes two widely used models as limiting cases namely it contains terms for bond as well as for stacking energies we numerically investigate possible changes in the qualitative and quantitative behavior while going from one model to the other in particular we test whether a transition occurs when continuously moving from one model to the other for this we calculate various thermodynamic quantities at both zero temperature and finite temperatures all calculations can be done efficiently in polynomial time by a dynamic programming algorithm we do not find a sign for the transition between the models but the critical exponent ensuremath nu of the correlation length describing the phase transition in all models to an ordered low temperature phase seems to depend continuously on the model finally we apply the ensuremath epsilon coupling method to study low energy excitations the exponent ensuremath theta describing the energy scaling of the excitations seems to depend not much on the energy model

statistical properties of randomly broken objects and of multivalley structures in disordered systems the statistical properties of the multivalley structure of disordered systems and of randomly broken objects have many features in common for all these problems if w denotes the weight of the sth piece we show that the probability distributions pi w of the largest piece w p2 w of the second largest piece and n y of y 1 wi always have singularities at w l n w2 l n and y ijn n 1 2 3

schrodinger operators in the twentieth century this paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics

asymptotic completeness for 3 particle long range systems we prove asymptotic completeness for 3 particle systems with pair potentials satisfying the virial condition and decreasing at infinity as for 1 2

constrained regional control problem of a bilinear plate equation this paper investigates a regional optimal control problem of a plate equation described by a bilinear system evolving in a spacial domain the control is distributed bounded and acts on the vel

compactification of complete kahler surfaces with negative ricci curvature it is a classical result of satake 17 baily borel 3 and ash mumford rapoport tai 2 that quotients of bounded symmetric domain by arithmetic groups of automorphism can be compactified the methods employed are essentially algebraic in nature along another direction andreott i grauert 1 siu yau 19 and nadel tsuji 14 obtained results which cover the above manifolds using the analytic properties of pseudoconcavity on the other hand it is believed that complete k ihler manifolds satisfying purely differential geometric conditions of bounded sectional curvature and negative ricci curvature can be compactified using differential geometric methods in 12 mok started a systematic scheme of attacking the problem and results in the work of mok zhong 13 the present article can be considered as a continuation of this scheme in particular we prove the conjecture in case of dimensional two more precisely we prove