stable self similar blowup in energy supercritical yang mills theory we consider the cauchy problem for an energy supercritical nonlinear wave equation that arises in 1 5 dimensional yang mills theory a certain self similar solution w 0 of this model is conjectured to act as an attractor for generic large data evolutions assuming mode stability of w 0 we prove a weak version of this conjecture namely that the self similar solution w 0 is nonlinearly stable phrased differently we prove that mode stability of w 0 implies its nonlinear stability the fact that this statement is not vacuous follows from careful numerical work by bizon and chmaj that verifies the mode stability of w 0 beyond reasonable doubt

global regularity and scattering for general non linear wave equations ii 4 1 dimensional yang mills equations in the lorentz gauge we continue here with previous investigations on the global behavior of general type nonlinear wave equations for a class of small scale invariant initial data in particular we show that the 4 1 dimensional yang mills equations are globally well posed with asymptotically free behavior for a wide class of initial data sets which include general charges the method here is based on the use of a new set of strichartz estimates for the linear wave equation which incorporates extra weighted smoothness assumptions with respect to the angular variable along with the construction of appropriate micro local function spaces which take into account this type of additional regularity

scattering below critical energy for the radial 4d yang mills equation and for the 2d corotational wave map system given g and f gg we consider solutions to the following non linear wave equation left begin array l displaystyle u tt u rr frac 1 r u r frac f u r 2 u u t t 0 u 0 u 1 end array right under suitable assumptions on g this equation admits non constant stationary solutions we denote q one with least energy we characterize completely the behavior as time goes to of solutions u ut corresponding to data with energy less than or equal to the energy of q either it is q 0 up to scaling or it scatters in the energy space

on the stability of self similar solutions to nonlinear wave equations we consider an explicit self similar solution to an energy supercritical yang mills equation and prove its mode stability based on earlier work by one of the authors we obtain a fully rigorous proof of the nonlinear stability of the self similar blowup profile this is a large data result for a supercritical wave equation our method is broadly applicable and provides a general approach to stability problems related to self similar solutions of nonlinear wave equations

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

strichartz estimates in similarity coordinates and stable blowup for the critical wave equation we establish strichartz estimates in similarity coordinates for the radial wave equation in three spatial dimensions with a time dependent self similar potential as an application we consider the critical wave equation and prove the asymptotic stability of the ode blowup profile in the energy space

h sub infinity control and quadratic stabilization of systems with parameter uncertainty via output feedback the article concerns linear systems which are subject to both time varying norm bounded parameter uncertainty and exogenous disturbance it addresses the robust h sub infinity control problem of designing a linear dynamic output feedback controller such that the closed loop system is quadratically stable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties it is shown that such a problem is equivalent to a scaled h sub infinity control problem

algebraic arctic curves in the domain wall six vertex model the arctic curve i e the spatial curve separating ordered or frozen and disordered or temperate regions of the six vertex model with domain wall boundary conditions is discussed for the root of unity vertex weights in these cases the curve is described by algebraic equations which can be worked out explicitly from the parametric solution for this curve some interesting examples are discussed in detail the upper bound on the maximal degree of the equation in a generic root of unity case is obtained

generic self similar blowup for equivariant wave maps and yang mills fields in higher dimensions we consider equivariant wave maps from the d 1 dimensional minkowski spacetime into the d sphere for d 4 we find a new explicit stable self similar solution and give numerical evidence that it plays the role of a universal attractor for generic blowup an analogous result is obtained for the so d symmetric yang mills field for d 6

quadratic stabilization of continuous time systems with state delay and norm bounded time varying uncertainties this paper develops a method for designing a feedback control law to stabilize a class of uncertain linear systems the class of systems under consideration is described by a continuous time model with variable state delay and depends on time varying unknown but bounded uncertain parameters it is shown that the construction of the stabilizing controller involves solving a certain algebraic riccati equation several previous results are derived as interesting special cases finally a simulation example is presented to illustrate the analytical developments

output feedback robust h sup spl infin control of uncertain fuzzy dynamic systems with time varying delay this paper presents an output feedback robust h sup spl infin control problem for a class of uncertain fuzzy dynamic systems with time varying delayed state the takagi sugeno fuzzy model is employed to represent an uncertain nonlinear systems with time varying delayed state using a single quadratic lyapunov function the globally exponential stability and disturbance attenuation of the closed loop fuzzy control system are discussed sufficient conditions for the existence of robust h sup spl infin controllers are given in terms of matrix inequalities constructive algorithm for design of robust h sup spl infin controller is also developed the resulting controller is nonlinear and automatically tuned based on fuzzy operation

delay dependent stability analysis and controller synthesis for discrete time t s fuzzy systems with time delays based on a novel delay dependent piecewise lyapunov krasovskii functional dplkf this paper presents delay dependent stability analysis and synthesis methods for discrete time takagi sugeno t s fuzzy systems with time delays it is shown that the stability and stabilization with some required performance can be established for the closed loop control system if there exists a dplkf and that the dplkf and the corresponding controller can be obtained by solving a set of linear matrix inequalities lmis new algorithms have also been developed to obtain the maximum value of the allowable constant delay and the suboptimal performance upper bound an example is finally presented to demonstrate the efficiency and advantage of the proposed methods

renormalization and blow up for the critical yang mills problem we consider the yangs mills equations in 4 1 dimensions this is the energy critical case and we show that it admits a family of solutions which blow up in finite time they are obtained by the spherically symmetric ansatz in the so 4 gauge group and result by rescaling of the instanton solution the rescaling is done via a prescribed rate which in this case is a modification of the self similar rate by a power of vertical bar log t vertical bar the powers themselves take any value exceeding 3 2 and thus form a continuum of distinct rates leading to blow up the methods are related to the authors previous work on wave maps and the energy critical semi linear equation however in contrast to these equations the linearized yang mills operator around an instanton exhibits a zero energy eigenvalue rather than a resonance this turns out to have far reaching consequences amongst which are a completely different family of rates leading to blow up logarithmic rather than polynomial corrections to the self similar rate c 2009 elsevier inc all rights reserved

the defocusing energy supercritical nonlinear wave equation in three space dimensions we consider the defocusing nonlinear wave equation u tt u u p u 0 in the energy supercritical regime p 4 for even values of the power p we show that blowup or failure to scatter must be accompanied by blowup of the critical sobolev norm an equivalent formulation is that solutions with bounded critical sobolev norm are global and scatter the impetus to consider this problem comes from recent work of kenig and merle who treated the case of spherically symmetric solutions

memoryless stabilization of uncertain dynamic delay systems riccati equation approach the authors present a procedure for obtaining the memoryless linear state feedback control of uncertain dynamic delay systems the uncertainties are time varying and within a given compact set this method is an extension of the riccati equation approach proposed by i r petersen and c v hollot 1986 the extension is straightforward also the uncertainties do not need to satisfy the matching conditions

an lmi approach to decentralized guaranteed cost control for a class of uncertain nonlinear large scale delay systems the guaranteed cost control problem via the decentralized robust control for nonlinear uncertain large scale systems that have delay in both state and control input is considered sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequality lmi it is shown that the decentralized local state feedback controllers can be obtained by solving the lmi

on blowup of co rotational wave maps in odd space dimensions abstract we consider co rotational wave maps from the 1 d dimensional minkowski space into the d sphere for d 3 odd this is an energy supercritical model which is known to exhibit finite time blowup via self similar solutions based on a method developed by the second author and schorkhuber we prove the asymptotic nonlinear stability of the ground state self similar solution

delay dependent guaranteed cost control for t s fuzzy systems with time delays this study introduces a guaranteed cost control method for nonlinear systems with time delays which can be represented by takagi sugeno t s fuzzy models with time delays the state feedback and generalized dynamic output feedback approaches are considered the generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base it considers both the dynamic part and the output part of t s fuzzy model which guarantees that the controller without any delay information can stabilize time delay t s fuzzy systems based on delay dependent lyapunov functional approach some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation pdc first second the corresponding conditions are extended into the generalized dynamic output feedback closed loop system via so called generalized pdc technique the upper bound of time delay can be obtained using convex optimization such that the system can be stabilized for all time delays whose sizes are not larger than the bound the minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function the effectiveness of the proposed method can be shown by the simulation examples

technical communique h state feedback control for generalized continuous discrete time delay system in this paper we consider the problem of designing h state feedback controller for the generalized time delay systems with delayed states and control inputs in continuous and discrete time cases respectively the generalized time delay system problems are solved on the basis of linear matrix inequality lmi technique considering time delays the sufficient condition for the existence of controller and h state feedback controller design methods are presented also using some changes of variables and schur complements the obtained sufficient condition can be rewritten as an lmi form in terms of transformed variables the proposed controller design method can be extended into the problem of robust h state feedback controller design method easily

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

the global existence of yang mills higgs fields in 4 dimensional minkowski space in this paper we complete the proof of global existence of yang mills higgs fields in 4 dimensional minkowski space by showing that an appropriate norm of the solutions cannot blow up in a finite time a key step in the proof is the demonstration that thel norm of the curvature is boundeda priori our results apply to any compact guage group and to any invariant higgs self coupling which is positive and of no higher than quartic degree

decentralized stabilization of uncertain systems with interconnection and feedback delays an lmi approach this note presents a broad lmi condition that can ascertain the stability of uncertain systems under decentralized feedback in the presence of interconnection and feedback delays based on the lyapunov s direct approach with a four term energy functional and a three term quadratic formulation of the given state dynamics this method has a larger search space than used so far numerical examples corroborate the superiority of this method vis a vis the existing ones for several subsets of the general problem

local well posedness of the yang mills equation in the temporal gauge below the energy norm abstract we show that the yang mills equation in three dimensions in the temporal gauge is locally well posed in hs for s 3 4 if the hs norm is sufficiently small the temporal gauge is slightly less convenient technically than the more popular coulomb gauge but has the advantage of uniqueness even for large initial data and does not require solving a nonlinear elliptic problem to handle the temporal gauge correctly we project the connection into curl and divergence free components and develop some new bilinear estimates of xs b type which can handle integration in the time direction

robust control for parameter uncertain delay systems in state and control input in this note we present a robust control design method for parameter uncertain systems that have delay in both state and control input through a certain algebraic riccati inequality approach a state feedback controller is obtained the controller guarantees a stability for parameter uncertainties and delays

an algebraic approach to robust h control via state feedback abstract this paper considers the problem of robust h control design for linear uncertain systems we show that for a certain type of time varying norm bounded parameter uncertainty the problem is equivalent to an h control problem therefore a complete solution is achieved by using the existing results of h control theory the paper presents a state feedback design which stabilizes the plant for all admissible uncertainties and also guarantees a prescribed level of disturbance attenuation in a certain sense

dimers and amoebae we study random surfaces which arise as height functions of random perfect matchings a k a dimer configurations on a weighted bipartite doubly periodic graph g embedded in the plane we derive explicit formulas for the surface tension and local gibbs measure probabilities of these models the answers involve a certain plane algebraic curve which is the spectral curve of the kasteleyn operator of the graph for example the surface tension is the legendre dual of the ronkin function of the spectral curve the amoeba of the spectral curve represents the phase diagram of the dimer model further we prove that the spectral curve of a dimer model is always a real curve of special type namely it is a harnack curve this implies many qualitative and quantitative statement about the behavior of the dimer model such as existence of smooth phases decay rate of correlations growth rate of height function fluctuations etc

optimal guaranteed cost control of uncertain discrete time delay systems this paper considers the problem of robust guaranteed cost control of linear discrete time delay systems with parametric uncertainties by matrix inequality approach the robust quadratic stability of the system is studied a control design method is developed such that the closed loop system with a cost function has a upper bound irrespective of all admissible parameter uncertainties and unknown time delays furthermore the upper bound cost can be optimized by incorporating with a minimization problem a numerical example is given to show the potential of the proposed techniques

finite energy solutions of the yang mills equations in mathbb r 3 1 yang mills equations in r3 1 is well posed in the energy norm this means that for an appropriate gauge condition we construct local unique solutions in a time interval which depends only on the size of the energy norm of the data since the energy norm is left invariant by the yang mills flow the local solution is automatically extended to the entire space time thus our results which settle a problem stated in str imply the well known fundamental regularity result of eardley and moncrief e m that result proved in the temporal gauge requires a higher degree of smoothness for the data our main result proved also in the temporal gauge allows us to extend the concept of solutions to arbitrary finite energy initial data the solutions are automatically unique in the class of solutions obtained by our procedure moreover the global regularity proof given by eardley and moncrief depends in an essential way on the specific properties of the fundamental solution of the wave equation in the flat minkowski space time r3 1 namely the strong huygens principle indeed due mainly to this fact their proof does not seem to extend to general curved space times we have reasons to hope that the very different approach we take here will resolve this difficulty the basic ingredients of our method are 1 the introduction of appropriate local coulomb gauges adapted to the causal structure of the equations 2 an appropriate method of localizing the new space time estimates for

nondispersive radial solutions to energy supercritical non linear wave equations with applications in this paper we establish optimal pointwise decay estimates for non dispersive compact radial solutions to non linear wave equations in 3 dimensions in the energy supercritical range as an application we show for the full energy supercritical range in the defocusing case that if the scale invariant sobolev norm of a radial solution remains bounded in its maximal interval of existence then the solution must exist for all times and scatter

the radial wave operator in similarity coordinates we present a rigorous functional analytic setting to study the radial wave equation in similarity coordinates as an application we analyze linear stability of the fundamental self similar solution of the wave equation with a focusing power nonlinearity this is part 1 in a series of papers donninger r asymptotics and analytic modes for the wave equation in similarity coordinates j evol equ 9 511 2009 donninger r nonlinear stability of self similar solutions for semilinear wave equations commun partial differ equ c 2010 american institute of physics doi 10 1063 1 3299302

robust control for uncertain neutral systems with time delays in state and control input via lmi and gas in this paper the problem of robust control for uncertain neutral delay systems in state and control input is considered the uncertainty under discussed is nonlinear time varying perturbations and does not require a matching condition but is norm bounded based on the constructive use of lyapunov functional delay dependent stabilization criteria are proposed to guarantee robust stability for the systems via linear control linear matrix inequality and genetic algorithms are used to design a memoryless state feedback controller an example is given to illustrate our result is less conservative than other

calculation of norms of bethe wave functions a class of two dimensional completely integrable models of statistical mechanics and quantum field theory is considered eigenfunctions of the hamiltonians are known for these models norms of these eigenfunctions in the finite box are calculated in the present paper these models include in particular the quantum nonlinear schrodinger equation and the heisenbergxxz model

robust l2 disturbance attenuation for a class of uncertain lipschitz nonlinear systems with input delay abstractin this paper we study a robust l2 disturbance attenuation problem that arises when applying the artstein kwon pearson reduction transformation for a class of uncertain lipschitz nonlinear systems with input delay and external disturbances a conventional predictor based feedback controller is adopted with the control gain matrix carefully identified by solving a couple of sufficient conditions in terms of linear matrix inequalities lyapunov krasovskii functionals are constructed to guarantee that the robust l2 disturbance attenuation problem can be solved by the proposed controller a numerical example is included to validate the performance of the proposed controller

determination of the blow up rate for a critical semilinear wave equation in this paper we determine the blow up rate for the semilinear wave equation with critical power nonlinearity related to the conformal invariance

stability and robust stabilization of discrete time switched systems with time delays lmi approach we present sufficient linear matrix inequality conditions for asymptotic stability and stabilizability of switched discrete time linear systems subject to time delays and norm bounded uncertainties namely if these lmis are solvable then the switched system is exponentially stable for arbitrary switching in fact we show that any family of switched time delay systems satisfying these conditions possesses a quadratic common lyapunov function we also discuss the implication of this result on the stabilizability of this class of systems by switching controllers that use common lyapunov functions we show that even the analysis is carried out through a common lyapunov function the applied controller is mode dependent

directed loop monte carlo simulations of vertex models we show how the directed loop monte carlo algorithm can be applied to study vertex models the algorithm is employed to calculate the arrow polarization in the six vertex model with the domain wall boundary conditions the model exhibits spatially separated ordered and disordered regions we show how the boundary between these regions depends on parameters of the model we give some predictions on the behavior of the polarization in the thermodynamic limit and discuss the relation to the arctic circle theorem

memoryless h sup spl infin controllers for state delayed systems in this note a memoryless h sup spl infin controller for the state delayed system is presented the controller is a delay independent stabilizer for the state delayed system which also reduces the h sup spl infin norm of the closed loop transfer function from the disturbance to the controlled output to a prescribed level the controller can be obtained by solving a modified riccati equation

genetic fuzzy control for time varying delayed uncertain systems with a robust stability safeguard this paper proposes a new delay independent stability criterion for uncertain systems with state time varying delay then a robust state feedback control law based on it is constructed via sequential quadratic programming method to stabilize uncertain systems add a proposed flc with a small number of rules and membership functions to the above mentioned robust state feedback control law such that not only closed loop uncertain systems with time varying delay are robust stable but also output performance approaches desired one an example given illustrates the availability of the proposed design method

limit shapes and the complex burgers equation in this paper we study surfaces in r 3 that arise as limit shapes in random surface models related to planar dimers these limit shapes are surface tension minimizers that is they minimize a functional of the form h dx dy among all lipschitz functions h taking given values on the boundary of the domain the surface tension has singularities and is not strictly convex which leads to formation of facets and edges in the limit shapes we find a change of variables that reduces the euler lagrange equation for the variational problem to the complex inviscid burgers equation complex hopf equation the equation can thus be solved in terms of an arbitrary holomorphic function which is somewhat similar in spirit to weierstrass parametrization of minimal surfaces we further show that for a natural dense set of boundary conditions the holomorphic function in question is in fact algebraic the tools of algebraic geometry can thus be brought in to study the minimizers and especially the formation of their singularities this is illustrated by several explicitly computed examples

weak solutions and development of singularities of the su 2 σ model pour toutes donnees initiales d energie finie le modele sigma o k a des solutions faibles globales en chaque dimension d espace temps

technical communique robust stabilization of uncertain systems with unknown input delay this paper is concerned with the robust controller design for uncertain input delayed systems the time delay is assumed to be an unknown constant a controller with delay feedback for the robust stabilization of the system is proposed the stability criterion of the closed loop system is derived in terms of linear matrix inequalities lmis examples show that in many cases our method can give less conservative results than those by the existing methods moreover for the same cases our controllers have lower feedback gains than the existing ones

h spl infin output feedback controller design for linear systems with time varying delayed state this paper considers the h spl infin controller design problem for linear systems with time varying delays in states the authors obtain sufficient conditions for the existence of h spl infin controllers in terms of three linear matrix inequalities lmis these sufficient conditions are dependent on the maximum value of the time derivative of time varying delay furthermore they briefly explain how to construct such controllers from the positive definite solutions of their lmis and give an example

observer based fuzzy control design with adaptation to delay parameter for time delay systems this paper is concerned with the problem of observer based fuzzy stabilization for time delay systems the time delay under consideration is assumed to be a constant time delay but not known exactly a new design method is proposed for an observer based fuzzy controller with adaptation to the time delay the designed controller simultaneously contains both the current and past state information of the systems and can be derived by solving a set of linear matrix inequalities lmis the existence of the controller is equivalent to that of a controller for time delay systems where the constant time delay is known exactly a numerical example is given to illustrate the effectiveness of the design method

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

existence and universality of the blow up profile for the semilinear wave equation in one space dimension in this paper we consider the semilinear wave equation with a power nonlinearity in one space dimension we exhibit a universal one parameter family of functions which stand for the blow up profile in self similar variables at a non characteristic point for general initial data the proof is done in self similar variables we first characterize all the solutions of the associated stationary problem as a one parameter family then we use energy arguments coupled with dispersive estimates to show that the solution approaches this family in the energy norm in the non characteristic case and to a finite decoupled sum of such a solution in the characteristic case finally in the case where this sum is reduced to one element which is the case for noncharacteristic points we use modulation theory coupled with a nonlinear argument to show the exponential convergence in the self similar time variable of the various parameters and conclude the proof this step provides us with a result of independent interest the trapping of the solution in self similar variables near the set of stationary solutions valid also for non characteristic points the proof of these results is based on a new analysis in the self similar variable 2007 elsevier inc all rights reserved

an adiabatic theorem for resonances we prove a robust extension of the quantum adiabatic theorem the theorem applies to systems that have resonances instead of bound states and to systems for which just an approximation to a bound state is known to demonstrate the theorem s usefulness in a concrete situation we apply it to shape resonances 2011 wiley periodicals inc

thermodynamic limit of the six vertex model with domain wall boundary conditions we address the question of the dependence of the bulk free energy on boundary conditions for the six vertex model here we compare the bulk free energy for periodic and domain wall boundary conditions using a determinant representation for the partition function with domain wall boundary conditions we derive toda differential equations and solve them asymptotically in order to extract the bulk free energy we find that it is different and bears no simple relation to the free energy for periodic boundary conditions the six vertex model with domain wall boundary conditions is closely related to algebraic combinatorics alternating sign matrices this implies new results for the weighted counting for large size alternating sign matrices finally we comment on the interpretation of our results in particular in connection with domino tilings dimers on a square lattice

planar dimers and harnack curves in this article we study the connection between dimers and harnack curves discovered in 15 we prove that every harnack curve arises as a spectral curve of some dimer model we also prove that the space of harnack curves of given degree is homeomorphic to a closed octant and that the areas of the amoeba holes and the distances between the amoeba tentacles give these global coordinates we characterize harnack curves of genus zero as spectral curves of isoradial dimers and also as minimizers of the volume under their ronkin function with given boundary conditions

technical communique robust stabilization of uncertain input delayed systems using reduction method this paper concerns a robust stabilization problem that arises when applying the so called reduction method to multiple input delayed systems with parametric uncertainties a robust stabilizing controller that can be constructed easily by solving convex problems in terms of linear matrix inequalities is presented numerical examples are provided to show that in many cases the proposed controller is less conservative and easier to obtain than the existing controllers

brief paper robust exponential stabilization for markovian jump systems with mode dependent input delay this paper is concerned with the problem of exponential stabilization for uncertain linear systems with markovian jump parameters and mode dependent input delays sufficient stabilization conditions are developed in terms of matrix inequalities which can be solved by a proposed iterative algorithm based on the cone complementarity linearization ccl method memory controllers are also designed such that the closed loop system is exponentially mean square stable for all admissible uncertainties numerical examples are given to show that the developed method is efficient and less conservative

six vertex model with domain wall boundary conditions and one matrix model the partition function of the six vertex model on a square lattice with domain wall boundary conditions dwbc is rewritten as a hermitian one matrix model or a discretized version of it similar to sums over young diagrams depending on the phase the expression is exact for finite lattice size which is equal to the size of the corresponding matrix in the thermodynamic limit the matrix integral is computed using traditional matrix model techniques thus providing a complete treatment of the bulk free energy of the six vertex model with dwbc in the different phases in particular in the antiferroelectric phase the bulk free energy and a subdominant correction are given exactly in terms of elliptic theta functions

determinant formula for the six vertex model the partition function of a six vertex model with domain wall boundary conditions is considered on the finite lattice the authors show that the partition function satisfies a recursive relation they solve the recursion relation by a determinant formula this gives a determinant representation for the partition function they use the quantum inverse scattering method qism

on stable self similar blowup for equivariant wave maps reference epfl article 166023doi 10 1002 cpa 20366 url http arxiv org abs 1003 0707 record created on 2011 05 23 modified on 2017 05 12