remarks on the multiplier operators associated with a cylindrical distance function abstract in this note we consider l p and maximal l p estimates for the generalized riesz means which are associated with the cylindrical distance function max d 1 d 1 r d r we prove these estimates up to the currently known range of the spherical bochner riesz and its maximal operators this is done by establishing implications between the corresponding estimates for the spherical bochner riesz and the cylindrical multiplier operators

the l2 boundedness of pseudodifferential operators on donne une nouvelle demonstration du theoreme de calderon vaillancourt on obtient la l 2 continuite de a x d si le symbole a x satisfait a certaines conditions

continuous feedback guaranteeing uniform ultimate boundedness for uncertain linear delay systems an application to river pollution control we employ the stability result of thowsen on a class of linear delay systems containing uncertain elements and subject to uncertain inputs to manage a simple one reach model of a river system with time delay and subject to uncertain but bounded input as well as parameter disturbances two important indices of water quality namely biochemical oxygen demand bod and dissolved oxygen do are used as state variables while controls in the form of effluent discharge rate of bod and in stream aeration rate of do are employed to steer the system to a calculable neighborhood of a desired steady state and then maintain it there

h sub infinity optimal control with state feedback a h sub infinity optimal control problem in which the measured outputs are the states of the plant is considered the main result shows that the infimum of the norm of the closed loop transfer function using linear static state feedback equals the infimum of the norm of the closed loop transfer function over all stabilizing dynamic even nonlinear time varying state feedback controllers

h sub spl infin control of systems under norm bounded uncertainties in all system matrices this paper concerns h sub spl infin control of systems under norm bounded uncertainties in all the system matrices this is an extension of the work by xie et al 1992 where only the a matrix is allowed to be uncertain it is found that the problem shares the same formulation with the h sub spl infin control problem for systems without uncertainties it can also be viewed as reducing the problem of dealing with systems with both structured uncertainties and unstructured uncertainties to one with unstructured uncertainties only

h sub infinity analysis and synthesis of discrete time systems with time varying uncertainty the problems of h sub infinity analysis and synthesis of discrete time systems with block diagonal real time varying uncertainty are considered it is shown that these problems can be converted into scaled h sub infinity analysis and synthesis problems the problems of quadratic stability analysis and quadratic stabilization of these types of systems are dealt with as a special case the results on synthesis are established for general linear dynamic output feedback control

radial fourier multipliers of lp r2 abstract we give sufficient conditions in terms of differentiability and growth properties for a radial function to be an lp r2 fourier multiplier these conditions are in the nature of best possible

propagation of singularities and maximal functions in the plane in this work we mainly generalize bourgain s circular maximal function to include variable coefficient averages our techniques involve a combination of bourgain s basic ideas plus microlocal analysis in particular to see the role of curvature we rely heavily on methods used in studying propogation of singularities for hyperbolic differential equations we also show that forp 2 there is local smoothing inl p for solutions to the wave equation

robust h control for uncertain discrete stochastic time delay systems this paper deals with the problems of robust stabilization and robust h control for discrete stochastic systems with time varying delays and time varying norm bounded parameter uncertainties for the robust stabilization problem attention is focused on the design of a state feedback controller which ensures robust stochastic stability of the closed loop system for all admissible uncertainties while for the robust h control problem a state feedback controller is designed such that in addition to the requirement of the robust stochastic stability a prescribed h performance level is also required to be satisfied a linear matrix inequality lmi approach is developed to solve these problems and delay dependent conditions for the solvability are obtained it is shown that the desired state feedback controller can be constructed by solving certain lmis an example is provided to demonstrate the effectiveness of the proposed approach

bochner riesz means associated with conical surfaces abstract let d 1 and d 2 be two nonnegative integers greater than 2 we study the fourier multiplier t associated with a conical surface s r d 1 r d 2 defined by t f 1 2 2 f r d 1 r d 2 where is a smooth function defined on r that is supported in 1 2 2

on the neighborhood structure of the traveling salesman problem generated by local search moves when trying to find approximate solutions for the traveling salesman problem with heuristic optimization algorithms small moves called lin k opts are often used in our paper we provide exact formulas for the numbers of possible tours into which a randomly chosen tour can be changed with a lin k opt furthermore we compare the quality of the results to which the various moves lead

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

robust h spl infin control for uncertain stochastic systems with state delay this note deals with the problems of robust stochastic stabilization and robust h control for uncertain stochastic systems with a time varying delay in the state the parameter uncertainties are assumed to be time varying norm bounded appearing in both the state and input matrices the purpose of the robust stochastic stabilization problem is the design of a memoryless state feedback controller such that the closed loop system is mean square asymptotically stable for all admissible uncertainties in the robust h control problem in addition to the mean square asymptotic stability requirement a prescribed h performance is required to be achieved in terms of a linear matrix inequality sufficient conditions for the solvability of these problems are proposed respectively the expressions of desired state feedback controllers are given an example illustrating the proposed approach is provided

on the cone multiplier in r3 abstract we prove the sharp l 3 bounds for the cone multiplier in r 3 and the associated square function which is known as mockenhaupt s square function

weighted sensitivity minimization for delay systems in this note we discuss the h infty sensitivity minimization problem for linear time invariant delay systems while the unweighted case reduces to simple nevanlinna pick interpolation the weighted case turns out to be much more complicated and demands certain functional analytic techniques for its solution

weighted estimates for conic fourier multipliers we prove a weighted inequality which controls conic fourier multiplier operators in terms of lacunary directional maximal operators by bounding the maximal operators this enables us to conclude that the multiplier operators are bounded on l p mathbb r 3 with 1 p infty

radial fourier multipliers in high dimensions given a fixed p 2 we prove a simple and effective characterization of all radial multipliers of mathcal f l p left mathbb r d right provided that the dimension d is sufficiently large the method also yields new l q space time regularity results for solutions of the wave equation in high dimensions

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

weak type estimates for maximal operators with a cylindric distance function we establish sharp weak type estimates for the maximal operators t associated with cylindric riesz means for functions on h p 3 when 4 5 3 p 5 2

on the maximal bochner riesz conjecture in the plane for p 2 we give a new estimate on the maximal bochner riesz operator in the plane for p 2 as a corollary we obtain an almost everywhere convergence result for certain bochner riesz means this work was inspired by discussions with michael christ and chris sogge

a computational study of smoothing heuristics for the traveling salesman problem abstract over the last five years or so data smoothing has been used to improve the performance of heuristics that solve combinatorial optimization problems data smoothing allows a local search heuristic to escape from a poor local optimum in practice data smoothing has worked well when applied to the traveling salesman problem in this paper we conduct an extensive computational study to test the performance of eight smoothing heuristics for the traveling salesman problem in particular we apply eight smoothing heuristics and standard versions of two opt and three opt to 40 randomly generated euclidean problems and 30 problems taken from a well known library of test problems we compare the solutions generated by the heuristics and provide insight into the behavior of the smoothing heuristics

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

wave front sets local smoothing and bourgain s circular maximal theorem the purpose of this paper is to improve certain known regularity results for the wave equation and to give a simple proof of bourgain s circular maximal theorem 1 we use easy wave front analysis along with techniques previously used in proofs of the carleson sj6lin theorem see 3 5 7 and in the proof of sharp regularity properties of fourier integral operators 13 the circular means operators are defined by

on the multilinear restriction and kakeya conjectures we prove d linear analogues of the classical restriction and kakeya conjectures in rd our approach involves obtaining monotonicity formulae pertaining to a certain evolution of families of gaussians closely related to heat flow we conclude by giving some applications to the corresponding variable coefficient problems and the so called joints problem as well as presenting some n linear analogues for n d

search space smoothing for combinatorial optimization problems commonly there are two types of local search approaches known to treat combinatorial optimization problems with very complex search space structure one is to introduce very complicated types of local move classes allowing a bypass of high energetic barriers separating different minima the second is introducing a control parameter i e temperature in physics terminology dependent state space walker which is depending on this control parameter more or less easily able to climb over barriers a third less well known but very obvious approach is to smooth the search space i e to eliminate barriers between low energy configurations and therefore to allow a fast and easy approach to the global optimum this procedure will be discussed in depth in the following work

functional calculus for generators of symmetric contraction semigroups we prove that every generator of a symmetric contraction semigroup on a finite measure space admits for 1 p a hormander type holomorphic functional calculus on lp in the sector of angle p arcsin 1 2 p the obtained angle is optimal

on the h optimal sensitivity problem for systems with delays in this paper we extend some of the results of ieee trans automat control ac 31 1986 pp 763 766 to more general delay systems in particular we analyze the effect of the interaction of delays and nonminimum phase zeros on the h infty optimal weighted sensitivity

linear and bilinear estimates for oscillatory integral operators related to restriction to hypersurfaces abstract we obtain bilinear estimates for oscillatory integral operators which are variable coefficient generalizations of bilinear restriction estimates for hypersurfaces as applications we improve the known estimates for oscillatory integrals

bochner riesz means with respect to a rough distance function the generalized bochner riesz operator s r may be defined as s r f x f 1 1 r f x where p is an appropriate distance function and f 1 is the inverse fourier transform the behavior of s r on l p r d x r is described for p d 1 max d 1 a rough distance function we conjecture that this operator is bounded on r d x r when max d 1 2 1 p 1 2 0 and p 2 6 d 3 and unbounded when p 2 6 d 3 this conjecture is verified for large ranges of p

sharp bounds for multiplier operators of negative indices associated with degenerate curves in this note we show the sharp l p l q boundedness of multiplier operators of bochner riesz type having negative indices of which singularity is located in degenerate curve in mathbb r 2 l p l q boundedness of their maximal operators is also obtained

the generalized localization for multiple fourier integrals in this paper we investigate almost everywhere convergence properties of the bochner riesz means of n fold fourier integrals under summation over domains bounded by the level surfaces of the elliptic polynomials it is proved that if the order of the bochner riesz means s n 1 1 p 1 2 then the bochner riesz means of a function f lp rn 1 p 2 converge to zero almost everywhere on rn supp f

new optimization heuristics in a former paper we introduced a very effective new general purpose optimization principle we compared this method which we called threshold accepting ta with the well known simulated annealing sa method for discrete optimization the empirical results demonstrated the superiority of the ta algorithm in further experiments with the ta principle we discovered two new powerful optimization heuristics the great deluge algorithm gda and the record to record travel rrt these algorithms resemble in their structure the formerly studied ta and the sa method the differences lie in their acceptance rules for worse intermediate solutions both the gda and the rrt are essentially one parameter algorithms i e for the achievement of best possible performance a good choice is necessary only for a single parameter this is in contrast for instance to the classical as algorithm where it is necessary to choose carefully a certain sequence of parameters the so called annealing schedule the quality of the computational results obtained so far by rrt and gda shows that the new algorithms behave equally well as ta and thus a fortiori better than sa

on the regularity of inverses of singular integral operators sur r d on considere un operateur de convolution sf f k ou k est une distribution homogene de degre d on suppose que s s etend a un operateur borne et inversible sur l 2 r d l inverse de s est donne par convolution avec une distribution l aussi homogene de degre d on montre qu une regularite possedee par k est partagee par l

a bilinear approach to the restriction and kakeya conjectures the purpose of this paper is to investigate bilinear variants of the restriction and kakeya conjectures to relate them to the standard formulations of these conjectures and to give applications of this bilinear approach to existing conjectures the methods used are based on several observations and results of bourgain see 2 6 together with some refinements by moyua vargas and vega 17 18 this paper is organized as follows in the first section we discuss bilinear restriction estimates and show how one can pass back and forth between these estimates and the standard restriction estimates we also generalize the 12 7 bilinear restriction estimate of 18 to higher dimensions in the second section we give analogues of the above results for the kakeya operator in particular we give a bilinear improvement to wolff s kakeya theorem in arbitrary dimension in the third section we give applications of these bilinear estimates in three dimensions for example we are able to improve the 42 11 exponent in wolff s restriction theorem to 34 9 we are also able to prove a sharp lp lq restriction theorem which improves on the classical l2 l4 tomas stein theorem and also give some concrete progress on a bilinear restriction conjecture of klainerman and machedon we also give a non bilinear approach to these estimates which gives weaker results but is more direct and probably has a wider range of application

technical communique robust h observer design of linear state delayed systems with parametric uncertainty the discrete time case in this note we consider the problem of h observer design for a class of uncertain linear discrete time systems with delayed state and parameter uncertainties the goal of this problem is to design a linear state observer such that for the positive integer state time delay and all admissible norm bounded parameter uncertainties the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified h norm upper bound constraint the observer structure does not depend on the parameter uncertainties a simple effective algebraic methodology is developed to derive the conditions for the existence of the desired robust h observers and the analytical expression of these observers is then characterized in terms of the matrix riccati like equations inequalities we provide a numerical example to demonstrate the validity and the applicability of the proposed approach

characterizations of hankel multipliers we give characterizations of radial fourier multipliers as acting on radial l p functions 1 p 2d d 1 in terms of lebesgue space norms for fourier localized pieces of the convolution kernel this is a special case of corresponding results for general hankel multipliers besides l p l q bounds we also characte rize weak type inequalities and intermediate inequalities involving lorentz spaces applications include results on interpolation of multiplier spaces

new estimates of the maximal bochner riesz operator in the plane we prove new l p estimates with 1 p 2 for the maximal bochner riesz operator in the plane

local smoothing estimates for some half wave operators in this paper we study the local smoothing estimates for some half wave operators associated to nondegenerate convex hypersurfaces

technical communique robust reliable control for a class of uncertain nonlinear state delayed systems this paper deals with the problem of robust reliable control design for a class of nonlinear uncertain state delayed systems the system under consideration involves state time delay parameter uncertainties and unknown nonlinear disturbances the nonlinearities are assumed to satisfy the boundedness condition and the parameter uncertainties are allowed to be time varying unstructured the purpose of this problem is to design the state feedback controller such that for all admissible uncertainties as well as actuator failures occuring among a prespecified subset of actuators the plant remains globally exponentially stable independently of the time delay an effective modified algebraic riccati equation approach is developed to solve the problem addressed it is shown that designed nonlinear time delay control systems provide guaranteed robust reliable stability despite possible actuator failures we present an illustrative example to demonstrate the applicability of the proposed design approach

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

robust observer based h controller design for linear uncertain time delay systems in this note we present a robust observer based h control design method for linear time delay systems with norm bounded time varying uncertainties using the riccati equation based approach we design observer based feedback control laws which guarantee the quadratic stability of the closed loop control system and reduce the effect of the disturbance input on the controlled output to a prescribed level

robust h sub infinity control for linear systems with norm bounded time varying uncertainty robust h sub infinity control design for linear systems with uncertainty in both the state and input matrices is treated a state feedback control design which stabilizes the plant and guarantees an h sub infinity norm bound constraint on disturbance attenuation for all admissible uncertainties is presented the robust h sub infinity control problem is solved via the notion of quadratic stabilization with an h sub infinity norm bound necessary and sufficient conditions for quadratic stabilization with an h sub infinity norm bound are derived the results can be regarded as extensions of existing results on h sub infinity control and robust stabilization of uncertain linear systems

mutually beneficial relationship in optimization between search space smoothing and stochastic search abstract the effectiveness of the metropolis algorithm ma constant temperature simulated annealing in optimization by the method of search space smoothing sss potential smoothing is studied on two types of random traveling salesman problems the optimization mechanism of this hybrid approach masss is investigated by analyzing the exploration dynamics observed in the rugged landscape of the cost function energy surface the results show that the ma can be successfully utilized as a local search algorithm in the sss approach it is also clarified that the optimization characteristics of these two constituent methods are improved in a mutually beneficial manner in the masss run specifically the relaxation dynamics generated by employing the ma work effectively even in a smoothed landscape and more advantage is taken of the guiding function proposed in the idea of sss this mechanism operates in an adaptive manner in the de smoothing process and therefore the masss method maintains its optimization function over a wider temperature range than the ma

improved bounds for stein s square functions supported in part by nrf grant 2009 0072531 korea micinn grant mtm2010 16518 spain erc grant 277778 europe and nsf grant 0652890 usa

robust h state feedback control for linear systems with state delay and parameter uncertainty this paper addresses the problem of robust h state feedback control design for linear systems with state delay and parameter uncertainty based on a positive definite solution of a modified algebraic riccati equation the proposed robust h static state feedback controller stabilizes uncertain time delay systems independently of delays and guarantees an h norm bound constraint on disturbance attenuation for all admissible uncertainties furthermore it is shown that no advantage can be obtained from the use of a proper linear dynamic state feedback compared with the use of static state feedback illustrative examples are given to demonstrate the applicability of the proposed approach

influence of rounding errors on the quality of heuristic optimization algorithms abstract search space smoothing and related heuristic optimization algorithms provide an alternative approach to simulated annealing and its variants while simulated annealing traverses barriers in the energy landscape at finite temperatures search space smoothing intends to remove these barriers so that a greedy algorithm is sufficient to find the global minimum several formulas for smoothing the energy landscape have already been applied one of them making use of the finite numerical precision on a computer in this paper we thoroughly investigate the effect of finite numerical accuracy on the quality of results achieved with heuristic optimization algorithms we present computational results for the traveling salesman problem