itd double edge diffraction for complex source beam illumination a new high frequency incremental theory of diffraction itd formulation for the double diffraction by metallic wedges when illuminated by complex source points csp is provided the main motivation is the extension of the class of problems that can be studied using asymptotic i e ray based and incremental methods by providing a double diffraction description for csp which are considered because they are efficient to analyze electrically large structures the new formulation provides an accurate asymptotic description of the interaction between two edges in an arbitrary configuration including slope diffraction contributions advantages of the itd formulation for csp illumination include avoiding the typical ray caustic impairments of the gtd utd ray techniques and not requiring ray tracing in complex space numerical results are presented and compared to a method of moments analysis to demonstrate the accuracy of the solution

an efficient algorithm for the computation of the utd t transition function we present an efficient algorithm for the numerical calculation of the t canonical transition function which is encountered in the uniform geometrical theory of diffraction utd such a transition function allows the uniform ray field description of various high frequency diffraction mechanisms such as double wedge or vertex diffraction the proposed algorithm is valid for both real and imaginary arguments as required to deal with the general case in utd applications

topological lower bounds on algebraic random access machines we prove general lower bounds for set recognition on random access machines rams that operate on real numbers with algebraic operations times as well as rams that use the operations times lfloor rfloor we do it by extending a technique formerly used with respect to algebraic computation trees in the case of algebraic computation trees the complexity was related to the number of connected components of the set w to be recognized for rams four similar results apply to the number of connected components of w circ the topological interior of w two results use overline w circ the interior of the topological closure of w we present theorems that can be applied to a variety of problems and obtain lower bounds many of them tight for the following models 1 a ram which operates on real numbers using integers to address memory and either the operations times or times lfloor rfloor 2 a ram of each of the above instruction sets extended by allowing arbitrary real numbers to be used as memory addresses and adding a test for integer instruction 3 a ram of each of the above instruction sets which can compute with arbitrary real numbers as well as use them for memory addressing while the input is restricted to the integers for one result on this model we require that all program constants be rational

stochastic theory of edge diffraction an alternative formulation an alternative formulation is presented for the derivation of the results in which allows to rigorously extend the validity range to any incidence observation aspect provided that the standard deviation of the edge roughness sigma is not large compared to the wavelength lambda while the observation distance r is r gt lambda this was heuristically conjectured by franceschetti ieee trans antennas propag vol 56 no 2 pp 437 449 2008 and supported by numerical examples but without a rigorous proof

a uniform double diffraction coefficient for a pair of wedges in arbitrary configuration an analytic closed form solution is presented for the double diffraction at a pair of arbitrarily placed wedges that is suitable to be used in a uniform theory of diffraction utd ray description framework here the particular assumption present in all the past literature that the two diffracting edges are coplanar is removed the doubly diffracted dd field at a pair of wedges is constructed via spectral synthesis such a procedure provides a double spectral integral representation of the dd field that is asymptotically evaluated by resorting to transition functions typical in double diffraction problems that can be expressed in terms of generalized fresnel integrals the final expression is arranged in the typical utd fashion and contains a uniform double diffraction dyadic coefficient the dd field behavior is analyzed in its transition regions to show how the dd field smoothly compensates for the total field discontinuities occurring at shadow boundaries where a singly diffracted field from a wedge is shadowed by the other wedge numerical examples are provided to verify such analysis and to test the accuracy of our utd ray description against method of moments full wave results

experimental and theoretical validation for the incremental theory of diffraction experimental and theoretical approaches to verify the validity of the incremental theory of diffraction itd are considered after providing a simple recipe for the application of the itd three geometries are examined for its validation first the itd formulation of the diffraction from a perfect electric conductor pec straight wedge is compared with the uniform theory of diffraction utd and with measurement results second the itd formulation of the diffraction from a pec disc is compared with measurement results and with the exact solution of a boundary value problem involving oblate spheroidal functions third the itd formulation of the diffraction from a hole in a pec plane is compared with the exact solution of a boundary value problem involving oblate spheroidal functions in particular this is the first time that itd results for diffraction from the disc and hole in a plane geometries are validated using exact solutions computed at a caustic in all cases examined very good agreement is found

double tip diffraction modeling 2 d numerical models versus high frequency asymptotics the subject of single and double diffraction phenomena has long been investigated by high frequency asymptotic techniques however integral or differential equation based numerical methods suffer from computational complexity due to electrically large geometries encountered in high frequency problems the main purpose of this paper is to present the finite element fem diffraction modeling of double tip structure and to compare its results with high frequency methods and other numerical models fem is made feasible for modeling of such an infinitely long structure by utilizing the locally conformal perfectly matched layer pml approach which enables the use of finite sized structure matlab codes are developed and various numerical examples are demonstrated in a comparative manner

a utd triple diffraction coefficient for straight wedges in arbitrary configuration a new utd solution is presented for the description of the ray triply diffracted by straight wedges in arbitrary configuration illuminated by a spherical wavefront field the proposed utd coefficient permits to uniformly describe the field at any aspect in particular including the case of overlapping transition regions where the subsequent application of utd single wedge diffraction coefficient fails the triple diffracted ray field is expressed in an analytical form providing physical insight into the triple diffraction mechanism and a new effective engineering tool within the utd framework as required in a modern ray based code

algorithm for the computation of the generalized fresnel integral the generalized fresnel integral appears as a canonical function in the uniform ray field representation of several high frequency diffraction mechanisms such as double wedge or vertex diffraction here we propose an algorithm for its calculation which is valid both for real and imaginary arguments as required for treating the general case in the uniform geometrical theory of diffraction framework

a lower bound for the integer element distinctness problem a lower bound of n log n is proved for the integer element distinctness problem given x1 xn zn are the xi s distinct on the bounded order algebraic decision tree model

complex symmetric differential operators on fock space abstract the space of entire functions which are integrable with respect to the gaussian weight known also as the fock space is one of the preferred functional hilbert spaces for modeling and experimenting harmonic analysis quantum mechanics or spectral analysis phenomena this space of entire functions carries a three parameter family of canonical isometric involutions we characterize the linear differential operators acting on fock space which are complex symmetric with respect to these conjugations in parallel as a basis of comparison we discuss the structure of self adjoint linear differential operators the computation of the point spectrum of some of these operators is carried out in detail

an efficient ray tracing algorithm for multiple straight wedge diffraction we present an efficient algorithm for the tracing of multiply edge diffracted rays the algorithm assumes a given sequence of infinite edges and complete visibility among them the ray tracing problem is formulated as the minimization of the ray total path length since such a cost function is strictly convex except for coplanar edges in the plane wave far field regime then the problem admits a unique global minimum and allows the use of a modified newton search algorithm which exhibits a very high converging rate we also propose a convenient starting point to effectively initialize the minimization algorithm the proposed algorithm is tested by some numerical examples that show its efficiency and effectiveness

a general uniform double wedge diffraction coefficient the uniform theory of diffraction utd is extended to include double diffraction by an arbitrary configuration of two wedges a scalar double diffraction coefficient is defined which is uniform throughout space while reducing to the product of single diffraction coefficients outside overlapping transition regions the result is formulated in terms of double fresnel integrals which can be rapidly evaluated

complex symmetric operators and applications ii a bounded linear operator t on a complex hilbert space h is called complex symmetric if t ct c where c is a conjugation an isometric antilinear involution of h we prove that t cj t where j is an auxiliary conjugation commuting with t t t we consider numerous examples including the poincare neumann singular integral bounded operator and the jordan model operator compressed shift the decomposition t cj t also extends to the class of unbounded c selfadjoint operators originally introduced by glazman in this context it provides a method for estimating the norms of the resolvents of certain unbounded operators

complex symmetric weighted composition operators on h2 d abstract in this paper we study complex symmetric weighted composition operators on the hardy space we provide some characterizations of and when a weighted composition operator w is complex symmetric we investigate which combinations of weights and maps of the open unit disk give rise to complex symmetric weighted composition operators with a special conjugation as some applications we obtain several examples for nonnormal complex symmetric operators in addition we give spectral properties of complex symmetric weighted composition operators we examine eigenvalues and eigenvectors of such operators and find some conditions for which a complex symmetric weighted composition operator is hilbert schmidt finally we consider cyclicity hypercyclicity and the single valued extension property for complex symmetric weighted composition operators

complex symmetry of weighted composition operators on the fock space abstract with the techniques of weighted composition operators we introduce a new concept of general weighted composition conjugations on the fock space f 2 c and completely solve the following problems the description of weighted composition operators which are conjugations the criteria for weighted composition operators to be complex symmetric the spectrum and the point spectrum of complex symmetric operators and the criteria for schatten class membership as well as for normality of such operators

lower bounds for algebraic computation trees with integer inputs let w subseteq r n be scale invariant and rationally dispersed i e tilde x in w implies lambda tilde x in w for all real lambda 0 and the rationale are dense in both w and r n w it is shown that in the algebraic computation tree model the problem of deciding whether an input tilde x in r n with integer coordinates is a member of w has complexity omega log 2 hat beta w 2n where hat beta w is the number of connected components of w that are not of measure 0 this theorem can be used to prove tight lower bounds for the integral constrained form of many basic problems such as element distinctness set disjointness finding convex hull etc through further transformations it leads to lower bounds for problems such as integer max gap and closest pair of a simple polygon the proof involves a nontrivial extension of the milnor thorn techniques for finding upper bounds on the betti numbers of algebraic varieties

speed scaling to manage energy and temperature speed scaling is a power management technique that involves dynamically changing the speed of a processor we study policies for setting the speed of the processor for both of the goals of minimizing the energy used and the maximum temperature attained the theoretical study of speed scaling policies to manage energy was initiated in a seminal paper by yao et al 1995 and we adopt their setting we assume that the power required to run at speed s is p s e s for some constant 1 we assume a collection of tasks each with a release time a deadline and an arbitrary amount of work that must be done between the release time and the deadline yao et al 1995 gave an offline greedy algorithm yds to compute the minimum energy schedule they further proposed two online algorithms average rate avr and optimal available oa and showed that avr is 2 1 competitive with respect to energy we provide a tight bound on the competitive ratio of oa with respect to energy we initiate the study of speed scaling to manage temperature we assume that the environment has a fixed ambient temperature and that the device cools according to newton s law of cooling we observe that the maximum temperature can be approximated within a factor of two by the maximum energy used over any interval of length 1 b where b is the cooling parameter of the device we define a speed scaling policy to be cooling oblivious if it is simultaneously constant competitive with respect to temperature for all cooling parameters we then observe that cooling oblivious algorithms are also constant competitive with respect to energy maximum speed and maximum power we show that yds is a cooling oblivious algorithm in contrast we show that the online algorithms oa and avr are not cooling oblivious we then propose a new online algorithm that we call bkp we show that bkp is cooling oblivious we further show that bkp is e competitive with respect to the maximum speed and that no deterministic online algorithm can have a better competitive ratio bkp also has a lower competitive ratio for energy than oa for 5 finally we show that the optimal temperature schedule can be computed offline in polynomial time using the ellipsoid algorithm

generalization of utd double diffraction to the case of impenetrable wedges with relatively general boundary conditions in the framework of the uniform geometrical theory of diffraction utd a novel high frequency solution is provided which allows the description of the rays doubly diffracted by a pair of impenetrable straight wedges with relatively general boundary conditions under a spherical wave illumination such a utd solution is heuristically derived by imposing the continuity of the total field at the shadow boundaries of the first order i e geometrical optics utd wedge single diffracted ray field utd solution it is the extension to the case of double diffraction of the first order solutions proposed by luebbers and by burnside and burgener it allows a uniform description of the field at any observation point including those aspects where transition regions overlap and the cascading of utd single wedge diffraction coefficients fails the proposed solution does not consider surface wave effects and for the special case of two perfectly conducting wedges it reduces to the formulation present in the literature of which it can be considered a generalization indeed it requires the same special functions involved in utd double diffraction by two perfectly conducting wedges the double diffracted ray field is expressed in analytical closed form providing a deeper understanding of the physics involved in double diffraction and a new powerful tool to be employed in any modern ray based code

complex symmetric composition operators on the newton space abstract a conjecture posed by macdonald and rosenthal states the composition operator c acting on the newton space n 2 p induced by z m z m 1 2 is bounded where m 0 1 our first result is proving that the aforementioned conjecture holds we investigate complex symmetry of composition operators acting on the newton space which is different from that on the hardy space in addition normality and co isometry of composition operators are studied finally we consider complex symmetric weighted composition operators

complex symmetric c0 semigroups on the fock space abstract in this paper we introduce a new concept in dynamical systems the complex symmetric operator c 0 semigroups groups acting on hilbert space using techniques of weighted composition operators we study these semigroups on the fock space f 2 and show in particular that complex symmetric operator c 0 semigroups contain the familiar unitary semigroups as a proper subclass

complex symmetric weighted composition operators on hγ d abstract we study the complex symmetric structure of weighted composition operators of the form w on the hilbert space h d of holomorphic functions over the open unit disk d with reproducing kernels k w 1 w z where n first we consider conjugations on h d of the form a u v f u f v such conjugations are also known as weighted composition conjugations and characterize them into two classes denoted by c 1 and c 2 then we obtain explicit conditions for w when it is c 1 symmetric and c 2 symmetric respectively

an efficient algorithm for computing optimal discrete voltage schedules we consider the problem of job scheduling on a variable voltage processor with d discrete voltage speed levels we give an algorithm which constructs a minimum energy schedule for n jobs in o d n log n time previous approaches solve this problem by first computing the optimal continuous solution in o n 3 time and then adjusting the speed to discrete levels in our approach the optimal discrete solution is characterized and computed directly from the inputs we also show that o n log n time is required hence the algorithm is optimal for fixed d

numerical diffraction of array guided surface waves on finite frequency selective surfaces in this paper an adaptation of hurst s method to take into account the presence of array guided surface waves in the calculation of the scattered field of finite frequency selective surfaces in free space is presented numerical approaches to determine the guided wave s wavenumber needed in this calculation namely prony s method and the discrete fourier transform dft are examined and compared the results show that the scattered fields obtained with the proposed method which is based on numerically extracted diffraction coefficients are in very good agreement with those obtained with the method of moments

energy optimal schedules for jobs with multiple active intervals in this paper we study the scheduling problem of jobs with multiple active intervals each job in the problem instance has n n 1 disjoint active time intervals where it can be executed and a workload characterized by the required number of cpu cycles previously people studied multiple interval job scheduling problem where each job must be assigned enough cpu cycles in one of its active intervals we study a different practical version where the partial work done by the end of an interval remains valid and each job is considered finished if total cpu cycles assigned to it in all its active intervals reach the requirement the goal is to find a feasible schedule that minimizes energy consumption by adapting the algorithm for single interval jobs proposed in yao demers and shenker 1995 1 one can still obtain an optimal schedule however the two phases in that algorithm critical interval finding and scheduling the critical interval can no longer be carried out directly we present polynomial time algorithms to solve the two phases for jobs with multiple active intervals and therefore can still compute the optimal schedule in polynomial time

algebraic decision trees and euler characteristics abstract for any set s r n let s denote its euler characteristic in this paper we show that any algebraic computation tree or fixed degree algebraic decision tree must have height log s cn for deciding the membership question of a compact semi algebraic set s this extends a result in bjorner et al 1992 where it was shown that any linear decision tree for deciding the membership question of a closed polyhedron s must have height greater than or equal to log 3 s