weightless cohomology of algebraic varieties abstract using morel s weight truncations in categories of mixed sheaves we attach to varieties over finite fields or the complex numbers a series of groups called the weightless cohomology groups these lie between the usual cohomology and intersection cohomology have natural ring structures and are functorial for certain morphisms

motivic weightless complex and the relative artin motive abstract we construct a motivic analogue of the weightless cohomology groups 18 and demonstrate several expected properties ring structure kunneth functoriality for certain morphisms etc we also demonstrate the expected relationship with the motivic intersection complex of wildeshaus 26 25 whenever it exists the methods also give another construction of the weightless cohomology groups over any base field in characteristic 0 this motive coincides with the motive e x of ayoub zucker 3 and recovers the motivic construction of the reductive borel serre compactification of shimura varieties

idempotent completion of triangulated categories we show that the idempotent completion of a triangulated category has a natural structure of a triangulated category the idempotent completion of the bounded derived category of an exact category gives the derived category of the idempotent completion in particular the derived category of an idempotent complete exact category is idempotent complete

a modified real ga for the sparse linear array synthesis with multiple constraints this paper describes a modified real genetic algorithm mga for the synthesis of sparse linear arrays the mga has been utilized to optimize the element positions to reduce the peak sidelobe level psll of the array and here the multiple optimization constraints include the number of elements the aperture and the minimum element spacing unlike standard ga using fixed corresponding relationship between the gene variables and their coding the mga utilized the coding resetting of gene variables to avoid infeasible solution during the optimization process also the proposed approach has reduced the size of the searching area of the ga by means of indirect description of individual the simulated results confirming the great efficiency and the robustness of this algorithm are provided in this paper

versatile beam forming with concentric excitations based on multiple weighted sinc or bessel function distribution in this paper we propose a beam forming approach capable of synthesizing versatile pre specified beam shapes using concentric excitations satisfying multiple weighted sinc or bessel function distribution we show by both theoretical calculation and full wave simulation that by tuning different weights of a sinc or bessel function distribution not only radiation beams with pencil flat topped and bimodal shapes can be synthesized but also the beam width and the side lobe level can be independently adjusted an example is provided to demonstrate how an isoflux beam aiming at a better coverage of the earth surface is synthesized and how an optimized continuous distribution is properly discretized for a physical realization of a satellite aperture array antenna the approach proposed in this paper can be applied to a wide range of applications that require performance optimization of concentric ring array antennas

optimization of sparse linear arrays using harmony search algorithms a sparse linear array composed of a uniformly spaced core subarray and an extended sparse subarray is synthesized using a harmony search hs and an exploratory harmony search ehs algorithms the optimal solution is searched by changing the amplitudes of all the elements and the positions of the extended elements under a set of practical constraints performance of the ehs the hs a genetic algorithm ga and a particle swarm optimization pso algorithm has also been compared in synthesizing these sparse linear arrays

sharp global nonlinear stability for temperature dependent viscosity convection with regard to the dependence of viscosity on temperature an unconditional non linear energy stability analysis for thermal convection according to navier stokes theory has not yet been developed we here analyse three models of fluid behaviour proposed by o a ladyzhenskaya we show that by using these theories we can develop an unconditional analysis directly two of the models lead directly to an unconditional development employing l2 theory while the third necessitates the introduction of a generalized energy also involving an l3 term the nonlinear stability boundaries in all three cases are sharp when compared with the instability thresholds of linear theory

a rigorous reduction of the l2 stability of the solutions to a nonlinear binary reaction diffusion system of pde s to the stability of the solutions to a linear binary system of ode s abstract a basic peculiar lyapunov functional v is introduced for the dynamical systems generated by a pair of nonlinear reaction diffusion pde s with nonconstant coefficients the sign of v and of its derivative along the solutions is linked through an immediate simple relation to the eigenvalues by using v and the l 2 norm the non linear l 2 stability instability is rigorously reduced to the stability instability of the solutions to a linear binary system of ode s

indecomposable higher chow cycles on jacobians we construct some natural indecomposable elements of ch g j c 1 with trivial regulator and in particular prove that ch g ind j c 1 mb q is uncountable for c a generic curve or a generic hyperelliptic curve of genus g geq 3

the application of a modified differential evolution strategy to some array pattern synthesis problems a high convergence rate and a robust exploration ability constitute a contradiction in modern heuristic optimization techniques this paper describes a modified differential evolution strategy mdes that builds up a balanced relationship between the two contradictive elements by introducing several modifications into the conventional differential evolution strategy des the novel mdes opens up an effective and robust approach for global optimization problems several representative mathematical functions are minimized using various optimization methods and the convergence rates are compared to evaluate the performance of mdes moreover array synthesis examples which can be formulated as non convex problems are presented including the optimal synthesis of sum and difference patterns and the synthesis of unequally spaced arrays numerical results demonstrate that the proposed approach improves the performance of the algorithm significantly in terms of both the convergence rate and the exploration ability

generalized analytical technique for the synthesis of unequally spaced arrays with linear planar cylindrical or spherical geometry an effective method for optimizing the performance of a fixed current distribution uniformly spaced antenna array has been to adjust its element positions to provide performance improvement in comparison with the default uniform structure this approach yields performance improvements such as smaller sidelobe levels or beamwidth values additionally it provides practical advantages such as reductions in size weight and number of antenna elements the objective of this paper is to describe a unified mathematical approach to nonlinear optimization of multidimensional array geometries the approach utilizes a class of limiting properties of sinusoidal bessel or legendre functions that are dictated by the array geometry addressed the efficacy of the method is demonstrated by its generalized application to synthesis of rectangular cylindrical and spherical arrays the unified mathematical approach presented below is a synthesis technique founded on the mathematical transformation of the desired field pattern followed by the application of limiting forms of the transformation and resulting in the development of a closed form expression for the element positions the method offers the following advantages over previous techniques such as direct nonlinear optimization or genetic algorithms first it is not an iterative searching algorithm and provides element spacing values directly in a single run of the algorithm thereby saving valuable cpu time and memory storage second it permits the array designer to place practical constraints on the array geometry e g the minimum maximum spacing between adjacent elements

a nonlinear fourth order diffusion problem convergence to the steady state and non negativity of solutions the paper deals with nonlinear diffusion both time dependent and time independent the spatial terms in the partial differential equation p d e contain a second order nonlinear part where the non negative diffusivity depends on the dependent variable and a fourth order linear part in the context of non null time independent boundary conditions convergence of the unsteady to the steady state is established the second part of the paper discusses criteria on data ensuring non negativity of the solutions this is done for the steady state irrespective of the spatial dimension and it is done for the unsteady state for the one dimensional rectilinear case only using a result from the first part of the paper

the effect of density dependent dispersal on the stability of populations abstract the nonlinear stability of two populations diffusing in a common bounded domain with nonlinear density dependent dispersal of a general type is studied under robin boundary conditions the stability and instability of the positive equilibrium are studied by the linear eigenvalues method the nonlinear stability is studied with the lyapunov direct method in a particular case global stability has been obtained

a nonlinear diffusion system with convection abstract this paper deals with a coupled nonlinear diffusion system with convection a characteristic matrix equation covering all the six nonlinear exponents of the system is introduced to get a simple description for the blow up criteria of the system in addition the influence of the four coefficients of the diffusion and the convection as well as the geometry of on global boundedness or not of the solutions is shown clearly especially for the situation with the critical sign of the characteristic parameters

synthesis of unequally spaced antenna arrays by using differential evolution synthesis of unequally spaced linear antenna arrays is considered in this paper a recently developed new differential evolution algorithm is applied to solve the problem both position only and position phase synthesis have been studied effect of angle resolution has also been investigated synthesis results show that our algorithm is able to obtain better synthesis result reliably and efficiently

near chebyshev pattern for nonuniformly spaced arrays using zeros matching method an analytic method is presented to design nonuniformly spaced uniform amplitude antenna arrays nsuaas to have near chebyshev radiation pattern in this method called zeros matching method zmm the zeros of array factors of nsuaas are matched with the zeros of the exact chebyshev pattern some examples are brought to verify the effectiveness of the zmm approach for both linear and planar nsuaas

a multi objective approach to subarrayed linear antenna arrays design based on memetic differential evolution in this paper we present a multi objective optimization approach to subarrayed linear antenna arrays design we define this problem as a bi objective one we consider two objective functions for directivity maximization and sidelobe level minimization memetic algorithms mas are hybrid algorithms that combine the benefits of a global search evolutionary algorithm ea with a local search method in this paper we introduce a new memetic multi objective evolutionary algorithm namely the memetic generalized differential evolution mgde3 this algorithm is a memetic extension of the popular generalized differential evolution gde3 algorithm another popular moea is the nondominated sorting genetic algorithm ii nsga ii mgde3 gde3 and nsga ii are applied to the synthesis of uniform and nonuniform subarrayed linear arrays providing an extensive set of solutions for each design case depending on the desired array characteristics the designer can select the most suitable solution the results of the proposed method are compared with those reported in the literature indicating the advantages and applicability of the multi objective approach

approximating the ideal free distribution via reaction diffusion advection equations abstract we consider reaction diffusion advection models for spatially distributed populations that have a tendency to disperse up the gradient of fitness where fitness is defined as a logistic local population growth rate we show that in temporally constant but spatially varying environments such populations have equilibrium distributions that can approximate those that would be predicted by a version of the ideal free distribution incorporating population dynamics the modeling approach shows that a dispersal mechanism based on local information about the environment and population density can approximate the ideal free distribution the analysis suggests that such a dispersal mechanism may sometimes be advantageous because it allows populations to approximately track resource availability the models are quasilinear parabolic equations with nonlinear boundary conditions

asymptotic and other properties of a nonlinear diffusion model let r 3 be a sufficiently smooth bounded fixed domain ensuring the validity of divergence like theorems and let us consider the initial boundary value problem i b v p u t delta f u quad x t in omega times r 1 u t left x 0 right u 0 left x right quad x in omega 2 u t left x t right u 1 left x right quad x in partial omega times r 3 where f c 2 r and u 0 in c left overline omega right u 1 c are assigned functions

on weight truncations in the motivic setting abstract using punctual gluing of t structures we construct an analogue of s morel s weight truncation functors for certain weight profiles in the setting of motivic sheaves as an application we construct a canonical motivic analogue of the intersection complex for an arbitrary threefold over any field k we are also able to recover certain invariants of singularities motivically

peak sidelobe level reduction with a hybrid approach based on gas and difference sets this paper presents an approach for the optimization of the beam pattern produced by massively thinned arrays the method which combines the most attractive features of a genetic algorithm and those of a combinatorial technique namely the difference sets method is aimed at synthesizing massively thinned antenna arrays in order to suitably reduce the peak sidelobe level selected numerical results are presented in order to assess the effectiveness and reliability of the proposed approach

electromagnetic inverse scattering of multiple two dimensional perfectly conducting objects by the differential evolution strategy electromagnetic inverse scattering of multiple two dimensional 2 d perfectly conducting objects with transverse magnetic tm wave incidence by the differential evolution strategy des is presented the governing electric field integral equations for the scattering problem are expressed as surface integral over the cylinder contours the cylinder contours are approximately represented by closed cubic b splines local shape functions in local polar coordinate system the inverse problem is to locate the cylinders and to reconstruct their shape with or without a priori knowledge of the number of cylinders it is cast into an optimization problem and is solved using the des both synthetic and real reconstructions are carried out the reconstruction results agree with the true profiles very well comparison with the real coded genetic algorithm has been carried out it has been observed that the des outperforms the real coded genetic algorithm

action of correspondences on filtrations on cohomology and 0 cycles of abelian varieties we prove that given a symmetrically distinguished correspondence of a suitable complex abelian variety which includes any abelian variety of dimension at most 5 powers of complex elliptic curves etc that vanishes as a morphism on a certain quotient of its middle singular cohomology then it vanishes as a morphism on the deepest part of a particular filtration on the chow group of 0 cycles of the abelian variety as a consequence we prove that an automorphism of such an abelian variety that acts as the identity on a certain quotient of its middle singular cohomology acts as the identity on the deepest part of this filtration on the chow group of 0 cycles of the abelian variety as an application we prove that for the generalized kummer variety associated to a complex abelian surface and the automorphism induced from a symplectic automorphism of the complex abelian surface the automorphism of the generalized kummer variety acts as the identity on a certain subgroup of its chow group of 0 cycles

the evolution to a steady state for a porous medium model abstract an initial boundary value problem is considered for a nonlinear diffusion equation the diffusivity being a function of the dependent variable dirichlet boundary conditions independent of time are considered and positive solutions are assumed this paper is mainly concerned with the rate of convergence in time of the unsteady to the steady state this is done by obtaining an upper estimate for a positive definite integral measure of the perturbation i e unsteady steady state using differential inequality techniques a previous result is recalled where the diffusivity k n n being a positive constant appropriate to mass transport or filtration in a porous medium the present paper treats an alternative model sharing some of the characteristics of the previous one k e 1 being non negative the paper concludes by considering a backwards in time initial boundary value problem for the perturbation amenable to the same techniques and establishes that the solution ceases to exist beyond a critical computable time

intermediate extension of chow motives of abelian type abstract in this article we give an unconditional construction of a motivic analogue of the intermediate extension in the context of chow motives of abelian type our main application concerns intermediate extensions of chow motives associated to kuga families to the baily borel compactification of a shimura variety

asymptotic behavior of the nonlinear diffusion equation nt n 1nx x the asymptotic behavior of the equation nt ln n xx is studied on the finite interval 0 x 1 with the boundary conditions n 0 t n 1 t n0 and initial data n x 0 n0 we prove that asymptotically ln n x t n0 a exp 2t n0 21 2 sin x and also provide rigorous upper and lower bounds on the asymptotic amplitude a in terms of integrals of nonlinear functions of the initial data the rigorous bounds are compared to values of a obtained from computer experiments the lower bound l 23 2 exp li 1 q where li is the logarithmic integral is euler s constant and q 2 f n x 0 n0 1 sin x dx is found to be the best known estimate of a

optimization of the difference patterns for monopulse antennas by a hybrid real integer coded differential evolution method the optimization of difference patterns of monopulse antennas is considered the synthesis problem is recast as an optimization problem by defining a suitable cost function in particular in this paper the cost function is based on constraints on the side lobe levels a subarray configuration is adopted and the excitations of the difference pattern are approximately determined the optimization problem is efficiently solved by a differential evolution algorithm which is able to contemporarily handle real and integer unknowns numerical results are reported concerning classical array configurations previously considered in the literature

chow groups are finite dimensional in some sense when s is a surface with pg s 0 mumford proved that its chow group a s is not finite dimensional in some sense in this paper we propose another definition of finite dimensionality for the chow groups using this new definition at least the chow group of some surface s with pg s 0 for example the product of two curves becomes finite dimensional the finite dimensionality of the chow groups follows from the finite dimensionality of the chow motives it turns out that the finite dimensionality of the chow motives is a very strong property for example we can prove bloch s conjecture representability of the chow groups of surfaces with pg s 0 under the assumption that the chow motive of s is finite dimensional

linear aperiodic array synthesis using an improved genetic algorithm a novel algorithm on beam pattern synthesis for linear aperiodic arrays with arbitrary geometrical configuration is presented in this paper linear aperiodic arrays are attractive for their advantages on higher spatial resolution and lower sidelobe however the advantages are attained at the cost of solving a complex non linear optimization problem in this paper we explain the improved genetic algorithm iga that simultaneously adjusts the weight coefficients and inter sensor spacings of a linear aperiodic array in more details and extend the investigations to include the effects of mutual coupling and the sensitivity of the peak sidelobe level psl to steering angles numerical results show that the psl of the synthesized beam pattern has been successfully lowered with the iga when compared with other techniques published in the literature in addition the computational cost of our algorithm can be as low as 10 of that of a recently reported genetic algorithm based synthesis method the excellent performance of iga makes it a promising optimization algorithm where expensive cost functions are involved