l 1 stability estimates for n x n conservation laws let u t f u x 0 be a strictly hyperbolic n times n system of conservation laws each characteristic field being linearly degenerate or genuinely nonlinear in this paper we explicitly define a functional phi phi u v equivalent to the l 1 distance which is almost decreasing i e phi big u t v t big phi big u s v s big leq o ve cdot t s quad hbox for all t s geq 0 for every pair of e approximate solutions u v with small total variation generated by a wave front tracking algorithm the small parameter e here controls the errors in the wave speeds the maximum size of rarefaction fronts and the total strength of all non physical waves in u and in v from the above estimate it follows that front tracking approximations converge to a unique limit solution depending lipschitz continuously on the initial data in the vec l 1 norm this provides a new proof of the existence of the standard riemann semigroup generated by a n n system of conservation laws

high frequency green s function for planar periodic phased arrays with skewed grid and polygonal contour the derivation of an uniform high frequency asymptotic representation of the array green s function agf for finite planar periodic phased arrays with arbitrary polygonal contour and skewed grid is presented this result generalizes those obtained in a series of recent papers in the case of rectangular phased arrays with rectangular grid for the treatment of the high frequency phenomena the actual finite array is rigorously decomposed in terms of canonical constituents i e infinite semi infinite and sectoral arrays the final result is a representation of the agf in terms of spatially truncated floquet waves fws and fw induced diffracted fields arising from the edges and vertices of the polygonal rim of the array consequently the number of field contributions necessary to reconstruct the total field is independent of the number of elements of the array leading to a very efficient algorithm a series of numerical results is provided to demonstrate the effectiveness of the high frequency representation

electromagnetic analysis of large scale periodic arrays using a two level cbfs method accelerated with fmm fft to realize efficient analysis of large scale planar periodic arrays a two level characteristic basis functions method accelerated with fast multipole method fast fourier transform fmm fft is developed in this paper the characteristic basis functions cbfs for each element are constructed in a two level framework in which the cbfs construction based on plane wave derivation for single element at child level and the cbfs construction based on local interaction between array elements at father level are combined the number of unknowns is reduced significantly by the two level cbfs further fmm fft is applied to expedite the computation of interaction between elements numerical results of large scale planar periodic arrays are given to demonstrate the validity and efficiency of the present method

l 1 stability of the boltzmann equation for the hard sphere model we study the l1 stability of classical solutions to the boltzmann equation for a hard sphere model when initial datum is a small perturbation of a vacuum and tends to zero exponentially fast at infinity in the phase space for this we introduce nonlinear functionals measuring potential interactions between particles with different velocities and l1 distance between classical solutions we use pointwise estimates for a solution and the gain term of a collision operator to control the time evolution of nonlinear functionals

acceleration of fast multipole method for large scale periodic structures with finite sizes using sub entire domain basis functions an acceleration technique to the fast multipole method fmm has been proposed to handle large scale problems of periodic structures in free space with finite sizes based on the accurate sub entire domain basis functions in the proposed algorithm only nine or 27 elements in the whole impedance matrix are required to be computed and stored for a two dimensional or three dimensional periodic structure and the matrix vector multiply can be performed efficiently using the combination of fast fourier transform and fmm the theoretical analysis and numerical results show that both the memory requirement and computational complexity are only of the order of o n with small constants where n is the total number of unknowns

asymptotic behavior of one dimensional discrete velocity models in a slab we prove results on the asymptotic behavior of solutions to discrete velocity models of the boltzmann equation in the one dimensional slab 0 x 1 with general stochastic boundary conditions at x 0 and x 1 assuming that there is a constant wall maxwellian m mi compatible with the boundary conditions and under a technical assumption meaning strong thermalization at the boundaries we prove three types of results i if no velocity has x component 0 there are real valued functions 1 t and 2 t such that in a measure theoretic sense fi 0 t 1 t m i fi 1 t 2 t mi as t 1 and 2 are closely related and satisfy functional equations which suggest that 1 t 1 and 2 t 1 as t ii under the additional assumption that there is at least one non trivial collision term containing a product f k f l with k l where k denotes the x component of the velocity associated with f k we show that in a measure theoretic sense 1 t and 2 t converge to 1 as t this entails l1 convergence of the solution to the unique wall maxwellian for this result k l 0 is admissible iii in the absence of any collision terms but under the assumption that there is an irrational quotient i j l k here i l 0 and j k 0 renewal theory entails that the solution converges to the unique wall maxwellian in l

electromagnetic scattering by finite periodic arrays using the characteristic basis function and adaptive integral methods we introduce a novel technique that combines the aim algorithm with the characteristic basis function method cbfm to solve the problem of electromagnetic scattering by large but finite periodic arrays an important advantage of using the cbfm for this problem is that we only need to analyze a single unit cell to construct the characteristic basis functions cbfs for the entire array the cbfs are generated by illuminating a single unit cell with a plane wave incident from different angles for both the and polarizations the initial set of cbfs generated in the manner described above are then downselected by applying a singular value decomposition svd procedure and retaining only the left singular vectors whose corresponding singular values fall above a threshold next in the conventional cbfm we derive a reduced matrix by applying the galerkin procedure and solve it directly if its size is manageable however when solving an array problem which precludes the direct solve option we can utilize the adaptive integral method aim algorithm detailed below not only to accelerate the solution but to reduce memory requirements as well numerical examples are included in this communication to demonstrate the accuracy and the numerical efficiency of the proposed technique

lyapunov functionals and l 1 stability for discrete velocity boltzmann equations we devise lyapunov functionals and prove uniform l 1 stability for one dimensional semilinear hyperbolic systems with quadratic nonlinear source terms these systems encompass a class of discrete velocity models for the boltzmann equation the lyapunov functional is equivalent to the l 1 distance between two weak solutions and non increasing in time they result from computations of two point interactions in the phase space for certain models with only transversal collisional terms there exist generalizations for three and multi point interactions

well posedness theory for hyperbolic conservation laws the paper presents a well posedness theory for the initial value problem for a general system of hyperbolic conservation laws we will start with the refinement of glimm s existence theory and discuss the principle of nonlinear through wave tracing our main goal is to introduce a nonlinear functional for two solutions with the property that it is equivalent to the l1 x distance between the two solutions and is time decreasing moreover the functional is constructed explicitly in terms of the wave patterns of the solutions through the nonlinear superposition it consists of a linear term measuring the l1 x distance a quadratic term measuring the coupling of waves and distance and a generalized entropy functional 1999 john wiley sons inc

the optimal trilinear restriction estimate for a class of hypersurfaces with curvature abstract in 4 nearly optimal l 1 trilinear restriction estimates in r n 1 are established under transversality assumptions only in this paper we show that the curvature improves the range of exponents by establishing l p estimates for any p 2 n 4 3 n 2 in the case of double conic surfaces the exponent 2 n 4 3 n 2 is shown to be the universal threshold for the trilinear estimate

a complete set of linear phase basis functions for scatterers with flat faces and for planar apertures entire domain basis functions are introduced for the analysis of scattering from bodies with flat portions and of radiation from planar apertures they are defined via the application of the sampling theorem of shannon these basis functions are particularly convenient for polygonal contours however arbitrary contours can be treated in the same framework with a very minor pre processing time a non redundant set of basis functions is determined a priori by explicit approximate formulas either for currents and for radiated field numerical results are presented to shown the accuracy of the method

l 1 stability of multi dimensional discrete velocity boltzmann equations we study the l 1 stability of multi dimensional discrete velocity boltzmann equations under suitable smallness assumption on initial data we show that bounded mild solutions are l 1 stable for a stability estimate we employ bony s multi dimensional analysis for total interactions over characteristic planes

time domain green s function for an infinite sequentially excited periodic planar array of dipoles the present paper is a continuation of previous explorations by the authors aimed at gaining a basic understanding of the time domain td behavior of large periodic phased i e sequentially turned on array antennas and related configurations our systematic investigation of the relevant canonical td dipole excited green s functions has so far included those for infinite and truncated sequentially pulsed line periodic arrays parameterized in terms of radiating propagating and nonradiating evanescent conical td floquet waves fw and truncation induced td fw modulated tip diffractions the present contribution extends these investigations to an infinite periodic sequentially pulsed planar array which generates pulsed plane propagating and evanescent fw starting from the familiar frequency domain fd transformation of the linearly phased element by element summation synthesis into summations of propagating and evanescent fws we access the time domain by fourier inversion the inversion integrals are manipulated in a unified fashion into exact closed forms which are parameterized by the single nondimensional quantity spl eta c v sup p sub u1 where v sup p sub u1 and c are the excitation phase speed along a preferred phasing direction u sub 1 in the array plane and the ambient wave speed respectively the present study deals with the practically relevant rapidly phased propagating case spl eta 1 regime for a future manuscript numerical reference data generated via element by element summation over the fields radiated by the individual dipoles with ultrawide band limited excitation are compared with results obtained much more efficiently by inclusion of a few td fws physical interpretation of the formal td fw solutions is obtained by recourse to asymptotics instantaneous frequencies and wavenumbers and related constructs of special interest is the demonstration that the td fws emerge along equal delay ellipses from the array plane this furnishes a novel and physically appealing interpretation of the planar array td fw phenomenology

frequency domain green s function for a planar periodic semi infinite phased array i truncated floquet wave formulation this two part sequence deals with the derivation and physical interpretation of a uniform high frequency solution for the field radiated at finite distance by a planar semi infinite phased array of parallel elementary electric dipoles the field obtained by direct summation over the contributions from the individual radiators is restructured into a double series of wavenumber spectral integrals whose asymptotic reduction yields a series encompassing propagating and evanescent floquet waves fws together with corresponding diffracted rays which arise from scattering of the fw at the edge of the array the formal aspects of the solution are treated in the present paper they involve a sequence of manipulations in the complex spectral wavenumber planes that prepare the integrands for subsequent efficient and physically incisive asymptotics based on the method of steepest descent different species of spectral poles define the various species of propagating and evanescent fw their interception by the steepest descent path sdp determines the variety of shadow boundaries for the edge truncated fw the uniform asymptotic reduction of the sdp integrals performed by the van der waerden 1951 procedure and yielding a variety of edge diffracted fields completes the formal treatment

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

efficient analysis of phased arrays of microstrip patches using a hybrid generalized forward backward method green s function technique with a dft based acceleration algorithm a hybrid method based on the combination of generalized forward backward method gfbm and green s function for the grounded dielectric slab together with the acceleration of the combination via a discrete fourier transform dft based algorithm is developed for the efficient and accurate analysis of electromagnetic radiation scattering from electrically large irregularly contoured two dimensional arrays consisting of finite number of probe fed microstrip patches in this method unknown current coefficients corresponding to a single patch are first solved by a conventional galerkin type hybrid method of moments mom green s function technique that uses the grounded dielectric slab s green s function because the current distribution on the microstrip patch can be expanded using an arbitrary number of subsectional basis functions the patch can have any shape the solution for the array currents is then found through gfbm where it sweeps the current computation element by element the computational complexity of this method which is originally being the total number of unknowns for each iteration is reduced to using a dft based acceleration algorithm making use of the fact that array elements are identical and the array is periodic numerical results in the form of array current distribution are given for various sized arrays of probe fed microstrip patches with elliptical and or circular boundaries and are compared with the conventional mom results to illustrate the efficiency and accuracy of the method

application of numerical regularization options to the integral equation analysis of printed antennas in this letter a novel numerical technique is applied to the analysis of printed antennas the technique transforms the first kind electric field integral equation efie into a regularized second kind equation via extraction of two singular frequency independent operators and their numerical inversion two options are presented in which the inversion is based on the eigenfunctions of these singular operators that appear to be a generalization of the tm and te modes of a magnetic wall cavity coupled by the edge singularities the example of application shows favorable convergence properties

discrete velocity models of the boltzmann equation a survey on the mathematical aspects of the theory discrete velocity models of the boltzmann equation are of considerable conceptual interest in the kinetic theory of gases and at the same time a fascinating mathematical subject the last decade has seen a lot of work on this subject which is reviewed here we put an emphasis on mathematical aspects in particular the global existence question qualitative properties of solutions explicit solutions and the fluid dynamical limit the mechanical background is discussed more concisely in part i numerous contributions concerning other questions are outlined we try to give a complete reference list up to and including 1985

global strong solution to a nonlinear dirac type equation in one dimension abstract this paper studies a class of nonlinear massless dirac equations in one dimension which include the equations for the massless thirring model and the massless gross neveu model under the assumptions of the initial data having small charge and being bounded the global existence of the strong solution is established the decay of the local charge is also proved

a truncated floquet wave diffraction method for the full wave analysis of large phased arrays ii generalization to 3 d cases for pt i see ibid vol 48 no 3 p 594 600 2000 this paper deals with the generalization to three dimensional 3 d arrays of the truncated floquet wave tfw diffraction method for the full wave analysis of large arrays this generalization potentially includes arrays consisting of microstrip excited slots cavity backed apertures and patches the formulation is carried out first by deriving an appropriate fringe integral equation ie and next by defining entire domain basis functions in terms of global array functions shaped as tfw diffracted rays whose analytical expression is derived on the basis of prototype canonical problems the efficiency and the accuracy of this method is demonstrated by comparison with the results of an element by element full wave approach for a rectangular slot array

l 1 continuous dependence property for systems of conservation laws this paper is concerned with the uniqueness and l 1 continuous dependence of entropy solutions for nonlinear hyperbolic systems of conservation laws

on the erdős distinct distances problem in the plane in this paper we prove that a set of n points in r 2 has at least c n log n distinct distances thus obtaining the sharp exponent in a problem of erd os we follow the setup of elekes and sharir which in the spirit of the erlangen program allows us to study the problem in the group of rigid motions of the plane this converts the problem to one of point line incidences in space we introduce two new ideas in our proof in order to control points where many lines are incident we create a cell decomposition using the polynomial ham sandwich theorem this creates a dichotomy either most of the points are in the interiors of the cells in which case we immediately get sharp results or alternatively the points lie on the walls of the cells in which case they are in the zero set of a polynomial of suprisingly low degree and we may apply the algebraic method in order to control points incident to only two lines we use the ecnode polynomial of the rev george salmon to conclude that most of the lines lie on a ruled surface then we use the geometry of ruled surfaces to complete the proof

asymptotic high frequency green s function for a large rectangular planar periodic phased array of dipoles with weakly tapered excitation in two dimensions this paper deals with the derivation and physical interpretation of a uniform high frequency representation of the green s function for a large planar rectangular phased array of dipoles with weakly varying excitation thereby our earlier published results valid for equiamplitude excitation and those for tapered illumination in one dimension are extended to tapering along both dimensions including dipole amplitudes tending to zero at the edges as previously the field obtained by direct summation over the contributions from the individual radiators is restructured into a double spectral integral whose high frequency asymptotic reduction yields a series of propagating and evanescent floquet waves fws together with corresponding fw modulated diffracted fields which arise from fw scattering at the array edges and vertexes to accommodate the weak amplitude tapering new generalized periodicity modulated edge and vertex slope transition functions are introduced accompanied by a systematic procedure for their numerical evaluation special attention is given to the analysis and physical interpretation of the complex vertex diffracted ray fields a sample calculation is included to demonstrate the accuracy of the asymptotic algorithm the resulting array green s function forms the basic building block for the full wave analysis of planar weakly amplitude tapered phased array antennas and for the description of electromagnetic radiation and scattering from weakly amplitude tapered rectangular periodic structures

global solution to nonlinear dirac equation for gross neveu model in 1 1 dimensions abstract this paper studies a class of nonlinear dirac equations with cubic terms in r 1 1 which include the equations for the massive thirring model and the massive gross neveu model under the assumption that the initial data has bounded l 2 norm the global existence and the uniqueness of the strong solution in c 0 l 2 r 1 are proved

nonlinear functionals of multi d discrete velocity boltzmann equations in this paper we study nonlinear functionals measuring potential interactions and l1 distance between two mild solutions for the multi dimensional discrete velocity boltzmann equations when the initial data are a small perturbation of a vacuum we employ bony s dispersion estimates to show that these functionals satisfy lyapunov type estimates which are useful for the study of time asymptotics and l1 stability of mild solutions

truncated floquet wave full wave analysis of large phased arrays of open ended waveguides with a nonuniform amplitude excitation recently an efficient hybrid asymptotic method of moments mom approach has been proposed for the analysis of large periodic planar arrays of elements excited with equal amplitude and linear phase the aforementioned method which is based on a floquet wave diffraction representation of the array green s function agf is here extended to treat arrays with tapered amplitude excitation to this end the asymptotic agf is refined by introducing additional slope diffraction contributions an appropriate fringe integral equation solved via a mom scheme provides the effects of array truncation in addition to the infinite array solution the dimension of the corresponding linear algebraic system is independent of the number of elements of the array numerical results are provided to prove the accuracy and the efficiency of this method with respect to an ordinary element by element mom

a hybrid spectral spatial method to evaluate the active green s function of large planar rectangular arrays a combined asymptotic numerical algorithm the article illustrates a formulation to evaluate the array green s function agf of large finite planar phased array for observation points on the array plane possibly close to the array contour the procedure is based on the agf representation in terms of a double spectral integral whose integration paths are properly deformed to have an exponential attenuation of the integrand the diffraction integral is evaluated numerically for point close to the array edges while an asymptotic treatment is proposed far from the edges this latter comprises higher order contributions thanks to the convergence properties the final algorithm is numerically accurate stable and more efficient with respect to the individual element summation for large arrays it also constitutes the basic step for the efficient evaluation of the agf of a multilayer environment

a truncated floquet wave diffraction method for the full wave analysis of large phased arrays i basic principles and 2 d cases this two part sequence deals with the formulation of an efficient method for the full wave analysis of large phased array antennas this is based on the method of moments mom solution of a fringe integral equation ie in which the unknown function is the difference between the exact solution of the finite array and that of the associated infinite array the unknown currents can be interpreted as produced by the field diffracted at the array edge which is excited by the floquet waves fws pertinent to the infinite configuration following this physical interpretation the unknown in the ie is efficiently represented by a very small number of basis functions with domain on the entire array aperture in order to illustrate the basic concepts the first part of this sequence deals with the two dimensional example of a linearly phased slit array it is shown that the dominant phenomenon fur describing the current perturbation with respect to the infinite array is accurately represented in most cases by only three diffracted ray shaped unknown functions this also permits a simple interpretation of the element by element current oscillation which was described by other authors

fast analysis of large antenna arrays using the characteristic basis function method and the adaptive cross approximation algorithm the characteristic basis function method cbfm has been hybridized with the adaptive cross approximation aca algorithm to construct a reduced matrix equation in a time efficient manner and to solve electrically large antenna array problems in core with a solve time orders of magnitude less than those in the conventional methods various numerical examples are presented that demonstrate that the proposed method has a very good accuracy computational efficiency and reduced memory storage requirement specifically we analyze large 1 d and 2 d arrays of electrically interconnected tapered slot antennas tsas the entire computational domain is subdivided into many smaller subdomains each of which supports a set of characteristic basis functions cbfs we also present a novel scheme for generating the cbfs that do not conform to the edge condition at the truncated edge of each subdomain and provide a minor overlap between the cbfs in adjacent subdomains as a result the cbfs preserve the continuity of the surface current across the subdomain interfaces thereby circumventing the need to use separate ldquoconnectionrdquo basis functions

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

restriction estimates using polynomial partitioning ii we improve the estimates in the restriction problem in dimension n geqslant 4 to do so we establish a weak version of a k linear restriction estimate for any k the exponents in this weak k linear estimate are sharp for all k and n

accelerated computation of the free space green s function gradient of infinite phased arrays of dipoles in this communication we provide an efficient algorithm for the evaluation of the semi infinite array green s function sagf for a semi infinite planar periodic phased array of dipoles in free space for observation points not too far from the array plane the algorithm uses a hybrid spectral spatial representation of the green s function accelerated with the levin t method that we show to be faster than the shanks method for observation points sufficiently far away from the array plane we show that the sagf is efficiently evaluated by using asymptotic field expressions asymptotics is also used to explain the loss of accuracy of the levin t accelerator in certain regions and a correction procedure is proposed to overcome this problem

truncated floquet wave full wave t fw sup 2 analysis of large periodic arrays of rectangular waveguides a new hybrid technique has been recently proposed for the analysis of large periodic arrays this method is based on a high frequency representation of the active green s function of a finite array involving a floquet wave fw expansion with the relevant edge and vertex diffracted ray fields originating at the array border using this representation the unknown current of an appropriate fringe integral equation is expanded in terms of a few basis functions shaped as fw induced diffracted rays this representation drastically reduces the numerical effort and provides a physical insight into the mechanism of the array truncation in this paper this method is applied to the analysis of large arrays of rectangular waveguides opened on an infinite ground plane numerical results are shown to demonstrate the effectiveness and the numerical efficiency of the method

implementation of a forward backward procedure for the fast analysis of electromagnetic radiation scattering from two dimensional large phased arrays forward backward method fbm was successfully developed for the analysis of electromagnetic radiation scattering from one dimensional 1 d phased array in an efficiency appealing fashion the fbm applications to treat 2 d array problems are developed in this paper acceleration algorithm performing better than the novel spectrum acceleration algorithm used for 1 d fbm computation is also developed for this 2 d fbm so the unique advantages of high efficiency and o n sub tot computational complexity as in the 1 d problems can be retained where n sub tot is the total number of array element numerical examples are presented to demonstrate its validity

large time behavior of discrete velocity boltzmann equations we study the asymptotic behavior of equations representing one dimensional motions in a fictitious gas with a discrete set of velocities the solutions considered have finite mass but arbitrary amplitude with certain assumptions every solution approaches a state in which each component is a traveling wave without interaction the techniques are similar to those in an earlier treatment of the broadwell model 1

initial boundary value problem for nonlinear dirac equation of gross neveu type in 1 1 dimensions abstract this paper studies an initial boundary value problem for a class of nonlinear dirac equations with cubic terms which include the equations for the massive thirring model and the massive gross neveu model under the assumptions that the initial data has bounded l 2 norm and the boundary satisfies suitable conditions the global existence and the uniqueness of the strong solution are proved

global weak solutions of the boltzmann equation in a slab with diffusive boundary conditions it is proved that under a physically realistic truncation of the collision kernel the boltzmann equation in the one dimensional slab 0 1 with general diffusive boundary conditions at 0 and 1 has a global weak solution in the traditional sense this solution satisfies the boundary conditions almost everywhere and has at worst exponentially growing total energy

a fast impedance and pattern computation scheme for finite antenna arrays a fast numerical method well suited to the analysis of moderate size arrays made of complex elements is presented it combines macro basis functions and multipole approaches without an iterative procedure this method is exploited to estimate the impedance matrix and active element patterns for the latter an efficient formulation is provided as a series of pattern multiplication problems examples are shown for arrays of broadband dipoles the computational gain obtained for the reduction of the original method of moments system of equations is briefly described

analysis of large complex structures with the synthetic functions approach an innovative procedure is presented that allows the method of moments mom analysis of large and complex antenna and scattering problems at a reduced memory and cpu cost bounded within the resources provided by a standard 32 bit personal computer the method is based on the separation of the overall geometry into smaller portions called blocks and on the degrees of freedom of the field the blocks need not be electrically unconnected on each block basis functions are generated with support on the entire block that are subsequently used as basis functions for the analysis of the complete structure only a small number of these functions is required to obtain an accurate solution therefore the overall number of unknowns is drastically reduced with consequent impact on storage and solution time these entire domain basis functions are called synthetic functions they are generated from the solution of the electromagnetic problem for the block in isolation under excitation by suitably defined sources the synthetic functions are obtained from the responses to all sources via a procedure based on the singular value decomposition because of the strong reduction of the global number of unknowns one can store the mom matrix and afford a direct solution the method is kernel free and can be implemented on existing mom codes

nonlinear functionals of the boltzmann equation and uniform stability estimates abstract we present nonlinear functionals measuring physical space variation and l 1 distance between two classical solutions for the boltzmann equation with a cut off inverse power potential in the case that initial datum is a small smooth perturbation of vacuum and decays fast enough in the phase space we show that these functionals satisfy stability estimates which lead to bv type estimates and a uniform l 1 stability