numerical analysis of conservative and entropy schemes for the fokker planck landau equation conservatives and entropy schemes for the fokker planck landau fpl equation are studied we prove the existence of a unique positive and global in time solution for the homogeneous linear and nonlinear discretized either in the velocity space or both in the velocity space and in time fpl equation the stability analysis of these schemes leads to sufficient conditions on the time step that guarantee positivity and entropy decay

multipole expansions for the fokker planck landau operator we give a sequence of operators approximating the fokker planck landau collision operator this sequence is obtained by aplying the fast multipole method based on the work by greengard and rokhlin 17 and tends to the exact fokker planck landau operator with an arbitrary accuracy these operators satisfy the physical properties such as the conservation of mass momentum energy and the decay of the entropy furthermore the quadratic structure due to the velocity coupling in the expression of the fokker planck landau operator is removed in the approximating operators this fact reduces seriously the computationnal cost of numerical simulations of the fokker planck landau equation finally we give numerical conservative and entropy discretizations solving the homogeneous fokker planck landau equation using the fast multipole method in addition to the deterministic character of these approximations they give satisfactory results in terms of accuracy and cpu time

long time convergence of the bose einstein condensation we study long time behavior of the bose einstein condensation of measure valued solutions f t of the space homogeneous and velocity isotropic boltzmann equation for bose einstein particles at low temperature we prove that if f 0 ge 0 is a non singular borel measure on mathbb r ge 0 satisfying a very low temperature condition and that the ratio f 0 0 varepsilon varepsilon alpha is sufficiently large for all varepsilon in 0 r for some constants 0 0 then there exists a solution f t of the equation on 0 infty with the initial datum f 0 such that f t 0 converges to the expected bose einstein condensation as t rightarrow infty we also show that such initial data f 0 exist extensively

fast conservative and entropic numerical methods for the boson boltzmann equation in this paper we derive accurate numerical methods for the quantum boltzmann equation for a gas of interacting bosons the schemes preserve the main physical features of the continuous problem namely conservation of mass and energy the entropy inequality and generalized bose einstein distributions as steady states these properties are essential in order to develop schemes that are able to capture the energy concentration behavior of bosons in addition we develop fast algorithms for the numerical evaluation of the resulting quadrature formulas which allow the final schemes to be computed only in o n2 log 2n operations instead of o n3

the boltzmann equation for bose einstein particles regularity and condensation we study regularity and finite time condensation of distributional solutions of the space homogeneous and velocity isotropic boltzmann equation for bose einstein particles for the hard sphere model global in time existence of distributional solutions had been proven before here we prove that the equation is locally and can be globally in time well posed for the class of distributional solutions having finite moment of the negative order 1 2 and solutions in this class with regular initial data are mild solutions in their regularity time intervals by observing a necessary condition on the initial data for the absence of condensation at some finite time we also propose a sufficient condition on the initial data for the occurrence of condensation at all large time and then using a positivity of a partial collision integral we prove further that the critical time of condensation can be strictly positive

numerical algorithms for axisymmetric fokker planck landau operators we establish a simplified form of the axisymmetric fokker planck landau operator in doing so we derive a weak formulation of this operator on which we get directly the conservation properties and the decay of the entropy as it is the case for the three dimensional operator a symmetrized version of this formulation leads to a class of numerical schemes which satisfy these physical properties at the discrete level fast numerical algorithms used in previous works are shown to be efficient in the cylindrical geometry finally some numerical tests are presented at the end of this paper

windowed green function method for layered media scattering this paper introduces a new windowed green function wgf method for the numerical integral equation solution of problems of electromagnetic scattering by obstacles in the presence of dielectric or conducting half planes the wgf method which is based on the use of smooth windowing functions and integral kernels that can be expressed directly in terms of the free space green function does not require evaluation of expensive sommerfeld integrals the proposed approach is fast accurate flexible and easy to implement in particular straightforward modifications of existing accelerated or unaccelerated integral equation solvers suffice to incorporate the wgf capability the method relies on a certain integral equation posed on the union of the boundary of the obstacle and a small flat section of the interface between the penetrable media our analysis and numerical experiments demonstrate that both the near and far field errors resulting from the proposed approach decrease faster than any negative power of the window size in the examples considered in this paper the proposed method is up to thousands of times faster for a given accuracy than a corresponding method based on use of sommerfeld integrals

a maxwellian lower bound for solutions to the boltzmann equation we prove that the solution of the spatially homogeneous boltzmann equation is bounded pointwise from below by a maxwellian i e a function of the formc1 exp c2v2 this holds for any initial data with bounded mass energy and entropy and for any positive timet t0 the constantsc1 andc2 depend on the mass energy and entropy of the initial data and ont0 0 only

a fast volume integral equation solver for electromagnetic scattering from large inhomogeneous objects in planarly layered media a newly developed iterative method the stabilized biconjugate gradient fast fourier transform bcgs fft method is applied to simulate electromagnetic scattering from large inhomogeneous objects embedded in a planarly layered medium in this fast solver the weak form formulation is applied to obtain a less singular discretization of the volume electric field integral equation several techniques are utilized to speed up the dyadic green s function evaluation to accelerate the operation of the dyadic green s function on an induced current i e the green s operation the green s function is split into convolutional and correlational components so that fft can be applied the cpu time and memory cost of this bcgs fft method is o nlogn and o n respectively where n is the number of unknowns significantly more efficient than the method of moments mom as a result this method is capable of solving large scale electromagnetic scattering problems in a planarly layered background a large scale scattering problem in a layered medium with more than three million unknowns has been solved on a sun ultra 60 workstation with 1 2 gbytes memory

well posedness for the spatially homogeneous landau fermi dirac equation for hard potentials we study the cauchy problem for the spatially homogeneous landau equation for fermi dirac particles in the case of hard and maxwellian potentials we establish existence and uniqueness of a weak solution for a large class of initial data

novel all pass factorization all solutions to rational matrix equation and control application for an arbitrary rational matrix rm a new descriptor realization of its all pass factorization is presented the coefficients of the factors are expressed explicitly in the solution of a linear matrix inequality which is well known in control theory using the all pass factorization necessary and sufficient conditions for existence of a solution of an equation with rms where the unknown rm has its poles in the left closed complex half plane and it can be improper are presented as well as all solutions as an application of the latter result the notion of almost disturbance decoupling i e when the infimum of the mathscr h infty norm of the transfer matrix from the disturbance input to the controlled output over the stabilizing controllers is zero is generalized the generalization is such that instead of the whole frequency axis the frequency axis with excluded intervals of small lengths is considered the controller consists of output feedback plus disturbance feedforward designed independently a necessary and sufficient solvability condition is presented which is expressed in terms of the given data the three main results are illustrated by an example

fast elliptic solvers in cylindrical coordinates and the coulomb collision operator in this paper we describe a new class of fast solvers for separable elliptic partial differential equations in cylindrical coordinates r q z with free space radiation conditions by combining integral equation methods in the radial variable r with fourier methods in q and z we show that high order accuracy can be achieved in both the governing potential and its derivatives a weak singularity arises in the fourier transform with respect to z that is handled with special purpose quadratures we show how these solvers can be applied to the evaluation of the coulomb collision operator in kinetic models of ionized gases

the h control problem with zeros on the boundary of the stability domain in this paper we study the discrete and continuous time h control problems without any assumptions on the system parameters our approach yields necessary and sufficient conditions for the existence of a suitable controller

rank conditions on the multiple view matrix geometric relationships governing multiple images of points and lines and associated algorithms have been studied to a large extent separately in multiple view geometry the previous studies led to a characterization based on multilinear constraints which have been extensively used for structure and motion recovery feature matching and image transfer in this paper we present a universal rank condition on the so called multiple view matrix m for arbitrarily combined point and line features across multiple views the condition gives rise to a complete set of constraints among multiple images all previously known multilinear constraints become simple instantiations of the new condition in particular the relationship between bilinear trilinear and quadrilinear constraints can be clearly revealed from this new approach the theory enables us to carry out global geometric analysis for multiple images as well as systematically characterize all degenerate configurations without breaking image sequence into pairwise or triple wise sets of views this global treatment allows us to utilize all incidence conditions governing all features in all images simultaneously for a consistent recovery of motion and structure from multiple views in particular a rank based multiple view factorization algorithm for motion and structure recovery is derived from the rank condition simulation results are presented to validate the multiple view matrix based approach

optimal boundary interpolation and one block optimal control problem with invariant zeros on the imaginary axis and infinity we formulate a matrix interpolation problem with existing interpolation points on the imaginary axis and infinity and existing equal left and right interpolation points using the concept of parametrisation of stabilising controllers then we solve the problem of obtaining all its solutions if interpolation points at infinity are absent we show that the introduced problem is equivalent to the existing one we apply this result to solve the problem of optimal interpolation with existent interpolation points on the imaginary axis and infinity we show by an example that the solution of optimal interpolation is directly applicable to the one block optimal control with existent invariant zeros on the imaginary axis and infinity it is seen from the example that not only the transfer matrix of the closed loop system is constrained on the extended imaginary axis but also its derivatives

on general ℋ2 control from frequency to time domain this article presents a general formula for discrete time 2 control it works with the regular and singular case of 2 control i e in the case of possibly non left invertible matrices g 12 and non right invertible matrices g 21 with possible unit circle invariant zeros in the generic case it can be simplified and adapted to work with the plant transfer matrix directly without invoking the matrices of the parameterisation of stabilising controllers a further result of this article is the presented necessary and sufficient conditions for state space 2 control under only stabilisability and detectability assumptions if the conditions are satisfied an observer based 2 controller is constructed the corresponding numerical algorithm consists of solving two discrete time algebraic riccati systems darss and two eigen problems

accurate calculation of green s function of the schrodinger equation in a block layered potential in this paper a new algorithm is presented for calculating the green s function of the schrodinger equation in the presence of block layered potentials such green s functions have various and practical applications in quantum modelling of electron transport within nano mosfet transistors the proposed method is based on expansions of the eigenfunctions of the subordinate sturm liouville problems and a collocation matching procedure along possibly curved interfaces of the potential blocks accurate numerical results are provided to validate the proposed algorithm

spectral methods for the non cut off boltzmann equation and numerical grazing collision limit in this paper we study the numerical passage from the spatially homogeneous boltzmann equation without cut off to the fokker planck landau equation in the so called grazing collision limit to this aim we derive a fourier spectral method for the non cut off boltzmann equation in the spirit of 21 23 we show that the kernel modes that define the spectral method have the correct grazing collision limit providing a consistent spectral method for the limiting fokker planck landau equation in particular for small values of the scattering angle we derive an approximate formula for the kernel modes of the non cut off boltzmann equation which similarly to the fokker planck landau case can be computed with a fast algorithm the uniform spectral accuracy of the method with respect to the grazing collision parameter is also proved

new results and application of singular control we reconsider the singular control problem with marginal stability of the closed loop system when the transfer matrix from the input to the output can have linearly dependent columns and zeros on the extended imaginary axis we present a new theoretical existence result and a new numerical algorithm based on finding an orthogonal transformation of the matrix pencil associated to the euler lagrange differential equations into a block triangular form we present an application in linear quadratic control of descriptor systems under the constraints of physical realizability of the control and impulse free and marginally stable closed loop system

windowed green function method for the helmholtz equation in the presence of multiply layered media this paper presents a new methodology for the solution of problems of two and three dimensional acoustic scattering and in particular two dimensional electromagnetic scattering by obstacles and defects in the presence of an arbitrary number of penetrable layers relying on the use of certain slow rise windowing functions the proposed windowed green function approach efficiently evaluates oscillatory integrals over unbounded domains with high accuracy without recourse to the highly expensive sommerfeld integrals that have typically been used to account for the effect of underlying planar multilayer structures the proposed methodology whose theoretical basis was presented in the recent contribution bruno et al 2016 siam j appl math 76 1871 1898 doi 10 1137 15m1033782 is fast accurate flexible and easy to implement our numerical experiments demonstrate that the numerical errors resulting from the proposed approach decrease faster than any negative power of the window size in a number of examples considered in this paper the proposed method is up to thousands of times faster for a given accuracy than corresponding methods based on the use of sommerfeld integrals

all solutions of a bitangential interpolation problem that includes boundary points all solutions of a matrix interpolation problem with purely imaginary interpolation points are given by a descriptor system realization if necessary and sufficient conditions are satisfied the first step is to reduce the interpolation problem to a minimal realization no assumptions are needed in the paper

a numerical method for the accurate solution of the fokker planck landau equation in the nonhomogeneous case abstract a new approach for the accurate numerical solution of the fokker planck landau fpl equation in the nonhomogeneous case is presented the method couples through a time splitting algorithm a finite volume scheme for the transport with a fast spectral solver for the efficient solution of the collision operator recently introduced the scheme allows the use of different grids in the velocity space for the transport and the collision phases the use of a suitable explicit runge kutta solver for the time integration of the collision phase permits avoid once of excessive small time steps induced by the stiffness of the diffusive collision operator numerical results for both space homogeneous and space nonhomogeneous situations show the efficiency and the accuracy of the present method

conservation of energy entropy identity and local stability for the spatially homogeneous boltzmann equation for nonsoft potential collision kernels with angular cutoff we prove that under the initial condition f0 v 1 v 2 logf0 v l1 r3 the classical formal entropy identity holds for all nonnegative solutions of the spatially homogeneous boltzmann equation in the class l 0 l12 r3 c1 0 l1 r3 where l1s r3 f f v 1 v 2 s 2 l1 r3 and in this class the nonincrease of energy always implies the conservation of energy and therefore the solutions obtained all conserve energy moreover for hard potentials and the hard sphere model a local stability result for conservative solutions i e satisfying the conservation of mass momentum and energy is obtained as an application of the local stability a sufficient and necessary condition on the initial data f0 such that the conservative solutions f belong to l1loc 0 l12 r3 is also given

simplified formula for a controller in optimal control problems we derive a simplified frequency domain formula for a controller transfer matrix for lq optimal output feedback control of stochastic systems for this purpose we apply a generalization of the wiener hopf method the generalization is characterized by the following three properties 1 we generalize the usual operator cdot on rational matrices in the traditional wiener hopf approach the same algorithms as for computation of cdot are applicable to compute the new operator 2 the matrices of the youla kuccera parametrization do not appear in the optimal controller transfer matrix bf c they appear only in its derivation even if the plant is unstable 3 unlike the traditional wiener hopf method d c youla h a jabr and j j bongiorno jr ieee trans automat control ac 21 1976 pp 319 338 where the spectral factors in the two spectral factorizations are both stable and minimum phase our spectral factors need to be minimum phase only finally three state space applications of the formula are presented

a newly developed formulation suitable for matrix manipulation of layered medium green s functions based on a recently developed formulation of the dyadic green s function for layered media dglm this work gives the matrix element representation of the dglm for general rwg basis functions including basis functions straddling across different layers and half rwg basis function attached to an infinite ground plane it has been rigorously proved that this representation is absent of any undesired line integrals the same as the popular michalski zheng s formulation of type c this work also gives the analytical solution for some typical cylindrically symmetric problems which can be used to validate any formulation for layered medium problems

implicit schemes for the fokker planck landau equation we propose time implicit schemes to solve the homogeneous fokker planck landau equation in both the isotropic and 3 dimensional geometries these schemes have properties of conservation and entropy moreover they allow for large time steps making them faster than the usual explicit schemes to solve the involved linear systems we prove that the use of krylov like solvers preserves the conservation properties we show in particular that the conjugate gradient method can be used numerical tests are performed for the isotropic case and demonstrate an important gain in terms of cpu time with the same accuracy as explicit schemes this work is a first step to the development of fast implicit schemes to solve a class of inhomogeneous kinetic equations

algorithms for optimal control with invariant zeros on the extended imaginary axis abstract we transform an control problem with invariant zeros on the extended imaginary axis into a regular problem then using the nevanlinna pick theorem we find necessary and sufficient existence conditions for the original control problem an algorithm and examples with invariant zeros on the extended imaginary axis are given by the same approach we also solve the singular 2 control problem

optimization criteria and geometric algorithms for motion and structure estimation prevailing efforts to study the standard formulation of motion and structure recovery have recently been focused on issues of sensitivity and robustness of existing techniques while many cogent observations have been made and verified experimentally many statements do not hold in general settings and make a comparison of existing techniques difficult with an ultimate goal of clarifying these issues we study the main aspects of motion and structure recovery the choice of objective function optimization techniques and sensitivity and robustness issues in the presence of noise we clearly reveal the relationship among different objective functions such as normalized epipolar constraints reprojection error or triangulation all of which can be unified in a new optimal triangulation procedure regardless of various choices of the objective function the optimization problems all inherit the same unknown parameter space the so called essential manifold based on recent developments of optimization techniques on riemannian manifolds in particular on stiefel or grassmann manifolds we propose a riemannian newton algorithm to solve the motion and structure recovery problem making use of the natural differential geometric structure of the essential manifold we provide a clear account of sensitivity and robustness of the proposed linear and nonlinear optimization techniques and study the analytical and practical equivalence of different objective functions the geometric characterization of critical points and the simulation results clarify the difference between the effect of bas relief ambiguity rotation and translation confounding and other types of local minima this leads to consistent interpretations of simulation results over a large range of signal to noise ratio and variety of configurations

entropy production estimates for boltzmann equations with physically realistic collision kernels we establish strict entropy production bounds for the boltzmann equation with the hard sphere collision kernel using these entropy production bounds we prove results asserting that the rate at which strongl 1 convergence to equilibrium occurs is uniform in wide classes of initial data this extends our previous results in this direction which applied only to a very special collision kernel moreover the present results provide computable lower bounds compactness arguments are entirely avoided the uniformity is an important ingredient in our study of scaling limits of solutions of the non spatially homogeneous boltzmann equation and is the main focus of this paper however the results obtained here provide the only framework known to us in which one can obtain computable estimates on the time it takes a solution of the spatially homogeneous boltzmann equation with initial data far from equilibrium to reach any given small strongl 1 neighborhood of equilibrium

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

taylor expansion based fast multipole method for 3 d helmholtz equations in layered media abstract in this paper we develop a taylor expansion te based fast multipole method fmm for low frequency 3d helmholtz green s function in layered media two forms of taylor expansions with either non symmetric or symmetric derivatives of layered media green s functions are used for the implementations of the proposed te fmm in the implementation with non symmetric derivatives an algorithm based on discrete complex image approximations and recurrence formulas is shown to be very efficient and accurate in computing the high order derivatives meanwhile the implementation based on symmetric derivatives is more robust and pre computed tables for the high order derivatives in translation operators are used numerical tests in layered media have validated the accuracy and o n complexity of the proposed algorithms

a fast algorithm for the energy space boson boltzmann collision operator abstract this paper introduces a fast algorithm for the energy space boson boltzmann collision operator compared to the direct o n3 calculation and the previous o n2 logn method markowich and pareschi 2005 the new algorithm runs in complexity o n log n which is optimal up to a logarithmic factor n is the number of grid points in energy space the basic idea is to partition the 3 d summation domain recursively into elementary shapes so that the summation within each shape becomes a special double convolution that can be computed efficiently by the fast fourier transform numerical examples are presented to illustrate the efficiency and accuracy of the proposed algorithm

global existence of solutions of the boltzmann equation for bose einstein particles with anisotropic initial data abstract in this paper we prove the global in time existence and uniqueness of solutions of the spatially homogeneous boltzmann equation for bose einstein particles for the hard sphere model for bounded anisotropic initial data the main idea of our proof is as follows we first establish an intermediate equation which is closely related to the original equation and is relatively easily proven to have global in time and unique solutions then we use the multi step iterations of the collision gain operator to obtain a desired uniform l bound for solutions of the intermediate equation so that if an initial datum is sufficiently small relative to the inverse of the planck constant which belongs to the case of very high temperature then the corresponding solution of the intermediate equation becomes the solution of the original equation

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

fast calculations of dyadic green s functions for electromagnetic scattering in a multilayered medium abstract in this paper we introduce a novel acceleration method for the calculation of dyadic green s functions for the mixed potential integral equation formulation of electromagnetic scattering of scatterers embedded in a multilayered medium numerical results are provided to demonstrate the efficiency and accuracy of the proposed method

fast multipole method for multivariable integrals we give a fast numerical algorithm to evaluate a class of multivariable integrals a direct numerical evaluation of these integrals costs n m where m is the number of variables and n is the number of the quadrature points for each variable for m 2 and m 3 and for only one dimensional variables we present an algorithm which is able to reduce this cost from n m to a cost of the order of o log epsilon mu m n where epsilon is the desired accuracy and mu m is a constant that depends only on m then we make some comments about possible extensions of such algorithms to number of variables m geq 4 and to higher dimensions this recursive algorithm can be viewed as an extension of fast multipole methods to situations where the interactions between particles are more complex than the standard case of binary interactions numerical tests illustrating the efficiency and the limitation of this method are presented

a parallel fast algorithm for computing the helmholtz integral operator in 3 d layered media in this paper we propose a parallel fast algorithm for computing the product of the discretized helmholtz integral operator in layered media and a vector in o n qn z 2n xn ylogn xn y operations here n xn yn z is the number of sources and n q is the number of quadrature points used in the evaluation of the sommerfeld integral in the definition of layered media green s function for problems in thin layer media n z o 1 such a product forms the key step of many iterative solvers such as the krylov subspace based gmres and bicgstab for linear systems arising from the integral equation methods for the helmholtz equations the fast solver is based on two important techniques which reduce the cost of quadrature summations in the sommerfeld contour integral for green s functions in 3 d layered media the first technique is the removal of surface pole effects along the real axis integration contour by identifying the pole locations with a discrete wavelet transform in the second technique we apply a window based high frequency filter to shorten the contour length as a result the integral operator for the 3 d layered media can be efficiently written as a sum of 2 d hankel cylindrical integral operators and the latter can be calculated by either a tree code or a 2 d wideband fast multipole method in a fast manner numerical results show the efficiency and parallelism of the proposed fast algorithm

reduced order controllers for the h control problem with unstable invariant zeros this paper addresses the existence and design methods of reduced order controllers for the h control problem with unstable invariant zeros in the state space realization of the transfer function matrix from the control input to the controlled error or from the exogenous input to the observation output where the realization is induced from a stabilizable and detectable realization of the generalized plant this paper presents a new controller degree bound for the h control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region when the unstable invariant zero exists this paper shows that reduced order controllers with orders strictly less than that of the generalized plant exist if the h control problem is solvable moreover this paper shows that the computational problem of finding the controllers with the new degree bound is convex by providing two linear matrix inequality based design methods algorithms for constructing the reduced order controllers the results developed in this paper are valid both for the continuous and discrete time h control problems

numerical approximation of the spatially homogeneous fokkerplancklandau equation a numerical method is developed for the spatially homogeneous fokkerplancklandau fpl equation for the case of coulomb collisions the equation is put into a form so that finite difference methods for parabolic type pdes can be applied through a transformation of variables the velocity space computation is reduced to a bounded domain and finite differencing is done with a well defined exact boundary condition corresponding to v at infinity for the discretization in time implicit differencing is used an analysis is carried out on the discrete approximation as applied to a linear fpl equation and for the linear equation it is proved that the numerical method is unconditionally stable and convergent computational work is then done that demonstrates the unconditional stability and accuracy of the numerical method for the nonlinear fpl equation

a differential geometric approach to multiple view geometry in spaces of constant curvature based upon an axiomatic formulation of vision system in a general riemannian manifold this paper provides a unified framework for the study of multiple view geometry in three dimensional spaces of constant curvature including euclidean space spherical space and hyperbolic space it is shown that multiple view geometry for euclidean space can be interpreted as a limit case when sectional curvature of a non euclidean space approaches to zero in particular we show that epipolar constraint in the general case is exactly the same as that known for the euclidean space but should be interpreted more generally when being applied to triangulation in non euclidean spaces a special triangulation method is hence introduced using trigonometry laws from absolute geometry based on a common rank condition we give a complete study of constraints among multiple images as well as relationships among all these constraints this idealized geometric framework may potentially extend extant multiple view geometry to the study of astronomical imaging where the effect of space curvature is no longer negligible e g the so called gravitational lensing phenomenon which is currently active study in astronomical physics and cosmology

sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous boltzmann equation we derive a new lower bound for the entropy dissipation associated with the spatially homogeneous boltzmann equation this bound is expressed in terms of the relative entropy with respect to the equilibrium and thus yields a differential inequality which proves convergence towards equilibrium in relative entropy with an explicit rate our result gives a considerable refinement of the analogous estimate by carlen and carvalho 9 10 under very little additional assumptions our proof takes advantage of the structure of boltzmann s collision operator with respect to the tensor product and its links with fokker planck and landau equations several variants are discussed

h control problem with jω axis zeros abstract in this paper we discuss the so called one block h control problem in the case where the plant has j axis including infinity poles and zeros first we derive a necessary and sufficient condition for the h model matching problem to have a solution in the transfer function setting second we give a solvability condition which enables us to check the solvability by i examining matrix norm conditions related to j axis zeros and ii solving two generalized riccati equations finally we extend our result to the standard h problem

mathscr h _ infty control of descriptor systems possessing invariant zeros on the imaginary axis and infinity we present an algorithm for suboptimal mathscr h infty control of descriptor systems possessing invariant zeros on the imaginary axis and infinity it is proved that the algorithm works also in an optimality case the algorithm is illustrated by examples

entropy dissipation and moment production for the boltzmann equation leth f m flog f m dv be the relative entropy off and the maxwellian with the same mass momentum and energy and denote the corresponding entropy dissipation term in the boltzmann equation byd f q f f logf dv an example is presented which shows that d f h f m can be arbitrarily small this example is a sequence of isotropic functions and the estimates are very explicitly given by a simple formula ford which holds for such functions the paper also gives a simplified proof of the so called povzner inequality which is a geometric inequality for the magnitudes of the velocities before and after an elastic collision that inequality is then used to prove that f v v s dt c t wheref is the solution of the spatially homogeneous boltzmann equation herec t is an explicitly given function dependings and the mass energy and entropy of the initial data

h control by state feedback for plants with zeros on the imaginary axis algebraic tests are derived for the suboptimality of some parameter in the h infty optimization problem by state feedback where the finite zero structure of the plant is not restricted as an application of these characterizations a quadratically convergent algorithm for the computation of the optimal value is presented the suboptimality tests are based on new solvability criteria for general algebraic riccati inequalities that are of independent interest

a new technique for the derivation of closed form electromagnetic green s functions for unbounded planar layered media a closed form electromagnetic green s function for unbounded planar layered media is derived in terms of a finite sum of hankel functions the derivation is based on the direct inverse hankel transform of a pole residue representation of the spectral domain form of the green s function such a pole residue form is obtained through the solution of the spectral domain form of the governing green s function equation numerically through a finite difference approximation rather than analytically the proposed methodology can handle any number of layers including the general case where the planar media exhibit arbitrary variation in their electrical properties in the vertical direction the numerical implementation of the proposed methodology is straightforward and robust and does not require any preprocessing of the spectrum of the green s function for the extraction of surface wave poles or its quasi static part the number of terms in the derived closed form expression is chosen adaptively with the distance between source and observation point as parameter the development of the closed form green s function is presented for both vertical and horizontal dipoles its accuracy is verified through a series of numerical examples and comparisons with results from other established methods

a characterization of all solutions to the four block general distance problem all solutions to the four block general distance problem which arises in h infty optimal control are characterized the procedure is to embed the original problem in an all pass matrix which is constructed it is then shown that part of this all pass matrix acts as a generator of all solutions special attention is given to the characterization of all optimal solutions by invoking a new descriptor characterization of all pass transfer functions as an application necessary and sufficient conditions are found for the existence of an h infty optimal controller following that a descriptor representation of all solutions is derived

a reformulation of augmented basic interpolation problem and an application to h control abstract in this paper we present a new formulation of the augmented basic interpolation problem abip with rational matrices in terms of the stability of four rational matrices so that the abip transforms into a purely linear algebraic problem actually the existing interpolation condition given by an integral is replaced by stability of a rational matrix the new condition is applied to the h optimal control of one block plants having imaginary axis invariant zeros a new parameter in the parametrization of h optimal controllers is revealed which is given in terms of the derivative of the closed loop system at the imaginary axis invariant zeros of the plant the h optimal control algorithm is illustrated by an example and compared to the existing algorithms

on spatially homogeneous solutions of a modified boltzmann equation for fermi dirac particles the paper considers a modified spatially homogeneous boltzmann equation for fermi dirac particles bfd we prove that for the bfd equation there are only two classes of equilibria the first ones are fermi dirac distributions the second ones are characteristic functions of the euclidean balls and they can be simply classified in terms of temperatures t 2 5tf and t 2 5tf where tf denotes the fermi temperature in general we show that the l bound 0 f 1 e derived from the equation for solutions implies the temperature inequality t 2 5tf and if t 2 5tf then f trend towards fermi dirac distributions if t 2 5tf then f are the second equilibria in order to study the long time behavior we also prove the conservation of energy and the entropy identity and establish the moment production estimates for hard potentials