analysis of bodies of revolution composed of conductors and dielectrics using only electric equivalent currents application to small horns with dielectric core a system of integral equations sie based on the uniqueness theorem that uses only electric equivalent currents is formulated to analyze problems composed of conductors and dielectrics this sie is solved using the moment method in its formulation for bodies of revolution for several short dielectric rod antennas radiation patterns were measured to test the sie formulation excellent agreement between measured and calculated values was obtained

hilbert space compression and exactness of discrete groups we show that the hilbert space compression of any unbounded finite dimensional cat 0 cube complex is 1 and deduce that any finitely generated group acting properly co compactly on a cat 0 cube complex is exact and hence has yu s property a the class of groups covered by this theorem includes free groups finitely generated coxeter groups finitely generated right angled artin groups finitely presented groups satisfying the b 4 t 4 small cancellation condition and all those word hyperbolic groups satisfying the b 6 condition another family of examples is provided by certain canonical surgeries defined by link diagrams

the cone of diffusions on finitely ramified fractals abstract like brownian motion on r d one would like to identify a natural unique diffusion on a fractal equivalently we look for abstract dirichlet integrals local regular irreducible symmetric dirichlet forms on strongly connected finitely ramified self similar fractals these forms have to be self similar in the sense that they scale by a fixed constant when the fractal is scaled by one of its defining contractions two necessary and sufficient uniqueness criteria are derived in the case of ambiguity we describe the shape and the location of the cone of self similar dirichlet forms technically we analyze a superlinear renormalization map which is non expansive with respect to hilbert s projective metric h it contracts h distances by irreducibility or super additivity

coarsely embeddable metric spaces without property a abstract we study guoliang yu s property a and construct metric spaces which do not satisfy property a but embed coarsely into the hilbert space

an efficient method for the analysis of a structure comprising an appendage attached to a planar surface of a conducting body a technique is presented to efficiently solve for the currents on an appendage e g antenna attached to a planar surface of a conducting body the appendage may be embedded in a homogeneous dielectric material the technique presented alleviates the complications associated with the point where the appendage is attached to the body to illustrate the method a wire antenna attached to an axisymmetric body is analyzed in detail a set of coupled integral equations are formulated appropriate quantities are expanded into fourier modes and coupled integral equations are derived for the fourier coefficients of the unknowns these equations are solved and the input admittance of the wire antenna is determined from the computed currents and is corroborated by measurements

robust use of supplementary conditions for moment method solution near internal resonances a robust and efficient general method is presented for stabilizing moment method calculations using supplemental information this method is then applied to the problem of exterior calculations using the electric field integral equation and the magnetic field integral equation for closed conducting bodies at frequencies near those of interior resonances a large number of well known techniques provide supplemental information thus this paper shows how the information in each of these may be used more efficiently in the sense of a smaller operation count the mathematical method used here is the modified truncated singular value decomposition which is both numerically stable and describes whether the supplemental conditions used are sufficient to allow an accurate solution of the integral equation the surface currents associated with the nearly resonant interior mode s are explicitly computed by this method

the short cut test abstract the short cut test detects existence and uniqueness of laplacians on finitely ramified graph directed fractals previous results by sabot nussbaum and the author are improved and extended it opens up the way for further studies because it combines well established spectral dynamical and analytic techniques its algorithmic and recursive structure is designed to provide computable and flexible criteria

a method for treating junctions between bodies of revolution and arbitrary surfaces a method to treat junctions between bodies of revolution bor and arbitrary surfaces is presented the method is applicable to formulations employing the method of moments to solve surface integral equations for structures consisting of combined bor and arbitrary surfaces harmonic entire domain basis functions are used on the bodies of revolution and triangular surface patches are used on the arbitrary surfaces a junction is formed by creating a spatially coincident region between a body of revolution and an arbitrary surface the geometry of the junction region is determined by the arrangement of the triangular surface patches used to form the junction it determines the accuracy with which the junction currents are modeled numerical results are presented to demonstrate the accuracy of the junction models for both radiation pattern and input impedance predictions

on delay independent stability of a class of nonlinear positive time delay systems we present a condition for delay independent stability of a class of nonlinear positive systems this result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

modal characteristic basis function method for solving scattering from multiple conducting bodies of revolution the analysis of scattering from multiple bodies of revolution bors has important applications in microwave remote sensing radar imaging and other areas for single bor three dimensional problem can be degenerated into 2 5 dimensional problem based on the modal green functions mgfs reducing the solving time and storage remarkably however it is difficult to extend the mgf to multiple arbitrarily orientated bors this paper presents a modal characteristic basis function method for solving the scattering from multiple bors it combines the mgf of bor with the characteristic basis function method named as the bor cbf method here the mgf of bor is first applied to efficiently solve the current distribution on the surface of each bor the singular value decomposition is then used to construct the global modal characteristic basis functions mcbfs for each bor finally the mcbfs are transformed into the rwg basis functions using a basis function mapping technique so that the filling of the interaction matrix can be accelerated by the multilevel fast multipole algorithm by using the bor cbf method the scattering of multiple arbitrarily orientated bors can be solved efficiently numerical results are presented to demonstrate the accuracy and efficiency of the bor cbf method

relative stability for ascending and positively homogeneous operators on banach spaces abstract for a closed convex cone k in a real banach space with a norm increasing on k and a selfmapping t of k which is continuous positively homogeneous and ascending it is shown that the nonlinear eigenvalue problem tx x has a unique solution x k 0 up to a scalar r which is relatively stable in the sense that for a suitable function c of k into r formula moreover an estimate for the speed of convergence is given

a spectral integral method for smooth multilayered bodies of revolution a spectral integral method sim is developed to solve the scattering problem from smooth multilayered bodies of revolution bors this sim is a spectral method to improve the accuracy and efficiency of the sim by the fast fourier transform fft algorithm this method can achieve high accuracy and greatly reduce the computational time consumption in our bor sim the bor generatrix current is expanded by the truncated fourier series then the impedance matrix is generated in the spectral domain to solve the scattering problem unlike the conventional methods that need eight to ten segments per wavelength in the bor sim two points per wavelength are adequate to achieve high accuracy according to the nyquist theorem being accelerated by fft this method shows a significant efficiency advantage over the conventional bor method numerical results demonstrate the accuracy and efficiency of our new method by combining with the poggio miller chang harrington wu tsai surface integral equations this method can be used to solve many practical scattering problems

concave perron frobenius theory and applications many important results of classical perron frobenius theory can be extended from linear selfmappings of the standard cone in finite dimensional real space to concave selfmappings of this cone this is in particular true for minima of linear mappings albeit the spectrum of these special concave mappings is more intricate than that for linear mappings as classical perron frobenius theory has numerous applications there are many new applications for its concave extension 1991 mathematical subject classification primary 39a11 15a48 secondary 47h07 47h12

isoperimetric inequalities and markov chains soit a i j i j n la matrice stochastique d une chaine de markov reversible sur n 1 2 soit n 2 tel que f r c f d f c 0 n ou r 2n n 2 ou c 0 est independant de f et ou r indique la norme dans l r n d pour la mesure i i alors on a sup i j j 1 a i j 0 n 2

combined field integral equation formulation for inhomogeneous two and three dimensional bodies the junction problem a combined field integral equation cfie formulation is presented for two and three dimensional bodies having discrete dielectric and conducting regions a three dimensional case is restricted to bodies of revolution bors the two dimensional case is analogous to the bor case when the fourier mode number is zero the method of moments mm is used to solve the cfie in terms of two integral operators it is shown that the cfie formulation yields accurate answers for scattering problems where the scatterer may be internally resonant the cfie results were validated using mie series results and measured data the junction problem associated with the cfie based formulation is explicated and several geometries with multiple junctions are used to validate the general cfie formulation a number of configurations are tested where the penetrable region consisted of a free space coating extensive numerical studies have shown that such limiting cases are sensitive indicators of the stability of mm solutions and allow direct comparison of different configurations

a comparison between two kinds of equivalent currents to analyze conducting bodies with apertures using moment methods application to horns with symmetry of revolution a system of integral equations sie based on the unique hess theorem that uses only electric equivalent currents eec is formulated to analyze conducting bodies with apertures this sie is compared with an sie that uses both electric and magnetic equivalent currents emec in general to solve both sie s numerically difficult computations of cauchy principal value integrals with highly singular kernels are required these integrals appear when computing electric magnetic fields created by magnetic electric currents their evaluation can be avoided using the eec approach in many practical cases when the main interest is in the radiation patterns of aperture antennas the two sie s are compared by carrying out an analysis of rotationally symmetric horns using the moment method mm in its formulation for bodies of revolution numerical results of electric currents and radiation patterns are presented for small horns of various geometries these results compare quite well with measurements for both sie s however the central processing unit cpu time for the eec formulation is an order of magnitude smaller than for the emec formulation

calculation of the field radiated by horn antennas using the mode matching method methods employed for evaluating fields radiated by horn antennas like the aperture field method and the spherical wave expansion have not taken into account the contribution by fields existing outside the horn aperture e g along the outer walls of the horn the use of the mode matching technique for analyzing the transition from horn antenna to free space makes it possible to include in the analysis even those fields which exist outside e g behind the horn aperture when determining the far as well as the near field furthermore the effects of the finite wall thickness and the discontinuity caused by the transition from waveguide to free space are also taken into account a suitable development of the fields at the transition of the conical corrugated horn to free space using the mode matching technique is presented two different convergence diagrams depending on the kind of modes excited in the horn antenna are given they show the results from extensive convergence investigations with the help of these diagrams a reliable evaluation of the fields radiated by horn antennas is guaranteed practical measurements of the fields radiated by horn antennas confirm the field distributions gained through analysis

stability and positivity of equilibria for subhomogeneous cooperative systems building on recent work on homogeneous cooperative systems we extend results concerning stability of such systems to subhomogeneous systems we also consider subhomogeneous cooperative systems with constant input and relate the global asymptotic stability of the unforced system to the existence and stability of positive equilibria for the system with input

maximizing sum rate and minimizing mse on multiuser downlink optimality fast algorithms and equivalence via max min sinr maximizing the minimum weighted signal to interference and noise ratio sinr minimizing the weighted sum mean square error mse and maximizing the weighted sum rate in a multiuser downlink system are three important performance objectives in nonconvex joint transceiver and power optimization where all the users have a total power constraint we show that through connections with the nonlinear perron frobenius theory jointly optimizing power and beamformers in the max min weighted sinr problem can be solved optimally in a distributed fashion then connecting these three performance objectives through the arithmetic geometric mean inequality and nonnegative matrix theory we solve the weighted sum mse minimization and the weighted sum rate maximization in the weak interference regimes using fast algorithms in the general case we first establish optimality conditions to the weighted sum mse minimization and the weighted sum rate maximization problems and provide their further connection to the max min weighted sinr problem we then propose a distributed weighted proportional sinr algorithm that leverages our fast max min weighted sinr algorithm to solve for local optimal solution of the two nonconvex problems and give conditions under which global optimality is achieved numerical results are provided to complement the analysis

a nonlinear extension of the birkhoff jentzsch theorem abstract the birkhoff jentzsch theorem for linear positive operators is extended to a certain class of nonlinear positive operators these so called p ascending operators include concave operators and suprema of such operators for the underlying positive cone to be complete for hilbert s metric a necessary and sufficient condition is given from which various criteria for completeness are derived the extension made yields in particular a concave version of jentzsch s theorem

an affine eigenvalue problem on the nonnegative orthant in this paper we consider the conditional affine eigenvalue problem lambda x ax b lambda is an element of r x 0 parallel to x parallel to 1 where a is an n x n nonnegative matrix b a nonnegative vector and parallel to center dot parallel to a monotone vector norm under suitable hypotheses we prove the existence and uniqueness of the solution lambda x and give its expression as the perron root and vector of a matrix a bc t where c has a maximizing property depending on the considered norm the equation x ax b parallel to ax b parallel to has then a unique nonnegative solution given by the unique perron vector of a bc t c 2005 elsevier inc all rights reserved

electromagnetic radiation from structures consisting of combined body of revolution and arbitrary surfaces a formulation is developed to treat radiation from structures consisting of a body of revolution bor in the presence of multiple arbitrarily shaped three dimensional objects an electric field integral equation is set up on the surface of the combined structure the resulting integro differential equation is solved using the method of moments on the bor harmonic entire domain expansion functions are used for the circumferential dependence while overlapping subdomain functions are used to model the axial curvature the arbitrarily shaped portions of the structure are modeled using triangular surface patches the resulting system matrix has a partial block diagonal nature which provides a more economical solution for structures that have some rational symmetry numerical results are presented and compared to measurements of a unique cavity backed patch fed antenna

max min sinr coordinated multipoint downlink transmission duality and algorithms this paper considers the max min weighted signal to interference plus noise ratio sinr problem subject to multiple weighted sum power constraints where the weights can represent relative power costs of serving different users first we study the power control problem we apply nonlinear perron frobenius theory to derive closed form expressions for the optimal value and solution and an iterative algorithm which converges geometrically fast to the optimal solution then we use the structure of the closed form solution to show that the problem can be decoupled into subproblems each involving only one power constraint next we study the multiple input single output miso transmit beamforming and power control problem we use uplink downlink duality to show that this problem can be decoupled into subproblems each involving only one power constraint we apply this decoupling result to derive an iterative subgradient projection algorithm for the problem

multifractal analysis of some multiple ergodic averages in this paper we study the multiple ergodic averages on the symbolic space m 0 1 m 1 n where m 2 l 2 q 2 are integers we give a complete solution to the problem of multifractal analysis of the limit of the above multiple ergodic averages actually we develop a non invariant and non linear version of thermodynamic formalism that is of its own interest we study a large class of measures called telescopic product measures the special case of telescopic product measures defined by the fixed points of some non linear transfer operators plays a crucial role in studying the level sets of the limit which are not shift invariant these measures share many properties with gibbs measures in the classical thermodynamic formalism our work also concerns variational principle pressure function and legendre transform in this new setting less

computation of the scattering from inhomogeneous objects with a discrete rotational symmetry and a nonsymmetric part using a specific solver for circulant matrices can reduce the cost of computing the scattering from a discrete rotational symmetric object by up to several orders of magnitude a solver is developed for symmetric objects with a nonsymmetrical part such as an antenna on a body of revolution this solver has been implemented in a finite element code based upon a hybrid formulation the hybrid formulation combines integral equations and partial differential equations it can handle inhomogeneous anisotropic objects of arbitrary shape results on inhomogeneous objects with defects are shown the solver can also be used to perform a parametric study of the defects

isoperimetry of group actions the isoperimetric profile of a discrete group was introduced by vershik however it is well defined only for a restrictive class amenable groups we generalize the notion of isoperimetric profile beyond the world of amenable groups by defining isoperimetric profiles of amenable actions of finitely generated groups on compact topological spaces this allows to extend the definition of the isoperimetric profile to all groups which are exact in such a way that for amenable groups it is equal to vershik s isoperimetric profile the main feature of our construction is that it preserves many of the properties known from the classical case we use these results to compute exact asymptotics of the isoperimetric profiles for several classes of non amenable groups

uniform non amenability abstract for any finitely generated group g an invariant fol g 0 is introduced which measures the amount of non amenability of g if g is amenable then fol g 0 if fol g 0 we call g uniformly non amenable we study the basic properties of this invariant for example its behaviour when passing to subgroups and quotients of g we prove that the following classes of groups are uniformly non amenable non abelian free groups non elementary word hyperbolic groups large groups free burnside groups of large enough odd exponent and groups acting acylindrically on a tree uniform non amenability implies uniform exponential growth we also exhibit a family of non amenable groups in particular including all non solvable baumslag solitar groups which are not uniformly non amenable that is they satisfy fol g 0 finally we derive a relation between our uniform folner constant and the uniform kazhdan constant with respect to the left regular representation of g

body of revolution phi flip matrix and bor patch system matrix optimization a new phi flip unit matrix is introduced into the body of revolution bor system matrix theory which aides in the development of negative mode expressions for the impedance admittance voltage current and row matrices a demonstration of the phi hip matrix provides a succinct proof of existing results for scattered fields using positive modes the bor patch system matrix equation and its solution are then presented using the phi flip matrix to optimize the partition solution it is shown that the z sub effective matrix is symmetric and may be computed using positive modes and that the row r sub effective measurement matrix may be obtained directly from the transpose of the v sub effective excitation column matrix for this work the entire polarization scattering matrix is the goal since the optimizations introduced operate better at this level of formulation

embedding of hyperbolic groups into products of binary trees we show that every gromov hyperbolic group admits a quasi isometric embedding into the product of n 1 binary trees where n dim is the topological dimension of the boundary at infinity of

uniqueness of the fixed point of nonexpansive semidifferentiable maps we consider semidifferentiable possibly nonsmooth maps acting on a subset of a banach space that are nonexpansive either in the norm of the space or in the hilbert s or thompson s metric inherited from a convex cone we show that the global uniqueness of the fixed point of the map as well as the geometric convergence of every orbit to this fixed point can be inferred from the semidifferential of the map at this point in particular we show that the geometric convergence rate of the orbits to the fixed point can be bounded in terms of bonsall s non linear spectral radius of the semidifferential we derive similar results concerning the uniqueness of the eigenline and the geometric convergence of the orbits to it in the case of positively homogeneous maps acting on the interior of a cone or of additively homogeneous maps acting on an am space with unit this is motivated in particular by the analysis of dynamic programming operators shapley operators of zero sum stochastic games

aperiodic tilings positive scalar curvature and amenability of spaces the object of this paper is to begin a geometric study of noncompact spaces whose local structure has bounded complexity manifolds of this sort arise as leaves of foliations of compact manifolds and as their universal covers we shall introduce a coarse homology theory using chains of bounded complexity and study some of its first properties the most interesting result characterizes when h uf x vanishes as an analogue and strengthening of f0lner s amenability criterion for groups in terms of isoperimetric inequalities see 4 one can view this result as producing a successful infinite ponzi scheme on any nonamenable space each point with only finite resources gives to some of its neighbors some of these resources yet receives more from the remaining neighbors as one can imagine this is useful for eliminating obstructions on noncompact spaces this has a number of applications we present two of them the first produces tilings that are unbalanced on any nonamenable polyhedron unbalanced tilings are automatically aperiodic and this gives many examples of sets of tiles that tile only aperiodically unfortunately imbalance is a particularly unsubtle reason for aperiodicity so that the aperiodic tilings of euclidean space penrose tilings are necessarily not accessible to our method on the other hand most other simply connected noncompact symmetric spaces even have unbalanced tilings using our criterion the second application regards characteristic numbers of manifolds whose universal covers have positive scalar curvature we prove a converse to a theorem of roe we show that for any nonamenable group f one can find a spin manifold with fundamental group f with nonzero a genus whose universal cover has a uniformly positive scalar curvature metric of bounded geometry in the natural strict quasi isometry class

on exactness and isoperimetric profiles of discrete groups abstract we introduce a quasi isometry invariant related to property a and explore its connections to various other invariants of finitely generated groups this allows to establish a direct relation between asymptotic dimension on one hand and isoperimetry and random walks on the other we apply these results to reprove sharp estimates on isoperimetric profiles of some groups and to answer some questions in dimension theory

integral equation analysis of dielectric and conducting bodies of revolution in the presence of arbitrary surfaces a formulation is developed to treat radiation from structures consisting of conducting and or dielectric bodies of revolution bor in the presence of multiple arbitrary shaped three dimensional objects a set of integral equations is developed on the surfaces of the combined structure and the resulting integro differential equations are solved using the method of moments on the bor harmonic entire domain expansion functions are used for the circumferential dependence while overlapping sub domain functions are used to model axial curvature the arbitrary shaped portions of the structure are modeled using triangular surface patch basis functions the resulting matrix has a partial block diagonal nature which provides a more economical solution for structures which have some rotational symmetry the accuracy of the bor and arbitrary surface formulation is verified using the self consistency method and measured data

a unified analysis of max min weighted sinr for mimo downlink system this paper studies the max min weighted signal to interference plus noise ratio sinr problem in the multiple input multiple output mimo downlink where multiple users are weighted according to priority and are subject to a weighted sum power constraint first we study the multiple input single output miso and single input multiple output simo problems using nonlinear perron frobenius theory as a by product we solve the open problem of convergence for a previously proposed miso algorithm by wiesel eldar and shamai in 2006 furthermore we unify our analysis with respect to the previous alternate optimization algorithm proposed by tan chiang and srikant in 2009 by showing that our miso result can in fact be derived from their algorithm next we combine our miso and simo results into an algorithm for the mimo problem we show that our proposed algorithm is optimal when the channels are rank one or when the network is operating in the low signal to noise ratio snr region finally we prove the parametric continuity of the mimo problem in the power constraint and we use this insight to propose a heuristic initialization strategy for improving the performance of our generally suboptimal mimo algorithm the proposed initialization strategy exhibits improved performance over random initialization

input impedance of wire antennas attached on axis to conducting bodies of revolution moment method calculations are presented for the input impedance of wire antennas attached on axis to a conducting body of revolution bor of arbitrary geometry the study of the wire antenna is carried out using integral equations of both reduced and exact kernel the analysis of the bor takes advantage of the symmetry of revolution that allows the expansion of the current in fourier series which takes advantage of the mode orthogonality and reduces the computer time required results for current distribution and input impedance are obtained for several structures such as vertical and nonvertical monopoles over circular ground planes and conical bodies measurements of impedance are presented to check numerical results these are also compared with results of other methods

amenability and exactness for dynamical systems and their c algebras we study the relations between amenability resp amenability at infinity of c dynamical systems and equality or nuclearity resp exactness of the corresponding crossed products

robust shrinkage estimation of high dimensional covariance matrices we address high dimensional covariance estimation for elliptical distributed samples which are also known as spherically invariant random vectors sirv or compound gaussian processes specifically we consider shrinkage methods that are suitable for high dimensional problems with a small number of samples large p small n we start from a classical robust covariance estimator tyler 1987 which is distribution free within the family of elliptical distribution but inapplicable when n p using a shrinkage coefficient we regularize tyler s fixed point iterations we prove that for all n and p the proposed fixed point iterations converge to a unique limit regardless of the initial condition next we propose a simple closed form and data dependent choice for the shrinkage coefficient which is based on a minimum mean squared error framework simulations demonstrate that the proposed method achieves low estimation error and is robust to heavy tailed samples finally as a real world application we demonstrate the performance of the proposed technique in the context of activity intrusion detection using a wireless sensor network

scattering from complex bodies using a combined direct and iterative technique an iterative technique is developed for frequency domain plane wave scattering from electrically large composite bodies an electric field integral equation efie formulation is employed in which the submatrices of the moment method matrix are uncoupled and the current on each geometrically separable region of the composite body is solved independently using a direct method the currents on the various subcomponents of the body are then recalculated within an outer iterative loop the technique is applied to the case of a multiwavelength body of revolution bor with two flat plate attachments this composite body iterative technique is shown to preserve the simplicity and attractiveness of an isolated bor while maintaining current continuity across the structure without the use of additional junction currents this new formulation also allows simple suppression of interior resonance effects normally associated with large closed conducting bodies

a nonlinear transfer operator theorem in recent papers kenyon et al ergod theory dyn syst 32 1567 1584 2012 and fan et al c r math acad sci paris 349 961 964 2011 adv math 295 271 333 2016 introduced a form of non linear thermodynamic formalism based on solutions to a non linear equation using matrices in this note we consider the more general setting of holder continuous functions

survey of numerical methods for solution of large systems of linear equations for electromagnetic field problems many of the popular methods for the solution of large matrix equations are surveyed with the hope of finding an efficient method suitable for both electromagnetic scattering and radiation problems and system identification problems

a simple technique for solving e field integral equations for conducting bodies at internal resonances a simple but effective method is presented to analyze electromagnetic radiation and scattering from condueting bodies at frequencies corresponding to internal resonances of a cavity of the same shape the advantage of this technique is that it requires only the e field integral equation and hot both e field and h field as required by the combined fields formulation it is shown theoretically that this method produces a solution with minimum norm and converges monotonically as the order of the approximation is increased the minimum norm solution for the current density given by the e field integral equation is not the correct current density as there is a portion of the resonant current that exists on the body however the minimum norm solution indeed provides the true scattering fields this technique may also be utilized for obtaining a minimum norm solution for nearly singular and singular matrix equations examples are presented to illustrate the application of this technique

nonlinear perron frobenius theory in finite dimensions abstract a nonlinear perron frobenius theory in finite dimensions is described which applies to positively homogeneous and increasing maps sufficient conditions for the existence and uniqueness of eigenvectors in the interior of a cone are developed even when eigenvectors at the boundary of the cone exist several ways to benefit from nonlinearities are pointed out in order to show that the classical linear theory truly deserves nonlinear generalization the main technical novelties are a link between collatz wielandt numbers and g teaux derivatives and the almost one dimensional dynamics of the nonlinear map

max min weighted downlink sinr with uplink sinr constraints for full duplex mimo systems in this paper we investigate a max min weighted signal to interference plus noise ratio sinr problem in a full duplex multiuser multiple input multiple output system where a full duplex capable base station bs equipped with multiple antennas communicates with multiple half duplex downlink and uplink users under the same system resources specifically we consider a practical scenario where the downlink minimum weighted sinr is maximized under specific sinr constraints for uplink users moreover the optimization is conducted by jointly considering the bs transmit power the transmit power of uplink users and bs transmit and receive beamforming this optimization problem is therefore subject to multiple uplink sinr constraints and multiple transmit power constraints due to the sinr constraints negative matrix components arise and hence the optimization problem cannot be directly solved by the standard approach i e perron frobenius theory we have provided an explicit iterative scheme to solve this joint optimization problem with a strict proof the proposed algorithm is proved to converge to karush kuhn tucker points simulation results show that our proposed algorithm has a fast convergence rate and leads to a better performance compared with other optimization techniques that do not jointly consider all parameters

the novikov conjecture for groups with finite asymptotic dimension recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology page 28 14 more precisely the asymptotic dimension for a metric space is the smallest integer n such that for any r 0 there exists a uniformly bounded cover c ui iei of the metric space for which the r multiplicity of c is at most n 1 i e no ball of radius r in the metric space intersects more than n 1 members of c 14 the class of finitely generated discrete groups with finite asymptotic dimension is hereditary in the sense that if a finitely generated group has finite asymptotic dimension as metric space with a word length metric then its finitely generated subgroups also have finite asymptotic dimension as metric spaces with word length metrics cf section 6 this together with a result of gromov in 14 implies that finitely generated subgroups of gromov s hyperbolic groups have finite asymptotic dimension currently no example of a finitely generated group with infinite asymptotic dimension and finite classifying space is known it should also be noted that two different definitions of asymptotic dimension