rank one property for derivatives of functions with bounded variation when u is a function of bounded variation of the open set r into r du is a measure on which takes values in the space rm n of all m n matrices such that du i j ui xj for every i j with 1 i m 1 j n and we denote by dsu the part of the measure du which is singular with respect to lebesgue measure we recall that the rank of a matrix a rm n is dimension of the space spanned by its columns in r or by its rows in r and in particular the rank of a is one if and only if there exist e r and r with e 6 0 6 0 so that a e i e ai j ei j for all i j cf remark 1 7 when is a measure which takes values in the space rm n and d d denotes the radon nikodym derivative of with respect to the total variation we say that has rank one when the rank of the matrix d d x is one for almost every x in this paper we prove we prove the following statement see theorem 4 5 corollary 4 6 and remark 4 9

the steiglitz mcbride identification algorithm revisited convergence analysis and accuracy aspects the convergence and accuracy properties of the steiglitz and mcbride identification method are examined the analysis is valid for a sufficiently large number of data it is shown that the method can converge to the true parameter vector only when the additive output noise is white in that case the method is proved to be locally convergent to the true parameters the global convergence properties are also investigated it is pointed out that the method is not always globally convergent some sufficient conditions guaranteeing global convergence are given assuming convergence takes place the estimates are shown to be asymptotically gaussian distributed an explicit expression is given for their asymptotic covariance matrix

the finite ei categories of cartan type abstract to each symmetrizable cartan matrix we associate a finite free ei category we prove that the corresponding category algebra is isomorphic to the algebra defined in geiss et al 2017 4 which is associated to another symmetrizable cartan matrix in certain cases the algebra isomorphism provides an algebraic enrichment of the well known correspondence between symmetrizable cartan matrices and graphs with automorphisms

a variational approach for the 2 dimensional semi geostrophic shallow water equations existence of weak solutions to the 3 d semi geostrophic equations with rigid boundaries was proved by benamou and brenier 3 using monge transport theory this paper extends the results to a free surface boundary condition which is more physically appropriate this extension is at present for the 2 d shallow water case only in addition we establish stronger time regularity than was possible in 3

korevaar schoen s directional energy and ambrosio s regular lagrangian flows we develop korevaar schoen s theory of directional energies for metric valued sobolev maps in the case of textsf rcd source spaces to do so we crucially rely on ambrosio s concept of regular lagrangian flow our review of korevaar schoen s spaces brings new even in the smooth category insights on some aspects of the theory in particular concerning the notion of differential of a map along a vector field and about the parallelogram identity for textsf cat 0 targets to achieve these one of the ingredients we use is a new even in the euclidean setting stability result for regular lagrangian flows

cellularity of diagram algebras as twisted semigroup algebras abstract the temperley lieb and brauer algebras and their cyclotomic analogues as well as the partition algebra are all examples of twisted semigroup algebras we prove a general theorem about the cellularity of twisted semigroup algebras of regular semigroups which allows us to easily reproduce the cellularity of these algebras this theorem generalizes a result of east about the cellularity of semigroup algebras of inverse semigroups

steady nearly incompressible vector fields in two dimension chain rule and renormalization given bounded vector field b mathbb r d to mathbb r d scalar field u mathbb r d to mathbb r and a smooth function beta mathbb r to mathbb r we study the characterization of the distribution rm div beta u b in terms of div b and div ub in the case of bv vector fields b and under some further assumptions such characterization was obtained by l ambrosio c de lellis and j mal up to an error term which is a measure concentrated on the so called tangential set of b we answer some questions posed in their paper concerning the properties of this term in particular we construct a nearly incompressible bv vector field b and a bounded function u for which this term is nonzero for steady nearly incompressible vector fields b and under some further assumptions in the case when d 2 we provide complete characterization of div beta u b in terms of div b and div ub our approach relies on the structure of level sets of lipschitz functions on mathbb r 2 obtained by g alberti s bianchini and g crippa extending our technique we obtain new sufficient conditions when any bounded weak solution u of partial t u b cdot nabla u 0 is renormalized that is when it also solves partial t beta u b cdot nabla beta u 0 for any smooth function beta colon mathbb r to mathbb r as a consequence we obtain new a uniqueness result for this equation

application of benveniste s convergence results in the study of adaptive iir filtering algorithms it is shown that the weak convergence results of a benveniste et al ieee trans automat contr vol ac 25 p 1042 58 dec 1980 can be used to prove convergence of some adaptive infinite impulse response iir filtering algorithms the association of the algorithms with some ordinary differential equations for constant gains which parallels the theory of l ljung et al 1983 is suitable for constant gain adaptive filtering applications convergence proofs for a prefiltering algorithm for a simple constant gain version of the recursive maximum likelihood algorithm and for the well known simple hyperstable adaptive recursive filter sharf algorithm are given as examples

a uniqueness result for the decomposition of vector fields in mathbb r d rd given a vector field rho 1 mathbf b in l 1 mathrm loc mathbb r times mathbb r d mathbb r d 1 such that mathrm div t x rho 1 mathbf b is a measure we consider the problem of uniqueness of the representation eta of rho 1 mathbf b mathcal l d 1 as a superposition of characteristics gamma t gamma t gamma rightarrow mathbb r d dot gamma t mathbf b t gamma t we give conditions in terms of a local structure of the representation eta on suitable sets in order to prove that there is a partition of mathbb r d 1 into disjoint trajectories wp mathfrak a mathfrak a in mathfrak a such that the pde begin aligned mathrm div t x big u rho 1 mathbf b big in mathcal m mathbb r d 1 quad u in l infty mathbb r times mathbb r d end aligned can be disintegrated into a family of odes along wp mathfrak a with measure r h s the decomposition wp mathfrak a is essentially unique we finally show that mathbf b in l 1 t mathrm bv x mathrm loc satisfies this local structural assumption and this yields in particular the renormalization property for nearly incompressible mathrm bv vector fields

weights for symmetric and general linear groups abstract an important feature of the theory of finite groups is the number of connections and analogies with the theory of lie groups the concept of a weight has long been useful in the modular representation theory of finite lie groups in the defining characteristic of the group the idea of a weight in the modular representation theory of an arbitrary finite group was recently introduced in alperin proc sympos pure math 41 1987 369 379 where it was conjectured that the number of weights should equal the number of modular irreducible representations moreover this equality should hold block by block the conjecture has created great interest since its truth would have important consequences a synthesis of known results and solutions of outstanding problems in this paper we prove the conjecture first for the modular representations of symmetric groups and second for modular representations in odd characteristic r for the finite general linear groups in the latter case r may be assumed to be different from the defining characteristic p of the group since the result is known when r is p the well known analogy between the representation theory of the symmetric and general linear groups holds here too

structure of metric cycles and normal one dimensional currents abstract we prove that every one dimensional real ambrosio kirchheim normal current in a polish i e complete separable metric space can be naturally represented as an integral of simpler currents associated to lipschitz curves as a consequence a representation of every such current with zero boundary i e a cycle as an integral of so called elementary solenoids which are very roughly speaking more or less the same as asymptotic cycles introduced by s schwartzman is obtained the latter result on cycles is in fact a generalization of the analogous result proven by s smirnov for classical whitney currents in a euclidean space the same results are true for every complete metric space under suitable set theoretic assumptions

decomposition of acyclic normal currents in a metric space abstract we prove that every acyclic normal one dimensional real ambrosio kirchheim current in a polish i e complete separable metric space can be decomposed in curves thus generalizing the analogous classical result proven by s smirnov in euclidean space setting the same assertion is true for every complete metric space under a suitable set theoretic assumption

comments on a weighted least squares method for the design of stable 1 d and 2 d iir digital filters with reply for original paper by lu et al see ieee trans signal processing vol 46 p 1 10 1998 january the iterative procedure by lu et al for designing iir filters is recognized as the sanathanan koerner or steiglitz mcbride iteration which was proposed originally in 1963 and 1965 respectively for system identification purposes we re examine some claims and issues related to lu et al s paper in view of various properties that have been deduced for the steiglitz mcbride iteration in the identification literature in particular the steiglitz mcbride procedure is known not to minimize a least squares distance measure contrary to lu et al s claim it can however provide good models and remain stable during successive iterations under specific conditions which are reviewed a reply is given by lu et al

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

acoustic echo cancellation do iir models offer better modeling capabilities than their fir counterparts the adequateness of iir models for acoustic echo cancellation is a long standing question and the answers found in the literature are conflicting we use the results from rational hankel norm and least squares approximation and we recall a test that provides a priori performance levels for fir and iir models we apply this test to the measured acoustic impulse responses upon comparing the performance levels of fir and iir models with the same number of free parameters we do not observe any significant gain from the use of iir models we attribute this phenomenon to the shape of the energy spectra of the acoustic impulse responses so tested which possess many strong and sharp peaks faithful modeling of these peaks requires many parameters irrespective of the type of the model

homotopy classification of self maps of bg via g actions to complete the classification of self maps of bg theorem 4 2 it remains to prove theorem 4 1 i e to show that the higher limits of certain functors n 1h 2 f p g z p wall vanish and that h0 mp g f i has the expected value in this section these limits h mp g hi will be calculated in the easy cases when g is a simply connected classical group i e one of the groups su n sp n or spin n or when i 2 the computation of h mp g hi for the simply connected exceptional lie groups will be put off until section 6 we begin with some general properties of higher limits let 6 be any small discrete category it is convenient when dealing with higher limits of functors on to let 4 moldenote the category of contravariant functors from v to ad then for any f e w muok we can identify

existence of stationary points for pseudo linear regression identification algorithms the authors prove the existence of a stable transfer function satisfying the nonlinear equations characterizing an asymptotic stationary point in undermodeled cases for a class of pseudo linear regression algorithms including landau s algorithm the feintuch algorithm and s harf the proof applies to all degrees of undermodeling and assumes only that the input power spectral density function is bounded and nonzero for all frequencies and that the compensation filter is strictly minimum phase some connections to previous stability analyses for reduced order identification in this algorithm class are brought out

optimally conditioned instrumental variable approach for frequency domain system identification accurate frequency domain system identification demands for reliable computational algorithms the aim of this paper is to develop a new algorithm for parametric system identification with favorable convergence properties and optimal numerical conditioning recent results in frequency domain instrumental variable identification are exploited which lead to enhanced convergence properties compared to classical identification algorithms in addition bi orthonormal polynomials with respect to a data dependent bi linear form are introduced for system identification hereby optimal numerical conditioning of the relevant system of equations is achieved this is shown to be particularly important for the class of instrumental variable algorithms for which numerical conditioning is typically quadratic compared to alternative frequency domain identification algorithms superiority of the proposed algorithm is demonstrated by means of both simulation and experimental results

a geometrical approach to monotone functions in r n this paper is concerned with the fine properties of monotone func tions on r n we study the continuity and differentiability properties of these functions the approximability properties the structure of the distributional derivatives and of the weak jacobians moreover we exhibit an example of a monotone function u which is the gradient of a c 1 convex function and

on the existence of stationary points for the steiglitz mcbride algorithm most convergence results for adaptive identification algorithms have been developed in sufficient order settings involving an unknown system with known degree reduced order settings in which the degree of the unknown system is underestimated are more common but more difficult to analyze deducing stationary points in these cases typically involves solving nonlinear equations hence the sparseness of results for reduced order cases if we allow ourselves the tractable case in which the input to an identification experiment is white noise we shall show that the steiglitz mcbride method 1965 indeed admits a stationary point in reduced order settings for which the resulting model is stable our interest in this study stems from a previous result showing an attractive a priori bound on the mismodeling error at any such stationary point

a version of alperinʼs weight conjecture for finite category algebras let p be a prime and k an algebraically closed field of characteristic p we construct a functor c oc on the category of finite categories with the property that if g c is a finite group then oc is the orbit category of p subgroups of g this leads to an extension of alperin s weight conjecture to any finite category c stating that the number of isomorphism classes of simple kc modules should be equal to that of the weight algebra w koc of oc we show that the versions of alperin s weight conjecture for finite groups and for finite categories are in fact equivalent 2013 elsevier inc

alperin s weight conjecture in terms of equivariant bredon cohomology alperin s weight conjecture 1 admits a reformulation in terms of the cohomology of a functor on a category obtained from a subdivision construction applied to a centric linking system 7 of a fusion system of a block which in turn can be interpreted as the equivariant bredon cohomology of a certain functor on the g poset of centric brauer pairs the underlying general constructions of categories and functors needed for this reformulation are described in 1 and 2 respectively and 3 provides a tool for computing the cohomology of the functors arising in 2 taking as starting point the alternating sum formulation of alperin s weight conjecture by knorr robinson 11 the material of the previous sections is applied in 4 to interpret the terms in this alternating sum as dimensions of cohomology spaces of appropriate functors using further work of robinson 15 16 17

duality theorems for marginal problems given topological spaces x1 xn with product space x probability measures i on xi together with a real function h on x define a marginal problem as well as a dual problem using an extended version of choquet s theorem on capacities an analogue of the classical duality theorem of linear programming is established imposing only weak conditions on the topology of the spaces xi and the measurability resp boundedness of the function h applications concern among others measures with given support stochastic order and general marginal problems