extensions of the method of poles for code construction the method of poles is a method introduced by franaszek 1969 for constructing a rate 1 1 finite state code from k ary data into a constrained channel of finite type whose capacity is strictly greater than log k the method is based on the computation of a set of states called poles with each pole is associated a set of paths going from this pole to others each set verifies an entropy condition the code produced by the method of poles has a sliding block decoder if each set of paths satisfies moreover an optimization condition based on the sum of the path lengths of the set we give a new optimization condition which guarantees the sliding block window decoding property and has a lower computational complexity than the previous one we also extend the method of poles to the more general case of sofic constrained channels

parameter identification of nonlinear aeroelastic system with time delayed feedback control in this paper an enhanced response sensitivity approach is proposed for parameter identification of nonlinear time delay aeroelastic systems two common aeroelastic models are investigated namely

structure arising from induction and jacquet modules of representations of classical p adic groups jacquet modules are very useful in the study of parabolically induced representations of reductive groups over a p adic field f we shall assume char f 2 in this paper it is very hard to describe explicitly the structure of jacquet modules of parabolically induced representations particularly in the most interesting cases there exists a description of factors of certain filtrations on them that description was done by j bernstein and a v zelevinsky in bz2 and by w casselman in c in the case of general linear groups the functor of parabolic induction and the jacquet functor induce a structure of z graded hopf algebra on the sum r of grothendieck groups of categories of smooth representations of gl n f s of finite length n 0 z1 the multiplication m r r r is defined using parabolic induction while the comultiplication m r r r is defined in terms of jacquet modules the most interesting part of the structure is the property that m r r r is a ring homomorphism hopf axiom this enables one to compute composition series of parabolically induced representations in a very simple way it is interesting to note that the existence of this strong structure did not have serious impact on the development of the representation theory of gl n f one of the reasons for that may lay in the fact that for gl n f there existed a very powerful theory of gelfandkazhdan derivatives and the main results of z1 were obtained using them nevertheless a v zelevinsky showed in z2 that some interesting parts of the representation theory of gl n over a finite field can be obtained as a structure theory of such hopf algebra defined in this setting besides that one of the main tools for the study of representation theory of gl n over a central division f algebra in t1 is such hopf algebra structure in this situation are not available gelfand kazhdan derivatives it is natural to ask does some structure of this kind exist for other simple split classical p adic groups since levi factors of classical groups are isomorphic to direct products of general linear groups and smaller groups from the same series one can expect for such structure to have some relation with r if it exists in the third section we define the direct sum of grothendieck groups r s which corresponds either to the series sp n f n 0 or so 2n 1 f n 0 in a similar way as r was defined for general linear groups the action of r on r s is defined using the parabolic induction in this way r s becomes z graded r module we can make r s a z graded comodule over r the comodule structure map r s r r s is again defined using the jacquet modules similarly as in the case of gl n f it is not hard to see that r s is not a hopf module over r see remark 7 3 in this paper we

computing nonnegative rank factorizations abstract the existence of nonnegative generalized inverses in terms of nonnegative rank factorizations is considered an algorithm is presented which computes a nonnegative rank factorization of a nonnegative matrix when a nonnegative 1 inverse exists

the backus gilbert method and their minimum norm solution abstractthis paper has two objectives one is to review the backus gilbert bg method backus and gilbert investigate continuous inverse problems in a radially symmetric earth using an approach completely different from that of standard inversion methods if m is an earth property of interest the bg method provides average values of m over some radial intervals if an interval w is relatively short and centered near a particular radius r0 the bg average will be a local average of m near r0 with a resolving length of w backus and gilbert also introduce the concept of trade off between resolution and error which is essential in inverse theory regardless of the inversion method in spite of its importance inverse theory texts neither describe the bg method in full nor show how to apply it in all its generality because the three papers that introduce the bg method are mathematically difficult this paper provides background material and a detailed derivation of the method as well as two completely wor

on 3d numerical inverse problems for the bidomain model in electrocardiology in the inverse problem en electrocardiology the goal is to recover electrophysiological activity in the heart without measuring directly on its surface without using catheter interventions note that today the inverse computation is frequently used by solving the quasi static model this model doesnt take into account the heart dynamic in time and may result in considerable errors in the reconstruction of the solution on the heart in this paper a 3d numerical inverse problem constrained by the bidomain equations in electrocardiology is investigated the state equations consisting in a coupled reaction diffusion system modelling the propagation of the intracelullar and extracellular electrical potentials and ionic currents are extended to further consider the effect of an external bathing medium thus we demonstrate that the novel concept of applying electrophysiological data might be useful to improve noninvasive reconstruction of electrical heart activity finally we present numerical experiments representing the effect of the heart dynamic on the inverse solutions

contrast source inversion methods in elastodynamics in this paper a nonlinear inversion method is presented for determining the mass density of an elastic inclusion from the knowledge of how the inclusion scatters known incident elastic waves the algorithm employed is an extension of the multiplicative regularized contrast source inversion method mr csi to elasticity this method involves alternate determination of the mass density contrast and the contrast sources the product of the contrast and the fields in each iterative step the simple updating schemes of the method allow the introduction of an extra regularization term to the cost functional as a multiplicative constraint this so called mr csi method mr csi has been proven to be very effective for the acoustic and electromagnetic inverse scattering problems numerical examples demonstrate that the mr csi method shows excellent edge preserving properties by robustly handling noisy data very well even for more complicated elastodynamic problems

minimum scope for sliding block decoder mappings some properties of state splitting are established the properties are then used to develop an algorithm for searching the sliding block decoder mapping of minimum scope obtained by state splitting the algorithm is applied to the d k constraints of magnetic recording

generalized circulants and class functions of finite groups abstract the regular representation of the ring of class functions of a finite group is used to construct families of matrices that enjoy many of the properties of circulant matrices for different choices of finite groups one gets different families of matrices the circulants block circulants block circulants with circulant blocks of all levels and many others the properties of these families are simple consequences of the character theory of finite groups many known properties of circulants and some of their generalizations are obtained as special cases of the properties of the families constructed some applications to character theory are also mentioned

sirt and cg type methods for the iterative solution of sparse linear least squares problems abstract sirt and cg type methods have been successfully employed for the approximate solution of least squares problems arising in tomography in this paper we study and compare their convergence and regularization properties it is pointed out that sirt methods apply an uncontrollable implicit rescaling which affects the statistical characteristics of the system whereas cg type methods do not for a large class of model problems it is shown that virtually the same solutions as obtained by sirt methods can be obtained by applying a cg type method to a properly rescaled system but with an amount of work proportional to the square root of the amount of work with sirt

on computing first and second order derivative spectra enhancing resolution in spectral response and an ability to differentiate spectral mixing in delineating the endmembers from the spectral response are central to the spectral data analysis first and higher order derivatives analysis of absorbance and reflectance spectral data is commonly used techniques in differentiating the spectral mixing but high sensitivity of derivative to the noise in data is a major problem in the robust estimation of derivative of spectral data an algorithm of robust estimation of first and second order derivative spectra from evenly spaced noisy normal spectral data is proposed the algorithm is formalized in the framework of an inverse problem where based on the fundamental theorem of calculus a matrix equation is formed using a volterra type integral equation of first kind a regularization technique where the balancing principle is used in selecting a posteriori optimal regularization parameter is designed to solve the inverse problem for robust estimation of first order derivative spectra the higher order derivative spectra are obtained while using the algorithm in sequel the algorithm is tested successfully with synthetically generated spectral data contaminated with additive white gaussian noise and also with real absorbance and reflectance spectral data for fresh and sea water respectively robust and efficient algorithm of computing first and second orders derivative spectra is designed the algorithm is based on the premise of inverse problem where a robust solution is achieved via regularization it couples discrepancy and balancing principles to determine regularization parameter and implement stopping rule respectively numerical experiments on noisy data suggest superiority of the method over finite difference and fourier transform based techniques the proposed method is applied on absorbance and reflectance spectral data for fresh and sea water

on the perron frobenius eigenvector for nonnegative integral matrices whose largest eigenvalue is integral abstract we first derive the bound det i a k k 0 0 where a is a k k nonnegative real matrix and 0 is the spectral radius of a if a is irreducible and integral and its largest nonnegative eigenvalue is an integer n then we use this inequality to derive the upper bound n k 1 on the components of the smallest integer eigenvector corresponding to n finer information on the components is also derived

the 2 norm of random matrices abstract numerical experiments show that it is possible to derive simple estimates for the expected 2 norm of random matrices a with elements from a normal distribution with zero mean and standard deviation and from a poisson distribution with mean value these estimates are max m n 2 max m n and e 2 mn respectively where m and n are the dimensions of a

a proof of langland s conjecture on plancherel measures complementary series of p adic groups analysis of p adic reductive groups our first result theorem 7 9 proves a conjecture of langlands on normalization of intertwining operators by means of local langlands root numbers and l functions at least when the group is quasi split and the inducing representation is generic assuming two natural conjectures in harmonic analysis of p adic groups we also prove the validity of the conjecture in general theorem 9 5 as our second result we obtain all the complementary series and special representations of quasi split p adic groups coming from rank one parabolic subgroups and generic supercuspidal represen

meshless thin plate spline methods for the modified helmholtz equation in this paper we investigate the application of the meshless radial basis function method for solving the helmholtz equation using thin plate splines we use a meshless method mixed with a boundary and a fundamental solution methods the numerical computation is achieved by using the generalized minimal residual gmres the least square lsqr methods associated with tikhonov regularization

unitary dual of the non split inner form of sp 8 f we classify the non cuspidal part of the unitary dual of the non quasi split inner form of sp 8 f where f is a non archimedean field of characteristic zero we obtain a conjectural description of the discrete l packets which contain representations of sp 4 f and its non split inner form

a 3d boundary optimal control for the bidomain bath system modeling the thoracic shock therapy for cardiac defibrillation this work is dedicated to study the cardiac defibrillation problem by using an optimal thoracic electroshock treatment the problem is formulated as an optimal control problem in a 3d domain surrounded by the bath and including the heart the control corresponds to the thoracic electroshock and the model describing the electrical activity in the heart is the bidomain model the bidomain model is coupled with the quasi static maxwell s equation to consider the effect of an external bathing medium the existence and uniqueness of a weak solution for the direct problem is assessed as well as the existence of a weak solution for the adjoint problem the numerical discretization is realized using a finite element method for the spatial discretization and linearly implicit runge kutta methods for the temporal discretization of the partial differential equations the numerical results are demonstrated for the termination of re entry waves

noninvasive reconstruction of three dimensional ventricular activation sequence from the inverse solution of distributed equivalent current density we propose a new electrocardiographic ecg inverse approach for imaging the three dimensional 3 d ventricular activation sequence based on the modeling and estimation of the equivalent current density throughout the entire volume of the ventricular myocardium the spatio temporal coherence of the ventricular excitation process has been utilized to derive the activation time from the estimated time course of the equivalent current density in the present study we explored four different linear inverse algorithms the minimum norm and weighted minimum norm estimates in combination with two regularization schemes the instant by instant regularization and the isotropy method to estimate the current density at each time instant during the ventricular depolarization the activation time at any given location within the ventricular myocardium was determined as the time point with the occurrence of the maximum local current density estimate computer simulations were performed to evaluate this approach using single and dual site pacing protocols in a physiologically realistic cellular automaton heart model the performance and stability of the proposed approach was evaluated with respect to the various levels of measurement noise 0 5 10 20 40 and 60 muv the various numbers of ecg electrodes and the modeling errors on the torso geometry and heart position the simulation results demonstrate that 1 the single site paced 3 d activation sequence can be well reconstructed from 200 channel body surface potential maps with additive gaussian white noise of 20 muv correlation coefficient 0 90 relative error 0 19 and localization error 5 49 mm 2 a higher imaging accuracy can be obtained when the activation is initiated from the left right ventricle lv rv compared to from the septum 3 the isotropy method gives rise to a better performance than the conventional instant by instant regularization 4 a decreased imaging accuracy results from a larger noise level a fewer number of electrodes or the volume conductor modeling errors however a reasonable imaging accuracy can still be obtained with a 60 muv noise level 64 electrodes or mild errors on both the torso geometry and heart position respectively 5 the dual site paced 3 d activation sequence can be imaged when the two sites are paced either simultaneously or with a time delay of 20 ms 6 two pacing sites can be resolved and localized in the imaged 3 d activation sequence when they are located at the contralateral sides of ventricles or at the ventricular lateral wall and the apex respectively

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

recovering the density of a string from only lowest frequency data a classical inverse problem is can you hear the density of a string clamped at both ends the answer as narrowly stated is negative one has to give an additional data sequence such as the energy in each mode norming constants or information on the string slope at the endpoints or alternatively change the boundary conditions and obtain the new frequencies what if neither of these options is possible one solution recently proposed was to add a known mass density and remeasure the dirichlet spectrum w rundell and p e sacks siam j appl math 73 2013 pp 1020 1037 in this work we take a related approach we are able to add any number of known mass densities but we can only measure the fundamental frequency that is the lowest eigenvalue in each case we will show that our problem can be closely approximated by a related problem for which there is uniqueness and we discuss a suite of reconstruction methods

bounds for determinants of perturbed m matrices abstract a sharp upper bound for the relative error of the determinant of an m matrix in terms of the relative errors of the matrix entries is given it improves and completes a bound derived by jungong and jiang

asymptotic theory of filtering for linear operator equations with discrete noisy data on considere les equations integrales de fredholm de premiere espece a noyaux continus avec echantillonnage des donnees et alteration par le bruit blanc on etablit une condition suffisante de convergence des methodes de filtrage

a linear bound for sliding block decoder window size ii for pt i see ibid vol 34 p 389 99 1988 an input constrained channel is the set s of finite sequences of symbols generated by the walks on a labeled finite directed graph g which is said to present s we introduce a new construction of finite state encoders for input constrained channels the construction is a hybrid of the state splitting technique of adler coppersmith and hassner 1983 and the stethering technique of ashley marcus and roth see ibid vol 41 p 55 76 1995 when s has finite memory and p and g are integers where p g is at most the capacity of s the construction guarantees an encoder at rate p g and having a sliding block decoder literally at rate q p with look ahead that is linear in the number of states of the smallest graph g presenting s this contrasts with previous constructions the straight adler coppersmith and hassner construction provides an encoder having a sliding block decoder at rate q p but the best proven upper bound on the decoder look ahead is exponential in the number of states of g a previous construction of ashley provides an encoder having a sliding block decoder whose look ahead has been proven to be linear in the number of states of g but the decoding is at rate tq tp where t is linear in the number of states of g

some remarks on a conjecture of boyle and handelman abstract boyle and handelman have conjectured that whenever a is an n n nonnegative matrix with rank a r and perron root 1 the inequality det i ta n r r 1r holds for all real numbers satisfying 1 we introduce an analogous conjecture involving nonnegative central class functions on the permutation group sn the analogue of the rank condition in this context is a condition on the support of the nonabelian fourier transform of the central function we are able to establish that both conjectures are true in case 2r n

planar crack identification in 3d linear elasticity by the reciprocity gap method abstract we study the reciprocity gap method andrieux et al 1999 for the identification of planar cracks in the framework of three dimensional linear elasticity in order to achieve better accuracy on thick domains we propose to use polynomial test functions instead of fourier series we also propose to improve the solution by various regularization techniques that are tested and compared numerical assessments are provided in 2d and 3d

a state space force identification method based on markov parameters precise computation and regularization technique a time domain force identification approach for linear system is proposed this approach can found a highly precise force identification model within the scope of general computer precision while it does not cost much computing time although the force identification model is accurate the force identification process like other inverse methods is still ill posed due to the inversion process and the white noise in measured structural responses the singular value decomposition is used to reveal the intrinsically matter of the ill posedness of force identification problem and a regularization technique is utilized to deal with this issue finally the proposed method with the aid of regularization technique is successfully applied to identify the input forces in two numerical simulations

nonnegative matrices brauer characters normal subsets and powers of representation modules abstract in a previous paper it was shown that some properties of ordinary characters of finite groups are consequences of the theory of nonnegative matrices in this article we observe that this method can be applied to brauer characters and normal subsets in particular conjugacy classes of finite groups results known ones and new ones on powers and values of brauer characters including ordinary characters on powers of normal subsets on values of central characters and on powers of representation modules are proved as consequences of results on nonnegative matrices

optimally scaled vector regularization method to solve ill posed linear problems instead of the tikhonov regularization method which with a scalar being the regularization parameter liu et al 1 have proposed a novel regularization method with a vector as being the regularization parameter as a continuation we further propose an optimally scaled vector regularization method osvrm to solve the ill posed linear problems which is better than the tikhonov regularization method the presently proposed vector regularization method is shown to be well conditioning to overcome the ill posedness of the linear equations system the osvrm causes a significant improvement of stability and accuracy in the numerical solution of ill posed linear problem and its convergence speed is as fast as by solving the well posed linear problem some tests of the linear inverse problems confirm the efficiency and accuracy of the osvrm

multilinear functional inequalities involving permanents determinants and other multilinear functions of nonnegative matrices and m matrices abstract motivated by a proof due to fiedler of an inequality on the determinants of m matrices and a recent paper by the authors we now obtain various inequalities on permanents and determinants of nonsingular m matrices this is done by extending the multilinear considerations of fiedler and subsequently of the authors to fractional multilinear functionals on pairs of nonnegative matrices two examples of our results for an n n nonsingular m matrix m i we give a sharp upper bound for det m per m when m is a nonsingular m matrix ii we determine an upper bound on the relative error per m e per m per m when m e is a certain componentwise perturbation of m

construction of discrete series for classical p adic groups in this paper the authors complete the classification of irreducible square integrable representations of classical p adic groups assuming a natural assumption which is expected to hold in general this classification implies a parameterization of irreducible tempered representations of these groups and it implies a classification of the non unitary duals of these groups modulo cuspidal data

boundary identification for a 3d laplace equation using a genetic algorithm in this paper we consider the identification of the geometric structure of the boundary of the solution domain for the three dimensional laplace equation we investigate the determination of the shape of an unknown portion of the boundary of a solution domain from cauchy data on the remaining portion of the boundary this problem arises in the study of quantitative non destructive evaluation of corrosion in materials in which boundary measurements of currents and voltages are used to determine the material loss caused by corrosion the domain identification problem is considered as a variational problem to minimize a defect functional which utilises some additional data on certain known parts of the boundary a real coded genetic algorithm rcga is used in order to minimise the objective functional the unknown boundary is parameterized using b splines the laplace equation is discretised using the method of fundamental solutions mfs numerical results are presented and discussed for several test examples

semisimple commutative algebras with positive bases abstract algebras that serve as models for concurrent studying of certain aspects of both the algebra of ordinary characters and the center of the group algebra of a finite group have been considered by various authors in this article we offer another such model the main differences between our model and the known ones are 1 our model includes brauer characters and principal indecomposable characters as special cases 2 our emphasis is on the eigenvalues of the regular representation of the algebra elements an approach that gives results on values of characters ordinary central brauer principal indecomposable as well as on their products

regular representations of semisimple algebras separable field extensions group characters generalized circulants and generalized cyclic codes let a be a semisimple n dimensional commutative algebra over a field f fix a basis b of a and denote by m a b the transpose of the matrix over f that represents a a regularly with respect to b it is easy to see that the set m a b a a can be simultaneously diagonalized over many fields including all perfect fields we use this fact in order to give an elementary proof that such an algebra over an infinite field is generated by a single element and to describe the subalgebras of a in terms of certain partitions of the set 1 2 3 n several applications of these results are shown 1 we give a new proof for the theorem stating that every finite dimensional separable field extension has a primitive element 2 we show that every finite group g has a character such that every other generalized character of g is a polynomial in with rational coefficients this is true for brauer characters as well 3 we give a necessary condition for two generalized characters or brauer characters and that forces the field of values of to contain that of 4 many collections of patterned matrices over a field f such as circulant matrices and some of their generalizations are known to be algebras generated by a single matrix we observe that each subalgebra of such a collection is also generated by a single matrix also if a and b are two elements of such a collection we give a necessary and sufficient condition in terms of the eigenvalue pattern of a and b for a to be a polynomial in b with coefficients in f 5 we show that if a is a generalized cyclic code then the eigenvalues of m a b are the so called matteson solomon coefficients of the codeword a other applications to coding to groups and to field extensions are discussed as well

the combination of self organizing feature maps and support vector regression for solving the inverse ecg problem noninvasive electrical imaging of the heart aims to quantitatively reconstruct transmembrane potentials tmps from body surface potentials bsps which is a typical inverse problem classically electrocardiography ecg inverse problem is solved by regularization techniques in this study it is treated as a regression problem with multi inputs bsps and multi outputs tmps then the resultant regression problem is solved by a hybrid method which combines the support vector regression svr method with self organizing feature map sofm techniques the hybrid sofm svr method conducts a two step process sofm algorithm is used to cluster the training samples and the individual svr method is employed to construct the regression model for each testing sample the cluster operation can effectively improve the efficiency of the regression algorithm and also helps the setup of the corresponding svr model for the tmps reconstruction the performance of the developed sofm svr model is tested using our previously developed realistic heart torso model the experiment results show that compared with traditional single svr method in solving the inverse ecg problem the proposed method can reduce the cost of training time and improve the reconstruction accuracy in solving the inverse ecg problem

primitive normal matrices and covering numbers of finite groups abstract a primitive matrix is a square matrix m with nonnegative real entries such that the entries of ms are all positive for some positive integer s the smallest such s is called the primitivity index of m primitive matrices of normal type namely mmt and mtm have the same zero entries occur naturally in studying the so called conjugacy class covering number and character covering number of a finite group we show that if m is a primitive n n matrix of normal type with minimal polynomial of degree m then the primitivity index of m is at most n 2 1 m 1 this bound is then applied to improve known bounds for the various covering numbers of finite groups

relations between svd and gsvd of discrete regularization problems in standard and general form abstract we consider an algorithm due to elden that transforms general discrete regularization problems into standard form we derive a simple relationship between the svd associated with the standard form problem and the gsvd associated with the general problem and we discuss the accuracy of the gsvd computed via this transformation

noninvasive transmural electrophysiological imaging based on minimization of total variation functional while tomographic imaging of cardiac structure and kinetics has improved substantially electrophysiological mapping of the heart is still restricted to the surface with little or no depth information beneath the progress in reconstructing 3 d action potential from surface voltage data has been hindered by the intrinsic ill posedness of the problem and the lack of a unique solution in the absence of prior assumptions in this work we propose a novel adaption of the total variation tv prior to exploit the unique spatial property of transmural action potential of being piecewise smooth with a steep boundary gradient separating depolarized and repolarized regions we present a variational tv prior instead of a common discrete tv prior for improved robustness to mesh resolution and solve the tv minimization by a sequence of weighted first order l2 norm minimization in a large set of phantom experiments the proposed method is shown to outperform existing quadratic methods in preserving the steep gradient of action potential along the border of infarcts as well as in capturing the disruption to the normal path of electrical wavefronts real data experiments also further demonstrate the potential of the proposed method in revealing the location and shape of infarcts when quadratic methods fail to do so

examining the impact of prior models in transmural electrophysiological imaging a hierarchical multiple model bayesian approach noninvasive cardiac electrophysiological ep imaging aims to mathematically reconstruct the spatiotemporal dynamics of cardiac sources from body surface electrocardiographic ecg data this ill posed problem is often regularized by a fixed constraining model however a fixed model approach enforces the source distribution to follow a pre assumed structure that does not always match the varying spatiotemporal distribution of actual sources to understand the model data relation and examine the impact of prior models we present a multiple model approach for volumetric cardiac ep imaging where multiple prior models are included and automatically picked by the available ecg data multiple models are incorporated as an lp norm prior for sources where p is an unknown hyperparameter with a prior uniform distribution to examine how different combinations of models may be favored by different measurement data the posterior distribution of cardiac sources and hyperparameter p is calculated using a markov chain monte carlo mcmc technique the importance of multiple model prior was assessed in two sets of synthetic and real data experiments compared to fixed model priors using laplace and gaussian priors the results showed that the posterior combination of models the posterior distribution of p as determined by the ecg data differed substantially when reconstructing sources with different sizes and structures while the use of fixed models is best suited in situations where the prior assumption fits the actual source structures the use of an automatically adaptive set of models may have the ability to better address model data mismatch and to provide consistent performance in reconstructing sources with different properties

the local langlands conjecture for gsp 4 ii the case of inner forms in an earlier paper of the first author and shuichiro takeda the local langlands correspondence for rm gsp 4 f over a non archimedean local field f of characteristic zero was established and several expected properties of the correspondence verified in this paper we extend the local langlands correspondence to the inner form rm gu 2 d of rm gsp 4

powers of characters of finite groups letg be a finite group and a complex character ofg define irr to be the set of all irreducible constituents of andirr g to be the set of all irreducible characters ofg thecharacter covering number of a finite groupg ccn g is defined as the smallest positive integer m such thatirr m irr g for all irr g 1g if no such positive integer exists we say that the character covering number ofg is infinite in this article we show that a finite nontrivial groupg has a finite character covering number if and only ifg is simple and non abelian and ifg is a nonabelian simple group thenccn g k2 3k 4 wherek is the number of conjugacy classes ofg then we show using the classification of the finite simple groups that the only finite group with a character covering number equal to two is the smallest janko s group j1 these results are analogous to results obtained previously concerning the covering of groups by powers of conjugacy classes other related results are shown

a new method for nmr data inversion based on double parameter regularization nuclear magnetic resonance nmr technology plays a significant role in petroleum exploration nmr data can be processed using inversion methods to reflect the relaxation information of all the components a new double parameter regularization dpr method was proposed for the inversion of nmr data whose regularization terms consist of tikhonov regularization and maximum entropy regularization the objective function for the dpr method was solved using the levenberg marquardt method the proportional coefficient of the regularization parameter was obtained using an iteration procedure the optimum regularization parameter of the dpr method was selected using an s curve the relationship between the optimum regularization parameter and the signal to noise ratio snr of the data was evaluated moreover we compared the results of the nmr inversion obtained from the norm smooth method the maximum entropy method and the dpr method for simulated data we evaluated how the proportional coefficient of the re

regularization parameter selection for nonlinear iterative image restoration and mri reconstruction using gcv and sure based methods regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values we focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive possibly complex gaussian noise generalized cross validation gcv and weighted mean squared error mse approaches based on stein s unbiased risk estimate sure need the jacobian matrix of the nonlinear reconstruction operator representative of the iterative algorithm with respect to the data we derive the desired jacobian matrix for two types of nonlinear iterative algorithms a fast variant of the standard iterative reweighted least squares method and the contemporary split bregman algorithm both of which can accommodate a wide variety of analysis and synthesis type regularizers the proposed approach iteratively computes two weighted sure type measures predicted sure and projected sure which require knowledge of noise variance 2 and gcv which does not need 2 for these algorithms we apply the methods to image restoration and to magnetic resonance image mri reconstruction using total variation and an analysis type l1 regularization we demonstrate through simulations and experiments with real data that minimizing predicted sure and projected sure consistently lead to near mse optimal reconstructions we also observe that minimizing gcv yields reconstruction results that are near mse optimal for image restoration and slightly suboptimal for mri theoretical derivations in this paper related to jacobian matrix evaluations can be extended in principle to other types of regularizers and reconstruction algorithms