topological conjugacy of linear endomorphisms of the 2 torus we describe two complete sets of numerical invariants of topological conjugacy for linear endomorphisms of the two dimensional torus i e continuous maps from the torus to itself which are covered by linear maps of the plane the trace and determinant are part of both complete sets and two candidates are proposed for a third and last invariant which in both cases can be understood from the topological point of view one of our invariants is in fact the ideal class of the latimer macduffee taussky theory reformulated in more elementary terms and interpreted as describing some topology merely one has to look at how closed curves on the torus intersect their image under the endomorphism part of the intersection information the intersection number counted with multiplicity can be captured by a binary quadratic form associated to the map so that we can use the classical theories initiated by lagrange and gauss to go beyond the intersection number and shortcut the classification theory for quadratic forms we use the rotation number of poincare

negativity compensation in the nonnegative inverse eigenvalue problem abstract if a set of complex numbers can be partitioned as 1 s in such a way that each i is realized as the spectrum of a nonnegative matrix say a i then is trivially realized as the spectrum of the nonnegative matrix a a i in linear algebra appl 369 2003 169 it was shown that in some cases a real set can be realized even if some of the i are not realizable themselves here we systematize and extend these results in particular allowing the sets to be complex the leading idea is that one can associate to any nonrealizable set a certain negativity n and to any realizable set a certain positivity m then under appropriate conditions if m n we can conclude that is the spectrum of a nonnegative matrix additionally we prove a complex generalization of suleimanova s theorem

algebraic shift equivalence and primitive matrices motivated by symbolic dynamics we study the problem given a unital subring s of the reals when is a matrix a algebraically shift equivalent over s to a primitive matrix we conjecture that simple necessary conditions on the nonzero spectrum of a are sufficient and establish the conjecture in many cases if s is the integers we give some lower bounds on sizes of realizing primitive matrices for dedekind domains we prove that algebraic shift equivalence implies algebraic strong shift equivalence

limit eigenvalues of nonnegative matrices abstract in this paper we give a simple closed formula for a certain limit eigenvalue of a nonnegative matrix we bound the spectral radius of a nonnegative matrix in terms of this limit eigenvalue

topological markov chains c algebras and k2 soit a x a x a la chaine de markov topologique provenant d une matrice 0 1 pouvant etre infinie et soit aut a le groupe des equivalences uniformes de a on etudie la relation entre aut a le foncteur algebrique de k theorie k 2 et des automorphismes de c algebre du type cuntz kreiger associees a a et de son groupe de dimension correspondant k 0 x a

regular article a fast adaptive multipole algorithm in three dimensions we present an adaptive fast multipole method for the laplace equation in three dimensions it uses both new compression techniques and diagonal forms for translation operators to achieve high accuracy at a reasonable cost

limiting performance of block fading channels with multiple antennas we derive the performance limits of a radio system consisting of a transmitter with t antennas and a receiver with r antennas a block fading channel with additive white gaussian noise awgn delay and transmit power constraints and perfect channel state information available at both the transmitter and the receiver because of a delay constraint the transmission of a codeword is assumed to span a finite and typically small number m of independent channel realizations therefore the relevant performance limits are the information outage probability and the delay limited or nonergodic capacity we derive the coding scheme that minimizes the information outage probability this scheme can be interpreted as the concatenation of an optimal code for the awgn channel without fading to an optimal beamformer for this optimal scheme we evaluate minimum outage probability and delay limited capacity among other results we prove that for the fairly general class of regular fading channels the asymptotic delay limited capacity slope expressed in bits per second per hertz b s hz per decibel of transmit signal to noise ratio snr is proportional to min t r and independent of the number of fading blocks m since m is a measure of the time diversity induced by interleaving or of the frequency diversity of the system this result shows that if channel state information is available also to the transmitter very high rates with asymptotically small error probabilities are achievable without the need of deep interleaving or high frequency diversity moreover for a large number of antennas delay limited capacity approaches ergodic capacity

spectral lines of codes given as functions of finite markov chains spectral lines of signals that are given by functions of finite markov chains are investigated a problem of characterizing encoders in such a manner that the messages emitted from these encoders have some amount of information about clock independent of the source statistics is considered necessary and sufficient conditions are established for the encoded message to have a spectral line of a given amplitude for every transition probability matrix of the underlying markov chain several other related results about spectral lines are given a biased coboundary condition is defined at a frequency f and it is shown that this condition is necessary and sufficient for the encoded message to have a spectral density null at f

eventual finite order generation for the kernel of the dimension group representation the finite order generation problem fog in symbolic dynamics asks whether every element in the kernel of the dimension group representation of a subshift of finite type xa aa is a product of elements of finite order in the group aut aa of homeomorphisms of xa commuting with ca we study the space of strong shift equivalences over the nonnegative integers and the first application is to prove eventual fog which says that every inert symmetry of ca is a product of finite order homeomorphisms of xa commuting with sufficiently high powers of ca then we discuss the relation of fog to williams lifting problem lift for symmetries of fixed points in particular either fog or lift is false finally we also discuss p adic convergence and other implications of eventual fog for gyration numbers

a fast high order algorithm for the solution of surface scattering problems basic implementation tests and applications we present a new algorithm for the numerical solution of problems of acoustic scattering by surfaces in three dimensional space this algorithm evaluates scattered fields through fast high order solution of the corresponding boundary integral equation the high order accuracy of our solver is achieved through use of partitions of unity together with analytical resolution of kernel singularities the acceleration in turn results from use of a novel approach which based on high order two face equivalent source approximations reduces the evaluation of far interactions to evaluation of 3 d fast fourier transforms ffts this approach is faster and substantially more accurate and it runs on dramatically smaller memories than other fft and k space methods the present algorithm computes one matrix vector multiplication in o n6 5logn to o n4 3logn operations where n is the number of surface discretization points the latter estimate applies to smooth surfaces for which our high order algorithm provides accurate solutions with small values of n the former more favorable count is valid for highly complex surfaces requiring significant amounts of subwavelength sampling further our approach exhibits super algebraic convergence it can be applied to smooth and nonsmooth scatterers and it does not suffer from accuracy breakdowns of any kind in this paper we introduce the main algorithmic components in our approach and we demonstrate its performance with a variety of numerical results in particular we show that the present algorithm can evaluate accurately in a personal computer scattering from bodies of acoustical sizes of several hundreds

fast multipole method for the biharmonic equation in three dimensions the evaluation of sums matrix vector products of the solutions of the three dimensional biharmonic equation can be accelerated using the fast multipole method while memory requirements can also be significantly reduced we develop a complete translation theory for these equations it is shown that translations of elementary solutions of the biharmonic equation can be achieved by considering the translation of a pair of elementary solutions of the laplace equations the extension of the theory to the case of polyharmonic equations in r 3 is also discussed an efficient way of performing the fmm for biharmonic equations using the solution of a complex valued fmm for the laplace equation is presented compared to previous methods presented for the biharmonic equation our method appears more efficient the theory is implemented and numerical tests presented that demonstrate the performance of the method for varying problem sizes and accuracy requirements in our implementation the fmm for the biharmonic equation is faster than direct matrix vector product for a matrix size of 550 for a relative l 2 accuracy e 2 10 4 and n 3550 for e 2 10 1 2

recovery of the absorption coefficient from diffused reflected light using a discrete diffusive model an algorithm based on a discrete model for photon migration is proposed for recovering the absorption coefficient in a semi infinite slab a pulsed light source is modeled and only reflected signals are used in the reconstruction the diffusion coefficient and speed of light are assumed constant and known the algorithm is based on the result that the earliest reflected signals obtained from a particular voxel depend either in a linear or in a quadratical fashion on the square of the absorption coefficient in that voxel by solving the discrete model in the forward direction in a region where the absorption coefficient has been calculated already the absorption coefficients in the voxels on the boundary of the region are calculated using interpolation results show that simple absorptive regions can be accurately recovered

strong shift equivalence of boolean and positive rational matrices abstract firstly we show that two primitive boolean matrices are strong shift equivalent if and only if the boolean traces of each of their powers are equal secondly we prove that if two matrices over q are strong shift equivalent through positive matrices over r then they are strong shift equivalent through matrices over q

elgenvalues of nonnegative matrices abstract in a partial continuation of work by fiedler some spectral properties of symmetric nonnegative matrices are extended to general nonnegative matrices

strong shift equivalence and positive doubly stochastic matrices abstract we give sufficient conditions for a positive stochastic matrix to be similar and strong shift equivalent over r to a positive doubly stochastic matrix through matrices of the same size we also prove that every positive stochastic matrix is strong shift equivalent over r to a positive doubly stochastic matrix consequently the set of nonzero spectra of primitive stochastic matrices over r with positive trace and the set of nonzero spectra of positive doubly stochastic matrices over r are identical we exhibit a class of 2 2 matrices pairwise strong shift equivalent over r through 2 2 matrices for which there is no uniform upper bound on the minimum lag of a strong shift equivalence through matrices of bounded size in contrast we show for any n n primitive matrix of positive trace that the set of positive n n matrices similar to it contains only finitely many sse r classes

power series with positive coefficients arising from the characteristic polynomials of positive matrices let a be an n times n entrywise positive matrix and let f t det i t a we prove the surprising result that there always exists a positive integer n such that the formal power series expansion of 1 f t 1 n around t 0 has positive coefficients

the spectra of nonnegative integer matrices via formal power series an old problem in matrix theory is to determine the n tuples of complex numbers which can occur as the spectrum of a matrix with nonnegative entries see bp94 chapter 4 or min88 chapter vii authors have studied the case where the ntuple is comprised of real numbers bor95 cia68 fri78 kel71 per53 sal72 sou83 sul49 the case where the matrices under consideration are symmetric fie74 jll96 and the general problem joh81 lm99 ll79 rea94 rea96 wuw97 various necessary conditions and sufficient conditions have been provided but a complete characterization is known for real n tuples only for n 4 kel71 sul49 and for complex n tuples only for n 3 ll79 motivated by symbolic dynamics boyle and handelman refocused attention on the nonzero part of the spectrum by making the following spectral conjecture bh91 bh93 see also boy93 8 and lm95 chapter 11 below a matrix a is primitive if all entries of a are nonnegative and for some n all entries of a are strictly positive also

second kind integral equations for the first kind dirichlet problem of the biharmonic equation in three dimensions a fredholm second kind integral equation skie formulation is constructed for the dirichlet problem of the biharmonic equation in three dimensions a fast numerical algorithm is developed based on the constructed skie its performance is illustrated via several numerical examples

strong shift equivalence and shear adjacency of nonnegative square integer matrices abstract for two square matrices a b of possibly different sizes with nonnegative integer entries write a 1 b if a rs and b sr for some two nonnegative integer matrices r s the transitive closure of this relation is called strong shift equivalence and is important in symbolic dynamics where it has been shown by r f williams to characterize the isomorphism of two topological markov chains with transition matrices a and b one invariant is the characteristic polynomial up to factors of however no procedure for deciding strong shift equivalence is known even for 2 2 matrices a b in fact for n n matrices with n 2 no nontrivial sufficient condition is known this paper presents such a sufficient condition that a and b are in the same component of a directed graph whose vertices are all n n nonnegative integer matrices sharing a fixed characteristic polynomial and whose edges correspond to certain elementary similarities for n 2 this result gives confirmation of strong shift equivalences that previously could not be verified for n 2 previous results are strengthened and the structure of the directed graph is determined

entropy at a weight per symbol and embeddings of markov chains in 11 krieger gave a remarkable embedding result for shifts of finite type he proved that two simple necessary conditions strict inequality of the topological entropies of the shifts and the existence of an embedding for their periodic points are in fact sufficient for markov chains when the appropriate definitions of embedding and subsystem were supplied in 10 analogous necessary conditions strict inequality of functions and the existence of a weight preserving embedding for periodic points became apparent however an example in 10 also revealed these conditions to not be sufficient in this paper we bring to bear on embeddings of markov chains the ideas we introduced in 16 in fact we work in the closely related setting of triples z a a a f where 2 a aa is a shift of finite type and f is a function assigning weights to the edges of the graph associated with sa aa the func t ionf takes values in ir or more generally in n q for some qen the weight of a periodic orbit which corresponds to a cycle in the graph is then the sum of the weights of the edges lying on the cycle division by the length of the cycle gives the weight per symbol in 16 we continued the rational linear span of the set wps i of weights per symbol is a finite dimensional vector space vs the convex hull of wps i in v i is a polytope wpsi called the weight per symbol polytope consideration of the faces of wps i gives subsystems of r a aa f which are ordered according to the ordering of the faces the resulting nesting of subsystems is the scaffold of a o a f an embedding of a triple i a a a f in another 2 b ab g is a continuous shift commuting injection q 2 a 12 which preserves weights of periodic orbits the two necessary conditions mentioned above imply w p s i c w when the boundary c wpsi meets wpsg that is when a face f of wps i meets a face g of wpsg any embedding must carry the subsystem corresponding to f into that corresponding to g and this gives rise to further necessary conditons a discussion of these complications and a description of the example of 10 in these terms will be given in sect 7 before that the main embedding

a phase field model for the mixture of two incompressible fluids and its approximation by a fourier spectral method abstract a phase field model for the mixture of two incompressible fluids is presented in this paper the model is based on an energetic variational formulation it consists of a navier stokes system linear momentum equation coupled with a cahn hilliard equation phase field equation through an extra stress term and the transport term the extra stress represents the phase induced capillary effect for the mixture due to the surface tension a fourier spectral method for the numerical approximation of this system is proposed and analyzed numerical results illustrating the robustness and versatility of the model are presented

quadrature over a pyramid or cube of integrands with a singularity at a vertex a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex

second kind integral equation formulation for the modified biharmonic equation and its applications a system of fredholm second kind integral equations skies is constructed for the modified biharmonic equation in two dimensions with gradient boundary conditions such boundary value problem arises naturally when the incompressible navier stokes equations are solved via a semi implicit discretization scheme and the resulting boundary value problem at each time step is then solved using the pure stream function formulation the advantages of such an approach greengard and kropinski 1998 14 are two fold first the velocity is automatically divergence free and second complicated nonlocal boundary conditions for the vorticity are avoided our construction though similar to that of farkas 1989 10 for the biharmonic equation is modified such that the skie formulation has low condition numbers for large values of the parameter we illustrate the performance of our numerical scheme with several numerical examples finally the scheme can be easily coupled with standard fast algorithms such as fft fast multipole methods greengard and rokhlin 1987 15 or fast direct solvers ho and greengard 2012 martinsson and rokhlin 2005 17 25 to achieve optimal complexity bringing accurate large scale long time fluid simulations within practical reach

short note a kernel independent fast multipole algorithm for radial basis functions we present a fast multipole algorithm for the evaluation of pairwise interaction through the radial basis functions such as 1 r a r 2 a 2 and 1 r 2 a 2 with a 0 in both two and three dimensions our algorithm is an extension of the kernel independent fast multipole method presented in ying et al l ying g biros d zorin a kernel independent adaptive fast multipole algorithm in two and three dimensions j comput phys 196 2 2004 591 626 numerical results are provided to illustrate the accuracy and complexity properties of the algorithm

the black box fast multipole method a new o n fast multipole formulation is proposed for non oscillatory kernels this algorithm is applicable to kernels k x y which are only known numerically that is their numerical value can be obtained for any x y this is quite different from many fast multipole methods which depend on analytical expansions of the far field behavior of k for x y large other black box or kernel independent fast multipole methods have been devised our approach has the advantage of requiring a small pre computation time even for very large systems and uses the minimal number of coefficients to represent the far field for a given l 2 tolerance error in the approximation this technique can be very useful for problems where the kernel is known analytically but is quite complicated or for kernels which are defined purely numerically

perron spectratopes and the real nonnegative inverse eigenvalue problem abstract call an n by n invertible matrix s a perron similarity if there is a real non scalar diagonal matrix d such that s d s 1 is entrywise nonnegative we give two characterizations of perron similarities and study the polyhedra c s x r n s d x s 1 0 d x diag x and p s x c s x 1 1 which we call the perron spectracone and perron spectratope respectively the set of all normalized real spectra of diagonalizable nonnegative matrices may be covered by perron spectratopes so that enumerating them is of interest the perron spectracone and spectratope of hadamard matrices are of particular interest and tend to have large volume for the canonical hadamard matrix as well as other matrices the perron spectratope coincides with the convex hull of its rows in addition we provide a constructive version of a result due to fiedler 9 theorem 2 4 for hadamard orders and a constructive version of the boyle handelman theorem 2 theorem 5 1 for sule manova spectra

williams s conjecture is false for reducible subshifts we show that for two subshifts of finite type having exactly two irreducible components strong shift equivalence is not the same as shift equiv alence this refutes the williams conjecture w in the reducible case the irreducible case remains an open problem mathematics research group alabama state university montgomery alabama 36101 this content downloaded from 207 46 13 180 on thu 08 sep 2016 04 22 09 utc all use subject to http about jstor org terms

on automorphisms of markov chains we prove several theorems about automorphisms of markov chains using the weight per symbol polytope

the nonnegative inverse eigenvalue problem abstract let 1 n be a list of complex numbers the nonnegative inverse eigenvalue problem niep is the problem of determining necessary and sufficient conditions in order that be the spectrum of an entrywise nonnegative n n matrix our purpose is to give an overview of the niep its history modern results and subproblems with particular emphasis on symmetric realizing matrices a substantial bibliography is included

strong shift equivalence and the generalized spectral conjecture for nonnegative matrices abstract given matrices a and b shift equivalent over a dense subring r of r with a primitive we show that b is strong shift equivalent over r to a primitive matrix this result shows that the weak form of the generalized spectral conjecture for primitive matrices implies the strong form the foundation of this work is the recent result that for any ring r the group nk 1 r of algebraic k theory classifies the refinement of shift equivalence by strong shift equivalence for matrices over r

maxentropic markov chains corresp the markov chain that has maximum entropy for given first and second moments is determined the solution provides a discrete analog to the continuous gauss markov process

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

conditional limit theorems under markov conditioning let x 1 x 2 cdots be independent identically distributed random variables taking values in a finite set x and consider the conditional joint distribution of the first m elements of the sample x 1 cdots x n on the condition that x 1 x 1 and the sliding block sample average of a function h cdot cdot defined on x 2 exceeds a threshold alpha eh x 1 x 2 for m fixed and n rightarrow infty this conditional joint distribution is shown to converge m the m step joint distribution of a markov chain started in x 1 which is closest to x l x 2 cdots in kullback leibler information divergence among all markov chains whose two dimensional stationary distribution p cdot cdot satisfies sum p x y h x y geq alpha provided some distribution p on x 2 having equal marginals does satisfy this constraint with strict inequality similar conditional limit theorems are obtained when x 1 x 2 cdots is an arbitrary finite order markov chain and more general conditioning is allowed

a hierarchical o n force calculation algorithm a novel code for the approximate computation of long range forces between n mutually interacting bodies is presented the code is based on a hierarchical tree of cubic cells and features mutual cell cell interactions which are calculated via a cartesian taylor expansion in a symmetric way such that total momentum is conserved the code benefits from an improved and simple multipole acceptance criterion that reduces the force error and the computational effort for n 104 the computational costs are found empirically to rise sublinearly with n for applications in stellar dynamics this is the first competitive code with complexity o n it is faster than the standard tree code by a factor of 10 or more

periodic points and automorphisms of the shift on etudie le groupe d automorphisme d un decalage de markov topologique a l aide des points periodiques et des ensembles instables

small polynomial matrix presentations of nonnegative matrices we investigate the use of polynomial matrices to give efficient presentations of nonnegative matrices exhibiting prescribed spectral and algebraic behavior

on the compression of low rank matrices a procedure is reported for the compression of rank deficient matrices a matrix a of rank k is represented in the form a u circ b circ v where b is a k times k submatrix of a and u v are well conditioned matrices that each contain a k times k identity submatrix this property enables such compression schemes to be used in certain situations where the singular value decomposition svd cannot be used efficiently numerical examples are presented

the error exponent for the noiseless encoding of finite ergodic markov sources a new approach to the classical fixed length noiseless source coding problem is proposed for the case of finite ergodic markov sources this approach is based on simple counting arguments the central notion of markov type a set containing all the source sequences having the same transition counts from letter to letter is introduced and the cardinality of such a set is evaluated via graph theoretical tools the error exponent is shown to be a weighted average of informational divergences and the universal character of the result is stressed as a corollary the classical source coding theorem determining the achievable rates is rederived

efficient spectral galerkin method ii direct solvers of second and fourth order equations using chebyshev polynomials efficient direct solvers based on the chebyshev galerkin methods for second and fourth order equations are presented they are based on appropriate base functions for the galerkin formulation that lead to discrete systems with special structured matrices that can be efficiently inverted numerical results indicate that the direct solvers presented in this paper are significantly more accurate and efficient than those based on the chebyshev tau method

a kernel independent adaptive fast multipole algorithm in two and three dimensions we present a new fast multipole method for particle simulations the main feature of our algorithm is that it does not require the implementation of multipole expansions of the underlying kernel and it is based only on kernel evaluations instead of using analytic expansions to represent the potential generated by sources inside a box of the hierarchical fmm tree we use a continuous distribution of an equivalent density on a surface enclosing the box to find this equivalent density we match its potential to the potential of the original sources at a surface in the far field by solving local dirichlet type boundary value problems the far field evaluations are sparsified with singular value decomposition in 2d or fast fourier transforms in 3d we have tested the new method on the single and double layer operators for the laplacian the modified laplacian the stokes the modified stokes the navier and the modified navier operators in two and three dimensions our numerical results indicate that our method compares very well with the best known implementations of the analytic fmm method for both the laplacian and modified laplacian kernels its advantage is the relative simplicity of the implementation and its immediate extension to more general kernels

the automorphism group of a shift of finite type let xt at be a shift of finite type and g aut vt denote the group of homeomorphisms of xt commuting with t we investigate the algebraic properties of the countable group g and the dynamics of its action on xt and associated spaces using marker constructions we show g contains many groups such as the free group on two generators however g is residually finite so does not contain divisible groups or the infinite symmetric group the doubly exponential growth rate of the number of automorphisms depending on n coordinates leads to a new and nontrivial topological invariant of crt whose exact value is not known we prove that modulo a few points of low period g acts transitively on the set of points with least at period n using padic analysis we generalize to most finite type shifts a result of boyle and krieger that the gyration function of a full shift has infinite order the action of g on the dimension group of at is investigated we show there are no proper infinite compact g invariant sets we give a complete characterization of the g orbit closure of a continuous probability measure and deduce that the only continuous g invariant measure is that of maximal entropy examples questions and problems complement our analysis and we conclude with a brief survey of some remaining open problems

automorphisms of the dimension group and gyration numbers o introduction 1 the sign gyration compatibility condition 2 gyration and orbit sign numbers 3 construction of sgcc a m 4 application of sgcc a summary let aut o a denote the group of automorphisms of a subshift of finite type xa o a built from a primitive matrix a we show that the sign gyrationcompatibility condition homomorphism sgcc a m defined on aut 0 a factors through the group aut s a of automorphisms of the dimension group this is used to find a mixing subshift of finite type with a permutation of fixed points that cannot be lifted to an automorphism of the shift we also give an example of a mixing subshift of finite type where the dimension group representation is not surjective this example is used in kr3 to give examples of subshifts of finite type reducible with two mixing components that are shift equivalent but not strong shift equivalent over the nonnegative integers o introduction

path components of matrices and strong shift equivalence over q abstract we show that two positive matrices over q or r which lie in the same component of a set m m n r m is conjugate over r to a are strong shift equivalent it is a simple corollary that 2 2 matrices over q are strong shift equivalent if they are shift equivalent conversely we prove that if two matrices a b over r are strong shift equivalent then a 0 b 0 can be joined by a path of nonnegative real matrices within the strong shift equivalence class of a up to conjugation of b 0 by a permutation matrix

improved gilbert varshamov bound for constrained systems nonconstructive existence results are obtained for block error correcting codes whose codewords lie in a given constrained system each such system is defined as a set of words obtained by reading the labels of a finite directed labeled graph for a prescribed constrained system and relative minimum distance delta the new lower bounds on the rate of such codes improve on those derived recently by v d kolesnik and v y krachkovsky 1991 the better bounds are achieved by considering a special subclass of sequences in the constrained system namely those having certain empirical statistics determined by delta

coded diversity on block fading channels this paper considers coded diversity schemes over block fading rician channels using random coding techniques two random coding upper bounds on the error probability of block codes are derived a new bound and a simpler but looser bound assuming binary input distribution also a new lower bound for any block code is derived using the strong converse to channel coding theorem the lower bound shows that the new random coding upper bound is quite tight furthermore it is shown that the maximum achievable diversity order in a block fading channel with finite interleaving depends not only on the number of subchannels l but also on the code rate r and that the performance can only marginally be improved by increasing the block length of the code the random coding upper bound and the lower bound are shown to converge to the capacity outage for large channel block lengths n demonstrating that the capacity outage can be used for estimating the error probability of coded diversity schemes

an integral equation approach to the incompressible navier stokes equations in two dimensions we present a collection of methods for solving the incompressible navier stokes equations in the plane that are based on a pure stream function formulation the advantages of this approach are twofold first the velocity is automatically divergence free and second complicated nonlocal boundary conditions for the vorticity are avoided the disadvantage is that the solution of a nonlinear fourth order partial differential equation is required by recasting this partial differential equation as an integral equation we avoid the ill conditioning which hampers finite difference and finite element methods in this environment by using fast algorithms for the evaluation of volume integrals we are able to solve the equations using o m or o m log m operations where m is the number of points in the discretization of the domain

efficient spectral galerkin method i direct solvers of second and fourth order equations using legendre polynomials this paper presents some efficient algorithms based on the legendre galerkin approximations for the direct solution of the second and fourth order elliptic equations the key to the efficiency of these algorithms is to construct appropriate base functions which lead to systems with sparse matrices for the discrete variational formulations the complexities of the algorithms are a small multiple of n d 1 operations for a d dimensional domain with n 1 d unknowns while the convergence rates of the algorithms are exponential for problems with smooth solutions in addition the algorithms can be effectively parallelized since the bottlenecks of the algorithms are matrix matrix multiplications

an efficient computational method for solving fractional biharmonic equation in this paper we first introduce the fractional biharmonic equation and an orthogonal system of basis functions for the space of continuous functions on the interval 0 l generated by the shifted chebyshev polynomials moreover we propose a computational method based on the operational matrix of fractional derivatives of these basis functions for solving the fractional biharmonic equation the main characteristic behind this approach is that it reduces the problem under consideration to solving a system of algebraic equations which greatly simplifies the problem convergence of the shifted chebyshev polynomials expansion in two dimensions is investigated also the power of this manageable method is illustrated

the correlation of length spectra of two hyperbolic surfaces we derive an asymptotic formula for the number of free homotopy classes on a closed surface which have approximately the same length with respect to two different hyperbolic structures on the surface the growth rate in the asymptotic formula is described in terms of the thermodynamic formalism for the geodesic flow