global holderian error bound for nondegenerate polynomials let f colon mathbb r n to mathbb r be a polynomial and s x in mathbb r n f x le 0 let f x max 0 f x if there exist c 0 alpha 0 beta 0 such that d x s le c f x alpha f x beta for all x in mathbb r n where d x s denotes the distance between x and s then we say that f has a global holderian error bound we prove that if f is convenient and nondegenerate with respect to its newton boundary at infinity in the sense of kouchnirenko invent math 32 1976 pp 1 32 then it has a global holderian error bound since the nondegenerate polynomials form a zariski open subset in a variety of polynomials with a given convenient newton boundary at infinity this result shows that global holderian error bounds hold for a large class of polynomials which can be relatively easy recognized

bit interleaved coded modulation with iterative decoding and 8 psk signaling we have suggested bit interleaved coded modulation with soft decision iterative decoding bicm id for bandwidth efficient transmission over gaussian and fading channels unlike trellis coded modulation bicm id has a small free euclidean distance but large diversity order due to bit interleaving with iterative decoding soft bit decisions can be employed to significantly improve the conditional intersignal euclidean distance this leads to a large coding gain comparable to that of turbo tcm over both gaussian and rayleigh fading channels with much less system complexity we address critical design issues to enhance the decoding performance and provide the analytical bounds on the performance with an ideal feedback assumption we investigate the performance characteristics of bicm id through extensive simulations and show that at high signal to noise ratios the performance of bicm id converges to the performance assuming error free feedback

endpoint estimates for one dimensional oscillatory integral operators abstract the one dimensional oscillatory integral operator associated to a real analytic phase s is given by t f x e i s x y x y f y d y in their fundamental work phong and stein established sharp l 2 estimates for t the goal of this paper is to extend their results to all endpoints in particular we obtain a complete characterization for the mapping properties for t on l p r more precisely we show that t f p f p holds for some 0 if and only if 1 p 1 p lies in the reduced newton polygon of s

lp zd estimates for discrete operators of radon type maximal functions and vector valued estimates abstract we prove l p z d bounds for p 1 of discrete maximal functions corresponding to averaging operators and truncated singular integrals of radon type and their applications to pointwise ergodic theory our new approach is based on a unified analysis of both types of operators and also yields an extension to the vector valued form of these results

responses of cross ply laminates with viscous interfaces in cylindrical bending the responses of a simply supported cross ply laminate in cylindrical bending with viscous interfaces are studied in this paper because of the introduction of viscous interfaces the elastic fields in the laminate will depend on the time variable the problem is solved exactly in the space domain but approximately in the time domain state space method which is very powerful for analyzing laminated structures is employed the variations of state variables with time are simulated using power series expansions numerical examples are considered and comparison with existent results validates the efficiency of the present method

ehresmann fibrations and palais smale conditions for morphisms of finsler manifolds the central result of this paper is a generalization of the ehresmann fibration theorem to the infinite dimensional and or non proper setting with this aim we introduce the concepts of strong submersion and of mapping with uniformly split kernels first applications include a global implicit function theorem and a necessary and sufficient version of hadamard s global invertibility criterion in the setting of finsler manifolds another major application makes use of the idea of asymptotic critical value not critical point which helps formulate various generalizations of the palais smale condition for morphisms of finsler manifolds not merely functionals we obtain a critical point theory for morphisms of finsler manifolds extending many results known only for functionals notably ekeland s variational principle these results are used to discuss a new approach to lagrange multiplier and nonlinear eigenvalue problems and to develop an intrinsic critical point theory for complex analytic functionals the latter reveals an intimate connection between conditions of palais smale type and the structure of polynomial automorphisms jacobian conjecture

resolution of singularities in two dimensions and the stability of integrals abstract for a small disk d centered at the origin in r 2 a smooth real valued function s x y on d and a positive epsilon we consider the measure of the points in d where s x y as well as oscillatory integral analogues specifically we consider the effect of perturbing s x y on these quantities besides being of intrinsic interest these questions are important in the analysis of fourier transforms of surface supported measures complex and higher dimensional analogues of these questions are also connected to various issues in algebraic and complex geometry for real analytic s x y this question has been investigated for example by karpushkin using versal deformation theory and by phong stein sturm who developed a method often referred to as the method of algebraic estimates in this paper we show how the use of resolution of singularities algorithms in two dimensions along with some one dimensional van der corput type lemmas provides another method for dealing with such questions as a result we prove new estimates and theorems for these and related quantities furthermore since these algorithms apply to all smooth functions the theorems will hold for all smooth functions as opposed to the earlier real analytic results

from harmonic analysis to arithmetic combinatorics arithmetic combinatorics or additive combinatorics is a fast developing area of research combining elements of number theory combinatorics harmonic analysis and ergodic theory its arguably best known result and the one that brought it to global prominence is the proof by ben green and terence tao of the long standing conjecture that primes contain arbitrarily long arithmetic progressions there are many accounts and expositions of the green tao theorem including the articles by kra 119 and tao 182 in the bulletin the purpose of the present article is to survey a broader highly interconnected network of questions and results built over the decades and spanning several areas of mathematics of which the green tao theorem is a famous descendant an old geometric problem lies at the heart of key conjectures in harmonic analysis a major result in partial differential equations invokes combinatorial theorems on intersecting lines and circles an unexpected argument points harmonic analysts towards additive number theory with consequences that could have hardly been anticipated we will not try to give a comprehensive survey of harmonic analysis combinatorics or additive number theory we will not even be able to do full justice to our specific areas of focus instead referring the reader to the more complete expositions and surveys listed in section 7 our goal here is to emphasize the connections between these areas we will thus concentrate on relatively few problems chosen as much for their importance to their fields as for their links to each other the article is written from the point of view of an analyst who in the course of her work was gradually introduced to the questions discussed here and found them fascinating we hope that the reader will enjoy a taste of this experience

on multilinear oscillatory integrals nonsingular and singular basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered l p norm inequalities are established for multilinear integral operators of calderon zygmund type which incorporate oscillatory factors e ip where p is a real valued polynomial

ell p left mathbb z d right estimates for discrete operators of radon type variational estimates we prove ell p left mathbb z d right bounds for p in 1 infty of r variations r in 2 infty for discrete averaging operators and truncated singular integrals of radon type we shall present a new powerful method which allows us to deal with these operators in a unified way and obtain the range of parameters of p and r which coincide with the ranges of their continuous counterparts

modal analysis of magneto electro elastic plates using the state vector approach the state vector approach is proposed to analyze the free vibration of magneto electro elastic laminate plates the extended displacements and stresses can be divided into the so called in plane and out of plane variables once the state equation for the out of plane variables is obtained a complex boundary value problem is converted into an equivalent simple initial value problem through the state equation the propagator matrix between the top and bottom interfaces of every layer can be easily derived the global propagator matrix can also be assembled using the continuity conditions it is obvious that the order of global propagator matrix is not related to the number of layers consequently this approach possesses certain virtues including simple formulation less expensive computation etc to test the formulation the developed solution is then applied to a simply supported multilayered plate constructed of piezoelectric and or piezomagnetic materials the natural frequencies and corresponding mode shapes are computed and compared with existing results furthermore the fundamental modes along with a couple of other higher modes which have never been reported in previous literature are presented therefore this completed set of frequencies and mode shapes can be used as benchmarks for future research in this field it is also believed that the approach could be useful in the analysis and design of smart structures constructed from piezoelectric piezomagnetic composites

recent improvements in the complexity of the effective nullstellensatz we bring up to date the estimates on the complexity of the effective nullstellensatz and the membership problem

three dimensional static analysis of multi layered piezoelectric hollow spheres via the state space method a general non axisymmetric exact analysis of the statics of a laminated piezoelectric hollow sphere is presented in the paper by using a state space method to select a proper set of state variables three displacement functions and two stress functions are introduced it is found that the basic equations of a spherically isotropic piezoelectric medium are eventually turned to two separated state equations with constant coefficients the solutions of which are then obtained by virtue of matrix theory the continuity conditions at each interface are then used to derive two relationships between respective boundary variables at the inner and outer spherical surfaces no matter how many layers the sphere contains the orders of the final solving equations remain unaltered

differential space time modulation space time coding and modulation exploit the presence of multiple transmit antennas to improve the performance on multipath radio channels thus far most work on space time coding has assumed that perfect channel estimates are available at the receiver in certain situations however it may be difficult or costly to estimate the channel accurately in which case it is natural to consider the design of modulation techniques that do not require channel estimates at the transmitter or receiver we propose a general approach to differential modulation for multiple transmit antennas based on group codes this approach ran be applied to any number of transmit and receive antennas and any signal constellation we also derive low complexity differential receivers error bounds and modulator design criteria which we use to construct optimal differential modulation schemes for two transmit antennas these schemes can be demodulated with or without channel estimates this permits the receiver to exploit channel estimates when they are available the performance degrades by approximately 3 db when estimates are not available

separation of algebraic sets and the łojasiewicz exponent of polynomial mappings we prove a sharp regular separation condition for arbitrary projective algebraic sets as a corollary an extension of kollar s results on the ojasiewicz exponent of polynomial mappings is obtained

injectivity of real polynomial maps and łojasiewicz exponents at infinity in this paper we give a lower bound for the ojasiewicz exponent at infinity of a special class of polynomial maps mathbb r n to mathbb r s s 1 as a consequence we detect a class of polynomial maps mathbb r n to mathbb r n that are global diffeomorphisms if their jacobian determinant never vanishes

uniform estimates for bilinear hilbert transforms and bilinear maximal functions associated to polynomials we study the bilinear hilbert transforms and bilinear maximal functions associated to non flat polynomial curves and obtain uniform l r estimates for r d 1 over d where d is the degree of the polynomial in addition the lower bound of r is sharp up to the end point

representation theory for high rate multiple antenna code design multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment but the practical success of using multiple antennas depends crucially on our ability to design high rate space time constellations with low encoding and decoding complexity it has been shown that full transmitter diversity where the constellation is a set of unitary matrices whose differences have nonzero determinant is a desirable property for good performance we use the powerful theory of fixed point free groups and their representations to design high rate constellations with full diversity furthermore we thereby classify all full diversity constellations that form a group for all rates and numbers of transmitter antennas the group structure makes the constellations especially suitable for differential modulation and low complexity decoding algorithms the classification also reveals that the number of different group structures with full diversity is very limited when the number of transmitter antennas is large and odd we therefore also consider extensions of the constellation designs to nongroups we conclude by showing that many of our designed constellations perform excellently on both simulated and real wireless channels

alternative state space formulations for magnetoelectric thermoelasticity with transverse isotropy and the application to bending analysis of nonhomogeneous plates abstract by introducing two displacement functions and two stress functions the governing equations of the linear theory of magneto electro thermo elasticity with transverse isotropy are simplified on selecting certain physical quantities as the basic unknowns two new state equations are established each of them is order reduced when compared with the one reported recently in literature leading to a higher numerical efficiency the material inhomogeneity along the axis of symmetry z direction can be taken into account and an approximate laminate model is employed to facilitate deriving analytical solutions the validity of new formulations is examined by considering a laminated magneto electro elastic rectangular plate and good agreement is obtained with existent results a plate with a functionally graded property is then analyzed the effect of magnetoelectric coupling in a batio3 cofe2o4 composite predicted from the micromechanics simulation is studied quantitatively

fractional time dependent schrodinger equation on the heisenberg group let be the kohn sublaplacian on the heisenberg group mathbb h n l delta alpha frac 2 3 0 and for all e 0

unitary space time modulation for multiple antenna communications in rayleigh flat fading motivated by information theoretic considerations we propose a signaling scheme unitary space time modulation for multiple antenna communication links this modulation is ideally suited for rayleigh fast fading environments since it does not require the receiver to know or learn the propagation coefficients unitary space time modulation uses constellations of t spl times m space time signals spl phi sub i l 1 l where t represents the coherence interval during which the fading is approximately constant and m t is the number of transmitter antennas the columns of each spl phi sub i are orthonormal when the receiver does not know the propagation coefficients which between pairs of transmitter and receiver antennas are modeled as statistically independent this modulation performs very well either when the signal to noise ratio snr is high or when t spl gt m we design some multiple antenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding we demonstrate that two antennas have a 6 db diversity gain over one antenna at 15 db snr

equivariant cohomology and the maurer cartan equation let g be a compact connected lie group acting smoothly on a manifold m goresky kottwitz macpherson described a small cartan model for the equivariant cohomology of m quasi isomorphic to the standard cartan complex of equivariant differential forms in this paper we construct an explicit cochain map from the small cartan model into the standard cartan model inducing an isomorphism in cohomology the construction involves the solution of a remarkable inhomogeneous maurer cartan equation this solution has further applications to the theory of transgression in the weil algebra and to the chevalley koszul theory of the cohomology of principal bundles

systematic design of unitary space time constellations we propose a systematic method for creating constellations of unitary space time signals for multiple antenna communication links unitary space time signals which are orthonormal in time across the antennas have been shown to be well tailored to a rayleigh fading channel where neither the transmitter nor the receiver knows the fading coefficients the signals can achieve low probability of error by exploiting multiple antenna diversity because the fading coefficients are not known the criterion for creating and evaluating the constellation is nonstandard and differs markedly from the familiar maximum euclidean distance norm our construction begins with the first signal in the constellation an oblong complex valued matrix whose columns are orthonormal and systematically produces the remaining signals by successively rotating this signal in a high dimensional complex space this construction easily produces large constellations of high dimensional signals we demonstrate its efficacy through examples involving one two and three transmitter antennas

a smooth variational principle with applications to subdifferentiability and to differentiability of convex functions we show that typically lower semicontinuous functions on a banach space densely inherit lower subderivatives of the same degree of smoothness as the norm in particular every continuous convex function on a space with a g teaux weak hadamard frechet smooth renorm is densely g teaux weak hadamard frechet differentiable our technique relies on a more powerful analogue of ekeland s variational principle in which the function is perturbed by a quadratic like function this smooth variational principle has very broad applicability in problems of nonsmooth analysis

sharp effective nullstellensatz the usual proofs of this result however give no information about the g1 s for instance they give no bound on their degrees this question was first considered by g hermann h she used elimination theory to get a bound on the degree of the gi s which was doubly exponential in the number of variables her results were later improved in mw and in th all these produce bounds that are doubly exponential in the number of variables a major breakthrough was achieved by brownawell b1 who proved the following result

on free vibration of non homogeneous transversely isotropic magneto electro elastic plates two independent state equations are established for transversely isotropic magneto electro elastic media by introducing proper stress and displacement functions the free vibration problem of simply supported rectangular plates with general inhomogeneous functionally graded material properties along the thickness direction is then considered an approximate laminate model is employed to transform the state equations with variable coefficients to the ones with constant coefficients two different classes of vibrations are found in particular the frequency of the first class is only related to the elastic property of the plate while that of the second class is affected by the couplings among the elastic electric and magnetic fields numerical results are presented and some important issues are discussed

optimal signaling and selection verification for single transmit antenna selection in marked contrast with the ideal error free feedback assumption that is common in the literature practical systems are likely to have severely bandwidth limited error prone feedback channels we consider the scenario where feedback from the receiver is used by the transmitter to select the best antenna out of many available antennas for data transmission feedback errors cause the transmitter to select an antenna different from the one signaled by the receiver we show that optimizing the signaling assignment which maps the antenna indices to the feedback codewords improves performance without introducing any additional redundancy for a system that uses error prone feedback to transmit quadrature phase shift keying modulated data from a single antenna selected from many available spatially correlated antennas we derive closed form approximations for the data symbol error probability for an arbitrary number of receive antennas we use these to systematically find the optimal signaling assignments using a low complexity algorithm the optimal signaling is intimately coupled to how the receiver performs selection verification i e how it decodes the data signal when due to feedback errors it does not always know which antenna was used for data transmission we show that ignoring feedback errors at the receiver can lead to an unacceptable performance degradation and develop optimal and suboptimal blind and nonblind selection verification methods with a small side information overhead nonblind verification approaches the ideal perfect selection verification performance

newton polygons and local integrability of negative powers of smooth functions in the plane let f x y be any smooth real valued function with f 0 0 0 for a sufficiently small neighborhood u of the origin we study the number sup u f x f it is known that sometimes this number can be expressed in a natural way using the newton polygon of f we provide necessary and sufficient conditions for this newton polygon characterization to hold the behavior of the integral at the supremal e is also analyzed

a global smooth version of the classical łojasiewicz inequality abstract let f r n r be a function of class c d d 1 such that d f x 1 d 0 on r n then the following global ojasiewicz inequality holds true c d dist x f 0 f x 1 0 d f x for all x r n where c d d 2 2 d 1 and dist x a denotes the euclidean distance from x to a as applications of this inequality we have the following statements if the sets f 0 and f x 1 0 are non asymptotic at infinity then there exist positive constants e and r such that c d dist x f 0 d f x whenever dist x f 0 e and x r if f is a polynomial of degree d with an isolated critical point at the origin the following effective ojasiewicz inequality holds true c dist x f 0 d 2 d 3 n 1 2 f x for all x r for some c 0 and r 0 finally we establish a relation between the above global ojasiewicz inequality and the phenomenon of singularities at infinity

uniform estimates for oscillatory integral operators abstract in this paper we prove the uniform l p boundedness of oscillatory singular integral operators with smooth phase functions which satisfy a certain finite type condition these phase functions include the class of real analytic functions the uniform boundedness does not hold if the finite type condition is removed we also obtained estimates for related operators including an optimal l 2 estimate for operators with singular kernels whose phase functions have non singular hessians

some l2 results for overline partial on projective varieties with general singularities let x be an irreducible n dimensional projective variety in bbb c p n with arbitrary singular locus we prove that the l 2 overline partial p 1 cohomology groups with respect to the fubini study metric of the regular part of x are finite dimensional

regularity of fourier integral operators with caustics the caustics of fourier integral operators are defined as caustics of the corresponding schwartz kernels lagrangian distributions on x y the caustic set c of the canonical relation is characterized as the set of points where the rank of the projection c x x y is smaller than its maximal value dim x x y 1 we derive the l p y l q x estimates on fourier integral operators with caustics of corank 1 such as caustics of type a m 1 m n for the values of p and q outside of a certain neighborhood of the line of duality q p the l p l q estimates are proved to be caustics insensitive we apply our results to the analysis of the blow up of the estimates on the half wave operator just before the geodesic flow forms caustics

radon transforms and finite type conditions the purpose of this paper is to study averaging operators of radon transform type we shall formulate suitable finite type conditions and prove lp sobolev and lplq estimates the results will be essentially sharp for operators associated with families of curves in the plane let xc and t be smooth manifolds dimx3 nl dim2 nr and let m be a submanifold in xc x t with conormal bundle n m we denote by t the codimension of m we shall always assume that the projections lry m x and 7rt m 42 are surjective with rank dirx nl rank dr9 nr this in particular implies that n m c t x o x t o where 0 refers to the zero sections in t x and t 2 respectively this is the usual assumption for the canonical relation associated with lagrangian distributions arising as kernels of fourier integral operators the assumptions on dirx d7rt imply that for fixed x e x y e 2 the sets amx y e t x y e mi m x ye2x x y em i

diophantine approximation by algebraic hypersurfaces and varieties questions on rational approximations to a real number can be generalized in two directions on the one hand we may ask about approximation to a point in r by hyperplanes defined over the rationals that is we seek hyperplanes with small distance from the given point on the other hand following wirsing we may ask about approximation to a real number by real algebraic numbers of degree at most d the present paper deals with a common generalization of both directions namely with approximation to a point in r n by algebraic hypersurfaces or more generally algebraic varieties defined over the rationals

endpoint l p l q estimates for degenerate radon transforms in mathbb r 2 associated with real analytic functions abstract we consider degenerate radon transforms of the form rf t x int mathbb r f t s x y y psi x y dy where psi is supported in a small neighborhood of the origin under the condition that s is real analytic we prove complete l p l q estimates for r

a topological tits alternative let k be a local eld and gln k a linear group over k we prove that either contains a relatively open solvable subgroup or it contains a relatively dense free subgroup this result has applications in dynamics riemannian foliations and pronite groups

free vibrations of piezoelectric cylindrical shells filled with compressible fluid abstract three displacement functions are introduced to represent each mechanical displacement according to the three dimensional theory after expanding these functions and the electric potential with orthogonal series the free vibration equation of piezoelectric cylindrical shells satisfying ss3 edge conditions can be obtained the equation was solved by utilizing bessel functions with complex arguments the effects of compressible fluid on shells are considered and some new phenomena which are exclusive for piezoelectric cylindrical shells are reported results of empty infinite piezoelectric cylindrical shells are compared to those presented in relative references some lowest frequencies that were missed by paul and venkatesan paul h s and venkatesan m 1987 vibrations of hollow circular cylinder of piezoelectric ceramics journal of the acoustic society of america82 852 856 were discovered

multilinear weighted convolution of l 2 functions and applications to nonlinear dispersive equations the x s b spaces as used by beals bourgain kenig ponce vega klainerman machedon and others are fundamental tools to study the low regularity behavior of nonlinear dispersive equations it is of particular interest to obtain bilinear or multilinear estimates involving these spaces by plancherel s theorem and duality these estimates reduce to estimating a weighted convolution integral in terms of the l 2 norms of the component functions in this paper we systematically study weighted convolution estimates on l 2 as a consequence we obtain sharp bilinear estimates for the kdv wave and schrodinger x s b spaces

sharp l p boundedness of oscillatory integral operators with polynomial phases in this paper we shall prove the l p endpoint decay estimates of oscillatory integral operators with homogeneous polynomial phases s in mathbb r times mathbb r as a consequence sharp l p decay estimates are also obtained when polynomial phases have the form s x m 1 y m 2 with m 1 and m 2 being positive integers

a note on the static behavior of simply supported laminated piezoelectric cylinders an exact three dimensional solution of the equations of linear piezoelectricity is given for the static response of a finite laminated piezoelectric cylinder with its ends simply supported the equilibrium equations and the conservation of charge equation are constructed in cylindrical coordinates the three displacement components and the electrostatic potential are expressed in terms of fourier series in the axial and circumferential directions leading to a coupled system of four ordinary differential equations in the radial coordinate the frobenious method is used to obtain the elastic and electric fields for each layer of the laminate which are a function of eight constants enforcing the boundary and continuity conditions across each interface yields the required number of equations to solve for these constants several examples are presented to study the fundamental behavior of these solids

global łojasiewicz type inequality for non degenerate polynomial maps abstract let f f 1 f p r n r p be a polynomial map this paper studies the existence of the following global ojasiewicz type inequality f x f x c d x f 1 0 for all x r n for some constants c 0 0 and 0 we show that the above inequality holds if one of the following conditions is satisfied i f is convenient and khovanskii non degenerate at infinity ii f is convenient and non degenerate at infinity iii f is mikhailov gindikin non degenerate further in cases ii and iii the exponents and can be determined explicitly

semialgebraic sard theorem for generalized critical values we prove that a semialgebraic differentiable mapping has a generalized critical values set of measure zero moreover if the mapping is c 2 we obtain bya generalisation of ehresmann s fibration theorem due to p j rabier 20 a locallytrivial fibration over the complement of this set in the complex case we prove that the set of generalized critical values of a polynomial mapping is a proper algebraic set

free axisymmetric vibration of transversely isotropic piezoelectric circular plates abstract based on three dimensional elastic theory of piezoelectric materials the axisymmetric state space formulation of piezoelectric laminated circular plates is derived finite hankel transforms are used and the boundary variables in free terms are replaced for two kinds of boundary conditions to obtain ordinary differential equations with constant coefficients regarding the axisymmetric free vibration problem two exact solutions for two different boundary conditions are found discarding piezoelectric effect the exact solutions for transversely isotropic circular laminates are also obtained through the same procedure numerical examples are given and compared with those of finite element method fem

a global lojasiewicz inequality for algebraic varieties let x be the locus of common zeros of polynomials f 1 f in n complex variables a global upper bound for the distance to x is given in the form of a lojasiewicz inequality the exponent in this inequality is bounded by d min n k where d max 3 deg f i the estimates are also valid over an algebraically closed field of any characteristic

coded unitary space time modulation with iterative decoding error performance and mapping design this paper studies the bit error probability of coded unitary space time modulation with iterative decoding where neither the transmitter nor the receiver knows the channel fading coefficients the tight error bound with respect to the asymptotic performance is first analytically derived for any given unitary constellation and mapping rule design criteria regarding the choice of unitary constellation and mapping are then established furthermore using the unitary constellation obtained from orthogonal design with quadrature phase shift keying qpsk or 4 psk and 8 psk two different mapping rules are proposed the first mapping rule gives the most suitable mapping for systems that do not implement iterative processing which is similar to a gray mapping in coherent channels the second mapping rule yields the best mapping for systems with iterative decoding in particular analytical and simulation results show that with the proposed mappings of the unitary constellations obtained from orthogonal designs the asymptotic error performance of the iterative systems can closely approach a lower bound which is applicable to any unitary constellation and mapping

pseudo gray coding a pseudo gray code is an assignment of n bit binary indexes to 2 points in a euclidean space so that the hamming distance between two points corresponds closely to the euclidean distance pseudo gray coding provides a redundancy free error protection scheme for vector quantization vq of analog signals when the binary indexes are used as channel symbols on a discrete memoryless channel and the points are signal codevectors binary indexes are assigned to codevectors in a way that reduces the average quantization distortion introduced in the reproduced source vectors when a transmitted index is corrupted by channel noise a globally optimal solution to this problem is generally intractable due to an inherently large computational complexity a locally optimal solution the binary switching algorithm is introduced based on the objective of minimizing a useful upper bound on the average system distortion the algorithm yields a significant reduction in average distortion and converges in reasonable running times the sue of pseudo gray coding is motivated by the increasing need for low bit rate vq based encoding systems that operate on noisy channels such as in mobile radio speech communications

noncoherent mimo communication grassmannian constellations and efficient detection this paper considers the design of both a transmitter and a receiver for noncoherent communication over a frequency flat richly scattered multiple input multiple output mimo channel the design is guided by the fact that at high signal to noise ratios snrs the ergodic capacity of the channel can be achieved by input signals that are isotropically distributed on the compact grassmann manifold the first part of the paper considers the design of grassmannian constellations that mimic the isotropic distribution a subspace perturbation analysis is used to determine an appropriate metric for the distance between grassmannian constellation points and using this metric greedy direct and rotation based techniques for designing constellations are proposed these techniques offer different tradeoffs between the minimum distance of the constellation and the design complexity in addition the rotation based technique results in constellations that have lower storage requirements and admit a natural ldquoquasi set partitioningrdquo binary labeling

further results on differential encoding by a table recently we proposed a novel differential encoder by a look up table in this paper we present further research results on this subject we first propose a bit assigning algorithm and construct some new tables for various constellations that maximize the minimum noncoherent distance then differential encoding for multiple symbol differential detection is proposed after that we indicate that differential encoding by a table is equivalent to differential encoding by a trellis so we propose a novel differential detector which uses the viterbi algorithm on the trellis a theorem about the sufficient number of states for various modulations is proposed in addition we further enhance the error performance of the proposed differential encoder by concatenating it with trellis coding for this noncoherent trellis coding scheme we propose augmented state viterbi decoding finally we extend the proposed differential encoding and detection to differential space time modulation dstm we propose a new definition of dstm by which the set of transmitted blocks is determined first the differential encoding is implemented by a look up table which can be optimized the proposed dstm has satisfactory error performance without constellation expansion

effective bezout identities in q z1 zn abstract if p sub 1 p sub m are n variate polynomials with integral coefficients and no common zeros in c exp n brownawell has shown in 1986 that there exist q sub 1 q sub m polynomials with integral coefficients and nu is an element of z such that p sub 1 q sub 1 p sub m q sub m nu and max deg q sub j max deg p sub j exp n on the other hand if h logarithm of the largest coefficient of all the p sub j and h sub 1 is the corresponding quantity for the q sub j then there is no sharp estimate of h sub 1 in terms of h and max deg p sub j in this paper we show that when the variety of common zeros at infinity of the p sub j is discrete then essentially we have h sub 1 d exp cn h for an absolute constant c if there were an algorithm to compute the q sub j in d exp cn time one would obtain exactly the above estimate current algorithms require about d exp n squared operations

discrete maximal functions in higher dimensions and applications to ergodic theory we establish a higher dimensional counterpart of bourgain s pointwise ergodic theorem along an arbitrary integer valued polynomial mapping we achieve this by proving variational estimates v r on l p spaces for all 1

unitary signal constellations for differential space time modulation with two transmit antennas parametric codes optimal designs and bounds we focus on the design of unitary signal constellations for differential space time modulation with double transmit antennas by using the parametric form of a two by two unitary matrix we present a class of unitary space time codes called parametric codes and show that this class of unitary space time codes leads to a five signal constellation with the largest possible diversity product and a 16 signal constellation with the largest known diversity product although the parametric code of size 16 is not a group by itself we show that it is a subset of a group of order 32 furthermore the unitary signal constellations of sizes 32 64 128 and 256 obtained by taking the subsets of the parametric codes of sizes 37 75 135 and 273 respectively have the largest known diversity products we also use large diversity sum of unitary space time signal constellations as another significant property for the signal constellations to have good performance in low snr scenarios the newly introduced unitary space time codes can lead to signal constellations with sizes of 5 and 9 through 16 that have the largest possible diversity sums subsequently we construct a few sporadic unitary signal constellations with the largest possible diversity product or diversity sum a four signal constellation which has both the largest possible diversity product and the largest possible diversity sum and three unitary signal constellations with the largest possible diversity sums for sizes of 6 7 and 8 are constructed respectively furthermore by making use of the existing results in sphere packing and spherical codes we provide several upper and lower bounds on the largest possible diversity product and the largest possible diversity sum that unitary signal constellations of any size can achieve

differential unitary space time modulation we present a framework for differential modulation with multiple antennas across a continuously fading channel where neither the transmitter nor the receiver knows the fading coefficients the framework can be seen as a natural extension of standard differential phase shift keying commonly used in single antenna unknown channel systems we show how our differential framework links the unknown channel system with a known channel system and we develop performance design criteria as a special ease we introduce a class of diagonal signals where only one antenna is active at any time and demonstrate how these signals may be used to achieve full transmitter diversity and low probability of error

the asymptotic behavior of degenerate oscillatory integrals in two dimensions abstract a theorem of varchenko gives the order of decay of the leading term of the asymptotic expansion of a degenerate oscillatory integral with real analytic phase in two dimensions his theorem expresses this order of decay in a simple geometric way in terms of its newton polygon once one is in certain coordinate systems called adapted coordinate systems in this paper we give explicit formulas that not only provide the order of decay of the leading term but also the coefficient of this term there are three rather different formulas corresponding to three different types of newton polygon analogous results for sublevel integrals are proven as are some analogues for the more general case of smooth phase the formulas require one to be in certain superadapted coordinates these are a type of adapted coordinate system which we show exists for any smooth phase

algebraic estimates stability of local zeta functions and uniform estimates for distribution functions a method of algebraic estimates is developed and used to study the stability properties of integrals of the form r b jf z j i dv under small deformations of the function f the estimates are described in terms of a stratiflcation of the space of functionsfr z jp z j jq z j g by algebraic varieties on each of which the size of the integral of r z is given by an explicit algebraic expression the method gives an independent proof of a result on stability of tian in 2 dimensions as well as a partial extension of this result to 3 dimensions in arbitrary dimensions combined with a key lemma of siu it establishes the continuity of the mapping c r b jf z c j i dv1 dvn when f z c is a holomorphic function of z c in particular the leading pole is semicontinuous in f strengthening also an earlier result of lichtin

l p bounds for marcinkiewicz integrals associated to surfaces of revolution abstract in this paper we prove the l p boundedness of some marcinkiewicz integral operators along surfaces of revolution some size conditions implying the l p r n 1 boundedness of these operators for some fixed 1 p are obtained

harmonic analysis on nilpotent groups and singular integrals i oscillatory integrals abstract this paper is devoted to the study of the operator given by where k is a standard calderon zygmund kernel and p is a real polynomial on r n r n we show t is bounded on lp to itself when 1

łojasiewicz inequality at infinity for polynomials in two real variables we propose different types of ojasiewicz inequality at infinity for polynomials in two real variables the formulas for the ojasiewicz exponents are given

maximal decay inequalities for trilinear oscillatory integrals of convolution type abstract in this paper we prove sharp l l l decay for certain trilinear oscillatory integral forms of convolution type on r 2 these estimates imply earlier l 2 l 2 l 2 results obtained by the second author as well as corresponding sharp stable sublevel set estimates of the form studied by christ 3 and christ li tao and thiele 5 new connections to the multilinear results of phong stein and sturm 13 are also considered

constellation mapping for space time matrix modulation with iterative demodulation decoding the mapping from binary sequences to space time matrices is an important issue in designing space time coded multiple antenna systems where different mapping schemes may lead to different bit error rate ber performance in this letter we use a binary switching algorithm to investigate the mappings of bit interleaved coded modulation with iterative demodulation decoding bicm id for space time modulation both coherent and noncoherent space time modulation in the cases of no a priori information and perfect a priori information of the coded bits for the demodulator are considered

l p improving bounds for averages along curves we establish local l p l q mapping properties for averages on curves the exponents are sharp except for endpoints let n 2 and let m1 and m2 be two smooth n 1 dimensional manifolds 1 each containing a preferred origin 0m1 and 0m2 we shall abuse notation and write 0 for both 0m1 and 0m2 for the purposes of integration we shall place a smooth riemannian metric on m1 and m2 although the exact choice of this metric will not be relevant all our considerations shall be local to the origin 0 we are interested in the local l p improving properties of averaging operators on curves before we give the rigorous description of these operators let us first give an informal discussion informally we assume that we have a smooth assignment x2 7 x2 taking points in m2 to curves in m1 with a corresponding dual assignment x1 x1 taking points in m1 to curves in m2 such that x1 x2 x2 1 we then form the operator r taking functions 2 on m1 to functions on m2 defined

some oscillatory integral estimates via real analysis we study oscillatory integrals in several variables with analytic smooth or c k phases satisfying a nondegeneracy condition attributed to varchenko with only real analytic methods varchenko s sharp estimates are rediscovered and generalized the same methods are pushed further to obtain full asymptotic expansions of such integrals with analytic and smooth phases and finite expansions with error assuming the phase is only c k the newton polyhedron appears naturally in the estimates in particular we show precisely how the exponents appearing in the asymptotic expansions depend only on the geometry of the newton polyhedron of the phase all estimates proven hold for oscillatory parameter real and nonzero not just asymptotically