on the spaces lp x ω and wm p x ω in this paper we present some basic results on the generalized lebesgue spaces l p x omega and generalized lebesgue sobolev spaces w m w p x omega these results provide the necessary framework for the study of variational problems and elliptic equations with non standard p x growth conditions c 2001 academic press

bit error rate of binary and quaternary dpsk signals with multiple differential feedback detection a differentially coherent detection scheme with improved bit error rate ber performance is presented for differentially encoded binary and quaternary phase shift keying psk modulation the improvement is based on using l symbol detectors with delays of 1 2 l symbol periods and on feeding back detected psk symbols exact formulas for the bit error probability are derived for the case that correct symbols are fed back the effect of symbol errors in the feedback path on the ber is determined by computer simulations

multiple symbol differential detection with interference suppression a multiple symbol differential detector is formulated for m ary differential phase shift keying modulation where the channel state information is unknown to the receiver the maximum likelihood decision statistic is derived for the detector and its performance is demonstrated by analysis and simulation under the gaussian assumption for the aggregate interference plus noise an exact expression for the symbol pairwise error probability is developed for m ary differential phase shift keying modulation over a diversity slow fading rayleigh channel in the presence of an interference source a simpler expression of the pairwise error probability is developed for the asymptotic case of large signal to noise ratio and small signal to interference ratio it is shown that with an increasing observation interval the performance of the differential detector over an unknown channel approaches that of optimum combining with known channel

error performance of multiple symbol differential detection of psk signals transmitted over correlated rayleigh fading channels the error performance of multiple symbol differential detection of uncoded qpsk signals transmitted over correlated rayleigh fading channels is studied the optimal detector is presented along with an exact expression for the corresponding pairwise error event probability it is shown that multiple symbol differential detection is a very effective strategy for eliminating the irreducible error floor associated with a conventional differential detector in all of the cases investigated a detector with an observation interval as small as two symbols is sufficient for this purpose it is also found that the error performance of a multiple symbol differential detector is not sensitive to the mismatch between the decoding metric and the channel fading statistics

galois module structure of the square root of the inverse different in even degree tame extensions of number fields abstract let g be a finite group and let n e be a tamely ramified g galois extension of number fields whose inverse different c n e is a square let a n e denote the square root of c n e then a n e is a locally free z g module which is in fact free provided n e has odd order as shown by erez using m taylor s theorem we can rephrase this result by saying that when n e has odd degree the classes of a n e and o n the ring of integers of n in cl z g are equal and in fact both trivial we show that the above equality of classes still holds when n e has even order assuming that n e is locally abelian this result is obtained through the study of the frohlich representatives of the classes of some torsion modules which are independently introduced in the setting of cyclotomic number fields jacobi sums together with the hasse davenport formula are involved in this study finally when g is the binary tetrahedral group we use our result in conjunction with taylor s theorem to exhibit a tame g galois extension whose square root of the inverse different has nontrivial class in cl z g

eigenvalues of p x laplacian dirichlet problem abstract this paper studies the eigenvalues of the p x laplacian dirichlet problem div u p x 2 u u p x 2 u in u 0 on where is a bounded domain in rn and p x is a continuous function on such that p x 1 we show that the set of eigenvalues is a nonempty infinite set such that sup we present some sufficient conditions for inf 0 and for inf 0 respectively

a multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids the goal of this correction is to correct a mistake that appears in the proof of both lemma 3 9 and 3 10 in the article mih ilescu r dulescu 2006 1 the mistake in the proof of lemma 3 9 and 3 10 is mainly owing to the fact that we wrongly computed the expression of function g x t

tamagawa numbers for motives with noncommutative coefficients ii we provide corroborative evidence for the equivariant tamagawa number conjecture which was formulated in the first part of this article

the root number class and chinburg s second invariant let n k be a finite normal extension of number fields with g gal n k by e noether s theorem the ring of integers on of n is a projective z g module if and only if n k is at most tamely ramified thus for such n k 0 defines a class q n k on k q z g in the class group cl z g the finite torsion subgroup of the grothendieck group k z g of finitely generated g modules of finite projective dimension in 14 m taylor proved that in this case q n k is equal to the root number class wnik which was defined by ph cassou nogds and friihlich by means of the artin root numbers of the irreducible symplectic representations of g cf s chap 1 or 3 p 183 in 4 t chinburg defined galois invariants q n k i i 1 2 3 of n k in cl z g and proved q n k 2 qjn k for arbitrary n k which are at most tamely ramified since both classes q n k 2 and w are defined for all n k including those which are wildly ramified one may be led to the following conjecture

multiple symbol differential detection with diversity reception in this letter we first consider the maximum likelihood sequence estimator for multiple symbol differential detection msdd over the slow fading diversity channel since this optimum decision metric results in a complex receiver implementation whose average bit error probability bep performance is difficult if not impossible to obtain analytically we then focus our attention on evaluating the average bep for msdd with diversity reception in the form of postdetection equal gain combining egc giving emphasis to its ability to bridge the gap between egc of conventional differentially detected m psk and maximal ratio combining of coherently detected m psk with differential encoding

on the equivariant tamagawa number conjecture for tate motives let l be a finite abelian extension of and let k be any subfield of l for each integer r with r 0 we prove the equivariant tamagawa number conjecture for the pair h0 spec l r gal l k

noncoherent sequence detection new noncoherent sequence detection algorithms for combined demodulation and decoding of coded linear modulations transmitted over additive white gaussian noise channels possibly affected by intersymbol interference are presented optimal sequence detection in the presence of a random rotation of the signal phase assumed to be constant during the entire transmission requires a receiver complexity exponentially increasing with the duration of the transmission based on proper approximations simple suboptimal detection schemes based on the viterbi algorithm are presented whose performance approaches that of coherent detection in a companion paper by colavolpe and raheli see ibid vol 47 no 9 p 1303 7 1999 noncoherent sequence detection is extended to continuous phase modulations in the proposed schemes the tradeoff between complexity and performance is simply controlled by a parameter referred to as implicit phase memory and the number of states of a trellis diagram besides being realizable these schemes have the convenient feature of allowing us to remove the constant phase assumption and encompass time varying phase models the proposed schemes compare favorably with other solutions previously proposed in the technical literature

existence results for schrodinger p laplace equations involving critical growth in rn abstract we establish some existence results for schrodinger p laplace equations in r n with various potentials and critical growth of nonlinearity that may occur on some nonempty set although not necessarily the whole space r n the proofs are mainly based on concentration compactness principles in a suitable weighted variable exponent sobolev space and its imbeddings

remarks on ricceri s variational principle and applications to the p x laplacian equations abstract in this paper we give some remarks on a variational principle of ricceri in the case of sequentially weakly lower semi continuous functionals defined on a reflexive real banach space in particular we introduce the notions of ricceri block and ricceri box which are more convenient in some applications than the weakly connected components using the variational principle of ricceri and a local mountain pass lemma we study the multiplicity of solutions of the p x laplacian equations with neumann dirichlet or no flux boundary condition and under appropriate hypotheses in which the integral functionals need not satisfy the ps condition on the global space we prove that the problem has at least seven solutions

multiple bit differential detection of offset qpsk analogous to multiple symbol differential detection of quadrature phase shift keying qpsk a multiple bit differential detection scheme is described for offset qpsk that also exhibits continuous improvement in performance with increasing observation interval being derived from maximum likelihood considerations together with the representation of differentially encoded offset qpsk as a continuous phase modulation the proposed scheme is purported to be the most power efficient scheme for such a modulation and detection method

on galois structure invariants associated to tate motives we establish the equivalence of two definitions of invariants measuring the galois module structure of k groups of rings of integers in number fields due to chinburg et al on the one hand and the authors on the other we also make some remarks concerning the possibility of yet another such definition via lichtenbaum complexes

the phase of a vector perturbed by gaussian noise and differentially coherent receivers some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by gaussian noise it is shown that for large signal to noise ratio the asymptotic distribution of the phase is of the tikhonov type this framework is then used for the synthesis of differentially coherent receiver structures one for m ary phase shift keying mpsk and the other for minimum shift keying msk the first structure bridges the performance gap between coherent and differentially coherent demodulation of mpsk the msk receiver uses matched filtering with differential demodulation

on equivariant global epsilon constants for certain dihedral extensions we consider a conjecture of bley and burns which relates the epsilon constant of the equivariant artin l function of a galois extension of number fields to certain natural algebraic invariants for an odd prime number p we describe an algorithm which either proves the conjecture for all degree 2p dihedral extensions of the rational numbers or finds a counterexample we apply this to show the conjecture for all degree 6 dihedral extensions of q the correctness of the algorithm follows from a finiteness property of the conjecture which we prove in full generality

on mordell weil groups and congruences between derivatives of twisted hasse weil l functions let a be an abelian variety defined over a number field k and let f be a finite galois extension of k let p be a prime number then under certain not too stringent conditions on a and f we compute explicitly the algebraic part of the p component of the equivariant tamagawa number of the pair h1 a f 1 z gal f k by comparing the result of this computation with the theorem of gross and zagier we are able to give the first verification of the p component of the equivariant tamagawa number conjecture for an abelian variety in the technically most demanding case in which the relevant mordell weil group has strictly positive rank and the relevant field extension is both non abelian and of degree divisible by p more generally our approach leads us to the formulation of certain precise families of conjectural p adic congruences between the values at s 1 of derivatives of the hasse weil l functions associated to twists of a normalised by a product of explicit equivariant regulators and periods and to explicit predictions concerning the galois structure of tate shafarevich groups in several interesting cases we provide theoretical and numerical evidence in support of these more general predictions

a critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations abstract for an even functional on a banach space the symmetric mountain pass lemma gives a sequence of critical values which converges to zero under the same assumptions on the functional this paper establishes a new critical point theorem which provides a sequence of critical points converging to zero the theorem is applied to sublinear elliptic equations then a sequence of solutions converging to zero is obtained

on the equivariant tamagawa number conjecture for tate motives and unconditional annihilation results dfg collaborative research center 701 spectral structures and topological methods in mathematics

galois structure of zariski cohomology for weakly ramified covers of curves we compute equivariant euler characteristics of locally free sheaves on curves thereby generalizing several results of kani and nakajima for instance we extend kani s computation of the galois module structure of the space of global meromorphic differentials which are logarithmic along the ramification locus from the tamely ramified to the weakly ramified case

existence of solutions for p x laplacian dirichlet problem this paper presents several sufficient conditions for the existence of solutions for the dirichlet problem of p x laplacian div u p x 2 u f x u x u 0 x especially an existence criterion for infinite many pairs of solutions for the problem is obtained the discussion is based on the theory of the spaces lp x and w01 p x

on noncoherent receivers for dstm in spatially correlated fading in this letter we derive a multiple symbol differential detection msdd and a novel msdd based decision feedback differential detection ms dfdd receiver for differential space time modulation transmitted over spatially correlated multiple input multiple output fading channels we show that ms dfdd outperforms previously proposed dfdd schemes that are based on scalar and vector prediction sp dfdd and vp dfdd in addition we prove that at high signal to noise ratio snr vp dfdd is equivalent to sp dfdd and thus fails to properly exploit the spatial fading correlations

on the llr metrics for dpsk modulations over two symbol observation intervals for the flat rician fading channel we consider the differential phase shift keying modulation over the flat rician fading channel with perfect channel model information pcmi and derive the two symbol observation interval log likelihood ratio llr metric from first principles the work generalizes the previous llr derivations in 16 19 and demonstrates the necessity of the knowledge of the statistical channel model in the exact llr computation assuming the channel is slowly time varying we also propose a simple approximate llr metric based on the generalized likelihood ratio test glrt which requires only the information of the noise spectral density the advantage of the newly derived pcmi llr metric over the approximate metric and the other llr metrics in the literature is explained from the information theoretic perspective via the generalized mutual information computer simulations are also provided to demonstrate the superiority of the pcmi llr metric in both error rate performance and convergence speed for iterative decoding of turbo and low density parity check codes in practical systems this paper aims to present the fundamental principles of llr computation emphasizing the importance of selecting the appropriate metric for iterative decoding over fading channels

maximum likelihood differential detection of uncoded and trellis coded amplitude phase modulation over awgn and fading channels spl minus metrics and performance this paper derives metrics for maximum likelihood differential detection of uncoded and trellis coded mpsk and qam transmitted over rayleigh and rician fading channels receiver structures based on these metrics are proposed and their error probability performance analyzed and or simulated the results represent a generalization of the notion of multiple symbol differential detection previously introduced by the authors for mpsk over an awgn to the fading channel and other modulations for the coded cases ideal interleaving deinterleaving is assumed and furthermore the presence or absence of channel state information an interesting side result is that for a constant envelope modulation transmitted over a fading channel with unknown but rapidly varying phase error the other extreme to the slowly varying phase error case normally assumed for differential detection under certain practical assumptions it is shown that the optimum receiver is of the limiter discriminator type

multiple symbol differential detection of mpsk a differential detection technique for mpsk multiple phase shift keying which uses a multiple symbol observation interval is presented and its performance is analyzed and simulated the technique makes use of maximum likelihood sequence estimation of the transmitted phases rather than symbol by symbol detection as in the conventional differential detection thus the performance of this multiple symbol detection scheme fills the gap between conventional two symbol observation differentially coherent detection of mpsk and ideal coherent of mpsk with differential encoding the amount of improvement gained over conventional differential detection depends on the number of phases m and the number of additional symbol intervals added to the observation what is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation the analysis and simulation results presented are for uncoded mpsk

on an open problem involving the p x laplacian a further study on the multiplicity of weak solutions to p x laplacian equations abstract by using a variational method and the truncation technique we show the multiplicity of weak solutions to a class of p x laplacian equations an open problem proposed by professor xianling fan is solved and more general results are given in this paper

computation of stark tamagawa units let k be a totally real number field and let l denote an odd prime number we design an algorithm which computes strong numerical evidence for the validity of the equivariant tamagawa number conjecture for the q g equivariant motive h0 spec l where l k is a cyclic extension of degree l and group g this conjecture is a very deep refinement of the classical analytic class number formula in the course of the algorithm we compute a set of special units which must be considered as a generalization of the conjecturally existing stark units associated to first order vanishing dirichlet l functions

a unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels we present a unified approach to determine the exact bit error rate ber of noncoherent and differentially coherent modulations with single and multichannel reception over additive white gaussian noise and generalized fading channels the multichannel reception results assume independent fading in the channels and are applicable to systems that employ post detection equal gain combining our approach relies on an alternate form of the marcum q function and leads to expressions of the ber involving a single finite range integral which can be readily evaluated numerically aside from unifying the past results the new approach also allows for a more general solution to the problem in that it includes many situations that in the past defied a simple solution the best example of this occurs for multichannel reception where the fading on each channel need not be identically distributed nor even distributed according to the same family of distributions

equivariant epsilon constant conjectures for weakly ramified extensions we study the local epsilon constant conjecture as formulated by breuning in breuning j london math soc 70 2 289 306 2004 this conjecture fits into the general framework of the equivariant tamagawa number conjecture etnc and should be interpreted as a consequence of the expected compatibility of the etnc with the functional equation of artin l functions let k mathbb q p be unramified under some mild technical assumption we prove breuning s conjecture for weakly ramified abelian extensions n k with cyclic ramification group as a consequence of breuning s local global principle we obtain the validity of the global epsilon constant conjecture as formulated in bley and burns proc lond math soc 87 3 545 590 2003 and of chinburg s omega 2 conjecture as stated in chinburg ann math 121 2 351 376 1985 for certain infinite families f e of weakly and wildly ramified extensions of number fields

solutions for p x laplacian dirichlet problems with singular coefficients using the critical point theory we investigate the existence and multiplicity of solutions for p x laplacian dirichlet problem with singular coefficients

existence results for the p laplacian with nonlinear boundary conditions in this paper we study the existence of nontrivial solutions for the problem pu u p 2u in a bounded smooth domain rn with a nonlinear boundary condition given by u p 2 u f u on the boundary of the domain the proofs are based on variational and topological arguments

a unified performance analysis framework for differential detection in mimo rayleigh fading channels in this paper a unified framework for the analysis of differential detection dd schemes in time variant multiple input multiple output rayleigh fading channels is provided the present results are very general in that they apply to transmission with differential phase shift keying unitary differential space time modulation dstm and block dstm and reception with conventional dd cdd multiple symbol dd msdd decision feedback dd dfdd and differentially coherent detection cd new result for general quadratic forms of gaussian random variables are derived which allows us to obtain elegant closed form expressions for the pairwise error probabilities peps of the dominant error events of the considered detectors furthermore it is shown that a unified treatment of all considered detectors is possible with a properly defined effective signal to noise ratio esnr and a useful connection between msdd and minimum mean squared error mmse interpolation is established interesting novel results obtained from this analysis include i dstm constellations designed for cdd and cd are also optimum for msdd and dfdd ii the error floor entailed by msdd and dfdd in time variant fading decreases exponentially with the observation window size n and iii in time variant fading with effective normalized fading bandwidth bh efft msdd with n rarr infin suffers only from an snr loss of 1 2bh efft compared to cd whereas dfdd suffers from a diversity loss of 1 2bh efft

overview of differential equations with non standard growth abstract differential equations with non standard growth have been a very active field of investigation in recent years in this survey we present an overview of the field as well as several of the most important results we consider both existence and regularity questions finally we provide a comprehensive list of papers published to date

existence and blow up rate of large solutions of p x laplacian equations with gradient terms abstract in this paper we investigate boundary blow up solutions of the problem p x u f x u k x u m x in u x as d x 0 where p x u div u p x 2 u is called the p x laplacian our results extend the previous work 25 of y liang q h zhang and c s zhao from the radial case to the non radial setting and 46 due to q h zhang and d motreanu from the assumption that k x u x m x is a small perturbation to the case in which k x u m x is a large perturbation we provide an exact estimate of the pointwise different behavior of the solutions near the boundary in terms of d x and in terms of the growth of the exponents furthermore the comparison principle is no longer applicable in our context since f x is not assumed to be monotone in this paper

density of smooth functions in wk p x ω kovacik rakosnik investigated the spaces l p x omega of functions which are integrable with variable power p x and the corresponding counterparts of the sobolev spaces w k p x omega we continue that investigation and describe a class of functions p x for which the set of smooth functions on omega is dense in w k p x omega as a corollary we obtain in terms of the distance function a condition on elements of w k p x omega sufficient to ensure that they belong to w 0 k p x omega

equivariant epsilon constants discriminants and etale cohomology let l k be a finite galois extension of number fields we formulate and study a conjectural equality between an element of the relative algebraic k group k 0 mathbb z mathrm gal l k mathbb r which is constructed from the equivariant artin epsilon constant of l k and a sum of structural invariants associated to l k the precise conjecture is motivated by the requirement that a special case of the equivariant refinement of the tamagawa number conjecture of bloch and kato as formulated by flach and the second named author should be compatible with the functional equation of the associated l function we show that more concretely our conjecture also suggests a completely systematic refinement of the central approach and results of classical galois module theory in particular the evidence for our conjecture that we present here already strongly refines many of the main results of galois module theory

reduced state sequence estimation with set partitioning and decision feedback a reduced state sequence estimator for linear intersymbol interference channels is described the estimator uses a conventional viterbi algorithm with decision feedback to search a reduced state subset trellis that is constructed using set partitioning principles the complexity of maximum likelihood sequence estimation mlse due to the length of the channel memory and the size of the signal set is systematically reduced an error probability analysis shows that a good performance complexity tradeoff can be obtained in particular the results indicate that the required complexity to achieve the performance of mlse is independent of the size of the signal set for large enough signal sets simulation results are provided for two partial response systems a simple technique for quadrature partial response signaling qprs is described that eliminates the quasicatastrophic nature of the ml trellis

on frohlich s conjecture for rings of integers of tame extensions where is the complex conjugate of z the constant w z is called the artin root number of in m l j martinet showed that om is not always a free zf module when n q and when f is a quaternion group of order 8 subsequently in f5 a frtihlich showed that the class of u in this special case is determined by the sign of the artin root number of the irreducible sympletic character of 2 we now return to the general case and let ci tif be the class group of locally free zf modules given a locally free 2 f module x we denote its class by x philippe cassou nogu6s defined a class t w in ci f which is defined solely in terms of the values of artin root numbers of sympletic characters this class will be defined in w after numerous computations by fr6hlich et al cf f6 c t3 for instance fr6hlich conjectured the result given below which we prove in this paper