probability of error for equal gain combiners over rayleigh channels some closed form solutions the probability of error of a general equal gain combiner eg in closed form is not available in the literature by formulating the problem in the framework of signal detection and evaluating the probability of error directly from the characteristic function cf of the signal at the combiner output we obtain closed form solutions for the probability of error of the eg combiner with two or three branches operating over a rayleigh fading channel

the weighted hardy s inequality for nonincreasing functions the purpose of this paper is to give an alternative proof of recent results of m arino and b muckenhoupt 1 and e sawyer 8 concerning hardy s inequality for nonincreasing functions and related applications to the boundedness of some classical operators on general lorentz spaces our approach will extend the results of 1 8 to the values of the parameters which are inaccessible by the methods of these papers

sensitivity to timing errors in egc and mrc techniques the effect of imperfect timing is analyzed in equal gain combining egc and maximal ratio combining mrc techniques over rayleigh and nakagami m fading channels with binary phase shift keying modulation in the case of egc the bit error probability is derived while in the case of mrc error rate bounds are presented theoretical results are justified by computer simulation numerical results demonstrate that both egc and mrc are fairly sensitive to timing errors and comparatively mrc is more sensitive

low dimensional real lie algebras all real lie algebras of dimension up to 8 that admit a nontrivial levi decomposition are found

symmetry reduction for nonlinear relativistically invariant equations symmetry reduction is studied for the relativistically invariant scalar partial differential equation h u u 2 u 0 in n 1 dimensional minkowski space m n 1 the introduction of k symmetry variables 1 k as invariants of a subgroup g of the poincare group p n 1 having generic orbits of codimension k n in m n 1 reduces the equation to a pde in k variables all codimension 1 symmetry variables in m n 1 n arbitrary reducing the equation studied to an ode are found as well as all codimension 2 and 3 variables for the low dimensional cases n 2 3 the type of equation studied includes many cases of physical interest in particular nonlinear klein gordon equations such as the sine gordon equation and hamilton jacobi equations

partially coherent ds ss performance in frequency selective multipath fading the bit error rate ber performance of a direct sequence spread spectrum ds ss signal operating over a multipath rayleigh fading channel is investigated when corrupted by phase noise as well as additive white gaussian noise awgn the phase noise arises from phase locked loop pll dynamics and results in imperfect receiver phase estimates whereby the phase errors assume tikhonov densities the phase estimates are used by a multipath combining rake receiver for demodulation approximate upper bounds on the bit error probability are obtained and evaluated for different combinations of channel parameters and for various values of the average loop signal to noise ratio snr results indicate that for a pll with loop snr 10 db above the system e sub b spl eta sub 0 the degradation is less than 3 db and for a loop snr of 20 db above e sub b spl eta sub 0 the degradation is less than 1 db

solvable lie algebras of dimension six six dimensional solvable lie algebras over the field of real numbers that possess nilradicals of dimension four are classified into equivalence classes this completes mubarakzyanov s classification of the real six dimensional solvable lie algebras

the poincare algebra in rank 3 simple lie algebras we classify embeddings of the poincare algebra p 3 1 into the rank 3 simple lie algebras up to inner automorphism we show that there are exactly two embeddings of p 3 1 into sl 4 c which are however related by an outer automorphism of sl 4 c next we show that there is a unique embedding of p 3 1 into so 7 c up to inner automorphism but no embeddings of p 3 1 into sp 6 c all embeddings are explicitly described as an application we show that each irreducible highest weight module of sl 4 c not necessarily finite dimensional remains indecomposable when restricted to p 3 1 with respect to any embedding of p 3 1 into sl 4 c

indecomposable representations of the diamond lie algebra we study classes of indecomposable representations of the diamond lie algebra a four dimensional solvable lie algebra which is the central extension of the poincare lie algebra in two dimensions these representations are obtained first inspired by douglas and premat commun algebra 35 1433 2007 by embedding the diamond lie algebra in the simple lie algebras a2 and c2 and then by regarding it as a subalgebra of a truncated current lie algebra

a classification of the embeddings of the diamond lie algebra into sl 3 c and sp 4 c and restrictions of irreducible modules the diamond lie algebra d is a four dimensional solvable lie algebra it is a central extension of the poincare lie algebra in two dimensions we classify the embeddings of d into each of the classical lie algebras of rank 2 namely sl 3 c and sp 4 c up to conjugation by elements of sl 3 c or sp 4 c respectively we then show that the irreducible representations of sl 3 c or sp 4 c remain indecomposable upon restriction to d under any embedding

regular subalgebras and nilpotent orbits of real graded lie algebras abstract for a semisimple lie algebra over the complex numbers dynkin 1952 developed an algorithm to classify the regular semisimple subalgebras up to conjugacy by the inner automorphism group for a graded semisimple lie algebra over the complex numbers vinberg 1979 showed that a classification of a certain type of regular subalgebras called carrier algebras yields a classification of the nilpotent orbits in a homogeneous component of that lie algebra here we consider these problems for graded semisimple lie algebras over the real numbers first we describe an algorithm to classify the regular semisimple subalgebras of a real semisimple lie algebra this also yields an algorithm for listing up to conjugacy the carrier algebras in a real graded semisimple real algebra we then discuss what needs to be done to obtain a classification of the nilpotent orbits from that such classifications have applications in differential geometry and theoretical physics our algorithms are implemented in the language of the computer algebra system gap using our package corelg we report on example computations

constructing semisimple subalgebras of semisimple lie algebras abstract algorithms are described that help with obtaining a classification of the semisimple subalgebras of a given semisimple lie algebra up to linear equivalence the algorithms have been used to obtain classifications of the semisimple subalgebras of the simple lie algebras of ranks 8 these have been made available as a database inside the sla package of gap 4 the subalgebras in this database are explicitly given as well as the inclusion relations among them

effect of channel estimation error on m qam ber performance in rayleigh fading we determine the bit error rate ber of multilevel quadrature amplitude modulation m qam in flat rayleigh fading with imperfect channel estimates despite its high spectral efficiency m qam is not commonly used over fading channels because of the channel amplitude and phase variation since the decision regions of the demodulator depend on the channel fading estimation error of the channel variation can severely degrade the demodulator performance among the various fading estimation techniques pilot symbol assisted modulation psam proves to be an effective choice we first characterize the distribution of the amplitude and phase estimates using psam we then use this distribution to obtain the ber of m qam as a function of the psam and channel parameters by using a change of variables our exact ber expression has a particularly simple form that involves just a few finite range integrals this approach can be used to compute the ber for any value of m we compute the ber for 16 qam and 64 qam numerically and verify our analytical results by computer simulation we show that for these modulations amplitude estimation error leads to a 1 db degradation in average signal to noise ratio and combined amplitude phase estimation error leads to 2 5 db degradation for the parameters we consider

separation of variables and subgroup bases on n dimensional hyperboloids a graphical formalism is introduced for describing subgroup type coordinates on n dimensional lorentzian hyperboloids imbedded into n 1 dimensional minkowski spaces the o n 1 group element is parametrized according to different subgroup chains involving lorentz rotation and euclidean subgroups the coordinates are then induced by the corresponding group action eigenfunctions of the laplace beltrami operator are obtained as products of jacobi functions associated legendre functions and modified bessel functions

global minimax approximations and bounds for the gaussian q function by sums of exponentials this paper presents a novel systematic methodology to obtain new simple and tight approximations lower bounds and upper bounds for the gaussian q function and functions thereof in the form of a weighted sum of exponential functions they are based on minimizing the maximum absolute or relative error resulting in globally uniform error functions with equalized extrema in particular we construct sets of equations that describe the behaviour of the targeted error functions and solve them numerically in order to find the optimized sets of coefficients for the sum of exponentials this also allows for establishing a trade off between absolute and relative error by controlling weights assigned to the error functions extrema we further extend the proposed procedure to derive approximations and bounds for any polynomial of the q function which in turn allows approximating and bounding many functions of the q function that meet the taylor series conditions and consider the integer powers of the q function as a special case in the numerical results other known approximations of the same and different forms as well as those obtained directly from quadrature rules are compared with the proposed approximations and bounds to demonstrate that they achieve increasingly better accuracy in terms of the global error thus requiring significantly lower number of sum terms to achieve the same level of accuracy than any reference approach of the same form

the classification of the perfect cyclic sl n 1 cn 1 modules abstract a perfect cyclic module of a perfect lie algebra g with solvable radical r and levi decomposition g s r is a finite dimensional module of g generated by an irreducible module of the semisimple lie algebra s in this paper we classify all the perfect cyclic finite dimensional indecomposable modules of the perfect lie algebras sl n 1 c n 1 given by the semidirect sum of the simple lie algebra a n with its standard representation furthermore using the embedding of the lie algebra sl n 1 c n 1 in sl n 2 we show that any finite dimensional irreducible module of sl n 2 restricted to sl n 1 c n 1 is a perfect cyclic module and that any perfect cyclic sl n 1 c n 1 module can be constructed as quotient module of the restriction to sl n 1 c n 1 of some finite dimensional irreducible sl n 2 module this explicit realization of the perfect cyclic sl n 1 c n 1 modules plays a role in their classification

maximal abelian subalgebras of pseudounitary lie algebras abstract the task of classifying and constructing all maximal abelian subalgebras of su p q p q 1 is reduced to that of classifying orthogonally indecomposable masas these are either maximal abelian nilpotent subalgebras represented by nilpotent matrices in any finite dimensional representation or for p q they can be nonorthogonally decomposable and their study can be reduced to a construction of manss of sl p c two types of manss of su p q are shown to exist one rowed and non one rowed numerous classification theorems are proven and applied to obtain all masas of su p 1 su p 2 and su p q with p q 6 physical applications are discussed

levi decomposable subalgebras of the symplectic algebra c2 the semisimple subalgebras of the symplectic algebra c2 are well known in this article we classify the levi decomposable subalgebras of the symplectic algebra c2 up to inner automorphism by levi s theorem a full classification of the subalgebras of c2 would be complete with a classification of its solvable subalgebras

embeddings of the euclidean algebra e 3 into sl 4 c and restrictions of irreducible representations of sl 4 c the euclidean group e 3 is the lie group of orientation preserving isometries of three dimensional euclidean space it is the noncompact semidirect product group e 3 so 3 r3 the euclidean algebra e 3 is the complexification of the lie algebra of e 3 we classify the embeddings of the euclidean algebra e 3 into the simple lie algebra sl 4 c and as an application of this classification discuss the restriction to various embeddings of e 3 of certain irreducible representations of sl 4 c in particular we consider which of these restrictions are e 3 indecomposable

a unified approach for calculating error rates of linearly modulated signals over generalized fading channels we present a unified analytical framework to determine the exact average symbol error rate ser of linearly modulated signals over generalized fading channels the results are applicable to systems employing coherent demodulation with maximal ratio combining multichannel reception the analyses assume independent fading paths which are not necessarily identically distributed in all cases the proposed approach leads to an expression of the average ser involving a single finite range integral which can be easily computed numerically in addition as special cases ser expressions for single channel reception are obtained these expressions reduce to well known solutions give alternative often simpler expressions for previous results or provide new formulas that are either closed form expressions or simple to compute numerically

the classical basis for the κ poincare hopf algebra and doubly special relativity theories several issues concerning the quantum poincare algebra are discussed and reconsidered here we propose two different formulations of the poincare quantum algebra firstly we present a complete hopf algebra formula of poincare in classical poincare basis further by adding one extra generator which modifies the classical structure of the poincare algebra we eliminate nonpolynomial functions in the parameter hilbert space representations of such algebras make doubly special relativity dsr similar to stueckelberg s version of proper time relativistic quantum mechanics

the schrodinger langevin equation special solutions and nonexistence of solitary waves two types of solutions of the schrodinger langevin equation are investigated it is proved that a special type of gaussian solutions exist globally in time for the harmonic oscillator hamiltonian furthermore it is shown that the schrodinger langevin equation can have no solitary wave type solutions in the damped free particle case which lie in l2

symmetry reduction for the kadomtsev petviashvili equation using a loop algebra the kadomtsev petviashvili kp equation ut 3uux 2 1 4 uxxx x 3 uyy 4 0 allows an infinite dimensional lie group of symmetries i e a group transforming solutions amongst each other the lie algebra of this symmetry group depends on three arbitrary functions of time t and is shown to be related to a subalgebra of the loop algebra a 1 4 low dimensional subalgebras of the symmetry algebra are identified specifically all those of dimension n 3 and also a physically important six dimensional lie algebra containing translations dilations galilei transformations and quasirotations new solutions of the kp equation are obtained by symmetry reduction using the one dimensional subalgebras of the symmetry algebra these solutions contain up to three arbitrary functions of t

a simple evaluation of dpsk error probability performance in the presence of bit timing error this paper presents a simple closed form expression for the conditional on the timing error bit error probability of an otherwise ideal dpsk receiver numerical results are given for average bit error probability obtained by averaging the conditional error probability over a tikhonov pdf which is a typical characterization of the timing error in practical bit synchronizers

variable rate and variable power mqam system based on bayesian bit error rate and channel estimation techniques the impact of inaccurate channel state information at the transmitter for a variable rate variable power multilevel quadrature amplitude modulation vrvp mqam system over a rayleigh flat fading channel is investigated a system model is proposed with rate and power adaptation based on the estimates of instantaneous signal to noise ratio snr and bit error rate ber a pilot symbol assisted modulation scheme is used for snr estimation the ber estimator is derived using a maximum a posteriori approach and a simplified closed form solution is obtained as a function of only the second order statistical characterization of the channel state imperfection based on the proposed system model rate and power adaptation is derived for the optimization of spectral efficiency subject to an average power constraint and an instantaneous ber requirement the performance of the vrvp mqam system under imperfect channel state information csi is evaluated we show that the proposed vrvp mqam system that employs optimal solutions based on the statistical characterization of csi imperfection achieves a higher spectral efficiency as compared to an ideal csi assumption based method

necessary and sufficient conditions for the boundedness of fractional maximal operators in local morrey type spaces the problem of the boundedness of the fractional maximal operator m 0 n in local and global morrey type spaces is reduced to the problem of the boundedness of the hardy operator in weighted lp spaces on the cone of non negative non increasing functions this allows obtaining sharp sufficient conditions for the boundedness for all admissible values of the parameters moreover in case of local morrey type spaces for some values of the parameters these sufficient conditions coincide with the necessary ones

maximal potential and singular operators in the local complementary variable exponent morrey type spaces abstract we consider local complementary generalized morrey spaces m x 0 p in which the p means of function are controlled over b x 0 r instead of b x 0 r where r n is a bounded open set p x is a variable exponent and no monotonicity type condition is imposed onto the function r defining the complementary morrey type norm in the case where is a power function we reveal the relation of these spaces to weighted lebesgue spaces in the general case we prove the boundedness of the hardy littlewood maximal operator and calderon zygmund singular operators with standard kernel in such spaces we also prove a sobolev type m x 0 p m x 0 q theorem for the potential operators i also of variable order in all the cases the conditions for the boundedness are given it terms of zygmund type integral inequalities on r which do not assume any assumption on monotonicity of r

weighted hardy and potential operators in the generalized morrey spaces abstract we study the weighted p q boundedness of the multi dimensional hardy type operators in the generalized morrey spaces l p r n w defined by an almost increasing function r and radial type weight w x we obtain sufficient conditions in terms of some integral inequalities imposed on and w for such a p q boundedness in some cases the obtained conditions are also necessary these results are applied to derive a similar weighted p q boundedness of the riesz potential operator

analysis of equal gain diversity on nakagami fading channels an infinite series for the complementary probability distribution function cdf of the signal to noise ratio snr at the output of l branch equal gain eg diversity combiners in nakagami 1960 fading channels is derived the bit error rate for a matched filter receiver is analyzed for the l branch eg combiner and different fading parameters both coherent phase shift keying cpsk and differential coherent phase shift keying dcpsk are considered the effects of gain unbalance between branches on the probability distribution of the snr and on the bit error rates are investigated bit error rate results are also obtained for coherent and noncoherent reception of frequency shift keying fsk the effects of gain unbalances on fsk modulations are also investigated bit error rates for eg combining on rayleigh fading channels are obtained for l 2 these results are presented as a special case of the more generalized nakagami fading model

2 generation of simple lie algebras and free dense subgroups of algebraic groups abstract we construct generating pairs of simple lie algebras in characteristic zero we apply this construction to exhibit infinite series of 2 generator zariski dense subgroups that are free of rank 2 of the simple algebraic groups sl n c sp n c g 2 c

on the error probability of linearly modulated signals on frequency flat ricean rayleigh and awgn channels the method used in aghamohammadi and meyr 1990 for finding the error probability of linearly modulated signals on rayleigh frequency flat fading channels has been applied to the more general case of ricean fading a signal received on a fading channel is subject to a multiplicative distortion md and to the usual additive noise following a compensation of the md the signal provided to the detector may be thought to include only a single additive distortion term final noise which comprises the effects of the original additive noise the md and the error in md compensation an exact expression for the probability density function of the final noise is derived this allows calculation of error probability for arbitrary types of linear modulations results for many cases of interest are presented furthermore as special cases of ricean fading error probability for rayleigh fading and non fading channels are obtained which either match the results or complete the approximate derivations formerly known from the literature

the subalgebras of the rank two symplectic lie algebra abstract the semisimple subalgebras of the rank 2 symplectic lie algebra sp 4 c are well known and we recently classified its levi decomposable subalgebras in this article we classify the solvable subalgebras of sp 4 c up to inner automorphism this completes the classification of the subalgebras of sp 4 c more broadly speaking in completing the classification of the subalgebras of sp 4 c we have completed the classification of the subalgebras of the rank 2 semisimple lie algebras

the euclidean algebra in rank 2 classical lie algebras we classify the embeddings of the euclidean algebra e 2 into the rank 2 semisimple classical lie algebras the classifications are up to inner automorphism we also examine the finite dimensional irreducible representations of the rank 2 semisimple classical lie algebras restricted to e 2 with respect to various embeddings all lie algebras and representations are over the complex numbers

closed subsets of root systems and regular subalgebras abstract we describe an algorithm for classifying the closed subsets of a root system up to conjugation by the associated weyl group our algorithm is implemented in the language of the computer algebra system gap 4 we discuss the implementation and give runtimes on some sample inputs the classification of the closed subsets of an irreducible root system is closely related to the classification of the regular subalgebras up to inner automorphism of the corresponding simple lie algebra we show how to obtain the regular subalgebras corresponding to a given closed set for the root systems of rank 3 the version of this paper on the arxiv has tables describing the subalgebras that were obtained

indecomposable representations of the poincare algebra the authors consider indecomposable representations of the poincare algebra iso 3 1 on the space omega omega omega h of its universal enveloping algebra a master representation is obtained on omega which induces representations on k the invariant subalgebra of translations and on omega and omega these representations are discussed in particular in view of finite dimensional indecomposable representations of iso 3 1 the approach taken is analogous to the approach chosen by the authors in their analysis of indecomposable representations of the lorentz algebra so 3 1 1983 thus under restriction of iso 3 1 to so 3 1 the earlier results are recovered the interpretation of the finite dimensional indecomposable representations of iso 3 1 then follows easily as a coupling of a finite number of irreducible so 3 1 representations to an indecomposable iso 3 1 representation with the dimension of the irreducible representations strictly increasing or strictly decreasing the bases for the finite dimensional indecomposable iso 3 1 representations are explicitly determined and thus also their matrix elements via the inducing representations a formula for their dimensionalities is obtained the methods employed are purely algebraic and follow the line of work of jacobson and dixmier 1962 1978

performance analysis of linear modulation schemes with generalized diversity combining on rayleigh fading channels with noisy channel estimates generalized diversity combining gdc also known as hybrid selection maximal ratio combining or generalized selection combining is a low complexity diversity combining technique by which a fixed subset of a large number of available diversity channels is chosen and then combined using the rules of maximal ratio combining in this paper we analyze the performance of gdc on time correlated rayleigh fading channels with noisy channel estimates we derive expressions for the probability of error for various linear modulation schemes with coherent detection and discuss the conditions under which the analysis can be extended to noncoherent and differentially coherent receiver structures throughout the paper using a fundamental approach to obtain the decision statistic at the combiner output a number of new expressions for the error probabilities are obtained in a rigorous way along with a presentation of their performance with channel estimation errors the final expressions have roughly the same complexity of evaluation as that for the channel with only additive gaussian noise our results correct various inaccuracies in the literature and show that coherent receivers based on imperfectly estimated channel knowledge incur a significant performance loss

levi decomposable algebras in the classical lie algebras abstract we examine embeddings of an important class of levi decomposable algebras into the classical lie algebras in particular we classify the embeddings of a n c n 1 b n c 2 n 1 c n c 2 n and d n c 2 n into the complex simple lie algebras a n 1 b n 1 c n 1 and d n 1 respectively up to inner automorphism