irreducible representations of the lie superalgebras b 0 n with finite degenerated vacuum ii the problem of getting irreducible representations of lie superalgebras b 0 n n 1 2 is studied starting with a recently constructed family of linear representations in terms of differential operators on the space c n of cn valued c functions equivalent formulation via creation annihilation operators of a para bose system with n degrees of freedom is used and the domain d of any is shown to be a subset of c n containing a nonzero vacuum subspace by assuming its dimension finite the necessary conditions for existence of are derived the method is applied to the superalgebra b 0 1 and a one parameter family of nonequivalent irreducible representations in terms of unbounded linear operators on l2 r c2 is obtained each representation has a nondegenerated vacuum and for all z b 0 1 satisfying z z the operators z are essentially self adjoint

the quantum superalgebra uq osp 1 2n deformed para bose operators and root of unity representations we recall the relation between the lie superalgebra osp 1 2n and para bose operators the quantum superalgebra uq osp 1 2n defined as usual in terms of its chevalley generators is shown to be isomorphic to an associative algebra generated by so called pre oscillator operators satisfying a number of relations from these relations and the analogue with the non deformed case one can interpret these pre oscillator operators as deformed para bose operators some consequences for uq osp 1 2n cartan weyl basis poincare birkhoff win basis and its hopf subalgebra uq gl n are pointed out finally using a realization in terms of q commuting q bosons we construct an irreducible finite dimensional unitary fock representation of uq osp 1 2n and its decomposition in terms of uq gl n representations when q is a root of unity

an extension of some theorems of l barreira and c valls for the nonuniform exponential dichotomous evolution operators abstract the aim of this paper is to study the connection between the non uniform exponential dichotomy of a non uniform exponentially bounded strongly continuous evolution family and the admissibility of some function spaces thus there are extended recent results established by l barreira and c valls 2010 2011 in 10 and 11

quantum deformation of bose parastatistics a q deformation of the transformation of the chevalley basis to an odd basis of generators of the universal enveloping of the lie superalgebra g n osp 1 2n is presented it is shown that one thus obtains a reasonable quantum deformation of the algebra of n para bose oscillators

q oscillator realizations of the quantum superalgebras slq m n andospq m 2n realizations of the quantum superalgebras corresponding to thea m n b m n c n 1 andd m n series are given in terms of the creation and annihilation operators ofq deformed bose and fermi oscillators

on a general framework for q particles paraparticles and q paraparticles through deformations the authors propose a unification of deformations associated with the descriptions of q para and q para bosons and fermions for complex values of q

finite dimensional irreducible representations of the quantum superalgebra u q gl n 1 it is shown that every finite dimensional irreducible module over the general linear lie superalgebragl n 1 can be deformed to an irreducible module ofu q gl n 1 aq analogue of the universal enveloping algebra ofgl n 1 the results are extended also to all kac modules which in the atypical cases remain indecomposible within each module expressions for the transformations of the gel fand zetlin basis under the action of the algebra generators are written down an analogoue of the poincare birkhoff witt theorem is formulated

on quantization of simple harmonic oscillators a general framework is presented of quantizing the system of a simple harmonic oscillator various methods of quantization so far proposed are accommodated here in a unified form some remarks are also made on quantization for the case of more than one oscillator

q analogues of the parabose and parafermi oscillators and representations of quantum algebras deformations of the one dimensional parabose oscillators are presented they are shown to provide fock representations of the quantum sp q 2 algebra and ospq 1 2 superalgebra the representations of suq 2 are used to define the q analogues of the parafermi oscillators

quantization of uq osp 1 2n with deformed para bose operators the observation that n pairs of para bose pb operators generate the universal enveloping algebra of the orthosymplectic lie superalgebra osp 1 2n is used in order to define deformed pb operators it is shown that these operators are an alternative to the chevalley generators on this background uq osp 1 2n its cartan weyl generators and their supercommutation relations are written down entirely in terms of deformed pb operators an analogue of the poincare birkhoff witt theorem is formulated

lyapunov functions for strong exponential contractions abstract our main aim is to give a complete characterization of an exponential contraction in terms of lyapunov sequences for discrete time or lyapunov functions for continuous time in particular we obtain inverse theorems giving explicitly a quadratic lyapunov function for each exponential contraction we consider the general cases of 1 nonautonomous dynamics either obtained from a product of linear operators or from a nonautonomous differential equation respectively for discrete and continuous time 2 nonuniform exponential contractions in which the uniform stability is replaced by a nonuniform stability 3 strong exponential behavior in the sense that we have simultaneously lower and upper contraction bounds we emphasize that the two last properties are ubiquitous in the context of ergodic theory and in particular for almost all trajectories of any measure preserving flow which justifies completely the study of this general type of exponential behavior as a nontrivial application of our work we establish the robustness of any strong nonuniform exponential contraction that is the persistence of the asymptotic stability of a strong nonuniform exponential contraction under sufficiently small linear perturbations

an alternative expression for the symbol error probability of mpsk in the presence of i q unbalance this letter provides a new expression for the probability of the phase angle between two vectors perturbed by gaussian noise with in phase quadrature phase i q unbalance in order to simplify the analysis of the error probabilities of m ary phase shift keying mpsk the error probabilities symbol error rates or bit error rates for mpsk with i q balance or unbalance can be presented straightforwardly from the derived expression because the newly derived result is provided in terms of the conventional first order gaussian q function and the joint gaussian q function with a correlation coefficient dependent on m it readily allows rapid evaluation for various cases of practical interest

q oscillator realizations of the metaplectic representation of quantum osp 3 2 q oscillator representations of the quantum superalgebra ospq 3 2 are discussed it is pointed out that the metaplectic representation of ospq 3 2 can be equivalently realized either in terms of one q boson and one q fermion or with one q boson and two q fermions

a description of the quantum superalgebrauq sl n 1 m via creation and annihilation generators a description of the quantum superalgebra uq sl n 1 m and in particular of the special linear superalgebra sl n 1 m via creation and annihilation generators cags is given it provides an alternative to the canonical description of uq sl n 1 m in terms of chevalley generators a conjecture that the fock representations of the cags provide microscopic realizations of exclusion statistics is formulated

computation of the exact bit error rate of coherent m ary psk with gray code bit mapping the problem of calculating the average bit error probability bep of coherent m ary phase shift keying psk over a gaussian channel has been studied previously in the literature a solution to the problem for systems using a binary reflected gray code brgc to map bits to symbols was first presented by p j lee see ibid vol com 34 p 488 91 1986 we show that the results obtained by lee are incorrect for m spl ges 16 we show that the reason for this is an invalid assumption that the bit error rate ber is independent of the transmitted symbols an assumption which has also propagated to textbooks we give a new expression for the ber of m psk systems using the brgc and compare this with lee s results

r matrix formulation of deformed boson algebra rewriting the pusz woronowicz q boson relations in terms of the standard r matrix for suq n the author gives the definition of a general deformed boson algebra a r depending upon a matrix r he investigates the conditions under which this algebra is associative for n 2 a set of matrices satisfying these conditions is classified and the corresponding twisted statistics is given

representations of osp 2 1 and the metaplectic representation shift operator techniques are used to treat the irreducible representations of the superalgebra osp 2 1 apart from obtaining the well known gradestar dispin representations which arise when the even part is the compact su 2 algebra the case when the star conditions on the even part are those satisfied by the noncompact su 1 1 algebra is also treated in this case no gradestar representations arise and the star representations are found to consist of the direct sum of two discrete series representations of su 1 1 one of these representations can be realized in terms of functions of a single complex variable and turns out to be a simple example of a metaplectic representation

parabosons virasoro type algebras and their deformations two parameter p q deformation of a parabosonic algebra underlying the two particle calogero model is considered the fock space representation bargmann fock representation coherent states spectrum generating algebra and a hidden supersymmetry are discussed the paraboson algebra induces a centreless virasoro type algebra with a doubling of the space of generators a two parameter deformation of this virasoro type algebra is studied

q deformed oscillator associated with the calogero model and its q coherent state we present the q deformed para bose oscillators associated with the two body calogero model the q deformed coherent state is also constructed and its resolution of unity is demonstrated

supersymmetry parastatistics and operator realizations of a lie algebra the algebraic structure of parastatistics has been generalized and it is found to be consistent with supersymmetric quantum mechanics with supercharges constructed out of the generalized para bose and para fermi operators it is further shown that the operator algebra of generalized parastatistics offers a realization of the graded orthosymplectic group similar to that of orthogonal and symplectic groups using conventional parastatistics

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

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

variants of bosonization in parabosonic algebra the hopf and super hopf structures in parabosonic algebra parabosonic algebra in finite or infinite degrees of freedom is considered as a 22 graded associative algebra and is shown to be a 22 graded or super hopf algebra the super hopf algebraic structure of the parabosonic algebra is established directly without appealing to its relation to the osp 1 2n lie superalgebraic structure the notion of super hopf algebra is equivalently described as a hopf algebra in the braided monoidal category cz 2 m the bosonization technique for switching a hopf algebra in the braided monoidal category h m where his a quasitriangular hopf algebra into an ordinary hopf algebra is reviewed in this paper we prove that for the parabosonic algebra p b beyond the application of the bosonization technique to the original super hopf algebra a bosonization like construction is also achieved using two operators related to the parabosonic total number operator both techniques switch the same super hopf algebra p b to an ordinary hopf algebra thus producing two different variants of p b with an ordinary hopf structure

highest weight irreducible representations of the lie superalgebra gl 1 two classes of irreducible highest weight modules of the general linear lie superalgebra gl 1 are constructed within each module a basis is introduced and the transformation relations of the basis under the action of the algebra generators are written down

geometry and representations of the quantum supergroup ospq 1 2n the quantum supergroup ospq 1 2n is studied systematically a haar functional is constructed and an algebraic version of the peter weyl theory is extended to this quantum supergroup quantum homogeneous superspaces and quantum homogeneous supervector bundles are defined following the strategy of connes theory parabolic induction is developed by employing the quantum homogeneous supervector bundles quantum frobenius reciprocity and a generalized borel weil theorem are established for the induced representations

stability of nonautonomous differential equations in hilbert spaces abstract we introduce a large class of nonautonomous linear differential equations v a t v in hilbert spaces for which the asymptotic stability of the zero solution with all lyapunov exponents of the linear equation negative persists in v a t v f t v under sufficiently small perturbations f this class of equations which we call lyapunov regular is introduced here inspired in the classical regularity theory of lyapunov developed for finite dimensional spaces that is nowadays apparently overlooked in the theory of differential equations our study is based on a detailed analysis of the lyapunov exponents essentially the equation v a t v is lyapunov regular if for every k the limit of t 1 t as t exists where t is any k volume defined by solutions v 1 t v k t we note that the class of lyapunov regular linear equations is much larger than the class of uniformly asymptotically stable equations

bit error probability for coherent m ary psk systems a simple technique for evaluating the bit error probability of coherent m ary phase shift keying psk with any bit mapping is proposed closed form expressions are given in terms of error functions for half and quadrant plane probabilities in the decision space avoiding the numerical evaluation of complicated integrals that occurs in the direct method bit error probability expressions for m ary psk with gray natural binary and folded binary bit mappings are derived

polynomial deformations of osp 1 2 and generalized parabosons we consider the algebra r generated by three elements a b h subject to three relations h a a h b b and a b f h when f h h this coincides with the lie superalgebra osp 1 2 when f is a polynomial we speak of polynomial deformations of osp 1 2 irreducible representations of r are described and in the case deg f 2 we obtain a complete classification showing some similarities but also some interesting differences with the usual osp 1 2 representations the relation with deformed oscillator algebras is discussed leading to the interpretation of r as a generalized paraboson algebra

efficient computation of erfc x for large arguments a new infinite series representation for the error function is developed it is especially suitable for computing erfc x for large x for instance for any x spl ges 4 the error function can be evaluated with a relative error less than 10 sup 10 by using only eight terms similarly the error function can be evaluated with a relative error less than 8 spl times 10 sup 7 for any x spl ges 2 using just six terms an analytical bound is derived to show that the total error due to series truncation and undersampling rapidly decreases as x increases comparisons with two other series are provided

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

a fast algorithm for learning a ranking function from large scale data sets we consider the problem of learning a ranking function that maximizes a generalization of the wilcoxon mann whitney statistic on the training data relying on an e accurate approximation for the error function we reduce the computational complexity of each iteration of a conjugate gradient algorithm for learning ranking functions from o m2 to o m where m is the number of training samples experiments on public benchmarks for ordinal regression and collaborative filtering indicate that the proposed algorithm is as accurate as the best available methods in terms of ranking accuracy when the algorithms are trained on the same data however since it is several orders of magnitude faster than the current state of the art approaches it is able to leverage much larger training data sets

quantum deformation of the ladder representations of u 1 1 for q 1 uq u 1 1 covariant creation and annihilation operators for q on the unit circle are constructed and the corresponding ladder and singleton representations are considered

versatile accurate and analytically tractable approximation for the gaussian q function the existing approximations for the gaussian q function have been developed bearing in mind applications that require high estimation accuracies e g derivation of the error probability for digital modulation schemes unfortunately the associated mathematical expressions are too complex to be easily employed in many other analytical studies even if they do not require such a high accuracy this letter proposes a simple yet accurate mathematical approximation to the gaussian q function when compared to other existing approximations the proposed model provides an adequate balance between accuracy and analytical tractability its simplicity enables its application over a wider range of analytical studies at reasonable accuracy levels as an illustrative example the proposed approximation is employed to obtain a new and simple closed form expression for the probability of detection of an energy detector under rayleigh fading channels

a superalgebra uq osp 3 2 generated by deformed paraoperators and its morphism onto a wq 1 1 clifford weyl algebra a deformed universal enveloping superalgebra uq of the lie superalgebra osp 3 2 which is a hopf algebra is defined as freely generated by deformed para bose operators b and deformed para fermi operators f the q analog of the cartan weyl basis and all deformed supercommutation relations between the generators are written down a morphism of uq onto a deformed clifford weyl superalgebra wq 1 1 a is constructed where wq 1 1 a is generated by q bosons b and q fermions f under the condition that the q bosons anticommute with the q fermions the corresponding oscillator representation is studied

very simple tight bounds on the q function we present new lower and upper bounds on the gaussian q function unified in a single and simple algebraic expression which contains only two exponential terms with a constant and a rational coefficient respectively lower and upper bounding properties are obtained from such unified expression by selecting the coefficients accordingly despite the remarkable simplicity the bounds are found to be as tight as multi term alternatives obtained e g from the exponential 2 and jensen cotes 3 families of bounds a corollary result is that the n th integer power of q x can also be tightly bounded both below and above with only n 1 algebraic terms in addition to offering remarkable accuracy and mathematical tractability combined the new bounds are very consistent in which both lower and upper counterparts are similarly tight over the entire domain

new solutions of the yang baxter equation based on root of 1 representations of the para bose superalgebra new solutions of the quantum yang baxter equation depending in general on three arbitrary parameters are written down they are based on the root of unity representations of the quantum orthosymplectic superalgebra which were found recently representations of the braid group are defined within any nth tensorial power of root of 1 modules

jensen cotes upper and lower bounds on the gaussian q function and related functions we present new families of lower and upper bounds on q functions first we consider the craig form of the gaussian q function q x and shown that its integrand phi thetas x can be partitioned into a pair of complementary convex and concave segments this property is then exploited in conjunction with the jensen inequality and the newton cotes quadrature rule to produce a complete family of upper and lower bounds on q x which can be made arbitrarily tight by finer segmentation the basic idea is then utilized to derive families of upper and lower bounds also for the squared gaussian q function q2 x the 2d joint gaussian q function q x y p and the generalized marcum q function qm x y the bounds are shown to be tighter than alternatives found in the literature and in some cases the lower bounds provided find no equivalent in current literature the generality of the principle is the elegant point of the method and the resulting jensen cotes bounds are easy to implement and evaluate since only elementary transcendental functions are involved as an example of application to the analysis of communication systems we consider the bit error rates ber s of decode and forward df cooperative relaying schemes with coherent and differential phase shift keying psk modulations which have been shown to have an intricate dependence on the gaussian q function complicated by crossproducts irrational functional arguments and multiple numerical integrations in that example the bounds substantially reduce the complexity required to evaluate the expressions retaining tightness despite multiple numerical integrations with infinite limits

uq covariant oscillators and vertex operators uq sl 2 covariant bose and fermi oscillators are studied systematically and applied to constructing vertex operators and uq invariant blocks for qp 1 p 2 3 a p2 dimensional unitary fock space representation of the bose oscillator algebra a q is constructed this representation does not allow however for the construction of all uq invariant blocks associated with an indecomposable representation of uq an extension of a is needed in this case which involves operators creating states of q spin projection p 2 from the fock vacuum the extended algebra only has infinite dimensional indefinite metric space representations an algebraic notion of trace is introduced provided q2 1 in the bose case this allows the introduction of a family of in general mixed uq invariant temperature states such that the vacuum expectation value appears in the zero temperature limit

sep performance of coherent mpsk over fading channels in the presence of phase quadrature error and i q gain mismatch this letter presents a joint approach to the symbol error probability sep of coherent m ary phase shift keying in a situation where the phase error quadrature error and in phase quadrature i q gain mismatch problems take place all concurrently over an additive white gaussian noise and arbitrary fading channel a set of equations that characterizes the conditional sep on an instantaneous fading signal to noise ratio is derived in the form of the craig representation

lyapunov functions and cone families we describe systematically the relation between lyapunov functions and nonvanishing lyapunov exponents both for maps and flows this includes a brief survey of the existing results in the area in particular we consider separately the cases of nonpositive and arbitrary lyapunov functions thus yielding optimal criteria for negativity and positivity of the lyapunov exponents of linear cocycles over measure preserving transformations moreover we describe converse results of these criteria with the explicit construction of eventually strict lyapunov functions for any map or flow with nonzero lyapunov exponents we also construct examples showing that in general the existence of an eventually strict invariant cone family does not imply the existence of an eventually strict lyapunov function

algebraic structure of parabose fock space i the green s ansatz revisited a description of the fock space of a parabose oscillator of order p based on commutation relations bilinear in creation and annihilation operators rather than trilinear ones is developed a new statement of the well known green s ansatz is introduced to help understand the significance of the bilinear commutation relations it is also applied to show how all parabose oscillators of even order respectively odd order can be obtained as irreducible constituents of the fock space associated with a green s ansatz of two three terms analogs of the form in which the parabose green s ansatz is presented are provided for one parafermi oscillator and for systems of many parabose and parafermi oscillators of the same order methods used in the paper allow various new results for q deformed parabose oscillators to be derived

dual diversity over correlated log normal fading channels a great deal of attention has been devoted in the literature to studying the bit error rate ber performance of diversity combining systems in the presence of rayleigh rice and nagakami m fading by comparison the literature is relatively sparse in comparable analyses over log normal channels which typically characterize shadowing from indoor obstacles and moving human bodies one reason for this disparity stems from the difficulty in evaluating the exact average ber when log normal variates are involved using for example the moment generating function mgf approach due to the inability of expressing the mgf itself in a simple closed form since it is possible to evaluate the marginal and joint statistical moments as well as the cumulative distribution function cdf associated with a log normal distribution in closed form we rather focus here on other performance measures namely average combined output signal to noise ratio amount of fading and outage probability the first two performance measures depend only on the moments whereas the outage probability depends solely on the cdf closed form expressions in terms of known functions single integral representations or upper and lower bounds are obtained for these measures corresponding to maximal ratio combining selection combining and switch and stay combining schemes allowing for the possibility of correlation between the two branches numerical evaluations of these expressions illustrating the performances of each individual diversity type as well as comparisons among them are also presented

chernoff type bounds for the gaussian error function we study single term exponential type bounds also known as chernoff type bounds on the gaussian error function this type of bound is analytically the simplest such that the performance metrics in most fading channel models can be expressed in a concise closed form we derive the conditions for a general single term exponential function to be an upper or lower bound on the gaussian error function we prove that there exists no tighter single term exponential upper bound beyond the chernoff bound employing a factor of one half regarding the lower bound we prove that the single term exponential lower bound of this letter outperforms previous work numerical results show that the tightness of our lower bound is comparable to that of previous work employing eight exponential terms

some new twists to problems involving the gaussian probability integral using an alternate form of the gaussian probability integral discovered a number of years ago it is shown that the solution to a number of previously considered communication problems can be simplified and in some cases made more accurate i e exact rather than bounded these problems include the evaluation of 1 the bit error probability of uncoded phase shift keying psk with costas loop tracking 2 word error probability of antipodal modulation in the presence of fading 3 bit error probability of coded m ary psk mpsk over the memoryless fading channel with given channel state information 4 conditional symbol error probability of mpsk in the presence of carrier synchronization error and 5 the average error probability for the binary additive white gaussian noise awgn intersymbol interference channel also obtained is a generalization of this new alternate form to the case of a two dimensional gaussian probability integral with arbitrary correlation which can be used to evaluate the symbol error probability of mpsk with i q unbalance

unitarizable representations of the deformed para bose superalgebra uq osp 1 2 at roots of 1 the unitarizable irreps of the deformed para bose superalgebra pbq which is isomorphic to uq osp 1 2 are classified at q being root of 1 new finite dimensional irreps of uq osp 1 2 are found explicit expressions for the matrix elements are written down

fock representations of the superalgebra sl n 1 m its quantum analogue uq sl n 1 m and related quantum statistics fock space representations of the lie superalgebra sl n 1 m and of its quantum analogue uq sl n 1 m are written down the results are based on a description of these superalgebras via creation and annihilation operators the properties of the underlying statistics are briefly discussed

envelope and phase distribution of two correlated gaussian variables probability density functions pdf s are derived for the phase and amplitude envelope of the complex gain x jy j radic 1 where x and y are two correlated non zero mean gaussian random variables the pdf of the amplitude is derived as an infinite series but reduces to a closed form expression when the means are zero the classical rayleigh and rician pdf s turn out to be special cases of the derived pdf this pdf is used to analyze the error performance of non coherent binary frequency shift keying bfsk with in phase quadrature i q imbalance over an additive white gaussian noise awgn channel the resulting bit error rate ber expression is derived as an infinite series the analytical expressions are validated by simulation and the i q imbalance related performance degradation is quantified convergence of the pdf series and the ber series is established

the evaluation of error probabilities for intersymbol and cochannel interference an efficient series that can be used to calculate the probability of error in a binary symmetric channel with intersymbol interference and additive noise is derived the series is derived by representing the noise complementary probability distribution function by an exact or approximate fourier series bounds on the accuracy of the estimate are derived for gaussian noise examples show that only a small numerical effort may be required to compute error probabilities of interest using the series applications to both finite and infinite intersymbol interference systems are discussed a similar technique is used to derive series representations for the probability of error of additive noise channels with cochannel interference or with combined intersymbol and cochannel interferences the accuracy of the results is bounded for gaussian noise

an infinite series for the computation of the complementary probability distribution function of a sum of independent random variables and its application to the sum of rayleigh random variables the properties of the series are studied for both bounded and unbounded random variables the technique is used to find efficient series for computation of the distributions of sums of uniform random variables and sums of rayleigh random variables a useful closed form expression for the characteristic function of a rayleigh random variable is presented and an efficient method for computing a confluent hypergeometric function is given an infinite series for the probability density function of a sum of independent random variables is also derived the inversion of characteristic functions a trapezoidal rule for numerical integration and the sampling theorem in the frequency domain are related to and interpreted in terms of the results

upper bounds on the symbol error probability of mpsk with phase error using pawula f function iv this letter presents an alternative derivation of the case iv of pawula f function and an approximation for the corresponding probability density function pdf in the presence of the tikhonov distributed phase error the pdf of case iv is used to obtain new upper bounds for the conditional and average symbol error probabilities of m ary phase shift keying with phase error over additive white gaussian noise channels numerical results demonstrate the validity of the upper bounds

a closed form expression for the exact ber of generalized pam and qam constellations we derive an explicit closed form expression for the exact bit error rate ber computation of generalized hierarchical m ary pulse amplitude modulations over additive white gaussian noise awgn and fading channels this expression can also be used to obtain the exact ber of generalized hierarchical quadrature amplitude modulations square and rectangular for the awgn case these expressions are in the form of a weighted sum of complementary error functions and are solely dependent on the constellation size m the carrier to noise ratio and a constellation parameter which controls the relative message importance

a description of the superalgebra osp 2 n 1 2 m via green generators an alternative description of the lie superalgebra osp 2n 1 2m in terms of generators and relations is given the generators called green generators are the root vectors of osp 2n 1 2m corresponding to the orthogonal roots

stability theory and lyapunov regularity abstract we establish the stability under perturbations of the dynamics defined by a sequence of linear maps that may exhibit both nonuniform exponential contraction and expansion this means that the constants determining the exponential behavior may increase exponentially as time approaches infinity in particular we establish the stability under perturbations of a nonuniform exponential contraction under appropriate conditions that are much more general than uniform asymptotic stability the conditions are expressed in terms of the so called regularity coefficient which is an essential element of the theory of lyapunov regularity developed by lyapunov himself we also obtain sharp lower and upper bounds for the regularity coefficient thus allowing the application of our results to many concrete dynamics it turns out that using the theory of lyapunov regularity we can show that the nonuniform exponential behavior is ubiquitous contrarily to what happens with the uniform exponential behavior that although robust is much less common we also consider the case of infinite dimensional systems

hopf algebraic structure of the parabosonic and parafermionic algebras and paraparticle generalization of the jordan schwinger map the aim of this paper is to show that there is a hopf structure of the parabosonic and parafermionic algebras and this hopf structure can generate the well known hopf algebraic structure of the lie algebras through a realization of lie algebras using the parabosonic and parafermionic extension of the jordan schwinger map the differences between the hopf algebraic and the graded hopf superalgebraic structure on the parabosonic algebra are discussed

nonuniform exponential contractions and lyapunov sequences abstract for a nonautonomous dynamics with discrete time obtained from the product of linear operators we show that a nonuniform exponential contraction can be completely characterized in terms of what we call strict lyapunov sequences we note that nonuniform exponential contractions include as a very particular case the uniform exponential contractions that correspond to have a uniform asymptotic stability of the dynamics we also obtain inverse theorems that give explicitly strict lyapunov sequences for each nonuniform exponential contraction essentially the lyapunov sequences are obtained in terms of what are usually called lyapunov norms that is norms with respect to which the behavior of a nonuniform exponential contraction becomes uniform we also show how the characterization of nonuniform exponential contractions in terms of quadratic lyapunov sequences can be used to establish in a very simple manner the persistence of the asymptotic stability of a nonuniform exponential contraction under sufficiently small linear or nonlinear perturbations moreover we describe an appropriate version of our results in the context of ergodic theory showing that the existence of an eventually strict lyapunov function implies that all lyapunov exponents are negative almost everywhere