the dirichlet problem for nonlinear second order elliptic equations iii functions of the eigenvalues of the hessian on etudie le probleme de dirichlet dans un domaine borne de r n a frontiere lisse f d 2 u dans u sur

conservation laws for equations of mixed elliptic hyperbolic and degenerate types for partial differential equations of mixed elliptic hyperbolic and degenerate types which are the euler lagrange equations for an associated lagrangian invariance with respect to changes in independent and dependent variables is investigated as are results in the classification of continuous one parameter symmetry groups for the variational and divergence symmetries conservation laws are derived via the method of multipliers the conservation laws resulting from anisotropic dilations are applied to prove uniqueness theorems for linear and nonlinear problems and the invariance under dilations of the linear part is used to derive critical exponent phenomena and to obtain localized energy estimates for supercritical problems

a two parameter deformation of the jaynes cummings model path integral representation a two parameter p q deformation of the jaynes cummings model is obtained using a recently developed p q deformed oscillator in the rotating wave approximation rwa the dynamical symmetry of the model is the quantum superalgebra up q 1 mod 1 the partition function of the model is obtained as a path integral over generalized perelomov coherent states corresponding to the quantum algebra up q 1 mod 1 the complete spectrum of the model is extracted for both the case when the coupling constants are grassman valued and when they are c number valued it is noted that a relaxation of the rwa extends the dynamical symmetry to the quantum superalgebra ospp q 2 mod 2

the linearized system for isometric embeddings and its characteristic variety abstract in this paper we prove a conjecture of bryant griffiths and yang concerning the characteristic variety for the determined isometric embedding system in particular we show that the characteristic variety is not smooth for any dimension greater than 4 this is accomplished by introducing a smaller yet equivalent linearized system in an appropriate way which facilitates analysis of the characteristic variety

multiple cumulants based spectrum sensing methods for cognitive radios in cognitive radios energy detector is considered for spectrum sensing in the literature however its performance deteriorates rapidly if the noise power is not known exactly moreover due to the presence of a colored channel interferer or some other reasons the conventional white gaussian noise may become colored in order to solve these problems this paper proposes several multicumulant based spectrum sensing methods generalized likelihood ratio test glrt based multicumulant glrtmc based detection method and multiantenna assisted multicumulant mamc based detection method glrtmc detection method is derived from generalized likelihood ratio test and assumed to be near optimum in theory mamc detection method on the other hand by using multiple antennas is a complexity reduced detector and allows us to make a compromise between performance and complexity it is well known that cumulants higher than second order are zero for gaussian distributions thus glrtmc detection method and mamc detection method can extract a non gaussian signal from gaussian noise even when the noise is colored in addition the proposed methods are nonparametric in the sense that they do not require any exact prior knowledge about the signal or the noise such as noise power or cyclic frequencies hence they are immune from noise uncertainty simulation experiments are provided to show the validity and the superiority over single cumulant based detector of the proposed multicumulant based detectors

dynkin like diagrams and representations of the strange superalgebra p n using an extension p n of the noncontragredient superalgebra p n on which a nondegenerate killing form can be constructed simple root systems srss are introduced to each srs is associated a dynkin like diagram then the maximal regular sub super algebras are obtained moreover a procedure to construct highest weight irreducible representations of p n is presented

an analysis of band limited communication systems from amplifier efficiency and distortion perspective considering growing concerns toward green communications not only their bandwidth efficiency but also their power consumption is expected to gain increasing importance for future communication systems a power amplifier pa is one of the most power consuming analog devices at the transmitter in communication systems and a precise estimation of the power consumption at the transmitter circuit requires the knowledge of its efficiency that depends on the distribution of input signal envelope and the amount of input back off in this paper we develop a simple analytical model that can be used for estimating achievable efficiency of a linear pa as well as the amount of resulting nonlinear distortion for a given modulated signal exclusively from its envelope distribution based on this model the trade off relationships between the efficiency and signal to distortion power ratio for several spectrally efficient linear modulations are examined it is also shown that in some special cases of gaussian input and memoryless nonlinearity pa models the results can be represented in simple closed form expressions

structure of basic lie superalgebras and of their affine extensions we generalize to the case of superalgebras several properties of simple lie algebras involving the use of dynkin diagrams if to a simple lie algebra can be associated one dynkin diagram it is a finite set of nonequivalent ones which can be constructed for a basic superalgebra or b s a the knowledge of these diagrams which can be obtained for each b s a in a systematic way allows us to deduce the regular subsuperalgebras of a b s a the symmetries of the dynkin diagrams are related to outer automorphisms of b s a and lead to some singular subsuperalgebras finally we consider the extended dynkin diagrams in order to classify the affine b s a and use their symmetries to construct the twisted basic superalgebras

geometric quantization on the super disk in this article we discuss the geometric quantization on a certain type of infinite dimensional super disk such systems are quite natural when we analyze coupled bosons and fermions the large n limit of a system like that corresponds to a certain super homogeneous space first we define an example of a super homogeneous manifold a super disk we show that it has a natural symplectic form and it can be used to introduce classical dynamics once a hamiltonian is chosen existence of moment maps provide a poisson realization of the underlying symmetry super group these are the natural operators to quantize via methods of geometric quantization and we show that this can be done

on monge ampere equations with homogenous right hand sides we study the regularity and behavior at the origin of solutions to the two dimensional degenerate monge ampere equation det d2u x with 2 we show that when 0 solutions admit only two possible behaviors near the origin radial and nonradial which in turn implies c2 regularity we also show that the radial behavior is unstable for 0 we prove that solutions admit only the radial behavior near the origin 2008 wiley periodicals inc

oscillator realization of the strange superalgebras p n and q n the strange superalgebra p n is realized in terms of bilinear products of oscillators of bosonic and fermionic type the even part is given by sums of bilinears in bosons and fermions and the odd part by bilinears in one boson and one fermion these oscillators can be used to build explicit realizations of some highest weight irreducible representations of p n this procedure is illustrated for p 3 where in particular the case of the adjoint representation of p 3 is worked out in detail finally an oscillator realization of the strange superalgebra q n is also given

global bv entropy solutions to the gauss codazzi system abstract the gauss codazzi system for the given metric whose gauss curvature is negative is considered in the present paper we provide some suitable conditions on the given metric such that the system admits a global bv entropy solution our main approach is applying the method of seeking global bv entropy solutions to the hyperbolic system of balance laws to the gauss codazzi system the global existence of bv solutions to the gauss codazzi system yields a c 1 1 isometric immersion of two dimensional manifold into r 3

the local isometric embedding in r3 of two dimensional riemannian manifolds with gaussian curvature changing sign cleanly on etudie le plongement isometrique local de surfaces a 2 dimensions dans r 3 on suppose que la premiere forme fondamentale edu 2 2fdudv gdv 2 on cherche trois fonctions c 2 x u v y u v z u v telles que dx 2 dy 2 dz 2 edu 2 2fdudv gdv 2 dans un voisinage de p

fock representations of the lie superalgebra q n 1 for the lie superalgebra q n 1 a description is given in terms of creation and annihilation operators in such a way that the defining relations of q n 1 are determined by quadratic and triple supercommutation relations of these operators fock space representations vp of q n 1 are defined by means of these creation and annihilation operators these new representations are introduced as quotient modules of some induced module of q n 1 the representations vp are not graded but they possess a number of properties that are of importance for physical applications for p a positive integer these representations vp are finite dimensional with a unique highest weight of multiplicity one the hermitian form that is consistent with the natural adjoint operation on q n 1 is shown to be positive definite on vp for q 2 these representations are dispin for the general case of q n 1 many structural properties of vp are derived

statistical tests for presence of cyclostationarity the presence of kth order cyclostationarity is defined in terms of nonvanishing cyclic cumulants or polyspectra relying upon the asymptotic normality and consistency of kth order cyclic statistics asymptotically optimal spl chi sup 2 tests are developed to detect the presence of cycles in the kth order cyclic cumulants or polyspectra without assuming any specific distribution on the data constant false alarm rate tests are derived in both time and frequency domain and yield consistent estimates of possible cycles present in the kth order cyclic statistics explicit algorithms for k spl les 4 are discussed existing approaches are rather empirical and deal only with k spl les 2 case simulation results are presented to confirm the performance of the given tests

dirichlet problems for general monge ampere equations here 172z denotes the hessian of z with respect to a given metric d s2 gu d u d u a in the local chart vzz z u f z where are the christoffel symbols there have been many papers to devoted to the boundary value problems of 1 1 for example cns1 2 t k tu h1 and most of them are only concerning the euclidean metric the purpose of the present paper is to deal with the dirichlet problem of 1 1 for any given metric as a moderate step in sect 2 and 3 we discuss the following problem

new coherent states of the lie superalgebra osp 1 2 r a new kind of coherent states css for lie superalgebra osp l 2 r are introduced some properties of these states are discussed it is shown that they can encompass the glauber css su 1 1 css and squeezed states within a common formalism the d algebra differential operator realization of the osp 1 2 r generators on the css and their diagonal projectors are constructed

the dirichlet problem for nonlinear second order elliptic equations i monge ampegre equation on considere le probleme de dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture d un domaine borne dans r n avec une frontiere c

hierarchical digital modulation classification using cumulants a simple method based on elementary fourth order cumulants is proposed for the classification of digital modulation schemes these statistics are natural in this setting as they characterize the shape of the distribution of the noisy baseband i and q samples it is shown that cumulant based classification is particularly effective when used in a hierarchical scheme enabling separation into subclasses at low signal to noise ratio with small sample size thus the method can be used as a preliminary classifier if desired computational complexity is order n where n is the number of complex baseband data samples this method is robust in the presence of carrier phase and frequency offsets and can be implemented recursively theoretical arguments are verified via extensive simulations and comparisons with existing approaches

boundary value problems for mixed type equations and applications abstract in this paper we outline a general method for finding well posed boundary value problems for linear equations of mixed elliptic and hyperbolic type which extends previous techniques of berezanskii didenko and friedrichs this method is then used to study a particular class of fully nonlinear mixed type equations which arise in applications to differential geometry

normally ordered bose fermi operator realization of the su n m group the technique of integration within an ordered product which is now generalized to the supersymmetric case together with the boson fermion coherent states is used to derive the normally ordered bose fermi operator realization of the group su n m the mapping of the su n m fundamental representation in classical complex number grassmann number space into the realization in hilbert space is manifestly shown in our formalism the corresponding antinormally ordered realization is also discussed

existence of c local solutions for the monge ampere equation on considere l equation de monge ampere det u ij f y u u dans un ouvert de r n on demontre l existence de solutions c locales

representations of quantum superalgebra uq gl 2 1 in a coherent state basis and generalization the coherent state method has proved to be useful in quantum physics and mathematics this method more precisely the vector coherent state method has been used by some authors to construct representations of superalgebras but almost to our knowledge it has not yet been extended to quantum superalgebras except uq osp 1 2 one of the smallest quantum superalgebras in this article the method is applied to a bigger quantum superalgebra namely uq gl 2 1 in constructing q boson fermion realizations and finite dimensional representations which when irreducible are classified into typical and nontypical representations this construction leads to a more general class of q boson fermion realizations and finite dimensional representations of uq gl 2 1 and thus at q 1 of gl 2 1 both gl 2 1 and uq gl 2 1 have found different physics applications therefore it is meaningful to construct their representations

high order moments and gaussianity of single carrier and ofdm signals this paper analyzes the high order moments of linearly modulated single carrier as well as orthogonal frequency division multiplexing ofdm signals assuming that the modulated symbols that form resulting continuous signal waveform are statistically independent for a single carrier case with the ideal low pass filter used for pulse shaping closed form expressions of the moments with up to the eighth order are derived the proposed approach is then extended to gaussianity assessment of ofdm signals we show how the moments of ofdm signals can approach to those of gaussian distribution as the number of subcarriers increases for a given modulation constraint on each subcarrier also reported is the peculiar nonstationary behavior of the fourth order moments in the case of bpsk modulated ofdm signals

bv weak solutions to gauss codazzi system for isometric immersions abstract the isometric immersion problem for surfaces embedded into r 3 is studied via the fluid dynamic framework introduced in chen et al 2010 6 as a system of balance laws of mixed type the techniques developed in the theory of weak solutions of bounded variation in continuum physics are employed to deal with the isometric immersions in the setting of differential geometry the so called bv framework is formed that establishes convergence of approximate solutions of bounded variation to the gauss codazzi system and yields the c 1 1 isometric realization of two dimensional surfaces into r 3 local and global existence results are established for weak solutions of small bounded variation to the gauss codazzi system for negatively curved surfaces that admit equilibrium configurations as an application the case of catenoidal shell of revolution is provided

existence of local sufficiently smooth solutions to the complex monge ampere equation we prove the c local solvability of the n dimensional complex monge ampere equation det u ij f z u u f 0 in a neighborhood of any point z 0 where f z 0 0

the existence of hypersurfaces of constant gauss curvature with prescribed boundary in this paper we are concerned with the problem of finding hypersurfaces of constant gauss kronecker curvature k hypersurfaces in r n 2 with prescribed boundary given a disjoint collection 1 m of closed smooth embedded n 1 dimensional submanifolds of r decide whether there exist immersed k hypersurfaces m in r with m locally this problem reduces to questions concerning monge ampere type equations and we seek solutions for which the resulting equation is elliptic this means that we must confine ourselves to the class of locally strictly convex hypersurfaces i e those whose principal curvatures are all positive such hypersurfaces locally lie on one side of their tangent planes at any point but need not do so globally as they have non empty boundary finding hypersurfaces with prescribed curvature and boundary has been a major challenge in geometric analysis because of the highly nonlinear nature of the problem and the lack of variational methods beginning around 1980 some success was achieved due to breakthroughs in the theory of monge ampere equations and general fully nonlinear equations but only for hypersurfaces which are globally graphs of functions over domains with geometric restrictions e g strictly convex domains this was the case even for k hypersurfaces where the only general existence results were consequences of the existence theory for monge ampere equations see 6 20 23 and was restricted to strictly convex domains this means that the resulting surfaces must be simply connected graphs a very strong restriction geometrically the first idea that a more general result was possible came in the paper of hoffmanrosenberg spruck 18 and subsequently such a general result was developed in 12 and 11 in these papers the authors proved an essentially optimal existence theorem for monge ampere equations in domains of arbitrary geometry and thus the limit of

simple space time symmetries generalizing conformal field theory we study simple space time symmetry groups g which act on a space time manifold m g h which admits a g invariant global causal structure we classify pairs g m which share the following additional properties of conformal field theory 1 the stability subgroup h of o m is the identity component of a parabolic subgroup of g implying factorization h man where m generalizes lorentz transformations a dilatations and n special conformal transformations 2 special conformal transformations n act trivially on tangent vectors v tom the allowed simple lie groups g are the universal coverings of su m m so 2 d sp l r so 4n and e7 25 and h are particular maximal parabolic subgroups they coincide with the groups of fractional linear transformations of euclidean jordan algebras whose use as generalizations of minkowski space time was advocated by gunaydin mod phys lett a 8 1407 1993 all these groups g admit positive energy representations it will also be shown that the classical confor

a new iterative method for solving the coefficient inverse problem of the wave equation on donne la definition de l equation operateur non lineaire du probleme inverse coefficient de l equation d onde dans le domaine des variables d espace et de temps sans les transformees de laplace et de fourier

existence of distributional solutions of a closed dirichlet problem for an elliptic hyperbolic equation abstract the closed dirichlet problem for an elliptic hyperbolic equation arising in linearizing the monge ampere type equation is shown to admit a distributional solution by using an a b c integral method

smooth tame frechet algebras and lie groups of pseudodifferential operators for pseudodifferential operator algebras with globally defined 0 order symbols belonging to either the hormander class s or certain prescribed subspaces it is shown that these algebras possess important smooth tame structures that make them amenable to nonlinear functional analysis of nash moser type

on the cauchy problem of degenerate hyperbolic equations in this paper we study a class of degenerate hyperbolic equations and prove the existence of smooth solutions for cauchy problems the existence result is based on a priori estimates of sobolev norms of solutions such estimates illustrate a loss of derivatives because of the degeneracy

the cumulant theory of cyclostationary time series ii development and applications for pt i see ibid vol 42 no 12 p 3387 3408 1994 the development of the theory of nonlinear processing of cyclostationary time series that is initiated in part i is continued a new type of cumulant for complex valued variables is introduced and used to generalize the temporal and spectral moments and cumulants for cyclostationary time series from real valued to complex valued time series the relations between the temporal and spectral moments and cumulants at the inputs and outputs of several signal processing operations are determined formulas for the temporal and spectral cumulants of complex valued pulse amplitude modulated time series are derived estimators for the temporal moments and cumulants and for the cyclic polyspectra are presented and their properties are discussed the performance of these estimators is illustrated by several computer simulation examples for pulse amplitude modulated time series the theory is applied to the problems of weak signal detection and interference tolerant time delay estimation

minimal unitary representation of su 2 2 and its deformations as massless conformal fields and their supersymmetric extensions we study the minimal unitary representation minrep of so 4 2 over a hilbert space of functions of three variables obtained by quantizing its quasiconformal action on a five dimensional space the minrep of so 4 2 which coincides with the minrep of su 2 2 similarly constructed corresponds to a massless conformal scalar in four space time dimensions there exists a one parameter family of deformations of the minrep of su 2 2 for positive negative integer values of the deformation parameter one obtains positive energy unitary irreducible representations corresponding to massless conformal fields transforming in 0 2 2 0 representation of the sl 2 c subgroup we construct the supersymmetric extensions of the minrep of su 2 2 and its deformations to those of su 2 2 n the minimal unitary supermultiplet of su 2 2 4 in the undeformed case simply corresponds to the massless n 4 yang mills supermultiplet in four dimensions for each given nonzero integer value of one obtains a uniq

isometric immersions and compensated compactness a fundamental problem in differential geometry is to characterize intrinsic metrics on a two dimensional riemannian manifold mathcal m 2 which can be realized as isometric immersions into mathbb r 3 this problem can be formulated as initial and or boundary value problems for a system of nonlinear partial differential equations of mixed elliptic hyperbolic type whose mathematical theory is largely incomplete in this paper we develop a general approach which combines a fluid dynamic formulation of balance laws for the gauss codazzi system with a compensated compactness framework to deal with the initial and or boundary value problems for isometric immersions in mathbb r 3 the compensated compactness framework formed here is a natural formulation to ensure the weak continuity of the gauss codazzi system for approximate solutions which yields the isometric realization of two dimensional surfaces in mathbb r 3

time domain tests for gaussianity and time reversibility statistical signal processing algorithms often rely upon gaussianity and time reversibility two important notions related to the probability structure of stationary random signals and their symmetry parametric models obtained via second order statistics sos are appropriate when the available data is gaussian and time reversible on the other hand evidence of nonlinearity non gaussianity or time irreversibility favors the use of higher order statistics hos in order to validate gaussianity and time reversibility and quantify the tradeoffs between sos and hos consistent time domain chi squared statistical tests are developed exact asymptotic distributions are derived to estimate the power of the tests including a covariance expression for fourth order sample cumulants a modification of existing linearity tests in the presence of additive gaussian noise is discussed briefly the novel gaussianity statistic is computationally attractive leads to a constant false alarm rate test and is well suited for parametric modeling because it employs the minimal hos lags which uniquely characterize arma processes simulations include comparisons with an existing frequency domain approach and an application to real seismic data time reversibility tests are also derived and their performance is analyzed both theoretically and experimentally

raising operators for the osp 1 2n r orthosymplectic lie superalgebras the branching rule is obtained for the decomposition of the osp 1 2n r oscillator like unitary irreducible representations into sp 2n r representations raising operators for osp 1 2n r sp 2n r are determined and used to construct a basis in the irreducible representation carrier space the matrix elements of the odd generators between two sp 2n r lowest weight states are calculated the general results so obtained are illustrated with the osp 1 4 r example

the full spectrum of ads5 cft4 i representation theory and one loop q system with the formulation of the quantum spectral curve for the ads5 cft4 integrable system it became potentially possible to compute its full spectrum with high efficiency this is the first paper in a series devoted to the explicit design of such computations with no restrictions to particular subsectors being imposed we revisit the representation theoretical classification of possible states in the spectrum and map the symmetry multiplets to solutions of the quantum spectral curve at zero coupling to this end it is practical to introduce a generalisation of young diagrams to the case of non compact representations and define algebraic q systems directly on these diagrams furthermore we propose an algorithm to explicitly solve such q systems that circumvents the traditional usage of bethe equations and simplifies the computation effort for example our algorithm quickly obtains explicit analytic results for all 495 multiplets that accommodate single trace operators in sym with classical conformal dimension up to we plan to use these results as the seed for solving the quantum spectral curve perturbatively to high loop orders in the next paper of the series

path integral for new coherent states of lie superalgebra osp 1 2 r a path integral formulation in the representation of new coherent states for the lie superalgebra osp l 2 r is introduced by the use of the completeness relation of the new coherent states a path integral expression for the transition amplitude between two osp l 2 r new coherent states for a hamiltonian which is linear in the generators of the superalgebra are obtained in the classical limit the equations of motion for the system are derived

vector coherent states of non compact orthosymplectic lie supergroups vector coherent states are defined for the generic lowest weight ladder irreducible representations of the non compact orthosymplectic lie supergroups osp 2m 2n r and osp 2m 1 2n r their simultaneous use with k matrix theory is shown to provide a powerful tool for the study of such representations this is illustrated with the detailed example of osp 1 2n r

unitary lowest weight representations of the noncompact supergroup osp 2n 2m r the oscillator construction of the unitary irreducible lowest highest weight representations of the noncompact supergroup osp 2n 2m r with even subgroup so 2n sp 2m r is given in particular simple rules for determining the so 2n sp 2m r decomposition of the unitary lowest weight representations of osp 2n 2m r are derived

super twistor realization of unitary super representations of u p q n this paper is concerned with demonstrating that the twistor realization of the ladder representation of u p q can be generalized to super representations of u p q n this is achieved by considering the generalization of twistor elementary states to a super algebraic category unitarity of these super representations follows from the positive definiteness of a super twistor scalar product constructed in this paper although generalizations of the ladder representations have been well studied by other means it will be shown that the super twistor generalization is especially natural and merits special investigation

unitary representations of non compact supergroups we give a general theory for the construction of oscillator like unitary irreducible representations uirs of non compact supergroups in a super fock space this construction applies to all non compact supergroupsg whose coset spaceg k with respect to their maximal compact subsupergroupk is hermitean supersymmetric we illustrate our method with the example of su m p n q by giving its oscillator like uirs in a particle state basis as well as supercoherent state basis the same class of uirs can also be realized over the super hilbert spaces of holomorphic functions of az variable labelling the coherent states

superunitary reduction of the orthosymplectic supertableaux the supertableaux of the orthosymplectic groups osp 2 2p and osp 2 1 2p are decomposed in sums of supertableaux of the superunitary group su p

cumulant based approach to harmonic retrieval and related problems a frequently encountered problem in signal processing is that of estimating the frequencies and amplitudes of harmonics observed in additive colored gaussian noise in practice the observed signals are contaminated with spatially and temporally colored noise of unknown power spectral density a cumulant based approach to these problems is proposed the cumulants of complex processes are defined and it is shown that specific 1 d slices of the fourth order cumulant of the noisy signal for the direction of arrival doa and retrieval of harmonics in noise rhn problems are identical to the autocorrelation of a related noiseless signal hence correlation based high resolution methods may be used with fourth order cumulants as well the effectiveness of the proposed methods is demonstrated through standard simulation examples

energy estimates for a class of degenerate hyperbolic equations we derive estimates in usual sobolev norms for solutions of degenerate hyperbolic equations if degenerate coefficients admit only real roots loss of derivatives occurs due to the degeneracy

harmonic fields on the extended projective disk and a problem in optics the hodge equations for 1 forms are studied on beltrami s projective disk model for hyperbolic space ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments an existence theorem for weakly harmonic 1 fields changing type on the unit circle is derived under dirichlet conditions imposed on the noncharacteristic portion of the boundary a similar system arises in the analysis of wave motion near a caustic a class of elliptic hyperbolic boundary value problems is formulated for those equations as well for both classes of boundary value problems an arbitrarily small lower order perturbation of the equations is shown to yield solutions which are strong in the sense of friedrichs

supercoherent states for the t j model the cartan structure of the dynamical superalgebra of the t j model of strongly correlated electrons is found this is used to define and explicitly construct the coherent states for this algebra and calculate the invariant measure for the completeness relation for the coherent states

regular subalgebras of lie superalgebras and extended dynkin diagrams using the method of extended cartan matrices and extended dynkin diagrams a classification of maximal regular semisimple subalgebras of the basic classical lie superalgebras is obtained especially in the case of exceptional lie superalgebras some curious inclusion relations are discovered

dimension and character formulas for lie supergroups a character formula is derived for lie supergroups the basic technique is that of symmetrization and antisymmetrization associated with young tableaux generalized to supergroups we rewrite the characters of the ordinary lie groups u n o n and sp 2n in terms of traces in the fundamental representation it is then shown that by simply replacing traces with supertraces the characters of certain representations for u n m and osp n 2m are obtained dimension formulas are derived by calculating the characters of a special diagonal supergroup element with 1 and 1 eigenvalues formulas for the eigenvalues of the quadratic casimir operators are given as applications the decomposition of a representation into representations of subgroups is discussed examples are given for the lie supergroup su 6 4 which has physical applications as a dynamical supersymmetry in nuclei

path integral for coherent states of the dynamical u2 group and u2 1 supergroup a path integral formulation in the representation of coherent states for the unitary u2 group and u2 1 supergroup is introduced u2 and u2 1 path integrals are shown to be defined on the coset spaces u2 u1 x u1 and u2 1 u1 1 x u1 respectively these cosets appear as curved classical phase spaces partition functions are expressed as path integrals over these spaces in the case when u2 and u2 1 are the dynamical groups the corresponding path integrals are evaluated with the help of linear fractional transformations that appear as the group supergroup action in the coset space superspace possible applications for quantum models are discussed

characteristics and existence of isometric embeddings soit m ds 2 une variete de riemann c a 3 dimensions et x 0 m un point tel que le tenseur d einstein 7b g x 0 n est pas l 2 ou l t x0 m alors il existe un plongement isometrique local c d un voisinage de x 0 dans e 6

the existence and singularity structures of low regularity solutions to higher order degenerate hyperbolic equations abstract this paper is a continuation of our partial work in 21 where we established that the bounded local solution u t x exists and is piecewise smooth for the second order degenerate hyperbolic equation t 2 t m x u f t x u with the initial data of c 1 piecewise smooth u 0 x and piecewise smooth t u 0 x in the present paper we will consider the lower regularity solution of the higher order degenerate hyperbolic equation in the category of discontinuous and even unbounded functions

compactness of alexandrov nirenberg surfaces we study a class of compact surfaces in 3 introduced by alexandrov and generalized by nirenberg and prove a compactness result under suitable assumptions on induced metrics and gauss curvatures 2017 wiley periodicals inc

oscillator like unitary representations of non compact groups with a jordan structure and the non compact groups of supergravity we give a general bosonic construction of oscillator like unitary irreducible representations uir of non compact groups whose coset spaces with respect to their maximal compact subgroups are hermitian symmetric with the exception of e7 7 they include all the non compact invariance groups of extended supergravity theories in four dimensions these representations have the remarkable property that each uir is uniquely determined by an irreducible representation of the maximal compact subgroup we study the connection between our construction the hermitian symmetric spaces and the tits koecher construction of the lie algebras of corresponding groups we then give the bosonic construction of the lie algebra ofe7 7 in su 8 so 8 and u 7 bases and study its properties application of our method toe7 7 leads to reducible unitary representations

the local isometric embedding in mathbb r 3 of two dimensional riemannian manifolds with gaussian curvature changing sign to finite order on a curve we consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of monge ampere type these two problems are the local isometric embedding problem for two dimensional riemannian manifolds and the problem of locally prescribed gaussian curvature for surfaces in r3 we prove a general local existence result for a large class of monge ampere equations in the plane and obtain as corollaries the existence of regular solutions to both problems in the case that the gaussian curvature vanishes to arbitrary finite order on a single smooth curve

deformation of the strange superalgebra p n a deformation uq p n pq n of the extended noncontragredient strange superalgebra of p n denoted by p n is proposed a realization of pq n in terms of q bosons and q fermions is presented then a procedure to build up a set of representations of pq n is briefly discussed as a by product a new realization of suq n is obtained

coherent states for the harmonic oscillator representations of the orthosymplectic supergroup osp 1 2n r coherent states for the harmonic oscillator representations of the noncompact supergroup osp 1 2n r are introduced and the invariant integration measure is calculated by studying transformation properties of supercoset variables the generalized bogoliubov transformation for mixed systems of bosons and fermions is also obtained an example for the simple harmonic oscillator is given

the cumulant theory of cyclostationary time series i foundation the problem of characterizing the sine wave components in the output of a polynomial nonlinear system with a cyclostationary random time series input is investigated the concept of a pure nth order sine wave is introduced and it is shown that pure nth order sine wave strengths in the output time series are given by scaled fourier coefficients of the polyperiodic temporal cumulant of the input time series the higher order moments and cumulants of narrowband spectral components of time series are defined and then idealized to the case of infinitesimal bandwidth such spectral moments and cumulants are shown to be characterized by the fourier transforms of the temporal moments and cumulants of the time series it is established that the temporal and spectral cumulants have certain mathematical and practical advantages over their moment counterparts to put the contributions of the paper in perspective a uniquely comprehensive historical survey that traces the development of the ideas of temporal and spectral cumulants from their inception is provided

on the existence of c 1 1 isometric immersions of several classes of negatively curved surfaces into mathbb r 3 we prove the existence of c 1 1 isometric immersions of several classes of negatively curved riemannian surfaces mathcal m g into the 3 dimensional euclidean space mathbb r 3 including the standard hyperbolic plane the generalised helicoid type metrics and the generalised enneper metrics our proof is based on the theory of compensated compactness and the method of invariant regions in hyperbolic conservation laws together with several new observations on relevant geometric quantities gauss curvature metric components etc for negatively curved surfaces

local smooth isometric embeddings of low dimensional riemannian manifolds into euclidean spaces on demontre l existence d un plongement isometrique lisse locale d une 3 variete de riemann lisse a courbure qui ne s annule pas dans un 6 espace euclidien

isometric immersions of surfaces with two classes of metrics and negative gauss curvature the isometric immersion of two dimensional riemannian manifolds or surfaces with negative gauss curvature into the three dimensional euclidean space is studied in this paper the global weak solutions to the gauss codazzi equations with large data in l infty are obtained through the vanishing viscosity method and the compensated compactness framework the l infty uniform estimate and h 1 compactness are established through a transformation of state variables and construction of proper invariant regions for two types of given metrics including the catenoid type and the helicoid type the global weak solutions in l infty to the gauss codazzi equations yield the c1 1 isometric immersions of surfaces with the given metrics

finite and infinite dimensional representations of the orthosymplectic superalgebra osp 3 2 the shift operator technique is used to give a complete analysis of all finite and infinite dimensional irreducible representations of the orthosymplectic superalgebra osp 3 2 for all cases the star or grade star conditions for the algebra are investigated only two finite dimensional representations are grade star representations if the representation space is required to be a graded hilbert space when the even part is so 3 sp 2 r su 2 su 1 1 an infinite class of infinite dimensional star representations is found one of them can be realized in terms of two valued functions of a complex variable this representation reduces to the sum of two metaplectic representations of sp 2 we show that it is precisely this metaplectic representation for osp 3 2 which gives the spin energy eigenstates for the one dimensional harmonic oscillator with spin 1 2 states