classification of matrix product unitaries with symmetries we prove that matrix product unitaries with on site unitary symmetries are completely classified by the chiral index and the cohomology class of the symmetry group g provided that we can add trivial and symmetric ancillas with arbitrary on site representations of g if the representations in both system and ancillas are fixed to be the same we can define symmetry protected indices spis which quantify the imbalance in the transport associated to each group element and greatly refines the classification these spis are stable against disorder and measurable in interferometric experiments our results lead to a systematic construction of two dimensional floquet symmetry protected topological phases beyond the standard classification and thus shed new light on understanding nonequilibrium phases of quantum matter

shift invariant spaces on lca groups in this article we extend the theory of shift invariant spaces to the context of lca groups we introduce the notion of h invariant space for a countable discrete subgroup h of an lca group g and show that the concept of range function and the techniques of fiberization are valid in this context as a consequence of this generalization we prove characterizations of frames and riesz bases of these spaces extending previous results that were known for rd and the lattice zd

nonlinear vibration of a coating fgm substrate cylindrical panel subjected to a temperature gradient this paper deals with the linear and nonlinear vibration analysis of a three layer coating fgm substrate cylindrical panel with general boundary conditions and subjected to a temperature gradient across the thickness due to steady heat conduction the theoretical formulation is based on geometric nonlinearity in von karman sense and the first order shear deformation theory which accounts for the effects of transverse shear strains and rotary inertia a nonlinear pre vibration analysis is conducted to determine the thermally induced deformation and pre stress state of the cylindrical panel due to the bending and stretching coupling effect being introduced by the graded layer the nonlinear governing differential equations of motion are obtained by adding an incremental dynamic state to the pre vibration state a numerical method that makes use of differential quadrature approximation together with iterative algorithms is employed to model the linear and nonlinear vibration behavior of the cylindrical panels numerical results are presented in both tabular and graphical forms showing that the linear and nonlinear vibration frequencies are significantly influenced by vibration amplitude temperature change out of plane boundary support and the values of a b a h and r a the effects of the in plane displacement constraints and the volume fraction index of the intermediate fgm thin layer are not very prominent

dilations for systems of imprimitivity acting on banach spaces abstract motivated by a general dilation theory for operator valued measures framings and bounded linear maps on operator algebras we consider the dilation theory of the above objects with special structures we show that every operator valued system of imprimitivity has a dilation to a probability spectral system of imprimitivity acting on a banach space this completely generalizes a well known result which states that every frame representation of a countable group on a hilbert space is unitarily equivalent to a subrepresentation of the left regular representation of the group we also prove that isometric group representation induced framings on a banach space can be dilated to unconditional bases with the same structure for a larger banach space this extends several known results on the dilations of frames induced by unitary group representations on hilbert spaces

a duality principle for groups the duality principle for gabor frames states that a gabor sequence obtained by a time frequency lattice is a frame for l2 rd if and only if the associated adjoint gabor sequence is a riesz sequence we prove that this duality principle extends to any dual pairs of projective unitary representations of countable groups we examine the existence problem of dual pairs and establish some connection with classification problems for ii1 factors while in general such a pair may not exist for some groups we show that such a dual pair always exists for every subrepresentation of the left regular unitary representation when g is an abelian infinite countable group or an amenable icc group for free groups with finitely many generators the existence problem of such a dual pair is equivalent to the well known problem about the classification of free group von neumann algebras

the buckling of functionally graded truncated conical shells under dynamic axial loading abstract the dynamic buckling of truncated conical shells made of functionally graded materials fgms subject to a uniform axial compressive load which is a linear function of time has been studied the material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell the variation of properties followed an arbitrary distribution in terms of the volume fractions of the constituents the fundamental relations the dynamic stability and compatibility equations of functionally graded truncated conical shells are obtained first applying galerkin s method these equations have been transformed to a pair of time dependent differential equation with variable coefficient and critical parameters obtained using the runge kutta method the results show that the critical parameters are affected by the configurations of the constituent materials compositional profile variations loading speed variations and the variation of the shell geometry comparing the results of this study with those in the literature validates the present analysis

on lipschitz analysis and lipschitz synthesis for the phase retrieval problem in this paper we prove two results regarding reconstruction from magnitudes of frame coefficients the so called phase retrieval problem first we show that phase retrievability as an algebraic property implies that nonlinear maps are bi lipschitz with respect to appropriate metrics on the quotient space second we prove that reconstruction can be performed using lipschitz continuous maps specifically we show that when nonlinear analysis maps h r m are injective with x hx fki m 1 and x hx fki 2 m 1 where f1 fm is a frame for a hilbert space h and

buckling of a conical thin shell with variable thickness under a dynamic loading this study considers the buckling of an elastic truncated conical shell having a meridional thickness expressed by an arbitrary function subject to a uniform external pressure which is a power function of time at first the fundamental relations and donnell type dynamic buckling equation of an elastic conical shell with variable thickness have been obtained then employing galerkin s method those equations have been reduced to a time dependent differential equation with variable coefficients finally applying the ritz type variational method the critical static and dynamic loads the corresponding wave numbers dynamic factor and critical stress impulse have been found analytically using the results thus obtained the effects of the thickness variations with a power or an exponential function the variation of the semi vertex angle and the variation of the power of time in the external pressure expression are studied through pertinent computations it is observed that these factors have appreciable effects on the critical parameters of the problem in the heading

quantum tomography under prior information we provide a detailed analysis of the question how many measurement settings or outcomes are needed in order to identify an unknown quantum state which is constrained by prior information we show that if the prior information restricts the possible states to a set of lower dimensionality then topological obstructions can increase the required number of outcomes by a factor of two over the number of real parameters needed to characterize the set of all states conversely we show that almost every measurement becomes informationally complete with respect to the constrained set if the number of outcomes exceeds twice the minkowski dimension of the set we apply the obtained results to determine the minimal number of outcomes of measurements which are informationally complete with respect to states with rank constraints in particular we show that the minimal number of measurement outcomes povm elements necessary to identify all pure states in a d dimensional hilbert space is 4d 3 c d d for some c d in 1 2 and d being the number of ones appearing in the binary expansion of d 1

multiplicative lidskii s inequalities and optimal perturbations of frames abstract in this paper we study two design problems in frame theory on the one hand given a fixed finite frame f f j j i n for c d we compute those dual frames g of f that are optimal perturbations of the canonical dual frame for f under certain restrictions on the norms of the elements of g on the other hand we compute those v f v f j j i n for invertible operators v which are close to the identity that are optimal perturbations of f that is we compute the optimal perturbations of f among frames g g j j i n that have the same linear relations as f in both cases optimality is measured with respect to submajorization of the eigenvalues of the frame operators hence our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error the key tool for these results is a multiplicative analogue of lidskii s inequality in terms of log majorization and a characterization of the case of equality

koiter circles in the buckling of axially compressed conical shells abstract as is well known the elastic stability of shell structures under certain loading conditions is characterised by a severely unstable postbuckling behaviour the presence of simultaneous buckling modes competing modes corresponding to the same critical buckling load is deemed to be largely responsible for such a behaviour in the present paper within the framework of the so called classical theory linear bifurcation eigenvalue analysis the buckling behaviour of axially compressed cylindrical shells is firstly reviewed accordingly doubly periodic eigenvectors buckling modes corresponding to the same eigenvalue critical buckling load can be determined and their locus in a dimensionless meridional and circumferential buckling wavenumber space is described by a circle known as the koiter circle in the case of axially compressed conical shells no clear evidence of the existence of simultaneous buckling modes can be found in the literature then such a problem is studied here via linear eigenvalue finite element analyses showing that simultaneous doubly periodic modes do also occur for cones and that their locus in a specifically defined dimensionless wavenumber space can be described by an ellipse hereafter termed as the koiter ellipse whose aspect ratio is dependent on the tapering angle of the cone

estimation risk for the var of portfolios driven by semi parametric multivariate models abstract joint estimation of market and estimation risks in portfolios is investigated when the individual returns follow a semi parametric multivariate dynamic model and the asset composition is time varying under ellipticity of the conditional distribution asymptotic theory for the estimation of the conditional value at risk var is developed an alternative method the filtered historical simulation which does not rely on ellipticity is also studied asymptotic confidence intervals for the conditional var which allow for simultaneous quantification of the market and estimation risks are derived the particular case of minimum variance portfolios is analyzed in more detail potential usefulness feasibility and drawbacks of the two approaches are illustrated via monte carlo experiments and an empirical study based on stock returns

aliasing and oblique dual pair designs for consistent sampling abstract in this paper we study some aspects of oblique duality between finite sequences of vectors f and g lying in finite dimensional subspaces w and v respectively we compute the possible eigenvalue lists of the frame operators of oblique duals to f lying in v we compute the spectral and geometrical structure of minimizers of convex potentials among oblique duals for f with norm restrictions as an application we show that these optimal duals are the closest to being tight frames and therefore have their spectrum as concentrated as possible among oblique duals with norm restrictions we obtain a complete quantitative analysis of the impact that the relative geometry between the subspaces v and w has in oblique duality we apply this analysis to compute those rigid rotations u for w such that the canonical oblique dual of u f minimize every convex potential we also introduce a notion of aliasing for oblique dual pairs and compute those rigid rotations u for w such that the canonical oblique dual pair associated to u f minimize the aliasing we point out that these two last problems are intrinsic to oblique duality within the context of consistent sampling

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics

phase retrievable operator valued frames and representations of quantum channels abstract we examine some connections among phase retrievable not necessarily self adjoint operator valued frames projective group representation frames and representations of quantum channels we first present some characterizations of phase retrievable frames for general operator systems acting on both finite and infinite dimensional hilbert spaces which generalize the known results for vector valued frames fusion frames and frames of hermitian matrices for an irreducible projective unitary representation of a finite group the image system is automatically phase retrievable and moreover it is a point wisely tight operator valued frames we generalize this notion to more general operator valued frames and prove that point wise tight operator valued frames are exactly the ones that are right equivalent to operator valued tight frames for an operator system that represent a quantum channel we show that phase retrievability of the system is independent of the choices of the representations of the quantum channel

dilations of operator valued measures with bounded p variations and framings on banach spaces abstract the dilations for operator valued measures ovms and bounded linear maps indicate that the dilation theory is in general heavily dependent on the banach space nature of the dilation spaces this naturally led to many questions concerning special type of dilations in particular it is not known whether ultraweakly continuous normal maps can be dilated to ultraweakly continuous homomorphisms we answer this question affirmatively for the case when the domain algebra is an abelian von neumann algebra it is well known that completely bounded hilbert space operator valued measures correspond to the existence of orthogonal projection valued dilations in the sense of naimark and stinespring and ovms with bounded total variations are completely bounded but not the vice versa with the aim of classifying ovms from the dilation point of view we introduce the concept of total p variations for ovms we prove that any completely bounded ovm has finite 2 variation and any ovm with finite p variation can be dilated to a but usually non hilbertian projection valued measure of the same type with the help of framing induced ovms we prove that conventional minimal dilation space of a non trivial framing contains c 0 then does not have bounded p variation

modelling dynamics of marathons a mixture model approach abstract in this paper statistical properties of marathon dynamics are studied we find that changes of velocity in marathons follow an unconventional mechanism in which the log change of velocity is highly dependent on current velocity with a complex relationship the conditional distributions of log change of velocity exhibit patterns of varying means variances and skewnesses as such the overall velocity distributions are also found to have departed from gaussian we illustrate the mechanism with a finite mixture of generalized linear regressions with varying weights and skew normal errors and we show that the completion time distribution can be approximated by skewed distributions

self organized criticality abstract dissipative dynamical systems with many degrees of freedom naturally evolve to a critical state with fluctuations extending over all length and time scales it is suggested and supported by simulations on simple toy model systems that turbulence earthquakes 1 f noise and economics may operate at the self organized critical state

the structure of shift invariant subspaces of l2 rn using the range function approach to shift invariant spaces in l2 rn we give a simple characterization of frames and riesz families generated by shifts of a countable set of generators in terms of their behavior on subspaces of l2 zn this in turn gives a simplified approach to the analysis of frames and riesz families done by gramians and dual gramians we prove a decomposition of a shift invariant space into the orthogonal sum of spaces each of which is generated by a quasi orthogonal generator as an application of this fact we characterize shift preserving operators in terms of range operators and prove some facts about the dimension function

scaling properties of marathon races abstract some regularities in popular marathon races are identified in this paper it is found for high performance participants i e racing times in the range 2 15 3 15 h the average velocity as a function of the marathoner s ranking behaves as a power law which may be suggesting the presence of critical phenomena elite marathoners with racing times below 2 15 h can be considered as outliers with respect to this behavior for the main marathon pack i e racing times in the range 3 00 6 00 h the average velocity as a function of the marathoner s ranking behaves linearly for this racing times the interpersonal velocity defined as the difference of velocities between consecutive runners displays a continuum of scaling behavior ranging from uncorrelated noise for small scales to correlated 1 f noise for large scales it is a matter of fact that 1 f noise is characterized by correlations extended over a wide range of scales a clear indication of some sort of cooperative effect

frame representations and parseval duals with applications to gabor frames let x n be a frame for a hilbert space h we investigate the conditions under which there exists a dual frame for x n which is also a parseval or tight frame we show that the existence of a parseval dual is equivalent to the problem whether x n can be dilated to an orthonormal basis under an oblique projection a necessary and sufficient condition for the existence of parseval duals is obtained in terms of the frame excess for a frame g g g induced by a projective unitary representation of a group g it is possible that g g g can have a parseval dual but does not have a parseval dual of the same type the primary aim of this paper is to present a complete characterization for all the projective unitary representations such that every frame g g g with a necessary lower frame bound condition has a parseval dual of the same type as an application of this characterization together with a result about lattice tiling we prove that every gabor frame g g l k again with the same necessary lower frame bound condition has a parseval dual of the same type if and only if the volume of the fundamental domain of l k is less than or equal to 1 2

random phaseless sampling for causal signals in shift invariant spaces a zero distribution perspective we proved that the phaseless sampling pls in the linear phase modulated shift invariant space sis v e bf i alpha cdot varphi alpha ne 0 is impossible even though the real valued function varphi enjoys the full spark property so does e bf i alpha cdot varphi stated another way the pls in the complex generated siss is essentially different from that in the real generated ones motivated by this we first establish the condition on the complex valued generator phi such that the pls of nonseparable causal nc signals in v phi can be achieved by random sampling the condition is established from the generalized haar condition ghc perspective based on the proposed reconstruction approach it is proved that if the ghc holds then with probability 1 the random sampling density sd 3 is sufficient for the pls of nc signals in the complex generated siss for the real valued case we also prove that if the ghc holds then with probability 1 the random sd 2 is sufficient for the pls of real valued nc signals in the real generated siss for the local reconstruction of highly oscillatory signals such as chirps a great number of deterministic samples are required compared with deterministic sampling the proposed random approach enjoys not only the greater sampling flexibility but the much smaller number of samples to verify our results numerical simulations were conducted to reconstruct highly oscillatory nc signals in the chirp modulated siss

parseval frames for icc groups abstract we analyze parseval frames generated by the action of an icc group on a hilbert space we parametrize the set of all such parseval frames by operators in the commutant of the corresponding representation we characterize when two such frames are strongly disjoint we prove an undersampling result showing that if the representation has a parseval frame of equal norm vectors of norm 1 n the hilbert space is spanned by an orthonormal basis generated by a subgroup as applications we obtain some sufficient conditions under which a unitary representation admits a parseval frame which is spanned by a riesz sequences generated by a subgroup in particular every subrepresentation of the left regular representation of a free group has this property

tests for conditional ellipticity in multivariate garch models tests are proposed for the assumption that the conditional distribution of a multivariate garch process is elliptic these tests are of kolmogorov smirnov and cramer von mises type and make use of the common geometry underlying the characteristic function of any spherically symmetric distribution the asymptotic null distribution of the test statistics as well as the consistency of the tests is investigated under general conditions it is shown that both the finite sample and the asymptotic null distribution depend on the unknown distribution of the euclidean norm of the innovations therefore a conditional monte carlo procedure is used to actually carry out the tests the validity of this resampling scheme is formally justified results on the behavior of the new tests in finite samples are included along with comparisons with other tests

free vibration of simply supported functionally graded and layered magneto electro elastic plates by finite element method in this article free vibration studies on functionally graded anisotropic and linear magneto electro elastic plates have been carried out by semi analytical finite element method a series solution is assumed in the plane of the plate and finite element procedure is adopted across the thickness of the plate such a way that the three dimensional 3 d character of the solution is preserved the finite element model is derived based on constitutive equation of magneto electro elastic material accounting for coupling between elasticity electric and magnetic effect the present finite element is modeled with displacement components electric potential and magnetic potential as nodal degree of freedom the functionally graded material is assumed to be exponential in the thickness direction the numerical results obtained by the present model are in good agreement with the isotropic 3 d exact benchmark solutions available in literature numerical study includes the influence of the different exponential factor magneto electro elastic properties and effect of mechanical and electrical type of loading on induced magneto electro elastic fields further study has been carried out on higher harmonic study has been extended on functionally graded and layered magneto electro elastic plate

buckling of laminated conical shells given the variations of the stiffness coefficients the buckling behavior of filament wound laminated conical shell is thoroughly investigated by consideration of the variation of the stiffness coefficients to date all analyses of laminated conical shells have been undertaken with constant stiffness coefficients in the laminate constitutive relations usually under the assumption of nominal material properties taken from the midlength of the cone the main object of the study is to investigate the influence of the variation of the stiffness coefficients on the buckling behavior of laminated conical shells an analytical and computational model was developed to calculate the variation of the stiffness coefficients under the assumption that in the case of filament wound truncated conical shells the fiber orientation changes using a geodesic path the model was added to the computer code stags a to calculate the buckling behavior of the laminated conical shell

inferential aspects of the skew exponential power distribution when the analysis of real data indicates that normality assumptions are untenable more flexible models that cope with the most prevalent deviations from normality can be adopted in this context the skew exponential power sep distribution warrants special attention because it encompasses distributions having both heavy tails and skewness it allows likelihood inference and it includes the normal model as a special case this article concerns likelihood inference about the parameters of the sep family in particular the information matrix of the maximum likelihood estimators mles is obtained and finite sample properties of the estimators are investigated numerically special attention is given to the properties of the mles and likelihood ratio statistics when the data are drawn from a normal distribution because this case is relevant for using the sep distribution to test for normality application of the sep distribution in robust estimation problems is considered for both independent and depend

subspaces of l2 g invariant under translation by an abelian subgroup abstract for a second countable locally compact group g and a closed abelian subgroup h we give a range function classification of closed subspaces in l 2 g invariant under left translation by h for a family a l 2 g this classification ties with a set of conditions under which the translations of a by h form a continuous frame or a riesz sequence when g is abelian our work relies on a fiberization map for the more general case we introduce an analogue of the zak transform both transformations intertwine translation with modulation and both rely on a new group theoretic tool for a closed subgroup g we produce a measure on the space g of right cosets that gives a measure space isomorphism g g outside of the group setting we consider a more general problem for a measure space x and a hilbert space h we investigate conditions under which a family of functions in l 2 x h multiplies with a basis like system in l 2 x to produce a continuous frame or a riesz sequence in l 2 x h finally we explore connections with dual integrable representations of lca groups as introduced by hernandez et al in 25

regression and time series model selection in small samples summary a bias correction to the akaike information criterion aic is derived for regression and autoregressive time series models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size the corrected method called aicc is asymptotically efficient if the true model is infinite dimensional furthermore when the true model is of finite dimension aicc is found to provide better model order choices than any other asymptotically efficient method applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed

wandering vector multipliers for unitary groups a wandering vector multiplier is a unitary operator which maps the set of wandering vectors for a unitary system into itself a special case of unitary system is a discrete unitary group we prove that for many and perhaps all discrete unitary groups the set of wandering vector multipliers is itself a group we completely characterize the wandering vector multipliers for abelian and icc unitary groups some characterizations of special wandering vector multipliers are obtained for other cases in particular there are simple characterizations for diagonal and permutation wandering vector multipliers similar results remain valid for irrational rotation unitary systems we also obtain some results concerning the wandering vector multipliers for those unitary systems which are the ordered products of two unitary groups there are applications to wavelet systems

symmetric approximation of frames and bases in hilbert spaces we introduce the symmetric approximation of frames by normalized tight frames extending the concept of the symmetric orthogonalization of bases by orthonormal bases in hilbert spaces we prove existence and uniqueness results for the symmetric approximation of frames by normalized tight frames even in the case of the symmetric orthogonalization of bases our techniques and results are new a crucial role is played by whether or not a certain operator related to the initial frame or basis is hilbert schmidt

modeling and inference with υ spherical distributions abstract a new class of continuous multivariate distributions on n is proposed we define these so called spherical distributions through properties of the density function in a location scale context we derive conditions for properness of spherical distributions and discuss how to generate them in practice the name spherical is motivated by the fact that these distributions generalize the classes of spherical when is the l 2 norm and l q spherical when is the l q norm distributions isodensity sets are still always situated around the location parameter but exchangeability and axial symmetry are no longer imposed as is illustrated in some examples as an important special case we define a class of distributions suggested by independent sampling from a generalization of exponential power distributions this allows us to model skewness interestingly all the robustness results found previously for spherical and l q spherical models carry over directly to spherical mo

properties and estimation of asymmetric exponential power distribution the new distribution class asymmetric exponential power distribution aepd proposed in this paper generalizes the class of skewed exponential power distributions sepd in a way that in addition to skewness introduces different decay rates of density in the left and right tails our parametrization provides an interpretable role for each parameter we derive moments and moment based measures skewness kurtosis expected shortfall it is demonstrated that a maximum entropy property holds for the aepd distributions we establish consistency asymptotic normality and efficiency of the maximum likelihood estimators over a large part of the parameter space by dealing with the problems created by non smooth likelihood function and derive explicit analytical expressions of the asymptotic covariance matrix where the results apply to the sepd class they enlarge on the current literature also we give a convenient stochastic representation of the distribution our monte carlo study illustrates the theoretical results we also provide some empirical evidence for the usefulness of employing aepd errors in garch type models for predicting downside market risk of financial assets

the zak transform and the structure of spaces invariant by the action of an lca group abstract we study closed subspaces of l 2 x where x is a finite measure space that are invariant under the unitary representation associated to a measurable action of a discrete countable lca group on x we provide a complete description for these spaces in terms of range functions and a suitable generalized zak transform as an application of our main result we prove a characterization of frames and riesz sequences in l 2 x generated by the action of the unitary representation under consideration on a countable set of functions in l 2 x finally closed subspaces of l 2 g for g being an lca group that are invariant under translations by elements on a closed subgroup of g are studied and characterized the results we obtain for this case are applicable to cases where those already proven in 5 7 are not

spaces invariant under unitary representations of discrete groups abstract we investigate the structure of subspaces of a hilbert space that are invariant under unitary representations of a discrete group we work with square integrable representations and we show that they are those for which we can construct an isometry intertwining the representation with the right regular representation that we call a helson map we then characterize invariant subspaces using a helson map and provide general characterizations of riesz and frame sequences of orbits these results extend to the nonabelian setting several known results for abelian groups they also extend to countable families of generators previous results obtained for principal subspaces

stability of imperfect stiffened conical shells abstract a general procedure is developed for stability of stiffened conical shells it is used for studying the sensitivity behavior with respect to the stiffener configurations the effect of the pre buckling nonlinearity on the bifurcation point as well as the limit point load level is examined the unique algorithm presented by the authors is an extended version of an earlier one adapted for determination of the limit point load level of imperfect conical shells the eigenvalue problem is iteratively solved with respect to the nonlinear equilibrium state up to the bifurcation point or to the limit point load level a general symbolic code using maple was programmed to create the differential operators based on donnell s type shell theory then the code uses the galerkin procedure the newton raphson procedure and a finite difference scheme for automatic development of an efficient fortran code which is used for the parametric study

extra invariance of shift invariant spaces on lca groups this article generalizes recent results in the extra invariance for shift invariant spaces to the context of lca groups let g be a locally compact abelian lca group and k a closed subgroup of g a closed subspace of l2 g is called k invariant if it is invariant under translations by elements of k assume now that h is a countable uniform lattice in g and m is any closed subgroup of g containing h in this article we study necessary and sufficient conditions for an h invariant space to be m invariant as a consequence of our results we prove that for each closed subgroup m of g containing the lattice h there exists an h invariant space s that is exactly m invariant that is s is not invariant under any other subgroup m containing h we also obtain estimates on the support of the fourier transform of the generators of the h invariant space related to its m invariance

long range correlation properties of coding and noncoding dna sequences genbank analysis an open question in computational molecular biology is whether long range correlations are present in both coding and noncoding dna or only in the latter to answer this question we consider all 33301 coding and all 29453 noncoding eukaryotic sequences each of length larger than 512 base pairs bp in the present release of the genbank to dtermine whether there is any statistically significant distinction in their long range correlation properties standard fast fourier transform fft analysis indicates that coding sequences have practically no correlations in the range from 10 bp to 100 bp spectral exponent beta 0 00 0 04 where the uncertainty is two standard deviations in contrast for noncoding sequences the average value of the spectral exponent beta is positive 0 16 0 05 which unambiguously shows the presence of long range correlations we also separately analyze the 874 coding and the 1157 noncoding sequences that have more than 4096 bp and find a larger region of power law behavior we calculate the probability that these two data sets coding and noncoding were drawn from the same distribution and we find that it is less than 10 10 we obtain independent confirmation of these findings using the method of detrended fluctuation analysis dfa which is designed to treat sequences with statistical heterogeneity such as dna s known mosaic structure patchiness arising from the nonstationarity of nucleotide concentration the near perfect agreement between the two independent analysis methods fft and dfa increases the confidence in the reliability of our conclusion

the structure of finitely generated shift invariant spaces in l2 rd a simple characterization is given of finitely generated subspaces of l2 rd which are invariant under translation by any multi integer and is used to give conditions under which such a space has a particularly nice generating set namely a basis and more than that a basis with desirable properties such as stability orthogonality or linear independence the last property makes sense only for local spaces i e shift invariant spaces generated by finitely many compactly supported functions and special attention is paid to such spaces as an application we prove that the approximation order provided by a given local space is already provided by the shift invariant space generated by just one function with this function constructible as a finite linear combination of the finite generating set for the whole space hence compactly supported this settles a question of some 20 years standing

singular value estimates of oblique projections abstract let w and m be two finite dimensional subspaces of a hilbert space h such that h w m and let p w m denote the oblique projection with range w and nullspace m in this article we get the following formula for the singular values of p w m 2 s k p w m 1 min f h x w m 2 where the minimum is taken over the set of all operator pairs f h on h such that r f w r h m and fh p w m and k 1 dim w we also characterize all the pairs where the minimum is attained

detrended fluctuation analysis of time series of a firing fusimotor neuron abstract we study the interspike intervals isi time series of the spontaneous fusimotor neuron activity by applying the detrended fluctuation analysis that is a modification of the random walk model analysis thus we have found evidence for the white noise characteristics of the isi time series which means that the fusimotor activity does not possess temporal correlations we conclude that such an activity represents the requisite noisy component for occurrence of the stochastic resonance mechanism in the neural coordination of muscle spindles

the existence of tight gabor duals for gabor frames and subspace gabor frames abstract let k and l be two full rank lattices in r d we give a complete characterization for all the gabor frames that admit tight dual of the same type the characterization is given in terms of the center valued trace of the von neumann algebra generated by the left regular projective unitary representations associated with the time frequency lattice k l two applications of this characterization were obtained i we are able to prove that every gabor frame has a tight dual if and only if the volume of k l is less than or equal to 1 2 ii we are able to obtain sufficient or necessary conditions for the existence of tight gabor pseudo duals for subspace gabor frames in various cases in particular we prove that every subspace gabor frame has a tight gabor pseudo dual if either the volume v k l 1 2 or v k l 2 moreover if k z d l z d with 1 then a subspace gabor frame g g l k has a tight gabor pseudo dual only when g g l k itself is already tight

dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading abstract in this paper a formulation for the dynamic stability analysis of functionally graded shells under harmonic axial loading is presented a profile for the volume fraction is assumed and a normal mode expansion of the equations of motion yields a system of mathieu hill equations the stability of which is analyzed by the bolotin s method the present study examines the effects of the volume fraction of the material constituents and their distribution on the parametric response in particular the positions and sizes of the instability regions

nonlinear dynamic response and active vibration control for piezoelectric functionally graded plate the nonlinear dynamic response and active vibration control of the piezoelectric functionally graded plate are analyzed in this paper based on higher order shear plate theory and elastic piezoelectric theory the nonlinear geometric and constitutive relations of the piezoelectric functionally graded plate are established and then the nonlinear motion equations of the piezoelectric functionally graded plate are obtained through hamilton s variational principle the nonlinear active vibration control of the structure is carried out with adoption of the negative velocity feedback control algorithm by applying finite difference method the whole problem is solved by using iterative method synthetically in numerical examples the effects of mechanical load electric load the volume fraction and the geometric parameters on the dynamic response and vibration control of the piezoelectric fgm plate are investigated

a character theory for projective representations of finite groups abstract in this paper we construct a character theory for projective representations of finite groups consequently we compute the number of distinct irreducible projective representations up to isomorphism of a finite group with a given associated schur multiplier and deduce properties on the degrees of such projective representations

football goal distributions and extremal statistics we analyse the distributions of the number of goals scored by home teams away teams and the total scored in the match in domestic football games from 169 countries between 1999 and 2001 the probability density functions pdfs of goals scored are too heavy tailed to be fitted over their entire ranges by poisson or negative binomial distributions which would be expected for uncorrelated processes log normal distributions cannot include zero scores and here we find that the pdfs are consistent with those arising from extremal statistics in addition we show that it is sufficient to model english top division and fa cup matches in the seasons of 1970 71 2000 01 on poisson or negative binomial distributions as reported in analyses of earlier seasons and that these are not consistent with extremal statistics

effect of the nonlinear pre buckling state on the bifurcation point of conical shells abstract the effect of pre buckling nonlinearity on the bifurcation point of a conical shell is examined on the basis of three shell theories donnell s sanders and timoshenko s the eigenvalue problem is solved iteratively about the nonlinear equilibrium state up to the bifurcation point a new algorithm is presented for the real buckling behavior dispensing with the need to cover the entire nonlinear pattern this algorithm is very important for structures characterized by a softening process in which the pre buckling nonlinearity depresses the buckling level relative to the classical one the procedure involves nonlinear partial differential equations which are separated into two sets using the perturbation technique for the pre buckling and buckling states respectively and solved with the variable expanded in fourier series in the circumferential direction and by finite differences in the axial direction a general computer code was developed and used in studying the effect of the pre buckling nonlinearity on the buckling level of the shell under axial compression in the context of the three shell theories

asymmetric elastic buckling of axially compressed conical shells with various end conditions two different solutions to the problem of simply supported conical shells under axial compression suggested by previous investigators are extensively compared and the problems associated with each type of solution are identified in terms of buckling load both solutions are in good agreement but significant differences are clearly shown in buckling mode comparisons it is also shown that in certain cases different modes correspond to the same value of critical load on the basis of the numerical performance of each solution a displacement function is selected and the study is extended to investigate mode effects in cones with clamped boundary conditions the numerical difficulties encountered in simply supported cones are reduced in this case clamping alters the shape of the buckling mode not only in the vicinity of the boundaries as may be expected but also in the center of the cone

buckling of laminated cylindrical shells in terms of different theories and formulations bifurcation buckling analysis of laminated cylindrical shells is presented on the basis of three different shell theories donnell s donnell l h stability of thin walled tubes under torsion naca tr 479 1933 sanders s sanders j l jr nonlinear theories of thin shells quarterly journal on applied mathematics vol 21 no 1 1963 pp 21 36 and timoshenko s timoshenko s theory of elastic stability mcgraw hill new york 1961 formulations in terms of the displacement components and of the airy stress function and normal displacement are examined the partial differential equations are derived via the variational principle and solved with variables expanded in fourier series in the circumferential direction and presented as finite differences in the axial direction the buckling behavior of an angle ply laminated cylindrical shell under different modes of loading was investigated parametrically showing in contrast to its isotropic counterparts a discrepancy between the two formulations

imperfection sensitivity of conical shells the sensitivity of isotropic conical shells to imperfection is considered via the initial postbuckling analysis on the basis of three different shell theories donnell s sanders s and timoshenko s the conical shell was chosen as a representative case exhibiting the entire range of imperfection sensitivity the procedure involves nonlinear partialdifferential equations whichareconverted into a sequenceofthreelinearsets thelatteraresolvedwiththe variablesexpandedinfourierseriesinthecircumferentialdirectionandine nitedifferencesintheaxialdirections a general code is developed and used in studying the effect of higher exactness of the shell theory on the sensitivity behaviorandinparametricanalysesofthesensitivity ofconicalshells especiallywithrespecttotheconesemivertex angle

postbuckling of laminated cylindrical shells in different formulations the sensitivity of laminated cylindrical shells to imperfection is investigated throughout their entire nonlinear behavior the study has two objectives 1 comparison of the simplest formulation using the airy stress function called the wf formulation with the more accurate one using the three displacement components called the uvw formulation and 2 examining the correlation between the sensitivity to imperfection according to this nonlinear analysis and that of koiter s process for the initial postbuckling behavior for laminated cylindrical shells in contrast to isotropic shells significant differences are observed between the two formulations wf and uvw and koiter s theory does not always represent the actual sensitivity behavior a general symbolic code using maple was programmed to create the differential operators then the code used the galerkin procedure the newton raphson procedure and a finite difference scheme for automatic development of an efficient fortran code which was used for the parametric study

frame vector multipliers for finite group representations abstract a frame vector or generator for a group representation of a countable or finite group g on a hilbert space h is a vector h such that g g g is a parseval frame for h frame vector multipliers are the unitary operators on h that map frame vectors to frame vectors based on a characterization of frame vectors with respect to the standard decomposition of a group representation as the direct sums of irreducible subrepresentations with multiplicity we obtain explicit characterizations of frame generator multipliers for two basic cases for finite group representations with the help of these characterizations we obtain some necessary conditions of frame vector multipliers for general frame representations and present several examples to demonstrate how these results can be used to get explicit characterizations for frame vector multipliers

2 d differential quadrature solution for vibration analysis of functionally graded conical cylindrical shell and annular plate structures this paper focuses on the dynamic behavior of functionally graded conical cylindrical shells and annular plates the last two structures are obtained as special cases of the conical shell formulation the first order shear deformation theory fsdt is used to analyze the above moderately thick structural elements the treatment is developed within the theory of linear elasticity when materials are assumed to be isotropic and inhomogeneous through the thickness direction the two constituent functionally graded shell consists of ceramic and metal that are graded through the thickness from one surface of the shell to the other two different power law distributions are considered for the ceramic volume fraction the homogeneous isotropic material is inferred as a special case of functionally graded materials fgm the governing equations of motion expressed as functions of five kinematic parameters are discretized by means of the generalized differential quadrature gdq method the discretization of the system leads to a standard linear eigenvalue problem where two independent variables are involved without using the fourier modal expansion methodology for the homogeneous isotropic special case numerical solutions are compared with the ones obtained using commercial programs such as abaqus ansys nastran straus pro mechanica very good agreement is observed furthermore the convergence rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good different typologies of non uniform grid point distributions are considered finally for the functionally graded material case numerical results illustrate the influence of the power law exponent and of the power law distribution choice on the mechanical behavior of shell structures

effectiveness of linear bifurcation analysis for predicting the nonlinear stability limits of structures as an effort to predict effectively the actual collapse load of a structure a series of numerical studies on the stability of shell structures are made the difference in formulation between the two types of linear buckling loads the classical and the fully linearized is first demonstrated their correlations with respect to the actual stability limit of the structure are compared and finally the two types of critical load approximations are obtained at various stages of a nonlinear analysis to study the pattern of convergence to the actual collapse load it is found that the fully linearized buckling analysis when combined with nonlinear analysis can serve as a useful tool for prediction of the stability limit of a structure while for most types of structures the approximation is within engineering accuracy the rate of convergence of the extrapolated critical load also gives some insight to the accuracy of the approximation

approximations for gabor and wavelet frames let be a frame vector under the action of a collection of unitary operators u motivated by the recent work of frank paulsen and tiballi and some application aspects of gabor and wavelet frames we consider the existence and uniqueness of the best approximation by normalized tight frame vectors we prove that for any frame induced by a projective unitary representation for a countable discrete group the best normalized tight frame ntf approximation exists and is unique therefore it applies to gabor frames including gabor frames for subspaces and frames induced by translation groups similar results hold for semi orthogonal wavelet frames

variational analysis applied to the problem of optical phase retrieval we apply nonsmooth analysis to a well known optical inverse problem phase retrieval the phase retrieval problem arises in many different modalities of electromagnetic imaging and has been studied in the optics literature for over forty years the state of the art for this problem in two dimensions involves iterated projections for solving a nonconvex feasibility problem despite widespread use of these algorithms current mathematical theory cannot explain their success at the heart of projection algorithms is a nonconvex nonsmooth optimization problem we obtain some insight into these algorithms by applying techniques from nonsmooth analysis in particular we show that the weak closure of the set of directions toward the projection generate the subdifferential of the corresponding squared set distance function following a pattern of proof described in f h clarke yu s ledyaev r j stern and p r wolenski nonsmooth analysis and control theory springer verlag new york 1998 this result is generalized to provide conditions under which the subdifferential of an integral function equals the integral of the subdifferential

the stability of functionally graded truncated conical shells subjected to aperiodic impulsive loading abstract in this work the stability of conical shells made of functionally graded materials fgms subject to a uniform external pressure which is a power function of time has been studied the material properties of functionally graded shells are assumed to vary continuously through his thickness of the shell according to a power law distribution of the volume fractions of the constituents the fundamental relations the dynamic stability and compatibility equations of functionally graded truncated conical shells are obtained first applying galerkin s method these equations have been transformed to a pair of time dependent differential equation with variable coefficient this differential equation is solved for different initial conditions by variational method by using lagrange hamilton type principle thus general formulas have been obtained for the critical parameters the results show that the critical parameters are affected by the configurations of the constituent materials loading parameters variations the variation of the semi vertex angle and the power of time in the external pressure expression variations comparing results with those in the literature validates the present analysis

geometric aspects of frame representations of abelian groups hhwe consider frames arising from the action of a unitary representation of a discrete countable abelian group we show that the range of the analysis operator can be determined by computing which characters appear in the representation this allows one to compare the ranges of two such frames which is useful for determining similarity and also for multiplexing schemes our results then partially extend to bessel sequences arising from the action of the group we apply the results to sampling on bandlimited functions and to wavelet and weyl heisenberg frames this yields a sufficient condition for two sampling transforms to have orthogonal ranges and two analysis operators for wavelet and weyl heisenberg frames to have orthogonal ranges the sufficient condition is easy to compute in terms of the periodization of the fourier transform of the frame generators

the nonlinear dynamic buckling response of functionally graded truncated conical shells abstract in this study the nonlinear dynamic buckling of functionally graded fg truncated conical shells subjected to axial compressive load varying as a linear function of time is investigated the material properties of the fg truncated shell are assumed to vary continuously through the thickness of the shell the nonlinear pre buckling deformations of the fg truncated conical shell are taken into account the fundamental relations and modified donnell type nonlinear dynamic stability and compatibility equations of the fg truncated conical shell are derived and solved by using the superposition principle galerkin and runge kutta methods the values of the dimensionless nonlinear critical time parameter have been found numerically finally carrying out some computations the effects of the compositional profiles the variation of the truncated conical shell geometric parameters and the axial loading speed on the dimensionless linear and nonlinear critical time parameters have been studied comparing the results of this study with those in the literature validates the present analysis

the structure of shift modulation invariant spaces the rational case in this paper we study structural properties of shift modulation invariant smi spaces also called gabor subspaces or weyl heisenberg subspaces in the case when shift and modulation lattices are rationally dependent we prove the characterization of smi spaces in terms of range functions analogous to the well known description of shift invariant spaces c de boor r devore a ron the structure of finitely generated shift invariant spaces in l2 r d j funct anal 119 1994 37 78 m bownik the structure of shift invariant subspaces of l2 r n j funct anal 177 2000 282 309 h helson lectures on invariant subspaces academic press new york london 1964 we also give a simple characterization of frames and riesz sequences in terms on their behavior of the fibers of the range function next we prove several orthogonal decomposition results of smi spaces into simpler blocks called principal smi spaces then this is used to characterize operators invariant under both shifts and modulations in terms of families of linear maps acting on the fibers of the range function we also introduce the fundamental concept of the dimension function for smi spaces as a result this leads to the classification of unitarily equivalent smi spaces in terms of their dimension functions finally we show several results illustrating our fiberization techniques to characterize dual gabor frames

wiener s lemma for twisted convolution and gabor frames as a consequence ca is invertible and bounded on all p zd for 1 p oo simultaneously in this article we study several non commutative generalizations of wiener s lemma and their application to gabor theory the paper is divided into two parts the first part sections 2 and 3 is devoted to abstract harmonic analysis and extends wiener s lemma to twisted convolution the second part section 4 is devoted to the theory of gabor frames specifically to the design of dual windows with good time frequency localization in particular we solve a conjecture of janssen feichtinger and one of us 17 18 9 these two topics appear to be completely disjoint but they are not the solution of the conjectures about gabor frames is an unexpected application of methods from non commutative harmonic analysis to application oriented mathematics it turns out that the connection between twisted convolution and the heisenberg group and the theory of symmetric group algebras are precisely the tools needed to treat the problem motivated by signal analysis to be more concrete we formulate some of our main results first and will deal with the details and the technical background later

on twisted group frames abstract in this paper we study g frames for finite dimensional hilbert spaces where g is a finite group and is a unitary schur multiplier of g we apply the characterizations for tight g frames and central g frames to investigation of g frames that have the maximal spanning property we apply the theory of twisted group frames to obtain a criterion for maximal spanning vectors that generalizes the main result of 16 theorem 1 7 moreover we prove that a projective representation does not admit any maximal spanning vector if it has an at least 2 dimensional subrepresentation that is equivalent to a central projection induced subrepresentation of the regular representation

optimal dual frames for erasures for any given frame for the purpose of encoding in a finite dimensional hilbert space we investigate its dual frames that are optimal for erasures for the purpose of decoding we show that in general the canonical dual is not necessarily optimal moreover optimal dual frames are not necessarily unique we present some sufficient conditions under which the canonical dual is the unique optimal dual frame for the erasure problem as an application we get that the canonical dual is the only optimal dual when either the frame is induced by a group representation or the frame is uniform tight

existence of parseval oblique duals of a frame sequence abstract we present a collection of necessary and sufficient conditions for the existence of a parseval oblique dual in an appropriate subspace of a frame sequence this result extends the previous results by han and larson antezana et al and han our proof shows that the problem is closely related with that of extending an operator with norm less than or equal to 1 to an isometry on a subspace

correlations in economic time series a financial index of the new york stock exchange the sp here f is called the crossover frequency iii we confirm these results using the dfa detrended fluctuation analysis method see fig 2b which allows accurate estimates of exponents independent of local trends

phaselift exact and stable signal recovery from magnitude measurements via convex programming suppose we wish to recover a signal input amssym font abc cmmib10 def bi 1 hbox abc 1 bi x in bbb c n from m intensity measurements of the form that is from data in which phase information is missing we prove that if the vectors are sampled independently and uniformly at random on the unit sphere then the signal x can be recovered exactly up to a global phase factor by solving a convenient semidefinite program a trace norm minimization problem this holds with large probability provided that m is on the order of and without any assumption about the signal whatsoever this novel result demonstrates that in some instances the combinatorial phase retrieval problem can be solved by convex programming techniques finally we also prove that our methodology is robust vis a vis additive noise 2012 wiley periodicals inc

optimal dual frames for communication coding with probabilistic erasures assume that a frame is preselected for encoding in a communication system we investigate the optimal dual frames for signal reconstruction decoding which minimize the maximal error when the probabilistic erasures occur in the transmission process from the perspective of mathematical theory of frames we set up a probability model under which we define the probability optimal po dual frames for a given frame when the frame based coding involves probabilistic erasures we obtain a sufficient and necessary condition under which the canonical dual frame is the unique po dual frame additionally we derive some general sufficient conditions for which the canonical dual frame is either not optimal or it is optimal but not the unique optimal one we present two simulation examples to compare the reconstruction effects when both the po dual frames and the general optimal go dual frames are used for reconstruction