natural frequencies of structures with interval parameters abstract this paper deals with the evaluation of the lower and upper bounds of the natural frequencies of structures with uncertain but bounded parameters the solution of the generalized interval eigenvalue problem is pursued by taking into account the actual variability and dependencies of uncertain structural parameters affecting the mass and stiffness matrices to this aim interval uncertainties are handled by applying the improved interval analysis via extra unitary interval eui recently introduced by the first two authors by associating an eui to each uncertain but bounded parameter the cases of mass and stiffness matrices affected by fully disjoint completely or partially coincident uncertainties are considered then based on sensitivity analysis it is shown that the bounds of the interval eigenvalues can be evaluated as solution of two appropriate deterministic eigenvalue problems without requiring any combinatorial procedure if the eigenvalues are monotonic functions of the uncertain parameters then the exact bounds are obtained the accuracy of the proposed method is demonstrated by numerical results concerning truss and beam structures with material and or geometrical uncertainties

the generalized eigenvalue problem for tridiagonal symmetric interval matrices an algorithm to compute the eigenintervals of the generalized eigenvalue problem for tridiagonal symmetric matrices a b with interval entries is developed the algorithm is based on the sturm sequences and requires twice as much computational effort as for point matrices the algorithm is applied to the problem of computing the natural frequencies of a vibrating beam where the manufacturing tolerance is taken into consideration

existence and uniqueness of weak solutions to ginzburg landau equation with external noise and stochastic perturbation abstract in this paper the ginzburg landau and fractional ginzburg landau equations with external noise and stochastic perturbations are studied and we obtain the global existence and uniqueness of weak l 1 solutions our proof is supported by the generalized ito formula and a careful analysis of the nonlinear transport equation after founding the well posedness for the nonlinear transport problem in the class of l p 1 p we also gain the well posedness of the ginzburg landau and fractional ginzburg landau equations in the same spaces correspondingly

local l estimates weak harnack inequality and stochastic continuity of solutions of spdes we consider stochastic partial differential equations under minimal assumptions the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition in particular the diffusion term is allowed to be scaling critical we derive local supremum estimates with a stochastic adaptation of de giorgi s iteration and establish a weak harnack inequality for the solutions the latter is then used to obtain pointwise almost sure continuity

on the complexity of sphere decoding in digital communications sphere decoding has been suggested by a number of authors as an efficient algorithm to solve various detection problems in digital communications in some cases the algorithm is referred to as an algorithm of polynomial complexity without clearly specifying what assumptions are made about the problem structure another claim is that although worst case complexity is exponential the expected complexity of the algorithm is polynomial herein we study the expected complexity where the problem size is defined to be the number of symbols jointly detected and our main result is that the expected complexity is exponential for fixed signal to noise ratio snr contrary to previous claims the sphere radius which is a parameter of the algorithm must be chosen to ensure a nonvanishing probability of solving the detection problem this causes the exponential complexity since the squared radius must grow linearly with problem size the rate of linear increase is however dependent on the noise variance and thus the rate of the exponential function is strongly dependent on the snr therefore sphere decoding can be efficient for some snr and problems of moderate size even though the number of operations required by the algorithm strictly speaking always grows as an exponential function of the problem size

eigenvalue bounds of structures with uncertain but bounded parameters many analysis and design problems in engineering and science involve uncertainty to varying degrees this paper is concerned with the structural vibration problem involving uncertain material or geometric parameters specified as bounds on these parameters this produces interval stiffness and mass matrices and the problem is transformed into a generalized interval eigenvalue problem in interval mathematics however tighter bounds on the eigenvalues may be obtained by using the formulation of the structural dynamic problem often the stiffness and mass matrices can be formed as a non negative decomposition in the uncertain structural parameters in this case the eigenvalue bounds may be obtained from the parameter vertex solutions even more efficiently using interval extension from interval mathematics the generalized interval eigenvalue problem may be divided into two generalized eigenvalue problems for real symmetric matrix pairs the parameter vertex solution algorithm is compared with deif s solution the eigenvalue inclusion principle and the interval perturbation method in numerical examples

reduced complexity ml detection and capacity optimized training for spatial modulation systems spatial modulation sm is a recently developed low complexity multiple input multiple output scheme that jointly uses antenna indices and a conventional signal set to convey information it has been shown that the maximum likelihood ml detector of an sm system involves joint detection of the transmit antenna index and of the transmitted symbol hence the ml search complexity grows linearly with the number of transmit antennas and the size of the signal set to circumvent the problem we show that the ml search complexity of an sm system may be rendered independent of the constellation size provided that the signal set employed is a square or a rectangular qam furthermore we derive bounds for the capacity of the sm system and derive the optimal power allocation between the data and the training sequences by maximizing the worst case capacity bound of the sm system operating with imperfect channel state information we show with the aid of our simulation results that the proposed detector is ml optimal despite its lowest complexity amongst the existing detectors furthermore we show that employing the proposed optimal power allocation provides a substantial gain in terms of the sm system s capacity as well as signal to noise ratio compared to its equal power allocation counterpart finally we compare the performance of the sm system to that of the conventional multiple input multiple output mimo system and show that the sm system is capable of outperforming the conventional mimo system by a significant margin when both the systems are employing optimal power splitting

on the ito wentzell formula for distribution valued processes and related topics we prove the ito wentzell formula for processes with values in the space of generalized functions by using the stochastic fubini theorem and the ito wentzell formula for real valued processes appropriate versions of which are also proved

a bmo estimate for stochastic singular integral operators and its application to spdes abstract in this paper we investigate kernel conditions on k t s x so that the stochastic singular integral operator 0 t k t s g s x d w s has a bounded mean oscillation as an application we prove that for the solution u of the stochastic heat equation 0 1 d u t x a i j t u x i x j d t g t k x d w t k u 0 0 t t the q th order bmo quasi norm of the derivatives of u is controlled by g l

an evolution strategy method for computing eigenvalue bounds of interval matrices in this paper a modified method by means of an evolution strategy es is introduced for computing eigenvalue bounds of interval matrices then a sufficient condition theorem of the evolutionary strategy is presented which guarantees the convergence in probability of the method the numerical examples show the method can effectively yield accurate bounds for interval eigenvalues

a non markovian liquidation problem and backward spdes with singular terminal conditions we establish the existence uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition the equation describes the value function of non markovian stochastic optimal control problem in which the terminal state of the controlled process is prespecified the analysis of such control problems is motivated by models of optimal portfolio liquidation

the k best sphere decoding for soft detection of generalized spatial modulation due to the interchannel interference and the varying active antennas in generalized spatial modulation gsm it is challenging to detect the transmitted data effectively while imposing low computational burden to the receiver in this paper we propose a novel algorithm based on the k best sphere decoding for the soft detection of the gsm signal which performs the breadth first tree search in two stages sequentially by exploiting the null space of the gsm channel the inactive antenna searching is carried out antennawise in the first stage in which a recursive algorithm for updating the ql decomposition a decomposition of a matrix into a product of an orthogonal matrix and a lower triangular matrix is proposed to calculate the branch metrics and an effective examination scheme is developed to prune those illegal or repetitive child nodes based on the available ql decomposition structure that has been updated recursively during the first stage the second stage of the proposed detector is then readily concatenated to search for the modulated symbols carried on the active antennas in a one by one manner moreover owing to the soft input soft output nature the proposed detector can be applied in a turbo decoder for a coded gsm system both complexity analysis and simulation results corroborate the superiority of the proposed soft detector for the gsm system

novel estimations for the eigenvalue bounds of complex interval matrices our work proposes two methods that estimate the eigenvalue bounds left right for real and imaginary parts of complex interval matrices the first method expresses each bound as an algebraic sum of weighted matrix measures where the measure corresponds to the spectral norm and the weighting matrix is diagonal and positive definite with unknown entries the optimization with respect to the entries of the weighting matrix yields the best value of the bound the computational approach is ensured as the minimization of a linear objective function subject to bilinear matrix inequality constraints and interval constraints the bounds are proved to be better than those provided by other estimation techniques the second method constructs four real matrices so that each of them can be exploited as a comparison matrix for the complex interval matrix and allows the estimation of one of the eigenvalue bounds the two methods we propose rely on different mathematical backgrounds and between the resulting bounds no firm inequality can be stated therefore they are equally useful in applications as reflected by the numerical case studies presented in the paper

an interval algorithm for uncertain dynamic stability analysis abstract analysis on the stability of dynamic systems is a very important field in structural elasticity theory for possible engineering situations where the system parameters are uncertain but bounded the propagation from the initial uncertainties of parameters to the consequent uncertainty of dynamic stability of structure is elaborately investigated by interval analysis for the first time the interval dynamic stability issue is studied through the column structure as a generalized interval eigenvalue problem and an analytic theorem is rigorously derived and numerically verified for solving the generalized interval eigenvalue problem moreover to avoid the exaggeration on actual bounds of solution an effective approach is established to limit the dependency phenomenon in the interval dynamic stability analysis the interval relationships of the excitation parameter and the critical load frequency with five types of system parameters are further bridged according to the interval arithmetic to propose a three stage interval scheme for evaluating the effects of interval system parameters on the dynamic stability of structures numerical studies demonstrate that the uncertainty of the constant part of load influences the boundaries of principal instability region much more than that of the variable part of load within all structural parameters the uncertainty of column length has the most effect on the boundaries which could make the critical frequency of load be magnified about ten times the uncertainty of parameter in particular if all the system parameters are interval with an identical uncertainty degree the uncertainty of parameter would be propagated in the system of dynamic stability and enlarged as high as 20 times the uncertainty of parameter consequently the impacts of parameter uncertainties on the dynamic stability of structures are fairly significant

transmit antenna selection for multiple input multiple output spatial modulation systems the benefits of transmit antenna selection tas invoked for spatial modulation sm aided multiple input multiple output mimo systems are investigated specifically we commence with a brief review of the existing tas algorithms and focus on the recently proposed euclidean distance based tas ed tas schemes due to their high diversity gain then a pair of novel ed tas algorithms termed as the improved qr decomposition qrd based tas qrd tas and the error vector magnitude based tas evm tas are proposed which exhibit an attractive system performance at low complexity moreover the proposed ed tas algorithms are amalgamated with the low complexity yet efficient power allocation pa technique termed as tas pa for the sake of further improving the system s performance our simulation results show that the proposed tas pa algorithms achieve signal to noise ratio snr gains of up to 9 db over the conventional tas algorithms and up to 6 db over the tas pa algorithm designed for spatial multiplexing systems

coherent and differential space time shift keying a dispersion matrix approach motivated by the recent concept of spatial modulation sm we propose a novel space time shift keying stsk modulation scheme for multiple input multiple output mimo communication systems where the concept of sm is extended to include both the space and time dimensions in order to provide a general shift keying framework more specifically in the proposed stsk scheme one out of q dispersion matrices is activated during each transmitted block which enables us to strike a flexible diversity and multiplexing tradeoff this is achieved by optimizing both the space time block duration as well as the number of the dispersion matrices in addition to the number of transmit and receive antennas we will demonstrate that the resultant equivalent system model does not impose any inter channel interference ici and hence the employment of single stream maximum likelihood ml detection becomes realistic at a low complexity furthermore we propose a differential stsk dstsk scheme assisted by the cayley unitary transform which does not require any channel state information csi at the receiver here the usual error doubling caused by the differential decoding gives rise to 3 db performance penalty in comparison to coherent stsk cstsk additionally we introduce an enhanced cstsk scheme which avoids the requirement of inter antenna synchronization ias between the rf chains associated with the transmit antenna elements aes by imposing a certain constraint on the dispersion matrix design where each column of the dispersion matrices includes only a single non zero component moreover according to the turbo coding principle the proposed cstsk and dstsk schemes are combined with multiple serially concatenated codes and an iterative bit to symbol soft demapper more specifically the associated stsk parameters are optimized with the aid of extrinsic information transfer exit charts for the sake of achieving a near capacity performance

well posedness for the fractional fokker planck equations in this paper we study the fractional fokker planck equation and obtain the existence and uniqueness of weak lp solutions 1 p under the assumptions that the coefficients are only in sobolev spaces moreover to l solutions we gain the well posedness for bv coefficients besides the non negative weak lp solutions and renormalized solutions are derived after then we achieve the stability for stationary solutions

reduced complexity coherent versus non coherent qam aided space time shift keying a novel reduced complexity near optimal detection algorithm is proposed for enhancing the recent coherently detected space time shift keying cstsk scheme employing arbitrary constellations such as cal l point phase shift keying psk and quadrature amplitude modulation qam the proposed detector relies on a modified matched filter mf concept more specifically we exploit both the constellation diagram of the modulation scheme employed as well as the inter element interference iei free stsk architecture furthermore we generalize the pulse amplitude modulation pam or psk aided differentially encoded stsk dstsk concept and conceive its more bandwidth efficient qam aided counterpart then the proposed reduced complexity cstsk detector is applied to the qam aided dstsk scheme which enables us to carry out low complexity non coherent detection while dispensing with channel estimation it is revealed that the proposed detector is capable of approaching the optimal maximum likelihood ml detector s performance while avoiding the exhaustive ml search interestingly our simulation results also demonstrate that the reduced complexity detector advocated may achieve the same performance as that of the optimal ml detector for the specific stsk scheme s parameters another novelty of this paper is that the star qam stsk scheme tends to outperform its square qam counterpart especially for high number of dispersion matrices furthermore we provided both the theoretical analysis and the simulations in order to support this unexpected fact

improved methods for calculating vectors of short length in a lattice including a complexity analysis the standard methods for calculating vectors of short length in a lattice use a reduction procedure followed by enumerating all vectors of z in a suitable box however it suffices to consider those x e z which lie in a suitable ellipsoid having a much smaller volume than the box we show in this paper that searching through that ellipsoid is in many cases much more efficient if combined with an appropriate reduction procedure our method allows to do computations in lattices of much higher dimensions several randomly constructed numerical examples illustrate the superiority of our new method over the known ones

on singularity as a function of time of a conditional distribution of an exit time we establish the singularity with respect to lebesgue measure as a function of time of the conditional probability distribution that the sum of two one dimensional brownian motions will exit from the unit interval before time t given the trajectory of the second brownian motion up to the same time on the way of doing so we show that if one solves the one dimensional heat equation with zero condition on a trajectory of a one dimensional brownian motion which is the lateral boundary then for each moment of time with probability one the normal derivative of the solution is zero provided that the diffusion of the brownian motion is sufficiently large

on the quasi linear reflected backward stochastic partial differential equations abstract this paper is concerned with the quasi linear reflected backward stochastic partial differential equation rbspde for short basing on the theory of backward stochastic partial differential equation and the parabolic capacity and potential we first associate rbspde to a variational problem and via the penalization method we prove the existence and uniqueness of the solution for linear rbspde with laplacian leading coefficients with the continuity approach we further obtain the well posedness of general quasi linear rbspdes related results including ito formulas for backward stochastic partial differential equations with stochastic regular measures the comparison principle for solutions of rbspdes and the connections with reflected backward stochastic differential equations and optimal stopping problems are addressed as well

generalized distributive law for ml decoding of space time block codes the problem of designing good space time block codes stbcs with low maximum likelihood ml decoding complexity has gathered much attention in the literature all the known low ml decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast decodable conditionally multigroup decodable structure of a code we refer to this well known technique of decoding stbcs as conditional ml cml decoding in this paper we introduce a new framework to construct ml decoders for stbcs based on the generalized distributive law gdl and the factor graph based sum product algorithm we say that an stbc is fast gdl decodable if the order of gdl decoding complexity of the code with respect to the constellation size m is strictly less than m where is the number of independent symbols in the stbc we give sufficient conditions for an stbc to admit fast gdl decoding and show that both multigroup and conditionally multigroup decodable codes are fast gdl decodable for any stbc whether fast gdl decodable or not we show that the gdl decoding complexity is strictly less than the cml decoding complexity for instance for any stbc obtained from cyclic division algebras which is not multigroup or conditionally multigroup decodable the gdl decoder provides about 12 times reduction in complexity compared to the cml decoder similarly for the golden code which is conditionally multigroup decodable the gdl decoder is only half as complex as the cml decoder

computation of bounds for eigenvalues of structures with interval parameters in this paper the computation of eigenvalue bounds for generalized interval eigenvalue problem is considered two algorithms based on the properties of continuous functions are developed for evaluating upper and lower eigenvalue bounds of structures with interval parameters the method can provide the tightest bounds within a given precision numerical examples illustrate the effectiveness of the proposed method

assessing the stability of linear time invariant continuous interval dynamic systems it is known that stability analysis of linear time invariant dynamic systems under parameter uncertainties can be equated to estimating the range of the eigenvalues of matrices whose elements are intervals in this note first the problem of finding tight outer bounds on the eigenvalue ranges is considered a method for computing such bounds is suggested which consists essentially of setting up and solving a system of n mildly nonlinear algebraic equations n being the size of the interval matrix investigated the main result of the note however is a method for determining the right end point of the exact eigenvalue ranges the latter makes use of the outer bounds it is applicable if certain computationally verifiable monotonicity conditions are fulfilled the methods suggested can be applied for robust stability analysis of both continuous and discrete time systems numerical examples illustrating the applicability of the new methods are also provided

eigenvalues of tridiagonal symmetric interval matrices an algorithm for the determination of the eigenvalues of tridiagonal symmetric interval matrices is presented the intervals of the eigenvalues are not overestimated but exactly calculated the algorithm is an efficient one because it only needs twice as many operations as the sturm algorithm which is used for real matrices

real eigenvalue bounds of standard and generalized real interval eigenvalue problems abstract in this paper we study the real eigenvalue bounds of standard and generalized real interval eigenvalue problems based on some known sufficient conditions for the regularity of interval matrices a new algorithm for computing real eigenvalue bounds for real interval matrices is proposed it can easily be extended for applying to generalized real interval eigenvalue problems one advantage of the method is that the computation procedure takes less time than former methods we have proposed therefore it can be applied for solving larger interval eigenvalue problems finally some numerical examples are presented which show the effectiveness of the method

generalised sphere decoding for spatial modulation in this paper sphere decoding sd algorithms for spatial modulation sm are developed to reduce the computational complexity of maximum likelihood ml detectors two sds specifically designed for sm are proposed and analysed in terms of bit error ratio ber and computational complexity using monte carlo simulations and mathematical analysis it is shown that by carefully choosing the initial radius the proposed sphere decoder algorithms offer the same ber as ml detection with a significant reduction in the computational complexity a tight closed form expression for the ber performance of sm sd is derived in the paper along with an algorithm for choosing the initial radius which provides near to optimum performance also it is shown that none of the proposed sds are always superior to the others but the best sd to use depends on the target spectral efficiency the computational complexity trade off offered by the proposed solutions is studied via analysis and simulation and is shown to validate our findings finally the performance of sm sds are compared to spatial multiplexing smx applying ml decoder and applying sd it is shown that for the same spectral efficiency sm sd offers up to 84 reduction in complexity compared to smx sd with up to 1 db better ber performance than smx ml decoder

an algorithm to determine linear independence of a set of interval vectors this paper presents an algorithm to determine the linear dependence and independence of a set of interval vectors the algorithm is developed on the basis of a necessary and sufficient condition for linear independence of an arbitrary interval vector relative to other linearly independent interval vectors the necessary and sufficient condition can be checked by a linear programming method then the developed necessary and sufficient condition will be employed to check the linear independence of a set of interval vectors through numerical examples the validity of the developed algorithm is illustrated

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

space shift keying ssk mimo with practical channel estimates in this paper we study the performance of space modulation for multiple input multiple output mimo wireless systems with imperfect channel knowledge at the receiver we focus our attention on two transmission technologies which are the building blocks of space modulation i space shift keying ssk modulation and ii time orthogonal signal design tosd ssk modulation which is an improved version of ssk modulation providing transmit diversity we develop a single integral closed form analytical framework to compute the average bit error probability abep of a mismatched detector for both ssk and tosd ssk modulations the framework exploits the theory of quadratic forms in conditional complex gaussian random variables rvs along with the gil pelaez inversion theorem the analytical model is very general and can be used for arbitrary transmit and receive antennas fading distributions fading spatial correlations and training pilots the analytical derivation is substantiated through monte carlo simulations and it is shown over independent and identically distributed i i d rayleigh fading channels that ssk modulation is as robust as single antenna systems to imperfect channel knowledge and that tosd ssk modulation is more robust to channel estimation errors than the alamouti scheme furthermore it is pointed out that only few training pilots are needed to get reliable enough channel estimates for data detection and that transmit and receive diversity of ssk and tosd ssk modulations are preserved even with imperfect channel knowledge