transmitter optimization for the multi antenna downlink with per antenna power constraints this paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the base station in contrast to the conventional sum power constraint on the transmit antennas this paper adopts a more realistic per antenna power constraint because in practical implementations each antenna is equipped with its own power amplifier and is limited individually by the linearity of the amplifier assuming perfect channel knowledge at the transmitter this paper investigates two different transmission schemes under the per antenna power constraint a minimum power beamforming design for downlink channels with a single antenna at each remote user and a capacity achieving transmitter design for downlink channels with multiple antennas at each remote user it is shown that in both cases the per antenna downlink transmitter optimization problem may be transformed into a dual uplink problem with an uncertain noise this generalizes previous uplink downlink duality results and transforms the per antenna transmitter optimization problem into an equivalent minimax optimization problem further it is shown that various notions of uplink downlink duality may be unified under a lagrangian duality framework this new interpretation of duality gives rise to efficient numerical optimization techniques for solving the downlink per antenna transmitter optimization problem

lsslp local structure sensitive label propagation label propagation is an approach to iteratively spread the prior state of label confidence associated with each of samples to its neighbors until achieving a global convergence state such process has been shown to hold close connection with a general graph based regularization framework within this framework a closed form linear system can be built to carry out label propagation in this paper to address several issues inherent with previous graph based label propagation framework we propose a reformulated one i e local structure sensitive label propagation lsslp by associating each graph vertex with a local structure sensitive tuning factor the empirical loss error on each vertex can be controlled preferably to keep consistent with the commonly preconditioned cluster assumption of data structure out of consideration for information conservation we relax the state conservation constraint of label confidence from labeled samples proposed by belkin et al 2004 to a more general form meanwhile an inverse warping procedure is incorporated into the proposed local structure sensitive label propagation framework to maintain large and stable enough classification margin based on the felicitous inversion technique for blocked matrix we extend lsslp to its incremental and inductive versions and also present computationally efficient implementation of it experimental results demonstrate the performance of the reformulated regularization framework for label propagation is much competitive

free vibration of a system of two elastically connected rectangular plates the free vibration problem of a system of two rectangular plates connected by a non homogeneous elastic layer is considered an integral formulation of the problem by using properties of green s functions is achieved and by application of a quadrature method to the integral equation the frequency equation of the combined system is obtained the comparison of an exact solution with the numerical results obtained by using the presented method for a system of two identical plates is given the numerical investigations have shown the effect of the area size as well as the stiffness of an elastic layer connecting the plates on the vibration frequencies of the combined systems

discriminative sparse flexible manifold embedding with novel graph for robust visual representation and label propagation abstract we explore the problem of robust visual representation and enhanced label prediction technically a discriminative sparse flexible manifold embedding sparsefme method with novel graph is proposed sparsefme enhances the representation and label prediction powers of fme by improving the reliability and robustness of distance metric such as using the l 2 1 norm to measure the flexible regression residue encoding the mismatch between embedded features and the soft labels and regularizing the l 2 1 norm on the soft labels directly to boost the discriminating power so that less unfavorable mixed signs that may result in negative effects on performance are included besides our sparsefme replaces the noise sensitive frobenius norm used in fme by l 2 1 norm to encode the projection that maps data into soft labels so the projection can be ensured to be sparse in rows so that discriminative soft labels can be learnt in the latent subspace thus more accurate identification of hard labels can be obtained to obtain high inter class separation and high intra class compactness of the predicted soft labels and encode the neighborhood of each sample more accurately we also propose a novel graph weight construction method by integrating class information and considering a certain kind of similarity dissimilarity of samples so that the true neighborhoods can be discovered the theoretical convergence analysis and connection to other models are also presented state of art performances are delivered by our sparsefme compared with several related criteria

transversal waves in beams via the network simulation method abstract in this paper the network simulation method nsm is proposed as a tool for solving the transverse motion of thin beams resulting from a bending action the reliability and robustness of the proposed technique is demonstrated with two examples in which a pinned pinned beam and a clamped mass load beam are respectively submitted to different flexural forces the nsm is a numerical technique for the solution of linear and non linear problems which are defined by a mathematical model assuming that the electrical variables of voltage and current are equivalent respectively to the displacement and the spatial variation of the displacement a network model for each volume element is designed such that electrical equations are formally equivalent to the spatial discretised equations of the mechanical model the whole network model including the devices associated with the boundary conditions is solved by the numerical computer code pspice the numerical results have been compared with those obtained by the mode superposition method the agreement between them is impressive the temporal behaviour of each quantity involved in the problem is obtained without transform complications since the whole study has been conducted in the time domain with the possibility of obtaining the corresponding spectral content at the end of calculation the main contribution of the present paper therefore is to employ the nsm numerical method in order to arrive at solutions in the time domain of dynamic mechanical problems one must also emphasize that nsm has not previously been used by other authors to solve physical problems like the ones presented here

unicast multi antenna relay beamforming with per antenna power control optimization and duality we consider amplify and forward multi antenna relaying between a single pair of source and destination under relay per antenna power constraints we design the optimal relay processing matrix to minimize the maximum per antenna power budget for a received snr target with given transmit and receive beamformers at the source and destination respectively we first focus on the equivalent system with single antenna source and destination although non convex we show that the optimization satisfies strong lagrange duality and can be solved in the lagrangian dual domain we reveal a prominent structure of this problem by establishing its duality with direct simo beamforming system with an uncertain noise this enables us to derive a semi closed form expression for the optimal relay processing matrix that depends on a set of dual variables which can be determined through numerical optimization with a significantly reduced problem space we further show that the dual problem has a semi definite programming form which enables efficient numerical optimization methods to determine the dual variables with polynomial complexity using this result the reverse problem of snr maximization under a set of relay per antenna power constraints is then addressed we then consider the maximum relay beamforming achievable rate under different combinations of antenna setups at source and destination in particular we generalize the duality to mimo relay beamforming vs direct mimo beamforming and establish the dual relation of the two systems for different multi antenna setups at source and destination

non linear vibrations of viscoelastic moving belts part i free vibration analysis abstract the non linear free vibration of viscoelastic moving belts is studied based on the linear viscoelastic differential constitutive law the generalized equation of motion is derived for a moving belt with geometric non linearities the method of multiple scales is applied directly to the governing equation which is in the form of continuous autonomous gyroscopic systems with weak non linearity this direct treatment does not involve a prior assumption regarding the spatial solutions the non linear natural frequencies and free response amplitude for autonomous systems are predicted by the perturbation method the results obtained with the quasi static assumption and those without this assumption are compared the effects of elastic and viscoelastic parameters axial moving speed and the geometric non linearity on natural frequencies and amplitudes of the free response are investigated from numerical examples

vibration analysis of a continuous system subject to generic forms of actuation forces and sensing devices this work provides a general formulation to solve vibration problems for continuous systems with damping effects including modal transient harmonic and spectrum response analyses in modal analysis the system eigenvalues and corresponding eigenfunctions can be determined the orthogonal relations of eigenfunctions are shown for transient harmonic and spectrum analyses the generic force actuator functions and response sensing operators are introduced respectively and used to derive the system response the time domain response is obtained for transient analysis the frequency response function is derived for harmonic analysis and statistical quantities of response variables due to random excitation are determined in spectrum analysis the solution for each type of analysis can be formulated and expressed in a concise format in terms of generic force actuator and response sensor mode shape functions in particular one dimensional beam and two dimensional plate vibration analyses are illustrated by following the developed generic formulation this work provides the complete analytical solutions of four types of vibration analyses for continuous systems and can be applied to other engineering structures as well

downlink mmse transceiver optimization for multiuser mimo systems duality and sum mse minimization we address the problem of minimum mean square error mmse transceiver design for point to multipoint transmission in multiuser multiple input multiple output mimo systems we focus on the problem of minimizing the downlink sum mse under a sum power constraint it is shown that this problem can be solved efficiently by exploiting a duality between the downlink and uplink mse feasible regions we propose two different optimization frameworks for downlink mmse transceiver design the first one solves an equivalent uplink problem then the result is transferred to the original downlink problem duality ensures that any uplink mmse scheme e g linear mmse reception or mmse decision feedback equalization dfe has a downlink counterpart we propose two globally optimum algorithms based on convex optimization the basic idea of the second framework is to perform optimization in an alternating manner by switching between the virtual uplink and downlink channels this strategy exploits that the same mse can be achieved in both links for a given choice of transmit and receive filters this iteration is proven to be convergent

robust adaptive embedded label propagation with weight learning for inductive classification we propose a robust inductive semi supervised label prediction model over the embedded representation termed adaptive embedded label propagation with weight learning aelp wl for classification aelp wl offers several properties first our method seamlessly integrates the robust adaptive embedded label propagation with adaptive weight learning into a unified framework by minimizing the reconstruction errors over embedded features and embedded soft labels jointly our aelp wl can explicitly ensure the learned weights to be joint optimal for representation and classification which differs from most existing lp models that perform weight learning separately by an independent step before label prediction second existing models usually precalculate the weights over the original samples that may contain unfavorable features and noise decreasing performance to this end our model adds a constraint that decomposes original data into a sparse component encoding embedded noise removed sparse representations of samples and a sparse error part fitting noise and then performs the adaptive weight learning over the embedded sparse representations third our aelp wl computes the projected soft labels by trading off the manifold smoothness and label fitness errors over the adaptive weights and the embedded representations for enhancing the label estimation power by including a regressive label approximation error for simultaneous minimization to correlate sample features with the embedded soft labels the out of sample issue is naturally solved by minimizing the reconstruction errors over features and embedded soft labels classification error and label approximation error jointly state of the art results are delivered

learning context sensitive similarity by shortest path propagation in this paper we introduce a novel shape object retrieval algorithm shortest path propagation ssp given a query object q and a target database object p we explicitly find the shortest path between them in the distance manifold of the database objects then a new distance measure between q and p is learned based on the database objects on the shortest path to replace the original distance measure the promising results on both mepg 7 shape dataset and a protein dataset demonstrate that our method can significantly improve the ranking of the object retrieval

the capacity region of the gaussian multiple input multiple output broadcast channel the gaussian multiple input multiple output mimo broadcast channel bc is considered the dirty paper coding dpc rate region is shown to coincide with the capacity region to that end a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality to show that a superposition of gaussian codes is optimal for the degraded vector broadcast channel and that dpc is optimal for the nondegraded case furthermore the capacity region is characterized under a wide range of input constraints accounting as special cases for the total power and the per antenna power constraints

linear precoding via conic optimization for fixed mimo receivers in this paper the problem of designing linear precoders for fixed multiple input multiple output mimo receivers is considered two different design criteria are considered in the first the transmitted power is minimized subject to signal to interference plus noise ratio sinr constraints in the second the worst case sinr is maximized subject to a power constraint it is shown that both problems can be solved using standard conic optimization packages in addition conditions are developed for the optimal precoder for both of these problems and two simple fixed point iterations are proposed to find the solutions that satisfy these conditions the relation to the well known uplink downlink duality in the context of joint transmit beamforming and power control is also explored the proposed precoder design is general and as a special case it solves the transmit rank one beamforming problem simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders

transverse vibrations of the elastically connected rectangular double membrane compound system abstract the free and forced vibrations of a system of two rectangular membranes attached together by a winkler elastic layer are studied analytically the motion of the system is described by two non homogeneous partial differential equations the solutions of the free vibrations are obtained by the bernoulli fourier method solving the boundary value problem the natural frequencies and the mode shape functions are found the initial value problem is also solved the free vibrations of the double membrane system are realised by synchronous and asynchronous deflections the forced vibrations of membranes subjected to arbitrarily distributed continuous loads are determined by using the classical method of the expansion in a series of the normal modes of vibrations discussing the vibrations caused by the harmonic exciting forces it is shown that the dynamic absorption phenomenon appears therefore the double membrane system can be used as a dynamic vibration absorber as a numerical example the vibrations of the system consisting of two identical membranes subjected to harmonic uniform distributed load are treated in detail

dynamic response of a double euler bernoulli beam due to a moving constant load in this paper the dynamic response of a double beam system traversed by a constant moving load is studied the system consists of two elastic homogeneous isotropic euler bernoulli beams the two simply supported prismatic beams are identical parallel one upon the other and connected continuously by a viscoelastic layer the dynamic deflections of both beams are given in analytical closed forms the effects of the moving speed of the load and the damping and the elasticity of the viscoelastic layer on the dynamic responses of the beams are investigated in detail also several plots of the deflections of the beams are given and discussed for different values of speed parameter damping ratio and stiffness parameter furthermore the force transmitted between the beams is determined and the effects of the system parameters on this force are studied plots of the maximum responses of the beams are presented

modelling of floating slab tracks with continuous slabs under oscillating moving loads this paper discusses modelling of floating slab tracks on rigid foundations the model consists of an upper euler bernoulli beam to account for both the rails and a lower euler bernoulli beam to account for the slab there are two continuous resilient layers in the model one to account for railpads between the rails and the slab and one to account for slab bearings underneath the slab the fourier transformation method is used to calculate displacements of such a track under an oscillating moving load these results are used to calculate the cut on frequencies and critical velocity of the track the work in this paper also demonstrates some basic concepts in the context of vibration of infinite systems including dispersion curves critical velocities load velocity lines and coupling of systems in the wavenumber frequency domain the paper offers a complete treatment of the issues important to the analysis of a double beam system not elsewhere available in the published literature

free transverse vibrations of an elastically connected rectangular plate membrane complex system abstract this paper theoretically analyzes undamped free transverse vibrations of an elastically connected rectangular plate membrane system solutions of the problem are formulated by using the navier method natural frequencies of the system in the form of two infinite sequences are determined normal mode shapes of vibration expressing two kinds of vibration synchronous and asynchronous are presented the initial value problem is also solved in a numerical example the effect of membrane tension on the natural frequencies of this mixed system is discussed

transverse vibrations of elastically connected double string complex system part i free vibrations this paper analyzes the forced transverse vibrations of an elastically connected double string complex continuous system the general solutions of forced vibrations of strings subjected to arbitrarily distributed continuous loads are found by using the method of expansion in a series of the mode shape functions different cases of exciting loadings are analyzed the action of stationary harmonic loads and moving concentrated forces is considered vibrations caused by the harmonic exciting forces are discussed and conditions of resonance and dynamic vibration absorption are formulated thus the string type dynamic absorber can be used to suppress the excessive vibrations of corresponding string systems the dynamic string type damper is a new concept of a continuous dynamic vibration absorber cdva it is shown that a corresponding two degree of freedom discrete system is an analogue of an elastically connected double string complex system theoretical analysis is illustrated by a numerical example

adaptive hypergraph learning and its application in image classification recent years have witnessed a surge of interest in graph based transductive image classification existing simple graph based transductive learning methods only model the pairwise relationship of images however and they are sensitive to the radius parameter used in similarity calculation hypergraph learning has been investigated to solve both difficulties it models the high order relationship of samples by using a hyperedge to link multiple samples nevertheless the existing hypergraph learning methods face two problems i e how to generate hyperedges and how to handle a large set of hyperedges this paper proposes an adaptive hypergraph learning method for transductive image classification in our method we generate hyperedges by linking images and their nearest neighbors by varying the size of the neighborhood we are able to generate a set of hyperedges for each image and its visual neighbors our method simultaneously learns the labels of unlabeled images and the weights of hyperedges in this way we can automatically modulate the effects of different hyperedges thorough empirical studies show the effectiveness of our approach when compared with representative baselines

on exact boundary controllability for linearly coupled wave equations in this paper we study exact boundary controllability for a system of two linear wave equations coupled by lower order terms we obtain square integrable control of neuman type for initial state with finite energy in nonsmooth domains of the plane

forced transverse vibrations of an elastically connected complex rectangular simply supported double plate system abstract the paper deals with forced transverse vibrations of an elastically connected rectangular double plate system this complex continuous system can represent a certain simplified model of a three layered structure consisting of two parallel thin plates separated by an elastic massless layer of a winkler type undamped motion of the system excited by arbitrarily distributed continuous loadings subjected transversely to both plates are governed by a linear set of two coupled non homogeneous partial differential equations based on the kirchhoff love plate theory the forced vibration problem is solved generally by the application of the modal expansion method in the case of simply supported boundary conditions for plates on the basis of general solutions obtained three particular cases of the action of exciting stationary harmonic loads are considered an analysis of harmonic responses of the system makes it possible to determine conditions of resonance and dynamic vibration absorption a numerical example is given to illustrate the theory presented

a nonparametric classification method based on k associated graphs graph is a powerful representation formalism that has been widely employed in machine learning and data mining in this paper we present a graph based classification method consisting of the construction of a special graph referred to as k associated graph which is capable of representing similarity relationships among data cases and proportion of classes overlapping the main properties of the k associated graphs as well as the classification algorithm are described experimental evaluation indicates that the proposed technique captures topological structure of the training data and leads to good results on classification task particularly for noisy data in comparison to other well known classification techniques the proposed approach shows the following interesting features 1 a new measure called purity is introduced not only to characterize the degree of overlap among classes in the input data set but also to construct the k associated optimal graph for classification 2 nonlinear classification with automatic local adaptation according to the input data contrasting to k nearest neighbor classifier which uses a fixed k the proposed algorithm is able to automatically consider different values of k in order to best fit the corresponding overlap of classes in different data subspaces revealing both the local and global structure of input data 3 the proposed classification algorithm is nonparametric implicating high efficiency and no need for model selection in practical applications

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

free transverse vibrations of elastically connected simply supported double beam complex system abstract in this paper the free vibration analysis of two parallel simply supported beams continuously joined by a winkler elastic layer is presented the motion of the system is described by a homogeneous set of two partial differential equations which is solved by using the classical bernoulli fourier method the natural frequencies of the system are determined the initial value problem is considered to find the final form of the free vibrations the free vibrations of an elastically connected double beam complex system are realized by synchronous and asynchronous deflections the presented theoretical analysis is illustrated by a numerical example in which the effect of physical parameters characterizing the vibrating system on the natural frequencies is investigated

vibration of a double beam system abstract an exact method is presented for solving the vibration of a double beam system subject to harmonic excitation the system consists of a main beam with an applied force and an auxiliary beam with a distributed spring k and dashpot c in parallel between the two beams the viscous damping and the applied forcing function can be completely arbitrary the damping is assumed to be neither small nor proportional and the forcing function can be either concentrated at any point or distributed the euler bernoulli model is used for the transverse vibrations of beams and the spring dashpot represents a simplified model of viscoelastic material the method involves a simple change of variables and modal analysis to decouple and to solve the governing differential equations respectively a case study is solved in detail to demonstrate the methodology and the frequency responses are shown in dimensionless parameters for low and high values of stiffness k k0 and damping c c0 the plots show that each natural mode consists of two submodes 1 the in phase submode whose natural frequencies and resonant peaks are independent of stiffness and damping and 2 the out of phase submode whose natural frequencies are increased with increasing stiffness and resonant peaks are decreased with increasing damping the closed form solution and the plots especially the three dimensional ones not only illustrate the principles of the vibration problem but also shed light on practical applications

free transverse vibrations of an elastically connected rectangular simply supported double plate complex system abstract in this paper the free transverse vibrations of a system of two rectangular simply supported thin plates connected by a homogeneous winkler elastic layer are investigated analytically the small vibrations of the system are described by a set of two partial differential equations based on the kirchhoff love plate theory next the homogeneous equations of motion are solved by using the classical navier method the natural frequencies of the system in the form of two infinite sequences are determined and the corresponding mode shapes of vibration are shown as a consequence an elastically connected double plate complex system executes two kinds of the free vibrations synchronous and asynchronous the initial value problem is then considered to find the final form of the free vibrations the theoretical analysis presented is illustrated by a numerical example in which the free vibrations of a system of two identical plates are discussed in detail

finding the best not the most classification on structure data such as graphs has drawn wide interest in recent years due to the lack of explicit features to represent graphs for training classification models extensive studies have been focused on extracting the most discriminative subgraphs features from the training graph dataset to transfer graphs into vector data however such filter based methods suffer from two major disadvantages 1 the subgraph feature selection is separated from the model learning process so the selected most discriminative subgraphs may not best fit the subsequent learning model resulting in deteriorated classification results 2 all these methods rely on users to specify the number of subgraph features k and suboptimally specified k values often result in significantly reduced classification accuracy in this paper we propose a new graph classification paradigm which overcomes the above disadvantages by formulating subgraph feature selection as learning a k dimensional feature space from an implicit and large subgraph space with the optimal k value being automatically determined to achieve the goal we propose a regularized loss minimization driven rlmd feature selection method for graph classification rlmd integrates subgraph selection and model learning into a unified framework to find discriminative subgraphs with guaranteed minimum loss w r t the objective function to automatically determine the optimal number of subgraphs k from the exponentially large subgraph space an effective elastic net and a subgradient method are proposed to derive the stopping criterion so that k can be automatically obtained once rlmd converges the proposed rlmd method enjoys gratifying property including proved convergence and applicability to various loss functions experimental results on real life graph datasets demonstrate significant performance gain highlightsour algorithm selects the optimal subgaphs for graph classification we generalize the column generation technique of gboost for graph classification we use the elastic net to produce sparse and robust solutions for subgraph selection we derive an effective pruning rule for search space reduction we demonstrate the effectiveness of our algorithm

zero forcing precoding and generalized inverses we consider the problem of linear zero forcing precoding design and discuss its relation to the theory of generalized inverses in linear algebra special attention is given to a specific generalized inverse known as the pseudo inverse we begin with the standard design under the assumption of a total power constraint and prove that precoders based on the pseudo inverse are optimal among the generalized inverses in this setting then we proceed to examine individual per antenna power constraints in this case the pseudo inverse is not necessarily the optimal inverse in fact finding the optimal matrix is nontrivial and depends on the specific performance measure we address two common criteria fairness and throughput and show that the optimal generalized inverses may be found using standard convex optimization methods we demonstrate the improved performance offered by our approach using computer simulations

free vibrations of elastically restrained non uniform plates abstract a simple and efficient method is presented to examine the levy type solutions for the free vibration of elastically restrained rectangular plates resting on a non uniform elastic winkler foundation under the action of constant in plane forces both the thickness of the plate and stiffness of the elastic foundation are uniform along one axis and variable along the other axis the frequency equation is derived and concisely expressed in terms of the four fundamental solutions of the governing characteristic differential equation if the closed form fundamental solutions of the system are not available then approximate fundamental solutions can be obtained through a numerical algorithm which is shown to be efficient convenient and accurate the results are compared with those in the literature finally the influence of the elastically restrained boundary conditions on the natural frequencies is investigated

free transverse vibrations of an elastically connected complex beam string system abstract the present work is devoted to theoretical vibration analysis of a complex mixed continuous system undamped free transverse vibrations of an elastically connected beam string system are considered solutions of the problem are formulated by using the modal expansion method two infinite sequences of the natural frequencies corresponding to two possible kinds of vibration motions synchronous and asynchronous are determined in a numerical example illustrating the theory presented the effect of string tension force on the natural frequencies of the system is investigated in detail

transverse vibration of an axially accelerating string abstract the transverse vibration of an axially accelerating string is investigated the equation of motion is developed using hamilton s principle the resulting partial differential equations are discretized using galerkin s method assuming the axial velocity to be periodic a stability analysis is performed using floquet theory one two three four six and eight term series approximations are considered in the galerkin s method the one term approximation leads to a mathieu equation the solution of which is well known the numerical results for one term are compared with the analytical solution for the mathieu equation and they are in full agreement the two term approximation leads to gyroscopically coupled equations and the solutions differ significantly from that of the one term approximation whereas the three term approximation solutions look similar to the one term approximation solutions the analysis is carried out for higher order even approximations and the solutions are in qualitative agreement the two and four term approximation solutions are compared with the analytical results from hsu s method and are in reasonable agreement the results show that instabilities occur at much higher amplitudes and frequencies of the periodic axial velocity than that of typical devices such as tape machines and band saws

free vibrations of elastically connected stretched beams abstract a general theory for the determination of natural frequencies and mode shapes for a set of elastically connected axially loaded euler bernoulli beams is developed a normal mode solution is applied to a set of non dimensional coupled partial differential equations the natural frequencies are the eigenvalues of a matrix of differential operators the matrix operator is shown to be self adjoint leading to an orthogonality condition for the mode shapes in the special case of identical beams it is shown that the natural frequencies are organized into sets of intramodal frequencies in which each mode shape is a product of a spatial mode and a discrete mode an exact solution is available for the general case however the natural frequencies and mode shapes are then determined using a complicated numerical method a rayleigh ritz method using mode shapes of the corresponding unstretched beams is developed as an alternative

new modified multi level residue harmonic balance method for solving nonlinearly vibrating double beam problem abstract in this study a new modified multi level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams although numerous nonlinear beam or linear double beam problems have been tackled and solved there have been few studies of this nonlinear double beam problem the geometric nonlinear formulations for a double beam model are developed the main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level this heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method the proposed method can generate the higher level nonlinear solutions that are neglected by the previous modified harmonic balance method the results from the proposed method agree reasonably well with those from the classical harmonic balance method the effects of damping axial force and excitation magnitude on the nonlinear vibrational behaviour are examined

damped vibration analysis of an elastically connected complex double string system abstract the main purpose of the present paper is to consider theoretically damped transverse vibrations of an elastically connected double string system this system is treated as two viscoelastic strings with a kelvin voigt viscoelastic layer between them a theoretical analysis has been made for a simplified model of the system in which assumed physical parameters make it possible to decouple the governing equations of motion by introducing the principal co ordinates applying the method of separation of variables and the modal expansion method exact analytical solutions for damped free and forced responses of the system subjected to arbitrarily distributed transverse continuous loads are determined in the case of arbitrary magnitude of linear viscous damping it is important to note that the solutions obtained are explicitly expressed in terms of parameters characterizing the physical properties of the system under discussion for the sake of completeness of the analysis solutions for undamped free and forced vibrations are also formulated

weighted fair multicast multigroup beamforming under per antenna power constraints a multiantenna transmitter that conveys independent sets of common data to distinct groups of users is considered this model is known as physical layer multicasting to multiple cochannel groups in this context the practical constraint of a maximum permitted power level radiated by each antenna is addressed the per antenna power constrained system is optimized in a maximum fairness sense with respect to predetermined quality of service weights in other words the worst scaled user is boosted by maximizing its weighted signal to interference plus noise ratio a detailed solution to tackle the weighted max min fair multigroup multicast problem under per antenna power constraints is therefore derived the implications of the novel constraints are investigated via prominent applications and paradigms what is more robust per antenna constrained multigroup multicast beamforming solutions are proposed finally an extensive performance evaluation quantifies the gains of the proposed algorithm over existing solutions and exhibits its accuracy over per antenna power constrained systems

free vibrations of periodically point supported rectangular plates abstract the basis and formulation of a new approach namely the flexibility function approach based on simulating point supports on free edges as zeros of a flexibility function representing a fictitious elastic restraint distribution over the edges was recently presented 1 2 its application to a variety of problems of free vibrations of point supported rectangular plates was presented subsequently 3 4 the present study provides an extension of its application to the problem of periodically point supported plates it is shown that by the use of a simple flexibility function the problem of periodically point supported plates can be easily analyzed numerical results for a range of problem parameters have been obtained which bring out the effect of the number of point supports on the natural frequencies edge displacements and edge reactions they also provide a quantitative estimate of the errors associated with the approximation of a large number of discrete supports by a continuous support condition or vice versa results have also been obtained for some typical problem parameters by using the impulse function approach based on representing the reactions at the point supports as fourier series expansion of the impulse function the comparison of the results clearly illustrates the fact that the flexibility function approach gives results which converge faster requires significantly less computation time and provides accurate results

statistically robust design of linear mimo transceivers the treatment of channel state information csi is critical in the design of mimo systems accurate csi at the transmitter is often not possible or may require high feedback rates herein we consider the robust design of linear mimo transceivers with perfect csi either at the transmitter or at both sides of the link the framework considers the design problem where the imperfect csi consists of the channel mean and covariance matrix or equivalently the channel estimate and the estimation error covariance matrix the robust transceiver design is based on a general cost function of the average mses as well as a design with individual mse based constraints in particular a lower bound of the average mse matrix is explored for the design when only the csi at the transmitter is imperfect under different csi conditions the proposed robust transceivers exhibit a similar structure to the transceiver designs for perfect csi but with a different equivalent channel and or noise covariance matrix

a generalized treatment of the energetics of translating continua part i strings and second order tensioned pipes the energetics of translating one dimensional uniform strings and highly tensioned pipes with vanishing bending stiffness and flowing fluid are analyzed for fixed free and damped boundary conditions the interaction between the translating continua and the boundary supports causes energy transfer at a fixed boundary the transverse component of tension does work and the coriolis forces at a free end cause energy flux into the second order continuum under a symmetric boundary configuration the total energy of free oscillation varies periodically at the fundamental natural frequency asymmetric boundary supports in the pipe fluid system lead to damped or self excited motions at a viscously damped boundary the condition for maximal energy dissipation the destabilizing effect of dissipation and the stabilizing effect of negative damping are examined analytically using travelling wave solutions the energies transferred at the different boundary supports are quantified by energy reflection coefficients which are determined completely by the boundary conditions numerical simulations verify the analytically predicted energy variations

analytic solution to free vibration of rectangular plates abstract the analytical strip method asm is presented for the free flexural vibration problem of rectangular plates with intermediate flexible supports and different edge conditions orthotropic plates and plates having single or multiple step variation in thickness are considered the plate is divided into strips the number of which depends on the geometric discontinuities the solution employs the classical method of separation of variables and the deflection for each plate strip is expressed in a single trigonometric series results are presented and when possible compared with previously published ones

transmitter optimization for per antenna power constrained multi antenna downlinks an slnr maximization methodology in this paper we consider signal to leakage plus noise ratio slnr maximized precoding for multi antenna downlinks under per antenna power constraints papcs in contrast to the conventional sum power constraint the per antenna power constrained slnr precoder design problem no longer admits a simple closed form solution and achieving its optimal solution turns out to be much more challenging to conquer the difficulty we first propose to perform the charnes cooper transformation on the problem of interest which yields a solvable simpler second order cone program socp moving beyond this approach we are then able to obtain a semi closed form solution to the optimal slnr precoder the power allocation among users is also optimized for further performance enhancement for which we devise two numerical methods based on gradient projection and a low complexity approximation finally focusing on the imperfect channel state information csi scenario we develop a robust slnr based precoder to combat the performance degradation caused by random csi errors the superiority of all proposed precoder designs in this work is confirmed by numerical simulations

graph based semisupervised learning graph based learning provides a useful approach for modeling data in classification problems in this modeling scenario the relationship between labeled and unlabeled data impacts the construction and performance of classifiers and therefore a semisupervised learning framework is adopted we propose a graph classifier based on kernel smoothing a regularization framework is also introduced and it is shown that the proposed classifier optimizes certain loss functions its performance is assessed on several synthetic and real benchmark data sets with good results especially in settings where only a small fraction of the data are labeled

robust joint design of linear relay precoder and destination equalizer for dual hop amplify and forward mimo relay systems this paper addresses the problem of robust linear relay precoder and destination equalizer design for a dual hop amplify and forward af multiple input multiple output mimo relay system with gaussian random channel uncertainties in both hops by taking the channel uncertainties into account two robust design algorithms are proposed to minimize the mean square error mse of the output signal at the destination one is an iterative algorithm with its convergence proved analytically the other is an approximated closed form solution with much lower complexity than the iterative algorithm although the closed form solution involves a minor relaxation for the general case when the column covariance matrix of the channel estimation error at the second hop is proportional to identity matrix no relaxation is needed and the proposed closed form solution is the optimal solution simulation results show that the proposed algorithms reduce the sensitivity of the af mimo relay systems to channel estimation errors and perform better than the algorithm using estimated channels only furthermore the closed form solution provides a comparable performance to that of the iterative algorithm

joint precoding optimization for multiuser multi antenna relaying downlinks using quadratic programming this paper studies the optimization problem for joint precoding design in a multi antenna downlink channel using relaying we formulate the joint source and relay precoding design by aiming at sum capacity maximization since this problem is in general nonconvex we first convert this problem into standard convex quadratic programs and then propose an iterative joint precoding optimization algorithm by utilizing efficient quadratic programming approaches we observe that the iterative method always yields optimal precoding matrices which diagonalize the compound channel of the backward source to relay and the forward relay to destination links at high snr regimes motivated by this observation we further develop an efficient structured precoding design simulation results are presented to verify the effectiveness of our proposed precoding schemes

rank constrained separable semidefinite programming with applications to optimal beamforming consider a downlink communication system where multiantenna base stations transmit independent data streams to decentralized single antenna users over a common frequency band the goal of the base stations is to jointly adjust the beamforming vectors to minimize the transmission powers while ensuring the signal to interference noise ratio requirement of each user within the system at the same time it may be necessary to keep the interference generated on other coexisting systems under a certain tolerable level in addition one may want to include general individual shaping constraints on the beamforming vectors this beamforming problem is a separable homogeneous quadratically constrained quadratic program and it is difficult to solve in general in this paper we give conditions under which strong duality holds and propose efficient algorithms for the optimal beamforming problem first we study rank constrained solutions of general separable semidefinite programs sdps and propose rank reduction procedures to achieve a lower rank solution then we show that the sdp relaxation of three classes of optimal beamforming problem always has a rank one solution which can be obtained by invoking the rank reduction procedures

vibrations of double string complex system under moving forces closed solutions in this paper the dynamic response of a double string system traversed by a constant or a harmonically oscillating moving force is considered the force is moving with a constant velocity on the top string the strings are identical parallel one upon the other and continuously coupled by a linear winkler elastic element the classical solution of the response of a double string system subjected to a force moving with a constant velocity has a form of an infinite series the main goal of this paper is to show that in the considered case a part of the solution can be presented in a closed analytical form instead of an infinite series the presented method of finding the solution in a closed analytical form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations

buckling and vibration of laminated composite plates using various plate theories analytical and finite element solutions of the classical first order and third order laminate theories are developed to study the buckling and free vibration behavior of cross ply rectangular composite laminates under various boundary conditions

linear transmit processing in mimo communications systems we examine and compare the different types of linear transmit processing for multiple input multiple output systems where we assume that the receive filter is independent of the transmit filter contrary to the joint optimization of transmit and receive filters we can identify three filter types similar to receive processing the transmit matched filter the transmit zero forcing filter and the transmit wiener filter we show that the transmit filters are based on similar optimizations as the respective receive filters with an additional constraint for the transmit power moreover the transmit wiener filter has similar convergence properties as the receive wiener filter i e it converges to the matched filter and the zero forcing filter for low and high signal to noise ratio respectively we give closed form solutions for all transmit filters and present the fundamental result that their mean square errors are equal to the errors of the respective receive filters if the information symbols and the additive noise are uncorrelated however our simulations reveal that the bit error ratio results of the transmit filters differ from the results for the respective receive filters

a parametrically driven harmonic analysis of a non linear stretched string with time varying length abstract this paper is concerned with the first second and third harmonic lateral vibrations of a string having a forced periodic small length variation account is taken of the non linear term arising from the correction to the tension of the string due to local elongation it is found that increasing the amplitude of the length variation of the string results in a narrowing of the frequency response range of each of the harmonic oscillation components both numerical and analytical calculations of the harmonic frequency responses have been carried out the relationships for initial values between the original differential equation and the approximate differential equations for the harmonic responses are discussed in detail