oscillation theorems for differential equations with a nonlinear damping term in this paper we are concerned with a class of nonlinear second order differential equations with a nonlinear damping term passage to more general class of equations allows us to remove a restrictive condition usually imposed on the nonlinearity and as a consequence our results apply to wider classes of nonlinear differential equations two illustrative examples are considered

a survey on oscillation of impulsive delay differential equations this paper presents a systematic development of the oscillatory results for the linear and nonlinear impulsive delay differential equations we also discuss linearized oscillation theory and give some applications to mathematical biology

suppression of vibration in the axially moving kirchhoff string by boundary control the lyapunov technique has been used to prove that the non linear axially moving kirchhoff string can be stabilized by the linear boundary control the boundary control is the negative feedback of the transversal velocity of the string at one end

fade statistics in nakagami lognormal channels new expressions for the average level crossing rate lcr and average time fade duration afd of the signal envelope in microcellular mobile radio channels characterized by nakagami 1960 fading and lognormal shadowing so called nakagami lognormal nln channels are derived new lcr and afd are computed and the effects of the nakagami m factor and shadowing spread spl sigma sub s on these fade statistics are discussed the generality of the nln model is demonstrated by matching some lcr curves with previously reported measurement for the land mobile satellite channel commonly described as the rice lognormal channels

new oscillation criteria for forced second order half linear differential equations with damping abstract using variational principle and riccati technique new oscillation criteria for forced second order half linear differential equation with damped term are established which improve a recent paper by li and cheng w t li s s cheng an oscillation criterion for nonhomogenuous half linear differential equations appl math lett 15 2002 259 263 and generalized some of the results in the literature

the transient amplitude of the viscoelastic travelling string an integral constitutive law abstract the problem considered is an initially stressed viscoelastic string subjected to steady state and harmonic variation of axial motion the string material is assumed to be constituted by the hereditary integral type the partial differential integral equation of motion is derived first then by applying galerkin s method the governing equation is reduced to a set of second order non linear differential integral equations which are solved by finite difference numerical integration procedures the viscoelastic string with a linear spring dashpot model is considered as the voigt element in series with a spring three parameter model the qualitative aspect of parametric excitation due to the non uniform travelling velocity of a viscoelastic string is investigated finally the results are compared with those obtained by a constitutive law of a differential type method the effects of elastic and viscoelastic parameters constant and non constant transport speeds the wave propagation speed ratio and the non linear term on the transient amplitudes are also investigated

random coding error exponents for two dimensional flat fading channels with complete channel state information in this correspondence we consider the random coding error exponent for nondispersive two dimensional 2 d quadrature fading channels for which the channel state information csi is perfectly known at the receiver and the input to the transmitter is constrained in its average power also the effect of space diversity on improving the performance is demonstrated the results obtained in this correspondence shed light on the effect of fading on communications reliability as well as the amount of coding complexity required to achieve a certain decoding error rate a treatment for the random coding error exponent for time correlated flat fading channels with rayleigh fading and bessel function correlation the jake s model is also provided

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

oscillation criteria for forced second order nonlinear differential equations with damping in this paper we are concerned with oscillations in a class of forced second order differential equations with nonlinear damping terms by using a classical variational principle and an averaging technique several new interval oscillation criteria for the equations are established which improve and extend some known results an example is also given to illustrate the results

supercritical speed stability of the trivial equilibrium of an axially moving string on an elastic foundation the stability of an axially moving string supported by a discrete or distributed elastic foundation is examined analytically particular attention is directed at the distribution of the critical speeds and identifying the divergence instability of the trivial equilibrium the elastically supported string shows unique stability behavior that is considerably different from unsupported axially moving string in particular any elastic foundation discrete or distributed leads to multiple critical speeds and a single region of divergence instability above the first critical speed whereas the unsupported string has one critical speed and is stable at all supercritical speeds additionally the elastically supported string critical speeds are bounded above and the maximum critical speed is the upper bound of the divergent speed region the analysis draws on the self adjoint eigenvalue problem for the critical speeds and a perturbation analysis about the critical speeds neither numerical solution nor spatial discretization which can produce substantially incorrect results are required the system falls in the class of dispersive gyroscopic continua and its behavior provides a useful comparison for general gyroscopic systems the analytical findings also serve as a benchmark for approximate methods applied to gyroscopic continua

oscillation of a forced super linear second order differential equation with impulses some oscillation criteria are established for a forced super linear second order differential equation with impulses those results extend some well known results for the equation without impulses which are different from most existing ones in that they are based only on information on a sequence of subintervals of t 0 rather than on the whole half linear interval

non linear non planar and non periodic vibrations of a string abstract we study the vibrations of a string subject to planar harmonic excitation both experimentally and theoretically we observe multiple periodic motions planar and non planar whirling as well as quasi periodic whirling and irregularly precessing oscillations when the forcing frequency is near that of a transverse normal mode a two degree of freedom model is derived and it is shown that these motions can be partially understood in terms of the completely integrable hamiltonian system obtained when damping and forcing tend to zero in that model

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

forced oscillation of super half linear impulsive differential equations by using a picone type formula in comparison with oscillatory unforced half linear equations we derive new oscillation criteria for second order forced super half linear impulsive differential equations having fixed moments of impulse actions in the superlinear case the effect of a damping term is also considered

fem analysis of transverse vibrations of an axially moving membrane immersed in ideal fluid transverse vibrations of an axially moving travelling in its own plane membrane submerged in ideal fluid are analysed using the fem the discrete equations differ from the equations of the common coupled problem in that there appear two additional inertia terms due to the convective acceleration the effect of the density of the element mesh the effect of the truncation distance and the effect of various lumping techniques on the accuracy of the results are studied the fem results are compared with available analytical and experimental results the agreement seems to be rather good

harmonic frequency spectra of vibrating stepped strings the frequency spectrum of a vibrating string with a step in density is investigated for proportions of length and 1 having different constant densities in corresponding ratio r if the quantity r r 1 is a rational number then the vibrations of the string with fixed ends exhibit harmonic and or odd harmonic frequency sub spectra expressible in simple analytical form if r 1 then the entire frequency spectrum is a pure harmonic series indistinguishable from that of a homogeneous string consideration of the string vibrating in the free fixed configuration serves to remove this coincidence the free free configuration is also dealt with in a similar approach

non linear string random vibration abstract an investigation is described of the concave shape generation mechanism in the displacement and its first derivative vibration velocity amplitude probability density functions of the narrow band random vibration of a non linear string three types of strings are studied in detail characterized as follows 1 constant damping factor and non linear stiffness 2 the damping factor an even function with respect to the displacement and its first derivative and non linear stiffness 3 the damping factor an even function of the displacement and its first derivative and linear stiffness it is verified by numerical calculation that for a response sample of relatively long duration of the order of eight representative periods of the oscillation the generation of the concave shape depends mainly upon 1 the saturation of the amplitude and the growth of higher harmonic oscillation due to the non linear stiffness or the even function damping and 2 a jump phenomenon in the input output relation

oscillation of second order nonlinear ode with damping we are concerned with a class of general type second order differential equations with a nonlinear damping term new oscillation criteria are established which are different from most known ones in the sense that they are based on a class of new functions t s l defined in the sequel

oscillation of solutions of second order mixed nonlinear differential equations under impulsive perturbations new oscillation criteria are obtained for second order forced mixed nonlinear impulsive differential equations of the form r t f a x q t f a x k 1nq k t f b k x e t t q ix q i a ix q i x q i b ix q i where f c s s c 1s and b 1 b 2 b m a b m 1 b n 0 if a 1 and the impulses are dropped then the results obtained by sun and wong y g sun j s w wong oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities j math anal appl 334 2007 549 560 are recovered examples are given to illustrate the results

unified framework for the effective rate analysis of wireless communication systems over miso fading channels this paper proposes a unified framework for the effective rate analysis over arbitrary correlated and not necessarily identical multiple input single output miso fading channels which uses the moment generating function mgf based approach and h transform representation the proposed framework has the potential to simplify the cumbersome analysis procedure compared with the probability density function based approach moreover the effective rates over two specific fading scenarios are investigated namely independent but not necessarily identical distributed i n i d miso hyper fox s h fading channels and arbitrary correlated generalized k fading channels the exact analytical representations for these two scenarios are also presented by substituting corresponding parameters the effective rates in various practical fading scenarios such as rayleigh nakagami m weibull gamma and generalized k fading channels are readily available in addition asymptotic approximations are provided for the proposed h transform and mgf based approach as well as for the effective rate over i n i d miso hyper fox s h fading channels simulations under various fading scenarios are also presented which support the validity of the proposed method

interval oscillation of a general class of second order nonlinear impulsive differential equations with nonlinear damping in this paper a general class of second order nonlinear impulsive differential equations with damping is studied several interval oscillation criteria which generalize and extend some known ones are established moreover examples are given to illustrate the effectiveness and non emptiness of our results

amplify and forward two way relay networks error exponents and resource allocation in a two way relay network two terminals exchange information over a shared wireless half duplex channel with the help of a relay due to its fundamental and practical importance there has been an increasing interest in this channel however there has been little work that characterizes the fundamental tradeoff between the communication reliability and transmission rate across all signal to noise ratios in this paper we consider amplify and forward af two way relaying due to its simplicity we first derive the random coding error exponent for the link in each direction from the exponent expression the capacity and cutoff rate for each link are also deduced we then put forth the notion of bottleneck error exponent which is the worst exponent decay between the two links to give us insight into the fundamental tradeoff between the rate pair and information exchange reliability in the two way relay network as applications of the error exponent analysis to design a reliable af two way relay network we present two optimization framework to maximize the bottleneck error exponent namely i the optimal rate allocation under a sum rate constraint and its closed form quasi optimal solution that requires only knowledge of the capacity and cutoff rate of each link and ii the optimal power allocation under a total power constraint and perfect global channel state information which is shown equivalently to a quasi convex optimization problem numerical results verify our analysis and the effectiveness of the optimal rate and power allocations in maximizing the bottleneck error exponent i e the network information exchange reliability

interval criteria for oscillation of second order linear ordinary differential equations abstract new oscillation criteria are established for the equation py qy 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are more natural according to the sturm separation theorem and sharper than some previous results and can be applied to extreme cases such as t 0 q t dt

interval oscillation criteria for second order forced impulsive differential equations with mixed nonlinearities abstract in this paper by arithmetic geometric mean inequality and riccati transformation interval oscillation criteria are established for second order forced impulsive differential equation with mixed nonlinearities of the form r t x t p 0 t x t i 1 n p i t i x t e t t k x k a k x k x k b k x k where t t 0 k n u u 1 u k is the impulse moments sequence with 0 t 0 0 1 2 k and lim k k p q p q are odds and the exponents satisfy 1 m m 1 n 0 some known results are generalized and improved examples are also given to illustrate the effectiveness and non emptiness of our results

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

the vibration and stability of a friction guided translating string abstract eyelets capstans and cylindrical surfaces are often used in thread fiber and paper handling machinery to guide the axially moving element in addition to providing positional control these guides introduce dry friction forces that alter the vibration and stability characteristics of the system this paper examines the lateral response of a string that slides through an elastically supported dry friction guide exact expressions are derived for the linear response under free and forced conditions solutions for the eigenvalue spectrum exhibit unusual features including multiple divergence instabilities regions of flutter instability and regions of curve veering associated with mode localization a second order perturbation solution is derived to examine the behavior of the eigenvalue spectrum in regions of flutter instability and curve veering the analysis highlights the common features of these two phenomena and suggests ways to minimize vibration by adjusting various design variables the analysis also demonstrates that the eigenvalue loci in regions of flutter instability and curve veering are naturally described by a local hyperbolic approximation

picone s formula for linear non selfadjoint impulsive differential equations in this paper we derive a picone type formula for second order linear non selfadjoint impulsive differential equations having fixed moments of impulse actions and obtain a wirtinger type inequality a leighton type comparison theorem and a sturm picone comparison theorem for such equations moreover several oscillation criteria are also derived as applications

wave synthesis in a non linear stretched string with time varying length or tension abstract this paper is concerned with the numerical tone synthesis of a non linear stretched string the length or tension of which varies with time 1 at a constant rate 2 at a cosine function rate and 3 at a rate determined by a handwritten input function listening to the results for the analytical waveforms transformed by a digital to analog converter indicates that the case of the constant rate time varying length corresponds closely to a guitar string positive or negative feedback compensation for the analytically obtained frequency brings the analytical waveforms close to the numerically calculated waveforms a simple method is proposed with lower order polynomials for smoothly connecting two discontinuous waveforms into continuous waveforms a fourier series synthesizer procedure is described to aid rapid real time synthesis of tones of desired timbre

nonlinear vibrations of axially moving timoshenko beams under weak and strong external excitations in this paper nonlinear vibrations under weak and strong external excitations of axially moving beams are analyzed based on the timoshenko model the governing nonlinear partial differential equation of motion is derived from newton s second law accounting for the geometric nonlinearity caused by finite stretching of the beams the complex mode approach is applied to obtain the transverse vibration modes and the natural frequencies of the linear equation the method of multiple scales is employed to investigate primary resonances nonsyntonic excitations superharmonic resonances and subharmonic resonances some numerical examples are presented to demonstrate the effects of a varying parameter such as axial speed external excitation amplitudes and nonlinearity on the response amplitudes for the first and second modes when other parameters are fixed the stability of the response amplitudes is investigated and the boundary of instability is located

free vibration of a membrane stretched by inextensible strings at opposite edges abstract an analysis of presented for the free vibration of a membrane stretched by inextensible strings along two opposite edges the membrane is transformed into a square membrane of unit length by a certain transformation of variables the transverse deflection of the membrane is expressed in a series of the products of the deflection functions of strings strips of membrane parallel to the edges of the square membrane and the frequency equation is derived by the ritz method the natural frequencies and the mode shapes are calculated numerically up to higher modes for membranes symmetrical with respect to the centre lines by the application of the present method

sturmian comparison theory for linear and half linear impulsive differential equations in this paper we investigate sturmian comparison theory for second order half linear differential equations with fixed moments of impulse actions it is shown that impulse actions may greatly change the behavior of solutions in comparison several oscillation criteria are also derived to illustrate the results

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 and stability analysis of a multi guided rotating string abstract the small displacement vibrations of a rotating circular string restrained by point and distributed springs are studied in the present paper the model used includes the translating string as a special case the governing equations and boundary conditions are derived using hamilton s principle analytical solutions are obtained for free vibrations and some specific cases are discussed in addition approximate solutions with trigonometric shape functions are constructed by the rayleigh ritz method numerical results are given showing the effectiveness of the rayleigh ritz formulation constructed and some features of the string vibration and stability are discussed

travelling load response of an axially moving string abstract the classical moving load problem in which a mass traverses an elastic structure is extended to systems in which the guideway also has prescribed axial motion a monocable ropeway such as a tramway or ski lift is an example of such a traveling structure traveling load system and it is modeled herein as an axially moving string that transports an attached discrete mass between two supports the green s function methods for the two constituent systems the particle and the uniform traveling string are combined to derive a volterra integral equation with delay that governs the interaction force in the coupled system the calculated response of the traveling string particle system to arbitrary initial conditions and external excitation is compared to that predicted by the derived asymptotic solution for vanishing discrete mass repeated scattering by the particle of transverse waves in the string dominates the motion transient vibration as the particle is transported between the supports is maximized at a transport speed that can be substantially lower than the critical speed of divergence instability for the uniform traveling string agreement between responses measured in the laboratory and those predicted by the traveling structure traveling load theory supports the analysis

the response of a non uniformly tensioned circular string to a moving load abstract a non uniformly tensioned circular string on a damped elastic foundation is acted upon by a moving concentrated load this configuration can be viewed as a very simplified representation of a spinning rectangularly orthotropic disk acted upon by a spatially fixed force or of a stationary orthotropic disk subjected to a circumferentially moving load the natural frequencies and normal modes of vibration of the string on elastic foundation are determined for a range of values of the tension inhomogeneity the response of the string to a moving load is then determined the results indicate that there are many speeds below the critical speed of the uniformly tensioned string for which the forced response is large it is anticipated that the response of this simple model to a moving load can provide insight into the behavior of the mathematically more complicated rectangularly orthotropic circular disk

h transforms for wireless communication the h transforms are integral transforms that involve fox s h functions as kernels a large variety of integral transforms can be put into particular forms of the h transform since h functions subsume most of the known special functions including meijer s g functions in this paper we embody the h transform theory into a unifying framework for modeling and analysis in wireless communication first we systematize the use of elementary identities and properties of the h transform by introducing operations on parameter sequences of h functions we then put forth h fading and degree 2 irregular h fading to model radio propagation under composite specular and or inhomogeneous conditions the h fading describes composite effects of multipath fading and shadowing as a single h variate including most of typical models such as rayleigh nakagami m weibull alpha mu n ast nakagami m generalized k fading and weibull gamma fading as its special cases as a new class of h variates called the degree zeta irregular h variate the degree 2 irregular h fading characterizes specular and or inhomogeneous radio propagation in which the multipath component consists of a strong specularly reflected or line of sight los wave as well as unequal power or correlated in phase and quadrature scattered waves this fading includes a variety of typical models such as rician nakagami q kappa mu eta mu rician los gamma and kappa mu los gamma fading as its special cases finally we develop a unifying h transform analysis for the amount of fading error probability channel capacity and error exponent in wireless communication using the new systematic language of transcendental h functions by virtue of two essential operations called mellin and convolution operations involved in the mellin transform and mellin convolution of two h functions the h transforms for these performance measures culminate in h functions using the algebraic asymptotic expansions of the h transform we further analyze the error probability and capacity at high and low signal to noise ratios in a unified fashion

the fading number of multiple input multiple output fading channels with memory the fading number of a general not necessarily gaussian regular multiple input multiple output mimo fading channel with arbitrary temporal and spatial memory is derived the channel is assumed to be noncoherent i e neither receiver nor transmitter have knowledge about the channel state but they only know the probability law of the fading process the fading number is the second term in the asymptotic expansion of channel capacity when the signal to noise ratio snr tends to infinity it is related to the border of the high snr region with double logarithmic capacity growth

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

interval oscillation criteria for a forced second order nonlinear differential equations with damping abstract in this paper we are concerned with the oscillations in a class of forced second order differential equations with nonlinear damping terms by using classical variational principle and averaging technique several new interval oscillation criteria for the equations are established which improve and extend some known results example is also given to illustrate the results

oscillation criteria for a forced mixed type emden fowler equation with impulses some oscillation criteria for a forced mixed type emden fowler equation with impulses are given when the impulses are dropped our results extend those of sun and meng y g sun f w meng interval criteria for oscillation of second order differential equations with mixed nonlinearities appl math comput 15 2008 375 381 sun and wong y g sun j s w wong oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities j math anal appl 334 2007 549 560 for second order forced ordinary differential equation with mixed nonlinearities nasr a h nasr sufficient conditions for the oscillation of forced superlinear second order differential equations with oscillatory potential proc am math soc 126 1998 123 125 yang q yang interval oscillation criteria for a forced second order nonlinear ordinary differential equations with oscillatory potential appl math comput 135 2003 49 64 for forced superlinear emden fowler equation kong q kong interval criteria for oscillation of second order linear differential equations j math anal appl 229 1999 483 492 for unforced second order linear differential equations and wong j s w wong oscillation criteria for a forced second order linear differential equation j math anal appl 231 1999 235 240 for forced second order linear differential equation

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

capacity bounds via duality with applications to multiple antenna systems on flat fading channels a technique is proposed for the derivation of upper bounds on channel capacity it is based on a dual expression for channel capacity where the maximization of mutual information over distributions on the channel input alphabet is replaced with a minimization of average relative entropy over distributions on the channel output alphabet we also propose a technique for the analysis of the asymptotic capacity of cost constrained channels the technique is based on the observation that under fairly mild conditions capacity achieving input distributions escape to infinity the above techniques are applied to multiple antenna flat fading channels with memory where the realization of the fading process is unknown at the transmitter and unknown or only partially known at the receiver it is demonstrated that for high signal to noise ratio snr the capacity of such channels typically grows only double logarithmically in the snr to better understand this phenomenon and the rates at which it occurs we introduce the fading number as the second order term in the high snr asymptotic expansion of capacity and derive estimates on its value for various systems it is suggested that at rates that are significantly higher than the fading number communication becomes extremely power inefficient thus posing a practical limit on practically achievable rates upper and lower bounds on the fading number are also presented for single input single output siso systems the bounds coincide thus yielding a complete characterization of the fading number for general stationary and ergodic fading processes we also demonstrate that for memoryless multiple input single output miso channels the fading number is achievable using beam forming and we derive an expression for the optimal beam direction this direction depends on the fading law and is in general not the direction that maximizes the snr on the induced siso channel using a new closed form expression for the expectation of the logarithm of a noncentral chi square distributed random variable we provide some closed form expressions for the fading number of some systems with gaussian fading including siso systems with circularly symmetric stationary and ergodic gaussian fading the fading number of the latter is determined by the fading mean fading variance and the mean squared error in predicting the present fading from its past it is not directly related to the doppler spread for the rayleigh ricean and multiple antenna rayleigh fading channels we also present firm nonasymptotic upper and lower bounds on channel capacity these bounds are asymptotically tight in the sense that their difference from capacity approaches zero at high snr and their ratio to capacity approaches one at low snr

solvability condition in multi scale analysis of gyroscopic continua abstract the solvability condition is investigated for the method of multiple scales applied to gyroscopic continua the general framework of the multi scale analysis is proposed for a linear gyroscopic continuous system under small nonlinear time dependent disturbances the solvability condition is derived from the properties of the systems the condition holds only for appropriate boundary conditions the appropriateness of the boundary conditions can be examined for unperturbed linear systems an example is presented to highlight the requirements on the boundary conditions

oscillation criteria for second order nonlinear differential equations with nonlinear damping this paper is concerned with the oscillation of a class of general type second order differential equations with nonlinear damping several new oscillation criteria are established under quite general assumptions which improve and extend the known results in the literature

product of two envelopes taken from alpha mu kappa mu and eta mu distributions this paper presents exact novel formulations for the probability density function and cumulative distribution function for the product of two independent and non identically distributed alpha mu kappa mu and eta mu variates the expressions are given in terms of both 1 generalized fox h function and 2 easily computable series expansions the formulations derived can be directly used to explore the performance of a number of wireless communication processes including multihop systems cascaded channels radar communications multiple input multiple output links and others due to the high flexibility of the above mentioned distributions the results presented here comprise a substantial number of useful product distributions as application examples performance metrics for the cascaded fading channel are derived the validity of the expressions is confirmed via monte carlo simulation it is noteworthy that because any composite multipath shadowing fading model is obtained as a particular case of the product of two fading variables the results given here provide a plethora of composite multipath shadowing fading scenarios

interval oscillation of a general class of second order nonlinear differential equations with nonlinear damping abstract the paper is concerned with the oscillation of a class of general type second order differential equations with nonlinear damping terms several new interval oscillation criteria are established for such a class of differential equations under quite general assumptions examples are also given to illustrate the results in particular it is shown that under some very mild conditions on k 1 k 2 and f the equation k 1 x x cos tk 2 x x x sin tf x 0 is oscillatory which extends the result obtained by kwong and wong j math anal appl 288 2003 15

free in plane vibration of an axially moving membrane the free in plane vibration of an axially moving membrane is studied considering the effects of both the translating speed and aspect ratio of the membrane two sets of boundary conditions which are free and fixed constraints in the lateral direction at boundaries with mass transport are discussed in this study from the extended hamilton principle the coupled equations of the longitudinal and lateral motions are derived these equations are then discretized by using the galerkin method from the discretized equations the natural frequencies and mode shapes are obtained for the variations of the translating speed and aspect ratio the results show that the translating speed aspect ratio and boundary conditions have significant effects on the in plane vibrations of the moving membrane

interval oscillation criteria for second order quasi linear nonhomogeneous differential equations with damping by using two inequalities due to holder and hardy littlewood and polya as well as averaging functions several interval oscillation criteria are established for the second order quasi linear differential equation with forced term of the form r t y t a 1y t p t y t a 1y t q t y t b 1y t e t that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line where b a 0 our results make use of the oscillatory properties of the forcing term and extend a recent result which is obtained by means of a picone identity

n ast nakagami a novel stochastic model for cascaded fading channels a generic and novel distribution referred to as nakagami constructed as the product of n statistically independent but not necessarily identically distributed nakagami m random variables rvs is introduced and analyzed the proposed distribution turns out to be a very convenient tool for modelling cascaded nakagami m fading channels and analyzing the performance of digital communications systems operating over such channels the moments generating probability density cumulative distribution and moments functions of the n nakagami distribution are developed in closed form using the meijer s g function using these formulas generic closed form expressions for the outage probability amount of fading and average error probabilities for several binary and multilevel modulation signals of digital communication systems operating over the n nakagami fading and the additive white gaussian noise channel are presented complementary numerical and computer simulation performance evaluation results verify the correctness of the proposed formulation the suitability of the n nakagami fading distribution to approximate the lognormal distribution is also being investigated using kolmogorov smirnov tests the rate of convergence of the central limit theorem as pertaining to the multiplication of nakagami m rvs is quantified

a novel unified expression for the capacity and bit error probability of wireless communication systems over generalized fading channels analysis of the average binary error probabilities abep and average capacity ac of wireless communications systems over generalized fading channels have been considered separately in past years this paper introduces a novel moment generating function mgf based unified expression for the abep and ac of single and multiple link communications with maximal ratio combining in addition this paper proposes the hyper fox s h fading model as a unified fading distribution of a majority of the well known generalized fading environments as such the authors offer a generic unified performance expression that can be easily calculated and that is applicable to a wide variety of fading scenarios the mathematical formulism is illustrated with some selected numerical examples that validate the correctness of the authors newly derived results

dynamic responses of the in plane and out of plane vibrations for an axially moving membrane the dynamic responses of both the in plane and out of plane vibrations are investigated for an axially moving membrane using the extended hamilton principle equations of motion are derived for the moving membrane with no slip boundary conditions at rollers the equations of motion are discretized by using the galerkin method and then the generalized a time integration method is applied to compute the dynamic responses of the membrane based on the computed results the responses are compared between the in plane and out of plane vibrations in addition the effects of translating velocity acceleration critical speeds and velocity profiles on the dynamic behaviours for displacements and stresses are investigated and discussed r 2006 elsevier ltd all rights reserved

stability analysis of an axially accelerating string the dynamic response of an axially accelerating string is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity approximate analytical solutions are sought using two different approaches in the first approach the equations are discretized first and then the method of multiple scales is applied to the resulting equations in the second approach the method of multiple scales is applied directly to the partial differential system principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for a band saw and a threadline problem

dynamic stability of a three dimensional string subjected to both magnetic and tensioned excitations this paper presents the dynamic stability of an axially moving string subjected to both actions of an alternating uniform transverse magnetic field and a periodic tension force owing to time varying actions terms with time dependent coefficients appear in the equations of motion which resutls in the existence of parametric instability

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

non linear resonance in strings under narrow band random excitation part i planar response and stability non linear planar response of a string to planar narrow band random excitation is investigated in this paper a response equation for the mean square deflection 2 is obtained under a single mode approximation by using the equivalent linearization technique it is shown that the response is triple valued as in the case of harmonic excitation if the centre frequency of excitation lies in a certain specified range the triple valued response occurs only if the excitation bandwidth is smaller than a critical value crit which is a monotonically increasing function of the intensity of excitation an approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the 2 plane have been charted it is shown that planar response can become unstable either due to an unbounded growth of the in plane component of motion or due to a spontaneous appearance of an out of plane component