two approaches for studying the impact response of viscoelastic engineering systems an overview two approaches for studying the impact response of viscoelastic engineering structures are considered by the example of the dynamic response of a viscoelastic bernoulli euler beam transversely impacted by an elastic sphere the young s modulus of the viscoelastic beam is the time dependent operator which is defined either via the kelvin voigt fractional derivative model or via the standard linear solid fractional derivative model the first approach assumes that poisson s ratio is not an operator but a constant while under the second approach the bulk modulus is considered to be constant the transverse impact of the elastic sphere upon the viscoelastic beam is investigated using both approaches the comparison of the results obtained shows that the solution obtained at the constant poisson s ratio is much simpler than that at the constant bulk modulus

analysis of d2d underlaid cellular networks sir meta distribution and mean local delay we study the performance of device to device d2d communication underlaying cellular wireless network in terms of the meta distribution of the signal to interference ratio sir which is the distribution of the conditional sir distribution given the locations of the wireless nodes modeling d2d transmitters and base stations as poisson point processes ppps moments of the conditional sir distribution are derived in order to calculate analytical expressions for the meta distribution and the mean local delay of the typical d2d receiver and cellular downlink user it turns out that for d2d users the total interference from the d2d interferers and base stations is equal in distribution to that of a single ppp while for downlink users the effect of the interference from the d2d network is more complicated we also derive the region of transmit probabilities for the d2d users and base stations that result in a finite mean local delay and give a simple inner bound on that region finally the impact of increasing the base station density on the mean local delay the meta distribution and the density of users reliably served is investigated with numerical results

closed form hop count distributions in random networks with arbitrary routing we contribute a new solution to the problem of establishing an analytical relationship between hop counts under a certain routing policy and euclidean distances in random networks both in the linear and planar cases the contributed solution is unified in that hop count distributions have similar expressions both in the 1d and the 2d cases general in terms of routing policies in that the effect of any given policy is accounted for by means of a single parameter closed form such that hop count probability mass functions pmf s are given in terms of scaled versions of the closed form pmf s of the number of nodes and mathematically tractable since the derived hop count distributions are in the form of a difference of the well known nakagami m cumulative density functions cdf s direct and kullback leibler divergence comparisons against empirical data demonstrate the high accuracy of our solution the simplicity accuracy and generality of the result owes partly to a self imposed confinement to connected networks defined formally in stochastic geometric terms which allows for the elimination of recursions and multivariate marginalization commonly required by existing solutions the contributed results find application in the design and analysis of ad hoc networks cooperative localization algorithms or latency and energy consumption analysis

a geometric interpretation of fading in wireless networks theory and applications in wireless networks with random node distribution the underlying point process model and the channel fading process are usually considered separately a unified framework is introduced that permits the geometric characterization of fading by incorporating the fading process into the point process model concretely assuming nodes are distributed in a stationary poisson point process in rd the properties of the point processes that describe the path loss with fading are analyzed the main applications are single hop connectivity and broadcasting

connecting toric manifolds by conical kahler einstein metrics abstract we give criterions for the existence of toric conical kahler einstein and kahler ricci soliton metrics on any toric manifold in relation to the greatest ricci and bakry emery ricci lower bound we also show that any two toric manifolds with the same dimension can be joined by a continuous path of toric manifolds with conical kahler einstein metrics in the gromov hausdorff topology

fractional calculus a different approach to the analysis of viscoelastically damped structures fractional calculus is used to construct stress strain relationships for viscoelastic materials these relationships are used in the finite element analysis of viscoelastically damped structures and closed form solutions to the equations of motion are found the attractive feature of this approach is that very few empirical parameters are required to model the viscoelastic material and calculate the response of the structure for general loading conditions

design modeling and performance analysis of multi antenna heterogeneous cellular networks this paper presents a stochastic geometry based framework for the design and analysis of downlink multi user multiple input multiple output mimo heterogeneous cellular networks with linear zero forcing transmit precoding and receive combining assuming rayleigh fading channels and perfect channel state information the generalized tiers of base stations may differ in terms of their poisson point process spatial density number of transmit antennas transmit power artificial biasing weight and number of user equipments served per resource block the spectral efficiency of a typical user equipped with multiple receive antennas is characterized using a non direct moment generating function based methodology with closed form expressions of the useful received signal and aggregate network interference statistics systematically derived in addition the area spectral efficiency is formulated under different space division multiple access and single user beamforming transmission schemes we examine the impact of different cellular network deployments propagation conditions antenna configurations and mimo setups on the achievable performance through theoretical and simulation studies based on the state of the art system parameters the results highlight the inherent limitations of baseline single input single output transmission and conventional sparse macro cell deployment as well as the promising potential of multi antenna communications and small cell solution in interference limited cellular environments

mean internodal distance in regular and random multihop networks the minimum necessary aggregate link capacity in a telecommunication network is directly proportional to the mean distance between nodes the mean internodal distance is therefore an important network characteristic it is shown that most network topologies including those constructed at random display mean internodal distances comparable to those of many carefully designed networks thus careful selection of network topology to minimize the mean internodal distance may be important in only the most sensitive applications furthermore even in such sensitive applications an almost randomly chosen network topology may be the best choice

kahler ricci solitons on toric manifolds with positive first chern class abstract in this paper we prove there exists a kahler ricci soliton unique up to holomorphic automorphisms on any toric kahler manifold with positive first chern class and the kahler ricci soliton is a kahler einstein metric if and only if the futaki invariant vanishes

greatest lower bounds on ricci curvature for toric fano manifolds abstract in this short note based on the work of wang and zhu 2004 8 we determine the greatest lower bounds on ricci curvature for all toric fano manifolds

on distances in uniformly random networks the distribution of euclidean distances in poisson point processes is determined the main result is the density function of the distance to the n nearest neighbor of a homogeneous process in ropfm which is shown to be governed by a generalized gamma distribution the result has many implications for large wireless networks of randomly distributed nodes

on kahler einstein metrics on certain kahler manifolds with c1 m 0 on demontre qu il existe une metrique de kahler einstein sur une hypersurface de fermat a m dimensions de degre superieur a m 1

distance statistics of the communication best neighbor in a poisson field of nodes in a wireless network while the signal attenuation due to the distance related path loss is minimum between a node and its nearest neighbor this is not the case for the overall attenuation when the fading effect is also taken into account hence the communication best neighbor cbn of a node is defined as the neighbor of that node with which it has the highest channel power gain recently the statistics of the physical neighborhood index of the cbn have been derived for a general fading environment in which the nodes have two dimensional poisson distribution in this paper the statistics of the distance between a node and its cbn as well as the joint cbn distance index statistics are obtained for the same scenario then the analytical expressions are specialized for the case where the communication channels follow the generalized gamma fading model also the results are verified and illustrated by computer simulations and numerical results further it is shown how the obtained analytical results can be used to identify the cbn more efficiently by limiting the search region and the number of neighbors that are examined

thresholds valuations and k stability abstract let x be a normal complex projective variety with at worst klt singularities and l a big line bundle on x we use valuations to study the log canonical threshold of l as well as another invariant the stability threshold the latter generalizes a notion by fujita and odaka and can be used to characterize when a q fano variety is k semistable or uniformly k stable it can also be used to generalize volume bounds due to fujita and liu the two thresholds can be written as infima of certain functionals on the space of valuations on x when l is ample we prove that these infima are attained in the toric case toric valuations achieve these infima and we obtain simple expressions for the two thresholds in terms of the moment polytope of l

dispersion curves of viscoelastic plane waves and rayleigh surface wave in high frequency range with fractional derivatives abstract the moduli of conventional elastic structural materials are extended to one of the viscoelastic materials through a modification whereby the dynamic moduli converge to the static moduli of elasticity as the fractional order approaches zero by plotting phase velocity curves and group velocity curves of plane waves and rayleigh surface wave for a viscoelastic material polyvinyl chloride foam the influence of the fractional order of viscoelasticity is examined the phase and group velocity curves in the high frequency range were derived for longitudinal transverse and rayleigh waves inherent to the viscoelastic material in addition the equation for the phase velocity was mathematically derived on the complex plane too and graphically illustrated a phenomenon was found that at the moment when the fractional order of the time derivative reaches an integer value 1 the curve on the complex plane becomes completely different exhibiting snap through behavior we examined the mechanism of the snap through mathematically numerical calculation examples were solved and good agreement was confirmed between the numerical calculation and the analytical expression mentioned above from the results of the numerical example regularities were derived for the absolute value of the complex phase and group velocities on the complex plane

event detection in wireless sensor networks in random spatial sensors deployments we develop a new class of event detection algorithms in wireless sensor networks where the sensors are randomly deployed spatially we formulate the detection problem as a binary hypothesis testing problem and design the optimal decision rules for two scenarios namely the poisson point process and binomial point process random deployments to calculate the intractable marginal likelihood density we develop three types of series expansion methods which are based on an askey orthogonal polynomials in addition we develop a novel framework to provide guidance on which series expansion is most suitable i e most accurate to use for different system parameters extensive monte carlo simulations are carried out to illustrate the benefits of this framework as well as the quality of the series expansion methods and the impacts that different parameters have on detection performance via the receiver operating curves roc

studying the sinr process of the typical user in poisson networks using its factorial moment measures based on a stationary poisson point process a wireless network model with random propagation effects shadowing and or fading is considered in order to examine the process formed by the signal to interference plus noise ratio sinr values experienced by a typical user with respect to all the base stations in the down link channel this sinr process is completely characterized by deriving its factorial moment measures which involve numerically tractable explicit integral expressions this novel framework naturally leads to expressions for the k coverage probability including the case of random sinr threshold values considered in multi tier network models while the k coverage probabilities correspond to the marginal distributions of the order statistics of the sinr process a more general relation is presented connecting the factorial moment measures of the sinr process to the joint densities of these order statistics this gives a way for calculating the exact values of the coverage probabilities arising in a general scenario of signal combination and interference cancellation between base stations the presented framework consisting of the mathematical representations of sinr characteristics with respect to the factorial moment measures holds for the whole domain of sinr and is amenable to considerable model extension

analysis of free vibrations of a viscoelastic oscillator via the models involving several fractional parameters and relaxation retardation times free damped vibrations of a linear viscoelastic oscillator based on the fractional derivative model involving more than one different fractional parameters and several relaxation retardation times are investigated the analytical solution is obtained in the form of two terms one of which governs the drift of the system s equilibrium position and is defined by the dynamic relaxation retardation processes occurring in the system and the other term describes damped vibrations around the equilibrium position and is determined by the system s inertia and energy dissipation the drift is governed by an improper integral taken along two sides of the cut of the complex plane while damped vibrations are determined according to the two complex conjugate roots of the characteristic equation which are located on the left half of the complex plane the behaviour of the characteristic equation roots as functions of the system s rheological parameters which enable the control of the dynamic response of the oscillator is shown in the complex plane

conical kahler einstein metrics revisited in this paper we introduce the interpolation degeneration strategy to study kahler einstein metrics on a smooth fano manifold with cone singularities along a smooth divisor that is proportional to the anti canonical divisor by interpolation we show the angles in 0 2 that admit a conical kahler einstein metric form a connected interval and by degeneration we determine the boundary of the interval in some important cases as a first application we show that there exists a kahler einstein metric on mathbb p 2 with cone singularity along a smooth conic degree 2 curve if and only if the angle is in 2 2 when the angle is 2 3 this proves the existence of a sasaki einstein metric on the link of a three dimensional a2 singularity and thus answers a question posed by gauntlett martelli sparks yau as a second application we prove a version of donaldson s conjecture about conical kahler einstein metrics in the toric case using song wang s recent existence result of toric invariant conical kahler einstein metrics

mechanism of complicated volume deformation in polymers and its fractional time based description abstract in tension and compression of polymers some abnormal phenomena of volume changes were often observed and its mechanism is still unclear in this paper based on the thermodynamics principle it is shown that the combined effects of internal energy and entropy are the basic reason of causing the anomaly in polymers moreover to describe the complicated deformation through a simple model and have a correct modelization of mechanical behaviors a volume strain model is presented in which the variation of volume strain resulted from the combined effects is characterized through a fractional integral expression comparison between fitting results and experimental results reveals the proposed model can describe the volume deformation of polymers

brief paper analytical computation of the h2 norm of fractional commensurate transfer functions 2 norm or impulse response energy of any fractional commensurate transfer function is computed analytically a general expression depending on transfer function coefficients and differentiation orders is established then more concise expressions are given for elementary fractional transfer functions unlike stable rational transfer functions it is proven that the 2 norm of stable fractional transfer functions may be infinite finiteness conditions are established in terms of transfer function relative degree moreover it is proven that the 2 norm of a fractional transfer function with a proper integrator of order less than 0 5 may be finite the obtained results are used to evaluate the integral squared error of closed loop control systems