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A family 풜 of sets is said to be intersecting if every two sets in 풜 intersect. An intersecting family is said to be trivial if its sets have a common element. A graph G is said to be r-EKR if at least one of the largest intersecting families of independent r-element sets of G is trivial. Let α (G) and ω (G) denote the independence number and the clique number of G, respectively. Hilton and Spencer recently showed that if G is the vertex-disjoint union of a cycle C raised to the power k and s cycles 1C,...,sC raised to the powers k1,..., ks, respectively, 1 ≤ r ≤ α (G), and min (ω (C 1 k 1 ) , ... , ω (C s k s )) ≥ ω ( C k) , then G is r-EKR. They had shown that the same holds if C is replaced by a path P and the condition on the clique numbers is relaxed to min (ω (C 1 k 1 ) , ... , ω (C s k s )) ≥ ω ( P k) , We use the classical Shadow Intersection Theorem of Katona to obtain a significantly shorter proof of each result for the case where the inequality for the minimum clique number is strict. [ABSTRACT FROM AUTHOR]

In this article we approach some of the basic questions in topological dynamics, concerning periodic points, transitivity, the shadowing and the gluing orbit properties, in the context of C 0 incompressible flows generated by Lipschitz vector fields. We prove that a C 0 -generic incompressible and fixed-point free flow satisfies the periodic shadowing property, it is transitive and has a dense set of periodic points in the non-wandering set. In particular, a C 0 -generic fixed-point free incompressible flow satisfies the reparametrized gluing orbit property. We also prove that C 0 -generic incompressible flows satisfy the general density theorem and the weak shadowing property, moreover these are transitive. [ABSTRACT FROM AUTHOR]

In this paper, we calculate the weak deflection angle by Casimir wormhole and its shadow. To do so, we derive the Gaussian optical curvature and use the Gauss–Bonnet theorem (GBT). Then we find the deflection angle by Casimir wormhole in weak field limits. Moreover, we obtain the weak deflection angle in the presence of plasma medium and see the effect of the plasma medium on the weak deflection angle. Moreover, we study a shadow of Casimir wormhole and we plot and discuss them. We show the shadow of Casimir wormhole's behavior when changing the value of a. [ABSTRACT FROM AUTHOR]

Let (M,ɗ ) be a metric G-space , ɸ ∶M→M be a continuous map. The notion of the G -average shadowing property (G ASP ) for a continuous map on G -space are introduced and the relation between the G ASP and average shadowing property(ASP)are investigated. We show that if ɸ has GASP, then ɸ^m has GASP for every m∈N. We proved that if a map ɸ be pseudo-equivariant with dense set of G_ɸ-periodic points and has the G ASP then ɸ is weakly G-mixing. We also showed that if ɸ is a G -expansive pseudo-equivariant homeomorphism has the GASP and ɸ is topologically G-mixing then ɸ has a G -specification. We obtained that the identity map ɸ on M has the G ASP if and only if the orbit space M⁄G of M is totally disconnected. Finally, we showed that if ɸ be a pseudo-equivariant map, and the trajectory map, Ψ∶M →M⁄G , is covering map then ɸ has the GASP if and only if the induced map ɸ ̆ ∶M⁄G → M⁄G , has GASP. [ABSTRACT FROM AUTHOR]

A qualitative model that relates the period of the surface roughness to the vertical and spherical growth rates of glancing angle deposited (GLAD) nanorods suggests that rod self-shadowing is responsible for the previously reported temperature dependence in the rod width. Atomic shadowing interactions between neighboring rods as well as surface islands on the rod growth fronts control the morphological evolution which is quantified by the growth exponent p that relates the rod width w (=Ahp) to their height h. An analytical formalism predicts linear dependences of p and A on the average island separation and provides an explanation for reported anomalous p values. Experimental validation using new and previously published GLAD data for Al, Cr, Nb, and Ta shows quantitative agreement for all metallic systems under consideration and confirms the predicted dependences. In addition, a discontinuity in the p versus homologous deposition temperature θ suggests a critical value θc=0.24±0.02 for a transition from two-dimensional to three-dimensional island growth, which is independently confirmed by a discontinuity in the measured island width. [ABSTRACT FROM AUTHOR]

Polymers are naturally polydisperse. Polydispersity may have a large effect on the phase behavior of polymer solutions, in particular, on the liquid-liquid phase equilibria. In this paper, we determine the cloud and shadow curves bounded by lower critical solution temperatures for a number of polymer+solvent systems where the polymer is polydisperse in terms of molecular weight (chain length). The moment method [P. Sollich, P. B. Warren, and M. E. Cates, Adv. Chem. Phys. 116, 265 (2001)] is applied with the SAFT approach to determine cloud and shadow curves with continuous Schulz-Flory distributions. It is seen that chain length polydispersity always enhances the extent of liquid-liquid phase equilibria. The predicted cloud curves obtained for continuous distributions are very similar to those obtained for simple ternary mixtures with the same polydispersity index, while the corresponding shadow curves can be very different depending on the composition of the parent distribution. The ternary phase behavior can be used to provide an understanding of the shape of the cloud and shadow curves. Regions of phase equilibria between three liquid phases are found for ternary systems when the chain length distribution is very asymmetrical; such regions are not observed for Schulz-Flory distributions even in the case of a large degree of polydispersity. [ABSTRACT FROM AUTHOR]

An r -uniform hypergraph is a tight r-tree if its edges can be ordered so that every edge e contains a vertex v that does not belong to any preceding edge and the set e - v lies in some preceding edge. A conjecture of Kalai personal communication published in Frankl and Füredi, J. Combin. Theory Ser. A, 45 (1987), pp. 226--262, generalizing the Erdõs-Sós conjecture for trees, asserts that if T is a tight r -tree with t edge\bigr)s and G is an n-vertex r-uniform hypergraph containing no copy of T, then G has at most t--1/r(n r-i) edges. A trunk T' of a tight r-tree T is a tight subtree such that every edge of T - T' has r - 1 vertices in some edge of T' and a vertex outside T'. For r ≥ 3, the only nontrivial family of tight r-trees for which this conjecture has been proved is the family of r-trees with trunk size one in J. Combin. Theory Se r. A, 45 (1987), pp. 226--262. Our main result is an asymptotic version of Kalai's conjecture for all tight trees T of bounded trunk size. This follows from our upper bound on the size of a T-free r-uniform hypergraph G in terms of the size of its shadow. We also give a short proof of Kalai's conjecture for tight r-trees with at most four edges. In particular, for 3-uniform hypergraphs, our result on the tight path of length 4 implies the intersection shadow theorem of Katona Acta Math. Acad. Sci. Hungar., 15 (1964), pp. 329--337. [ABSTRACT FROM AUTHOR]

Some characterizations on the chain recurrence, chain transitivity, chain mixing property, shadowing and h-shadowing for Zadeh's extension are obtained. Besides, it is proved that a dynamical system is spatiotemporally chaotic provided that the Zadeh's extension is Li-Yorke sensitive. [ABSTRACT FROM AUTHOR]

This paper considers near-equilibrium systems of ordinary differential equations with explicit separation of the slow and stable manifolds. Formal B-series like those previously used to analyze highly oscillatory systems or to construct modified equations are employed here to construct expansions of the change of variables, the center invariant manifold and the reduced model. The new approach may be seen as a process of reduction to a normal form, with the surprising advantage, as compared to the standard view conveyed by the celebrated center manifold theorem, that it is possible to recover the complete solution at any time through an explicitly computable way. [ABSTRACT FROM AUTHOR]

Abstract In this paper we introduce a concept of weak stability for non-autonomous dynamical systems. We characterize the set of weak stable points and show that the set of weak stable points is residual, and investigate the relation between weak stability and shadowing property. We also discuss the relation between weak stability of a non-autonomous dynamical system and its induced set-valued system. [ABSTRACT FROM AUTHOR]

A shadowable point for a flow is a point where the shadowing lemma holds for pseudo-orbits passing through it. We prove that this concept satisfies the following properties: the set of shadowable points is invariant and a Gδ set. A flow has the pseudo-orbit tracing property if and only if every point is shadowable. The chain recurrent and nonwandering sets coincide when every chain recurrent point is shadowable. The chain recurrent points which are shadowable are exactly those that can be are approximated by periodic points when the flow is expansive. These results extends those presented in Morales (Dyn Syst. 2016;31(3):347-356). We study the relations between shadowable points of a homeomorphism and the shadowable points of its suspension flow. We characterize the set of forward shadowable points for transitive flows and chain transitive flows. We prove that the geometric Lorenz attractor does not have shadowable points. We show that in the presence of shadowable points chain transitive flows are transitive and that transitivity is a necessary condition for chain recurrent flows with shadowable points whenever the phase space is connected. Finally, as an application, these results we give concise proofs of some well known theorems establishing that flows with POTP admitting some kind of recurrence are minimal. [ABSTRACT FROM AUTHOR]

In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by work on assimilation in the unstable subspace [Carrassi et al., Chaos, 18 (2008), 023112; Trevisan, D'Isidoro, and Talagrand, Q. J. R. Meteorol. Soc., 136 (2010), pp. 487--496; Palatella, Carrassi, and Trevisan, J. Phys. A, 46 (2013), 254020] and pseudo-orbit data assimilation [Judd and Smith, Phys. D, 151 (2001), pp. 125--141; Judd et al., J. Atmos. Sci., 65 (2008), pp. 1749--1772; Du and Smith, J. Atmos. Sci., 71 (2014), pp. 469--482]. The algorithm utilizes time dependent projections onto the nonstable subspace determined by employing computational techniques for Lyapunov exponents/vectors. The method is extended to parameter estimation without changing the problem dynamics and we address techniques for adapting the method when (as is commonly the case) observations are not available in the full model state space. We use a combination of analysis and numerical experiments (with the Lorenz 63 and Lorenz 96 models) to illustrate the efficacy of the techniques and show that the results compare favorably with other variational techniques. [ABSTRACT FROM AUTHOR]

We prove the genericity of the shadowing and periodic shadowing properties for both conservative and dissipative homeomorphisms on a compact connected manifold. Our proof is valid for topological manifolds and still holds in the dissipative case. As a consequence of this result, we establish the genericity of the specification property, the average shadowing property, and the asymptotic average shadowing property, in the conservative case. [ABSTRACT FROM AUTHOR]

In this paper we investigate the quasi-shadowing property for C1 random dynamical systems on their random partially hyperbolic sets. It is shown that for any pseudo orbit {xk}−∞+∞ on a random partially hyperbolic set there exists a “center” pseudo orbit {yk}−∞+∞ shadowing it in the sense that yk+1 is obtained from the image of yk by a motion along the center direction. Moreover, when the random partially hyperbolic set has a local product structure, the above “center” pseudo orbit {yk}−∞+∞ can be chosen such that yk+1 and the image of yk lie in their common center leaf. [ABSTRACT FROM AUTHOR]

We present a variational implementation of the Verlet algorithm for molecular dynamics which is both conceptually and computationally attractive. Given an approximate path, this variational Verlet algorithm computes an actual trajectory close to the path. Instead of initial conditions, we specify end-point conditions, which makes it possible to compute trajectories with fixed end points as well as trajectories that are exactly periodic (nonlinear modes of vibration). With a simple sign change, the method yields approximate reaction pathways. We present several applications which illustrate how this alternative approach to dynamics can yield unusual trajectories that are difficult to attain by conventional means. In our first model system, a simple double well, we examine the seemingly paradoxical shadowing lemma of classical mechanics which claims that, in spite of the cumulative numerical errors which cause rapid deviation from the correct path, a calculated trajectory can still be close to some true trajectory of the system over a relatively long time period. We explicitly calculate such so-called shadowing trajectories. We also study isomerization events in which trajectories cross from one potential well to another, obtaining guesses from simple line segments and from dynamics on a perturbed version of the double-well potential. A closed loop of briefly recurrent motion in a trajectory can serve as an initial guess in the computation of a large-amplitude nonlinear mode of vibration. Finally, we use a model AB+C reaction in rare-gas solution to demonstrate the feasibility of calculations on molecular systems with many degrees of freedom. A gas-phase reactive trajectory of the A, B, and C atoms is, with the variational Verlet algorithm, transformed into a similar solution-phase trajectory and vice versa. This calculation suggests that rare events, such as reactions in solution, may be obtained through refining initial paths of perturbed or decoupled systems... [ABSTRACT FROM AUTHOR]

In this study, the authors propose a simple yet tighter approximations for the special two-dimensional Gaussian Q functions using the Trapezoidal rule of numerical integration. This enables a simplified and accurate symbol error probability (SEP) approximation of the hexagonal-quadrature amplitude modulation (HQAM) in additive white Gaussian noise channel. The proposed approximation further simplifies the SEP calculation of HQAM in parametric α - μ, η - μ, and λ - μ fading distributions. Also, the SEP of HQAM over log-normal shadowing is calculated in this study. The accuracy of the analytical framework is verified using computer simulations. [ABSTRACT FROM AUTHOR]

In this article, an accurate and fast approach is proposed to calculate the electromagnetic wave propagation characteristics over the sea surface under tropospheric ducting conditions. The method is based on the parabolic equation and an asymptotic model of a rough sea surface and is used to calculate the electromagnetic characteristics and to model the sea surface reflection. In the proposed model, termed the extremum approximation of the shadowing effect (EA of SE) model, the shadowing effect is considered and simplified to improve the accuracy and shorten the computation time. The probability density functions and the propagation factors of different models are compared, the influence of the rough sea surface and the shadowing effect on the electromagnetic wave propagation is analyzed and the model accuracy and efficiency are evaluated. Some comparisons are made with experimental data. The results show that the average error is about 1 dB less after the shadowing effect is considered; and the proposed approach shortens the computation time about 600 times while maintaining a high accuracy. [ABSTRACT FROM AUTHOR]

A free-molecular flow past two parallel circular flat plates is analyzed by the test particle Monte Carlo (TPMC) method. Flow shadowing and multiple reflections have a vital influence on aerodynamic coefficients of the two plates. At the pitch angle of 0, lift coefficients of each plate do not equal to zero. Flow shadowing has a significant effect on the front side of the shaded plate while multiple reflections play a dominant role on the back side of the shading one. The area ratio of the two plates has an evident effect on flow shadowing and multiple reflections, and different area ratios lead to different pressure distributions on the front side of the shaded plate and the back side of the shading one. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new notion, named controlled shadowing property and we relate it to some notions in dynamical systems such as topological ergodicity, topologically mixing and specification properties. The relation between the controlled shadowing and chaos in sense of Li-Yorke is studied. At the end we give some examples to investigate the controlled shadowing property. [ABSTRACT FROM AUTHOR]

We define topological pseudo orbital specification, topological weak specification, topological ergodic shadowing, topological d̲-shadowing for a continuous map on a uniform space and show that they are equivalent for a uniformly continuous map with topological shadowing on a totally bounded uniform space. [ABSTRACT FROM AUTHOR]

In this paper we consider shadowing and weak shadowing properties for iterated function systems IFS and give some results on these concepts. At first, a sufficient condition for shadowing property is given and by this result we present two IFS which have the shadowing property. It is proved that every uniformly expanding as well as every uniformly contracting IFS has the weak shadowing property. By an example we show that in IFS's shadowing property does not imply weak shadowing property. Finally we have the main result of the paper and prove that the weak shadowing is a generic property in the set of all IFS's. [ABSTRACT FROM AUTHOR]

We show that if a C¹ generic diffeomorphism of a closed smooth two-dimensional manifold has the average shadowing property or the asymptotic average shadowing property, then it is Anosov. Moreover, if a C¹ generic vector field of a closed smooth three-dimensional manifold has the average shadowing property or the asymptotic average shadowing property, then it satisfies singular Axiom A without cycles. [ABSTRACT FROM AUTHOR]

This paper firstly proves that every dynamical system defined on a Hausdorff uniform space with topologically ergodic shadowing is topologically mixing, thus topologically chain mixing. Then, the following is proved: (1) every weakly mixing dynamical system defined on a second countable Baire-Hausdorff uniform space is chaotic in the sense of both Li-Yorke and Auslander-Yorke; (2) every point transitive dynamical system defined on a Hausdorff uniform space is either almost equicontinuous or sensitive. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

We characterize product Anosov diffeomorphisms in terms of the two-sided limit shadowing property. It is proved that an Anosov diffeomorphism is a product Anosov diffeomorphism if and only if any lift to the universal covering has the unique two-sided limit shadowing property. Then we introduce two maps in a suitable Banach space such that fixed points of these maps are related with shadowing orbits on the universal covering. [ABSTRACT FROM AUTHOR]

In this paper we extend the concept of topological stability from homeomorphisms to group actions on compact metric spaces and prove that if an action of a finitely generated group is expansive and has the pseudoorbit tracing property, then it is topologicaly stable. This represents a group action version of P. Walter's stability theorem [Lecture Notes in Math., vol. 668, Springer, 1978, pp. 231-244]. Moreover we give a class of group actions with topological stability or pseudo-orbit tracing property. In particular, we establish a characterization of subshifts of finite type over finitely generated groups in terms of the pseudo-orbit tracing property. [ABSTRACT FROM AUTHOR]

We present a novel algorithm to calculate radiative energy transfer rates in Discrete Element Method (DEM)-based simulations of mono-disperse spheres. To verify our algorithm we use the Finite Volume Method (FVM) which enables us to picture relevant radiation phenomena in a dense bed of particles. These phenomena include (i) shadowing, (ii) emission and (iii) adsorption by a constant gray medium. After careful verification, we embed our algorithm in LIGGGHTS , a solver for the DEM. A combination of LIGGGHTS and a solver for intra-particle temperature gradients, i.e., ParScale , is then used to quantify the relevance of radiative heat transfer rates in sheared particles beds. Specifically, we evaluate the relative contributions of conductive, convective and radiative thermal fluxes in granular shear flows of frictional inelastic spheres. We find that the radiative flux can be collapsed onto single curve if it is related to an appropriate dimensionless group. Our analysis establishes a rationale on when radiative heat transfer in dense granular flows should be considered or not. Also, our results can be used to close continuum-based granular dynamics model that aim on predicting the particle temperature distribution under extreme temperature scenarios. [ABSTRACT FROM AUTHOR]

Many methods have been employed to detect, compare, and correct errors to increase communication reliability and efficiency in wireless sensor networks (WSNs). However, to the best of our knowledge, no existing study has compared the performance of error control codes by using different modulation techniques in a smart grid communication environment when multichannel scheduling is used. This paper presents a detailed performance evaluation and makes a comparison of different modulation techniques, such as frequency shift keying (FSK), differential phase shift keying (DPSK), binary phase shift keying (BPSK), and offset quadrature phase-shift keying (OQPSK), using Hamming codes in a 500-kV line-of-sight substation smart grid environment with multichannel scheduling. A link-quality-aware routing algorithm is used as a routing protocol and a log-normal shadowing channel is employed as a channel model. Simulations are performed in MATLAB and the performance of the Hamming code with various modulation techniques is compared with the results obtained without using any error correction codes for throughput, delay, and bit error rate. The results show that the performance of the Hamming code with OQPSK modulation is better than its performance with other modulation techniques. Moreover, the results show that the performance of Hamming code improves with multichannel scheduling for all modulation techniques. [ABSTRACT FROM AUTHOR]

The notion of shadowable points was introduced by Morales in his recent paper (2016,Dynamical Systems). A shadowable point of a continuous map or a homeomorphism is defined to be a point such that the shadowing lemma holds for pseudo orbits passing through the point. In this paper, as a quantitative version of the shadowable points, we study shadowable points with a given shadowing accuracy, and prove a quantitative version of Morales’ theorem in his paper above. In addition, we answer two questions on shadowable points asked in the paper. [ABSTRACT FROM PUBLISHER]

In this work we consider a dissipative reaction–diffusion equation in a d -dimensional thin domain shrinking to a one dimensional segment and obtain good rates for the convergence of the attractors. To accomplish this, we use estimates on the convergence of inertial manifolds as developed previously in [6] and Shadowing theory. [ABSTRACT FROM AUTHOR]

We study the computational complexity of some problems which arise in the dynamics of certain hyperbolic toral automorphisms, using the shadowing lemma. Given p , q ∈ T 2 , saddles of common period n , and rational r > 0 sufficiently small, we study how quickly orbits ( f n ) N ( z ) ​transit from a basin of p , the open ball B ( p , r ) to one of q , B ( q , r ) . A priori, z is of arbitrary precision. We compute a finite precision L , polynomial in the size of an instance, so that if an orbit ( f n ) N ( z ) makes such a transition, so does a reliable L -precision pseudo-orbit, but at the price of possibly using duration N + 1 . If we allow duration N + 2 , this precision depends on n and r but is independent of N . It follows that in an appropriate model of computation such a saddle transition problem is in Oracle NP i.e. in NP up to a restricted oracle, and we show there exist closely related problems which are in NP . [ABSTRACT FROM AUTHOR]

Facets shadowing test is time-consuming and inefficient in calculation of radar cross section utilizing physical optics (PO). A novel method is proposed in this paper by covering the target by overlapped spheres which divide the facets to several consistent groups. In order to ensure that every facet is included by at least one sphere, the adjacent spheres must have a common area and some facets may be included by more than one sphere. Spheres’ shadowing tests are conducted before the facets’ tests. If one sphere does not shadow the facet under testing, then the facet cannot be shadowed by any facet within the sphere. Otherwise, every facet within the sphere should be judged whether to shadow the facet. Numerical simulation is conducted to validate the efficiency and accuracy of the algorithm. The spheres’ size on performance of the algorithm is also discussed in this paper and an optional choice of the parameter is achieved resulting 89% time saving. [ABSTRACT FROM AUTHOR]

Miniature GPS devices now allow for measurement of the movement of animals in real time and provide high- quality and high-resolution data. While these new data sets are a great improvement, one still encounters some measurement errors as well as device failures. Moreover, these devices only measure position and require further reconstruction techniques to extract the full dynamical state space with the velocity and acceleration. Direct differentiation of position is generally not adequate. We report on the successful implementation of a shadowing filter algorithm that (1) minimizes measurement errors and (2) reconstructs at the same time the full phase-space from a position recording of a flying pigeon. This filter is based on a very simple assumption that the pigeon's dynamics are Newtonian. We explore not only how to choose the filter's parameters but also demonstrate its improvements over other techniques and give minimum data requirements. In contrast to competing filters, the shadowing filter's approach has not been widely implemented for practical problems. This article addresses these practicalities and provides a prototype for such application. [ABSTRACT FROM AUTHOR]

We prove that the geodesic flow on closed surfaces displays a hyperbolic set if the shadowing property holds C 2 -robustly on the metric. Similar results are obtained when considering even feeble properties like the weak shadowing and the specification properties. Despite the Hamiltonian nature of the geodesic flow, the arguments in the present paper differ completely from those used in Bessa et al. (2013) for Hamiltonian systems. [ABSTRACT FROM AUTHOR]

We call that a flow has the orbital shadowing property if for any ε > 0 there is d > 0 such that, for any d -pseudo orbit g ( t ) there exists an orbit Orb ( x ) satisfying d i s t H ( g ( t ) ‾ , Orb ( x ) ‾ ) < ε . In this paper, we show that the C 1 -interior of the set of 3-dimensional flows having the orbital shadowing property is contained in the set of Ω-stable 3-flows. [ABSTRACT FROM AUTHOR]

This paper analyse and investigate the performance of communication system with maximal ratio combining (MRC) and selection combining (SC) over Inverse Gaussian (IG) fading distribution. All formats of coherent and non-coherent modulation schemes are considered and novel analytical expressions of average symbol error probability (ASEP) with diversity are derived. Gamma and IG fading distributions are popularly used as a mathematically less complex solution to lognormal in the open literature. Hence, we provide a comparative analysis between IG and gamma fading with the aim to provide a quantitative measure of the difference between the two distributions in the context of ASEP. Moreover, the novel closed-form expressions of channel capacity under transmission schemes such as optimal rate adaptation (ORA) and channel inversion fixed rate (CIFR) are derived and analysed with MRC and SC diversity over IG fading. The analytical results have been validated with the Monte Carlo simulations and the exact numerical results. [ABSTRACT FROM AUTHOR]

We present a mechanism for Arnold diffusion based on intertwining homoclinic orbits to a normally hyperbolic invariant manifold, followed for long time intervals, with orbits of the dynamics restricted to that manifold, followed for short time intervals. The resulting trajectories are rather fast, and their construction is explicit, so they can be used in concrete applications. The method to construct such orbits relies mainly on correctly aligned windows and does not require the use of delicate analytical methods such as averaging or KAM, nor the convexity assumptions of variational methods. It only requires control of the inner dynamics over short times, and so it allows easy verification of the hypotheses with finite precision numerical calculations. As an illustration of this mechanism, we consider a geodesic flow on a compact manifold with a generic (Riemannian, Finsler or Lorentz) metric, subject to time-dependent perturbations via a generic potential. The genericity conditions are given explicitly. The perturbation is driven by a flow on an external manifold which satisfies some mild recurrence condition. Periodic and quasiperiodic perturbations are included, and there are many others. We show the existence of trajectories whose energy grows to infinity, as well as of trajectories that follow prescribed energy paths. The trajectories can be constructed to diffuse at speeds that match upper bounds. While the study of perturbations of the geodesic flow is a classical problem, we use it mainly to showcase the main ingredients of the method in a simple way. Other results related to ours exist in the literature, but the trajectories we obtain are different from the previously constructed ones. Our approach is flexible enough to be widely applicable; some applications to the restricted three-body problem involving also numerical calculations are in progress. [ABSTRACT FROM AUTHOR]

We consider the point process of signal strengths emitted from transmitters in a wireless network and observed at a fixed position. In our model, transmitters are placed deterministically or randomly according to a hard core or Poisson point process, and the signals are subjected to power law propagation loss and random propagation effects that may be correlated between transmitters. We provide bounds on the distance between the point process of signal strengths and a Poisson process with the same mean measure, assuming correlated log-normal shadowing. For “strong shadowing” and moderate correlations, we find that the signal strengths are close to a Poisson process, generalizing a recently shown analogous result for independent shadowing. [ABSTRACT FROM AUTHOR]

Physical optics (PO) is an efficient method in calculation of complex electrically large object’s (CELO) radar cross section (RCS). According to PO’s assumptions, only the illuminated part of the target has contributions to electromagnetic scattering. This paper represents a novel method that covers the target by overlapped cubes which separate the facets to several consistent groups. To make sure every facet is contained in at least one cube, the cubes might have common domain and some facets in the domain are included in more than one cube. Cubes’ shadowing tests are conducted before facets’ tests. If the cube does not shadow the point to be tested, then it means that all of the facets within the cube cannot shadow the point and they needn’t more test. Otherwise, every facet within the cube should be tested whether or not shadowing the point. Through this process, much time in shadowing tests is saved. Computation experiment validates the accuracy and efficiency of the algorithm. This paper also discussed the influence of the cubes’ size on performance of the algorithm. If proper parameters are chosen, the time saved can be up to 90%. [ABSTRACT FROM AUTHOR]

This paper describes the effective solid angle improvement achieved using a large-area silicon drift detector together with a virtual-pivot double-tilt specimen holder. The virtual-pivot mechanism enables various designs of specimen-retaining and can reduce the shadowing effect. Energy-dispersive X-ray spectra were measured and converted into effective solid angles using different types of specimen holders and specimens. The investigated shadowing-free mechanical system yielded effective solid angles approaching the nominal solid angle of 0.464 sr. In addition, we have demonstrated the availability of the plastic (polyetheretherketone) specimen holder for low system noise. [ABSTRACT FROM AUTHOR]

This paper develops a variant of the Least Squares Shadowing (LSS) method, which has successfully computed the derivative for several chaotic ODEs and PDEs. The development in this paper aims to simplify Least Squares Shadowing method by improving how time dilation is treated. Instead of adding an explicit time dilation term as in the original method, the new variant uses windowing, which can be more efficient and simpler to implement, especially for PDEs. [ABSTRACT FROM AUTHOR]

We report a study on prediction in shadowing and simultaneous interpreting (SI), both considered as forms of real-time, 'online' spoken language processing. The study comprised two experiments, focusing on: (i) shadowing of German headfinal sentences by 20 advanced students of German, all native speakers of English; (ii) SI of the same sentences into English head-initial sentences by 22 advanced students of German, again native English speakers, and also by 11 trainee and practising interpreters. Latency times for input and production of the target verbs were measured. Drawing on studies of prediction in English-language reading production, we examined two cues to prediction in both experiments: contextual constraints (semantic cues in the context) and transitional probability (the statistical likelihood of words occurring together in the language concerned). While context affected prediction during both shadowing and SI, transitional probability appeared to favour prediction during shadowing but not during SI. This suggests that the two cues operate on different levels of language processing in SI. [ABSTRACT FROM AUTHOR]

Path loss models are the most fundamental part of wireless propagation channel models. Path loss is typically modelled as a (single-slope or multi-slope) power-law dependency on distance plus a log-normally distributed shadowing attenuation. Determination of the parameters of this model is usually done by fitting the model to results from measurements or ray tracing. The authors show that the typical least-square fitting to those data points is inherently biased to give the best fitting to the link distances that happen to have more evaluation points. A weighted fitting method is developed that emphasises the accuracy at the distance range that is consciously chosen by the user as most important for a system simulation. As a further important point that is typically not taken into account for path loss parameter extraction, the authors show that typically measurement data (but also ray tracing) is censored, i.e. path loss values above a certain threshold cannot be measured. The authors present examples of weighted fitting models, and models with and without the censored data, for 28 GHz channels in urban macrocells, and show that these effects have a significant impact on the extracted parameters and that the fitting accuracy can be improved with the presented methods. [ABSTRACT FROM AUTHOR]

Prior work has addressed the effects of multipath fading and path loss separately for broadcast and multiple-access channels. It has been shown that the number of simultaneously active users are of the order $$\Theta (\ln (\ln (n)))$$ for random channel gains with exponentially-decaying tails, where n is the total number of users. Furthermore, it has been shown that assuming path loss is dominant and ignoring multipath fading, the user capacity (i.e. the maximum number of simultaneously active users in a wireless system) of multi-user channels is of the order $$\Theta (\ln (n))$$ when the users are spatially distributed on the plane with a Gaussian or Uniform distribution. In this paper, we study the shadowing effects on the number of active users for broadcast and multiple-access channels in which the users are randomly distributed on the plane. It is shown that as the total number of users in the multi-user channel goes to infinity, the number of active users is of the order $$\Theta (\sqrt{\ln (n)}).$$ [ABSTRACT FROM AUTHOR]

Shadow effects at collisions of hadrons with light nuclei at high energies were subject of scientific interest of V.N. Gribov, first, we mean his study of the hadron-deuteron scattering, see Sov. Phys. JETP 29, 483 (1969) [ Zh. Eksp. Teor. Fiz. 56, 892 (1969)] and discovery of the reinforcement of shadowing due to inelastic diffractive rescatterings. It turns out that the similar effect exists on hadron level though at ultrahigh energies. Diffractive production is considered in the ultrahigh energy region where pomeron exchange amplitudes are transformed into black disk ones due to rescattering corrections. The corresponding corrections in hadron reactions with small momenta transferred (, ) are calculated in terms of the -matrix technique modified for ultrahigh energies. Small values of the momenta transferred are crucial for introducing equations for amplitudes. The three-body equation for hadron diffractive production reaction is written and solved precisely in the eikonal approach. In the black disk regime final state scattering processes do not change the shapes of amplitudes principally but dump amplitudes by a factor ; initial state rescatterings result in additional factor . In the resonant disk regime initial and final state scatterings damp strongly the production amplitude that corresponds to at in this mode. [ABSTRACT FROM AUTHOR]

The dipole phenomenology, which has been quite successfully applied to various hard reactions, especially on nuclear targets, is applied for calculation of Gribov inelastic shadowing. This approach does not include ad hoc procedures, which are unavoidable in calculations done in hadronic representation. Several examples of Gribov corrections evaluated within the dipole description are presented. [ABSTRACT FROM AUTHOR]

The intersection shadow theorem of Katona is an important tool in extremal set theory. The original proof is purely combinatorial. The aim of the present paper is to show how it is using linear independence latently. [ABSTRACT FROM AUTHOR]