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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]

Abstract. In this article, a comparison of signal-to-noise ratio (SNR) and shadowing-based algorithms for ocean wave height estimation from ship-borne X-band nautical radar sea surface images is presented. Modifications, including selecting a subarea along the upwind direction and smoothing the edge pixel intensity histogram, are made to the original shadowing algorithm to achieve more accurate wave height measurements. Tests of the algorithms are conducted using radar and buoy data acquired in a sea trial in the North Atlantic Ocean off the east coast of Canada. Compared with the original shadowing algorithm, the modified algorithm improves the wave height estimation with a decrease of about 1.70 m in the root mean square (RMS) difference with respect to in situ measurements. In addition, the result of the comparison shows that the modified shadowing algorithm produces more accurate wave heights than the SNR method with improvements of about 0.05 in the correlation coefficient and about 0.04 m in the RMS difference. [ABSTRACT FROM PUBLISHER]

In this article, macro-diversity structure with macro-diversity selection combining (SC) receiver and two micro-diversity SC receivers operating over correlated shadowed multipath fading channel are analysed. Received signal is subjected simultaneously to α–µshort-term fading and gamma long-term fading (shadowing) resulting in system performance degradation. Macro-diversity SC receiver aims to reduce gamma shadowing effect while micro-diversity SC receivers aim to mitigate α–μ small-scale multipath fading effects. Useful infinite series expressions for the second-order statistical measure such as level crossing rate (LCR) of macro-diversity SC receiver output signal is efficiently derived. Numerical results are presented to examine the influence of various gamma shadowing and α–µmultipath fading parameters on LCR of the proposed system. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the detection performance of cooperative spectrum sensing (CSS) using energy detector in several fading scenarios. The fading environments comprise relatively less-studied Hoyt and Weibull channels in addition to the conventional Rayleigh, Rician, Nakagami-mand log-normal shadowing channels. We have presented an analytical framework for evaluating different probabilities related to spectrum sensing, i.e. missed detection, false alarm and total error due to both of them, for all the fading/shadowing models mentioned. The major theoretical contribution is, however, the derivation of closed-form expressions for probability of detection. Based on our developed framework, we present performance results of CSS under various hard decision fusion strategies such as OR rule, AND rule and Majority rule. Effects of sensing channel signal-to-noise ratio, detection threshold, fusion rules, number of cooperating cognitive radios (CRs) and fading/shadowing parameters on the sensing performance have been illustrated. The performance improvement achieved with CSS over a single CR-based sensing is depicted in terms of total error probability. Further, an optimal threshold that minimises total error probability has been indicated for all the fading/shadowing channels. [ABSTRACT FROM PUBLISHER]

A shadowing test technique for analysis of practical objects by a non-uniform rational B-spline based high-frequency asymptotic method is presented in this article. A hierarchical space volumetric partitioning data structure is proposed for the shadowing test. The surface area heuristic strategy is employed to govern the construction of the hierarchical space volumetric partitioning in an adaptive and optimized way. The fast ray-patch intersection solving algorithm with linear complexity is developed based on the hierarchical space volumetric partitioning. Finally, using the proposed hierarchical space volumetric partitioning in combination with the methods of the uniform theory of diffraction or physical optics, some electromagnetic scattering and radiation problems are solved successfully. [ABSTRACT FROM AUTHOR]

We introduce a notion of shadowing property for actions of finitely generated groups and study its basic properties. We formulate and prove a shadowing lemma for actions of nilpotent groups. We construct an example of a faithful linear action of a solvable Baumslag–Solitar group and show that the shadowing property depends on quantitative characteristics of hyperbolicity. Finally, we show that any linear action of a non-abelian free group does not have the shadowing property. [ABSTRACT FROM AUTHOR]

Absorption enhancement and shadowing effects were investigated for nigrosin-laden quartz (fibrous), Teflon (matted), and polycarbonate (membrane) filters in inert surroundings at different sample steady-state temperatures and particle mass loadings. Sample absorptivity was determined using a novel laser-heating technique, which is based on perturbing the sample steady-state temperature and monitoring the thermal response during decay back to steady state, along with a model for thermal energy conservation. In addition, transmissivity measurements were carried out to enable determination of the sample absorption coefficient. The results indicated that the isolated-nigrosin absorption coefficient decreased with steady-state temperature and increased with mass loading and filter pore size. Comparing the absorption coefficient for both the isolated nigrosin and nigrosin-laden filters, indicated that absorption enhancement was most significant for the Teflon filters and least significant for the polycarbonate filters. The effect became more significant as the pore size decreased, steady-state temperature increased, and particle mass loading decreased. The decrease in the isolated-nigrosin, mass-specific absorption cross-section with heavier sample loadings was attributed to shadowing effects. Copyright 2014 American Association for Aerosol Research [ABSTRACT FROM AUTHOR]

We prove that Lipschitz inverse shadowing for non-singular flows is equivalent to structural stability. [ABSTRACT FROM AUTHOR]

Language has been proposed as a medium that serves to promote spatial orientation through integrating geometric and featural information (Spelke, 2003). This proposal has been explored in dual-task experiments where linguistic resources are blocked by verbal shadowing. Although some studies report disruption in using environmental cues for spatial reorientation, findings have not been consistently replicated, and the source of disruption to reorientation by verbal shadowing remains unclear. We examined conditions under which verbal shadowing affects reorientation. Shadowing of meaningful language disrupted healthy adults' use of geometric and featural information to reorient only when task instructions were unclear and when extraneous visual information provided a source of nonlinguistic interference. Reorientation was examined during the shadowing of meaningful prose or nonword syllables and was similar under both concurrent task conditions. These results indicate that language is not necessary for spatial cue integration. [ABSTRACT FROM AUTHOR]

Let f be a diffeomorphism of a closed C ∞ manifold M, and let Λ ⊂ M be a closed f-invariant set. We show that if f |Λ is robustly chain transitive with orbital shadowing property, then Λ is a basic set. [ABSTRACT FROM PUBLISHER]

Let Diff(M) be the space of diffeomorphisms of a closed C ∞ manifold M endowed with the C 1-topology, and denote by ℛ(f) the chain recurrent set of f ∈ Diff(M). In this article, we show that C 1-generically f |ℛ(f) has the s-limit shadowing property if and only if f satisfies both Axiom A and no-cycle condition. [ABSTRACT FROM PUBLISHER]

This article introduces the notion of weakly parametrized (wp) shadowing for actions of groups ℤ m  × ℝ n , where m, n ≥ 0 and m + n > 0. The possibility of coexistence of distality and shadowing for actions of ℝ n is discussed. It is proven that an equicontinuous action of ℝ n on a compact connected space possessing wp-shadowing is actually minimal. Moreover, distal real flows (ℝ-actions) on one-dimensional compact metric spaces are characterized as constant-one suspensions over adding machines. [ABSTRACT FROM PUBLISHER]

Mather characterized uniform hyperbolicity of a discrete dynamical system as equivalent to invertibility of an operator on the set of all sequences bounded in norm in the tangent bundle of an orbit. We develop a similar characterization of nonuniform hyperbolicity and show that it is equivalent to invertibility of the same operator on a larger, Fréchet space. We apply it to obtain a condition for a diffeomorphism on the boundary of the set of Anosov diffeomorphisms to be nonuniformly hyperbolic. Finally, we generalize the Shadowing lemma in the same context. [ABSTRACT FROM AUTHOR]

Let f be a C2-diffeomorphism on a closed surface. In this article, we show that if f has the C2-stably inverse shadowing property with respect to the class of continuous methods then (i) f is Kupka-Smale, and (ii) if the periodic points are dense in the non-wandering set Ω(f) and there is a dominated splitting on the closure of periodic points of the saddle type Ph(f), then f satisfies both Axiom A and the strong transversality condition. [ABSTRACT FROM AUTHOR]

When solving scattering or emissivity problems for rough surfaces, the shadowing effect is often taken into account. Furthermore, for rough surfaces with large root mean square slope, surface reflections of the incidence or emission ray should not be neglected, especially at large observation angles. In this paper, a model of the monostatic statistical illumination function for one-dimensional rough surfaces with single surface reflection is developed, which is based on the Smith illumination function. A Monte Carlo ray-tracing algorithm is used to evaluate the accuracy of the present model. It is shown that, when neglecting the correlation between heights and slopes of the surface, the present model agrees quite well with the Monte Carlo result. Moreover, the result is improved if the correlation between heights and slopes is taken into account. For practical purposes, an empirical factor is introduced to improve the performance of the uncorrelated first-order illumination function to avoid computing the correlated one, which takes a long computation time. Besides, the first-order illumination function is significant at large observation angles, which could be promising to overcome problems in models of surface infrared emissivity where underestimation occurs compared with experimental measurements. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to relate a recently introduced notion of the asymptotic average shadowing property (AASP) with other notions known from topological dynamics. For a compact metric space X and a continuous map [image omitted] we prove the following facts: If f has the AASP and the minimal points of f are dense in X then f is totally transitive.If f is a surjection and has the specification property then f has the AASP.If f is c-expansive and has the shadowing property then f is mixing if and only if f has the AASP. [ABSTRACT FROM AUTHOR]

Let M be a topological manifold admitting a finite decomposition into sets homeomorphic to a closed ball. In this paper, we prove that a C0 generic discrete dynamical system on M has a (periodic) inverse shadowing property with respect to some class of continuous methods. [ABSTRACT FROM AUTHOR]

Measurement results for human body shadowing and local environmental effects in short-range indoor radio channels are presented. A narrowband measurement system, comprising a signal generator, two identical triangular monopoles and a spectrum analyser, was used in the measurements. When the radio link was periodically blocked by a human body with various objects in and around the link, fading depths of up to 15 dB and even more were observed at spot frequencies of 3-11 GHz band. Standard deviation and its range for human body blockage are estimated for different radio link scenarios simulating real environments. The distribution of human body shadowing was analysed and compared with known distribution functions. [ABSTRACT FROM AUTHOR]

It is shown how known results for autonomous difference equations can be adapted to definitions of semi-hyperbolicity and bi-shadowing generalized to nonautonomous difference equations with Lipschitz continuous mappings. In particular, invertibility and smoothness of the mappings are not required and, for greater applicability, the mappings are allowed to act between possibly different Banach spaces. [ABSTRACT FROM AUTHOR]

In order to accurately predict the effects of ocean roughness on forward radar propagation, it is important to incorporate the relevant physical scattering mechanisms. Shadowing is one such mechanism that is particularly important for low-grazing incidence yet it is often not taken into account. One broad class of approximations defines a roughness reduction factor in terms of an ensemble average over surface heights of a Rayleigh phase factor. The widely used Ament approximation and Miller-Brown approximation are two examples from this class of approximations that do not incorporate shadowing. In this paper, we use this class of approximations to develop a 'shadowed' approximation that implements a probability density function (PDF) for a rough sea surface illuminated at grazing incidence. A rigorous method of moments calculation is used to compare and quantitatively assess the accuracy of the Ament, Miller-Brown, and shadowed approximations at horizontal polarization. It is shown that the shadowed approximation yields significantly more accurate results than either the Ament or Miller-Brown approximation. In addition, these three approximations are compared with experimental data and it is shown that the shadowed approximation is in good agreement with the data. Finally, numerical curve fitting is used to develop a simple analytical expression for a roughness reduction factor that incorporates shadowing. [ABSTRACT FROM AUTHOR]

This paper proposes a secret image sharing scheme based on only ADDITION operation to embed a grey level or colour secret image into two or more shadow images. In this scheme, the secret image cannot be reconstructed until all the shadow images have been collected. The secret image can be losslessly recovered. Since only ADDITION operation is used in both creating the shadow images and recovering the secret image, it can be easily and quickly implemented so that this property is very important for many embedded systems, i.e. mobile equipments. [ABSTRACT FROM AUTHOR]

In this article, we study a certain shadowing property on well-known two-dimensional maps presented by Lozi with the y-axis as their singularity set and strange attractors. Our main theorem shows that there exists a nonempty open subset [image omitted] of the Misiurewicz domain [image omitted] such that, for any [image omitted], the Lozi map La, b with strange attractor has the parameter-shifted shadowing property. [ABSTRACT FROM AUTHOR]

Mantissa distributions generated by dynamical processes continue to attract much interest. In this article, it is demonstrated that one-dimensional projections of (at least) almost all orbits of many multi-dimensional nonautonomous dynamical systems exhibit a mantissa distribution that is a convex combination of a trivial point mass and Benford's Law, i.e. the mantissa distribution of the non-trivial part of the orbit is asymptotically logarithmic, typically for all bases. Both linear and power-like systems are considered, and Benford behaviour is found to be ubiquitous for either class. The results unify previously known facts and extend them to the nonautonomous setting, with many of the conclusions being best possible in general. [ABSTRACT FROM AUTHOR]

We introduce the notion of inverse shadowing for continuous flows, and show that a structurally stable flow generated by a C1 vector field on a compact smooth manifold has the inverse shadowing property with respect to the classes of continuous methods. [ABSTRACT FROM AUTHOR]

We show how to obtain information about the dynamics of a two-dimensional discrete-time system from its homoclinic and heteroclinic orbits. The results obtained are based on the theory of ' trellises ', which comprise finite-length subsets of the stable and unstable manifolds of a collection of saddle periodic orbits. For any collection of homoclinic or heteroclinic orbits, we show how to associate a canonical ' trellis type ' which describes the orbits. Given a trellis type, we show how to compute a ' graph representative ' which gives a combinatorial invariant of the trellis type. The orbits of the graph give the dynamics forced by the homoclinic/heteroclinic orbits in the sense that every orbit of the graph representative is ' globally shadowed ' by some orbit of the system, and periodic, homoclinic/heteroclinic orbits of the graph representative are shadowed by similar orbits. [ABSTRACT FROM AUTHOR]

Let f be a C[sup 2]-diffeomorphism on a closed surface. In this paper, we show that if f satisfies shadowing stably in the C[sup 2]-topology, then (i) f is Kupka-Smale, (ii) if, in addition, the periodic points are dense in the non-wandering set and there is a dominated splitting on the closure of periodic points of saddle type, then f satisfies both Axiom A and the strong transversality condition. [ABSTRACT FROM AUTHOR]

Areas of high concentrations of particulates in the urban atmosphere are hypothesized to strongly influence the solar receipt in nearby nonpolluted regions. Reductions of solar radiation in oonpolluted areas by upsun high aerosol regions are computed using a three-dimensional multi-scattering radiation model for specified solar-elevation classes. Numerical simulations from this model indicate that reductions exceeding 10 percent can occur several kilometers downsun of even moderately polluted regions in the early morning (i.e., periods of low solar-elevation angle). Although the reductions in global radiation are quite pronounced in the early day, they are generally overwhelmed in the daily total because of the relatively small amount of radiation associated with low-elevation angles. A series of simulations for three representative latitudes (33°N, 43°N and 53°N) demonstrate that the areal extent of the shadowing is highly dependent on latitude. Reductions in solar radiation exceeding 3 percent occur 15 km down range of the center of pollution for high-latitude (53°N) locations during early-morning, low-elevation angle periods. Such excessive solar attenuation in nonpolluted regions may affect the site selection of solar power facilities, the planning and siting of parks, golf courses and other recreational activities, the migration and tourism trends in areas experiencing seasonal population changes (i.e., the sunbelt states), and the temperature regime of the region. [ABSTRACT FROM AUTHOR]