Sharif Digital Repository

A new method is proposed to analyze stability of descriptor systems with multiple commensurate time-delays. In this method, purely imaginary roots of the system are calculated, asymptotic behavior of root path at these roots is studied, and unstable regions of the system in the space of delays are determined. Moreover, the number of roots in each unstable region is calculated. Also necessary and sufficient conditions for τ-stabilizability of these systems are presented. Examples are provided to illustrate the effectiveness and validity of the proposed method. © 2019 The Franklin Institute  

In this paper, we consider abnormality detection via diffusive molecular communications (MCs) for a network consisting of several sensors and a fusion center (FC). If a sensor detects an abnormality, it injects a number of molecules into the medium which is proportional to its sensing output. Two transmission schemes for releasing molecules into the medium are considered. In the first scheme, each sensor releases a different type of molecule (DTM), whereas in the second scheme, all sensors release the same type of molecule (STM). The molecules released by the sensors propagate through the MC channel and some may reach the FC where the final decision regarding whether or not an abnormality... 

The waist parameter is a particularly important factor for functional expansion in terms of localized orthogonal basis functions. We present a systematic approach to evaluate an asymptotic trend for the optimum waist parameter in truncated orthogonal localized bases satisfying several general conditions. This asymptotic behavior is fully introduced and verified for Hermite - Gauss and Laguerre-Gauss bases. As a special case of importance, a good estimate for the optimum waist in projection of discontinuous profiles on localized basis functions is proposed. The importance and application of the proposed estimation is demonstrated via several optical applications  

Modeling the mechanical behavior of asphalt binders and mixtures has been the subject of intensified research in recent decades. Master curves of the norm of the complex modulus |G*| in the linear viscoelastic domain are frequently used for modeling, while phase angle master curves are less frequently considered for this purpose. Therefore in this research, an empirical model is introduced for phase angle master curves of modified and neat bituminous binders. The model is based on a general form of a double-logistic (DL) mathematical function. The |GG*| master curve was then modeled using a mutual relationship between the phase angle and |GG*|. Master curves of three neat and seven modified... 

We introduce a definition of the notion of compressibility for infinite deterministic and i.i.d. random sequences which is based on the asymptotic behavior of truncated subsequences. For this purpose, we use asymptotic results regarding the distribution of order statistics for heavy-tail distributions and their link with α -stable laws for 1<α<2. In many cases, our proposed definition of compressibility coincides with intuition. In particular, we prove that heavy-tail (polynomial decaying) distributions fulfill the requirements of compressibility. On the other hand, exponential decaying distributions like Laplace and Gaussian do not. The results are such that two compressible distributions... 

Sufficient conditions for the boundedness and regularity of a function, whose partial derivatives satisfy a certain set of equations, are presented. Energy methods are used to establish these results. The asymptotic behavior of the gradient toward a constant function is also investigated. © Sharif University of Technology  

We study the asymptotic behavior of the capacity of erasure networks under a restricted class of network coding schemes, called spatial network coding. In spatial network coding, nodes are permitted to only combine data units received from distinct incoming links; multiple data units arriving on the same link may not be coded together. Elsewhere, it has been shown that the network capacity under spatial network coding is the statistical mean of the minimum cut value. In this paper, we come up with a new concept in the random graph theory referred to as typical min-cut family, which parallels the information theoretic notion of typical sequences, and use it to develop an analytical tool for... 

We study the homogenization of semilinear elliptic equations in divergence form with discontinuous oscillating coefficients in the whole ℝN. As is well known, the homogenization process in a classical framework is concerned with the study of asymptotic behavior of solutions u Isin; of boundary value problems when the period ∈ > 0 of the coefficients is small. By extending some of the classical homogenization results for quasi-linear elliptic equations to unbounded domains and, making use of various variational techniques, we shall establish some stability results under Γ-convergence of least energy solutions for such boundary value problems  

Conducting interfaces and nano conducting layers can support surface electromagnetic waves. Uniform charge layers of non-zero thickness and their asymptotic behavior toward conducting interfaces of infinitely small thicknesses, where the thin charge layer is modeled via a surface conductivity σ s , are already studied. Here, the possible effects of inhomogeneity in the conductivity profile of the thin conducting layers are investigated for the first time and a new approximate yet accurate enough analytical formulation for mode extraction in such structures is given. In order to rigorously analyze the structure and justify the proposed approximate formulation, the Galerkin's method with... 

Recently, electromagnetic slow wave propagation in Kronig-Penny photonic crystals composed of conducting interfaces constituted of extremely thin charge layers has been studied, where analytic expressions for Bloch wave numbers in terms of normalized frequency were derived, asymptotic behavior of electromagnetic slow wave propagation in these structures was investigated at different regimes, and the possibility of observing forbidden spatial frequencies was numerically demonstrated. In this manuscript, the existence and electromagnetic behavior of such waves together with the possibility of having forbidden spatial frequency are investigated by taking the finiteness of charge layer thickness... 

Recently, a group of novel devices based on conducting interfaces has been proposed. These conducting interfaces can be implemented by using the inversion layer of MOS structures, trapped charges or depletion layer charges. It has been shown that these structures can support surface electromagnetic waves. In this paper, the coupling of surface electromagnetic waves supported by nano charge layers is analyzed and its asymptotic behavior toward conducting interfaces, where the thin charge layer of finite thickness is modeled via a surface conductivity σs, is numerically studied for the first time. The numerical results driven by coupled mode theory approach are justified by solving exact... 

In this paper, the analytical solution to a new class of nonlinear solitons is presented with cubic nonlinearity, subject to a dissipation term arising as a result of a first-order derivative with respect to time, in the weakly nonlinear regime. Exact solutions are found using the combination of the perturbation and Green's function methods up to the third order. We present an example and discuss the asymptotic behavior of the Green's function. The dissipative solitary equation is also studied in the phase space in the non-dissipative and dissipative forms. Bounded and unbounded solutions of this equation are characterized, yielding an energy conversation law for non-dissipative waves....