Sharif Digital Repository

The purpose of this paper is to describe a simple proof for a result originally presented by H. Brezis in [B], with roots in J. Bourgain, H. Brezis and P. Mironescu [BBM]. © 2020 University of Houston  

We present in this paper a general analytical solution to the integral equations of liquid state theories (Born-Green-Yvon, hyper-netted-chain, and Percus-Yevick Equations) at low-density limit for potentials with a hard core. For the specific case of the Lennard-Jones potential with a hard core, we have derived an analytical function for the radial distribution function at high temperature and low density. We have noted that this function has two humps which is the characteristic feature of the radial distribution function at low densities. In addition, this function has been used to calculate the third virial coefficient for such a fluid exactly. We see that for the especial case of... 

In this article, we solve the problem of minimizing the difference of dual functions of two coradiant functions. We do this by applying a type of duality, that is used in microeconomic theory. Indeed, the dual function of a co-radiant function is decreasing and inverse coradiant. So, we first give various characterizations for the maximal elements of the support sets of this class of functions. Next, by using these results, we obtain the necessary and sufficient conditions for the global minimizers of the difference of two decreasing and inverse coradiant functions. Finally, as an application, we present the necessary and sufficient conditions for the global minimizers of the difference of... 

This paper deals with the question of nonexistence of limit cycles in two famous classes of predator-prey systems. We present some sufficient conditions for the nonexistence of limit cycles in these systems. Our results extend and improve the results presented by Moghadas. © 2005 Elsevier Inc. All rights reserved  

Tailoring the electronic properties of graphene is of fundamental interest regarding its application in electronic devices. One of the key strategies is chemical functionalization which modifies the p-electron system and thus can induce band gaps. However, in order to control the degree of functionalization it is crucial to know the exact amount of the chemisorbed species. We show with angle-resolved photoemission spectroscopy (ARPES) the formation of a band gap in graphene and estimate the hydrogen coverage from the scattering rate. Using X-ray photoemission spectroscopy (XPS) we identify the chemical environments in hydrogenated graphene and determine the total hydrogen to carbon... 

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  

We propose a theoretical scheme for teleportation of a general wave function of a quantum object. In principle, this protocol provides teleportation of discrete N-level spatial states of an object with various degrees of freedom, e.g. spin, in ordinary three-dimensional space. All necessary Bell states and their corresponding operators to measure and reconstruct the initial state are represented. © 2006 World Scientific Publishing Company  

In this paper, the third order differential equation x‴ + ψ (x′)x″ + (κ2 +ø (x))x′ + f(t, x = e(t) is considered. Under certain conditions on the functions appearing in the differential equation, the existence of periodic solutions is proved. Similar problems have been treated by authors in [4,6,7]. However, the method employed here is used by Reissig [1] and the results obtained are, in fact, a generalization of those in [1-3]. The conditions imposed on the nonlinear terms do not require the ultimate boundedness of all solutions. © Sharif University of Technology  

Performance enhancement of supercapacitors has been recently discussed. In this paper a novel and facile procedure for functionalization of graphene with some electroactive molecules is presented. The graphene has been functionalized by catechol-based molecules, which are electroactive molecules with electrochemically reversible properties. The functionalized graphene exhibits very effective pseudocapacitor behaviorfor charge storage. For the first time, with the aim of an electrosynthesis procedure, catechol is covalently attached on graphene sheets. This attachment has been investigated by electrochemical, X-ray photoelectron spectroscopy and attenuated total reflectance methods. Catechol... 

This paper makes a case for writing unrestricted eBPF network functions which then get automatically decomposed between kernel and user-space. © 2021 Owner/Author  

This paper deals with the identification of fractional-order systems through orthogonal rational functions. Fractional systems are characterized by their non-exponential aperiodic multimodes; therefore, fractional orthogonal rational functions provide better approximating models with fewer parameters. In spite of the fact that the Laguerre-based model is simple, it is, to some extent, deficient at high frequencies. Motivated by this objective, the use of a Legendre basis which has progressive pole locations and can be expected to perform better at high frequencies is studied  

In this paper, we introduce the problem of private sequential function computation, where a user wishes to compute a composition of a sequence of K linear functions, in a specific order, for an arbitrary input. The user does not run these computations locally, rather it exploits the existence of N non-colluding servers, each can compute any of the K functions on any given input. However, the user does not want to reveal any information about the desired order of computations to the servers. For this problem, we study the capacity, defined as the supremum of the number of desired computations, normalized by the number of computations done at the servers, subject to the privacy constraint. In... 

Multivariate interpolation and approximation is a powerful tool for intuition of real world. In this paper we study Lebesgue function and Lebesgue constant for multivariate interpolation by conditionally positive definite RBFs. Also we give a conjecture about similar Bernstein and Erdös problem to multivariate case. © 2006 Elsevier Inc. All rights reserved  

Let D be a division ring with center F. An element of the form xyx -1y-1 ∈ D is called a multiplicative commutator. Let T(D) be the vector space over F generated by all multiplicative commutators in D. In this paper it is shown that if D is algebraic over F and Char(D) = 0, then D = T(D). We conjecture that it is true in general. Among other results it is shown that in characteristic zero if T(D) is algebraic over F, then D is algebraic over F  

As it is found in the related published literatures, the transfer function (TF) evaluation method is the most feasible method for detection of winding mechanical faults in transformers. Therefore, investigation of an accurate method for evaluation of the TFs is very important. This paper presents three new indices to compare the transformer TFs and consequently to detect the winding mechanical faults. These indices are based on estimated rational functions. To develop the method, the necessary measurements are carried out on a 1.3 MVA transformer winding, under intact condition, as well as different fault conditions (axial displacement of winding). The obtained results demonstrate the high... 

A gauge invariant partition function is defined for gauge theories which leads to the standard quantization. It is shown that the descent equations and consequently the consistent anomalies and Schwinger terms can be extracted from this modified partition function naturally  

The fracture phenomenon is defined via the change of state of structure (entity) between the intact and the fractured end states as the function of the state variable. The twin state functions are defined for the transition of unit of the entity between its two end states. The state ratio is defined as the ratio of the two state functions. The property of the cracked structure is defined as the product of the structure property and the state ratio. The work is then used to derive the main parameters of the fracture mechanics. The work is verified via five examples. © 2016, Springer-Verlag Berlin Heidelberg  

A utility function is an important tool for representing a DM’s preference. We adjoin utility functions to multi-objective optimization problems. In current studies, usually one utility function is used for each objective function. Situations may arise for a goal to have multiple utility functions. Here, we consider a constrained multi-objective problem with each objective having multiple utility functions. We induce the probability of the utilities for each objective function using Bayesian theory. Illustrative examples considering dependence and independence of variables are worked through to demonstrate the usefulness of the proposed model. © 2017, The Author(s)