Sharif Digital Repository

This article presents a new model for pricing a new product considering a skimming pricing strategy in the presence of competition. We consider two periods for price setting, including skimming and an economy period. The problem is to decide on skimming as well as economy price, in order to maximize total profit. The derived model is a non-linear programming model and we have analyzed the structure and properties of an optimal solution to develop a solution method. Analytical results, as well as managerial insights, are presented by mathematical and numerical analyses  

In this paper, we present a multi-user resource allocation framework using fragmented-spectrum synchronous OFDM-CDMA modulation over a frequency-selective fading channel. In particular, given pre-existing communications in the spectrum where the system is operating, a channel sensing and estimation method is used to obtain information of subcarrier availability. Given this information, some real-valued multi-level orthogonal codes, which are orthogonal codes with values of {±1, ±2, ±3, ±4,...}, are provided for emerging new users, i.e., cognitive radio users. Additionally, we have obtained a closed form expression for bit error rate of cognitive radio receivers in terms of detection... 

This paper deals with the problem of static instability of nano switches under the effect of Casimir force and electrostatic actuation. The nonlinear fringing field effect has been accounted for in the model. Using a Galerkin decomposition method and considering only one mode, the nonlinear boundary value problem describing the static behavior of nano-switch, is reduced to a nonlinear boundary value ordinary differential equation which is solved using the homotopy perturbation method (HPM). In order to ensure the precision of the results, the number of included terms in the perturbation expansion has been investigated. Results have been compared with numerical results and also with... 

At the present research, a new analytical model is developed for the impact of a deformable blunt projectile to metallic targets using the plastic stress wave propagation theory and the momentum equations. At this model, the deformation of the projectile is considered, too. Also, the effects of dishing and plugging phenomena on failure of the target are investigated. All of the obtained results are compared with the experimental and other available analytical results where good agreement has been observed. The other outcome of this research is a new definition for the penetration stages which includes 9 ones. Motion equations are derived for each of these stages, accordingly  

In this work, we study the conductance of a general periodic quantum dot (QD) attached to ideal semi-infinite uniform metallic leads (nanocrystals), fully analytically. We propose a new general formula which relates conductance to transfer matrix (TM) for an isolated cell in the periodic dot. The equation describes exactly the dependence of the transmission coefficient (TC) on Fermi energy, dot-size, dot-lead coupling, and gate voltage for an arbitrary periodic dot. Then, we derive a nonlinear equation which gives the resonance, bound, and surface state energies. Finally, the TC has been calculated for gapless, single, and double gap models exactly. Moreover, we have also calculated the... 

In this paper, we study the coherent electronic transport of a periodic quantum wire (P-QW) such as poly-acetylene connected to uniform metallic leads, within the tight-binding (TB) approach and in the ballistic regime. We have calculated the Green's function (GF), density of states (DOS) and the coherent transmission coefficient (TC) fully exactly for a quantum wire. The quasi gap and the energy and wire-length dependence of the GF and conductance for the system are also derived. Finally, we obtain a non-linear equation which gives the bound state energies. Our calculation can be generalized to arbitrary leads and can be applied to molecular wires, polymers, nanocrystals, where results may... 

A general model for superconducting synchronous machines in which the rotor can be considered as a magnetic or a nonmagnetic material is proposed and analytically investigated. Analytical equations for magnetic flux in different regions of the machine have been developed. Furthermore, nonlinear magnetization of the iron core is studied. In order to solve the equations in the case of the iron saturation, a reiterative algorithm is proposed. Finite-element simulation has also been performed to verify the equations and the proposed algorithm. The obtained analytical results show good agreement with finite-element method results  

In this research, the developing turbulent swirling flow in the entrance region of a pipe is investigated analytically by using the boundary layer integral method. The governing equations are integrated through the boundary layer and obtained differential equations are solved with forth-order Adams predictor-corrector method. The general tangential velocity is applied at the inlet region to consider both free and forced vortex velocity profiles. The comparison between present model and available experimental data demonstrates the capability of the model in predicting boundary layer parameters (e.g. boundary layer growth, shear rate and swirl intensity decay rate). Analytical results showed... 

Resonant interaction between one surface wave and two oblique interfacial waves is analyzed in a three dimensional system of a finite-depth, two-layer fluid. A third order perturbation analysis is carried out to obtain the evolution equations of the waves amplitudes. Taking the waves amplitudes as the perturbation small parameter, the evolution equations of the waves are solved simultaneously to obtain the short and long term behavior of the interfacial waves. In contrast to the second order analysis, the current analysis shows that after an initial exponential growth period, the interfacial waves stop growing and stabilize. Furthermore, the influences of surface wave frequency, density... 

In this paper by solving Dirac equation, we present an analytical solution to calculate energy levels and wave functions of mono- and bilayer graphene quantum dots. By supposing circular quantum dots, we solve Dirac equation and obtain energy levels and band gap with relations in a new closed and practical form. The energy levels are correlated with a radial quantum number and radius of quantum dots. In addition to monolayer quantum dots, AA- and AB-stacked bilayer quantum dots are investigated and their energy levels and band gap are calculated as well. Also, we analyze the influence of the quantum dots size on their energy spectrum. It can be observed that the band gap decreases as quantum... 

In this paper, nonlinear oscillation of a pendulum wrapping and unwrapping around two cylindrical bases is studied and an analytical solution is obtained using multiple scales method. Equations of motion are derived based on energy conservation technique. Applying perturbation method on the equations, nonlinear natural frequency of the system is calculated along with its time response. Analytical results are compared with numerical findings and good agreement is found. Effect of nonlinearity due to large amplitude and radius of cylinders on the system frequency is evaluated. Results indicate that as the radius of cylinder is increased, nonlinear frequency is enhanced. Initial amplitude plays... 

We consider chaperone-assisted translocation of biopolymers with two distinct monomers or bases A and B, with the size of the chaperones being λα, where α is a monomer's size. The probability that A and B are neighbors in the biopolymer is PAB. A master equation is used, together with the detailed-balanced condition, in order to derive analytical results for the statistics of the first-passage times of the biopolymer as a function of PAB, λ, and the biopolymer's configuration. Monte Carlo simulations have also been carried out in order to compute the same quantities for biopolymers with 100-900 monomers and several λ. The results indicate nontrivial dependence of the variance of the... 

Previous studies of analysis and prediction of marine risers responses usually focus on vortex-induced vibration (VIV) of cross-flow (CF) direction rather than in-line (IL). Recent studies show that responses of IL direction tend to dominate in some cases. Responses of long riser due to biaxial bending of IL and CF VIV are investigated. Closed-form formulas are derived for estimating maximum normal stress due to the biaxial moment of CF/IL VIV and relations for estimating biaxial stress using CF values are presented. Analytical results are compared with numerical results of the time domain model and a good correlation is observed. It is shown that for tension and bending-controlled modes of... 

Previous studies of analysis and prediction of marine risers responses usually focus on vortex-induced vibration (VIV) of cross-flow (CF) direction rather than in-line (IL). Recent studies show that responses of IL direction tend to dominate in some cases. Responses of long riser due to biaxial bending of IL and CF VIV are investigated. Closed-form formulas are derived for estimating maximum normal stress due to the biaxial moment of CF/IL VIV and relations for estimating biaxial stress using CF values are presented. Analytical results are compared with numerical results of the time domain model and a good correlation is observed. It is shown that for tension and bending-controlled modes of... 

In this study, the average throughput maximisation of a secondary user (SU) by optimising its spectrum sensing time is formulated, assuming that a priori knowledge of the presence and absence probabilities of the primary users (PUs) is available. The energy consumed to find a transmission opportunity is evaluated, and a discussion on the impacts of the number of PUs on SU throughput and consumed energy are presented. To avoid the challenges associated with the analytical method, as a second solution, a systematic adaptive neural network-based sensing time optimisation approach is also proposed. The proposed scheme is able to find the optimum value of the channel sensing time without any... 

Frame aggregation (FA) mechanisms improve the throughput of WLANs. In this paper, the effect of the FA mechanism on the throughput of wireless local area networks (WLANs) has been investigated. To this end, we propose an analytical model in order to analyze an IEEE 802.11n network comprised of an access point (AP) and several conventional nodes (CNs), all in the coverage area of each other. With respect to the heavier download traffic compared to the upload one, in our scenario, only the AP uses an FA mechanism and the other nodes use the basic IEEE 802.11 standard. In our proposed analytical model, the maximum downlink (DL) throughput is derived. Regarding the asymmetry among nodes, our... 

Link lifetime (LL) analysis is crucially important in designing and evaluating wireless mobile network protocols. Although a considerable amount of research has been conducted on this issue, the current paper studies several aspects of link lifetime for the first time, e.g. a closed form expression for the probability distribution of the residual link lifetime (RLL) for the constant velocity mobility model is obtained, which facilitates marginal studies on the behavior of link lifetime. As a case, using a tail analysis of LL and RLL distributions, we analytically prove that they are heavy-tailed. Using this outcome, a self-similar behavior in the traffic pattern of a sample delay tolerant... 

k-Neigh is a basic neighbor-based topology control protocol based on the construction of k-neighbor graph as logical communication graph. Although k-Neigh is based on a connectivity theory, several topological aspects of the constructed topology are not yet analytically investigated. In this paper, several topological properties of the constructed topology after execution of the protocol, including probability density function of the distance between each node to its ith neighbor, probability of unidirectional links after execution of the first phase of the protocol, average logical degree, and average final transmission range, are investigated analytically. Moreover, an extensive simulation... 

In this paper, the behavior of a fractional order Van der Pol-like oscillator is investigated using a describing function method. A parametric function for the boundary between oscillatory and nonoscillatory regions of this system is extracted. The analytical results are evaluated by numerical simulations which demonstrate sufficient reliability of the proposed analyzing method  

We introduce the new concept of "metalines" for manipulating the amplitude and phase profile of an incident wave locally and independently. Thanks to the highly confined graphene plasmons, a transmit-array of graphene-based metalines is used to realize analog computing on an ultracompact, integrable, and planar platform. By employing the general concepts of spatial Fourier transformation, a well-designed structure of such meta-transmit-array, combined with graded index (GRIN) lenses, can perform two mathematical operations, i.e., differentiation and integration, with high efficiency. The presented configuration is about 60 times shorter than the recent structure proposed by Silva et al....