Some properties of a cayley graph of a commutative ring

, Article Communications in Algebra ; Vol. 42, issue. 4 , Dec , 2014 , pp. 1582-1593 ; ISSN: 00927872 Aalipour, G ; Akbari, S ; Sharif University of Technology

2014

Abstract

Let R be a commutative ring with unity and R+, U(R), and Z*(R) be the additive group, the set of unit elements, and the set of all nonzero zero-divisors of R, respectively. We denote by ℂAY(R) and GR, the Cayley graph Cay(R+, Z*(R)) and the unitary Cayley graph Cay(R+, U(R)), respectively. For an Artinian ring R, Akhtar et al. (2009) studied GR. In this article, we study ℂAY(R) and determine the clique number, chromatic number, edge chromatic number, domination number, and the girth of ℂAY(R). We also characterize all rings R whose ℂAY(R) is planar. Moreover, we determine all finite rings R whose ℂAY(R) is strongly regular. We prove that ℂAY(R) is strongly regular if and only if it is edge...

Phase shift calibration based on Fresnel diffraction from phase plates

, Article Journal of Optics (United Kingdom) ; Volume 14, Issue 12 , 2012 ; 20408978 (ISSN) Aalipour, R ; Aminjafari, M ; Sharif University of Technology

2012

Abstract

When a transparent plane-parallel plate is illuminated at a boundary region by a parallel monochromatic beam of light, Fresnel diffraction occurs because of the abrupt change in phase imposed by the finite change in refractive index at the plate boundary. The intensity of the diffraction fringes varies periodically with changes in the optical path difference of the light passing through the plate edge. The optical path difference depends on the incident angle of the light, the refractive index of the plate and surrounding medium, and the wavelength of the light. Plotting the intensity of the diffraction fringes versus optical path difference provides a general phase shift method for phase...

On the cayley graph of a commutative ring with respect to its zero-divisors

, Article Communications in Algebra ; Volume 44, Issue 4 , 2016 , Pages 1443-1459 ; 00927872 (ISSN) Aalipour, G ; Akbari, S ; Sharif University of Technology

Taylor and Francis Inc 2016

Abstract

Let R be a commutative ring with unity and R+ and Z*(R) be the additive group and the set of all nonzero zero-divisors of R, respectively. We denote by ℂ𝔸𝕐(R) the Cayley graph Cay(R+, Z*(R)). In this article, we study ℂ𝔸𝕐(R). Among other results, it is shown that for every zero-dimensional nonlocal ring R, ℂ𝔸𝕐(R) is a connected graph of diameter 2. Moreover, for a finite ring R, we obtain the vertex connectivity and the edge connectivity of ℂ𝔸𝕐(R). As a result, ℂ𝔸𝕐(R) gives an algebraic construction for vertex transitive graphs of maximum connectivity. In addition, we characterize all zero-dimensional semilocal...

Laplacian spectral characterization of two families of trees

, Article Linear and Multilinear Algebra ; Volume 62, Issue 7 , July , 2014 , Pages 965-977 ; ISSN: 03081087 Aalipour, G ; Akbari, S ; Shajari, N ; Sharif University of Technology

2014

Abstract

It is well known that all starlike trees, i.e. trees with exactly one vertex of degree at least three, are determined by their Laplacian spectrum. A double starlike tree is a tree with exactly two vertices of degree at least three. In 2009, the following question was posed: Are all the double starlike trees determined by their Laplacian spectra? In this direction, it was proved that one special double starlike tree Hn(p,p) is determined by its Laplacian spectrum, where Hn(p,q) is a tree obtained by joining p pendant vertices to an end vertex of a path of order and then joining pendant vertices to another end of the path. Also, the banana tree Bn,k is a tree obtained by joining a vertex to...

On D-equivalence class of complete bipartite graphs

, Article Ars Combinatoria ; Vol. 117, issue , Oct , 2014 , p. 275-288 ; 03817032 Aalipour-Hafshejani, G ; Akbari, S ; Ebrahimi, Z ; Sharif University of Technology

2014

Abstract

Let G be a simple graph of order n. We mean by dominating set, a set S C V(G) such that every vertex of G is either in S or adjacent to a vertex in S. The domination polynomial of G is the polynomial Σni=1 (G,i)xi where d((g,i) is the number of dominating sets of G of size i. Two graphs G and H are said to be V-equivalent, written G H, if D((G, x) = D(H, x). The D-equivalence class of G is [G] = { H H G }. Recently, the determination of D-equivalence class of a given graph, has been of interest. In this paper, it is shown that for n ≥ 3, [Kn, n] has size two. We conjecture that the complete bipartite graph Km,n for n - m ≥ 2, is uniquely determined by its domination polynomial

Cayley Graphs and Annihilating-Ideal Graph of a Ring

, Ph.D. Dissertation Sharif University of Technology Aalipour Hafshejani, Ghodratollah (Author) ; Akbari, Saeed (Supervisor)

Abstract

In the recent years, the role of combinatorics and graph theory have grown in the progress of computer sciences. For instance, the circulant graphs have applications in design of interconnection networks and the graphs with integer eigenvalues are applied in modelling quantum spin networks supporting the perfect state transfer. The circulant graphs with integer eigenvalues also found applications in molecular graph energy. In 2006, it was shown that an n-vertex circulant graph G has integer eigenvalues if G=Cay(Zn; T ) or G= Cay(Zn; T)∪Cay(Zn;U(Zn)), where T Z(Zn). The Cayley graph Cay(Zn;U(Zn)) is known as the unitary Cayley graph. Fuchs defined the unitary Cayely graph of a commutative...

Introducing a Simulation-Based Model to Improve the Design and Layout of Workstations Inside Airport Terminals in Iran

, M.Sc. Thesis Sharif University of Technology Amini Esfidvajani, Amin Mohammad (Author) ; Alvanchi, Amin (Supervisor)

Abstract

The airport terminal is difficult to plan and design due to the different components and the intricate complexity of its parts. At the airport terminal, we face a queue system which simulation is always a good way to analyze. In addition, computer simulation using modern softwares with the capability to model different types of systems, including the airport terminal, while being less realistic than analytical models, is less costly than operational Exercise.In this study, a supportive approach for better and specific management of Iranian airport terminal buildings with discrete-event simulation is proposed, considering the need for managing the airport terminals building in the country and...

Minimal prime ideals and cycles in annihilating-ideal graphs

, Article Rocky Mountain Journal of Mathematics ; Volume 43, Issue 5 , 2013 , Pages 1415-1425 ; 00357596 (ISSN) Aalipour, G ; Akbari, S ; Nikandish, R ; Nikmehr, M. J ; Shaveisi, F ; Sharif University of Technology

2013

Abstract

Let R be a commutative ring with identity, and let A(R) be the set of ideals with non-zero annihilator. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R)* = A(R) {0}, and two distinct vertices I and J are adjacent if and only if IJ = 0. In this paper, we study some connections between the graph theoretic properties of this graph and some algebraic properties of a commutative ring. We prove that if AG(R) is a tree, then either AG(R) is a star graph or a path of order 4 and, in the latter case, R = F × S, where F is a field and S is a ring with a unique non-trivial ideal. Moreover, we prove that if R has at least three minimal prime ideals, then AG(R) is...

On the coloring of the annihilating-ideal graph of a commutative ring

, Article Discrete Mathematics ; Volume 312, Issue 17 , 2012 , Pages 2620-2626 ; 0012365X (ISSN) Aalipour, G ; Akbari, S ; Nikandish, R ; Nikmehr, M. J ; Shaveisi, F ; Sharif University of Technology

Elsevier 2012

Abstract

Suppose that R is a commutative ring with identity. Let A(R) be the set of all ideals of R with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A( R)*=A(R)(0) and two distinct vertices I and J are adjacent if and only if IJ=(0). In Behboodi and Rakeei (2011) [8], it was conjectured that for a reduced ring R with more than two minimal prime ideals, girth(AG(R))=3. Here, we prove that for every (not necessarily reduced) ring R, ω(AG(R))<|Min(R)|, which shows that the conjecture is true. Also in this paper, we present some results on the clique number and the chromatic number of the annihilating-ideal graph of a commutative ring. Among...

A modified method for barium titanate nanoparticles synthesis

, Article Materials Research Bulletin ; Volume 46, Issue 12 , 2011 , Pages 2291-2295 ; 00255408 (ISSN) Ashiri, R ; Nemati, A ; Sasani Ghamsari, M ; Sanjabi, S ; Aalipour, M ; Sharif University of Technology

2011

Abstract

In this research, a modified, cost effective sol-gel procedure applied to synthesize BaTiO3 nanoparticles. XRD and electron microscopy (SEM and TEM) applied for microstructural characterization of powders. The obtained results showed that the type of precursors, their ratio and the hydrolysis conditions had a great effect on time, temperature and therefore the costs of the synthesis process. By selection, utilization of optimized precursor's type, hydrolysis conditions, fine cubic BaTiO3 nanoparticles were synthesized at low temperature and in short time span (1 h calcination at 800 °C). The proposed procedure seems to be more preferable for mass production. The result indicated that the...

On the structure of the power graph and the enhanced power graph of a group

, Article Electronic Journal of Combinatorics ; Volume 24, Issue 3 , 2017 ; 10778926 (ISSN) Aalipour, G ; Akbari, S ; Cameron, P. J ; Nikandish, R ; Shaveisi, F ; Sharif University of Technology

2017

Abstract

Let G be a group. The power graph of G is a graph with the vertex set G, having an edge between two elements whenever one is a power of the other. We characterize nilpotent groups whose power graphs have finite independence number. For a bounded exponent group, we prove its power graph is a perfect graph and we determine its clique/chromatic number. Furthermore, it is proved that for every group G, the clique number of the power graph of G is at most countably infinite. We also measure how close the power graph is to the commuting graph by introducing a new graph which lies in between. We call this new graph the enhanced power graph. For an arbitrary pair of these three graphs we...

, M.Sc. Thesis Sharif University of Technology (Author) ; Alvanchi, Amin (Supervisor)

Abstract

Limited water resources in Iran have made dams an important part of the country’s infrastructure. As a result of the large number of in-progress and expected dam projects in the country, consideration of sustainability factors during planning, construction and operation phases of dam projects can create significant economical, social and environmental impacts in the long term. To come up with an inclusive sustainable development, new sustainability assessment approaches seek for sustainable development at the entire project’s life-cycle; they are looking for sustainable development at all design, construction, operation, maintenance and even demolition phases. In this research we have...

Black Hole Complementarity, An Approach To The Information Problem

, M.Sc. Thesis Sharif University of Technology Aalipour, Amin (Author) ; Bahmanabadi, Mahmud (Supervisor) ; Sheikh Jabbari, Mohammad Mehdi (Supervisor)

Abstract

In this survey we explore the black hole information problem, one of the most challenging issues in theoretical physics over the past few decades. According to the theory of general relativity, black holes can form through gravitational collapse of matter. At semiclassical level, however, black holes emit thermal Hawking-radiation and eventually completely evaporate. After evaporation the radiation state cannot retain all the information about the initial matter that underwent gravitational collapse, contradicting the principles of quantum mechanics. Various approaches have been proposed to address this issue. One such approach is the black hole complementarity principle, introduced by...

The Insider Threat: Analyzing and Modeling

, M.Sc. Thesis Sharif University of Technology Amin, Assiabi (Author) ; Hendesi, Faramarz (Supervisor)

Abstract

Nowadays, most of businesses are becoming computer-based. This trend causes the organizations to become more vulnerable to internal and external threats. Internal threats are done through insiders. Insiders unlike outsiders have capabilities which aid them to easily carry out their illicit activities. Unfortunately, most of research in computer security has focused on the outsider threats, whereas the most damaging is the result of insiders’ illicit activities.This dissertation addresses three primary necessities of the research in the area of insider threat: a consistent definition of insider threat, a classification of types of insider threats, and a classification of vulnerabilities which...

Design of a Plantwide Decentrlized Structure Controller for the Tennessee Eastman Challenge Problem

, M.Sc. Thesis Sharif University of Technology Molamofrad, Foozhan (Author) ; Nobakhti, Amin (Supervisor)

Abstract

This project focuses on the Tennessee East-man challange problem(TEP) and the impact of setpoint changes and controller tunning on plant performance and profitability. TE has four major units. it is an unstable system due to the reaction within the reactor and a recycle streamcausing snow ball effect. As a result the control of this system is not easy. The study has been conducted along two main directions. First, selecting the optimal values for the setpoints and applying them in the simulation. secondly, try to find better parameter for controller in simulation. Simulation is based on working of Ricker. In TEP like the other multivariable systems, it is ameanable to use a centralized...

Convex Methods for the Design of Low Order Dynamic Pre-Compensators

, M.Sc. Thesis Sharif University of Technology Shamgah, Laya (Author) ; Nobakhti, Amin (Supervisor)

Abstract

Decentralized control is a typical method for the design of industrial MIMO control systems. However, in most multivariable systems, the existence of large interactions limit the achievable performance of such controllers. In the Nyquist Array design method proposed by Rosenbrock, the system interactions can be reduced using a precompensator, such that a decentralized controller may be used with acceptable performance. A well designed pre-compensator will effectively decouple the system and the multivariable systems may be considered as a set of SISO systems. It is therefore obvious that the key element in the Nyquist Array design method is the design of the pre-compensator. There are two...

Integrity Analysis in the Time-Delay Systems

, M.Sc. Thesis Sharif University of Technology Eslami, Mostafa (Author) ; Nobakhti, Amin (Supervisor)

Abstract

Integrity of closed-loop systems with integral action control is characterized by using a series of successively more difficult to obtain conditions: Integral Stabilizable (IS), Integral Controllable (IC), Integral Controllable with Integrity (ICI), and Decentralized Integral Controllability (DIC). The IS condition requires that for a Linear Time-Invariant (LTI) finitedimensional (FD) plant, G(s), one finds a stabilizing decentralized controller with integral action. For G(s) to be IC, in addition to being IS, one should be able to reduce the gain of
all control loops by the same factor from a finite value to (but not including) zero without introducing instabilities. ICI requires that...

A Thesis Submitted in Partial Fulfillment of the Requirement for the Degree of Master of Science in Electrical Engineering

, M.Sc. Thesis Sharif University of Technology Negim, Mostafa (Author) ; Nobakhti, Amin (Supervisor)

Abstract

Intraction in multi input multi output (MIMO) system makes control of these systems difficult.There are two ways to control such systems; Centralized and Decentralized control. One way in which a centralized controller is designed is using a precompensator. With application of the pre-compensator, the MIMO sytem is decoupled into several SISO systems and one can control these seperatly. Almost all previews methods for the design of pre-compensator assume that the model of the plant containsno uncertainties.In this thesis a new method is proposed which takes into account model uncertaintes in the design of the pre-compensator.The form of the uncertainties considred an interval-parametric

Conditions for Integrity of Multivariable Systems with Input Saturation

, M.Sc. Thesis Sharif University of Technology Asgharzadeh, Abbas (Author) ; Nobakhti, Amin (Supervisor)

Abstract

Multivariable control systems as used in the industry usually contain integral action in order to improve tracking of the output with respect to step reference changes. These systems are usually subject to input saturation due to actuator or sensor nonlinearities. The aim of this work is find the conditions for the integrity concept of such multivariable system, e.g. IS, IC, ICI and DIC. First we develop the conditions on the controller gains necessary stabilize the systems and then show that these conditions can changes when one examines integrity conditions

Disturbance Reduction Servo Motor Controller Design and Implementation

, M.Sc. Thesis Sharif University of Technology Ahi, Behzad (Author) ; Nobakhti, Amin (Supervisor)

Abstract

The servomechanisms have wide industrial application such as robotics, Computer Numerical Control (CNC) machines, automated manufacturing and solar tracking. Several methods have already been proposed for servo motor control that the most important of them are Proportional Integral Derivative (PID), H2/H--, intelligent based controllers, and model predictive control. Problem specifications and user requirements, will determine the appropriate approach in each case. The aim of this thesis is construction of a real-life camera stabilizer to be used in the motion picture industry. Effects of base movement on the performance should be decreased by choosing appropriate sensors and control...