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Some Applications of Combinatorial Nullstellensatz in Graph Theory and Combinatorics

, M.Sc. Thesis Sharif University of Technology Fakhari, Amin (Author) ; Akbari, Saeed (Supervisor)

Stanley depth of the integral closure of monomial ideals

, Article Collectanea Mathematica ; Volume 64, Issue 3 , November , 2013 , Pages 351-362 ; 00100757 (ISSN) Seyed Fakhari, S. A ; Sharif University of Technology

2013

Abstract

Let I be a monomial ideal in the polynomial ring S=K [x1,... xn]. We study the Stanley depth of the integral closure Ī of I. We prove that for every integer k ≥ 1, the inequalities (S/Ik) ≤ sdepth (S/Ī) and sdepth(Ik) ≤ sdepth(Ī) hold. We also prove that for every monomial ideal I⊂ S there exist integers k1,k2≥ 1, such that for every s≥ 1, the inequalities sdepth (S/Isk1) ≤ sdepth(S/Ī) and sdepth (Isk2) ≤ sdepth (Ī) hold. In particular, mink{sdepth(S/Ik)} ≤ sdepth(S/Ī) and min̄k {sdepth (Ik)}≤ sdepth(Ī). We conjecture that for every integrally closed monomial ideal I, the inequalities sdepth(S/I)≥ n-l (I) and sdepth (I)≥ n-l (I)+1 hold, where l (I) is the analytic spread of I. Assuming the...

On the h-vector of a simplicial complex with Serre's condition

, Article Journal of Pure and Applied Algebra ; Volume 216, Issue 1 , January , 2012 , Pages 91-94 ; 00224049 (ISSN) Goodarzi, A ; Pournaki, M. R ; Seyed Fakhari, S. A ; Yassemi, S

2012

Abstract

Let δ be a (d-1)-dimensional simplicial complex and let h(δ)=(h0,h1,...,hd) be its h-vector. A recent result of Murai and Terai guarantees that if δ satisfies Serre's condition (Sr), then (h0,h1,...,hr) is an M-vector and hr+hr+1+...+hd is nonnegative. In this article, we extend the result of Murai and Terai by giving r extra necessary conditions. More precisely, we prove that if δ satisfies Serre's condition (Sr), then iihr+i+1ihr+1+...+i+d-rihd, 0≤i≤r≤d, are all nonnegative

The clique numbers of regular graphs of matrix algebras are finite

, Article Linear Algebra and Its Applications ; Volume 431, Issue 10 , 2009 , Pages 1715-1718 ; 00243795 (ISSN) Akbari, S ; Jamaali, M ; Seyed Fakhari, S. A ; Sharif University of Technology

2009

Abstract

Let F be a field, char (F) ≠ 2, and S ⊆ GLn (F), where n is a positive integer. In this paper we show that if for every distinct elements x, y ∈ S, x + y is singular, then S is finite. We conjecture that this result is true if one replaces field with a division ring. © 2009 Elsevier Inc. All rights reserved

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...

Stanley depth of powers of the edge ideal of a forest

, Article Proceedings of the American Mathematical Society ; Volume 141, Issue 10 , 2013 , Pages 3327-3336 ; 00029939 (ISSN) Pournaki, M. R ; Seyed Fakhari, S. A ; Yassemi, S ; Sharif University of Technology

2013

Abstract

Let K be a field and S = K[x1,...,xn] be the polynomial ring in n variables over the field K. Let G be a forest with p connected components G1,...,Gp and let I = I(G) be its edge ideal in S. Suppose that di is the diameter of Gi, 1 ≤ i ≤ p, and consider d = max{di I 1 ≤ i ≤ p}. Morey has shown that for every t ≥ 1, the quantity max is a lower bound for depth(S/It). In this paper, we show that for every t ≥ 1, the mentioned quantity is also a lower bound for sdepth(S/It). By combining this inequality with Burch's inequality, we show that any sufficiently large powers of edge ideals of forests are Stanley. Finally, we state and prove a generalization of our main theorem

On the Stanley depth of weakly polymatroidal ideals

, Article Archiv der Mathematik ; Volume 100, Issue 2 , 2013 , Pages 115-121 ; 0003889X (ISSN) Pournaki, M. R ; Seyed Fakhari, S. A ; Yassemi, S ; Sharif University of Technology

2013

Abstract

Let K be a field and S = K[x1,...,xn] be the polynomial ring in n variables over the field K. In this paper, it is shown that Stanley's conjecture holds for I and S/I if I is a product of monomial prime ideals or I is a high enough power of a polymatroidal or a stable ideal generated in a single degree

On the h-triangles of sequentially (S r) simplicial complexes via algebraic shifting

, Article Arkiv for Matematik ; Volume 51, Issue 1 , 2013 , Pages 185-196 ; 00042080 (ISSN) Pournaki, M. R ; Seyed Fakhari, S. A ; Yassemi, S ; Sharif University of Technology

2013

Abstract

Recently, Haghighi, Terai, Yassemi, and Zaare-Nahandi introduced the notion of a sequentially (Sr) simplicial complex. This notion gives a generalization of two properties for simplicial complexes: being sequentially Cohen-Macaulay and satisfying Serre's condition (Sr). Let Δ be a (d-1)-dimensional simplicial complex with Γ(Δ) as its algebraic shifting. Also let (hi,j(Δ))0≤j≤i≤d be the h-triangle of Δ and (hi,j(Γ(Δ)))0≤j≤i≤d be the h-triangle of Γ(Δ). In this paper, it is shown that for a Δ being sequentially (Sr) and for every i and j with 0≤j≤i≤r-1, the equality hi,j(Δ)=hi,j(Γ(Δ)) holds true

New Classes of Set-theoretic Complete Intersection Monomial Ideals

, Article Communications in Algebra ; Volume 43, Issue 9 , Jun , 2015 , Pages 3920-3924 ; 00927872 (ISSN) Pournaki, M. R ; Seyed Fakhari, S. A ; Yassemi, S ; Sharif University of Technology

Taylor and Francis Inc 2015

Abstract

Let Δ be a simplicial complex and χ be an s-coloring of Δ. Biermann and Van Tuyl have introduced the simplicial complex Δχ. As a corollary of Theorems 5 and 7 in their 2013 article, we obtain that the Stanley–Reisner ring of Δχ over a field is Cohen–Macaulay. In this note, we generalize this corollary by proving that the Stanley–Reisner ideal of Δχ over a field is set-theoretic complete intersection. This also generalizes a result of Macchia

On the size of graphs whose cycles have length divisible by a fixed integer

, Article Australasian Journal of Combinatorics ; Volume 45 , 2009 , Pages 67-72 ; 10344942 (ISSN) Akbari, S ; Jamaali, M ; Mahmoody, A ; Seyed Fakhari, A ; Sharif University of Technology

2009

Abstract

Let G be a simple graph of order n and size m which is not a tree. If ℓ; ≤ 3 is a natural number and the length of every cycle of G is divisible by ℓ, then m ≤l/l-2 (n -2), and the equality holds if and only if the following hold: (i) ℓ is odd and G is a cycle of order ℓ or (ii) ℓ is even and G is a generalized 6>-graph with paths of length |l/2 It is shown that for a (0 mod ℓ)-cycle graph, m/n < l/l-1 if ℓ is odd, and for a given e > 0, there exists a (0 mod ℓ)-cycle graph G with m/n > l/l-2 - e. Also m/n > l/l-2 if ℓ is even, and for a given e > 0, there exists a (0 mod ℓ)-cycle graph G with m/n l/l-2-e

Investigation of Temperature Effect on MOSFET Parameters and Modeling of Carrier Mobility in Temperature Range of 77 - 300K

, M.Sc. Thesis Sharif University of Technology Seyed Fakhari, Moein (Author) ; Fardmanesh, Mahdi (Supervisor) ; Medi, Ali (Supervisor)

Abstract

Temperature reduction from room temperature to liquid nitrogen temperature has a significant effect in improvement of semiconductor devices operation such as field effect transistors. Nowadays cryoelectronics as a considerable branch of electronics is concerned by several groups. In order to optimize the procedure of low temperature IC design and fabrication we investigated the temperature effects on different parameters of MOSFET in this thesis. Several transistors in a variety of channel lengths were fabricated in different technology files. Wide measurement experiments were done on these transistors in order to find their drain current vs. drain to source voltage characteristics. From...

What is... Stanley depth?

, Article Notices of the American Mathematical Society ; Volume 56, Issue 9 , 2009 , Pages 1106-1108 ; 00029920 (ISSN) Pournaki, M. R ; Seyed Fakhari, A ; Tousi, M ; Yassemi, S ; Sharif University of Technology

2009

, 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...

Survey article: Simplicial complexes satisfying Serre's condition: A survey with some new results

, Article Journal of Commutative Algebra ; Vol. 6, issue. 4 , 2014 , p. 455-483 Pournaki, M. R ; Seyed Fakhari, S. A ; Terai, N ; Yassemi, S ; Sharif University of Technology

2014

Abstract

The problem of finding a characterization of Cohen-Macaulay simplicial complexes has been studied intensively by many authors. There are several attempts at this problem available for some special classes of simplicial complexes satisfying some technical conditions. This paper is a survey, with some new results, of some of these developments. The new results about simplicial complexes with Serre's condition are an analogue of the known results for Cohen-Macaulay simplicial complexes

Combinatorics comes to the rescue: h-vectors in commutative algebra

, Article Mathematical Intelligencer ; 2018 ; 03436993 (ISSN) Chin, A. Y. M ; Pournaki, M.R ; Seyed Fakhari, S.A ; Yassemi, S ; Sharif University of Technology

Springer New York LLC 2018

Comparative thermoeconomic analysis of geothermal energy recovery via super/transcritical CO2 and subcritical organic Rankine cycles

, Article Energy Conversion and Management ; Volume 251 , 2022 ; 01968904 (ISSN) Habibollahzade, A ; Petersen, K. J ; Aliahmadi, M ; Fakhari, I ; Brinkerhoff, J. R ; Sharif University of Technology

Elsevier Ltd 2022

Abstract

Transcritical-CO2, supercritical-CO2, and organic Rankine cycles are numerically investigated and compared in simple Rankine, Rankine with internal heat exchanger, and regenerative Rankine configurations to assess their thermodynamic and thermoeconomic performance indicators. Subsequently, the systems are optimized using a multi-objective optimization method. Pareto optimal solutions are provided to present the trade-off between thermodynamic and thermoeconomic indicators. In addition, scatter plots of decision variables are presented to ascertain the optimal operating range of input variables. The results show that transcritical-CO2 systems can generate the highest power. The levelized cost...

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...

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...

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...

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