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#### A Counting Formula for the Kervaire Semi-Characteristic

, M.Sc. Thesis Sharif University of Technology ; Esfahani Zadeh, Mustafa (Supervisor)
Abstract

Similar to the classical Poincare-Hopf index formula for the Euler characteristic, Zhang gave a counting formula for the Kervaire semi-characteristic of a 4q+1 manifold. We first study Witten deformation techniques in the proof of the Poincare-Hopf formula. Then we will represent Zhang’s formula which uses similar analysis. Both these formulas establish a connection between topological and geometrical data on a manifold. Both proofs will be analytical. Index theory will play the ’bridge’ between the topology and analysis. We begin with an analytic interpretation of the topologically defined quantities as indices of differential operators. We deform the operators with respect to appropriate...

#### A higher index theorem for foliated manifolds with boundary

, Article Bulletin des Sciences Mathematiques ; Volume 136, Issue 2 , 2012 , Pages 201-238 ; 00074497 (ISSN) ; Sharif University of Technology
2012

Abstract

Following Gorokhovsky and Lott and using an extension of the b-pseudodifferential calculus of Melrose, we give a formula for the Chern character of the Dirac index class of a longitudinal Dirac type operators on a foliated manifold with boundary. For this purpose we use the Bismut local index formula in the context of noncommutative geometry. This paper uses heavily the methods and technical results developed by E. Leichtnam and P. Piazza

#### On vanishing of low-degree higher Â-genera

, Article Differential Geometry and its Application ; Volume 43 , 2015 , Pages 56-59 ; 09262245 (ISSN) ; Sharif University of Technology
2015

Abstract

In this short note we apply methods introduced by B. Hanke and T. Schick to prove the vanishing of (low degree) higher Â-genera for spin manifolds admitting a positive scalar curvature metric. Our aim is to provide a short proof for this beautiful result

#### Sutures, Taut Manifolds and the Topology of 3-Manifolds

, M.Sc. Thesis Sharif University of Technology ; Esfahani Zadeh, Mostafa (Supervisor)
Abstract

In this essay we focus on the question of whether a 3-manifold (possibly with bound- ary) like M supports a codimension-1 transversely oriented foliation like F , such that F is transverse to ∂M and does not have Reeb components. If such foliation exists, then ∂M is necessarily a (possibly

empty) union of tori and (based on the works of Novikov, Reeb and Rosenberg) M is either S2 × S1(with F being the prod- uct foliation) or M is irreducible. In a paper by David Gabai, which we discuss, the suﬃciency of these conditions is proved in case of non-trivial second homology group.Furthermore, from the works of Thurston it is concluded that compact leaves of such foliation are norm minimizing...

empty) union of tori and (based on the works of Novikov, Reeb and Rosenberg) M is either S2 × S1(with F being the prod- uct foliation) or M is irreducible. In a paper by David Gabai, which we discuss, the suﬃciency of these conditions is proved in case of non-trivial second homology group.Furthermore, from the works of Thurston it is concluded that compact leaves of such foliation are norm minimizing...

#### Chern–Weil Theory Extended to a Class of Infinite Dimensional Bundles

, M.Sc. Thesis Sharif University of Technology ; Esfahani Zadeh, Mostafa (Supervisor)
Abstract

Given a principal bundle a characteristic class is an element of the cohomology al- gebra of the classifying space of structure group of the bundle with coeﬃcients in a commutative ring with unit ,which have a functorial property .When the structure groupe of the bundle is a Lie group and the coeﬃcient ring is the real or complex num- bers , the Chern–Weil approach provides a geometric construction of char-acteristic classes. Classical Chern–Weil formalism relates geometry to topology, assigning to the cur- vature of a connection, de Rham cohomology classes of the underlying manifold.This theory developped in the 40’s by Shiing-ShenChern and Andre Weil which can be seen as a generalisation...

#### Gravity in Noncommutative Geometry

, M.Sc. Thesis Sharif University of Technology ; Esfahani Zadeh, Mostafa (Supervisor)
Abstract

In this thesis, the aim is to stating some of the noncommutative geometry(NCG) applications in formulating and describing the gravity. So, in the first chapter, we will work on some of metric aspects of NCG. In this chapter, we will review elements of the spin geometry, specifically we will define the Dirac operator which is the most important object in this thesis. Then, we will try to find counterparts of some of Riemannian geometric notions like integral and distance in the NCG framework. We will define some notions such as noncommutative infinitesimals, Dixmier trace, Wodzicki residue, noncommutative integral and spectral triples. Then, in the second chapter, we will work on some of the...

#### Ricci Curvature on Graphs

, M.Sc. Thesis Sharif University of Technology ; Esfahani Zadeh, Mostafa (Supervisor) ; Daneshgar, Amir (Supervisor)
Abstract

In the present study, the Ricci curvature is defined on the graphs by using two methods and the lower bounds are obtained. In the first method, which is related to Bakry and Emery, a definition for Ricci curvature and lower bounds would be obtained by using Curvature-Dimension inequalities.The second method which is related to Ollivier, is based on the fact that in Riemannian Geometry,the Ricci Curvature controls the velocity of convergence and divergence of emanated geodesics from a same source. Next, the more Curvature-Dimension inequalities for Ricci curvature would be obtained by using local clustering. Finally, the Bonnet-Myers theorem would be proved on the graphs.

#### Discrete Exterior Calculus

, M.Sc. Thesis Sharif University of Technology ; Esfahani Zadeh, Mostafa (Supervisor) ; Daneshgar, Amir (Supervisor)
Abstract

In this thesis, a discrete exterior calculus is studied. Discrete exterior calculus is an attempt to create a discrete analogy of differential geometry and topology which is potentially applicable in computer science and physics. At first, simplicial complexes are presented as approximation of smooth manifolds. Then discrete forms and discrete exterior derivative are defined. We will observe that Stokes, theorem can be stated and proved in discrete analogy too. We will obtain Hodge operator by using dual complex and after that discrete Laplacian and Heat kernel will be calculated by using Hodge operator. In addition, we will define discrete vector field independent of discrete forms and then...

#### Conformal Invariance in the 2D Ising Model

, M.Sc. Thesis Sharif University of Technology ; Esfahani Zadeh, Mostafa (Supervisor) ; Alishahi, Kasra (Co-Advisor)
Abstract

Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, . . .This has led to numerous exact (but non-rigorous) predictions of their scaling exponents and dimensions. We will discuss how to prove the conformal invariance conjectures, especially in relation to Schramm-Loewner Evolution

#### The Geometry of the Group of Symplectic Diffeomorphisms

, M.Sc. Thesis Sharif University of Technology ; Eftekhary, Eiman (Supervisor) ; Esfahani Zadeh, Mostafa (Supervisor)
Abstract

In this thesis, we first define the pseudo-distance p on the group of Hamiltonian diffeomorphisms.Using the concept of displacement energy, we show that the pseudo-distance p is degenerate and if the manifold is closed, p will be zero for each p = 1; 2; 3; : : : Then, we introduce Lagrangian submanifolds and prove that if L R2n is a rational Lagrangian submanifold, we have the following inequality e(L) ≥ 1γ(L). : Finally, using the above inequality and the concept of displacement energy, for M = R2n we prove that 1 is non-degenerate. Therefore, the hypothesis for 1 to be a metric, are satisfied. This metric is called Hofer’s metric

#### Deep Compositional Captioner

, M.Sc. Thesis Sharif University of Technology ; Esfahani Zadeh, Mostafa (Supervisor) ; Kamali Tabrizi, Mostafa (Co-Supervisor) ; Moghadasi, Jamshid (Co-Supervisor)
Abstract

One of the most important applications of artificial intelligence, and especially deep learning is image captioning. Given an image, the task is to automatically produce a sentence, describing the image. Image captioning has several real world applications like helping the blind understanding the images, generating automatic captions for the social media, etc. In the past, several different methods for image captioning have been used, but after the emergence of deep learning, like many other areas, image captioning algorithms have been improved significantly. In this thesis, I talk about a specific method for image captioning, called ”Deep Compositional Captioning. In this method, at first...

#### Load Shedding in Microgrids to preserve System Stability In The Islanded Operation Mode

, M.Sc. Thesis Sharif University of Technology ; Parniani, Mustafa (Supervisor)
Abstract

In the near future, it is expected that the microgrids become widespreed due to issues such as reliability, increased penetration of renewable energy sources and distributed generation, environmental concerns and shortage of fossil fuels. Different control methods have been suggested to regulate the frequency and voltage of the system so that these quantities remain in their permissible range upon islanding and in the islanded operation mode. However, in emergency conditions, such as shortage of generated power compared to the load of microgrid, frequency or voltage reduction occures due to imbalance. In this situation, it is invitable to shed extra load to maintain the stability and...

#### MiR-9-5p and miR-106a-5p dysregulated in CD4+ T-cells of multiple sclerosis patients and targeted essential factors of T helper17/regulatory T-cells differentiation

, Article Iranian Journal of Basic Medical Sciences ; Volume 21, Issue 3 , March , 2018 , Pages 277-283 ; 20083866 (ISSN) ; Hosseini, A ; Ghaedi, K ; Kiani Esfahani, A ; Tanhaei, S ; Shiralian Esfahani, H ; Rahnamaee, S. Y ; Mowla, S. J ; Nasr Esfahani, M. H ; Sharif University of Technology
Mashhad University of Medical Sciences
2018

Abstract

Objective(s): Multiple sclerosis (MS) is considered as a chronic type of an inflammatory disease characterized by loss of myelin of CNS. Recent evidence indicates that Interleukin 17 (IL-17)-producing T helper cells (Th17 cells) population are increased and regulatory T cells (Treg cells) are decreased in MS. Despite extensive research in understanding the mechanism of Th17 and Treg differentiation, the role of microRNAs in MS is not completely understood. Thereby, as a step closer, we analyzed the expression profile of miR-9-5p and miR-106a-5p, and protein level of retinoic acid receptor (RAR)-related orphan receptor C (RORC; Th17 master transcription factor) as direct target of miR-106a-5p...

#### Robust Design Optimization for Fatigue Life with Geometric and Material Uncertainties of Mechanical Parts Under Random Loading Based on Maximizing Fatigue Life and Minimizing Uncertainty in Fatigue Llife Prediction

, M.Sc. Thesis Sharif University of Technology ; Khodaygan, Saeed (Supervisor)
Abstract

Fatigue life prediction of a mechanical part is one of issues which a group of engineers are engaged with it and always they try to design the parts with the maximum of lifetime. Although many researches have been done in this field but yet we can see that predicted life are different from that happens in the reality because there are some uncertainties in the phenomena. Our effort in this project is creating an algorithm design so that the parts are designed by it, have the maximum fatigue life and the minimum uncertainty in prediction. In this project we have considered geometrical, material and random loading uncertainties as error resources. Older methods those are presented in this...

#### The Correlation between Science & Abrahamic Religions (Emphasizing on Evolutionary Biology & Islam)

, Ph.D. Dissertation Sharif University of Technology ; Tagavi, Mustafa (Supervisor) ; Miandari, Hassan (Supervisor)
Abstract

While the science–religion debate on human creation has been widely explored in the Muslim world، Iranian Muslim opinions have been missed in the mainstream literature. To see whether they follow the lead of the majority of Muslim thinkers or not، here is an overview of the Qur’anic Perspective of Iranian Muslim Scholars. After reviewing the previously categorized approaches of Muslims encountering evolution mentioned in the literature، this thesis will survey the Qur’anic verses related to the biological creation of man with the “scientific-lexical” method of all possible states. Afterward، the views of the most-cited Iranian scholars، such as Saḥābī، Ṭabāṭabā’ī، Muṭahharī، and Jawādī، will...

#### Efficient recyclable catalytic system for deoxygenation of sulfoxides: Catalysis of ionic liquid-molybdenum complexes in ionic liquid solution

, Article New Journal of Chemistry ; Volume 36, Issue 4 , Dec , 2012 , Pages 971-976 ; 11440546 (ISSN) ; Ghazali Esfahani, S ; Sharif University of Technology
2012

Abstract

Three newly synthesized room temperature ionic liquids containing molybdate anion, [DMIm][MoO 2(NCS) 4], [RPy][MoO 2(NCS) 4] (R = butyl or decyl), and previously reported [BMIm][MoO 2(NCS) 4] were used as catalysts for the reduction of sulfoxides. For facilitating the recyclability of the catalysts, the ionic liquids [RMIm][PF 6] and [RPy][PF 6] (RMIm = 1-n-alkyl-3-methylimidazolium, RPy = 1-n-alkylpyridinium) were applied as ionic solvents and toluene is used as solvent for the organic phase. Molybdenum salts immobilized in RTILs constituted a reusable and efficient heterogeneous catalyst system. A maximum conversion (>99%) was achieved for reduction of diphenyl sulfoxide to diphenyl...

#### Molybdenum liquid salts immobilized on ionic liquid-modified silica as efficient heterogeneous catalysts for sulfoxide reduction

, Article Tetrahedron Letters ; Volume 54, Issue 29 , 2013 , Pages 3765-3768 ; 00404039 (ISSN) ; Ghazali Esfahani, S ; Sharif University of Technology
2013

Abstract

Two room temperature liquid salts containing molybdenum(VI), [BMIM] 2[MoO2(NCS)4] (1) and [DMIM] 2[MoO2(NCS)4] (2), were immobilized on ionic liquid-modified silica leading to materials which showed notable catalytic activity for the reduction of sulfoxides into sulfides with triphenylphosphine (PPh3). The molybdenum liquid salts immobilized on the supported ionic liquid phase could be reused at least for three catalytic cycles without significant loss of activity

#### Epoxidation of olefins catalyzed by some cis-dioxomolybdenum(VI)-tridentate schiff base complexes with tert-butyl hydroperoxide

, Article Scientia Iranica ; Volume 17, Issue 2 C , 2010 , Pages 131-138 ; 10263098 (ISSN) ; Ghazali Esfahani, S ; Sharif University of Technology
2010

Abstract

Some cis-dioxomolybdenum (VI) complexes with tridentate Schiff base ligands derived from salicylaldehyde and aminophenols, aminoalcohol or o-aminobenzenethiol were examined as catalysts for epoxidation of different aliphatic and aromatic olefins, with tert-butyl hydroperoxide as oxidant. All complexes exhibited high activity and selectivity for epoxidation of aliphatic substrates during a short time period (95% conversion of cyclooctene after 30 min). The epoxide yield increased with the nucleophilic character of olefin. The catalysts activation strongly depends on the reaction temperature and nature of the solvent. Epoxidation of olefins by these catalysts is inhibited by ligands or...

#### The maximum disjoint routing problem

, Article 22nd International Conference on Computing and Combinatorics, COCOON 2016, 2 August 2016 through 4 August 2016 ; Volume 9797 , 2016 , Pages 319-329 ; 03029743 (ISSN); 9783319426334 (ISBN) ; Sharif Zadeh, A. S ; Zarrabi Zadeh, H ; Sharif University of Technology
Springer Verlag
2016

Abstract

Motivated by the bus escape routing problem in printed circuit boards, we revisit the following problem: given a set of n axis-parallel rectangles inside a rectangular region R, find the maximum number of rectangles that can be extended toward the boundary of R, without overlapping each other. We provide an efficient algorithm for solving this problem in O(n2 log3 n log log n) time, improving over the current best O(n3)-time algorithm available for the problem

####
The Particle-Field Theory On The Possibility of New Formulation of Micro-phenomena

,
M.Sc. Thesis
Sharif University of Technology
;
Shafiee, Afshin
(Supervisor)
Abstract

In this thesis we are going to explore a new formalism in micro domain which describes quantum phenomena in a realistic casual fashion by introducing an unified concept of matter, energy, and Information. In this theory, a micro-entity, e.g. an electron, is a combination of a particle and its associated field integrated to a new entity called particle-field. The dynamics of such system will be analyzed. Then, some quantum examples which have controversial aspects will be discussed within the new theory. In a generalized form of formalism, the non-linear Schrödinger Equation is introduced, which enables us to predict some experimental data for common Quantum Mechanical stationary systems....