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rastegar-talzali--sajjad
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Optimization of Valgus Anatomy Angle of the Fractured Hip for Overcoming the Bone Unhealing Due to Increased Shear Stress at the Fixation Site, Considering Patient Bone Characteristics
, M.Sc. Thesis Sharif University of Technology ; Firoozbakhsh, Keikhosrow (Supervisor)
Abstract
In femoral neck fracture when the non-union happens in the fractured zone, valgus osteotomy is a surgery method to overcome bone non-union. In this method, a wedge osteotomy-with specific depth and angle- at the femoral neck is created. By changing the bone angle at the fracture site and the angle of the wedge osteotomy it is desired to convert the shear stress to the normal stress. Clinically it is believed that this would facilitate bone healing and prevent bone fracture. This surgery method also changes the anatomy of muscles due to changing hip anatomy, joint reaction force , and it’s direction. This procedure while minimizing shear stress it also reduces the blood supply to the area and...
Experimental Investigation of Fretting Fatigue of Titanium Specimens Made by Additive Manufacturing Method
, M.Sc. Thesis Sharif University of Technology ; Adibnazari, Saeed (Supervisor)
Abstract
Additive manufacturing (AM) has gained significant attention in recent years as a novel approach to fabricate three-dimensional parts. Its advantages, including high speed, low-cost production for small-scale batches, and greater design freedom, have made it a competitive alternative to traditional manufacturing methods. However, the application of AM for components subjected to fretting fatigue requires careful evaluation. Fretting fatigue is a major cause of failure in turbines, particularly at the contact interface between turbine blade roots and disk. In this study, the influence of AM and post-processing treatments on the fretting fatigue life of Ti-6Al-4V alloy was investigated. Five...
Deformation of outer representations of galois group II
, Article Iranian Journal of Mathematical Sciences and Informatics ; Volume 6, Issue 2 , 2011 , Pages 33-41 ; 17354463 (ISSN) ; Sharif University of Technology
2011
Abstract
This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained several universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for functors on Artin local rings. In the second part, we use a version of Schlessinger criteria for functors on the Artinian category of nilpotent Lie algebras which is formulated by Pridham, and explore arithmetic applications
Deformation of outer representations of Galois group
, Article Iranian Journal of Mathematical Sciences and Informatics ; Volume 6, Issue 1 , 2011 , Pages 35-52 ; 17354463 (ISSN) ; Sharif University of Technology
2011
Abstract
To a hyperbolic smooth curve defined over a number-field one naturally associates "ananabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than those coming from deformations of "abelian" Galois representations induced by the Tate module of associated Jacobian variety. We develop an arithmetic deformation theory of graded Lie algebras with finite dimensional graded components to serve our purpose
Arithmetic Teichmuller theory
, Article Iranian Journal of Mathematical Sciences and Informatics ; Volume 14, Issue 2 , 2019 , Pages 157-171 ; 17354463 (ISSN) ; Sharif University of Technology
Iranian Academic Center for Education, Culture and Research
2019
Abstract
By Grothendieck’s anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number-fields encode all the arithmetic information of these curves. The Goal of this paper is to develop an arithmetic Teichmuller theory, by which we mean, introducing arithmetic objects summarizing the arithmetic information coming from all curves of the same topological type defined over number-fields. We also introduce Hecke-Teichmuller Lie algebra which plays the role of Hecke algebra in the anabelian framework. © 2019 Academic Center for Education, Culture and Research TMU
Arithmetic teichmuller theory
, Article Iranian Journal of Mathematical Sciences and Informatics ; Volume 14, Issue 2 , 2019 , Pages 157-171 ; 17354463 (ISSN) ; Sharif University of Technology
Iranian Academic Center for Education, Culture and Research
2019
Abstract
By Grothendieck’s anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number-fields encode all the arithmetic information of these curves. The Goal of this paper is to develop an arithmetic Teichmuller theory, by which we mean, introducing arithmetic objects summarizing the arithmetic information coming from all curves of the same topological type defined over number-fields. We also introduce Hecke-Teichmuller Lie algebra which plays the role of Hecke algebra in the anabelian framework. © 2019 Academic Center for Education, Culture and Research TMU
Ihara-Type results for siegel modular forms
, Article Bulletin of the Iranian Mathematical Society ; Volume 46, Issue 3 , 2020 , Pages 693-716 ; Sharif University of Technology
Springer
2020
Abstract
Let p be a prime not dividing the integer n. By an Ihara result, we mean existence of a cokernel torsion-free injection from a full lattice in the space of p-old modular forms into a full lattice in the space of all modular forms of level pn. In this paper, we will prove an Ihara result in the number field case, for Siegel modular forms. The case of elliptic modular forms is discussed in Ihara (Discrete subgroups of Lie groups and applications to moduli, Oxford University Press, Bombay, 1975). We will use a geometric formulation for the notion of p-old Siegel modular forms (Rastegar in BIMS 43(7):1–23, 2017). Then, we apply an argument by Pappas, and prove the Ihara result using density of...
On a theorem of Ihara
, Article Scientia Iranica ; Volume 12, Issue 1 , 2005 , Pages 1-9 ; 10263098 (ISSN) ; Sharif University of Technology
Sharif University of Technology
2005
Abstract
Let p be a prime number and let n be a positive integer prime to p. By an Ihara-result, one means the existence of an injection with torsion-free cokernel, from a full lattice, in the space of p-old modular forms, into a full lattice, in the space of all modular forms of level np. In this paper, Ihara-results are proven for genus two Siegel modular forms, Siegel-Jacobi forms and Hilbert modular forms. Ihara did the genus one case of elliptic modular forms [1]. A geometric formulation is proposed for the notion of p-old Siegel modular forms of genus two, using clarifying comments by R. Schmidt [2] and, then, following suggestions in an earlier paper [3] on how to prove Ihara results. The main...
Arithmetic deformation theory of lie algebras
, Article Iranian Journal of Mathematical Sciences and Informatics ; Volume 18, Issue 1 , 2023 , Pages 19-32 ; 17354463 (ISSN) ; Sharif University of Technology
Iranian Academic Center for Education, Culture and Research
2023
Abstract
This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations. In the second part, we use a version of Schlessinger criteria for functors on the Artinian category of nilpotent Lie algebras which is formulated by Pridham, and explore arithmetic deformations using this technique. © 2023 Academic Center for Education, Culture and Research TMU
Investigating the impacts of plug-in hybrid electric vehicles on power distribution systems
, Article IEEE Transactions on Smart Grid ; Volume 4, Issue 3 , 2013 , Pages 1351-1360 ; 19493053 (ISSN) ; Fotuhi Firuzabad, M ; Rastegar, M
2013
Abstract
Despite the economic and environmental advantages of plug-in hybrid electric vehicles (PHEVs), the increased utilization of PHEVs brings up new concerns for power distribution system decision makers. Impacts of PHEVs on distribution networks, although have been proven to be noticeable, have not been thoroughly investigated for future years. In this paper, a comprehensive model is proposed to study the PHEV impacts on residential distribution systems. In so doing, PHEV fundamental characteristics, i.e., PHEV battery capacity, PHEV state of charge (SOC), and PHEV energy consumption in daily trips, are accurately modeled. As some of these effective characteristics depend on vehicle owner's...
Analytical Investigation and Evaluation of Vulnerability of Deep Networks to Adversarial Perturbations
, M.Sc. Thesis Sharif University of Technology ; Ghaemmaghami, Shahrokh (Supervisor) ; Amini, Sajjad (Co-Supervisor)
Abstract
One of the most important problems in machine learning is investigating the performance of the learning algorithms, and especially deep neural networks, on adversarial examples, which are generated by imperceptibly perturbing input images, so that cause the model make a wrong prediction. Not only this line of research is important for making deep neural networks dependable, but also can help with understanding the fundamental limitations of deep neural networks, and the nature of their operation, which can in turn provide researchers with valuable insights into artificial intelligence. In this research work, we have tried to approach the topic with a mainly theoretical mindset. The method we...
Face Forgery Detection Through Statistical Analysis and Local Correlation Investigation
, M.Sc. Thesis Sharif University of Technology ; Ghaemmaghami, Shahrokh (Supervisor) ; Amini, Sajjad (Supervisor)
Abstract
Existing face forgery detection methods mainly focus on certain features of images, such as features related to image noise, local textures or frequency statistics of images for forgery detection. This makes the extracted representations and the final decision depend on the data in the database and makes it difficult to detect forgery with unknown manipulation methods. Solving this challenge, which is called the generalization challenge in artificial intelligence literature, has become the main goal of researchers in this field. In this thesis, the focus is on extracting effective features for success in forgery detection and preventing the performance of the forgery detection network from...
Investigation of Deepfake Methods for Face Images and it‘s Detection with Deep Learning Networks
, M.Sc. Thesis Sharif University of Technology ; Amini, Sajjad (Supervisor) ; Amini, Arash (Supervisor)
Abstract
Free access to large-scale public datasets, together with the rapid advancement of deep learning techniques and networks, particularly generative models, has led to the production of forged content whose distinction from authentic content has become impossible for humans and many classical forgery detection methods. The well-known term deepfake refers to a deep learning–based technique capable of generating forged images and videos by manipulating their content. A common example of deepfake forgery is identity manipulation in images and videos through facial alteration. In this research, three main objectives related to deepfake methods are considered. First, deepfake generation techniques...
About Space Time
, M.Sc. Thesis Sharif University of Technology ; Rastegar, Arash (Supervisor)
Abstract
Einstein's general theory of relativity is an admirable successful and unifier geometrical modeling among concepts of space, time and gravity. This theory along with special theory of relativity made a massive change in our physical view and this, especially in its historical context, has deep and interesting consequences in man's philosophical viewpoint which can be studied. Some parts of this thesis relates to these consequences. Some of these interesting consequences may be hidden by computional or mathematical viewpoint and often these equations do not contain enough intuition. in one part, we provide a formulizatin of Einstein's equaion that is intuitional which can be translated in...
Synthesis and Characterization of Electrospun Ceramic Nanofibers
, M.Sc. Thesis Sharif University of Technology ; Bagheri, Habib (Supervisor)
Abstract
Electrospinning is a simple and versatile technique for producing polymeric and ceramic nanofibers. The conventional procedure for fabrication of ceramic nanofibers is a combination of sol-gel techniques and electrospinning. The main challenge is the spin polymer nanofiber in fabricate of fibers with diameter from 1 to 100 nm, while their standard deviation are as low as possible. Uniform beads free polyamidenanofibers with lower diameter were fabricated.A 18% w/w of polyamide in formic acid was chosen and the effect of magnetic field, adding magnetic ionic liquid surfactant, auxiliary electrode on the main fiber were investigated. They termsfiber 1 to fiber 5. The mean diameters of 489,...
Tropical Algebraic Geometry
, M.Sc. Thesis Sharif University of Technology ; Rastegar, Arash (Supervisor)
Abstract
Tropical algebraic geometry is a fairly new branch in geometry which is called so in honor of Brazilian mathematician Imre Simon who was pioneer of this field.The set equipped with the addition and multiplication is a semifield.Algebraic geometry objects like algebraic varieties can be defined over.Polynomials and rational functions are defined over.The functions that they define are piecewise linear and concave functions and the set of points where they are nonlinear is a tropical variety which is a concave polyhedral. Thus, tropical algebraic geometry is a piecewise linear version of algebraic geometry.Another approach to tropical algebraic geometry comes back to the works of Russian...
Deep Learning for Multimodal Data
, M.Sc. Thesis Sharif University of Technology ; Soleymani, Mahdieh (Supervisor)
Abstract
Recent advances in data recording has lead to different modalities like text, image, audio and video. Images are annotated and audio accompanies video. Because of distinct modality statistical properties, shallow methods have been unsuccessful in finding a shared representation which maintains the most information about different modalities. Recently, deep networks have been used for extracting high-level representations for multimodal data. In previous methods, for each modality, one modality-specific network was learned. Thus, high-level representations for different modalities were extracted. Since these high-level representations have less difference than raw modalities, a shared...
A New Approach Based on Mathematical Modelling and Fuzzy Multi Criteria Decision Making for Supplier Selection in Green Supply Chain
, M.Sc. Thesis Sharif University of Technology ; Hajji, Alireza (Supervisor)
Abstract
Recently, reducing greenhouse gas emissions and the damage to the environment is very important. Due to the increasing environmental awareness of the people on the one hand, and government pressure to reduce damage to the environment on the other hand, has led organizations to pay more attention to this important issue. In addition, these organizations in order to participate in the global competition, should consider green criteria along with other criteria. Hence, the organizations to outsourcing part of their work are looking for Suppliers who along with other criteria also meet the criteria for being green. In this study, a new two-stage approach based on fuzzy...
, M.Sc. Thesis Sharif University of Technology ; Rastegar, Arash (Supervisor)
Abstract
Our goal is to reformulate MKR-dictionary for geodesic foliations on hyperbolic 3-manifolds. Where the closed geodesic is considered as a knot. In this new perspective, by topological interpretation at arithmetical objects and considering the etale fundamental group, the ground has been prepared to obtain an analogy between the theory of knots and the algebraic numbers theory. The analogy between knots and prime numbers was pointed out by B. Mazur and also by Y. Manin and developed by the work of Kapranov and Reznikov. Using this analogy, Mazur formulated the Chebotarev density theorem related to prime numbers in number fields for an infinite sequence of knot on a three-dimensional manifold,...
Discovery of Effective Genes Via Differential Gene Expression Networks
, M.Sc. Thesis Sharif University of Technology ; Motahari, Abolfazl (Supervisor)
Abstract
With the emergence of high-throughput gene expression data collection methods, the development of more precise analytical techniques to extract patterns from these data is increasingly necessary. These methods, of course, vary depending on the specific pattern being targeted for extraction. However, identifying key genes and biological pathways responsible for major changes remains the primary challenge in understanding the structure of gene regulatory networks. Understanding these regulatory networks serves as a foundation for a wide range of biological intervention strategies, which can have diverse objectives. In the field of gene expression network inference, numerous challenges exist,...