Sharif Digital Repository

In this paper, the Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformation is presented for the noncommutative U(N) gauge theory. The nilpotency of the charge associated with this symmetry is then proved. As a consequence of the spacelike noncommutativity parameter, the Hubert space of physical states is determined by the cohomology space of the BRST operator as in the commutative case. Further, the unitarity of the S-matrix elements projected onto the subspace of the physical states is deduced. © 2003 The American Physical Society  

In this paper, the Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformation is presented for the noncommutative [Formula Presented] gauge theory. The nilpotency of the charge associated with this symmetry is then proved. As a consequence of the spacelike noncommutativity parameter, the Hilbert space of physical states is determined by the cohomology space of the BRST operator as in the commutative case. Further, the unitarity of the S-matrix elements projected onto the subspace of the physical states is deduced. © 2003 The American Physical Society  

The aim of this study was to determine the workspace of surgeon's body for designing more efficient surgical robots in the operation rooms. Five wearable inertial sensors were placed near the wrist and elbow joints and also on the thorax of surgeons to track the orientation of upper limb. Assuming that the lengths of five segments of an upper limb were known, measurements of the inertial sensors were used to determine the position of the wrist and elbow joints via an established kinematic model. subsequently, to assess the workspace of surgeon upper body, raw data were collected in the arthroscopy and laparoscopy operations. Experimental results demonstrated that the workspaces of surgeon's... 

When properties of the displacing fluid are considered, the rising profile of the penetrating fluid in a capillary tube deviates from its classical Lucas-Washburn profile. Also, shape of capillary tube can affect the rising profile in different aspects. In this article, effect of capillary tube's shape on the vertical capillary motion in presence of gravity is investigated by considering the properties of the displacing fluid. According to the fact that the differential equation of the capillary rising for a non-simple wall type is very difficult to solve analytically, a finite element simulation model is used for this study. After validation of the simulation model with an experiment that... 

A novel method based on EEG nonlinear analysis and analysis of steady-state visual evoked potentials (SSVEPs) has been processed. The EEG phase space is reconstructed, and some new geometrical features are extracted. Statistical analysis is carried out based on ANOVA, and most significant features are selected and then fed into a multi-class support vector machine (MSVM). Both offline and online phases are considered to fully address SSVEP detection. In the offline mode, the whole design evaluation, feature selection, and classifier training are performed. In the online scenario, the proposed method is evaluated and the detection rate is reported for both phases. Subject-dependent and... 

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  

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  

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  

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  

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... 

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... 

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  

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... 

Multi-sensor tracking is widely used for augmentation of tracking accuracy using data fusion. A basic requirement for such applications is the real time temporal synchronization and spatial registration of two sensory data. In this study a new method for time and space coordination of two tracking sensor measurements has been presented. For spatial registration we used a body coordinate system and then applied the effect of the level arm. The time synchronization was done based on least mean square (LMS) error method. This method was implemented to synchronize the position and orientation of an object using Inertial (1IMU) and Optical (Optotrak) tracking systems. The results of synchronized... 

The fusion of the optical and inertial tracking systems seems an attractive solution to solve the shadowing problem of the optical tracking systems, and remove the time integration troubles of the inertial sensors. We developed a fusion algorithm for this purpose, based on the Kalman filter, and examined its efficacy to improve the position and orientation data, obtained by each individual system. Experimental results indicated that the proposed fusion algorithm could effectively estimate the 2 seconds missing data of the optical tracker  

Steady State Visual Evoked Potential (SSVEP) based Brain Computer Interfaces (BCI) can be great assistance for people suffering from physical disabilities due to their high accuracy, high speed, an acceptable number of possible targets, etc. Many researchers have managed to design such systems. Most of these BCIs utilize methods for frequency detection which cause the system to need a training phase for each new user, making the system a user-based one. That is why our goal was to design a BCI that not only has accuracy and speed comparable to similar systems, but also does not need any training phase and thus can be used by new users right away. Our final design got a mean accuracy of...