Sharif Digital Repository

For a ternary quadratic form over the rational numbers, we characterize the set of rational numbers represented by that form over the rational numbers. Consequently, we reprove the classical fact that any positive definite integral ternary quadratic form must fail to represent infinitely many positive integers over the rational numbers. Our proof uses only the quadratic reciprocity law and the Hasse-Minkowski theorem, and is elementary. © 2022, Institute of Mathematics, Czech Academy of Sciences  

We present an exactly solvable extension of the quantum XY chain with longer range multi-spin interactions. Topological phase transitions of the model are classified in terms of the number of Majorana zero modes, n M which are in turn related to an integer winding number, nW. The present class of exactly solvable models belong to the BDI class in the Altland-Zirnbauer classification of topological superconductors. We show that time reversal symmetry of the spin variables translates into a sliding particle-hole (PH) transformation in the language of Jordan-Wigner fermions - a PH transformation followed by a π shift in the wave vector which we call it the πPH. Presence of πPH symmetry... 

The effect of the variation in the femoral groove geometry on patellofemoral joint stability was studied using a two dimensional transverse plane model with deformable articular surfaces. The femoral and patellar bony structures were modelled as rigid bodies with their profiles expressed by splines. The articular cartilage was discretized into compression springs, distributed along the femoral and patellar profiles, based on the rigid-body spring model. The medial and lateral retinacula were modelled as linear tensile springs, and the quadriceps muscles and patellar tendon as strings with known tension. The anatomical data were obtained from the transverse plane magnetic resonance images of... 

Patellar lateral stability was studied using a 2D transverse plane model with deformable articular surfaces. Quadriceps muscles and patellar tendon were considered as strings with predefined forces and lateral and medial retinaculum as tensile springs. Deformation behavior of articular cartilage was modeled by a set of compression springs perpendicular to articular surfaces, based on rigid body spring model method (RBSM). Patellar lateral stability was investigated using restraining force method (the external force required to cause up to 10 mm lateral displacement on patella). The results were in good agreement with experimental reports for normal joint, vastus lateralis and vastus medialis... 

Based on the analogy between the B-spline curve modeling and the force-deflection behavior of a beam subjected to lateral point loads, an extension to the B-spline surface modeling method was introduced. The proposed method has strong extrapolating capability and can develop accurate surface models over an incomplete net of data points without affecting the original data. Extrapolation of the incomplete part of the data net Is conducted simultaneously with interpolation of the existing part, with no need to recalculation. Approximation or data smoothing is a natural extension of the method, however, the smoothing intensity can be controlled continuously without reducing the number of spline... 

We study an S = 1/2 Heisenberg model on the honeycomb lattice with first and second neighbor antiferromagnetic exchange (J1-J2 model), employing exact diagonalization in both the Sz = 0 basis and nearest neighbor singlet valence bond (NNVB) basis. We find that for 0.2 < J2/J1 < 0.3, the NNVB basis gives a proper description of the ground state in comparison with the exact results. By analyzing the dimer-dimer as well as the plaquette-plaquette correlations and also defining appropriate structure factors, we investigate possible symmetry breaking states as the candidates for the ground state in the frustrated region. We provide a body of evidence in favor of plaquette valence bond ordering... 

This paper deals with mathematical modeling and simulation of methanol carbonylation reactor in acetic acid production plant that consisted of a continuous stirred tank reactor (CSTR), a flash drum, a Joule-Thomson valve, and a condenser. The model was based on material and energy balances that considered liquid-gas mass transfer, thermodynamics, and reactor hydrodynamics. The most important aspect of the model was the selection of an appropriate correlation for prediction of mass transfer coefficient. Several correlations were examined and comparison of the model results with plant data indicated that the correlation reported by Lemoine was most appropriate. The simulation results were... 

The motivation of this work is to synthesize a kicking pattern for a humanoid robot with consideration of various objectives such as retaining its balance even after the kick is done and reducing the undesired angular momentum using both hands and torso. This kick pattern is designed so that a desirable ball velocity is achieved. In this paper, the law of conservation of angular momentum is used to generate a less energy consuming trajectory. Effectiveness of the proposed method is verified using computer simulation and is tested on Sharif CEDRA humanoid robot. Copyright © 2006 by ASME  

Surface registration is a necessary step and widely used in medical image-aided surgery. It's relevance to medical imaging is that there is much useful anatomical information in the form of collected surface points which originate from complimentary modalities. In this study, the kinematic relations between two point clouds with different coordinate definitions have been generated. Using Influence Method of surface modeling for extracting point clouds functions, the transformation matrix would be resulted. The proposed method was applied for an experimental femur data points(651 points) using the MRI images. These data points were transformed in a 30 degrees flexion of knee. This... 

Assessing the durability of concrete is of prime importance to provide an adequate service life and reduce the repairing cost of structures. Freeze-thaw is one such test that indicates the ability of concrete to last a long time without a significant loss in its performance. In this study, the freeze-thaw resistance of polymer concrete containing different polymer contents was explored and compared to various conventional cement concretes. Concretes’ fresh and hardened properties were assessed for their workability, air content, and compressive strength. The mass loss, length change, dynamic modulus of elasticity, and residual compressive strength were determined for all types of concretes... 

This article proposes two novel approaches to improve the superimposed frequency droop scheme for the control of dc microgrids (MGs). Conventional voltage-based control strategies suffer from issues such as undesirable voltage regulations, poor power sharing among the sources, and negative effects of line resistances on the equivalent droop characteristics. To overcome these challenges, a superimposed frequency droop scheme has been introduced. However, this method suffers from three major issues: 1) instability in terms of load variation, which is due to the location of system dominant poles; 2) limitation in system loading due to the limitation in the transferred reactive power; and 3)... 

A highly chemoselective methodology is described for the N-methylation of functionalized anilines with dimethyl carbonate (MeOCO2Me, DMC) in the presence of ZrOCl2·8H2O. Dimethyl carbonate, which usually promotes methylation at T > 120 C and eventually under inert atmosphere, was activated in the presence of zirconium oxychloride for the desired transformation at 90 C under aerobic conditions. Aminophenols showed good reactivity in this transformation and produced the corresponding N-methylanilines, as the major products, with high selectivity. Catalyst reusability study confirmed that ZrOCl2·8H2O is a recyclable catalyst and its catalytic activity was remained unchanged at least after eight... 

A detailed 3D anatomical model of the patellofemoral joint was developed to study the tracking, force, contact and stability characteristics of the joint. The quadriceps was considered to include six components represented by 15 force vectors. The patellar tendon was modeled using four bundles of viscoelastic tensile elements. Each of the lateral and medial retinaculum was modeled by a three-bundle nonlinear spring. The femur and patella were considered as rigid bodies with their articular cartilage layers represented by an isotropic viscoelastic material. The geometrical and tracking data needed for model simulation, as well as validation of its results, were obtained from an in vivo... 

In this paper design and fabrication of a wrist exoskeleton robot (ROBOWRIST) has been discussed. The robot has 3 degree of freedom, including flexion/extension, abduction/ adduction and pronation/supination based on the anatomical axis of the body. Four stepper motors are responsible for creating the motion. The exoskeleton can be used for neurorehabilitation and also post-surgery of wrist and forearm. Various therapeutic procedures with a precise tracking can be handled using the control algorithms. Each motor has a separate encoder to measure the angular position and send feedback to the controller. The design goal is to construct a reliable robot that is robust and applicable for... 

Based on the force-deflection equation for a beam subjected to lateral point loads, a C2 continuous piecewise bicubic mathematical representation was proposed to model complicated geometrical surfaces, e.g. the articular surfaces of human joints. The method was then extended so that it could be used for mathematical modelling of incomplete nets of data points, as well as smoothing of noisy and/or filtering of erroneous data points. Mathematical techniques were also developed to calculate the required unknown parameters explicitly, with no need to solve the system of equations simultaneously. The performance of the proposed method was evaluated on a number of surface modelling problems,... 

Biological oxidation of ferrous sulfate by Acidithiobacillus ferrooxidans has proved to be a significant step in the bioleaching of sulfide minerals and the treatment of acid mine drainage. The same bioreaction also has beneficial applications in the desulphurization of coal and removal of hydrogen sulfide from gaseous effluents. In this research, the effects of some process variables such as pH, temperature, elemental sulfur, amount of initial ferrous and magnesium ions on oxidation of ferrous sulfate by a native A. ferrooxidans, which was isolated from a chalcopyrite concentrate, were investigated. All experiments carried out in shake flasks at 33 °C that was obtained as optimum... 

The phase diagram of the Kane-Mele-Heisenberg model in a classical limit [47] contains disordered regions in the coupling space, as the result of competition between different terms in the Hamiltonian, leading to frustration in finding a unique ground state. In this work we explore the nature of these phases in the quantum limit, for a S = 1/2. Employing exact diagonalization in Sz and nearest neighbour valence bond bases, and bond and plaquette valence bond mean field theories, we show that the disordered regions are divided into ordered quantum states in the form of plaquette valence bond crystals and staggered dimerized phases  

We consider load balancing problem in a cache network consisting of storage-enabled servers forming a distributed content delivery scenario. Previously proposed load balancing solutions cannot perfectly balance out requests among servers, which is a critical issue in practical networks. Therefore, in this paper, we investigate a coded cache content placement where coded chunks of original files are stored in servers based on the files popularity distribution. In our scheme, upon each request arrival at the delivery phase, by dispatching enough coded chunks to the request origin from the nearest servers, the requested file can be decoded. Here, we show that if $n$n requests arrive randomly at... 

In this paper, we investigate the statistical and scaling properties of the California earthquakes' inter-events over a period of the recent 40 years. To detect long-term correlations behavior, we apply detrended fluctuation analysis (DFA), which can systematically detect and overcome nonstationarities in the data set at all time scales. We calculate for various earthquakes with magnitudes larger than a given M. The results indicate that the Hurst exponent decreases with increasing M; characterized by a Hurst exponent, which is given by, H = 0:34 + 1:53/M, indicating that for events with very large magnitudes M, the Hurst exponent decreases to 0:50, which is for independent events. © Versita... 

The government and industry have given the recent development of the Internet of Things in the healthcare sector significant respect. Health service providers retain data gathered from many sources and are useful for patient diagnostics and research for pivotal analysis. However, sensitive personal information about a person is contained in healthcare data, which must be protected. Individual privacy protection is a crucial concern for both people and organizations, particularly when those firms must send user data to data centers due to data mining. This article investigated two general states of increasing entropy by changing the entropy of the class set of characteristics based on...