Sharif Digital Repository

For every rotation (Formula presented.) of the Euclidean space (Formula presented.) ((Formula presented.)), we find an upper bound for the number (Formula presented.) such that (Formula presented.) is a product of (Formula presented.) rotations by an angle (Formula presented.) ((Formula presented.)). We also find an upper bound for the number (Formula presented.) such that (Formula presented.) can be written as a product of (Formula presented.) full rotations by an angle (Formula presented.). © 2017 Australian Mathematical Publishing Association Inc  

For every rotation of the Euclidean space ℝ(n≥3), we find an upper bound for the number such that is a product of rotations by an angle α( 0<≤π). We also find an upper bound for the number such that ρ can be written as a product of full rotations by an angle α. © 2017 Australian Mathematical Publishing Association Inc  

We use a third-order perturbation theory and Melnikov's method to prove the existence of chaos in spinning circular disks subject to a lateral point load. We show that the emergence of transverse homoclinic and heteroclinic points lead, respectively, to a random reversal in the traveling direction of circumferential waves and a random phase shift of magnitude π for both forward and backward wave components. These long-term phenomena occur in imperfect low-speed disks sufficiently far from fundamental resonances. © 2007 American Institute of Physics  

This study presents the removal performance of phenol in a three-stages cross flow laboratory-scale rotating biological contactor (RBC). The impact of major process and operating variables, such as input hydraulic loading (HL), input COD loading, and temperature of wastewater on the total removal efficiency of the system were examined. It was observed that the phenol removal performance worsened when the HL increased, and optimum total phenol removal efficiency of 99.9% was observed at loading of 4 × 10-3 m-3 m-2 per day and COD concentration of 800 mg dm-3. On the basis of overall treatment of phenol containing wastewater in the RBC, the optimal removal performance was noted at the end of... 

An exact vibration-rotation kinetic energy operator for polyatomic molecules has been obtained. Using this Hamiltonian for sequentially bonded tetra-atomic molecules, all rovibrational terms have been derived with internal coordinates as the vibrational variables. The present approach is greatly simplified with less algebra compared with conventional methods. Also, simple and explicit expressions for the vibration-rotation coupling terms in internal coordinates are presented  

In this study, effects of geometric factors and material properties are investigated on stress behavior of circular rotating disk with constant rotation in various industrial mechanisms using equilibrium equations, geometric relations and stress functions. In this way, research on a thin uniform and homogeneous circular disk under constant rotation is considered. The rotating motion produces centrifugal acceleration on each element of the rotating disk, and this rotating motion becomes the source of external loading for the mentioned problem. Additional exterior loadings are not assumed in this problem. It is comfortable to handle the centrifugal force loading by relating it to a body force... 

The upgradation of the Kerman cement plant in Iran was discussed. It produces type 2,5 and pozzolanic cements which constitute almost 4.2% of the cement used in Iran. A short description of the process used, and some observations and recommendations about the plant were also provided  

A fourth-order Hamiltonian describing the planar full two body problem is obtained, allowing for a mapping out of the geography of spin-spin-orbit resonances. The expansion of the mutual potential function up to the fourth-order results in the angles to come through one single harmonic and consequently the rotation of both bodies and mutual orbit are coupled. Having derived relative equilibria, stability analysis showed that the stability conditions are independent of physical and orbital characteristics. Simultaneously chaotic motion of bodies is investigated through the Chirikov diffusion utilizing geographic information of the complete resonances. The results show that simultaneous chaos... 

In many sensor fusion algorithms, the vision based RANdom Sample Consensus (RANSAC) method is used for estimating motion parameters for autonomous robots. Usually such algorithms estimate both translation and rotation parameters together which makes them inefficient solutions for merely rotation estimation purposes. This paper presents a novel 3-point RANSAC algorithm for estimating only the rotation parameters between two camera frames which can be utilized as a high rate source of information for a camera-IMU sensor fusion system. The main advantage of our proposed approach is that it performs less computations and requires fewer iterations for achieving the best result. Despite many... 

In this study, we discuss the postural stability of a nonprehensile manipulation problem, which deals with multibody objects. As a metric for postural stability, we define PRI. Then, the system is posturally stable, if PRI is inside the convex hull of the object-manipulator contact surface. We then discuss that dynamic biped locomotion is a special case of dynamic nonprehensile manipulation in all aspects; we prove that ZMP (zero-moment point) and FRI (zoot rotation indicator) are special cases of PRI (palm rotation indicator). Simulations and experiments corresponding to simple examples support the results  

Using a general relativistic exact model for spherical structures in a cosmological background, we have put forward an algorithm to calculate the test particle geodesics within such cosmological structures in order to obtain the velocity profile of stars or galaxies. The rotation curve thus obtained is based on a density profile and is independent of any mass definition which is not unique in general relativity. It is then shown that this general relativistic rotation curves for a toy model and a NFW density profile are almost identical to the corresponding Newtonian one, although the general relativistic masses may be quite different  

Knowing the exact position and rotation is a crucial necessity for the navigation of autonomous robots. Even in outdoor environments GPS signals are not always accessible for estimating online rotation and position of robots. Also inertial aided navigation methods have their own defects such as the drift of gyroscope or inaccuracy of accelerometer in agile motions and environmental sensitivity of compass. In this article, we have introduced a novel online visual gyroscope that can estimate the rotation of a moving car with analyzing the images of a monocular camera installed on it. Our real time visual gyroscope utilizes an efficient method of rotation estimation between each pair of camera... 

In this study, we present results of a mathematical model in which the governing equations of electroforming process were solved using a robust finite element solver (COMSOL Multiphysics). The effects of different parameters including applied current density, solution electrical conductivity, electrode spacing, and anode height on the copper electroforming process have been investigated. An electroforming experiment using copper electroforming cell was conducted to verify the developed model. The obtained results show that by increasing the applied current density, the electroforming process takes place faster, thereby resulting in a higher thickness of the electroformed layer. In addition,... 

By watermarking an image, we hide a pattern in it in such a way that the pattern is not visible but can be extracted using a decomposition algorithm and a key in the receiver side. The watermark pattern can be a character string or any small image (pattern). One of the main applications of watermarking is its application in proving digital image ownership in widely used Internet. In this paper, we present a watermarking method for color images which is robust with respect to usual attacks such as noise addition, smoothing, compression and also rotation. The validity of correctness of retrieved watermark is based on the result of a Naive-Bayes classifier. This classier was trained on a set of... 

The behavior of an isolated bubble in a single-phase swirling flow is investigated theoretically and experimentally. The Rossby number is such that the liquid flow can be approximated by a solid-body rotation superposed to a uniform axial velocity. The equations of the motion of the bubble are solved analytically and numerically, by assuming that the bubble is small and does not modify the water flow. Two kinds of bubbles have been considered: clean bubbles and bubbles with a contaminated interface. In the latter case the bubble is treated as a solid sphere. In both cases a critical angular velocity ωc for the rotating device is found. When ω<ωc the trajectory of the bubble is a conical... 

The calculation of loading and residual stresses, and associated strains and displacements, are reported for shrink fitted rotating discs at elevated temperatures. A range of material behaviour is considered including unloading described by an actual material curve, or modelled by isotropic of kinematic hardening with a variable Bauschinger effect. Various collapse loads are obtained and discussed for design boundaries. The influence of reloading on the residual stresses is also studied. It is shown that after the first few loadings of a disc, the residual stress field becomes constant. © 2001 Elsevier Science Ltd. All rights reserved  

Arvand is a robot specially designed and constructed for playing soccer according to RoboCup rules and regulations for the medium size robots. This robot consists of three main parts: mechanics (motion mechanism and kicker), hardware (image acquisition, processing unit and control unit) and software (image processing, wireless communication, motion control and decision making). The motion mechanism is based on a drive unit, a steer unit and a castor wheel. We designed a special control board which uses two microcontrollers to carry out the software system decisions and transfers them to the robot mechanics. The software system written in C++ performs real time image processing and object... 

In this paper the analytical and simulation modelling of the combined heat and mass transfer processes that occur in a solid desiccant wheel is carried out. Using the numerical method, the performance of an adiabatic rotary dehumidifier is parametrically studied, and the optimal rotational speed is determined by examining the outlet adsorption-side humidity profiles. An approach to compare the solutions for different conditions used in air dehumidifier has been investigated according to the previous published studies. Comparing the simulated results with the published actual values of an experimental work substantiates the validity of model. The model accuracy with respect to the key... 

Dynamic stability of machine tools during operations is dependent on many parameters including the spindle speed. In high and ultra high speed machining, the gyroscopic on the spindle dynamics becomes more pronounced and can affect the borders of stability of the rotating system. In this paper, a finite element based model of spindle, tool holder and cutting tool based on Timoshenko beam theory is used to obtain the dynamic response of the system when gyroscopic terms are included. An iterative scheme is used to update the speed dependent frequency response of the system for obtaining system stability characteristics. It is shown that the gyroscopic effect reduces the critical depth of cut...