**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**591

# Search results for: rational Ball curve.

##### 591 Generating Arabic Fonts Using Rational Cubic Ball Functions

**Authors:**
Fakharuddin Ibrahim,
Jamaludin Md. Ali,
Ahmad Ramli

**Abstract:**

^{1}continuity. The conditions considered are known as the G

^{1}Hermite condition. A simple application of the proposed method is to generate an Arabic font satisfying the required continuity.

**Keywords:**
Continuity,
data interpolation,
Hermite condition,
rational Ball curve.

##### 590 The Number of Rational Points on Singular Curvesy 2 = x(x - a)2 over Finite Fields Fp

**Authors:**
Ahmet Tekcan

**Abstract:**

**Keywords:**
Singular curve,
elliptic curve,
rational points.

##### 589 The Number of Rational Points on Elliptic Curves and Circles over Finite Fields

**Authors:**
Betül Gezer,
Ahmet Tekcan,
Osman Bizim

**Abstract:**

**Keywords:**
Elliptic curves over finite fields,
rational points on
elliptic curves and circles.

##### 588 Arc Length of Rational Bezier Curves and Use for CAD Reparametrization

**Authors:**
Maharavo Randrianarivony

**Abstract:**

**Keywords:**
Adaptivity,
Length,
Parametrization,
Rational Bezier

##### 587 The Number of Rational Points on Conics Cp,k : x2 − ky2 = 1 over Finite Fields Fp

**Authors:**
Ahmet Tekcan

**Abstract:**

Let p be a prime number, Fp be a finite field, and let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively.

**Keywords:**
Elliptic curve,
conic,
rational points.

##### 586 An Approach to Polynomial Curve Comparison in Geometric Object Database

**Authors:**
Chanon Aphirukmatakun,
Natasha Dejdumrong

**Abstract:**

**Keywords:**
Bezier curve,
Said-Ball curve,
Wang-Ball curve,
DP curve,
CAGD,
comparison,
geometric object database.

##### 585 Rational Points on Elliptic Curves 2 3 3y = x + a inF , where p 5(mod 6) is Prime

**Authors:**
Gokhan Soydan,
Musa Demirci,
Nazli Yildiz Ikikardes,
Ismail Naci Cangul

**Abstract:**

In this work, we consider the rational points on elliptic curves over finite fields Fp where p ≡ 5 (mod 6). We obtain results on the number of points on an elliptic curve y2 ≡ x3 + a3(mod p), where p ≡ 5 (mod 6) is prime. We give some results concerning the sum of the abscissae of these points. A similar case where p ≡ 1 (mod 6) is considered in [5]. The main difference between two cases is that when p ≡ 5 (mod 6), all elements of Fp are cubic residues.

**Keywords:**
Elliptic curves over finite fields,
rational points.

##### 584 Dynamics and Control of Bouncing Ball

**Authors:**
A. K. Kamath,
N. M. Singh,
R. Pasumarthy

**Abstract:**

**Keywords:**
Bouncing Ball,
impact dynamics,
intermittent
control,
model predictive control.

##### 583 Circular Approximation by Trigonometric Bézier Curves

**Authors:**
Maria Hussin,
Malik Zawwar Hussain,
Mubashrah Saddiqa

**Abstract:**

We present a trigonometric scheme to approximate a circular arc with its two end points and two end tangents/unit tangents. A rational cubic trigonometric Bézier curve is constructed whose end control points are defined by the end points of the circular arc. Weight functions and the remaining control points of the cubic trigonometric Bézier curve are estimated by variational approach to reproduce a circular arc. The radius error is calculated and found less than the existing techniques.

**Keywords:**
Control points,
rational trigonometric Bézier curves,
radius error,
shape measure,
weight functions.

##### 582 The Control Vector Scheme for Design of Planar Primitive PH curves

**Authors:**
Ching-Shoei Chiang,
Sheng-Hsin Tsai,
James Chen

**Abstract:**

**Keywords:**
PH curve,
hodograph,
Bézier curve.

##### 581 Numerical Simulation and Experimental Validation of the Hydraulic L-Shaped Check Ball Behavior

**Authors:**
Shinji Kajiwara

**Abstract:**

The spring-driven ball-type check valve is one of the most important components of hydraulic systems: it controls the position of the ball and prevents backward flow. To simplify the structure, the spring must be eliminated, and to accomplish this, the flow pattern and the behavior of the check ball in L-shaped pipe must be determined. In this paper, we present a full-scale model of a check ball made of acrylic resin, and we determine the relationship between the initial position of the ball, the position and diameter of the inflow port. The check flow rate increases in a standard center inflow model, and it is possible to greatly decrease the check-flow rate by shifting the inflow from the center.

**Keywords:**
Hydraulics,
Pipe Flow,
Numerical Simulation,
Flow
Visualization,
Check ball,
L-shaped Pipe.

##### 580 The Number of Rational Points on Elliptic Curves y2 = x3 + a3 on Finite Fields

**Authors:**
Musa Demirci,
Nazlı Yıldız İkikardeş,
Gökhan Soydan,
İsmail Naci Cangül

**Abstract:**

**Keywords:**
Elliptic curves over finite fields,
rational points,
quadratic residue.

##### 579 Internal Loading Distribution in Statically Loaded Ball Bearings Subjected to a Centric Thrust Load: Numerical Aspects

**Authors:**
Mário C. Ricci

**Abstract:**

**Keywords:**
Ball,
Bearing,
Static,
Load,
Iterative,
Numerical,
Method.

##### 578 The Elliptic Curves y2 = x3 - t2x over Fp

**Authors:**
Ahmet Tekcan

**Abstract:**

Let p be a prime number, Fp be a finite field and t ∈ F*p= Fp- {0}. In this paper we obtain some properties of ellipticcurves Ep,t: y2= y2= x3- t2x over Fp. In the first sectionwe give some notations and preliminaries from elliptic curves. In the second section we consider the rational points (x, y) on Ep,t. Wegive a formula for the number of rational points on Ep,t over Fnp for an integer n ≥ 1. We also give some formulas for the sum of x?andy?coordinates of the points (x, y) on Ep,t. In the third section weconsider the rank of Et: y2= x3- t2x and its 2-isogenous curve Et over Q. We proved that the rank of Etand Etis 2 over Q. In the last section we obtain some formulas for the sums Σt∈F?panp,t for an integer n ≥ 1, where ap,t denote the trace of Frobenius.

**Keywords:**
Elliptic curves over finite fields,
rational points onelliptic curves,
rank,
trace of Frobenius.

##### 577 Comparison of the Distillation Curve Obtained Experimentally with the Curve Extrapolated by a Commercial Simulator

**Authors:**
Lívia B. Meirelles,
Erika C. A. N. Chrisman,
Flávia B. de Andrade,
Lilian C. M. de Oliveira

**Abstract:**

**Keywords:**
Distillation curve,
petroleum distillation,
simulation,
true boiling point curve.

##### 576 Internal Loading Distribution in Statically Loaded Ball Bearings Subjected to a Centric Thrust Load: Alternative Approach

**Authors:**
Mário C. Ricci

**Abstract:**

**Keywords:**
Ball,
Bearing,
Static,
Load,
Iterative,
Numerical,
Method.

##### 575 Highly Accurate Tennis Ball Throwing Machine with Intelligent Control

**Authors:**
Ferenc Kovács,
Gábor Hosszú

**Abstract:**

**Keywords:**
Control system,
robot programming,
robot control,
sports equipment,
throwing machine.

##### 574 Method of Intelligent Fault Diagnosis of Preload Loss for Single Nut Ball Screws through the Sensed Vibration Signals

**Authors:**
Yi-Cheng Huang,
Yan-Chen Shin

**Abstract:**

**Keywords:**
Empirical Mode Decomposition,
Hilbert-Huang Transform,
Multi-scale Entropy,
Preload Loss,
Single-nut Ball Screw

##### 573 Fractional Order Feedback Control of a Ball and Beam System

**Authors:**
Santosh Kr. Choudhary

**Abstract:**

In this paper, fractional order feedback control of a ball beam model is investigated. The ball beam model is a particular example of the double Integrator system having strongly nonlinear characteristics and unstable dynamics which make the control of such system a challenging task. Most of the work in fractional order control systems are in theoretical nature and controller design and its implementation in practice is very small. In this work, a successful attempt has been made to design a fractional order PIλDμcontroller for a benchmark laboratory ball and beam model. Better performance can be achieved using a fractional order PID controller and it is demonstrated through simulations results with a comparison to the classic PID controller.

**Keywords:**
Fractional order calculus,
fractional order controller,
fractional order system,
ball and beam system,
PIλDμ controller,
modelling,
simulation.

##### 572 The Conceptual and Procedural Knowledge of Rational Numbers in Primary School Teachers

**Authors:**
R. M. Kashim

**Abstract:**

The study investigates the conceptual and procedural knowledge of rational number in primary school teachers, specifically, the primary school teachers level of conceptual knowledge about rational number and the primary school teachers level of procedural knowledge about rational numbers. The study was carried out in Bauchi metropolis in Bauchi state of Nigeria. A Conceptual and Procedural Knowledge Test was used as the instrument for data collection, 54 mathematics teachers in Bauchi primary schools were involved in the study. The collections were analyzed using mean and standard deviation. The findings revealed that the primary school mathematics teachers in Bauchi metropolis posses a low level of conceptual knowledge of rational number and also possess a high level of Procedural knowledge of rational number. It is therefore recommended that to be effective, teachers teaching mathematics most posses a deep understanding of both conceptual and procedural knowledge. That way the most knowledgeable teachers in mathematics deliver highly effective rational number instructions. Teachers should not ignore the mathematical concept aspect of rational number teaching. This is because only the procedural aspect of Rational number is highlighted during instructions; this often leads to rote - learning of procedures without understanding the meanings. It is necessary for teachers to learn rational numbers teaching method that focus on both conceptual knowledge and procedural knowledge teaching.

**Keywords:**
Conceptual knowledge,
primary school teachers,
procedural knowledge,
rational numbers.

##### 571 Control of A Cart-Ball System Using State-Feedback Controller

**Authors:**
M. Shakir Saat,
M. Noh Ahmad,
Dr,
Amat Amir

**Abstract:**

**Keywords:**
Cart-Ball System,
Integral Control,
Pole-PlacementMethod,
State-Feedback Controller.

##### 570 Best Proximity Point Theorems for MT-K and MT-C Rational Cyclic Contractions in Metric Spaces

**Authors:**
M. R. Yadav,
A. K. Sharma,
B. S. Thakur

**Abstract:**

The purpose of this paper is to present a best proximity point theorems through rational expression for a combination of contraction condition, Kannan and Chatterjea nonlinear cyclic contraction in what we call MT-K and MT-C rational cyclic contraction. Some best proximity point theorems for a mapping satisfy these conditions have been established in metric spaces. We also give some examples to support our work.

**Keywords:**
Cyclic contraction,
rational cyclic contraction,
best proximity point and complete metric space.

##### 569 Determination of Surface Roughness by Ball Burnishing Process Using Factorial Techniques

**Authors:**
P. S. Dabeer,
G. K. Purohit

**Abstract:**

Burnishing is a method of finishing and hardening machined parts by plastic deformation of the surface. Experimental work based on central composite second order rotatable design has been carried out on a lathe machine to establish the effects of ball burnishing parameters on the surface roughness of brass material. Analysis of the results by the analysis of variance technique and the F-test show that the parameters considered, have significant effects on the surface roughness.

**Keywords:**
Ball burnishing,
Response surface Methodology.

##### 568 Motion Control of a Ball Throwing Robot with a Flexible Robotic Arm

**Authors:**
Yizhi Gai,
Yukinori Kobayashi,
Yohei Hoshino,
Takanori Emaru

**Abstract:**

Motion control of flexible arms is more difficult than that of rigid arms, however utilizing its dynamics enables improved performance such as a fast motion in short operation time. This paper investigates a ball throwing robot with one rigid link and one flexible link. This robot throws a ball at a set speed with a proper control torque. A mathematical model of this ball throwing robot is derived through Hamilton’s principle. Several patterns of torque input are designed and tested through the proposed simulation models. The parameters of each torque input pattern is optimized and determined by chaos embedded vector evaluated particle swarm optimization (CEVEPSO). Then, the residual vibration of the manipulator after throwing is suppressed with input shaping technique. Finally, a real experiment is set up for the model checking.

**Keywords:**
Motion control,
flexible robotic arm,
CEVEPSO,
ball
throwing robot.

##### 567 Primary School Teachers’ Conceptual and Procedural Knowledge of Rational Number and Its Effects on Pupils’ Achievement in Rational Numbers

**Authors:**
R. M. Kashim

**Abstract:**

**Keywords:**
Achievement,
conceptual knowledge,
procedural knowledge,
rational numbers.

##### 566 Approximating Maximum Speed on Road from Curvature Information of Bezier Curve

**Authors:**
M. Y. Misro,
A. Ramli,
J. M. Ali

**Abstract:**

**Keywords:**
Speed estimation,
path constraints,
reference
trajectory,
Bezier curve.

##### 565 Fracture Control of the Soda-Lime Glass in Laser Thermal Cleavage

**Authors:**
Jehnming Lin

**Abstract:**

The effects of the contact ball-lens on the soda lime glass in laser thermal cleavage with a cw Nd-YAG laser were investigated in this study. A contact ball-lens was adopted to generate a bending force on the crack formation of the soda-lime glass in the laser cutting process. The Nd-YAG laser beam (wavelength of 1064 nm) was focused through the ball-lens and transmitted to the soda-lime glass, which was coated with a carbon film on the surface with a bending force from a ball-lens to generate a tensile stress state on the surface cracking. The fracture was controlled by the contact ball-lens and a straight cutting was tested to demonstrate the feasibility. Experimental observations on the crack propagation from the leading edge, main section and trailing edge of the glass sheet were compared with various mechanical and thermal loadings. Further analyses on the stress under various laser powers and contact ball loadings were made to characterize the innovative technology. The results show that the distributions of the side crack at the leading and trailing edges are mainly dependent on the boundary condition, contact force, cutting speed and laser power. With the increase of the mechanical and thermal loadings, the region of the side cracks might be dramatically reduced with proper selection of the geometrical constrains. Therefore the application of the contact ball-lens is a possible way to control the fracture in laser cleavage with improved cutting qualities.

**Keywords:**
Laser cleavage,
controlled fracture,
contact ball lens.

##### 564 Influence of Ball Milling Time on Mechanical Properties of Porous Ti-20Nb-5Ag Alloy

**Authors:**
M. J. Shivaram,
Shashi Bhushan Arya,
Jagannath Nayak,
Bharat Bhooshan Panigrahi

**Abstract:**

_{4}HCO

_{3}). The resultant powder particles, fabricated solid and porous samples were characterized by scanning electron microscopy (SEM). The compressive strength, elastic modulus and microhardness properties were investigated. Solid and porous Ti-20Nb-5Ag alloy samples showed good mechanical properties for 20 h ball milling time as compare to 5 h ball milling.

**Keywords:**
Ball Milling,
compressive strengths,
microstructure,
porous Titanium alloy.

##### 563 Analysis of Chatter in Ball End Milling by Wavelet Transform

**Authors:**
S. Tangjitsitcharoen

**Abstract:**

The chatter is one of the major limitations of the productivity in the ball end milling process. It affects the surface roughness, the dimensional accuracy and the tool life. The aim of this research is to propose the new system to detect the chatter during the ball end milling process by using the wavelet transform. The proposed method is implemented on the 5-axis CNC machining center and the new three parameters are introduced from three dynamic cutting forces, which are calculated by taking the ratio of the average variances of dynamic cutting forces to the absolute variances of themselves. It had been proved that the chatter can be easier to detect during the in-process cutting by using the new parameters which are proposed in this research. The experimentally obtained results showed that the wavelet transform can provide the reliable results to detect the chatter under various cutting conditions.

**Keywords:**
Ball end milling,
wavelet transform,
fast fourier transform,
chatter.

##### 562 Fast and Efficient Algorithms for Evaluating Uniform and Nonuniform Lagrange and Newton Curves

**Authors:**
Taweechai Nuntawisuttiwong,
Natasha Dejdumrong

**Abstract:**

**Keywords:**
Newton interpolation,
Lagrange interpolation,
linear
complexity.