**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**519

# Search results for: Reynold’s numbers

##### 519 Experimental Study on Using the Aluminum Sacrificial Anode as a Cathodic Protection for Marine Structures

**Authors:**
A. Radwan,
A. Elbatran,
A. Mehanna,
M. Shehadeh

**Abstract:**

**Keywords:**
Corrosion,
Reynold’s numbers,
sacrificial anode,
velocity.

##### 518 A Class of Recurrent Sequences Exhibiting Some Exciting Properties of Balancing Numbers

**Abstract:**

**Keywords:**
Recurrent sequences,
Balancing numbers,
Lucas balancing
numbers,
Binet form.

##### 517 On λ− Summable of Orlicz Space of Gai Sequences of Fuzzy Numbers

**Authors:**
N.Subramanian,
S.Krishnamoorthy,
S. Balasubramanian

**Abstract:**

**Keywords:**
Fuzzy numbers,
statistical convergence,
Orlicz space,
gai sequence.

##### 516 Strong Law of Large Numbers for *- Mixing Sequence

**Authors:**
Bainian Li,
Kongsheng Zhang

**Abstract:**

Strong law of large numbers and complete convergence for sequences of *-mixing random variables are investigated. In particular, Teicher-s strong law of large numbers for independent random variables are generalized to the case of *-mixing random sequences and extended to independent and identically distributed Marcinkiewicz Law of large numbers for *-mixing.

**Keywords:**
mixing squences,
strong law of large numbers,
martingale differences,
Lacunary System

##### 515 Applying Half-Circle Fuzzy Numbers to Control System: A Preliminary Study on Development of Intelligent System on Marine Environment and Engineering

**Authors:**
Chen-Yuan Chen,
Wan-I Lee,
Yi-Chaio Sui,
Cheng-Wu Chen

**Abstract:**

This study focuses on the development of triangular fuzzy numbers, the revising of triangular fuzzy numbers, and the constructing of a HCFN (half-circle fuzzy number) model which can be utilized to perform more plural operations. They are further transformed for trigonometric functions and polar coordinates. From half-circle fuzzy numbers we can conceive cylindrical fuzzy numbers, which work better in algebraic operations. An example of fuzzy control is given in a simulation to show the applicability of the proposed half-circle fuzzy numbers.

**Keywords:**
triangular fuzzy number,
half-circle fuzzy numbers,
predictions,
polar coordinates,
Lyapunov method

##### 514 A New Class χ2 (M, A,) of the Double Difference Sequences of Fuzzy Numbers

**Authors:**
N.Subramanian,
U.K.Misra

**Abstract:**

The aim of this paper is to introduce and study a new concept of strong double χ2 (M,A, Δ) of fuzzy numbers and also some properties of the resulting sequence spaces of fuzzy numbers were examined.

**Keywords:**
Modulus function,
fuzzy number,
metric space.

##### 513 On λ− Summable of Orlicz Space of Entire Sequences of Fuzzy Numbers

**Authors:**
N. Subramanian,
U. K. Misra,
M. S. Panda

**Abstract:**

**Keywords:**
Fuzzy numbers,
statistical convergence,
Orlicz space,
entire sequence.

##### 512 On the Numerical and Experimental Analysis of Internal Pressure in Air Bearings

**Authors:**
Abdurrahim Dal,
Tuncay Karaçay

**Abstract:**

**Keywords:**
Air bearing,
internal pressure,
Reynold’s equation,
rotor.

##### 511 Ranking Fuzzy Numbers Based On Epsilon-Deviation Degree

**Authors:**
Vincent F. Yu,
Ha Thi Xuan Chi

**Abstract:**

Nejad and Mashinchi (2011) proposed a revision for ranking fuzzy numbers based on the areas of the left and the right sides of a fuzzy number. However, this method still has some shortcomings such as lack of discriminative power to rank similar fuzzy numbers and no guarantee the consistency between the ranking of fuzzy numbers and the ranking of their images. To overcome these drawbacks, we propose an epsilon-deviation degree method based on the left area and the right area of a fuzzy number, and the concept of the centroid point. The main advantage of the new approach is the development of an innovative index value which can be used to consistently evaluate and rank fuzzy numbers. Numerical examples are presented to illustrate the efficiency and superiority of the proposed method.

**Keywords:**
Ranking fuzzy numbers,
Centroid,
Deviation degree.

##### 510 Ranking Fuzzy Numbers Based on Lexicographical Ordering

**Authors:**
B. Farhadinia

**Abstract:**

**Keywords:**
Ranking fuzzy numbers,
Lexicographical ordering.

##### 509 Winding Numbers of Paths of Analytic Functions Zeros in Finite Quantum Systems

**Authors:**
Muna Tabuni

**Abstract:**

The paper contains an investigation of winding numbers of paths of zeros of analytic theta functions. We have considered briefly an analytic representation of finite quantum systems ZN. The analytic functions on a torus have exactly N zeros. The brief introduction to the zeros of analytic functions and there time evolution is given. We have discussed the periodic finite quantum systems. We have introduced the winding numbers in general. We consider the winding numbers of the zeros of analytic theta functions.

**Keywords:**
Winding numbers,
period,
paths of zeros.

##### 508 A New Approach For Ranking Of Generalized Trapezoidal Fuzzy Numbers

**Authors:**
Amit Kumar,
Pushpinder Singh,
Parampreet Kaur,
Amarpreet Kaur

**Abstract:**

**Keywords:**
Ranking function,
Generalized trapezoidal fuzzy numbers

##### 507 Dependent Weighted Aggregation Operators of Hesitant Fuzzy Numbers

**Authors:**
Jing Liu

**Abstract:**

In this paper, motivated by the ideas of dependent weighted aggregation operators, we develop some new hesitant fuzzy dependent weighted aggregation operators to aggregate the input arguments taking the form of hesitant fuzzy numbers rather than exact numbers, or intervals. In fact, we propose three hesitant fuzzy dependent weighted averaging(HFDWA) operators, and three hesitant fuzzy dependent weighted geometric(HFDWG) operators based on different weight vectors, and the most prominent characteristic of these operators is that the associated weights only depend on the aggregated hesitant fuzzy numbers and can relieve the influence of unfair hesitant fuzzy numbers on the aggregated results by assigning low weights to those “false” and “biased” ones. Some examples are given to illustrated the efficiency of the proposed operators.

**Keywords:**
Hesitant fuzzy numbers,
hesitant fuzzy dependent weighted averaging(HFDWA) operators,
hesitant fuzzy dependent weighted geometric(HFDWG) operators.

##### 506 A Quadratic Approach for Generating Pythagorean Triples

**Authors:**
P. K. Rahul Krishna,
S. Sandeep Kumar,
Jayanthi Sunder Raj

**Abstract:**

The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

**Keywords:**
Arithmetic progression,
hypotenuse leg difference method,
natural numbers,
Pythagorean triplets,
quadratic equation.

##### 505 Lower Bounds of Some Small Ramsey Numbers

**Authors:**
Decha Samana,
Vites Longani

**Abstract:**

**Keywords:**
Lower bound,
Ramsey numbers,
Graphs,
Distance line.

##### 504 The Orlicz Space of the Entire Sequence Fuzzy Numbers Defined by Infinite Matrices

**Authors:**
N.Subramanian,
C.Murugesan

**Abstract:**

This paper is devoted to the study of the general properties of Orlicz space of entire sequence of fuzzy numbers by using infinite matrices.

**Keywords:**
Fuzzy numbers,
infinite matrix,
Orlicz space,
entiresequence.

##### 503 Strong Limit Theorems for Dependent Random Variables

**Authors:**
Libin Wu,
Bainian Li

**Abstract:**

**Keywords:**
Lacunary System,
Generalized Gaussian,
NA sequences,
strong law of large numbers.

##### 502 IFDewey: A New Insert-Friendly Labeling Schemafor XML Data

**Authors:**
S. Soltan,
A. Zarnani,
R. AliMohammadzadeh,
M. Rahgozar

**Abstract:**

XML has become a popular standard for information exchange via web. Each XML document can be presented as a rooted, ordered, labeled tree. The Node label shows the exact position of a node in the original document. Region and Dewey encoding are two famous methods of labeling trees. In this paper, we propose a new insert friendly labeling method named IFDewey based on recently proposed scheme, called Extended Dewey. In Extended Dewey many labels must be modified when a new node is inserted into the XML tree. Our method eliminates this problem by reserving even numbers for future insertion. Numbers generated by Extended Dewey may be even or odd. IFDewey modifies Extended Dewey so that only odd numbers are generated and even numbers can then be used for a much easier insertion of nodes.

**Keywords:**
XML,
tree labeling,
query processing.

##### 501 Evolution of Fuzzy Neural Networks Using an Evolution Strategy with Fuzzy Genotype Values

**Authors:**
Hidehiko Okada

**Abstract:**

Evolution strategy (ES) is a well-known instance of evolutionary algorithms, and there have been many studies on ES. In this paper, the author proposes an extended ES for solving fuzzy-valued optimization problems. In the proposed ES, genotype values are not real numbers but fuzzy numbers. Evolutionary processes in the ES are extended so that it can handle genotype instances with fuzzy numbers. In this study, the proposed method is experimentally applied to the evolution of neural networks with fuzzy weights and biases. Results reveal that fuzzy neural networks evolved using the proposed ES with fuzzy genotype values can model hidden target fuzzy functions even though no training data are explicitly provided. Next, the proposed method is evaluated in terms of variations in specifying fuzzy numbers as genotype values. One of the mostly adopted fuzzy numbers is a symmetric triangular one that can be specified by its lower and upper bounds (LU) or its center and width (CW). Experimental results revealed that the LU model contributed better to the fuzzy ES than the CW model, which indicates that the LU model should be adopted in future applications of the proposed method.

**Keywords:**
Evolutionary algorithm,
evolution strategy,
fuzzy number,
feedforward neural network,
neuroevolution.

##### 500 Modified Diffie-Hellman Protocol By Extend The Theory of The Congruence

**Authors:**
Rand Alfaris,
Mohamed Rushdan MD Said,
Mohamed Othman,
Fudziah Ismail

**Abstract:**

**Keywords:**
Extended theory of the congruence,
modified Diffie-
Hellman protocol.

##### 499 Fuzzy Numbers and MCDM Methods for Portfolio Optimization

**Authors:**
Thi T. Nguyen,
Lee N. Gordon-Brown

**Abstract:**

**Keywords:**
Fuzzy numbers,
SAW,
TOPSIS,
portfolio
optimization,
higher moments,
risk management.

##### 498 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.

##### 497 A Two-Stage Multi-Agent System to Predict the Unsmoothed Monthly Sunspot Numbers

**Authors:**
Mak Kaboudan

**Abstract:**

**Keywords:**
Computational techniques,
discrete wavelet transformations,
solar cycle prediction,
sunspot numbers.

##### 496 Genetic Algorithm with Fuzzy Genotype Values and Its Application to Neuroevolution

**Authors:**
Hidehiko Okada

**Abstract:**

The author proposes an extension of genetic algorithm (GA) for solving fuzzy-valued optimization problems. In the proposed GA, values in the genotypes are not real numbers but fuzzy numbers. Evolutionary processes in GA are extended so that GA can handle genotype instances with fuzzy numbers. The proposed method is applied to evolving neural networks with fuzzy weights and biases. Experimental results showed that fuzzy neural networks evolved by the fuzzy GA could model hidden target fuzzy functions well despite the fact that no training data was explicitly provided.

**Keywords:**
Evolutionary algorithm,
genetic algorithm,
fuzzy number,
neural network,
neuroevolution.

##### 495 A Reduced-Bit Multiplication Algorithm for Digital Arithmetic

**Authors:**
Harpreet Singh Dhillon,
Abhijit Mitra

**Abstract:**

A reduced-bit multiplication algorithm based on the ancient Vedic multiplication formulae is proposed in this paper. Both the Vedic multiplication formulae, Urdhva tiryakbhyam and Nikhilam, are first discussed in detail. Urdhva tiryakbhyam, being a general multiplication formula, is equally applicable to all cases of multiplication. It is applied to the digital arithmetic and is shown to yield a multiplier architecture which is very similar to the popular array multiplier. Due to its structure, it leads to a high carry propagation delay in case of multiplication of large numbers. Nikhilam Sutra, on the other hand, is more efficient in the multiplication of large numbers as it reduces the multiplication of two large numbers to that of two smaller numbers. The framework of the proposed algorithm is taken from this Sutra and is further optimized by use of some general arithmetic operations such as expansion and bit-shifting to take advantage of bit-reduction in multiplication. We illustrate the proposed algorithm by reducing a general 4x4-bit multiplication to a single 2 x 2-bit multiplication operation.

**Keywords:**
Multiplication,
algorithm,
Vedic mathematics,
digital
arithmetic,
reduced-bit.

##### 494 Method for Solving Fully Fuzzy Assignment Problems Using Triangular Fuzzy Numbers

**Authors:**
Amit Kumar,
Anila Gupta,
Amarpreet Kaur

**Abstract:**

In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy assignment problems by representing all the parameters as triangular fuzzy numbers. The advantages of the pro-posed method are also discussed. To illustrate the proposed method a fuzzy assignment problem is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy assignment problems occurring in real life situations.

**Keywords:**
Fuzzy assignment problem,
Ranking function,
Triangular fuzzy numbers.

##### 493 A New Class F2 (M, 0, N)L„ p)F of The Double Difference Sequences of Fuzzy Numbers

**Authors:**
N. Subramanian,
C. Murugesan

**Abstract:**

The double difference sequence space I2 (M, of fuzzy numbers for both 1 < p < oo and 0 < p < 1, is introduced. Some general properties of this sequence space are studied. Some inclusion relations involving this sequence space are obtained.

**Keywords:**
Orlicz function,
solid space,
metric space,
completeness

##### 492 CFD Simulation of Non-Newtonian Fluid Flow in Arterial Stenoses with Surface Irregularities

**Authors:**
R. Manimaran

**Abstract:**

**Keywords:**
Blood flow,
Roughness,
Computational fluid
dynamics,
Bio fluid mechanics.

##### 491 Solution of Interval-valued Manufacturing Inventory Models With Shortages

**Authors:**
Susovan Chakrabortty,
Madhumangal Pal,
Prasun Kumar Nayak

**Abstract:**

**Keywords:**
EOQ,
Inventory,
Interval Number,
Demand,
Production,
Simulation

##### 490 Force Statistics and Wake Structure Mechanism of Flow around a Square Cylinder at Low Reynolds Numbers

**Authors:**
Shams-Ul-Islam,
Waqas Sarwar Abbasi,
Hamid Rahman

**Abstract:**

Numerical investigation of flow around a square cylinder are presented using the multi-relaxation-time lattice Boltzmann methods at different Reynolds numbers. A detail analysis are given in terms of time-trace analysis of drag and lift coefficients, power spectra analysis of lift coefficient, vorticity contours visualizations, streamlines and phase diagrams. A number of physical quantities mean drag coefficient, drag coefficient, Strouhal number and root-mean-square values of drag and lift coefficients are calculated and compared with the well resolved experimental data and numerical results available in open literature. The Reynolds numbers affected the physical quantities.

**Keywords:**
Code validation,
Force statistics,
Multi-relaxation-time lattice Boltzmann method,
Reynolds numbers,
Square cylinder.