**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2889

# Search results for: weak law of large numbers.

##### 2889 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

##### 2888 The Convergence Theorems for Mixing Random Variable Sequences

**Authors:**
Yan-zhao Yang

**Abstract:**

**Keywords:**
Complete convergence,
mixing random variables,
weak law of large numbers.

##### 2887 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.

##### 2886 Talent in Autism: Cognitive Style based on Weak Central Coherence and Special Sensory Characteristics in State of Kuwait: Case Study

**Authors:**
Mariam Abdulaziz Y.Esmaeel

**Abstract:**

**Keywords:**
Autism,
Central Coherence,
Savant,
Sensory
characteristics,
Talent.

##### 2885 Banach Lattices with Weak Dunford-Pettis Property

**Authors:**
Khalid Bouras,
Mohammed Moussa

**Abstract:**

We introduce and study the class of weak almost Dunford-Pettis operators. As an application, we characterize Banach lattices with the weak Dunford-Pettis property. Also, we establish some sufficient conditions for which each weak almost Dunford-Pettis operator is weak Dunford-Pettis. Finally, we derive some interesting results.

**Keywords:**
Almost Dunford-Pettis operator,
weak Dunford-Pettis operator,
eak almost Dunford-Pettis operator,
almost Dunford-Pettis operator,
weak Dunford-Pettis operator

##### 2884 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.

##### 2883 A Class of Recurrent Sequences Exhibiting Some Exciting Properties of Balancing Numbers

**Abstract:**

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

##### 2882 On Strong(Weak) Domination in Fuzzy Graphs

**Authors:**
C.Natarajan,
S.K.Ayyaswamy

**Abstract:**

Let G be a fuzzy graph. Then D Ôèå V is said to be a strong (weak) fuzzy dominating set of G if every vertex v ∈ V -D is strongly (weakly) dominated by some vertex u in D. We denote a strong (weak) fuzzy dominating set by sfd-set (wfd-set). The minimum scalar cardinality of a sfd-set (wfd-set) is called the strong (weak) fuzzy domination number of G and it is denoted by γsf (G)γwf (G). In this paper we introduce the concept of strong (weak) domination in fuzzy graphs and obtain some interesting results for this new parameter in fuzzy graphs.

**Keywords:**
Fuzzy graphs,
fuzzy domination,
strong (weak) fuzzy domination number.

##### 2881 The Giant Component in a Random Subgraph of a Weak Expander

**Authors:**
Yilun Shang

**Abstract:**

In this paper, we investigate the appearance of the giant component in random subgraphs G(p) of a given large finite graph family Gn = (Vn, En) in which each edge is present independently with probability p. We show that if the graph Gn satisfies a weak isoperimetric inequality and has bounded degree, then the probability p under which G(p) has a giant component of linear order with some constant probability is bounded away from zero and one. In addition, we prove the probability of abnormally large order of the giant component decays exponentially. When a contact graph is modeled as Gn, our result is of special interest in the study of the spread of infectious diseases or the identification of community in various social networks.

**Keywords:**
subgraph,
expander,
random graph,
giant component,
percolation.

##### 2880 Large Deviations for Lacunary Systems

**Authors:**
Bainian Li,
Kongsheng Zhang

**Abstract:**

**Keywords:**
Lacunary system,
larger deviations,
Locally GeneralizedGaussian,
Strong law of large numbers.

##### 2879 Efficient Large Numbers Karatsuba-Ofman Multiplier Designs for Embedded Systems

**Authors:**
M.Machhout,
M.Zeghid,
W.El hadj youssef,
B.Bouallegue,
A.Baganne,
R.Tourki

**Abstract:**

**Keywords:**
finite field,
Karatsuba-Ofman,
long numbers,
multiplication,
mathematical model,
recursivity.

##### 2878 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.

##### 2877 Numerical Analysis of Turbulent Natural Convection in a Square Cavity using Large- Eddy Simulation in Lattice Boltzmann Method

**Authors:**
H. Sajjadi,
M. Gorji,
GH.R. Kefayati,
D. D. Ganji,
M. Shayan Nia

**Abstract:**

**Keywords:**
Turbulent natural convection,
Large Eddy
Simulation,
Lattice Boltzmann Method

##### 2876 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

##### 2875 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.

##### 2874 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.

##### 2873 Common Fixed Point Theorems for Co-Cyclic Weak Contractions in Compact Metric

**Authors:**
Alemayehu Geremew Negash

**Abstract:**

In this paper, we prove some common fixed point theorems for co-cyclic weak contractions in compact metric spaces.

**Keywords:**
Cyclic weak contraction,
Co-cyclic weak contraction,
Co-cyclic representation,
Common fixed point.

##### 2872 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.

##### 2871 How are Equalities Defined, Strong or Weak on a Multiple Algebra?

**Authors:**
Mona Taheri

**Abstract:**

For the purpose of finding the quotient structure of multiple algebras such as groups, Abelian groups and rings, we will state concepts of ( strong or weak ) equalities on multiple algebras, which will lead us to research on how ( strong or weak) are equalities defined on a multiple algebra over the quotients obtained from it. In order to find a quotient structure of multiple algebras such as groups, Abelian groups and loops, a part of this article has been allocated to the concepts of equalities (strong and weak) of the defined multiple functions on multiple algebras. This leads us to do research on how defined equalities (strong and weak) are made in the multiple algebra on its resulted quotient.

**Keywords:**
Multiple algebra,
mathematics,
universal algebra.

##### 2870 An Alternative Method for Generating Almost Infinite Sequence of Gaussian Variables

**Authors:**
Nyah C. Temaneh,
F. A. Phiri,
E. Ruhunga

**Abstract:**

**Keywords:**
Gaussian variable,
statistical analysis,
simulation ofCommunication Network,
Random numbers.

##### 2869 Ranking Fuzzy Numbers Based on Lexicographical Ordering

**Authors:**
B. Farhadinia

**Abstract:**

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

##### 2868 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.

##### 2867 The Analogue of a Property of Pisot Numbers in Fields of Formal Power Series

**Authors:**
Wiem Gadri

**Abstract:**

This study delves into the intriguing properties of Pisot and Salem numbers within the framework of formal Laurent series over finite fields, a domain where these numbers’ spectral characteristics, Λm(β) and lm(β), have yet to be fully explored. Utilizing a methodological approach that combines algebraic number theory with the analysis of power series, we extend the foundational work of Erdos, Joo, and Komornik to this setting. Our research uncovers bounds for lm(β), revealing how these depend on the degree of the minimal polynomial of β and thus offering a characterization of Pisot and Salem formal power series. The findings significantly contribute to our understanding of these numbers, highlighting their distribution and properties in the context of formal power series. This investigation not only bridges number theory with formal power series analysis but also sets the stage for further interdisciplinary research in these areas.

**Keywords:**
Pisot numbers,
Salem numbers,
Formal power series,
Minimal polynomial degree.

##### 2866 Behaviours of Energy Spectrum at Low Reynolds Numbers in Grid Turbulence

**Authors:**
Md. Kamruzzaman,
L. Djenidi,
R. A. Antonia

**Abstract:**

This paper reports an experimental investigation of the energy spectrum of turbulent velocity fields at low Reynolds numbers in grid turbulence. Hot wire measurements are carried out in grid turbulence with subjected to a 1.36:1 contraction of the wind tunnel. Three different grids are used: (i) large square perforated grid (mesh size 43.75mm), (ii) small square perforated grid (mesh size 14. and (iii) woven mesh grid (mesh size 5mm). The results indicate that the energy spectrum at small Reynolds numbers does not follow Kolmogorov’s universal scaling. It is further found that the critical Reynolds number, below which the scaling breaks down, is around 25.

**Keywords:**
Decay exponent,
Energy spectrum,
Taylor microscale Reynolds number,
Taylor microscale,
Turbulent kinetic energy.

##### 2865 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

##### 2864 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.

##### 2863 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.

##### 2862 Weak Instability in Direct Integration Methods for Structural Dynamics

**Authors:**
Shuenn-Yih Chang,
Chiu-Li Huang

**Abstract:**

**Keywords:**
Dynamic analysis,
high frequency,
integration method,
overshoot,
weak instability.

##### 2861 Retail Strategy to Reduce Waste Keeping High Profit Utilizing Taylor's Law in Point-of-Sales Data

**Authors:**
Gen Sakoda,
Hideki Takayasu,
Misako Takayasu

**Abstract:**

Waste reduction is a fundamental problem for sustainability. Methods for waste reduction with point-of-sales (POS) data are proposed, utilizing the knowledge of a recent econophysics study on a statistical property of POS data. Concretely, the non-stationary time series analysis method based on the Particle Filter is developed, which considers abnormal fluctuation scaling known as Taylor's law. This method is extended for handling incomplete sales data because of stock-outs by introducing maximum likelihood estimation for censored data. The way for optimal stock determination with pricing the cost of waste reduction is also proposed. This study focuses on the examination of the methods for large sales numbers where Taylor's law is obvious. Numerical analysis using aggregated POS data shows the effectiveness of the methods to reduce food waste maintaining a high profit for large sales numbers. Moreover, the way of pricing the cost of waste reduction reveals that a small profit loss realizes substantial waste reduction, especially in the case that the proportionality constant of Taylor’s law is small. Specifically, around 1% profit loss realizes half disposal at =0.12, which is the actual value of processed food items used in this research. The methods provide practical and effective solutions for waste reduction keeping a high profit, especially with large sales numbers.

**Keywords:**
Food waste reduction,
particle filter,
point of sales,
sustainable development goals,
Taylor's Law,
time series analysis.

##### 2860 Isomorphism on Fuzzy Graphs

**Authors:**
A.Nagoor Gani,
J.Malarvizhi

**Abstract:**

**Keywords:**
complementary fuzzy graphs,
co-weak isomorphism,
equivalence relation,
fuzzy relation,
weak isomorphism.