Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1114

Search results for: Random numbers.

1114 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

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1113 Strong Limit Theorems for Dependent Random Variables

Authors: Libin Wu, Bainian Li

Abstract:

In This Article We establish moment inequality of dependent random variables,furthermore some theorems of strong law of large numbers and complete convergence for sequences of dependent random variables. In particular, independent and identically distributed Marcinkiewicz Law of large numbers are generalized to the case of m0-dependent sequences.

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

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1112 A Very Efficient Pseudo-Random Number Generator Based On Chaotic Maps and S-Box Tables

Authors: M. Hamdi, R. Rhouma, S. Belghith

Abstract:

Generating random numbers are mainly used to create secret keys or random sequences. It can be carried out by various techniques. In this paper we present a very simple and efficient pseudo random number generator (PRNG) based on chaotic maps and S-Box tables. This technique adopted two main operations one to generate chaotic values using two logistic maps and the second to transform them into binary words using random S-Box tables. The simulation analysis indicates that our PRNG possessing excellent statistical and cryptographic properties.

Keywords: Chaotic map, Cryptography, Random Numbers, Statistical tests, S-box.

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1111 An Alternative Method for Generating Almost Infinite Sequence of Gaussian Variables

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

Abstract:

Most of the well known methods for generating Gaussian variables require at least one standard uniform distributed value, for each Gaussian variable generated. The length of the random number generator therefore, limits the number of independent Gaussian distributed variables that can be generated meanwhile the statistical solution of complex systems requires a large number of random numbers for their statistical analysis. We propose an alternative simple method of generating almost infinite number of Gaussian distributed variables using a limited number of standard uniform distributed random numbers.

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

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1110 The Convergence Theorems for Mixing Random Variable Sequences

Authors: Yan-zhao Yang

Abstract:

In this paper, some limit properties for mixing random variables sequences were studied and some results on weak law of large number for mixing random variables sequences were presented. Some complete convergence theorems were also obtained. The results extended and improved the corresponding theorems in i.i.d random variables sequences.

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

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1109 A Class of Recurrent Sequences Exhibiting Some Exciting Properties of Balancing Numbers

Authors: G.K.Panda, S.S.Rout

Abstract:

The balancing numbers are natural numbers n satisfying the Diophantine equation 1 + 2 + 3 + · · · + (n - 1) = (n + 1) + (n + 2) + · · · + (n + r); r is the balancer corresponding to the balancing number n.The nth balancing number is denoted by Bn and the sequence {Bn}1 n=1 satisfies the recurrence relation Bn+1 = 6Bn-Bn-1. The balancing numbers posses some curious properties, some like Fibonacci numbers and some others are more interesting. This paper is a study of recurrent sequence {xn}1 n=1 satisfying the recurrence relation xn+1 = Axn - Bxn-1 and possessing some curious properties like the balancing numbers.

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

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1108 Estimated Production Potential Types of Wind Turbines Connected to the Network Using Random Numbers Simulation

Authors: Saeid Nahi, Seyed Mohammad Hossein Nabavi

Abstract:

Nowadays, power systems, energy generation by wind has been very important. Noting that the production of electrical energy by wind turbines on site to several factors (such as wind speed and profile site for the turbines, especially off the wind input speed, wind rated speed and wind output speed disconnect) is dependent. On the other hand, several different types of turbines in the market there. Therefore, selecting a turbine that its capacity could also answer the need for electric consumers the efficiency is high something is important and necessary. In this context, calculating the amount of wind power to help optimize overall network, system operation, in determining the parameters of wind power is very important. In this article, to help calculate the amount of wind power plant, connected to the national network in the region Manjil wind, selecting the best type of turbine and power delivery profile appropriate to the network using Monte Carlo method has been. In this paper, wind speed data from the wind site in Manjil, as minute and during the year has been. Necessary simulations based on Random Numbers Simulation method and repeat, using the software MATLAB and Excel has been done.

Keywords: wind turbine, efficiency, wind turbine work points, Random Numbers, reliability

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1107 Deterministic Random Number Generator Algorithm for Cryptosystem Keys

Authors: Adi A. Maaita, Hamza A. A. Al_Sewadi

Abstract:

One of the crucial parameters of digital cryptographic systems is the selection of the keys used and their distribution. The randomness of the keys has a strong impact on the system’s security strength being difficult to be predicted, guessed, reproduced, or discovered by a cryptanalyst. Therefore, adequate key randomness generation is still sought for the benefit of stronger cryptosystems. This paper suggests an algorithm designed to generate and test pseudo random number sequences intended for cryptographic applications. This algorithm is based on mathematically manipulating a publically agreed upon information between sender and receiver over a public channel. This information is used as a seed for performing some mathematical functions in order to generate a sequence of pseudorandom numbers that will be used for encryption/decryption purposes. This manipulation involves permutations and substitutions that fulfill Shannon’s principle of “confusion and diffusion”. ASCII code characters were utilized in the generation process instead of using bit strings initially, which adds more flexibility in testing different seed values. Finally, the obtained results would indicate sound difficulty of guessing keys by attackers.

Keywords: Cryptosystems, Information Security agreement, Key distribution, Random numbers.

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1106 Topological Properties of an Exponential Random Geometric Graph Process

Authors: Yilun Shang

Abstract:

In this paper we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process. The transition probability matrix and stationary distribution are derived for the Markov chains concerning connectivity and the number of components. We analyze the algorithm for hitting time regarding disconnectivity. In addition to dynamical properties, we also study topological properties for static snapshots. We obtain the degree distributions as well as asymptotic precise bounds and strong law of large numbers for connectivity threshold distance and the largest nearest neighbor distance amongst others. Both exact results and limit theorems are provided in this paper.

Keywords: random geometric graph, autoregressive process, degree, connectivity, Markovian, wireless network.

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1105 On λ− Summable of Orlicz Space of Gai Sequences of Fuzzy Numbers

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

Abstract:

In this paper the concept of strongly (λM)p - Ces'aro summability of a sequence of fuzzy numbers and strongly λM- statistically convergent sequences of fuzzy numbers is introduced.

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

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1104 Software Product Quality Evaluation Model with Multiple Criteria Decision Making Analysis

Authors: C. Ardil

Abstract:

This paper presents a software product quality evaluation model based on the ISO/IEC 25010 quality model. The evaluation characteristics and sub characteristics were identified from the ISO/IEC 25010 quality model. The multidimensional structure of the quality model is based on characteristics such as functional suitability, performance efficiency, compatibility, usability, reliability, security, maintainability, and portability, and associated sub characteristics. Random numbers are generated to establish the decision maker’s importance weights for each sub characteristics. Also, random numbers are generated to establish the decision matrix of the decision maker’s final scores for each software product against each sub characteristics. Thus, objective criteria importance weights and index scores for datasets were obtained from the random numbers. In the proposed model, five different software product quality evaluation datasets under three different weight vectors were applied to multiple criteria decision analysis method, preference analysis for reference ideal solution (PARIS) for comparison, and sensitivity analysis procedure. This study contributes to provide a better understanding of the application of MCDMA methods and ISO/IEC 25010 quality model guidelines in software product quality evaluation process.

Keywords: ISO/IEC 25010 quality model, multiple criteria decisions making, multiple criteria decision making analysis, MCDMA, PARIS, Software Product Quality Evaluation Model, Software Product Quality Evaluation, Software Evaluation, Software Selection, Software

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1103 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

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1102 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.

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1101 On λ− Summable of Orlicz Space of Entire Sequences of Fuzzy Numbers

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

Abstract:

In this paper the concept of strongly (λM)p - Ces'aro summability of a sequence of fuzzy numbers and strongly λM- statistically convergent sequences of fuzzy numbers is introduced.

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

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1100 Auto Tuning PID Controller based on Improved Genetic Algorithm for Reverse Osmosis Plant

Authors: Jin-Sung Kim, Jin-Hwan Kim, Ji-Mo Park, Sung-Man Park, Won-Yong Choe, Hoon Heo

Abstract:

An optimal control of Reverse Osmosis (RO) plant is studied in this paper utilizing the auto tuning concept in conjunction with PID controller. A control scheme composing an auto tuning stochastic technique based on an improved Genetic Algorithm (GA) is proposed. For better evaluation of the process in GA, objective function defined newly in sense of root mean square error has been used. Also in order to achieve better performance of GA, more pureness and longer period of random number generation in operation are sought. The main improvement is made by replacing the uniform distribution random number generator in conventional GA technique to newly designed hybrid random generator composed of Cauchy distribution and linear congruential generator, which provides independent and different random numbers at each individual steps in Genetic operation. The performance of newly proposed GA tuned controller is compared with those of conventional ones via simulation.

Keywords: Genetic Algorithm, Auto tuning, Hybrid random number generator, Reverse Osmosis, PID controller

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1099 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.

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1098 Some Application of Random Fuzzy Queueing System Based On Fuzzy Simulation

Authors: Behrouz Fathi-Vajargah, Sara Ghasemalipour

Abstract:

This paper studies a random fuzzy queueing system that the interarrival times of customers arriving at the server and the service times are independent and identically distributed random fuzzy variables. We match the random fuzzy queueing system with the random fuzzy alternating renewal process and we do not use from α-pessimistic and α-optimistic values to estimate the average chance of the event ”random fuzzy queueing system is busy at time t”, we employ the fuzzy simulation method in practical applications. Some theorem is proved and finally we solve a numerical example with fuzzy simulation method.

Keywords: Random fuzzy variables, Fuzzy simulation, Queueing system, Interarrival times.

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1097 Ranking Fuzzy Numbers Based on Lexicographical Ordering

Authors: B. Farhadinia

Abstract:

Although so far, many methods for ranking fuzzy numbers have been discussed broadly, most of them contained some shortcomings, such as requirement of complicated calculations, inconsistency with human intuition and indiscrimination. The motivation of this study is to develop a model for ranking fuzzy numbers based on the lexicographical ordering which provides decision-makers with a simple and efficient algorithm to generate an ordering founded on a precedence. The main emphasis here is put on the ease of use and reliability. The effectiveness of the proposed method is finally demonstrated by including a comprehensive comparing different ranking methods with the present one.

Keywords: Ranking fuzzy numbers, Lexicographical ordering.

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1096 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.

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1095 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.

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1094 Synchronization Technique for Random Switching Frequency Pulse-Width Modulation

Authors: Apinan Aurasopon, Worawat Sa-ngiavibool

Abstract:

This paper proposes a synchronized random switching frequency pulse width modulation (SRSFPWM). In this technique, the clock signal is used to control the random noise frequency which is produced by the feedback voltage of a hysteresis circuit. These make the triangular carrier frequency equaling to the random noise frequency in each switching period with the symmetrical positive and negative slopes of triangular carrier. Therefore, there is no error voltage in PWM signal. The PSpice simulated results shown the proposed technique improved the performance in case of low frequency harmonics of PWM signal comparing with conventional random switching frequency PWM.

Keywords: Random switching frequency pulse - width modulation.

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1093 A New Approach For Ranking Of Generalized Trapezoidal Fuzzy Numbers

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

Abstract:

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (2009) 6833-6842) is incorrect. The main aim of this paper is to propose a new approach for the ranking of generalized trapezoidal fuzzy numbers. The main advantage of the proposed approach is that the proposed approach provide the correct ordering of generalized and normal trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets and Systems 118 (2001) 375-385).

Keywords: Ranking function, Generalized trapezoidal fuzzy numbers

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1092 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.

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1091 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.

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1090 Meta Random Forests

Authors: Praveen Boinee, Alessandro De Angelis, Gian Luca Foresti

Abstract:

Leo Breimans Random Forests (RF) is a recent development in tree based classifiers and quickly proven to be one of the most important algorithms in the machine learning literature. It has shown robust and improved results of classifications on standard data sets. Ensemble learning algorithms such as AdaBoost and Bagging have been in active research and shown improvements in classification results for several benchmarking data sets with mainly decision trees as their base classifiers. In this paper we experiment to apply these Meta learning techniques to the random forests. We experiment the working of the ensembles of random forests on the standard data sets available in UCI data sets. We compare the original random forest algorithm with their ensemble counterparts and discuss the results.

Keywords: Random Forests [RF], ensembles, UCI.

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1089 Deterministic Random Number Generators for Online Applications

Authors: Natarajan Vijayarangan, Prasanna S. Bidare

Abstract:

Cryptography, Image watermarking and E-banking are filled with apparent oxymora and paradoxes. Random sequences are used as keys to encrypt information to be used as watermark during embedding the watermark and also to extract the watermark during detection. Also, the keys are very much utilized for 24x7x365 banking operations. Therefore a deterministic random sequence is very much useful for online applications. In order to obtain the same random sequence, we need to supply the same seed to the generator. Many researchers have used Deterministic Random Number Generators (DRNGs) for cryptographic applications and Pseudo Noise Random sequences (PNs) for watermarking. Even though, there are some weaknesses in PN due to attacks, the research community used it mostly in digital watermarking. On the other hand, DRNGs have not been widely used in online watermarking due to its computational complexity and non-robustness. Therefore, we have invented a new design of generating DRNG using Pi-series to make it useful for online Cryptographic, Digital watermarking and Banking applications.

Keywords: E-tokens, LFSR, non-linear, Pi series, pseudo random number.

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1088 Vision Based Hand Gesture Recognition Using Generative and Discriminative Stochastic Models

Authors: Mahmoud Elmezain, Samar El-shinawy

Abstract:

Many approaches to pattern recognition are founded on probability theory, and can be broadly characterized as either generative or discriminative according to whether or not the distribution of the image features. Generative and discriminative models have very different characteristics, as well as complementary strengths and weaknesses. In this paper, we study these models to recognize the patterns of alphabet characters (A-Z) and numbers (0-9). To handle isolated pattern, generative model as Hidden Markov Model (HMM) and discriminative models like Conditional Random Field (CRF), Hidden Conditional Random Field (HCRF) and Latent-Dynamic Conditional Random Field (LDCRF) with different number of window size are applied on extracted pattern features. The gesture recognition rate is improved initially as the window size increase, but degrades as window size increase further. Experimental results show that the LDCRF is the best in terms of results than CRF, HCRF and HMM at window size equal 4. Additionally, our results show that; an overall recognition rates are 91.52%, 95.28%, 96.94% and 98.05% for CRF, HCRF, HMM and LDCRF respectively.

Keywords: Statistical Pattern Recognition, Generative Model, Discriminative Model, Human Computer Interaction.

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1087 Lower Bounds of Some Small Ramsey Numbers

Authors: Decha Samana, Vites Longani

Abstract:

For positive integer s and t, the Ramsey number R(s, t) is the least positive integer n such that for every graph G of order n, either G contains Ks as a subgraph or G contains Kt as a subgraph. We construct the circulant graphs and use them to obtain lower bounds of some small Ramsey numbers.

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

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1086 Large Deviations for Lacunary Systems

Authors: Bainian Li, Kongsheng Zhang

Abstract:

Let Xi be a Lacunary System, we established large deviations inequality for Lacunary System. Furthermore, we gained Marcinkiewicz Larger Number Law with dependent random variables sequences.

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

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1085 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.

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