**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1410

# Search results for: Generating functions

##### 1410 Bilinear and Bilateral Generating Functions for the Gauss’ Hypergeometric Polynomials

**Authors:**
Manoj Singh,
Mumtaz Ahmad Khan,
Abdul Hakim Khan

**Abstract:**

The object of the present paper is to investigate several general families of bilinear and bilateral generating functions with different argument for the Gauss’ hypergeometric polynomials.

**Keywords:**
Appell’s functions,
Gauss hypergeometric functions,
Heat polynomials,
Kampe’ de Fe’riet function,
Laguerre polynomials,
Lauricella’s function,
Saran’s functions.

##### 1409 The Gerber-Shiu Functions of a Risk Model with Two Classes of Claims and Random Income

**Authors:**
Shan Gao

**Abstract:**

In this paper, we consider a risk model involving two independent classes of insurance risks and random premium income. We assume that the premium income process is a Poisson Process, and the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Both of the Gerber- Shiu functions with zero initial surplus and the probability generating functions (p.g.f.) of the Gerber-Shiu functions are obtained.

**Keywords:**
Poisson process,
generalized Erlang risk process,
Gerber-Shiu function,
generating function,
generalized Lundberg equation.

##### 1408 A Study on Stochastic Integral Associated with Catastrophes

**Authors:**
M. Reni Sagayaraj,
S. Anand Gnana Selvam,
R. Reynald Susainathan

**Abstract:**

We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).

**Keywords:**
Stochastic integrals,
single–server queue model,
catastrophes,
busy period.

##### 1407 Moment Generating Functions of Observed Gaps between Hypopnea Using Saddlepoint Approximations

**Authors:**
Nur Zakiah Mohd Saat,
Abdul Aziz Jemain

**Abstract:**

**Keywords:**
Exponential,
maximum likehood estimators,
observed gap,
Saddlepoint approximations.

##### 1406 The Bent and Hyper-Bent Properties of a Class of Boolean Functions

**Authors:**
Yu Lou,
Chunming Tang,
Yanfeng Qi,
Maozhi Xu

**Abstract:**

This paper considers the bent and hyper-bent properties of a class of Boolean functions. For one case, we present a detailed description for them to be hyper-bent functions, and give a necessary condition for them to be bent functions for another case.

**Keywords:**
Boolean functions,
bent functions,
hyper-bent functions,
character sums.

##### 1405 New Classes of Salagean type Meromorphic Harmonic Functions

**Authors:**
Hakan Bostancı,
Metin Öztürk

**Abstract:**

In this paper, a necessary and sufficient coefficient are given for functions in a class of complex valued meromorphic harmonic univalent functions of the form f = h + g using Salagean operator. Furthermore, distortion theorems, extreme points, convolution condition and convex combinations for this family of meromorphic harmonic functions are obtained.

**Keywords:**
Harmonic mappings,
Meromorphic functions,
Salagean
operator.

##### 1404 Zeros of Bargmann Analytic Representation in the Complex Plane

**Authors:**
Muna Tabuni

**Abstract:**

The paper contains an investigation of zeros Of Bargmann analytic representation. A brief introduction to Harmonic oscillator formalism is given. The Bargmann analytic representation has been studied. The zeros of Bargmann analytic function are considered. The Q or Husimi functions are introduced. The The Bargmann functions and the Husimi functions have the same zeros. The Bargmann functions f(z) have exactly q zeros. The evolution time of the zeros μn are discussed. Various examples have been given.

**Keywords:**
Bargmann functions,
Husimi functions,
zeros.

##### 1403 Subclasses of Bi-Univalent Functions Associated with Hohlov Operator

**Authors:**
Rashidah Omar,
Suzeini Abdul Halim,
Aini Janteng

**Abstract:**

The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function *f *ϵ* A *is said to be bi-univalent in the open unit disk *D* if both *f *and *f ^{-1}* are univalent in

*D*. The symbol

*A*denotes the class of all analytic functions

*f*in

*D*and it is normalized by the conditions

*f*(0) =

*f’*(0) – 1=0. The class of bi-univalent is denoted by The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function

*f*is subordinate to an analytic function

*g*if there is an analytic function

*w*defined on

*D*with

*w*(0) = 0 and |

*w*(z)| < 1 satisfying

*f*(

*z*) =

*g*[

*w*(

*z*)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

**Keywords:**
Analytic functions,
bi-univalent functions,
Hohlov operator,
subordination.

##### 1402 Unconventional Calculus Spreadsheet Functions

**Authors:**
Chahid K. Ghaddar

**Abstract:**

**Keywords:**
Calculus functions,
nonlinear systems,
differential algebraic equations,
solvers,
spreadsheet.

##### 1401 On Generalized New Class of Matrix Polynomial Set

**Authors:**
Ghazi S. Kahmmash

**Abstract:**

New generalization of the new class matrix polynomial set have been obtained. An explicit representation and an expansion of the matrix exponential in a series of these matrix are given for these matrix polynomials.

**Keywords:**
Generating functions,
Recurrences relation and Generalization of the new class matrix polynomial set.

##### 1400 Rating and Generating Sudoku Puzzles Based On Constraint Satisfaction Problems

**Authors:**
Bahare Fatemi,
Seyed Mehran Kazemi,
Nazanin Mehrasa

**Abstract:**

Sudoku is a logic-based combinatorial puzzle game which people in different ages enjoy playing it. The challenging and addictive nature of this game has made it a ubiquitous game. Most magazines, newspapers, puzzle books, etc. publish lots of Sudoku puzzles every day. These puzzles often come in different levels of difficulty so that all people, from beginner to expert, can play the game and enjoy it. Generating puzzles with different levels of difficulty is a major concern of Sudoku designers. There are several works in the literature which propose ways of generating puzzles having a desirable level of difficulty. In this paper, we propose a method based on constraint satisfaction problems to evaluate the difficulty of the Sudoku puzzles. Then we propose a hill climbing method to generate puzzles with different levels of difficulty. Whereas other methods are usually capable of generating puzzles with only few number of difficulty levels, our method can be used to generate puzzles with arbitrary number of different difficulty levels. We test our method by generating puzzles with different levels of difficulty and having a group of 15 people solve all the puzzles and recording the time they spend for each puzzle.

**Keywords:**
Constraint satisfaction problem,
generating Sudoku
puzzles,
hill climbing.

##### 1399 Geometric Properties and Neighborhood for Certain Subclasses of Multivalent Functions

**Authors:**
Hesam Mahzoon

**Abstract:**

By using the two existing operators, we have defined an operator, which is an extension for them. In this paper, first the operator is introduced. Then, using this operator, the subclasses of multivalent functions are defined. These subclasses of multivalent functions are utilized in order to obtain coefficient inequalities, extreme points, and integral means inequalities for functions belonging to these classes.

**Keywords:**
Coefficient inequalities,
extreme points,
integral means,
multivalent functions,
Al-Oboudi operator,
and Sãlãgean operator.

##### 1398 Some Issues of Measurement of Impairment of Non-Financial Assets in the Public Sector

**Authors:**
Mariam Vardiashvili

**Abstract:**

The economic value of the asset impairment process is quite large. Impairment reflects the reduction of future economic benefits or service potentials itemized in the asset. The assets owned by public sector entities bring economic benefits or are used for delivery of the free-of-charge services. Consequently, they are classified as cash-generating and non-cash-generating assets. IPSAS 21 - Impairment of non-cash-generating assets, and IPSAS 26 - Impairment of cash-generating assets, have been designed considering this specificity. When measuring impairment of assets, it is important to select the relevant methods. For measurement of the impaired Non-Cash-Generating Assets, IPSAS 21 recommends three methods: Depreciated Replacement Cost Approach, Restoration Cost Approach, and Service Units Approach. Impairment of Value in Use of Cash-Generating Assets (according to IPSAS 26) is measured by discounted value of the money sources to be received in future. Value in use of the cash-generating asserts (as per IPSAS 26) is measured by the discounted value of the money sources to be received in the future. The article provides classification of the assets in the public sector as non-cash-generating assets and cash-generating assets and, deals also with the factors which should be considered when evaluating impairment of assets. An essence of impairment of the non-financial assets and the methods of measurement thereof evaluation are formulated according to IPSAS 21 and IPSAS 26. The main emphasis is put on different methods of measurement of the value in use of the impaired Cash-Generating Assets and Non-Cash-Generation Assets and the methods of their selection. The traditional and the expected cash flow approaches for calculation of the discounted value are reviewed. The article also discusses the issues of recognition of impairment loss and its reflection in the financial reporting. The article concludes that despite a functional purpose of the impaired asset, whichever method is used for measuring the asset, presentation of realistic information regarding the value of the assets should be ensured in the financial reporting. In the theoretical development of the issue, the methods of scientific abstraction, analysis and synthesis were used. The research was carried out with a systemic approach. The research process uses international standards of accounting, theoretical researches and publications of Georgian and foreign scientists.

**Keywords:**
Non-cash-generating assets,
cash-generating assets,
recoverable value,
recoverable service amount,
value in use.

##### 1397 Learning Styles Difference in Difficulties of Generating Idea

**Authors:**
M. H. Yee,
J. Md Yunos,
W. Othman,
R. Hassan,
T. K. Tee,
M. M. Mohamad

**Abstract:**

The generation of an idea that goes through several phases is affected by individual factors, interests, preferences and motivation. The purpose of this research was to analyze the difference in difficulties of generating ideas according to individual learning styles. A total of 375 technical students from four technical universities in Malaysia were randomly selected as samples. The Kolb Learning Styles Inventory and a set of developed questionnaires were used in this research. The results showed that the most dominant learning style among technical students is Doer. A total of 319 (85.1%) technical students faced difficulties in solving individual assignments. Most of the problem faced by technical students is the difficulty of generating ideas for solving individual assignments. There was no significant difference in difficulties of generating ideas according to students’ learning styles. Therefore, students need to learn higher order thinking skills enabling students to generate ideas and consequently complete assignments.

**Keywords:**
Difference,
difficulties,
generating idea,
learning
styles.

##### 1396 Design of MBMS Client Functions in the Mobile

**Authors:**
Jaewook Shin,
Aesoon Park

**Abstract:**

**Keywords:**
BM-SC,
Broadcast,
MBMS,
Mobile,
Multicast.

##### 1395 A Class of Formal Operators for Combinatorial Identities and its Application

**Authors:**
Ruigang Zhang,
Wuyungaowa,
Xingchen Ma

**Abstract:**

In this paper, we present some formulas of symbolic operator summation, which involving Generalization well-know number sequences or polynomial sequences, and mean while we obtain some identities about the sequences by employing M-R‘s substitution rule.

**Keywords:**
Generating functions,
operators sequence group,
Riordan arrays,
R. G operator group,
combinatorial identities.

##### 1394 Performance Evaluation of Complex Valued Neural Networks Using Various Error Functions

**Authors:**
Anita S. Gangal,
P. K. Kalra,
D. S. Chauhan

**Abstract:**

**Keywords:**
Complex backpropagation algorithm,
complex errorfunctions,
complex valued neural network,
split activation function.

##### 1393 Performance Evaluation of Popular Hash Functions

**Authors:**
Sheena Mathew,
K. Poulose Jacob

**Abstract:**

**Keywords:**
Cryptography,
Hash function,
JERIM-320,
Messageintegrity

##### 1392 Operational Representation of Certain Hypergeometric Functions by Means of Fractional Derivatives and Integrals

**Authors:**
Manoj Singh,
Mumtaz Ahmad Khan,
Abdul Hakim Khan

**Abstract:**

The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral.

**Keywords:**
Fractional Derivatives and Integrals,
Hypergeometric
functions.

##### 1391 Q-Learning with Eligibility Traces to Solve Non-Convex Economic Dispatch Problems

**Authors:**
Mohammed I. Abouheaf,
Sofie Haesaert,
Wei-Jen Lee,
Frank L. Lewis

**Abstract:**

Economic Dispatch is one of the most important power system management tools. It is used to allocate an amount of power generation to the generating units to meet the load demand. The Economic Dispatch problem is a large scale nonlinear constrained optimization problem. In general, heuristic optimization techniques are used to solve non-convex Economic Dispatch problem. In this paper, ideas from Reinforcement Learning are proposed to solve the non-convex Economic Dispatch problem. Q-Learning is a reinforcement learning techniques where each generating unit learn the optimal schedule of the generated power that minimizes the generation cost function. The eligibility traces are used to speed up the Q-Learning process. Q-Learning with eligibility traces is used to solve Economic Dispatch problems with valve point loading effect, multiple fuel options, and power transmission losses.

**Keywords:**
Economic Dispatch,
Non-Convex Cost Functions,
Valve Point Loading Effect,
Q-Learning,
Eligibility Traces.

##### 1390 Numerical Solution of Riccati Differential Equations by Using Hybrid Functions and Tau Method

**Authors:**
Changqing Yang,
Jianhua Hou,
Beibo Qin

**Abstract:**

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

**Keywords:**
Hybrid functions,
Riccati differential equation,
Blockpulse,
Chebyshev polynomials,
Tau method,
operational matrix.

##### 1389 Proposal of Additional Fuzzy Membership Functions in Smoothing Transition Autoregressive Models

**Authors:**
Ε. Giovanis

**Abstract:**

**Keywords:**
Forecast ,
Fuzzy membership functions,
Smoothingtransition,
Time-series

##### 1388 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.

##### 1387 Continuous Functions Modeling with Artificial Neural Network: An Improvement Technique to Feed the Input-Output Mapping

**Authors:**
A. Belayadi,
A. Mougari,
L. Ait-Gougam,
F. Mekideche-Chafa

**Abstract:**

The artificial neural network is one of the interesting techniques that have been advantageously used to deal with modeling problems. In this study, the computing with artificial neural network (CANN) is proposed. The model is applied to modulate the information processing of one-dimensional task. We aim to integrate a new method which is based on a new coding approach of generating the input-output mapping. The latter is based on increasing the neuron unit in the last layer. Accordingly, to show the efficiency of the approach under study, a comparison is made between the proposed method of generating the input-output set and the conventional method. The results illustrated that the increasing of the neuron units, in the last layer, allows to find the optimal network’s parameters that fit with the mapping data. Moreover, it permits to decrease the training time, during the computation process, which avoids the use of computers with high memory usage.

**Keywords:**
Neural network computing,
information processing,
input-output mapping,
training time,
computers with high memory.

##### 1386 Synthesis of a Control System of a Deterministic Chaotic Process in the Class of Two-Parameter Structurally Stable Mappings

**Authors:**
M. Beisenbi,
A. Sagymbay,
S. Beisembina,
A. Satpayeva

**Abstract:**

In this paper, the problem of unstable and deterministic chaotic processes in control systems is considered. The synthesis of a control system in the class of two-parameter structurally stable mappings is demonstrated. This is realized via the gradient-velocity method of Lyapunov vector functions. It is shown that the gradient-velocity method of Lyapunov vector functions allows generating an aperiodic robust stable system with the desired characteristics. A simple solution to the problem of synthesis of control systems for unstable and deterministic chaotic processes is obtained. Moreover, it is applicable for complex systems.

**Keywords:**
Control system synthesis,
deterministic chaotic processes,
Lyapunov vector function,
robust stability,
structurally stable mappings.

##### 1385 Orthogonal Functions Approach to LQG Control

**Authors:**
B. M. Mohan,
Sanjeeb Kumar Kar

**Abstract:**

In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed. To demonstrate the validity of the proposed approaches a numerical example is included.

**Keywords:**
Linear quadratic Gaussian control,
linear quadratic estimator,
linear quadratic regulator,
time-invariant systems,
orthogonal functions,
block-pulse functions,
shifted legendre polynomials.

##### 1384 Screened Potential in a Reverse Monte Carlo (RMC) Simulation

**Authors:**
M. Habchi,
S. M. Mesli,
M. Kotbi

**Abstract:**

**Keywords:**
RMC simulation; Screened potential; partial and pair
distribution functions; glassy and liquid state

##### 1383 Transient Analysis of a Single-Server Queue with Fixed-Size Batch Arrivals

**Authors:**
Vitalice K. Oduol,
C. Ardil

**Abstract:**

The transient analysis of a queuing system with fixed-size batch Poisson arrivals and a single server with exponential service times is presented. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. These functions are shown to be a generalization of the modified Bessel functions of the first kind, with the batch size B as the generalizing parameter. Results for the case of single-packet arrivals are obtained first. The similarities between the two families of functions are then used to obtain results for the general case of batch arrival queue with a batch size larger than one.

**Keywords:**
batch arrivals,
generalized Bessel functions,
queuetransient analysis,
time-varying probabilities.

##### 1382 A Computational Model of Minimal Consciousness Functions

**Authors:**
Nabila Charkaoui

**Abstract:**

Interest in Human Consciousness has been revived in the late 20th century from different scientific disciplines. Consciousness studies involve both its understanding and its application. In this paper, a computational model of the minimum consciousness functions necessary in my point of view for Artificial Intelligence applications is presented with the aim of improving the way computations will be made in the future. In section I, human consciousness is briefly described according to the scope of this paper. In section II, a minimum set of consciousness functions is defined - based on the literature reviewed - to be modelled, and then a computational model of these functions is presented in section III. In section IV, an analysis of the model is carried out to describe its functioning in detail.

**Keywords:**
Consciousness,
perception,
attention.

##### 1381 Computable Function Representations Using Effective Chebyshev Polynomial

**Authors:**
Mohammed A. Abutheraa,
David Lester

**Abstract:**

We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.

**Keywords:**
Approximation Theory,
Chebyshev Polynomial,
Computable Functions,
Computable Real Arithmetic,
Integration,
Numerical Analysis.