Search results for: Univalent functions
1089 Subclasses of Bi-Univalent Functions Associated with Hohlov Operator
Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9431088 A Sandwich-type Theorem with Applications to Univalent Functions
Authors: Sukhwinder Singh Billing, Sushma Gupta, Sukhjit Singh Dhaliwal
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In the present paper, we obtain a sandwich-type theorem. As applications of our main result, we discuss the univalence and starlikeness of analytic functions in terms of certain differential subordinations and differential inequalities.Keywords: Univalent function, Starlike function, Differential subordination, Differential superordination.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13211087 New Classes of Salagean type Meromorphic Harmonic Functions
Authors: Hakan Bostancı, Metin Öztürk
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13011086 Differential Sandwich Theorems with Generalised Derivative Operator
Authors: Maslina Darus, Khalifa Al-Shaqsi
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In this paper, a generalized derivatives operator n λ,βf introduced by the authors will be discussed. Some subordination and superordination results involving this operator for certain normalized analytic functions in the open unit disk will be investigated. Our results extend corresponding previously known results.Keywords: Analytic functions, Univalent functions, Derivative operator, Differential subordination, Differential superordination.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14661085 Univalence of an Integral Operator Defined by Generalized Operators
Authors: Salma Faraj Ramadan, Maslina Darus
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In this paper we define generalized differential operators from some well-known operators on the class A of analytic functions in the unit disk U = {z ∈ C : |z| < 1}. New classes containing these operators are investigated. Also univalence of integral operator is considered.
Keywords: Univalent functions, integral operators, differential operators.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12591084 The Bent and Hyper-Bent Properties of a Class of Boolean Functions
Authors: Yu Lou, Chunming Tang, Yanfeng Qi, Maozhi Xu
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12271083 Zeros of Bargmann Analytic Representation in the Complex Plane
Authors: Muna Tabuni
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18051082 Bilinear and Bilateral Generating Functions for the Gauss’ Hypergeometric Polynomials
Authors: Manoj Singh, Mumtaz Ahmad Khan, Abdul Hakim Khan
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16421081 Unconventional Calculus Spreadsheet Functions
Authors: Chahid K. Ghaddar
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The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.Keywords: Calculus functions, nonlinear systems, differential algebraic equations, solvers, spreadsheet.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24561080 Geometric Properties and Neighborhood for Certain Subclasses of Multivalent Functions
Authors: Hesam Mahzoon
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6961079 Design of MBMS Client Functions in the Mobile
Authors: Jaewook Shin, Aesoon Park
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MBMS is a unidirectional point-to-multipoint bearer service in which data are transmitted from a single source entity to multiple recipients. For a mobile to support the MBMS, MBMS client functions as well as MBMS radio protocols should be designed and implemented. In this paper, we analyze the MBMS client functions and describe the implementation of them in our mobile test-bed. User operations and signaling flows between protocol entities to control the MBMS functions are designed in detail. Service announcement utilizing the file download MBMS service and four MBMS user services are demonstrated in the test-bed to verify the MBMS client functions.Keywords: BM-SC, Broadcast, MBMS, Mobile, Multicast.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19261078 Performance Evaluation of Complex Valued Neural Networks Using Various Error Functions
Authors: Anita S. Gangal, P. K. Kalra, D. S. Chauhan
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The backpropagation algorithm in general employs quadratic error function. In fact, most of the problems that involve minimization employ the Quadratic error function. With alternative error functions the performance of the optimization scheme can be improved. The new error functions help in suppressing the ill-effects of the outliers and have shown good performance to noise. In this paper we have tried to evaluate and compare the relative performance of complex valued neural network using different error functions. During first simulation for complex XOR gate it is observed that some error functions like Absolute error, Cauchy error function can replace Quadratic error function. In the second simulation it is observed that for some error functions the performance of the complex valued neural network depends on the architecture of the network whereas with few other error functions convergence speed of the network is independent of architecture of the neural network.Keywords: Complex backpropagation algorithm, complex errorfunctions, complex valued neural network, split activation function.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24211077 Performance Evaluation of Popular Hash Functions
Authors: Sheena Mathew, K. Poulose Jacob
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This paper describes the results of an extensive study and comparison of popular hash functions SHA-1, SHA-256, RIPEMD-160 and RIPEMD-320 with JERIM-320, a 320-bit hash function. The compression functions of hash functions like SHA-1 and SHA-256 are designed using serial successive iteration whereas those like RIPEMD-160 and RIPEMD-320 are designed using two parallel lines of message processing. JERIM-320 uses four parallel lines of message processing resulting in higher level of security than other hash functions at comparable speed and memory requirement. The performance evaluation of these methods has been done by using practical implementation and also by using step computation methods. JERIM-320 proves to be secure and ensures the integrity of messages at a higher degree. The focus of this work is to establish JERIM-320 as an alternative of the present day hash functions for the fast growing internet applications.Keywords: Cryptography, Hash function, JERIM-320, Messageintegrity
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26371076 Operational Representation of Certain Hypergeometric Functions by Means of Fractional Derivatives and Integrals
Authors: Manoj Singh, Mumtaz Ahmad Khan, Abdul Hakim Khan
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15131075 Numerical Solution of Riccati Differential Equations by Using Hybrid Functions and Tau Method
Authors: Changqing Yang, Jianhua Hou, Beibo Qin
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25851074 Proposal of Additional Fuzzy Membership Functions in Smoothing Transition Autoregressive Models
Authors: Ε. Giovanis
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In this paper we present, propose and examine additional membership functions for the Smoothing Transition Autoregressive (STAR) models. More specifically, we present the tangent hyperbolic, Gaussian and Generalized bell functions. Because Smoothing Transition Autoregressive (STAR) models follow fuzzy logic approach, more fuzzy membership functions should be tested. Furthermore, fuzzy rules can be incorporated or other training or computational methods can be applied as the error backpropagation or genetic algorithm instead to nonlinear squares. We examine two macroeconomic variables of US economy, the inflation rate and the 6-monthly treasury bills interest rates.Keywords: Forecast , Fuzzy membership functions, Smoothingtransition, Time-series
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15231073 Winding Numbers of Paths of Analytic Functions Zeros in Finite Quantum Systems
Authors: Muna Tabuni
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17091072 Orthogonal Functions Approach to LQG Control
Authors: B. M. Mohan, Sanjeeb Kumar Kar
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18571071 Screened Potential in a Reverse Monte Carlo (RMC) Simulation
Authors: M. Habchi, S. M. Mesli, M. Kotbi
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A structural study of an aqueous electrolyte whose experimental results are available. It is a solution of LiCl-6H2O type at glassy state (120K) contrasted with pure water at room temperature by means of Partial Distribution Functions (PDF) issue from neutron scattering technique. Based on these partial functions, the Reverse Monte Carlo method (RMC) computes radial and angular correlation functions which allow exploring a number of structural features of the system. The obtained curves include some artifacts. To remedy this, we propose to introduce a screened potential as an additional constraint. Obtained results show a good matching between experimental and computed functions and a significant improvement in PDFs curves with potential constraint. It suggests an efficient fit of pair distribution functions curves.Keywords: RMC simulation; Screened potential; partial and pair distribution functions; glassy and liquid state
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15221070 Transient Analysis of a Single-Server Queue with Fixed-Size Batch Arrivals
Authors: Vitalice K. Oduol, C. Ardil
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17501069 A Computational Model of Minimal Consciousness Functions
Authors: Nabila Charkaoui
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18871068 Multi-Objective Optimal Threshold Selection for Similarity Functions in Siamese Networks for Semantic Textual Similarity Tasks
Authors: Kriuk Boris, Kriuk Fedor
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This paper presents a comparative study of fundamental similarity functions for Siamese networks in semantic textual similarity (STS) tasks. We evaluate various similarity functions using the STS Benchmark dataset, analyzing their performance and stability. Additionally, we present a multi-objective approach for optimal threshold selection. Our findings provide insights into the effectiveness of different similarity functions and offer a straightforward method for threshold selection optimization, contributing to the advancement of Siamese network architectures in STS applications.
Keywords: Siamese networks, Semantic textual similarity, Similarity functions, STS Benchmark dataset, Threshold selection.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 711067 Computable Function Representations Using Effective Chebyshev Polynomial
Authors: Mohammed A. Abutheraa, David Lester
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 30841066 Numerical Solution for Integro-Differential Equations by Using Quartic B-Spline Wavelet and Operational Matrices
Authors: Khosrow Maleknejad, Yaser Rostami
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In this paper, Semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions
Keywords: Integro-differential equations, Quartic B-spline wavelet, Operational matrices.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 31481065 A Localized Interpolation Method Using Radial Basis Functions
Authors: Mehdi Tatari
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Finding the interpolation function of a given set of nodes is an important problem in scientific computing. In this work a kind of localization is introduced using the radial basis functions which finds a sufficiently smooth solution without consuming large amount of time and computer memory. Some examples will be presented to show the efficiency of the new method.
Keywords: Radial basis functions, local interpolation method, closed form solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15441064 Certain Subordination Results For A Class Of Analytic Functions Defined By The Generalized Integral Operator
Authors: C. Selvaraj, K. R. Karthikeyan
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We obtain several interesting subordination results for a class of analytic functions defined by using a generalized integral operator.Keywords: Analytic functions, Hadamard product, Subordinating factor sequence
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15581063 Virtual Routing Function Allocation Method for Minimizing Total Network Power Consumption
Authors: Kenichiro Hida, Shin-Ichi Kuribayashi
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In a conventional network, most network devices, such as routers, are dedicated devices that do not have much variation in capacity. In recent years, a new concept of network functions virtualisation (NFV) has come into use. The intention is to implement a variety of network functions with software on general-purpose servers and this allows the network operator to select their capacities and locations without any constraints. This paper focuses on the allocation of NFV-based routing functions which are one of critical network functions, and presents the virtual routing function allocation algorithm that minimizes the total power consumption. In addition, this study presents the useful allocation policy of virtual routing functions, based on an evaluation with a ladder-shaped network model. This policy takes the ratio of the power consumption of a routing function to that of a circuit and traffic distribution between areas into consideration. Furthermore, the present paper shows that there are cases where the use of NFV-based routing functions makes it possible to reduce the total power consumption dramatically, in comparison to a conventional network, in which it is not economically viable to distribute small-capacity routing functions.
Keywords: Virtual routing function, NFV, resource allocation, minimum power consumption.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13021062 A Survey on Positive Real and Strictly Positive Real Scalar Transfer Functions
Authors: Mojtaba Hakimi-Moghaddam
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Positive real and strictly positive real transfer functions are important concepts in the control theory. In this paper, the results of researches in these areas are summarized. Definitions together with their graphical interpretations are mentioned. The equivalent conditions in the frequency domain and state space representations are reviewed. Their equivalent electrical networks are explained. Also, a comprehensive discussion about a difference between behavior of real part of positive real and strictly positive real transfer functions in high frequencies is presented. Furthermore, several illustrative examples are given.Keywords: Real rational transfer functions, positive realness property, strictly positive realness property, equivalent conditions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23851061 Comparison of Fricative Vocal Tract Transfer Functions Derived using Two Different Segmentation Techniques
Authors: K. S. Subari, C. H. Shadle, A. Barney, R. I. Damper
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The acoustic and articulatory properties of fricative speech sounds are being studied using magnetic resonance imaging (MRI) and acoustic recordings from a single subject. Area functions were derived from a complete set of axial and coronal MR slices using two different methods: the Mermelstein technique and the Blum transform. Area functions derived from the two techniques were shown to differ significantly in some cases. Such differences will lead to different acoustic predictions and it is important to know which is the more accurate. The vocal tract acoustic transfer function (VTTF) was derived from these area functions for each fricative and compared with measured speech signals for the same fricative and same subject. The VTTFs for /f/ in two vowel contexts and the corresponding acoustic spectra are derived here; the Blum transform appears to show a better match between prediction and measurement than the Mermelstein technique.
Keywords: Area functions, fricatives, vocal tract transferfunction, MRI, speech.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16491060 Cross Layer Optimization for Fairness Balancing Based on Adaptively Weighted Utility Functions in OFDMA Systems
Authors: Jianwei Wang, Timo Korhonen, Yuping Zhao
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Cross layer optimization based on utility functions has been recently studied extensively, meanwhile, numerous types of utility functions have been examined in the corresponding literature. However, a major drawback is that most utility functions take a fixed mathematical form or are based on simple combining, which can not fully exploit available information. In this paper, we formulate a framework of cross layer optimization based on Adaptively Weighted Utility Functions (AWUF) for fairness balancing in OFDMA networks. Under this framework, a two-step allocation algorithm is provided as a sub-optimal solution, whose control parameters can be updated in real-time to accommodate instantaneous QoS constrains. The simulation results show that the proposed algorithm achieves high throughput while balancing the fairness among multiple users.Keywords: OFDMA, Fairness, AWUF, QoS.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1824