Search results for: Functions of random variables.

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.

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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.

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Authors: M. Nayeemuddin, T. Bramhananda Reddy, M. Vijaya Kumar

Abstract:

Acoustic noise becoming ever more obnoxious radiated by voltage source inverter fed induction motor drive in modern and industrial applications. The drive utilized for industrial and modern applications should use “spread spectrum” innovation known as Random pulse width modulation (PWM) algorithms where acoustic noise emanates through the machine should be critically concerned. This paper illustrates three types of random PWM control algorithms with fixed switching frequency namely 1) Random modulating PWM 2) Random carrier PWM and 3) Random modulating-carrier PWM. The spectrum plots of the motor stator current demonstrate the strength and robustness of the proposed PWM algorithms. To affirm the proposed algorithms, experimental tests have been conducted using dSPACE rt1104 control board on a v/f control three phase induction motor drive fed by DC link cascaded multilevel inverter.

Keywords: Multilevel inverter, acoustic noise, CSVPWM, total harmonic distortion, random PWM algorithm.

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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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Authors: Ε. Giovanis

Abstract:

In this paper we propose and examine an Adaptive Neuro-Fuzzy Inference System (ANFIS) in Smoothing Transition Autoregressive (STAR) modeling. Because STAR models follow fuzzy logic approach, in the non-linear part fuzzy rules can be incorporated or other training or computational methods can be applied as the error backpropagation algorithm instead to nonlinear squares. Furthermore, additional fuzzy membership functions can be examined, beside the logistic and exponential, like the triangle, Gaussian and Generalized Bell functions among others. We examine two macroeconomic variables of US economy, the inflation rate and the 6-monthly treasury bills interest rates.

Keywords: Forecasting, Neuro-Fuzzy, Smoothing transition, Time-series

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Authors: L. Basha, E. Gjika

Abstract:

This study is focused on analyzing climate change in Albania and its potential effects on cereal yields. Initially, monthly temperature and rainfalls in Albania were studied for the period 1960-2021. Climacteric variables are important variables when trying to model cereal yield behavior, especially when significant changes in weather conditions are observed. For this purpose, in the second part of the study, linear and nonlinear models explaining cereal yield are constructed for the same period, 1960-2021. The multiple linear regression analysis and lasso regression method are applied to the data between cereal yield and each independent variable: average temperature, average rainfall, fertilizer consumption, arable land, land under cereal production, and nitrous oxide emissions. In our regression model, heteroscedasticity is not observed, data follow a normal distribution, and there is a low correlation between factors, so we do not have the problem of multicollinearity. Machine learning methods, such as Random Forest (RF), are used to predict cereal yield responses to climacteric and other variables. RF showed high accuracy compared to the other statistical models in the prediction of cereal yield. We found that changes in average temperature negatively affect cereal yield. The coefficients of fertilizer consumption, arable land, and land under cereal production are positively affecting production. Our results show that the RF method is an effective and versatile machine-learning method for cereal yield prediction compared to the other two methods: multiple linear regression and lasso regression method.

Keywords: Cereal yield, climate change, machine learning, multiple regression model, random forest.

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Authors: Fabrice Poirion, Benedicte Puig

Abstract:

Mathematical justifications are given for a simulation technique of multivariate nonGaussian random processes and fields based on Rosenblatt-s transformation of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrelation function.

Keywords: Simulation, nonGaussian, random field, multivariate, stochastic process.

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Authors: Hatice Özbek, Caner Çil, Ahmet Rodoplu

Abstract:

Automotive lighting is the leading function in the configuration of vehicle architecture. Especially headlights and taillights from external lighting functions are among the structures that determine the stylistic character of the vehicle. At the same time, the fact that lighting functions are related to many other functions brings along difficulties in design. Customers expect maximum quality from the vehicle. In these circumstances, it is necessary to make designs that aim to keep the performance of bulbs with limited working lives at the highest level. With this study, the factors that influence the working lives of filament lamps were examined and bulb explosions that can occur sooner than anticipated in the future were prevented while the vehicle was still in the design phase by determining the relations with electrical, dynamical and static variables. Especially the filaments of the bulbs used in the front lighting of the vehicle are deformed in a shorter time due to the high voltage requirement. In addition to this, rear lighting lamps vibrate as a result of the tailgate opening and closing and cause the filaments to be exposed to high stress. With this study, the findings that cause bulb explosions were evaluated. Among the most important findings: 1. The structure of the cables to the lighting functions of the vehicle and the effect of the voltage values are drawn; 2. The effect of the vibration to bulb throughout the life of the vehicle; 3 The effect of the loads carried to bulb while the vehicle doors are opened and closed. At the end of the study, the maximum performance was established in the bulb lifetimes with the optimum changes made in the vehicle architecture based on the findings obtained.

Keywords: Vehicle architecture, automotive lighting functions, filament lamps, bulb lifetime.

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Authors: Oscar E. Ruiz, S. Arroyave, J. F. Cardona

Abstract:

In the context of computer numerical control (CNC) and computer aided manufacturing (CAM), the capabilities of programming languages such as symbolic and intuitive programming, program portability and geometrical portfolio have special importance. They allow to save time and to avoid errors during part programming and permit code re-usage. Our updated literature review indicates that the current state of art presents voids in parametric programming, program portability and programming flexibility. In response to this situation, this article presents a compiler implementation for EGCL (Extended G-code Language), a new, enriched CNC programming language which allows the use of descriptive variable names, geometrical functions and flow-control statements (if-then-else, while). Our compiler produces low-level generic, elementary ISO-compliant Gcode, thus allowing for flexibility in the choice of the executing CNC machine and in portability. Our results show that readable variable names and flow control statements allow a simplified and intuitive part programming and permit re-usage of the programs. Future work includes allowing the programmer to define own functions in terms of EGCL, in contrast to the current status of having them as library built-in functions.

Keywords: CNC Programming, Compiler, G-code Language, Numerically Controlled Machine-Tools.

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Authors: Nabilah Filzah Mohd Radzuan, Andi Putra, Zalinda Othman, Azuraliza Abu Bakar, Abdul Razak Hamdan

Abstract:

Precipitation forecast is important in avoid incident of natural disaster which can cause loss in involved area. This review paper involves three techniques from artificial intelligence namely logistic regression, decisions tree, and random forest which used in making precipitation forecast. These combination techniques through VAR model in finding advantages and strength for every technique in forecast process. Data contains variables from rain domain. Adaptation of artificial intelligence techniques involved on rain domain enables the process to be easier and systematic for precipitation forecast.

Keywords: Logistic regression, decisions tree, random forest, VAR model.

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Authors: Farnaz G. Nezami, Mir B. Aryanezhad, Seyed J. Sadjadi

Abstract:

In this paper a nonlinear model is presented to demonstrate the relation between production and marketing departments. By introducing some functions such as pricing cost and market share loss functions it will be tried to show some aspects of market modelling which has not been regarded before. The proposed model will be a constrained signomial geometric programming model. For model solving, after variables- modifications an iterative technique based on the concept of geometric mean will be introduced to solve the resulting non-standard posynomial model which can be applied to a wide variety of models in non-standard posynomial geometric programming form. At the end a numerical analysis will be presented to accredit the validity of the mentioned model.

Keywords: Geometric programming, marketing, nonlinear optimization, production.

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Authors: Bita Payami-Shabestari, Dariush Eslami

Abstract:

The purpose of this paper is to develop a multi-product economic production quantity model under vendor management inventory policy and restrictions including limited warehouse space, budget, and number of orders, average shortage time and maximum permissible shortage. Since the “costs” cannot be predicted with certainty, it is assumed that data behave under uncertain environment. The problem is first formulated into the framework of a bi-objective of multi-product economic production quantity model. Then, the problem is solved with three multi-objective decision-making (MODM) methods. Then following this, three methods had been compared on information on the optimal value of the two objective functions and the central processing unit (CPU) time with the statistical analysis method and the multi-attribute decision-making (MADM). The results are compared with statistical analysis method and the MADM. The results of the study demonstrate that augmented-constraint in terms of optimal value of the two objective functions and the CPU time perform better than global criteria, and goal programming. Sensitivity analysis is done to illustrate the effect of parameter variations on the optimal solution. The contribution of this research is the use of random costs data in developing a multi-product economic production quantity model under vendor management inventory policy with several constraints.

Keywords: Economic production quantity, random cost, supply chain management, vendor-managed inventory.

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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.

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Authors: Yusuke Kuramitsu, Tomoaki Hashimoto, Hirokazu Tahara

Abstract:

The control problem of underactuated spacecrafts has attracted a considerable amount of interest. The control method for a spacecraft equipped with less than three control torques is useful when one of the three control torques had failed. On the other hand, the quantized control of systems is one of the important research topics in recent years. The random dither quantization method that transforms a given continuous signal to a discrete signal by adding artificial random noise to the continuous signal before quantization has also attracted a considerable amount of interest. The objective of this study is to develop the control method based on random dither quantization method for stabilizing the rotational motion of a rigid spacecraft with two control inputs. In this paper, the effectiveness of random dither quantization control method for the stabilization of rotational motion of spacecrafts with two torque inputs is verified by numerical simulations.

Keywords: Spacecraft control, quantized control, nonlinear control, random dither method.

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Authors: A. Habibizad Navin, M. Naghian Fesharaki, M. Mirnia, M. Kargar

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In this paper we introduce Digital Probability Hyper Digraph for modeling random variable as the hierarchical data-oriented model.

Keywords: Data-Oriented Models, Data Structure, DigitalProbability Hyper Digraph, Random Variable, Statistic andProbability.

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

Abstract:

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

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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.

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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.

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Authors: Pavlo Selyshchev

Abstract:

We consider fluctuations of defects density taking into account their interaction. Stochastic field of displacement generation rate gives random defect distribution. We determinate statistical characteristics (mean and dispersion) of random field of point defect distribution as function of defect generation parameters, temperature and properties of irradiated crystal.

 

Keywords: Irradiation, Primary Defects, Interaction, Fluctuations.

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Authors: Kriuk Boris, Kriuk Fedor

Abstract:

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.

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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.

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Authors: Yong-can Cao, Wei-dong Zhang

Abstract:

To deal with random delays in Networked Control System (NCS), Modified Fuzzy PID Controller is introduced in this paper to implement real-time control adaptively. Via adjusting the control signal dynamically, the system performance is improved. In this paper, the design process and the ultimate simulation results are represented. Finally, examples and corresponding comparisons prove the significance of this method.

Keywords: Fuzzy Control, Networked Control System, PID, Random Delays

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Authors: Khosrow Maleknejad, Yaser Rostami

Abstract:

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.

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Authors: Mehdi Tatari

Abstract:

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.

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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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Authors: Guilan Huang

Abstract:

In 2013 and 2014, the U.S. Food and Drug Administration (FDA) collected data from selected fast food restaurants and full service restaurants for tracking changes in the occurrence of foodborne illness risk factors. This paper discussed how we customized spatial random sampling method by considering financial position and availability of FDA resources, and how we enriched restaurants data with location. Location information of restaurants provides opportunity for quantitatively determining random sampling within non-government units (e.g.: 240 kilometers around each data-collector). Spatial analysis also could optimize data-collectors’ work plans and resource allocation. Spatial analytic and processing platform helped us handling the spatial random sampling challenges. Our method fits in FDA’s ability to pinpoint features of foodservice establishments, and reduced both time and expense on data collection.

Keywords: Geospatial technology, restaurant, retail food risk factors study, spatial random sampling.

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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

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Authors: Kenichiro Hida, Shin-Ichi Kuribayashi

Abstract:

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.

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Authors: Kailash C. Madan

Abstract:

We study four models of a three server queueing system with Bernoulli schedule optional server vacations. Customers arriving at the system one by one in a Poisson process are provided identical exponential service by three parallel servers according to a first-come, first served queue discipline. In model A, all three servers may be allowed a vacation at one time, in Model B at the most two of the three servers may be allowed a vacation at one time, in model C at the most one server is allowed a vacation, and in model D no server is allowed a vacation. We study steady the state behavior of the four models and obtain steady state probability generating functions for the queue size at a random point of time for all states of the system. In model D, a known result for a three server queueing system without server vacations is derived.

Keywords: A three server queue, Bernoulli schedule server vacations, queue size distribution at a random epoch, steady state.

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Authors: Maslina Darus, Khalifa Al-Shaqsi

Abstract:

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.

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