Search results for: generalization

Authors: Kunal Tongaria, Abhishek Mangal, S. Mandal, Devendra Mohan

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The carbonation of concrete is a phenomenon which is a function of various interdependent parameters. Therefore, in spite of numerous literature and database, the useful generalization is not an easy task. These interdependent parameters can be grouped under the category of internal and external factors. This paper focuses on the internal parameters which govern and increase the probability of the ingress of deleterious substances into concrete. The mechanism of effects of internal parameters such as microstructure for with and without supplementary cementing materials (SCM), water/binder ratio, the age of concrete etc. has been discussed. This is followed by the comparison of various proposed mathematical models for the deterioration of concrete. Based on existing laboratory experiments as well as field results, this paper concludes the present understanding of mechanism, modeling and future research needs in this field.

Keywords: carbonation, diffusion coefficient, microstructure of concrete, reinforced concrete

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Authors: A. Giniatoulline

Abstract:

A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid

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Authors: Jiahau Guo, Yihe Zhang

Abstract:

This paper proposes solutions for pricing options on stocks paying discrete dividends in markets with daily price limits. We first extend the intraday density function of Guo and Chang (2020) to a multi-day one and use the framework of Haug et al. (2003) to value European options on stocks paying discrete dividends. Next, we adopt the fast Fourier transform (FFT) to derive accurate and efficient formulae for American options and further employ the three-point Richardson extrapolation to accelerate the computation. Finally, the accuracy of our proposed methods is verified by simulations.

Keywords: daily price limit, discrete dividend, early exercise, fast Fourier transform, multi-day density function, Richardson extrapolation

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Authors: N. K. Mohd Affendi, T. A. R. Tuan Abdullah, S. A. Syed Mustaffa

Abstract:

In power industry transformer is an important component and most of us familiar by the functioning principle of a transformer electrically. There are many losses occur during the operation of a transformer that causes heat generation. This heat, if not dissipated properly will reduce the lifetime and effectiveness of the transformer. Transformer cooling helps in maintaining the temperature rise of various paths. This paper proposed to minimize the ambient temperature of the transformer room in order to lower down the temperature of the transformer. A simulation has been made using finite element methods programs called FEMM (Finite Elements Method Magnetics) to create a virtual model based on actual measurement of a transformer. The generalization of the two-dimensional (2D) FEMM results proves that by minimizing the ambient temperature, the heat of the transformer is decreased. The modeling process and of the transformer heat flow has been presented.

Keywords: heat generation, temperature rise, ambient temperature, FEMM

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Authors: Sadia Arshad, Ayesha Sohail, Sana Javed, Khadija Maqbool, Salma Kanwal

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The dynamical study of the carriers play an essential role in the evolution and global transmission of infectious diseases and will be discussed in this study. To make this approach novel, we will consider the fractional order model which is generalization of integer order derivative to an arbitrary number. Since the integration involved is non local therefore this property of fractional operator is very useful to study epidemic model for infectious diseases. An extended numerical method (ODE solver) is implemented on the model equations and we will present the simulations of the model for different values of fractional order to study the effect of carriers on transmission dynamics. Global dynamics of fractional model are established by using the reproduction number.

Keywords: Fractional differential equation, Numerical simulations, epidemic model, transmission dynamics

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Authors: Aydin Teymourifar, Gurkan Ozturk

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In this paper, a new hybrid Hopfield neural network is proposed for the dynamic, flexible job shop scheduling problem. A new heuristic based and easy to implement energy function is designed for the Hopfield neural network, which penalizes the constraints violation and decreases makespan. Moreover, for enhancing the performance, several heuristics are integrated to it that achieve active, and non-delay schedules also, prevent early convergence of the neural network. The suggested algorithm that is designed as a generalization of the previous studies for the flexible and dynamic scheduling problems can be used for solving real scheduling problems. Comparison of the presented hybrid method results with the previous studies results proves its efficiency.

Keywords: dynamic flexible job shop scheduling, neural network, heuristics, constrained optimization

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Authors: Andrey Norov

Abstract:

Based on the generalization of scientific and production experience and the latest developments of JSC “NIUIF”, the oldest (founded in September 1919) and the only Russian research institute for phosphorus-containing fertilizers, this paper shows the factors that determine the reasonable choice of a method for processing phosphate raw materials into complex fertilizers. These factors primarily include the composition of phosphate raw materials and the impurities contained in it, as well as some parameters of the process mode, wastelessness, ecofriendliness, energy saving, maximum use of the heat of chemical reactions, fire and explosion safety, efficiency, productive capacity, the required product range and the possibility of creating flexible technologies, compliance with BAT principles, etc. The presented data allow to choose the right technology for complex granular fertilizers, depending on the abovementioned factors.

Keywords: BAT, ecofriendliness, energy saving, phosphate raw materials, wastelessness

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Authors: Abdelouaheb Rouabhi

Abstract:

In order to study the plastic resource of structures, the elastic-plastic single degree of freedom model described by Prandtl diagram is widely used. The generalization of this model to tow degree of freedom beyond the scope of a simple rigid-plastic system allows investigating the plastic resource of structures under complex disproportionate by individual components of deformation (earthquake). This macro-model greatly increases the accuracy of the calculations carried out. At the same time, the implementation of the proposed macro-model calculations easier than the detailed dynamic elastic-plastic calculations existing software systems such as ANSYS.

Keywords: elastic-plastic, single degree of freedom model, rigid-plastic system, plastic resource, complex plastic deformation, macro-model

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Authors: Abhishek Mangal, Kunal Tongaria, S. Mandal, Devendra Mohan

Abstract:

Carbonation of reinforced concrete structures has emerged as one of the major challenges for Civil engineers across the world. With increasing emissions from various activities, carbon dioxide concentration in the atmosphere has been eve rising, enhancing its penetration in porous concrete, reaching steel bars and ultimately leading to premature failure. Several literatures have been published dealing with the various interdependent variables related to carbonation. However, with innumerable variability a generalization of these data proves to be a troublesome task. This paper looks into this carbonation anomaly in concrete structures caused by various external variables such as relative humidity, concentration of CO2, curing period and ambient temperature. Significant discussions and comparisons have been presented on the basis of various studies conducted with an aim to predict the depth of carbonation as a function of these multidimensional parameters using various numerical and statistical modelling techniques.

Keywords: carbonation, curing, exposure conditions, relative humidity

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Authors: Muna Tabuni

Abstract:

The paper contains an investigation of the notion of Q algebras. A brief introduction to quantum mechanics is given, in that systems the state defined by a vector in a complex vector space H which have Hermitian inner product property. H may be finite or infinite-dimensional. In quantum mechanics, operators must be hermitian. These facts are saved by Lie algebra operators but not by those of quantum algebras. A Hilbert space H consists of a set of vectors and a set of scalars. Lie group is a differentiable topological space with group laws given by differentiable maps. A Lie algebra has been introduced. Q-algebra has been defined. A brief introduction to BCI-algebra is given. A BCI sub algebra is introduced. A brief introduction to BCK=BCH-algebra is given. Every BCI-algebra is a BCH-algebra. Homomorphism maps meanings are introduced. Homomorphism maps between two BCK algebras are defined. The mathematical formulations of quantum mechanics can be expressed using the theory of unitary group representations. A generalization of Q algebras has been introduced, and their properties have been considered. The Q- quantum algebra has been studied, and various examples have been given.

Keywords: Q-algebras, BCI, BCK, BCH-algebra, quantum mechanics

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Authors: Mohamed Othmani, Yassine Khlifi

Abstract:

This paper presents a technique for compact three dimensional (3D) object model reconstruction using wavelet networks. It consists to transform an input surface vertices into signals,and uses wavelet network parameters for signal approximations. To prove this, we use a wavelet network architecture founded on several mother wavelet families. POLYnomials WindOwed with Gaussians (POLYWOG) wavelet families are used to maximize the probability to select the best wavelets which ensure the good generalization of the network. To achieve a better reconstruction, the network is trained several iterations to optimize the wavelet network parameters until the error criterion is small enough. Experimental results will shown that our proposed technique can effectively reconstruct an irregular 3D object models when using the optimized wavelet network parameters. We will prove that an accurateness reconstruction depends on the best choice of the mother wavelets.

Keywords: 3d object, optimization, parametrization, polywog wavelets, reconstruction, wavelet networks

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Authors: Stylianos Kampakis

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This paper presents a new algorithm for neural networks called “Input Dropout with Aggressive Re-weighting” (IDAR) aimed specifically at datasets with many useless features. IDAR combines two techniques (dropout of input neurons and aggressive re weighting) in order to eliminate the influence of noisy features. The technique can be seen as a generalization of dropout. The algorithm is tested on two different benchmark data sets: a noisy version of the iris dataset and the MADELON data set. Its performance is compared against three other popular techniques for dealing with useless features: L2 regularization, LASSO and random forests. The results demonstrate that IDAR can be an effective technique for handling data sets with many useless features.

Keywords: neural networks, feature selection, regularization, aggressive reweighting

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Authors: M. Y. Bakeir

Abstract:

Rough set theory is a recent approach for reasoning about data. It has achieved a large amount of applications in various real-life fields. The main idea of rough sets corresponds to the lower and upper set approximations. These two approximations are exactly the interior and the closure of the set with respect to a certain topology on a collection U of imprecise data acquired from any real-life field. The base of the topology is formed by equivalence classes of an equivalence relation E defined on U using the available information about data. The theory of generalized topology was studied by Cs´asz´ar. It is well known that generalized topology in the sense of Cs´asz´ar is a generalization of the topology on a set. On the other hand, many important collections of sets related with the topology on a set form a generalized topology. The notion of Nano topology was introduced by Lellis Thivagar, which was defined in terms of approximations and boundary region of a subset of an universe using an equivalence relation on it. The purpose of this paper is to introduce a new generalized topology in terms of rough set called nano generalized topology

Keywords: rough sets, topological space, generalized topology, nano topology

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Authors: Praveen S. Muthukumarana, Achala C. Aponso

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A large percentage of global crop harvest is lost due to crop diseases. Timely identification and treatment of crop diseases is difficult in many developing nations due to insufficient trained professionals in the field of agriculture. Many crop diseases can be accurately diagnosed by visual symptoms. In the past decade, deep learning has been successfully utilized in domains such as healthcare but adoption in agriculture for plant disease detection is rare. The literature shows that models trained with popular datasets such as PlantVillage does not generalize well on real world images. This paper attempts to find out how to make plant disease identification models that generalize well with real world images.

Keywords: agriculture, convolutional neural network, deep learning, plant disease classification, plant disease detection, plant disease diagnosis

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Authors: E. A. Mlybari, M. S. Elbisy, A. H. Alshahri, O. M. Albarakati

Abstract:

Sea level rise threatens to increase the impact of future storms and hurricanes on coastal communities. Accurate sea level change prediction and supplement is an important task in determining constructions and human activities in coastal and oceanic areas. In this study, support vector machines (SVM) is proposed to predict daily tidal levels along the Jeddah Coast, Saudi Arabia. The optimal parameter values of kernel function are determined using a genetic algorithm. The SVM results are compared with the field data and with back propagation (BP). Among the models, the SVM is superior to BPNN and has better generalization performance.

Keywords: tides, prediction, support vector machines, genetic algorithm, back-propagation neural network, risk, hazards

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Authors: Sabri Arik

Abstract:

In this paper, we study the global asymptotic robust stability of delayed neural networks with norm-bounded uncertainties. By employing the Lyapunov stability theory and Homeomorphic mapping theorem, we derive some new types of sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slopebounded activation functions. An important aspect of our results is their low computational complexity as the reported results can be verified by checking some properties symmetric matrices associated with the uncertainty sets of network parameters. The obtained results are shown to be generalization of some of the previously published corresponding results. Some comparative numerical examples are also constructed to compare our results with some closely related existing literature results.

Keywords: neural networks, delayed systems, lyapunov functionals, stability analysis

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Authors: Michele Aleandri, Matteo Colangeli, Davide Gabrielli

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We study a generalization to a continuous setting of the classical Markov chain tree theorem. In particular, we consider an irreducible diffusion process on a metric graph. The unique invariant measure has an atomic component on the vertices and an absolutely continuous part on the edges. We show that the corresponding density at x can be represented by a normalized superposition of the weights associated to metric arborescences oriented toward the point x. A metric arborescence is a metric tree oriented towards its root. The weight of each oriented metric arborescence is obtained by the product of the exponential of integrals of the form ∫a/b², where b is the drift and σ² is the diffusion coefficient, along the oriented edges, for a weight for each node determined by the local orientation of the arborescence around the node and for the inverse of the diffusion coefficient at x. The metric arborescences are obtained by cutting the original metric graph along some edges.

Keywords: diffusion processes, metric graphs, invariant measure, reversibility

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Authors: Safeer Hussain Khan, H. Fukhar-ud-Din

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The concept of quasi-contractive type operators was given by Berinde and extended by Imoru and Olatinwo. They named this new type as contractive-like operators. On the other hand, Xu and Noo introduced a three-step-one-mappings iterative process which can be seen as a generalization of Mann and Ishikawa iterative processes. Approximating common fixed points has its own importance as it has a direct link with minimization problem. Motivated by this, in this paper, we first extend the iterative process of Xu and Noor to the case of three-step-three-mappings and then prove a strong convergence result using contractive-like operators for this iterative process. In general, this generalizes corresponding results using Mann, Ishikawa and Xu-Noor iterative processes with quasi-contractive type operators. It is to be pointed out that our results can also be proved with iterative process involving error terms.

Keywords: contractive-like operator, iterative process, common fixed point, strong convergence

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Authors: Xiangyu Yang

Abstract:

Xiao Qian (1910-1999) was a prolific literary translator between Chinese and English in both directions and an influential commentator on Chinese translation practices for nearly 70 years (1931-1998). During his stay in Britain from 1939 to 1946, Xiao self-translated and published a series of short stories, essays, and feature articles. With Pedersen's theoretical framework, the paper finds that Xiao flexibly adopted seven translation strategies (i.e. phonemic retention, specification, direct translation, generalization, substitution, omission, and official equivalent) to deal with the expressions specific to Chinese culture, struggling to seek a balance between adequate translation and acceptable translation in a historical condition of the huge gap between China and the west in the early twentieth century. Besides, the study also discovers that Xiao's translation strategies were greatly influenced by his own translational purpose as well as the literary systems, ideologies, and patronage in China and Britain in the 1940s.

Keywords: self-translation, extralinguistic cultural reference, Xiao Qian, Pedersen

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Authors: Van Dong Phung, Igor Hawryszkiewycz, Kyeong Kang, Muhammad Hatim Binsawad

Abstract:

Knowledge sharing (KS) is the key to creativity and innovation in any organizations. Overcoming the KS barriers has created new challenges for designing in dynamic and complex environment. There may be interrelations and interdependences among the barriers. The purpose of this paper is to present a review of literature of KS barriers and impute the relative importance of them through the fuzzy analytic network process that is a generalization of the analytical hierarchy process (AHP). It helps to prioritize the barriers to find ways to remove them to facilitate KS. The study begins with a brief description of KS barriers and the most critical ones. The FANP and its role in identifying the relative importance of KS barriers are explained. The paper, then, proposes the model for research and expected outcomes. The study suggests that the use of the FANP is appropriate to impute the relative importance of KS barriers which are intertwined and interdependent. Implications and future research are also proposed.

Keywords: FANP, ANP, knowledge sharing barriers, knowledge sharing, removing barriers, knowledge management

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Authors: S. Oudjemia, F. Alim, S. Seddiki

Abstract:

This paper shows the application of multifractal analysis for additional help in cancer diagnosis. The medical image processing is a very important discipline in which many existing methods are in search of solutions to real problems of medicine. In this work, we present results of multifractal analysis of brain MRI images. The purpose of this analysis was to separate between healthy and cancerous tissue of the brain. A nonlinear method based on multifractal detrending moving average (MFDMA) which is a generalization of the detrending fluctuations analysis (DFA) is used for the detection of abnormalities in these images. The proposed method could make separation of the two types of brain tissue with success. It is very important to note that the choice of this non-linear method is due to the complexity and irregularity of tumor tissue that linear and classical nonlinear methods seem difficult to characterize completely. In order to show the performance of this method, we compared its results with those of the conventional method box-counting.

Keywords: irregularity, nonlinearity, MRI brain images, multifractal analysis, brain tumor

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Authors: Vinayaka Gude Divya Sampath

Abstract:

The research introduces an integrated prediction model to assess the susceptibility of roads in a future flooding event. The model consists of deep learning algorithm for forecasting gauge height data and Flood Inundation Mapper (FIM) for spatial flooding. An optimal architecture for Long short-term memory network (LSTM) was identified for the gauge located on Tangipahoa River at Robert, LA. Dropout was applied to the model to evaluate the uncertainty associated with the predictions. The estimates are then used along with FIM to identify the spatial flooding. Further geoprocessing in ArcGIS provides the susceptibility values for different roads. The model was validated based on the devastating flood of August 2016. The paper discusses the challenges for generalization the methodology for other locations and also for various types of flooding. The developed model can be used by the transportation department and other emergency response organizations for effective disaster management.

Keywords: deep learning, disaster management, flood prediction, urban flooding

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Authors: Khenfer-Koummich Fatima, Mesbahi Larbi, Hendel Fatiha

Abstract:

This paper presents a recognition system for isolated words like robot commands. It’s carried out by Time Delay Neural Networks; TDNN. To teleoperate a robot for specific tasks as turn, close, etc… In industrial environment and taking into account the noise coming from the machine. The choice of TDNN is based on its generalization in terms of accuracy, in more it acts as a filter that allows the passage of certain desirable frequency characteristics of speech; the goal is to determine the parameters of this filter for making an adaptable system to the variability of speech signal and to noise especially, for this the back propagation technique was used in learning phase. The approach was applied on commands pronounced in two languages separately: The French and Arabic. The results for two test bases of 300 spoken words for each one are 87%, 97.6% in neutral environment and 77.67%, 92.67% when the white Gaussian noisy was added with a SNR of 35 dB.

Keywords: TDNN, neural networks, noise, speech recognition

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Authors: Tian Lan, Yixiang Wang, Wenxin Tai, Yilan Lyu, Zufeng Wu

Abstract:

The monaural speech enhancement task in the time-frequencydomain has a myriad of approaches, with the stacked con-volutional neural network (CNN) demonstrating superiorability in feature extraction and selection. However, usingstacked single convolutions method limits feature represen-tation capability and generalization ability. In order to solvethe aforementioned problem, we propose an attention-basedadaptive convolutional network that integrates the multi-scale convolutional operations into a operation-specific blockvia input dependent attention to adapt to complex auditoryscenes. In addition, we introduce a two-stage progressivelearning method to enlarge the receptive field without a dra-matic increase in computation burden. We conduct a series ofexperiments based on the TIMIT corpus, and the experimen-tal results prove that our proposed model is better than thestate-of-art models on all metrics.

Keywords: speech enhancement, adaptive convolu-tion, progressive learning, time-frequency domain

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Authors: Amit Ghosh, Chanchal Kundu

Abstract:

Recently, the notion of past cumulative inaccuracy (CPI) measure has been proposed in the literature as a generalization of cumulative past entropy (CPE) in univariate as well as bivariate setup. In this paper, we introduce the notion of CPI of order α (alpha) and study the proposed measure for conditionally specified models of two components failed at different time instants called generalized conditional CPI (GCCPI). We provide some bounds using usual stochastic order and investigate several properties of GCCPI. The effect of monotone transformation on this proposed measure has also been examined. Furthermore, we characterize some bivariate distributions under the assumption of conditional proportional reversed hazard rate model. Moreover, the role of GCCPI in reliability modeling has also been investigated for a real-life problem.

Keywords: cumulative past inaccuracy, marginal and conditional past lifetimes, conditional proportional reversed hazard rate model, usual stochastic order

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Authors: Sultan Noman Qasem

Abstract:

This paper presents an evolutionary algorithm for solving multi-objective optimization problems-based artificial neural network (ANN). The multi-objective evolutionary algorithm used in this study is genetic algorithm while ANN used is radial basis function network (RBFN). The proposed algorithm named memetic elitist Pareto non-dominated sorting genetic algorithm-based RBFNN (MEPGAN). The proposed algorithm is implemented on medical diseases problems. The experimental results indicate that the proposed algorithm is viable, and provides an effective means to design multi-objective RBFNs with good generalization capability and compact network structure. This study shows that MEPGAN generates RBFNs coming with an appropriate balance between accuracy and simplicity, comparing to the other algorithms found in literature.

Keywords: radial basis function network, hybrid learning, multi-objective optimization, genetic algorithm

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Authors: Prashant Malavadkar, Santosh Dhotre, Maruti Shikare

Abstract:

The n-point splitting operation on graphs is used to characterize 4-connected graphs with some more operations. Element splitting operation on binary matroids is a natural generalization of the notion of n-point splitting operation on graphs. The element splitting operation on a graphic (cographic) matroid may not yield a graphic (cographic) matroid. Characterization of graphic (cographic) matroids whose element splitting matroids are graphic (cographic) is known. The element splitting operation on a co-graphic matroid, in general may not yield a graphic matroid. In this paper, we give a necessary and sufficient condition for the cographic matroid to yield a graphic matroid under the element splitting operation. In fact, we prove that the element splitting operation, by any pair of elements, on a cographic matroid yields a graphic matroid if and only if it has no minor isomorphic to M(K4); where K4 is the complete graph on 4 vertices.

Keywords: binary matroids, splitting, element splitting, forbidden minor

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Authors: Arindam Chaudhuri

Abstract:

The research presents epsilon- hierarchical fuzzy twin support vector regression (epsilon-HFTSVR) based on epsilon-fuzzy twin support vector regression (epsilon-FTSVR) and epsilon-twin support vector regression (epsilon-TSVR). Epsilon-FTSVR is achieved by incorporating trapezoidal fuzzy numbers to epsilon-TSVR which takes care of uncertainty existing in forecasting problems. Epsilon-FTSVR determines a pair of epsilon-insensitive proximal functions by solving two related quadratic programming problems. The structural risk minimization principle is implemented by introducing regularization term in primal problems of epsilon-FTSVR. This yields dual stable positive definite problems which improves regression performance. Epsilon-FTSVR is then reformulated as epsilon-HFTSVR consisting of a set of hierarchical layers each containing epsilon-FTSVR. Experimental results on both synthetic and real datasets reveal that epsilon-HFTSVR has remarkable generalization performance with minimum training time.

Keywords: regression, epsilon-TSVR, epsilon-FTSVR, epsilon-HFTSVR

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Authors: Hui Wei, Zheng Dong

Abstract:

Object recognition has long been a challenging task in computer vision. Yet the human brain, with the ability to rapidly and accurately recognize visual stimuli, manages this task effortlessly. In the past decades, advances in neuroscience have revealed some neural mechanisms underlying visual processing. In this paper, we present a novel model inspired by the visual pathway in primate brains. This multi-layer neural network model imitates the hierarchical convergent processing mechanism in the visual pathway. We show that local image features generated by this model exhibit robust discrimination and even better generalization ability compared with some existing image descriptors. We also demonstrate the application of this model in an object recognition task on image data sets. The result provides strong support for the potential of this model.

Keywords: biological model, feature extraction, multi-layer neural network, object recognition

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Authors: Rajkumar N. Ingle

Abstract:

In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.

Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon

Procedia PDF Downloads 455