Showing papers in "International journal of pure and applied mathematics in 2018"

Existence and uniqueness theorems for fractional volterra-fredholm integro-differential equations

Abstract: In this article, the homotopy perturbation method has been successfully applied to find the approximate solution of a Caputo fractional Volterra-Fredholm integro-differential equation. The reliability of the method and reduction in the size of the computational work give this method a wider applicability. Also, the behavior of the solution can be formally determined by the analytical approximate. Moreover, we proved the existence and uniqueness results of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed technique. AMS Subject Classification: 26A33, 35C10, 65H20

Well-posedness of nonlinear fractional schrodinger and wave equations in sobolev spaces

Abstract: In this paper, we establish the local well-posedness results in sub-critical and critical cases for the pure power-type nonlinear fractional Schrodinger and wave equations on $\mathbb{R}^d$, namely $$ i\partial_t u + \Lambda^\sigma u + \mu |u|^{ u−1}u = 0, \quad u_{\vert=0} = \phi, $$ and $$ \partial^2_t v + \Lambda^{2\sigma} v + \mu |v|^{ u−1} v = 0, \quad v_{\vert t=0} = \phi,\quad \partial_t v_{\vert t=0} = \varphi, $$ where $\sigma \in (0,∞)\backslash \{1\}, u > 1,\mu \in \{\pm 1\}$ and $\Lambda =\sqrt{−\Delta}$ is the Fourier multiplier by $|\xi|$. For the nonlinear fractional Schrodinger equation, we extend the previous results in [22] for $\sigma \geq 2$. These results cover the well-known results for Schrodinger equation $\sigma = 2$ given in [4]. In the case $\sigma \in (0,2)\backslash \{1\}$, we show the local well-posedness in the sub-critical case for $ u > 1$ in contrast to $ u \geq 2$ when $d = 1$, and $ u \geq 3$ when $d geq 2$ of [22]. These results also generalize the ones of [11] when $d = 1$ and of [18] when $d \geq 2$, where the authors considered the cubic fractional Schrodinger equation with $\sigma \in (1,2)$. To our knowledge, the nonlinear fractional wave equation does not seem to have been much considered, up to [37] on the scattering operator with $\sigma$ an even integer and [6], [7] in the context of the damped fractional wave equation.

Extraction of Facial Features for Depression Detection among Students

Abstract: Psychological health of college students prove a vital role on their overall academic performance. Neglecting this can result in several problems such as stress, anxiety, depression etc. These problems need to be detected and controlled at the initial stages itself for the better mental health of the student. Detecting depression in a vast no of college students is challenging task. Most of the students are totally unaware that they may be having depression. If at all they are aware of it, some students conceal their depression from everyone. So an automated system is required that will pick out the students who are dealing with depression. A system has been proposed here which captures frontal face videos of college students, extracts the facial features from each frame and analyses these facial features to detect signs of depression in them. This system will be trained with of frontal face images of happy, contempt and disgust faces. The presence of these features in the video frames will be analyzed to predict depression in the students. Keywords— Keywords—Image processing, Feature Extraction, Facial Features, Depression Detection.

Cosine similarity measure for rough intuitionistic fuzzy sets and its application in medical diagnosis

Abstract: Similarity measure is an important mathematical tool used in medical diagnosis, pattern recognition etc. In this paper a cosine similarity for rough intuitionistic fuzzy set is proposed. Also we apply the notion of weighted rough intuitionistic fuzzy approach to cosine similarity measure for further investigation. Finally a medical diagnosis problem is defined to verify the proposed similarity measure. AMS Subject Classification: 03E72, 04A72, 28E10, 26E50, 94D05

A note on the yamada--exponential software reliability model

Abstract: In this paper we study the Hausdorff approximation of the Heaviside step function hr(t) by deterministic curve models based on Yamada–exponential software reliability model, Yamada–Rayleigh model and Yamada–Weibul model and find an expression for the error of the best approximation. Some comparisons are made.

Some deterministic reliability growth curves for software error detection: approximation and modeling aspects

Abstract: In the context of reliability engineering, the Gompertz curve (or deterministic curve model) is, for example, used to assess the reliability growth phenomenon of hardware products. In this paper we study the one–sided Hausdorff approximation of the Heaviside step function hr(t) by deterministic curve model and find an expression for the error of the best approximation. We propose a new transmuted deterministic software reliability model. Some comparisons are made.

IOT enabled smart charging stations for electric vehicle

Abstract: As more countries are moving towards pollution free traffic, EVs are gaining more popularity across the globe. As the number of EVs increases, EV charging infrastructure will be also a basic need. A system with IoT will definitely streamline the performance of EV charging and looks the impacts. This method is helpful for transportation systems, and V2G systems. This proposed system will improve the city planning and makes the city life easy. With IoT we can easily manage the whole V2G system which will definitely saves time and money. This work is to make a smart application to connect with the grid and to know the different tariff rates of the grid.The tariff rates will have both the rate for power delivery to the grid and tariff rate for taking power from the grid. If the user is having the car battery fully charged,he can deliver some power to the grid and can earn some money. SoC is measured using the ARM Mbed controller and transmitted to cloud. The application will also displays the battery status(SoC) of the user when he comes to the grid.

Nabla integral for fuzzy functions on time scales

Abstract: In this paper, we define fuzzy nabla integrals for fuzzy functions on time scales and obtain some of its fundamental properties and also we establish the relationship between nabla differentiation and integration. AMS Subject Classification: 03E72, 34A07, 26E07

Scaffolding Model for Efficient Programming Learning Based on Cognitive Load Theory

Abstract: Programming learning for beginners requires tremendous amount of exposure to understand the logic in each programming solution using the basic concepts despite the overwhelming syntax it might carries. Learning programming through examples with careful walkthrough builds learners’ confidence to embark with problems of any designs, avoids frustration due to syntax error and unintentional bugs. Scaffolding involves meta-programming approach of building software applications using supported materials that provides some inspiration of how the program could be developed. This research identifies important attributes in programming and proposes a scaffold model to enhance programming learning efficiency especially among novice programmers. The study applies cognitive load theory by providing users with two types of instructional design as learning support to reduce mental effort applied in the working memory i.e. worked-example and goal free programming problem solutions. The model is expected to help instructors in systematically organizing programming materials for any language or programming environment for efficient programming learning. Keywords—programming, scaffolding, learning support, cognitive load, worked-example

Adomian decomposition method applied to linear stochastic differential equations

Abstract: The paper deals with an application of Adomian Decomposition Method for solving linear stochastic differential equations. We derive new formulas such as the analytical approximate solution which convergces rapidely to the exact solution. The numerical experiments which are obtained show the efficiency of this method in the field of stochastic differential equations. AMS Subject Classification: 40A05, 40A25, 45G05

A note on adaptation of the knuth's extended euclidean algorithm for computing multiplicative inverse

Abstract: In this note we refresh realization of Adaptation of the Knuth’s Extended Euclidean Algorithm for Computing Multiplicative Inverse (EEACMI). The motivation of this work is that this algorithm is used in many directions [48], [32] as well as that this is variant of Euclidean algorithm which is given on many places as the oldest algorithm ever [1]-[27] and [29]-[48]. Internet sources gave many links and forums dealing with similar research of ‘greatest common divisor’. In our implementation we reduce the number of iterations and now they are 50% of Adaption of Knuth’s realization of EEACMI. For all algorithms we have use the implementations in Visual C# 2017 programming environment. AMS Subject Classification: 11A05, 68W01

On the extended chen's and pham's software reliability models. some applications

Abstract: The Hausdorff approximation of the impulse function σ∗∗(t) by sigmoidal functions based on the extended Chen’s and Pham’s cumulative functions are studied and an expression for the error of the best approximation is found. The received results are of independent significance in the study of issues related to neural networks and impulse technics. Using programming environment Mathematica we give results of many numerical examples which confirm the theory presented here. We give also real examples with data provided in [4] using extended Chen’s software reliability model and extended Pham’s deterministic software reliability model. Dataset included [5] Year 2000 compatibility modifications, operating system upgrade, and signaling message processing. Some direct comparisons are made. AMS Subject Classification: 41A46

Some deterministic growth curves with applications to software reliability analysis

Abstract: The Hausdorff approximation of the shifted Heaviside function ht0(t) by sigmoidal functions based on the Pham [1] and Song–Chang–Pham [2] cumulative functions is investigated and an expression for the error of the best approximation is obtained in this paper. The results of numerical examples confirm theoretical conclusions and they are obtained using programming environment Mathematica. We give real examples with data provided by IBM entry software package [3] using Song– Chang–Pham [2] software reliability model. AMS Subject Classification: 68N30, 41A46

Investigations of the k--stage erlangian software reliability growth model

Abstract: The Hausdorff approximation of the shifted Heaviside function ht0(t) by sigmoidal K–stage Erlangian growth curve based on the Khoshgoftaar’s [1] software reliability model is investigated and an expression for the error of the best approximation is obtained in this paper. The results of numerical examples confirm theoretical conclusions and they are obtained using programming environment Mathematica. We give real examples with dataset proposed in [8] using Khoshgoftaar’s model. AMS Subject Classification: 68N30, 41A46

A note on knuth's implementation of extended euclidean greatest common divisor algorithm

Abstract: In this note we give new and faster natural realization of Extended Euclidean Greatest Common Divisor (EEGCD) algorithm. The motivation of this work is that this algorithm is used in numerous scientific fields [36], [24]. Internet search engines show very high appearance of ‘greatest common divisor’. In our implementation we reduce the number of iterations and now they are 50% of Knuth’s realization of EEGCD. For all algorithms we have use the implementations in Visual C# 2017 programming environment. This paper is dedicated to Prof. Donald Knuth on occasion on his 80th anniversary AMS Subject Classification: 11A05, 68W01

A note on the ``mean value'' software reliability model

Abstract: In this paper we study the Hausdorff approximation of the Heaviside step function ht0(t) by sigmoidal curve based on the ”mean value” software reliability model and find an expression for the error of the best approximation. AMS Subject Classification: 68M15, 68N30

A new improvement of harris-stein modification of euclidean algorithm for greatest common divisor. ii

Abstract: In this note we gave new interpretation of Harris-Stein modification of Euclidean algorithm for calculation of greatest common divisor (GCD). Our results are different optimized ways of approaches presented in [1]–[26], [42]–[65]. For computer implementation Visual C# 2017 programming environment is used. AMS Subject Classification: 11A05, 68W01

A note on euclidean and extended euclidean algorithms for greatest common divisor for polynomials

Abstract: In this note we gave new interpretations of Euclid idea for Greatest Common Divisor for Polynomials (GCDP) and Extended Euclidean Algorithm for Greatest Common Divisor for Polynomials (EEAGCDP). The reason of this interest is wide usage of these algorithms [50], [34]. In our implementation we reduce the number of iterations and now they are 50% of wide spread implementation of Euclidean GCDP and EEAGCDP. In every serious book of algorithms the Euclidean algorithms are part of basic examples [1]-[29], [31]-[50]. Visual C# 2017 programming environment is used. AMS Subject Classification: 11A05, 68W01

A note on knuth's implementation of euclid's greatest common divisor algorithm

Abstract: In this note we give new and faster natural realization of Euclid’s Greatest Common Divisor (GCD) algorithm. The reason of interest in this topic is widely application of this algorithm in various mathematics and computer science topics [13]. Particularly via Google you can see that there are more than 400 000 pages indexed for keyword ‘greatest common divisor’. In our implementation we reduce the number of iterations and now they are 50% of Knuth’s realization of Euclid’s GCD. For all algorithms we have use the implementations in Visual C# 2017 programming environment. To the bright memory of Prof. Iliya Iliev AMS Subject Classification: 11A05, 68W01

Existence of fundamental matrix for neutral linear fractional system with distributed delays

Abstract: Abstract: The aim of the present paper is to obtain sufficient conditions for existing and uniqueness of the solution of the Cauchy problem with discontinuous initial conditions for nonhomogeneous neutral linear fractional differential system with distributed delay and Caputo type derivatives. As an application is obtained that the homogeneous system has a continuous in [a,∞), a ∈ R fundamental matrix, which result extends the corresponding ones even in the particular case of fractional system with one constant delay and lower terminal at zero of the fractional derivatives.

A Selective Generation of Hybrid Random Numbers via Android Smart Phones

Abstract: The True Random Number Generator (TRNG) is an important module for countless cryptographically secure appliances. TRNG generation technique requires custom made hardware with quantum phenomena, which on the whole are expensive research components. A secure and sound TRNG design is anticipated at this time, which is based on the permutation of sensor feeds and combination of noise patterns from the peripherals of any Android smartphone. The source for this generator is the selected features from the in-built hardware components namely accelerometer, gyroscope, magnetometer, WiFi signal measure, cell tower information, GPS coordinates and battery thermal noise. Additionally, Process ID (PID) of the corresponding Android processes is given as key vector to augment the entropy and also addresses some of the security concern like confidentiality, integrity and availability of the authentic sources. . Hardware-Based Random Number Generator (HRNG) can be achieved by combing the source of the user, their corresponding parameters and the measure of imperfection. Keywords— PID; TID; Mobile Sensors; TRNG; Thermal Noise; HRNG;

Some properties of the joint numerical range of the aluthge transform

Abstract: The study of the Aluthge transform T̃ was introduced and studied by Aluthge in his study of p-hyponormal operators in 1990. Several researchers have since studied various properties of the transform for a single operator T . For instance, quite a lot has been researched on the numerical range of T̃ of an operator T. In contrast to this, nothing is known about the joint numerical range of Aluthge transform T̃ of an m−tuple operator T = (T1, ..., Tm). The main reason for this limitation is that the notion of Aluthge transform is still a new area of study. The focus of this paper is on the study of the properties of the joint numerical range of Aluthge transform for an m−tuple operator T = (T1, ..., Tm). Among other results, we show that the joint approximate point spectrum of T̃ is contained in the closure of the joint numerical range of of T̃ . This study is therefore helpful in the development of the research on numerical ranges and Aluthge transform. AMS Subject Classification: 47LXX

A Modern approach to identify the fake news using machine learning

Abstract: Information technology has been improvising day by day. Key reason is that the usage of internet is increasing every year. This increases the data size as per the wiki statistics, majority of the people are interested in using social medias, thus the social media especially like Facebook and Twitter has lots audience all over the world. Controlling and validating the information source in these social media are really toughest challenge. Recently social media is used as a platform to spread the rumor and fake information such as morphed videos and images that affects social status of many innocent victims. There are also many people who lost their life due to the social media rumors. Identifying and reporting the rumor source before it spreads virally is the toughest challenge in current social media sites. In this paper, we have proposed an architecture and design to identify the rumor sources using machine learning model. Our base idea is to collect the common features vectors from various fake news source dataset. Then we used machine learning algorithms to train our model to predict the rumor news. We have implemented and tested our model with twitter dataset for various cases along with empirical results.

Neighborhood-based approach of collaborative filtering techniques for book recommendation system

Abstract: Recommendation System or Recommender System help the user to predict the "rating" or "preference" a user would give to an item. Recommender systems in general helps the users to find content, products, or services (such as digital products, books, music, movie, TV programs, and web sites) by combining and analyzing suggestions from other users, which mean rating from various people, and users. These recommendation systems use analytic technology to calculate the results that a user is willing to purchase, and the users will receive recommendations to a product of their interest. The aim of the System is to provide a recommendation based on users likes or reviews or ratings. Recommendation system comprises of content based and collaborative based filtering techniques. In this paper, collaborative based filtering has been used to get the expected outcome. The expected outcome has been achieved through collaborative filtering with the help of correlation techniques which in turn comprises of Pearson correlation, cosine similarity, Kendall’ s Tau correlation, Jaccard similarity, Spearman Rank Correlation, Mean-squared distance, etc. This paper tells about which similarity metrics such us Pearson correlation (PC), constrained Pearson correlation (CPC), spearman rank correlation (SRC) which is good in the context of book recommendation system and then applied with neighborhood algorithm.

Construction of complex nested ideal lattices for complex-valued channel quantization

Abstract: In this work we develop a new algebraic methodology which quantizes complex-valued channels in order to realize interference alignment (IA) onto a complex ideal lattice. Also we make use of the minimum mean square error (MMSE) criterion to estimate complex-valued channels contaminated by additive Gaussian noise. Received: March 14, 2018 c © 2018 Academic Publications §Correspondence author 550 C.C. Trinca Watanabe et al AMS Subject Classification: 03G10, 06B05, 06B10, 11RXX, 13F10, 97N20

Enhanced mutual authentication scheme for cloud of things

Abstract: In recent years, technologies play a vital role in day to day activities, of which cloud computing and Internet of Things form a primary role. The integration of these two technologies would be a huge advancement wherein there is a large pool of embedded devices communicating with the cloud. However, there are a lot of issues when we go for this integration. One of the main concerns is security, where device authentication and data privacy plays a vital role. In this paper, a mutual authentication scheme using Elliptic Curve Cryptography has been proposed. The proposed scheme has been analyzed against the work of Kalra et al. and the possible drawbacks with resolutions have been presented. The proposed scheme is verified using AVISPA and is proved to be strong against several attacks which prove it is more secure, powerful and efficient.