Advances in Mathematics and Computer Science Vol. 4

Tank Level Prediction Using Kalman and Lainiotis Filters

N. Assimakis, G. Tziallas, I. Anagnostopoulos, A. Polyzos Polyzos — Wed, 20 Nov 2019 00:00:00 +0000

Tank level knowledge is very important in many applications, as in oil tank. The liquid in the tank can be static, filling or emptying, or sloshing, resulting to uncertain knowledge of tank level. In this work the tank level is predicted using prediction algorithms based on Kalman and Lainiotis filters. Time invariant and steady state prediction algorithms for static model and filling/emptying model are implemented. Time varying prediction algorithms for sloshing and filling/emptying and sloshing models are also implemented. The prediction algorithms’ behavior is examined concluding that the obtained predictions are very close to the real tank level. The calculation burdens of the prediction algorithms are derived, determining the faster prediction algorithm for each model.

The Impact of Consumption on an Investor’s Strategy under Stochastic Interest Rate and Correlating Brownian Motions

Silas A. Ihedioha, Ubani, Sunday Iheanyi, Njoku, Iheanyi Odochi — Wed, 20 Nov 2019 00:00:00 +0000

In this work, we consider that an investor’s portfolio comprises of two assets- a risk-free asset driven by Ornstein-Uhlenbeck Stochastic interest rate of return model and the second asset a risky stock with a price process governed by the geometric Brownian motion. It is also considered that there are withdrawals for consumption and taxes, transaction costs and dividends are in involved. The aim was to investigate the effect of consumption on an investor’s trading strategy under correlating Brownian motions. The relating Hamilton-Jacobi-Bellman (HJB) equation was obtained using maximum principle. The application of elimination of variable dependency gave the optimal investment strategy for the investor’s problem. Among the findings is that more fund should be made available for investment on the risky asset when there is consumption to keep the investor solvent.

A Queuing Model to Analyze Data Center Performances in a Cloud Computing Environment

Mohamed Hanini, Fatima Oumellal, Abdelkrim Haqiq — Wed, 20 Nov 2019 00:00:00 +0000

In the last decades cloud computing has been the focus of a lot of research in both academic and industrial fields, however, implementation-related issues have been developed and have received more attention than performance analysis which is an important aspect of cloud computing and it is of crucial interest for both cloud providers and cloud users. Successful development of cloud computing paradigm necessitates accurate performance evaluation of cloud data centers. Because of the nature of cloud centers and the diversity of user requests, an exact modeling of cloud centers is not practicable; in this work we report an approximate analytical model based on an approximate Markov chain model for performance evaluation of a cloud computing center. Due to the nature of the cloud environment, we considered, based on queuing theory, a MMPP task arrivals, a general service time for requests as well as large number of physical servers and a finite capacity. This makes our model more flexible in terms of scalability and diversity of service time. We used this model in order to evaluate the performance analysis of cloud server farms and we solved it to obtain accurate estimation of the complete probability distribution of the request response time and other important performance indicators such as: the Mean number of Tasks in the System, the distribution of Waiting Time, the Probability of Immediate Service, the Blocking Probability and Buffer Size

Some S-degree Based Topological Indices of Silicates (SiO2) Layer

Budheswar Deka, Abhigyan Mahanta, A. Bharali — Wed, 20 Nov 2019 00:00:00 +0000

A topological index is a graph invariant, which is generated as a real number from a set of finite graphs. A large number of topological indices have been developed based on vertex degree, eccentricity, etc. and studied extensively. In this paper we propose a new version of the inverse sum indeg index (ISI), sum-connectivity index (SCI), redefined third Zagreb index and - Zagreb index based on S-degrees of vertices a graph and discuss them in connection with SiO₂layer structure in a graph theoretic perspective.

A zeta function Computation of Casimir Energy

Louis Omenyi — Wed, 20 Nov 2019 00:00:00 +0000

A computation of Casimir energy via spectral zeta function is considered in this Chapter. The original computations deriving the Casimir energy and force consists of first taking limits of the spectral zeta function and afterwards analytically extending the result. This process of computation presents a weakness in Hendrik Casimir’s original argument since limit and analytic continuation do not commute. A case of the Laplacian on a parallelepiped box representing the space as the vacuum between two plates modelled with Dirichlet and periodic Neumann boundary conditions is constructed to address this anomaly. It involves the derivation of the regularised zeta function in terms of the Riemann zeta function on the parallelepiped. The values of the Casimir energy and Casimir force obtained from our derivation agree with those of Hendrik Casimir.

Improving Method of Evaluating Semantic Filtering for Human Computer Interaction in an Adaptive Collaborative Learning Environment

A. A. Adigun, A. O. Osofisan, O. Longe, M. O. Kolawole — Wed, 20 Nov 2019 00:00:00 +0000

Human Computer Interaction Semantic filtering techniques are used in learning environment to track problems in collaborative systems. However, as noted in Adigun et al. [1], when sharing and dynamism are promoted, a problem of redundancy and integrity appeared not to have been well addressed. An improved ASF-based method of evaluating semantic filtering for social network systems in a collaborative learning environment is developed, which assisted participants to achieve greater levels of performance with information sharing from other collaborators, as well as in reusing ideas across the period of collaboration.

Finding the Location of the Axes, the Vertices and the Foci of a Parabola, an Ellipse and a Hyperbola Using a Straightedge and a Compass

Moshe Stupel, Avi Sigler, Shula Weissman — Wed, 20 Nov 2019 00:00:00 +0000

We present geometrical constructions using a straightedge and a compass in order to find the location of the axes, the vertices and the foci of a parabola, an ellipse and a hyperbola from their plots. The constructions are based on familiarity with theorems and special properties characterizing these loci, which therefore can be used for implementing and applying knowledge acquired during the studies of analytical geometry.

Image Segmentation Using N - Cut Based Graph Partitioning

Sheetal Ghorpade — Wed, 20 Nov 2019 00:00:00 +0000

The process of image segmentation is one of the most important steps in computer vision for image retrieval, visual summary, image-based modeling and in many other processes. The goal of segmentation is typically to locate certain objects of interest. In this paper, we have studied and investigated graph based normalized cut segmentation methods and proposed a technique for adding flexibility to the parameters for performance improvement. These methods are examined analytically and tested their performance for the standard images. The results obtained for the important metrics show that these methods perform better than others approach and are computationally efficient, and useful for precise image segmentation.

Bayesian Approach to Reliability Estimation

Arun Kumar Rao, Himanshu Pandey — Wed, 20 Nov 2019 00:00:00 +0000

In this chapter Bayes estimators of the reliability function R(t) under Type II censoring of Weibull distribution have been obtained by taking non-informative and beta prior distributions. The loss functions used are squared error, linex, precautionary and entropy.

Reliability Measurement of Square Model to Develop IVR Software

Devesh Kumar Srivastava — Wed, 20 Nov 2019 00:00:00 +0000

Square model is a software process model to develop Interactive Voice Response (IVR) software, used in call center industry. In this article, we measured the reliability of Square Model in the presence of covariate information. For this, we derived a failure intensity function which is used to measure the reliability of model using fix number of calls, failure intensity parameter value, failures / CPU hour and mean failures observed empirically for all components to estimate failure intensity of IVR software over various time periods when it is assumed that the software is changed after each time period and that software metrics information is available after each update.

Proposition of a Recursive Formula to Calculate the Higher Order Derivative of a Composite Function without Using the Resolution of the Diophantine Equation

El Khomssi Mohammed, Chaachoui Ghizlane, Ez-Zriouli Rachid — Wed, 20 Nov 2019 00:00:00 +0000

The formula of Fa`a Di Bruno provides a powerful tool to calculate the higher order derivative of a composite function. Unfortunately it has three weaknesses: it is not a recursive formula, it totally depends on the resolution of the diophantine equation and a change in the order of the derivative requires the total change of the calculation. With these weaknesses and the absence of a formula to program, Fa`a Di Bruno’s formula is less useful for formal computation.
Other complicated techniques based on ﬁnite diﬀerence calculation (see [ 1]) are recursive, however the complexity of the calculation algorithm is very high. There is as well some techniques based on graphs (see [2]) to calculate the coeﬃcients to a certain order, but without giving the general formula.
In our work we propose a new formula to calculate the higher order derivative of a composite function gof. It is of great interest, because it is recursive and it is not based on the resolution of the diophantine equation. We complete this work by giving an expression that allows to ﬁnd directly the n-th derivative of a composite function.

Square Difference Prime Labeling –More Results on Path Related Graphs

B. S. Sunoj, T. K. Mathew Varkey — Wed, 20 Nov 2019 00:00:00 +0000

Vertices of the graph G are labeled with first p-1 whole numbers, where p is the number of vertices of the graph and edges are labeled with absolute difference of the squares of the labels of the end vertices. If the greatest common divisor of the labels of all edges incident on a vertex of degree greater than one is one then the graph admits square difference prime labeling.

Here we investigate, strong duplicate graph of path, splitting graph of path, tortoise graph of path and some more path related graphs for square difference prime labeling.