##### Some New Solutions of the Landau-Lifshitz Equation in Cylindrical Symmetric System

Jie Zhang

Journal of Advances in Mathematics and Computer Science, Page 39-52
DOI: 10.9734/jamcs/2020/v35i130238

This paper is devoted to obtaining various explicit dynamic solutions of the Landau-Lifshitz equation in 2-dimensional cylindrical symmetric system. By suitably establishing explicit transformation, we here construct explicit dynamic solutions depending on the angle θ and time t for Landau-Lifshitz equation with anisotropy field or external magnetic field. Besides, we introduce certain indeterminate solution form of the Landau-Lifshitz equation by solving the indeterminate coefficients to derive explicit magnetic vortex or traveling wave solution. In this paper, we provide some specific examples and attain their some explicit dynamic solutions.

##### A Mathematical Model of Rabies Transmission Dynamics in Dogs Incorporating Public Health Education as a Control Strategy -A Case Study of Makueni County

Jane S. Musaili, Isaac Chepkwony

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/jamcs/2020/v35i130235

Rabies is a zoonotic viral disease that aects all mammals including human beings. Dogs are responsible for 99% of human rabies cases and the disease is always fatal once the symptoms appear. In Kenya the disease is still endemic despite the fact that there are ecient vaccines for controlling the disease. In this project, we developed SIRS mathematical model using a system of ordinary dierential equations from the model to study the transmission dynamics of rabies virus
in dogs using public health education as a control strategy. The reproduction number R0 was calculated using the Next Generation Matrix. Both disease free and endemics equilibrium points were determined and their stability analysis performed. From the stability analysis results it was found out that the disease free equilibrium point is both locally and globally asymptotically stable when R0 < 1 and the endemic equilibrium point is both locally and globally asymptotically stable when R0 > 1. Numerical simulations done using Matlab indicated that education of the public on administration of both pre and post exposure vaccines to dogs and responsible dog ownership leads to a decrease in the numbers of rabies virus infected dogs which shows that public health education is an ecient means for controlling rabies.

##### Some Results for Feng-Liu type Mappings in Modular Metric Spaces

Duran Turkoglu, Emine Kilinc

Journal of Advances in Mathematics and Computer Science, Page 12-22
DOI: 10.9734/jamcs/2020/v35i130236

In this paper we investigate some fixed point results of Feng and Liu type multi-valued mappings in modular metric spaces. We also give an example to show that these results are more general versions of Feng and Liu’s theorem.

##### Use of Signed Permutations in Cryptography

Iharantsoa Vero Raharinirina

Journal of Advances in Mathematics and Computer Science, Page 23-38
DOI: 10.9734/jamcs/2020/v35i130237

In this paper we consider cryptographic applications of the arithmetic on the hyperoctahedral group. On an appropriate subgroup of the latter, we particularly propose to construct public key cryptosystems based on the discrete logarithm. The fact that the group of signed permutations has rich properties provides fast and easy implementation and makes these systems resistant to attacks like the Pohlig-Hellman algorithm. The only negative point is that storing and transmitting permutations need large memory. Using together the hyperoctahedral enumeration system and what is called subexceedant functions, we define a one-to-one correspondence between natural numbers and signed permutations with which we label the message units.

##### A Slacks-based Measure in the Presence of Ratio Variable with Convexity Consideration

Farzaneh Ghaffari, Morteza Haghiri

Journal of Advances in Mathematics and Computer Science, Page 53-62
DOI: 10.9734/jamcs/2020/v35i130239

The nature of input-output relationships in general and ratio data in particular has important consequences for practitioners when the data envelopment analysis method is used to  measure technical efficiency of decision making units or production units. Since the data envelopment analysis approach was introduced several studies tried to develop the model from different aspects including when the model deals with ratio data. To date, none of these studies was able to address the aforementioned problem properly and as a result most of them suffered from a lack of clarity in the presence of input-and-output ratios. This study proposes a slacks-based measure of efficiency in the presence of ratio variable. Our approach deals directly with the input excess and the output shortfalls of the decision making units’ concerns, and as a result, improved measuring efficiency scores.

##### Odd Lindley-Rayleigh Distribution: Its Properties and Applications to Simulated and Real Life Datasets

Terna Godfrey Ieren, Sauta Saidu Abdulkadir, Adekunle Abdulmumeen Issa

Journal of Advances in Mathematics and Computer Science, Page 63-88
DOI: 10.9734/jamcs/2020/v35i130240

This article develops an extension of the Rayleigh distribution with two parameters and greater flexibility which is an improvement over Lindley distribution, Rayleigh distribution and other generalizations of the Rayleigh distribution. The new model is known as “odd Lindley-Rayleigh Distribution”. The definitions of its probability density function and cumulative distribution function using the odd Lindley-G family of distributions are provided. Some properties of the new distribution are also derived and studied in this article with applications and discussions. The estimation of the unknown parameters of the proposed distribution is also carried out using the method of maximum likelihood. The performance of the proposed probability distribution is compared to some other generalizations of the Rayleigh distribution using three simulated datasets and a real life dataset. The results obtained are compared using the values of some information criteria evaluated with the parameter estimates of the fitted distributions based on the four datasets and it is revealed that the proposed distribution outperforms all the other fitted distributions. This performance has shown that the odd Lindley-G family of distribution is an adequate generator of probability models and that the odd Linley-Rayleigh distribution is a very flexible distribution for fitting different kinds of datasets better than the other generalizations of the Rayleigh distribution considered in this study.

##### Generalized Fibonacci Numbers: Sum Formulas

Yüksel Soykan

Journal of Advances in Mathematics and Computer Science, Page 89-104
DOI: 10.9734/jamcs/2020/v35i130241

In this paper, closed forms of the summation formulas for generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery.

##### Cubic Transmuted Gompertz Distribution: As a Life Time Distribution

A. A. Ogunde, Fatoki Olayode, Audu Adejumoke

Journal of Advances in Mathematics and Computer Science, Page 105-116
DOI: 10.9734/jamcs/2020/v35i130242

In this work, we proposed and studied the Cubic Transmuted Gompertz (CTG) distribution using the Cubic Transmuted family of distributions which was introduced by Rahman et al. [8] and based on cubic transmutation map. We studied the statistical properties of the new distribution which includes: rth moment, moment generating function order statistics, mean, variance, Renyl entropy. The CTG distribution was fitted to a real data set to demonstrate its flexibility and tractability in modelling real life data.

##### Study of RL-Connectedness and RL-Compactness

J. M. U. D. Wijerathne, P. Elango

Journal of Advances in Mathematics and Computer Science, Page 117-123
DOI: 10.9734/jamcs/2020/v35i130243

In this paper, we introduce a new kind of locally closed sets called regular locally closed sets (brie y RL-closed sets) in a topological space which are weaker than the locally closed sets. Regular locally continuous maps and regular locally irresolute maps are also introduced and studied some of their properties. Finally, we introduce the concept of regular locally connectedness and regular locally compactness on a topological space using the RL-closed sets.

##### Large Deviation Principle for Stochastic Differential System Pertubated by a Rapid Process in the Besov-Orlicz Topology

Randrianomenjanahary Rado Abraham, Rabeherimanana Toussaint Joseph

Journal of Advances in Mathematics and Computer Science, Page 124-138
DOI: 10.9734/jamcs/2020/v35i130244