##### Reliability Analysis of a Commodity-Supply Multi-State System Using the Map Method

Ali Muhammad Ali Rushdi, Abdulghani Bakur Alsayegh

Journal of Advances in Mathematics and Computer Science, Page 1-17
DOI: 10.9734/jamcs/2019/v31i230107

A multi-state k-out-of-n: G system is a multi-state system whose multi-valued success is greater than or equal to a certain value j (lying between 1 (the lowest non-zero output level) and M (the highest output level)) whenever at least km components are in state m or above for all m such that 1 m j. This paper is devoted to the analysis of a commodity-supply system that serves as a standard gold example of a non-repairable multi-state k-out-of-n: G system with independent non-identical components. We express each instance of the multi-state system output as an explicit function of the multi-valued inputs of the system. The ultimate outcome of our analysis is a Multi-Valued Karnaugh Map (MVKM), which serves as a natural, unique, and complete representation of the multi-state system. To construct this MVKM, we use “binary” entities to relate each of the instances of the output to the multi-valued inputs. These binary entities are represented via an eight-variable Conventional Karnaugh Map (CKM) that is adapted to a map representing four variables that are four-valued each. Despite the relatively large size of the maps used, they are still very convenient, thanks to their regular structure. No attempt was made to draw loops on the maps or to seek minimal formulas. The maps just served as handy tools for combinatorial representation and for collectively implementing the operations of ANDing, ORing, and complementation. The MVKM obtained serves as a means for symbolic analysis yielding results that agree numerically with those obtained earlier. The map is a useful tool for visualizing many system properties, and is a valuable resource for computing a plethora of Importance Measures for the components of the system.

##### Lomax-Gumbel {Fréchet}: A New Distribution

M. R. Mahmoud, R. M. Mandouh, R. E. Abdelatty

Journal of Advances in Mathematics and Computer Science, Page 1-19
DOI: 10.9734/jamcs/2019/v31i230108

In this paper the T-R{Y} framework is used for proposing a new distribution that called The Lomax-Gumbel{Fréchet} distribution. We study in details the properties of this distribution including hazard function, quantile Function, the skewness, the kurtosis, transformation, Renyi entropy, and moment generating function. Estimate of the parameters will be obtained using the MLE method. We present a simulation study and t the distribution to two real data sets.

##### Convergence Analysis and Network Properties of Wagner's Artificial Gene Regulatory Network Model

Yifei Wang

Journal of Advances in Mathematics and Computer Science, Page 1-18
DOI: 10.9734/jamcs/2019/v31i230109

The gene regulatory network (GRN) is essential to life, as it governs all levels of gene products that enable cell survival and numerous cellular functions. Wagner's GRN model, which has mathematical roots origin from the Ising model and neural networks, is a powerful computation tool that helps integrate network thinking into biology, and motivated a new research theme focusing on the evolution of genetic networks. However, except the formal mathematical
foundation described in [1], few papers have focused on providing further mathematical analysis of the model. Moreover, network characteristics of Wagner's GRN model when varying key parameters are unclear. Therefore, in this paper, I present a convergence analysis of Wagner's GRN model by using the Markov chain theory. I show mathematically that if we consider the evolution process as an optimisation process, then the probability of nding the optimal conguration (a certain target phenotype) converges to probability one. In addition, I investigate network characteristics such as stability, robustness and path length in initial populations. I find that generally small networks with a sparse connectivity have a higher initial stability.The robustness is also observed to be higher in initial stable networks with a low network connectivity. These results are partly explained by the pattern, as shown in this paper, that small networks with a sparse connectivity generally have a shorter path length and, therefore, they are not only able to quickly reach equilibrium phenotypic states but also more likely to resist genetic perturbations.

##### Generalized (α,β )-higher Derivations on Lie Ideals of Rings with Involution

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/jamcs/2019/v31i230110

In this manuscript, we investigate the behaviour of additive mappings which satisfy a functional identity associated with generalized (α, β)-higher derivations on Lie ideals of a prime ring with involution. As the consequences of our main theorem, many well known results can be deduced.

##### Cloud Computing: Securing without Losing Control

Mubarak S. Almutairi

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/jamcs/2019/v31i230106

Computing virtualization is the key technology in cloud computing as it can reduce the investment in the hardware component drastically. The present research work carefully analyse some of the major security threats to the cloud services based on the security threat analysis produced by Cloud Security Alliance (CSA). The physical network components are not necessarily located on the same geographical area but yet are doing the necessary processing and storage. As such, “cloud computing” will be the driving force behind most of today's promising computing technologies. Security will be always an issue which needs to be addresses at two different levels: front-end and back-end. In a nutshell, cloud computing is hugely beneficial for the enterprise and while still evolving, will be around for the long-term. It is crucially important for those enterprises which will adopt the cloud computing model to put long-term security strategy in place. Knowledge of cloud architecture, technology, process, services, and deployment models is vital in specifying security models and identifying security concerns in cloud computing. As the providers and end users increase, standardization and security techniques will play an important role in helping organizations to reduce risks involved. This survey also illustrates the view of cloud providers’ actions and assessment of the cloud-computing services provided by them to the IT users.