Analytical Construction of Uniformly Convergent Method for Convection Diffusion Problem

In this paper, we study the uniformly convergent method on equidistant meshes for the convection-diffusion problem of type; where the formal adjoint operator of L. Lu=-εu''+bu'+c u=f(x), u(0)=0, u(1)=0 At the end of the this paper we will generate the scheme; -e^(ρ_i )/(e^(ρ_i )+1) U_(i-1)+U_i-1/(e^(ρ_i )+1) U_(i+1)=(f_i-c_i U_i ) h/b ((e^(ρ_i )-1)/(e^(ρ_i )+1))

Compactly Completeness and Finitarily Completeness on Continuous Information System

The plane here, introduce and study the concepts of bounded completeness and finitely completeness on continuous information system. Further more compactly completeness, finitarily completeness and strongly compactly completeness for continuous information system. Some interactions between these concepts are investigated. Some corresponding results in posets and domains due to R.Hechmann [5] are generalized.

A Sustainable Approach for Smart Supply Chain with Quality Humiliation and Carbon Emission Cost

Most decisive principles affecting customers’ ordering decision is quality of the products. The intention of the work is to provide the sustainable decisions such as order lot-size and total number of lot-size to create a smart SC in view of minimum carbon emissions and joint total cost. This research considers an imperfect production vendor-buyer inventory system involving quality degradation of raw material and carbon emission cost. The vendor’s production process produces some imperfect products, even manufactured products inspect twice, which are examined by buyer and those are return back to vendor in the subsequent shipment. We incorporate the emissions throughout the production processes, transport and storage. Mathematical based inventory model is developed to attain the sustainable decisions which are illustrated numerically.

Unknown Values Estimation in Incomplete Fuzzy Soft and Interval Valued Soft Matrices

In day-to-day problems, incomplete information due to unknown values in data is the cause of the loss of information which leads to uncertainly, ambiguity and vagueness. There are many reasons for unknown values in data, like errors in data collection, lack of data information, inappropriate technique, and illegibility of data which cause incompleteness in data. Thus, estimating the unknown values in data of various information systems is an important area of research. In this communication, the definitions of incomplete Fuzzy soft and interval-valued fuzzy soft matrices are given with application in numerical problems. An algorithm is proposed for unknown values estimation in an incomplete fuzzy soft matrix and applied in solving a numerical problem. An application of an incomplete fuzzy soft matrix after inserting the unknown values in dimension reduction is studied. The unknown values in the incomplete interval-valued fuzzy soft matrix are also estimated and applied in the multi-criteria decision-making method.

Non-Convex Penalized Estimation of Count Data Responses via Generalized Linear Model (GLM)

This study provided a non-convex penalized estimation procedure via Smoothed Clipped Absolute Deviation (SCAD) and Minimax Concave Penalty (MCP) for count data responses to checkmate the problem of covariates exceeding the sample size . The Generalized Linear Model (GLM) approach was adopted in obtaining the penalized functions needed by the MCP and SCAD non-convex penalizations of Binomial, Poisson and Negative-Binomial related count responses regression. A case study of the colorectal cancer with six (6) covariates against sample size of five (5) was subjected to the non-convex penalized estimation of the three distributions. It was revealed that the non-convex penalization of Binomial regression via MCP and SCAD best explained four un-penalized covariates needed in determining whether surgical or therapy ideal for treating the turmoil.

An Applied Component Modeling to the Irreversibility from a New Configurationally Perspective of the Statistical Physics

From the perspective of statistical physics (Boltzmann equation), configurational entropy can be calculated using the study of the microstates of the system. When a physical process is performed, identifying the entropy production can be used to investigate the irreversibility, but from the perspective of the Boltzmann equation, to study entropy production, both all microstates and macrostates must be studied. Therefore, a very large volume of calculations will be needed. In this report, using a new innovative energy structure equation, a new macroscopic component modeling is extracted to investigate the configurational irreversibility. To investigate the irreversibility in physical systems, the energy structure equation of the system can be studied in different paths. During performing a physical process, some activated energy components related to the reversible process and remain will be related to the irreversible process. In this report, also using a quasi-statistical approach, the structure of irreversible components is studied. When macroscopic energy components are the base of the equations, a very large volume of the needed calculations will be less than Boltzmann equation and in fact, studying all particles isn’t needed, but it is enough that a few macroscopic components to be investigated. Also, considering the theories of dissipated energy, the extracted equations have the same base as the different formulations of the second law of thermodynamics.

Use of Fuzzy Matrices for the Diagnosis of Diabetes, Anaemia and Hypertension

The mathematical model presented here aims to enhance the precision in diagnostic process of diabetes, anaemia and hypertension by means of fuzzy interface. In real life, the imprecise nature of medical documentation and uncertain information provided by patients often do not give the desired degree of confidence to the diagnosis. To that end using the capability of fuzzy logic in representing, interpreting and utilizing data and information that are vague and lack certainty, a new algorithm based on different fuzzy matrices and fuzzy relations is developed. In the process a medical knowledge base is developed with the help of 51 doctors. The model achieved 94.44% accuracy in the diagnosis, which shows its usefulness. To implement this model-based diagnosis procedure a user-friendly Excel program is designed.

A Mathematical Study on a Diseased Prey-Predator Model with Predator Harvesting

In this paper, we present a mathematical model for a prey-predator system with infectious disease in the prey population. We assumed that there is harvesting from the predator and a defensive property against predation. This model is constituted by a system of nonlinear decoupled ordinary first order differential equations, which describe the interaction among the healthy prey, infected prey and predator. The existence, uniqueness and boundedness of the system solutions are investigated. Local stability of the system at equilibrium points is discussed.

Some Results on Fuzzy Topological Modules and Fuzzy Topological Submodules

In this paper, we bring together the structure of fuzzy topological space ,fuzzy module and that of fuzzy ring to form a combined structure, that of a fuzzy topological R-module. Properties of fuzzy topological R-module ,topological R-submodule and its Properties are also briefly examined. we proved many theorems and corollaries as results shown in this paper.

A New Generalized Entropy Measure and its Properties

 In this research article, a new two parametric measure of Entropy  and its corresponding code word length  has been developed. The developed measures are the generalizations to some well known existing measures. Besides, some noiseless coding theorems for discrete noiseless channel have been developed, and the results thus obtained have been verified with the support of an numerical example. Also, at the end of this research article, a comparative study in terms of  monotonic behavior  among the proposed entropy  , Matahi’s entropy  and Tsallis entropy  together  with their respective average code word length measures have been made and graphically displayed.