The m-consecutive-k-out-of-n: F linear and circular system consists of n sequentially connected components; the components are ordered on a line or a circle; it fails if there are at least m non-overlapping runs of consecutive-k failed components. This paper proposes the reliability and failure probability functions for both linearly and circularly m-consecutive-k-out-of-n: F systems. More precisely, the failure states of the system components are separated into two collections (the working and the failure collections); where each one is defined as a collection of finite mutual disjoint classes of the system states. Illustrative example is provided.

Community structures are fundamental in understanding the structure and functionality of complex networks. Different optimization algorithms, including both single-objective and multi-objective approaches, have been employed to address the challenge of community detection. Recently, multi-objective evolutionary algorithms (MOEAs) have attracted many researchers to identify communities in static networks. Many algorithms have been proposed to find a solution that achieves a trade-off between exploring new areas of the solution space and improving the quality of existing solutions. In this trade-off is crucial; whereas exploitation improves existing solutions, it may fail to find better solutions from insufficiently explored regions o

Abstract

The use of modern scientific methods and techniques, is considered important topics to solve many of the problems which face some sector, including industrial, service and health. The researcher always intends to use modern methods characterized by accuracy, clarity and speed to reach the optimal solution and be easy at the same time in terms of understanding and application.

the research presented this comparison between the two methods of solution for linear fractional programming models which are linear transformation for Charnas & Cooper , and denominator function restriction method through applied on the oil heaters and gas cookers plant , where the show after reac

Background: Venous leg ulcers (VLUs) affect 1-3% of the population and impose substantial pain-related morbidity, yet vascular pain remains underrecognized in clinical practice and research. Objectives: This narrative review synthesizes current evidence on the pathophysiology, clinical manifestations, and management strategies for VLU-associated pain. Methods: A comprehensive literature search was conducted across PubMed/MEDLINE, Scopus, Embase, and Web of Science (January 2015-July 2025) following SANRA guidelines. Search terms included "vascular pain", "venous leg ulcer", "chronic venous disease" and related terminology. Studies addressing pathophysiology, clinical characteristics, diagnostic approaches, and therapeutic interventi

The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approximation. This paper's main purpose is to introduce new types of proximal contraction for nonself mappings in fuzzy normed space and then proved the best proximity point theorem for these mappings. At first, the definition of fuzzy normed space is given. Then the notions of the best proximity point and - proximal admissible in the context of fuzzy normed space are presented. The notion of α ̃–ψ ̃- proximal contractive mapping is introduced.

       In the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented.

Some relations of inclusion and their properties are investigated for functions of type " -valent that involves the generalized operator of Srivastava-Attiya by using the principle of strong differential subordination.

Transport is a problem and one of the most important mathematical methods that help in making the right decision for the transfer of goods from sources of supply to demand centers and the lowest possible costs, In this research, the mathematical model of the three-dimensional transport problem in which the transport of goods is not homogeneous was constructed. The simplex programming method was used to solve the problem of transporting the three food products (rice, oil, paste) from warehouses to the student areas in Baghdad, This model proved its efficiency in reducing the total transport costs of the three products. After the model was solved in (Winqsb) program, the results showed that the total cost of transportation is (269,

The purpose behind building the linear regression model is to describe the real linear relation between any explanatory variable in the model and the dependent one, on the basis of the fact that the dependent variable is a linear function of the explanatory variables and one can use it for prediction and control. This purpose does not cometrue without getting significant, stable and reasonable estimatros for the parameters of the model, specifically regression-coefficients. The researcher found that "RUF" the criterian that he had suggested accurate and sufficient to accomplish that purpose when multicollinearity exists provided that the adequate model that satisfies the standard assumpitions of the error-term can be assigned. It