Area of Any Quadrilateral from Side Lengths
A Perishable Inventory Model with Variable Cycle Length Having Weibull Decay and Selling Price Dependent Demand
Design and Analysis of LMI for Stability and Static Output Feedback Control of Discrete-Time Matrix Sylvester System
Hewer Controllability and Kalman Controllability of Lyapunov Matrix Periodic Systems
Quantitative Research Method in the Spatial Analysis of Geographical Phenomenon: The GIS Nexus
An Introduction to Various Types of Mathematics Teaching Aids
A Simple Method of Numerical Integration for a Class of Singularly Perturbed Two Point Boundary Value Problems
A New Approach to Variant Assignment Problem
A Homotopy Based Method for Nonlinear Fredholm Integral Equations
Proof of Beal's Conjecture and Fermat Last Theorem using Contra Positive Method
Trichotomy–Squared – A Novel Mixed Methods Test and Research Procedure Designed to Analyze, Transform, and Compare Qualitative and Quantitative Data for Education Scientists who are Administrators, Practitioners, Teachers, and Technologists
Algorithmic Triangulation Metrics for Innovative Data Transformation: Defining the Application Process of the Tri–Squared Test
A New Hilbert-Type Inequality In Whole Plane With The Homogeneous Kernel Of Degree 0
Introducing Trinova: “Trichotomous Nomographical Variance” a Post Hoc Advanced Statistical Test of Between and Within Group Variances of Trichotomous Categorical and Outcome Variables of a Significant Tri–Squared Test
Surfaces in R3 with density
In this paper we show that the area of any quadrilateral can be estimated from the four lengths sides. With the Triangle Inequality Theorem and a novel provided diagonal's formula, the boundaries of quadrilateral diagonals are found. Finally, Bretschneider's formula can be applied to find a set of possible areas.
An inventory model is presented for deteriorating items with selling price dependent demand having different cycle lengths through assuming the lifetime commodity is random and follows Weibull distribution. In this inventory model, demand is considered as a function of selling price and cycle length of successive replenishment in a planning period. It is also considered that the cycle length in each cycle reduces by arithmetic progression, and shortages are completely backlogged and allowed with feasible cost consideration. The instantaneous state of inventory and total cost function is derived. The optimal ordering and pricing policies of this model are also obtained. In this work, numerical illustrations and sensitive analysis are utilized to observe the sensitivity of optimal values of the ordering and pricing with respect to deterioration parameters and cost. This model also includes several earlier inventory models as specific cases.
This paper deals with the design of static output feedback (SOF) control for the discrete matrix sylvester system. The design principles of SOF formulation based on the linear matrix inequality (LMI) are expressed in terms of Bilinear Matrix Inequalities (BMIs). Non-convex stability conditions that emerge in the design of SOF control are to be transferred into convex stability conditions by using suitable techniques. This paper presents the results that are necessary to address the convexity problem. This paper also presents a novel approach for the transformation of BMI constraints into LMIs. The developed theory and established results are verified and validated by numerical simulations.
This paper explores the relationship between Kalman Controllability (K-Controllability) and Hewer Controllability (H- Controllability) of Lyapunov Matrix periodic systems, which have extensive applications in cyber physical systems, power systems, robotics and the analysis and design of control systems. This paper establishes the equivalence of K- Controllability and H- Controllability of Lyapunov matrix periodic systems through the period of the system and degree of the minimal polynomial of the monodromy matrix of the system.
Understanding the spatial structure and environmental link of physical, economic, social, and political processes, or the spatial evidence of their consequences, is significant in many areas of endeavor. As a result, a variety of analytical techniques have previously been developed to explain the spatial behavior of this geographical phenomenon. For example, the quantitative approach has proven to be a successful scientific approach for researching geographical issues and occurrences. The creation of a model, usually with a substantial spatial context, is a key component of quantitative geographical research. Additionally, the Geographic Information System (GIS) is a suitable and efficient tool that provides the fundamental answers to a number of geospatial issues, including the representation, analysis, and knowledge of their spatial dimensions. The application of the quantitative method in spatial analysis, with a focus on the GIS relationship, is the goal of this paper. In summary, the evaluated publications show that mathematical and statistical abilities are necessary for the quantitative approach to geospatial analysis. It aimed to create a more exacting and methodical approach to resolving issues pertaining to geography. Furthermore, it is impossible to overstate the importance of computer and data management abilities in quantitative methodologies. As a computer-based instrument for the collection, storing, processing, and visualization of geographical data, GIS is therefore a crucial method in the quantitative approach to spatial analysis. Similarly, the quantitative method is important to GIS in various ways, such as in the basic ideas of GIS architecture, the concept of attribute table, and the abstraction of geographic space.
