Matrix Science Mathematic (MSMK)

In the ordinal theory, maximum utility is achieved by determining the tangent point of the budget constraint line to one of the difference curves of equal satisfaction of a consumer. The model is a simplified model to determine the choices of buying two products such that maximum consumer satisfaction is reached. Market conditions frequently change due to inflation, deflation or price fluctuations. It may also happen that the individual income may change in time. In both cases, the budget constraint line shifts to the right or left. In this work, budget constraint line changes are modeled by assuming changes in the intercepts of the line. In the first scenario, the ratio of intercept changes are proportional in time while in the second scenario, the intercept changes are modeled by arbitrary functions of time. For both cases, by combining the optimal points, maximum utility curves are formed. Numerical examples are treated to outline the calculations.

In recent times, the conditional marginal modeling approach has emerged as a new area in longitudinal studies; a new multivariate Poisson regression model has been proposed for count data, the model’s validity was assessed using simulation techniques, followed by fitting the model to real data from the Health and Retirement Study, and the correlation coefficients of the response variable’s impact among the first, second, and third follow-up were estimated.

This paper attempts to describe the Fibonacci numbers, their qualities, completeness, and mathematical completeness; the Fibonacci sequence may be seen in a number of stunning natural events; as a result, this paper begins by introducing the Fibonacci sequence and then goes on to discuss some of its properties; the Fibonacci sequence is mathematically complete, as well as having natural and artistic manifestations; the series itself is infinite, and any positive integer may be expressed as the sum of individual Fibonacci numbers; the Fibonacci sequence and golden ratio act as testimonies; the Fibonacci sequence, which has ancient mathematical foundations, continues to fascinate our minds and show subtle patterns in a variety of fields; as we interpret the complexities of these mathematical masterworks, we develop a better understanding of how mathematics and the world around us.

The approximate equivalence of functions is defined with respect to Taylor series expansions first. Based on the approximate equivalence, approximation of a given function with other functional series is discussed. The theory is first applied to root finding iteration algorithms. Then the solution of ordinary differential equations is treated as the next application. Several numerical sample problems are considered. It is shown that the formalism can be effectively used in determining the roots of algebraic equations or finding the solutions of differential equations. To increase the precision of the solutions, higher order approximations should be taken.

This paper considers the conventional logistic model and how to obtain the solutions of fractional differential equations. It examines using a hybrid of Sumudu transform method, which is an approximate analytical method for solving fractional differential equations that are associated with time delay. Furthermore, the paper introduces the fractional Caputo-Fabrizio derivative and proportional time delay into the conventional logistic model to propose a general and more logistic model for the population growth. The paper considers different cases of the newly introduced general logistic model and using a hybrid of Sumudu transform method, their solutions were obtained. Using MATLAB, it displays and compares the behaviour of different cases of the general logistic model with fractional Caputo-Fabrizio derivative and proportional time delay.

Bernoulli bases are developed to approximate the solutions of two-point BVP in modelling viscoelastic flows in which the shifted Chebyshev collocation points are used as collocation nodes. Properties of Bernoulli bases are then used to reduce the two-point BVP in modelling viscoelastic flows to systems of nonlinear algebraic equations. The results show the agreement between the exact solutions and the approximate solutions. Form the numerical results we see that the proposed method gives accurate results.

A new 2-point hybrid block method for the numerical solution of first-order stiff systems of ordinary differential equations in initial value problems with optimal stability property is presented. The necessary and sufficient conditions for the convergence of the proposed implicit block numerical scheme for solving stiff ODEs are established. The stability and convergence analysis of the method show that it is consistent, zero-stable, and convergent. The absolute stability region of the method is plotted, indicating that the method is A-stable. The method is implemented in Microsoft Dev C++ environment using the C programming language and Newton’s iteration, and some selected first-order stiff initial value problems are solved. The numerical results obtained for the proposed method are compared with the existing fifth order fully implicit 2-point block backward differentiation formula and 2-point block backward differentiation formula with two off-step points methods. The comparison reveals that the new method outperforms both methods in terms of accuracy but are competing in terms of computation time as we reduce the step size. It is evident that the method converges faster.

Intelligent weighing systems play a significant role in guiding coal production and assisting production decisions. However, the traditional weighing method not only cannot guarantee efficiency, but also is prone to artificial fraud, causing economic losses to enterprises. In view of the needs of industrial production, this paper studies a visual weighing method for mining dump trucks with ResNet deep learning network as the core. Firstly, the collected dataset is processed by the Resize function and the Blend function, and then the ResNet neural network is trained with the processed dataset, and finally the cross-entropy loss function and Adam optimization strategy are used to improve the recognition accuracy. The results show that the final recognition accuracy is 60%.

Soft set theory gained popularity as a cutting-edge approach to handling uncertainty-related problems and modeling uncertainty when it was introduced by Molodtsov in 1999. It may be applied in a variety of contexts, both theoretical and practical. This paper introduces a new soft set operation called the “soft binary piecewise star operation.” Its basic algebraic characteristics are thoroughly examined. Moreover, this operation’s distributions over various soft set operations are obtained. We prove that the soft binary piecewise star operation is a commutative semigroup under certain conditions and is also a right-left system. Furthermore, we show that the collection of soft sets over the universe, along with the soft binary piecewise star operation and some other types of soft sets, form many important algebraic structures, such as semirings and near-semirings, by considering the algebraic properties of the operation and its distribution rules together.

This paper considers the conventional logistic model and how to obtain the solutions of fractional differential equations. It examines using a hybrid of Sumudu transform method, which is an approximate analytical method for solving fractional differential equations that are associated with time delay. Furthermore, the paper introduces the fractional Caputo-Fabrizio derivative and proportional time delay into the conventional logistic model to propose a general and more logistic model for the population growth. The paper considers different cases of the newly introduced general logistic model and using a hybrid of Sumudu transform method, their solutions were obtained. Using MATLAB, it displays and compares the behaviour of different cases of the general logistic model with fractional Caputo-Fabrizio derivative and proportional time delay.