JOURNAL OF ADVANCES IN MATHEMATICS

Exponential Fit to Food Degradation Experiment

T.X. Truedell — 2023-10-01

Students in the Principles of Biology I course use a lot of course time preparing solutions each week in their course
based research experience. This experiment was designed to determine the degradation rates of prepared solutions of
various plant-based foods (i.e., Napa cabbage, rice, peanuts, and apple) under refrigeration as a means of reducing the
amount of time for solution preparation. Scaling from the original lab procedures, approximately sixty milliliters of
filtrate were prepared from the listed foods and testing was conducted on a thrice-weekly schedule. The concentration
of proteins and carbohydrates were measured using the Bradford’s assay and Benedict’s test, respectively. The data
revealed a noticeable trend in degradation in protein for all the samples. The rice sample proved to be an outlier with
a marked increase in reducing sugars, while the other samples gradually decreased.

Research and Application of Digital Classroom Teaching Development in the Post-Pandemic Era

Tongxing Li — 2023-09-25

With the continuous development of information technology, digital classrooms are becoming more adapted to the demands of talent cultivation in the modern era. The digital classroom teaching model is a reform of traditional teaching methods, and constructing a digital classroom allows for more flexible organization of instructional design, fostering students' creative thinking and enhancing their overall qualities. Seizing the opportunity for the development of applied universities, our school is constructing a locally distinctive path of information technology. This article takes higher mathematics as an example to elaborate on the practical application experience of digital classroom teaching development. In conclusion, this article summarizes the shortcomings in the process of digital classroom construction, which holds certain reference value and significance for future work.

THE FEKETE -SZEGO ̈ PROBLEM OF ANALYTIC FUNCTIONS BASED ON THE DEFERENtIAL OPERTOR AND CERTAIN SUBCLASSES

LY VAN AN — 2023-08-17

In this paper I use the operators D^m_β,η(η, φ)f, S_m(d, β, η) and C_m(d, β, η).To establish |a₃−μa²₂ | -functional inequalities for the Fekete-Szeg ̈o problem. That’s my main result.

Oscillatory Behavior of Higher Order Nonlinear Mixed Type Difference Equations With a Nonlinear Neutral Term

Ali Çakır — 2023-07-27

This paper discusses higher order nonlinear neutral mixed type difference equations of the form

Δ^{m}[x(n)+p(n)h(x(σ(n)))]+q(n)f(x(τ(n)))=0, n=0,1,2,…,

where (p(n)), (q(n)) are sequences of nonnegative real numbers, h, f:R→R are continuous and nondecreasing with uh(u)>0, uf(u)>0 for all u≠0, and (σ(n)) and (τ(n)) are sequences of integers such that

lim_{n→∞}τ(n)=lim_{n→∞}σ(n)=∞.

In general, we will examine the oscillatory behavior of the solutions for the above equation. Especially, when m is even, the result obtained here complements studies related to the oscillation of the above equation. In addition, examples showing the accuracy of the results are given.

Some Statistical Approximation based on Post-Widder operators

prerna Sharma — 2023-06-26

In the present paper, we study the convergence of real and modified Post-Widder operators in C, which is known as the extension of approximation of these operators from the real axis in the complex plane. In this direction, we also investigate error estimation in simultaneous approximation and a Voronovskaya-type asymptotic formula.

Quasi Triple Operator on Hilbert Space

Dr.Alaa Hussein Mohammed — 2023-03-06

In this pepar we given a newclass of operators onHilbert space calledquasi triple operatorand -Quasi Triple Operator . We study the operator and introdus some properties ofit

Applications of the ideals in the measure theory and integration

Doris DODA — 2023-02-28

In this paper, we will represent some applications to various problems of mass theory and integration, by using the concept of local convergences and exhaustive sequences. We will continue the idea of point-wise I -convergence, Ideal exhaustiveness that was introduced by Komisarski [3], and Kostyrko, Sal´at and Wilczy´nski [4]. The equi-integrable introduced in Bohner-type ideal integrals and a new study on the application of symmetric differences have been presented in the theory of mass and continuous functions, continuing the results of Boccuto, Das, Dimitriou, Papanastassiou [2].

Use of Mixed Operator Method to a fractional Hadamard Dirichlet boundary value problem

Lakhdar Ragoub — 2023-02-08

The purpose of this paper is to deal with the following nonlinear Hadamard fractional boundary value problem

^HD^α₁+ u(t) + f(t, u(t), u(t)) + g(t, u(t)) = 0,
1 < t < e, 1 < α ≤ 2,
u(1) = u(e) = 0,

where ^HD^α ₁+ is the Hadamard fractional derivative operator. Using the mixed monotone operator method, we prove an existence and uniqueness result for this mixed fractional Hadamard boundary value problem. As an application of this result, we give one example to establish an existence and uniqueness of a positive solution.