Non-linear creep of polypropylene utilizing multiple integral

<p>Multiple integral representation (MIR) has been used to represent studying the effect of temperature on the amount of nonlinear creep on the semi- crystalline polypropylene (PP) under the influence of axial elastic stress. To complete this research, the Kernel functions were selected, for the purpose of performing an analogy, and for arranging the conditions for the occurrence of the first, second and third expansion in a temperature range between 20 °C-60 °C, i.e., between the glass transition and softening temperatures, within the framework of the energy law. It was observed that the independent strain time increased non-linearly with increasing stress, and non-linearly decreased with increase in temperature, although the time parameter increased non-linearly with stress and temperature directly. In general, a very satisfactory agreement between theoretical and practical results on the MIR material was observed.</p>

Students' Perceptions of Mathematical Physics E-Module on Multiple Integral Material

Mathematical physics is often considered a very difficult subject to study, one of the reasons that makes this happen is the lack of learning media that supports students. In addition, most of the existing media are in foreign languages, so in this case we need an Indonesian language learning media, namely the mathematical physics e-module on dual integral material. This study aims to see the level of students' perceptions of the mathematics physics e-module on the dual integral material that has been made. The approach of this study uses a mixed method with an explanatory model. The sampling technique in this research was purposive sampling with 68 research subjects active physics education students who contracted Mathematics Physics courses. The instrument used in this study was a student perception questionnaire with 15 questions and an interview sheet with 10 questions.. The data analysis used in this research is descriptive statistics. The results of physics education students' perceptions of the mathematics physics e-module of multiple internal material were categorized as good with a percentage of 66.17% and in the very good category with a percentage of 33.83%. From the results it can be seen that the mathematical physics e-module on dual integral material can support the learning process and increase student motivation.

Investigating Student Perceptions Based on Gender Differences Using E-Module Mathematics Physics in Multiple Integral Material

Mathematics physics is a difficult learning and becomes a scourge in studies in physics education. Learning physics and mathematics itself will be very effective when using e-modules, but in terms of making e-modules, students' opinions or perceptions are needed regarding this matter. This study aims to look at student perceptions and also compare these perceptions with other classes based on gender or gender. The research conducted is a survey type quantitative research. The sampling technique used in this study was simple random sampling with the research subject as many as 92 physics education students who contracted the mathematics physics course. The instrument used in collecting data is 15 questions containing 4 choices that must be filled out by students. Analysis of the data used in this study in the form of descriptive analysis and ANOVA test to determine whether there is an average difference in each student's perception. The results obtained indicate that girls have different perceptions in class A and class B, while for boys there is a difference between class A and class C. These results indicate that girls have a fairly large average difference in perception with each other, while for boys the perception tends to be uniform compared to girls.

On Well-Posedness of Some Constrained Variational Problems

By considering the new forms of the notions of lower semicontinuity, pseudomonotonicity, hemicontinuity and monotonicity of the considered scalar multiple integral functional, in this paper we study the well-posedness of a new class of variational problems with variational inequality constraints. More specifically, by defining the set of approximating solutions for the class of variational problems under study, we establish several results on well-posedness.

Well Posedness of New Optimization Problems with Variational Inequality Constraints

In this paper, we studied the well posedness for a new class of optimization problems with variational inequality constraints involving second-order partial derivatives. More precisely, by using the notions of lower semicontinuity, pseudomonotonicity, hemicontinuity and monotonicity for a multiple integral functional, and by introducing the set of approximating solutions for the considered class of constrained optimization problems, we established some characterization results on well posedness. Furthermore, to illustrate the theoretical developments included in this paper, we present some examples.

Synchronization Analysis of Multiple Integral Inequalities Driven by Steklov Operator

We construct a subclass of Copson’s integral inequality in this article. In order to achieve this goal, we attempt to use the Steklov operator for generalizing different inequalities of the Copson type relevant to the situations ρ>1 as well as ρ<1. We demonstrate the inequalities with the guidance of basic comparison, Holder’s inequality, and the integration by parts approach. Moreover, some new variations of Hardy’s integral inequality are also presented with the utilization of Steklov operator. We also formulate many remarks and two examples to show the novelty and authenticity of our results.

Second-Order PDE Constrained Controlled Optimization Problems with Application in Mechanics

The present paper deals with a class of second-order PDE constrained controlled optimization problems with application in Lagrange–Hamilton dynamics. Concretely, we formulate and prove necessary conditions of optimality for the considered class of control problems driven by multiple integral cost functionals involving second-order partial derivatives. Moreover, an illustrative example is provided to highlight the effectiveness of the results derived in the paper. In the final part of the paper, we present an algorithm to summarize the steps for solving a control problem such as the one investigated here.

On a Class of Second-Order PDE&PDI Constrained Robust Modified Optimization Problems

In this paper, by using scalar multiple integral cost functionals and the notion of convexity associated with a multiple integral functional driven by an uncertain multi-time controlled second-order Lagrangian, we develop a new mathematical framework on multi-dimensional scalar variational control problems with mixed constraints implying second-order partial differential equations (PDEs) and inequations (PDIs). Concretely, we introduce and investigate an auxiliary (modified) variational control problem, which is much easier to study, and provide some equivalence results by using the notion of a normal weak robust optimal solution.

A Conservative and Implicit Second-Order Nonlinear Numerical Scheme for the Rosenau-KdV Equation

In this paper, for solving the nonlinear Rosenau-KdV equation, a conservative implicit two-level nonlinear scheme is proposed by a new numerical method named the multiple integral finite volume method. According to the order of the original differential equation’s highest derivative, we can confirm the number of integration steps, which is just called multiple integration. By multiple integration, a partial differential equation can be converted into a pure integral equation. This is very important because we can effectively avoid the large errors caused by directly approximating the derivative of the original differential equation using the finite difference method. We use the multiple integral finite volume method in the spatial direction and use finite difference in the time direction to construct the numerical scheme. The precision of this scheme is O(τ2+h3). In addition, we verify that the scheme possesses the conservative property on the original equation. The solvability, uniqueness, convergence, and unconditional stability of this scheme are also demonstrated. The numerical results show that this method can obtain highly accurate solutions. Further, the tendency of the numerical results is consistent with the tendency of the analytical results. This shows that the discrete scheme is effective.