Exploring the effects of prescribed fire on ticks spread and propagation in a spatial setting

Lyme disease is one of the most prominent tick-borne diseases in the United States and prevalence of the disease has been steadily increasing over the past several decades due to a number of factors, including climate change. Methods for control of the disease have been considered, one of which is prescribed burning. In this paper the effects of prescribed burns on the abundance of ticks present in a spatial domain are assessed. A spatial stage-structured tick-host model with an impulsive differential equation system is developed to simulate the effect that controlled burning has on tick populations. Subsequently, a global sensitivity analysis is performed to evaluate the effect of various model parameters on the prevalence of infectious nymphs. Results indicate that while ticks can recover relatively quickly following a burn, yearly, high-intensity prescribed burns can reduce the prevalence of ticks in and around the area that is burned. The use of prescribed burns in preventing the establishment of ticks into new areas is also explored and it is observed that frequent burning can slow establishment considerably.

Compact Model for Bipolar and Multilevel Resistive Switching in Metal-Oxide Memristors

The article presents the results of the development and study of a combined circuitry (compact) model of thin metal oxide films based memristive elements, which makes it possible to simulate both bipolar switching processes and multilevel tuning of the memristor conductivity taking into account the statistical variability of parameters for both device-to-device and cycle-to-cycle switching. The equivalent circuit of the memristive element and the equation system of the proposed model are considered. The software implementation of the model in the MATLAB has been made. The results of modeling static current-voltage characteristics and transient processes during bipolar switching and multilevel turning of the conductivity of memristive elements are obtained. A good agreement between the simulation results and the measured current-voltage characteristics of memristors based on TiOx films (30 nm) and bilayer TiO2/Al2O3 structures (60 nm/5 nm) is demonstrated.

Optimal Path Analysis for Solving Nonlinear Equations with Finite Local Error

Because the traditional method of solving nonlinear equations takes a long time, an optimal path analysis method for solving nonlinear equations with limited local error is designed. Firstly, according to the finite condition of local error, the optimization objective function of nonlinear equations is established. Secondly, set the constraints of the objective function, solve the optimal solution of the nonlinear equation under the condition of limited local error, and obtain the optimal path of the nonlinear equation system. Finally, experiments show that the optimal path analysis method for solving nonlinear equations with limited local error takes less time than other methods, and can be effectively applied to practice

An Efficient Method for Analytically Solving (1+2)-dimensional Chiral Non-linear Schrödinger Equation

In this paper, we have successfully extracted novel analytic solutions for the (1+2)-dimensional Chiral non-linear Schrödinger (NLS) equation by modified extended tanh expansion method combined with new Riccati solutions (METEM-cNRCS) as far as we know. When a wave transformation is applied to the considered Chiral NLS equation, a nonlinear ODE is obtained. Assuming the solutions of ODE have a form as the method suggests, and substituting the trial solutions to the ODE, we get a polynomial. Gathering the coefficients with the same power in the polynomial, we acquire an algebraic equation system. So, we may obtain the abundant solutions of the (1+2)-dimensional Chiral NLS equation by solving the system via Maple. The plots of some solutions are demonstrated to explain the dynamics of the solutions. It is expected that the results of the paper are a guide for future works in traveling wave theory.

The hunting cooperation of a predator under two prey's competition and fear-effect in the prey-predator fractional-order model

<abstract><p>This paper investigates a fractional-order mathematical model of predator-prey interaction in the ecology considering the fear of the prey, which is generated in addition by competition of two prey species, to the predator that is in cooperation with its species to hunt the preys. At first, we show that the system has non-negative solutions. The existence and uniqueness of the established fractional-order differential equation system were proven using the Lipschitz Criteria. In applying the theory of Routh-Hurwitz Criteria, we determine the stability of the equilibria based on specific conditions. The discretization of the fractional-order system provides us information to show that the system undergoes Neimark-Sacker Bifurcation. In the end, a series of numerical simulations are conducted to verify the theoretical part of the study and authenticate the effect of fear and fractional order on our model's behavior.</p></abstract>

Teaching Materials of Problem-Based Linear Equation System with Two-Variables for Eighth-Grade Students in Junior High School

This research is motivated by the lack of mathematics teaching materials that can make students learn on their own. The teaching material can be created by teachers as they are the ones who possess the knowledge about their students’ characteristics. Further, learning materials are a set of materials (information, tools, or texts) that can aid teachers and students to carry out the learning process. The two-variable linear equation system (SPLDV) is one of the mathematics materials taught to eighth-grade students of junior high school; it contains problems related to daily life. However, it is found that this material is still difficult to master by most students. Therefore, it is necessary to develop the SPLDV teaching materials that can help students learn and solve problems as well as be used as examples by teachers in developing other materials. This research aimed to make problem-based SPLDV teaching materials. The research method refers to the Four-D Model by Thiagarajan, Semmel, and Semmel (1974). It consisted of defining, designing, developing, and disseminating. The results showed that problem-based SPLDV teaching materials could be used in learning activities as the students and the teachers had shown their positive responses after going through expert assessments. This study also suggested that the teachers use this teaching material and adopt teaching materials for other similar materials.

The Parametric Optimization of Voltage Multiplier

The evolutionary model of voltage multiplier parametric optimization which includes 5 diodes and 5 capacitors is reviewed. It executes the transformation of alternating into constant voltage using a five times larger amplitude. The valve work is modelled according to the scheme of an ideal key. The original mathematical model of voltage multiplier which includes additional logical variables is deducted. It aссepts binary meanings 0 and 1, where 0 corresponds to closed valve status and 1 corresponds to open. In order to receive such a model, it is necessary to indicate the amount of open and closed valve combinations. Then for each of them, it is necessary to write the system of differential equations. Comparing them with each other the single differential equation system with additional logical variables is written as a generalization. The evolutional model is used in order to select the capacitor volume meaning. The goal function forecasts two conditions: maximum meaning of output voltage 1 kV and its minimal fluctuations in the stable regime.

Efektivitas Pembelajaran Matematika Berbasis E-Learning Pada Materi Sistem Persamaan Linear Dua Variabel Kelas VIII di MTsN 1 Mataram

The purpose of this study was to determine the effectiveness of e-learning based mathematics learning on the material of the two-variable linear equation system for class VIII at MTsN 1 Mataram. This type of research is a descriptive study using a quantitative approach. The research design used a post-test-only control design. All students of class VIII at MTsN 1 Mataram were the population and the sampling technique used cluster random sampling. The sample used was class VIII-8 and VIII-9 who were a member of one sample group. The data in the study were analyzed using descriptive statistics and paired sample t-test to determine whether or not e-learning based mathematic learning was effective in the material of the two-variable linear equation system. Based on the results of data analysis, it is known that e-learning-based mathematics learning with learning video is effectively applied to the material of the two-variable linear equation system for class VIII students at MTsN 1 Mataram the academic year 2020/2021.

Students’ Intuition in Solving Mathematics Problems: The Case of High Mathematics Ability and Gender Differences

Students are required to find their appropriate strategies to solve mathematics problems so that intuition is needed. Male and female students have different intuition on mathematical problem-solving. Thus, gender is influencing how to obtain mathematical knowledge. This descriptive qualitative study aimed to analize the intuition differences of male and female students who have high-level mathematical abilities at secondary school in solving mathematics problems. Data was collected through tests of mathematical problem-solving and interviews then analysed through data reduction, data presentation, and conclusion. This study found that: (1) There are differences in the characteristics of male and female intuition in mathematical problems solving, (2) The intuition of male and female in mathematical problems solving based on Polya's steps is different in re-checking the answers, (3) There are differences in intuition when students solve linear equation system problems. There are differences in intuition between male and female students with high matematical abilities in each material. Students with problem-solving abilities have affirmative intuition to understand problems, anticipatory intuition for problem-solving plans and solutions, and conclusive intuition to re-examine problems.