On Asymptotics of Optimal Stopping Times

We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward. In this analysis, we obtained asymptotic expressions for the expectation and variance of the optimal stopping time as the number of drawn variables became large. In the case of distributions with infinite upper bound, the asymptotic behaviour of these statistics depends solely on the algebraic power of the probability distribution decay rate in the upper limit. In the case of densities with finite upper bound, the asymptotic behaviour of these statistics depends on the algebraic form of the distribution near the finite upper bound. Explicit calculations are provided for several common probability density functions.

Analisis Kesalahan dalam Menyelesaikan Soal Bentuk Aljabar Ditinjau dari Taksonomi SOLO

The aim of this study is to describe the types of errors and their causes made by the seven grade students of SMPN 7 PUJUT in the academic year 2020/2021 in solving algebraic form questions based on the SOLO taxonomy level. This research is a qualitative descriptive study and the instruments used are test questions and interview guides. The subjects of this study were 32 grade seven students of SMPN 7 PUJUT who were selected using purposive sampling technique. After selecting one class, several students were selected according to the SOLO taxonomy level. The results showed that all students made the types of errors according to the basic objects of mathematics, namely fact errors, concept errors, operating errors, and principle errors. The results also showed that the questions given to 32 class seven students of SMPN 7 PUJUT obtained a percentage of the structural level of 31.25%, the unistructural level of 37.5%, the multistructural level of 21.9%, the relational level of 9.38%, and the extended abstract level is 0%. The causes of students making mistakes in solving questions, namely: the cause of factual errors is that students do not understand the meaning of the questions which include what is known and asked and in determining the final result; the cause of misconceptions is that students do not understand the formula used; the cause of the operation error is that the students are not careful in calculating; and the cause of the principle error is that students do not understand the steps to solve it.

PENGEMBANGAN SOAL TES UNTUK MENGUKUR KEMAMPUAN PEMECAHAN MASALAH SISWA PADA MATERI BENTUK ALJABAR

Problem-solving ability became a learned process as well as a goal that must be achieved in learned mathematics so it is important for students to have these abilities, especially in algebraic form material. But in fact, in the material of algebraic forms, the ability was still minimally mastered by students. Based on the results of the interview, it shows that the lack of ability was due to the questions given by the teacher only in the form of routine questions taken from LKS or textbooks that did not require the use of problem-solving skills but only require the used of procedural formulas. Therefore, it was necessary to develop test questions that contain question items that could measure students' problem-solving abilities in the algebraic form of material. This type of research was developed researched using the ADDIE model which stands for analysis, design, development, implementation, and evaluation. Data collection techniques used in this study were validation questionnaires and tests. Meanwhile, the data collection instruments were validation questionnaire sheets and test sheets. The test subjects in this study were class VII C students of MTs Salafiyah Syafi'iyah Seblak Jombang. The results showed that the product developed in the form of a test was declared valid by the expert with an average validity of 3.75 and was in very valid criteria. Meanwhile, the results of the empirical validity test showed that only four of the five items on the test developed were declared valid and of the four items that were valid, the reliability value of 0.786 with high criteria was obtained. The research findings prove that the developed test contains only four items that were valid both theoretically and empirically and reliably so that they could be used to measure students' problem-solving abilities on the algebraic form of material.

Applications of Haar Wavelet-Finite Difference Hybrid Method and Its Convergence for Hyperbolic Nonlinear Schrödinger Equation with Energy and Mass Conversion

This article is concerned with the numerical solution of nonlinear hyperbolic Schro¨dinger equations (NHSEs) via an efficient Haar wavelet collocation method (HWCM). The time derivative is approximated in the governing equations by the central difference scheme, while the space derivatives are replaced by finite Haar series, which transform it to full algebraic form. The experimental rate of convergence follows the theoretical statements of convergence and the conservation laws of energy and mass are also presented, which strengthens the proposed method to be convergent and conservative. The Haar wavelets based on numerical results for solitary wave shape of |φ| are discussed in detail. The proposed approach provides a fast convergent approximation to the NHSEs. The reliability and efficiency of the method are illustrated by computing the maximum error norm and the experimental rate of convergence for different problems. Comparisons are performed with various existing methods in recent literature and better performance of the proposed method is shown in various tables and figures.

SMIS: A Stepwise Multiple Integration Solver Using a CAS

Multiple Integration is a very important topic in different applications in Engineering and other Sciences. Using numerical software to get an approximation to the solution is a normal procedure. Another approach is working in an algebraic form to obtain an exact solution or to get general solutions depending on different parameters. Computer Algebra Systems (CAS) are needed for this last approach. In this paper, we introduce SMIS, a new stepwise solver for multiple integration developed in a CAS. The two main objectives of SMIS are: (1) to increase the capabilities of CAS to help the user to deal with this topic and (2) to be used in Math Education providing an important tool for helping with the teaching and learning process of this topic. SMIS can provide just the final solution or an optional stepwise solution (even including some theoretical comments). The optional stepwise solutions provided by SMIS are of great help for (2). Although SMIS has been developed in the specific CAS Derive, since the code is provided, it can be easily migrated to any CAS which deals with integrals and text management that allow us to display comments for intermediate steps.

Two-phase modelling for sediment water mixtures above the limit deposit velocity in horizontal pipelines

In dredging applications, deep sea mining and land reclamation projects typically large amounts of sediments are transported through pipes in the form of hyper concentrated (40% sediment or more) sediment-water mixtures or slurries. In this paper it is investigated how well a generic Euler-Euler CFD-model is capable to model velocity, concentration profiles and the pressure gradient of sediment above deposition limit velocity in a pipeline. This Euler-Euler solver treats both phases as a continuum with its own momentum and continuity equations. The full kinetic theory for granular flows is accounted for (no algebraic form is used) and is combined with a buoyant k-ε turbulence model for the fluid phase. The influence of the mesh size has been checked and grid convergence is achieved. All numerical schemes used are of second-order accuracy in space. The pressure gradient was calibrated by adjusting the specularity coefficient in one calibration case and kept constant afterwards. Simulations were carried out in a wide range of slurry flow parameters, in situ volume concentration (9–42%), pipe diameter (0.05–0.90 m), particle diameter (90–440 μm) and flow velocity of (3–7 m/s). The model shows satisfactory agreement to experimental data from existing literature.

Meningkatkan Hasil Belajar Matematika Pokok Bahasan Pengoperasian Bentuk Aljabar Melalui Model Pemberian Tugas

Implementation of this research was conducted in Oktober to Nopember 2020. The purpose of this study is to obtain information about student learning outcomes in the subject matter in the algebra class VIID SMPN 1 Margomulyo after using the method of giving gssignment model. The subject of this research is the students of class VIID SMPN 1 Margomulyo in odd semester of academic year 2020-2021 with the number of students 26 students consisting of 10 men and 16 women. This classroom action research is implemented in 3 cycles consisting of one meetings each. Data collection is done by using learning result test, observation, and student's response. Then the research analyzed qualitatively and quantitatively. From the analysis results of third cycles obtained learners' learning completeness on the subject of Operation Calculate Algebraic Form is increased. This can be seen from the improvement of students' learning mastery that is the result of post test prasiklus value that experienced 15.38% completeness, in cycle 1 to 23.08%, in cycle 2 increased to 33.33%, and in cycle 3 increased to 92.31%.. This it can be concluded that from the third complete test result of learning as much as 92.31% so it can be said that learners learn mastery can be achieved. From the observation of the three cycles also experienced increased learning activities of learners, learners are increasingly more enthusiastic to follow the learning, active cooperative, daring to ask

Efektivitas Model Pembelajaran Kooperatif Tipe Teams Games Tournaments (TGT) Terhadap Hasil Belajar Matematika Siswa Kelas VII SMP Negeri 3 Kempo

This research aims to determine the effectiveness of the Teams Games Tournaments (TGT) cooperative learning model on the learning outcomes of VII grade students SMPN 3 Kempo academic year 2020/2021 on the material algebraic form. The type of research is pre-experimental research with one shot case study design. The research was conducted in 4 meeting for using the TGT cooperative learning and 1 meeting for the implementation of the posttest. The sample is done by purposive sampling technique, the sample was class VII-A as the experimental class which is using the TGT cooperative learning. Data collection using observation and test techniques. Instruments include: observation sheets and learning outcomes tests. The learning outcome data is used to determine how far the students understand the material being taught and the observation data is used to determine the quality of the teaching and learning process which is analyzed descriptively. The research indicator is model TGT cooperative learning, effective if the students’ learning with a classical learning completeness percentage ≥ 85%. Based on the results obtained 16 students who had completed their studies or equal to 88.89% and 2 students who did not complete their studies or 11.11%. The results of observations teacher activities obtained 85% with good criteria, and observations students activities obtained 80% with active criteria. Based on the research results, the cooperative learning model type Teams Games Tournaments (TGT) is effective on the learning students outcomes.

Modal Analysis Problem Solution for a Mathematical Model Formed by the Extended Nodal Method

The article proposes an option for transforming a mathematical model of the object, formed by the extended nodal method in the time-domain solution for modal analysis. Since finding the eigenvalues ​​and eigenvectors for systems of ordinary equations given in the Cauchy normal form is possible, calculations are presented that allow us to obtain a system of equations in the Cauchy normal form from a mathematical model in a differential-algebraic form through linearization. The extended nodal method contains derivatives of state variables in the vector of unknown, and the Jacobi matrix obtained at each Newton iteration of each step of numerical integration can be used to obtain a linearized mathematical model, but the equilibrium equations, as a rule, contain several derivatives with respect to time. By introducing additional variables, it is possible to reduce the linearized mathematical model to the Cauchy normal form, while the Jacobi matrix structure remains essentially unchanged.The proposed solution is implemented in the mathematical core of the PRADIS Gen2 PA-8 software package, which made it possible to expand its functionality by an operator of modal analysis.The presented calculations of test schemes have shown the correctness of the method proposed.

Thermally fully developed CNTs suspended nano fluid flow through annular sector duct

Here we simulate hydrodynamically and thermally fully developed carbon nano tubes, ( CNTs) suspended nano fluid flow through annular sector duct. Hydrodynamic results are found by using no slip boundary condition on the solid walls of duct; whereas H1 and T thermally fully developed conditions are accounted to evaluate the thermal results. CNTs are considered to be single wall, ( SW)/multi walls, ( MW). Power-law discretized scheme is used to transform the non-linear cross sectional convection-diffusion terms in algebraic form by using the control volume based method. With the help semi-implicit method for pressure-linked equations-revised, ( SIMPLER), a system of discretized algebraic equations is solved. Forced convective flow is carried out for different annular configuration parameters and contribution of CNTs in base fluid (i.e. pure water) at Pr = 6.2. Limiting case friction factor and heat transfer results show good agreement with already published data.