Screw dislocation pileups in a two-phase thin film

The method of continuously distributed dislocations is used to study the distribution of screw dislocations in a linear array piled up near the interface of a two-phase isotropic elastic thin film with equal thickness in each phase. The resulting singular integral equation is solved numerically using the Gauss–Chebyshev integration formula to arrive at the dislocation distribution function and the number of dislocations in the pileup.

An approximation of one-dimensional nonlinear Kortweg de Vries equation of order nine

This research presents the approximate solution of nonlinear Korteweg-de Vries equation of order nine by a hybrid staggered one-dimensional Haar wavelet collocation method. In literature, the underlying equation is derived by generalizing the bilinear form of the standard nonlinear KdV equation. The highest order derivative is approximated by Haar series, whereas the lower order derivatives are attained by integration formula introduced by Chen and Hsiao in 1997. The findings are shown in the form of tables and a figure, demonstrating the proposed technique’s convergence, robustness, and ease of application in a small number of collocation points.

How to Integrate STEM Education in The Indonesian Curriculum? A Systematic Review

STEM education has received a lot of attention, including in Indonesia, because it is considered capable of preparing competitive students in the 21st century. However, the implementation of STEM learning is constrained because there are no standard guidelines according to the curriculum 2013 (education curriculum in Indonesia). Therefore, the aim of this study is to find an integration formula for STEM learning and the curriculum 2013 based on the synthesis of various literature to find a formula for implementing STEM learning in accordance with the curriculum 2013. This study is a systematic review. The data sources in this research are 46 selected literatures and relevant to the research objectives published between 1996 and 2020. The data sources are literature published in ISBN books, government documents, and journals. The data collected from the literature were analyzed with a thematic model starting with data introduction, initial coding, compiling code within a theme, analyzing themes, naming themes, and relating findings to research questions. The research resulted in a learning step that combines EDP in STEM, the scientific approach in the 2013 curriculum, and project learning steps. The merger produces a guideline for implementing STEM learning in the 2013 curriculum starting from problem identification, making problem-solving designs, design realization, testing and studying product deficiencies, improving products, drawing conclusions, and communicating the findings of the learning process.

On Functional Hamilton–Jacobi and Schrödinger Equations and Functional Renormalization Group

We consider the functional Hamilton–Jacobi (HJ) equation, which is the central equation of the holographic renormalization group (HRG), functional Schrödinger equation, and generalized Wilson–Polchinski (WP) equation, which is the central equation of the functional renormalization group (FRG). These equations are formulated in D-dimensional coordinate and abstract (formal) spaces. Instead of extra coordinates or an FRG scale, a “holographic” scalar field Λ is introduced. The extra coordinate (or scale) is obtained as the amplitude of delta-field or constant-field configurations of Λ. For all the functional equations above a rigorous derivation of corresponding integro-differential equation hierarchies for Green functions (GFs) as well as the integration formula for functionals are given. An advantage of the HJ hierarchy compared to Schrödinger or WP hierarchies is that the HJ hierarchy splits into independent equations. Using the integration formula, the functional (arbitrary configuration of Λ) solution for the translation-invariant two-particle GF is obtained. For the delta-field and the constant-field configurations of Λ, this solution is studied in detail. A separable solution for a two-particle GF is briefly discussed. Then, rigorous derivation of the quantum HJ and the continuity functional equations from the functional Schrödinger equation as well as the semiclassical approximation are given. An iterative procedure for solving the functional Schrödinger equation is suggested. Translation-invariant solutions for various GFs (both hierarchies) on delta-field configuration of Λ are obtained. In context of the continuity equation and open quantum field systems, an optical potential is briefly discussed. The mode coarse-graining growth functional for the WP action (WP functional) is analyzed. Based on this analysis, an approximation scheme is proposed for the generalized WP equation. With an optimized (Litim) regulator translation-invariant solutions for two-particle and four-particle amputated GFs from approximated WP hierarchy are found analytically. For Λ=0 these solutions are monotonic in each of the momentum variables.

Meet Andréief, Bordeaux 1886, and Andreev, Kharkov 1882–1883

The paper “Note sur une relation entre les intégrales définies des produits des fonctions” by C. Andréief is an often cited paper in random matrix theory, due to it containing what is now referred to as Andréief’s integration formula. Nearly all citing works state the publication year as 1883. However, the journal containing the paper, Mémories de la Societé des Sciences physiques et naturelles de Bordeaux, issue 3 volume 2 actually appeared in 1886. In addition to clarifying this point, some historical information relating to C. Andréief (better known as K. A. Andreev) and the lead up to this work is given, as is a review of some of the context of Andréief’s integration formula.