scholarly journals Quantitative ergodicity for the symmetric exclusion process with stationary initial data

2021 ◽  
Vol 26 (none) ◽  
Author(s):  
Lorenzo Bertini ◽  
Nicoletta Cancrini ◽  
Gustavo Posta
Keyword(s):  
Initial Data ◽  
Exclusion Process

scholarly journals Dynamic ASEP, Duality, and Continuous q−1-Hermite Polynomials

2018 ◽  
Vol 2020 (3) ◽  
pp. 641-668 ◽  
Author(s):  
Alexei Borodin ◽  
Ivan Corwin
Keyword(s):  
Initial Data ◽  
Moment Problem ◽  
Hermite Polynomials ◽  
Exclusion Process ◽  
Asymmetric Simple Exclusion Process ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion

Abstract We demonstrate a Markov duality between the dynamic asymmetric simple exclusion process (ASEP) and the standard ASEP. We then apply this to step initial data, as well as a half-stationary initial data (which we introduce). While investigating the duality for half-stationary initial data, we uncover and utilize connections to the continuous q−1-Hermite polynomials. Finally, we introduce a family of stationary initial data which are related to the indeterminate moment problem associated with these q−1-Hermite polynomials.

scholarly journals THE KARDAR–PARISI–ZHANG EQUATION AND UNIVERSALITY CLASS

2012 ◽  
Vol 01 (01) ◽  
pp. 1130001 ◽  
Author(s):  
IVAN CORWIN
Keyword(s):  
Initial Data ◽  
Random Media ◽  
Interacting Particle Systems ◽  
Exclusion Process ◽  
Universality Class ◽  
Distribution Functions ◽  
Great Success ◽  
Kpz Equation ◽  
Point Distribution ◽  
The Kpz Equation

Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its universality class. Over the past 25 years a new universality class has emerged to describe a host of important physical and probabilistic models (including one-dimensional interface growth processes, interacting particle systems and polymers in random environments) which display characteristic, though unusual, scalings and new statistics. This class is called the Kardar–Parisi–Zhang (KPZ) universality class and underlying it is, again, a continuum object — a non-linear stochastic partial differential equation — known as the KPZ equation. The purpose of this survey is to explain the context for, as well as the content of a number of mathematical breakthroughs which have culminated in the derivation of the exact formula for the distribution function of the KPZ equation started with narrow wedge initial data. In particular we emphasize three topics: (1) The approximation of the KPZ equation through the weakly asymmetric simple exclusion process; (2) The derivation of the exact one-point distribution of the solution to the KPZ equation with narrow wedge initial data; (3) Connections with directed polymers in random media. As the purpose of this article is to survey and review, we make precise statements but provide only heuristic arguments with indications of the technical complexities necessary to make such arguments mathematically rigorous.

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

ON THE EXPERT’S RIGHT TO BE PRESENT AT LEGAL PROCEEDINGS

2016 ◽  
Vol 15 ◽  
pp. 163-171
Author(s):  
M. G. Shcherbakovskiy
Keyword(s):  
Initial Data ◽  
Legal Proceedings ◽  
Reliable Assessment ◽  
Data Acquiring ◽  
Selection Of

The article discusses the reasonsfor an expert to participate in legal proceedings. The gnoseological reason for that consists of the bad quality of materials subject to examination that renders the examination either completely impossible or compromises objective, reasoned and reliable assessment of the findings. The procedural reason consists ofa proscription for an expert to collect evidence himself or herself. The author investigates into the ways of how an expert can participate in legal proceedings. If the defense invites an expert to participate in the proceedings, then it is recommended that his or her involvement should be in the presence of attesting witnesses and recorded in the protocol. In the course of the legal proceedings an expert has the following tasks: adding initial data, acquiring new initial data, understanding the situation of the incident, acquiring new objects to be studied, including samples for examination. An expert’s participation in legal proceedings differs from the participation of a specialist or an examination on the scene of the incident. The author describes the tasks that an expert solves in the course of legal proceedings, the peculiarities ofan investigation experiment practices, the selection of samples for an examination, inspection, interrogation.

UPAYA MENINGKATKAN KEMAMPUAN MEMBACA MELALUI METODE SCRAMBLE PADA PESERTA DIDIK KELAS I SD NEGERI 002 BENTENG KECAMATAN SUNGAI BATANG

2017 ◽  
Vol 6 (2) ◽  
pp. 409
Author(s):  
Reni Marlina
Keyword(s):  
Cooperative Learning ◽  
Initial Data ◽  
Learning Outcomes ◽  
Reading Ability ◽  
First Grade ◽  
Student Learning Outcomes ◽  
Female Students ◽  
Male Students ◽  
Average Analysis ◽  
Before And After

This study aims to improve students' reading ability through the first grade scramble students of SD Negeri 002 Benteng, Kecamatan Sungai Batang, which are 28 students with 11 male students and 17 female students with heterogeneous ability. This study is based on the low ability of students' learning outcomes and lack of awareness of teachers to implement an effective, innovative, and cooperative learning. The study was conducted from September 3, 2016 to October 8, 2016. This study is a classroom action research (PTK) consisting of two cycles. Minimum completeness criteria (KKM) and average analysis are used to determine whether or not improvement of student learning outcomes before and after using the scramble learning model. The results of this study indicate that the number of students who reach KKM in the initial data is only 10 people (36%), cycle I is 16 people (57%), and the second cycle is 25 people (89%). The average student score at baseline was 68.4; cycle I increased to 75,9; in the second cycle increased again to 83,6. Based on the results of this study it can be concluded that the model of learning scramble can improve reading ability in Indonesian language students class I of SD Negeri 002 Benteng, Kecamatan Sungai Batang.

PENERAPAN METODE DISKUSI UNTUK MENINGKATKAN HASIL BELAJAR IPS SISWA KELAS VA SD NEGERI 004 TEMBILAHAN KECAMTAN TEMBILAHAN KABUPATEN INDRAGIRI HILIR

2017 ◽  
Vol 6 (1) ◽  
pp. 296
Author(s):  
Rosmida Rosmida
Keyword(s):  
Action Research ◽  
Social Studies ◽  
Initial Data ◽  
Learning Outcomes ◽  
Mastery Learning ◽  
Class V ◽  
Average Value ◽  
Class Average ◽  
Classroom Action Research

The background of this study is the lack of IPS students' learning outcomes, from 22 students only 36.36% or 8 students who managed to achieve a minimum completeness criteria (KKM) established school with a class average value of 61.75. Based on this the researchers conducted a classroom action research with the aim to improve learning outcomes IPS students through the application of methods of discussion. This research is a class act, who performed a total of two cycles consisting of two meetings, the data of this study focuses on the data increase learning outcomes and increase student mastery learning outcomes IPS. The study states that the results of social studies students has increased in each cycle, the initial data is the number of students who completed 8 students (36.36%) with an average of learning outcomes at 61.75. In the first cycle has increased the number of students who completed up to 16 students (72.73%) with an average of learning outcomes at 73.90, and the second cycle the number of students who pass the increase to 22 students (100.00%) with a mean -rata learning outcomes at 87.75. Based on these results it can be concluded that the application of the method of discussion to improve learning outcomes IPS students of class V A SD Negeri 004 Tembilahan Kecamatan Tembilahan.

UPAYA MENINGKATKAN AKTIVITAS DAN HASIL BELAJAR MAHASISWA MELALUI PENERAPAN MODEL PEMBELAJARAN INKUIRI PADA MATA KULIAH KONSEP DASAR IPA 2 DI PROGRAM STUDI PENDIDIKAN GURU SEKOLAH DASAR TAHUN AKADEMIK 2013/2014

2014 ◽  
Vol 3 (1) ◽  
pp. 23
Author(s):  
Mahmud Alpusari
Keyword(s):  
Initial Data ◽  
Learning Outcomes ◽  
Inquiry Learning ◽  
Learning Activities ◽  
Simple Experiment ◽  
Competency Based ◽  
Basic Concepts ◽  
Using Data ◽  
The University ◽  
Daily Test

In line with the competency-based curriculum at the University of Riau, the effort to improvelearning basic concepts of science 2 courses puts emphasis on understanding the concept ofmatter, which is based on students' learning activities through scientific inquiry.Implementation of action research consists of two cycles in PGSD JIP University of Riau onthe odd semester of 2013/2014 with 55 third semester students. Based on the research results,lecturing process by applying the model of inquiry learning, students’ activity increased inwhich in the first cycle all activities are good category except activity I and II are faircategory. Meanwhile students’ activity in first and fourth in cycle II is good category, andvery good category in second, third, fifth, and sixth activity. Temporarily student’s learningoutcomes increased from pre-tests with an average65.45 into 77,0 in daily test I and 77.45onthe daily test II. Improvement from initial data to the first cycle was 11.55, while the datafrom the beginning to the second cycle increased 12 points. In general the improvement ofstudents’learning is possible because the learning model used is inquiry learning so thatlearning becomes active which centered into students by presenting a problem, then studentsare asked to carry out a simple experiment using equipment and tools, using data, arrangingreports, communicating the results of observations based on concepts and learned principles.Keywords: Inquiry, students’ activity, learning outcomes.

PENERAPAN METODE STORY READING UNTUK MENINGKATKAN KEMAMPUAN BERBICARA ANAK USIA 5 - 6 TAHUN DI TK MELATI / ABA 005 PULAU BALAI

2015 ◽  
Vol 4 (2) ◽  
pp. 143
Author(s):  
Hasnidar '
Keyword(s):  
Data Collection ◽  
Initial Data ◽  
Research Data ◽  
Class Action ◽  
Percentage Increase ◽  
Story Reading ◽  
Reading Methods ◽  
Number Of Children ◽  
Class Actions ◽  
Speaking Skills

This study aims to improve speaking skills of children aged 5-6 through methods Story Reading in TK Melati/ ABA 005 Pulau Balai. The method used is a Class Action Research. Class actions that researchers do the research is to use the method Story Reading to improve speaking skills of children aged 5-6 years in TK Melati TK Melati/ ABA 005 Pulau Balai, and is observed by the observer. Samples taken are TK Melati/ ABA 005 Pulau Balai with the number of children of 20 people, consisting of 13 men and 7 women. Data collection techniques in this research is through observation of teachers and children as well as data capability speaking children aged 5-6 years with use of methods Story Reading. Hipotesis in this study is if the method will be applicable Story Reading can improve speaking skills of children aged 5-6 years in TK Melati/ ABA Pulau Balai 005 can be enhanced through storytelling. Results of the research data obtained by using the method Story Reading can improve the ability to speak of children aged 5-6 years in TK Melati / ABA 005 Pulau Balai. The percentage increase in the ability to speak the child at the age of 5-6 years using Story Reading methods in TK Melati/ ABA 005 Pulau Balai, from initial data to the second cycle increased by 32.2%. The implication of this study is the use of methods Story Reading used properly, can improve speaking skills of children aged 5-6 years in TK Melati/ ABA 005 Pulau BalaiKeywords: story reading, speech

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