scholarly journals Bessenrodt-Stanley Polynomials and the Octahedron Recurrence

10.37236/4434 ◽  
2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Philippe Di Francesco
Keyword(s):  
Initial Data ◽  
Partition Functions ◽  
Multivariate Polynomials ◽  
Suitable Initial Data ◽  
Octahedron Recurrence ◽  
Explicit Expressions

We show that a family of multivariate polynomials recently introduced by Bessenrodt and Stanley can be expressed as solution of the octahedron recurrence with suitable initial data. This leads to generalizations and explicit expressions as path or dimer partition functions.

scholarly journals Solutions to the T-Systems with Principal Coefficients

10.37236/5698 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Panupong Vichitkunakorn
Keyword(s):  
Recurrence Relation ◽  
Cluster Algebra ◽  
Perfect Matchings ◽  
Partition Functions ◽  
Initial Condition ◽  
Free Cluster ◽  
Octahedron Recurrence ◽  
T System

The $A_\infty$ T-system, also called the octahedron recurrence, is a dynamical recurrence relation. It can be realized as mutation in a coefficient-free cluster algebra (Kedem 2008, Di Francesco and Kedem 2009). We define T-systems with principal coefficients from cluster algebra aspect, and give combinatorial solutions with respect to any valid initial condition in terms of partition functions of perfect matchings, non-intersecting paths and networks. This also provides a solution to other systems with various choices of coefficients on T-systems including Speyer's octahedron recurrence (Speyer 2007), generalized lambda-determinants (Di Francesco 2013) and (higher) pentagram maps (Schwartz 1992, Ovsienko et al. 2010, Glick 2011, Gekhtman et al. 2016).

scholarly journals On a Fractional in Time Nonlinear Schrödinger Equation with Dispersion Parameter and Absorption Coefficient

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1197 ◽  
Author(s):  
Mohamed Jleli ◽  
Bessem Samet ◽  
Calogero Vetro
Keyword(s):  
Initial Data ◽  
Global Solutions ◽  
Combined Effects ◽  
Nonlinear Capacity ◽  
Nonlinear Schrödinger ◽  
Special Cases ◽  
Dispersion Terms ◽  
Absorption And Dispersion ◽  
Suitable Initial Data ◽  
Capacity Method

This paper is concerned with the nonexistence of global solutions to fractional in time nonlinear Schrödinger equations of the form i α ∂ t α ω ( t , z ) + a 1 ( t ) Δ ω ( t , z ) + i α a 2 ( t ) ω ( t , z ) = ξ | ω ( t , z ) | p , ( t , z ) ∈ ( 0 , ∞ ) × R N , where N ≥ 1 , ξ ∈ C \ { 0 } and p > 1 , under suitable initial data. To establish our nonexistence theorem, we adopt the Pohozaev nonlinear capacity method, and consider the combined effects of absorption and dispersion terms. Further, we discuss in details some special cases of coefficient functions a 1 , a 2 ∈ L l o c 1 ( [ 0 , ∞ ) , R ) , and provide two illustrative examples.

scholarly journals Quantum $A_r$ $Q$-System Solutions as q-Multinomial Series

10.37236/663 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Philippe Di Francesco
Keyword(s):  
Data Structure ◽  
Initial Data ◽  
Fundamental Solutions ◽  
Generating Series ◽  
Multinomial Coefficients ◽  
Q System ◽  
Explicit Expressions

We derive explicit expressions for the generating series of the fundamental solutions of the $A_r$ quantum $Q$-system of Di Francesco and Kedem [ Non-commutative integrability, paths and quasi-determinants, Adv. in Math. 228(1) (2011) 97–152], expressed in terms of any admissible initial data. These involve products of quantum multinomial coefficients, coded by the initial data structure.

scholarly journals A UNIFIED SCHEME FOR MODULAR INVARIANT PARTITION FUNCTIONS OF WZW MODELS

1994 ◽  
Vol 09 (16) ◽  
pp. 2707-2739 ◽  
Author(s):  
M.R. ABOLHASSANI ◽  
F. ARDALAN
Keyword(s):  
Discrete Group ◽  
Partition Functions ◽  
Modular Invariant ◽  
Group Manifold ◽  
Arbitrary Level ◽  
Unified Method ◽  
Explicit Expressions

We introduce a unified method which can be applied to any WZW model at arbitrary level to search systematically for modular invariant physical partition functions. Our method is based essentially on modding out a known theory on group manifold G by a discrete group Γ. We apply our method to [Formula: see text] with n=2, 3, 4, 5, 6, and to [Formula: see text] models, and obtain all the known partition functions and some new ones, and give explicit expressions for all of them.

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.

Myocarditis in Paediatric Patients: Age and Gender Are Influencing Incidence, Severity, and Clinical Course: Initial Data Analysis from the German Multi-Centre Registry (“MYKKE”)

2016 ◽  
Vol 64 (S 02) ◽  
Author(s):  
S. Schubert ◽  
B. Opgen-Rhein ◽  
G. Haverkämper ◽  
E. zu Knyphausen ◽  
A. Weise ◽  
...  
Keyword(s):  
Data Analysis ◽  
Initial Data ◽  
Clinical Course ◽  
Age And Gender ◽  
Paediatric Patients ◽  
And Gender

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.

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