Educational chat on the website of the teacher

The article discusses the practice of using the original training chat on the web site of the teacher. Set out different ways of registration of students in the chat, especially the communication with the teacher and chat options when you use in the educational process for consultations, discussions and on-line knowledge testВ статье рассматривается практика использования оригинального учебного чата на web-сайте преподавателя. Изложены различные способы регистрации студентов в чате, особенности общения с преподавателем и возможности чата при использовании в учебном процессе для консультаций, обсуждений и on-line проверки знани

The student module of the educational portal

In the article the results of long operation of the educational web-portal of PFUR the basic factors that determine the learning ability of students when using for the transfer of knowledge of modern information technologies. Student discusses a specific designed module educational portal of PFUR, which greatly improves the efficiency of remote work with the studentsВ статье по результатам длительной эксплуатации учебного web-портала РУДН изложены основные факторы, которые определяют обучаемость студентов при использовании для передачи знаний современных информационных технологий. Рассматривается конкретный разработанный студенческий модуль учебного портала РУДН, который значительно повышает эффективность удаленной работы со студентам

A possible combinatorial point for XYZ-spin chain

We formulate and discuss a number of conjectures on the ground state vectors of the XYZ-spin chains of odd length with periodic boundary conditions and a special choice of the Hamiltonian parameters. In particular, arguments for the validity of a sum rule for the components, which describes in a sense the degree of antiferromagneticity of the chain, are given.Comment: AMSLaTeX, 15 page

The Wave Functions for the Free-Fermion Part of the Spectrum of the SUq(N)SU_q(N) Quantum Spin Models

We conjecture that the free-fermion part of the eigenspectrum observed recently for the $SU_q(N)$ Perk-Schultz spin chain Hamiltonian in a finite lattice with $q=\exp (i\pi (N-1)/N)$ is a consequence of the existence of a special simple eigenvalue for the transfer matrix of the auxiliary inhomogeneous $SU_q(N-1)$ vertex model which appears in the nested Bethe ansatz approach. We prove that this conjecture is valid for the case of the SU(3) spin chain with periodic boundary condition. In this case we obtain a formula for the components of the eigenvector of the auxiliary inhomogeneous 6-vertex model ($q=\exp (2 i \pi/3)$), which permit us to find one by one all components of this eigenvector and consequently to find the eigenvectors of the free-fermion part of the eigenspectrum of the SU(3) spin chain. Similarly as in the known case of the $SU_q(2)$ case at $q=\exp(i2\pi/3)$ our numerical and analytical studies induce some conjectures for special rates of correlation functions.Comment: 25 pages and no figure

Spin chains and combinatorics: twisted boundary conditions

The finite XXZ Heisenberg spin chain with twisted boundary conditions was considered. For the case of even number of sites $N$, anisotropy parameter -1/2 and twisting angle $2 \pi /3$ the Hamiltonian of the system possesses an eigenvalue $-3N/2$. The explicit form of the corresponding eigenvector was found for $N \le 12$. Conjecturing that this vector is the ground state of the system we made and verified several conjectures related to the norm of the ground state vector, its component with maximal absolute value and some correlation functions, which have combinatorial nature. In particular, the squared norm of the ground state vector is probably coincides with the number of half-turn symmetric alternating sign $N \times N$ matrices.Comment: LaTeX file, 7 page

Bethe roots and refined enumeration of alternating-sign matrices

The properties of the most probable ground state candidate for the XXZ spin chain with the anisotropy parameter equal to -1/2 and an odd number of sites is considered. Some linear combinations of the components of the considered state, divided by the maximal component, coincide with the elementary symmetric polynomials in the corresponding Bethe roots. It is proved that those polynomials are equal to the numbers providing the refined enumeration of the alternating-sign matrices of order M+1 divided by the total number of the alternating-sign matrices of order M, for the chain of length 2M+1.Comment: LaTeX 2e, 12 pages, minor corrections, references adde

Original Learning Platform «Quick-Study»

В статье дается описание оригинальной учебной веб-платформы, которая может использоваться в различных режимах обучения: автоматизированный - без прямого контакта преподавателя со слушателями; гибридный - для проведения дистанционного обучения при On-Line общении преподавателя со слушателями с помощью встроенной системы проведения видеоконференций;аудиторный, который обеспечивает демонстрацию учебного материала лекции или семинара в аудитории (через проектор или на компьютерах слушателей), а также заданий на семинаре и самостоятельную работу слушателей дома.The article describes the original educational web platform, that can be used in various learning modes:automated - without direct contact between the teacher and the students;hybrid - for conducting distance learning with On-Line communication between the teacher and students using the built-in videoconferencing system;classroom - which provides a demonstration of the educational material of a lecture or seminar in the audience (through a projector or on students' computers), as well as assignments at a seminar and independent work of students at home

The Complex of Solutions of the Nested Bethe Ansatz. The A_2 Spin Chain

The full set of polynomial solutions of the nested Bethe Ansatz is constructed for the case of A_2 rational spin chain. The structure and properties of these associated solutions are more various then in the case of usual XXX (A_1) spin chain but their role is similar

Exact and simple results for the XYZ and strongly interacting fermion chains

We conjecture exact and simple formulas for physical quantities in two quantum chains. A classic result of this type is Onsager, Kaufman and Yang's formula for the spontaneous magnetization in the Ising model, subsequently generalized to the chiral Potts models. We conjecture that analogous results occur in the XYZ chain when the couplings obey J_xJ_y + J_yJ_z + J_x J_z=0, and in a related fermion chain with strong interactions and supersymmetry. We find exact formulas for the magnetization and gap in the former, and the staggered density in the latter, by exploiting the fact that certain quantities are independent of finite-size effects