The twistor geometry of three-qubit entanglement

A geometrical description of three qubit entanglement is given. A part of the transformations corresponding to stochastic local operations and classical communication on the qubits is regarded as a gauge degree of freedom. Entangled states can be represented by the points of the Klein quadric ${\cal Q}$ a space known from twistor theory. It is shown that three-qubit invariants are vanishing on special subspaces of ${\cal Q}$. An invariant vanishing for the $GHZ$ class is proposed. A geometric interpretation of the canonical decomposition and the inequality for distributed entanglement is also given.Comment: 4 pages RevTeX

Dynamical Structure Factors for Dimerized Spin Systems

We discuss the transition strength between the disordered ground state and the basic low-lying triplet excitation for interacting dimer materials by presenting theoretical calculations and series expansions as well as inelastic neutron scattering results for the material KCuCl_3. We describe in detail the features resulting from the presence of two differently oriented dimers per unit cell and show how energies and spectral weights of the resulting two modes are related to each other. We present results from the perturbation expansion in the interdimer interaction strength and thus demonstrate that the wave vector dependence of the simple dimer approximation is modified in higher orders. Explicit results are given in 10th order for dimers coupled in 1D, and in 2nd order for dimers coupled in 3D with application to KCuCl_3 and TlCuCl_3.Comment: 17 pages, 6 figures, part 2 is based on cond-mat/021133

Minimal distance transformations between links and polymers: Principles and examples

The calculation of Euclidean distance between points is generalized to one-dimensional objects such as strings or polymers. Necessary and sufficient conditions for the minimal transformation between two polymer configurations are derived. Transformations consist of piecewise rotations and translations subject to Weierstrass-Erdmann corner conditions. Numerous examples are given for the special cases of one and two links. The transition to a large number of links is investigated, where the distance converges to the polymer length times the mean root square distance (MRSD) between polymer configurations, assuming curvature and non-crossing constraints can be neglected. Applications of this metric to protein folding are investigated. Potential applications are also discussed for structural alignment problems such as pharmacophore identification, and inverse kinematic problems in motor learning and control.Comment: Submitted to J. Phys.:Condens. Matte

On the relation between p-adic and ordinary strings

The amplitudes for the tree-level scattering of the open string tachyons, generalised to the field of p-adic numbers, define the p-adic string theory. There is empirical evidence of its relation to the ordinary string theory in the p_to_1 limit. We revisit this limit from a worldsheet perspective and argue that it is naturally thought of as a continuum limit in the sense of the renormalisation group.Comment: 13 pages harvmac (b), 2 eps figures; v2: revtex, shortened, published versio

PLAGIARISM IN DISSERTATIONS

Introduction. Originality and independence is the first, absolute and general requirement to the content of dissertations, regardless of an academic degree and research direction. At the same time, recently a considerable fraction of different types of plagiarism have been found out in the Russian dissertation works. The aim is an analysis of the most frequent plagiarism in candidate and doctoral dissertations. Results. We consider the established practices in the evaluation of independence in academic works. Unethical use of someone else’s work and materials by the authors of dissertations include, in particular, copying from official documents and abstracts without acknowledgement the source and with no citation; replication of existing reviews and chapters from already defended dissertations; falsification by refreshing of outdated data with substituted dates, and or wordfor-word copy-pasting with substitution of the research object. The latter type of the plagiarism involving fraud in experimental and statistical data constitutes a special peril for the science and for the society in general. The primary principle for assessment of independence in dissertations has to be proper citing and referencing that should allow a reader to distinguish the author’s contribution from someone else’s text. Undocumented verbatim quotations in dissertations are inadmissible, whether the author claims scientific novelty or not. At that, it does not matter whether well-known or unique data are provided, and whether the source is protected by a copyright. Practical significance. The qualitative analysis of the factual material, based on the author’s observations, can serve as a starting point for the subsequent quantitative analysis of plagiarism in scientific texts. Введение. Оригинальность и самостоятельность – первое, абсолютное и не подлежащее каким-либо исключениям и оговоркам общее требование, предъявляемое к содержанию диссертаций, независимо от ученой степени, на которую претендует соискатель, и от научного направления исследования. Вместе с тем в последние годы различные виды плагиата приобрели в российских диссертационных работах массовый характер. Цель статьи – типологический анализ неправомерных заимствований, наиболее часто встречающихся в текстах кандидатских и докторских диссертаций. Результаты. С критических позиций рассмотрена сложившаяся практика оценки степени самостоятельности научного текста. Показаны и разобраны распространенные варианты недобросовестного использования диссертантами фрагментов чужих работ и материалов: копирование без указания источников частей из официальных документов и авторефератов, тиражирование обзорных глав и шаблонных изложений, фальсификации посредством «осовременивания» устаревших данных или дословного плагиата с подменой объекта исследования. Последняя разновидность заимствований, сопряженных с подлогом экспериментальных и статистических данных, представляет особую опасность для науки и для общества в целом. Подчеркивается, что базовым принципом экспертной оценки самостоятельности диссертационной работы должно быть требование адекватного оформления в ней заимствований, позволяющего отделить собственный текст диссертанта от чужого текста. Независимо от того, претендует автор на научную новизну или нет, недокументированные заимствования в диссертациях недопустимы. При этом не имеет значения, приводятся ли общеизвестные или уникальные сведения и охраняется ли источник заимствования авторским правом. Практическая значимость. Предлагаемый к обсуждению качественный анализ фактического материала, основанный на наблюдениях автора, может служить отправной точкой для последующего количественного анализа плагиата в научных текстах

Recursion relations and branching rules for simple Lie algebras

The branching rules between simple Lie algebras and its regular (maximal) simple subalgebras are studied. Two types of recursion relations for anomalous relative multiplicities are obtained. One of them is proved to be the factorized version of the other. The factorization property is based on the existence of the set of weights $\Gamma$ specific for each injection. The structure of $\Gamma$ is easily deduced from the correspondence between the root systems of algebra and subalgebra. The recursion relations thus obtained give rise to simple and effective algorithm for branching rules. The details are exposed by performing the explicit decomposition procedure for $A_{3} \oplus u(1) \to B_{4}$ injection.Comment: 15p.,LaTe