Александр Запрягаев

Presburger Arithmetic $\mathop{\mathbf{PrA}}\nolimits$ is the true theory of natural numbers with addition. We consider linear orderings interpretable in Presburger Arithmetic and establish various necessary and sufficient conditions for interpretability depending on dimension $n$ of interpretation. We note this problem is relevant to the interpretations of Presburger Arithmetic in itself, as well as the characterization of automatic orderings. For $n=2$ we obtain the complete criterion of interpretability.

Presburger arithmetic \(\mathop {\mathbf {PrA}}\nolimits \) is the true theory of natural numbers with addition. We study interpretations of \(\mathop {\mathbf {PrA}}\nolimits \) in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in \((\mathbb {N},+)\) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of \(\mathop {\mathbf {PrA}}\nolimits \) it follows that \(\mathop {\mathbf {PrA}}\nolimits \) isn’t one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.

The report deals with the axiomatic approach to the phenomena of quantum computation and algorithms. It gives an overview of the classical approach (due to von Neumann) using the structures of Hilbert spaces, as well as mentions some major results in the field and discusses the flaws of the model and its current dominance. This leads to the introduction of a new axiomatization, first proposed by S. Abramsky and B. Coecke in 2007, which relies on the modern concepts of category theory. It is a field of mathematics originally created in the 1940s by specialists in algebraic topology but currently gaining popularity in other branches because of its abstract nature and emphasis on operations rather than objects. Most importantly, category theory is a powerful tool in functional analysis allowing mathematicians to reformulate the statements of Hilbert space theory in a more intuitive way, without matrix calculus. Finally, the logic behind quantum operations is discussed: it is revealed t...

Presburger arithmetic PrA is the true theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the result we show that all linear orders that are interpretable in (N,+) are scattered orders with finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.

Presburger arithmetic is the true theory of natural numbers with addition. We study interpretations of Presburger arithmetic in itself. The main result of this paper is that all self-interpretations are definably isomorphic to the trivial one. Here we consider interpretations that might be multi-dimensional. We note that this resolves a conjecture by Visser (1998, An overview of interpretability logic. Advances in Modal Logic, pp. 307–359). In order to prove the result, we show that all linear orderings that are interpretable in $({\mathbb{N}},+)$ are scattered orderings with the finite Hausdorff rank and that the ranks are bounded in the terms of the dimensions of the respective interpretations.

Within the verbal morphology of Old Japanese (OJ) language, the verbs se- ‘to do’ and ko- ‘to come’ have a unique position. Resembling both the paradigms of vocalic and consonantal stems, they provide unique combinations of forms that might shed light on the diachronic development of the pre-OJ verb. The verb se- is especially complicated by its possible etymological connections to one of the copulas, as well as a focus particle, and shows a number of highly unexpected forms, including the main focus of the current research, two competing infinitival stems. This article aims to assemble current data on the morphology of this vital verb and discuss the possible hypotheses on the developments that led to the distribution depicted in written sources. Internal reconstruction , as well as Ryūkyūan comparative data are used in order to establish the most probable explanations.

Presburger Arithmetic PrA is the true theory of natural numbers with addition. We consider linear orderings interpretable in Presburger Arithmetic and establish various necessary and sufficient conditions for interpretability depending on dimension n of interpretation. We note this problem is relevant to the interpretations of Presburger Arithmetic in itself, as well as the characterization of automatic orderings. For n = 2 we obtain the complete criterion of interpretability.

This proposal offers to encode an additional character (small version of U+1B06A HENTAIGANA LETTER TU-2). The motivation lies in the correct and unambiguous representation of earlier forms of Japanese language, especially Late Middle Japanese, in academic contexts, scientific articles and dictionaries.

Since Andrew West’s inaugural proposal of soon to be 10 years ago,
there has been a journey towards encoding second stage simplifications in Unicode, for uses such as correctly representing the texts published during the short implementation, as well as rendering correctly the ancient texts which used the forms sometimes taken as inspiration. However, since then some of the characters were successfully encoded, and the original proposal did not include explicit generalizations of schemes offered as generic simplifications, and contained a small number of unfortunate misprints. Hence, I believe there is now time to review the charts against the current information and remake the list with as much data as possible.

This is Version 2.2, synchronized with the changes in the BabelStone Erjian fonts.

The current version is now available under link: https://drive.google.com/open?id=1NYAWfzGFBBLXRs-1BZXZBJzd2XN57Azd

В работе рассматриваются поэтические произведения на эльдарских языках, разработанных Дж.Р.Р.Толкином, размер которых отличается от традиционной для английского языка силлаботоники. Сопоставление творчества самого Толкина, с одной стороны, с образцами поэзии классических и древних языков, служившей для него источником вдохновения, а с другой стороны-с опытами современных поэтов по созданию эльдарских стихов на заложенной им основе позволяет нам избавиться от распространённого заблуждения о том, что квенья и синдарин допускают лишь формы, максимально приближенные к английским, и раскрывает нам Толкина как выдающегося филолога, знатока древних языков и одну из крупнейших фигур в воскрешении английского аллитерационного языка в XX в. Мы рассмотрим цитаты из произведений Толкина, позволяющие реконструировать формы и размеры поэзии, особенно синдаринской, оставшейся за кадром повествования и выясним, почему именно писатель часто ограничивался словесными описаниями и не предпринимал попыток предоставить свои собственные примеры.

Presburger arithmetic PrA is the true theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomor-phic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in (N, +) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.

Together with the borrowing of the writing system and a mass adaptation of the lexicon , Japan has also become aware of China's tonal distinctions. However, the readings of the names applied to these distinctions in Japanese leave an impression of an idiosyncratic mess, not matching exactly neither the the most popular readings of the same sinograms in ordinary language nor to any of the formally defined types of readings. In this article, we try to trace the reasoning that led to the establishment of the forms currently used and, specifically, explain the highly aberrant form hyō that denoted the level tone.

The 'imperfect' or continuous present tense form is a rather late addition to the roster of Quenya verbal tenses, expressed only analytically in Early Quenya Grammar and emerging as a part of basic Common Eldarin system in the 40s. However, the concept of the present and aorist formed differently in the case of 'derived' verbs postdates the last comprehensive Quenya grammar and can only be extrapolated out of a disassembled number of sources, most of which were now made available in Parma Eldalamberon 22. This article attempts to flesh out the grammatical features behind the tabulated forms.