On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix

For $e$ a positive integer, we find restrictions modulo $2^e$ on the coefficients of the characteristic polynomial $\chi_S(x)$ of a Seidel matrix $S$. We show that, for a Seidel matrix of order $n$ even (resp. odd), there are at most $2^{\binom{e-2}{2}}$ (resp. $2^{\binom{e-2}{2}+1}$) possibilities for the congruence class of $\chi_S(x)$ modulo $2^e\mathbb Z[x]$. As an application of these results, we obtain an improvement to the upper bound for the number of equiangular lines in $\mathbb R^{17}$, that is, we reduce the known upper bound from $50$ to $49$.Comment: 21 pages, fixed typo in Lemma 2.

Innovative analytical and statistical technology as a corruption counteraction tool: conceptual analysis

The article is devoted to conceptual analysis of the problem of innovative analytical and statistical technologies implementations as a corruption prevention tool. This study defines corruption as the unlawful use of administrative resources for personal or group benefits, violating both formal and informal norms. It is stated that “corruption counteraction” means actions to prevent, combat, and mitigate corruption in society. The paper introduces several approaches for analytical and statistical technologies classification with grouping such technologies into high, middle and low technologies. Hi-tech is applied to the most advanced technologies based on scientific and technical progress and associated with automated technology. Automated analytical and statistical technologies are innovative in utilizing machine learning, deep learning, neural networks, NLP, network analysis, and real-time data analysis. The use of such technologies, which autonomously perform tasks previously reserved for humans, has shown potential for more effective corruption counteraction. So, “innovative analytical and statistical technology” is defined as a modern collection of methods and tools for data analysis, designed to identify complex dependencies and useful patterns in data, improving decision-making, and detecting anomalies

Lichens of Historical Manor Parks in Northwest-central Belarus.

В результате изучения шести усадебных парков, расположенных в Минской области и взятых в качестве пробных участков, идентифицировано 119 видов лихенизированных сумчатых грибов. Парки были распределены по двум категориям: богатые видами (65‒72 вида лишайников) и бедные видами (38‒47 видов лишайников). Кластерный анализ, основанный на относительном обилии видов, показал малые различия в лихенобиоте между парками, бедными видами, и значительные различия между парками, богатыми видами. В качестве факторов, увеличивающих видовое богатство лишайников, рассматриваются наличие многочисленных старовозрастных деревьев, заболоченных участков местности, скоплений валунов, руин, а также усложненный рельеф. Главными характеристиками, описывающими различия в лихенобиоте парков, были: число редких видов, число видов накипной жизненной формы, число видов, населяющих минеральные субстраты. В то же время число видов листоватой жизненной формы, процент эпифитных видов, число видов на бетоне и гниющей древесине были сходны в изученных парках. Семь видов, в особенности Oxneria fallax, Parmelina tiliacea и Pleurosticta acetabulum, были вычленены как приуроченные по преимуществу к парковых экосистемам. Впервые для Беларуси были определены Candelaria pacifica, Lecania erysibe, L. sylvestris и Thelidium minutulum. Diplotomma alboatrum, Leptogium cyanescens и Pyrrhospora quernea были подтверждены для лихенобиоты Беларуси образцами из изученных парков. = As a result of the study of lichenized Ascomycota in six sample manor parks, situated in Minsk region, 119 species were identified. The parks belong to the two categories: species-rich (with 65–72 lichen species) and species-poor (with 38–47 species). Cluster analysis based on relative abundance of the species showed small differences between species-poor parks and significant differences between species-rich parks. The presence of numerous old-aged trees, wetlands, stone aggregations, ruins, and complicated relief are considered. as the factors, rising species richness in parks. The main characteristics making dif-ferences in lichen biota of the parks were number of rare species, number of species belonging to crustose growth form, and number of species inhabiting mineral substrata. In the same time number of foliose spe-cies, per cent of epiphytic species, number of species on concrete and wood were similar in the parks studied. Seven taxa, especially Oxneria fallax, Parmelina tiliacea, and Pleurosticta acetabulum, were distinguished as confined mostly to park ecosystems. Candelaria pacifica, Lecania erysibe, L. sylvestris, and Thelidium minutulum were recorded for the first time in Belarus. Diplotomma alboatrum, Leptogium cyanescens, and Pyrrhospora quernea were confirmed for lichen biota of Belarus by recent collections. Key words: epilithes, epiphytes, phorophyte, substratum type, thallus morphotype

Real quadratic fields with a universal form of given rank have density zero

We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadratic form of a given rank, thus establishing a density zero statement. More generally, we obtain such a result for totally positive definite quadratic lattices that represent all the multiples of a given rational integer. Our main tools are short vectors in quadratic lattices combined with an estimate for the number of periodic continued fractions with bounded coefficients.Comment: 18 pages, minor change