116 research outputs found
On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix
For a positive integer, we find restrictions modulo on the
coefficients of the characteristic polynomial of a Seidel matrix
. We show that, for a Seidel matrix of order even (resp. odd), there are
at most (resp. ) possibilities for
the congruence class of modulo . As an application
of these results, we obtain an improvement to the upper bound for the number of
equiangular lines in , that is, we reduce the known upper bound
from to .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 βcorruption counteractionβ 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, βinnovative analytical and statistical technologyβ 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.
Π ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΠΈΠ·ΡΡΠ΅Π½ΠΈΡ ΡΠ΅ΡΡΠΈ ΡΡΠ°Π΄Π΅Π±Π½ΡΡ
ΠΏΠ°ΡΠΊΠΎΠ², ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½Π½ΡΡ
Π² ΠΠΈΠ½ΡΠΊΠΎΠΉ ΠΎΠ±Π»Π°ΡΡΠΈ ΠΈ Π²Π·ΡΡΡΡ
Π² ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΏΡΠΎΠ±Π½ΡΡ
ΡΡΠ°ΡΡΠΊΠΎΠ², ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½ΠΎ 119 Π²ΠΈΠ΄ΠΎΠ² Π»ΠΈΡ
Π΅Π½ΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΡΠΌΡΠ°ΡΡΡ
Π³ΡΠΈΠ±ΠΎΠ². ΠΠ°ΡΠΊΠΈ Π±ΡΠ»ΠΈ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Ρ ΠΏΠΎ Π΄Π²ΡΠΌ ΠΊΠ°ΡΠ΅Π³ΠΎΡΠΈΡΠΌ: Π±ΠΎΠ³Π°ΡΡΠ΅ Π²ΠΈΠ΄Π°ΠΌΠΈ (65β72 Π²ΠΈΠ΄Π° Π»ΠΈΡΠ°ΠΉΠ½ΠΈΠΊΠΎΠ²) ΠΈ Π±Π΅Π΄Π½ΡΠ΅ Π²ΠΈΠ΄Π°ΠΌΠΈ (38β47 Π²ΠΈΠ΄ΠΎΠ² Π»ΠΈΡΠ°ΠΉΠ½ΠΈΠΊΠΎΠ²). ΠΠ»Π°ΡΡΠ΅ΡΠ½ΡΠΉ Π°Π½Π°Π»ΠΈΠ·, ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΡΠΉ Π½Π° ΠΎΡΠ½ΠΎΡΠΈΡΠ΅Π»ΡΠ½ΠΎΠΌ ΠΎΠ±ΠΈΠ»ΠΈΠΈ Π²ΠΈΠ΄ΠΎΠ², ΠΏΠΎΠΊΠ°Π·Π°Π» ΠΌΠ°Π»ΡΠ΅ ΡΠ°Π·Π»ΠΈΡΠΈΡ Π² Π»ΠΈΡ
Π΅Π½ΠΎΠ±ΠΈΠΎΡΠ΅ ΠΌΠ΅ΠΆΠ΄Ρ ΠΏΠ°ΡΠΊΠ°ΠΌΠΈ, Π±Π΅Π΄Π½ΡΠΌΠΈ Π²ΠΈΠ΄Π°ΠΌΠΈ, ΠΈ Π·Π½Π°ΡΠΈΡΠ΅Π»ΡΠ½ΡΠ΅ ΡΠ°Π·Π»ΠΈΡΠΈΡ ΠΌΠ΅ΠΆΠ΄Ρ ΠΏΠ°ΡΠΊΠ°ΠΌΠΈ, Π±ΠΎΠ³Π°ΡΡΠΌΠΈ Π²ΠΈΠ΄Π°ΠΌΠΈ. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΡΠ°ΠΊΡΠΎΡΠΎΠ², ΡΠ²Π΅Π»ΠΈΡΠΈΠ²Π°ΡΡΠΈΡ
Π²ΠΈΠ΄ΠΎΠ²ΠΎΠ΅ Π±ΠΎΠ³Π°ΡΡΡΠ²ΠΎ Π»ΠΈΡΠ°ΠΉΠ½ΠΈΠΊΠΎΠ², ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ Π½Π°Π»ΠΈΡΠΈΠ΅ ΠΌΠ½ΠΎΠ³ΠΎΡΠΈΡΠ»Π΅Π½Π½ΡΡ
ΡΡΠ°ΡΠΎΠ²ΠΎΠ·ΡΠ°ΡΡΠ½ΡΡ
Π΄Π΅ΡΠ΅Π²ΡΠ΅Π², Π·Π°Π±ΠΎΠ»ΠΎΡΠ΅Π½Π½ΡΡ
ΡΡΠ°ΡΡΠΊΠΎΠ² ΠΌΠ΅ΡΡΠ½ΠΎΡΡΠΈ, ΡΠΊΠΎΠΏΠ»Π΅Π½ΠΈΠΉ Π²Π°Π»ΡΠ½ΠΎΠ², ΡΡΠΈΠ½, Π° ΡΠ°ΠΊΠΆΠ΅ ΡΡΠ»ΠΎΠΆΠ½Π΅Π½Π½ΡΠΉ ΡΠ΅Π»ΡΠ΅Ρ. ΠΠ»Π°Π²Π½ΡΠΌΠΈ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠ°ΠΌΠΈ, ΠΎΠΏΠΈΡΡΠ²Π°ΡΡΠΈΠΌΠΈ ΡΠ°Π·Π»ΠΈΡΠΈΡ Π² Π»ΠΈΡ
Π΅Π½ΠΎΠ±ΠΈΠΎΡΠ΅ ΠΏΠ°ΡΠΊΠΎΠ², Π±ΡΠ»ΠΈ: ΡΠΈΡΠ»ΠΎ ΡΠ΅Π΄ΠΊΠΈΡ
Π²ΠΈΠ΄ΠΎΠ², ΡΠΈΡΠ»ΠΎ Π²ΠΈΠ΄ΠΎΠ² Π½Π°ΠΊΠΈΠΏΠ½ΠΎΠΉ ΠΆΠΈΠ·Π½Π΅Π½Π½ΠΎΠΉ ΡΠΎΡΠΌΡ, ΡΠΈΡΠ»ΠΎ Π²ΠΈΠ΄ΠΎΠ², Π½Π°ΡΠ΅Π»ΡΡΡΠΈΡ
ΠΌΠΈΠ½Π΅ΡΠ°Π»ΡΠ½ΡΠ΅ ΡΡΠ±ΡΡΡΠ°ΡΡ. Π ΡΠΎ ΠΆΠ΅ Π²ΡΠ΅ΠΌΡ ΡΠΈΡΠ»ΠΎ Π²ΠΈΠ΄ΠΎΠ² Π»ΠΈΡΡΠΎΠ²Π°ΡΠΎΠΉ ΠΆΠΈΠ·Π½Π΅Π½Π½ΠΎΠΉ ΡΠΎΡΠΌΡ, ΠΏΡΠΎΡΠ΅Π½Ρ ΡΠΏΠΈΡΠΈΡΠ½ΡΡ
Π²ΠΈΠ΄ΠΎΠ², ΡΠΈΡΠ»ΠΎ Π²ΠΈΠ΄ΠΎΠ² Π½Π° Π±Π΅ΡΠΎΠ½Π΅ ΠΈ Π³Π½ΠΈΡΡΠ΅ΠΉ Π΄ΡΠ΅Π²Π΅ΡΠΈΠ½Π΅ Π±ΡΠ»ΠΈ ΡΡ
ΠΎΠ΄Π½Ρ Π² ΠΈΠ·ΡΡΠ΅Π½Π½ΡΡ
ΠΏΠ°ΡΠΊΠ°Ρ
. Π‘Π΅ΠΌΡ Π²ΠΈΠ΄ΠΎΠ², Π² ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠΈ Oxneria fallax, Parmelina tiliacea ΠΈ Pleurosticta acetabulum, Π±ΡΠ»ΠΈ Π²ΡΡΠ»Π΅Π½Π΅Π½Ρ ΠΊΠ°ΠΊ ΠΏΡΠΈΡΡΠΎΡΠ΅Π½Π½ΡΠ΅ ΠΏΠΎ ΠΏΡΠ΅ΠΈΠΌΡΡΠ΅ΡΡΠ²Ρ ΠΊ ΠΏΠ°ΡΠΊΠΎΠ²ΡΡ
ΡΠΊΠΎΡΠΈΡΡΠ΅ΠΌΠ°ΠΌ. ΠΠΏΠ΅ΡΠ²ΡΠ΅ Π΄Π»Ρ ΠΠ΅Π»Π°ΡΡΡΠΈ Π±ΡΠ»ΠΈ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Ρ Candelaria pacifica, Lecania erysibe, L. sylvestris ΠΈ Thelidium minutulum. Diplotomma alboatrum, Leptogium cyanescens ΠΈ Pyrrhospora quernea Π±ΡΠ»ΠΈ ΠΏΠΎΠ΄ΡΠ²Π΅ΡΠΆΠ΄Π΅Π½Ρ Π΄Π»Ρ Π»ΠΈΡ
Π΅Π½ΠΎΠ±ΠΈΠΎΡΡ ΠΠ΅Π»Π°ΡΡΡΠΈ ΠΎΠ±ΡΠ°Π·ΡΠ°ΠΌΠΈ ΠΈΠ· ΠΈΠ·ΡΡΠ΅Π½Π½ΡΡ
ΠΏΠ°ΡΠΊΠΎΠ². = 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 65β72 lichen species) and species-poor (with 38β47 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
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