A Projective Invariant Description of Ovals with Three Possible Symmetry Genera

Nikolaev, Petr P.

doi:10.22204/2410-4639-2016-092-04-38-54

Cited by 2 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to the physical-geographical zoning of Kazakhstan, the territory of the national park is located within the Central Kazakhstan hills [3]. The main ecosystems are represented by semi-arid and drought steppes with an altitudinal belt in the province of the Karaganda-Chingiztau dry-steppe low-hill terrain and in the area of the Yereymentau-Karkaraly mountainous hillocky territory (Karamysheva, Rachkovskaya, 1973) [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Protected, Rare and Medicinal Plant Species of the Buiratau State National Natural Park (Republic of Kazakhstan)

Kali,

Kenzhina,

Turlybekova

et al. 2023

Preprint

View full text Add to dashboard Cite

The biodiversity of the State National Natural Park (SNNP) "Buiratau" has not been studied, as it is young in Kazakhstan. The purpose of our study was an independent botanical and geographical study of the vegetation cover of the SNNP "Buiratau". This study have been carried out using the method route-reconnaissance and identifying plants, according to plant guide “Flora of Kazakhstan” (1999), “Key to Plants of Central Asia” (1974). The results showed that depending on the geographical location (Kazakh highland, steppe zone) of the SNNP "Buiratau" territory this natural complex has a very diverse botanical feature. In these types of vegetation of this territory, there are both Red Data Book and rare and endemic plants, such as black alder and birch forests, the peculiarity of which is that some species (Alnus glutinosa (L) Gaertn, Betula Kirghisorum Sav. - Rysz.) are listed in the Red book and very few. Medicinal, plant species and their resource potential are an important component of the flora. The analysis showed that the SNNP "Buiratau" is a unique natural environment, which is characterized by 10 species of plants listed in the Red Book, and 26 species of rare and endangered species.

show abstract

Section: Introductionmentioning

confidence: 99%

Protected, Rare and Medicinal Plant Species of the Buiratau State National Natural Park (Republic of Kazakhstan)

Kali,

Kenzhina,

Turlybekova

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Recognition of projectively transformed planar figures. XVII. Using plucker’s reciprocity theorem to describe ovals with an external fixed point

Nikolaev

2024

Sensornye sistemy

View full text Add to dashboard Cite

An approach to a projectively invariant description of a family of ovals (o) in scenes where the figure o is given in a composition with an external point, P, fixed in its plane is considered, and in cases where o has hidden symmetries (central or axial), the position of P is not specified in the form of an additional condition defining the scene, but can be calculated through the symmetry parameters. The invariant description, as a general universal method for numerical processing of compositions like “o + ext-P”, is proposed to be implemented in the form of Wurf mappings.The method uses the apparatus of dual pairs (DP) and wurf functions,previously developed and described by us, which are a product of decomposition of statements of the reciprocity theorem proposed by J. Plьcker to describe the properties of quadratic curves (conics).Illustrated examples of special cases of the “o + ext-P”composition are considered and discussed, actually completing the topic of studying the scenes like “an oval and a linear element of the plane”, which are classified according to the types of symmetry of o.

show abstract

A Projective Invariant Description of Ovals with Three Possible Symmetry Genera

Cited by 2 publications

References 0 publications

Protected, Rare and Medicinal Plant Species of the Buiratau State National Natural Park (Republic of Kazakhstan)

Protected, Rare and Medicinal Plant Species of the Buiratau State National Natural Park (Republic of Kazakhstan)

Recognition of projectively transformed planar figures. XVII. Using plucker’s reciprocity theorem to describe ovals with an external fixed point

Contact Info

Product

Resources

About