Distribution of landslides in the area of the town of Polski Trambesh, Northern Bulgaria

Abstract

The article presents the results of the landslide mapping in the area of the town of Polski Trambesh, central Northern Bulgaria. A total of 37 new landslides have been described, which have not been included in the landslide register so far. Landslides are classified by area, type and activity. Their location is mapped in a GIS environment.

The de Sitter (dS) Group and its Representations

“…The dS 4 and AdS 4 are indeed the two curved spacetimes of constant curvature (respectively, of negative and positive curvatures), which like Minkowski (zero curvature) spacetime, admit continuous groups of motion of maximal symmetry such that, as Minkowski spacetime is the zero-curvature limit of dS 4 and AdS 4 spacetimes, the Poincaré group can be realized by a contraction limit of either the dS 4 relativity group SO 0 (1,4) or the AdS 4 one SO 0 (2,3). On the representation level, and quite similar to the Poincaré case, the (A)dS 4 UIR's are labelled by two invariant parameters of the spin and energy scales (the latter, in the AdS 4 case, is actually the rest energy) [18][19][20][21][22][23][24][25][26][27]. From the point of view of a local ("tangent") Minkowskian observer, the (A)dS 4 UIRs fall basically into three sets: the set of (A)dS 4 "massive" UIRs, in the sense that they contract to the Poincaré massive UIRs and exhaust the whole set of the latter [20,28,29]; the set of (A)dS 4 "massless" UIRs constituting by those (A)dS 4 UIRs with a unique extension to the conformal group (SO 0 (2, 4)) UIRs, while that extension is equivalent to the conformal extension of the Poincaré massless UIRs (of course, this correspondence exhaust the whole set of the Poincaré massless UIRs) [30][31][32]; and finally, the set of those (A)dS 4 UIRs with either no physical Poincaré contraction limit or no Poincaré contraction limit at all.…”

“…In this section, we study the construction of the AdS 4 UIRs relevant to the quantum reading of the described classical systems above. The so-called "massive" elementary systems living in AdS 4 spacetime on the quantum level are associated with the discrete series UIRs U (ς,s) of Sp(4, R) or of its universal covering Sp(4, R) [18][19][20][21][22][23]; the parameters ς ∈ R + and s ∈ N/2 (spin) are dimensionless, and satisfy ς > s + 1 (the lowest limit ς = s + 1 is the "massless" case). For ς > s + 2, the representation Hilbert spaces are denoted by Fock-Bargmann spaces F (ς,s) and their elements are holomorphic (2s + 1)-vector functions:…”

“…3), it is sufficient to combine A, B, and C. In this regard, we invoke Eq. (E 22),. and then we obtain:√ a ς,l,k det −bz z z + a −ς (g −1 ⋄ z z z) • (g −1 ⋄ z z z) k Y l−2k,m g −1 ⋄ z z z = l ′′′ k ′′′ m ′′′ U (ς,0) l,k,m;l ′′′ ,k ′′′ ,m ′′′ (g) √ a ς,l ′′′ ,k ′′′ (z z z • z z z) k ′′′ Y l ′′′ −2k ′′′ ,m ′′′ (z z z) ,,m;l ′′′ ,k ′′′ ,m ′′′ (g) are the matrix elements of the Sp(4, R) scalar representations U (ς,0) such that:U (ς,0) l,k,m;l ′′′ ,k ′′′ ,m ′′′ (g) = ′ L ′′ m ′′ L ′ −L ′′ =even L √ a ς,l,k a (ς,k),l,k a ′ k,l,k √ a ς,l ′′′ ,k ′′′ U L,k,m;L ′ ,L ′′ ,m ′′ (g) × δ l ′′′ ,l+l+L ′ δ 2k ′′′ ,l ′′′ −L ′′′ det a −ς−k+1 det b k (w • w) k Y l−2k,m (w) (u • u) k Y l−2k,m (u) × (−1) m (2l − 4k + 1)(2l − 4k + 1)(2L + 1) 4π 1/2 l − 2k l − 2k L m m −m l − 2k l − 2k L 0 0 (−1) m ′′′ (2L ′′ + 1)(2L + 1)(2L ′′′ + 1) 4π 1/2 L L ′′ L ′′′ m m ′′ −m ′′′ L L ′′ L ′′′ 0…”

Peculiarities of the materials involved in the debris flows in Kresna Gorge, Southwest Bulgaria

“…Въпросът за кално-каменните порои сравнително отскоро е обект на интерес в геоложките и геоморфоложките разработки (Dobrev, 1994;Kenderova, Vassilev, 1997;Dobrev, Georgieva, 2010;Gerdjikov et al, 2012Gerdjikov et al, , 2022Baltakova et al, 2018, и др.). Описани са случаи, регистрирани основно в поречието на р. Струма, Източните Родопи, ЮЗ България и Задбалканските котловини, като последният случай бе от 02.09.2022 г. в Карловско, при който бяха засегнати селата Каравелово, Богдан, Розино и Слатина.…”

“…Обект на настоящото изследване е северната част на Кресненския пролом, където периодично се случват такива явления (фиг. 1) (Dobrev, 1999;Георгиева, 2010 1 ;Dobrev, Georgieva, 2010). Проявленията им носят висок риск за трафика по главен път Е79.…”