The existence of n-Auslander–Reiten sequences via determined morphisms

Let [Formula: see text] be a commutative artinian ring and [Formula: see text] a small Ext-finite Krull–Schmidt [Formula: see text]-abelian [Formula: see text]-category with enough projectives and injectives. We introduce two full subcategories [Formula: see text] and [Formula: see text] of [Formula: see text] in terms of the representable functors from the stable category of [Formula: see text] to category of finitely generated [Formula: see text]-modules. Moreover, we define two additive functors [Formula: see text] and [Formula: see text], which are mutually quasi-inverse equivalences between the stable categories of this two full subcategories. We give an equivalent characterization on the existence of [Formula: see text]-Auslander–Reiten sequences using determined morphisms.

Quantified Desistance: A Scoping Review of Conventions in the Scientific Literature

This paper adopts a conventionalist approach to shed light on the measurement and reification problems that underlie the quantification of desistance from crime in the scientific literature. Analysis of 100 papers spanning three decades indicates that approaches based on theoretical classification have recently lost ground in favor of more sophisticated techniques aimed at empirically identifying subgroups. These techniques convey the impression of objectiveness among statistics users and consumers and, as a result, the classification “desisters” and “persisters” are increasingly reified. Findings suggest that the quantification of desistance is intimately linked to the maintenance of a classification system that constitutes delinquency as a stable category and contributes to “making” up new kinds of people over which institutions can legitimately intervene.

The STRUKTUR KOMUNITAS TERIPANG (Holothuroidea) DI PERAIRAN PANTAI DESA NAMTABUNG, KECAMATAN SELARU, KABUPATEN KEPULAUAN TANIMBAR

Sea cucumber is an invertebrate which is widely used by the community as food and medicine. The purpose of this study is to analyze the community structure of sea cucumber (Holothuroidea) in the coastal waters of Namtabung Village, Selaru District, Tanimbar Islands Regency. The used method to collect sea cucumber samples was the linear quadratic transect method with the number of observation stations as many as three stations, the samples of sea cucumbers obtained will be identified using an identification book. The results showed that there were four species of sea cucumber from the Holothuridea family, genus Holothuria and Bohadschia with the types namely Holothuria scabra, Holothuria edulis, Holothuria atra, and Bohadschia marmorata. Holothuria scabra has the highest density of 0.202 ind / m2. The highest relative abundance was shown by Holothuria edulis at 28.12%. The type of diversity index value is 1.3662 which means moderate diversity, and the dominance index is 0.2533, which means that there are no dominant species. The relative distribution pattern is at ˃ 1, which means that the distribution pattern is clustered. The highest index of importance was Holothuria scabra with a value of 91.07%. Overall, the sea cucumber community structure in the coastal waters of Namtabung Village is in the stable category. The highest index of importance was Holothuria scabra with a value of 91.07%. Overall, the community structure of sea cucumber in the coastal waters of Namtabung Village is in the stable category. ABSTRAK Teripang merupakan hewan tidak bertulang belakang yang banyak dimanfaatkan oleh masyarakat sebagai bahan pangan dan obat-obatan. Tujuan dari penelitian ini adalah menganalisis struktur komunitas teripang (Holothuroidea) di perairan pantai Desa Namtabung Kecamatan Selaru, Kabupaten Kepulauan Tanimbar. Metode yang digunakan untuk pengambilan sampe teripang adalah metode transek linear kuadrat dengan jumlah stasiun pengamatan sebanyak tiga stasiun, sampel teripang yang diperoleh akan diidentifikasi menggunakan buku identifikasi. Hasil penelitian menunjukan terdapat empat spesies teripang dari famili Holothuridea, genus Holothuria dan Bohadschia dengan jenis-jenis yaitu Holothuria scabra, Holothuria edulis, Holothuria atra, dan Bohadschia marmorata. Kepadatan tertinggi dimiliki oleh jenis Holothuria scabra sebesar 0,202 ind/m2. Kelimpahan relative tertinggi ditunjukkan oleh Holothuria edulis sebesar 28,12%. jenis Nilai indeks keanekaragaman sebesar 1,3662 yang artinya keanekaragaman sedang, dan indeks dominansi 0,2533 yang artinya tidak terdapat spesies yang mendominansi. Pola penyebaran relatif berada pada angka ˃ 1 yang artinya pola sebaran bersifat mengelompok. Indeks nilai penting tertinggi adalah Holothuria scabra dengan nilai 91,07%. Secara keseluruhan, struktur komunitas teripang di daerah perairan pantai Desa Namtabung berada dalam kategori stabil. Kata kunci: Struktur komunitas, teripang, indeks ekologi, Desa Namtabung, Maluku

Combinatorial study of stable categories of graded Cohen–Macaulay modules over skew quadric hypersurfaces

In this paper, we present a new connection between representation theory of noncommutative hypersurfaces and combinatorics. Let S be a graded ($$\pm 1$$ ± 1 )-skew polynomial algebra in n variables of degree 1 and $$f =x_1^2 + \cdots +x_n^2 \in S$$ f = x 1 2 + ⋯ + x n 2 ∈ S . We prove that the stable category $$\mathsf {\underline{CM}}^{\mathbb Z}(S/(f))$$ CM ̲ Z ( S / ( f ) ) of graded maximal Cohen–Macaulay module over S/(f) can be completely computed using the four graphical operations. As a consequence, $$\mathsf {\underline{CM}}^{\mathbb Z}(S/(f))$$ CM ̲ Z ( S / ( f ) ) is equivalent to the derived category $$\mathsf {D}^{\mathsf {b}}({\mathsf {mod}}\,k^{2^r})$$ D b ( mod k 2 r ) , and this r is obtained as the nullity of a certain matrix over $${\mathbb F}_2$$ F 2 . Using the properties of Stanley–Reisner ideals, we also show that the number of irreducible components of the point scheme of S that are isomorphic to $${\mathbb P}^1$$ P 1 is less than or equal to $$\left( {\begin{array}{c}r+1\\ 2\end{array}}\right) $$ r + 1 2 .