Absolutely Koszul algebras and the Backelin-Roos property

We study absolutely Koszul algebras, Koszul algebras with the Backelin-Roos property and their behavior under standard algebraic operations. In particular, we identify some Veronese subrings of polynomial rings that have the Backelin-Roos property and conjecture that the list is indeed complete. Among other things, we prove that every universally Koszul ring defined by monomials has the Backelin-Roos property

The theoretical DFT study of electronic structure of thin Si/SiO2 quantum nanodots and nanowires

The atomic and electronic structure of a set of proposed thin (1.6 nm in diameter) silicon/silica quantum nanodots and nanowires with narrow interface, as well as parent metastable silicon structures (1.2 nm in diameter), was studied in cluster and PBC approaches using B3LYP/6-31G* and PW PP LDA approximations. The total density of states (TDOS) of the smallest quasispherical silicon quantum dot (Si85) corresponds well to the TDOS of the bulk silicon. The elongated silicon nanodots and 1D nanowires demonstrate the metallic nature of the electronic structure. The surface oxidized layer opens the bandgap in the TDOS of the Si/SiO2 species. The top of the valence band and the bottom of conductivity band of the particles are formed by the silicon core derived states. The energy width of the bandgap is determined by the length of the Si/SiO2 clusters and demonstrates inverse dependence upon the size of the nanostructures. The theoretical data describes the size confinement effect in photoluminescence spectra of the silica embedded nanocrystalline silicon with high accuracy.Comment: 22 pages, 5 figures, 1 tabl

Evolutionary biology studies on the Iris pumila clonal plant: Advantages of a good model system, main findings and directions for further research

Evolutionary studies on the dwarf bearded iris, Iris pumila L., a perennial clonal monocot with hermaphroditic enthomophylous flowers, have been conducted during the last three decades on plants and populations from the Deliblato Sands in Serbia. In this review we discuss the main advantages of this model system that have enabled various studies of several important genetic, ecological, and evolutionary issues at different levels of biological organization (molecular, physiological, anatomical, morphological and population). Based on published research and its resonance in international scientific literature, we present the main findings obtained from these studies, and discuss possible directions for further research

On the cohomological spectrum and support varieties for infinitesimal unipotent supergroup schemes

We show that if $G$ is an infinitesimal elementary supergroup scheme of height $\leq r$, then the cohomological spectrum $|G|$ of $G$ is naturally homeomorphic to the variety $\mathcal{N}_r(G)$ of supergroup homomorphisms $\rho: \mathbb{M}_r \rightarrow G$ from a certain (non-algebraic) affine supergroup scheme $\mathbb{M}_r$ into $G$. In the case $r=1$, we further identify the cohomological support variety of a finite-dimensional $G$-supermodule $M$ as a subset of $\mathcal{N}_1(G)$. We then discuss how our methods, when combined with recently-announced results by Benson, Iyengar, Krause, and Pevtsova, can be applied to extend the homeomorphism $\mathcal{N}_r(G) \cong |G|$ to arbitrary infinitesimal unipotent supergroup schemes.Comment: Fixed some algebra misidentifications, primarily in Sections 1.3 and 3.3. Simplified the proof of Proposition 3.3.

Koszul binomial edge ideals

It is shown that if the binomial edge ideal of a graph $G$ defines a Koszul algebra, then $G$ must be chordal and claw free. A converse of this statement is proved for a class of chordal and claw free graphs

(Contravariant) Koszul duality for DG algebras

A DG algebras $A$ over a field $k$ with $H(A)$ connected and $H_{<0}(A)=0$ has a unique up to isomorphism DG module $K$ with $H(K)\cong k$. It is proved that if $H(A)$ is degreewise finite, then RHom_A(?,K): D^{df}_{+}(A)^{op} \equiv D_{df}^{+}}(RHom_A(K,K)) is an exact equivalence of derived categories of DG modules with degreewise finite-dimensional homology. It induces an equivalences of $D^{df}_{b}(A)^{op}$ and the category of perfect DG $RHom_A(K,K)$-modules, and vice-versa. Corresponding statements are proved also when $H(A)$ is simply connected and $H^{<0}(A)=0$.Comment: 33 page

GG-prime and GG-primary GG-ideals on GG-schemes

Let $G$ be a flat finite-type group scheme over a scheme $S$, and $X$ a noetherian $S$-scheme on which $G$-acts. We define and study $G$-prime and $G$-primary $G$-ideals on $X$ and study their basic properties. In particular, we prove the existence of minimal $G$-primary decomposition and the well-definedness of $G$-associated $G$-primes. We also prove a generalization of Matijevic-Roberts type theorem. In particular, we prove Matijevic-Roberts type theorem on graded rings for $F$-regular and $F$-rational properties.Comment: 54pages, added Example 6.16 and the reference [8]. The final versio