Quasi-complete intersection homomorphisms

Extending a notion defined for surjective maps by Blanco, Majadas, and Rodicio, we introduce and study a class of homomorphisms of commutative noetherian rings, which strictly contains the class of locally complete intersection homomorphisms, while sharing many of its remarkable properties.Comment: Final version, to appear in the special issue of Pure and Applied Mathematics Quarterly dedicated to Andrey Todorov. The material in the first four sections has been reorganized and slightly expande

Free resolutions over short local rings

The structure of minimal free resolutions of finite modules M over commutative local rings (R,m,k) with m^3=0 and rank_k(m^2) < rank_k(m/m^2)is studied. It is proved that over generic R every M has a Koszul syzygy module. Explicit families of Koszul modules are identified. When R is Gorenstein the non-Koszul modules are classified. Structure theorems are established for the graded k-algebra Ext_R(k,k) and its graded module Ext_R(M,k).Comment: 17 pages; number of minor changes. This article will appear in the Journal of the London Math. So

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

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

Nonlinear vibration of continuous systems

Continuous systems, such as beams, membranes, plates, shells, and other structural/mechanical components, represent fundamental elements of mechanical systems in any field of engineering: Aerospace, Aeronautics, Automation, Automotive, Civil, Nuclear, Petroleum, and Railways. The modern designer is required to optimize structural elements to improve the performance-to-cost ratio, produce lightweight machines, and improve the efficiency. Such optimizations easily lead to a magnification of vibration/dynamic problems such as resonances, instabilities, and nonlinear behaviors. Therefore, the development of new methods of analysis, testing, and monitoring is greatly welcome. This special issue focuses on sharing recent advances and developments of theories, algorithms, and applications that involve the dynamics and vibrations of continuous systems. The contributions to this special issue include innovative theoretical studies, advanced numerical simulations, and new experimental approaches to investigate and better understand complex dynamic phenomena; more specifically, methods and theories for beams, membranes, plates, and shells; numerical approaches for structural elements; fluid-structure interaction; nonlinear acoustics; identification, diagnosis, friction models, and vehicle dynamics. Seventeen contributions have been received from all over the world: Canada, China, Kazakhstan, Italy, Macau, Spain, and USA. This shows the generalized interest on the topic. The following short description of the special issue content is organized by grouping the contributions in coherent subtopics

Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension

Let $R$ be a local ring, and let $M$ and $N$ be finitely generated $R$-modules such that $M$ has finite complete intersection dimension. In this paper we define and study, under certain conditions, a pairing using the modules \Ext_R^i(M,N) which generalizes Buchweitz's notion of the Herbrand diference. We exploit this pairing to examine the number of consecutive vanishing of \Ext_R^i(M,N) needed to ensure that \Ext_R^i(M,N)=0 for all $i\gg 0$. Our results recover and improve on most of the known bounds in the literature, especially when $R$ has dimension at most two

(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

Shapes of free resolutions over a local ring

We classify the possible shapes of minimal free resolutions over a regular local ring. This illustrates the existence of free resolutions whose Betti numbers behave in surprisingly pathological ways. We also give an asymptotic characterization of the possible shapes of minimal free resolutions over hypersurface rings. Our key new technique uses asymptotic arguments to study formal Q-Betti sequences.Comment: 14 pages, 1 figure; v2: sections have been reorganized substantially and exposition has been streamline