Dynamic Considerations for Control of Closed Life Support Systems

Reliability of closed life support systems depend on their ability to continue supplying the crew's needs during perturbations and equipment failures. The dynamic considerations interact with the basic static design through the sizing of storages, the specification of excess capacities in processors, and the choice of system initial state. A very simple system flow model was used to examine the possibilities for system failures even when there is sufficient storage to buffer the immediate effects of the perturbation. Two control schemes are shown which have different dynamic consequences in response to component failures

Redefining the performing arts archive

This paper investigates representations of performance and the role of the archive. Notions of record and archive are critically investigated, raising questions about applying traditional archival definitions to the performing arts. Defining the nature of performances is at the root of all difficulties regarding their representation. Performances are live events, so for many people the idea of recording them for posterity is inappropriate. The challenge of creating and curating representations of an ephemeral art form are explored and performance-specific concepts of record and archive are posited. An open model of archives, encouraging multiple representations and allowing for creative reuse and reinterpretation to keep the spirit of the performance alive, is envisaged as the future of the performing arts archive

Mutation in triangulated categories and rigid Cohen-Macaulay modules

We introduce the notion of mutation of $n$-cluster tilting subcategories in a triangulated category with Auslander-Reiten-Serre duality. Using this idea, we are able to obtain the complete classifications of rigid Cohen-Macaulay modules over certain Veronese subrings.Comment: 52 pages. To appear in Invent. Mat

About multiplicities and applications to Bezout numbers

Let $(A,\mathfrak{m},\Bbbk)$ denote a local Noetherian ring and $\mathfrak{q}$ an ideal such that $\ell_A(M/\mathfrak{q}M) < \infty$ for a finitely generated $A$-module $M$. Let \au = a_1,\ldots,a_d denote a system of parameters of $M$ such that $a_i \in \mathfrak{q}^{c_i} \setminus \mathfrak{q}^{c_i+1}$ for $i=1,\ldots,d$. It follows that \chi := e_0(\au;M) - c \cdot e_0(\mathfrak{q};M) \geq 0, where $c = c_1\cdot \ldots \cdot c_d$. The main results of the report are a discussion when $\chi = 0$ resp. to describe the value of $\chi$ in some particular cases. Applications concern results on the multiplicity e_0(\au;M) and applications to Bezout numbers.Comment: 11 pages, to appear Springer INdAM-Series, Vol. 20 (2017

Optimal Leapfrogging

No abstract provided in this article

Automorphism groups of polycyclic-by-finite groups and arithmetic groups

We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construct examples of polycyclic-by-finite groups which have an automorphism group which does not contain an arithmetic group of finite index. Finally we discuss applications of our results to the groups of homotopy self-equivalences of K(\Gamma, 1)-spaces and obtain an extension of arithmeticity results of Sullivan in rational homotopy theory

Applications of BGP-reflection functors: isomorphisms of cluster algebras

Given a symmetrizable generalized Cartan matrix $A$, for any index $k$, one can define an automorphism associated with $A,$ of the field $\mathbf{Q}(u_1, >..., u_n)$ of rational functions of $n$ independent indeterminates $u_1,..., u_n.$ It is an isomorphism between two cluster algebras associated to the matrix $A$ (see section 4 for precise meaning). When $A$ is of finite type, these isomorphisms behave nicely, they are compatible with the BGP-reflection functors of cluster categories defined in [Z1, Z2] if we identify the indecomposable objects in the categories with cluster variables of the corresponding cluster algebras, and they are also compatible with the "truncated simple reflections" defined in [FZ2, FZ3]. Using the construction of preprojective or preinjective modules of hereditary algebras by Dlab-Ringel [DR] and the Coxeter automorphisms (i.e., a product of these isomorphisms), we construct infinitely many cluster variables for cluster algebras of infinite type and all cluster variables for finite types.Comment: revised versio

On Hausdorff dimension of the set of closed orbits for a cylindrical transformation

We deal with Besicovitch's problem of existence of discrete orbits for transitive cylindrical transformations $T_\varphi:(x,t)\mapsto(x+\alpha,t+\varphi(x))$ where $Tx=x+\alpha$ is an irrational rotation on the circle \T and \varphi:\T\to\R is continuous, i.e.\ we try to estimate how big can be the set D(\alpha,\varphi):=\{x\in\T:|\varphi^{(n)}(x)|\to+\infty\text{as}|n|\to+\infty\}. We show that for almost every $\alpha$ there exists $\varphi$ such that the Hausdorff dimension of $D(\alpha,\varphi)$ is at least $1/2$. We also provide a Diophantine condition on $\alpha$ that guarantees the existence of $\varphi$ such that the dimension of $D(\alpha,\varphi)$ is positive. Finally, for some multidimensional rotations $T$ on \T^d, $d\geq3$, we construct smooth $\varphi$ so that the Hausdorff dimension of $D(\alpha,\varphi)$ is positive.Comment: 32 pages, 1 figur