Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product

The injective stabilization of the tensor product is subjected to an iterative procedure that utilizes its bifunctor property. The limit of this procedure, called the asymptotic stabilization of the tensor product, provides a homological counterpart of Buchweitz's asymptotic construction of stable cohomology. The resulting connected sequence of functors is isomorphic to Triulzi's J-completion of the Tor functor. A comparison map from Vogel homology to the asymptotic stabilization of the tensor product is constructed and shown to be always epic. The category of finitely presented functors is shown to be complete and cocomplete. As a consequence, the inert injective stabilization of the tensor product with fixed variable a finitely generated module over an artin algebra is shown to be finitely presented. Its defect and consequently all right-derived functors are determined. New notions of asymptotic torsion and cotorsion are introduced and are related to each other.

Graphical-analytical method for constructing load characteristics

The article discusses a graphical-analytical method for constructing the load characteristics of a three-element resonant circuit in the current stabilization mode. The current stabilization mode is observed when compensating the negative section of the S-shaped characteristics of the parallel resonant circuit of the connected sequence with a linear inductance and with a linear capacitor characteristic. The equation of the load mode in a dimensionless form represents the equation of an ellipse, which makes it possible to construct the necessary characteristics of a three-element resonant circuit for various types of load.

Graphical-analytical method for constructing load characteristics

The article discusses a graphical-analytical method for constructing the load characteristics of a three-element resonant circuit in the current stabilization mode. The current stabilization mode is observed when compensating the negative section of the S-shaped characteristics of the parallel resonant circuit of the connected sequence with a linear inductance and with a linear capacitor characteristic. The equation of the load mode in a dimensionless form represents the equation of an ellipse, which makes it possible to construct the necessary characteristics of a three-element resonant circuit for various types of load.

Network Analysis of Sequence-Function Relationships and Exploration of Sequence Space of TEM β-Lactamases

ABSTRACTThe Lactamase Engineering Database (www.LacED.uni-stuttgart.de) was developed to facilitate the classification and analysis of TEM β-lactamases. The current version contains 474 TEM variants. Two hundred fifty-nine variants form a large scale-free network of highly connected point mutants. The network was divided into three subnetworks which were enriched by single phenotypes: one network with predominantly 2be and two networks with 2br phenotypes. Fifteen positions were found to be highly variable, contributing to the majority of the observed variants. Since it is expected that a considerable fraction of the theoretical sequence space is functional, the currently sequenced 474 variants represent only the tip of the iceberg of functional TEM β-lactamase variants which form a huge natural reservoir of highly interconnected variants. Almost 50% of the variants are part of a quartet. Thus, two single mutations that result in functional enzymes can be combined into a functional protein. Most of these quartets consist of the same phenotype, or the mutations are additive with respect to the phenotype. By predicting quartets from triplets, 3,916 unknown variants were constructed. Eighty-seven variants complement multiple quartets and therefore have a high probability of being functional. The construction of a TEM β-lactamase network and subsequent analyses by clustering and quartet prediction are valuable tools to gain new insights into the viable sequence space of TEM β-lactamases and to predict their phenotype. The highly connected sequence space of TEM β-lactamases is ideally suited to network analysis and demonstrates the strengths of network analysis over tree reconstruction methods.

A Characterization of LCn Compacta in Terms of Gromov-Hausdorff Convergence

It is proved that a compactum is locally n-connected if and only if it is the limit (in the sense of Gromov-Hausdorff convergence) of an "equi-locally n-connected" sequence of (at most) (n + 1)-dimensional compacta.

Parataxis in Provençal

Comparative philologists have long since recognized that the logical relation of mental concepts need not find expression by means of words. Viewed from the standpoint of pure logic a sentence like “I think he will come” contains a subordination; but the student of historical grammar rightly regards it as exhibiting two independent, if not unrelated, sentences. It is altogether likely that such a method of juxtaposing concepts was the only one that prevailed in remote antiquity and that in the course of time such a loosely connected sequence of clauses developed into one organic whole. The fact of parataxis is now established for all branches of the Indo-European family, and Hermann has proved that grammatical subordination was unknown in the “Ursprache,” being developed in the daughter tongues by means of the specific determinants of the originally independent sentence. Notwithstanding these results, there is still a plentiful lack of agreement among scholars in regard to the definition of the term parataxis and to the degree of extension to be ascribed to it.