let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...

We introduce a classification of locally compact Hausdorff topological spaces with respect to the behavior $$ \sigma -compact subsets and, relying on this classification, we study properties corresponding $$C^*$$ -algebras in terms frame theory and {\mathscr A} operators Hilbert -modules; some pathological examples are constructed.

We construct tilting modules over Jacobian algebras arising from knots. To a two-bridge knot L [ 1 , … n ] we associate quiver Q with potential and its algebra A . family of canonical indecomposable -modules M ( i ) each supported on different specific subquiver Each the is expected to parametrize Jones polynomial knot. study direct sum = ? these indecomposables inside module category as well i...

System integration is one of the market driving issues in power electronics. In this paper the integration of precise shunts into IGBT modules, like it is done in Infineons MIPAQ family, is compared to on-IGBT-chip current sense functionality. Temperature measurement via NTC-resistor on DBC-level or on-IGBT-chip integrated temp-sense-diodes will be treated as well. Further processing of the low...

We construct superconformal gauged sigma models with extended rigid supersymmetry in three dimensions. Those with N > 4 have necessarily flat targets, but the models with N ≤ 4 admit non-flat targets, which are cones with appropriate Sasakian base manifolds. Superconformal symmetry also requires that the three dimensional spacetimes admit conformal Killing spinors which we examine in detail. We...

The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super Yang-Mills theory in four dimensions. The key ingredients are electric-magnetic duality of gauge theory, mirror symmetry of sigma-models, branes, Wilson and ’t Hooft operators, and topological field theory. Seemingly esoteric notions of the geometric Langlan...

We implemented a novel approach to score water mediation and displacement in the protein-ligand docking program GOLD. The method allows water molecules to switch on and off and to rotate around their three principal axes. A constant penalty, sigma(p), representing the loss of rigid-body entropy, is added for water molecules that are switched on, hence rewarding water displacement. We tested the...

In the paper semantic simulation engine for supervision of mobile robotic system is described. Semantic simulation engine provides tools to implement mobile robot simulation based on real data delivered by robot observations in INDOOR environment. The supervision of real objects such as robots is performed by association with its virtual representation in the simulation, therefore events such a...