Koszul differential graded algebras and BGG correspondence

The concept of Koszul differential graded algebra (Koszul DG algebra) is introduced. Koszul DG algebras exist extensively, and have nice properties similar to the classic Koszul algebras. A DG version of the Koszul duality is proved. When the Koszul DG algebra $A$ is AS-regular, the Ext-algebra $E$ of $A$ is Frobenius. In this case, similar to the classical BGG correspondence, there is an equivalence between the stable category of finitely generated left $E$-modules, and the quotient triangulated category of the full triangulated subcategory of the derived category of right DG $A$-modules consisting of all compact DG modules modulo the full triangulated subcategory consisting of all the right DG modules with finite dimensional cohomology. The classical BGG correspondence can derived from the DG version.Comment: 29 page

A search algorithm for a class of optimal finite-precision controller realization problems with saddle points

With game theory, we review the optimal digital controller realization problems that maximize a finite word length (FWL) closed-loop stability measure. For a large class of these optimal FWL controller realization problems which have saddle points, a minimax-based search algorithm is derived for finding a global optimal solution. The algorithm consists of two stages. In the first stage, the closed form of a transformation set is constructed which contains global optimal solutions. In the second stage, a subgradient approach searches this transformation set to obtain a global optimal solution. This algorithm does not suffer from the usual drawbacks associated with using direct numerical optimization methods to tackle these FWL realization problems. Furthermore, for a small class of optimal FWL controller realization problems which have no saddle point, the proposed algorithm also provides useful information to help solve them

Precise near-earth navigation with GPS: A survey of techniques

The tracking accuracy of the low earth orbiters (below about 3000 km altitude) can be brought below 10 cm with a variety of differential techniques that exploit the Global Positioning System (GPS). All of these techniques require a precisely known global network of GPS ground receivers and a receiver aboard the user satellite, and all simultaneously estimate the user and GPS satellite orbits. Three basic approaches are the geometric, dynamic, and nondynamic strategies. The last combines dynamic GPS solutions with a geometric user solution. Two powerful extensions of the nondynamic strategy show considerable promise. The first uses an optimized synthesis of dynamics and geometry in the user solution, while the second uses a novel gravity-adjustment method to exploit data from repeat ground tracks. These techniques will offer sub-decimeter accuracy for dynamically unpredictable satellites down to the lowesst possible altitudes

Dopant site selectivity in BaCe0.85M0.15O3-δ by extended x-ray absorption fine structure

Rare earth doped BaCeO3 has been widely investigated as a proton conducting material. Trivalent dopants are generally assumed to fully occupy the Ce4+-site, and thereby introduce oxygen vacancies into the perovskite structure. Recent studies indicate the possibility of partial dopant incorporation onto the Ba2+-site concomitant with BaO evaporation, reducing the oxygen vacancy content. Because proton incorporation requires, as a first step, the generation of oxygen vacancies such dopant partitioning is detrimental to protonic conductivity. A quantitative Extended X-ray Absorption Fine Structure (EXAFS) study of BaCe0.85M0.15O3-δ (M=Yb,Gd) is presented here along with complementary x-ray powder diffraction and electron probe chemical analyses. The EXAFS results demonstrate that as much as 4.6% of the ytterbium and 7.2% of the gadolinium intended for incorporation onto the Ce site, in fact, resides on the Ba site. The results are in qualitative agreement with the diffraction and chemical analyses, which additionally show an even greater extent of Nd incorporation on the Ba site

Structural Relaxation and Mode Coupling in a Simple Liquid: Depolarized Light Scattering in Benzene

We have measured depolarized light scattering in liquid benzene over the whole accessible temperature range and over four decades in frequency. Between 40 and 180 GHz we find a susceptibility peak due to structural relaxation. This peak shows stretching and time-temperature scaling as known from $\alpha$ relaxation in glass-forming materials. A simple mode-coupling model provides consistent fits of the entire data set. We conclude that structural relaxation in simple liquids and $\alpha$ relaxation in glass-forming materials are physically the same. A deeper understanding of simple liquids is reached by applying concepts that were originally developed in the context of glass-transition research.Comment: submitted to New J. Phy

Charge pumping in monolayer graphene driven by a series of time-periodic potentials

We applied the Floquet scattering-matrix formalism to studying the electronic transport properties in a mesoscopic Dirac system. Using the method, we investigate theoretically quantum pumping driven by a series of time-periodic potentials in graphene monolayer both in the adiabatic and non-adiabatic regimes. Our numerical results demonstrate that adding harmonic modulated potentials can break the time reversal symmetry when no voltage bias is applied to the graphene monolayer. Thus, when the system is pumped with proper dynamic parameters, these scatterers can produce a nonzero dc pumped current. We also find that the transmission is anisotropic as the incident angle is changed.Comment: 8 pages, 6 figure