Matrix factorizations for nonaffine LG-models

We propose a natural definition of a category of matrix factorizations for nonaffine Landau-Ginzburg models. For any LG-model we construct a fully faithful functor from the category of matrix factorizations defined in this way to the triangulated category of singularities of the corresponding fiber. We also show that this functor is an equivalence if the total space of the LG-model is smooth.Comment: 12 pages, minor corrections of TEX fil

P∞P_\infty algebra of KP, free fermions and 2-cocycle in the Lie algebra of pseudodifferential operators

The symmetry algebra $P_\infty = W_\infty \oplus H \oplus I_\infty$ of integrable systems is defined. As an example the classical Sophus Lie point symmetries of all higher KP equations are obtained. It is shown that one (``positive'') half of the point symmetries belongs to the $W_\infty$ symmetries while the other (``negative'') part belongs to the $I_\infty$ ones. The corresponing action on the tau-function is obtained for the positive part of the symmetries. The negative part can not be obtained from the free fermion algebra. A new embedding of the Virasoro algebra into $gl(\infty )$n describes conformal transformations of the KP time variables. A free fermion algebra cocycle is described as a PDO Lie algebra cocycle.Comment: 21 pages, Latex, no figures (some references added and misprints are corrected

Effect of 6-day hypokinesia on oxygen metabolism indices in elderly and senile subjects

After a strict 6 day confinement to bed of elderly and senile subjects the oxygen supply of the subcutaneous cellular tissue was impaired, and the intensity of its tissue respiration was somewhat reduced. The vacat-oxygen of the blood and urine, the coefficient of incomplete oxidation, and the oxygen deficiency in the organism were increased

Derived categories of Burniat surfaces and exceptional collections

We construct an exceptional collection $\Upsilon$ of maximal possible length 6 on any of the Burniat surfaces with $K_X^2=6$, a 4-dimensional family of surfaces of general type with $p_g=q=0$. We also calculate the DG algebra of endomorphisms of this collection and show that the subcategory generated by this collection is the same for all Burniat surfaces. The semiorthogonal complement $\mathcal A$ of $\Upsilon$ is an "almost phantom" category: it has trivial Hochschild homology, and K_0(\mathcal A)=\bZ_2^6.Comment: 15 pages, 1 figure; further remarks expande

ANALOG-DIGITAL DEVICES FOR PARAMATER ESTIMATION OF THE TRANSFER FUNCTION

In this paper comparatively simple method is presented for identifying linear and nonlinear dynamic units. It is based on the analysis of steady-state response and makes use of the sequential integrating procedure. Analog-digital devices needed for realizing this method are described. It is shown that use of the microprocessor made it possible to continuously contol the elements in the function control systems

Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation

The critical behavior of the two-dimensional N-vector cubic model is studied within the field-theoretical renormalization-group (RG) approach. The beta-functions and critical exponents are calculated in the five-loop approximation, RG series obtained are resummed using Pade-Borel-Leroy and conformal mapping techniques. It is found that for N = 2 the continuous line of fixed points is well reproduced by the resummed RG series and an account for the five-loop terms makes the lines of zeros of both beta-functions closer to each another. For N > 2 the five-loop contributions are shown to shift the cubic fixed point, given by the four-loop approximation, towards the Ising fixed point. This confirms the idea that the existence of the cubic fixed point in two dimensions under N > 2 is an artifact of the perturbative analysis. In the case N = 0 the results obtained are compatible with the conclusion that the impure critical behavior is controlled by the Ising fixed point.Comment: 18 pages, 4 figure

Single-electron latch with granular film charge leakage suppressor

A single-electron latch is a device that can be used as a building block for Quantum-dot Cellular Automata (QCA) circuits. It consists of three nanoscale metal "dots" connected in series by tunnel junctions; charging of the dots is controlled by three electrostatic gates. One very important feature of a single-electron latch is its ability to store ("latch") information represented by the location of a single electron within the three dots. To obtain latching, the undesired leakage of charge during the retention time must be suppressed. Previously, to achieve this goal, multiple tunnel junctions were used to connect the three dots. However, this method of charge leakage suppression requires an additional compensation of the background charges affecting each parasitic dot in the array of junctions. We report a single-electron latch where a granular metal film is used to fabricate the middle dot in the latch which concurrently acts as a charge leakage suppressor. This latch has no parasitic dots, therefore the background charge compensation procedure is greatly simplified. We discuss the origins of charge leakage suppression and possible applications of granular metal dots for various single-electron circuits.Comment: 21 pages, 4 figure