[en] The van der Pauw method for 2D samples of arbitrary shape with an isolated hole is considered. Correlations between extreme values of the resistances allow one to determine the specific resistivity of the sample and the dimensionless parameter related to the geometry of the isolated hole, known as the Riemann modulus. The parameter is invariant under conformal mappings. Experimental verification of the method is presented. (paper)

[en] A six-point generalization of the van der Pauw method is presented. The method is applicable for 2D homogeneous systems with an isolated hole. A single measurement performed on the contacts located arbitrarily on the sample edge allows us to determine the specific resistivity and a dimensionless parameter related to the hole, known as the Riemann modulus. The parameter is invariant under conformal mappings of the sample shape. The hole can be regarded as a high resistivity defect. Therefore, the method can be applied for the experimental determination of the sample inhomogeneity. (paper)

[en] In this work, we prove the generalized Covariant Entropy Bound, $\mathrm{\Delta <!--\; ??\; -->}S\le <!--\; ???\; -->(A-<!--\; ???\; -->A^{\prime })/4G\mathrm{\hslash <!--\; ???\; -->}$, for light-sheets with initial area $A$ and final area $A^{\prime }$. The entropy $\mathrm{\Delta <!--\; ??\; -->}S$ is defined as a difference of von Neumann entropies of an arbitrary state and the vacuum, with both states restricted to the light-sheet under consideration. The proof applies to free fields, in the limit where gravitational backreaction is small. We do not assume the null energy condition. In regions where it is violated, we postulate that the bound is protected by the defining property of light-sheets: that their null generators are nowhere expanding.

[en] We prove that if two conformal embeddings between Riemann surfaces with finite topology are homotopic, then they are isotopic through conformal embeddings. Furthermore, we show that the space of all conformal embeddings in a given homotopy class is homotopy equivalent to a point, a circle, a torus, or the unit tangent bundle of the codomain, depending on the induced homomorphism on fundamental groups. Quadratic differentials play a central role in the proof.

No abstract available

[en] We derive a local index theorem in Quillen’s form for families of Cauchy–Riemann operators on orbifold Riemann surfaces (or Riemann orbisurfaces) that are quotients of the hyperbolic plane by the action of cofinite finitely generated Fuchsian groups. Each conical point (or a conjugacy class of primitive elliptic elements in the Fuchsian group) gives rise to an extra term in the local index theorem that is proportional to the symplectic form of a new Kähler metric on the moduli space of Riemann orbisurfaces. We find a simple formula for a local Kähler potential of the elliptic metric and show that when the order of elliptic element becomes large, the elliptic metric converges to the cuspidal one corresponding to a puncture on the orbisurface (or a conjugacy class of primitive parabolic elements). We also give a simple example of a relation between the elliptic metric and special values of Selberg’s zeta function.

[en] Magnetized highly ionized sheet plasmas are created in steady state with sheet thickness of about the ion cyclotron diameter. The difference between the characters of slab and sheet plasmas are discussed and some ways of practical applications of the slab or the sheet plasmas are shown. (author)

[en] New methods of sheet stamping were developed: the gas forming with double-sided heating of a blank part and the gas molding with backpressure. In case of the first method the blank part is heated to the set temperature by means of a double-sided impact of combustion products of gas mixtures, after which, under the influence of gas pressure a stamping process is performed. In case of gas molding with backpressure, the blank part is heated to the set temperature by one-sided impact of the combustion products, while backpressure is created on the opposite side of the blank part by compressed air. In both methods the deformation takes place in the temperature range of warm or hot treatment due to the heating of a blank part. This allows one to form parts of complicated shape within one technological operation, which significantly reduces the cost of production. To implement these methods, original devices were designed and produced, which are new types of forging and stamping equipment. Using these devices, an experimental research on the stamping process was carried out and high-quality parts were obtained, which makes it possible to recommend the developed methods of stamping in the industrial production. Their application in small-scale production will allow one to reduce the cost price of stamped parts 2 or 3 times. (paper)

No abstract available

[en] The cylindrical plasma flow caused by dc discharge along a magnetic field is transformed into a sheet plasma flow (13 cm in width, 40 cm in length and about 3 mm in thickness) while electron components (up to 100 A) in the plasma flow are accelerated by a power supply of 80 V to 220 V. In the first experiment, the sheet plasma where an argon ion current density of 19 mA/cm² is extracted is produced under an argon gas pressure of 1.3 x 10^-1 Pa, an electron acceleration voltage V_A=100 V and an electron acceleration current I_A=50 A. In the second experiment, the sheet plasma is produced under an argon pressure of 5.3 Pa, V_A=100 V and I_A=100 A. In the third experiment, the sheet plasma is produced under a hydrogen gas pressure of 52 Pa, V_A=220 V and I_A=100 A. These electron acceleration sheet plasmas are very useful for large-area and high-speed plasma processes. It should be noted that the ordinary vacuum conductance of the electron acceleration anode slit is greatly reduced to 1/8 of the original value when an electron acceleration current of 100 A enters the acceleration anode region through the slit. (author)