Integration of differential forms on manifolds with locally-finite variations. II

In part I of the paper, we have defined n-dimensional C⁰-manifolds in ℝⁿ(m ≥ n) with locally-finite n-dimensional variations (a generalization of locally-rectifiable curves to dimensionn > 1) and integration of measurable differential n-forms over such manifolds. The main result of part II states that an n-dimensional manifold that is C¹-embedded into ℝ^m has locally-finite variations and the integral of a measurable differential n-form defined in part I can be calculated by the well-known formula. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 66–85.     

On the instability of parallel weakly interacting dislocations in soft-mode crystals

The instability of the rectilinear form of parallel weakly interacting dislocations, manifesting itself in their spontaneous wave-like bending, has been investigated. It is shown that softening of a crystal leads to the enhancement of this instability.     

Magnetic calorimeter for registration of small energy release

A scheme of magnetic calorimeter for registration of rare events characterized by small energy release (cosmic rays, WIMPs, solitary X-ray quanta) is proposed. The calorimeter is brought to operation by adiabatic demagnetization, and its magnetic response is measured by a quantum interferometer (SQUID, A. Barone and G. Paterno, Physics and applications of Josephson Effect). Special consideration is given to the specific features of calorimeter operation in the ferromagnetic transition region. The trigger registration of ultrasmall energy release by a ferromagnetic system in the metastable state is described.     

Evidence for the short-period oscillations in spin-resolved photoemission of thin Cr(110) films

The spin-resolved electronic structure of thin Cr overlayers on top of the Fe(110) surface was investigated by means of spin- and angle-resolved photoelectron spectroscopy. The initial fast drop of photoelectron spin-polarization at the Fermi level, followed by weak oscillatory behavior with the period of about 2 ML, can give an evidence for the first time spectroscopic observation of the short period oscillations in (110)-oriented thin Cr films.     

The (1+1) Dimensional Dirac Equation With Pseudoscalar Potentials: Path Integral Treatment

The supersymetric path integrals in solving the problem of relativistic spinning particle interacting with pseudoscalar potentials is examined. The relative propagator is presented by means of path integral, where the spin degrees of freedom are described by odd Grassmannian variables and the gauge invariant part of the effective action has a form similar to the standard pseudoclassical action given by Berezin and Marinov. After integrating over fermionic variables (Grassmannian variables), the problem is reduced to a nonrelativistic one with an effective supersymetric potential. Some explicit examples are considered, where we have extracted the energy spectrum of the electron and the wave functions. PACS numbers: 03.65. Ca-Formalism, 03.65. Db-Functional analytical methods, 03.65. Pm-Relativistic wave equations.     

Preparation and crystal structure of Na3SbO(PO4)2

The single phase compound Na₃SbO(PO₄)₂ was prepared by a solid state reaction. It crystallizes in the orthorhombic system, space group P2₁2₁2₁ with a = 6.964(1) Å, b = 9.284(2) Å, c = 12.425(2) Å, Z = 4. The structure was determined from 968 reflections collected on a Nonius CAD4 automatic diffractometer with MoKα radiation. The final R index and weighted R_w index are 0.031 and 0.039, respectively. The structure is built up from strings of corner-sharing SbO₆ octahedra to which phosphate groups are linked by two of their vertices. These chains, running parallel to the a-axis, are separated from each other by sodium atoms.     

AdS/CFT duality at strong coupling

We study the strong-coupling limit of the AdS/CFT correspondence in the framework of a recently proposed fermionic formulation of the Bethe ansatz equations governing the gauge theory anomalous dimensions. We give examples of states that do not follow the Gubser-Klebanov-Polyakov law at a large ’t Hooft coupling λ, in contrast to recent results on the quantum string Bethe equations that are valid in that regime. This result indicates that the fermionic construction cannot be trusted at large λ, although it remains an efficient tool for computing the weak-coupling expansion of anomalous dimensions. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 213–224, August, 2007.