Extended structures and new infinite-dimensional hidden symmetries for the Einstein–Maxwell-dilaton-axion theory with multiple vector fields

A so-called extended elliptical-complex (EEC) function method is proposed and used to further study the Einstein–Maxwell-dilaton-axion theory with p vector fields (EMDA-p theory, for brevity) for . An Ernst-like matrix EEC potential is introduced and the motion equations of the stationary axisymmetric EMDA-p theory are written as a so-called Hauser–Ernst-like self-dual relation for the EEC matrix potential. In particular, for the EMDA-2 theory, two Hauser–Ernst-type EEC linear systems are established and based on their solutions some new parametrized symmetry transformations are explicitly constructed. These hidden symmetries are verified to constitute an infinite-dimensional Lie algebra, which is the semidirect product of the Kac–Moody algebra and Virasoro algebra (without centre charges). These results show that the studied EMDA-p theories possess very rich symmetry structures and the EEC function method is necessary and effective.     

On isogeny graphs of supersingular elliptic curves over finite fields

We study the isogeny graphs of supersingular elliptic curves over finite fields, with an emphasis on the vertices corresponding to elliptic curves of j-invariant 0 and 1728.     

Magneto-bound polaron in CdSe spherical quantum dots: strong coupling approach

The effect of a magnetic field on the ground-state energy of a donor impurity confined in a polar CdSe spherical quantum dot embedded in a nonpolar matrix is studied theoretically. The interaction between the all charge carriers (electron and ion) and the confined longitudinal optical phonons (LO-phonons) is taken into account by considering the strong coupling method (Landau–Pekar approach). A variational calculation is performed in the framework of the effective mass approximation using a trial wave function deduced from the second-order perturbation and assuming that the quantum dot has a finite depth potential.     

Deformation measurements using mutual information: principle and applications

The paper presents a new method applied to measure displacement fields using mutual information concept. Based on analysis of digital image sequences, we propose the formulation derived from the mutual information between subsets in the un-deformed and deformed image. The quantity of the mutual information between two subsets establishes a criterion of their mutual dependence based on the notion of information connection between them. We can obtain the integer pixel displacement for the corresponding subset. And the accurate displacement field is obtained by using sub-pixel technique. In the experiments, the method is validated and the resulting solution can show accuracy to 0.02 pixels. This method was also applied successfully to determine the displacement fields of laminated composites of AS4/PEEK[0/±45/90]_7s under uniaxial compression.     

Optically detected nuclear magnetic resonance at the sub-micron scale

Nuclear magnetic resonance is arguably one of the most powerful techniques available today to characterize diverse systems. However, the low sensitivity of the standard detection method constrains the applicability of this technique to samples having effective dimensions not less than a few microns. Here, we propose a novel scheme and device for the indirect detection of the nuclear spin signal at a submicroscopic scale. This approach--for which the name Dipolar Field Microscopy is suggested--is based on the manipulation of the long-range nuclear dipolar interaction created between the sample and a semiconductor tip located close to its surface. After a preparation interval, the local magnetization of the sample is used to modulate the nuclear magnetization in the semiconductor tip, which, in turn is determined by an optical inspection. Based on results previously reported, it is shown that, in principle, images and/or localized high-resolution spectra of the sample can be retrieved with spatial resolution proportional to the size of the tip.     

The Difference Between the Standard and The Lorentz Transformations of the Electric and the Magnetic Fields

In this paper it is shown by using the Clifford algebra formalism that the usual Lorentz transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B (which will be named as standard transformations (ST)) are different than the Lorentz transformations (LT) of well-defined quantities from the 4D spacetime. This difference between the ST and the LT is obtained regardless of the used algebraic objects (1-vectors or bivectors) for the representation of the electric and magnetic fields in the usual observer dependent decompositions of F. The LT correctly transform the whole 4D quantity, e.g., E_f : F · γ₀, whereas the ST are the result of the application of the LT only to the part of E_f, i.e., to F, but leaving γ₀ unchanged. The new decompositions of F in terms of 4D quantities that are defined without reference frames, i.e., the absolute quantities, are introduced and discussed. It is shown that the LT of the 4D quantities representing electric and magnetic fields correctly describe the motional electromotive force (emf) for all relatively moving inertial observers, whereas it is not the case with the ST of the 3D E and B.     

Crystal field in RPdIn (R=Ce, Pr, Nd) compounds

The RPdIn compounds (R = rare earth) crystallise in the hexagonal ZrNiAl-type crystal structure. The compounds from this family exhibit a great variety of interesting magnetic properties including heavy fermion behaviour. In order to get a deeper insight into nature of magnetism of RPdIn with light rare earths elements (La–Nd) an inelastic neutron scattering experiment was performed. For compounds with Pr and Nd excitations due to crystal field were clearly distinguished. On the other hand, interesting behaviour for the CePdIn sample was observed. The sample exhibits no signs of crystal field excitations, likely due to highly delocalised Ce 4f states leading to its heavy fermion behaviour.     

Shape-dependent local internal stress of α-Cr2O3 nanocrystal fabricated by pulsed laser ablation

The α-Cr₂O₃ single-crystal nanocondensates were fabricated by pulsed laser ablation in air and characterized by analytical electron microscopy regarding shape-dependent local internal stress of the anisotropic crystal. The nanocondensates formed predominantly as rhombohedra with well-developed surfaces and occasionally hexagonal plate with thin edges and blunt corners. Such nanocondensates showed Raman shift for the CrO₆ polyhedra, indicating a local compressive stress up to ca. 4 GPa on the average. Careful analysis of the lattice fringes revealed a local compressive stress (0.5% strain) at the thin edge of the hexagonal plates and a local tensile stress (0.3–1.0% strain) near the relaxed , , and (0 0 0 1) surfaces of truncated rhombohedra. The combined effects of nanosize, capillarity force at sharp edge, and specific surface relaxation account for the retention of a local internal compressive stress built up in an anisotropic crystal during a very rapid heating–cooling process.     

Montgomery Multiplication in GF(2k)

We show that the multiplication operation c=a · b · r^-1 in the field GF(2^k can be implemented significantly faster in software than the standard multiplication, where r is a special fixed element of the field. This operation is the finite field analogue of the Montgomery multiplication for modular multiplication of integers. We give the bit-level and word-level algorithms for computing the product, perform a thorough performance analysis, and compare the algorithm to the standard multiplication algorithm in GF(2^k. The Montgomery multiplication can be used to obtain fast software implementations of the discrete exponentiation operation, and is particularly suitable for cryptographic applications where k is large.     

A nullstellensatz and a positivstellensatz for ordered differential fields

We use the model completeness and axiomatisation of the theory of closed ordered differential fields to give a differential version of Dubois, Krivine and Risler's nullstellensatz and Stengle's positivstellensatz for ordered fields.