Computing automorphisms of abelian number fields

Let be an abelian number field of degree . Most algorithms for computing the lattice of subfields of require the computation of all the conjugates of . This is usually achieved by factoring the minimal polynomial of over . In practice, the existing algorithms for factoring polynomials over algebraic number fields can handle only problems of moderate size. In this paper we describe a fast probabilistic algorithm for computing the conjugates of , which is based on -adic techniques. Given and a rational prime which does not divide the discriminant of , the algorithm computes the Frobenius automorphism of in time polynomial in the size of and in the size of . By repeatedly applying the algorithm to randomly chosen primes it is possible to compute all the conjugates of .

     

Indivisibility of Class Numbers of Real Quadratic Fields

Let D denote the fundamental discriminant of a real quadratic field, and let h(D) denote its associated class number. If p is prime, then the Cohen and Lenstra Heuristics give a probability that ph(D). If pgt;3 is prime, then subject to a mild condition, we show that

Singular cycles of vector fields on regular parts of the boundary of Morse-Smale systems

At the boundary of the class of Morse-Smale vector fields there are vector fields whose unique degenerate phenomena is a singular cycle. We first characterize and classify all singular cycles which contains only one degeneracy (thesimple singular cycles: ssc). Each of these cycles defines a condimension one submanifold of vector fields. For some ssc its codimension one submanifold is a regular part of the boundary of the Morse-Smale systems. We characterize those ssc that defines this type of submanifold. Our ambient space isn dimensional,n2.Supported by Fondecyt, Proyecto 1930863.     

Complex multiplication of exactly solvable Calabi–Yau varieties

We propose a conceptual framework that leads to an abstract characterization for the exact solvability of Calabi–Yau varieties in terms of abelian varieties with complex multiplication. The abelian manifolds are derived from the cohomology of the Calabi–Yau manifold, and the conformal field theoretic quantities of the underlying string emerge from the number theoretic structure induced on the varieties by the complex multiplication symmetry. The geometric structure that provides a conceptual interpretation of the relation between geometry and conformal field theory is discrete, and turns out to be given by the torsion points on the abelian varieties.     

Vergleichbare Kraftfelder vieratomiger Formylverbindungen

Comparable force fields for HCOO^–, HFCO, HClCO and HDCO have been calculated on the basis of internal coordinates. Linear relations between (i) the carbonyl bond order and the carbonyl stretching force constant, (ii) the sum of the three in-plane bending force constants and the hydrogen out-of-plane force constantf , (iii) a combination of orbital electronegativities andf , have been obtained. The observed in-plane vibrational frequencies have been calculated with an average error of 6.3 cm^–1 or 0.4%.

     

The global Markov property for lattice systems

We prove the global Markov property for lattice systems of classical statistical mechanics, with bounded spins and finite range interactions. The method uses the one developed by two of us to prove the global Markov property of Euclidean generalized random fields. The result shows that the systems considered have a transition matrix, which together with a distribution on a hyperplane, describes completely the system.     

Magnetic fields associated with a nuclear magnetic resonance medical imaging system

Measurements were made of magnetic and electric field levels in and around a nuclear magnetic resonance imaging system undergoing a clinical trial. Magnetic field levels ranged from 0.04 tesla (T) in the imaging volume down to about 0.0006 T at the end of the patient table. The peak radio-frequency magnetic field level was 15 amperes per meter (A/m) in the imaging volume, while the rms value was 4.6 A/m. The specific absorption rate resulting from the radio-frequency magnetic field was calculated to be no more than 0.017 watts per kilogram (W/kg). The radio-frequency electric field was detectable only within a few centimeters of the coil assembly, and does not significantly contribute to the specific absorption rate. These exposure levels were much lower than existing guidelines for clinical NMR procedures.     

Hall coefficient in solution for a simple dynamical model

A model Liouville equation is proposed for a system composed of an ion moving in a solvent fluid. Using this model, explicit results are obtained for the Ohmic conductivityL and the Hall conductivityh. These results are then used to calculate the Hall coefficientR = ehL^–2, which is a measure of the effect of non-Brownian motion, for several charge carriers of interest. Our results are in agreement with earlier findings based on a stochastic model which predictR > 1 for H⁺(aq). Our results also indicate thatR 1 for charge carriers such as Na⁺, Cl^–, and K⁺ which have a mass greater than that of a solvent molecule (here taken as 18 amu).This research was supported in part by grants from the National Science Foundation and by the Research Foundation of the State University of New York.     

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.     

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.