Towards understanding astrophysical effects of nuclear symmetry energy

The European Physical Journal A - The properties of the quantum electrodynamic (QED) vacuum in general, and of the nuclear vacuum (ground) state in particular, are determined by virtual processes...     

Enamines of 3-acyltetramic acids from β-enamino amides and amino acids

A novel approach for the synthesis of enamine derivatives of N-protected 3-acyltetramic acids is described. The synthetic procedure relies on α-C-acylation of β-enamino amides with N-protected α-amino acids and subsequent cyclisation of the obtained intermediates in refluxing TFA. The tetramic derivatives are obtained with very good enantiopurity (e.r. ≥95:5). Ring-enlarged analogues (piperidine-2,4-diones) can also be obtained from β-amino acids.     

Ammonia/desorption chemical ionization mass spectrometry of some cyclopentane iridoid glucosides

The ammonia/desorption chemical ionization (DCI) mass spectra of nine cyclopentane iridoid glucosides were measured. The dependences cf the intensities of different peaks on the structures and stereochemistries of the compounds investigated is discussed.     

Finite heat kernel expansions on the real line

Let be the one-dimensional Schrödinger operator and let be the corresponding heat kernel. We prove that the th Hadamard's coefficient is equal to 0 if and only if there exists a differential operator of order such that . Thus, the heat expansion is finite if and only if the potential is a rational solution of the KdV hierarchy decaying at infinity studied by Adler and Moser (1978) and Airault, McKean and Moser (1977). Equivalently, one can characterize the corresponding operators as the rank one bispectral family given by Duistermaat and Grünbaum (1986).

     

Quantitative relations between corruption and economic factors

We report quantitative relations between corruption level and economic factors, such as country wealth and foreign investment per capita, which are characterized by a power law spanning multiple scales of wealth and investment per capita. These relations hold for diverse countries, and also remain stable over different time periods. We also observe a negative correlation between level of corruption and long-term economic growth. We find similar results for two independent indices of corruption, suggesting that the relation between corruption and wealth does not depend on the specific measure of corruption. The functional relations we report have implications when assessing the relative level of corruption for two countries with comparable wealth, and for quantifying the impact of corruption on economic growth and foreign investment.     

Multiplicities of the eigenvalues of periodic Dirac operators

Let us consider the Dirac operator

     

Improvement of some bounds on the stability of fast Helmholtz solvers

Three fast Helmholtz solvers based on the Fast Fourier Transform are studied with respect to their stability. It is proved that they are strongly stable, and that the backward relative errors can grow at most like O(log₂ n)₀, where ₀ is the machine roundoff unit.     

A Basis for the Graded Identities of the Matrix Algebra of Order Two over a Finite Field of Characteristic p≠2

Let K be a finite field of characteristic p>2, and let M₂(K) be the matrix algebra of order two over K. We describe up to a graded isomorphism the 2-gradings of M₂(K). It turns out that there are only two nonisomorphic nontrivial such gradings. Furthermore, we exhibit finite bases of the graded polynomial identities for each one of these two gradings. One can distinguish these two gradings by means of the graded polynomial identities they satisfy.     

On the stability of the cyclic reduction without back substitution for tridiagonal systems

Componentwise error analysis for a modification of the cyclic reduction without back substitution for a tridiagonal system is presented. We consider relative roundoff errors and equivalent perturbations, so the main supposition is that all the data is nonzero. First, backward analysis for the computation of each component of the solution in separate is presented. Bounds on the relative equivalent perturbations are obtained depending on two constants. From these bounds it is easy to obtain a componentwise forward error analysis. Then the two constants are defined for some special classes of matrices, i.e. diagonally dominant (row or column), symmetric positive definite, totally nonnegative andM-matrices, and it is shown that the bounds for these classes of matrices are small.The author was supported by Grants MM-211/92 and MM-434/94 from the National Scientific Research Fund of the Bulgarian Ministry of Education and Science.     

Uniqueness of the multi-dimensional inverse scattering problem for time dependent potentials

Partially supported by Bulgarian Committee of Science, Contract No. 52/1988