Oscillation of linear ordinary differential equations: on a theorem by A. Grigoriev

We give a simplified proof and an improvement of a recent theorem by A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equations with polynomial or rational coefficients.Comment: 16 page

A search for neutrino-antineutrino mass inequality by means of sterile neutrino oscillometry

The investigation of the oscillation pattern induced by the sterile neutrinos might determine the oscillation parameters, and at the same time, allow to probe CPT symmetry in the leptonic sector through neutrino-antineutrino mass inequality. We propose to use a large scintillation detector like JUNO or LENA to detect electron neutrinos and electron antineutrinos from MCi electron capture or beta decay sources. Our calculations indicate that such an experiment is realistic and could be performed in parallel to the current research plans for JUNO and RENO. Requiring at least 5$\sigma$ confidence level and assuming the values of the oscillation parameters indicated by the current global fit, we would be able to detect neutrino-antineutrino mass inequality of the order of 0.5% or larger, which would imply a signal of CPT anomalies.Comment: 14 pages, 10 figure

Gregor Mendel: my time will come

Gregor Mendel and his work have traditionally attracted well-deserved attention of scientific society. The purpose of this article is to study the background and prerequisites of Mendel’s formation as a personality and scientist, the motivation of his scientific interests and discoveries which marked a beginning to the emergency of genetics as a science. Comparative analysis of literature have pointed at the way of his life in childhood, father’s work and mastering fine methods of handling plants as highly motivational factors. Obviously, Mendel’s personality developed due to his natural gift, love of knowledge and passion for studying. He was greatly inspired by studying with the theorist of hybridization and selection Professor Franz Diebel. According to the author, studies at the university of Vienna and in particular Professor Franz Unger, a botanist and cytologist, played a key role in Mendel’s becoming a scientist and developing the idea of hereditary factors (Anlagen) transmitted to the subsequent generation by gametes. The article gives description of Mendel’s experiments and his interpretation of patterns revealed. A conclusion is made that the reproducibility of Mendel’s experiments using different objects and traits, confirms his research objectivity and makes his results invulnerable to criticism. Mechanisms providing realization of numerical patterns discovered by Mendel got clarified after establishing of their complete correspondence with structure and function of heredity system. In conclusion, main achievements of Mendel which formed the basis of genetics and stimulated the development of several branches of general biology are mentioned

Quantum geometrodynamics for black holes and wormholes

The geometrodynamics of the spherical gravity with a selfgravitating thin dust shell as a source is constructed. The shell Hamiltonian constraint is derived and the corresponding Schroedinger equation is obtained. This equation appeared to be a finite differences equation. Its solutions are required to be analytic functions on the relevant Riemannian surface. The method of finding discrete spectra is suggested based on the analytic properties of the solutions. The large black hole approximation is considered and the discrete spectra for bound states of quantum black holes and wormholes are found. They depend on two quantum numbers and are, in fact, quasicontinuous.Comment: Latex, 32 pages, 5 fig

Twist-3 distribution amplitudes of scalar mesons from QCD sum rules

We study the twist-3 distribution amplitudes for scalar mesons made up of two valence quarks based on QCD sum rules. By choosing the proper correlation functions, we derive the moments of the scalar mesons up to the first two order. Making use of these moments, we then calculate the first two Gegenbauer coefficients for twist-3 distribution amplitudes of scalar mesons. It is found that the second Gegenbauer coefficients of scalar density twist-3 distribution amplitudes for $K^{*}_0$ and $f_0$ mesons are quite close to that for $a_0$, which indicates that the SU(3) symmetry breaking effect is tiny here. However, this effect could not be neglected for the forth Gegenbauer coefficients of scalar twist-3 distribution amplitudes between $a_0$ and $f_0$. Besides, we also observe that the first two Gegenbauer coefficients corresponding to the tensor current twist-3 distribution amplitudes for all the $a_0$, $K^{*}_0$ and $f_0$ are very small. The renormalization group evolution of condensates, quark masses, decay constants and moments are considered in our calculations. As a byproduct, it is found that the masses for isospin I=1, ${1 \over 2}$ scalar mesons are around $1.27 \sim 1.41$ GeV and $1.44 \sim 1.56$ GeV respectively, while the mass for isospin state composed of $\bar{s} s$ is $1.62 \sim 1.73$ GeV.Comment: replaced with revised version, to be published in Phys. Rev.

Explicitly solvable cases of one-dimensional quantum chaos

We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are explicitly solvable. The proof is constructive: we present exact periodic orbit expansions for individual energy levels, thus obtaining an analytical solution for the spectrum of regular quantum graphs that is complete, explicit and exact

Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

For the Schrodinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Novikov, Multidimensional inverse spectral problem for the equation -\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22, (1988)]

New Spin-Two Gauged Sigma Models and General Conformal Field Theory

Recently, we have studied the general Virasoro construction at one loop in the background of the general non-linear sigma model. Here, we find the action formulation of these new conformal field theories when the background sigma model is itself conformal. In this case, the new conformal field theories are described by a large class of new spin-two gauged sigma models. As examples of the new actions, we discuss the spin-two gauged WZW actions, which describe the conformal field theories of the generic affine-Virasoro construction, and the spin-two gauged g/h coset constructions. We are able to identify the latter as the actions of the local Lie h-invariant conformal field theories, a large class of generically irrational conformal field theories with a local gauge symmetry.Comment: LaTeX, 28 pages, references and clarifying remarks adde