Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms

Let $l$ and $m$ be two integers with $l>m\ge 0$, and let $a$ and $b$ be integers with $a\ge 1$ and $a+b\ge 1$. In this paper, we prove that $\log {\rm lcm}_{mn<i\le ln}\{ai+b\} =An+o(n)$, where $A$ is a constant depending on $l, m$ and $a$.Comment: 8 pages. To appear in Archiv der Mathemati

Electro-optic scanning of light coupled from a corrugated LiNbO3 waveguide

Light diffracted from a grating output coupler in a Ti-diffused LiNbO3 waveguide is scanned electro-optically. Using a coupling length of 2.5 mm in our arrangement we have demonstrated a scanning capability of one resolved spot per 3 V/µm applied field

The least common multiple of a sequence of products of linear polynomials

Let $f(x)$ be the product of several linear polynomials with integer coefficients. In this paper, we obtain the estimate: $\log {\rm lcm}(f(1), ..., f(n))\sim An$ as $n\rightarrow\infty$, where $A$ is a constant depending on $f$.Comment: To appear in Acta Mathematica Hungaric

The GEMS Approach to Stationary Motions in the Spherically Symmetric Spacetimes

We generalize the work of Deser and Levin on the unified description of Hawking radiation and Unruh effect to general stationary motions in spherically symmetric black holes. We have also matched the chemical potential term of the thermal spectrum of the two sides for uncharged black holes.Comment: Latex file, 12 pages, no figure; v2: typos fixed; v3: minor corrections, final version published in JHE

Extended Optical Model Analyses of Elastic Scattering and Fusion Cross Section Data for the 12^{12}C+208^{208}Pb System at Near-Coulomb-Barrier Energies by using a Folding Potential

Simultaneous $\chi^{2}$ analyses are performed for elastic scattering and fusion cross section data for the $^{12}$C+$^{208}$Pb system at near-Coulomb-barrier energies by using the extended optical model approach in which the polarization potential is decomposed into direct reaction (DR) and fusion parts. Use is made of the double folding potential as a bare potential. It is found that the experimental elastic scattering and fusion data are well reproduced without introducing any normalization factor for the double folding potential and also that both DR and fusion parts of the polarization potential determined from the $\chi^{2}$ analyses satisfy separately the dispersion relation. Furthermore, it is shown that the imaginary parts of both DR and fusion potentials at the strong absorption radius change very rapidly, which results in a typical threshold anomaly in the total imaginary potential as observed with tightly bound projectiles such as $\alpha$-particle and $^{16}$O.Comment: 26 pages, 7 figures, submitted to Physical Review

Flavor symmetry breaking effects on SU(3) Skyrmion

We study the massive SU(3) Skyrmion model to investigate the flavor symmetry breaking (FSB) effects on the static properties of the strange baryons in the framework of the rigid rotator quantization scheme combined with the improved Dirac quantization one. Both the chiral symmetry breaking pion mass and FSB kinetic terms are shown to improve $c$ the ratio of the strange-light to light-light interaction strengths and $\bar{c}$ that of the strange-strange to light-light.Comment: 12 pages, latex, no figure

Spinning String and Giant Graviton in Electric/Magnetic Field Deformed AdS3×S3×T4AdS_3 \times S^3 \times T^4

We apply the transformation of mixing azimuthal and internal coordinate or mixing time and internal coordinate to the 11D M-theory with a stack of M2-branes $\bot$ M2-branes, then, through the mechanism of Kaluza-Klein reduction and a series of the T duality we obtain the corresponding background of a stack of D1-branes $\bot$ D5-branes which, in the near-horizon limit, becomes the magnetic or electric Melvin field deformed $AdS_3 \times S^3 \times T^4$. We find the giant graviton solution in the deformed spacetime and see that the configuration whose angular momentum is within a finite region could has a fixed size and become more stable than the point-like graviton, in contrast to the undeformed giant graviton which only exists when its angular momentum is a specific value and could have arbitrary size. We discuss in detail the properties of how the electric/magnetic Melvin field will affect the size of the giant gravitons. We also adopt an ansatz to find the classical string solutions which are rotating in the deformed $S^3$ with an angular momentum in the rotation plane. The spinning string and giant graviton solutions we obtained show that the external magnetic/electric flux will increase the solution energy. Therefore, from the AdS/CFT point of view, the corrections of the anomalous dimensions of operators in the dual field theory will be positive. Finally, we also see that the spinning string and giant graviton in the near-horizon spacetime of Melvin field deformed D5-branes background have the similar properties as those in the deformed $AdS_3 \times S^3 \times T^4$.Comment: Latex 21 pages, slightly detail calculation

Extended Optical Model Analyses of Elastic Scattering and Fusion Cross Section Data for the 7Li+208Pb System at Near-Coulomb-Barrier Energies using the Folding Potential

Simultaneous $\chi^{2}$ analyses previously made for elastic scattering and fusion cross section data for the $^{6}$Li+$^{208}$Pb system is extended to the $^{7}$Li+$^{208}$Pb system at near-Coulomb-barrier energies based on the extended optical model approach, in which the polarization potential is decomposed into direct reaction (DR) and fusion parts. Use is made of the double folding potential as a bare potential. It is found that the experimental elastic scattering and fusion data are well reproduced without introducing any normalization factor for the double folding potential and that both the DR and fusion parts of the polarization potential determined from the $\chi^{2}$ analyses satisfy separately the dispersion relation. Further, we find that the real part of the fusion portion of the polarization potential is attractive while that of the DR part is repulsive except at energies far below the Coulomb barrier energy. A comparison is made of the present results with those obtained from the Continuum Discretized Coupled Channel (CDCC) calculations and a previous study based on the conventional optical model with a double folding potential. We also compare the present results for the $^7$Li+$^{208}$Pb system with the analysis previously made for the $^{6}$Li+$^{208}$Pb system.Comment: 7 figures, submitted to PR

Relations between Neutrino and Charged Fermion Masses

We find an intriguing relation between neutrino and charged fermion masses, $|m_{\nu_3^{}}^2- m_{\nu_1^{}}^2| : (m_{\nu_2^{}}^2- m_{\nu_1^{}}^2):: V_{tb}^4 m_\tau^2 m_b^2/m_t^2 : V_{cs}^4 m_\mu^2 m_s^2/m_c^2$. We further indicate this relation can be predicted by a left-right symmetric model.Comment: 4 pages, 1 figure. Model is slightly corrected. Title is changed. Journal versio