A generalization of a 4-dimensional Einstein manifold

A weakly Einstein manifold is a generalization of a 4-dimensional Einstein manifold, which is defined as an application of a curvature identity derived from the generalized Gauss-Bonnet formula for a 4-dimensional compact oriented Riemannian manifold. In this paper, we shall give a characterization of a weakly Einstein manifold.Comment: 16 page

A Curvature identity on a 4-dimensional Riemannian manifold

We give a curvature identity derived from the generalized Gauss-Bonnet formula for 4-dimensional compact oriented Riemannian manifolds. We prove that the curvature identity holds on any 4-dimensional Riemannian manifold which is not necessarily compact. We also provide some applications of the identity.Comment: 10 page

Spectrophotometric Dating of Elliptical Galaxies in the Ultraviolet

The UV upturn phenomenon observed in elliptical galaxies is attractive for its potential value as an age indicator of old stellar systems. We present our most recent population models for the UV evolution of elliptical galaxies. We confirm that the dominant UV sources are either metal-poor or metal-rich hot horizontal-branch (HB) stars in local giant ellipticals, but we also note that the contribution from post-asymptotic-giant-branch (PAGB) stars overwhelms the UV spectrum at higher redshifts (look-back times). The model UV spectral energy distribution (SED) is therefore strongly affected by the current uncertainty of the mean mass of PAGB stars at higher redshifts. Fortunately, our models suggest that the far-UV observations at z > 0.35 could produce strong constraint on the PAGB mass, while observations at could produce strong constraint on the PAGB mass, while observations at lower redshifts (0.15 < z < 0.30) would still provide constraints on the models on the origin of the UV upturn. Future observations of ellipticals from the STIS/HST and planned GALEX space UV facility will provide crucial database required for more concrete calibration of our UV dating techniques for old stellar systems.Comment: 4 pages, 2 figures, LaTex ps files, in Spectro-Photometric Dating of Stars & Galaxies, in pres

Finiteness of the total first curvature of a non-closed curve in En\mathbb{E}^{n}

We consider a regular smooth curve in $\mathbb{E}^n$ such that its coordinates' components are the fundamental solutions of the differential equation $y^{(n)} (x) - y(x) = 0 ,$ $x \in \mathbb{R}$ of order $n$. We show that the total first curvature of this curve is infinite for odd $n$ and is finite for even $n$.Comment: 22 page

Nanoscale Topographical Replication of Graphene Architecture by Artificial DNA nanostructures

Despite many studies on how geometry can be used to control the electronic properties of graphene, certain limitations to fabrication of designed graphene nanostructures exist. Here, we demonstrate controlled topographical replication of graphene by artificial deoxyribonucleic acid (DNA) nanostructures. Owing to the high degree of geometrical freedom of DNA nanostructures, we controlled the nanoscale topography of graphene. The topography of graphene replicated from DNA nanostructures showed enhanced thermal stability and revealed an interesting negative temperature coefficient of sheet resistivity when underlying DNA nanostructures were denatured at high temperatures.Comment: 12 pages, 3 figure

Transplanting geometrical structures

We say that a germ G of a geometric structure can be transplanted into a manifold M if there is a suitable geometric structure on M which agrees with G on a neighborhood of some point P of M. We show for a wide variety of geometric structures that this transplantation is always possible provided that M does in fact admit some such structure of this type. We use this result to show that a curvature identity which holds in the category of compact manifolds admitting such a structure holds for germs as well and we present examples illustrating this result. We also use this result to show geometrical realization problems which can be solved for germs of structures can in fact be solved in the compact setting as well

Strong ferromagnetic-dielectric coupling in multiferroic Lu2CoMnO6 single crystals

We have grown single crystals of multiferroic double-perovskite Lu2CoMnO6 and studied the directional dependence of their magnetic and dielectric properties. The ferromagnetic order emerges below TC ~ 48K along the crystallographic c axis. Dielectric anomaly arises along the b axis at TC, contrary to the polycrystalline work suggesting ferroelectricity along the c axis. Through the strongly coupled ferromagnetic and dielectric states, the highly non-linear variation of both dielectric constant and magnetization was achieved in application of magnetic fields. This concurrent tunability provides an efficient route to manipulation of multiple order parameters in multiferroics

Measurement of low-energy background events due to 222^{222}Rn contamination on the surface of a NaI(Tl) crystal

It has been known that decays of daughter elements of $^{222}$Rn on the surface of a detector cause significant background at energies below 10 keV. In particular $^{210}$Pb and $^{210}$Po decays on the crystal surface result in significant background for dark matter search experiments with NaI(Tl) crystals. In this report, measurement of $^{210}$Pb and $^{210}$Po decays on surfaces are obtained by using a $^{222}$Rn contaminated crystal. Alpha decay events of $^{210}$Po on the surface are measured by coincidence requirements of two attached crystals. Due to recoiling of $^{206}$Pb, rapid nuclear recoil events are observed. A mean time characterization demonstrates that $^{206}$Pb recoil events can be statistically separated from those of sodium or iodine nuclear recoil events, as well as electron recoil events.Comment: 6 pages, 8 figure

Study of Solar Active Regions Based on BOAO Vector Magnetograms

In this study we present the study of solar active regions based on BOAO vector magnetograms and $H\alpha$ filtergrams. With the new calibration method we analyzed BOAO vector magnetograms taken from the SOFT observational system to compare with those of other observing systems. In this study it has been demonstrated that (1) our longitudinal magnetogram matches very well the corresponding Mitaka's magnetogram to the extent that the maximum correlation yields r=0.962 between our re-scaled longitudinal magnetogram and the Mitaka's magnetogram; (2) according to a comparison of our magnetograms of AR 8422 with those taken at Mitaka solar observatory their longitudinal fields are very similar to each other while transverse fields are a little different possibly due to large noise level; (3) main features seen by our longitudinal magnetograms of AR 8422 and AR 8419 and the corresponding Kitt Peak magnetograms are very similar to each other; (4) time series of our vector magnetograms and H-alpha observations of AR 8419 during its flaring (M3.1/1B) activity show that the filament eruption followed the sheared inversion line of the quadrupolar configuration of sunspots, indicating that the flare should be associated with the quadrupolar field configuration and its interaction with new filament eruption. Finally, it may be concluded that the Solar Flare Telescope at BOAO works normally and it is ready to do numerous observational and theoretical works associated with solar activities such as flares.Comment: 8 pages, 8 figures, uses jkas99.sty, submitted to JKA

Four-dimensional almost Hermitian manifolds with vanishing Tricerri-Vanhecke Bochner curvature tensor

We study curvature properties of four-dimensional almost Hermitian manifolds with vanishing Bochner curvature tensor as defined by Tricerri and Vanhecke. We give local structure theorems for such Kaehler manifolds, and find out several examples related to the theorems.Comment: 16 page