Certain homotopy properties related to map(ΣnCP2,Sm)\text{map}(\Sigma^n \mathbb{C} P^2,S^m)

For given spaces $X$ and $Y$, let $map(X,Y)$ and $map_\ast(X,Y)$ be the unbased and based mapping spaces from $X$ to $Y$, equipped with compact-open topology respectively. Then let $map(X,Y;f)$ and $map_\ast(X,Y;g)$ be the path component of $map(X,Y)$ containing $f$ and $map_\ast(X,Y)$ containing $g$, respectively. In this paper, we compute cohomotopy groups of suspended complex plane $\pi^{n+m}(\Sigma^n \mathbb{C} P^2)$ for $m=6,7$. Using these results, we classify path components of the spaces $map(\Sigma^n \mathbb{C} P^2,S^m)$ up to homotopy equivalent. We also determine the generalized Gottlieb groups $G_n(\mathbb{C} P^2,S^m)$. Finally, we compute homotopy groups of mapping spaces $map(\Sigma^n \mathbb{C}P^2,S^m;f)$ for all generators $[f]$ of $[\Sigma^n \mathbb{C} P^2,S^m]$, and Gottlieb groups of mapping components containing constant map $map(\Sigma^n \mathbb{C} P^2,S^m;0)$

Understanding the Complex Position in a PT-symmetric Oscillator

We study how to understand the complex coordinates involved in the non-Hermitian but PT-symmetric systems. We explore a PT-symmetric oscillator model to show that the entire information on the complex position is attainable. Its real part is from the observation while its imaginary part is from the non-Hermiticity parameter. We also propose a new complex extension of P-transformation and T-transformation (the `parity' and `time reflection' respectively). Particularly, the P-transformation realizes the left-right reflection in the complex plane.Comment: 4 pages with 1 figure, uses revtex4-1.cl

AdS_3 Black Hole Entropy and the Spectral Flow on the Horizon

We consider the entropy problem of AdS_3 black holes using the conformal field theory at the horizon. We observe that the supersymmetry is enhanced at the horizon of massless AdS_3 black hole. This allows us to determine the vacuum of the modular invariant conformal field theory to be the NS-ground state (which corresponds to AdS_3 spacetime). This is smoothly related to the R-ground state (corresponding to massless black hole) by a spectral flow, which can be understood as a superconformal transformation.Comment: 14 pages using REVTeX macr

Beam dynamics at the main LEBT of RAON accelerator

The high-intensity rare-isotope accelerator (RAON) of the Rare Isotope Science Project (RISP) in Daejeon, Korea, has been designed to accelerate multiple-charge-state beams. The ion beams, which are generated by Electron Cyclotron Resonance Ion Source (ECR-IS), will be transported through the main Low Energy Beam Transport (LEBT) system to the Radio Frequency Quadrupole (RFQ). While passing the beams through LEBT, we should keep the transverse beam size and longitudinal emittance small. Furthermore, the matching of required twiss parameter at the RFQ entrance will be performed by using electro-static quadrupoles at the main LEBT matching section which is from the multi-harmonic buncher (MHB) to the entrance of RFQ. We will briefly review the new aspects of main LEBT lattice and the beam matching at the main LEBT matching section will be presented. In addition, the effects of various errors on the beam orbit and the correction of distorted orbit will be discussed

Mutation invariance of the arc index for some Montesinos knots

For the alternating knots or links, mutations do not change the arc index. In the case of nonalternating knots, some semi-alternating knots or links have this property. We mainly focus on the problem of mutation invariance of the arc index for nonalternating knots which are not semi-alternating. In this paper, we found families of infinitely many mutant pairs/triples of Montesinos knots with the same arc index.Comment: 19 pages, 24 figures, 1 tabl

Rotating Supertubes

We study the rotating tubular D2-brane as a time dependent supersymmetric solution of type-IIA string theory. We show that the Poynting angular momentum of the supertube can be replaced by the mechanical angular momentum without disturbing the 8 supersymmetries. Unlike the non-rotating supertube, whose cross section can take an arbitrary shape, the rotating supertube admits only the circular cross section. When there is no electric field on the world volume, the supersymmetry dictates the angular velocity of the tubular D2-brane to be inversely proportional to the magnetic field. This rotating supertube can be considered as the `blown-up' configuration of an array of spinning D0-particles and is T-dual to the spiraling D-helix whose pitch moves at the speed of light.Comment: V2. added one more figure, comments on the reparametrization symmetry, and a referenc

Lifting graph automorphisms along solvable regular covers

A {\em solvable} cover of a graph is a regular cover whose covering transformation group is solvable. In this paper, we show that a solvable cover of a graph can be decomposed into layers of abelian covers, and also, a lift of a given automorphism of the base graph of a solvable cover can be decomposed into layers of lifts of the automorphism in the layers of the abelian covers. This procedure is applied to classify metacyclic covers of the tetrahedron branched at face-centers.Comment: 23 pages, 1 figure

Living Near de Sitter Bubble Walls

We study various bubble solutions in string/M theories obtained by double Wick rotations of (non-)extremal brane configurations. Typically, the geometry interpolates de Sitter space-time times non-compact extra-dimensional space in the near-bubble wall region and the asymptotic flat Minkowski space-time. These bubble solutions provide nice background geometries reconciling string/M theories with de Sitter space-time. For the application of these solutions to cosmology, we consider multi-bubble solutions and find landscapes of varying cosmological constant. Double Wick rotation in string/M theories, used in this paper, introduces imaginary higher-form fields. Rather than regard these fields as classical pathologies, we interpret them as semi-classical decay processes of de Sitter vacuum via the production of spherical branes. We speculate on the possibility of solving the cosmological constant problem making use of the condensation of the spherical membranes.Comment: 51 pages, 8 figures, additional sections on the ghosts and on the wave function of the Univese, and additonal reference

Certain maps preserving self-homotopy equivalences

Let $\mathcal{E}(X)$ be the group of homotopy classes of self homotopy equivalences for a connected CW complex $X$. We observe two classes of maps $\mathcal{E}$-maps and co-$\mathcal{E}$-maps. They are defined as the maps $X\to Y$ that induce the homomorphisms $\mathcal{E}(X)\to \mathcal{E}( Y)$ and $\mathcal{E}(Y)\to \mathcal{E}(X)$, respectively. We give some rationalized examples related to spheres, Lie groups and homogeneous spaces by using Sullivan models. Furthermore, we introduce an $\mathcal{E}$-equivalence relation between rationalized spaces $X_{\mathbb{Q}}$ and $Y_{\mathbb{Q}}$ as a geometric realization of an isomorphism $\mathcal{E}(X_{\mathbb{Q}})\cong \mathcal{E}(Y_{\mathbb{Q}})$

Start-to-end simulation with rare isotope beam for post accelerator of the RAON accelerator

The RAON accelerator of the Rare Isotope Science Project (RISP) has been developed to create and accelerate various kinds of stable heavy ion beams and rare isotope beams for a wide range of the science applications. In the RAON accelerator, the rare isotope beams generated by the Isotope Separation On-Line (ISOL) system will be transported through the post accelerator, namely, from the post Low Energy Beam Transport (LEBT) system and the post Radio Frequency Quadrupole (RFQ) to the superconducting linac (SCL3). The accelerated beams will be put to use in the low energy experimental hall or accelerated again by the superconducting linac (SCL2) in order to be used in the high energy experimental hall. In this paper, we will describe the results of the start-to-end simulations with the rare isotope beams generated by the ISOL system in the post accelerator of the RAON accelerator. In addition, the error analysis and correction at the superconducting linac SCL3 will be presented