On the strategic choice of spatial price policy: the role of the pricing game rules.

The strategic choice of spatial price policy under duopoly crucially depends on the rules of price competition. We show that under simultaneous price competition and under leader-follower price competition (with the discriminatory firm being the leader), the pricing policy game is not, as stated by Thisse and Vives (1988), a Prisoner's Dilemma.

Numerical experiments of adjusted BSSN systems for controlling constraint violations

We present our numerical comparisons between the BSSN formulation widely used in numerical relativity today and its adjusted versions using constraints. We performed three testbeds: gauge-wave, linear wave, and Gowdy-wave tests, proposed by the Mexico workshop on the formulation problem of the Einstein equations. We tried three kinds of adjustments, which were previously proposed from the analysis of the constraint propagation equations, and investigated how they improve the accuracy and stability of evolutions. We observed that the signature of the proposed Lagrange multipliers are always right and the adjustments improve the convergence and stability of the simulations. When the original BSSN system already shows satisfactory good evolutions (e.g., linear wave test), the adjusted versions also coincide with those evolutions; while in some cases (e.g., gauge-wave or Gowdy-wave tests) the simulations using the adjusted systems last 10 times as long as those using the original BSSN equations. Our demonstrations imply a potential to construct a robust evolution system against constraint violations even in highly dynamical situations.Comment: to be published in PR

GLOBAL SOLUTIONS FOR ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered

Detecting local establishment strategies of wild cherry (Prunus avium L.)

BACKROUND: P. avium, a pioneer tree species that colonizes early forest successional stages, is assumed to require an effective strategy allowing stably repeatable rounds of local establishment, dispersal and local extinction. Consequently, the early replacement of cherry by climax tree species makes the establishment of several local generations very unlikely, especially in central European continuous cover forests. This has to be seen in connection with the mixed reproduction system involving asexual reproduction as a complementary adaptational strategy. Tests of the local establishment of wild cherry must therefore consider the possibility of first generation establishment via seedling recruitment potentially followed by an asexual generation (root suckering). Successful establishment can therefore be determined only among adult individuals with the option of detecting vegetative reproduction at these stages. To test the implied suggestion about local establishment strategies of wild cherry, nuclear microsatellites were used to analyse patterns of asexual propagation among adult stages that have been subjected to one of two major types of forest management. These management types, the historical "coppice with standards system" (CWS) and the "high forest system" (HFS), can be reasonably assumed to have affected the reproduction system of P. avium. RESULTS: Clear differences were found in the reproduction pattern between two stands representing the two forest management types: 1) Clonal propagation is observed in both management systems, but with a distinctly higher frequency in the CWS. Hence, sexual recruitment as a first local generation is followed by a second asexual generation in both, whereas in the CWS there is evidence for an additional clonal generation. 2) The estimation of amounts of clonal reproduction critically depends on the assumptions about multilocus gene associations. This is revealed by the application of newly developed methods of quantifying gene associations. 3) Haplotype diversities are higher in the CWS and found to be associated with a large degree of heterozygosity for the second largest clonal group. 4) Seed set was sparse over the last eight years of observation in the CWS stand. CONCLUSION: This study provides useful guidelines for more comprehensive investigations, particularly on the interrelationships between degrees of cloning and capacity of sexual reproduction, amounts of multilocus gene associations, effects of heterozygosity on cloning success, and sustainability of different forest management types

Constructing hyperbolic systems in the Ashtekar formulation of general relativity

Hyperbolic formulations of the equations of motion are essential technique for proving the well-posedness of the Cauchy problem of a system, and are also helpful for implementing stable long time evolution in numerical applications. We, here, present three kinds of hyperbolic systems in the Ashtekar formulation of general relativity for Lorentzian vacuum spacetime. We exhibit several (I) weakly hyperbolic, (II) diagonalizable hyperbolic, and (III) symmetric hyperbolic systems, with each their eigenvalues. We demonstrate that Ashtekar's original equations form a weakly hyperbolic system. We discuss how gauge conditions and reality conditions are constrained during each step toward constructing a symmetric hyperbolic system.Comment: 15 pages, RevTeX, minor changes in Introduction. published as Int. J. Mod. Phys. D 9 (2000) 1

Electronic Structures of N-doped Graphene with Native Point Defects

Nitrogen doping in graphene has important implications in graphene-based devices and catalysts. We have performed the density functional theory calculations to study the electronic structures of N-doped graphene with vacancies and Stone-Wales defect. Our results show that monovacancies in graphene act as hole dopants and that two substitutional N dopants are needed to compensate for the hole introduced by a monovacancy. On the other hand, divacancy does not produce any free carriers. Interestingly, a single N dopant at divacancy acts as an acceptor rather than a donor. The interference between native point defect and N dopant strongly modifies the role of N doping regarding the free carrier production in the bulk pi bands. For some of the defects and N dopant-defect complexes, localized defect pi states are partially occupied. Discussion on the possibility of spin polarization in such cases is given. We also present qualitative arguments on the electronic structures based on the local bond picture. We have analyzed the 1s-related x-ray photoemission and adsorption spectroscopy spectra of N dopants at vacancies and Stone-Wales defect in connection with the experimental ones. We also discuss characteristic scanning tunneling microscope (STM) images originating from the electronic and structural modifications by the N dopant-defect complexes. STM imaging for small negative bias voltage will provide important information about possible active sites for oxygen reduction reaction.Comment: 40 pages, 2 tables, 16 figures. The analysis of Clar sextets is added. This version is published on PHYSICAL REVIEW B 87, 165401(2013

R-Process Nucleosynthesis in MHD Jet Explosions of Core-Collapse Supernovae

We investigate $r$-process nucleosynthesis during the magnetohydrodynamical (MHD) explosion of supernova in a massive star of 13 $M_{\odot}$. Contrary to the case of the spherical explosion, jet-like explosion due to the combined effects of the rotation and magnetic field lowers the electron fraction significantly inside the layers above the iron core. We find that the ejected material of low electron fraction responsible for the $r$-process comes out from the silicon rich layer of the presupernova model. This leads to the production up to the third peak in the solar $r$-process elements. We examine whether the fission affects the $r$-process paths by using the full nuclear reaction network with both the spontaneous and $\beta$-delayed fission included. Moreover, we pay particular attention how the mass formula affects the $r$-process peaks with use of two mass formulae. It is found that both formulae can reproduce the global abundance pattern up to the third peak though detailed distributions are rather different. We point out that there are variations in the $r$-process nucleosynthesis if the MHD effects play an important role in the supernova explosion.Comment: 19 pages with 7 figures, submitted to Ap

Optical Coronagraphic Spectroscopy of AU Mic: Evidence of Time Variable Colors?

We present coronagraphic long slit spectra of AU Mic's debris disk taken with the STIS instrument aboard the Hubble Space Telescope (HST). Our spectra are the first spatially resolved, scattered light spectra of the system's disk, which we detect at projected distances between approximately 10 and 45 AU. Our spectra cover a wavelength range between 5200 and 10200 angstroms. We find that the color of AU Mic's debris disk is bluest at small (12-35 AU) projected separations. These results both confirm and quantify the findings qualitatively noted by Krist et al. (2005), and are different than IR observations that suggested a uniform blue or gray color as a function of projected separation in this region of the disk. Unlike previous literature that reported the color of AU Mic's disk became increasingly more blue as a function of projected separation beyond approximately 30 AU, we find the disk's optical color between 35-45 AU to be uniformly blue on the southeast side of the disk and decreasingly blue on the northwest side. We note that this apparent change in disk color at larger projected separations coincides with several fast, outward moving "features" that are passing through this region of the southeast side of the disk. We speculate that these phenomenon might be related, and that the fast moving features could be changing the localized distribution of sub-micron sized grains as they pass by, thereby reducing the blue color of the disk in the process. We encourage follow-up optical spectroscopic observations of the AU Mic to both confirm this result, and search for further modifications of the disk color caused by additional fast moving features propagating through the disk.Comment: Accepted by AJ, 13 pages, 8 figures, 1 tabl