The solution to Wheeler-DeWitt is eight

We describe a new geometrical solution to the Wheeler-DeWitt equation in two dimensional quantum gravity. The solution is the amplitude of a surface whose boundary consists of two tangent loops. We further discuss a new method for estimating singular geometries amplitudes, which uses explicit recursive counting of discrete surfaces.Comment: 10 tex pages + 5 ps figure

ANALISIS PORTOFOLIO SEBAGAI ALAT UNTUK MENGOPTIMALKAN KEUNTUNGAN INVESTASI SAHAM PADA PERUSAHAAN TEKSTIL YANG TERDAFTAR DI BURSA EFEK INDONESIA (BEI) BERDASARKAN MODEL INDEKS TUNGGAL

This research represent case study at Effect Exchange Indonesia (BEI) with title “Analyze Portofolio As a Means Of To Be Is Optimal Advantage Of Investment Share at Company Of Textile Which Enlist in Effect Exchange Indonesia (BEI) Pursuant To Single Model Index”. Target of this research is to to analyze portofolio as a means of to be is optimal of advantage of share investment at company of Textile which enlist in Effect Exchange Indonesia (BEI) Pursuant To Single Model Index. Analyzer the used is with single index model. This model can be used to make moderate calculation [in] model of Markowitz by providing required input parameters in calculation of model of Markowitz. Despitefully, model single index earn is also used to calculate expects return and risk of portofolio. relied on single Index model of perception that price from an securities have unidirectional fluctuation to with consumer price index. Peculiarly can perceive that most share tend to experience of increase of price if share price index go up. On the contrary also correctness, that is if share price index go down, most natural share of degradation of price. This matter suggest that return-return of securities possible have correlation to caused by reaction of public (response common) to changes of market value. Result of from single index model analysis of shares company of textile which enter in optimal portofolio is FMII equal to 59,82305152% and SRSN equal to 40,17694848%. Pursuant to this research, the optimal portofolio give portofolio return expected equal to 0,064948187 ( 6,4948187%) with risk storey; level of portofolio which must be accounted on equal to 0,166060271 ( 16,6060271%). Level of risk storey; level of portofolio the smaller in comparison with individual share risk. This matter indicate that forming of portofolio can degrade lower risk of individual share risk so that risk which must be accounted on investor become smaller

General Relativistic Self-Similar Solutions in Cosmology

We present general relativistic solutions for self-similar spherical perturbations in an expanding cosmological background of cold pressure-less gas. We focus on solutions having shock discontinuities propagating in the surrounding cold gas. The pressure, $p$, and energy-density, $\mu$, in the shock-heated matter are assumed to obey $p=w\mu$, where $w$ is a positive constant. Consistent solutions are found for shocks propagating from the symmetry center of a region of a positive density excess over the background. In these solutions, shocks exist outside the radius marking the event horizon of the black hole which would be present in a shock-less collapse. For large jumps in the energy-density at the shock, a black hole is avoided altogether and the solutions are regular at the center. The shock-heated gas does not contain any sonic points, provided the motion of the cold gas ahead of the shock deviates significantly from the Hubble flow. For shocks propagating in the uniform background, sonic points always appear for small jumps in the energy-density. We also discuss self-similar solutions without shocks in fluids with $w<-1/3$.Comment: 6 pages, 3 figures, mnras styl