The theorem of consumer surplus and demand elasticity at equilibrium price in a monopolist competition case

In the market of a monopolistically competition the price of a long-run equilibrium, the consumers’ surplus is equal to a half of fixed cost value, and the price elasticity is equal to the ratio of total to fixed costs.consumer surplus; price elasticity

Synthetic Light Curves of Shocked Dense Circumstellar Shells

We numerically investigate light curves (LCs) of shocked circumstellar shells which are suggested to reproduce the observed LC of superluminous SN 2006gy analytically. In the previous analytical model, the effects of the recombination and the bolometric correction on LCs are not taken into account. To see the effects, we perform numerical radiation hydrodynamic calculations of shocked shells by using STELLA, which can numerically treat multigroup radiation transfer with realistic opacities. We show that the effects of the recombination and the bolometric correction are significant and the analytical model should be compare to the bolometric LC instead of a single band LC. We find that shocked circumstellar shells have a rapid LC decline initially because of the adiabatic expansion rather than the luminosity increase and the shocked shells fail to explain the LC properties of SN 2006gy. However, our synthetic LCs are qualitatively similar to those of superluminous SN 2003ma and SN 1988Z and they may be related to shocked circumstellar shells.Comment: 7 pages, 7 figures, 1 table, accepted by Monthly Notices of the Royal Astronomical Societ

A proposal for a generalized canonical osp(1,2) quantization of dynamical systems with constraints

The aim of this paper is to consider a possibility of constructing for arbitrary dynamical systems with first-class constraints a generalized canonical quantization method based on the osp(1,2) supersymmetry principle. This proposal can be considered as a counterpart to the osp(1,2)-covariant Lagrangian quantization method introduced recently by Geyer, Lavrov and M\"ulsch. The gauge dependence of Green's functions is studied. It is shown that if the parameter m^2 of the osp(1,2) superalgebra is not equal to zero then the vacuum functional and S-matrix depend on the gauge. In the limit $m\to 0$ the gauge independence of vacuum functional and S - matrix are restored. The Ward identities related to the osp(1,2) symmetry are derived.Comment: Revised version. To appear in Mod.Phys.Lett.

Relation between the 0νββ0\nu\beta\beta and 2νββ2\nu\beta\beta nuclear matrix elements revisited

We show that the dominant Gamow-Teller part, $M^{0\nu}_{GT}$, of the nuclear matrix element governing the neutrinoless $\beta\beta$ decay is related to the matrix element $M^{2\nu}_{cl}$ governing the allowed two-neutrino $\beta\beta$ decay. That relation is revealed when these matrix elements are expressed as functions of the relative distance $r$ between the pair of neutrons that are transformed into a pair of protons in the $\beta\beta$ decay. Analyzing this relation allows us to understand the contrasting behavior of these matrix elements when $A$ and $Z$ is changed; while $M^{0\nu}_{GT}$ changes slowly and smoothly, $M^{2\nu}$ has pronounced shell effects. We also discuss the possibility of phenomenological determination of the $M^{2\nu}_{cl}$ and from them of the $M^{0\nu}_{GT}$ values from the experimental study of the $\beta^{\pm}$ strength functions

Violation of Lorentz Invariance and neutral component of UHECR

The observed clustering of ultra-high energy cosmic rays suggests the existence of a neutral component. The models with violation of Lorentz invariance may explain this component by neutrons becoming stable above some threshold energy E_0. The protons, in turn, may become unstable above some energy E_1>E_0. We calculate the dependence of the threshold energies E_0 and E_1 on the parameters of the model and find E_1/E_0\gsim 1.5. We argue that the characteristic threshold behavior of charged and neutral components may be used as the specific signature of models with violation of Lorentz invariance. The existence of the neutron stability threshold E_0 can be investigated with already existing data.Comment: 14 pages, 2 figure

Eclipsing Binaries Showing Light Time Effect

Four eclipsing binaries, which show apparent changes of period, have been studied with respect to a possible presence of the light time effect. With a least squares method we calculated new light elements of these systems, the mass function of the predicted third body, and its minimum mass. We discuss the probability of the presence of such bodies in terms of mass function, changes in radial velocity and third light in solution of light curves.Comment: 4 pages, 4 figures, 1 table, conference proceeding

A search for peculiar stars in the open cluster Hogg 16

The study of chemically peculiar (CP) stars in open clusters provides valuable information about their evolutionary status. Their detection can be performed using the $\Delta a$ photometric system, which maps a characteristic flux depression at $\lambda \sim 5200$ \AA. This paper aims at studying the occurrence of CP stars in the earliest stages of evolution of a stellar population by applying this technique to Hogg 16, a very young Galactic open cluster (about 25 Myr). We identified several peculiar candidates: two B-type stars with a negative $\Delta a$ index (CD-60 4701, CPD-60 4706) are likely emission-line (Be) stars, even though spectral measurements are necessary for a proper classification of the second one; a third object (CD-60 4703), identified as a Be candidate in literature, appears to be a background B-type supergiant with no significant $\Delta a$ index, which does not rule out the possibility that it is indeed peculiar as the normality line of $\Delta a$ for supergiants has not been studied in detail yet. A fourth object (CD-60 4699) appears to be a magnetic CP star of 8 M$_\odot$, but obtained spectral data seem to rule out this hypothesis. Three more magnetic CP star candidates are found in the domain of early F-type stars. One is a probable nonmember and close to the border of significance, but the other two are probably pre-main sequence cluster objects. This is very promising, as it can lead to very strong constraints to the diffusion theory. Finally, we derived the fundamental parameters of Hogg 16 and provide for the first time an estimate of its metal content.Comment: Accepted for publication in New Astronomy. 9 pages, 4 figures, and 4 tables. A complete data table is available via CDS or upon request from the corresponding autho