A NOTE ON INTERNATIONAL OLIGOPOLY WITH FREE ENTRY

The purpose of this note is a reconsideration of the relationship between the equilibrium number of firms and cost differences under an international oligopoly setting. We show that both cost differences across countries and the degree of product differentiation have strong implications in the free entry case

Inversion of complex body waves—III

We have developed a method that inverts seismic body waves to determine the mechanism and rupture pattern of earthquakes. The rupture pattern is represented as a sequence of subevents distributed on the fault plane. This method is an extension of our earlier method in which the subevent mechanisms were fixed. In the new method, the subevent mechanisms are determined from the data and are allowed to vary during the sequence. When subevent mechanisms are allowed to vary, however, the inversion often becomes unstable because of the complex trade-offs between the mechanism, the timing, and the location of the subevents. Many different subevent sequences can explain the same data equally well, and it is important to determine the range of allowable solutions. Some constraints must be imposed on the solution to stabilize the inversion. We have developed a procedure to explore the range of allowable solutions and appropriate constraints. In this procedure, a network of grid points is constructed on the τ - I plane, where τ and I are, respectively, the onset time and the distance from the epicenter of a subevent; the best-fit subevent is determined at all grid points. Then the correlation is computed between the synthetic waveform for each subevent and the observed waveform. The correlation as a function of τ and I and the best-fit mechanisms computed at each τ - I grid point depict the character of allowable solutions and facilitate a decision on the appropriate constraints to be imposed on the solution. The method is illustrated using the data for the 1976 Guatemala earthquake

Inversion of complex body waves

A numerical method to deconvolve complex body waves into a multiple shock sequence is developed. With the assumption that all the constituent events of a multiple shock have identical fault geometry and depth, the far-field source time function is obtained as a superposition of ramp functions. The height and the onset time of the ramp functions are determined by matching the synthetic waveforms with the observed ones in the least-square sense. The individual events are then identified by pairs of ramp functions or discrete trapezoidal pulses in the source time sequence. The method can be used for the analysis of both single and multi-station data. Teleseismic long-period P waves from the 1976 Guatemala earthquake are analyzed as a test of our method. The present method provides a useful tool for a systematic analysis of multiple event sequences

The Shikotan Earthquake of October 4, 1994: Lithospheric earthquake

A large M_w=8.2 earthquake occurred off Shikotan Is., one of the Kurile Is., on October 4, 1994. We inverted 32 body-wave records to determine the rupture pattern using an iterative deconvolution method. The mechanisms of the subevents were allowed to vary during rupture. The source parameters obtained are: the location of the initial break = (43.48°N, 147.40°E); the centroid depth = 56 km; (strike, dip, rake) = (49°, 75°, 125°) for the total source; the seismic moment M_o = 2.6×10^(21) Nm (M_w=8.2); source time duration T = 42 s; the average rupture velocity ν = 2.5 km/s. We also determined the mechanism using long-period Love and Rayleigh waves from 14 stations. The solution for a finite source distributed over a depth range from 0 to 90 km is (strike, dip, rake) = (54°, 76°, 129°) with Mo = 2.3×10^(21) Nm, in good agreement with that from body waves. Referring to the extent of the aftershock area and the subevent distribution, we estimated the fault area S = 120 × 60 km², the average slip D=5.6m, and the stress drop Δσ=11 MPa. We computed synthetic waveforms as well as static displacements using either the steep or the low-angle plane as the fault plane, and found that the steep-dip fault model fits the data better. Our result (the mechanism, large centroid depth, high stress drop) strongly suggests that the 1994 Shikotan earthquake is a lithospheric earthquake: an intra-plate event that ruptures through a substantial part of the subducting oceanic lithosphere. This type of lithospheric earthquake is relatively common

Using Conservative Estimation for Conditional Probability instead of Ignoring Infrequent Case

There are several estimators of conditional probability from observed frequencies of features. In this paper, we propose using the lower limit of confidence interval on posterior distribution determined by the observed frequencies to ascertain conditional probability. In our experiments, this method outperformed other popular estimators.Comment: The 2016 International Conference on Advanced Informatics: Concepts, Theory and Application (ICAICTA2016

The virtual-state character of the {9}^Be 1/2^+ state in the {9}^Be({\gamma},n){8}^Be reaction

We study the character of the first excited 1/2^{+} state of {9}^Be, which is observed as a low-lying sharp peak in the cross section of 9^Be({\gamma},n)2{\alpha} just above the {8}^Be+n threshold. Using the {\alpha}+{\alpha}+n three-body model, we describe the ground and excited unbound states of {9}^Be above the {\alpha}+{\alpha}+n threshold. Applying the complex scaling method to the three-body model, we find no 1/2^{+} resonant solutions, while the low-lying peak in the photodisintegration cross section is reproduced in the present calculation. It is found that the low-lying peak is dominantly explained by the 8^Be+n component. Furthermore, using the analytical continuation of the coupling constant of the three-body interaction for the {\alpha}+{\alpha}+n system, we discuss the virtual-state character of the 1/2^{+} state.Comment: 5 page

A Spectrophotometric Method to Determine the Inclination of Class I Objects

A new method which enables us to estimate the inclination of Class I young stellar objects is proposed. Since Class I objects are not spherically symmetric, it is likely that the observed feature is sensitive to the inclination of the system. Thus, we construct a protostar model by carefully treating two-dimensional (2D) radiative transfer and radiative equilibrium. We show from the present 2D numerical simulations that the emergent luminosity L_SED,which is the frequency integration of spectral energy distribution (SED), depends strongly on the inclination of the system i, whereas the peak flux is insensitive to i. Based on this result, we introduce a novel indicator f_L, which is the ratio of L_SED to the peak flux, as a good measure for the inclination. By using f_L, we can determine the inclination regardless of the other physical parameters. The inclination would be determined by f_L within the accuracy of +- 5 degree, if the opening angle of bipolar outflows is specified by any other procedure. Since this spectrophotometric method is easier than a geometrical method or a full SED fitting method, this method could be a powerful tool to investigate the feature of protostars statistically with observational data which will be provided by future missions, such as SIRTF, ASTRO-F, and ALMA.Comment: 14 pages, 9 figures, accepted by Ap

Effect of high molecular weight hyaluronan on cartilage degeneration in a rabbit model of osteoarthritis

SummaryThe effects of high molecular weight hyaluronan (HA) on cartilage degeneration were investigated in a partial menisectomy model of osteoarthritis (OA) in the rabbit knee. This study compared HA80 (0.8 × 106 Da, 1%), HA190 (1.9 × 106 Da, 0.01–1%) and saline. HA (0.1 ml/kg) or saline were injected intra-articularly twice a week immediately after surgery. Degenerative changes in femoral and tibial cartilages were graded histopathologically 2 and 4 weeks after surgery. Two weeks after surgery, HA190, only when used at a 1% concentration, resulted in a dramatic inhibition of cartilage degeneration in both the femoral condyle and the tibial plateau (P < 0.01). Two weeks after surgery, the protection against cartilage degeneration was significantly (P < 0.05) greater with HA190 than with HA80. Four weeks after surgery, only the femoral cartilage degeneration was significantly and similarly inhibited with HA190 (P < 0.01) and HA80 (P < 0.05). Scanning electron micrographs of femoral cartilage showed that cartilage degeneration was less severe with HA190 than with saline. These results might suggest that, in the rabbit model, intra-articular administration of higher molecular weight HA is more effective than lower molecular weight HA in inhibiting cartilage degeneration in early OA

Some general lagrange interpolations over simplex finite elements with reference to derivative singularities

For simplex finite elements, the native Lagrange family with arbitrarily placed nodes is presented in hierarchy-ranking expressions. It includes the well-known complete Lagrange family as well as the mid-edge Lagrange family to be proposed in this paper. This new family enables us to utilize harmonious combinations of interpolations of different orders in finite element analysis. As an application of developed simplex interpolations to fracture mechanics where some derivative singularities are needed, we then describe the semi-radial singularity mapping with examinations of peculiar trial function spaces.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24285/1/0000551.pd