Pricing Corporate Defaultable Bond using Declared Firm Value

We study the pricing problem for corporate defaultable bond from the viewpoint of the investors outside the firm that could not exactly know about the information of the firm. We consider the problem for pricing of corporate defaultable bond in the case when the firm value is only declared in some fixed discrete time and unexpected default intensity is determined by the declared firm value. Here we provide a partial differential equation model for such a defaultable bond and give its pricing formula. Our pricing model is derived to solving problems of partial differential equations with random constants (de- fault intensity) and terminal values of binary types. Our main method is to use the solving method of a partial differential equation with a random constant in every subinterval and to take expectation to remove the random constants.Comment: 12 pages, version 5 is written in tex and accepted in EJMAA(Electronic Journal of Mathematical Analysis and Applications

The power-law distribution in the geometrically growing system: Statistic of the COVID-19 pandemic

The power-law distribution is ubiquitous and its mechanism seems to be various. We find a general mechanism for the distribution. The distribution of a geometrically growing system can be approximated by a log - completely squared chi distribution with 1 degree of freedom (log-CS$\chi_1$), which reaches asymptotically a power-law distribution, or by a log-normal distribution, which has an infinite asymptotic slope, at the upper limit. For the log-CS$\chi_1$, the asymptotic exponent of the power-law or the slope in a log-log diagram seems to be related only to the variances of the system parameters and their mutual correlation but independent of an initial distribution of the system or any mean value of parameters. We can take the log-CS$\chi_1$ as a unique approximation when the system should have a singular initial distribution. The mechanism shows a comprehensiveness to be applicable to wide practice. We derive a simple formula for the Zipf's exponent, which will probably demand that the exponent should be near -1 rather than exactly -1. We show that this approach can explain statistics of the COVID-19 pandemic

Revealing the formation and electrochemical properties of bis(trifluoromethanesulfonyl) imide intercalated graphite with first-principles calculations

Graphite has been reported to have anion as well as cation intercalation capacities as both cathode and anode host materials for the dual ion battery. In this work, we study the intercalation of bis(trifluoromethanesulfonyl) imide (TFSI) anion from ionic liquid electrolyte into graphite with first-principles calculations. We build models for TFSI-C$_n$ compounds with systematically increasing unit cell sizes of graphene sheet and investigate their stabilities by calculating the formation energy, resulting in the linear decrease and arriving at the limit of stability. With identified unit cell sizes for stable compound formation, we reveal that the interlayer distance and relative volume expansion ratio of TFSI-C$_n$ increase as increasing the concentration of TFSI intercalate during the charge process. The electrode voltage is determined to be ranged from 3.8 V to 3.0 V at the specific capacity ranging from 30 mAh g$^{-1}$ to 54 mAh g$^{-1}$ in agreement with experiment. Moreover, a very low activation barrier of under 50 meV for TFSI migration and good electronic conductivity give a proof of using these compounds as a promising cathode. Through the analysis of charge transfer, we clarify the mechanism of TFSI-C$_n$ formation, and reveal new prospects for developing graphite based cathode

Ionic Diffusion and Electronic Transport in Eldfellite Nax_xFe(SO4_4)2_2

Discovering new electrodes for sodium-ion battery requires clear understanding of the material process during battery operation. Using first-principles calculations, we identify mechanisms of ionic diffusion and electronic transfer in newly developed cathode material, eldfellite Na$_x$Fe(SO$_4$)$_2$, reproducing the electrochemical properties in good agreement with experiment. The inserted sodium atom is suggested to diffuse along the two-dimensional pathway with preceding movement of the host sodium atom, and the activation energy is calculated to be reasonable for fast insertion. We calculate the electronic properties, showing the band insulating at low composition of inserted sodium, for which the electron polaron formation and hoping are also suggested. Our results may contribute to opening a new way of developing innovative cathode materials based on iron and sulfate ion

A new distance law of planets and satellites in the solar system

In the 1960s, it has been substantiated that an equation of Schrodinger type could describe the diffusion phenomena, and the main consequence from this finding has been that there would be wave property in the diffusion processes as well. This theory has been immediately proved through laboratorial experiments. Afterwards the theory was applied to the primordial nebula which was thought to surround the protosun, and has found the consistency of the prediction of the theory with current distance distribution of the planets to be excellent. At the end of 20th century new satellites of planets were discovered. On the basis of the new data, the theory is tested thoroughly and the result allows us to come to the conclusion that the basic process for the distances of the planets from the protosun to be determined has been the diffusion of the primordial nebula consisting of mainly molecular gas.Comment: 24 pages, 5 table

Influence of halide composition on the structural, electronic, and optical properties of mixed CH3_3NH3_3Pb(I1−x_{1-x}Brx_x)3_3 perovskites calculated using the virtual crystal approximation method

We investigate the structural, electronic and optical properties of mixed bromide-iodide lead perovskite solar cell CH$_3$NH$_3$Pb(I$_{1-x}$Br$_x$)$_3$ by means of the virtual crystal approximation (VCA) within density functional theory (DFT). Optimizing the atomic positions and lattice parameters increasing the bromide content $x$ from 0.0 to 1.0, we fit the calculated lattice parameter and energy band gap to the linear and quadratic function of Br content, respectively, which are in good agreement with the experiment, respecting the Vegard's law. With the calculated exciton binding energy and light absorption coefficient, we make sure that VCA gives consistent results with the experiment, and the mixed halide perovskites are suitable for generating the charge carriers by light absorption and conducting the carriers easily due to their strong photon absorption coefficient, low exciton bindign energy, and high carrier mobility at low Br contents. Furthermore analyzing the bonding lengths between Pb and X (I$_{1-x}$Br$_x$: virtual atom) as well as C and N, we stress that the stability of perovskite solar cell is definitely improved at $x$=0.2

Two-dimensional hybrid composites of SnS2 with graphene and graphene oxide for improving sodium storage: A first-principles study

Among the recent achievements of sodium-ion battery (SIB) electrode materials, hybridization of two-dimentional (2D) materials is one of the most interesting appointments. In this work, we propose to use the 2D hybrid composites of SnS2 with graphene or graphene oxide (GO) layers as SIB anode, based on the first-principles calculations of their atomic structures, sodium intercalation energetics and electronic properties. The calculations reveal that graphene or GO film can effectively support not only the stable formation of hetero-interface with the SnS2 layer but also the easy intercalation of sodium atom with low migration energy and acceptable low volume change. The electronic charge density differences and the local density of state indicate that the electrons are transferred from the graphene or GO layer to the SnS2 layer, facilitating the formation of hetero-interface and improving the electronic conductance of the semiconducting SnS2 layer. These 2D hybrid composites of SnS2/G or GO are concluded to be more promising candidates for SIB anodes compared with the individual monolayers

First-principles study on the electronic and optical properties of inorganic perovskite Rb1-xCsxPbI3 for solar cell applications

Recently, replacing or mixing organic molecules in the hybrid halide perovskites with the inorganic Cs or Rb cations has been reported to increase the material stability with the comparable solar cell performance. In this work, we systematically investigate the electronic and optical properties of all-inorganic alkali iodide perovskites Rb1-xCsxPbI3 using the first-principles virtual crystal approximation calculations. Our calculations show that as increasing the Cs content x, lattice constants, band gaps, exciton binding energies, and effective masses of charge carriers decrease following the quadratic (linear for effective masses) functions, while static dielectric constants increase following the quadratic function, indicating an enhancement of solar cell performance upon the Rb addition to CsPbI3. When including the many-body interaction within the GW approximation and incorporating the spin-orbit coupling (SOC), we obtain more reliable band gap compared with experiment for CsPbI3, highlighting the importance of using GW+SOC approach for the all-inorganic as well as organic-inorganic hybrid halide perovskite materials

Apparent Positions of Planets

The apparent positions of planets are determined by means of the fundamental ephemerides, the precession-nutation models of the Earth, the gravitational effects and aberrations et al. Around 2000, many astrometrical conceptions, models and theories had been newly defined and updated:for the fiducial celestial reference system, the ICRS is introduced, the fundamental ephemerides - DE405/LE405 et al.,precession-nutation model - IAU 2000A/IAU 2006 model. Using the traditional algorithm and the updated models, we develop the system of calculating the apparent positions of planets. The results are compared with the Astronomical Almanac and proved in their correctness.Comment: 9 pages, 3 figure

Ab initio study of sodium cointercalation with diglyme molecule into graphite

The cointercalation of sodium with the solvent organic molecule into graphite can resolve difficulty of forming the stage-I Na-graphite intercalation compound, which is a predominant anode of Na-ion battery. To clarify the mechanism of such cointercalation, we investigate the atomistic structure, energetics, electrochemical properties, ion and electron conductance, and charge transferring upon de/intercalation of the solvated Na-diglyme ion into graphite with {\it ab initio} calculations. It is found that the Na(digl)$_2$C$_n$ compound has the negatively lowest intercalation energy at $n\approx$21, the solvated Na(digl)$_2$ ion diffuses fast in the interlayer space, and their electronic conductance can be enhanced compared to graphite. The calculations reveal that the diglyme molecules as well as Na atom donates electrons to the graphene layer, resulting in the formation of ionic bonding between the graphene layer and the moiety of diglyme molecule. This work will contribute to the development of innovative anode materials for alkali-ion battery applications