We consider the heat kernel for a spinor with spin 1/2 in the presence of various non-Abelian fields, i.e. vector, axial-vector, scalar, pseudo-scalar and antisymmetric tensor fields in $d=4$ Riemannian spacetime. In this model we study the irreducible forms of Hadamard-Minakshisundaram-DeWitt-Seeley(HMDS) coefficients, which are asymptotic expansion coefficients of the heat kernel. The irreducible forms of the first two HMDS coefficients are explicitly given. These forms are useful for the derivation of anomalies in $d=4$ Riemannian spacetime.

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From a point of view that the Fermi fields minimally interact with the axial part of torsion, we evaluate the asymptotic expansion coefficients of the heat kernel in four dimensional Riemannian space with the particular chiral $U(1)$ fields, where the covariant Taylor expansion is used in the calculation method following the algorithm given by Avramidi. The coefficients are compared with those in Riemann-Cartan space which has the totally antisymmetric torsion tensor. As a result, it is shown that the coincidence limits of these corresponding coefficients are identified each other.

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We analytically derive transition probabilities for four-neutrino oscillations in matter. The mixing angles in matter are also caluculated. From these results, the resonance among the active neutrinos ($\nu_e$, $\nu_{\mu}$ and $\nu_{\tau}$) may occur near the earth, while it is realistically difficult to observe the resonance between the e-neutrino and the sterile neutrino near the earth, even if the sterile neutrino exists.

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The response of the macroscopic system as quantum system is investigated with a coarse-grained position operator. It is shown that the irreversibility and reversibility in the macroscopic system are deeply related with the decoherence and coherence, respectively. It is also poinetd out that the appearance of reversible process in the macroscopic system can be possible even if the fluctuation exists.

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We investigate p-process nucleosynthesis in a supernova-driven supercritical accretion disk (SSAD) around a compact object of 1.4 $M_{\odot}$. Compositions of fallback material far from the compact object, or initial compositions, are taken to those of explosively burned oxygen/neon layers (ONeLs) of a 20$M_{\odot}$ progenitor. Profiles of the overproduction factors (OPFs) of p-nuclei ejected from SSADs via jets and/or winds highly depend on initial amounts of s-process seeds in fallback material. Not only neutron rich isotopes than p-nuclei but slightly neutron deficient isotopes are relevant for seeds of p-nuclei inside SSADs. This is due to transformation of slightly neutron deficient isotopes to s-process seeds via radiative neutron captures during accretion. When the peak temperature $T_{9, \rm peak}$ in units of 10$^9$ K is less than 2.24 for an explosively burned layer, composition of p-nuclei ejected from SSADs is very similar to that for fallback of ONeLs of progenitors. If an explosively burned layer with $T_{9, \rm peak} \ge 3.97$ falls back, p-nuclei cannot be ejected from SSADs due to destruction of s-process seeds. For fallback of intermediate layers with $2.24 < T_{9, \rm peak} < 3.97$, OPFs of p-nuclei have various profiles. There exist no overproduction of Mo, Ru, and La for any initial compositions of explosively burned ONeLs.

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We construct a steady model of optically thin accretion flows around a black hole of 10 $M_{\odot}$ with including energy loss through pair neutrinos. It is found that neutrino cooling is predominant over both advective and radiative cooling in a middle region of the flows when the accretion rate in Eddington units $\dot{m} = 10^{-7} - 10^{-3}$ and the viscosity parameter $\alpha < 0.5$. In this region, accreting gas becomes nearly isothermal with $T \simeq 10^9$ K, which is much less than that of optically thin advection dominated accretion flows (ADAFs). Moreover, density varies as $r^{-5/2}$, radial velocity remains roughly constant and angular velocity is close to Keplerian in this region. These physical quantities have the same dependence on both $\dot{m}$ and $\alpha$ as those in ADAFs. Near the inner edge of the disk the angular velocity becomes super-Keplerian, which leads to the existence of a maximum pressure point.

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Using the shell flash model and the full reaction network, we have investigated the relation between the final products of the rp-process and the ignition pressure. It is found that nuclear fuel is almost burned out after the flash and the mass number of synthesized nuclei reaches to $\sim 100$ in the pressure from $10^{23}$ to $10^{23.5}$ dyn cm$^{-2}$. Furthermore, p-nuclei up to $^{126}$Xe are found to be synthesized after the flash. It is concluded that our results affect the construction of the model of the type I X-ray burst concerned with the nuclear fuel after the burst.

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We investigate the helium flash (He-flash) on neutron stars where accreted matter is assumed to be pure helium. Our results of numerical calculations are compared with the observed data of 4U 1820-30 which is considered to be a site of the He-flash. In case of the high accretion rate, we found that except for the persistent luminosity our results agree with the burst parameters of 4U 1820-30. Furthermore, we examined the effect of the NCO reaction on the ignition of the He-flash and found that the NCO reaction affects the time difference until the ignition. The theoretical problems associated with the superburst have been elucidated in close relation to the flash occurred in the deep accreted layers.

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We investigate the thermal history in the universe with a variable cosmological term. In particular, we show how the formation of important molecules such as H$_2$ and HD is influenced during the epoch for the redshift from $10^4$ to 1. These molecules should dominate the cooling process of primordial gas clouds which triggers their collapse. It is found that the molecular formation is quickened by $\Delta z \sim 10^3$ compared with the case in the standard Big Bang theory due to the variable cosmological term. The qualitative estimate of the mass of the first objects has been performed with use of the time scales related to the thermal evolution. It is suggested that the formation scenarios of the first objects studied so far could be changed drastically if the variable cosmological term is included in the thermal history in the universe.

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Regarding the composition dependence of photodoping rate of Ag in As$_x$S$_{1-x}$ glasses, many authors have noted a maximum in the composition range $0.2 < x < 0.4.$ In the present paper, the origin of such composition dependence has been investigated by using two different approaches. In the first approach, the possibility to relate the concentration fluctuation of the host glass to the photodoping rate has been studied. In the second approach, the composition dependence of the photodoping rate has been compared with the excess volume. Although not conclusive, the result of the second approach pointed out a possible correlation.

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In order to examine whether the magnetoresistance effect concerning the tunnering occurs even in polycrystalline films, we prepared Fe-Al films by introducing oxygen during evaporation at the substrate temperatures $T_{\rm S}$ of 173, 300 and 433 K.Partial pressure of O$_2$ gas $p$(O$_2$) ranged from 0 to 0.08 Pa. The structure of Fe columns in the films was investigated magnetically and the magnetoresistance was measured. At $p$(O$_2$) of 0 Pa, the nonmagnetic Fe-Al alloys are considered to be more formed in the films for $T_{\rm S}$ of 300 and 433 K than for 173 K. With increasing $p$(O$_2$) relative gaps between Fe columns increase and become more isotropic. At $p$(O$_2$) of 0.08 Pa, their anisotropies almost disappear for 433 K, while remain for 300 K. At $p$(O$_2)=0.04$ Pa and $T_{\rm S}=433$ K negative magnetoresistance, which is considered to originate from the spin-dependent tunneling, was observed.

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We have measured optical constants and the anisotropic alignment of obliquely deposited aluminum thin films using ellipsometry. The purpose of this measurement is to compare with a previous work using films deposited at a deposition rate of about 10 nm/s were reported. Substrate temperature dependence of average optical constants and the anisotropy of the reflection coefficient is similar to the previous work in spite of a slow deposition rate. It can be considered that there is no effect of the deposition rate for the surface configuration within our experiments.

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Luminescence spectra have been measured in TlBr doped with iodine ions under the pulse light excitation. Two broad emission bands were observed at 2.2 eV and 2.45 eV. The emission band at 2.2 eV decayed nonexponentially and was attributed to the radiative recombination of trapped holes and electrons from the measurements of the decay properties and the spectral shape of the emission band. The emission band at 2.45 eV decayed with two time constants of 0.5 $\mu$s and less than 20 ns. The fast decay component was assigned to the radiative annihilation of the singlet-triplet mixed state of the self-trapped exciton. The slow decay component was attributed to be due to the triplet state of the exciton, which will be weakly allowed by an iodine ion. The luminescence decay of the 2.45 eV band was analyzed by the rate equations, assuming that initial states of the emission are composed of doubly degenerated singlet-triplet mixed states and a triplet state.

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We have carried out NMR measurements by a conventional spin echo method without external magnetic field in a series of M(HCOO)$_2\cdot$2H$_2$O, where M stands for transition metals, at millikelvin temperatures using a dilution refrigerator especially constructed for NMR experiments. These substances have two types of layers from a viewpoint of magnetism. One layer is in magnetic ordered state while the other remains paramagnetic below transition temperature. In this series the nuclear magnetic resonance of $^{59}$Co nuclei is observed on powdered sample of Co(HCOO)$_2\cdot$2H$_2$O in the temperature range between 40 mK and 200 mK in the NMR frequency range between 150 MHz and 300 MHz. Two peaks are observed in Co NMR spectra.

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We study spontaneous magnetization of K$_2$CuF$_4$ at low temperatures.The temperature dependence of the NMR frequencies of the $1/2\leftrightarrow3/2$ transition for $^{63}$Cu and $^{65}$Cu nuclei is measured. The experimental results are discussed in the framework of the two-dimensional spin wave theory at millikelvin temperatures.

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