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Hidden metallic iron in amorphous silicate dust? Insights from condensation experiments and mid-infrared spectroscopy
Authors:
Hanako Enomoto,
Aki Takigawa,
Hiroki Chihara,
Chiyoe Koike
Abstract:
Amorphous silicate dust is a major component in the interstellar and circumstellar dust formed in the outflow of asymptotic giant branch (AGB) stars. Although iron depletion is observed in the interstellar medium (ISM), the exact form and fraction of iron in solid remains under debate. In particular, it is unclear whether amorphous silicate dust around AGB stars contains metallic iron. We aimed to…
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Amorphous silicate dust is a major component in the interstellar and circumstellar dust formed in the outflow of asymptotic giant branch (AGB) stars. Although iron depletion is observed in the interstellar medium (ISM), the exact form and fraction of iron in solid remains under debate. In particular, it is unclear whether amorphous silicate dust around AGB stars contains metallic iron. We aimed to provide optical constants of amorphous silicate nanoparticles and examine the effects of metallic iron on their spectral features to better constrain the dust properties by producing amorphous silicate nanoparticles with and without metallic cores. We performed condensation experiments using an induction thermal plasma system to produce dust analogues of the CI chondritic composition in the Mg-Ca-Na-Al-Si-Fe-Ni-O and Mg-Ca-Na-Al-Si-O systems. We measured the absorbance and reflectance of the samples, observed the structure of the products, and determined the optical constants. Two types of amorphous silicate nanoparticles (10-200 nm in diameter) with nearly CI chondritic composition were produced: one contained kamacite (Fe: Ni=0.9: 0.1) cores with a diameter ratio ranging 0-0.87 (average ~0.50), and the other was iron-free homogeneous amorphous silicate. The amorphous silicates of the CI chondritic composition with various sized metallic cores may be prevalent in circumstellar and interstellar dust.
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Submitted 7 December, 2025; v1 submitted 20 November, 2025;
originally announced November 2025.
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The matrix weighted real-analytic double fibration transforms
Authors:
Hiroyuki Chihara,
Shubham R. Jathar,
Jesse Railo
Abstract:
We show that the real-analytic matrix-weighted double fibration transform determines the analytic wavefront set of a vector-valued function. We apply this result to show that the matrix weighted ray transform is injective on a two-dimensional, non-trapping, real-analytic Riemannian manifold with strictly convex boundary. Additionally, we show that a real-analytic Higgs field can be uniquely determ…
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We show that the real-analytic matrix-weighted double fibration transform determines the analytic wavefront set of a vector-valued function. We apply this result to show that the matrix weighted ray transform is injective on a two-dimensional, non-trapping, real-analytic Riemannian manifold with strictly convex boundary. Additionally, we show that a real-analytic Higgs field can be uniquely determined from the nonabelian ray transform on real-analytic Riemannian manifolds of any dimension with a strictly convex boundary point.
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Submitted 6 May, 2026; v1 submitted 30 June, 2025;
originally announced June 2025.
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The symbol of the normal operator for the d-plane transform on the Euclidean space
Authors:
Hiroyuki Chihara
Abstract:
We directly compute the symbol of the normal operator for the d-plane transform on the Euclidean space. We show that this symbol is the product of the symbol of the power of the Laplacian of order -d/2 and a constant given by an invariant integral over excess-dimensional spaces. This leads to an alternative derivation of the filtered backprojection formula for the d-plane transform.
We directly compute the symbol of the normal operator for the d-plane transform on the Euclidean space. We show that this symbol is the product of the symbol of the power of the Laplacian of order -d/2 and a constant given by an invariant integral over excess-dimensional spaces. This leads to an alternative derivation of the filtered backprojection formula for the d-plane transform.
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Submitted 24 December, 2024;
originally announced December 2024.
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Microlocal analysis of double fibration transforms with conjugate points
Authors:
Hiroyuki Chihara
Abstract:
We study the structure of normal operators of double fibration transforms with conjugate points. Examples of double fibration transforms include Radon transforms, $d$-plane transforms on the Euclidean space, geodesic X-ray transforms, light-ray transforms, and ray transforms defined by null bicharacteristics associated with real principal type operators. We show that, under certain stable conditio…
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We study the structure of normal operators of double fibration transforms with conjugate points. Examples of double fibration transforms include Radon transforms, $d$-plane transforms on the Euclidean space, geodesic X-ray transforms, light-ray transforms, and ray transforms defined by null bicharacteristics associated with real principal type operators. We show that, under certain stable conditions on the distribution of conjugate points, the normal operator splits into an elliptic pseudodifferential operator and several Fourier integral operators, depending on the degree of the conjugate points. These problems were first studied for geodesic X-ray transforms by Stefanov and Uhlmann (Analysis \& PDE, {\bf 5} (2012), pp.219--260). After that Holman and Uhlmann (Journal of Differential Geometry, {\bf 108} (2018), pp.459--494) proved refined results according to the degree of regular conjugate points.
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Submitted 24 December, 2025; v1 submitted 18 December, 2024;
originally announced December 2024.
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Geodesic X-ray transform and streaking artifacts on simple surfaces or on spaces of constant curvature
Authors:
Hiroyuki Chihara
Abstract:
The X-ray transform on the plane or on the three-dimensional Euclidean space can be considered as the measurements of CT scanners for normal human tissue. If the human body contains metal regions such as dental implants, stents in blood vessels, metal bones, etc., the beam hardening effect for the energy level of the X-ray causes streaking artifacts in its CT image. More precisely, if there are tw…
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The X-ray transform on the plane or on the three-dimensional Euclidean space can be considered as the measurements of CT scanners for normal human tissue. If the human body contains metal regions such as dental implants, stents in blood vessels, metal bones, etc., the beam hardening effect for the energy level of the X-ray causes streaking artifacts in its CT image. More precisely, if there are two strictly convex metal regions contained in the cross-section of normal human tissue, then streaking artifacts occur along the common tangent lines of the two regions. In this paper we study the geodesic X-ray transform and streaking artifacts on nontrapping simple compact Riemannian manifolds with strictly convex boundaries. We show that the streaking artifacts result from the propagation of conormal singularities on the boundary of metal regions along the common tangent geodesics under the strong and seemingly strange assumption that the manifolds are two dimensional or spaces of constant curvature. This condition ensures that every Jacobi field takes the form of the product of a scalar function and parallel transport along the geodesic. Our results clarify the geometric meaning of the theory, which was imperceptible in the known results on the Euclidean space.
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Submitted 24 February, 2026; v1 submitted 10 February, 2024;
originally announced February 2024.
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Microlocal analysis of d-plane transform on the Euclidean space
Authors:
Hiroyuki Chihara
Abstract:
We study the basic properties of d-plane transform on the Euclidean space as a Fourier integral operator, and its application to the microlocal analysis of streaking artifacts in its filtered back-projection. The d-plane transform is defined by integrals of functions on the n-dimensional Euclidean space over all the d-dimensional planes, where 0<d<n. This maps functions on the Euclidean space to t…
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We study the basic properties of d-plane transform on the Euclidean space as a Fourier integral operator, and its application to the microlocal analysis of streaking artifacts in its filtered back-projection. The d-plane transform is defined by integrals of functions on the n-dimensional Euclidean space over all the d-dimensional planes, where 0<d<n. This maps functions on the Euclidean space to those on the affine Grassmannian G(d,n). This is said to be X-ray transform if d=1 and Radon transform if d=n-1. When n=2 the X-ray transform is thought to be measurements of CT scanners. In this paper we obtain concrete expression of the canonical relation of the d-plane transform and quantitative properties of the filtered back-projection of the product of the images of the d-plane transform. The latter one is related to the metal streaking artifacts of CT images, and some generalization of recent results of Park-Choi-Seo (2017) and Palacios-Uhlmann-Wang (2018) for the X-ray transform on the plane.
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Submitted 6 October, 2022; v1 submitted 25 August, 2021;
originally announced August 2021.
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Bargmann transform on the space of hyperplanes
Authors:
Hiroyuki Chihara
Abstract:
We introduce a Bargmann transform on the space of hyperplanes by applying the Plancherel formula of the Radon transform to the definition of the Bargmann transform on the Euclidean space. Some basic facts on microlocal analysis are also discussed.
We introduce a Bargmann transform on the space of hyperplanes by applying the Plancherel formula of the Radon transform to the definition of the Bargmann transform on the Euclidean space. Some basic facts on microlocal analysis are also discussed.
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Submitted 25 January, 2022; v1 submitted 24 July, 2020;
originally announced July 2020.
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Radiative equilibrium estimates of dust temperature and mass in high-redshift galaxies
Authors:
Akio K. Inoue,
Takuya Hashimoto,
Hiroki Chihara,
Chiyoe Koike
Abstract:
Estimating the temperature and mass of dust in high-$z$ galaxies is essential for discussions of the origin of dust in the early Universe. However, this suffers from limited sampling of the infrared spectral-energy distribution. Here we present an algorithm for deriving the temperature and mass of dust in a galaxy, assuming dust to be in radiative equilibrium. We formulate the algorithm for three…
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Estimating the temperature and mass of dust in high-$z$ galaxies is essential for discussions of the origin of dust in the early Universe. However, this suffers from limited sampling of the infrared spectral-energy distribution. Here we present an algorithm for deriving the temperature and mass of dust in a galaxy, assuming dust to be in radiative equilibrium. We formulate the algorithm for three geometries: a thin spherical shell, a homogeneous sphere, and a clumpy sphere. We also discuss effects of the mass absorption coefficients of dust at ultraviolet and infrared wavelengths, $κ_{\rm UV}$ and $κ_{\rm IR}$, respectively. As an example, we apply the algorithm to a normal, dusty star-forming galaxy at $z=7.5$, A1689zD1, for which three data points in the dust continuum are available. Using $κ_{\rm UV}=5.0\times10^4$ cm$^2$ g$^{-1}$ and $κ_{\rm IR}=30(λ/100μm)^{-β}$ cm$^2$ g$^{-1}$ with $β=2.0$, we obtain dust temperatures of 38--70~K and masses of $10^{6.5-7.3}$ M$_\odot$ for the three geometries considered. We obtain similar temperatures and masses from just a single data point in the dust continuum, suggesting the usefulness of the algorithm for high-$z$ galaxies with limited infrared observations. In the clumpy-sphere case, the temperature becomes equal to that of the usual modified black-body fit, because an additional parameter describing the clumpiness works as an adjuster. The best-fit clumpiness parameter is $ξ_{\rm cl}=0.1$, corresponding to $\sim10$\% of the volume filling factor of the clumps in this high-$z$ galaxy if the clump size is $\sim10$ pc, similar to that of giant molecular clouds in the local Universe.
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Submitted 27 April, 2020;
originally announced April 2020.
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Inversion of higher dimensional Radon transforms of seismic-type
Authors:
Hiroyuki Chihara
Abstract:
We study integral transforms mapping a function on the Euclidean space to the family of its integration on some hypersurfaces, that is, a function of hypersurfaces. The hypersurfaces are given by the graphs of functions with fixed axes of the independent variables, and are imposed some symmetry with respect to the axes. These transforms are higher dimensional version of generalization of the parab…
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We study integral transforms mapping a function on the Euclidean space to the family of its integration on some hypersurfaces, that is, a function of hypersurfaces. The hypersurfaces are given by the graphs of functions with fixed axes of the independent variables, and are imposed some symmetry with respect to the axes. These transforms are higher dimensional version of generalization of the parabolic Radon transform and the hyperbolic Radon transform arising from seismology. We prove the inversion formulas for these transforms under some vanishing and symmetry conditions of functions.
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Submitted 5 June, 2020; v1 submitted 14 October, 2019;
originally announced October 2019.
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Inversion of seismic-type Radon transforms on the plane
Authors:
Hiroyuki Chihara
Abstract:
We study integral transforms mapping a function on the Euclidean plane to the family of its integration on plane curves, that is, a function of plane curves. The plane curves we consider in the present paper are given by the graphs of functions with a fixed axis of the independent variable, and are imposed some symmetry with respect to the axes. These transforms contain the parabolic Radon transfo…
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We study integral transforms mapping a function on the Euclidean plane to the family of its integration on plane curves, that is, a function of plane curves. The plane curves we consider in the present paper are given by the graphs of functions with a fixed axis of the independent variable, and are imposed some symmetry with respect to the axes. These transforms contain the parabolic Radon transform and the hyperbolic Radon transform arising from seismology. We prove the inversion formulas for these transforms under some vanishing and symmetry conditions of functions.
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Submitted 23 May, 2020; v1 submitted 7 October, 2019;
originally announced October 2019.
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Mid-infrared spectroscopy of zodiacal emission with AKARI/IRC
Authors:
Aoi Takahashi,
Takafumi Ootsubo,
Hideo Matsuhara,
Itsuki Sakon,
Fumihiko Usui,
Hiroki Chihara
Abstract:
Interplanetary dust (IPD) is thought to be recently supplied from asteroids and comets. Grain properties of the IPD can give us the information about the environment in the proto-solar system, and can be traced from the shapes of silicate features around 10 $μ$m seen in the zodiacal emission spectra. We analyzed mid-IR slit-spectroscopic data of the zodiacal emission in various sky directions obta…
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Interplanetary dust (IPD) is thought to be recently supplied from asteroids and comets. Grain properties of the IPD can give us the information about the environment in the proto-solar system, and can be traced from the shapes of silicate features around 10 $μ$m seen in the zodiacal emission spectra. We analyzed mid-IR slit-spectroscopic data of the zodiacal emission in various sky directions obtained with the Infrared Camera on board AKARI satellite. After we subtracted the contamination due to instrumental artifacts, we have successfully obtained high S/N spectra and have determined detailed shapes of excess emission features in the 9 -- 12 $μ$m range in all the sky directions. According to a comparison between the feature shapes averaged over all directions and the absorption coefficients of candidate minerals, the IPD was found to typically include small silicate crystals, especially enstatite grains. We also found the variations in the feature shapes and the related grain properties among the different sky directions. From investigations of the correlation between feature shapes and the brightness contributions from dust bands, the IPD in dust bands seems to have the size frequency distribution biased toward large grains and show the indication of hydrated minerals. The spectra at higher ecliptic latitude showed a stronger excess, which indicates an increase in the fraction of small grains included in the line of sight at higher ecliptic latitudes. If we focus on the dependence of detailed feature shapes on ecliptic latitudes, the IPD at higher latitudes was found to have a lower olivine/pyroxene ratio for small amorphous grains. The variation of the mineral composition of the IPD in different sky directions may imply different properties of the IPD from different types of parent bodies, because the spatial distribution of the IPD depends on the type of the parent body.
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Submitted 27 August, 2019;
originally announced August 2019.
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Holomorphic Hermite functions in Segal-Bargmann spaces
Authors:
Hiroyuki Chihara
Abstract:
We study systems of holomorphic Hermite functions in the Segal-Bargmann spaces, which are Hilbert spaces of entire functions on the complex Euclidean space, and are determined by the Bargmann-type integral transform on the real Euclidean space. We prove that for any positive parameter which is strictly smaller than the minimum eigenvalue of the positive Hermitian matrix associated with the transfo…
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We study systems of holomorphic Hermite functions in the Segal-Bargmann spaces, which are Hilbert spaces of entire functions on the complex Euclidean space, and are determined by the Bargmann-type integral transform on the real Euclidean space. We prove that for any positive parameter which is strictly smaller than the minimum eigenvalue of the positive Hermitian matrix associated with the transform, one can find a generator of holomorphic Hermite functions whose anihilation and creation operators satisfy canonical commutation relations. In other words, we find the necessary and sufficient conditions so that some kinds of entire functions can be such generators. Moreover, we also study the complete orthogonality, the eigenvalue problems and the Rodrigues formulas.
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Submitted 18 May, 2018; v1 submitted 19 December, 2017;
originally announced December 2017.
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Holomorphic Hermite functions and ellipses
Authors:
Hiroyuki Chihara
Abstract:
In 1990 van Eijnghoven and Meyers introduced systems of holomorphic Hermite functions and reproducing kernel Hilbert spaces associated with the systems on the complex plane. Moreover they studied the relationship between the family of all their Hilbert spaces and a class of Gelfand-Shilov functions. After that, their systems of holomorphic Hermite functions have been applied to studying quantizati…
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In 1990 van Eijnghoven and Meyers introduced systems of holomorphic Hermite functions and reproducing kernel Hilbert spaces associated with the systems on the complex plane. Moreover they studied the relationship between the family of all their Hilbert spaces and a class of Gelfand-Shilov functions. After that, their systems of holomorphic Hermite functions have been applied to studying quantization on the complex plane, combinatorics, and etc. On the other hand, the author recently introduced systems of holomorphic Hermite functions associated with ellipses on the complex plane. The present paper shows that their systems of holomorphic Hermite functions are determined by some cases of ellipses, and that their reproducing kernel Hilbert spaces are some cases of the Segal-Bargmann spaces determined by the Bargmann-type transforms introduced by Sjoestrand.
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Submitted 8 May, 2018; v1 submitted 17 March, 2017;
originally announced March 2017.
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Hermite expansions of some tempered distributions
Authors:
Hiroyuki Chihara,
Takashi Furuya,
Takumi Koshikawa
Abstract:
We compute Hermite expansions of some tempered distributions by using the Bargmann transform. In other words, we calculate the Taylor expansions of the corresponding entire functions. Our method of computations seems to be superior to the direct computations in the shifts of singularities and the higher dimensional cases.
We compute Hermite expansions of some tempered distributions by using the Bargmann transform. In other words, we calculate the Taylor expansions of the corresponding entire functions. Our method of computations seems to be superior to the direct computations in the shifts of singularities and the higher dimensional cases.
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Submitted 2 May, 2017; v1 submitted 22 February, 2017;
originally announced February 2017.
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Bargmann-type transforms and modified harmonic oscillators
Authors:
Hiroyuki Chihara
Abstract:
We study some complete orthonormal systems on the real-line. These systems are determined by Bargmann-type transforms, which are Fourier integral operators with complex-valued quadratic phase functions. Each system consists of eigenfunctions for a second-order elliptic differential operator like the Hamiltonian of the harmonic oscillator. We also study the commutative case of a certain class of sy…
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We study some complete orthonormal systems on the real-line. These systems are determined by Bargmann-type transforms, which are Fourier integral operators with complex-valued quadratic phase functions. Each system consists of eigenfunctions for a second-order elliptic differential operator like the Hamiltonian of the harmonic oscillator. We also study the commutative case of a certain class of systems of second-order differential operators called the non-commutative harmonic oscillators. By using the diagonalization technique, we compute the eigenvalues and eigenfunctions for the commutative case of the non-commutative harmonic oscillators. Finally, we study a family of functions associated with an ellipse in the phase plane. We show that the family is a complete orthogonal system on the real-line.
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Submitted 19 April, 2019; v1 submitted 21 February, 2017;
originally announced February 2017.
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Absorption and scattering by interstellar dust in the silicon K-edge of GX 5-1
Authors:
S. T. Zeegers,
E. Costantini,
C. P. de Vries,
A. G. G. M. Tielens,
H. Chihara,
F. de Groot,
H. Mutschke,
L. B. F. M. Waters,
S. Zeidler
Abstract:
We study the absorption and scattering of X-ray radiation by interstellar dust particles, which allows us to access the physical and chemical properties of dust. The interstellar dust composition is not well understood, especially on the densest sight lines of the Galactic Plane. X-rays provide a powerful tool in this study. We present newly acquired laboratory measurements of silicate compounds t…
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We study the absorption and scattering of X-ray radiation by interstellar dust particles, which allows us to access the physical and chemical properties of dust. The interstellar dust composition is not well understood, especially on the densest sight lines of the Galactic Plane. X-rays provide a powerful tool in this study. We present newly acquired laboratory measurements of silicate compounds taken at the Soleil synchrotron facility in Paris using the Lucia beamline. The dust absorption profiles resulting from this campaign were used in this pilot study to model the absorption by interstellar dust along the line of sight of the low-mass X-ray binary (LMXB) GX 5-1. The measured laboratory cross-sections were adapted for astrophysical data analysis and the resulting extinction profiles of the Si K-edge were implemented in the SPEX spectral fitting program. We derive the properties of the interstellar dust along the line of sight by fitting the Si K-edge seen in absorption in the spectrum of GX 5-1. We measured the hydrogen column density towards GX 5-1 to be $3.40\pm0.1\times10^{22} \rm cm^{-2}$. The best fit of the silicon edge in the spectrum of GX 5-1 is obtained by a mixture of olivine and pyroxene. In this study, our modeling is limited to Si absorption by silicates with different Mg:Fe ratios. We obtained an abundance of silicon in dust of $4.0\pm0.3\times10^{-5}$ per H atom and a lower limit for total abundance, considering both gas and dust, of $>4.4\times10^{-5}$ per H atom, which leads to a gas to dust ratio of >0.22. Furthermore, an enhanced scattering feature in the Si K-edge may suggest the presence of large particles along the line of sight.
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Submitted 23 December, 2016;
originally announced December 2016.
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Fourth-order dispersive systems on the one-dimensional torus
Authors:
Hiroyuki Chihara
Abstract:
We present the necessary and sufficient conditions of the well-posedness of the initial value problem for certain fourth-order linear dispersive systems on the one-dimensional torus. This system is related with a dispersive flow for closed curves into compact Riemann surfaces. For this reason, we study not only the general case but also the corresponding special case in detail. We apply our result…
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We present the necessary and sufficient conditions of the well-posedness of the initial value problem for certain fourth-order linear dispersive systems on the one-dimensional torus. This system is related with a dispersive flow for closed curves into compact Riemann surfaces. For this reason, we study not only the general case but also the corresponding special case in detail. We apply our results on the linear systems to the fourth-order dispersive flows. We see that if the sectional curvature of the target Riemann surface is constant, then the equation of the dispersive flow satisfies our conditions of the well-posedness.
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Submitted 5 February, 2014; v1 submitted 20 September, 2013;
originally announced September 2013.
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A fourth-order dispersive flow into Kähler manifolds
Authors:
Hiroyuki Chihara,
Eiji Onodera
Abstract:
We discuss a short-time existence theorem of solutions to the initial value problem for a fourth-order dispersive flow for curves parametrized by the real line into a compact Kähler manifold. Our equations geometrically generalize a physical model describing the motion of a vortex filament or the continuum limit of the Heisenberg spin chain system. Our results are proved by using so-called the ene…
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We discuss a short-time existence theorem of solutions to the initial value problem for a fourth-order dispersive flow for curves parametrized by the real line into a compact Kähler manifold. Our equations geometrically generalize a physical model describing the motion of a vortex filament or the continuum limit of the Heisenberg spin chain system. Our results are proved by using so-called the energy method. We introduce a bounded gauge transform on the pullback bundle, and make use of local smoothing effect of the dispersive flow a little.
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Submitted 26 August, 2013;
originally announced August 2013.
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A third order dispersive flow for closed curves into almost Hermitian manifolds
Authors:
Hiroyuki Chihara,
Eiji Onodera
Abstract:
We discuss a short-time existence theorem of solutions to the initial value problem for a third order dispersive flow for closed curves into a compact almost Hermitian manifold. Our equations geometrically generalize a physical model describing the motion of vortex filament. The classical energy method cannot work for this problem since the almost complex structure of the target manifold is not…
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We discuss a short-time existence theorem of solutions to the initial value problem for a third order dispersive flow for closed curves into a compact almost Hermitian manifold. Our equations geometrically generalize a physical model describing the motion of vortex filament. The classical energy method cannot work for this problem since the almost complex structure of the target manifold is not supposed to be parallel with respect to the Levi-Civita connection. In other words, a loss of one derivative arises from the covariant derivative of the almost complex structure. To overcome this difficulty, we introduce a bounded pseudodifferential operator acting on sections of the pullback bundle, and eliminate the loss of one derivative from the partial differential equation of the dispersive flow.
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Submitted 29 July, 2008;
originally announced July 2008.
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Schroedinger flow into almost Hermitian manifolds
Authors:
Hiroyuki Chihara
Abstract:
We present a short-time existence theorem of solutions to the initial value problem for Schroedinger maps of a closed Riemannian manifold to a compact almost Hermitian manifold. The classical energy method cannot work for this problem since the almost complex structure of the target manifold is not supposed to be parallel with respect to the Levi-Civita connection. In other words, a loss of one…
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We present a short-time existence theorem of solutions to the initial value problem for Schroedinger maps of a closed Riemannian manifold to a compact almost Hermitian manifold. The classical energy method cannot work for this problem since the almost complex structure of the target manifold is not supposed to be parallel with respect to the Levi-Civita connection. In other words, a loss of one derivative arises from the covariant derivative of the almost complex structure. To overcome this difficulty, we introduce a bounded pseudodifferential operator acting on sections of the pullback bundle, and essentially eliminate the loss of one derivative from the partial differential equation of the Schroedinger map.
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Submitted 2 November, 2008; v1 submitted 22 July, 2008;
originally announced July 2008.
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Bounded Berezin-Toeplitz operators on the Segal-Bargmann space
Authors:
Hiroyuki Chihara
Abstract:
We discuss the boundedness of Berezin-Toeplitz operators on a generalized Segal-Bargmann space (Fock space) over the complex $n$-space. This space is characterized by the image of a global Bargmann-type transform introduced by Sjöstrand. We also obtain the deformation estimates of the composition of Berezin-Toeplitz operators whose symbols and their derivatives up to order three are in the Wiene…
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We discuss the boundedness of Berezin-Toeplitz operators on a generalized Segal-Bargmann space (Fock space) over the complex $n$-space. This space is characterized by the image of a global Bargmann-type transform introduced by Sjöstrand. We also obtain the deformation estimates of the composition of Berezin-Toeplitz operators whose symbols and their derivatives up to order three are in the Wiener algebra of Sjöstrand. Our method of proofs is based on the pseudodifferential calculus and the heat flow determined by the phase function of the Bargmann transform.
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Submitted 22 January, 2009; v1 submitted 1 June, 2008;
originally announced June 2008.
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Gain of analyticity for semilinear Schroedinger equations
Authors:
Hiroyuki Chihara
Abstract:
We discuss gain of analyticity phenomenon of solutions to the initial value problem for semilinear Schroedinger equations with gauge invariant nonlinearity. We prove that if the initial data decays exponentially, then the solution becomes real-analytic in the space variable and a Gevrey function of order 2 in the time variable except in the initial plane. Our proof is based on the energy estimat…
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We discuss gain of analyticity phenomenon of solutions to the initial value problem for semilinear Schroedinger equations with gauge invariant nonlinearity. We prove that if the initial data decays exponentially, then the solution becomes real-analytic in the space variable and a Gevrey function of order 2 in the time variable except in the initial plane. Our proof is based on the energy estimates developed in our previous work and on fine summation formulae concerned with a matrix norm.
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Submitted 15 June, 2008; v1 submitted 16 August, 2007;
originally announced August 2007.
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Resolvent estimates related with a class of dispersive equations
Authors:
Hiroyuki Chihara
Abstract:
We present a simple proof of the resolvent estimates of elliptic Fourier multipliers on the Euclidean space, and apply them to the analysis of time-global and spatially-local smoothing estimates of a class of dispersive equations. For this purpose we study in detail the properties of the restriction of Fourier transform on the unit cotangent sphere associated with the symbols of multipliers.
We present a simple proof of the resolvent estimates of elliptic Fourier multipliers on the Euclidean space, and apply them to the analysis of time-global and spatially-local smoothing estimates of a class of dispersive equations. For this purpose we study in detail the properties of the restriction of Fourier transform on the unit cotangent sphere associated with the symbols of multipliers.
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Submitted 2 August, 2007; v1 submitted 3 April, 2007;
originally announced April 2007.
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The initial value problem for a third order dispersive equation on the two-dimensional torus
Authors:
Hiroyuki Chihara
Abstract:
We present the necessary and sufficient condition for the $L^2$-well-posedness of the initial problem for a third order linear dispersive equation on the two dimensional torus. Birkhoff's method of asymptotic solutions is used to prove the necessity. Some properties of a system for quadratic algebraic equations associated to the principal symbol play crucial role in proving the sufficiency.
We present the necessary and sufficient condition for the $L^2$-well-posedness of the initial problem for a third order linear dispersive equation on the two dimensional torus. Birkhoff's method of asymptotic solutions is used to prove the necessity. Some properties of a system for quadratic algebraic equations associated to the principal symbol play crucial role in proving the sufficiency.
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Submitted 30 April, 2004; v1 submitted 1 April, 2004;
originally announced April 2004.
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Third order semilinear dispersive equations related to deep water waves
Authors:
Hiroyuki Chihara
Abstract:
We present local existence theorem of the initial value problem for third order semilinear dispersive partial differential equations in two space dimensions. This type of equations arises in the study of gravity wave of deep water, and cannot be solved by the classical energy method. To solve the initial value problem, we make full use of pseudodifferential operators with nonsmooth coefficients.
We present local existence theorem of the initial value problem for third order semilinear dispersive partial differential equations in two space dimensions. This type of equations arises in the study of gravity wave of deep water, and cannot be solved by the classical energy method. To solve the initial value problem, we make full use of pseudodifferential operators with nonsmooth coefficients.
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Submitted 27 July, 2004; v1 submitted 1 April, 2004;
originally announced April 2004.
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Photo-Luminescence and Possible Forsterite nanoparticles Model of Extended Red Emission
Authors:
K. Koike,
H. Chihara,
C. Koike,
M. Nakagawa,
M. Okada,
M. Matsumura,
J. Takada
Abstract:
Possible forsterite nanoparticle model of the Extended Red Emission(ERE) is proposed on the basis of photo-luminescence of forsterite after gamma-ray and neutron irradiation. Forsterite exhibits interesting thermoluminescence spectrum similar to ERE of Red Rectangle after irradiation in low temperature. It is shown that the forsterite after thermoluminescence is over exhibits photo-luminescence(…
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Possible forsterite nanoparticle model of the Extended Red Emission(ERE) is proposed on the basis of photo-luminescence of forsterite after gamma-ray and neutron irradiation. Forsterite exhibits interesting thermoluminescence spectrum similar to ERE of Red Rectangle after irradiation in low temperature. It is shown that the forsterite after thermoluminescence is over exhibits photo-luminescence(PL) when Ultraviolet ray is irradiated. The structure of PL spectrum is almost similar to that of thermoluminescence. In order to explain small variations of the peak position of wavelength of ERE spectrum, possible nanoparticle model of forsterite is investigated. Our model is consistent to the ISO observation data in near and middle infrared region, which suggest the existence of forsterite.
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Submitted 23 March, 2004;
originally announced March 2004.
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PAHs and crystalline silicates in the post-AGB star IRAS 16279-4757
Authors:
M. Matsuura,
A. A. Zijlstra,
F. J. Molster,
S. Hony,
L. B. F. M. Waters,
F. Kemper,
J. E. Bowey,
H. Chihara,
C. Koike,
L. P. Keller
Abstract:
IRAS 16279-4757 belongs to a group of post-AGB stars showing both PAH bands and crystalline silicates. We present mid-infrared images, that resolve the object for the first time. The morphology is similar to that of the `Red Rectangle' (HD 44179), the prototype object with PAHs and crystalline silicates. A two-component model and images suggest a dense oxygen-rich torus, an inner, low-density ca…
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IRAS 16279-4757 belongs to a group of post-AGB stars showing both PAH bands and crystalline silicates. We present mid-infrared images, that resolve the object for the first time. The morphology is similar to that of the `Red Rectangle' (HD 44179), the prototype object with PAHs and crystalline silicates. A two-component model and images suggest a dense oxygen-rich torus, an inner, low-density carbon-rich region and a carbon-rich bipolar outflow. The PAH bands are enhanced at the outflow, while the continuum emission is concentrated towards the center. Our findings support the suggestion that mixed chemistry and morphology are closely related. We discuss the ISO/SWS spectra of IRAS 16279-4757. Several bands in the ISO/SWS spectrum show a match with anorthite: this would be the first detection of this mineral outside the solar system. Compared to HD 44179, the shapes of PAH bands are closer to those of planetary nebulae, possibly related to a population of small PAHs present HD 44179, but absent around IRAS 16279-4757. Detailed examination of the spectra shows the individual character of these two objects. The comparison suggests that the torus found in IRAS 16279-4757 may have formed more recently than that in HD 44179.
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Submitted 2 February, 2004;
originally announced February 2004.
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Thermoluminescence of Simulated Interstellar Matter after Gamma-ray Irradiation
Authors:
K. Koike,
M. Nakagawa,
C. Koike,
M. Okada,
H. Chihara
Abstract:
Interstellar matter is known to be strongly irradiated by radiation and several types of cosmic ray particles. Simulated interstellar matter, such as forsterite $\rm Mg_{2}SiO_{4}$, enstatite $\rm MgSiO_{3}$ and magnesite $\rm MgCO_{3}$ has been irradiated with the $\rm ^{60}Co$ gamma-rays in liquid nitrogen, and also irradiated with fast neutrons at 10 K and 70 K by making use of the low-temper…
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Interstellar matter is known to be strongly irradiated by radiation and several types of cosmic ray particles. Simulated interstellar matter, such as forsterite $\rm Mg_{2}SiO_{4}$, enstatite $\rm MgSiO_{3}$ and magnesite $\rm MgCO_{3}$ has been irradiated with the $\rm ^{60}Co$ gamma-rays in liquid nitrogen, and also irradiated with fast neutrons at 10 K and 70 K by making use of the low-temperature irradiation facility of Kyoto University Reactor (KUR-LTL. Maximum fast neutron dose is $10^{17}n_f{\rm /cm^{2}}$).
After irradiation, samples are stored in liquid nitrogen for several months to allow the decay of induced radioactivity. We measured the luminescence spectra of the gamma ray irradiated samples during warming to 370K using a spectrophotometer. For the forsterite and magnesite, the spectra exhibit a rather intense peak at about 645 -- 655 nm and 660 nm respectively, whereas luminescence scarcely appeared in olivine sample. The spectra of forsterite is very similar to the ERE of the Red Rectangle.
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Submitted 4 February, 2002; v1 submitted 1 February, 2002;
originally announced February 2002.
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Crystalline silicate dust around evolved stars III. A correlations study of crystalline silicate features
Authors:
F. J. Molster,
L. B. F. M. Waters,
A. G. G. M. Tielens,
C. Koike,
H. Chihara
Abstract:
We have carried out a quantitative trend analysis of the crystalline silicates observed in the ISO spectra of a sample of 14 stars with different evolutionary backgrounds. We have modeled the spectra using a simple dust radiative transfer model and have correlated the results with other known parameters. We confirm the abundance difference of the crystalline silicates in disk and in outflow sour…
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We have carried out a quantitative trend analysis of the crystalline silicates observed in the ISO spectra of a sample of 14 stars with different evolutionary backgrounds. We have modeled the spectra using a simple dust radiative transfer model and have correlated the results with other known parameters. We confirm the abundance difference of the crystalline silicates in disk and in outflow sources, as found by Molster et al. (1999, Nature 401, 563). We found some indication that the enstatite over forsterite abundance ratio differs, it is slightly higher in the outflow sources with respect to the disk sources. It is clear that more data is required to fully test this hypothesis. We show that the 69.0 micron feature, attributed to forsterite, may be a very suitable temperature indicator. We found that the enstatite is more abundant than forsterite in almost all sources. The temperature of the enstatite grains is about equal to that of the forsterite grains in the disk sources but slightly lower in the outflow sources. Crystalline silicates are on average colder than amorphous silicates. This may be due to the difference in Fe content of both materials. Finally we find an indication that the ratio of ortho to clino enstatite, which is about 1:1 in disk sources, shifts towards ortho enstatite in the high luminosity (outflow) sources.
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Submitted 18 January, 2002;
originally announced January 2002.