A solution of radiative transfer in isotropic plane-parallel atmosphere by integrating Milne equation

In this paper we solve the inversion problem of the radiative transfer process in the isotropic plane-parallel atmosphere by iterative integrations of the Milne integral equation. As a result, we obtain the scattering function in the form of a cubic polynomial in optical thickness. The author has already solved the same problem by iterative integrations of Chandrasekhar's integral equation. In the Milne integral equation, both the cosines of the viewing angles and the optical thickness are integral variables, while in Chandrasekhar's integral equation the cosines of the viewing angles are variables but the optical thickness is not. We derive several series of exponential-like functions as intermediate derivations. Their convergences are evaluated by the author's previous work in the solution of Chandrasekhar's integral equation. The truncated scattering function up to the third order in optical thickness thus obtained is identical to that obtained from Chandrasekhar's integral equation, though their apparent forms are different. Chandrasekhar pointed out that the solution of Chandrasekhar's integral equation does not have a uniqueness of solution. The Milne equation, in contrast, has been proven to have a unique solution. We discuss the uniqueness of the solution by these two methods.     

Integration of Chandrasekhar's integral equation

We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA “explicitly” in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness.     

Development of a Sensitive Bioluminogenic Probe for Imaging Highly Reactive Oxygen Species in Living Rats

A sensitive bioluminogenic probe for highly reactive oxygen species (hROS), SO₃H‐APL, was developed based on the concept of dual control of bioluminescence emission by means of bioluminescent enzyme‐induced electron transfer (BioLeT) and modulation of cell‐membrane permeability. This probe enables non‐invasive visualization of physiologically relevant amounts of hROS generated deep inside the body of living rats for the first time. It is expected to serve as a practical analytical tool for investigating a wide range of biological functions of hROS in vivo. The design concept should be applicable to other in vivo bioluminogenic probes.     

Complexation behavior of mono- and disaccharides by the vinylbenzeneboronic acid–divinylbenzene copolymer resins packed in a high-performance liquid chromatographic column

Using an HPLC column packed with monodispersed vinylbenzeneboronic acid–divinylbenzene (V–D) copolymer resins, the elution behaviors of the mono- and disaccharides were studied under different pH mobile phases. The monodispersed V–D copolymer resins were prepared by the copolymerization of 4-vinylbenzeneboronic acid and divinylbenzene in the presence of template silica gel particles (particle size: 5 μm; pore size: 10 nm), followed by dissolution of the template silica gel using a NaOH solution. Similarly, styrene–divinylbenzene (S–D) copolymer resins as the control resins were also synthesized. The transmission electron micrographs of these polymer resins revealed a good monodispersity. The complexation behavior of the saccharides was evaluated by comparison of the peak area eluted through the V–D column for that through the S–D column. Four aldopentoses (d-ribose, d-arabinose, d-xylose, and d-lyxose) and four aldohexoses (d-glucose, d-mannose, d-galactose, and d-talose) were retained completely at pH 11.9. Especially, ribose and talose were totally retained even under acidic and neutral conditions. For the disaccharides, unlike sucrose and maltose, palatinose was completely retained in basic mobile phases.     

Development of a far-red to near-infrared fluorescence probe for calcium ion and its application to multicolor neuronal imaging

To improve optical imaging of Ca(2+) and to make available a distinct color window for multicolor imaging, we designed and synthesized CaSiR-1, a far-red to near-infrared fluorescence probe for Ca(2+), using Si-rhodamine (SiR) as the fluorophore and the well-known Ca(2+) chelator BAPTA. This wavelength region is advantageous, affording higher tissue penetration, lower background autofluorescence, and lower phototoxicity in comparison with the UV to visible range. CaSiR-1 has a high fluorescence off/on ratio of over 1000. We demonstrate its usefulness for multicolor fluorescence imaging of action potentials (visualized as increases in intracellular Ca(2+)) in brain slices loaded with sulforhodamine 101 (red color; specific for astrocytes) that were prepared from transgenic mice in which some neurons expressed green fluorescent protein.     

Effect of basic amino acids on photoreaction of ketoprofen in phosphate buffer solution

Photoreaction of ketoprofen (KP), one of the widely used nonsteroidal anti-inflammatory drugs (NSAIDs), was studied with transient absorption spectroscopy in phosphate buffer solution (pH 7.4) in the presence of basic amino acids of histidine (His), lysine (Lys) and arginine (Arg). Deprotonated form of KP (KP(-)) excited with UV-light irradiation gave rise to carbanion through a decarboxylation reaction. It was found that carbanion abstracted a proton from the side chain of the protonated amino acids to yield 3-ethylbenzophenone ketyl biradical (EBPH); however, no reaction was observed with alanine. The relative yield of EBPH by the proton transfer reaction with His was ca. 40 times larger than that of the other two basic amino acids, suggesting that the proton-donating ability of His (protonated His) should be quite high. The information on the photoreaction mechanism of NSAIDs with basic amino acids was essential to understand primary reaction of excited NSAIDs in vivo causing photosensitization on human skin.     

Single-molecule magnets of ferrous cubes: structurally controlled magnetic anisotropy

Tetranuclear Fe(II) cubic complexes were synthesized with Schiff base ligands bridging the Fe(II) centers. X-ray structural analyses of six ferrous cubes, [Fe4(sap)4(MeOH)4].2H2O (1), [Fe4(5-Br-sap)4(MeOH)4] (2), [Fe4(3-MeO-sap)4(MeOH)4].2MeOH (3), [Fe4(sae)4(MeOH)4] (4), [Fe4(5-Br-sae)4(MeOH)4].MeOH (5), and [Fe4(3,5-Cl2-sae)4(MeOH)4] (6) (R-sap and R-sae were prepared by condensation of salicylaldehyde derivatives with aminopropyl alcohol and aminoethyl alcohol, respectively) were performed, and their magnetic properties were studied. In 1-6, the alkoxo groups of the Schiff base ligands bridge four Fe(II) ions in a mu3-mode forming [Fe4O4] cubic cores. The Fe(II) ions in the cubes have tetragonally elongated octahedral coordination geometries, and the equatorial coordination bond lengths in 4-6 are shorter than those in 1-3. Dc magnetic susceptibility measurements for 1-6 revealed that intramolecular ferromagnetic interactions are operative to lead an S = 8 spin ground state. Analyses of the magnetization data at 1.8 K gave the axial zero-field splitting parameters (D) of +0.81, +0.80, +1.15, -0.64, -0.66, and -0.67 cm(-1) for 1-6, respectively. Ac magnetic susceptibility measurements for 4-6 showed both frequency dependent in- and out-of-phase signals, while 1-3 did not show out-of-phase signals down to 1.8 K, meaning 4-6 are single-molecule magnets (SMMs). The energy barriers to flip the spin between up- and down-spin were estimated to 28.4, 30.5, and 26.2 K, respectively, for 4-6. The bridging ligands R-sap2- in 1-3 and R-sae2- in 4-6 form six- and five-membered chelate rings, respectively, which cause different steric strain and Jahn-Teller distortions at Fe(II) centers. The sign of the D value was discussed by using angular overlap model (AOM) calculations for irons with different coordination geometry.     

Photodissociation of CO from [Ru3(mu3-O)(mu-OOCCH3)6(CO)L2] in acetonitrile, where L = pyridine, 4-cyanopyridine and methanol

Photodissociation of CO from oxo-centered trinuclear ruthenium clusters [Ru3(mu3-O)(mu-OOCCH3)6(CO)L2] (L = pyridine (py): 1; 4-cyanopyridine (cpy): 2; methanol: 3) dissolved in organic solvents has been examined. Upon photolysis (> or = 290 nm, a 450-W Xe lamp), an absorption peak at 585 nm observed for 1 in CH3CN decreases its intensity and a new absorption band appears and grows at 896 nm. This spectral change, presenting isosbestic points, corresponds to photosubstitution of CO in 1 to form [Ru3(mu3-O)(mu-OOCCH3)6(CH3CN)(py)2] 4. Photoexcitation of carbonyl complexes 2 and 3 in CH3CN also affords the corresponding CH3CN-coordinated complexes [Ru3(mu3-O)(mu-OOCCH3)6(CH3CN)(cpy)2] 6 and [Ru3(mu3-O)(mu-OOCCH3)6(CH3CN)3] 7, respectively. The photosubstitution reactions (excitation wavelength, > or = 290 nm) are well described by the first-order kinetics: k = 7.3 x 10(-4) s(-1) for 1, 4.9 x 10(-4) s(-1) for 2 and 5.1 x 10(-4) s(-1) for 3 (298 K). In the presence of a 100-fold excess of py, photolysis of 1 yields a tris(py) complex [Ru3(mu3-O)(mu-OOCCH3)6(py)3] 5 via photochemical loss of CO followed by coordination of py. The overall reaction (photochemical and thermal) is also confirmed by 1H NMR spectroscopy. The dissociative character of the photosubstitution is supported by negligible effects of the concentration of the entering pyridine molecule, the nature of solvents and the type of terminal monodentate ligands (other than CO) attached to the cluster. Quantum yield measurements with varied excitation wavelengths have shown that absorption bands located in the UV region (< 400 nm) play a principal role in photosubstitution, whereas an absorption band in the visible region (centered at approximately 580 nm), ascribed to an "intracluster" charge transfer, is not at all responsible for photosubstitution.     

Syntheses, structures, and properties of trinuclear complexes [M(bpca)(2)(M'(hfac)(2))(2)], constructed with the complexed bridging ligand [M(bpca)(2)] [M, M' = Ni(II), Mn(II); Cu(II), Mn(II); Fe(II), Mn(II); Ni(II), Fe(II); and Fe(II), Fe(II); Hbpca = Bis(2-pyridylcarbonyl)amine, Hhfac = Hexafluoroacetylacetone

Five trinuclear complexes [M(bpca)(2)(M'(hfac)(2))(2)] (where MM'(2) = NiMn(2), CuMn(2), FeMn(2), NiFe(2), and FeFe(2); Hbpca = bis(2-pyridylcarbonyl)amine; and Hhfac = hexafluoroacetylacetone) were synthesized almost quantitatively by the reaction of [M(bpca)(2)] and [M'(hfac)(2)] in 1:2 molar ratio, and their structures and magnetic properties were investigated. Three complexes, with M' = Mn, crystallize in the same space group, Pna2(1), whereas two complexes, with M' = Fe, crystallize in P4(1), and complexes within each set are isostructural to one another. In all complexes, [M(bpca)(2)] acts as a bis-bidentate bridging ligand to form a linear trinuclear complex in which three metal ions are arranged in the manner M'-M-M'. The central metal ion is in a strong ligand field created by the N(6) donor set, and hence the Fe(II) in the [Fe(bpca)(2)] moiety is in a low-spin state. The terminal metal ions (M') are surrounded by O(6) donor sets with a moderate ligand field, which leads to the high-spin configuration of Fe(II). Three metal ions in all complexes are almost collinear, and metal-metal distances are ca. 5.5 A. The magnetic behavior of NiMn(2) and NiFe(2) shows a weak ferromagnetic interaction between the central Ni(II) ion and the terminal Mn(II) or Fe(II) ions. In these complexes, sigma-spin orbitals of the central Ni(II) ion and those of terminal metal ions have different symmetry about a 2-fold rotation axis through the Ni-N(amide)-M'(terminal) atoms, and this results in orthogonality between the neighboring sigma-spin orbitals and thus ferromagnetic interactions.