Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping

In the previous work, it was shown that, in supersymmetric (matrix) discretized quantum mechanics, inclusion of an external field twisting the boundary condition of fermions enables us to discuss spontaneous breaking of supersymmetry (SUSY) in the path-integral formalism in a well-defined way. In the present work, we continue investigating the same systems from the points of view of localization and Nicolai mapping. The localization is studied by changing of integration variables in the path integral, which is applicable whether or not SUSY is explicitly broken. We examine in detail how the integrand of the partition function with respect to the integral over the auxiliary field behaves as the auxiliary field vanishes, which clarifies a mechanism of the localization. In SUSY matrix models, we obtain a matrix-model generalization of the localization formula. In terms of eigenvalues of matrix variables, we observe that eigenvalues' dynamics is governed by balance of attractive force from the localization and repulsive force from the Vandermonde determinant. The approach of the Nicolai mapping works even in the presence of the external field. It enables us to compute the partition function of SUSY matrix models for finite N (N is the rank of matrices) with arbitrary superpotential at least in the leading nontrivial order of an expansion with respect to the small external field. We confirm the restoration of SUSY in the large-N limit of a SUSY matrix model with a double-well scalar potential observed in the previous work.     

Rapid enantioseparation of 1-aminoindan by microchip electrophoresis with linear-imaging UV detection.

Chiral separations of 1-aminoindan (AI) by cyclodextrin electrokinetic chromatography (CDEKC) were investigated on microfluidic quartz chips. By using a microchip electrophoresis (MCE) instrument equipped with a linear-imaging UV detector, the separation process of the enantiomeric compounds was observed. When sulfated beta-cyclodextrin was employed as a chiral selector, the baseline separation of AI could be achieved within 1 min with a high repeatability. The relative standard deviation of the migration time was less than 6%. The fastest separation was achieved in 14 s, utilizing a separation length of only 6.1 mm. These results show that the MCE analysis employing a linear imaging UV detector has a significant potential for fast chiral analysis.     

Gel formation with multiple interunit junctions. II—mixture of different functional molecules

Number‐ and weight‐average molecular weight of condensation polymers formed in the mixture of primary molecules carrying different species of functional groups A and B are derived by the cascade theory. These functional groups are allowed to form multiple junctions of arbitrary multiplicity k. From the weight average, the gel point condition is found to be given by 1 ? (f_w ? 1)(μ_A,A ? 1) ? (g_w ? 1)(μ _B,B ? 1) + (f_w ? 1)(g_w ? 1)D_μ = 0, where f_w and g_w are average functionality of the primary molecules, μ _αβ the average multiplicity of β groups in the junctions where a path of an α‐group enters, and D_μ ≡ (μ_A,A ? 1)(μ _B,B ? 1) ? μ _A,Bμ _B,A the multiplicity determinant. Possible applications to thermoreversible gelation are suggested. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2413–2421, 2003     

Light Scattering Changes in Isolated Brain Mitochondria during Anoxia - Magnesium Effect on Morphological Changes and Respiration -

Under pathological conditions, morphological changes of the cells and tissues may differ from those of normal conditions, which can be reflected by changes in light scattering (LS). Consequently, LS has been recognized as a potential non-invasive tool for optical diagnosis of living tissue. This paper aimed to identify the basic properties of LS of isolated brain mitochondria in vitro under normoxic and anoxic conditions in the presence and absence of Mg²⁺. An increase in LS was observed during anoxia in both the presence and absence of Mg²⁺. In both cases, the changes in LS initiated by anoxia and reoxygenation started concomitantly with the reduction of heme aa₃. The rates of LS changes were slower than those of heme aa₃, particularly in the presence of Mg²⁺. Mg²⁺ inhibited the morphological responses of mitochondria caused by the addition of ADP and ATP, and significantly reduced the oxygen consumption rate in state 4. These results are due to modulation of the K⁺/H⁺ antiporter affected by Mg²⁺. In addition, the mitochondria were well coupled, although the basal level of LS fell after addition of Mg²⁺. Therefore, the observed responses of mitochondria at anoxia were physiological and independent of the presence or absence of Mg²⁺. The relationship between LS and redox state of cytochrome c oxidase, an anoxic indicator, provides a basis to assess the tissue conditions in vivo.     

Spectrophotometric determination of titanium with o-carboxyphenylfluorone in cationic micellar media, and its equilibrium and kinetic studies

Spectrophotometric determination of titanium(IV) was accomplished with o-carboxyphenylfluorone (OCPF) in the presence of hexadecyltrimethyl ammonium chloride (HTAC) under strongly acidic media. In the determination of titanium(IV), Beer's law was obeyed in the range of 24-340 ng mL⁻¹ with an effective molar absorption coefficient (at 530 nm) and relative standard deviation of 2.24 × 10⁵ dm³ mol⁻¹ cm⁻¹ and 0.64% (n = 8), respectively. The severe interference of iron ions was easily eliminated by the addition of ethylenediaminetetraacetic acid (EDTA); the effects of other foreign substances were low. Equilibrium and kinetic studies under analytical conditions were investigated to quantitatively evaluate the reaction mechanism. The obtained orange complex is considered to be Ti(OCPF)₄. Its stability log K_f and rate constant K_obs are 16.88 and 1.65 × 10⁻² s⁻¹, respectively. It is suggested that the color of the complex is related to the species of OCPF in the solution.     

Sesquarterpenes (C35 terpenes) biosynthesized via the cyclization of a linear C35 isoprenoid by a tetraprenyl-β-curcumene synthase and a tetraprenyl-β-curcumene cyclase: identification of a new terpene cyclase

In this study, mono- and pentacyclic C(35) terpenes from Bacillus subtilis were biosynthesized via the cyclization of C(35) isoprenoid using purified enzymes, including the first identified new terpene cyclase that shows no sequence homology to any of the known terpene cyclases. On the basis of these findings, we propose that these C(35) terpenes should be called the new family of "sesquarterpenes."     

On energy estimates for second order hyperbolic equations with Levi conditions for higher order regularity

We consider energy estimates for second order homogeneous hyperbolic equations with time dependent coefficients. The property of energy conservation, which holds in the case of constant coefficients, does not hold in general for variable coefficients; in fact, the energy can be unbounded as t → ∞ in this case. The conditions to the coefficients for the generalized energy conservation (GEC), which is an equivalence of the energy uniformly with respect to time, has been studied precisely for wave type equations, that is, only the propagation speed is variable. However, it is not true that the same conditions to the coefficients conclude (GEC) for general homogeneous hyperbolic equations. The main purpose of this paper is to give additional conditions to the coefficients which provide (GEC); they will be called as C ^k -type Levi conditions due to the essentially same meaning of usual Levi condition for the well-posedness of weakly hyperbolic equations.     

Non-Newtonian laminar boundary-layer heat transfer in stirred tanks

 A laminar boundary-layer heat transfer in a jacketed, stirred tank with non-Newtonian fluids has been experimentally and theoretically examined. Heat transfer rates from jacket to process liquid through the stirred tank wall were measured for different large-scale impeller designs and rheological properties. On the basis of the laminar boundary-layer theory, we developed a theoretical correlation for non-Newtonian laminar tank-side film heat transfer coefficients in stirred tanks. The correlation was derived using von Karman's integral technique. Satisfactory agreement between the predictions of the proposed correlation and the present experimental data for viscous Newtonian and non-Newtonian laminar heat transfer in stirred tanks was obtained. Received on 20 February 2001 / Published online: 29 November 2001     

The Repulsion Between Localization Centers in the Anderson Model

In this note we show that, a simple combination of deep results in the theory of random Schrödinger operators yields a quantitative estimate of the fact that the localization centers become far apart, as corresponding energies are close together.