Fluorination of 2-alkyl-substituted oxanes. The synthesis and purification of perfluoro(2-alkyl-substituted oxane)s

Five kinds of 2-alkyl-substituted oxanes like 2-ethyloxane, 2-n-propyloxane, 2-iso-propyloxane, 2-n-butyloxane and 2-n-amyloxane were fluorinated electrochemically to give the corresponding perfluoro(2-alkyloxane)s. The perfluoro(2-alkyloxane)s were obtained in good yields from these starting materials together with isomeric perfluoro(2-alkyloxolane)s, perfluoro(2-alkyl-5-methyloxolane)s and perfluoro(dialkyl ether)s. The purification of the perfluoro(2-alkyloxane)s which contained small amounts of isomeric perfluoro(2-alkyloxolane)s was successfully achieved by recovering the former unreacted after treating these mixture with anhydrous aluminum chloride at 150 /sR 160 °C during /sR 48 hrs in order to convert the latter into the easy-separable perfluoro(2,5,5- trichloro-2-alkyloxolane)s. Small quantities of new perfluoro(5,5-dichloroalkanoyl chloride)s were also among the chlorination products. The spectroscopic data as well as the physical properties of these new fluorination products, and perfluoro(2,5,5-trichloro-2-alkyloxolane)s and perfluoro(5,5-dichloroalkanoyl chloride)s are presented.     

A Remark on the Global Existence of a Third Order Dispersive Flow into Locally Hermitian Symmetric Spaces

We prove time-global existence of solutions to the initial value problem for a third order dispersive flow into compact locally Hermitian symmetric spaces. The equation under consideration generalizes two-sphere-valued completely integrable systems modeling the motion of vortex filament. Unlike one-dimensional Schrödinger maps, our third order equation is not completely integrable under the curvature condition on the target manifold in general. The idea of our proof is to exploit two conservation laws and an “almost conserved quantity” which prevents the formation of a singularity in finite time.     

Standing Pulse Solutions in Reaction-Diffusion Systems with Skew-Gradient Structure

The purpose of this paper is to introduce a reaction-diffusion system with skew-gradient structure and discuss the stability of standing pulse solutions. In short, the skew-gradient system is a reaction-diffusion system which resembles a gradient system but has nonlinearities with different sign. We assume the existence of a standing pulse solution and define its orientation in some geometrical manner. Then we show that the stationary solution becomes unstable if time constants satisfy some inequality. The Evans function plays a crucial role for the stability analysis.     

Simple linear approximations to the likelihood equation for combining evidence in multiple 2×2 tables: A critique of conventional procedures

Summary The conventional procedures for a common odds ratio in multiple 2×2 tables are explored and critiqued. Three types of linear approximation to the likelihood equations under some models of common measures of association are used to derive the popular conventional estimators and test statistics. Some of them are derived using the model of the common standardized difference which is an unacceptable measure. The derivation provides us with some characteristics of the procedures. The advantages of procedures based on the conditional and unconditional likelihoods are discussed. The Institute of Statistical Mathematics     

Fast image enlargement using predefined codebook and eigenspace backprojection for lost pixel

In this paper, a new image enlargement method applying the backprojection for lost pixel (BPLP) to the predefined codebook-based method is proposed. BPLP is a method for image restoration. In BPLP, the eigenspace reflecting the characteristics of an input image is generated from the remained pixels and is used to restore the missing pixels. In the proposed method, the eigenspace is replaced by one generated from the predefined codebook (PDC). PDC represents edge-blurring properties in a small image patch and consists of pairs of low- and high-frequency image patches on various edge patterns. By replacing the PDC-based estimation of lost high-frequency components with BPLP, a fast image enlargement method retaining its performance can be developed. Through some experiments, the effectiveness of the proposed method was demonstrated. Especially, it was confirmed that the processing time of the proposed method was shortened to about 1/50 that of the PDC-based method.     

Throughput Measurement of a Multilayer-Coated Schwarzschild Objective Using Synchrotron Radiation

The throughput of a Schwarzschild objective using undulator synchrotron radiation was measured. Conventionally, the throughput was estimated from the squared reflectivity of one multilayer mirror and from the obstruction ratio. However, we evaluated the transmission ratio from the input and output photon flux using a precisely calibrated monochromatic beam from an undulator light source. It was found that the objective has a maximum throughput of 8.5% at a wavelength of 13.9 nm.     

Differences between PREMIER combustion in a natural gas spark-ignition engine and knocking with pressure oscillations

PREMIER (PREmixed Mixture Ignition in the End-gas Region) combustion occurs with auto-ignition in the end-gas region when the main combustion flame propagation is nearly finished. Auto-ignition is triggered by the increases in pressure and temperature induced by the main combustion flame. Similarly to engine knocking, heat is released in two stages when engines undergo this type of combustion. This pattern of heat release does not occur during normal combustion. However, engine knocking induces pressure oscillations that cause fatal damage to engines, whereas PREMIER combustion does not. The purpose of this study was to elucidate PREMIER combustion in natural gas spark-ignition engines, and differentiate the causes of knocking and PREMIER combustion. We applied combustion visualization and in-cylinder pressure analysis using a compression–expansion machine (CEM) to investigate the auto-ignition characteristics in the end-gas region of a natural gas spark-ignition engine. We occasionally observed knocking accompanied by pressure oscillations under the spark timings and initial gas conditions used to generate PREMIER combustion. No pressure oscillations were observed during normal and PREMIER combustion. Auto-ignition in the end-gas region was found to induce a secondary increase in pressure before the combustion flame reached the cylinder wall, during both knocking and PREMIER combustion. The auto-ignited flame area spread faster during knocking than during PREMIER combustion. This caused a sudden pressure difference and imbalance between the flame propagation region and the end-gas region, followed by a pressure oscillation.     

A third order dispersive flow for closed curves into almost Hermitian manifolds

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.     

The Change of Grip Strength in a Patient with Congenital Myotonic Dystrophy Over a 4-year Period

Myotonic dystrophy (MyD) is a neuromuscular disease that is autosomal dominant and the most common form of muscular dystrophy affecting adults. The clinical features of MyD include a multisystemic disorder characterized by myotonia, progressive muscle weakness and wasting, cataracts, premature balding and mental retardation. The most severe type of MyD is classified as congenital MyD (CMyD). The muscle weakness in CMyD is very severe, but muscle development can be observed in the period of growth. However, no clinical case of this type has been reported yet. Therefore, we report on a girl with CMyD who had an increase in muscle strength over a four-year period. The girl with CMyD participated in this study from the age of 9 to the age of 12. The measurement of muscle strength was recorded as the maximum score of grip strength with the use of dynamometers. Grip strength was assessed once a year by the same two physical therapists. Grip strength of CMyD for each year was markedly weak when compared with the normal controls, but muscle strength changed within some specific growth areas. The muscle weakness in CMyD was remarkable, but the result showed that specific muscle strength of CMyD in childhood was actually increased.