Time periodic solutions to the Navier–Stokes equations in the rotational framework

We consider the Navier–Stokes equations in the rotational framework with the time periodic external force. We give sufficient conditions on the size of the external forces for the existence of time periodic solutions in terms of the Coriolis parameter. It follows from our conditions that the unique existence of time periodic solutions is guaranteed for large external forces provided the speed of rotation is sufficiently fast.     

An unknotting theorem for delta and sharp edge‐homotopy

Two spatial embeddings of a graph are said to be delta (resp. sharp) edge‐homotopic if they are transformed into each other by self delta (resp. sharp) moves and ambient isotopies. We show that any two spatial embeddings of a graph are delta (resp. sharp) edge‐homotopic if and only if the graph does not contain a subgraph which is homeomorphic to the theta graph or the disjoint union of two 1‐spheres, or equivalently G is homeomorphic to a bouquet. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Energy decay rates of elastic waves in unbounded domain with potential type of damping

In this paper we first show that the total energy of solutions for a semilinear system of elastic waves in Rn with a potential type of damping decays in an algebraic rate to zero. We study the critical potential case and we assume that the initial data have a compact support. An application for the Euler-Poisson-Darboux type dissipation V(t,x) is obtained and in this case the compactness of the support on the initial data is not necessary. Finally, we shall discuss the energy concentration region for the linear system of elastic waves in an exterior domain.     

Effect of Interventions for Improving Lumbar Motor Control on Low Back Pain in Sedentary Office Workers: A Randomized Controlled Trials

Objective: To clarify the effect of intervention with dynamic motor control exercise (DMCE) for the lumbar region on low back pain in sedentary office workers (SOWs). Methods: The participants comprised 32 SOWs with low back pain who were randomly categorized into two groups: the DMCE group and the normal trunk exercise (NTE) group. Both groups performed each exercise for three days per week for 8 weeks. The primary endpoints were evaluated for the lumbar and hip flexion angles during trunk forward bending, effect of low back pain on activities of daily living (using the Oswestry Disability Index), and intensity of low back pain (using the Visual Analog Scale) pre- and post-intervention. The extent of changes was calculated by subtracting the pre-intervention value from the post-intervention value and was compared between the two groups using an unpaired t-test. Results: The extent of changes in the lumbar flexion and hip flexion angles at 10° of trunk forward bending were significantly greater in the DMCE group than in the NTE group, and no significant differences were noted between the two groups at other angles of trunk forward bending. The extent of changes in the Oswestry Disability Index and the Visual Analog Scale scores were significantly greater in the DMCE group than in the NTE group. Conclusion: DMCE is effective in improving motor control in the lumbar region and hip joints, thereby ameliorating low back pain in SOWs.     

Self-oscillation of polymer chains with rhythmical soluble-insoluble changes

Self-oscillation of polymer chains in an aqueous solution has been achieved. The ruthenium catalyst for the Belousov-Zhabotinsky reaction was polymerized by using N-isopropylacrylamide and dissolved into the solution containing the BZ substrates. Periodical soluble-insoluble changes of the polymer chain were spontaneously induced by the BZ reaction. The conformational oscillations of the polymer were measured as the optical transmittance changes of the solution. This is the first report that rhythmical and reversible soluble-insoluble changes of polymer chains are realized under constant and homogeneous conditions. The transducing system from chemical energy of the BZ reaction to optical information has been constructed.     

Site-selective RNA scission at two sites for precise genotyping of SNPs by mass spectrometry

Short RNA fragments containing single nucleotide polymorphism (SNP) sites have been selectively clipped out of substrate RNA by using complementary DNA having two acridine residues and Lu(III), and the genotype of the substrate is accurately and easily determined by mass analysis of these fragments.     

pH-responsive aqueous foams stabilized by ionizable latex particles

We have designed a type of colloidal particle whose surface characteristics are sensitive to the pH of the aqueous phase in which they are dispersed. Particles of polystyrene latex stabilized by poly(acrylic acid) can act as stabilizers of aqueous foams by adsorbing at the air-water surface. Foams can be prepared and stabilized only at pH values below the isoelectric point where particles are either uncharged and flocculated or acquire a positive charge. At high pH where particles are anionic, no foam forms. This influence of pH on foamability and stability applies to both pH-dependent and pH-responsive systems.     

Asymmetric and efficient synthesis of homophenylalanine derivatives via Friedel-Crafts reaction with trifluoromethanesulfonic acid

An efficient Friedel-Crafts reaction of TFA-Asp(Cl)-OMe and stoichiometric amounts of benzene was established by using neat trifluoromethanesulfonic acid (TfOH) as solvent and catalyst under a mild condition. This methodology has been applied to many aromatic compounds and enabled synthesis of several homophenylalanine derivatives.     

Freeze-dried cellulose acetate membrane fine structure observation

A freeze-dried cellulose acetate membrane fine structure was observed with an ultrathin sectioning electron microscope. The fine structure for the top surface in this membrane could be seen by lead citrate staining ultrathin sectioning. This network structure was observed among pores, which existed in porous substrate. The pore diameter in the top surface was about 50 Å, a value that agrees approximately with the value estimated by gas permeation.