Periodic orbits in the Euler method for a class of delay differential equations

Recently, we have proved that Naimark-Sacker bifurcations occur in the Euler method applied to a delay differential equation [1]. By slightly modifying the proof, it is verified that the same result holds, e.g., for another equation obtained from the equation by a change of the dependent variable. However, in computer experiments, the Euler method presents different behavior for the two equations: an invariant circle is observed in the former case; a stable periodic orbit is observed in the latter case.

We show that it is reasonable to consider the behavior in the latter case as a weak resonance in the Naimark-Sacker bifurcation. More specifically, we study a class of delay differential equations which includes the second equation, paying attention to special periodic solutions found by Kaplan and Yorke [2], and prove constructively that the Euler method applied to each equation of the class has at least two periodic orbits. Numerical experiments are presented which indicate that one orbit is stable and the other orbit is unstable, whose unstable manifold forms an invariant circle.     

Effects of follicle size and electrolytes and glucose in maturation medium on nuclear maturation and developmental competence of bovine oocytes

The concentrations of electrolytes (Na, K, Cl, Mg and Ca) and glucose in small follicle (SF) follicular fluid (SFF) and large follicle (LF) follicular fluid (LFF) from slaughterhouse-derived ovaries were studied. Oocytes were matured in medium based on synthetic oviductal fluid. The effects of various concentrations of electrolytes (Na, K, Ca and Mg) and glucose in the maturation medium on the progression of nuclear maturation and subsequent development were also studied. K in SFF was significantly greater than that in LFF. The Mg concentration in follicular fluid (FF) is 2.0-2.3 mM, which is greater than the concentration present in medium generally used for culture. The glucose concentration in FF is about 3.5-3.9 mM and rapidly decreases during the preservation of ovaries. LF oocytes resumed nuclear maturation and progressed to the M2 stage significantly faster than those collected from SF oocytes. In addition, more LF oocytes developed to blastocysts than did SF oocytes. Changing the Na/K ratio in the maturation medium from 16 to 24 did not affect either the progression of nuclear maturation or the rate of development. A low concentration of Mg (0.5 mM) combined with a low Ca concentration (0.5 mM) inhibited the rate of development, but did not affect the progression of nuclear maturation. On the other hand, increasing the Mg concentration to 2.0 mM from 0.5 mM hastened the progression of nuclear maturation and improved the rate of blastulation, irrespective of the Ca concentration. The progression of nuclear maturation was faster and the rate of development was greater with 5.56 mM glucose than with 1.5 mM glucose. The difference in time needed to progress to M2 among the experiment was about 2-3 h. Therefore, prolonging the maturation periods from 21 to 24 h did not change the rate of development. Our results show that the concentrations of Mg and glucose in the maturation medium and the follicle size enveloping the oocyte affect the progression of nuclear maturation and subsequent development. The time requirement for oocytes to reach M2 is strongly related to the developmental competence of the oocytes.     

Superstructures and phase transitions of Bi2O3

Polymorphs of bismuth sesquioxide were studied by TG-DTA and X-ray diffraction methods and by electron microscopy. Phase transitions of the polymorphs are influenced not only by the temperature before cooling and the cooling rate but also by the duration of melting. New commensurate and incommensurate superstructure phases, observed under the electron microscope, are described as the Naxa types, where N is various value between 2 and 2.48. Here a stands for the cell dimension of the δ form, the fluorite-type structure. The superstructures can be derived by a scheme for ordering oxygen vacancies in the defective fluorite-type structure.     

Simultaneous multicolor imaging of five different lymphatic basins using quantum dots

Quantum dots can be used to perform multicolor images with high fluorescent intensity and are of a nanosize suitable for lymphatic imaging via direct interstitial injection. Here simultaneous multicolor in vivo wavelength-resolved spectral fluorescence lymphangiography is shown using five quantum dots with similar physical sizes but different emission spectra. This allows noninvasive and simultaneous visualization of five separate lymphatic flows draining and may have implications for predicting the route of cancer metastasis into the lymph nodes.     

Steep fronts at transient recovery voltages appearing with the interruption of inrush currents of transformers

High lightning overvoltages do not appear in underground substations connected to transmission cables. Consequently, it is very important to thoroughly investigate switching overvoltages and to achieve rational insulation coordination for apparatus installed in such underground substations. This paper discusses the occurrence of steep fronts at transient recovery voltages (TRV) appearing at circuit breakers when the inrush currents of transformers are interrupted. Caused by a steep front at the TRV, reignitions occur at circuit breakers, resulting in the generation of high overvoltages with high frequencies. The overvoltages are among the highest switching overvoltages appearing at the terminal of a transformer. The authors clarified the mechanism of the generation of steep fronts at TRV by means of EMTP analysis, as well as by carrying out tests in a high‐power laboratory. © 2001 Scripta Technica, Electr Eng Jpn, 135(1): 24–32, 2001     

Circulating Vitreous microRNA as Possible Biomarker in High Myopic Eyes with Macular Hole

High myopia is a major cause of irreversible visual impairment globally. In the present study, we investigated the microRNA (miRNA) profile in the vitreous of macular hole (MH) and high myopic MH. We performed miRNA analysis using TaqMan^® Low Density Arrays (Thermo Fisher Scientific, Waltham, MA, USA) to investigate the circulating vitreous miRNA profile from patients with MH (axial length < 26.5 mm, n = 11) and high myopic MH (axial length ≥ 26.5 mm, n = 11) who underwent pars plana vitrectomy. The vitreous inflammatory cytokine signature was examined in high myopic MH eyes using a multiplex assay. A miRNA-Array analysis revealed that let-7c was significantly up-regulated and miR-200a was significantly down-regulated in high myopic MH eyes compared to those in MH eyes. The bioinformatics analysis for up-regulated miRNA targeted gene identified 23 pathways including mitogen-activated protein kinase (MAPK) and several inflammatory signaling pathways, whereas the bioinformatics analysis for down-regulated miRNA targeted genes showed 32 enriched pathways including phosphoinositide 3-kinase/protein kinase B (PI3K/AKT). The levels of inflammatory cytokines including IP-10, IFN-γ, and MCP-1 were significantly higher in the vitreous of high myopic MH eyes. These results suggest that specific miRNAs expressed in the vitreous may be associated with the pathological condition of high myopic MH and the above mentioned miRNAs may contribute to the development of inflammatory status in the vitreous of high myopic eyes.     

Performance of Y2O3∕Al multilayer coatings for the He-II radiation at 30.4 nm

We briefly report on the performance and stability of periodic multilayer mirrors containing Y(2)O(3) and Al layers designed for normal incidence reflection at the He-II emission line (30.4 nm). We found that Y(2)O(3)∕Al multilayer coatings had higher reflectivity (24.9%) at 30.4 nm and significantly lower reflectivity (1.3%) at 58.4 nm than the conventional coatings such as Mo∕Si. Furthermore, we investigated the temporal stability of the Y(2)O(3)∕Al multilayer coatings. Our sample was kept under vacuum, dry N(2) purge, and normal atmosphere for over three months, and there were no measurable changes in the reflectivity. These results suggest that we can use Y(2)O(3)∕Al multilayer coatings as standard mirrors for the He-II radiation.