Weierstrass Gap Sets for Quadruples of Points on Compact Riemann Surfaces

AbstractLet M be a compact Riemann surface of genus g, and let P1,…,P4 be distinct points on M. We study the Weierstrass gap set G(P1,…,P4) and prove the conjecture of Ballico and Kim on the upper bound of #G(P1,…,P4) affirmatively in case M is d-gonal curve of genus g≥5 with d=2 or d≥5

A way of computer use in mathematics teaching -The effectiveness that visualization brings-

We report a class of the mathematics in which an animation technology (calculating and plotting capabilities) of the software Mathematica is utilized. This class is taught for university students in a computer laboratory during a second semester. It is our purpose to make a student realize the usefulness and the importance of mathematics easily through visualization. In addition, we hope that students will acquire a new power of mathematics needed in the 21st century. For several years, we have continued this kind of class, and have continued to investigate the effectiveness that our teaching method (especially visualization) brings in the understanding of the mathematics. In this paper, we present some of this teaching method, which is performed in our class. From the questionnaire survey, it is found that our teaching method not only convinces students that the mathematics is useful or important but also deepens the mathematic understanding of students more

Physiological and Ultrastructural Studies on the Origin of Activator Calcium in Body Wall Muscles of Spoon Worms

To examine the origin of activator Ca and its translocation during contraction in body wall muscles (BWM) of spoon worms, Urechis unicinctus , physiological and ultrastructural studies, including cytochemistry, were performed. The potassium (K-) contracture tension was significantly reduced by the removal of external Ca, and by the application of Mn, La and verapamil. On the other hand, caffeine induced a prolonged contraction. The removal of Ca and Mg from the external solution, and the rapid cooling caused an irregular or oscillatory contraction. These results suggested that, in BWM fibers, the activator Ca is supplied partially from both external solution and intracellular Ca-accumulating structures. Ultrastructural observations revealed that the muscle fibers contain a relatively large amount of sarcoplasmic reticulum (SR). The fractional volume of the SR relative to the fiber volume was 2~5% in all fibers of three muscle layers. To demonstrate the Ca localization, the muscle fibers were fixed by pyroantimonate (PA) methods at resting and contracting states. In the resting fibers, the PA precipitates were exclusively localized in the SR and the inner surface of plasma membrane. On the other hand, in the contracting fibers, they were diffusely distributed in the central regions of myoplasm, and had disappeared from the SR and plasma membrane. X-ray microanalysis revealed that the PA precipitates contain Ca. With the results of physiological experiments, these results indicate that the activator Ca originates not only from the external solution, but also from the intracellular Ca-accumulating structures, the SR and the inner surface of plasma membrane.Full-Length Pape

A way of computer use in mathematics teaching -The effectiveness that visualization brings-

We report a class of the mathematics in which an animation technology (calculating and plotting capabilities) of the software Mathematica is utilized. This class is taught for university students in a computer laboratory during a second semester. It is our purpose to make a student realize the usefulness and the importance of mathematics easily through visualization. In addition, we hope that students will acquire a new power of mathematics needed in the 21st century. For several years, we have continued this kind of class, and have continued to investigate the effectiveness that our teaching method (especially visualization) brings in the understanding of the mathematics. In this paper, we present some of this teaching method, which is performed in our class. From the questionnaire survey, it is found that our teaching method not only convinces students that the mathematics is useful or important but also deepens the mathematic understanding of students more

A way of computer use in mathematics teaching -The effectiveness that visualization brings-

We report a class of the mathematics in which an animation technology (calculating and plotting capabilities) of the software Mathematica is utilized. This class is taught for university students in a computer laboratory during a second semester. It is our purpose to make a student realize the usefulness and the importance of mathematics easily through visualization. In addition, we hope that students will acquire a new power of mathematics needed in the 21st century. For several years, we have continued this kind of class, and have continued to investigate the effectiveness that our teaching method (especially visualization) brings in the understanding of the mathematics. In this paper, we present some of this teaching method, which is performed in our class. From the questionnaire survey, it is found that our teaching method not only convinces students that the mathematics is useful or important but also deepens the mathematic understanding of students more