An extension of Stieltjes-Young integrals

Department of Mathematics, Faculty of Science, Kanazawa University.Let ƒﾓ(t) and f(t) be real-valued functions defined on a closed interval [a, b]. The Riemann-Stieltjes integral of f with respect to ƒﾓ is usually denoted by [numerical formula] When ƒﾓ(x) is of bounded variation on the interval [a, b], we can treat this integral in the framework of measure theory. Let p and q are positive numbers such that [numerical formula] L. C. Young showed that the integral [numerical formula] in the case that f(t) and ƒﾓ(t) have finite mean variation of order p and q, respectively. In this paper we shall try to extend the Stieltjes-Young integration theory when f(t) and ƒﾓ(t) are stochastic processes

A representation of continuous additive functionals of zero energy

Department of Mathematics, Faculty of Science, Kanazawa University.The notion of the continuous additive functionals of zero energy of symmetric Markov processes was introduced by M. Fukushima. There are two typical types of continuous additive functionals of zero energy. We shall decide the class of continuous additive functionals of zero energy of symmetric Markov processes which are represented by the sum of the above two typical additive functionals

N4-methylation changes the conformation of (3S,6S)-3-alkyl-6-benzylpiperazine-2,5-diones from folded to extended

N4-Methylation of (3S,6S)-3-alkyl-6-benzylpiperazine-2,5-diones (S,S)-1a–c was found to change their folded conformation to an extended conformation. Conformational aspects of N1- and/or N4-methylated (S,S)-1a–c were revealed by single crystal X-ray crystallography and 1H NMR spectroscopy

Full thickness macular hole case after intravitreal aflibercept treatment

BACKGROUND: The pathogenesis of macular hole formation is widely accepted as a tractional force at the vitreo-retinal interface in fovea. We report a case of macular hole after intravitreous aflibercept injection for age-related macular degeneration (AMD) associated with contraction of the retinal pigment epithelium (RPE) at the edge of a fibrovascular pigment epithelial detachment (PED). CASE PRESENTATION: A 94-year old man with neovascular AMD affecting his left eye accompanied by a fibrovascular PED was examined for severe vision loss. Although RPE tear in his left eye was identified before the first aflibercept intravitreous injection performed in order to treat neovascular AMD, he received three aflibercept injections as induction treatment. After induction treatment, a full thickness macular hole was identified associated with the contracted rolled RPE edge beneath the retina. CONCLUSION: Macular hole is commonly formed associated with tangential vitreous traction. Current report suggests that rapid contraction of the RPE underneath the retina can be one of the causes of a macular hole, and one of the side effects of anti-VEGF therapy for neovascular AMD