Towards the Green-Griffiths-Lang conjecture

The Green-Griffiths-Lang conjecture stipulates that for every projective variety X of general type over C, there exists a proper algebraic subvariety of X containing all non constant entire curves f : C $\rightarrow$ X. Using the formalism of directed varieties, we prove here that this assertion holds true in case X satisfies a strong general type condition that is related to a certain jet-semistability property of the tangent bundle TX . We then give a sufficient criterion for the Kobayashi hyperbolicity of an arbitrary directed variety (X,V). This work is dedicated to the memory of Professor Salah Baouendi.Comment: version 2 has been expanded and improved (15 pages

Orbifold transversality

We prove a best possible transversality theorem for maps from manifolds to orbifolds, and, more generally arbitrary differentiable Deligne-Mumford classifying champs, 0.1, of groupoids R -> U in separated, 0.2, manifolds. En passant, the essentially finite dimensional linear algebra nature of jet transversality is isolated

In-Situ Aberration Metrology Using Phase Wheel Targets

Aberration metrology and monitoring of lithography projection systems in the semiconductor industry are becoming more important as today’s ICs are printed at sub-100 nm resolution. All lenses suffer from lens aberrations and it is important that the lithographer knows which aberration and the magnitude of the aberration in order to understand its impact on the process window and resolution limitations. A technique and process to recognize and measure lens aberrations in-situ has been developed using a phase wheel target at 157nm and 193nm lithography. This project will use the phase wheel target technique to extend aberration monitoring into i-line lithography using RIT’s Canon exposure tool. Test reticle design, layout and fabrication, as well as the exposure process optimization will be carried out for the technique to work at 365nm. First order aberrations from the Canon exposure tool will be identified using this system

A Truly Beautiful Theorem: Demonstrating the Magnificence of the Fundamental Theorem of Calculus

In standard treatments of calculus, the Fundamental Theorem of Calculus is often presented as a computational method to evaluate definite integrals, with such powerful utility that one is tempted to overlook its beauty. To improve students\u27 appreciation for the first part of the Fundamental Theorem of Calculus, we suggest a few classroom examples focusing on the accumulation function, to be introduced early and often throughout an introductory calculus course. These examples are small enough that they would not necessarily result in changes to a typical course schedule; yet we believe their contribution to student understanding can be significant. Furthermore, such examples might allow students to share more of the excitement that the pioneers of the subject surely experienced along the way

Sur le lemme de Brody

Brody's lemma is a basic tool in complex hyperbolicity. We present a version of it making more precise the localization of an entire curve coming from a diverging sequence of holomorphic discs. As a byproduct we characterize hyperbolicity in terms of an isoperimetric inequality

Intersections of Hyperconics in Projective Planes of Even Order

AbstractWe show how to lift the even intersection equivalence relation from the hyperovals of PG(2, 4) to an equivalence relation amongst sets of hyperconics in π=PG(2, F). Here, F is any finite or infinite field of characteristic two that contains a subfield of order 4, but does not contain a subfield of order 8. Moreover, we are able to determine the number of points that two hyperconics in π will have in common provided some projective subplane of order 4 intersects both of them in hexads

Responding to Infertility: Lessons From a Growing Body of Research and Suggested Guidelines for Practice

Infertility is a common, yet often misunderstood, experience. Infertility is an important topic for family scientists because of its effects on families; its relevance to research in related areas, such as fertility trends and reproductive health; and its implications for practitioners who work with individuals and couples experiencing infertility. In this review, we focus on common misperceptions in knowledge and treatment of infertility and highlight insights from recent research that includes men, couples, and people with infertility who are not in treatment. The meaning of parenthood, childlessness, awareness of a fertility problem, and access to resources are particularly relevant for treatment seeking and psychosocial outcomes. On the basis of insights from family science research, we provide specific guidelines for infertility practice within broader social contexts such as trends in health care, education, employment, and relationships. Guidelines are presented across three areas of application: infertility education for individuals, families, and practitioners; steps to support the emotional well-being of those affected by infertility; and understanding of treatment approaches and their implications for individuals and couples

Pregnancy Loss and Distress Among U.S. Women

Although pregnancy loss—especially miscarriage— is a relatively common experience among reproductive-aged women, much of our understanding about the experience has come from small clinic-based or other nonrepresentative samples. We compared fertility-specific distress among a national sample of 1,284 women who have ever experienced a stillbirth or miscarriage. We found that commitment/attachment to pregnancy that ended in loss as well as current childbearing contexts and attitudes were associated with distress following pregnancy loss. Practitioners working with women or couples who have experienced pregnancy loss should be aware of the importance of characteristics associated with higher distress, such as whether the pregnancy had been planned, recency of the loss, no subsequent live births, having a medical explanation for the loss, a history of infertility, current childbearing desires, importance of motherhood, and locus of control over fertility