Similarity transformations for the two-dimensional, unsteady, stream-function equation

The methods described by Bluman & Cole (1974) are used to derive the infinitesimals of the general invariance group of the unsteady, two-dimensional, stream-function equation for the case where the kinematic viscosity v is equal to a constant and the case where v = 0. The infinitesimals in each case involve ten independent parameters, seven of which appear explicitly and three of which are contained implicitly in three arbitrary functions of time. The various finite groups and similarity transformations which may be derived from the infinitesimals are discussed through examples. Two of the arbitrary functions of time are non-trivial and represent invariance of the stream-function equation under a transformation to a co-ordinate system which moves in a non-uniform irrotational fashion. A general similarity form is derived for which the equations dx/dt = u(x, y, t) and dy/dt = v(x, y, t) for the particle paths may be reduced to an autonomous system. This form is general enough to suggest the hypothesis that, under certain restrictions, the entrainment processes of unsteady flows dominated by two-dimensional large-scale motions may be displayed diagrammatically on a phase-plane plot of particle trajectories

Enduring myths: smrang, rabs and ritual in the Dunhuang texts on Padmasambhava

Revue d’Etudes Tibétaines Number 15, November 200

Tandem wheel drop-legs for standard truck trailer

Tandem wheel drop-leg device provides a semitrailer with fore and aft mobility that allows it to be moved without a prime mover. The modified drop-legs have trunnion dual wheels and an adjustable brace

The Potential Effects of Hormonal Therapy and Stress on the Oral Health of the Transitioning Population

Problem: In terms of healthcare, the transgender population is underserved. Unfortunately, these individuals often experience stress related to seeking preventative care and fear discrimination. These factors preventing them from seeking care, in addition to hormone therapy taken during the transition process, could have severe impacts on their dental health. The purpose of this study is to establish a link between the hormone therapy used during gender transitioning and the effect on oral health. While there is a correlation between hormone replacement therapy and clinical evidence that sex hormones can impact on periodontal tissues, few studies have linked this knowledge to the healthcare needs of the transitioning population. Methods: Research was obtained from PubMed, the database of Dental and Oral Sciences Sources, Google Scholar, and LGBTQ+ databases. Recent studies and literature reviews were analyzed to determine if there was a correlation between hormone therapy and the health of the oral cavity. All sources found were published within five years. Major Findings: Many studies have revealed that there is an effect on sex hormones on the oral cavity. If it can happen to those that are taking sex hormone then there has to be a correlation to those who are transitioning taking the same hormone. Few studies have been conducted proving this correlation; this topic deserves more research and investigation. Conclusions: There is a clinical correlation between hormone replacement therapy and sex hormones and their effects on the oral cavity. Therefore, there is a possible correaltion to the transgender population that is taking hormones. As this population continues to grow, and more individuals identify as a part of the community, it is important to continue to research this topic.https://scholarscompass.vcu.edu/denh_student/1018/thumbnail.jp

Endperiodic Automorphisms of Surfaces and Foliations

We extend the unpublished work of M. Handel and R. Miller on the classification, up to isotopy, of endperiodic automorphisms of surfaces. We give the Handel-Miller construction of the geodesic laminations, give an axiomatic theory for pseudo-geodesic lamaniations, show the geodesic laminations satisfy the axioms, and prove that paeudo-geodesic laminations satisfying our axioms are ambiently isotopic to the geodesic laminations. The axiomatic approach allows us to show that the given endperiodic automorphism is isotopic to a smooth endperiodic automorphism preserving smooth laminations ambiently isotopic to the original ones. Using the axioms, we also prove the "transfer theorem" for foliations of 3-manifolds., namely that, if two depth one foliations are transverse to a common one-dimensional foliation whose monodromy on the noncompact leaves of the first foliation exhibits the nice dynamics of Handel-Miller theory, then the transverse one-dimensional foliation also induces monodromy on the noncompact leaves of the second foliation exhibiting the same nice dynamics. Our theory also applies to surfaces with infinitely many ends.Comment: Added Sergio Fenley as author. Moved material from Section 12.6 to a new Section 6.7. Rewrote Section 7. Deleted material from Section 6.1 and combined Sections 6.1 and 6.2 into new Section 6.1. Rewrote Section 4.6. Corrected typos and errors and improved expositio