Let H, K be a couple of vector fields class C1 in an open set U ? ?N+m, $${\cal M}$$ N-dimensional submanifold and define T}: = \left\{{z \in {\cal M}:H\left(z \right),K\left(z \right) {T_z}{\cal M}} \right\}$$ . Then the obvious property If z0 ? is interior point (relative to )of T}$$ then $$\left[{H,K} \right]\left({{z_0}} {T_{{z_0}}}{\cal admits following generalization: superdensity As coro...

An exposition of the 1918 paper of Lattès, together with its historical antecedents, and its modern formulations and applications. 1. The Lattès paper. 2. Finite Quotients of Affine Maps 3. A Cyclic Group Action on C/Λ . 4. Flat Orbifold Metrics 5. Classification 6. Lattès Maps before Lattès 7. More Recent Developments 8. Examples References §1. The Lattès paper. In 1918, some months before his...

A polymer chain near a penetrable interface is studied in the Gaussian model, in the lattice random walk model and by a scaling analysis. The interface is modeled as an external potential u of a Heaviside step-function form. One end of the chain is fixed at a distance z0 away from this interface. When the end point is fixed in the high potential region, a first-order coil-to-flower transition t...

we mean an equivalence class of paths modulo reparametrizations. Write CD for the set of chords in D. Given a path γ, we write [γ] for the associated chord; more generally, if γ is a continuous map from any compact subinterval I of [0,∞] to Û , starting at z0 and ending at z1, we can obtain a chord [γ] in D by choosing an increasing homeomorphism φ : [0, 1] → I and setting [γ] = [γ ◦ φ]. Write ...

Chronic hypoxia causes chronic mountain sickness through hypoxia-induced pulmonary hypertension (HPH) and increased hematocrit. Here, we investigated the impact of increased hematocrit and HPH on right ventricular (RV) afterload via pulmonary vascular impedance. Mice were exposed to chronic normobaric hypoxia (10% oxygen) for 10 (10H) or 21 days (21H). After baseline hemodynamic measurements, ∼...

Changes in the aerodynamic characteristics of a site can have a major influence on the wind regime at the surface/air interface along a road which in turn has a local effect on road surface temperatures. Traditionally a parameter known as roughness length (Z0) is used as the primary measure of the aerodynamic roughness of a surface, but Z0 is notoriously difficult to estimate. This study takes ...

In a vascular network blood flow rate is proportional to the arteriovenous pressure difference and inversely proportional to the viscous and geometric resistances. The geometric resistance to tumor blood flow was determined by perfusing tissue-isolated mammary adenocarcinoma (R3230AC; N = 40; tumor weight, 1.8 +/- 1.2 (SD) g; range, 0.5-6.6 g) ex vivo with an acellular Krebs-Henseleit medium (v...