Isotopic Equivalence from Bezier Curve Subdivision

We prove that the control polygon of a Bezier curve B becomes homeomorphic and ambient isotopic to B via subdivision, and we provide closed-form formulas to compute the number of iterations to ensure these topological characteristics. We first show that the exterior angles of control polygons converge exponentially to zero under subdivision.Comment: arXiv admin note: substantial text overlap with arXiv:1211.035

Design of helicopter rotor blades for optimum dynamic characteristics

The mass and stiffness distributions for helicopter rotor blades are tailored in such a way to give a predetermined placement of blade natural frequencies. The optimal design is pursued with respect of minimum weight, sufficient inertia, and reasonable dynamic characteristics. Finite element techniques are used as a tool. Rotor types include hingeless, articulated, and teetering

Malarial Fever in Horses

This disease is also called swamp fever by farmers, and pernicious anaemia by veterinarians. In Nebraska many of the farmers call the disease typhoid fever, for it resembles this fever very much. The manner in which the disease is contracted by horses is not definitely understood. In the last few years, the veterinarians in the Philippines have discovered a disease, prevalent in India under the name of surra, the description of which corresponds very much to that of malarial fever of horses in this country, with the exception that bacteriologists have not been able to find the surra parasite in the blood of affected animals in this country. As the parasite of surra is very easily detected in the blood of affected animals, and as we have not been able to discover it, the conclusion seems reasonable that the diseases are not identical. It is difficult to ascertain how the disease first made its appearance in Nebraska. We find it on the marshy pastures during very \u27wet seasons. It is the general opinion of those who have studied the disease that it is caused by feeding on certain low, marshy pastures and on hay that comes from such pastures. Whatever its origin, the disease has spread on these pastures during the last few years. Horses die from this disease on the Missouri river bottom and in the Elkhorn valley and farther up in the western part of the state. In these districts the loss is very great, especially in wet seasons, such as we have had in the last few years. To the stockman the loss is very heavy, for when it once makes its appearance on a ranch, it is very apt to recur, and carry off every horse. Many ranch-men in these districts lost all of their hores and were seriously crippled in finishing up their season\u27s work, many farmers losing from two to eight head of horses. This is the most serious disease among horses that this state has been called upon to investigate

Malarial Fever in Horses

This disease is also called swamp fever by farmers, and pernicious anaemia by veterinarians. In Nebraska many of the farmers call the disease typhoid fever, for it resembles this fever very much. The manner in which the disease is contracted by horses is not definitely understood. In the last few years, the veterinarians in the Philippines have discovered a disease, prevalent in India under the name of surra, the description of which corresponds very much to that of malarial fever of horses in this country, with the exception that bacteriologists have not been able to find the surra parasite in the blood of affected animals in this country. As the parasite of surra is very easily detected in the blood of affected animals, and as we have not been able to discover it, the conclusion seems reasonable that the diseases are not identical. It is difficult to ascertain how the disease first made its appearance in Nebraska. We find it on the marshy pastures during very \u27wet seasons. It is the general opinion of those who have studied the disease that it is caused by feeding on certain low, marshy pastures and on hay that comes from such pastures. Whatever its origin, the disease has spread on these pastures during the last few years. Horses die from this disease on the Missouri river bottom and in the Elkhorn valley and farther up in the western part of the state. In these districts the loss is very great, especially in wet seasons, such as we have had in the last few years. To the stockman the loss is very heavy, for when it once makes its appearance on a ranch, it is very apt to recur, and carry off every horse. Many ranch-men in these districts lost all of their hores and were seriously crippled in finishing up their season\u27s work, many farmers losing from two to eight head of horses. This is the most serious disease among horses that this state has been called upon to investigate

Representations of C*-dynamical systems implemented by Cuntz families

Given a dynamical system (A,\al) where $A$ is a unital \ca-algebra and \al is a (possibly non-unital) *-endomorphism of $A$, we examine families $(\pi,\{T_i\})$ such that $\pi$ is a representation of $A$, $\{T_i\}$ is a Toeplitz-Cuntz family and a covariance relation holds. We compute a variety of non-selfadjoint operator algebras that depend on the choice of the covariance relation, along with the smallest \ca-algebra they generate, namely the \ca-envelope. We then relate each occurrence of the \ca-envelope to (a full corner of) an appropriate twisted crossed product. We provide a counterexample to show the extent of this variety. In the context of \ca-algebras, these results can be interpreted as analogues of Stacey's famous result, for non-automorphic systems and $n>1$. Our study involves also the one variable generalized crossed products of Stacey and Exel. In particular, we refine a result that appears in the pioneering paper of Exel on (what is now known as) Exel systems.Comment: 29 pages; changes in subsection 1.2; close to publicatio