A note on the hypercomplex riemann-cauchy like relations for quaternions and laplace equations

In this Note it is worked out a new set of Laplace-Like equations for quaternions through Riemann-Cauchy hypercomplex relations otained earlier [1]. As in the theory of functions of a complex variable, it is expected that this new set of Laplace-Like equations might be applied to a large number of Physical problems, providing new insights in the Classical Fields Theory.

A note on pairs of regular foliations on the solid torus

We discuss the geometry of the pair of foliations on a solid torus given by the Reeb foliation together with discs transverse to the boundary of the torus.

An Informatics Technical Note on Interaction of DNA - Graphene Chemical Sensor System as Reaction-Diffusion Wave-Based Computing System in Ionised Gaseous environments and their Applications Using Theoretical Studies and Scientific Computation Overview

The physics of plasmas encompasses basic problems from the universe and has assured us of promises in diverse applications to be implemented in a wider range of scientific and engineering domains, linked to most of the evolved and evolving fundamental problems. Substantial part of this domain could be described by R–D mechanisms involving two or more species (reaction–diffusion mechanisms). These could further account for the simultaneous non-linear effects of heating, diffusion and other related losses. We mention here that in laboratory scale experiments, a suitable combination of these processes is of vital importance and very much decisive to investigate and compute the net behaviour of plasmas under consideration. Plasmas are being used in the revolution of information processing, so we considered in this technical note a simple framework to discuss and pave the way for better formalisms and Informatics, dealing with diverse domains of science and technologies. The challenging and fascinating aspects of plasma physics is that it requires a great deal of insight in formulating the relevant design problems, which in turn require ingenuity and flexibility in choosing a particular set of mathematical (and/or experimental) tools to implement them.

A note on the integral trace form in cyclotomic fields

Let m >= 3 be an integer, zeta(m) is an element of C a primitive mth root of unity, and K-m the cyclotomic field Q(zeta(m)). An explicit description of the integral trace form Tr-Km/Q(x (x) over bar)vertical bar Z[zeta(m)] where (x) over bar is the complex conjugate of x is presented. In the case where m is prime, a procedure for finding the minimum of the form subject to x being a nonzero element of a certain Z- module in Z[zeta(m)] is presented.

Inicial nasal mucosa detachment using piezoelectric device in the Le Fort I osteotomy: A technical note

In maxillary Le Fort I type osteotomy the detachment of the nasal mucosa should be done carefully. Piezoelectric surgery contributed much to increase the safety of osteotomies, despite the initial advantage of minimizing the risk of injury in nervous tissue, mainly in bilateral sagittal split osteotomy; we use the piezoelectric device for the initial detachment of the nasal mucosa in the maxillary osteotomy.

The use of a bite fork to help mobilize the maxilla after downfracture during the Le Fort I osteotomy: a technical note

Introduction The Le Fort I osteotomy is indicated to reposition the maxilla in the surgical correction of dentofacial deformities. Although it is a known surgical step, like any surgical procedure, it can have complications and difficulties; among these, the initial mobility of the jaw is very common after completing all corticotomies. Methods The authors present a technique in which the bite fork is used as an auxiliary tool in maxilla downfracture, especially in cases of maxillary impaction where vertical space is created on the walls of the corticotomy. Findings As the bite fork acts as a scraper with a long leverage arm, an advantage would be the better distribution of forces along the corticotomy, minimizing the risk of bad fracture and facilitating maxillary downfracture movement.

Spontaneous intracerebral hemorrhage treated by neuroendoscopy: technical note

Spontaneous intracerebral hemorrhage (SICH) is responsible for 10%-15% of the acute stroke. Hematoma or the occlusion of cerebrospinal fluid (CSF) flow by ventricular clotting can result in obstructive hydrocephalus, increasing intracranial pressure, which needs urgent decompression. We report our results of management of spontaneous deep cerebral hematoma by endoscopic approach.

A note on the unprecedented strandings of 56 deep-diving whales along the UK and Irish coast

In the first seven months of 2008, eighteen Cuvier’s beaked whales (Ziphius cavirostris), four Sowerby’s beaked whales (Mesoplodon bidens), five unidentified beaked whales and twenty-nine long-finned pilot whales (Globicephala melas) were reported stranded in the UK and Ireland. Decomposition of those animals investigated puts the predicted time of death at mid-January. Concerns that an unusual mortality event had taken place prompted further investigations. Most carcasses were too decomposed for necropsy. A summary of findings is presented here. Although the initial stranding of five Cuvier’s beaked whales in Scotland shared some similarities with atypical mass stranding events linked in time and space to mid-frequency naval sonars, there were two important differences with the remaining strandings during this period. First, the geographical range of the event was very wide and second, the strandings occurred over a prolonged period of several months. Both of these factors could be related to the fact that the mortalities occurred offshore and the carcasses drifted ashore. The cause(s) of this high number of strandings of mixed offshore cetacean species during this period remain undetermined.

A Preliminary Note on Trichinosis Investigations in Alaska

Trichinosis in the arctic regions of the world has received considerable attention during recent years, particularly since the work of Roth (1948) in Greenland. In Connell's (1949) review of arctic trichinosis some Alaskan and Canadian records were included but, until now, little has been known of the status of the disease in Alaska. Information available at the present time indicates that the incidence of trichinosis is high in circumpolar carnivores and that marine mammals have a definite place in its epizootiology. Present knowledge cannot explain the survival of trichinosis in marine mammal populations, but it is evident that they may serve as important sources of human infection. Up to the present time the following mammals from Alaska have been found to be infected: From the arctic coast-polar bear, Thalarctas maritimus; arctic fox, Alapex lagapus irmuitus; red fox, Vulpes fulva alascemis; white whale, Delphinapterus leucas; Eskimo dog. From south of the Brooks Range--brown and grizzly bears, Ursus spp.; wolf, Canis lupus ssp.; wolverine. Gula l. luscus. At the time of writing, nearly ail species of land carnivores in Alaska have been examined as well as many other mammalian species less likely to be infected, including various rodents, shrews, and others.

A note on a mineralogical analysis of the sediments associated with the Plata River and Patos Lagoon outflows

Riverine waters bring to seas a variety of suspended materials, which are ultimately deposited on the shelf or exported to the deep ocean. Investigation of the mineralogical contents of these continental-borne constituents on seafloors may reveal valuable information about the environmental conditions in the drainage basin. In this note we report results of X-ray diffraction and other analysis of sediments in bottom samples collected on the continental shelf under influence of the Plata River and the Patos Lagoon, in South America. The analysis reveals that non-clay materials are mostly concentrated south of 33 degrees S, while clay sediments are relatively more abundant further north. We propose that such distributions are controlled by the circulation pattern and water mass distribution of the lower and upper layers, respectively. (C) 2008 Elsevier Ltd. All rights reserved.

A note on permutation regularity

The existence of a small partition of a combinatorial structure into random-like subparts, a so-called regular partition, has proven to be very useful in the study of extremal problems, and has deep algorithmic consequences. The main result in this direction is the Szemeredi Regularity Lemma in graph theory. In this note, we are concerned with regularity in permutations: we show that every permutation of a sufficiently large set has a regular partition into a small number of intervals. This refines the partition given by Cooper (2006) [10], which required an additional non-interval exceptional class. We also introduce a distance between permutations that plays an important role in the study of convergence of a permutation sequence. (C) 2011 Elsevier B.V. All rights reserved.

A note on the local power of the LR, Wald, score and gradient tests

This paper examines the local power of the likelihood ratio, Wald, score and gradient tests under the presence of a scalar parameter, phi say, that is orthogonal to the remaining parameters. We show that some of the coefficients that define the local powers remain unchanged regardless of whether phi is known or needs to be estimated, where as the others can be written as the sum of two terms, the first of which being the corresponding term obtained as if phi were known, and the second, an additional term yielded by the fact that phi is unknown. The contribution of each set of parameters on the local powers of the tests can then be examined. Various implications of our main result are stated and discussed. Several examples are presented for illustrative purposes

A NOTE ON OPEN 3-MANIFOLDS SUPPORTING FOLIATIONS BY PLANES

We show that if N, an open connected n-manifold with finitely generated fundamental group, is C-2 foliated by closed planes, then pi(1)(N) is a free group. This implies that if pi(1)(N) has an abelian subgroup of rank greater than one, then F has at least a nonclosed leaf. Next, we show that if N is three dimensional with fundamental group abelian of rank greater than one, then N is homeomorphic to T-2 x R. Furthermore, in this case we give a complete description of the foliation.

A Note on Large Deviations for the Stable Marriage of Poisson and Lebesgue with Random Appetites

Let IaS,a"e (d) be a set of centers chosen according to a Poisson point process in a"e (d) . Let psi be an allocation of a"e (d) to I in the sense of the Gale-Shapley marriage problem, with the additional feature that every center xi aI has an appetite given by a nonnegative random variable alpha. Generalizing some previous results, we study large deviations for the distance of a typical point xaa"e (d) to its center psi(x)aI, subject to some restrictions on the moments of alpha.