A class of generalized special Weingarten surfaces

2019 ◽  
Vol 30 (14) ◽  
pp. 1950075
Author(s):  
Armando M. V. Corro ◽  
Diogo G. Dias ◽  
Carlos M. C. Riveros
Keyword(s):  
Fixed Point ◽  
Holomorphic Functions ◽  
Gauss Map ◽  
Type Representation ◽  
The Third ◽  
Weingarten Surfaces ◽  
Lines Of Curvature ◽  
Third Fundamental Form ◽  
Pass Through ◽  
Weierstrass Type Representation

In [Classes of generalized Weingarten surfaces in the Euclidean 3-space, Adv. Geom. 16(1) (2016) 45–55], the authors study a class of generalized special Weingarten surfaces, where coefficients are functions that depend on the support function and the distance function from a fixed point (in short EDSGW-surfaces), this class of surfaces has the geometric property that all the middle spheres pass through a fixed point. In this paper, we present a Weierstrass type representation for EDSGW-surfaces with prescribed Gauss map which depends on two holomorphic functions. Also, we classify isothermic EDSGW-surfaces with respect to the third fundamental form parametrized by planar lines of curvature. Moreover, we give explicit examples of EDSGW-surfaces and isothermic EDSGW-surfaces.

Classes of generalized Weingarten surfaces in the Euclidean 3-space

2016 ◽  
Vol 16 (1) ◽  
Author(s):  
Diogo G. Dias ◽  
Armando M. V. Corro
Keyword(s):  
Fixed Point ◽  
Distance Function ◽  
Special Class ◽  
Support Function ◽  
The Other ◽  
Isolated Singularity ◽  
Type Representation ◽  
Weingarten Surfaces ◽  
Parallel Surfaces ◽  
Weierstrass Type Representation

AbstractWe present surfaces with prescribed normal Gaussmap. These surfaces are obtained as the envelope of a sphere congruencewhere the other envelope is contained in a plane. We introduce classes of surfaces that generalize linear Weingarten surfaces, where the coefficients are functions that depend on the support function and the distance function from a fixed point (in short, DSGW-surfaces). The linear Weingarten surfaces, Appell’s surfaces and Tzitzeica’s surfaces are all DSGW-surfaces. From them we obtain new classes of DSGWsurfaces applying inversions, dilatations and parallel surfaces. For a special class of DSGW-surfaces, which is invariant under dilatations and inversions, we obtain a Weierstrass type representation (in short, EDSG Wsurfaces). As applications we classify the EDSGW-surfaces of rotation and present a 2-parameter family of complete cyclic EDSGW-surfaces with an isolated singularity and foliated by non-parallel planes.

Ribaucour surfaces of harmonic type

2021 ◽  
Author(s):  
Armando M. V. Corro ◽  
Carlos M. C. Riveros ◽  
Karoline V. Fernandes
Keyword(s):  
Holomorphic Functions ◽  
Parameter Family ◽  
Isolated Singularities ◽  
Type Representation ◽  
Lines Of Curvature ◽  
Weierstrass Type Representation

We introduce the class of Ribaucour surfaces of harmonic type (in short HR-surfaces) that generalizes the Ribaucour surfaces related to a problem posed by Élie Cartan. We obtain a Weierstrass-type representation for these surfaces which depends on three holomorphic functions. As application, we classify the HR-surfaces of rotation, present examples of complete HR-surfaces of rotation with at most two isolated singularities and an example of a complete HR-surface of rotation with one catenoid type end and one planar end. Also, we present a 5-parameter family of cyclic HR-surfaces foliated by circles in non-parallel planes. Moreover, we classify the isothermic HR-surfaces with planar lines of curvature.

scholarly journals The Principal Curvatures and the Third Fundamental Form of Dini-Type Helicoidal Hypersurface in 4-Space

2020 ◽  
pp. 62-68
Author(s):  
Erhan G¨uler
Keyword(s):  
Euclidean Space ◽  
Characteristic Polynomial ◽  
Fundamental Form ◽  
Shape Operator ◽  
Gauss Map ◽  
Dimensional Euclidean Space ◽  
Operator Matrix ◽  
Principal Curvatures ◽  
The Third ◽  
Third Fundamental Form

We consider the principal curvatures and the third fundamental form of Dini-type helicoidal hypersurface D(u, v, w) in the four dimensional Euclidean space E4. We find the Gauss map e of helicoidal hypersurface in E4. We obtain characteristic polynomial of shape operator matrix S. Then, we compute principal curvatures ki=1;2;3, and the third fundamental form matrix III of D.

Experimental Third Ventriculostomy Performed Using Endovascular Surgical Techniques and Their Adaptation to Percutaneous Intradural Neuronavigation: Proof of Concept Cadaver Study

Neurosurgery ◽  
2003 ◽  
Vol 53 (2) ◽  
pp. 387-392 ◽  
Author(s):  
Michael B. Horowitz ◽  
Kamal Ramzipoor ◽  
Ajit Nair ◽  
Susan Miller ◽  
George Rappard ◽  
...  
Keyword(s):  
Third Ventricle ◽  
Surgical Techniques ◽  
Cadaver Study ◽  
Brain Parenchyma ◽  
Third Ventriculostomy ◽  
General Anesthetic ◽  
The Third ◽  
Noncommunicating Hydrocephalus ◽  
Pass Through ◽  
The Brain

Abstract OBJECTIVE Endoscopic third ventriculostomy has developed into a therapeutic alternative to shunting for the management of carefully selected patients with primarily noncommunicating hydrocephalus. This procedure, however, requires a general anesthetic and necessitates violation of the brain parenchyma and manipulation near vital neural structures to access the floor of the third ventricle. Using two cadavers and off-the-shelf angiographic catheters, we sought to determine whether it was possible to navigate a catheter, angioplasty balloon, and stent percutaneously through the subarachnoid space from the thecal sac into the third ventricle so as to perform a third ventriculostomy from below. METHODS Using biplane angiography and off-the-shelf angiographic catheters along with angioplasty balloons and stents, we were able to pass a stent coaxially from the thecal sac to and across the floor of the third ventricle so as to achieve a third ventriculostomy from below. RESULTS Coaxial catheter techniques allowed for the percutaneous insertion of a stent across the floor of the third ventricle. Ventriculostomy was confirmed by injecting contrast medium into the lateral ventricle and seeing it pass through the stent and into the chiasmatic cistern. CONCLUSION We describe the performance of third ventriculostomies in two cadavers by use of the new concept of percutaneous intradural neuronavigation. This procedure may obviate the need for general anesthetic and minimize the potential for brain and vascular injury, especially if ultimately combined with magnetic resonance fluoroscopy.

Winter Navigation through the Strait of Belle Isle

1964 ◽  
Vol 17 (4) ◽  
pp. 364-375
Author(s):  
R. E. G. Simmons
Keyword(s):  
The Third ◽  
The Past ◽  
Shortest Route ◽  
Pack Ice ◽  
Normal Period ◽  
Ice Conditions ◽  
Short Season ◽  
Pass Through ◽  
Alternative Routes ◽  
St Lawrence River

The shortest route from the Great Lakes and St. Lawrence River to Europe passes through the Strait of Belle Isle. The alternative routes pass through the Cabot Strait and are between 100 and 400 miles longer according to the European port of destination. The Strait of Belle Isle is, however, normally closed to navigation from the end of December until the middle of July due to the presence of pack ice and icebergs.Air reconnaissance patrols flown over the Labrador, Belle Isle and East Newfoundland areas seem to indicate that, for the past few years at least, ice conditions have not been so severe as to hamper navigation throughout the normal period of closure. Consolidated ice is only present from the third week of January to mid-February and clears in mid-April to mid-May; only icebergs present a problem in May and June. It is hoped t o show that with proper air reconnaisance at the beginning and end of the ice season, navigation through the Strait could be extended to eight or nine months of the year, or even longer, instead of the present short season of only 5½ months.

scholarly journals Health care logistics: mapping and optimization of patients logistics

2021 ◽  
Vol 12 (8) ◽  
pp. 2161-2179
Author(s):  
Daiane Maria de Genaro Chiroli ◽  
Raíza Conde Coradazi ◽  
Fabio Jose Ceron Branco ◽  
Yslene Rocha Kachba ◽  
Franciely Velozo Aragão ◽  
...  
Keyword(s):  
Linear Programming ◽  
Computational Simulation ◽  
Transportation Of Patients ◽  
Patient Transport ◽  
Specific Approach ◽  
Health Region ◽  
The Third ◽  
City Hall ◽  
Pass Through ◽  
The One

Healthcare logistics play an important role in management, being attributed the activities of acquisition, distribution and movement of materials, professionals and patients. This work aims to develop a study, using the healthcare logistics in the movement of patients in the third health region of Paraná, proposing a linear programming problem that will pass through a computational simulation, considering the existing demands and constraints in the system, aiming to optimize the flow of patients from this region. The present study developed four mathematical models, based on demands and constraints followed by linear programming in order to find the best possible solution for the flow of patients from the third health region of the state of Paraná. The study developed reached its goal of optimization, generating an economy in the transportation of patients. Through the analysis of the results, it is concluded that the model that best suits the presented problem is the one of costs minimization, since the one of vehicles presented higher costs. Possibly the model that minimizes the vehicles would bring better results if the vehicles were not outsourced, but of the Ponta Grossa City Hall (PMPG). Was possible to verify the importance of the theme, especially when referring to the flow of patients in the health services due to the lack of studies with this specific approach. Even with the scarcity of data, it is possible to notice the potential for improvements on this patient transport system.

scholarly journals Extreme points and support points of conformal mappings

2019 ◽  
Vol 17 (1) ◽  
pp. 23-31
Author(s):  
Ronen Peretz
Keyword(s):  
Remainder Term ◽  
Linear Functional ◽  
Convex Combination ◽  
Extreme Points ◽  
Holomorphic Functions ◽  
Support Point ◽  
Continuous Linear ◽  
Continuous Linear Functional ◽  
The Third ◽  
Support Points

Abstract There are three types of results in this paper. The first, extending a representation theorem on a conformal mapping that omits two values of equal modulus. This was due to Brickman and Wilken. They constructed a representation as a convex combination with two terms. Our representation constructs convex combinations with unlimited number of terms. In the limit one can think of it as an integration over a probability space with the uniform distribution. The second result determines the sign of ℜ L(z0(f(z))2) up to a remainder term which is expressed using a certain integral that involves the Löwner chain induced by f(z), for a support point f(z) which maximizes ℜ L. Here L is a continuous linear functional on H(U), the topological vector space of the holomorphic functions in the unit disk U = {z ∈ ℂ | |z| < 1}. Such a support point is known to be a slit mapping and f(z0) is the tip of the slit ℂ − f(U). The third demonstrates some properties of support points of the subspace Sn of S. Sn contains all the polynomials in S of degree n or less. For instance such a support point p(z) has a zero of its derivative p′(z) on ∂U.

scholarly journals F-Metric, F-Contraction and Common Fixed-Point Theorems with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 586 ◽  
Author(s):  
Awais Asif ◽  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Third ◽  
Set Valued Mappings ◽  
Common Fixed Point Theorems

In this paper, we noticed that the existence of fixed points of F-contractions, in F -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function F : ( 0 , ∞ ) → R . We obtain fixed points as well as common fixed-point results for Reich-type F-contractions for both single and set-valued mappings in F -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

Normality operators and classical recapture in many-valued logic

2018 ◽  
Vol 28 (5) ◽  
pp. 657-683
Author(s):  
Roberto Ciuni ◽  
Massimiliano Carrara
Keyword(s):  
Fixed Point ◽  
Final Part ◽  
The Third ◽  
Truth Value ◽  
Formal Behaviour ◽  
Classical Truth

AbstractIn this paper, we use a ‘normality operator’ in order to generate logics of formal inconsistency and logics of formal undeterminedness from any subclassical many-valued logic that enjoys a truth-functional semantics. Normality operators express, in any many-valued logic, that a given formula has a classical truth value. In the first part of the paper we provide some setup and focus on many-valued logics that satisfy some (or all) of the three properties, namely subclassicality and two properties that we call fixed-point negation property and conservativeness. In the second part of the paper, we introduce normality operators and explore their formal behaviour. In the third and final part of the paper, we establish a number of classical recapture results for systems of formal inconsistency and formal undeterminedness that satisfy some or all the properties above. These are the main formal results of the paper. Also, we illustrate concrete cases of recapture by discussing the logics $\mathsf{K}^{\circledast }_{3}$, $\mathsf{LP}^{\circledast }$, $\mathsf{K}^{w\circledast }_{3}$, $\mathsf{PWK}^{\circledast }$ and $\mathsf{E_{fde}}^{\circledast }$, that are in turn extensions of $\mathsf{{K}_{3}}$, $\mathsf{LP}$, $\mathsf{K}^{w}_{3}$, $\mathsf{PWK}$ and $\mathsf{E_{fde}}$, respectively.

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