On the inseparable degrees of the Gauss map and the projection of the conormal variety to the dual of higher order for space curves

1992 ◽  
Vol 292 (1) ◽  
pp. 529-532 ◽  
Author(s):  
Hajime Kaji
Keyword(s):  
Gauss Map ◽  
Higher Order ◽  
Space Curves ◽  
Conormal Variety

scholarly journals On the inseparable degree of the Gauss map of higher order for space curves

1992 ◽  
Vol 68 (1) ◽  
pp. 11-14 ◽  
Author(s):  
Masaaki Homma ◽  
Hajime Kaji
Keyword(s):  
Gauss Map ◽  
Higher Order ◽  
Space Curves

ON THE UMBILICITY OF HYPERSURFACES IN THE HYPERBOLIC SPACE

2016 ◽  
Vol 103 (1) ◽  
pp. 45-58
Author(s):  
C. P. AQUINO ◽  
M. BATISTA ◽  
H. F. DE LIMA
Keyword(s):  
Hyperbolic Space ◽  
Mean Curvature ◽  
Warped Product ◽  
Gauss Map ◽  
Higher Order ◽  
Totally Umbilical ◽  
Totally Umbilical Hypersurfaces ◽  
Product Models ◽  
Higher Order Mean Curvature ◽  
Complete Hypersurfaces

In this paper, we establish new characterization results concerning totally umbilical hypersurfaces of the hyperbolic space$\mathbb{H}^{n+1}$, under suitable constraints on the behavior of the Lorentzian Gauss map of complete hypersurfaces having some constant higher order mean curvature. Furthermore, working with different warped product models for$\mathbb{H}^{n+1}$and supposing that certain natural inequalities involving two consecutive higher order mean curvature functions are satisfied, we study the rigidity and the nonexistence of complete hypersurfaces immersed in$\mathbb{H}^{n+1}$.

scholarly journals Osculating surfaces of curves on surfaces

2020 ◽  
Vol 55 ◽  
Author(s):  
Kazimieras Navickis
Keyword(s):  
Differential Geometry ◽  
Euclidean Space ◽  
Higher Order ◽  
Space Curves ◽  
Classical Differential Geometry ◽  
Surfaces In Euclidean Space ◽  
Curves On Surfaces

Oosculating sphere have been studied in classical differential geometry [1]. In this article the osculating surfaces of higher order of space curves on surfaces in Euclidean space is considered. We study the intrinsic differential geometry of curves  on surfaces by analyzing their contact with surfaces of higher order.

scholarly journals Osculating curves and surfaces

2012 ◽  
Vol 54 ◽  
Author(s):  
Kazimieras Navickis
Keyword(s):  
Differential Geometry ◽  
Higher Order ◽  
Space Curves ◽  
Curves And Surfaces ◽  
Classical Differential Geometry

Osculating circle and osculating sphere have been studied in classical differential geometry [1]. In this article the osculating curves and surfaces of higher order of plane and space curves in Euclideann-space (n = 2, 3) is considered. We study the intrinsic differential geometry of curves by analyzing their contact with curves and surfaces of higher order.

Strangeness of higher order for space curves

1992 ◽  
Vol 20 (6) ◽  
pp. 1535-1548 ◽  
Author(s):  
Hajime Kaji
Keyword(s):  
Higher Order ◽  
Space Curves

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Quantitative EPMA of nitrogen : A tricky element in the electron-probe microanalyzer

1992 ◽  
Vol 50 (2) ◽  
pp. 1622-1623
Author(s):  
G.F. Bastin ◽  
H.J.M. Heijligers
Keyword(s):  
Background Subtraction ◽  
Electron Probe ◽  
Detection System ◽  
Higher Order ◽  
Light Elements ◽  
Strong Suppression ◽  
Electron Probe Microanalyzer ◽  
Quantitative Epma ◽  
Peak Count ◽  
Lead Stearate

Among the ultra-light elements B, C, N, and O nitrogen is the most difficult element to deal with in the electron probe microanalyzer. This is mainly caused by the severe absorption that N-Kα radiation suffers in carbon which is abundantly present in the detection system (lead-stearate crystal, carbonaceous counter window). As a result the peak-to-background ratios for N-Kα measured with a conventional lead-stearate crystal can attain values well below unity in many binary nitrides . An additional complication can be caused by the presence of interfering higher-order reflections from the metal partner in the nitride specimen; notorious examples are elements such as Zr and Nb. In nitrides containing these elements is is virtually impossible to carry out an accurate background subtraction which becomes increasingly important with lower and lower peak-to-background ratios. The use of a synthetic multilayer crystal such as W/Si (2d-spacing 59.8 Å) can bring significant improvements in terms of both higher peak count rates as well as a strong suppression of higher-order reflections.

Effects of Higher-Order Laue Zone reflections on structure images

1993 ◽  
Vol 51 ◽  
pp. 450-451
Author(s):  
H. S. Kim ◽  
S. S. Sheinin
Keyword(s):  
Wave Vector ◽  
Theoretical Calculations ◽  
Reciprocal Lattice ◽  
Image Plane ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Higher Order ◽  
Lattice Image ◽  
Lattice Vector ◽  
Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

Models of higher order structure—foldamers and beyond

2001 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
M Cubberley
Keyword(s):  
Higher Order

Higher Order Logic and Hardware Verification

1993 ◽  
Author(s):  
T. F. Melham
Keyword(s):  
Higher Order ◽  
Order Logic ◽  
Hardware Verification ◽  
Higher Order Logic
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