The variation of curves along a fixed direction

1964 ◽  
pp. 1-14
Author(s):  
V. A. Zalgaller
Keyword(s):  
Fixed Direction

scholarly journals Slice holomorphic solutions of some directional differential equations with bounded L-index in the same direction

2019 ◽  
Vol 52 (1) ◽  
pp. 482-489 ◽  
Author(s):  
Andriy Bandura ◽  
Oleh Skaskiv ◽  
Liana Smolovyk
Keyword(s):  
Partial Differential Equations ◽  
Continuous Function ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Holomorphic Functions ◽  
Positive Continuous Function ◽  
Partial Differential ◽  
Partial Derivatives ◽  
Fixed Direction

AbstractIn the paper we investigate slice holomorphic functions F : ℂn → ℂ having bounded L-index in a direction, i.e. these functions are entire on every slice {z0 + tb : t ∈ℂ} for an arbitrary z0 ∈ℂn and for the fixed direction b ∈ℂn \ {0}, and (∃m0 ∈ ℤ+) (∀m ∈ ℤ+) (∀z ∈ ℂn) the following inequality holds{{\left| {\partial _{\bf{b}}^mF(z)} \right|} \over {m!{L^m}(z)}} \le \mathop {\max }\limits_{0 \le k \le {m_0}} {{\left| {\partial _{\bf{b}}^kF(z)} \right|} \over {k!{L^k}(z)}},where L : ℂn → ℝ+ is a positive continuous function, {\partial _{\bf{b}}}F(z) = {d \over {dt}}F\left( {z + t{\bf{b}}} \right){|_{t = 0}},\partial _{\bf{b}}^pF = {\partial _{\bf{b}}}\left( {\partial _{\bf{b}}^{p - 1}F} \right)for p ≥ 2. Also, we consider index boundedness in the direction of slice holomorphic solutions of some partial differential equations with partial derivatives in the same direction. There are established sufficient conditions providing the boundedness of L-index in the same direction for every slie holomorphic solutions of these equations.

Response of a Rotating Beam Subject to an Accelerating Force

1991 ◽  
Author(s):  
A. Argento ◽  
R. A. Scott
Keyword(s):  
Constant Velocity ◽  
Integral Transforms ◽  
Beam Model ◽  
Rotating Beam ◽  
Velocity Function ◽  
Distributed Load ◽  
Fixed Direction ◽  
Convolution Integrals ◽  
Rotating Timoshenko Beam ◽  
Set Up

Abstract A method is given by which the response of a rotating Timoshenko beam subjected to an accelerating fixed direction force can be determined. The beam model includes the gyroscopically induced displacement transverse to the direction of the load. The solution for pinned supports is set up in general form using multi-integral transforms and the inversion is expressed in terms of convolution integrals. These are numerically integrated for a uniformly distributed load having an exponentially varying velocity function. Results are presented for the displacement under the load’s center as a function of position. Comparisons are made between the responses to a constant velocity load and a load which accelerates up to the same velocity.

Generalized evolutes of planar curves

2021 ◽  
Author(s):  
Yongqiao Wang ◽  
Yuan Chang ◽  
Haiming Liu
Keyword(s):  
Euclidean Plane ◽  
Singular Points ◽  
Moving Frames ◽  
Planar Curves ◽  
Fixed Direction ◽  
Spatial Curves

The evolutes of regular curves in the Euclidean plane are given by the caustics of regular curves. In this paper, we define the generalized evolutes of planar curves which are spatial curves, and the projection of generalized evolutes along a fixed direction are the evolutes. We also prove that the generalized evolutes are the locus of centers of slant circles of the curvature of planar curves. Moreover, we define the generalized parallels of planar curves and show that the singular points of generalized parallels sweep out the generalized evolute. In general, we cannot define the generalized evolutes at the singular points of planar curves, but we can define the generalized evolutes of fronts by using moving frames along fronts and curvatures of the Legendre immersion. Then we study the behaviors of generalized evolutes at the singular points of fronts. Finally, we give some examples to show the generalized evolutes.

scholarly journals A Five Species Cyclically Dominant Evolutionary Game with Fixed Direction: A New Way to Produce Self-Organized Spatial Patterns

Entropy ◽  
2016 ◽  
Vol 18 (8) ◽  
pp. 284 ◽  
Author(s):  
Yibin Kang ◽  
Qiuhui Pan ◽  
Xueting Wang ◽  
Mingfeng He
Keyword(s):  
Spatial Patterns ◽  
Evolutionary Game ◽  
Self Organized ◽  
Fixed Direction

An early formulation by Stokes of the theories of the rotatory polarizations of light

1924 ◽  
Vol 22 (1) ◽  
pp. 76-81 ◽  
Author(s):  
Joseph Larmor
Keyword(s):  
Magnetic Field ◽  
Frame Of Reference ◽  
Spatial Frame ◽  
Fixed Direction ◽  
Early Formulation ◽  
Magneto Optic

AbstractThe two letters now communicated are from G. G. Stokes to W. Thomson, of dates Dec. 12–13, 1848, three years after Faraday's great magneto-optic discovery. They formulated already the permissible types for general equations of propagation, virtually on the basis of the very modern criterion of covariance,—relative to all changes of the spatial frame of reference in the case of active fluids, but having regard to the fixed direction of the extraneous magnetic field in the Faraday case. Their form was elucidated in each case by correlation with a remarkable and significant type of rotational stress in a propagating medium.

scholarly journals Interaction of magnetite-based receptors in the beak with the visual system underlying 'fixed direction' responses in birds

2010 ◽  
Vol 7 (1) ◽  
pp. 24 ◽  
Author(s):  
Roswitha Wiltschko ◽  
Dennis Gehring ◽  
Susanne Denzau ◽  
Onur Güntürkün ◽  
Wolfgang Wiltschko
Keyword(s):  
Visual System ◽  
Fixed Direction

scholarly journals A 3D-Printed Hybrid Water Antenna with Tunable Frequency and Beamwidth

Electronics ◽  
2018 ◽  
Vol 7 (10) ◽  
pp. 230 ◽  
Author(s):  
Zeng-Pei Zhong ◽  
Jia-Jun Liang ◽  
Guan-Long Huang ◽  
Tao Yuan
Keyword(s):  
Beam Steering ◽  
Ground Plane ◽  
Fixed Direction ◽  
Gain Variation ◽  
Measurement Results ◽  
Feeding Structure ◽  
Operating Bandwidth ◽  
3D Printed ◽  
Metallic Strip ◽  
Tunable Frequency

A novel hybrid water antenna with tunable frequency and beamwidth is proposed. An L-shaped metallic strip is adopted as the feeding structure of the antenna in order to effectively broaden the operating bandwidth. The L-shaped strip feeder and a rectangular water dielectric resonator constitute the driven element. Five identical rectangular water dielectric elements are mounted linearly with respect to the driven element, which act as the directors and contribute to narrow the beamwidth. By varying the height of the liquid water level in the driven element, the proposed antenna is able to tune to different operational frequencies. Furthermore, it is also able to adjust to different beamwidths and gains via varying the number of director elements. A prototype is fabricated by using 3-D printing technology, where the main parts of the antenna are printed with photopolymer resin, and then the ground plane and L-shaped strip feeder are realized by using adhesive copper tapes. Measurement results agree well the simulation ones. A tunable frequency ranging from 4.66 GHz to 5.65 GHz is obtained and a beam steering along a fixed direction with a gain variation less than 0.5 dB is realized.

Node Information Collection Routing Algorithm Using Mobile Agent in WSN Initialization Stage

2013 ◽  
Vol 462-463 ◽  
pp. 64-67 ◽  
Author(s):  
Jia Jun Chen ◽  
Chang Feng Xing ◽  
Zhi Feng Cheng ◽  
Xiao Bei Wang
Keyword(s):  
Data Collection ◽  
Mobile Agent ◽  
Routing Algorithm ◽  
Total Energy Consumption ◽  
Fixed Direction ◽  
Collection Data ◽  
One Step ◽  
Three Stages ◽  
Direction Information ◽  
Start Node

We propose a mobile agent fixed-direction one step routing algorithm based on modeling WSN node data collection task. This algorithm divides the data collection task into three stages to finish and they are searching start node for MA data collection, data collection and returning the sink node. MA determines the next hop node according to the surrounding node information sensed and current move direction information. Simulation result shows that the proposed algorithm can ensure that all nodes information in WSN is collected. Then, it can effectively reduce the total number of hops for information transferring and the node total energy consumption compared to LGF algorithm in C\S mode

REIDEMEISTER MOVES FOR SURFACE ISOTOPIES AND THEIR INTERPRETATION AS MOVES TO MOVIES

1993 ◽  
Vol 02 (03) ◽  
pp. 251-284 ◽  
Author(s):  
J. SCOTT CARTER ◽  
MASAHICO SAITO
Keyword(s):  
Cross Sections ◽  
Height Function ◽  
The Other ◽  
Projection Direction ◽  
Reidemeister Moves ◽  
Link Diagrams ◽  
Fixed Direction ◽  
The Cross ◽  
Knot Diagrams

A movie description of a surface embedded in 4-space is a sequence of knot and link diagrams obtained from a projection of the surface to 3-space by taking 2-dimensional cross sections perpendicular to a fixed direction. In the cross sections, an immersed collection of curves appears, and these are lifted to knot diagrams by using the projection direction from 4-space. We give a set of 15 moves to movies (called movie moves) such that two movies represent isotopic surfaces if and only if there is a sequence of moves from this set that takes one to the other. This result generalizes the Roseman moves which are moves on projections where a height function has not been specified. The first 7 of the movie moves are height function parametrized versions of those given by Roseman. The remaining 8 are moves in which the topology of the projection remains unchanged.

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