The Koch Curve: A Geometric Proof

2007 ◽  
Vol 114 (1) ◽  
pp. 61-66 ◽  
Author(s):  
Šime Ungar
Keyword(s):  
Geometric Proof ◽  
Koch Curve

A Geometric Proof of lim d →0 +(-dln d) = 0

1992 ◽  
Vol 23 (3) ◽  
pp. 209
Author(s):  
John H. Mathews
Keyword(s):  
Geometric Proof

Fractal Koch curve for UHF band application

2007 ◽  
Author(s):  
Mohd Nazri A. Karim ◽  
Mohamad Kamal A. Rahim ◽  
Mohamad Irfan ◽  
Thelaha Masri
Keyword(s):  
Koch Curve ◽  
Uhf Band

A Lattice-Geometric Proof of Wedderburn’s Theorem

1993 ◽  
Vol 23 (3-4) ◽  
pp. 384-386 ◽  
Author(s):  
Stefan E. Schmidt
Keyword(s):  
Geometric Proof

A Simple Geometric Proof of the Addition Formula for the Sine

1994 ◽  
Vol 25 (3) ◽  
pp. 229
Author(s):  
Jeffrey Li-chieh Ho
Keyword(s):  
Geometric Proof ◽  
Addition Formula

A Geometric Proof of Machin's Formula

1990 ◽  
Vol 63 (5) ◽  
pp. 336
Author(s):  
Roger B. Nelsen
Keyword(s):  
Geometric Proof

The Koch curve as a smooth manifold

2008 ◽  
Vol 38 (2) ◽  
pp. 334-338 ◽  
Author(s):  
Marcelo Epstein ◽  
Jędrzej Śniatycki
Keyword(s):  
Smooth Manifold ◽  
Koch Curve

scholarly journals Non-defectivity of Grassmannian bundles over a curve

2016 ◽  
Vol 27 (07) ◽  
pp. 1640002 ◽  
Author(s):  
Insong Choe ◽  
George H. Hitching
Keyword(s):  
Vector Bundles ◽  
Manuscripta Math ◽  
Maximal Degree ◽  
Geometric Proof ◽  
Secant Varieties ◽  
Grassmann Bundle ◽  
Positive Rank

Let [Formula: see text] be the Grassmann bundle of two-planes associated to a general bundle [Formula: see text] over a curve [Formula: see text]. We prove that an embedding of [Formula: see text] by a certain twist of the relative Plücker map is not secant defective. This yields a new and more geometric proof of the Hirschowitz-type bound on the isotropic Segre invariant for maximal isotropic sub-bundles of orthogonal bundles over [Formula: see text], analogous to those given for vector bundles and symplectic bundles in [I. Choe and G. H. Hitching, Secant varieties and Hirschowitz bound on vector bundles over a curve, Manuscripta Math. 133 (2010) 465–477, I. Choe and G. H. Hitching, Lagrangian sub-bundles of symplectic vector bundles over a curve, Math. Proc. Cambridge Phil. Soc. 153 (2012) 193–214]. From the non-defectivity, we also deduce an interesting feature of a general orthogonal bundle of even rank over [Formula: see text], contrasting with the classical and symplectic cases: a general maximal isotropic sub-bundle of maximal degree intersects at least one other such sub-bundle in positive rank.

scholarly journals Modified Koch Fractal Antenna for Multi and Wideband Wireless Applications

2021 ◽  
Vol 19 (2) ◽  
pp. 182-189
Author(s):  
Shweta Rani ◽  
Sushil Kakkar
Keyword(s):  
Numerical Simulations ◽  
Impedance Matching ◽  
Optimization Procedure ◽  
Design Parameters ◽  
Impedance Bandwidth ◽  
Fractal Antenna ◽  
Bacterial Foraging Optimization ◽  
Koch Curve ◽  
Wireless Applications ◽  
Koch Fractal

This paper focuses on the design and development of modified Koch fractal antenna. Compared to traditional Koch curve antenna, the presented antenna possesses a greater number of frequency bands and better impedance matching. Furthermore, the bacterial foraging optimization (BFO) approach is implemented to enhance the impedance bandwidth. The developed technique has been verified by employing various numerical simulations. The design parameters generated from the optimization procedure have been utilized to manufacture the antenna and the respective experimental and simulated results compared. The measured results show that the designed antenna exhibits multi and wideband behavior, covering WLAN, WIMAX, and various other wireless applications.

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