Microstrip Low Pass · 2010
In this article, a microstrip structure for a small-sized elliptic function low pass filter (LPF) is developed from a modified dumbbell-shaped defected ground structure (DGS) and additional open stubs. The steps taken in developing the structure are presented. Cross-junction open stubs are placed right above rectangular- and I-shaped slots in the ground plane of the microstrip line. A comparison with previous work 11 shows that this approach provides a steeper attenuation slope and a smaller circuit size. Since the study did not use a periodic or array configuration of DGS cells, considerable circuit size reduction, less than one fifth, is possible, compared with a conventional stepped impedance LPF having an identical cutoff frequency (2.665 GHz) to that of this LPF. Furthermore, the fine tuning capability of the stopband can provide precise manufacturing conditions for applications such as IF filters for downconverters and the bias circuits of oscillators and amplifiers to reject harmonic and spurious signals, since the stopband tuning rate with respect to frequency variation is small compared to that of a conventional DGS. 11 Defected ground structures (DGS) etched in the metallic ground plane of microstrip lines, also known as photonic
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Henri Cohen, Fredrik Strömberg · Graduate studies in mathematics · 2017
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J. Cassels · Acta Arithmetica · 1971
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Ju Young Lee, Sanghyuk Lee, Sewook Oh · Journal of Functional Analysis · 2024
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Ju Young Lee, Sanghyuk Lee, Sewook Oh · arXiv (Cornell University) · 2023
We study the elliptic maximal functions defined by averages over ellipses and rotated ellipses which are multi-parametric variants of the circular maximal function. We prove that those maximal functions are bounded on $L^p$ for some $p\neq \infty$. For this purpose, we obtain some sharp multi-parameter local smoothing estimates.
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Hidetoshi Awata, Hiroaki Kanno, Andrei Mironov et al. · Journal of High Energy Physics · 2020
A bstract As a development of [1], we note that the ordinary Shiraishi functions have an insufficient number of parameters to describe generic eigenfunctions of double elliptic system (Dell). The lacking parameter can be provided by substituting elliptic instead of the ordinary Gamma functions in the coefficients of the series. These new functions (ELS-functions) are conjectured to be functions governed by compactified DIM networks which can simultaneously play the three roles: solutions to non-stationary Dell equations, Dell conformal blocks with the degenerate field (surface operator) insertion, and the corresponding instanton sums in 6 d SUSY gauge theories with adjoint matter. We describe the basics of the corresponding construction and make further conjectures about the various limits and dualities which need to be checked to make a precise statement about the Dell description by double-periodic network models with DIM symmetry. We also demonstrate that the ELS-functions provide symmetric polynomials, which are an elliptic generalization of Macdonald ones, and compute the generation function of the elliptic genera of the affine Laumon spaces. In the particular U(1) case, we find an explicit plethystic formula for the 6 d partition function, which is a non-trivial elliptic generalization of the ( q, t ) Nekrasov-Okounkov formula from 5 d .
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E. V. Brumberg, Toshio Fukushima · Celestial Mechanics and Dynamical Astronomy · 1994
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Douglas Ulmer · IAS/Park City mathematics series · 2011
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Prisuelos Arribas, María Cruz · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2017
Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas. Fecha de lectura: 06-04-2017
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R.J. Wenzel · 1970
A type of elliptic-function filter is described that is easy to design and construct, has low passband loss, and is very compact. With simple scaling, a broad range of cutoff frequencies can be obtained with a limited number of standard parts. Experimental results are presented for three filters with cutoff frequencies of 0.75, 1.0, and 1.5 GHz. Each filter occupies a volume of about 0.5 in/sup3/.
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E. Yu. Bunkova · Proceedings of the Steklov Institute of Mathematics · 2016
The article is devoted to the theory of elliptic functions of level n. An elliptic function of level n determines a Hirzebruch genus called an elliptic genus of level n. Elliptic functions of level n are also of interest because they are solutions of the Hirzebruch functional equations. The elliptic function of level 2 is the Jacobi elliptic sine function, which determines the famous Ochanine–Witten genus. It is the exponential of the universal formal group of the form F(u, v) = (u 2 − v 2)/(uB(v) − vB(u)), B(0) = 1. The elliptic function of level 3 is the exponential of the universal formal group of the form F(u, v) = (u 2 A(v) − v 2 A(u))/(uA(v)2 − vA(u)2), A(0) = 1, A″(0) = 0. In the present study we show that the elliptic function of level 4 is the exponential of the universal formal group of the form F(u, v) = (u 2 A(v) − v 2 A(u))/(uB(v) − vB(u)), where A(0) = B(0) = 1 and for B′(0) = A″(0) = 0, A′(0) = A 1, and B″(0) = 2B 2 the following relation holds: (2B(u) + 3A 1 u)2 = 4A(u)3 − (3A 1 2 − 8B 2)u 2 A(u)2. To prove this result, we express the elliptic function of level 4 in terms of the Weierstrass elliptic functions.
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E. H. Neville · Elsevier eBooks · 1971
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E. H. Neville · Elsevier eBooks · 1971
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ERIC HAROLD NEVILLE · Elsevier eBooks · 1971
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S Hofmann, S, A Amenta et al. · Tesis Doctorals en Xarxa (Consorci de Serveis Universitaris de Catalunya)
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I. Rubinstein, R.L. Sleven, A.F. Hinte · IEEE Transactions on Microwave Theory and Techniques · 1969
This paper describes the development of a practical circuit for realizing narrow-bandwidth elliptic-function filters at microwave frequencies. The design procedure is presented for TEM filters of any bandwidth up to about 10 percent. Experimental verification of the low-loss feature of the elliptic-function response is demonstrated with measured data on 1-percent-bandwidth strip-transmission-line S-band filters.
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Triebel, Hans · French digital mathematics library (Numdam) · 1973
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Adam Beran · Digital Repository (National Repository of Grey Literature) · 2023
In this thesis, we study twisted Edwards curves using the theory of algebraic function fields. After summarizing the basic theory, we focus on the structure of the function field for curves that are given by an equation of the form x2 2 = f(x1), where f is a monic polynomial of degree four. We show that twisted Edwards curves correspond to a special case when f(x1) = g(x2 1), where g is a quadratic polynomial with two distinct nonzero roots. We describe the basic properties of twisted Edwards curves, with special attention given to possible places at infinity. Next, we derive formulas for the point addition, which is achieved by using the relation between points on the curve, places of degree one and elements of the Picard group. Furthermore, we summarize how the point addition can be interpreted geometrically, and outline several alternative coordinate systems based on projective coordinates. Finally, we present two examples of twisted Edwards curves that are nowadays being used in cryptographic applications. 1
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Norbert Schappacher · Lecture notes in mathematics · 1988
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McKean, Henry P. 1930-2024, Moll, Victor H. 1956-, Kasman, Alex 1967- · 2025
The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book, reissued with a new Foreword, presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic. After an informal preparatory chapter, the book follows an historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text
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