Zobrazeno 1 - 10
of 536
pro vyhledávání: '"McPhedran, R."'
Autor:
McPhedran, R. C.
We consider a system of three analytic functions, two of which are known to have all their zeros on the critical line $\Re (s)=\sigma=1/2$. We construct inequalities which constrain the third function, $\xi(s)$, on $\Im(s)=0$ to lie between the other
Externí odkaz:
http://arxiv.org/abs/2407.00060
Autor:
McPhedran, R C
This article contains work associated with a resolution of the Riemann hypothesis, following work by Taylor \cite{prt}, Lagarias and Suzuki \cite{lagandsuz} and Ki \cite{ki}, as well as Pustyl'nikov \cite{pust, pust2} and Keiper \cite{keiper}. Functi
Externí odkaz:
http://arxiv.org/abs/2003.14241
Autor:
McPhedran, R. C., Stout, B.
We consider integrals of products of Bessel functions and of spherical Bessel functions, combined with a Gaussian factor guaranteeing convergence at infinity. Explicit representations are obtained for the integrals, building on those in the 1992 pape
Externí odkaz:
http://arxiv.org/abs/1811.07132
Autor:
McPhedran, R. C.
Four propositions are considered concerning the relationship between the zeros of two combinations of the Riemann zeta function and the function itself. The first is the Riemann hypothesis, while the second relates to the zeros of a derivative functi
Externí odkaz:
http://arxiv.org/abs/1811.04867
In this paper, we present an asymptotic model describing localised flexural vibrations along a structured ring containing point masses or spring-mass resonators in an elastic plate. The values for the required masses and stiffnesses of resonators are
Externí odkaz:
http://arxiv.org/abs/1806.11512
Autor:
McPhedran, R. C.
We consider analytic functions of the Riemann zeta type, for which, if $s$ is a zero, so is $1-s$. We use infinite product representations of these functions, assuming their zeros to be of first order. We use exponential factors to accelerate converg
Externí odkaz:
http://arxiv.org/abs/1801.07415
Autor:
McPhedran, R. C.
A proof is reconstructed for a useful theorem on the zeros of derivatives of analytic functions due to H. M. Macdonald, which appears to be now little known. The Theorem states that, if a function $f(z)$ is analytic inside a bounded region bounded by
Externí odkaz:
http://arxiv.org/abs/1702.03458
Autor:
McPhedran, R. C.
The location of zeros of the basic double sum over the square lattice is studied. This sum can be represented in terms of the product of the Riemann zeta function and the Dirichlet beta function, so that the assertion that all its non-trivial zeros l
Externí odkaz:
http://arxiv.org/abs/1602.06330
Autor:
O'Neill, J., Selsil, O., McPhedran, R. C., Movchan, A. B., Movchan, N. V., Moggach, C. Henderson
The dynamic response of a coated inclusion is considered in the context of active cloaking. The active cloak is achieved for a coated inclusion in the presence of membrane and flexural waves. In this paper, we investigate the design of an active cloa
Externí odkaz:
http://arxiv.org/abs/1505.06138
This paper discusses the properties of flexural waves obeying the biharmonic equation, propagating in a thin plate pinned at doubly-periodic sets of points. The emphases are on the properties of dispersion surfaces having the Dirac cone topology, and
Externí odkaz:
http://arxiv.org/abs/1410.0393