On page 188 of his lost notebook, Ramanujan introduced distinct classes of exquisite infinite series, representing them in terms of Eisenstein series. The objective of this paper is to develop ...various differential identities related to Borwein's cubic theta functions and h-functions. Also, we present certain identities containing Eisenstein series of level 6 and h-functions that are used to establish relations involving class one infinite series and h-functions. Additionally, we present a straightforward approach to evaluate a discrete convolution sum by employing relationships involving Eisenstein series and h-functions.
The (p, k)-parametrization method, as introduced by Alaca, offers an innovative approach to derive a variety of new Eisenstein series identities that incorporate Borweins' theta functions. This paper ...presents new Eisenstein series identities that involve Borweins' cubic theta functions, achieved through the (p, k)-parameterization technique.
It is well known that every bivariate copula induces a positive measure on the Borel σ-algebra on 0,12, but there exist bivariate quasi-copulas that do not induce a signed measure on the same ...σ-algebra. In this paper we show that a signed measure induced by a bivariate quasi-copula can always be expressed as an infinite combination of measures induced by copulas. With this we are able to give the first characterization of measure-inducing quasi-copulas in the bivariate setting.
Two summation theorems concerning the F12(1/2)-series due to Gauss and Bailey will be examined by employing the “coefficient extraction method”. Forty infinite series concerning harmonic numbers and ...binomial/multinomial coefficients will be evaluated in closed form, including eight conjectured ones made by Z.-W. Sun. The presented comprehensive coverage for the harmonic series of convergence rate “1/2” may serve as a reference source for readers.
This paper is concerned with the delay-dependent stability for the linear systems with a time-varying delay. To get a result in the form of LMI from a Lyapunov–Krasovskii functional, an integral ...inequality is necessary and Jensen inequality has been a most powerful inequality in the last few years. Recently, based on Wirtinger inequality, an improved integral inequality, encompassing Jensen inequality, was proposed and its application to the stability showed a quite improvement. In this paper, without using Wirtinger inequality, a further improved integral inequality in the form of infinite series is derived, and, based on this, a delay-dependent stability condition in the form of LMI is derived. Finally, its contribution on the stability criterion is shown by well-known two examples.
Recently, arguments for a refined de Sitter conjecture were put forward in 1. Using the large distance conjecture of 2, the authors provide evidence for this dS conjecture in asymptotic regimes of ...field space, where the parametric control of string theory becomes arbitrarily good. Their main tool is Bousso's covariant entropy bound.3 Here, we describe a simpler way to reach a similar conclusion. The argument is based on the fact that the cutoff of an effective theory with gravity decreases as the number of species grows. We then discuss a loophole in this argument and its possible counterpart in the assumptions underlying the entropy‐based derivation. The idea is to consider potentials which, while they remain below an exponentially falling bound, have small oscillations leading locally to relatively flat regions or even to an infinite series of dS minima.
Recently, arguments for a refined de Sitter conjecture were put forward in 1. Using the large distance conjecture of 2, the authors provide evidence for this dS conjecture in asymptotic regimes of field space, where the parametric control of string theory becomes arbitrarily good. Their main tool is Bousso's covariant entropy bound3. Here, we describe a simpler way to reach a similar conclusion. The argument is based on the fact that the cutoff of an effective theory with gravity decreases as the number of species grows. We then discuss a loophole in this argument and its possible counterpart in the assumptions underlying the entropy‐based derivation. The idea is to consider potentials which, while they remain below an exponentially falling bound, have small oscillations leading locally to relatively at regions or even to an infinite series of dS minima.
The Photon Ring in M87 Broderick, Avery E.; Pesce, Dominic W.; Gold, Roman ...
The Astrophysical journal,
08/2022, Letnik:
935, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Abstract
We report measurements of the gravitationally lensed secondary image—the first in an infinite series of so-called “photon rings”—around the supermassive black hole M87* via simultaneous ...modeling and imaging of the 2017 Event Horizon Telescope (EHT) observations. The inferred ring size remains constant across the seven days of the 2017 EHT observing campaign and is consistent with theoretical expectations, providing clear evidence that such measurements probe spacetime and a striking confirmation of the models underlying the first set of EHT results. The residual diffuse emission evolves on timescales comparable to one week. We are able to detect with high significance a southwestern extension consistent with that expected from the base of a jet that is rapidly rotating in the clockwise direction. This result adds further support to the identification of the jet in M87* with a black hole spin-driven outflow, launched via the Blandford–Znajek process. We present three revised estimates for the mass of M87* based on identifying the modeled thin ring component with the bright ringlike features seen in simulated images, one of which is only weakly sensitive to the astrophysics of the emission region. All three estimates agree with each other and previously reported values. Our strongest mass constraint combines information from both the ring and the diffuse emission region, which together imply a mass-to-distance ratio of
4.20
−
0.06
+
0.12
μ
as
and a corresponding black hole mass of (7.13 ± 0.39) × 10
9
M
⊙
, where the error on the latter is now dominated by the systematic uncertainty arising from the uncertain distance to M87*.
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