11,872 research outputs found
The Reason for the Incompleteness of Some Theorems in Modern Mathematics: Non Numbers Enter Mathematical Analysis or the Concept Definition Is Incomplete
The concept of non-number and number is found, and the concept of non-number and number is defined by symbols. The basic theory of number theory is solved; it is proved that {Godel's Incomplete Theorem} are incomplete. and it is also proved that the first number of natural number must be 1, not 0
Overview: How Does the Paper "The Continuity of Prime Numbers Can Lead to the Continuity of Even Numbers" Relate to the Goldbach Conjecture
The paper "The continuity of prime numbers can lead to the continuity of even numbers" proposes three clever methods to prove the Goldbach conjecture from another path that humans never anticipated and was also the correct path. "The continuity of prime numbers can lead to the continuity of even numbers" A preprint has previously been published (Xie ling. 2021). 
5-(4-BromoÂphenÂyl)-1,2,3,4-tetraÂhydroÂbenzo[a]phenanthridine
The title compound, C23H18BrN, was synthesized by the reaction of 4-bromoÂbenzaldehyde, naphthalen-2-amine and cycloÂhexaÂnone in tetraÂhydroÂfuran, catalyzed by iodine. The saturated six-membered ring adopts a half-chair conformation, and the four vicinal rings form a helical conformation, which results in a significant deviation from planarity for the pyridine ring. In the crystal, a weak C—H⋯π interÂaction occurs, leading to inversion dimers
Enhanced quantum teleportation in the background of Schwarzschild spacetime by weak measurements
It is commonly believed that the fidelity of quantum teleportation in the
gravitational field would be degraded due to the heat up by the Hawking
radiation. In this paper, we point out that the Hawking effect could be
eliminated by the combined action of pre- and post-weak measurements, and thus
the teleportation fidelity is almost completely protected. It is intriguing to
notice that the enhancement of fidelity could not be attributed to the
improvement of entanglement, but rather to the probabilistic nature of weak
measurements. Our work extends the ability of weak measurements as a quantum
technique to battle against gravitational decoherence in relativistic quantum
information.Comment: 9 pages, 5 figures, comments are welcom
Robust Spin Squeezing Preservation in Photonic Crystal Cavities
We show that the robust spin squeezing preservation can be achieved by
utilizing detuning modification for an ensemble of N separate two-level atoms
embedded in photonic crystal cavities (PCC). In particular, we explore the
different dynamical behaviors of spin squeezing between isotropic and
anisotropic PCC cases when the atomic frequency is inside the band gap. In both
cases, it is shown that the robust preservation of spin squeezing is completely
determined by the formation of bound states. Intriguingly, we find that unlike
the isotropic case where steady-state spin squeezing varies smoothly when the
atomic frequency moves from the inside to the outside band edge, a sudden
transition occurs for the anisotropic case. The present results may be of
direct importance for, e.g., quantum metrology in open quantum systems.Comment: 6 pages, 4 figures, accepted by Laser Physics Letter
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