An extension of an inequality for ratios of gamma functions

In this paper, we prove that for $x+y>0$ and $y+1>0$ the inequality {equation*} \frac{[\Gamma(x+y+1)/\Gamma(y+1)]^{1/x}}{[\Gamma(x+y+2)/\Gamma(y+1)]^{1/(x+1)}} 1$and reversed if$x<1$and that the power$\frac12$is the best possible, where$\Gamma(x)$ is the Euler gamma function. This extends the result in [Y. Yu, \textit{An inequality for ratios of gamma functions}, J. Math. Anal. Appl. \textbf{352} (2009), no.~2, 967\nobreakdash--970.] and resolves an open problem posed in [B.-N. Guo and F. Qi, \emph{Inequalities and monotonicity for the ratio of gamma functions}, Taiwanese J. Math. \textbf{7} (2003), no.~2, 239\nobreakdash--247.].Comment: 8 page

Erratum: First-principles study on the intrinsic stability of the magic Fe13O8 Cluster [Phys. Rev. B 61, 5781 (2000)]

See Also: Original Article: Q. Sun, Q. Wang, K. Parlinski, J. Z. Yu, Y. Hashi, X. G. Gong, and Y. Kawazoe, First-principles studies on the intrinsic stability of the magic Fe13O8 cluster, Phys. Rev. B 61, 5781 (2000)

Higher randomness and forcing with closed sets

[Kechris, Trans. Amer. Math. Soc. 1975] showed that there exists a largest Pi_1^1 set of measure 0. An explicit construction of this largest Pi_1^1 nullset has later been given in [Hjorth and Nies, J. London Math. Soc. 2007]. Due to its universal nature, it was conjectured by many that this nullset has a high Borel rank (the question is explicitely mentioned by Chong and Yu, and in [Yu, Fund. Math. 2011]). In this paper, we refute this conjecture and show that this nullset is merely Sigma_3^0. Together with a result of Liang Yu, our result also implies that the exact Borel complexity of this set is Sigma_3^0. To do this proof, we develop the machinery of effective randomness and effective Solovay genericity, investigating the connections between those notions and effective domination properties

Bilateral Hipoglossal Nerve Palsy In Necrotizing Otitis Externa

[No abstract available]734576Benecke Jr., J.A., Management of osteomyelitis of the skull base (1989) Laryngoscope, 99 (12), pp. 1220-1223Boringa, J.B., Hoekstra, O.S., Roos, J.W., Bertelsmann, F.W., Multiple cranial nerve palsy after otitis externa: A case report (1995) Clin Neurol Neurosurg, 97, pp. 332-335Rubin, J., Yu, V.L., Malignant external otitis: Insights into pathogenesis, clinical manifestations and therapy (1998) Am J Med, 85, pp. 391-39

Rabi oscillations and macroscopic quantum superposition states

A two-level atom interacting with a single radiation mode is considered, without the rotating-wave approximation, in the strong coupling regime. It is shown that, in agreement with the recent results on Rabi oscillations in a Josephson junction (Y. Nakamura, Yu. A. Pashkin and J. S. Tsai, Phys. Rev. Lett. {\bf 87}, 246601 (2001)), the Rabi frequency is indeed proportional to first kind integer order Bessel functions in the limit of a large number of photons and the dressed states are macroscopic quantum superposition states. To approach this problem analytically use is made of the dual Dyson series and the rotating-wave approximation.Comment: 7 pages, revtex, no figures. I have to thank Kazuyuki Fujii for pointing me out some corrections to introduce into the paper. Besides, the title and the nomenclature has been changed in agreement to editorial requirements. Finally, the correct citation for the paper by Nakamura et al. has been introduce

Comment on "Observation of a push force on the end face of a nanometer silica filament exerted by outgoing light," Phys. Rev. Lett. 101, 243601 (2008)

In a recent paper, W. She, J. Yu and R. Feng reported the slight deformations observed upon transmission of a light pulse through a fairly short length of a silica glass nano-fiber. Relating the shape and magnitude of these deformations to the momentum of the light pulse both inside and outside the fiber, these authors concluded that, within the fiber, the photons carry the Abraham momentum. In my view, the authors' claim that they have resolved the Abraham-Minkowski controversy surrounding the momentum of photons inside dielectric media is premature. A correct interpretation of the experiments of She et al requires precise calculations that would properly account not only for the electromagnetic momentum (both inside and outside the fiber) but also for the Lorentz force exerted on the fiber by the light pulse in its entire path through this nano-waveguide.Comment: 2 pages, 4 reference

One to Rule Them All: A Unique TAU Therapy for Neurodevelopmental Encephalopathies

TAU Ablation in Excitatory Neurons and Postnatal TAU Knockdown Reduce Epilepsy, SUDEP, and Autism Behaviors in a Dravet Syndrome Model Shao E, Chang C-W, Li Z, Yu X, Ho K, Zhang M, Wang X, Simms J, Lo I, Speckart J, Holtzman J, Yu G-Q, Roberson ED, Mucke L. Sci Transl Med. 2022;14(642):eabm5527. doi:10.1126/scitranslmed.abm5527 Intracellular accumulation of TAU aggregates is a hallmark of several neurodegenerative diseases. However, global genetic reduction of TAU is beneficial also in models of other brain disorders that lack such TAU pathology, suggesting a pathogenic role of nonaggregated TAU. Here, conditional ablation of TAU in excitatory, but not inhibitory, neurons reduced epilepsy, sudden unexpected death in epilepsy, overactivation of the phosphoinositide 3-kinase-AKT-mammalian target of rapamycin pathway, brain overgrowth (megalencephaly), and autism-like behaviors in a mouse model of Dravet syndrome, a severe epileptic encephalopathy of early childhood. Furthermore, treatment with a TAU-lowering antisense oligonucleotide, initiated on postnatal day 10, had similar therapeutic effects in this mouse model. Our findings suggest that excitatory neurons are the critical cell type in which TAU has to be reduced to counteract brain dysfunctions associated with Dravet syndrome and that overall cerebral TAU reduction could have similar benefits, even when initiated postnatally

On bosonic limits of two recent supersymmetric extensions of the Harry Dym hierarchy

Two generalized Harry Dym equations, recently found by Brunelli, Das and Popowicz in the bosonic limit of new supersymmetric extensions of the Harry Dym hierarchy [J. Math. Phys. 44:4756--4767 (2003)], are transformed into previously known integrable systems: one--into a pair of decoupled KdV equations, the other one--into a pair of coupled mKdV equations from a bi-Hamiltonian hierarchy of Kupershmidt.Comment: 7 page