Why Is Π < 2 Φ ?
نویسنده
چکیده
We give a combinatorial proof of the inequality in the title in terms of Fibonacci numbers and Euler numbers. The result is motivated by Sidorenko’s theorem on the number of linear extensions of the poset and its complement. We conclude with some open problems. November 5, 2016. ⋆Department of Mathematics, UCLA, LA, CA 90095. Email: {ahmorales,pak}@math.ucla.edu. Department of Mathematics, UPenn, Philadelphia, PA 19104. Email: [email protected]. 1 2 ALEJANDRO MORALES, IGOR PAK AND GRETA PANOVA
منابع مشابه
0 Observation of the φ → π + π − π + π − Decay
Using 11.6 pb of data collected in the energy range 0.984–1.06 GeV by CMD-2 at VEPP-2M, the cross section of the reaction e+e− → π+π−π+π− has been studied. For the first time an interference pattern was observed in the energy dependence of the cross section near the φ meson. The branching ratio of the φ → π+π−π+π− decay double suppressed by the G-parity and OZI rule is measured Br(φ → ππππ) = (...
متن کاملComposition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane
and Applied Analysis 3 In two main theorems in 20 , the authors proved the following results, which we now incorporate in the next theorem. Theorem A. Assume p ≥ 1 and φ is a holomorphic self-map of Π . Then the following statements true hold. a The operator Cφ : H Π → A∞ Π is bounded if and only if sup z∈Π Im z ( Imφ z )1/p < ∞. 1.8 b The operator Cφ : H Π → B∞ Π is bounded if and only if sup ...
متن کاملErratum to: Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equation
We show that the existence of a principal eigenvalue of a linear differential operator claimed in [4] does not always hold; hence, the proof of the stability and uniqueness of positive steady-state solution in [4] are not correct. For the linearized operator (φ ∈ X = {v ∈ C 2 [−1, 1] : v(±1) = 0}) L[φ] = φ (x) + λφ(x) − λφ(x) 1 −1 f (x, y)u(y)dy − λu(x) 1 −1 f (x, y)φ(y)dy, (1) where f ∈ L 2 ((...
متن کاملWeighted Composition Operators from Weighted Bergman Spaces to Weighted-Type Spaces on the Upper Half-Plane
and Applied Analysis 3 Let β > 0. The weighted-type space or growth space on the upper half-planeA∞ β Π consists of all f ∈ H Π such that ∥ ∥f ∥ ∥ A∞ β Π sup z∈Π Iz β ∣ ∣f z ∣ ∣ < ∞. 1.7 It is easy to check thatA∞ β Π is a Banach space with the norm defined above. For weightedtype spaces on the unit disk, polydisk, or the unit ball see, for example, papers 10, 32, 33 and the references therein....
متن کاملUniversal Manipulation of a Single Qubit
We find the optimal universal way of manipulating a single qubit, |ψ(θ, φ)〉, such that (θ, φ) → (θ− k, φ− l). Such optimal transformations fall into two classes. For 0 ≤ k ≤ π/2 the optimal map is the identity and the fidelity varies monotonically from 1 (for k = 0) to 1/2 (for k = π/2). For π/2 ≤ k ≤ π the optimal map is the universal-NOT gate and the fidelity varies monotonically from 1/2 (fo...
متن کاملResolution to the quantum phase problem
Defining the observable φ canonically conjugate to the number observable N has long been an open problem in quantum theory. The problem stems from the fact that N is bounded from below. Here we show how to define the absolute phase observable Φ ≡ |φ| by suitably restricting the Hilbert space of x and p like variables. This Φ is actually the absolute value of the phase and has the correct classi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016