منابع مشابه
Horizon ratio bound for inflationary fluctuations.
We demonstrate that the gravity wave background amplitude implies a robust upper bound on the wavelength-to-horizon ratio at the end of inflation: lambda/H(-1) less than or approximately equal e(60), as long as the cosmic energy density does not drop faster than radiation subsequent to inflation. This limit implies that N, the number of e-folds between horizon exit and the end of inflation for ...
متن کاملA Horizon Ratio Bound for Inflationary Fluctuations
Inflation predicts a spectrum of scalar and tensor perturbations that can be tested by present cosmological observations. The precise nature of this spectrum depends on, among other things, the amount of expansion between the time the scales of interest leave the horizon and the end of inflation. The scale factor grows by e between these two times. Here we point out that N is bounded from above...
متن کاملA lower bound for ratio of power means
holds for r > 0 and n∈N. We call the left-hand side of this inequality Alzer’s inequality [1] and the right-hand side Martins’ inequality [8]. Let {ai}i∈N be a positive sequence. If ai+1ai−1 ≥ ai for i ≥ 2, we call {ai}i∈N a logarithmically convex sequence; if ai+1ai−1 ≤ ai for i≥ 2, we call {ai}i∈N a logarithmically concave sequence. In [2], Martins’ inequality was generalized as follows: let ...
متن کاملAn upper and lower bound of the Medication Possession Ratio
BACKGROUND The Medication Possession Ratio (MPR) is a ubiquitous and central measurement for adherence in the health care industry. However, attempts to standardize its calculation have failed, possibly due to the opacity of a single, static MPR, incapability of directly lending itself to a variety of studies, and challenges of comparing the value across studies. This work shows that the MPR st...
متن کاملAn Improved Bound for Characterizing Integer-valued Factorial Ratio Sequences
We study the nonnegativity of a certain class of step functions, associated with the integrality of sequences of ratios of factorial products. In particular, we extend the work of previous authors Bell and Bober [1], obtaining tighter lower bounds on the mean square of such step functions, allowing us to find better asymptotic and general restrictions on when the factorial ratio sequences can b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2021
ISSN: 0024-3795
DOI: 10.1016/j.laa.2021.02.010