scholarly journals The Gravitational Compression of an Elastic Sphere

1955 ◽  
Vol 8 (1) ◽  
pp. 167
Author(s):  
A Keane
Keyword(s):  
Lower Bound ◽  
Elastic Material ◽  
Upper Bound ◽  
Moment Of Inertia ◽  
Elastic Sphere ◽  
The Moment ◽  
Gravitational Compression ◽  
Gravitational Equilibrium

On considering a sphere in hydrostatic gravitational equilibrium, composed of a homogeneous elastic material for which the variation of incompressibility x with pressure p is given by dx/dp=n, a constant, we find that there is an upper bound to the radius R of the sphere provided n=2, and that for all values of n there is a lower bound to the value of I/MR2, where I is the moment of inertia about a diameter and M is the mass of the sphere.

scholarly journals Almost Simplicial Polytopes: The Lower and Upper Bound Theorems

2019 ◽  
Vol 72 (2) ◽  
pp. 537-556
Author(s):  
Eran Nevo ◽  
Guillermo Pineda-Villavicencio ◽  
Julien Ugon ◽  
David Yost
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Independent Interest ◽  
Upper Bound Theorem ◽  
Moment Curve ◽  
Simplicial Polytopes ◽  
Cyclic Polytopes ◽  
Bound Theorem ◽  
The Moment

AbstractWe study $n$-vertex $d$-dimensional polytopes with at most one nonsimplex facet with, say, $d+s$ vertices, called almost simplicial polytopes. We provide tight lower and upper bound theorems for these polytopes as functions of $d,n$, and $s$, thus generalizing the classical Lower Bound Theorem by Barnette and the Upper Bound Theorem by McMullen, which treat the case where $s=0$. We characterize the minimizers and provide examples of maximizers for any $d$. Our construction of maximizers is a generalization of cyclic polytopes, based on a suitable variation of the moment curve, and is of independent interest.

scholarly journals Optimal sup norm bounds for newforms on GL2 with maximally ramified central character

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Félicien Comtat
Keyword(s):  
Number Theory ◽  
Lower Bound ◽  
Modular Forms ◽  
Upper Bound ◽  
Upper Bounds ◽  
Central Character ◽  
Ramanujan Conjecture ◽  
The Moment ◽  
Level Aspect

AbstractRecently, the problem of bounding the sup norms of {L^{2}}-normalized cuspidal automorphic newforms ϕ on {\mathrm{GL}_{2}} in the level aspect has received much attention. However at the moment strong upper bounds are only available if the central character χ of ϕ is not too highly ramified. In this paper, we establish a uniform upper bound in the level aspect for general χ. If the level N is a square, our result reduces to\|\phi\|_{\infty}\ll N^{\frac{1}{4}+\epsilon},at least under the Ramanujan Conjecture. In particular, when χ has conductor N, this improves upon the previous best known bound {\|\phi\|_{\infty}\ll N^{\frac{1}{2}+\epsilon}} in this setup (due to [A. Saha, Hybrid sup-norm bounds for Maass newforms of powerful level, Algebra Number Theory 11 2017, 1009–1045]) and matches a lower bound due to [N. Templier, Large values of modular forms, Camb. J. Math. 2 2014, 1, 91–116], thus our result is essentially optimal in this case.

Perception of the moment of inertia of hand tools

1982 ◽  
Author(s):  
Carol Zahner ◽  
M. Stephen Kaminaka
Keyword(s):  
Moment Of Inertia ◽  
Hand Tools ◽  
The Moment

Research on the identification of the moment of inertia of PMSM for industrial robots

2020 ◽  
Author(s):  
Chuanwen Zhang ◽  
Guangxu Zhou ◽  
Ting Yang ◽  
Ningran Song ◽  
Xinli Wang ◽  
...  
Keyword(s):  
Industrial Robots ◽  
Moment Of Inertia ◽  
The Moment

scholarly journals Statistical Estimates of the Pulsar Glitch Activity

Universe ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 8
Author(s):  
Alessandro Montoli ◽  
Marco Antonelli ◽  
Brynmor Haskell ◽  
Pierre Pizzochero
Keyword(s):  
Linear Regression ◽  
Upper Bound ◽  
Bootstrap Method ◽  
Waiting Times ◽  
Statistical Estimates ◽  
Equal Variance ◽  
Linear Fit ◽  
The Moment ◽  
The Bootstrap Method

A common way to calculate the glitch activity of a pulsar is an ordinary linear regression of the observed cumulative glitch history. This method however is likely to underestimate the errors on the activity, as it implicitly assumes a (long-term) linear dependence between glitch sizes and waiting times, as well as equal variance, i.e., homoscedasticity, in the fit residuals, both assumptions that are not well justified from pulsar data. In this paper, we review the extrapolation of the glitch activity parameter and explore two alternatives: the relaxation of the homoscedasticity hypothesis in the linear fit and the use of the bootstrap technique. We find a larger uncertainty in the activity with respect to that obtained by ordinary linear regression, especially for those objects in which it can be significantly affected by a single glitch. We discuss how this affects the theoretical upper bound on the moment of inertia associated with the region of a neutron star containing the superfluid reservoir of angular momentum released in a stationary sequence of glitches. We find that this upper bound is less tight if one considers the uncertainty on the activity estimated with the bootstrap method and allows for models in which the superfluid reservoir is entirely in the crust.

scholarly journals Multiple closed orbits for N-body-type problems

1998 ◽  
Vol 58 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Shiqing Zhang
Keyword(s):  
Lower Bound ◽  
Periodic Solutions ◽  
Upper Bound ◽  
Critical Value ◽  
Body Type ◽  
Fixed Energy ◽  
Closed Orbits

Using the equivariant Ljusternik-Schnirelmann theory and the estimate of the upper bound of the critical value and lower bound for the collision solutions, we obtain some new results in the large concerning multiple geometrically distinct periodic solutions of fixed energy for a class of planar N-body type problems.

On the nuclear equilibrium deformation and the moment of inertia of the band

1971 ◽  
Vol 34 (4) ◽  
pp. 255-256 ◽  
Author(s):  
S.A. Hjorth ◽  
J. Oppelstrup ◽  
G. Ehrling
Keyword(s):  
Moment Of Inertia ◽  
Equilibrium Deformation ◽  
The Moment

Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop

2016 ◽  
Vol 26 (12) ◽  
pp. 1650204 ◽  
Author(s):  
Jihua Yang ◽  
Liqin Zhao
Keyword(s):  
Lower Bound ◽  
Limit Cycle ◽  
Hamiltonian Systems ◽  
Limit Cycles ◽  
Upper Bound ◽  
Melnikov Function ◽  
Piecewise Smooth ◽  
First Order ◽  
Period Annulus

This paper deals with the limit cycle bifurcations for piecewise smooth Hamiltonian systems. By using the first order Melnikov function of piecewise near-Hamiltonian systems given in [Liu & Han, 2010], we give a lower bound and an upper bound of the number of limit cycles that bifurcate from the period annulus between the center and the generalized eye-figure loop up to the first order of Melnikov function.

Isolated minima of the product of n linear forms

1953 ◽  
Vol 49 (1) ◽  
pp. 59-62 ◽  
Author(s):  
E. S. Barnes
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Linear Forms ◽  
Image Position

Letbe n linear forms with real coefficients and determinant Δ = ∥ aij∥ ≠ 0; and denote by M(X) the lower bound of | X1X2 … Xn| over all integer sets (u) ≠ (0). It is well known that γn, the upper bound of M(X)/|Δ| over all sets of forms Xi, is finite, and the value of γn has been determined when n = 2 and n = 3.

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