The Bounds on the Coefficients of Restitution for the Frictional Impact of Rigid Pendulum Against a Fixed Surface

2009 ◽  
Vol 77 (1) ◽  
Author(s):  
V. A. Lubarda
Keyword(s):  
Lower Bound ◽  
Coefficient Of Friction ◽  
Upper Bound ◽  
Kinetic Coefficient ◽  
Geometric Mean ◽  
Upper Bounds ◽  
Coefficient Of Restitution ◽  
Tangential Impact ◽  
Impact Coefficient ◽  
Vertical Impact

Upper bounds on Newton’s, Poisson’s, and energetic coefficients of normal restitution for the frictional impact of rigid pendulum against a fixed surface are derived, demonstrating that the upper bound on Newton’s coefficient is smaller than 1, while the upper bound on Poisson’s coefficient is greater than 1. The upper bound on the energetic coefficient of restitution, which is a geometric mean of Newton’s and Poisson’s coefficients of normal restitution, is equal to 1. Lower bound on all three coefficients is equal to zero. The bounds on the tangential impact coefficient, defined by the ratio of the frictional and normal impulses, are also derived. Its lower bound is negative, while its upper bound is equal to the kinetic coefficient of friction. Simplified bounds in the case of a nearly vertical impact are also derived.

The Heine-Borel theorem in extended basic logic

1949 ◽  
Vol 14 (1) ◽  
pp. 9-15 ◽  
Author(s):  
Frederic B. Fitch
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Fundamental Theorem ◽  
Upper Bounds ◽  
Basic Logic ◽  
Real Numbers ◽  
Consistent Theory

A demonstrably consistent theory of real numbers has been outlined by the writer in An extension of basic logic1 (hereafter referred to as EBL). This theory deals with non-negative real numbers, but it could be easily modified to deal with negative real numbers also. It was shown that the theory was adequate for proving a form of the fundamental theorem on least upper bounds and greatest lower bounds. More precisely, the following results were obtained in the terminology of EBL: If С is a class of U-reals and is completely represented in Κ′ and if some U-real is an upper bound of С, then there is a U-real which is a least upper bound of С. If D is a class of (U-reals and is completely represented in Κ′, then there is a U-real which is a greatest lower bound of D.

scholarly journals A Computational Perspective on Network Coding

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Qin Guo ◽  
Mingxing Luo ◽  
Lixiang Li ◽  
Yixian Yang
Keyword(s):  
Graph Theory ◽  
Computational Complexity ◽  
Lower Bound ◽  
Network Coding ◽  
Upper Bound ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Multicast Networks ◽  
Computational Perspective ◽  
Source Rate

From the perspectives of graph theory and combinatorics theory we obtain some new upper bounds on the number of encoding nodes, which can characterize the coding complexity of the network coding, both in feasible acyclic and cyclic multicast networks. In contrast to previous work, during our analysis we first investigate the simple multicast network with source rateh=2, and thenh≥2. We find that for feasible acyclic multicast networks our upper bound is exactly the lower bound given by M. Langberg et al. in 2006. So the gap between their lower and upper bounds for feasible acyclic multicast networks does not exist. Based on the new upper bound, we improve the computational complexity given by M. Langberg et al. in 2009. Moreover, these results further support the feasibility of signatures for network coding.

Minimization of Bounded Cable Tensions in Cable-Based Parallel Manipulators

2007 ◽  
Author(s):  
Mahir Hassan ◽  
Amir Khajepour
Keyword(s):  
Lower Bound ◽  
Numerical Method ◽  
Upper Bound ◽  
Task Force ◽  
Parallel Manipulators ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Alternating Projection ◽  
Alternating Projection Method ◽  
Cable Forces

In this work, the application of the Dykstra’s alternating projection method to find the minimum-2-norm solution for actuator forces is discussed in the case when lower and upper bounds are imposed on the actuator forces. The lower bound is due to specified pretension desired in the cables and the upper bound is due to the maximum allowable forces in the cables. This algorithm presents a systematic numerical method to determine whether or not a solution exists to the cable forces within these bounds and, if it does exist, calculate the minimum-2-norm solution for the cable forces for a given task force. This method is applied to an example 2-DOF translational cable-driven manipulator and a geometrical demonstration is presented.

scholarly journals Crossings in Grid Drawings

10.37236/3025 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Vida Dujmović ◽  
Pat Morin ◽  
Adam Sheffer
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Geometric Graph ◽  
Upper Bounds ◽  
Crossing Number ◽  
Geometric Graphs ◽  
Vertex Sets

We prove tight crossing number inequalities for geometric graphs whose vertex sets are taken from a $d$-dimensional grid of volume $N$ and give applications of these inequalities to counting the number of crossing-free geometric graphs that can be drawn on such grids.In particular, we show that any geometric graph with $m\geq 8N$ edges and with vertices on a 3D integer grid of volume $N$, has $\Omega((m^2/N)\log(m/N))$ crossings. In $d$-dimensions, with $d\ge 4$, this bound becomes $\Omega(m^2/N)$. We provide matching upper bounds for all $d$. Finally, for $d\ge 4$ the upper bound implies that the maximum number of crossing-free geometric graphs with vertices on some $d$-dimensional grid of volume $N$ is $N^{\Theta(N)}$. In 3 dimensions it remains open to improve the trivial bounds, namely, the $2^{\Omega(N)}$ lower bound and the $N^{O(N)}$ upper bound.

Asymptotic bounds for the fluid queue fed by sub-exponential On/Off sources

2000 ◽  
Vol 32 (01) ◽  
pp. 244-255 ◽  
Author(s):  
V. Dumas ◽  
A. Simonian
Keyword(s):  
Lower Bound ◽  
Finite Number ◽  
Upper Bound ◽  
Content Distribution ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Fluid Queue ◽  
Asymptotic Bounds ◽  
Multiplicative Factor ◽  
Buffer Content

We consider a fluid queue fed by a superposition of a finite number of On/Off sources, the distribution of the On period being subexponential for some of them and exponential for the others. We provide general lower and upper bounds for the tail of the stationary buffer content distribution in terms of the so-called minimal subsets of sources. We then show that this tail decays at exponential or subexponential speed according as a certain parameter is smaller or larger than the ouput rate. If we replace the subexponential tails by regularly varying tails, the upper bound and the lower bound are sharp in that they differ only by a multiplicative factor.

Doubling up: Two upper bounds for scalars

Linguistics ◽  
2015 ◽  
Vol 53 (3) ◽  
Author(s):  
Mira Ariel
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Upper Bounds ◽  
Bound Analysis

AbstractMost theories of scalar quantifiers, of whatever persuasion, assume a lexical lower-bound-only, ‘at least’ meaning for scalar quantifiers, offering pragmatic or grammatical mechanisms for deriving the upper bound (Carston 1990; Chierchia 2004; Horn 1972 and onwards). I have challenged the lower-bound analysis in Ariel (2004), proposing instead a

scholarly journals Almost simplicial polytopes: the lower and upper bound theorems

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Eran Nevo ◽  
Guillermo Pineda-Villavicencio ◽  
Julien Ugon ◽  
David Yost
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Upper Bound Theorem ◽  
Simplicial Polytopes ◽  
Full Version ◽  
The Face ◽  
International Audience ◽  
Bound Theorem

International audience this is an extended abstract of the full version. We 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 bounds for the face numbers of these polytopes as functions of d, n and s, thus generalizing the classical Lower Bound Theorem by Barnette and Upper Bound Theorem by McMullen, which treat the case s = 0. We characterize the minimizers and provide examples of maximizers, for any d.

scholarly journals Iterative estimation of total π-electron energy

2005 ◽  
Vol 70 (10) ◽  
pp. 1193-1197 ◽  
Author(s):  
Lemi Türker ◽  
Ivan Gutman
Keyword(s):  
Lower Bound ◽  
Electron Energy ◽  
Upper Bound ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Benzenoid Hydrocarbons ◽  
Total Electron ◽  
Iterative Estimation ◽  
Total Electron Energy ◽  
Almost All

In this work, the lower and upper bounds for total ?-electron energy (E) was studied. A method is presented, by means of which, starting with a lower bound EL and an upper bound EU for E, a sequence of auxiliary quantities E0 E1, E2,? is computed, such that E0 = EL, E0 < E1 < E2 < ?, and E = EU. Therefore, an integer k exists, such that Ek E < Ek+1. If the estimates EL and EU are of the McClelland type, then k is called the McClelland number. For almost all benzenoid hydrocarbons, k = 3.

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.

BOUNDS ON THE MINIMAL SUMSET SIZE FUNCTION IN GROUPS

2007 ◽  
Vol 03 (04) ◽  
pp. 503-511 ◽  
Author(s):  
SHALOM ELIAHOU ◽  
MICHEL KERVAIRE
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Solvable Groups ◽  
Upper Bounds ◽  
Minimal Size ◽  
Lower And Upper Bounds ◽  
Numerical Function ◽  
Size Function

In this paper, we give lower and upper bounds for the minimal size μG(r,s) of the sumset (or product set) of two finite subsets of given cardinalities r,s in a group G. Our upper bound holds for solvable groups, our lower bound for arbitrary groups. The results are expressed in terms of variants of the numerical function κG(r,s), a generalization of the Hopf–Stiefel function that, as shown in [6], exactly models μG(r,s) for G abelian.

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