Upper estimate of a combinatorial sum

2018 ◽  
Vol 28 (1) ◽  
pp. 53-64
Author(s):  
Pavel V. Roldugin
Keyword(s):  
Binomial Sum ◽  
Upper Estimate

Abstract We give an upper estimate for the binomial sum $\begin{array}{} U_{d} \left(x\right)=\sum _{r\ge 0}\binom {d-r+1} r\cdot x^{r} \end{array} $ with natural d and real nonnegative x. In particular, this estimate implies that $\begin{array}{} U_{d} \left(x\right)=O\bigl((0.5+\sqrt{x+0.25} )^{d} \bigr) \end{array} $ with fixed x > 0 and d → ∞.

Estimation of Firing Temperature and Compositional Variability of Archaeological Pottery by Differential Scanning Calorimetry

2004 ◽  
Vol 852 ◽  
Author(s):  
A. Giordana ◽  
E. Peacock ◽  
M. McCarthy ◽  
K. Guilbeau ◽  
P. Jacobs ◽  
...  
Keyword(s):  
Firing Temperature ◽  
Thermal Characterization ◽  
Small Sample ◽  
Scanning Calorimetry ◽  
Blind Test ◽  
Vitrification Temperature ◽  
Archaeological Pottery ◽  
Digital Scanning ◽  
Different Temperatures ◽  
Upper Estimate

ABSTRACTDigital Scanning Calorimetry (DSC), a thermal characterization technique, can be used to rapidly obtain a rough upper estimate of the firing temperature of archaeological pottery as well as an indication of its composition. The technique involves heating a small sample (10–20 mg) of ground ceramic above the vitrification temperature, cooling and reheating. The curves of the two heating cycles are then compared. The validity of the technique was evaluated by a blind test in which 35 tiles fired at different temperatures were analyzed without knowing their firing point, and by analysis of archaeological pottery samples assumed to be local or imported based upon stylistic criteria.

scholarly journals Rational interpolation of the function |x|α by an extended system of Chebyshev – Markov nodes

2020 ◽  
Vol 55 (4) ◽  
pp. 391-405
Author(s):  
E. A. Rovba ◽  
V. Yu. Medvedeva
Keyword(s):  
Rational Functions ◽  
Rational Interpolation ◽  
Asymptotic Equality ◽  
Fixed Number ◽  
Theoretical Research ◽  
Extended System ◽  
Uniform Approximations ◽  
Upper Estimate ◽  
Interpolation Functions ◽  
Interpolation Nodes

In this paper, we study the approximations of a function |x|α, α > 0 by interpolation rational Lagrange functions on a segment [–1,1]. The zeros of the even Chebyshev – Markov rational functions and a point x = 0 are chosen as the interpolation nodes. An integral representation of an interpolation remainder and an upper bound for the considered uniform approximations are obtained. Based on them, a detailed study is made:a) the polynomial case. Here, the authors come to the famous asymptotic equality of M. N. Hanzburg;b) at a fixed number of geometrically different poles, the upper estimate is obtained for the corresponding uniform approximations, which improves the well-known result of K. N. Lungu;c) when approximating by general Lagrange rational interpolation functions, the estimate of uniform approximations is found and it is shown that at the ends of the segment [–1,1] it can be improved.The results can be applied in theoretical research and numerical methods. 

An upper estimate for the reciprocal sum of a sum-free sequence

1977 ◽  
Vol 34 (1) ◽  
pp. 9-24 ◽  
Author(s):  
Eugene Levine ◽  
Joseph O'Sullivan
Keyword(s):  
Reciprocal Sum ◽  
Upper Estimate

scholarly journals On the time it takes to judge grammaticality

2020 ◽  
Vol 73 (9) ◽  
pp. 1460-1465 ◽  
Author(s):  
Jonathan Mirault ◽  
Jonathan Grainger
Keyword(s):  
Stimulus Duration ◽  
Presentation Duration ◽  
Percent Correct ◽  
Rate Of Increase ◽  
Syntactic Information ◽  
Variable Duration ◽  
Masking Stimulus ◽  
Upper Estimate ◽  
Models Of Reading ◽  
Decision Times

The presentation duration of five-word sequences was varied and participants were asked to judge their grammaticality. The five-word sequences were presented for a variable duration randomly selected between 50 and 500 ms with 50-ms steps and were immediately followed by a masking stimulus. Half of the sequences were correct sentences which were randomly intermixed with ungrammatical sequences formed of the same words in scrambled order. We measured the proportion of correct responses for each presentation duration in the grammatical and ungrammatical conditions, and calculated sensitivity and bias from these measures. Both the sensitivity measure ( d′) and the probability correct responses to grammatical and ungrammatical sequences increased as the stimulus duration increased, with a d′ of 2 and an average percent correct close to 87% for the grammatical sequences already attained at 300 ms. The rate of increase in performance diminished beyond 300 ms. Grammatical decision times were faster and more accurate for the grammatically correct sequences, thus indicating that participants were not responding by detecting illegal word combinations in the ungrammatical sequences. On the basis of these findings, we provide an upper estimate of 300 ms as the time it takes to access reliable syntactic information from five-word sequences in French, and we discuss the implications of this constraint for models of reading.

scholarly journals Particle motion around generic black holes coupled to non-linear electrodynamics

2019 ◽  
Vol 79 (9) ◽  
Author(s):  
Jaroslav Vrba ◽  
Ahmadjon Abdujabbarov ◽  
Arman Tursunov ◽  
Bobomurat Ahmedov ◽  
Zdeněk Stuchlík
Keyword(s):  
Black Hole ◽  
Energy Conditions ◽  
Test Particles ◽  
Stable Circular Orbit ◽  
Spin Parameter ◽  
Non Linear ◽  
Innermost Stable Circular Orbit ◽  
Charge Parameter ◽  
Upper Estimate ◽  
Black Hole Solutions

Abstract We study spherically symmetric magnetically charged generic black hole solutions of general relativity coupled to non-linear electrodynamics (NED). For characteristic values of the generic spacetime parameters we give the position of horizons in dependence on the charge parameter, demonstrating separation of the black hole and no-horizon solutions, and possibility of existence of solutions containing three horizons. We show that null, weak and strong energy conditions are violated when the outer horizon is approaching the center. We study effective potentials for photons and massive test particles and location of circular photon orbits (CPO) and innermost stable circular orbit (ISCO). We show that the unstable photon orbit can become stable, leading to the possibility of photon capture which affects on silhouette of the central object. The position of ISCO approaches the horizon with increasing charge parameter q and the energy at ISCO decreases with increasing charge parameter. We investigate this phenomenon and summarize for a variety of the generic spacetime parameters the upper estimate on the spin parameter of the Kerr black which can be mimicked by the generic charged black hole solutions.

scholarly journals Global and Blow-Up Solutions for a Class of Nonlinear Parabolic Problems under Robin Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Lingling Zhang ◽  
Hui Wang
Keyword(s):  
Global Solution ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Parabolic Problems ◽  
Maximum Principles ◽  
Gradient Term ◽  
Nonlinear Parabolic Problems ◽  
Nonlinear Parabolic ◽  
Robin Boundary ◽  
Upper Estimate

We discuss the global and blow-up solutions of the following nonlinear parabolic problems with a gradient term under Robin boundary conditions:(b(u))t=∇·(h(t)k(x)a(u)∇u)+f(x,u,|∇u|2,t), inD×(0,T),(∂u/∂n)+γu=0, on∂D×(0,T),u(x,0)=u0(x)>0, inD¯, whereD⊂RN  (N≥2)is a bounded domain with smooth boundary∂D. Under some appropriate assumption on the functionsf,h,k,b, andaand initial valueu0, we obtain the sufficient conditions for the existence of a global solution, an upper estimate of the global solution, the sufficient conditions for the existence of a blow-up solution, an upper bound for “blow-up time,” and an upper estimate of “blow-up rate.” Our approach depends heavily on the maximum principles.

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