101.28 The versatile exponential inequality ex ⩾ 1 + x

2017 ◽  
Vol 101 (552) ◽  
pp. 470-475
Author(s):  
Nick Lord
Keyword(s):  
Exponential Inequality

scholarly journals On the Exponential Inequality for Weighted Sums of a Class of Linearly Negative Quadrant Dependent Random Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Guodong Xing ◽  
Shanchao Yang
Keyword(s):  
Random Variables ◽  
Weighted Sums ◽  
Exponential Inequality ◽  
Precise Asymptotics ◽  
Dependent Random Variables

The exponential inequality for weighted sums of a class of linearly negative quadrant dependent random variables is established, which extends and improves the corresponding ones obtained by Ko et al. (2007) and Jabbari et al. (2009). In addition, we also give the relevant precise asymptotics.

An Intriguing Exponential Inequality

2009 ◽  
Vol 103 (1) ◽  
pp. 50-55
Author(s):  
John Robert Perrin
Keyword(s):  
Analytical Solution ◽  
Exponential Inequality ◽  
Graphical Solution ◽  
Calculus Students

An algebra problem with a graphical solution challenges precalculus and calculus students to determine an analytical solution.

On the size of a random sphere of influence graph

1999 ◽  
Vol 31 (3) ◽  
pp. 596-609 ◽  
Author(s):  
T. K. Chalker ◽  
A. P. Godbole ◽  
P. Hitczenko ◽  
J. Radcliff ◽  
O. G. Ruehr
Keyword(s):  
Upper And Lower Bounds ◽  
Exponential Inequality ◽  
Nearest Neighbour ◽  
Expected Number ◽  
Spheres Of Influence ◽  
Influence Graph ◽  
Influence Graphs ◽  
Sphere Of Influence ◽  
Proximity Graph ◽  
Sharp Concentration

We approach sphere of influence graphs (SIGs) from a probabilistic perspective. Ordinary SIGs were first introduced by Toussaint as a type of proximity graph for use in pattern recognition, computer vision and other low-level vision tasks. A random sphere of influence graph (RSIG) is constructed as follows. Consider n points uniformly and independently distributed within the unit square in d dimensions. Around each point, Xi, draw an open ball (‘sphere of influence’) with radius equal to the distance to Xi's nearest neighbour. Finally, draw an edge between two points if their spheres of influence intersect. Asymptotically exact values for the expected number of edges in a RSIG are determined for all values of d; previously, just upper and lower bounds were known for this quantity. A modification of the Azuma-Hoeffding exponential inequality is employed to exhibit the sharp concentration of the number of edges around its expected value.

A note on the exponential inequality for a class of dependent random variables

2011 ◽  
Vol 40 (1) ◽  
pp. 109-114 ◽  
Author(s):  
Soo Hak Sung ◽  
Patchanok Srisuradetchai ◽  
Andrei Volodin
Keyword(s):  
Random Variables ◽  
Exponential Inequality ◽  
Dependent Random Variables

scholarly journals FUNCTIONS ON GROUPS AND COMPUTATIONAL COMPLEXITY

2004 ◽  
Vol 14 (04) ◽  
pp. 409-429 ◽  
Author(s):  
JEAN-CAMILLE BIRGET
Keyword(s):  
Computational Complexity ◽  
Symmetric Space ◽  
Word Problem ◽  
Exponential Inequality ◽  
Isoperimetric Function ◽  
Length Functions ◽  
Finitely Presented Groups ◽  
Double Exponential ◽  
Context Free ◽  
Finitely Presented

We give some connections between various functions defined on finitely presented groups (isoperimetric, isodiametric, Todd–Coxeter radius, filling length functions, etc.), and we study the relation between those functions and the computational complexity of the word problem (deterministic time, nondeterministic time, symmetric space). We show that the isoperimetric function can always be linearly decreased (unless it is the identity map). We present a new proof of the Double Exponential Inequality, based on context-free languages.

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