Class of tight bounds on the Q ‐function with closed‐form upper bound on relative error

2019 ◽  
Vol 42 (6) ◽  
pp. 1786-1794 ◽  
Author(s):  
Zoran H. Perić ◽  
Jelena R. Nikolić ◽  
Marko D. Petković
Keyword(s):  
Closed Form ◽  
Relative Error ◽  
Upper Bound ◽  
Q Function

A closed-form upper-bound for the distribution of the weighted sum of rayleigh variates

2005 ◽  
Vol 9 (7) ◽  
pp. 589-591 ◽  
Author(s):  
G.K. Karagiannidis ◽  
T.A. Tsiftsis ◽  
N.C. Sagias
Keyword(s):  
Closed Form ◽  
Upper Bound ◽  
Weighted Sum

A MEAN–VARIANCE BOUND FOR A THREE-PIECE LINEAR FUNCTION

2007 ◽  
Vol 21 (4) ◽  
pp. 611-621 ◽  
Author(s):  
Karthik Natarajan ◽  
Zhou Linyi
Keyword(s):  
Convex Function ◽  
Closed Form ◽  
Linear Function ◽  
Upper Bound ◽  
Random Variable ◽  
Expected Value ◽  
Variance Bound ◽  
The Mean ◽  
Mean Variance

In this article, we derive a tight closed-form upper bound on the expected value of a three-piece linear convex function E[max(0, X, mX − z)] given the mean μ and the variance σ2 of the random variable X. The bound is an extension of the well-known mean–variance bound for E[max(0, X)]. An application of the bound to price the strangle option in finance is provided.

The Effective Thermal Conductivity of a Packing of Spheres

1990 ◽  
Vol 57 (3) ◽  
pp. 789-791 ◽  
Author(s):  
A. Jagota ◽  
C. Y. Hui
Keyword(s):  
Thermal Conductivity ◽  
Temperature Field ◽  
Closed Form ◽  
Effective Thermal Conductivity ◽  
Granular Materials ◽  
Upper Bound ◽  
Random Packing ◽  
Fabric Tensor ◽  
Mean Temperature

The anisotropic effective thermal conductivity of a random packing of spheres is derived. The conductivity is closely related to the fabric tensor of the theory of granular materials. The derivation involves a mean temperature field assumption which is shown to render the model an upper bound. Closed-form expressions for the conductivity are obtained in the isotropic and axisymmetric cases.

On Buckling Loads of Timoshenko Columns with Elastically Supported Ends

2012 ◽  
Vol 446-449 ◽  
pp. 578-581
Author(s):  
Hua Zhang ◽  
Xiang Fang Li
Keyword(s):  
Lower Bound ◽  
Closed Form ◽  
Upper Bound ◽  
Intermediate State ◽  
Critical Loads ◽  
Compressive Force ◽  
Buckling Loads ◽  
Characteristic Equations ◽  
The Stability ◽  
Elastically Supported

The stability of Timoshenko columns with elastically supported ends under axially compressive force is analyzed. Characteristic equations are obtained according to an intermediate state between Haringx’s and Engesser’s models. For clamped-free, clamped-clamped, and pinned-pinned columns, buckling loads are given in closed form. The influences of elastic restraint stiffness on the critical loads are elucidated. Haringx’s and Engesser’s models are two extreme cases of the present. Critical buckling loads using Haringx’s model are upper bound, and those using Engesser’s model are lower bound.

AN ORDERING OF MEASURES OF THE WELFARE COST OF INFLATION IN ECONOMIES WITH INTEREST-BEARING DEPOSITS

2012 ◽  
Vol 16 (5) ◽  
pp. 732-751 ◽  
Author(s):  
Rubens Penha Cysne ◽  
David Turchick
Keyword(s):  
Closed Form ◽  
Relative Error ◽  
Welfare Cost ◽  
Opportunity Costs ◽  
Maximum Relative Error ◽  
Elementary Functions ◽  
Closed Form Solutions ◽  
Welfare Measure ◽  
Welfare Cost Of Inflation ◽  
Alternative Measures

This paper builds on Lucas [Econometrica 68 (2000), 247–274] and on Cysne [Journal of Money, Credit and Banking 35 (2003), 221–238] to derive and order six alternative measures of the welfare costs of inflation (five of them already existing in the literature) for any vector of opportunity costs. We provide examples and closed-form solutions for each welfare measure based both on log–log and on semilog money demands, whenever possible in terms of elementary functions. Estimates of the maximum relative error a researcher can incur when using any of these measures are given. Everything is done for economies with or without interest-bearing deposits.

scholarly journals Real-Time Inverse Kinematics of the Human Arm

1996 ◽  
Vol 5 (4) ◽  
pp. 393-401 ◽  
Author(s):  
Deepak Tolani ◽  
Norman I. Badler
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Upper Bound ◽  
Multiple Solutions ◽  
Inverse Kinematics ◽  
Additional Constraint ◽  
Degree Of Freedom ◽  
Empirical Results ◽  
Human Arm ◽  
Real Time Applications

A simple inverse kinematics procedure is proposed for a seven degree of freedom model of the human arm. Two schemes are used to provide an additional constraint leading to closed-form analytical equations with an upper bound of two or four solutions, Multiple solutions can be evaluated on the basis of their proximity from the rest angles or the previous configuration of the arm. Empirical results demonstrate that the procedure is well suited for real-time applications.

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