CLOSED-FORM SOLUTIONS FOR NATURAL FREQUENCY FOR INHOMOGENEOUS BEAMS WITH ONE SLIDING SUPPORT AND THE OTHER PINNED

2000 ◽  
Vol 238 (3) ◽  
pp. 529-539 ◽  
Author(s):  
I. ELISHAKOFF ◽  
R. BECQUET
Keyword(s):  
Closed Form ◽  
Natural Frequency ◽  
The Other ◽  
Closed Form Solutions

scholarly journals Reliability of Sampling Inspection Schemes Applied to Replacement Steam Generators

2006 ◽  
Vol 129 (1) ◽  
pp. 109-117 ◽  
Author(s):  
Guy Roussel ◽  
Leon Cizelj
Keyword(s):  
Closed Form ◽  
Steam Generator ◽  
The State ◽  
The Other ◽  
Prior Density ◽  
Steam Generators ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Sampling Inspection ◽  
Steam Generator Tubing

The basis for determining the size of the random sample of tubes to be inspected in replacement steam generators is revisited in this paper. A procedure to estimate the maximum number of defective tubes left in the steam generator after no defective tubes have been detected in the randomly selected inspection sample is proposed. A Bayesian estimation is used to obtain closed-form solutions for uniform, triangular, and binomial prior densities describing the number of failed tubes in steam generators. It is shown that the particular way of selecting the random inspection sample (e.g., one sample from both SG, one sample from each SG, etc.) does not affect the results of the inspection and also the information obtained about the state of the uninspected tubing, as long as the inspected steam generators belong to the same population. Numerical examples further demonstrate two possible states of the knowledge existing before the inspection of the tubing. First, virtually no knowledge about the state of the steam generator tubing before the inspection is modeled using uniform and triangular prior densities. It is shown that the knowledge about the uninspected part of the tubing strongly depends on the size of the sample inspected. Further, even small inspection samples may significantly improve our knowledge about the uninspected part. On the other hand, rather strong belief on the state of the tubing prior to the inspection is modeled using binomial prior density. In this case, the knowledge about the uninspected part of the tubing is virtually independent on the size of the sample. Furthermore, it is shown qualitatively and quantitatively that such inspection brings no additional knowledge on the uninspected part of the tubing.

Synthesis of Seven-Link Mechanisms

1973 ◽  
Vol 95 (2) ◽  
pp. 533-540 ◽  
Author(s):  
D. Kohli ◽  
A. H. Soni
Keyword(s):  
Closed Form ◽  
Nonlinear Equations ◽  
Degrees Of Freedom ◽  
The Other ◽  
Linear Superposition ◽  
Two Degrees Of Freedom ◽  
Closed Form Solutions ◽  
Highly Nonlinear ◽  
Principle Of Linear Superposition

The mechanisms derived from the seven-link chains with five links in their two loops and having two degrees of freedom are examined for six synthesis problems. Using displacement matrices, closed form synthesis equations are derived. It is shown that three synthesis problems may be solved using the principle of linear superposition, and closed form solutions may be obtained. The other three synthesis problems involve highly nonlinear equations and must be solved numerically.

scholarly journals Multi-bidder First Price Auction with Beliefs

2019 ◽  
Vol 7 (1) ◽  
pp. 140-160
Author(s):  
Hyeon Park
Keyword(s):  
Closed Form ◽  
Arbitrary Number ◽  
Value Of Information ◽  
Jel Classification ◽  
The Other ◽  
Type Space ◽  
Closed Form Solutions ◽  
Price Auction ◽  
Equilibrium Bidding

This paper characterizes the set of equilibria in the first price auction with multiple bidders—specifically three bidders, each of whose type space is multi-dimensional, incorporating a bidder’s beliefs about others’ valuations. In this auction, each bidder independently and privately learns the other two opponents’ valuations with some probability. This paper derives closed form solutions for equilibrium bidding behaviours parameterized by the degree of information when the bidder has homogeneous beliefs regarding each opponent. This paper demonstrates how much the level of information affects the bidding behaviours of the informed bidders. In addition, this paper extends the model into [Formula: see text] bidders when a high value bidder has fixed beliefs that all other bidders are identical types, and show how the value of information changes as the number of participants increases. Finally, this paper speculates on the possible changes in the efficiency of the model from increasing the valuation space to an arbitrary number. JEL Classification: D44, D82, D83

Statics and Geometry of Underconstrained Axisymmetric 3-Nets

1984 ◽  
Vol 51 (4) ◽  
pp. 827-830 ◽  
Author(s):  
E. N. Kuznetsov
Keyword(s):  
Closed Form ◽  
The Other ◽  
Geometric Shapes ◽  
Closed Form Solutions ◽  
The Subject

A 3-net is a system formed by three intersecting arrays of linear flexible members such that every intersection involves one member of each array. The subject of this study is an axisymmetric 3-net where the first array is meridional and the other two are inclined to a meridian at equal but opposite angles. If the net intersections are not fixed the system is underconstrained and, generally, does not possess a unique configuration. However, such systems allow exceptional configurations in which they lack kinematic mobility and admit prestress. Pertinent equations governing the intricately interrelated statics and geometry of axisymmetric 3-nets are developed and some closed-form solutions are obtained. On this basis, two particular classes of immobile (static) 3-nets are synthesized and two corresponding sets of feasible geometric shapes are investigated.

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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