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Mechanical Structure Including Mechanisms and Load Analysis
Published in Seong-woo Woo, Design of Mechanical Systems Based on Statistics, 2021
A variety of mechanisms in automobiles, refrigerators, bicycles, etc. are a mechanical portion that can transfer motion and forces from a power source to the other. Most mechanisms are designed to provide a mechanical advantage. They also form a kinematic chain in which at least one link is attached to a frame of reference (ground) and makes four different motions, namely, rotary motion, oscillation, linear motion, and reciprocating motion. Rotary motion is the starting point for many mechanisms, mostly provided by an engine or dc motors. Oscillation is a back and forth motion about a pivot point. Linear motion is a one-dimensional motion along a straight line. Reciprocating motion is again a back and forth motion.
Simulation of mechanical behavior of carbonate gravel with hybrid PSO–SVR algorithm
Published in Marine Georesources & Geotechnology, 2023
QianBiao Liu, Sa Li, JiangSong Yin, TingTing Li, Molin Han
For an SVR model, we let be a set of training patterns where is the input, stands for the corresponding desired output, is the N-dimensional vector space and is the one-dimensional vector space. The primary goal of SVR is to find a linear or nonlinear regression function representing the relationship between and This function can be formulated by: where is weight vector; is bias parameter; and are the optimized parameters obtained from training; is the nonlinear mapping about which transforms the linear inseparable samples in a low dimensional space into a high dimensional space to make them linearly separable.
Analyticity of the Lyapunov exponent of meromorphic monotonic cocycles
Published in Dynamical Systems, 2022
In order to apply the techniques in [1], we introduce the following notations. Denote For we write , where If one identifies the complex one-dimensional projective space with , by associating to the line through the complex number , the action of on is given precisely by . In this identification, the real one-dimensional projective space corresponds to the unit circle , and matrices preserve the unit disk .
Investigation on the effect of boost pressure on performance characteristics of a diesel engine
Published in Numerical Heat Transfer, Part A: Applications, 2019
Consider a given training set of N data points with input data and output where denotes n-dimensional vector space, and denotes one dimensional vector space. In LSSVM for regression analysis, the optimization problem can be formulated as follows [22, 23]: Subjected to the equality constraints where is a nonlinear function which maps the input space into a higher dimensional space; = weight matrix; denotes a regularization constant; = error; = bias.