let $pounds$ be the category of locally compact abelian groups and $a,cin pounds$. in this paper, we define component extensions of $a$ by $c$ and show that the set of all component extensions of $a$ by $c$ forms a subgroup of $ext(c,a)$ whenever $a$ is a connected group. we establish conditions under which the component extensions split and determine lca groups which are component projective. ...

introduction: gutta-percha, the concrete milky juice of the sapotaceae family tree, is the most commonly used material for obturation of prepared canal space. natural 1-4 trans stereochemical structure of gutta-percha is taken to a heating- inclusion process of various organic and inorganic elements by manufacturers. the purpose of this study is to detect the presence and percentage of inorgani...

the principle of dimensionality reduction with pca is the representation of the dataset ‘x’in terms of eigenvectors ei ∈ rn  of its covariance matrix. the eigenvectors oriented in the direction with the maximum variance of x in rn carry the most      relevant information of x. these eigenvectors are called principal components [8]. assume that n images in a set are originally represented in mat...

this paper presents a mathematical model for the vibration analysis of a three-component piezoelectric force sensor. the cubic theory of weakly nonlinear electroelasticity is applied to the model for describing the electromechanical coupling effect in the piezoelectric sensing elements which operate in thickness-shear and thickness-stretch vibration modes. hamilton's principle is used to d...

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