Introduction: The aim of this study was to evaluate the effect of proximal contour of class II composite restorations placed with straight or contoured matrix band using composite resins with different modulus of elasticity on stress distribution by finite element method. Methods: In order to evaluate the stress distribution of class II composite restorations using finite element method, upper ...

1. The algorithm. Huang [1] gives an algorithm for computing the powers of a triangular matrix where the diagonal elements are unique. However, in contrast to Huang’s algorithm, the method presented here has the unique advantage of producing the result in closed form, which shows explicitly how the behavior of any element of the matrix varies with varying powers of the matrix. Also, the closed ...

We describe an algorithm for decomposing a fundamental matrix computed from point correspondences over two images into the focal lengths of the two images and the camera motion parameters in a closed-form expression. Our algorithm is based on the decomposability condition of the essential matrix expressed in terms of its scalar invariants. We give a complete analysis for degenerate camera con g...

The charged lepton mass formula can be explained when the masses are propotinal to the squared vacuum expectation values (VEVs) of scalar fields. We introduce U(3) flavor symmetry and its nonet scalar field Φ, whose VEV structure plays an essential role for generating the fermion mass spectrum. We can naturally obtain bilinear form of the Yukawa coupling Yij ∝ ∑ k〈Φik〉〈Φkj〉 without the non-reno...

In this paper we prove theorems related to the Ramanujan-type series for 1/π (type 3F2) and to the Ramanujan-like series, discovered by the author, for 1/π (type 5F4). Our developments for the cases 3F2 and 5F4 connect with the theory of modular functions and with the theory of CalabiYau differential equations, respectively.

introduction: cleaner productions in textile industry is achieved by reducing water and chemicals’ consumption, saving energy, reducing production of air pollution and solid wastes, reducing toxicity and noise pollution through many solutions. the purpose of the present research was to apply strengths, weaknesses, opportunities, threats (swot) and quality systems planning matrix (qspm) techniqu...

Regular linear matrix pencils A − E∂ ∈ K[∂], where K = Q, R or C, and the associated differential algebraic equation (DAE) Eẋ = Ax are studied. The Wong sequences of subspaces are investigate and invoked to decompose the Kn into V⊕W, where any bases of the linear spaces V and W transform the matrix pencil into the Quasi-Weierstraß form. The Quasi-Weierstraß form of the matrix pencil decouples t...

We present a new algorithm to compute the Integer Smith normal form of large sparse matrices. We reduce the computation of the Smith form to independent, and therefore parallel, computations modulo powers of word-size primes. Consequently, the algorithm does not suuer from coef-cient growth. We have implemented several variants of this algorithm (Elimination and/or Black-Box techniques) since p...

The two-by-two ABCD matrix plays a central role in optical sciences. The four elements of this matrix are all real, and its determinant is one. Thus, it has three independent parameters. Yet, it has a rich mathematical content which could lead to interesting results in physics. It is generally assumed that this matrix can be diagonalized by a rotation, but this is not the case as shown in our p...