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 ...

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 ...

‎in this paper‎, ‎the type-{rm ii} matrices on (negative) latin square graphs are considered and it is proved that‎, ‎under‎ ‎certain conditions‎, ‎the nomura algebras of such type-{rm ii} matrices are trivial‎. ‎in addition‎, ‎we construct type-{rm ii} matrices‎ ‎on doubly regular tournaments and show that the nomura algebras of such matrices are also trivial‎.

The Painlev\'e--Kovalevskaya test is applied to find three matrix versions of the Painlev\'e II equation. All these equations are interpreted as group-invariant reductions integrable evolution equations, which makes it possible construct isomonodromic Lax pairs for them.

In this paper, we determine the symmetrised density of a nonsingular doubly noncentral matrix variate beta type I and II distributions under different definitions.

In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.

These notes started their life as a lecture given at the Toronto Student Seminar on February 9, 2012. The material is taken mostly from the classic paper by Coppersmith and Winograd [CW]. Other sources are §15.7 of Algebraic Complexity Theory [ACT], Stothers’s thesis [Sto], V. Williams’s recent paper [Wil], and the paper by Cohn at al. [CKSU]. Starred sections are the ones we didn’t have time t...