INTRODUCTION It is not clear whether increasing the ultrasonic intensity would enhance the cleaning efficacy of passive ultrasonic irrigation (PUI) inside a root canal. The aim of this study was to evaluate the effect of the ultrasonic intensity on PUI to remove dentin debris and whether there is any lateral effect beyond the ultrasonic tip. METHODS Each of 15 in vitro root canal models with ...

In this paper, the relationship between the (P,Q)-orthogonal symmetric and symmetric matrices is derived. By applying the generalized singular value decomposition, the general expression of the least square (P,Q)-orthogonal symmetric solutions for the matrix equation AXB = C is provided. Based on the projection theorem in inner space, and by using the canonical correlation decomposition, an ana...

The effect of different concentrations of sugar solution (hypertonic) (30%, 45% and 60% w/v) and carboxyl methyl cellulose (CMC) (0%, 1% and 2% w/v) coating on freeze drying of apple slices was studied. In total, nine treatments with respect to concentrations of hypertonic solution and coating layer were prepared to analyze their influence on the physical and chemical properties of freeze dried...

A system ofM(≥ 2) coupled singularly perturbed linear reaction-diffusion equations is considered on the unit square. Under certain hypotheses on the coupling, a maximum principle is established for the differential operator. The relationship between compatibility conditions at the corners of the square and the smoothness of the solution on the closed domain is fully described. A decomposition o...

This paper concerns the square-mean almost periodic solutions to a class of nonautonomous stochastic differential equations on a separable real Hilbert space. Using the so-called ‘Acquistapace-Terreni’ conditions, we establish the existence and uniqueness of a square-mean almost periodic mild solution to those nonautonomous stochastic differential equations.

Motivated by the definition of P†-matrix ([9]), another generalization of a P -matrix for square singular matrices called PD-matrix is proposed first. Then the uniqueness of solution of Linear Complementarity Problems for square singular matrices is proved using PD-matrices. Finally some results which are true for P -matrices are extended to PD-matrices.

We consider so-called “squaring the square”-puzzles where a given square (or rectangle) should be dissected into smaller squares. For a specific instance of such problems we demonstrate that a mathematically rigorous solution can be quite involved. As an alternative to exhaustive enumeration using tailored algorithms we describe the general approach of formulating the problem as an integer line...