Solution of 2D Navier–Stokes equation by coupled finite difference-dual reciprocity boundary element method

Computation of viscous fluid flow is an area of research where many authors have tried to present different numerical methods for solution of the Navier–Stokes equations. Each of these methods has its own advantages and weaknesses. In the meantime, many researchers have attempted to develop coupled numerical algorithms in order to save storage for computational purposes and to save computational time.     

Comparison of Pulsed and Continuous Wave Diode Laser at 940 nm on the Viability and Migration of Gingival Fibroblasts

Gingival fibroblasts have critical roles in oral wound healing. Photobiomodulation (PBM) has been shown to promote mucosal healing and is now recommended for managing oncotherapy-associated oral mucositis. This study examined the effects of the emission mode of a 940 nm diode laser on the viability and migration of human gingival fibroblasts. Cells were cultured in a routine growth media and treated with PBM (average power 0.1 W cm⁻², average fluence 3 J cm⁻², every 12 h for six sessions) in one continuous wave and two pulsing settings with 20% and 50% duty cycles. Cell viability was assessed using MTT, and digital imaging quantified cell migration. After 48 and 72 h, all treatment groups had significantly higher viability (n = 6, P < 0.05) compared with the control. The highest viability was seen in the pulsed (20% duty cycle) group at the 72-h time point. PBM improved fibroblast migration in all PBM-treated groups, but differences were not statistically significant (n = 2, P > 0.05). PBM treatments can promote cell viability in both continuous and pulsed modes. Further studies are needed to elucidate the optimal setting for PBM-evoked responses for its rationalized use in promoting specific phases of oral wound healing.     

Semistar-Krull and valuative dimension of integral domains

Given a stable semistar operation of finite type ⋆ on an integral domain D, we show that it is possible to define in a canonical way a stable semistar operation of finite type ⋆[X] on the polynomial ring D[X], such that, if n := ⋆-dim(D), then n+1 ≤ ⋆[X]-dim(D[X]) ≤ 2n+1. We also establish that if D is a ⋆-Noetherian domain or is a Prüfer ⋆-multiplication domain, then ⋆[X]-dim(D[X]) = ⋆- dim(D)+1. Moreover we define the semistar valuative dimension of the domain D, denoted by ⋆-dim _v (D), to be the maximal rank of the ⋆-valuation overrings of D. We show that ⋆-dim _v (D) = n if and only if ⋆[X ₁, . . . , X _n ]-dim(D[X ₁, . . . , X _n ]) = 2n, and that if ⋆-dim _v (D) < ∞ then ⋆[X]-dim _v (D[X]) = ⋆-dim _v (D) + 1. In general ⋆-dim(D) ≤ ⋆-dim _v (D) and equality holds if D is a ⋆-Noetherian domain or is a Prüfer ⋆-multiplication domain. We define the ⋆-Jaffard domains as domains D such that ⋆-dim(D) < ∞ and ⋆-dim(D) = ⋆-dim _v (D). As an application, ⋆-quasi-Prüfer domains are characterized as domains D such that each (⋆, ⋆′)-linked overring T of D, is a ⋆′-Jaffard domain, where ⋆′ is a stable semistar operation of finite type on T. As a consequence of this result we obtain that a Krull domain D, must be a w _D -Jaffard domain.