First,Second, and Third Change of Rings Theorems for Gorenstein Homological dimensions

In this article, we investigate the change of rings theorems for the Gorenstein dimensions over arbitrary rings. Namely, by the use of the notion of strongly Gorenstein modules, we extend the well-known first, second, and third change of rings theorems for the classical projective and injective dimensions to the Gorenstein projective and injective dimensions, respectively. Each of the results established in this article for the Gorenstein projective dimension is a generalization of a G-dimension of a finitely generated module M over a noetherian ring R.     

C 1 Quadratic and C 2 Quartic Macro-Elements on a Modified Morgan-Scott Triangulation

In this paper, we construct a quadratic composite finite element of class C ¹ and quartic composite finite element of class C ² on a new triangulation τ ₁₀ which is obtained by splitting each triangle of a given triangulation τ into ten smaller subtriangles. These new elements can be used for constructing spline spaces with local basis that can be applied for solving some Hermite interpolation problems with optimal approximation order.     

On the powers and the inverse of a tridiagonal matrix

In this paper, we present an eigendecomposition of a tridiagonal matrix. Tridiagonal matrix powers and inverse are derived. As consequence, we get some relations verified by the coefficients of the inverse and the powers of a tridiagonal matrix.     

Exploring the Palynological,Chemical, and Bioactive Properties of Non-Studied Bee Pollen and Honey from Morocco

Bee products are known for their beneficial properties widely used in complementary medicine. This study aims to unveil the physicochemical, nutritional value, and phenolic profile of bee pollen and honey collected from Boulemane–Morocco, and to evaluate their antioxidant and antihyperglycemic activity. The results indicate that Citrus aurantium pollen grains were the majority pollen in both samples. Bee pollen was richer in proteins than honey while the inverse was observed for carbohydrate content. Potassium and calcium were the predominant minerals in the studied samples. Seven similar phenolic compounds were found in honey and bee pollen. Three phenolic compounds were identified only in honey (catechin, caffeic acid, vanillic acid) and six phenolic compounds were identified only in bee pollen (hesperidin, cinnamic acid, apigenin, rutin, chlorogenic acid, kaempferol). Naringin is the predominant phenolic in honey while hesperidin is predominant in bee pollen. The results of bioactivities revealed that bee pollen exhibited stronger antioxidant activity and effective α-amylase and α-glycosidase inhibitory action. These bee products show interesting nutritional and bioactive capabilities due to their chemical constituents. These features may allow these bee products to be used in food formulation, as functional and bioactive ingredients, as well as the potential for the nutraceutical sector.     

Catalytic performances of Ni/mesoporous SiO2 catalysts for dry reforming of methane to hydrogen

Several mesoporous silicas with different morphologies were controllably prepared by sol-gel method with adjustable ratio of dual template,and they were further impregnated with aqueous solution of nickel nitrate,followed by calcination in air.The synthesized silica supports and supported nickel samples were characterized using N₂-adsorption/desorption,X-ray diffraction（XRD）,H₂ temperature-programmed reduction（H₂-TPR）,Scanning electron microscope（SEM）,Transmission electron microscope（TEM） and thermo-gravimetric analysis（TGA-DTG） techniques.The Ni nanoparticles supported on shell-like silica are highly dispersed and yielded much narrower nickel particle-size than those on other mesoporous silica.The methane reforming with dioxide carbon reaction results showed that Ni nanoparticles supported on shell-like silica carrier exhibited the better catalytic performance and catalytic stability than those of nickel catalyst supported on other silica carrier.The thermo-gravimetric analysis on used nickel catalysts uncovered that catalyst deactivation depends on the type and nature of the coke deposited.The heterogeneous nature of the deposited coke was observed on nickel nanoparticles supported on spherical and peanut-like silica.Much narrower and lower TGA derivative peak was founded on Ni catalyst supported on the shell-like silica.     

A finite volume approach for unsteady viscoelastic fluid flows

A finite volume, time‐marching for solving time‐dependent viscoelastic flow in two space dimensions for Oldroyd‐B and Phan Thien–Tanner fluids, is presented. A non‐uniform staggered grid system is used. The conservation and constitutive equations are solved using the finite volume method with an upwind scheme for the viscoelastic stresses and an hybrid scheme for the velocities. To calculate the pressure field, the semi‐implicit method for the pressure linked equation revised method is used. The discretized equations are solved sequentially, using the tridiagonal matrix algorithm solver with under‐relaxation. In both, the full approximation storage multigrid algorithm is used to speed up the convergence rate. Simulations of viscoelastic flows in four‐to‐one abrupt plane contraction are carried out. We will study the behaviour at the entrance corner of the four‐to‐one planar abrupt contraction. Using this solver, we show convergence up to a Weissenberg number We of 20 for the Oldroyd‐B model. No limiting Weissenberg number is observed even though a Phan Thien–Tanner model is used. Several numerical results are presented. Smooth and stable solutions are obtained for high Weissenberg number. Copyright © 2002 John Wiley & Sons, Ltd.     

AgCo3PO4(HPO4)2

The structure of the hydro­thermally synthesized compound AgCo₃PO₄(HPO₄)₂, silver tricobalt phosphate bis­(hydrogen phosphate), consists of edge‐sharing CoO₆ chains linked together by the phosphate groups and hydrogen bonds. The three‐dimensional framework delimits two types of tunnels which accommodate Ag⁺ cations and OH groups. The title compound is isostructural with the compounds AM₃H₂(XO₄)₃ (A = Na or Ag, M = Co or Mn, and X = P or As) of the alluaudite structure type.