A counterexample to the paper ��Weakly associated primes and primary decomposition of modules over commutative rings��

In this note we will show that finitely generated condition is necessary in Theorem 1.2 of the above mentioned paper.     

Monitoring the effects of homogeneity methanol/water/monomer on the mode of polymerization of styrene: dispersion polymerization versus emulsion polymerization

The polymerization of styrene (St) was carried out with varying amounts of methanol in aqueous medium. As methanol content decreased (to 50 %), the phase of polymerization mixture (methanol/water/monomer) changed to a heterogeneous state; the homogeneous state was obtained in samples that contain 75 and 100 % methanol. In order to verify the mechanism of polymerization in heterogeneous and homogeneous mixtures, the nucleus formation rate during polymerization, the stability equilibrium of the media and seeded particles, and the size of particles and their growth in polymerization were experimentally being monitored. With the homogeneous mixture in 75 wt% methanol, dumbbell, triangle, and peanut-like particles have been formed. On the other hand, the characteristics of the polymerization products were different from those typically obtained in the emulsion polymerization and in the sample with 100 wt% methanol dispersion polymerization. In the sample with 100 % methanol and in one with 50 % methanol, monodispersed spherical particles are formed in the final conversion. Thus, homogeneity in the aqueous methanol mixture can be a critical factor in determining the polymerization modes between dispersion and emulsion polymerization.     

A deterministic,multi-item inventory model with supplier selection and imperfect quality

This paper considers the scenario of supply chain with multiple products and multiple suppliers, all of which have limited capacity. We assume that received items from suppliers are not of perfect quality. Items of imperfect quality, not necessarily defective, could be used in another inventory situation. Imperfect items are sold as a single batch, prior to receiving the next shipment, at a discounted price. The demand over a finite planning horizon is known, and an optimal procurement strategy for this multi-period horizon is to be determined. Each of products can be sourced from a set of approved suppliers, a supplier-dependent transaction cost applies for each period in which an order is placed on a supplier. A product-dependent holding cost per period applies for each product in the inventory that is carried across a period in the planning horizon. Also a maximum storage space for the buyer in each period is considered. The decision maker, the buyer, needs to decide what products to order, in what quantities, with which suppliers, and in which periods. Finally, a genetic algorithm (GA) is used to solve the model.     

Three-dimensional modelling of GeSi growth in presence of axial and rotating magnetic fields

A three-dimensional numerical simulation has been performed to study the growth of Ge_0.98Si_0.02 by the Traveling Solvent Method. We attempted to suppress the buoyancy convection, in the Ge_0.98Si_0.02 melt zone, by applying axial and rotating magnetic fields. The effects of the applied magnetic field intensity, on the transport structures in the melt (flow and concentration fields, heat and mass transfer), have been investigated in detail. The steady-state full Navier–Stokes equations, as well as energy, mass species transport and continuity equations are numerically solved using the finite element method. By applying an axial magnetic field of various intensities (2, 10, and 22 mT), we found that as the axial magnetic field increases, the silicon distribution nearby the growth interface becomes more uniform. In the case of a rotating magnetic field, with different applied rotational speeds (2, 7 and 10 rpm), we found that such kind of magnetic field has a marked effect on the silicon concentration, which changes its shape from a convex one to a nearly flat shape as the magnetic field intensity increases. An alternative method to reduce or suppress buoyancy convection, in the melt zone, is the growing of the sample in a microgravity environment, with a gravity level of at least 10^?4 the earth normal gravity level; in this case the results revealed smooth and almost perfect straight concentration contours, due to the buoyancy convection weakness.     

A predictive, simple and rapid method for thermodynamic study on the binding of copper ion with Alzheimer''s amyloid β peptide

The interaction of CuC12 to the first 16 residues of the Alzbeimer's amyliod β peptide, Aβ(1-16) was studied by isothermal titration calorimetry at pH 7.2 and 37 ℃ in aqueous solution.     

Recent strategies in the synthesis of thiophene derivatives: highlights from the 2012–2020 literature

Molecular Diversity - Thiophene-based analogs have been fascinated by a growing number of scientists as a potential class of biologically active compounds. Furthermore, they play a vital role for...