On the Auslander–Reiten conjecture for Cohen–Macaulay rings and path algebras

In this note, it is shown that the validity of the Auslander–Reiten conjecture for a given d-dimensional Cohen–Macaulay local ring R depends on its validity for all direct summands of d-th syzygy of R-modules of finite length, provided R is an isolated singularity. Based on this result, it is shown that under a mild assumption on the base ring R, satisfying the Auslander–Reiten conjecture behaves well under completion and reduction modulo regular elements. In addition, it will turn out that, if R is a commutative Noetherian ring and 𝒬 a finite acyclic quiver, then the Auslander–Reiten conjecture holds true for the path algebra R𝒬, whenever so does R. Using this result, examples of algebras satisfying the Auslander–Reiten conjecture are presented.     

Synthesis and application of a thermosensitive tri-block copolymer as an efficient sample treatment technique for preconcentration and ultra-trace detection of lead ions

We have designed and synthesized a thermosensitive tri-block copolymer for selective trace extraction of Pb(II) ions from biological and food samples. The polymer was characterized by Fourier transform IR and NMR spectroscopy, and by gel permeation chromatography. The critical aggregation concentration and lower critical solution temperature were determined via fluorescence and UV spectrophotometry, respectively. The effects of solution pH value, amount of copolymer, of the temperature on extraction and on phase separation, and of the matrix on the extraction of Pb(II) were optimized. Pb(II) ions were then quantified by FAAS. The use of this copolymer resulted in excellent figures of merit including a calibration plot extending from 0.5 to 160 μg L^?1 (with an R² of >0.99), a limit of detection (LOD) as low as 90 pg L^?1, an extraction efficiency of >98 %, and relative standard deviations of <4 % for eight separate extraction experiments.

Totally acyclic complexes over noetherian schemes

We define a notion of total acyclicity for complexes of flat quasi-coherent sheaves on a semi-separated noetherian scheme, and study these complexes using the pure derived category of flat quasi-coherent sheaves. We prove that a scheme is Gorenstein if and only if every acyclic complex of flat quasi-coherent sheaves is totally acyclic. Our formalism also removes the need for a dualising complex in several known results for rings, including Jørgensen's proof of the existence of Gorenstein projective precovers.     

Characterizing local rings via homological dimensions and regular sequences

Let (R,m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If the G_C-dimension of M/aM is finite for all ideals a generated by an R-regular sequence of length at most d−t then either the G_C-dimension of M is at most t or C is a dualizing complex. Analogous results for other homological dimensions are also given.     

A 3-local Characterization for M 11

We identify M ₁₁ by the structure of the normalizer of its Sylow 3-subgroup.     

Effect of C60-SiO2 hybrid nanoparticles on thermophysical and tribological properties of a multigrade engine oil: an experimental study

Journal of Thermal Analysis and Calorimetry - In this study, the thermophysical and tribological properties of a hybrid nanofluid containing fullerene-silica nanoparticles in a multigrade engine...     

Electrochemical Sensing Platform Based on Graphene Oxide-chitosan for Simultaneous Determination of some Antihypertensive Drugs

The development of selective and simple methods for the determination of different analytes is of great interest. This is the first time to show the applicability of graphene oxide-chitosan (GO-CS) nanocomposite for designing an electrochemical nanosensor for determination of Amlodipine, Valsartan, and Hydrochlorothiazide, simultaneously. Differential pulse voltammetrics current of AML, HCT, and VAL increased linearly in the ranges of 0.1–110, 0.1–110, and 1–230 μM with LOD of 5.5×10⁻², 3.5×10⁻² and 8.6×10⁻² μM, respectively. Finally, GO-CS/GCE was used for the detection of these drugs in commercial tablets and compared with the reference method (HPLC).     

Faltings' theorem for the annihilation of local cohomology modules over a Gorenstein ring

In this paper we study the Annihilator Theorem and the Local-global Principle for the annihilation of local cohomology modules over a (not necessarily finite-dimensional) Noetherian Gorenstein ring.