Dielectric behavior of nano-structured and bulk Li Ni Zn ferrite samples

The ac conductivity and dielectric properties of spinel ferrite nanoparticles of Li_0.1(Ni_1−xZn_x)_0.8Fe_2.1O₄ (x=0.0–1.0) prepared by the chemical co-precipitation method were investigated as functions of frequency and temperature by using a complex impedance technique. Parts of the precipitated powders were pressed into a disk-shape and were sintered at 1473 K for 2 h to increase the particle size to the bulk scale (dimensions >100 nm). The ac conductivity of the samples increases with increasing temperature, ensuring the semiconducting behavior of both nano and bulk samples, in agreement with the Koops model to describe heterogeneous structures. The significant decrease in ac conductivity σ′_ac, dielectric constant, and dielectric loss of the as-prepared nanosamples compared to their bulk counterparts is correlated to the small size of the grain compared to the grain boundary size. This might be useful for many applications requiring the reduction of eddy current effects.     

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.     

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.     

Particle size distribution, magnetic permeability and dc conductivity of nano-structured and bulk LiNiZn-ferrite samples

Nanoparticles of Li_0.1(Ni_1−xZn_x)_0.8Fe_2.1O₄ (x=0-1.0) were prepared by a chemical co-precipitation method. A part of the precipitated powders was sintered at 1473 K for 2 h to obtain bulk samples via increasing the particle sizes. The particle size distribution, dc conductivity and magnetic permeability were investigated for the nano-structured samples and their bulk counterparts. The permeability as a function of temperature revealed the size effect of nano-structure in agreement with the literature. In some of the samples the permeability was almost constant over a considerable range of temperature, which may be useful in practical applications that require stability. Moreover, the nano-size structure caused a significant decrease in dc conductivity values.     

Spanier–Whitehead Categories of Resolving Subcategories and Comparison with Singularity Categories

Algebras and Representation Theory - Let $\mathcal {A}$ be an abelian category with enough projective objects, and let $\mathcal {X}$ be a quasi-resolving subcategory of $\mathcal {A}$ . In this...     

Cohomology theories based on Gorenstein injective modules

In this paper we study relative and Tate cohomology of modules of finite Gorenstein injective dimension. Using these cohomology theories, we present variations of Grothendieck local cohomology modules, namely Gorenstein and Tate local cohomology modules. By applying a sort of Avramov-Martsinkovsky exact sequence, we show that these two variations of local cohomology are tightly connected to the generalized local cohomology modules introduced by J. Herzog. We discuss some properties of these modules and give some results concerning their vanishing and non-vanishing.

     

Approximation of fuzzy integrals using fuzzy bernstein polynomials

In this paper, we approximate the integration of continuous fuzzy real number valued function of one and two variables. To do this, we use Bernstein-type fuzzy polynomials. Moreover, we obtain the error estimates for these approximations in terms of the modulus of continuity.