Abstract:
In the present study, 3D-finite element method was conducted to investigate the deformation characteristics of Al7075 alloy during integrated extrusion-equal channel angular pressing. Effective strain, strain rate, mean stress, and damage distributions were evaluated. Severe cracking was observed at Al7075 sample after extrusion-equal channel angular pressing. Finite element results show that cracking is due to the positive mean stress and damage accumulation at the top surface of sample.

Abstract:
In this study, a multilayer Al/Ni/Cu composite reinforced with SiC particles was produced using an accumulative roll bonding (ARB) process with different cycles. The microstructure and mechanical properties of this composite were investigated using optical and scanning microscopy and hardness and tensile testing. The results show that by increasing the applied strain, the Al/Ni/Cu multilayer composite converted from layer features to near a particle-strengthening characteristic. After the fifth ARB cycle, a composite with a uniform distribution of reinforcements (Cu, Ni, and SiC) was fabricated. The tensile strength of the composite increased from the initial sandwich structure to the first ARB cycle and then decreased from the first to the third ARB cycle. Upon reaching five ARB cycles, the tensile strength of the composite increased again. The variation in the elongation of the composite exhibited a tendency similar to that of its tensile strength. It is observed that with increasing strain, the microhardness values of the Al, Cu, and Ni layers increased, and that the dominant fracture mechanisms of Al and Cu were dimple formation and ductile fracture. In contrast, brittle fracture in specific plains was the main characteristic of Ni fractures.

Abstract:
We determine some stability results concerning the cubic func-tional equation in non-Archimedean fuzzy normed spaces. Our result can be regarded as a generalization of the stability phenomenon in the framework of L-fuzzy normed spaces.

Abstract:
The equations of motion of a super non-Abelian T-dual sigma model on the Lie supergroup $(C^1_1+A)$ in the curved background are explicitly solved by the super Poisson-Lie T-duality. To find the solution of the flat model we use the transformation of supercoordinates, transforming the metric into a constant one, which is shown to be a supercanonical transformation. Then, using the super Poisson-Lie T-duality transformations and the dual decomposition of elements of Drinfel'd superdouble, the solution of the equations of motion for the dual sigma model is obtained. The general form of the dilaton fields satisfying the vanishing $\beta-$function equations of the sigma models is found. In this respect, conformal invariance of the sigma models built on the Drinfel'd superdouble $((C^1_1+A),I_{(2|2)})$ is guaranteed up to one-loop, at least.

Abstract:
This paper at first concerns some criteria on Artinianness and vanishing of formal local cohomology modules. Then we consider the cosupport and the set of coassociated primes of these modules more precisely.

Abstract:
Let $(R,\fm)$ be a local ring and $\fa$ be an ideal of $R$. The inequalities $$\begin{array}{ll} \ \Ht(\fa) \leq \cd(\fa,R) \leq \ara(\fa) \leq l(\fa) \leq \mu(\fa) \end{array}$$ are known. It is an interesting and long-standing problem to find out the cases giving equality. Thanks to the formal grade we give conditions in which the above inequalities become equalities.

Abstract:
Let $\fa$ be an ideal of a $d$-dimensional commutative Noetherian ring $R$. In this paper we give some information on some last non-zero local cohomology modules known as top local cohomology modules in particular, $H^{d-1}_{\fa}(R)$.

Abstract:
Let $\fa$ be an ideal of a local ring $(R, \fm)$ with $d = \dim R.$ For $i > d$ the local cohomology module $H^i_{\fa}(R)$ vanishes. In the case that $H^d_{\fa}(R) \not= 0,$ at first we give a bound for $\depth D(H^d_{\fa}(R))$, where $d>2$ and $(R,\fm)$ is complete. More precisely we show $$\begin{array}{ll} \ \grade (\fb, D(H^d_{\fa} (R)))+\dim R/\fb \geq \depth (D(H^d_{\fa} (R))) \geq 2, \end{array}$$ where $\fb$ is an ideal of $R$ of dimension $\leq 2$ and D(-) denotes the Matlis duality functor. Later we give conditions that Cohen-Macaulayness of $D(H^d_{\fa}(R))$ fails, where $d \geq 3$. Finally, $H^d_{\fa}(R) \otimes_R H^d_{\fa}(R)$, $D(H^d_{\fa}(R)) \otimes_R D(H^d_{\fa}(R))$ and $H^d_{\fa}(R) \otimes_R D(H^d_{\fa}(R))$ are examined. In particular, we give the necessary and sufficient condition for Cohen-Macaulayness of $D(H^d_{\fa}(R)) \otimes_{R/Q} D(H^d_{\fa}(R))$, where $Q$ is a certain ideal of $R$.

Abstract:
The Frobenius depth denoted by $\Fdepth$ defined by Hartshorne-Speiser in 1977 and later by Lyubeznik in 2006, in a different way, for rings of positive characteristic. The aim of the present paper is to compare the $\Fdepth$ with formal grade, and $\depth$ to shed more light on the notion of Frobenius depth from a different point of view.