A Note on Gorenstein Flat Dimension

Unlike the Gorenstein projective and injective dimensions, the majority of results on the Gorenstein flat dimension have been established only over Noetherian (or coherent) rings. Naturally, one would like to generalize these results to any associative ring. In this direction, we show that the Gorenstein flat dimension is a refinement of the classical flat dimension over any ring; and we investigate the relations between the Gorenstein projective dimension and the Gorenstein flat dimension

Weak Gorenstein global dimension

In this paper, we investigate the weak Gorenstein global dimensions. We are mainly interested in studying the problem when the left and right weak Gorenstein global dimensions coincide. We first show, for GF-closed rings, that the left and right weak Gorenstein global dimensions are equal when they are finite. Then, we prove that the same equality holds for any two-sided coherent ring. We conclude the paper with some examples and a brief discussion of the scope and limits of our results

Gorenstein Global Dimensions and Cotorsion Dimension of Rings

In this paper, we establish, as a generalization of a result on the classical homological dimensions of commutative rings, an upper bound on the Gorenstein global dimension of commutative rings using the global cotorsion dimension of rings. We use this result to compute the Gorenstein global dimension of some particular cases of trivial extensions of rings and of group rings

Global Gorenstein dimensions

In this paper, we prove that the global Gorenstein projective dimension of a ring $R$ is equal to the global Gorenstein injective dimension of $R$, and that the global Gorenstein flat dimension of $R$ is smaller than the common value of the terms of this equality.Comment: 4 page

Derivations and the first cohomology group of trivial extension algebras

In this paper we investigate in details derivations on trivial extension algebras. We obtain generalizations of both known results on derivations on triangular matrix algebras and a known result on first cohomology group of trivial extension algebras. As a consequence we get the characterization of trivial extension algebras on which every derivation is inner. We show that, under some conditions, a trivial extension algebra on which every derivation is inner has necessarily a triangular matrix representation. The paper starts with detailed study (with examples) of the relation between the trivial extension algebras and the triangular matrix algebras.Comment: Mediterranean Journal of Mathematics; 201

On n-Perfect Rings and Cotorsion Dimension

A ring is called $n$-perfect ($n\geq 0$), if every flat module has projective dimension less or equal than $n$. In this paper, we show that the $n$-perfectness relate, via homological approach, some homological dimension of rings. We study $n$-perfectness in some known ring constructions. Finally, several examples of $n$-perfect rings satisfying special conditions are given

A new approach to muscle fatigue evaluation for Push/Pull task

Pushing/Pulling tasks is an important part of work in many industries. Usually, most researchers study the Push/Pull tasks by analyzing different posture conditions, force requirements, velocity factors, etc. However few studies have reported the effects of fatigue. Fatigue caused by physical loading is one of the main reasons responsible for MusculoSkeletal Disorders (MSD). In this paper, muscle groups of articulation is considered and from joint level a new approach is proposed for muscle fatigue evaluation in the arms Push/Pull operations. The objective of this work is to predict the muscle fatigue situation in the Push/Pull tasks in order to reduce the probability of MSD problems for workers. A case study is presented to use this new approach for analyzing arm fatigue in Pushing/Pulling.Comment: 19th CISM-IFToMM Symposium on Robot Design, Dynamics, and Control, Paris : France (2012

Rings over which all modules are strongly Gorenstein projective

One of the main results of this paper is the characterization of the rings over which all modules are strongly Gorenstein projective. We show that these kinds of rings are very particular cases of the well-known quasi-Frobenius rings. We give examples of rings over which all modules are Gorenstein projective but not necessarily strongly Gorenstein projective

Context-Aware Mobility Management in HetNets: A Reinforcement Learning Approach

The use of small cell deployments in heterogeneous network (HetNet) environments is expected to be a key feature of 4G networks and beyond, and essential for providing higher user throughput and cell-edge coverage. However, due to different coverage sizes of macro and pico base stations (BSs), such a paradigm shift introduces additional requirements and challenges in dense networks. Among these challenges is the handover performance of user equipment (UEs), which will be impacted especially when high velocity UEs traverse picocells. In this paper, we propose a coordination-based and context-aware mobility management (MM) procedure for small cell networks using tools from reinforcement learning. Here, macro and pico BSs jointly learn their long-term traffic loads and optimal cell range expansion, and schedule their UEs based on their velocities and historical rates (exchanged among tiers). The proposed approach is shown to not only outperform the classical MM in terms of UE throughput, but also to enable better fairness. In average, a gain of up to 80\% is achieved for UE throughput, while the handover failure probability is reduced up to a factor of three by the proposed learning based MM approaches

Context-Aware Scheduling of Joint Millimeter Wave and Microwave Resources for Dual-Mode Base Stations

One of the most promising approaches to overcome the drastic channel variations of millimeter wave (mmW) communications is to deploy dual-mode base stations that integrate both mmW and microwave (\muW) frequencies. Reaping the benefits of a dual-mode operation requires scheduling mechanisms that can allocate resources efficiently and jointly at both frequency bands. In this paper, a novel resource allocation framework is proposed that exploits users' context, in terms of user application (UA) delay requirements, to maximize the quality-of-service (QoS) of a dual-mode base station. In particular, such a context-aware approach enables the network to dynamically schedule UAs, instead of users, thus providing more precise delay guarantees and a more efficient exploitation of the mmW resources. The scheduling of UAs is formulated as a one-to-many matching problem between UAs and resources and a novel algorithm is proposed to solve it. The proposed algorithm is shown to converge to a two-sided stable matching between UAs and network resources. Simulation results show that the proposed approach outperforms classical CSI-based scheduling in terms of the per UA QoS, yielding up to 36% improvement. The results also show that exploiting mmW resources provides significant traffic offloads reaching up to 43% from \muW band.Comment: In Proc. of the IEEE International Conference on Communications (ICC), Mobile and Wireless Networks Symposium, Kualalumpur, Malaysia, May 201