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Abstract. Let R be a commutative Noetherian ring, a an ideal of R and M a finitely generated R-module. Let t be a non-negative integer. It is known that if the local cohomology module H i a (M) is finitely generated for all i < t, then Hom R (R/a, H t a (M)) is finitely generated. In this paper it is shown that if H i a (M) is Artinian for all i < t, then Hom R (R/a, H t a (M)) need not be Artinian, but it has a finitely generated submodule N such that Hom R (R/a, H t a (M))/N is Artinian.

Text classification has always been an important and practical issue so that we need to use the computer to classify and discover the information in the text. If we want to recognize the offending words in a text without human intervention, we should use this. In this article we will compare recurrent neural networks, convolutional neural networks and hierarchical attention networks with detailed information about each of which. We will represent a HAN model using Theano framework, which indicates more accurate validation for large datasets. For text classification problem in large datasets, we will use hierarchical attention networks to get a better result.

Traveling salesman problem (TSP) is a well-established NP-complete problem and many evolutionary techniques like particle swarm optimization (PSO) are used to optimize existing solutions for that. PSO is a method inspired by the social behavior of birds. In PSO, each member will change its position in the search space, according to personal or social experience of the whole society. In this paper, we combine the principles of PSO and crossover operator of genetic algorithm to propose a heuristic algorithm for solving the TSP more efficiently. Finally, some experimental results on our algorithm are applied in some instances in TSPLIB to demonstrate the effectiveness of our methods which also show that our algorithm can achieve better results than other approaches.Keywords: traveling salesman problem; particle swarm optimization; genetic algorithm; optimization Related worksThe origins of the traveling salesman problem (TSP) are unclear. A handbook for traveling salesmen from 1832 mentions the problem and includes example tours through Germany and Switzerland, but contains no mathematical treatment.Mathematical problems related to the TSP were treated in the 1800s by the Irish mathematician W. R. Hamilton and by the British mathematician Thomas Kirkman. Hamiltons Icosian Game was a