0

in this paper, we first define spaces of single difference sequences defined by a sequence of orlicz functions without convexity and investigate their properties. then we extend this idea to spaces of double sequences and present a new matrix theoretic approach construction of such double sequence spaces.

let  be a sequence of arbitrary random variables with  and , for every  and  be an array of real numbers. we will obtain two maximal inequalities for partial sums and weighted sums of random variables and also, we will prove complete convergence for weighted sums , under some conditions on  and sequence .

Representation learning is important for solving sequence-to-sequence problems in natural language processing. transforms raw data into vector-form representations while preserving their features. However, with significantly different features leads to heterogeneity representations, which may increase the difficulty of convergence. We design a multi-filter encoder-decoder model resolve problem ...