In this paper, a state-of-the-art neuron mathematical model of neural tensor network (NTN) is proposed to RDF knowledge base completion problem. One of the difficulties with the parameter of the network is that representation of its neuron mathematical model is not possible. For this reason, a new representation of this network is suggested that solves this difficulty. In the representation, th...

We obtain a finite-sum representation for the general solution of the equation ∆ (p(n− 1)∆u(n − 1)) + q(n)u(n) = λr(n)u(n) in terms of a nonvanishing solution corresponding to some fixed value of λ = λ0. Applications of this representation to some results on the boundedness of solutions are given as well as illustrating examples.

Recently integral representations for the eigenfunctions of quadratic open Toda chain Hamiltonians for classical groups was proposed. This representation generalizes Givental representation for An. In this note we verify that the wave functions defined by these integral representations are common eigenfunctions for the complete set of open Toda chain Hamiltonians. We consider the zero eigenvalu...

We propose a framework to prove Malle's conjecture for the compositum of two number fields based on proven results and good uniformity estimates. Using this method we can $S_n\times A$ over any field $k$ $n=3$ with $A$ an abelian group order relatively prime 2, $n= 4$ 6 $n=5$ 30. As consequence, that is true $C_3\wr C_2$ in its $S_9$ representation, whereas $S_6$ representation first counter ex...

The concept of b-linear functional and its different types continuity in linear n-normed space are presented some their properties being established. We derive the Uniform Boundedness Principle Hahn-Banach extension Theorem with help bounded functionals case spaces discuss examples applications. Finally, we present weak*convergence for sequence space.