breast cancer is the second largest cause of cancer deaths among women. at the same time, it is also among the most curable cancer types if it can be diagnosed early. this paper presents a novel hybrid intelligent method for recognition of breast cancer tumors. the proposed method includes three main modules: the feature extraction module, the classifier module and the optimization module. in t...

Let R be a ring, M a right R-module and (S,≤) a strictly ordered monoid. In this paper we will show that if (S,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a uniserial right [[RS,≤]] ]]-module if and only if M is a simple right R-module and S is a chain monoid.

By considering two important factors involved in the codon-anticodon interactions, the hydrogen bond number and the chemical type of bases, a codon array of the genetic code table as an increasing code scale of interaction energies of amino acids in proteins was obtained. Next, in order to consecutively obtain all codons from the codon AAC, a sum operation has been introduced in the set of codo...

The combinatorial q, t-Catalan numbers are weighted sums of Dyck paths introduced by J. Haglund and studied extensively by Haglund, Haiman, Garsia, Loehr, and others. The q, t-Catalan numbers, besides having many subtle combinatorial properties, are intimately connected to symmetric functions, algebraic geometry, and Macdonald polynomials. In particular, the n’th q, t-Catalan number is the Hilb...

It is well known that a square zero pattern matrix guarantees non-singularity if and only if it is permutationally equivalent to a triangular pattern with nonzero diagonal entries. It is also well known that a nonnegative square pattern matrix with positive main diagonal is sign nonsingular if and only if its associated digraph does not have any directed cycles of even length. Any m × n matrix ...

A general A∞-infinity bialgebra is a DG module (H, d) equipped with a family of structurally compatible operations ωj,i : H ⊗i → H,where i, j ≥ 1 and i+ j ≥ 3 (see [6]). In special A∞-bialgebras, ωj,i = 0 whenever i, j ≥ 2, and the remaining operationsmi = ω1,i and ∆j = ωj,1 define the underlying A∞-(co)algebra substructure. Thus special A∞-bialgebras have the form (H, d,mi,∆j)i,j≥2 subject to ...

The combinatorial q, t-Catalan numbers are weighted sums of Dyck paths introduced by J. Haglund and studied extensively by Haglund, Haiman, Garsia, Loehr, and others. The q, t-Catalan numbers, besides having many subtle combinatorial properties, are intimately connected to symmetric functions, algebraic geometry, and Macdonald polynomials. In particular, the n’th q, t-Catalan number is the Hilb...

let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...