Several notions of multiplicativity are introduced for forms of degree d ≥ 3 over a field of characteristic 0 or greater than d. Examples of multiplicative and strongly multiplicative forms of higher degree are given. Conditions restricting the structure of a strongly multiplicative form are found.

In this paper we present a new feature of texture images which can scale the uniformity degree of image texture directions. The feature value is obtained by examining the statistic characteristic of the gradient information of the image pixels. Simulation results illustrate that this feature can exactly coincide with the uniformity degree of image texture directions according to the perception ...

The cardinal growth characteristics of Myxococcus xanthus were examined from 14 to 40 degree C, and the examinations indicated that the organism is mesophilic in character. The maximum growth rate (0,3 doublings per h) was between 34 and 36 degree C and the temperature characteristic (micron) is 17,000 cal/mol (71,162 J/mol).

Let k be a field of characteristic two. We prove that monic polynomial f∈k[X] degree n≥1 is the minimal/characteristic symmetric matrix with entries in if and only it not product pairwise distinct inseparable irreducible polynomials. In this case, we f minimal size n. also any element α∈kalg eigenvalue n or n+1, first case happening α separable.

The algebras of the title are infinite-dimensional graded Lie L=?i=1?Li, over a field positive characteristic p, which generated by an element degree 1 and satisfy [Li,L1]=Li+1 for i?p. In case p=2 such were classified Caranti Vaughan-Lee in 2003. We announce extension that classification to arbitrary prime characteristic, prove several major steps its proof.

We sketch the solution to a simple enumerative problem in linear series in characteristic p: given points Pi on the projective line, integers ei < p and d satisfying P i (ei − 1) = 2d − 2, how many maps from P 1 to itself are there of degree d and having ramification index precisely ei at the Pi? Limit linear series are a tool for solving this problem. I’ll explain what they are, and some of th...

an equitable domination has interesting application in the contextof social networks. in a network, nodes with nearly equal capacitymay interact with each other in a better way. in the societypersons with nearly equal status, tend to be friendly. in thispaper, we introduce new variant of equitable domination of agraph. basic properties and some interesting results have beenobtained.

In this paper, characterizations of the degree to which a mapping $mathcal{T} : L^{X}longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail.What is more, the degree to which an $L$-subset is an $L$-open set with respect to $mathcal{T}$ is introduced.Based on that, the degrees to which a mapping $f: Xlongrightarrow Y$ is continuous,open, closed or a quotient mapping with respect t...

We present two noncommutative algebras over a field of characteristic zero that each possesses family actions by cyclic groups order $2n$, represented in $2 \times 2$ matrices, requiring generators degree $3n$.