In K-mean algorithm, every pixel in super space is required to calculate Euclidean distance for clustering, so it is one time-consuming hard work when there are a great many class centers. Improved K-mean clustering algorithm presented here can save clustering time by making initial division based on previous clustering results, and maintaining the relationship among stable classes during clust...

this study setout to investigate the effect of wheat residue, tillage, and nitrogen fertilizer management on some agronomic traits of soybean as a split split plot based on randomized complete block design with three replications. the main plots included wheat residue management: collecting and leaving residue and sub plot included tillage (without tillage and conventional tillage), and the sub...

For a prime p > 2 let Zp be the group of invertible elements modulo p, and let Hp denote the modular hyperbola xy ≡ 1 (mod p) where x, y ∈ Z. Following [1] we define Hp = Hp ∩ [1, p− 1], that is, Hp = {(x, y) ∈ Z : xy ≡ 1 (mod p), 1 ≤ x, y ≤ p− 1}. We note that the lines l1 : y = x and l2 : y + x = p are lines of symmetry of Hp. In this note we use these two symmetries to prove the following ba...

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, discuss some of its basic properties, and characterize the G-fuzzy congruence generated by a fuzzy relation on a semigroup. We also give certain lattice theoretic properties of Gfuzzy congruences on semigroups.

We study the distribution of spacings between squares in Z/QZ as the number of prime divisors of Q tends to infinity. In [3] Kurlberg and Rudnick proved that the spacing distribution for square free Q is Poissonian, this paper extends the result to arbitrary Q.

We show that for any fixed ε > 0, there are numbers δ > 0 and p 0 2 with the following property: for every prime p p 0 , there is an integer p δ < N p 1/(4 √ e)+ε such that the sequence 1, 2,. .. , N contains at least δN quadratic non-residues modulo p. We then apply this result to obtain a new estimate on the smallest quadratic nonresidue in a Beatty sequence.

Plots of quadratic residues display some visual features that are analyzed mathematically in this paper. The graphical patterns of quadratic residues modulo m depend only on the residues of m modulo the lowest positive integers.

The projective special linear group PSL2(n) is 2-transitive for all primes n and 3-homogeneous for n≡ 3 (mod 4) on the set {0,1, · · · ,n−1,∞}. It is known that the extended odd-like quadratic residue codes are invariant under PSL2(n). Hence, the extended quadratic residue codes hold an infinite family of 2-designs for primes n≡ 1 (mod 4), an infinite family of 3-designs for primes n≡ 3 (mod 4)...

The super-Poincaré covariant formalism for the superstring is used to compute mass-less four-point two-loop amplitudes in ten-dimensional superspace. The computations are much simpler than in the RNS formalism and include both external bosons and fermions.

(here b and a run over the quadratic nonresidues and quadratic residues, respectively, that lie between 0 and p) is a unit of the real quadratic field R(y/p), and that 77> 1. The fact that -n > 1 is usually deduced from the theory of the classnumber of quadratic fields. We present a short proof independent of the theory of the class-number. As in the paper of Chowla and Mordell [Note on the non...