Gronau, Mullin, and Rosa conjectured that for every tree T with n vertices except for P4 there exists an ODC of Kn by T . They also proved the conjecture for all caterpillars of diameter 3. Later, Leck and Leck proved it for all caterpillars of diameter 4 and all trees with up to 14 vertices. We prove the conjecture for all carerpillars of diameter 5 and order n ≥ 24; for orders 15 ≤ n ≤ 23 we ...

Many scales in psychology, education and social measurement in general, which are constructed to measure a single variable, are nevertheless composed of subscales which measure different aspects of the variable. Although the presence of subscales captures better the complexity of a variable and increases its validity, it compromises its unidimensionality. This paper reconciles the measurement p...

Using pitaya as raw material, this paper used ethanol subsiding method to study the extraction technology of polysaccharide by single factor test and orthogonal test. Through test, we have found optimum conditions follows: temperature 60℃, solid-liquid ratio 1:30, time 3h. Under optimal conditions, yield was 1.13%.

The existence of fixed point in orthogonal metric spaces has been initiated by Eshaghi and et. al [7]. In this paper, we prove existence and uniqueness theorem of fixed point for mappings on $varepsilon$-connected orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point for analytic function of one complex variable. The paper concludes with some i...