Let Q(ζm) be the mth cyclotomic field, where ζm is a primitive mth root of unity for an integer m ≥ 1. Let hm denote the class number of Q(ζm) and hm be the class number of its maximal real subfield Q(ζm + ζ −1 m ). Kummer proved that the relative class number hm = hm/h + m is an integer, and in 1851 he claimed ([7], pg. 473) that the rule for the asymptotic growth of hp as the prime p → ∞ is g...

firstly, in this paper, we apply the fuzzy restricted variation method to achieve an analytical and approximate unsymmetrical fuzzy solution for fully fuzzy quadratic equation. in this application, after finding the real root of 1-cut of $tilde{a}tilde{x}^{2}+tilde{b}tilde{x}+tilde{c}=tilde{d}$, initial guess is always chosen with possible unknown parameters that leads to highly accurate soluti...

abstract. in the case of process capability index several methods are identified. in this paper ,a new process capability index using fuzzy number and fuzzy probability concept, in order to remove the weakness of other famous method is suggested. after introduction of fuzzy index in univariate case, fuzzy multivariate process capability index is investigated. finally, this new method is compare...

in this paper, rstly, it is proved that, for a fuzzy vector space, the set of its fuzzy bases de ned by shi and huang, is equivalent to the family of its bases de ned by p. lubczonok. secondly, for two fuzzy vector spaces, it is proved that they are isomorphic if and only if they have the same fuzzy dimension, and if their fuzzy dimensions are equal, then their dimensions are the same, however,...

the investigation was conducted on wet and dry seasons of ethiopia during the year 2012/2013 at wondo genet agricultural research center nursery site. four levels of cutting size and three levels of cutting positions were arranged in randomized complete block design with three replications. data on seedling height, branch number/seedling, root number/seedling, root weigh/seedling, root length/s...

In this paper, a new method is proposed to find the fuzzy optimal solution of fully fuzzy linear programming (abbreviated to FFLP) problems. Also, we employ linear programming (LP) with equality constraints to find a nonegative fuzzy number vector x which satisfies Ax =b, where A is a fuzzy number matrix. Then we investigate the existence of a positive solution of fully fuzzy linear system (FFLS).

the research has been done for assessment of effects of different concentrations of indole-3-butyric acid (iba) on rhizogenesis of scions of c. phlomidis in 2010.  the research has been done on randomized complete-blocks for five replications and three treatments with zero, 2000ppm and 3000pmm concentration. different characters such as number of root of each scion, length of root, length of ne...

n this paper we study the hyers-ulam-rassias stability of cauchyequation in felbin's type fuzzy normed linear spaces. as a resultwe give an example of a fuzzy normed linear space such that thefuzzy version of the stability problem remains true, while it failsto be correct in classical analysis. this shows how the category offuzzy normed linear spaces differs from the classical normed linearspac...

fuzzy decision tree (fdt) classifiers combine decision trees with approximate reasoning offered by fuzzy representation to deal with language and measurement uncertainties. when a fdt induction algorithm utilizes stopping criteria for early stopping of the tree's growth, threshold values of stopping criteria will control the number of nodes. finding a proper threshold value for a stopping crite...