We introduce the notion of Smarandache BCH-algebra and Smarandache (fresh, clean and fantastic) ideals, some example are given and related properties are investigated. Relationship between
Q-Smarandache (fresh, clean and fantastic) ideals and other types of ideals are given. Extension properties for Q-Smarandache (fresh, clean and fantastic) ideals are established.
Authors: Florentin Smarandache
Comments: 2 Pages.
In this note the author presents a new proof for the theorem of I. Patrascu.
Authors: Florentin Smarandache
Comments: 1 Page.
It is possible to cover all (positive) integers with n geometrical progressions of integers?
Find a necessary and sufficient condition for a general class of positive integer sequences
such that, for a fixed n , there are n (distinct) sequences of this class which cover all integers.
Ideea centrală a lucrarii este prezentarea unor transformări noi, anterior inexistente în Matematica ordinară, denumită centrică (MC), dar, care au devenit posibile graţie apariţiei matematicii excentrice şi, implicit, a supermatematicii.
Lucrarea prezintă corespondentele din matematica excentrică ale funcţiilor cardinale şi integrale din matematica centrică, sau matematica ordinară, funcţii centrice prezentate şi în introducerea lucrării, deoarece sunt prea puţin cunoscute, deşi sunt utilizate pe larg în fizica ondulatorie
The first prime number with the special property that its addition with its reversal gives as result a prime number too is 299. The prime numbers with this property will be called Luhn prime numbers. In this article we intend to present a performing
algorithm for determining the Luhn prime numbers.
In this paper , we have defined First Zadeh’s implication , First Zadeh’s intuitionistic fuzzy conjunction and intuitionistic fuzzy disjunction of two intuitionistic fuzzy soft sets and some their basic properties are studied with proofs and examples.
Construct, using a ruler and a compass, two non-congruent triangles, which have equal
perimeters and arias.
In preparation for the proof of this problem we recall several notions and we prove a
In this paper we extend the Smarandache function.
Authors: Ion Patrascu
Comments: 6 Pages.
In this article, we review some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles.
Authors: Suhoparov Stanislav Yurievich
Comments: 5 Pages.
Derivation of the recurrence relation for orthogonal polynomials and usage.
Вывод рекуррентного соотношения ортогональных многочленов из процесса ортогонализации Грама-Шмидта, а также схема применения полученного рекуррентного соотношения
Authors: Jean Claude Dutailly
Comments: 16 Pages.
The purpose of this paper is to present a general method to estimate the probability of transitions of a system between phases. The system must be represented in a quantitative model, with vectorial variables depending on time, satisfying general conditions which are usually met. The method can be implemented in Physics, Economics or Finances.
Missing values for some genotype-environment combinations are commonly encountered in multienvironment trials. The recommended methodology for analyzing such unbalanced data combines the Expectation-Maximization (EM) algorithm with the additive main effects and multiplicative interaction (AMMI) model. Recently, however, four imputation algorithms based on the Singular Value Decomposition of a matrix (SVD) have been reported in the literature (Biplot imputation, EM+SVD, GabrielEigen imputation, and distribution free multiple imputation - DFMI). These algorithms all fill in the missing values, thereby removing the lack of balance in the original data and permitting simpler standard analyses to be performed. The aim of this paper is to compare these four algorithms with the gold standard EM-AMMI. To do this, we report the results of a simulation study based on three complete sets of real data (eucalyptus, sugar cane and beans) for various imputation percentages. The methodologies were compared using the normalised root mean squared error, the Procrustes similarity statistic and the Spearman correlation coefficient. The conclusion is that imputation using the EM algorithm plus SVD provides competitive results to those obtained with the gold standard. It is also an excellent alternative to imputation with an additive model, which in practice ignores the genotype-by-environment interaction and therefore may not be appropriate in some cases.