Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: powers

Sortuj według:

Ogranicz wyniki do:

Some Remarkable Identities Involving Numbers

100%

Ziobro R.

Formalized Mathematics

2014

tom 22

nr 3

205-208

The article focuses on simple identities found for binomials, their divisibility, and basic inequalities. A general formula allowing factorization of the sum of like powers is introduced and used to prove elementary theorems for natural numbers. Formulas for short multiplication are sometimes referred in English or French as remarkable identities. The same formulas could be found in works concerning polynomial factorization, where there exists no single term for various identities. Their usability is not questionable, and they have been successfully utilized since for ages. For example, in his books published in 1731 (p. 385), Edward Hatton [3] wrote: “Note, that the differences of any two like powers of two quantities, will always be divided by the difference of the quantities without any remainer...”. Despite of its conceptual simplicity, the problem of factorization of sums/differences of two like powers could still be analyzed [7], giving new and possibly interesting results [6].

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

On two families of tests for normality with empirical description of their performances

63%

Szynal D., Wołyński W.

Discussiones Mathematicae Probability and Statistics

2014

tom 34

nr 1-2

169-185

We discuss two families of tests for normality based on characterizations of continuous distributions via order statistics and record values. Simulations of their powers show that they are competitive to widely recommended tests in the literature.

Ograniczanie wyników

1 Discussiones Mathematicae Probability and Statistics

1 Formalized Mathematics

1 Szynal D.

1 Wołyński W.

1 Ziobro R.

2 2014

Wyniki wyszukiwania

Some Remarkable Identities Involving Numbers

On two families of tests for normality with empirical description of their performances