Some inequalities concerning $\Pi$-isomorphisms

Some inequalities concerning Smarandache's function

The objectives of this article are to study the sum IS(d) and to find some upper din bounds for Smarandache's function. This sum is proved to satisfy the inequality IS(d) ~ n at most all the composite numbers, Using this inequality, some new din upper bounds for Smarandache's function are found. These bounds improve the well-known inequality Sen) ~ n.

On Some Inequalities Concerning π(x)

Some Inequalities Concerning Cross-Intersecting Families

Combinatorics, Probability and Computing / Volume 7 / Issue 03 / September 1998, pp 247 260 DOI: null, Published online: 08 September 2000 Link to this article: http://journals.cambridge.org/abstract_S0963548398003575 How to cite this article: P. FRANKL and N. TOKUSHIGE (1998). Some Inequalities Concerning Cross-Intersecting Families. Combinatorics, Probability and Computing, 7, pp 247-260 Requ...

Some Best Possible Inequalities Concerning Cross-Intersecting Families

Let I be a non-empty family of a-subsets of an n-element set and 1 a non-empty family of b-subsets satisfying A A B# 0 for all A ES/, BEG. Suppose that n>a+b, baa. It is proved that in this case ~~~+~.4Y~<(~)-(" ;L1)+l holds. Various extensions of this result are proved. Two new proofs of the Hilton-Milner theorem on non-trivial intersection families are given as well.

Some Inequalities concerning Derivative and Maximum Modulus of Polynomials

In this paper, we prove some compact generalizations of some well-known Bernstein type inequalities concerning the maximum modulus of a polynomial and its derivative in terms of maximum modulus of a polynomial on the unit circle. Besides, an inequality for self-inversive polynomials has also been obtained, which in particular gives some known inequalities for this class of polynomials. All the ...