58 research outputs found
On the Sum of Dilations of a Set
We show that for any relatively prime integers and for any finite
one has |p \cdot A + q \cdot A | \geq (p + q) |A| -
(pq)^{(p+q-3)(p+q) + 1}.$
A low-energy decomposition theorem
We prove that any finite set of real numbers can be split into two parts, one
part being highly non-additive and the other highly non-multiplicative.Comment: 16 page
Challenges of marketing management in the non-governmental sector of South-Eastern Europe in the context of global recession
During the process of social and economic transition in the SEE countries numerous non-governmental organisations found a fertile ground for their activities. In spite of unstable political and general conditions these organisations have managed to survive and contribute to the creation of social capital. Non-governmental organisations have gradually become efficient subjects of civil society (or the third sector) and their role in the processes of social and economic transition of post-communist societies was recognized and accepted by all the social participants, both domestic and from abroad. It is generally assumed that the turbulent processes of social and economic transition of these countries would have probably had a different course without the social engagement of non-governmental organisations that catalysed and amortized the social processes in which they took part. The main goal of this paper is to point out the importance of applying the marketing concept integrated into the crisis management of non-governmental organisations (NGOs) in transitional countries of South-Eastern Europe (SEE) during the economic recession starting in 2008. Although the main purpose of marketing is to secure the organisational survival on the public scene, this is also an opportunity for non-governmental organisations to additionally profile themselves and improve the image they have in society
On the Number of Solutions of Exponential Congruences
For a prime and an integer we obtain nontrivial upper bounds
on the number of solutions to the congruence , . We use these estimates to estimate the number of solutions to the
congruence , , which is of
cryptographic relevance
On the Convex Hull of the Integer Points
Let P r denote the convex hull of the integer points in the disc of radius r . We prove that the number of vertices of P r is essentially r 2 /3 as r approaches infinity
Sum of dilates in vector spaces
Let , be finite and not contained in a
translate of any hyperplane, and such that . We
show |A+ q \cdot A| \geq (|q|+d+1)|A| - O_{q,d}(1).$
New Sum-Product Estimates for Real and Complex Numbers
A variation on the sum-product problem seeks to show that a set which is defined by additive and multiplicative operations will always be large. In this paper, we prove new results of this type. In particular, we show that for any finite set A of positive real numbers, it is true that |{a+bc+d:a,b,c,d∈A}|≥2|A|2-1.As a consequence of this result, it is also established that |4k-1A(k)|:=|A…A⏟ktimes+⋯+A…A⏟4k-1times|≥|A|k.Later on, it is shown that both of these bounds hold in the case when A is a finite set of complex numbers, although with smaller multiplicative constants. © 2015, Springer Science+Business Media New York
On the Convex Hull of the Integer Points
Let P_{r} denote the convex hull of the integer points in the disc of radius r. We prove that the number of vertices of P_{r} is essentially r^{2/3} as r approaches infinity.
- …