Let M be a set and F a family of its subsets. F is said by E. W. MILLER [5] to possess property B if there exists a subset K of M so that no set of the family F is contained either in K or in K (K is the complement of K in M) . HAJNAL and 1 [2] recently published a paper on the property B and its generalisations . One of the unsolved problems we state asks : What is the smallest integer in (n) ...

The two part Sperner theorem of Katona and Kleitman states that if X is an n-element set with partition X1 ∪X2, and F is a family of subsets of X such that no two sets A,B ∈ F satisfy A ⊂ B (or B ⊂ A) and A ∩ Xi = B ∩ Xi for some i, then |F| ≤ ( n ⌊n/2⌋ ) . We consider variations of this problem by replacing the Sperner property with the intersection property and considering families that satis...

Intellectual Property Rights, Migration, and Diaspora In this paper we study theoretically and empirically the role of the interaction between skilled migration and intellectual property rights (IPRs) protection in determining innovation in developing countries (South). We show that although emigration from the South may directly result in the well-known concept of brain drain, it also causes a...

We consider the following classical autonomous variational problem minimize { F (v) = ∫ b a f(v(x), v′(x)) dx : v ∈ AC([a, b]), v(a) = α, v(b) = β } , where the Lagrangian f is possibly neither continuous, nor convex, nor coercive. We prove a monotonicity property of the minimizers stating that they satisfy the maximum principle or the minimum one. By virtue of such a property, applying recent ...

It is shown that the first-order theory T of a non-surjective injection (of the universe into itself) is connected. By a criterion for connectedness, due to J. Mycielski, one reduces this result to the following theorem: If A, B are any structures and ε is a definable equivalence relation on their disjoint product A ×̇B such that (A ×̇B)/ε is a model of T, then either A has the property that for ...

Let X = {a}∪ {ai | i ∈ N} be a subspace of Euclidean space E such that limi→∞ ai = a and ai 6= aj for i 6= j. Then it is well known that the space X has no expansive homeomorphisms with the shadowing property. In this paper we show that the set of all expansive homeomorphisms with the shadowing property on the space Y is dense in the space H(Y ) of all homeomorphisms on Y , where Y = {a, b} ∪ {...

An L{structure is called internally presented in a nonstandard universe if its base set and interpretation of every symbol in L are internal. A nonstandard universe is said to satisfy the {isomorphism property if for any two internally presented L{structures A and B, where L has less than many symbols, A is elementarily equivalent to B implies that A is isomorphic to B. In this paper we prove t...

Abstract A $$\sigma $$ σ -ideal $$\mathcal {I}$$ I on a Polish group $$(X,+)$$ ( X , + ) has the Smital Property if for every dense set D and Borel -positive B algebraic sum $$D+B$$ <mm...

A graph G is said to have property P(m,n,k) if for any disjoint sets A and B of vertices of G with IAI = m and IBI = n there exist at least k other vertices, each of which is adjacent to every vertex of A but not adjacent to any vertex of B. We know that almost all graphs have property P(m,n.k). However, almost no graphs have been constructed. In this paper. we construct classes of graphs havin...

Obtaining essential intellectual property rights (IPRs) is important for innovation competition in the network industry, where technical standardization plays a critical role in development. In this study, we empirically investigate the determinants of essential IPRs for wireless communications standards by using the patent database. More specifically, we use the technological capabilities of b...