We consider a property stronger than the Sacks property which holds between the ground model and the Sacks forcing extension. 1. The Shrink Wrapping Property Suppose that V is a Sacks forcing extension of a model M . Then the Sacks property holds between V and M . That is, for each x ∈ ω, there exists a tree T ⊆ ω in M such that x ∈ [T ] and each level of T is finite. The following is a stronge...

Let α be an algebraic number of degree d > 2 over Q. Suppose for some pairwise coprime positive integers n1, . . . , nr we have deg(αj ) < d for j = 1, . . . , r, where deg(α) = d for each positive proper divisor n of nj . We prove that then φ(n1 . . . nr) 6 d, where φ stands for the Euler totient function. In particular, if nj = pj , j = 1, . . . , r, are any r distinct primes satisfying deg(α...

Given a graph G = (V,E) on n vertices, the MAXIMUM r-REGULAR INDUCED CONNECTED SUBGRAPH (r-MaxRICS) problems ask for a maximum sized subset of vertices S ⊆ V such that the induced subgraph G[S] on S is connected and r-regular. For r = 2, it is known that 2-MaxRICS is NP-hard and cannot be approximated within a factor of n1−ε in polynomial time for any ε > 0 if P 6 = NP . In this paper, we show ...

The large N1 wave of the auditory event-related potentials (ERPs) typically occurring to the first stimulus after a long silent interval seems to be associated with the involuntary initial-orienting response. Since the mechanisms involved in the generation of this brain response are assumed to be activated automatically, the present study aims at determining whether this electrophysiological re...

Management of solid wastes with high nicotine content, such as those accumulated during tobacco manufacturing, poses a major challenge, which can be addressed by using bacteria such as Pseudomonas and Arthrobacter. In this study, a new species of Pseudomonas geniculata, namely strain N1, which is capable of efficiently degrading nicotine, was isolated and identified. The optimal growth conditio...

(d) Suppose list1 contains N1 elements and list2 contains N2 elements. The first while loop is executed O(N1) times. The body of this loop takes O(N1) since GetNextItem takes O(1) and InsertItem takes O(N1). So, the complexity of the first loop is O(N1N1). The second while loop is executed O(N2) times. The body of that loop takes O(N1+N2) time since GetNextItem takes O(1), RetrieveItem takes O(...

The respiratory-related evoked potential (RREP) is increasingly used to study the neural processing of respiratory signals. However, little is known about the cortical origins of early (Nf, P1, N1) and later RREP components (P2, P3). By using high-density EEG, we studied cortical sources of RREP components elicited by short inspiratory occlusions in 18 healthy volunteers (6 female, mean age 20....

The papers [18], [9], [21], [14], [23], [6], [24], [2], [3], [8], [10], [1], [22], [7], [11], [20], [16], [19], [4], [5], [13], [12], [17], and [15] provide the terminology and notation for this paper. For simplicity, we adopt the following convention: k, l, m, n, i, j denote natural numbers, K, N denote non empty subsets of N, K1, N1, M1 denote subsets of N, and X, Y denote sets. Let us consid...

This study reports the synthesis of some substituted 5-iodouracils and their bioactivities. Alkylation of 5-iodouracils gave predominately N1-substituted-(R)-5-iodouracil compounds 7a-d (R = n-C(4)H(9), s-C(4)H(9), CH(2)C(6)H(11), CH(2)C(6)H(5)) together with N1,N3-disubstituted (R) analogs 8a-b (R = n-C(4)H(9), CH(2)C(6)H(11)). Their antimicrobial activity was tested against 27 strains of micr...