Appendix A. Notation N = {1, 2, ..., N} =: [N ] is the whole set of data points. i, j ∈ N denote points. dij := D(xi,xj). D is the number of data sets. Td ⊆ N denotes the set of points in the d-th dataset, i.e. ∪d=1Td = N . Nd = |Td| is the number of points in Dataset d. d(i) ∈ [D] denotes the dataset index of Point i. M ⊆ N is the set of medoids. k, l ∈ M denote clusters and themselves are med...

Two new steroidal saponins, cynanside A (1) and B (2) were isolated together with three known compounds (3-5) from the roots of Cynanchum paniculatum (Bunge) Kitag. The structures of 1 and 2 were elucidated on the basis of spectroscopic analyses, including extensive 2D NMR and acid hydrolysis. We evaluated the cytotoxicity of isolates (1-5) against A549, SK-OV-3, SK-MEL-2, and HCT-15 cell lines...

We introduce some Π1–expressible combinatorial principles which may be treated as axioms for some bounded arithmetic theories. The principles, denoted Sk(Σn, length log k) and Sk(Σn, depth log k) (where ‘Sk’ stands for ‘Skolem’), are related to the consistency of Σn–induction: for instance, they provide models for Σn–induction. However, the consistency is expressed indirectly, via the existence...

We answer the following question: given any n ∈ N, which is the minimum number of endpoints en of a tree admitting a zero-entropy map f with a periodic orbit of period n? We prove that en = s1s2 ···sk − ∑k i=2 sisi+1 ···sk, where n = s1s2 ···sk is the decomposition of n into a product of primes such that si ≤ si+1 for 1 ≤ i < k. As a corollary, we get a criterion to decide whether a map f defin...

As we have reported recently, the human neuroblastoma cell line SK-N-SH is able to take up and store m-iodobenzylguanidine (mIBG). This is in contrast to several other neuroblastoma cell lines, among which are SK-N-LO cells. Both cell lines were used in cell killing experiments with unlabeled and radioactive-labeled mIBG. Using 1-200 microCi m-[131I]IBG (1 h incubation time), only SK-N-SH cells...

Generalized knot groups Gn(K) were introduced first by Wada and Kelly independently. The classical knot group is the first one G1(K) in this series of finitely presented groups. For each natural number n, G1(K) is a subgroup of Gn(K) so the generalized knot groups can be thought of as extensions of the classical knot group. For the square knot SK and the granny knot GK, we have an isomorphism G...

This is a sketch about Boucherie paper on product form. It is quite informal, for a deeper view we suggest to study the interesting paper [2]. Our aim is just to point out the main main conditions for this product form. 1 The Boucherie result on the product form The starting CTMCs In this section we summarize the results presented in [2]. Let us consider K stable and regular CTMCs. The state sp...