Notes on some Specimens of Lower Silurian Trilobites

Notes on Silurian Fossils from Ohio and Other Central States

Some notes on two lower bound methods for communication complexity

We compare two methods for proving lower bounds on standard two-party model of communication complexity, the Rank method and Fooling set method. We present bounds on the number of functions f(x, y), x, y ∈ {0, 1}n, with rank of size k and fooling set of size at least k, k ∈ [1, 2n]. Using these bounds we give a novel proof that almost all Boolean functions f are hard, i.e., the communication co...

Some Notes on the Dynamic Connectivity Lower Bound?

We want to encode a graph of n vertices in a data structure supporting the following operations: – insert edge(u, v): inserts and edge connecting vertex u to vertex v in the graph encoding. – delete edge(u, v): removes from the encoding the edge between u and v. – connected(u, v): answers yes if there is a path connecting u to v in the encoded graph, otherwise answers no. The first two are upda...

Notes on Three Pathological Specimens

NOTES ON SOME SPECIES OF THE GENUS EUPHORBIA IN IRAN

During the study on newly collected and herbarium specimens belonging to the genus Euphorbia, three species, namely, E. gorenfloti, E. cheirolepioides and E. splendida were found to be synonymous with E. chamaepeplus, E. grossheimii and E. decipiens, respectively. Euphorbia sahendi as an interesting and rare species has been recognized after long time again among my material and Euphorbia delto...