where c#,Jr) is the number of F-partitions of r using h colors with (at most) s repetitions where s can be any positive integer or 00 (to represent no restriction on repetitions). The proofs of these congruences were based on some interesting congruence properties of compositions and were combinatorial in nature. Though the proofs were straightforward, they were somewhat lengthy and tedious. Du...

A number of different formal analyses of relative clauses have been proposed over the years. For example, the adjunction analysis states that the relative clause is adjoined to the modified noun; the antisymmetry analysis (formulated in Kayne 1994) posits that the complementizer phrase (CP) is the direct complement of the determiner (the determiner being the head of the nominal projection), and...

Defined as the differential extent to which rich countries and poor countries benefit from various forms of information technology (IT), the global digital divide has been extensively measured and described in national as well as international debates. The problem, however, is that the topic is highly fragmented in the literature, with few attempts to put the parts into a coherent analytical fr...

Africa is a large continen features and-a wide range of natural resources. Although hard demographic fa about Africa's population are almost non that it is increasing fast. Countries in the world; These countri (HIPCs), where a combination of extreme poverty and financial insolvency mark them for a special kind of despa of industrialized West almost entirely, unless war or an exotic disease bre...

We show that the CKM phase 2β +γ can be extracted from measurement of the time dependent rates in the decays B̄ → D(∗)±M∓ and B → D(∗)±M∓, where M = a0, π(1300), b1, a2, π2, ρ3. These channels have a large asymmetry between decays of B̄ 0 and B into the same final state. Even though the branching ratios are small, their sensitivity to γ can be competitive with decays into D(∗) and (π, ρ, a1). ∗Wo...

The purpose of this note is to provide yet another example of the link between certain conformal geometries and ordinary differential equations, along the lines of the examples discussed by Nurowski [3]. In this particular case, I consider the equivalence problem for 3-plane fields D ⊂ TM on a 6-manifold M satisfying the nondegeneracy condition that D + [D, D] = TM . I give a solution of the eq...

In this list there is an arithmetic progression: 1, 25, 49 (common difference 24). If we search further along, another arithmetic progression of squares is found: 289, 625, 961 (common difference 336). Yet another is 529, 1369, 2209 (common difference 840). How can these examples, and all others, be found? In Section 2 we will use plane geometry to describe the 3-term arithmetic progressions of...

The Yet Another Workflow Language (YAWL) language and environment has been used to prototype, verify, execute and analyse business processes in a wide variety of industrial domains, such as telephony, construction, supply chain, insurance services, medical environments, personnel management and the creative arts. These engagements offer the YAWL researcher community a great opportunity to valid...