We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on set of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order for various combinatorial objects.

Canfield and Mason have conjectured that for all subgroups G of the automorphism group of the Boolean lattice Bn (which can be regarded as the symmetric group Sn) the quotient order Bn/G is a symmetric chain order. We provide a straightforward proof of a generalization of a result of K. K. Jordan: namely, Bn/G is an SCO whenever G is generated by powers of disjoint cycles. In addition, the Bool...

Thermal printers are widely adopted in receipt issuance applications in distribution terminals including POS terminals and ECR, payment terminals, and financial terminals such as ATMs, CDs, and change machines due to their highspeed printing, easy maintenance, improved thermal paper conservation, and so forth. Furthermore, adoption of thermal printers is growing in label printing for distributi...

following the formation of the persian empire by cyrus the great and its extension by darius i, from indus river in india to nile in egypt, persian kings felt that there is a need to use an international language to be understandable by all nations of this great empire. this need was greater when they sent orders and messages to these different nations. when darius i defeated his enemies and su...

We propose a renormalon-inspired resummation of QCD perturbation theory based on approximating the renormalization scheme (RS) invariant effective charge beta-function coefficients by the portion containing the highest power of b=16(11N– 2Nf ), for SU(N) QCD with Nf quark flavours. This can be accomplished using exact large-Nf all-orders results. The resulting resummation is RS-invariant and th...

We prove that for any nonnegative integers n and r the binomial sum n ∑ k=−n ( 2n n− k ) k is divisible by 22n−min{α(n),α(r)}, where α(n) denotes the number of 1s in the binary expansion of n. This confirms a recent conjecture of Guo and Zeng [J. Number Theory, 130(2010), 172–186]. In 1976 Shapiro [3] introduced the Catalan triangle ( k n ( 2n n−k ) )n>k>1 and determined the sum of entries in t...

The roles of smoking and alcohol on the development of Alzheimer's disease (AD) remain unclear. We performed a case-control study on the effects of both exposures before the age of onset of the disease in the cases (and same reference age for their age-matched controls) on disease risk. Interviews were conducted with population controls (n=246) and relatives of cases (n=176) identified through ...

An alignment is developed between the terminology of outcome oriented decision taking and a terminology for promise issuing. Differences and correspondences are investigated between the concepts of decision and promise. For decision taking, two forms are distinguished: the external outcome delivering form and internalized decision taking. Internalized decision taking is brought in connection wi...