The Chebyshev polynomials have many beautiful properties and countless applications, arising in a variety of continuous settings. They are a sequence of orthogonal polynomials appearing in approximation theory, numerical integration, and differential equations. In this paper we approach them instead as discrete objects, counting the sum of weighted tilings. Using this combinatorial approach, on...

Let c(Tn) denote the number of 3-cycles in the tournament Tn and let u(Tn) denote the number of nodes i in Tn such that each arc oriented towards i belongs to at least one 3-cycle. We determine the minimum value of c(Tn) when u(Tn) = n and the maximum value of c(Tn) when u(Tn) = 3.

and Applied Analysis 3 limn→∞tn 1, ∑∞ n 1 tn 1 − tn ∞, and limn→∞ kn − 1 / kn − tn 0, where ξn min{ 1 − α kn/ kn − α , 1/kn}. For an arbitrary z0 ∈ K let the sequence {zn} be iteratively defined by zn 1 ( 1 − tn kn ) f zn tn kn Tzn, n ∈ N. 1.7 Then i for each integer n ≥ 0, there is a unique xn ∈ K such that xn ( 1 − tn kn ) f xn tn kn Txn; 1.8

To mutate the Ice Nucleation Active (INA) gene in Erwinia herbicola strains, Tn-5 transposon carried by Psup2021 plasmid was used. This plasmid was transferred to the bacterial cells by electroporation. Electrotransformation was carried out for 2.5 ms at 1800 v and 1 mm distance between the electrodes. Polymerase chain reaction was used for determination of presence or loss of INA gene, using a...

In the present study, we further examined (see Kamhi & Catts, 1986) the phonological processing abilities of language-impaired (LI) and reading-impaired (RI) children. We also evaluated these children's ability to process spatial information. Subjects were 10 LI, 10 RI, and 10 normal children between the ages of 6:8 and 8:10 years. Each subject was administered eight tasks: four word repetition...

in early 1990, an outbreak of measles occurred in kerman, (population 257, 284) iran. overall, 475 cases were identified and four died (case fatality ratio 5.4 per thousand). illness was limited primarily to children below 15 years of age 166 (22.3%) were in children under five, 573 (77%) between 5-14 and six (0.8%) above 15 years of age. the age of the cases ranged from five months to 35 years...

CCP program 1 simulation(S):2 Init=[[I1|_], [I2|_], ..., [In|_]], 3 run(1,S,Init) || 4 run(2,S,Init) || 5 ... || 6 run(n,S,Init). 7 run(ID, S, [P1, P2, ..., Pn]):8 getTails([P1, ..., Pn],[T1, ..., Tn]), 9 ask(T1=[_|_]) -> skip + 10 ask(T2=[_|_]) -> skip + 11 ... + 12 ask(Tn=[_|_]) -> skip, 13 getLast([P1, ..., Pn],[L1, ..., Ln]), 14 updatePosition(ID,S,[L1,..,Ln],NP), 15 tell(TID=[NP|_]), 16 ru...

Microfabricated thermoelectric controllers can be employed to investigate mechanisms underlying myosin-driven sliding of Ca(2+)-regulated actin and disease-associated mutations in myofilament proteins. Specifically, we examined actin filament sliding-with or without human cardiac troponin (Tn) and α-tropomyosin (Tm)-propelled by rabbit skeletal heavy meromyosin, when temperature was varied cont...