We give some simple examples of applying the well-known elementary probability theory inequalities and properties in field logical argumentation. A probabilistic version hypothetical syllogism inference rule is as follows: if propositions A, B, C, A→B, B→C have probabilities a, b, c, r, s, respectively, then for p A→C, we f(a,b,c,r,s)≤p≤g(a,b,c,r,s), functions f g given parameters. In this pape...

bisphenol-a (bpa) is an industrial xenoestrogen used widely in our living environment. recently, several studies suggested that bpa has destructive effects on dna and chromosomes in normal body cells via estrogen receptors (er). therefore, bpa could be considered as an important mediator in many diseases such as cancer. however, there are still many controversial issues which need clarification...

the recognition of the biologically and environmentally important ions is of great interest in the field of chemical sensors in recent years. the fluorescent sensors as a powerful optical analytical technique for the detection of low level of various analytes such as anions and metal cations have been progressively developed due to the simplicity, cost effective, and selectivity for monitoring ...

1.2 Algorithm for GCD The Euclidean algorithm is a simple algorithm for finding the gcd of two numbers. The basis of the algorithm is the fact that if a = qb+ c, a, q, b, c ∈ Z,⇒ (a, b) = (b, c). (4) This is very easy to see. Let s = (a, b)⇒ s|a, s|b⇒ a = sa1, b = sb1 t = (b, c)⇒ t|b, t|c⇒ b = tb2, c = tc2 Also c = a− qb = s(a1 − qb1)⇒ s|c Also as s|b (as s is the gcd of (a, b), s divides b and...

Notation and Basic Facts a, b, and c are the sides of ∆ABC opposite to A, B, and C respectively. [ABC] = area of ∆ABC s = semi-perimeter =) c b a (2 1 + + r = inradius R = circumradius Sine Rule: R 2 C sin c B sin b A sin a = = = Cosine Rule: a 2 = b 2 + c 2 − 2bc cos A [ABC] = B sin ac 2 1 A sin bc 2 1 C sin ab 2 1 = = = R 4 abc =) c s)(b s)(a s (s − − − (Heron's Formula) = 2 cr 2 br 2 ar + + ...

background: the human t-cell lymphotropic virus type i is the first retrovirus idenfied in humans. the virus has been associated with adult t-cell leukemia/lymphoma, human t-lymphotropic virus type i, myelopathy/tropical spasc paraparesis, uveis, arthris, pulmonary lymphocyc alveolis, keratoconjuncvis sicca, and infecous dermas. human t-lymphotropic virus type iis endemic in japan, p...

tumors of t h e male u ret h ra are r a re, co m prising <1% of urolo g ic malignancies. this is a re po rt of a 44-ye a r-old man pre s ented with a 4 -month history of gross initi a l h e maturia and d y s u ri a . af t e r exami n ing the pa t ien t , we found a firm mass ex t ending 1 c m within the p roxim a l bulb a r uret h ra and a pathologic report of moderately differen t iated sq u a...