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Generating functions are obtained for certain types of permutations analogous to up-down and down-up permutations. In each case the generating function is a quotient of entire functions; the denominator in each case is φ02(x) ? φ1(x)φ3(x), where 相似文献
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ABSTRACT Copolymers of 1,5-dioxepan-2-one (DXO) and e-caprolactone (?-CL), δ-valerolactone (δ-VL) or L-lactide (LLA) have been synthesized and characterized. High molecular weight copolymers were obtained using stannous-2-ethyl hexanoate as catalyst in bulk. Reactivity ratios for the copolymerization of DXO and δ-VL were determined at 110°C as rVL=0.5 and rDXO=2.3. At high conversion, depolymerization of δ-VL occurred, resulting in lower molecular weight and variations in the copolymer composition. Physical properties, such as crystallinity and melting temperature of the DXO-copolymers proved to be strongly dependent on the choice of comonomer and on the molar composition of the copolymers. DXO appears to be incorporated into the poly-?-caprolactone (PCL) crystals and to some extent into the poly-δ-valerolactone (PVL) crystals, resulting in a more gradual decrease in crystallinity with increasing amount of DXO. 相似文献
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Instantons and anti-instantons can profoundly influence the structure of a non-Abelian gauge theory involving N flavors of massless quarks. Interactions of the quarks with these pseudoparticles can spontaneously generate a quark mass, break the theory's SU(N) × SU(N) chiral symmetry and bind quark-antiquark pairs to form N2 ? 1 Goldstone bosons. If the spontaneously generated quark mass is small, multipseudoparticle configurations can be treated in a dilute gas approximation. 相似文献
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The authors determine the number of (n+m)×t matrices A1 of rank r+v, over a finite field GF(q), whose last m rows are those of a given matrix A of rank r+v over GF(q) and whose first n rows have a given rank u. 相似文献
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Experimental measurements of the electric form factor of the neutron indicate a spatially inhomogeneous distribution of charge. The quark model, with a spatially dependent spin-spin interaction, can accurately describe this inhomogeneity. We relate the neutron's charge radius to the nucleon-delta mass difference and discuss other experimental consequences of the inhomogeneity. 相似文献
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Letn = (a1.a2 … aN) denote a sequence of integers ai={1.2.…n}. A rise is a part ai.ai+1 with ai <ai+1: a fall is a pair with aiai+1: a level is a pair with ai = ai+1. A maximum is a triple ai-1.aiai+1 with ai-1?ai.ai?ai+1. If ei is the number of aj?n withaj = i, then [e1…en] is called the specification of n. In addition, a conventional rise is counted to the left of a1 and a conventional fall to the right of aN: ifa1?a2, then a1 is counted as a conventional maximum, similarly if aN-1 ? aN thenaN is a conventional maximum. Simon Newcomb's problem is to find the number of sequences n with given specification and r rises; the refined problem of determining the number of sequences of given specification with r rises and s falls has also been solved recently. The present paper is concerned with the problem of finding the number of sequences of given specification with r rises, s falls. λ levels and λ maxima. A generating function for this enumerant is obtained as the quotient of two continuants. In certain special cases this result simplifies considerably. 相似文献