In the Bézier formalism, an arc of a conic is a rational curve of degree 2 with control polygon {P, Q, R} for which the weights can be normalized to {1, w, 1}. The parametrization of the conic arc is C(t) = (1 − t) 2 P + 2wt(1 − t)Q + t 2 R (1 − t) 2 + 2wt(1 − t) + t 2 , t ∈ [0, 1]. Abstract Synthetic derivation of closed for-mulae of the geometric characteristic of a conic given in Bézier form...

We present conjectures giving formulas for the Macdonald polynomials of type B, C, D which are indexed by a multiple of the first fundamental weight. The transition matrices between two different types are explicitly given. Introduction Among symmetric functions, the special importance of Schur functions comes from their intimate connection with representation theory. Actually the irreducible p...

This article studies the existence of homoclinic solutions for the second-order non-autonomous Hamiltonian system q̈ − L(t)q + Wq(t, q) = 0, where L ∈ C(R, Rn ) is a symmetric and positive definite matrix for all t ∈ R. The function W ∈ C1(R × Rn, R) is not assumed to satisfy the global Ambrosetti-Rabinowitz condition. Assuming reasonable conditions on L and W , we prove the existence of at leas...

and Applied Analysis 3 The aim of this paper is to prove the equivalence of convergent results of above Ishikawa andMann iterations with errors for generalized asymptoticallyΦ-strongly pseudocontractive mappings without bounded range assumptions in uniformly smooth real Banach spaces. For this, we need the following concepts and lemmas. Definition 1.4 see 4 . The mapping T is called generalized...

We present conjectures giving formulas for the Macdonald polynomials of type B, C, D which are indexed by a multiple of the first fundamental weight. The transition matrices between two different types are explicitly given. Introduction Among symmetric functions, the special importance of Schur functions comes from their intimate connection with representation theory. Actually the irreducible p...

Let T be a positive operator on a Banach lattice E. Some properties of Weyl essential spectrum σew(T ), in particular, the equality σew(T ) = ⋂ 0≤K∈K(E) σ(T +K), where K(E) is the set of all compact operators on E, are established. If r(T ) does not belong to Fredholm essential spectrum σef(T ), then r(T ) 6∈ σ(T +a|T−1|) for every a 6= 0, where T−1 is a residue of the resolvent R(., T ) at r(T...

T ro i s c a r a c t è r e s d o m i n e n t la f a u n e d e P o i s s o n s d ' e a u d o u c e m a l g a c h e : sa p a u v r e t é , s o n o r ig ine e x c l u s i v e m e n t m a r i n e e t sa r i c h e s s e en f o r m e s e n d é m i q u e s (vo i r K I E N E R , 1963 , e t B Â N Â R E S C U , 1969) . Il n o u s a p a r u i n t é r e s s a n t d ' é t u d i e r , en r e l a t i o n a v ...

and Applied Analysis 3 In 2005, C. E. Chidume and C. O. Chidume 3 proved the convergence theorems for fixed points of uniformly continuous generalized Φ-hemicontractive mappings and published in 3 . However, there exists a gap in the proof course of their theorems. The aim of this paper is to show the convergence of the multistep iteration with errors for fixed points of uniformly continuous Φ-...

Renewable resources can p r o v i d e a s u b s t a n t i a l energy resource f o r t h e Un i ted States. however, i s l i m i t e d t o t h e use o f b i o f u e l s . L i q u i d s are p r e f e r r e d f o r use as t r a n s p o r t a t i o n f u e l s because o f t h e i r h igh energy d e n s i t y and hand l ing ease and safety. feedstock f o r p roduc t ion o f l i q u i d f u e l s [l]...

Note that, by (4 .4) and (4 .5), (7 .6) holds for all nonnegatíve p. Substituting from (7 .6) in (6 .1) and (6 .2) and evaluating coefficients of xm, we obtain the following two identities. r-1 m (p + q)T rP~+4) = pTrpm + ~,(q) + T (P)-L q r, m pq E a l i r-a-1, m-j s-0 j-0 r-1 m-1 pq ~-~ T(P)Tr(9a-l. m-i-1 a L-0 i-0 r-1 m (r + i)Tr m+q) _ (r + 1)Tr + p (r-s)T (P)T (q) a. j r-8-1, M-j 8-0 j-0 r...