An abelian pattern describes the set of strings that comprise of the same combination of characters. Given an abelian pattern P and a text T ∈ Σ, the task is to find all occurrences of P in T , i.e. all substrings S = Ti...Tj such that the frequency of each character in S matches the specified frequency of that character in P . In this report we present simple online algorithms for abelian patt...

BACKGROUND To determine the temperament and character profile of glaucoma patients. METHODS A total of 234 patients (104 with primary open angle glaucoma, and 130 control subjects without any ocular disease) were selected for this prospective, cross-sectional study. All the participants underwent a comprehensive ophthalmological examination, including the best corrected visual acuity, intraoc...

The molecular mechanism of the reaction between N-methyl-3-chloroindole and methyl coumalate yielding carbazole has been studied using DFT methods at the MPWB1K/6-311G(d,p) level in toluene. This reaction is a domino process that comprises three consecutive reactions: (i) a polar Diels-Alder (P-DA) reaction between indole and methyl coumalate yielding two stereoisomeric [2 + 4] cycloadducts (CA...

Let k be a nite eld of characteristic p and cardinality q, a nontrivial C -valued additive character of k, and a nontrivial C -valued multiplicative character of k . We extend to a function on all of k by de ning (0) := 0: Recall that, given an integer n, a number 2 C is said to be pure of weight n (relative to q) if it and all its Aut(C =Q)-conjugates have absolute value p q. Such an is necess...

Let p be an odd prime and {χ(m) = (m/p)}, m = 0,1, . . . ,p − 1 be a finite arithmetic sequence with elements the values of a Dirichlet character χ modp which are defined in terms of the Legendre symbol (m/p), (m,p)= 1. We study the relation between the Gauss and the quadratic Gauss sums. It is shown that the quadratic Gauss sumsG(k;p) are equal to the Gauss sums G(k,χ) that correspond to this ...

The dual diene/1,3-dipolar character of 1-H-imidazole 3-oxide, HIO 1, allows this compound toparticipate in a competitive Diels-Alder (DA)/1,3-dipolar cycloaddition (13DC) reaction toward C=Sdouble bond of the electro-deficient sulfonyl methane SFM 2. The B3LYP/6-311++G(d,p) calculatedrelative Gibbs free energies indicate that among the studied 13DC and DA reactions, former iscompletely preferr...

Deformity and Character: Dr. Little’s Diagnosis of Richard lll ACCARDO Dr. P. J. Description: From Journal of the American Medical Association, Vol. 244 Date of publication: 19 December 1980 Synopsis: 19-century obstetrician accepting of the traditional list of Richard lll’s ‘deformities’ suggests that they were caused by hemiplegia resulting from a difficult birth, and speculates on the influe...

Let χ be a nontrivial multiplicative character of Fpn . We obtain the following results. (1). Let ε > 0 be given. If B = {Pnj=1 xjωj : xj ∈ [Nj + 1, Nj + Hj ] ∩ Z, j = 1, . . . , n} is a box satisfying n Π j=1 Hj > p ( 2 5, then for p > p(ε) we have, denoting χ a nontrivial multiplicative character | X x∈B χ(x)| ¿n p− ε 2 4 |B| unless n is even, χ is principal on a subfield F2 of size pn/2 and ...