on the xy-plane are bounded regions, called bases of digital plane segments. So, if the plane a is digitized and if a In this paper we prove that digital plane segments and their least-squares plane fit are in one-to-one correspondence, which region Q in the xy-plane is given, then the digital plane gives a simple representation of a digital plane segment by its segment P(a, Q) (more precisely,...

Let pq be a rational number. Numeration in base p q is defined by a function that evaluates each finite word over Ap = {0, 1, . . . , p− 1} to a rational number in some set Np q . In particular, Np q contains all integers and the literature on base pq usually focuses on the set of words that are evaluated to integers; it is a rather chaotic language which is not context-free. On the contrary, w...

We demonstrate an elegant combinatorial formula for the operation which adds a column on the homogeneous symmetric functions when this function acts on the Schur basis. A q-analog of this formula adds a column on the Hall-Littlewood basis. Résumé. Nous demontrons une formule élégante et combinatoire pour l’opérateur qui ajoute une colonne sur les fonctions symétriques homogène quand cet opérate...

We prove that, given any $n\geqslant 3$ and $2\leqslant q\leqslant n-1$, there is a closed $n$-manifold $M^{n}$ admitting chaotic lamination of codimension $q$ whose support has the topological dimension ${n-q+1}$. For $n=3$ $q=2$, such laminations can be represented as nontrivial 2-dimensional basic sets axiom A flows on 3-manifolds. show that are two types compactification (called casings) fo...

A new elliptic curve scalar multiplication algorithm is proposed. The algorithm o ers about twice the troughput of some conventional OEF-base algorithms because it combines the Frobenius map with the table reference method based on baseexpansion. Furthermore, since this algorithm suits conventional computational units such as 16, 32 and 64 bits, its base eld F p m is expected to enhance ellipti...

In the presence of alkali and LAuCl one or two —N H — groups of a purine or pyrimidine base can be transformed into -N (AuL)groups giving stable and soluble compounds containing one or two two-coordinated gold(I) nuclei; mononuclear L A u-Q ' or binuclear LA u-Q -A uL with a monodentate Q " or an exobidentate O '" ligand, resp. (Q 'H = adenine, guanine, theobromine, theophylline, azaguanine or ...

In the previous lecture we proved the Kronecker-Weber theorem: every abelian extension L of Q lies in a cyclotomic extension Q(ζm)/Q. The isomorphism Gal(Q(ζm)/Q) ' (Z/mZ)× allows us to view Gal(L/Q) as a quotient of (Z/mZ)×. Conversely, for each quotient H of (Z/mZ)×, there is a subfield L of Q(ζm) for which H ' Gal(L/Q). We now want make the correspondence between H and L explicit, and then g...

A new feature description method based on the fusion of fast retina keypoint (FREAK) and rotation-aware binary robust independent elementary features (rRBRIEF) is proposed to realize effective combination efficiency accuracy two descriptions. In addition, in elimination stage mismatched point pairs, by setting base its neighborhood, an improved neighborhood parallel random sample consensus (RAN...

The multireference Møller-Plesset perturbation (MRMP) theory with complete active space self-consistent field (CASSCF) reference functions is applied to the study of the Q and B bands of free-base, magnesium, and zinc porphyrins and their derivatives. The Q band of free-base porphyrin is so weak because the transition is pseudoparity-forbidden because of the alternancy symmetry. The Q band in t...

In the Lecture 20 we proved the Kronecker-Weber theorem: every abelian extension L of Q lies in a cyclotomic extension Q(ζm)/Q. The isomorphism Gal(Q(ζm)/Q) ' (Z/mZ)× allows us to view Gal(L/Q) as a quotient of (Z/mZ)×. Conversely, for each quotient H of (Z/mZ)×, there is a subfield L of Q(ζm) for which H ' Gal(L/Q). We would like to make the correspondence between H and L explicit, and then ge...