root fracture injuries affect up to 7% of permanent teeth. this type of injury is rarely seen in teeth with open apices and depending on the fracture site, the prognosis is good. this case report describes a horizontal intra-alveolar root fracture in the middle third of a maxillary central incisor associated with an extrusive luxation of the coronal segment and its treatment in a 6-year-old gir...

We show that the Faddeev-Pyatov SL q (N) differential algebra [1] is a subalgebra of the GL q (N) differential algebra constructed by Schupp, Watts and Zumino [2]. In the paper [1], the bicovariant differential algebra on SL q (N) (see below (10), (11)) with generators {T ij , L ij , ˜ Ω ij } i, j = 1,. .. N has been constructed. The elements T ij are generators of the algebra F un(SL q (N)), w...

By using a fixed point theorem of strict-set-contraction, some sufficient conditions are obtained for the existence of positive periodic solutions for a periodic neutral Lotka-Volterra competition system on time scales of the form x ∆ i (t) = x i (t) r i (t) − n j=1 a ij (t)x j (t) − n j=1 b ij (t)x j (t − τ ij (t, x 1 (t),. .. , x n (t))) − n j=1 c ij (t)x

Open-answer questions are resistant to guesswork; they stimulate students’ thinking. However, the number of correct answers rises quickly with answer length both in natural and formal languages. One template can define many variants answers. The article presents a question plugin Preg for popular Moodle LMS, which uses Perl-compatible regular expressions as templates hint next character lexeme....

We consider a square matrix Aǫ whose entries have asymptotics of the form (Aǫ) ij = a ij ǫ A ij + o(ǫ A ij) when ǫ goes to 0, for some complex coefficients a ij and real exponents A ij. We look for asymptotics of the same type for the eigenvalues of Aǫ. We show that the sequence of exponents of the eigenvalues of Aǫ is weakly (super) majorized by the sequence of corners of the min-plus characte...

Transportation networks play a vital role in modern societies. Structural optimization of a transportation system under a given set of constraints is an issue of great practical importance. For a general transportation system whose total cost C is determined by C = Sigma(i<j)C(ij)(I(ij)), with C(ij) (I(ij)) being the cost of the flow I(ij) between node i and node j, Banavar and co-workers [Phys...

The aim of this paper is to introduce the concepts of τ1τ2-regular generalized star star closed sets , τ1τ2-regular generalized star star open sets and study their basic properties in bitopological spaces. Keywords—τ1τ2-regular closed sets; τ1τ2-regular open sets; τ1τ2-regular generalized closed sets; τ1τ2-regular generalized star closed sets; τ1τ2-regular generalized star star closed sets.

Consider a N × n random matrix Yn = (Y n ij ) where the entries are given by Y n ij = σ(i/N,j/n) √ n X ij , the X n ij being centered i.i.d. and σ : [0, 1] 2 → (0,∞) being a continuous function called a variance profile. Consider now a deterministic N×n matrix Λn = ( Λij ) whose non diagonal elements are zero. Denote by Σn the non-centered matrix Yn+Λn. Then under the assumption that limn→∞ N n...