Let (W,Σ) be a finite Coxeter system, and θ an involution such that θ(∆) = ∆, where ∆ is a basis for the root system Φ associated with W , and Iθ = {w ∈ W | θ(w) = w−1} the set of θ-twisted involutions in W . The elements of Iθ can be characterized by sequences in Σ which induce an ordering called the Bruhat poset. The main algorithm of this paper computes this poset. Algorithms for finding con...

This paper introduces a generalization of the operation of catenation: u[k]lv, the left-k-insertion, is the set of all words obtained by inserting v into u in positions that are at most k letters away from the left extremity of the word u. We define k-suffix codes using the left-kinsertion operation and extend the concept of k-prefix and k-suffix codes to involution k-prefix and involution k-su...

Let G(V,E) be a graph with p vertices and q edges. A graph G is said to have an odd mean labeling if there exists a function f : V (G) → {0, 1, 2,...,2q - 1} satisfying f is 1 - 1 and the induced map f* : E(G) → {1, 3, 5,...,2q - 1} defined by f*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is evenf*(uv) = (f(u) + f(v) + 1)/2 if f(u) + f(v) is odd is a bijection. A graph that admits an odd mean labelin...

We consider a d-dimensional C∞-manifold M such that M = Mc ∪ M∞, where Mc is relatively compact open submanifold, and M∞ is the noncompact part which is diffeomorphic to (0,∞)×∂M . Here ∂M is a compact manifold without boundary. In the following, we designate a point in M∞ by (r, θ) with r ∈ (0,∞) and θ ∈ ∂M . Often we also denote by θ ∈ ∂M a variables in a local coordinate of ∂M . Let H(θ)dθ b...

We are given a finite set of m points (guards) G in the plane R 2 and an angle 0 ≤ Θ ≤ 2π. A Θ-cone is a cone with apex angle Θ. We call a Θ-cone empty (with respect to G) if it does not contain any point of G. A point p ∈ R is called Θ-guarded if every Θ-cone with apex located at p is non-empty. Moreover, the set of all Θ-guarded points is called Θ-region. We first show how to construct a data...

1 Problem Discuss the motion of an unbalanced tire that rolls without slipping on a horizontal surface, subject to conservation of energy. In what sense(s) can this system be said to contain " hidden momentum? " 2 Solution 2.1 The Motion We consider the tire to be a hoop of radius a and mass M that is unbalanced due to an additional mass m at some fixed point on the rim, as shown in the figure ...

In this article, we introduce the lacunary difference sequence spaces w0(M , θ,∆ n m, p, q), w1(M , θ,∆ n m, p, q) and w∞(M , θ,∆ n m, p, q) using a sequence M = (Mk) of Orlicz functions and investigate some relevant properties of these spaces. Then, we define and study the notion of qlacunary ∆nm-statistical convergent sequences. Further, we study the relationship between q-lacunary ∆nm-statis...

Theory of Sturmian and episturmian sequences is a subject of great interest in combinatorics on words with applications in several fields. The aim of this talk is to present very recent research results concerning some extensions of episturmian sequences which have been obtained in a joint work with Alessandro De Luca, Michelangelo Bucci, and Luca Q. Zamboni [?, ?, ?]. As is well known palindro...

Let Θ(M,K) denote the 2-loop piece of (the logarithm of) the LMO invariant of a knot K in M , a ZHS . Forgetting the knot (by which we mean setting diagrams with legs to zero) specialises Θ(M,K) to λ(M), Casson’s invariant. This note describes an extension of Casson’s surgery formula for his invariant to Θ(M,K). To be precise, we describe the effect on Θ(M,K) of a surgery on a knot which togeth...

Let M = (E,F) be a matroid on a set E, and B one of its bases. A closed set θ ⊆ E is saturated with respect to B when |θ ∩B| = r(θ), where r(θ) is the rank of θ. The collection of subsets I of E such that |I ∩ θ| ≤ r(θ) for every closed saturated set θ turns out to be the family of independent sets of a new matroid on E, called base-matroid and denoted by MB . In this paper we prove that a grap...