In this paper we consider the ip operation for combinatorial pointed pseudo-triangulations where faces have size 3 or 4, so-called combinatorial 4-PPTs. We show that every combinatorial 4-PPT is stretchable to a geometric pseudo-triangulation, which in general is not the case if faces may have size larger than 4. Moreover, we prove that the ip graph of combinatorial 4-PPTs with triangular outer...

We define semi-pointed partition posets, which are a generalisation of partition posets and show that they are Cohen-Macaulay. We then use multichains to compute the dimension and the character for the action of the symmetric groups on their homology. We finally study the associated incidence Hopf algebra, which is similar to the Faà di Bruno Hopf algebra.

let $a$ be a banach algebra and $x$ be a banach $a$-bimodule. then ${mathcal{s}}=a oplus x$, the $l^1$-direct sum of $a$ and $x$ becomes a module extension banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ in this paper, we investigate biflatness and biprojectivity for these banach algebras. we also discuss on automatic continuity of derivations on ${mathcal{s...

We investigate the problem of detecting rigid components (maximal Laman subgraphs) in a pseudotriangulation mechanism and in arbitrary pointed planar frameworks. For general Laman graphs with some missing edges, it is known that rigid components can be computed in O(n) time. Here we make substantial use of the special geometry of pointed pseudo-triangulation mechanisms to achieve linear time. T...

The aim of this study was to determine whether there was any relationship between body fat and pseudo(or plasma) cholinesterase. Hutchinson, McCance & Widdowson (I~sI), in reporting their studies of undernutrition and feeding, pointed out that, at the end of rehabilitation when men became ‘fat’, the average pseudo-cholinesterase was higher than normal. It therefore seemed of interest to investi...

Let G be a locally compact group, 1 < p < ∞ and let ω be a weight function on G. Recently, we introduced the Lebesgue weighted L−algebra L ω (G). Here, we establish necessary and sufficient conditions for L ω (G) to be φ−contractible, pseudo-contractible or contractible. Moreover we give some similar results about L(G,ω).

Let G be a Poisson–Lie group equipped with left invariant contravariant pseudo-Riemannian metric. There are many ways to lift the Poisson structure on tangent bundle TG of G. In this paper, we induce metric TG, and express in different cases Levi-Civita connection curvature terms We prove that space differential forms Ω*(G) is graded algebra if, only Ω*(TG) algebra. Moreover, show Sanchez de Al...

In the paper [8], we introduced the notions of pseudo-hyperplane and pseudoembedding of a point-line geometry and proved that every generalized quadrangle of order (s, t), 2 ≤ s <∞, has faithful pseudo-embeddings. The present paper focuses on generalized quadrangles of order (3, t). Using the computer algebra system GAP [12] and invoking some theoretical relationships between pseudo-hyperplanes...

Boolean constraints play an important role in various constraint logic programming languages. In this paper we consider pseudo-Boolean constraints, that is equations and inequalities between pseudo-Boolean functions. A pseudoBoolean function is an integer-valued function of Boolean variables and thus a generalization of a Boolean function. Pseudo-Boolean functions occur in many application area...

We construct cocycles on the Lie algebra of pseudoand q-pseudodifferential symbols of one variable and on their close relatives: the sine-algebra and the Poisson algebra on two-torus. A “quantum” Godbillon-Vey cocycle on (pseudo)differential operators appears in this construction as a natural generalization of the Gelfand-Fuchs 3-cocycle on periodic vector fields. We describe a nontrivial embed...