We obtain the following characterization of Q-polynomial distance-regular graphs. Let Γ denote a distance-regular graph with diameter d ≥ 3. Let E denote a minimal idempotent of Γ which is not the trivial idempotent E0. Let {θ∗ i }i=0 denote the dual eigenvalue sequence for E. We show that E is Q-polynomial if and only if (i) the entry-wise product E ◦ E is a linear combination of E0, E, and at...

This paper deals with a class of 2-step solvable simply connected Lie groups G in which we construct certain lattices Γ . It turns out that these are all the lattices in such groups. We then apply our results to study the decomposition of the quasi-regular representation of G on G/Γ .

The assignment (nonstable K0-theory), that to a ring R associates the monoid V(R) of Murray-von Neumann equivalence classes of idempotent infinite matrices with only finitely nonzero entries over R, extends naturally to a functor. We prove the following lifting properties of that functor: (i) There is no functor Γ, from simplicial monoids with order-unit with normalized positive homomorphisms t...

Orbital motion in triaxial nuclei with central point masses, representing supermassive black holes, is investigated. The stellar density is assumed to follow a power law, ρ ∝ r −γ , with γ = 1 or γ = 2. At low energies the motion is essentially regular; the major families of orbits are the tubes and the pyramids. Pyramid orbits are similar to box orbits but have their major elongation parallel ...

In this paper, we study the right regular representation RΓ of a finite group G on the vector space consisting of vector valued functions on Γ\G with a subgroup Γ of G and give a trace formula using the work of M.-F. Vignéras.

We state a sparse approximate version of the blow-up lemma, showing that regular partitions in sufficiently pseudorandom graphs behave almost like complete partite graphs for embedding graphs with maximum degree ∆. We show that (p, γ)-jumbled graphs, with γ = o(pmax(2∆,∆+3/2)n), are “sufficiently pseudorandom”. The approach extends to random graphs Gn,p with p ( log n n )1/∆.

With the usual notation for congruences on a regular semigroup S, in a previous communication we studied the lattice Λ generated by Γ = {σ, τ, μ, β} relative to properties such as distributivity and similar conditions. For K and T the kernel and trace relations on the congruence lattice of S, we form an abstraction of the triple (Λ;K|Λ, TΛ) called a c-triple. In this study a number of relations...

A finite simple graph Γ is called a Nest if it regular of valency 6 and admits an automorphism ρ with two orbits the same length such that at least one subgraphs induced by these cycle. We say core-free no non-trivial subgroup group generated normal in Aut(Γ). In this paper, we show that, edge-transitive core-free, then isomorphic to following graphs: complement Petersen graph, Hamming H(2,4), ...

We prove the existence of solutions to the differential inclusion ẍ(t) ∈ F (x(t), ẋ(t)) + f(t, x(t), ẋ(t)), x(0) = x0, ẋ(0) = y0, where f is a Carathéodory function and F with nonconvex values in a Hilbert space such that F (x, y) ⊂ γ(∂g(y)), with g a regular locally Lipschitz function and γ a linear operator.

Let T be a d-regular tree (d ≥ 3) and A = Aut(T ) its automorphism group. Let Γ be the group generated by n independent Haar-random elements of A. We show that almost surely, every nontrivial element of Γ has finitely many fixed points on T .