Let g = g0 ⊕ g1 be a simple Z2-graded Lie algebra and let b0 be a fixed Borel subalgebra of g0. We describe and enumerate the abelian b0-stable subalgebras of g1.

Differences between lattice Monte Carlo data and perturbation theory (for example the lack of asymptotic scaling) are usually associated with the ‘bad’ behaviour of the bare lattice coupling g0 due to the effects of large (and unknown) higher order terms in g0. In this philosophy a new, renormalised coupling g ′ is defined with the aim of making the higher order coefficients of the perturbative...

There is a known hyperkähler structure on any complexified Hermitian symmetric space G/K, whose construction relies identifying G/K with both (co)adjoint orbit and the cotangent bundle to compact Gu/K0. Via family of explicit diffeomorphisms, we show that almost all complex structures are equivalent one G/K; via related symplectic $T^{*}\left (G_{u}/K_{0}\right )$ . We highlight intermediate Kä...

Let G0 = K ⋉ p be the Cartan motion group associated with a noncompact semisimple Riemannian symmetric pair (G, K). Let a be a maximal abelian subspace of p and let p = a+ q be the corresponding orthogonal decomposition. A flat horocycle in p is a G0-translate of q. A conical distribution on the space Ξ0 of flat horocycles is an eigendistribution of the algebra D(Ξ0) of G0-invariant differentia...

An expansion graph of a directed weighted graph G0 is obtained fromG0 by replacing some edges by disjoint chains. The adjacency matrix of an expansion graph is a partial linearization of a matrix polynomial with nonnegative coefficients. The spectral radii for different expansion graphs of G0 and correspondingly the spectral radii of matrix polynomials with nonnegative coefficients, which sum u...

An expansion graph of a directed weighted graph G0 is obtained fromG0 by replacing some edges by disjoint chains. The adjacency matrix of an expansion graph is a partial linearization of a matrix polynomial with nonnegative coefficients. The spectral radii for different expansion graphs of G0 and correspondingly the spectral radii of matrix polynomials with nonnegative coefficients, which sum u...

Small-conductance Ca2+-activated K+ (SK2) channel plays an important role in the activation of Jurkat T-lymphocytes by maintaining electrical gradients for the sustained Ca2+ influx. Apamin-sensitive K+ current was significantly decreased with cell-cycle progression from G0/G1 into G2/M phases, and protein expression of SK2 channels showed parallel down-regulation, with its highest expression a...

1 WHEN IS A SEQUENCE DENSE IN A COMPACT ABELIAN GROUP We denote by G a compact abelian group; we denote by μ its normalized Haar measure and by Γ = Ĝ its dual group (which is discrete). We consider sequences Λ ⊂ G and ask when is Λ dense in G. Our first approach is based on the duality theorem which tells us that the topology on G is the weak topology determined by Γ; thus if g0 ∈ G, then a bas...

One of the long-standing problems on logic programming is to express exception handling in a high-level way. We argue that this problem can be solved by adopting computability logic and sequential-choice disjunctive goal formulas of the form G0 ▽ G1 where G0, G1 are goals. These goals have the following intended semantics: sequentially choose the first true goal Gi and execute Gi where i(= 0 or...

If G is a plane graph and x, y ∈ V (G), then the dual distance of x and y is equal to the minimum number of crossings of G with a closed curve in the plane joining x and y. Riskin [7] proved that if G0 is a 3connected cubic planar graph, and x, y are its vertices at dual distance d, then the crossing number of the graph G0 + xy is equal to d. Riskin asked if his result holds for arbitrary 3-con...