This article deals with necessary and sufficient conditions for a family of elements in Euclidean Jordan algebra to have simultaneous (order) spectral decomposition. Motivated by well-known matrix theory result that any pairwise commuting complex Hermitian matrices is simultaneously (unitarily) diagonalizable, we show the setting general algebra, operator has decomposition, i.e. there exists co...

The Theorem of Bahadur an Rao is a refinement of the classical Cramér’s Theorem. Instead of just calculating the exponential rate of decay of large deviation events, it gives a precise estimate of the large deviation probabilities. We use this theorem as well as Cramér’s Theorem to calculate the tail distributions of total financial losses of a large portfolio and compare the quality of both ap...

We introduce the notion of λ-double Lie algebra, which coincides with usual double algebra when λ=0. show that every for λ≠0 provides structure modified Poisson on free associative algebra. In particular, it confirms conjecture S. Arthamonov (2017). prove there are no simple finite-dimensional algebras.

Abstract. Let 1 ≤ p < ∞, f ∈ Lp(R) and Λ ⊆ R. We consider the closed subspace of Lp(R), Xp(f,Λ), generated by the set of translations f(λ) of f by λ ∈ Λ. If p = 1 and {f(λ) : λ ∈ Λ} is a bounded minimal system in L1(R), we prove that X1(f,Λ) embeds almost isometrically into `1. If {f(λ) : λ ∈ Λ} is an unconditional basic sequence in Lp(R), then {f(λ) : λ ∈ Λ} is equivalent to the unit vector ba...

We consider the semilinear problem Δu=λ+(− log u+)1{u>0}−λ−(− u−)1{u<0} in B1, where B1 is unit ball Rn and assume λ+,λ−>0. Using a monotonicity formula argument, we prove an optimal regularity result for solutions: ∇u log-Lipschitz function. This introduces two main difficulties. The first lack of invariance scaling blow-up problem. other (more serious) issue term Weiss energy which potentiall...

A result of Farahat and Higman shows that there is a “universal” algebra, FH, interpolating the centres symmetric group algebras, Z(ℤS n ). We explain this algebra isomorphic to ℛ⊗Λ, where ℛ ring integer-valued polynomials Λ functions. Moreover, isomorphism via “evaluation at Jucys–Murphy elements”, which leads character formulae for groups. Then, we generalise wreath products Γ≀S fixed finite ...

Let H and K be subsets of the vertex set V(Qd) d-cube Qd (we call configurations in Qd). We say is an exact copy if there automorphism which sends to K. If d a positive integer configuration Qd, we define λ(H,d) limit as n goes infinity maximum fraction, over all S V(Qn), sub-d-cubes Qn whose intersection with H. determine λ(C8,4) λ(P4,3) where C8 “perfect” 8-cycle Q4 P4 path 4 vertices Q3, mak...