The $q$-Onsager algebra $\mathcal O_q$ is defined by two generators $W_0, W_1$ and relations called the $q$-Dolan/Grady relations. Recently Baseilhac Kolb obtained a PBW basis for with elements denoted $\lbrace B_{n \delta+ \alpha_0} \rbrace_{n=0}^\infty, \lbrace \alpha_1} \delta} \rbrace_{n=1}^\infty $. In their recent study of current A_q$, Belliard conjecture that there exist W_{-k}\rbrace_{...

and Applied Analysis 3 f : [0, τ] ×N ×N → N is smooth enough and there are constants a, c ∈ N, with c ̸ = − 1, such that sup (t,z,u)∈q τ 󵄨󵄨󵄨󵄨f (t, z, u) − az − cu 󵄨󵄨󵄨󵄨 < ∞, (12) where q τ = [0, τ] ×N ×N. (2) The interior controllability of the semilinear Laguerre equation

We present a silicon optomechanical nanobeam design with a dynamically tunable acoustic mode at 10.2 GHz. The resonance frequency can be shifted by 90 kHz/V2 with an on-chip capacitor that was optimized to exert forces up to 1 µN at 10 V operation voltage. Optical resonance frequencies around 190 THz with Q-factors up to 2.2 × 106 place the structure in the well-resolved s...

In 1975 Philipp showed that for any increasing sequence (nk) of positive integers satisfying the Hadamard gap condition nk+1/nk > q > 1, k ≥ 1, the discrepancy DN of (nkx) mod 1 satisfies the law of the iterated logarithm 1/4 ≤ lim sup N→∞ NDN(nkx)(N log logN) −1/2 ≤ Cq a.e. Recently, Fukuyama computed the value of the lim sup for sequences of the form nk = θ , θ > 1, and in a preceding paper t...

If q is an algebraic Lie algebra and Q is an algebraic group with Lie algebra q, then ind q equals the transcendence degree of the field of Q-invariant rational functions on q. If q is reductive, then q and q are isomorphic as q-modules and hence ind q = rk q. It is an important invariant-theoretic problem to study index and, more generally, the coadjoint representation for non-reductive Lie al...

Let A be a unital simple separable C*-algebra satisfying the UCT. Assume that dr(A) < +∞, A is Jiang-Su stable, and K0(A)⊗Q ∼= Q. Then A is an ASH algebra (indeed, A is a rationally AH algebra).