We consider Baxter Q-operators for various versions of quantum affine Toda chain. The interpretation of eigenvalues of the finite Toda chain Baxter operators as local Archimedean L-functions proposed recently is generalized to the case of affine Lie algebras. We also introduce a simple generalization of Baxter operators and local L-functions compatible with this identification. This gives a con...

Tropical and non-Archimedean curves

Let π = ⊗ p≤∞ πp be a cuspidal automorphic representation of GL(n) over Q. The adelic representation π is composed of π∞, an archimedean representation of GL(n,R), and nonarchimedean representations πp of GL(n,Qp) for each prime p. For all places p < ∞ outside of a finite set S, πp is unramified and parameterized by principal series parameters {αp,j}. Letting Ap ∈ GL(n,C) denote the diagonal ma...

In the title compound, [Hf(C(5)H(4)F(3)O(2))(4)]·2C(7)H(8), the Hf(IV) atom, lying on a twofold rotation axis, is coordinated by eight O atoms from four 1,1,1-trifluoro-acetyl-acetonate ligands with an average Hf-O distance of 2.173 (1) Å and O-Hf-O bite angles of 75.69 (5) and 75.54 (5)°. The coordination polyhedron shows a slightly distorted Archimedean square antiprismatic geometry. The asym...

The problem of characterization of the structure of MTL-algebras, which form an equivalent algebraic semantics for Monoidal T-norm Based Logic (see [9]) in the sense of Blok and Pigozzi (see [3]), is still far from being solved. Since MTL-algebras are in fact subdirect products of chains, it suffices to investigate only the structure of MTL-chains if we want to characterize the structure of MTL...

Within the categoryW of archimedean lattice-ordered groups with weak order unit, we show that the objects of the form C (L), the set of continuous real-valued functions on a locale L, are precisely those which are divisible and complete with respect to a variant of uniform convergence, here termed indicated uniform convergence. We construct the corresponding completion of aW-object A purely alg...

Let K be a basic closed semialgebraic set in R defined by polynomial inequalities g1 ≥ 0, . . . , gs ≥ 0, where g1, . . . , gs ∈ R[x1, . . . , xn], and let f ∈ R[x1, . . . , xn]. In [12], Schmüdgen proves that, if K is compact and f is strictly positive on K, then f belongs to the quadratic preordering generated by g1, . . . , gs. Denote by M the (smaller) quadratic module generated by g1, . . ...

In this paper, we prove some stability results concerning the generalized quadratic and quartic type functional equation in the context of nonArchimedean fuzzy normed spaces in the spirit of Hyers-Ulam-Rassias. As applications, we establish some results of approximately generalized quadratic and quartic type mapping in non-Archimedean normed spaces. Also, we show that the assumption of the non-...

Probability distributions are central tools for probabilistic modeling in data mining. In functional data analysis (FDA) they are weakly studied in the general case. In this paper we discuss a probability distribution law for functional data considered as stochastic process. We define first a new kind of stationarity linked t o the Archimedean copulas, and then we build a probability distributi...