We consider a 5-axis CNC machine whose tool axis maintains a fixed angle with respect to the surface normal as the machine tool cuts a given path on a smooth surface. The tool axis a(ξ) lies on a cone of constant angle ψ about the surface normal n(ξ) at each point of the path, but its azimuthal position on this cone remains indeterminate. Geometrically speaking, given a curve n(ξ) on the unit s...

Let U = Tri(A,M,B) be a triangular algebra, where A, B are unital algebras over a field F and M is a faithful (A,B)-bimodule. Assume that ξ ∈ F and L : U → U is a map. It is shown that, under some mild conditions, L is linear and satisfies L([X, Y ]) = [L(X), Y ] + [X,L(Y )] for any X,Y ∈ U with [X, Y ] = XY − Y X = 0 if and only if L(X) = φ(X) + ZX + f(X) for all A, where φ is a linear derivat...

This paper is concerned with the extension of the concepts and theories of traveling wave solutions of time and space periodic monostable equations to time recurrent and space periodic ones. It first introduces the concept of generalized traveling wave solutions of time recurrent and space periodic monostable equations, which extends the concept of periodic traveling wave solutions of time and ...

Let U = Tri(A,M,B) be a triangular algebra, where A, B are unital algebras over a field F and M is a faithful (A,B)-bimodule. Assume that ξ ∈ F and L : U → U is a map. It is shown that, under some mild conditions, L is linear and satisfies L([X, Y ]) = [L(X), Y ] + [X,L(Y )] for any X,Y ∈ U with [X, Y ] = XY − Y X = 0 if and only if L(X) = φ(X) + ZX + f(X) for all A, where φ is a linear derivat...

ly seen, the main problem of the theory of Eisenstein series is to analyze thespace L(ξ) or the spaces L({P}, ξ) in terms of the cusp forms on the various M . Thisanalysis is carried out—in principle—in the text. However, one can be satisfied with amore perspicuous statement if one is content to analyze L(ξ) in terms of the representationsoccurring discretely in the spaces of au...

Using (448.1±2.9)×106 ψ(3686) events collected with the BESIII detector and a single-baryon tagging technique, we present first observation of decays ψ(3686)→Ξ(1530)0Ξ¯(1530)0 Ξ(1530)0Ξ¯0. The branching fractions are measured to be B(ψ(3686)→Ξ(1530)0Ξ¯(1530)0)=(6.77±0.14±0.39)×10−5 B(ψ(3686)→Ξ(1530)0Ξ¯0)=(0.53±0.04±0.03)×10−5. Here, second uncertainties statistical systematic, respectively. In ...

has infinitely many solutions in rational numbers p/q. It follows from the theory of continued fractions that μ(ξ) is always greater than or equal to 2, and an easy covering argument shows that μ(ξ) is equal to 2 for almost all real numbers ξ (with respect to the Lebesgue measure). Furthermore, Roth’s theorem asserts that the irrationality exponent of every algebraic irrational number is equal ...

The subword complexity of an infinite word ξ is a function f (ξ, n) returning the number of finite subwords (factors, infixes) of length n of ξ. In the present paper we investigate infinite words for which the set of subwords occurring infinitely often is a regular language. Among these infinite words we characterise those which are eventually recurrent. Furthermore, we derive some results comp...

– Let ξ be a real number and let n be a positive integer. We define four exponents of Diophantine approximation, which complement the exponents w n (ξ) and w * n (ξ) defined by Mahler and Koksma. We calculate their six values when n = 2 and ξ is a real number whose continued fraction expansion coincides with some Sturmian sequence of positive integers, up to the initial terms. In particular, we...