We document the discovery of two generating functions for ζ(2n + 2), analogous to earlier work for ζ(2n + 1) and ζ(4n + 3), initiated by Koecher and pursued further by Borwein, Bradley and others.

At Rolls-Royce, a study determined that manufacturing part cost can be estimated from dimensional data in the part definition. The method appears to be more accurate than mass-based parametric models or process simulation cost models. Additional advantages are: part definition information is causally related to part manufacturing cost; part definition information is easily available during the ...

‘Scientific community’ is common currency in the study of science, largely due to Kuhn’s use of the term in his highly influential book The Structure of Scientific Revolutions. As this article explains, however, ‘scientific community’ was not of Kuhn’s coining. It was hinted at by Peirce, and expressly designated by Royce. On a few occasions Fleck affirmed a scientific community, while Polanyi ...

We prove the boundedness of non-local operator $$\begin{aligned} \mathcal {L}^a u(x)=\int _{\mathbb {R}^d} \left( u(x+y)-u(x)-\chi _\alpha (y)\big (\nabla u(x),y\big )\right) a(x,y)\frac{dy}{|y|^{d+\alpha }} \end{aligned}$$ from $$H_{p,w}^\alpha (\mathbb {R}^d)$$ to $$L_{p,w}(\mathbb for whole range $$p \in (1,\infty )$$ , where w is a Muckenhoupt weight. The coefficient a(x, y) bounded, merely...

We denote by Conc L the (∨, 0)-semilattice of all finitely generated congruences of a lattice L. For varieties (i.e., equational classes) V and W of lattices such that V is contained neither in W nor in its dual, and such that every simple member of W contains a prime interval, we prove that there exists a bounded lattice A ∈ V with at most א2 elements such that Conc A is not isomorphic to Conc...

Let Ω ⊂ R, n > 2, be a bounded connected domain of the class C for some θ ∈ (0, 1]. Applying the generalized Moser-Trudinger inequality without boundary condition, the Mountain Pass Theorem and the Ekeland Variational Principle, we prove the existence and multiplicity of nontrivial weak solutions to the problem u ∈ W L(Ω), − div ( Φ(|∇u|) ∇u |∇u| ) + V (x)Φ(|u|) u |u| = f(x, u) + μh(x) in Ω, ∂u...

In this paper we will discuss why in some circumstances people express their intentions indirectly: the use of Indirect Speech Acts (ISA). Based in Parikh’s game of part information and Franke’s IBR model, we develop a game-theoretic model of ISA, which is divided into two categories, namely non-conventional ISA and conventional ISA. We assume that non-conventional ISA involves two types of com...