Papert Strauss (Proc. London Math. Soc. 18(3), 217–230, 1968) used Pontryagin duality to prove that a compact Hausdorff topological Boolean algebra is a powerset algebra. We give a more elementary proof of this result that relies on a version of Bogolyubov’s lemma.

Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This result generalizes the classical identification of exponentiable topological spaces as those whose lattice of open subsets forms a continuous lattice.

We analyze structure theories of the power-set of ω1 and compare them relative to Cantor’s Continuum Problem. We also compare these theories with the structure theory of the powerset of ω under the assumption of the axiom of definable determinacy.

We study the backward shift operator on Hilbert spaces Hα (for α ≥ 0) which are norm equivalent to the Dirichlet-type spaces Dα. Although these operators are unitarily equivalent to the adjoints of the forward shift operator on certain weighted Bergman spaces, our approach is direct and completely independent of the standard Cauchy duality. We employ only the classical Hardy space theory and an...

The other technique is to learn some form of control knowledge, which helps to determine which control action to try next. Ideally the former “blind” search with exponential complexity is replaced by a strategy to move straight forward in direction of the goal. The control knowledge can take many forms including evaluation functions, operator strengths, and operator-selection and rejection rule...

Hereditarily finite (HF) set theory provides a standard universe of sets, but with no infinite sets. Its utility is demonstrated through a formalisation of the theory of regular languages and finite automata, including the Myhill-Nerode theorem and Brzozowski’s minimisation algorithm. The states of an automaton are HF sets, possibly constructed by product, sum, powerset and similar operations.

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

The Compton amplitude is calculated in terms of expectation values of light–ray quark operators. As a technical tool we apply the nonlocal light–cone expansion. Thereby we express the expectation value of the vector light–ray operator with the help of the expectation value of the corresponding scalar operator of twist 2. This allows important simplifications. In the limit of forward scattering ...

In this paper, through comparison of different reconstruction algorithms for volume rendering, we put forward Ray Casting algorithm as the scheme of 3D reconstruction of medical image. We improved the image synthesis operator, and combined section sampling mode to reconstruct the image. Finally, we rendered images on GPU. By using improved operator, we not only made the rendering speed accelera...

where Δ is the forward difference operator Δxn = xn+1 − xn, Δxn = Δ(Δxn), φp(s) is p-Laplacian operator φp(s) = |s|p−2s (1 < p < ∞), and f : Z×R3 → R is a continuous functional in the second, the third, and fourth variables and satisfies f (t +m,u,v,w) = f (t,u,v,w) for a given positive integerm. We may think of (1.1) as being a discrete analogue of the second-order functional differential equa...