Two lower bag domain constructions are introduced: the initial construction which gives free lower monoids, and the final construction which is defined explicitly in terms of second order functions. The latter is analyzed closely. For sober dcpo's, the elements of the final lower bag domains can be described concretely as bags. For continuous domains, initial and final lower bag domains coincid...

The objective of the present paper is twofold: first, to establish explicit conditions for the elicitation of consistent a priori and conditional probabilities for a set of events representing pieces of evidence and hypotheses. Furthermore, an algorithm is proposed which uses these consistent input probabilities to compute lower and upper bounds for higher order joint probabilities. Secondly, p...

In this work, we study the volume ratio of the projective tensor products `p ⊗π `q ⊗π `r with 1 ≤ p ≤ q ≤ r ≤ ∞. We obtain asymptotic formulas that are sharp in almost all cases. As a consequence of our estimates, these spaces allow for a nearly Euclidean decomposition of Kašin type whenever 1 ≤ p ≤ q ≤ r ≤ 2 or 1 ≤ p ≤ 2 ≤ r ≤ ∞ and q = 2. Also, from the Bourgain-Milman bound on the volume rat...

Present bias is an old idea. The notion that people are susceptible to the over-pursuit of immediate gratification dates (at least) to the ancient Greeks. In academic research, psychologists working with animals in the 1960s and 1970s proposed “hyperbolic discounting”—a functional form of discounting that generates present bias—as a natural way to represent how animals respond to time delays, a...

Correspondence: gaoyingimu@163. com Department of Mathematics, Chongqing Normal University, Chongqing 400047, China Abstract In this paper, a pair of nondifferentiable multiobjective fractional programming problems is formulated. For a differentiable function, we introduce the definition of higher-order (F, a, r, d)-convexity, which extends some kinds of generalized convexity, such as second or...

State-of-the-art first-order automated theorem proving systems have reached considerable strength over recent years. However, in many areas of mathematics they are still a long way from reliably proving theorems that would be considered relatively simple by humans. For example, when reasoning about sets, relations, or functions, first-order systems still exhibit serious weaknesses. While it has...

This paper presents two views of stepwise enhancement, one a pragmatic syntax-based approach and the other a semantic approach based on higher-order functions and relating to shape and polytypism. The approaches are outlined, and the perhaps surprisingly close relationship between the two described. By combining the advantages of both approaches, it is shown how more code in both functional and...

Let $X$ be a Banach space of $dim X > 2$ and $B(X)$ be the space of bounded linear operators on X. If $L : B(X)to B(X)$ be a Lie higher derivation on $B(X)$, then there exists an additive higher derivation $D$ and a linear map $tau : B(X)to FI$ vanishing at commutators $[A, B]$ for all $A, Bin B(X)$ such that $L = D + tau$.