We show that function types which have only initial algebras for regular functors in the domains, i.e. first order function types, can be represented by terminal coalgebras for certain nested functors. The representation exploits properties of ω-limits and local ω-colimits.

Logic programs can be synthesized as a by-product of the planning of their verification proofs. This is achieved by using higher-order variables at the proof planning level, which become instantiated in the course of planning. We illustrate two uses of such variables in proof planning for program synthesis, one for synthesis proper and one for the selection of induction schemes. We demonstrate ...

Fold functions are a general mechanism for computing over recursive data structures. First-order folds compute results bottom-up. With higher-order folds, computations that inherit attributes from above can also be expressed. In this paper, we explore folds over a form of recursive higher-order function, called hyperfunctions, and show that hyperfunctions allow fold computations to coroutine ac...

We use high precision lattice simulations to calculate the plaquette expectation value in three-dimensional SU(Nc) gauge theory for Nc = 2, 3, 4, 5, 8. Using these results, we study the Nc-dependence of the first non-perturbative coefficient in the weak-coupling expansion of hot QCD. We demonstrate that, in the limit of large Nc, the functional form of the plaquette expectation value with ultra...

The scalar version of the pathway model of Mathai (2005) is shown to be associated with a large number of probability models used in physics. Different families of densities are listed here, which are all connected through the pathway parameter α, generating a distributional pathway. The idea is to switch from one functional form to another through this parameter and it is shown that one can pr...

ion X → X ′ 〈λx.X〉(t)→ 〈λx.X ′〉(t) +Lambda ¬X → ¬X ′ ¬〈λx.X〉(t)→ ¬〈λx.X ′〉(t) −Lambda Quantification For new variables x1, . . . , xn, ¬φ(x)→ ¬φ1(x) . . . ¬φ(x)→ ¬φn(x) ¬(∀x)φ(x)→ ¬[φ1(x1) ∧ . . . ∧ φn(xn)] −Quant Binding For x not free in X, X → X ′ X → 〈λx.X ′〉(t) +Bind ¬X → ¬X ′ ¬X → ¬〈λx.X ′〉(t) −Bind Definition 5.2 We say Y is a modal Herbrand expansion of X provided there is a formula X∗ ...

The slow roll approximation is studied for cosmological models in Hyperextended Scalar-Tensor Theories of Gravity. A procedure to obtain slow roll solutions in non-minimally coupled gravity is outlined and some examples are provided. An integral condition over the functional form of the non-minimal coupling is imposed in order to obtain intermediate in ationary behavior. e-mail: dtorres@venus. ...

Unfortunately, the incorrect version of [1, Theorem 4.3] was published. The correct version of [1, Theorem 4.3] is given in this paper. By employing the generalized higher-order contingent derivatives of set-valued maps, Wang et al. [1] established a sufficient optimality condition of weakly efficient solutions for (SV P): (SV P) min F(x), s.t. G(x) (−D) = ∅, x ∈ E. Theorem 1 (see [1, Theorem 4...

According to David Rosenthal, a mental state is conscious just in case its subject suitably represents herself as being in that state, where this entails that the mental state " is accompanied by a noninferential, nondispositional, assertoric thought to the effect that one is in that very state " (2002a, p. 410; see also Rosenthal, 1997, p. 742). This assertoric thought, since it is about anoth...