After it has been successfully done in probability and possibility theories, the paper is the first attempt to introduce the operator of composition also for belief functions. We prove that the proposed definition preserves all the necessary properties of the operator enabling us to define compositional models as an efficient tool for multidimensional models representation.

Consider a decision problem whose instance is a function. Its degree of undecidability, measured by the corresponding class of the arithmetic (or Kleene-Mostowski) hierarchy hierarchy, may depend on whether the instance is a partial recursive or a primitive recursive function. A similar situation happens for results like Rice Theorem (which is false for primitive recursive functions). Classical...

We introduce a concept called good oscillation. A function is called good oscillation, if its m-tuple integrals are bounded by functions having mild orders. We prove that if the error terms coming from summatory functions of arithmetical functions are good oscillation, then the Dirichlet series associated with those arithmetical functions can be continued analytically over the whole plane. We a...

In this paper, we give a simple proof of Mirzakhani's recursion formula of Weil-Petersson volumes of moduli spaces of curves using the Witten-Kontsevich theorem. We also briefly describe a very general recursive phenomenon in the intersection theory of moduli spaces of curves. In particular, we present several new recursion formulas for higher degree κ classes.

Corrected version Nov.20: a confused slide on the functional interpretation of weak compactness as well as a slide stating a bound on Browder's theorem have been deleted as the latter has been superseded meanwhile: weak compactess can be bypassed resulting in a primitive recursive bound.

Perfectly balanced functions were introduced by Sumarokov in [1]. A well known class of such functions are those linear either in the first or in the last variable. We present a novel technique to construct perfectly balanced functions not in the above class.

Pseudodifferential operators of several variables are formal Laurent series in the formal inverses of ∂1, . . . , ∂n with ∂i = d/dxi for 1 ≤ i ≤ n. As in the single variable case, Lax equations can be constructed using such pseudodifferential operators, whose solutions can be provided by Baker functions. We extend the usual notion of tau functions to the case of pseudodifferential operators of ...

Johnson [1] evaluated the sum d[n [C(d;r)[, where C(n;r) denotes Ramanujan’s trigonometric sum. This evaluation has been generalized to a wide class of arithmetical functions of two variables. In this paper, we generalize this evaluation to a wide class of arithmetical functions f several variables and deduce as special cases the previous evaluations.

We suggest several new ways to compare fully primitive recursive presentations of a structure. Properties of this kind have never been seen in computable structure theory. We prove that these new definitions are nonequivalent. In this note we give only proof sketches, complete proof will appear in the full version of the paper.

We deal with some relatives of the Hales Jewett theorem with primitive recursive bounds.