The ISOP-model or model of twodimensional or bi-isotonicity (Scheiblechner, 1995) postulates that the probabilities of ordered response categories increase isotonically in the order of subject “ability” and item ”easiness”. Adding a conventional cancellation axiom for the factors of subjects and items gives the ADISOP model where the c.d.f.s of response categories are functions of an additive item and subject parameter and an ordinal category parameter. Extending cancellation to the interactions of subjects and categories as well as of items and categories (independence axiom of the category factor from the subject and item factor) gives the CADISOP model (completely additive model) in which the parallel c.d.f.s are functions of the sum of subject, item and category parameters. The CADISOP model is very close to the unidimensional version of the polytomous Rasch model with the logistic item/category characteristic(s) replaced by nonparametric axioms and statistics. The axioms, representation theorems and algorithms for model fitting of the additive models are presented.

Recently, Indrek Reiland proposed a new version of the act-type theory of propositions (ATT) in which predication is still committal. However, the Frege-Geach problem can be addressed without resorting to Peter Hanks's cancellation manoeuvre. In this article, I argue that if we take predication as a committal act, we will then have to tackle another problem: non-committal representational acts. I argue that Reiland still needs a notion of cancellation to deal with the latter problem. On this account, he cannot avoid the major flaw he attributes to Hanks's version.

Similar to research on risky choice, the traditional analysis of intertemporal choice takes the view that an individual behaves so as to maximize the discounted sum of all future utilities. The well-known Allais paradox contradicts the fundamental postulates of maximizing the expected value or utility of a risky option. We describe a violation of the law of diminishing marginal utility as well as an intertemporal version of the Allais paradox.

Recent research reported evidence that contradicts cumulative prospect theory and the priority heuristic. The same body of research also violates two editing principles of original prospect theory: cancellation (the principle that people delete any attribute that is the same in both alternatives before deciding between them) and combination (the principle that people combine branches leading to the same consequence by adding their probabilities). This study was designed to replicate previous results and to test whether the violations of cumulative prospect theory might be eliminated or reduced by using formats for presentation of risky gambles in which cancellation and combination could be facilitated visually. Contrary to the idea that decision behavior contradicting cumulative prospect theory and the priority heuristic would be altered by use of these formats, however, data with two new graphical formats as well as fresh replication data continued to show the patterns of evidence that violate cumulative prospect theory, the priority heuristic, and the editing principles of combination and cancellation. Systematic violations of restricted branch independence also contradicted predictions of “stripped” prospect theory (subjectively weighted additive utility without the editing rules).

We establish bounds for triple exponential sums with mixed exponential and linear terms. The method we use is by Shparlinski [‘Bilinear forms with Kloosterman and Gauss sums’, Preprint, 2016, arXiv:1608.06160] together with a bound for the additive energy from Roche-Newton et al. [‘New sum-product type estimates over finite fields’, Adv. Math.293 (2016), 589–605].

Let $A$ be a unital $C^*$-algebra and for each $n\in\mathbb{N}$ let $M_n$ be the $n\times n$ matrix algebra over $\mathbb{C}$. In this paper we shall give a necessary and sufficient condition that there is a unital $C^*$-algebra $B$ satisfying $A\not\cong B$ but for which $A\otimes M_n\cong B\otimes M_n$ for some $n\in\mathbb{N}\setminus\{1\}$. Also, we shall give some examples of unital $C^*$-algebras satisfying the above property.

AMS 2000 Mathematics subject classification: Primary 46L05