相关论文: When is a quantity additive, and when is it extens…

The problems of conditional entropy's definition and the formula to compute conditional entropy are analyzed from various perspectives, and the corrected computing formula is presented. Examples are given to prove the conclusion that…

Problems in additive number theory related to sum and difference sets, more general binary linear forms, and representation functions of additive bases for the integers and nonnegative integers.

This note is about using computational effects for scalability. With this method, the specification gets more and more complex while its semantics gets more and more correct. We show, from two fundamental examples, that it is possible to…

In this paper, we investigate two-parameter entropies and obtain some conditions for their extensivity. By using a generalized $(k,r)-product$, correlations for subsystems are related to the joint probabilities, so that the entropy remains…

Expressions with an aspectual variant of a light verb, e.g. 'take on debt' vs. 'have debt', are frequent in texts but often difficult to classify between verbal idioms, light verb constructions or compositional phrases. We investigate the…

This is a survey article on the recent developments of semipositivity, injectivity, and vanishing theorems for higher-dimensional complex projective varieties.

We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of…

It is plausible that quantum gravity effects may lead us to a description of Nature beyond the framework of special relativity. In this case, either the relativity principle is broken or it is maintained. These two scenarios (a violation or…

We treat the classical notion of convexity in the context of hard real analysis. Definitions of the concept are given in terms of defining functions and quadratic forms, and characterizations are provided of different concrete notions of…

Starting from a small number of well-motivated axioms, we derive a unique definition of sums with a noninteger number of addends. These "fractional sums" have properties that generalize well-known classical sum identities in a natural way.…

If a compact closed category has finite products or finite coproducts then it in fact has finite biproducts, and so is semi-additive.

We introduce the notion of a definable category--a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are…

Argumentation is an important topic of AI for modelling and reasoning about arguments. In abstract argumentation, we consider directed graphs, so-called argumentation frameworks (AF), that express conflicts between arguments. The semantics…

We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more…

After some general remarks about the interrelation between philosophical and statistical thinking, the discussion centres largely on significance tests. These are defined as the calculation of $p$-values rather than as formal procedures for…

We formulate and explore two basic axiomatic systems of typefree subjective probability. One of them explicates a notion of finitely additive probability. The other explicates a concept of infinitely additive probability. It is argued that…

Two models of integral theory based on the concept of a differential as a certain infinitesimal quantity are considered. One theory treats an infinitesimal quantity as a zero-tending sequence. The second is as an infinitesimal Hyper-real.

In this article we introduce associative Look-Up Tables. With their help, pseudo sums are correctly determined. The set of limit distributions in a pseudo-summation scheme of i.i.d. random variables is described. Also, two special cases…

We review some aspects of theories with compact extra dimensions. We consider the motivation and the theoretical basis of Large, Universal and Warped Extra Dimensions. We focus on those aspects that are potentially relevant in the…

The tension between qualitative theorizing and quantitative methods is pervasive in the social sciences, and poses a constant challenge to empirical research. But in science studies as an interdisciplinary specialty, there are additional…