Extending the work of [7] on groups definable in compact complex manifolds and of [1] on strongly minimal groups definable in nonstandard compact complex manifolds, we classify all groups definable in nonstandard compact complex manifolds showing that if G is such a group then there are a linear algebraic group L, a definably compact group T , and definable exact sequence 1→ L → G → T → 1.

We give an overview of the F–product construction and the corresponding nonstandard constructions and show that (in the case of bounded ultrapowers) both constructs are isomorphic (theorem 3.15). From this we also follow a little “classical” corollary (3.14). The nonstandard construction has been investigated in [Wol84] and [Wol], the corresponding classical constructions first appeared in [Der...

Using techniques of nonstandard analysis Abraham Robinson showed that it is possible to represent each Schwartz distribution T as an integral T () = R f, where f is some nonstandard smooth function. We show that the theory based on this representation can be developed within a constructive setting.

We give a survey of the study of nonstandard models in recursion theory and reverse mathematics. We discuss the key notions and techniques in effective computability in nonstandard models, and their applications to problems concerning combinatorial principles in subsystems of second order arithmetic. Particular attention is given to principles related to Ramsey’s Theorem for Pairs.

We rederive a form of Joachims’ ξα method for tuning Support Vector Machines by the same approach as was used to derive the GACV, and show how the two methods are related. We generalize the ξα method to the nonstandard case of nonrepresentative training set and unequal misclassification costs and compare the result to the GACV estimate for the standard and nonstandard cases.

Using Nonstandard Analysis, we will provide a rigorous computation for the harmonic oscillator Feynman path integral. The computation will be done without having prior knowledge of the classical path. We will see that properties of classical physics falls out naturally from a purely quantum mechanical point of view. We will assume that the reader is familiar with Nonstandard Analysis.

We investigate order-theoretic properties of the nonstandard real line, by isolating the basic order-types involved, and the possible relations among them. We focus on order-isomorphisms between the infinitesimals, the infinites, and the whole hyperreal line. We also compute the main cardinal invariants of the order-topology of the nonstandard real line.

BACKGROUND Theoretical models on shift work fall short of describing relevant health-related pathways associated with the broader concept of nonstandard working schedules. Shift work models neither combine relevant working time characteristics applicable to nonstandard schedules nor include the role of rest periods and recovery in the development of health complaints. Therefore, this paper aime...