We explore a more general class of soft supersymmetry-breaking masses and interactions than that usually considered, both in general and in the MSSM context, where our results for the one-loop β-functions correct some errors in the literature. We identify a new class of one-loop finite supersymmetric theories.

In addition to ordinary words and names, real text contains non-standard “words” (NSWs), including numbers, abbreviations, dates, currency amounts and acronyms. Typically, one cannot find NSWs in a dictionary, nor can one find their pronunciation by an application of ordinary “letter-to-sound” rules. Non-standard words also have a greater propensity than ordinary words to be ambiguous with resp...

Positively graded algebras are fairly natural objects which are arduous to be studied. In this article we query quotients of non-standard graded polynomial rings with combinatorial and commutative algebra methods.

The presen t s tudy examines the s eman t i c problems involved in comput ing the meaning of the non s tandard uses of if. The cen t r a l ques t ion is whe the r or not it is necessary to in t roduce d i f f e r en t meanings of if. Austin proposed two non s tandard meanings for if. We show that these can be accoun ted for by the s t andard meaning t oge the r with shi f ts in the posi t ion o...

Noises: a nonstandard analysis. Thanks to the nonstandard formalization of fast oscillating functions, due to P. Cartier and Y. Perrin, an appropriate mathematical framework is derived for new non-asymptotic estimation techniques, which do not necessitate any statistical analysis of the noises corrupting any sensor. Various applications are deduced for multiplicative noises, for the length of t...

The study sets out to examine the achievements Junior Secondary Schools students in essay writing in French using activity based and lecture methods. It adopts the quasi experimental research design. A French achieving test for junior secondary school III was used for data collection, it was analysed using mean, standard deviation and analysis of covariance. It eventually comes out with the vie...

We describe how non-standard analysis can be used to prove real analysis theorems, and how these proofs can be automated using proof-planning. In particular we borrow from the constructive analysis notions of inductive partitioning, and show how transferring to the non-standard model for the reals allows us a simple proof of the correctness of partitioning algorithms for certain real analysis t...

A large variety of supervised or unsupervised learning algorithms is based on a metric or similarity measure of the patterns in input space. Often, the standard euclidean metric is not sufficient and much more efficient and powerful approximators can be constructed based on more complex similarity calculations such as kernels or learning metrics. This procedure is benefitial for data in euclide...