Jumping numbers of a simple complete ideal in a two-dimensional regular local ring

The multiplier ideals of an ideal in a regular local ring form a family of ideals parametrized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.

Describing syntax with star-free regular expressions

Koskenniemen Äärellistilaisen leikkauskieliopin (FSIG) lauseopilliset rajoitteet ovat loogisesti vähemmän kompleksisia kuin mihin niissä käytetty formalismi vittaisi. Osoittautuukin että vaikka Voutilaisen (1994) englannin kielelle laatima FSIG-kuvaus käyttää useita säännöllisten lausekkeiden laajennuksia, kieliopin kuvaus kokonaisuutenaan palautuu äärelliseen yhdistelmään unionia, komplementtia ja peräkkäinasettelua. Tämä on oleellinen parannus ENGFSIG:n descriptiiviseen kompleksisuuteen. Tulos avaa ovia FSIG-kuvauksen loogisten ominaisuuksien syvemmälle analyysille ja FSIG kuvausten mahdolliselle optimoinnillle. Todistus sisältää uuden kaavan, joka kääntää Koskenniemien rajoiteoperaation ilman markkerimerkkejä.

Colours as Non-Verbal Signs on Packages

Colour is an essential aspect of our daily life, and still, it is a neglected issue within marketing research. The main reason for studying colours is to understand the impact of colours on consumer behaviour, and thus, colours should be studied when it comes to branding, advertising, packages, interiors, and the clothes of the employees, for example. This was an exploratory study about the impact of colours on packages. The focus was on low-involvement purchasing, where the consumer puts limited effort into the decision-making. The basis was a scenario in which the consumer faces an unpredictable problem needing immediate action. The consumer may be in hurry, which indicate time pressure. The consumer may lack brand preferences, or the preferred brand may be out of stock. The issue is that the choice is to be made at the point of purchase. Further, the purchasing involves product classes where the core products behind the brands are indistinguishable from each other. Three research questions were posed. Two questions were answered by conjoint analysis, i.e. if colours have an impact on decision-making and if a possible impact is related to the product class. 16 hypothetical packages were designed in two product classes within the healthcare, i.e. painkillers and medicine against sore throats. The last research question aimed at detecting how an analysis could be carried out in order to understand the impact of colours. This question was answered by conducting interviews that were analysed by applying laddering method and a semiotics approach. The study found that colours do indeed have an impact on consumer behaviour, this being related to the context, such as product class. The role of colours on packages was found to be threefold: attention, aesthetics, and communication. The study focused on colours as a means of communication, and it proposes that colours convey product, brand, and product class meanings, these meanings having an impact on consumers’ decision-making at the point of purchase. In addition, the study demonstrates how design elements such as colours can be understood by regarding them as non-verbal signs. The study also presents an empirical design, involving quantitative and qualitative techniques that can be used to gain in depth understanding of the impact of design elements on consumer behaviour. Hannele Kauppinen is associated with CERS, the Centre for Relationship Marketing and Service Management of the Swedish School of Economics and Business Administration