The Method and the Results of the Direct Comparison of the Laser Interferometers Renishaw Xl-80

The method of the direct comparison of the laser interferometers and method processing of the interferometry measurement results by the least square method (LSM) is present. The additive part of the measurement error for each pair of the interferometers is evaluated and the multiplicative part of the measurement error for each interferometer is evaluated too by LSM. Uncertainty by A tape by LSM is evaluated for all parameters. Results of the comparison of the three interferometers are presented.

Hypernear-rings with a defect of distributivity

Since in a near-ring the distributivity holds just on one side (left or right), it seems naturally to study the behaviour and properties of the set of elements that ?correct? the lack of distributivity, in other words that elements that assure the validity of the distributivity. The normal subgroup of the additive structure of a near-ring generated by these elements is called a defect of distributivity of the near-ring. The purpose of this note is to initiate the study of the hypernear-rings (generalizations of near-rings, having the additive part a quasicanonical hypergroup) with a defect of distributivity, making a comparison with similar properties known for near-rings.

One-generated semirings and additive divisibility

We study the structure of one-generated semirings from the symbolical point of view and their connections to numerical semigroups. We prove that such a semiring is additively divisible if and only if it is additively idempotent. We also show that every at most countable commutative semigroup is contained in the additive part of some one-generated semiring.

Modeling Noncompensatory Choices With a Compensatory Model for a Product Design Search

Market-based product design has typically used compensatory models that assume a simple additive part-worth rule. However, marketing literature has demonstrated that consumers use various heuristics called noncompensatory choices to simplify their choice decisions. This study aims to explore the suitability of compensatory modeling of these noncompensatory choices for the product design search. This is motivated by the limitations of the existing Bayesian-based noncompensatory mode, such as the screening rule assumptions, probabilistic representation of noncompensatory choices, and discontinuous choice probability functions in the Bayesian-based noncompensatory model. Results from using compensatory models show that noncompensatory choices can lead to distinct segments with extreme part-worths. In addition, the product design search problem suggests that the compensatory model would be preferred due to small design errors and inexpensive computational burden.