Magnitude is a numerical invariant of compact metric spaces, originally inspired by category theory and now known to be related to myriad other geometric quantities. Generalizing earlier results in $\ell _1^n$ and Euclidean space, we prove an upper bound for the magnitude of a convex body in a hypermetric normed space in terms of its Holmes–Thompson intrinsic volumes. As applications of this bound, we give short new proofs of Mahler’s conjecture in the case of a zonoid and Sudakov’s minoration inequality.

The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often misunderstood text, dealing with the status of infinite divisibility in nature, rather than in mathematics. In line with this distinction, we offer a reading of the fictionality of infinitesimals. The letter has been claimed to support a reading of infinitesimals according to which they are logical fictions, contradictory in their definition, and thus absolutely impossible. The advocates of such a reading have lumped infinitesimals with infinite wholes, which are rejected by Leibniz as contradicting the part–whole principle. Far from supporting this reading, the letter is arguably consistent with the view that infinitesimals, as inassignable quantities, are mentis fictiones, i.e., (well-founded) fictions usable in mathematics, but possibly contrary to the Leibnizian principle of the harmony of things and not necessarily idealizing anything in rerum natura. Unlike infinite wholes, infinitesimals—as well as imaginary roots and other well-founded fictions—may involve accidental (as opposed to absolute) impossibilities, in accordance with the Leibnizian theories of knowledge and modality.

Upper German dialects make heavy use of diminutive strategies, but little is known about the actual conceptual effects of those devices. This paper is the first to present two large-scale psycholinguistic experiments that investigate this issue in East Franconian, a dialect spoken in Bavaria. Franconian uses both the diminutive suffix -la and the quantifying construction a weng a lit. ‘a little bit a’ to modify noun phrases. Our first experiment shows that diminutization has no effect on conceptualization of magnitude: People do not think of a smaller/weaker/shorter etc. referent when the NP is modified by the morphological diminutive, the quantifying construction, or their combination. The second experiment involves gradable NPs and shows that, again, the morphological diminutive has no effect on how people conceptualize the degree to which a gradable nominal predicate holds; in contrast, a weng a reduces it significantly. These experiments suggest that diminutization does not have uniform effects across semantic domains, and our results act as a successful example of extending the avenue of cognitive psychology into dialectology with the active participation of a speaker community.*

The aim of this paper is to show that attention to Kant’s philosophy of mathematics sheds light on the doctrine that there are two stems of the cognitive capacity, which are distinct, but equally necessary for cognition. Specifically, I argue for the following four claims: (i) The distinctive structure of outer sensible intuitions must be understood in terms of the concept of magnitude. (ii) The act of sensibly representing a magnitude involves a special act of spontaneity Kant ascribes to a capacity he calls the productive imagination. (iii) Contrary to what is assumed by many commentators, it is not the case that the Two Stems Doctrine implies that a representation is either sensible or spontaneity-dependent, but not both. (iv) Outer sensible intuitions are both sensible and spontaneity-dependent – they are sensible because they exhibit the kind of structure Kant takes to be distinctive of outer sensible intuitions, and they depend on spontaneity because they are cases of sensibly representing a magnitude.

Discrimination between quarry blasts and earthquakes has gained importance due to signature of the Comprehensive Test Ban Treaty. In this context, large chemical explosions are significant. In the routine analysis of data from local seismograph networks, discrimination between smaller blasts and micro-earthquakes is not always clear. Many quarries are in operation and blasts far outnumber natural earthquakes in the highly industrialized northern Rhine area.

We compiled a list of active quarries in the Northern Rhine Area and mapped their locations. We then created a database from a questionnaire sent out to all quarries on the list. From the 33% of questionnaires that were returned, we discerned some representative values for the main blasting parameters and explosive consumption. In the study area of 72,000 km2, approx. 21,000 blasts are fired per year (80 per working day). Most of the blasts (72%) have total explosive charges between 400 and 4500 kg. Shots with charges above 10 tons are rare (20-30 per year). Some 80% of the blasts are ripple-fired with a nominal firing time interval of 20 ms.

Based on empirical amplitude vs. distance curves from vibration control measurements, a relation between maximum charge weight per delay time, L (kg), and a ‘quarry blast’ magnitude, MQB, is derived: MQB = 0.6·log10(L) + 0.131. Using this relation and extrapolating the database from the questionnaire shows that for magnitudes between 1 and 2, blasts occur 200–250 times more frequently than micro-earthquakes in the Northern Rhine area.

We present GalevNB (Galev for N-body simulations), an utility that converts fundamental stellar properties of N-body simulations into observational properties using the GALEV (GAlaxy EVolutionary synthesis models) package, and thus allowing direct comparisons between observations and N-body simulations. It converts the fundamental stellar properties of N-body simulations, i.e., stellar mass, temperature, stellar luminosity and metallicity, into observational magnitudes for a variety of filters of widely used instruments/telescopes (HST, ESO, SDSS, 2MASS), and into spectra that span from far-UV (90 Å) to near-IR (160 μm).

We report on GalevNB (Galev for N-body simulations), an integrated software solution that provides N-body users direct access to the software package GALEV (GALaxy EVolutionary synthesis models). GalevNB is developed for the purpose of a direct comparison between N-body simulations and observations. It converts the fundamental stellar properties of N-body simulations, i.e., stellar mass, temperature, stellar luminosity and metallicity, into observational magnitudes for a variety of filters of widely used instruments/telescopes (HST, ESO, SDSS, 2MASS), and into spectra that span from far-UV (90 Å) to near-IR (160 μm).

Four discrete issues demonstrate how complex the crime of aggression under the Rome Statute of the International Criminal Court will be following the amendments approved in Kampala in June 2010. First, the absence of an explicit magnitude, or gravity, requirement for determining an act of aggression ignores the reality of how matters are referred to the ICC as well as how one first determines the existence of aggression. The gravity test of a crime of aggression is insufficient and misleading in arriving at a methodology for a logical determination of both acts and crimes of aggression. An agreed understanding in Kampala to resolve the dilemma is fraught with contradictions. Second, the amendments fail to address how the ICC should respond to a Security Council determination that an act of aggression has not occurred. Third, the lingering debate over how the Rome Statute should have been amended to activate the crime of aggression will burden the Assembly of States Parties, which should focus on arriving at a united interpretation of the procedures used to approve the Kampala amendments. Fourth, given the many permutations of how states will fall within or outside the jurisdiction of the International Criminal Court regarding the crime of aggression, the resulting patchy landscape of coverage should surprise no one.

It is not possible for persons within and between the many disciplines involved in disasters to communicate with each other without clear definitions of the specific terms that are used. In many instances, the same terms have different meanings in different disciplines. Thus, a standardized set of definitions is provided in this chapter and in the associated Glossary of Terms. Some definitions discussed in this Chapter include: (1) disaster; (2) medical disaster; (3) hazard; (4) risk; (5) prevention; (6) modification; (7) event (including onset, duration, amplitude, intensity, scale, and magnitude); (8) impact; (9) mitigation; (10) preparedness; (11) damage; (12) vulnerability; (13) resilience; (14) absorbing capacity; (15) buffering capacity; (16) disaster management; (17) response; and (18) recovery. An annotated, comprehensive set of definitions is provided in the Glossary of Terms in these Guidelines.

Establishing the magnitude and frequency of floods within upland catchments on the basis of short-term gauged runoff records is crucially dependent upon the extent to which the record is truly representative. In the case of the River Dee, upstream of Crathie in Aberdeenshire, gauged discharge records are limited in length. Although the middle Dee has been gauged since 1929, the gauge within the upper catchment has only ten years of record. Thus, reliable estimates of the return intervals of extreme floods for this part of the Dee can only be obtained by using a variety of historical sources to extend the flood series.

Long-term rainfall records, where available, provide a valuable independent check on the reconstructed flood series. Such rainfall records, when analysed in terms of the magnitude, frequency and duration of major events, should, in general terms, correspond with the flood series. In this paper, the recurrence interval of extreme rainfalls of varying magnitude and duration in upper Deeside is estimated by extreme value analysis of the annual maximum series. The frequency of rainfall events above varying thresholds is also assessed. The existence of climatic fluctuations giving highly variable recurrence intervals for rainfall events of the same magnitude is demonstrated. Finally, the seasonality of frequent flood-producing storms is analysed. Patterns observed within the rainfall record are compared with those previously established within the historic flood series to substantiate and augment the flood record.