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Large deviations for Brownian bridges with prescribed terminal densities

100%

Saize S. , Yang X.

Probability and Mathematical Statistics

2023

tom Vol. 43, Fasc. 1

141--154

We consider a family of Brownian bridges (depending on some small parameter) over a finite time interval whose initial position is deterministically fixed, and whose terminal position possesses a prescribed density. Large deviations for this family are studied with the help of the Girsanov transformation.

Ke dvojznačnosti kvantovacích sloves a recipročních výrazů v konstrukcích s násobnými číslovkami

63%

Veselý V.

Naše řeč (Our Speech)

2023

tom 106

nr 4

195-226

The paper presents an analysis of two types of syntactic constructions: constructions with a quantized verb like zaklepat ‘knock’ and a quantifier like dvakrát ‘twice’ on the one hand and constructions with reciprocals like navštívit se (vzájemně) ‘visit each other’ and a quantifier like dvakrát ‘twice.’ Both of these syntactic construction types display a similar ambiguity: for instance, dvakrát zaklepat ‘to knock twice’ means either ‘to make two knocks’ or ‘to make two series of knocks’ while dvakrát se vzájemně navštívit means either ‘to make two visits’ or ‘to make four visits (two and two),’ with the former senses being instances of “internal” quantification (what is quantified is part of the meaning of the quantized verb and the reciprocal, but it cannot be directly expressed with it). Through this analysis a group of conditions has been identified which arguably have to be met so that the ambiguity could arise: 1. The denotation of the predicate can be divided into separate actions. If reciprocals like navštívit se (vzájemně) ‘to visit (each other)’ are considered autonomous verbs (i.e. not syntactic constructions), then it is the case that: 2. The separate actions can be expressed with a verb which is a base for the respective quantized verb or the reciprocal verb in a derivational sense; 3. The verb is syntactically intransitive. A general condition for the observed ambiguity is an interaction of two quantifiers. It can be assumed that when an “external” quantification is opted for, i.e., sets of events are counted, the quantification carried out by the quantized verb or by the reciprocal usually happens before the quantification related to a quantifier like dvakrát ‘twice.’

The Unstable Behaviour of Reciprocally Rotating Shafts in Textile Machines

63%

Zajączkowski J.

Fibres & Textiles in Eastern Europe

2007

tom Vol. 15, no. 3 (62)

102--104

The stability of the reciprocal rotary motion of a motor-driven elastic shaft is studied in this paper. It is found that unstable critical behaviour arises when the average value of the second power of angular velocity is close to the second power of the circular frequency of natural vibrations.

Analizowano stabilność ruchu wirowego, o zmiennym kierunku wirowania, elastycznych wałów maszyn włókienniczych napędzanych silnikiem elektrycznym. Stwierdzono, że krytycznym warunkiem przejścia pracy wału w stan niestabilny jest zbliżenie średniej wartości kwadratu prędkości kątowej do kwadratu częstotliwości kołowej.