Let K be a convex body in the Euclidean space Rn, n ≥ 2, equipped with its standard inner product 〈·, ·〉 and Euclidean norm | · |. Consider K as a probability space equipped with its uniform (normalized Lebesgue) measure μ. We are interested in k-dimensional marginals of μ, that is, the push-forward μ◦P−1 E of μ by the orthogonal projection PE onto a k-dimensional subspace E ⊂ Rn. The question ...

Tässä kriittisessä esseessä luon yleiskatsauksen koulutuksen digitaalisen datafikaation erilaisiin muotoihin ja merkityksiin erityisesti kotimaisessa kontekstissa. Esseessä käyn läpi suhdetta muihin koulutusta ohjaaviin trendeihin, digitalisaatioon, oppimiskeskeisyyteen tulosvastuullisuuteen. Lisäksi tarkastelen datan diskursiivisen tuottamisen välistä epäsuhtaa, josta jatkan koulun dataintensi...

For stationary ergodic diffusions satisfying nonlinear homogeneous Itô stochastic differential equations, this paper obtains the Berry–Esseen bounds on rates of convergence to normality distributions quasi maximum likelihood estimators based Taylor approximation, under some regularity conditions, when diffusion is observed at equally spaced dense time points over a long interval, high-frequency...

convexity theory and duality theory are important issues in math- ematical programming. within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. finally,...

in this paper the bagley-torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. the results reveal that the present method is very effective and accurate.

A Chernoff-type distribution is a nonnormal defined by the slope at zero of greatest convex minorant two-sided Brownian motion with polynomial drift. While known to appear as distributional limit in many nonregular statistical estimation problems, accuracy approximations has remained largely unknown. In present paper, we tackle this problem and derive Berry–Esseen bounds for distributions canon...

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...