Holonomy groups of stable vector bundles

We define the notion of holonomy group for a stable vector bundle F on a variety in terms of the Narasimhan-Seshadri unitary representation of its restriction to curves. Next we relate the holonomy group to the minimal structure group and to the decomposition of tensor powers of F. Finally we illustrate the principle that either the holonomy is large or there is a clear geometric reason why it should be small

Numerical Stability Analysis in Respiratory Control System Models

Stability of the unique equilibrium in two mathematical models (based on chemical balance dynamics) of human respiration is examined using numerical methods. Due to the transport delays in the respiratory control system these models are governed by delay differential equations. First, a simplified two-state model with one delay is considered, then a five-state model with four delays (where the application of numerical methods is essential) is investigated. In particular, software is developed to perform linearized stability analysis and simulations of the model equations. Furthermore, the Matlab package DDE-BIFTOOL v. 2.00 is employed to carry out numerical bifurcation analysis. Our main goal is to study the effects of transport delays on the stability of the model equations. Critical values of the transport delays (i.e., where Hopf bifurcations occur) are determined, and stable periodic solutions are found as the delays pass their critical values. The numerical findings are in good agreement with analytic results obtained earlier for the two-state model

Dynamics of delayed piecewise linear systems

In this paper the dynamics of the controlled pendulum is investigated assuming backlash and time delays. The upper equilibrium of the pendulum is stabilized by a piecewise constant control force which is the linear combination of the sampled values of the angle and the angular velocity of the pendulum. The control force is provided by a motor which drives one of the wheels of the cart through an elastic teeth belt. The contact between the teeth of the gear (rigid) and the belt (elastic) introduces a nonlinearity known as "backlash" and causes the oscillation of the controlled pendulum around its upper equilibrium. The processing and sampling delays in the determination of the control force tend to destabilize the controlled system as well. We obtain conditions guaranteeing that the pendulum remains in the neighborhood of the upper equilibrium. Experimental findings obtained on a computer controlled inverted pendulum cart structure are also presented showing good agreement with the simulation results

SEMI-NORMAL LOG CENTRES AND DEFORMATIONS OF PAIRS

We show that some of the properties of log canonical centres of a log canonical pair also hold for certain subvarieties that are close to being a log canonical centre. As a consequence, we obtain that, in working with deformations of pairs where all the coefficients of the boundary divisor are bigger than 1/2, embedded points never appear on the boundary divisor

Neighborhoods of subvarieties in homogeneous spaces

We study the holomorphic/meromorphic function theory and the fundamental group of Euclidean open neighborhoods of compact subvarieties in homogeneous spaces; building on results of Hironaka, Hartshorne, Napier and Ramachandran in the ample normal bundle case

Deformations of elliptic Calabi–Yau manifolds

We investigate deformations and characterizations of elliptic Calabi-Yau varieties, building on earlier works of Wilson and Oguiso. We show that if the second cohomology of the structure sheaf vanishes, then every deformation is again elliptic. More generally, all non-elliptic deformations derive from abelian varieties or K3 surfaces. We also give a numerical characterization of elliptic Calabi-Yau varieties under some positivity assumptions on the second Todd class. These results lead to a series of conjectures on fibered Calabi-Yau varieties

GAMIFICATION IN EDUCATION: CHANGING THE ATTITUDE OF MEDICAL STUDENTS TOWARDS DEMENTIA BY USING VIRTUAL REALITY (PILOT STUDY)

The aim of the study was to change the attitudes of medical students towards elderly people with dementia in a positive way and to raise awareness of the importance of studying dementia in the elderly by using virtual reality tools. Hungarian (n = 20) and foreign (n = 20) medical students could experience what it would be like to be an elderly, demented person for 5 minutes by using a virtual reality application. Before and after the experiment, they completed a questionnaire and expressed their opinion on a Likert scale (0-6 points). The evaluation was made by using the Wilcoxon signed-rank test. The attitude of foreign and Hungarian medical students changed significantly in a positive way regarding the importance of studying dementia in the elderly (Z = 18, p < 0.078 and Z = 7.5, p < 0.187 respectively), judging the difficulty of lives of elderly people with dementia (Z = 20, p < 0.0078 and Z = 27.5, p < 0.002 respectively), judging their empathy for elderly people with dementia (Z = 32, p < 0.00112 and Z = 55.5, p < 0.0005 respectively), understanding thinking of elderly people with dementia (Z = 79 p < 0.0001 and Z = 59, p < 0.026 respectively), regarding the likelihood of taking steps to prevent their own dementia (Z = 27.5 p < 0.002 and Z = 27.5, p < 0.002 respectively). The study demonstrated the importance and the effectiveness of applying virtual reality tools in educating medical students