On Weak Solutions of an Integral Equation Driven by a p-Semimartingale of Special Type

We consider the integral equation driven by a standard Brownian motion and by a fractional Brownian motion. Sufficient conditions under which the equation has a weak solution are obtained.     

Exact Confidence Intervals of the Extended Orey Index for Gaussian Processes

In this paper exact confidence intervals for the Orey index of Gaussian processes are obtained using concentration inequalities for Gaussian quadratic forms and discrete observations of the underlying process. The obtained result is applied to Gaussian processes with the Orey index which not necessarily have stationary increments.     

Investigation of intracranial media ultrasonic monitoring model

The objectives are to investigate the peculiarities of the ultrasound pulse propagation through human extra/intracranial media by mathematical simulation and to confirm the simulation results experimentally by proving the suitability of the ultrasonic time-of-flight measurement method for human intracranial media (IM) physiological non-invasive monitoring. The mathematical model of ultrasound pulse propagation through the human extra/intracranial media is described. The simulation of various physiological phenomena were performed to determine the relationship between the characteristics of the transmitted ultrasound pulse through the human head and the acoustic properties of the IM. It is shown that non-invasive monitoring of the IM acoustic properties is possible by measuring the changes of the ultrasonic signal time-of-flight and the oscillation period. The influence made by variations in acoustic parameters of the external tissue/skull bones on the non-invasive measurement data is investigated and methods of compensation of that influence are presented. The models were applied for developing of a new non-invasive sonographic intracranial pressure (ICP) monitor (Vittamed). Comparative studies of this monitor with the invasive ICP monitor (Camino) have shown the possibility of achieving clinically acceptable accuracy of the long term non-invasive ICP monitoring of head injured patients in intensive care units.     

On the rate of convergence in the multidimensional CLT for martingales

Institute of Mathematics and Informatics, Lithuanian Academy of Science. Published in Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 31, No. 4, pp. 633–645, October–December, 1991.     

Modified graphitized carbon black as transducing material for reagentless H2O2 and enzyme sensors

Direct electron transfer between redox enzymes and electrodes is the basis for the third generation biosensors. We established direct electron transfer between quinohemoprotein alcohol dehydrogenase (PQQ-ADH) and modified carbon black (CBs) electrodes. Furthermore, for the first time, this phenomenon was observed for pyrroloquinoline quinone (PQQ)-dependent glucose dehydrogenase (PQQ-GDH). Reagentless enzyme biosensors suitable for the determination of ethanol, glucose and sensors for hydrogen peroxide were designed using CB electrodes and screen-printing technique. Aiming to create an optimal transducing material for biosensors, a set of CB batches was synthesized using the matrix of Plackett-Burman experimental design. Depending on the obtained surface functional groups as well as the nano-scale carbon structures in CBs batches, the maximal direct electron transfer current of glucose and ethanol biosensors can vary from 20 to 300 nA and from 30 to 6300 nA for glucose and ethanol, respectively. Using modified CB electrodes, an electrocatalytic oxidation of H₂O₂ takes place at more negative potentials (0.1-0.4 V versus Ag/AgCl). Moreover, H₂O₂ oxidation efficiency depends on the amount and morphology of fine fraction in the modified CBs.