Teresa Rajba

Wireless sensor networks in application to patients health monitoring

This work presents an application of Wireless Sensor Network (WSN) of random access with one-way transmission to the monitoring of hospital patients. In the paper, we consider WSN single-hop network using one single radio frequency, such that all nodes are divided into several groups depending on the average time between the transmission due to the different state of health of patients. We apply the Poisson Arrivals See Time Averages (PASTA) to modeling of WSN. We present formula for the probability of collisions which has been verified by simulation studies of network.

Functions Generating Strongly Schur-Convex Sums

The notion of strongly Schur-convex functions is introduced and functions generating strongly Schur-convex sums are investigated. The results presented are counterparts of the classical Hardy–Littlewood–Polya majorization theorem and the theorem of Ng characterizing functions generating Schur-convex sums. It is proved, among others, that for some (for every) n≥2, the function F(x 1,…,x n )=f(x 1)+⋯+f(x n ) is strongly Schur-convex with modulus c if and only if f is of the form f(x)=g(x)+a(x)+c∥x∥2, where g is convex and a is additive.

On Some Recent Applications of Stochastic Convex Ordering Theorems to Some Functional Inequalities for Convex Functions: A Survey

This is a survey paper concerning some theorems on stochastic convex ordering and their applications to functional inequalities for convex functions. We present the recent results on those subjects.

Muirhead inequality for convex orders and a problem of I. Raşa on Bernstein polynomials

We present a new, very short proof of a conjecture by I. Ra\c{s}a, which is an inequality involving basic Bernstein polynomials and convex functions. It was affirmed positively very recently by J. Mrowiec, T. Rajba and S. W\k{a}sowicz (2017) by the use of stochastic convex orderings, as well as by Abel (2017) who simplified their proof. We give a useful sufficient condition for the verification of some stochastic convex ordering relations, which in the case of binomial distributions are equivalent to the I. Ra\c{s}a inequality. We give also the corresponding inequalities for other distributions. Our methods allow us to give some extended versions of stochastic convex orderings as well as the I. Ra\c{s}a type inequalities. In particular, we prove the Muirhead type inequality for convex orderings for convolution polynomials of probability distributions.

Research of time characteristics of search methods of inverse element by the module

The method for finding inverse element by the module is based on the stepwise addition of residue is developed in this paper. This method allows avoiding performing the complex arithmetic operations and implementing calculations on numbers much lower bit compared to the classical approach based on the Euclids algorithm and its consequences. Analytical expressions of time complexity characteristics are obtained and their graphic depending is built. Software and hardware modules of specified methods on the basis of environment of the development AldecActive-HDL 9.1 are implemented and studies of their temporal characteristics that point to the advantages of the proposed method are conducted.

Development of simulator automated dispatch control system for implementation in learning process

Article deals with the automated dispatch control system (ADCS) is designed to improve the reliability and efficiency of operational dispatch and process control facilities that are part of the power system. ADCS is a set of hardware and information of the software used in the dispatching management of energy facilities based on computer. The proposed model of simulator ADCS and automated system commercial electric power accounting (ASCEA) allows to study the principles of functional tasks, structure, hardware and software of the ADCS of power networks and power consumption. The automated system was developed at the Department of power consumption systems and computer technology in the power industry. The system includes a model simulator substation, standard functional devices (telemechanics, a system of automated energy accounting) and a computer with appropriate software.

Wireless sensor networks with randomized parameters

In this paper we present a model of single-hop type wireless sensor network with random access and oneway transmission. In the paper, we analyze the WSN single-hop network using one single radio frequency, such that all nodes are divided into several groups depending on the average time between the transmissions. We replaced deterministic number of nodes in groups by random variables. We apply the Poisson Arrivals See Time Averages (PASTA) to modeling the WSN. We present the formula for the collision probability in the new model. The purpose of this approach is to match better the network model with random access to real world applications. In the paper we present an application of Wireless Sensor Network with random access and one-way transmission to monitoring hospital patients, such that all nodes are divided into several groups depending on the average time between the transmission due to the different state of health of patients.

The implementation of wireless sensor networks for environmental monitoring of water facilities

In the paper we present original solution for remote monitoring of water facilities using wireless sensor networks. We present both the mathematical model of the sensor network and the results of computer simulation.

Extremal measures with prescribed moments

Abstract In the approximate integration some inequalities between the quadratures and the integrals approximated by them are called extremalities . On the other hand, the set of all quadratures is convex. We are trying to find possible connections between extremalities and extremal quadratures (in the sense of extreme points of a convex set). Of course, the quadratures are the integrals with respect to discrete measures and, moreover, a quadrature is extremal if and only if the associated measure is extremal. Hence the natural problem arises to give some description of extremal measures with prescribed moments in the general (not only discrete) case. In this paper we deal with symmetric measures with prescribed first four moments. The full description (with no symmetry assumptions, and/or not only four moments are prescribed and so on) is far to be done.

Моделювальні дослідження випадкового керування доступом в безпровідній сенсорній мережі

У статті представлено результати дослідження роботи мережі БСМ з випадковим керуванням доступом, використовуючи систему PASTA (середнє значення за час спостереження надходження пуассонівського потоку). Наведено результати моделювальних тестувань ефективності функціонування мережі для двох випадків: 1) коли всі вузли мережі передають протоколи з тим самим середнім часом між передачами, 2) якщо вузли мережі поділено на групи, які мають різні середні часи між передачами. Цей підхід має багато практичних переваг, які висвітлено у статті.