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An operator-based approach for the construction of closed-form solutions to fractional differential equations is presented in this paper. The technique is based on the analysis of Caputo and Riemann-Liouville algebras of fractional power series. Explicit solutions to a class of linear fractional differential equations are obtained in terms of Mittag-Leffler and fractionally-integrated exponential functions in order to demonstrate the viability of the proposed technique.

The generalization of the classical Korteweg-de-Vries (KdV) solitary wave solution is presented in this paper. The amplitude and the propagation speed of generalized KdV solitary waves vary in time. Generating partial differential equations and conditions of existence of the generalized KdV solitary waves are derived using the inverse balancing method. Computational experiments illustrate the variety of new solitary solutions and their generating equations.

Hypotension is type of secondary insult and it is related to poor outcome. The ability to predict adverse hypotensive events, where a patient's arterial blood pressure drops to abnormally low levels, would be of major benefit to the fields of primary and secondary health care. The aim of the paper is to present the novel method for predicting of acute hypotensive episodes, based on ECG analysis by the complex system theory approach. 45 patients (in four neurointensive care facilities throughout Europe) data were selected for the analysis. 11 patients had EUSIG-defined hypotensive events. The method includes determining of time varying biomarkers corresponding to plurality of physiological processes in patient's organism as a non-linear dynamic complex system and generating an acute hypotension prediction classifier. The calculations of biomarkers are based on complex system approach and algebraic matrix analysis of ECG parameters. The classifier is based on the comparison of biomarkers behaviour in 3D images. It is demonstrated that the presented method allows us to predict arterial hypotension events 40-50 minutes ahead with a sensitivity of 81 %, specificity 94 %. This result was obtained from prospective real-time data collection in a live clinical intensive care environment.

The imitation model of bursty and batch data packet flow is presented in this paper. The proposed imitation model was created using the convolution of Mooreand Mealy automata., Telekomunikacinių sistemų sėkmingam funkcionavimo aprašymui ypač daug reikšmės turi įvairios duomenų srautų charakteristikos. Todėl aktualu turėti minėtų srautų analizines išraiškas. Kadangi analiziniai modeliai arba yra ganėtinai sudėtingi, arba iš viso jų neįmanoma bendresniu atveju sudaryti, tai imitacinis modeliavimas galbūt vienintelis įmanomas sudėtingesnių srautų tyrimo metodas. Vienas iš telekomunikacinių sistemų tyrimo uždavinių – turėti patogų vartotojui neordinarinio pliūpsninio srauto imitacinį modelį, kad, gautas duomenų imtis apdorojus statistiniais paketais, būtų galima naudoti toliau tirti telekomunikacines sistemas. Taigi straipsnyje pasiūlytas neordinarinio pliūpsninio paraiškų srauto imitacinis modelis, sudarytas naudojant Muro ir Milio automatų sąsūką.

The conditions when solutions of Huxley equation can be expressed in special form and the procedure of finding exact solutions are presented in this paper. Huxley equation is an evolution equation that describes the nerve propagation in biology. It is often useful to obtain a generalized solitary solution for fully understanding its physical meanings. It is shown that the solution produced by the Exp-function method may not hold for all initial conditions. It is proven that the analytical condition describing the existence of the produced solution in the space of initial conditions (or even in the space of the system's parameters) can not be derived by the Exp-function method because the question about the existence of that solution is omitted. The proposed operator method, on the contrary, brings the load of symbolic computations before the structure of the solution is identified. The method for the derivation of the solution is based on the concept of the rank of the Hankel matrix constructed from the sequence of coefficients representing formal solution in the series form. Moreover, the structure of the algebraic-analytic solution is generated automatically together with all conditions of the solution's existence. Computational experiments are used to illustrate the properties of derived analytical solutions.

Tyrimo tikslas — nustatyti duomenų grupavimo metodo panaudojimo galimybę Tepingo testo metu. Vertinant centrinės nervų sistemos (CNS) darbingumo ir funkcinės būklės rodiklius, plačiai taikomas Tepingo testas. Duomenys registruojami naudojant specialias kompiuterines programas, sukurtas Lietuvos kūno kultūros akademijos (LKKA) Kineziologijos laboratorijoje pagal Ukrainos kūno kultūros universiteto mokslininkų parengtą CNS funkcinės būklės ir darbingumo rodiklių vertinimo metodiką. Kompiuterinės tyrimų programos pateikia normalizuotas registruojamų rodiklių reikšmes — CNS darbingumo ir funkcinės būklės rodiklius: CNS paslankumo, asimetrijos, nuovargio, bendrojo darbingumo, anaerobinio darbingumo ir anaerobinio darbo talpos reikšmes. Buvo ištirta 10 sportuojančių asmenų, kurių amžius 17—25 metai. Tyrimai atlikti LKKA Kineziologijos laboratorijoje. Visi tiriamieji atliko klasikinį 60 sekundžių trukmės Tepingo testą, milisekundėmis matuojant laiko intervalus tarp atskirų judesių. Tepingo testo duomenų grupavimas atliktas Kauno technologijos universiteto Taikomosios matematikos katedroje. Duomenų grupavimo metodas naudojamas tyrimo duomenų tarpusavio panašumams ir skirtumams analizuoti. Turint duomenų seką — vadinamąją laiko eilutę (matuojant milisekundėmis), po atskiro kompiuterio klaviatūros spustelėjimo atliekamas Tepingo testas. Iš jų galime sudaryti informatyviuosius vektorius, t. y. atlikti duomenų grupavimą. Skaičiavimai atliekami priklausomai nuo to, kokios informacijos... [toliau žr. visą tekstą] Finger Tapping Test and other performance based tests are widely used in the assessment of the functional state of the central nervous system. The aim of the study was to assess the Tapping Test data by method of nonlinear dimensional reduction (by grouping them to various components). The study was performed in the Laboratory of Human Kinetics at the Lithuanian Academy of Physical Education. The finger movements data were registered by using a special computer program, created in the laboratory of Kinesiology, Lithuanian Academy of Physical Education. The subjects of the study were 10 athletes aged 12—25 years. All the subjects did a classical 60 seconds Finger Tapping Test, and the time intervals of each finger movement were recorded in milliseconds. All the subjects took part in two investigations: before and after an exhausting training session. The method of nonlinear dimensional reduction of data was created in Kaunas University of Technology in the Department of Applied Mathematics. The results obtained during the study showed that the correlation index helped to get new information about the peculiarities of the central nervous system of the subjects, actualizing the motor acts, and we could also compare different experimental groups. In conclusion we can to point out that the method of nonlinear dimensional reduction allows us to obtain new information about the peculiarities of functioning of the central nervous system. The most sensitive changes can be obtained in... [to full text]