An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs

We propose a new algorithm for computing validated bounds for the solutions to the first order variational equations associated to ODEs. These validated solutions are the kernel of numerics computer-assisted proofs in dynamical systems literature. The method uses a high-order Taylor method as a predictor step and an implicit method based on the Hermite-Obreshkov interpolation as a corrector step. The proposed algorithm is an improvement of the $C^1$-Lohner algorithm proposed by Zgliczy\'nski and it provides sharper bounds. As an application of the algorithm, we give a computer-assisted proof of the existence of an attractor set in the R\"ossler system, and we show that the attractor contains an invariant and uniformly hyperbolic subset on which the dynamics is chaotic, that is, conjugated to subshift of finite type with positive topological entropy.Comment: 33 pages, 11 figure

Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems

We propose a general framework for computer-assisted verification of the presence of symmetry breaking, period-tupling and touch-and-go bifurcations of symmetric periodic orbits for reversible maps. The framework is then adopted to Poincar\'e maps in reversible autonomous Hamiltonian systems. In order to justify the applicability of the method, we study bifurcations of halo orbits in the Circular Restricted Three Body Problem. We give a computer-assisted proof of the existence of wide branches of halo orbits bifurcating from $L_{1,2,3}$-Lyapunov families and for wide range of mass parameter. For two physically relevant mass parameters we prove, that halo orbits undergo multiple period doubling, quadrupling and third-order touch-and-go bifurcations.Comment: 36 pages, 9 Figure

The Effect of Structure Modification of Sodium Compounds on the SO2 and HCl Removal Efficiency from Fumes in the Conditions of Circulating Fluidised Bed

The article presents the effects of mechanical and thermal modification on the surface area of sodium bicarbonate and its ability to remove SO2 and HCl from exhaust fumes. The mechanical modification consisted of grinding in an impact mill. The thermal modification consisted of heating in the temperature range from 373 K to 673 K. The applied modifications caused a change in the grain structure of sodium bicarbonate and parameters such as specific surface area and the pore size. The parameters were determined by low-pressure nitrogen adsorption (LPNA) and mercury porosimetry (MIP) methods. The largest development of the active surface, which was up to 6 m2 g–1 (LPNA), was achieved after crushing and heating in the temperature range of 423–523 K. The efficiency of a simultaneous purification of fumes from SO2 i HCl on a continuous-combustion installation with a circular fluidised bed CFB was determined. The samples were fed into the installation in three different molar ratios 2Na/S (0.5; 1.0; 2.1) in a gas jet of 573 K. It was shown that the removal of SO2 and HCl took place simultaneously and mainly on the grain surface. The average efficiency of SO2 purification was between 17 % and 89 %, and it depended on the comminution degree and the amount of the sorbent. The efficiency of HCl removal was between 54 and 78 %. This work is licensed under a Creative Commons Attribution 4.0 International License

Reclamation of reactive metal oxides from complex minerals using alkali roasting and leaching- an improved approach to process engineering

In nature, the commonly occurring reactive metal oxides of titanium, chromium, aluminium, and vanadium often chemically combine with the transition metal oxides such as iron oxides and form complex minerals. Physico-chemical separation of transition metal oxides from the remaining reactive metal oxides is therefore an important step in the purification of reactive oxide constituents. Each purification step has quite a high energy requirement at present. Current practice in industry yields sulphate and neutralized chloride waste from titanium dioxide enrichment, red mud from bauxite refining, slag and leach residues from vanadium extraction and chromite ore process residue (COPR) from chromate processes. In this review article, a novel alkali-based oxidative roasting and aqueous leaching for the extraction of mineral oxides is explained in the context of the original work of Le Chatelier in 1850, which was unsuccessful in the industrialization of bauxite processing for alumina extraction. However, much later in the 19th century the alkali-based oxidative mineral roasting was successfully developed for industrial scale manufacturing of chromate chemicals, which yields COPR. The crystal chemistry of mineral oxides, namely alumina, titanium dioxide, and chromium oxide in naturally occurring minerals is briefly reviewed in the context of chemical extraction, which is then developed as a model for developing thermodynamic chemical equilibrium principles for analyzing the physical separation and enrichment of such reactive metal oxides by forming water-soluble and water-insoluble alkali complexes. The involvement of the alkali roasting chemistry of non-magnetic titaniferous mineral waste is also reported in the initial separation of rare-earth oxide mixtures for subsequent separation of individual oxides. The paper concludes with a generic approach to process chemistry which minimizes waste generation and therefore helps in reducing the overall process and energy costs. Examples of recovering alkali from high pH solution using carbon dioxide are also demonstrated

Anatomia funkcjonalna ośrodkowego układu nerwowego cz.1.

Central nervous system (CNS) seems to be the most sophisticated system of the human body. Its proper functioning requires enough blood supply. The development of CNS starts very early in the foetal life. The neural tube and the neural crest are formed from ectoderm in the third week of the foetal life. The brain, the spinal cord and the peripheral nerves develop from these structures. Physiologists describe three functional brain levels, that is – spinal, lower and higher cerebral. The spinal cord is considered to be the first and the oldest phylogenetic functional part of CNS. Its work is reflexive and automatic, thus enabling a quick reaction to a stimulus. The lower brain level consists mainly of subcortical centres – the hypothalamus and the thalamus. Both of them are responsible for homeostasis. The cerebral cortex is the highest brain level. It integrates all kinds of stimuli, movement planning and the development of learning. The cerebrum provides the proper motor coordination and the sense of balance. Vasomotor, respiratory centres and the nucleus of cerebral nerves are located in the brain stem. It also contains reticular formation, which modulates pain sensation and is responsible for the maintenance of the proper level of consciousness

Professional exposure's frequency on potenionally contagious material among te staff of the th 5 Military Clnical Hospital in Cracow

Wstęp: Personel medyczny, w szczególny sposób narażony jest na ryzyko ekspozycji zawodowej na krew i potencjalnie infekcyjny materiał. Działania profilaktyczne oraz właściwe postępowanie poekspozycyjne minimalizuje ryzyko zakażenia, w wyniku zdarzenia niepożądanego.Cel pracy: Ocena częstości występowania ekspozycji zawodowej na materiał potencjalnie zakaźny wśród personelu 5 Wojskowym Szpitalu Klinicznym z Polikliniką. Materiał i metody: Analizowano dokumentację medyczną, natomiast źródłem informacji była Indywidualna Karta Ekspozycji Zawodowej na krew lub inny infekcyjny materiał zakaźny. Badaniem objęto wszystkie zgłoszone przypadki, które miały miejsce w latach 2013-2016 w 5 Wojskowym Szpitalu Klinicznym z Polikliniką w Krakowie.Wyniki: Najliczniej ekspozycji zawodowej ulegały kobiety- 70,8 %, w tym pielęgniarki 50%. Najczęściej ekspozycja zawodowa miała miejsce na Bloku Operacyjnym (N=23, tj. 24%), w godzinach 7-19.- 81,3%. Zabieg/ operacja oraz pobieranie materiału do badań (21,9%) to czynności, które były obarczone największym ryzykiem ekspozycji zawodowej. Ekspozycja ewidentna miała miejsce w 72,9 %. Pracownicy służby zdrowia najczęściej byli narażeni na zakażenie Wirusem HCV, w 13 przypadkach odnotowano wynik badania p/c anty HCV dodatni. Nie stwierdzono, by w badanym okresie doszło do zakażenia personelu medycznego.Wnioski: W 5 Wojskowym Szpitalu Klinicznym, w latach 2013-2016 odnotowano wzrost częstości zgłaszania ekspozycji zawodowej przez pracowników. Badania wykazały, że personel medyczny najczęściej eksponowany był poprzez zakłucie igłą, a materiałem potencjalnie infekcyjnymi była krew.Introduction: Medical personnel are particularly exposed to the risk of occupational exposure to blood and potentially infectious material. Preventive actions and proper post-exposure procedures minimize the risk of infection as a result of an adverse event.Aim of the study: To assess the frequency of occupational exposure to potentially infectious material among staff of the 5th Military Clinical Hospital with a Polyclinic.Material and methods: Medical documentation was analyzed, while the source of information was the Individual Occupational Exposure Card for blood or other infectious infectious material. The study covered all reported cases that took place in 2013-2016 at the 5th Military Clinical Hospital with the Polyclinic in Krakow.Results: The largest number of occupational exposures were women - 70.8%, including nurses 50%. The most common occupational exposure took place on the Operational Block (N = 23, ie 24%), from 7-19 hours - 81.3%. The treatment / operation and the collection of material for examinations (21.9%) are activities that were burdened with the highest risk of occupational exposure. The evident exhibition took place at 72.9%. Health workers were most often exposed to HCV infection, in 13 cases the result of the p / c anti HCV positive test was recorded. In the examined period, it would not be detected that the medical personnel were infected.Conclusions: In the 5th Military Clinical Hospital, in 2013-2016 an increase in the frequency of professional exposure by employees was noted. Studies have shown that medical personnel were most often exposed through needle sticking, and potentially infectious material was blood