Publikační činnost Katedry matematiky a deskriptivní geometrie / Publications of Department of Mathematics and Descriptive Geometry (714)

Permanent URI for this collectionhttp://hdl.handle.net/10084/64639

Kolekce obsahuje bibliografické záznamy publikační činnosti (článků) akademických pracovníků Katedry matematiky a deskriptivní geometrie (714) v časopisech registrovaných ve Web of Science od roku 2003 do roku 2018.
Katedra byla zrušena jako celoškolský subjekt a převedena pod 310 - Katedru matematiky a deskriptivní geometrie na Fakultě strojní.
Do kolekce jsou zařazeny:
a) publikace, u nichž je v originálních dokumentech jako působiště autora (adresa) uvedena Vysoká škola báňská-Technická univerzita Ostrava (VŠB-TUO),
b) publikace, u nichž v originálních dokumentech není v adrese VŠB-TUO uvedena, ale autoři prokazatelně v době jejich zpracování a uveřejnění působili na VŠB-TUO.

Bibliografické záznamy byly původně vytvořeny v kolekci Publikační činnost akademických pracovníků VŠB-TUO, která sleduje publikování akademických pracovníků od roku 1990.

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Relationships among coking coals and related cokes characteristics: a statistical evaluation
(Akademie věd České republiky, Ústav struktury a mechaniky hornin, 2018) Serenčíšová, Jana; Klika, Zdeněk; Kolomazník, Ivan; Bartoňová, Lucie; Baran, Pavel
From 61 coking coals, 36 coal blends were prepared. Using a pilot coke oven, cokes were prepared from both 61 coking coals (Type I cokes) and 36 coal blends (Type II cokes). Coals were characterized by 14 coal characteristics and cokes by Coke Reactivity Index CRI and Coke Strength after Reaction with CO2 CSR. For the study of mutual statistic relationships among experimentally determined characteristics of coals and cokes, the Factor (FA) and Regression Analyses (RA) were used. FA distributed characteristics of coals and Type I cokes into 4 factors while characteristics of coal blends and Type II cokes were distributed into 7 factors. In case of pure coals and Type I cokes, strong relationships with high correlation coefficients (R > vertical bar 0.60 vertical bar) were more abundant than in case of coal blends and Type II cokes. FA was used for the selection of coal characteristics that influence the coke quality the most significantly. These characteristics were then recalculated by RA for the predictions of CRI/CSR of Type I cokes. Predictions of CRI/CSR of Type II cokes were calculated from coal blends by the same procedure. The comparison of the predicted and experimentally determined CRI and CSR indexes showed much more reliable prediction of CRI/CSR indexes calculated from coals than calculated from coal blends. This study also explains the dominant reasons of this observation.
A domain decomposition algorithm for contact problems: Analysis and implementation
(EDP Sciences, 2009) Haslinger, Jaroslav; Kučera, Radek; Sassi, T.
The paper deals with an iterative method for numerical solving frictionless contact problems for two elastic bodies. Each iterative step consists of a Dirichlet problem for the one body, a contact problem for the other one and two Neumann problems to coordinate contact stresses. Convergence is proved by the Banach fixed point theorem in both continuous and discrete case. Numerical experiments indicate scalability of the algorithm for some choices of the relaxation parameter.
Asociace vybraných rizikových faktorů s tíží aterosklerotického postižení v karotické bifurkaci
(Česká neurologická společnost ČLS JEP. Česká neurochirurgická společnost ČLS JEP. Slovenská neurologická spoločnosť. Slovenská neurochirurgická spoločnosť. Společnost dětské neurologie ČLS JEP., 2008) Václavík, Daniel; Školoudík, David; Škoda, Ondřej; Praks, Pavel; Axmanová, Kateřina; Vlachová, Ivanka
Kromě tradičních rizikových faktorů aterosklerózy, jako jsou cholesterol, arteriální hypertenze, kouření a diabetes mellitus jsou v posledních letech zkoumány i vlivy dalších faktorů na rozvoj aterosklerózy. Ve své práci jsme se snažili zjistit rozdíly mezi hladinami apolipoproteinu B, homocysteinu, hypersenzitivního CRP (C-reaktivní protein) a lipoproteinu(a) u pacientů s počínajícím aterosklerotickým postižením karotických tepen s přítomnosti pouze aterosklerotických plátů a pacientů s výrazným postižením karotického řečiště – přítomností stenózy vnitřní karotidy nad 50 %. Skupinu č. 1 tvořilo 92 pacientů s aterosklerotickým plátem v karotidách, bez přítomnosti stenózy tepny. Skupinu č. 2 tvořilo 77 pacientů se stenózou karotické tepny nad 50 %. Stupeň postižení karotid byl hodnocen ultrazvukovým vyšetřením. V obou skupinách byly provedeny odběry uvedených faktorů a srovnány mezi sebou s následným provedením lineární regresivní analýzy k posouzení nezávislosti na tradičních rizikových faktorech. Soubory byly srovnávány pomocí Mannova-Whitneyova (Wilcoxonova) W testu. Ve skupině č. 2 jsme nalezli signifikantně vyšší hladiny hypersenzitivního CRP (p = 0,026 ) a apolipoproteinu B (p = 0,00063). Následná lineární regresivní analýza byla provedena pomocí obecného lineární modelu a vyhodnocena ANOVA testem. Analýza ukázala nezávislost apolipoproteinu B i hypersenzitivního CRP na tradičních rizikových faktorech (arteriální hypertenze, věk, kouření, diabetes mellitus). V naší práci byl apolipoprotien B a hypersenzitivní CRP signifikantně vyšší u pacientů se stenotickým postižením karotid ve srovnání s pacienty, kteří měli v karotických tepnách pouze aterosklerotické pláty bez přítomnosti stenózy.
The Society for the Protection of Science and Learning as a patron of refugee mathematicians
(Taylor & Francis, 2015) Nossum, Rolf T.; Kotůlek, Jan
The Society for the Protection of Science and Learning (SPSL, which started out as the Academic Assistance Council (AAC) 1933-36) distinguished itself from many other aid organizations set up in response to Nazi policies towards Jews and political dissidents in its focus on academic excellence as a criterion for support. Its archives are deposited in the Bodleian Library. Today, the organization is known as the Council for At-Risk Academics (CARA, http:// www. cara1933. org/). In the archives of the SPSL, there are files on two and a half thousand scientists, victims of persecution in their home countries, who appealed to the Society for assistance in finding refuge and work in Britain. Almost a hundred are mathematicians, of which about one in four found temporary or permanent employment in British academia. Many others found their way to the US, in most cases aided by the Emergency Committee, an American organization with priorities similar to those of the SPSL. The paths of some of the most successful SPSL grantees are described, and contrasted with those of some less fortunate applicants.
On unbounded solutions of singular IVPs with phi-Laplacian
(Bolyai Institute, University of Szeged and the Hungarian Academy of Sciences, 2017) Rohleder, Martin; Burkotová, Jana; López-Somoza, Lucía; Stryja, Jakub
The paper deals with a singular nonlinear initial value problem with a phi-Laplacian (p(t)phi(u'(t)))' + p(t)f(phi(u(t))) = 0, t > 0, u (0) = u(0)is an element of[L-0, L], u' (0) = 0. Here, f is a continuous function with three roots phi(L-0) < 0 < phi(L), phi : R -> R is an increasing homeomorphism and function p is positive and increasing on (0, infinity). The problem is singular in the sense that p (0) = 0 and 1/p may not be integrable in a neighbourhood of the origin. The goal of this paper is to prove the existence of unbounded solutions. The investigation is held in two different ways according to the Lipschitz continuity of functions phi(-1) and f. The case when those functions are not Lipschitz continuous is more involved that the opposite case and it is managed by means of the lower and upper functions method. In both cases, existence criteria for unbounded solutions are derived.
Uniform motions in central fields
(AIMS, 2017) Swaczyna, Martin; Volný, Petr
We present a theoretical problem of uniform motions, i.e. motions with constant magnitude of the velocity in central fields as a nonholonomic system of one particle with a nonlinear constraint. The concept of the article is in analogy with the recent paper [21]. The problem is analysed from the kinematic and dynamic point of view. The corresponding reduced equation of motion in the Newtonian central gravitational field is solved numerically. Appropriate trajectories for suitable initial conditions are presented. Symmetries and conservation laws are investigated using the concept of constrained Noetherian symmetry [9] and the corresponding constrained Noetherian conservation law. Isotachytonic version of the conservation law of mechanical energy is found as one of the corresponding constraint Noetherian conservation law of this nonholonomic system.
Vermiculite as efficient sorbent of Ce-III and Ce-IV
(CSIRO, 2017) Klika, Zdeněk; Seidlerová, Jana; Kolomazník, Ivan; Hundáková, Marianna
This study focussed on the mechanism of CeIII and CeIV uptake on vermiculite (Ver), which has been studied sporadically. Chemical equilibrium and leaching experiments in acid solutions were evaluated using batch experiments and changes of mineral composition were monitored by X-ray powder diffraction analysis. The concentrations of Ce, Na, K, Ca, Mg, Al and Si were determined by atomic emission spectroscopy coupled with inductively coupled plasma (AES-ICP). The data for CeIII uptake on Ver in neutral aqueous solution were fitted both with adsorption and ion-exchange models. The latter, with a calculated selectivity constant EN16112_IE1.gif = 14.30 (L mmol–1)k–1, showed a better fit with experimental data than adsorption models. The uptake of CeIII on Ver at pH 2 was also controlled by intensive leaching of cations from 2 : 1 layers and therefore these data were not fitted. A much higher uptake of CeIV on Ver (~6 mequiv. g–1, i.e. ~210 mg g–1) at pH 2 and 6 in comparison with the cation-exchange capacity of original vermiculite (1.28 mequiv. g–1) was found and explained. With regard to the different rate of CeIV species fixation on Ver, their different CeIV solubility in NaCl solution, aqueous acid solution (pH 2), and 3 M H2SO4, three species of CeIV bonded on vermiculite are proposed. They are ion-exchanged CeIV, CeIV–complex 1 and CeIV–complex 2. The CeIV species uptake on Ver was quantitatively determined both for pH 2 and 6. The new findings show a very effective method of cerium uptake, especially from acidic aqueous solutions.
Existence and uniqueness of damped solutions of singular IVPs with phi-Laplacian
(Bolyai Institute, University of Szeged and the Hungarian Academy of Sciences, 2016) Burkotová, Jana; Rachůnková, Irena; Rohleder, Martin; Stryja, Jakub
We study analytical properties of a singular nonlinear ordinary differential equation with a phi-Laplacian. In particular we investigate solutions of the initial value problem (p(t)phi(u'(t)))' + p(t)f(phi(u(t))) = 0, u(0) = u(0) is an element of [L-0, L], u'(0) = 0 on the half-line [0, infinity). Here, f is a continuous function with three zeros phi(L0) < 0 < phi(L), function p is positive on (0, infinity) and the problem is singular in the sense that p(0) - 0 and 1/p(t) may not be integrable on [0,1]. The main goal of the paper is to prove the existence of damped solutions defined as solutions u satisfying sup{u(t), t is an element of [0, infinity)} < L. Moreover, we study the uniqueness of damped solutions. Since the standard approach based on the Lipschitz property is not applicable here in general, the problem is more challenging. We also discuss the uniqueness of other types of solutions.
Uptake of Ce(III) and Ce(IV) on montmorillonite
(Elsevier, 2016) Klika, Zdeněk; Seidlerová, Jana; Valášková, Marta; Kliková, Christiana; Kolomazník, Ivan
Montmorillonite (Mt) doped by Ce(III) has good antimicrobial properties and doped by Ce(IV) has high permanent porosity, surface area and catalytic properties. The present study is focused on the mechanismof Ce(III) and Ce(IV) uptake onmontmorillonite in neutral and acid aqueous solutions. Chemical equilibria and leaching experiments in acid solutions were evaluated using batch experiments, changes of mineral structure were monitored by X-ray diffraction (XRD), and Ce uptake onMt surface by scanning electron microscopy (SEM). The concentrations of Ce, Na, K, Ca,Mg, Al, and Siwere determined fromaqueous solutions using atomic emission spectroscopy with Inductively Coupled Plasma (AES-ICP). The isothermfor Ce(III) uptake onMtwere fitted both by adsorption and ion exchange models. The exchange model with the calculated selectivity constant K = 15.2 L/mmolk−1 showed a better fitwith experimental data than adsorptionmodels. The uptake of Ce(III) onMt at pH 2was controlled by ion exchange, accompanied by increasing leaching of cations from 2:1 montmorillonite layers. A high uptake of Ce(IV) on Mt (~ 6 meq/g, i.e. ~ 210 mg/g) at pH 2 and 6 in excess of the cation exchange capacity (0.76 meq/g) was found and explained by the formation of a mixture of two Ce(IV) complexes fixed on Mt; the first was insoluble and the second soluble in 3 M H2SO4 but insoluble in acid aqueous solution at pH 2. A small amount of ion exchanged Ce (IV) (~ 0.27 meq/g) was also determined in samples of Ce(IV)-Mt prepared at pH 2. The Ce(III) and Ce(IV) uptake on Mt at pH 6 reached equilibrium in b30 min, while the uptake of Ce (IV) at pH 2 needed at least 24 h. The new findings show a very effective way for cerium uptake, especially from acidic aqueous solutions.
Bezpečnost karotického stentingu - srovnání protekčních systémů
(Česká neurologická společnost ČLS JEP. Česká neurochirurgická společnost ČLS JEP. Slovenská neurologická spoločnosť. Slovenská neurochirurgická spoločnosť. Společnost dětské neurologie ČLS JEP., 2016) Pavlík, Ondřej; Václavík, Daniel; Kučera, Dušan; Návratová, Jitka; Solná, Gabriela; Rabasová, Marcela
Cíl: Porovnat účinnost a bezpečnost distálního protekčního zařízení (Filtr) s proximální protekcí (Mo.Ma systém) během karotického stentingu (KAS) a potvrdit či vyvrátit nižší výskyt mikroembolizací při použití Mo.Ma systému. Určit efekt mikroembolizací na kognitivní funkce. Metodika: Padesát šest pacientů bylo randomizováno do dvou skupin dle použité protekce (skupina Filtr vs. Mo.Ma). Všichni pacienti podstoupili magnetickou rezonanci (MR) mozku před výkonem a po něm. Třicet dva pacientů podstoupilo revidovaný Adenbrookský kognitivní test (ACE-R) před a měsíc po výkonu. Dále byl sledován výskyt 30denní mortality a morbidity. Výsledky: Nové ischemické léze po KAS byly nalezeny celkem u 32,14 % pacientů (n = 18). Ve skupině Filtr (n = 37) u 32,43 % pacientů (n = 12), ve skupině Mo.Ma (n = 19) u 31,58 % (n = 6; p = 0,4741). Pouze 38,89 % lézí bylo lokalizováno čistě v povodí intervenované tepny, ve skupině Filtr 16,67 % (p = 0,006), ve skupině Mo.Ma 83,33 % (p = 0,037). Signifikantní pokles v ACE-R testu byl zaznamenán jednou. Závěr: Nové ischemické léze po KAS jsme našli v obou sledovaných skupinách, předpokládaný nižší výskyt ve skupině Mo.Ma se nepotvrdil. Ve skupině Filtr bylo signifikantně více lézí lokalizováno mimo povodí intervenované tepny nebo ve více povodích současně. Ve skupině Mo.Ma bylo signifikantně více nových lézí v povodí intervenované tepny. Negativní vliv mikroembolizací na výsledek v ACE-R testech se nám nepodařilo prokázat.
The metrizability problem for Lorentz-invariant affine connections
(World Scientific Publishing, 2016) Urban, Zbyněk; Volná, Jana
The invariant metrizability problem for affine connections on a manifold, formulated by Tanaka and Krupka for connected Lie groups actions, is considered in the particular cases of Lorentz and Poincaré (inhomogeneous Lorentz) groups. Conditions under which an affine connection on the open submanifold R×(R 3 \{(0,0,0)}) of the Euclidean space R 4 coincides with the Levi-Civita connection of some SO(3,1), respectively (R 4 × s SO(3,1)) -invariant metric field are studied. We give complete description of metrizable Lorentz-invariant connections. Explicit solutions (metric fields) of the invariant metrizability equations are found and their properties are discussed. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0219887816501103
Geometric concept of isokinetic constraint for a system of particles
(University of Miskolc, 2013) Swaczyna, Martin; Volný, Petr
The paper deals with the geometric concept of mechanical systems of N particles. The systems are modelled on the Cartesian product R XN and its first jet prolongation J 1.R XN / D R TXN , where X is a 3-dimensional Riemannian manifold with a metric G. The kinetic energy T of the system of N-particles is interpreted by means of the weighted quadratic form NQ G associated with the weighted metric tensor G which arises from the original metric tensor G and the system of N particles m1; : : : ;mN . A requirement for the kinetic energy of the system of N particles to be constant is regarded as a nonholonomic, so-called isokinetic constraint and it is defined as a fibered submanifold T of the jet space R TXN endowed with a certain distribution C called canonical distribution, which has the meaning of generalized admissible displacements of the system of particles subject to the isokinetic constraint. Vector generators of the canonical distribution are found.
On a bicomplex induced by the variational sequence
(World Scientific Publishing, 2015) Krupka, Demeter; Moreno, Giovanni; Urban, Zbyněk; Volná, Jana
The construction of a finite-order bicomplex whose morphisms are the horizontal and vertical derivatives of differential forms on finite-order jet prolongations of fibered manifolds over one-dimensional bases is presented. In particular, relationship between the morphisms and classes entering the variational sequence and the associated finite-order bicomplex is studied. Properties of classes entering the infinite-order bicomplex, induced from the finite-order variational sequences by means of an infinite canonical construction, are formulated as a remark, insisting further research.
Critical evaluation of a new method for quantitative determination of minerals in solid samples
(Wiley-VCH, 2016) Klika, Zdeněk; Kolomazník, Ivan; Matýsek, Dalibor; Kliková, Christiana
The new method for the Chemical Quantitative Mineral Analysis (CQMA) is presented and critically evaluated. The percentages of minerals are calculated of the elemental bulk chemical analysis using identified minerals and their crystallochemical formulas. For this calculation an optimization procedure is used. CQMA enables also the feedback calculation of the bulk chemical analysis from CQMA calculated mineral contents. Subsequent comparison of the feedback calculated bulk chemical analysis and actual bulk chemical analysis of the same sample is used for critical evaluation of the input data. If necessary the input data are completed and/or reanalyzed and used for repeated calculation to achieve better match between the feedback calculated and actual chemical analyses, which consequently leads to more accurate mineral analysis. Moreover the feedback bulk chemical analysis can be also separately calculated from any mineral analyses determined e.g. by XRD, FTIR and/or optical method. Six German rock reference samples representing a very wide range of minerals and chemical composition of materials were selected and their mineral analyses carried out by CQMA and Rietveld X-ray diffraction methods. The results were compared with reference mineral analyses and critically evaluated.
Surface plasmon resonance based sensing of aqueous solutions using spectral interferometry
(Polish Institute of Physics, 2016) Luňáček, Jiří; Hlubina, Petr; Ciprian, Dalibor; Duliaková, Michaela; Luňáčková, Milena
This paper deals with a polarimetric setup to measure the refractive index change of aqueous solutions. The experimental method is based on the surface plasmon resonance effect in the Kretschmann configuration combined with spectral interferometry. In order to retrieve surface plasmon resonance-induced differential phase change, a windowed Fourier transform was adopted to extract the phases from two spectral interferograms, one corresponding to the reference material (air) and the second to the analyte (NaCl aqueous solution). The shift of phase curve is related to the analyte refractive index change. The refractive index of the NaCl aqueous solutions (0, 2 and 5 percent) was measured by the Abbe refractometer at a wavelength of 589.3 nm and compared with theoretical one, calculated by the Lorentz–Lorenz equation. An excellent agreement between the values was confirmed. The resonance wavelengths as extremes of the surface plasmon resonance-induced differential phase changes retrieved from spectral interference signals were compared with the resonance wavelengths determined from spectral reflectance measurements. A good agreement between the values was confirmed.
Mining of protection pillars without subsidence
(Springer, 2015) Hummel, Martin; Hummelová, Ilona; Koudelková, Jaroslava; Černá, Kristýna
The special mining method called as mining without subsidence was used for mining in the protection pillar at the CSM mine in Czech Republic. The room and pillar method with different modification was applied for these reasons. The experience of this pilot project is described in the paper.
Baire classes of complex L-1-preduals
(Springer, 2015) Ludvík, Pavel; Spurný, Jiří
Let X be a complex L 1-predual, non-separable in general. We investigate extendability of complex-valued bounded homogeneous Baire-α functions on the set ext B X* of the extreme points of the dual unit ball B X* to the whole unit ball B X*. As a corollary we show that, given α ∈ [1, ω 1), the intrinsic α-th Baire class of X can be identified with the space of bounded homogeneous Baire-α functions on the set ext B X* when ext B X* satisfies certain topological assumptions. The paper is intended to be a complex counterpart to the same authors’ paper: Baire classes of non-separable L 1-preduals (2015). As such it generalizes former work of Lindenstrauss and Wulbert (1969), Jellett (1985), and ourselves (2014), (2015).
On the existence and properties of three types of solutions of singular IVPs
(Bolyai Institute, University of Szeged and the Hungarian Academy of Sciences, 2015) Burkotová, Jana; Rohleder, Martin; Stryja, Jakub
The paper studies the singular initial value problem (p(t)u 0 (t))0 + q(t)f(u(t)) = 0, t > 0, u(0) = u0 ∈ [L0, L] , u 0 (0) = 0. Here, f ∈ C(R), f(L0) = f(0) = f(L) = 0, L0 < 0 < L and x f(x) > 0 for x ∈ (L0, 0) ∪ (0, L). Further, p, q ∈ C [ 0, ∞ ) are positive on (0, ∞) and p(0) = 0. The integral R 1 0 ds p(s) may be divergent which yields the time singularity at t = 0. The paper describes a set of all solutions of the given problem. Existence results and properties of oscillatory solutions and increasing solutions are derived. By means of these results, the existence of an increasing solution with u(∞) = L (a homoclinic solution) playing an important role in applications is proved.
Lower and upper functions in a singular Dirichlet problem with o-Laplacian
(Elsevier, 2015) Rachůnková, Irena; Stryja, Jakub
The paper investigates the Dirichlet problem with ø-Laplacian of the form $(\varphi (u'))' + f(t,u,u') = 0,u(0) = u(T) = 0.$ An existence principle which can be used for problems where f(t, x, y) may have singularities at t = 0, t = T and also at x = 0, y = 0, is proved here. As an application of this principle, new conditions that guarantee the solvability of the above problem are found.
Multivariate statistical assessment of coal properties
(Elsevier, 2014) Klika, Zdeněk; Serenčíšová, Jana; Kožušníková, Alena; Kolomazník, Ivan; Študentová, Soňa; Vontorová, Jiřina
A set of 42 coal samples consisting of coal blends prepared for coking (subset A-blends) and lump coal from coal seams (subset B-single coals) was subjected to multicomponent statistical analysis. For these samples, the study determined their structural properties (total intrusion volume TIV, total pore area TPA, bulk density BD, average pore diameter APD, and porosity PS), proximate characteristics (moisture Wa, ash content Ad and volatile matter Vdaf), ultimate characteristics (total sulfur content Sd and carbon content Cd), coal maceral characteristics (reflectance of vitrinite Rr, vitrinite Vitr, inertinite Inert and liptinite Lipt) and coking properties (contraction a, dilation b and swelling index SI). Using factor analysis (FA), 3 factors were separated. These include the most important coal characteristics with significant mutual correlations. The distribution of the entire set of 42 samples was performed by principal components analysis (PCA) and hierarchical clustering (HC). The coal samples were divided into two clusters, numbered I and II. Cluster I completely matched the samples included in subset A (blends), while cluster II matched the samples in subset B (single coals). A basic statistical evaluation of the investigated properties in both clusters I and II was performed, including correlation and regression analyses. Based on the results of FA, the reduced number of 9 relevant characteristics was selected. These were then gradually reduced from 9 to 3; HC separations were calculated for each of them. It was found that almost the same differentiation of 42 samples into clusters I and II (corresponding to blends and single coals, respectively) can be calculated using only 7 instead of the original 16 properties. These properties are TPA, Ad, Vdaf, Rr, Vitr, Lipt and b.

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