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Almost homoclinics for nonautonomous second order Hamiltonian systems by a variational approach
PublikacjaW artykule badamy problem istnienia rozwiązań prawie homoklinicznych dla nieautonomicznych układów Hamiltona w R^n z potencjałem V(t,x) postaci -1/2(L(t)x,x)+W(t,x) oraz zaburzeniem f(t) (ang. forcing term) z L^2. Zakładamy, że L jest funkcją ciągłą z prostej w zbiór macierzy kwadratowych nxn taką, że macierze L(t) są symetryczne i dodatnio określone jednostajnie względem zmiennej t. Potencjał W(t,x) jest klasy C^1 i nadkwadratowy...
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Homoclinic solutions for a class of the second order Hamiltonian systems
PublikacjaW niniejszej pracy badamy istnienie orbit homoklinicznych dlaukładu Hamiltonowskiego drugiego rzędu: q^{..} + V_{q}(t,q) = f(t), gdzie V z iloczynu kartezjańskiego R x R^{n} do R jest postaciV(t,q) = -K(t,q) + W(t,q). Zakładamy, ze V jest T-okresowe ze względuna zmienną t, K spełnia tzw. ''pinching'' warunek, W jest superliniowew nieskończoności, a norma f w L^{2} jest wystarczająco mała.Orbitę homokliniczną takiego układu znajdujemy...
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Charge density wave and large nonsaturating magnetoresistance in YNiC2 and LuNiC2
PublikacjaWe report a study of physical properties of two quasi-low-dimensional metals YNiC2 and LuNiC2 including the investigation of transport, magnetotransport, galvanomagnetic, and specific heat properties. In YNiC2 we reveal two subsequent transitions associated with the formation of weakly coupled charge density wave at TCDW=318K and its locking in with the lattice at T1=275K. These characteristic temperatures follow the previously...
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Novel amides of mycophenolic acid and some heterocyclic derivatives as immunosuppressive agents
PublikacjaThe group of new amide derivatives of mycophenolic acid (MPA) and selected heterocyclic amines was synthesised as potential immunosuppressive agents functioning as inosine-5'-monophosphate dehydrogenase (IMPDH) uncompetitive inhibitors. The synthesis employed uronium-type activating system (TBTU/HOBt/DIPEA) while or phosphonic acid anhydride method (T3P/Py) facilitating amides to be obtained in moderate to excellent yields without...
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Products of Photo- and Thermochemical Rearrangement of 19-Membered di-tert-Butyl-Azoxybenzocrown
PublikacjaThe preparation and characterization of products of the photochemical and thermochemical rearrangements of 19-membered azoxybenzocrowns with two, bulky, tert-butyl substituents in benzene rings in the para positions to oligooxyethylene fragments (meta positions to azoxy group, i.e., t-Bu-19-Azo-O have been presented. In photochemical rearrangement, two colored typical products were expected, i.e., 19-membered o-hydroxy-m,m′-di-tert-butyl-azobenzocrown...
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Reactivity of Phosphanylphosphinidene Complex of Tungsten(VI) toward Phosphines: A New Method of Synthesis of catena-Polyphosphorus Ligands
PublikacjaThe reactivity of an anionic phosphanylphosphinidene complex of tungsten(VI), [(2,6-i-Pr2C6H3N)2(Cl)- W(η2-t-Bu2P=P)]Li·3DME toward PMe3, halogenophosphines, and iodine was investigated. Reaction of the starting complex with Me3P led to formation of a new neutral phosphanylphosphinidene complex, [( 2,6-i-Pr2C6H3N)2(Me3P)W(η2-t-Bu2P=P)]. Reactions with halogenophosphines yielded new catena-phosphorus complexes. From reaction with...
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A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions
PublikacjaIn this paper we discuss a topological treatment for the planar system z' = f (t, z) + g(t, z) where f and g are T -periodic in time and g(t, z) is bounded. Namely, we study the effect of g(t, z) in two different frameworks: isochronous centers and time periodic systems having subharmonics. The main tool employed in the proofs consists of a topological strategy to locate fixed points in the class of orientation preserving embedding...
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The reactivity of 1,1-dichloro-2,2-di-tert-butyldiphosphane towards lithiated metal carbonyls: a new entry to phosphanylphosphinidene dimers
PublikacjaReactions of [Cp*(OC)3M]Li (Cp* = C5Me5, M = Mo, W) towards t-Bu2P–PCl2 lead to the formation of phosphanylphosphinidene dimers [Cp*(OC)3M(η2-t-Bu2P–P)]2 in fairly good yields. The formation of a tetraphosphorus ligand proceeds via reductive dimerization of t-Bu2P–P units. NMR, X-ray investigations and DFT calculations show that the resulting tetraphosphorus ligand has a structure of dication t-Bu2P+=P–P=P+t-Bu2.
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Almost homoclinic solutions for the second order Hamiltonian systems
PublikacjaW niniejszej pracy badam istnienie rozwiązań prawie homoklinicznych (almost homoclinic) dla układu Hamiltona rzędu drugiego (układu Newtona): ü(t) + V_{u}(t,u) = f(t), gdzie t є R, u є R^{n}, V(t,u) = -K(t,u) + W(t,u), K,W: R x R^{n} → R są klasy C^{1}, K spełnia warunek ''pinching'', W_{u}(t,u)=o(|u|), gdy |u| → 0 jednostajnie względem t, f: R → R^{n} jest funkcją ciągłą, niezerową i odpowiednio małą w L^{2}(R,R^{n}). Przy tych...
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Super Dominating Sets in Graphs
PublikacjaIn this paper some results on the super domination number are obtained. We prove that if T is a tree with at least three vertices, then n2≤γsp(T)≤n−s, where s is the number of support vertices in T and we characterize the extremal trees.
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Isolation Number versus Domination Number of Trees
PublikacjaIf G=(VG,EG) is a graph of order n, we call S⊆VG an isolating set if the graph induced by VG−NG[S] contains no edges. The minimum cardinality of an isolating set of G is called the isolation number of G, and it is denoted by ι(G). It is known that ι(G)≤n3 and the bound is sharp. A subset S⊆VG is called dominating in G if NG[S]=VG. The minimum cardinality of a dominating set of G is the domination number, and it is denoted by γ(G)....
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Study of nanomechanical properties of (1-y)BST-yMgO thin films
PublikacjaIn the present study thin films of MgO – modified Ba0.6Sr0.4TiO3 (BST60/40) solid solution were prepared by the sol-gel-type chemical solution deposition method on stainless steel substrates. A multilayer spin-coating approach was utilized for the Ba0.6Sr0.4TiO3-MgO thin film deposition with subsequent thermal annealing at T=650-750C. Dried BST60/40-MgO gel powders were studied with thermogravimetric and differential thermal analysis...
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T-SL, T-SLF i T-DSATUR - nowe heurystyki dla problemu przydziału częstotliwości
PublikacjaNiniejszy artykuł poświęcony został algorytmom T-SL, T-SLF i T-DSATUR - nowym heurystykom dla problemu przydziału częstotliwości. Zawiera opis algorytmów, omówienie ich teoretycznych własności oraz wyniki testów komputerowych, którym zostały poddane.
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Interpolation properties of domination parameters of a graph
PublikacjaAn integer-valued graph function π is an interpolating function if a set π(T(G))={π(T): T∈TT(G)} consists of consecutive integers, where TT(G) is the set of all spanning trees of a connected graph G. We consider the interpolation properties of domination related parameters.
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Evaluation of a PCR Melting Profile method for intra-species differentiation of Trichophyton rubrum and Trichophyton interdigitale
PublikacjaW celu identyfikacji źródła infekcji spowodowanych przez dermatofity, jak i drogi ich transmisji, istnieje potrzeba szukania nowych metod, które pozwolą na głębokie zróżnicowanie genetyczne szczepów w obrębie rodzaju. W pracy po raz pierwszy pokazano zastosowanie techniki PCR MP opartej o adaptory oligonukleotydowe i różnice w temperaturze topnienia fragmentów restrykcyjnych DNA w reakcji PCR do wewnątrzgatunkowego typowania dermatofitów....
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Design, synthesis and high antitumor potential of new unsymmetrical bisacridine derivatives towards human solid tumors, specifically pancreatic cancers and their unique ability to stabilize DNA G-quadruplexes
PublikacjaNew promising unsymmetrical bisacridine derivatives (UAs), have been developed. Three groupsincluding 36 compounds were synthesized by the condensation of 4-nitro or 4-methylacridinone, imi-dazoacridinone and triazoloacridinone derivatives with 1-nitroacridine compounds linked with anaminoalkyl chain. Cytotoxicity screening revealed the high potency of these compounds against severaltumor cell lines. Particularly, imidazoacridinone-1-nitroacridine...
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Cubane Like Structure of a Silanethiol Primary Amine Assembly a Novel, Unusual Hydrogen Bond Pattern.
PublikacjaMetodą rentgenowskiej analizy strukturalnej wyznaczono struktury krystaliczne i cząsteczkowe trzech soli amoniowych: (t-BuO)3SiS(-)H3N(+)Bu-t, (i-PrO)3SiS(-)H3N(+)Bu-t i (t-BuO)3SiS(-)H3N(+)(CH2)2CH(CH3)2. Wszystkie trzy związki w ciele stałym tworzą tetramery w których atomy S i N wyznaczają w przybliżeniu naroża sześcianu. Trwałość tych agregatów, oprócz sił elektrostatycznego przyciągania, zapewnia sieć wiązań wodorowych N-H
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Parity vertex colouring of graphs
PublikacjaA parity path in a vertex colouring of a graph is a path along which each colour is used an even number of times. Let Xp(G) be the least number of colours in a proper vertex colouring of G having no parity path. It is proved that for any graph G we have the following tight bounds X(G) <= Xp(G) <=|V(G)|− a(G)+1, where X(G) and a(G) are the chromatic number and the independence number of G, respectively. The bounds are improved for...
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Recovery of silver metallization from damaged silicon cells
PublikacjaMetallization is one of the key process steps to fabricate solar cells with high performance in a cost-effective way. Majority of photovoltaic solar cell manufacturing uses thick film screen print metallization with Ag containing paste to produce solar cells. The average lifetime of PV modules can be expected to be more than 25 years. The disposal of PV systems will become a problem in view of the continually increasing production...
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New Alternative Passive Networks to Improve the Range Output Voltage Regulation of the PWM Inverters
PublikacjaThis paper presents different topologies of buck-boost converters with passive input networks that have alternative topologies; this is known in the literature as a Z-source inverter. Alternative passive networks were named by the authors as T-inverters; these improve output voltage regulation of the PWM inverters. T-inverter has fewer reactive components in comparison to conventional Z-source inverter. The most significant advantage...
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Subarachnoid Space: New Tricks by an Old Dog
PublikacjaPurpose: The purpose of the study was to: (1) evaluate the subarachnoid space (SAS) width and pial artery pulsation in both hemispheres, and (2) directly compare magnetic resonance imaging (MRI) to near-infrared transillumination/backscattering sounding (NIR-T/BSS) measurements of SAS width changes in healthy volunteers.Methods: The study was performed on three separate groups of volunteers, consisting in total of 62 subjects (33...
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New type T-Source inverter
PublikacjaThis paper presents different topologies of voltage inverters with alternative input LC networks. The basic topology is known in the literature as a Z-source inverter (ZSI). Alternative passive networks were named by the authors as T-sources. T-source inverter has fewer reactive components in comparison to conventional Z-source inverter. The most significant advantage of the T-source inverter (TSI) is its use of a common voltage...
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A lower bound on the double outer-independent domination number of a tree
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D, and the set V(G)D is independent. The double outer-independent domination number of a graph G, denoted by gamma_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We...
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Frequency and phase analysis of daily reprocessed solutions from selected EPN stations relating to geological phenomena,
PublikacjaThe main assumption of this research was to check and verify the behaviour of a few EPN (European Permanent Network) stations on both sides of the Teisseyre-Tornquist zone (T-T zone), which is located on Polish territory and crosses Poland almost in half. The selected EPN stations’ time series were a subject of frequency and phase analysis. The main purpose of the research was to verify if there is any correspondence between stations...
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Intermetallic disordered magnet Gd2Pt1.1Ge2.9 and its relation to other AlB2 -type compounds
PublikacjaThe intermetallic germanide Gd 2 Pt 1.1 Ge 2.9 was synthesized using an arc-melting method. The crystal structure was characterized using powder x-ray diffraction, revealing a disordered ternary AlB 2 -type structure (space group P 6 / m m m , No. 191) with lattice parameters a = 4.2092 ( 1 ) Å and c = 4.0546 ( 2 ) Å . Physical properties were investigated by magnetic susceptibility and heat capacity measurements, which...
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Fabrication of La-Doped Bi4Ti3O12 Ceramics
PublikacjaLa-modified Bi4Ti3O12 is a typical ferroelectric, piezoelectric and electro-optic material, having relatively low coercive field, low dielectric constant, high Curie temperature and high breakdown strength. Goal of the present research was to apply mixed oxide method for fabrication of BiTLax ceramics, study its chemical composition, crystalline structure and microstructure. The compound BiTLax for x=0, 0.25, 0.5, 0.75 ceramic...
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Numerical analysis of CO2-water separation in a horizontal double T-junction
PublikacjaCarbon dioxide is considered one of the main factors leading to global warming. Considering the significant impacts of CO2 on climate change, various technologies have been developed in recent decades to control carbon emission, such as for example CO2 capture and storage. The developed cycle of a negative CO2 emission power plant includes some devices, out of which, separator plays an indispensable role. To this end, T-junction...
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Limiting distribution of the three-state semi-Markov model of technical state transitions of ship power plant machines and its applicability in operational decision-making.
PublikacjaThe article presents the three-state semi-Markov model of the process {W(t): t 0} of state transitions of a ship power plant machine, with the following interpretation of these states: s1 – state of full serviceability, s2 – state of partial serviceability, and s3 – state of unserviceability. These states are precisely defined for the ship main engine (ME). A hypothesis is proposed which explains the possibility of application...
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Analysis of Interspike-Intervals for the General Class of Integrate-and-Fire Models with Periodic Drive
PublikacjaWe study one-dimensional integrate-and-fire models of the general type x˙=F (t, x) and analyze properties of the firing map which iterations recover consecutive spike timings. We impose very week constraints for the regularity of the function F (t, x), e.g. often it suffices to assume that F is continuous. If additionally F is periodic in t, using mathematical study of the displacement sequence of an orientation preserving circle...
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Inline Waveguide Filter With Compact Frequency-Dependent Coupling Producing Two Additional Poles and Three Transmission Zeros
PublikacjaThis work reports a compact frequency-dependent coupling (FDC) structure introduced in a rectangular waveguide, which allows to generate two additional in-band transmission poles and three transmission zeros (TZs). This serves to increase the order/selectivity of the waveguide bandpass filter in a compact inline topology, thus without the need for any additional space/volume or cross coupling. The proposed FDC consists of a partial-height...
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Bounds on the vertex-edge domination number of a tree
PublikacjaA vertex-edge dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every edge of $G$ is incident with a vertex of $D$ or a vertex adjacent to a vertex of $D$. The vertex-edge domination number of a graph $G$, denoted by $\gamma_{ve}(T)$, is the minimum cardinality of a vertex-edge dominating set of $G$. We prove that for every tree $T$ of order $n \ge 3$ with $l$ leaves and $s$ support vertices we have $(n-l-s+3)/4...
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An investigation on the chemistry of the R2P=P ligand: reactions of a phosphanylphosphinidene complex of tungsten(VI) with electrophilic reagents
PublikacjaThe nucleophilic properties of the title compound [(2,6-i-Pr2C6H3N)2(Cl)W(η2-t-Bu2PvP)]Li·3DME (1) were investigated in reactions with selected electrophilic reagents such as MeI, M(CO)5THF (M = Cr, Mo, W), AlCl3, and GaCl3. Methylation of 1 by MeI yields phosphanylphosphido complexes [(2,6-i-Pr2C6H3N)2W(X)(1,2-η-t-Bu2PvP–CH3)] (X = Cl, I) (2-Cl/2-I) with the formation of a new P–C bond. Moreover, 1 reacts with electrophilic compounds...
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IgG Avidity Test as a Tool for Discrimination between Recent and Distant Toxoplasma gondii Infection—Current Status of Studies
PublikacjaToxoplasma gondii, an obligate intracellular protozoan parasite, is the causative agent of one of the most prevalent zoonoses worldwide. T. gondii infection is extremely important from a medical point of view, especially for pregnant women, newborns with congenital infections, and immunocompromised individuals. Thus, an accurate and proper diagnosis of this infection is essential. Among the available diagnostic tests, serology...
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Adaptive fuzzy modelling and control for discrete-time nonlinear uncertain systems
PublikacjaReferat przedstawia metodę adaptacyjnego rozmytego modelowania i sterowania dla nieliniowego systemu dyskretnego z niepewnością. Proponowana metoda adaptacyjna składa się z dwóch części: rozmyte modelowanie on-line z zastosowaniem systemu Takagi - Sugeno (T-S) oraz sterowanie adaptacyjne z modelem referencyjnym. Model rozmyty T-S posiada samoorganizującą się strukturę, tzn. reguły rozmyte mogą być dodawane, zamieniane lub usuwane...
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Incremental construction of Minimal Tree Automata [online]
PublikacjaWe describe an algorithm that allows the incremental addition or removal of unranked ordered trees to minimal frontier-to-root deterministic tree automaton (DTA). The algorithm takes a tree t and a minimal DTA A as input; it outputs a minimal DTA A' which accepts the language L(A) accepted by A incremented (or decremented) with the tree t. The algorithm can be used to efficiently maintain dictionaries which store large collections...
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Strong mixing Markov semigroups on C1 are meager
PublikacjaDowodzi się, że zbiór tych półgrup operatorów Markowa na klasie Schattena C1, dla których w mocnej topologii operatorowej T(t) jest zbieżne do operatora Markowa Q, gdzie Q jest 1-wymiarową projekcją, jest zbiorem rzadkim w zbiorze wszystkich półgrup Markowa.
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Systems of Nonlinear Fractional Differential Equations
PublikacjaUsing the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives D(T)(q)x and D(T)(q)y. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.
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Method of evaluation of lubricating ability of lube oils and fuels in energetistic formulation
PublikacjaThe paper presents an interpretation of operation of a boundary layer of a lubricating medium. A model of the homogeneous Poisson process has been proposed to assess the deterioration process of the layer's operation. The assessment considers the original interpretation of operation of a boundary layer, as a lubricity measure of a boundary layer of any lubricant. In the submitted proposal the operation of a boundary layer is understood...
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Phosphanylphosphido and phosphanylphosphinidene complexes of zirconium(IV) supported by bidentate N,N ligands
PublikacjaPhosphanylphosphido complexes of zirconium, [NacNacZrCl2(η2-R2P–PSiMe3)] (R = t-Bu, i-Pr), were synthesized in the reaction of R2P–P(SiMe3)Li·nTHF (R = t-Bu, i-Pr) with a β-diketiminate complex, [NacNacZrCl3], in toluene. Elimination of Me3SiCl from [NacNacZrCl2(η2-R2P–PSiMe3)] provided the phosphanylphosphinidene complexes [NacNacZrCl(η2-R2P–P)] (R = t-Bu, i-Pr). Moreover, the reaction of [NacNacZrCl2(η2-R2P–PSiMe3)] with R2P–P(SiMe3)Li·nTHF...
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Positive solutions to second-order differential equations with dependence on the first-order derivative and nonlocal boundary conditions
PublikacjaIn this paper, we consider the existence of positive solutions for second-order differential equations with deviating arguments and nonlocal boundary conditions. By the fixed point theorem due to Avery and Peterson, we provide sufficient conditions under which such boundary value problems have at least three positive solutions. We discuss our problem both for delayed and advanced arguments α and also in the case when α(t)=t, t∈[0,1]....
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Macro-elements and Model Order Reduction for Efficient Three-Dimensional FEM Analysis
PublikacjaAn efficient model order reduction (MOR) methodology for three dimensional vector finite element method (FEM) is developed to accelerate simulations of the structures containing features that cause strong variations of mesh density. As the result of presented algorithm, FEM subsystems of equations corresponding to the selected refined region are converted into a very compact sets of linear equations, called macro-elements.Numerical...
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Spinon excitations in the quasi-one-dimensional S=12 chain compound Cs4CuSb2Cl12
PublikacjaThe spin−1/2 Heisenberg antiferromagnetic chain is ideal for realizing one of the simplest gapless quantum spin liquids (QSLs), supporting a many-body ground state whose elementary excitations are fractional fermionic excitations called spinons. Here we report the discovery of such a one-dimensional (1D) QSL in Cs4CuSb2Cl12. Compared to previously reported S=1/2 1D chains, this material possesses a wider temperature range over...
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Fabrication and Crystal Structure of Sol-Gel Deposited BST Thin Films with Compositional Gradient
PublikacjaIn the present research technology of compositionally graded barium strontium titanate Ba1-xSrxTiO3 thin films deposited on stainless steel substrates by sol-gel spin coating followed with thermal annealing at T = 650°C is reported. Results of thermal behavior of the sol-gel derived powders with compositions used for fabrication of graded structure (i.e. with Sr mole fraction x = 0.5, 0.4 and 0.3) are described. X-ray diffraction...
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Chronographic Imprint of Age-Induced Alterations in Heart Rate Dynamical Organization
PublikacjaBeat-to-beat changes in the heart period are transformed into a network of increments between subsequent RR-intervals, which enables graphical descriptions of short-term heart period variability. Three types of such descriptions are considered: (1) network graphs arising from a set of vertices and directed edges, (2) contour plots of adjacency matrices A, representing the networks and transition matrices T, resulting from A, and (3)...
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Właściwości interpolacyjne parametrów dominowania w grafach
PublikacjaFunkcję Pi o wartościach całkowitych nazywamy funkcją interpolującą, jeżeli dla każdego spójnego grafu G, Pi(T(G)) jest interwałem, przy czym T(G) jest zbiorem wszystkich drzew spinających grafu G. W artykule tym przedstawia się interpolacyjny charakter parametrów związanych z różnymi rodzajami dominowania.
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Fixed point theorems for weakly commuting and compatible multi-valued mappings.
PublikacjaW pracy podano twierdzenia o wspólnych punktach stałych czwórki odwzorowań: dwóch jednowartościowych T i S oraz dwóch wielowartościowych F i G, spełniających nieliniowy uogólniony warunek kontrakcyjny, przy pewnych założeniach dotyczących uogólnionej komutatywności T,S i F,G. W pracy zamieszczono przykłady ilustrujące udowodnione twierdzenia.
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STUDY OF CuO AND V2O5 EFFECT ON IR SPECTRA OF POLYCRYSTALLINE BISMUTH NIOBATE
PublikacjaBismuth niobate (BiNbO4) ceramics were fabricated by mixed oxide method and sintered by presureless sintering method. BiNbO4 ceramics doped with V2O5 additive in amount 0.125 wt%, 0.250 wt% and 1 wt% of was sintered at T = 910°C whereas BiNbO4 ceramics doped with 2 wt% of CuO additive was sintered at T = 890°C and T = 910°C. It was found that V2O5 additive improved morphology of the ceramic samples. However, the chemical composition...
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Four-Port Circulator Using Reduced Ground Plane Ferrite Coupled Line Junction
PublikacjaIn this paper the investigations of four-port circula-tor using longitudinally magnetized ferrite coupled line section are presented. The device is designed by cascading ferrite section with magic-T junction ensuring its even and odd mode excitation. The scattering parameters of ferrite coupled line junction are calculated using own software and verified with the use of commercial software. The even and odd excitation of ferrite...
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Stabilization of the pyrochlore phase of Mn2Sb2O7 by double substitution
PublikacjaPolycrystalline samples of (Ce4+Mn2+3)(Ga3+Sb5+3)O14 were synthesized by a high-temperature solid-state reaction. In contrast with the parent Mn2Sb2O7 compound that adopts a rhombohedral or monoclinic structure at T > 600 °C, the pyrochlore structure of CeMn3GaSb3O14 is retained up to at least T = 1070°C. High-resolution synchrotron x-ray diffraction measurements show no sign of a superstructure or distortion from cubic symmetry...
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Assessment of Tensile Strength Reserve of Asphalt Mixtures at Low Temperatures
PublikacjaDuring winter conditions, low-temperature cracks develop at the surface of the asphalt pavement when tensile thermal stress induced in the asphalt layer during cooling equals and exceeds the tensile strength of the material. The paper presents the results of tensile strength reserve assessment of asphalt mixtures with neat and SBS-polymer modified bitumen application. The tensile strength reservewas calculated as difference between...