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Invariant Measures for Uncountable Random Interval Homeomorphisms
PublikacjaA necessary and sufficient condition for the iterated function system { f (·, ω) | ω ∈ } with probability P to have exactly one invariant measure μ∗ with μ∗((0, 1)) = 1 is given. The main novelty lies in the fact that we only require the transformations f (·, ω) to be increasing homeomorphims, without any smoothness condition, nei- ther we impose conditions on the cardinality of . In particular, positive Lyapunov exponents conditions...
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Algebraic periods and minimal number of periodic points for smooth self-maps of 1-connected 4-manifolds with definite intersection forms
PublikacjaLet M be a closed 1-connected smooth 4-manifolds, and let r be a non-negative integer. We study the problem of finding minimal number of r-periodic points in the smooth homotopy class of a given map f: M-->M. This task is related to determining a topological invariant D^4_r[f], defined in Graff and Jezierski (Forum Math 21(3):491–509, 2009), expressed in terms of Lefschetz numbers of iterations and local fixed point indices of...
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Aktywność amylolityczna ciałek inkluzyjnych izolowanych z Escherichia coli BL21(DE3)pLysS transformowanej plazmidem pTYB2alfa-Amyl.
PublikacjaBadania ekspresji rekombinantowej alfa-amylazy izolowanej z Escherichia coli BL21(DE3)pLysS transformowanej plazmidem pTYB2alfa-Amyl wykazały, że około 49 % wytwarzanego enzymu występuje w postaci ciałek inkluzyjnych. Źródłem genu termostabilnej alfa-amylazy był szczep Pyrococcus woesei (DSM 3773). W celu uzyskania aktywnych białek z ciałek inkluzyjnych odwirowane komórki bakterii inkubowano w roztworze CaCl2 i po trawieniu lizozymem...
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Active Suppression of Nonstationary Narrowband Acoustic Disturbances
PublikacjaIn this chapter, a new approach to active narrowband noise control is presented. Narrowband acoustic noise may be generated, among others, by rotating parts of electro-mechanical devices, such as motors, turbines, compressors, or fans. Active noise control involves the generation of “antinoise”, i.e., the generation of a sound that has the same amplitude, but the opposite phase, as the unwanted noise, which causes them to interfere...
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Synthesis, structural and spectroscopic properties of asymmetric schiff bases derived from 2,3-diaminopyridine
PublikacjaTwo Schiff base derivatives, 4-(2-amino-3-pyridyliminomethyl)phenol (I) and 3-(2-amino-3- pyridyliminomethyl)nitrobenzene (II ), were synthesised and characterised by spectroscopy. The structure of I was determined by single crystal X-ray diffraction studies. The asymmetric Schiff base derived from 2,3-diaminopyridine selectively recognise transition and heavy metal cations, and some anion. Ligands I and II form stable complexes...
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Systems, Environments, and Soliton Rate Equations: Toward Realistic Modeling
PublikacjaIn order to solve a system of nonlinear rate equations one can try to use some soliton methods. The procedure involves three steps: (1) find a ‘Lax representation’ where all the kinetic variables are combined into a single matrix ρ, all the kinetic constants are encoded in a matrix H; (2) find a Darboux–Bäcklund dressing transformation for the Lax representation iρ˙=[H,f(ρ)], where f models a time-dependent environment; (3) find...
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Fluctuation-Enhanced Sensing of Organic Vapors by Ink-Printed MoS2 Devices under UV Irradiation
PublikacjaThis work presents the results of fluctuationenhanced sensing (FES) of selected organic gases by MoS2 sensor fabricated via a simple ink printing method. We demonstrate that low-frequency noise measured under UV irradiation (275 nm) is more sensitive to different gases than measured in the dark. The noise at 1 Hz under UV light increased 3.3, 3.5, 1.6, and 2.9 times for chloroform, tetrahydrofuran, acetonitrile, and acetone ambiances, respectively....
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High-performance analog circuits : bipolar noise
PublikacjaOmówiono typowe źródła szumów występujące w tranzystorach bipolarnych, a mianowicie: cieplne, śrutowe, generacyjno-rekombinacyjne, 1/f, 1/f2, wybuchowe (RTS),lawinowe. Przedstawiono szumowy schemat zastępczy tranzystora bipolarnego oraz opisano wydajności poszczególnych źródeł szumów. Przytoczono informacje o zastępczej rezystancji tranzystora szumów oraz współczynniku szumów.
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Pavement ageing influence on tyre/road noise
PublikacjaRoad surface should be constructed in a way that ensures safe and comfortable traffic conditions, not only when it is newly paved but also during its entire lifetime. An important factor in the asphalt mixture design process is also the expected pavement durability and stability of pavement properties over time. In many countries, road surface starts to play a significant role in traffic noise reduction actions. Selecting a particular...
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Noise in semiconductor devices
PublikacjaOmówiono typowe źródła szumów występujące w przyrządach pólprzewodnikowych, a mianowicie: cieplne, śrutowe, generacyjno-rekombinacyjne, 1/f, 1/f2, wybuchowe (RTS), lawinowe. Przedstawiono szumowe schematy zastępcze tranzystora bipolarnego, JFET i MOSFET oraz opisano wydajności poszczególnych źródeł szumów. Zasugerowano jak dobierać przyrządy półprzewodnikowe do małoszumowych układów w zakresie małych częstotliwości.
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Tripping of F-type RCDs for high-frequency residual currents
PublikacjaResidual current devices (RCDs) are apparatus commonly used for protection against electric shock in low-voltage electrical installations. They protect people in the case of an earth fault or even in the case of direct contact with the live parts. However, to be effective protective devices, RCDs have to detect residual currents of various waveform shapes which appear in modern electrical installations. For this purpose, RCDs are...
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Tripping of F-type RCDs for High-Frequency Residual Currents
PublikacjaResidual current devices (RCDs) are apparatus commonly used for protection against electric shock in low-voltage electrical installations. They protect people in the case of an earth fault or even in the case of direct contact with the live parts. However, to be effective protective devices, RCDs have to detect residual currents of various waveform shapes which appear in modern electrical installations. For this purpose, RCDs...
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Fluorine ions in photocatalysts’ synthesis: an obstacle or an ally? The investigation of photocatalysts in Ti-O-F system
PublikacjaTitanium(IV) oxide (TiO2) is one of the most promising photocatalysts, which is expected to be applied in the photocatalytic degradation of xenobiotics. For sustainable development and green chemistry approach recently, much effort has been paid to enhance TiO2 photocatalytic activity in UV-vis light by modifying its structure. The photocatalytic process’s complexity cannot be simply described as electron-hole pairs generations...
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Modelowanie szumów RTS
PublikacjaPrzytoczono charakterystyczne parametry szumu wybuchowego (Random Telegraph Signal, RTS). Przedstawiono algorytm programowego generatora szumów RTS. Algorytm został wyposażony w możliwość dodawania do wygenerowanych impulsów RTS szumu białego oraz szumu typu 1/f. Przedstawiono przykładowe realizacje wygenerowanych przebiegów.
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Modelowanie szumów RTS
PublikacjaPrzytoczono charakterystyczne parametry szumu wybuchowego (Random Telegraph Signal, RTS). Przedstawiono algorytm programowego generatora szumów RTS. Algorytm został wyposażony w możliwość dodawania do wygenerowanych impulsów RTS szumu białego oraz szumu typu 1/f. Przedstawiono przykładowe realizacje wygenerowanych przebiegów.
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METHODS OF TEACHING NOISE PROTECTION AT ENVIRONMENTAL ENGINEERING
PublikacjaNoise strongly influences both our health and behavior in everyday life and as employees or employers. The lost of hearing and other effects of noise on humans result not only in a significant decrease in the quality of life or work efficiency but have also have economic consequences. As noise can be preventable in part by the Environmental Engineers, but it is necessary to introduce them noise issues during their education process....
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ROSANNE Project: New Procedure for Noise Characterisation of Road Surfaces in Europe
PublikacjaROSANNE is a collaborative project in the 7th EU Framework Programme which aims at harmonising measurement methods for skid resistance, noise emission and rolling resistance of road pavements as a preparation for standardization. The project started in November 2013 and is developing and improving standards in the field of working group CEN/TC 227/WG 5. Regarding the influence of the pavement on the road traffic noise emission,...
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Speed dependency of temperature effects on road traffic noise
PublikacjaRecently, a new literature review on the influence of temperature on tire/road noise became available, based on a compilation of large amounts of data from empirical research. This review showed that the effect of temperature is roughly double of that previously assumed and taken account of in international standards. This makes temperature one of the main sources of error in measurement results. Furthermore, it suggested that...
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Expression of Deinococcus geothermalis Trehalose Synthase Gene in Escherichia coli and Its Enzymatic Properties
PublikacjaA novel trehalose synthase gene from Deinococcus geothermalis (DSMZ 11300) containing 1,692 bp reading-frame encoding 564 amino acids was amplified using PCR. The gene was ligated into pET30Ek/LIC vector and expressed after isopropyl alfa-D-thiogalactopyranoside induction in Escherichia coli BL21(DE3)pLysS. The recombinant trehalose synthase (DgeoTreS) containing a His6 tag at the C-terminus was purified by metal affinity chromatography...
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Metody zwiększenia czułości dwukanałowego systemu pomiaru szumów.
PublikacjaZnajomość właściwości szumowych elementów elektronicznych w zakresie małych częstotliwości, gdzie dominują szumy o widmie typu 1/f, stanowi efektywne narzędzie oceny jakości procesu technologicznego wytwarzania tych elementów oraz predykcji ich niezawodności. Przeprowadzenie dokładnych pomiarów parametrów i charakterystyk szumowych stwarza jednak często wiele problemów.
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Parseval Wavelet Frames on Riemannian Manifold
PublikacjaWe construct Parseval wavelet frames in L 2 (M) for a general Riemannian manifold M and we show the existence of wavelet unconditional frames in L p (M) for 1 < p < ∞. This is made possible thanks to smooth orthogonal projection decomposition of the identity operator on L 2 (M), which was recently proven by Bownik et al. (Potential Anal 54:41–94, 2021). We also show a characterization of Triebel–Lizorkin F sp,q (M) and Besov B...
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The best porous asphalt pavement in Sweden so far
PublikacjaIn 2010 a double-layer porous asphalt concrete (DPAC) pavement was constructed in various versions on the E4 motorway through the Swedish city Huskvarna. As a result of a court decision the Swedish Transport Administration had to reduce noise emission by applying a low noise road surface that would reduce A-weighted noise levels by 5 dB, as an average. Earlier experience in Sweden indicated that it was possible to obtain a high...
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Compact Electromagnetic Lens Antennas Using Cascaded Metasurfaces for Gain Enhancement and Beam Steering Applications
PublikacjaElectromagnetic (EM) lens antenna designs using cascaded metasurfaces for gain enhancement and beam steering applications are proposed. Two different lens aperture designs are proposed and populated with aperiodic unit cells of size 0.2λo × 0.2λo. In lens Design 1, the unit cells of different phases are distributed in concentric circular zones, whereas in lens Design 2, the unit cells of different phases are distributed in vertical...
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Dynamical description of quantum computing: generic nonlocality of quantumnoise
PublikacjaWe develop a dynamical non-Markovian description of quantum computing in the weak-coupling limit, in the lowest-order approximation. We show that the long-range memory of the quantum reservoir (such as the 1/t4 one exhibited by electromagnetic vacuum) produces a strong interrelation between the structure of noise and the quantum algorithm, implying nonlocal attacks of noise. This shows that the implicit assumption of quantum error...
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Impact of the anion and chalcogen on the crystal structure and properties of 4,6-dimethyl-2-pyrimido(thio)nium halides
PublikacjaBy the reaction of urea or thiourea, acetylacetone and hydrogen halide (HF, HBr or HI), we have obtained seven new 4,6-dimethyl-2-pyrimido(thio)nium salts, which were characterized by single-crystal X-ray diffraction, namely, 4,6-dimethyl-2-oxo-2,3-dihydropyrimidin-1-ium bifluoride, C₆H₉N₂O⁺·HF₂⁻ or (dmpH)F₂H, 4,6-dimethyl-2-oxo-2,3-dihydropyrimidin-1-ium bromide, C₆H₉N₂O⁺·Br⁻ or (dmpH)Br, 4,6-dimethyl-2-oxo-2,3-dihydropyrimidin-1-ium...
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Ocena przyczyn awarii wrzeciona frezarki CNC Fidia BT 8555/15
PublikacjaOpinia powstała na zamówienie firmy Zakłady Porcelany Stołowej ''Lubiana'' S.A. (ul. Zakładowa 1, 83-407 Łubiana) i dotyczy frezarki sterowanej numerycznie (CNC) FIDIA F 8555/15.Przedmiotem ekspertyzy jest ocena prawdopodobnych przyczyn awarii obrabiarki. Udział doradczy niezależnych specjalistów okazał się niezbędny z uwagi na problemy związane z realizacją obsługi gwarancyjnej obrabiarki.
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New lanthanide–CB[6] coordination compounds: relationships between the crystal structure and luminescent properties
PublikacjaThe reaction between cucurbit[6]uril (CB[6]) and lanthanide chlorides (Eu, Sm, Tb and Tm) in acidic aqueous media led to four new structures. The compounds obtained are isostructural with general formula [Ln2(H2O)12(H2O@CB[6])]Cl6(H2O)4 (Ln = Eu3+ (1), Sm3+ (2), Tb3+ (3) and Tm3+ (4)) and crystallize in the P21/c space group. For the complexes with Eu3+, Sm3+ and Tb3+, the luminescent properties in the solid state and aqueous media...
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Anion binding by p-aminoazobenzene-derived aromatic amides: spectroscopic and electrochemical studies
PublikacjaThe synthesis and complexing properties of p-aminoazobenzene-derived mono-, bis-, and trisamides were described. Ligands 3 and 4 bind anions, including fluorides, chlorides, bromides, acetates, benzoates, dihydrogen phosphates, hydrogen sulfates, and p-toluenesulfonates, in chloroform forming 1 : 1 complexes. The highest value of stability constant was evaluated for the 4-F− complex (log K = 5.63 ± 0.21). On the basis of 1H NMR,...
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N-doped carbon materials as electrodes for highly stable supercapacitors
PublikacjaThis article reports a strategy to use nitrogen-doped carbon materials as electrodes for supercapacitors. Depending on the carbon precursor, the porous structure is changed with specific surface area reached up to 2270 m2 g−1. The capacitance of carbon materials used as electrodes is related strictly to pore size. The microstructure and nitrogen functionalities enable a high capacitance (327 F g−1) and cycle durability. The nanoporous...
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Modulation of cellular response to anticancer treatment by caffeine:inhibition of cell cycle checkpoints, DNA repair and more
PublikacjaKofeina i inne metyloksantyny wywołują bardzo różne efekty fizjologiczne w organizmie człowieka. W pracy przedstawiamy, które z tych efektów mogą wpływać na skuteczność terapii przeciwnowotworowych. Kofeina może bezpośrednio wpływać na transport oraz aktywację metaboliczną cząsteczek leków do komórki, poprzez tworzenie kompleksów z lekami zawierającymi układy poliaromatyczne. Kofeina hamuje aktywność kinaz ATM/ATR co prowadzi do...
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Hydrothermal reactions: From the synthesis of ligand to new lanthanide 3D-coordination polymers
PublikacjaThe organic ligand 2,5-piperazinedione-1,4-diaceticacid (H2PDA) was synthesized under hydrothermal conditions starting from the iminodiacetic acid and catalyzed by oxalic acid. The X-ray powder diffraction data indicates that the compound crystallizes in the P21/c space group as reported in the literature. The ligand was also characterized by elemental analysis, magnetic nuclear resonance, infrared spectroscopy and thermogravimetric...
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Investigation of noises in the EPN weekly time series
PublikacjaThe constantly growing needs of permanent stati ons’ velocities users cause their stability level to increase. To this research we included more than 150 stations located across Europe operating within the EUREF Permanent Network (EPN) w ith weekly changes in the ITRF2005 reference frame. The obvious long-range dependencies in the stochastic part of GPS time series were p roven by Ljung-Box...
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Temperature influence on tyre/road noise frequency spectra
PublikacjaThe correction for temperature effect on measured tyre/road noise is very important as it may be one of the main sources of errors in measurement results due to substantial influence of this parameter on obtained values. The latest version of the Technical Specification ISO/CD TS 13471-1 about Temperature Corrections contains a proposal of correction procedure for normalizing measured noise levels to a reference air temperature...
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Photophysics of Ru(II) Dyads Derived from Pyrenyl-Substitued Imidazo[4,5-f][1,10]phenanthroline Ligands.
PublikacjaThe photophysics of a series of Ru(II) dyads based on the 2-(1-pyrenyl)-1H-imidazo[4,5-f][1,10]-phenanthroline ligand was investigated. The ability of these metal complexes to intercalate DNA and induce cell death upon photoactivation makes them attractive photosensitizers for a range of photobiological applications, including photodynamic therapy. In the present study, time-resolved transient absorption and emission spectroscopy...
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A Framework for Searching in Graphs in the Presence of Errors
PublikacjaWe consider a problem of searching for an unknown target vertex t in a (possibly edge-weighted) graph. Each vertex-query points to a vertex v and the response either admits that v is the target or provides any neighbor s of v that lies on a shortest path from v to t. This model has been introduced for trees by Onak and Parys [FOCS 2006] and for general graphs by Emamjomeh-Zadeh et al. [STOC 2016]. In the latter, the authors provide...
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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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Investigation of long-range dependencies in the stochastic part of daily GPS solutions
PublikacjaThe long-range dependence (LRD) of the stochastic part of GPS-derived topocentric coordinates change (North, East, Up) results with relatively high autocorrelation values with a focus on self-similarity. One of the reasons for such self-similarity in the GPS time series are noises that are commonly recognised to prevail in the form of the flicker noise model. To prove the self-similarity of the stochastic part of GPS time series...
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Szerokopasmowy, zminiaturyzowany, wielodrożny dzielnik mocy typu 1:6
PublikacjaW referacie zaprezentowano metodykę projektowania szerokopasmowego, wielodrożnego dzielnika mocy typu 1:6 wykonanego w technologii niesymetrycznych linii paskowych. Zaburzenie ciągłości metalizacji paska sygnałowego poprzez implementację struktur PBG (ang. Photonic Bandgap) umożliwiło osiągnięcie zarówno 15% miniaturyzacji, jak i poszerzenia pasma pracy do 141% dla częstotliwości f=4 [GHz]. Wyniki eksperymentu wykazujące dużą zgodność...
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Temperature influence on tyre/road noise on poroelastic road surface based on laboratory measurements
PublikacjaThe temperature effect on measured tyre/road noise is very important phenomena as it may lead to significant errors in measurement results due to substantial influence of this parameter on the obtained values. It depends mainly on the particular tyre-road combination. It is different for dense and porous as well as for bituminous and cement concrete pavements. It differs also depending on tested tyre. The correction procedure for...
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CeIr3: superconductivity in a phase based on tetragonally close packed clusters
PublikacjaWe present the crystallographic analysis, superconducting and spectroscopic characterization, and theoretical modeling of CeIr3. Lattice parameters a = 5.2945(1) Å and c = 26.219(1) Å are found for the R-3m symmetry crystal structure, which are close to the literature values. CeIr3 is a moderate type-II superconductor (κ GL = 17, λ e–p = 0.65) below 2.5 K. Ce ions exhibit a strongly intermediate valence character as evidenced by...
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Comparison of hydrogen bonds and diverse weak interactions of the nitro group in 2-methyl-4-nitroanilinium nitrate, bisulfate and two hexafluoridosilicates: elementary graph-set approach
PublikacjaCrystal structures of (H2m4na)NO3 (1), (H2m4na)HSO4 (2), (H2m4na)2SiF6 (3) and (H2m4na)2SiF6*2H2O (4), where 2m4na = 2-methyl-4-nitroaniline, are presented. Two layers of interactions occur in the structures, N—H...O/F hydrogen bonds and interactions with the nitro group. Although diverse, hydrogen-bonding patterns are compared with each other by means of interrelations among elementary graph-set descriptors and descriptors of hydrogen-bonding...
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Analysis of Lombard speech using parameterization and the objective quality indicators in noise conditions
PublikacjaThe aim of the work is to analyze Lombard speech effect in recordings and then modify the speech signal in order to obtain an increase in the improvement of objective speech quality indicators after mixing the useful signal with noise or with an interfering signal. The modifications made to the signal are based on the characteristics of the Lombard speech, and in particular on the effect of increasing the fundamental frequency...
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Loudness Scaling Test Based on Categorical Perception
PublikacjaThe main goal of this research study is focused on creating a method for loudness scaling based on categorical perception. Its main features, such as: way of testing, calibration procedure for securing reliable results, employing natural test stimuli, etc., are described in the paper and assessed against a procedure that uses 1/2-octave bands of noise (LGOB) for the loudness growth estimation. The Mann-Whitney U-test is employed...
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Acoustic evaluation of road surfaces using different Close Proximity testing devices
PublikacjaAccording to the valid standard, Close Proximity (CPX) method intends to evaluate the influence of road surfaces on traffic noise. Measurements may be carried out with the use of a self-powered vehicle or a special test trailer equipped with testing tyre towed by another vehicle. Two different testing devices took part in the research organized in Poland in order to determine the ranking of road surfaces in terms of acoustic parameters....
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Multiple bifurcation in the solution set of the von Karman equations with S^{1}-symmetries
PublikacjaRozważmy cienką, sprężystą, kołową płytę, położoną na sprężystym podłożu, poddawaną działaniu sił ściskających koncentrycznie wzdłuż jej brzegu. Formy równowagi takiej płyty są rozwiązaniami równań von Karmana z dwoma parametrami określonych na dysku w R^{2}. Są to równania różniczkowe cząstkowe rzędu czwartego. Można je zapisać jako równanie operatorowe F(x,p)=0 w przestrzeniach Höldera, gdzie zmienna x odpowiada formom równowagi...
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Error analysis for European IGS stations
PublikacjaEach of the GPS time series that describes the changes of topocentric components consists of a deterministic and a stochastic part, whose character influences the errors of the deterministic parameters. As to the uncertainties of reliable velocities of permanent satellite station systems, surveys that estimate and take into account any dependencies that may affect subsequent operational efficiency are very important. For this analysis,...
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Noise and Electro-Ultrasonic Spectroscopy of Conducting PolymerThick Films
PublikacjaThick conducting films based on conducting polymer are characterized by DC conductivity and noise in temperature range 10 to 300 K. Conducting polymers could be used e.g. for the top electrode (cathode) in the solid tantalum or niobium capacitors. On the conducting polymer layer the top layer of carbon/graphite and/or silver polymer based pastes is applied in the capacitor technology. Our samples structure consists of conducting...
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Problemy pomiarów szumów diod z węglika krzemu
PublikacjaPrzedstawiono system do pomiaru szumów m.cz. diod Schottky'ego wykonanych z węglika krzemu (SiC) spolaryzowanych w kierunku przewodzenia i zaporowym, z uwzględnieniem specyfiki pomiaru szumów wybuchowych (RTS). Badane diody charakteryzują się wysokim prądem przewodzenia (do 12A) i wysokim napięciem zaporowym (typowo 600V i 1200V). Omówiono zagadnienia związane ze sposobami polaryzacji badanych diod i ich wpływ na wyniki pomiarów....
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Spektroskopia szumowa. Część II. Badania przyrządów półprzewodnikowych, szumy elektrochemiczne i emisja akustyczna w diagnostyce.
PublikacjaPrzedstawiono wyniki pomiaru szumów 1/f tranzystorów z GaAs i ich analizę w spektroskopii. Opisano procedurę klasyfikacji na grupy o zróżnicowanej jakości półprzewodnikowych elementów mocy na podstawie wyników pomiaru szumów małoczęstotliwościowych. Szumy elektrochemiczne stanowią dogodne narzędzie do analizy korozji, zwłaszcza korozji wżerowej. Przedstawiono wyniki pomiaru szumów ogniw słonecznych i ich porównanie z analizą niejednorodności...
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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...