Search results for: mountain pass theorem
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Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator
PublicationUsing the Mountain Pass Theorem we show that the problem \begin{equation*} \begin{cases} \frac{d}{dt}\Lcal_v(t,u(t),\dot u(t))=\Lcal_x(t,u(t),\dot u(t))\quad \text{ for a.e. }t\in[a,b]\\ u(a)=u(b)=0 \end{cases} \end{equation*} has a solution in anisotropic Orlicz-Sobolev space. We consider Lagrangian $\Lcal=F(t,x,v)+V(t,x)+\langle f(t), x\rangle$ with growth conditions determined by anisotropic G-function and some geometric conditions...
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A convergence result for mountain pass periodic solutions of perturbed Hamiltonian systems
PublicationIn this work, we study second-order Hamiltonian systems under small perturbations. We assume that the main term of the system has a mountain pass structure, but do not suppose any condition on the perturbation. We prove the existence of a periodic solution. Moreover, we show that periodic solutions of perturbed systems converge to periodic solutions of the unperturbed systems if the perturbation tends to zero. The assumption on...
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Mountain pass type periodic solutions for Euler–Lagrange equations in anisotropic Orlicz–Sobolev space
PublicationUsing the Mountain Pass Theorem, we establish the existence of periodic solution for Euler–Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part and a forcing term. We consider two situations: G satisfying at infinity and globally. We give conditions on the growth of the potential near zero for both situations.
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Module structure in Conley theory with some applications
PublicationA multiplicative structure in the cohomological versjon of Conley index is described . In the case of equivariant flows we apply the normalization procedure known from equivariant degree theory and we propose a new continuation invariant. The theory is then applied to obtain a mountain pass type theorem. Another application is a result on multiple bifurcations for some elliptic PDE.
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Existence of Two Periodic Solutions to General Anisotropic Euler-Lagrange Equations
PublicationAbstract. This paper is concerned with the following Euler-Lagrange system d/dtLv(t,u(t), ̇u(t)) =Lx(t,u(t), ̇u(t)) for a.e.t∈[−T,T], u(−T) =u(T), Lv(−T,u(−T), ̇u(−T)) =Lv(T,u(T), ̇u(T)), where Lagrangian is given by L=F(t,x,v) +V(t,x) +〈f(t),x〉, growth conditions aredetermined by an anisotropic G-function and some geometric conditions at infinity.We consider two cases: with and without forcing termf. Using a general version...
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On the Existence of Homoclinic Type Solutions of a Class of Inhomogenous Second Order Hamiltonian Systems
PublicationWe show the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems, where a C1-smooth potential satisfies a relaxed superquadratic growth condition, its gradient is bounded in the time variable, and a forcing term is sufficiently small in the space of square integrable functions. The idea of our proof is to approximate the original system by time-periodic ones, with larger and larger...
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Approximative sequences and almost homoclinic solutions for a class of second order perturbed Hamiltonian systems
PublicationIn this work we will consider a class of second order perturbed Hamiltonian systems with a superquadratic growth condition on a time periodic potential and a small aperiodic forcing term. To get an almost homoclinic solution we approximate the original system by time periodic ones with larger and larger time periods. These approximative systems admit periodic solutions, and an almost homoclinic solution for the original system...
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BIOVAC® WASTEWATER TREATMENT PLANTS IN THE MOUNTAIN NATIONAL PARKS.
PublicationThis paper presents characteristics of the Biovac® wastewater treatment plants operating in the mountain areas of the Polish national parks (NP): Tatrzanski NP and Babiogórski NP as well as in the West Spitsbergen NP. On the basis of the laboratory tests performed on raw sewage and the final effluent the efficiency of the wastewater treatment plants was evaluated. It was found that high COD values and rather high COD / BOD5 ratios...
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A Measurable Selector in Kadison’s Carpenter’s Theorem
PublicationWe show the existence of a measurable selector in Carpenter’s Theorem due to Kadison. This solves a problem posed by Jasper and the first author in an earlier work. As an application we obtain a characterization of all possible spectral functions of shift-invariant subspaces of L 2 (R d ) and Carpenter’s Theorem for type I ∞ von Neumann algebras.
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A Hopf type theorem for equivariant local maps
PublicationWe study otopy classes of equivariant local maps and prove a Hopf type theorem for such maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group.
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Contra Bellum: Bell's Theorem as a Confusion of Languages
PublicationBell's theorem is a conflict of mathematical predictions formulated within an infinite hierarchy of mathematical models. Inequalities formulated at level k ∈ Z are violated by probabilities at level k+1. We are inclined to think that k=0 corresponds to the classical world, while k=1 — to the quantum one. However, as the k=0 inequalities are violated by k=1 probabilities, the same relation holds between k=1 inequalities violated...
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The Hopf theorem for gradient local vector fields on manifolds
PublicationWe prove the Hopf theorem for gradient local vector fields on manifolds, i.e., we show that there is a natural bijection between the set of gradient otopy classes of gradient local vector fields and the integers if the manifold is connected Riemannian without boundary.
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No-local-broadcasting theorem for multipartite quantum correlations
PublicationWe prove that the correlations present in a multipartite quantum state have an operational quantum character even if the state is unentangled, as long as it does not simply encode a multipartite classical probability distribution. Said quantumness is revealed by the new task of local broadcasting, i.e., of locally sharing preestablished correlations, which is feasible if and only if correlations are stricly classical. Our operational...
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Risk of incorrect pass-fail decisions associated with assessment uncertainty
PublicationA mathematical framework for calculation teacher's and student's risks of incorrect pass-fail decisions under uncertainty of assessment, is presented. The probabilistic model of assessment process is adapted from interdisciplinary probabilistic theory of measurement.
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On the Peano Theorem for Some Functional Differential Equations on Time Scale
PublicationThe Peano Theorem for some functional differential equations on time scale is proved. Assumptions are of Caratheodory type. Two counter examples for false Peano theorems in the literature are presented.
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On the theorem of Tverberg
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A note on a Wiener-Wintner theorem for mean ergodic Markov amenable semigroups
PublicationWe prove a Wiener-Wintner ergodic type theorem for a Markov representation of a right amenable semitopological semigroup.
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Environmental Role of Rime Chemistry at Selected Mountain Sites in Poland
PublicationThe results of field experiments on fog pollutantdeposition enhanced by local mountain climate, completed by thedendrochronological analysis of the forest response, are presentedin this paper. In spite of their low absolute altitude (1,000-1,600 ma.s.l), the Sudetes and the Silesian Beskid form a noticeable orographicbarrier for the airflow of the humid Atlantic air masses.This results in the increase of cloudiness and fog frequency...
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About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof
PublicationRecently, the fractional Noether's theorem derived by G. Frederico and D.F.M. Torres in [10] was proved to be wrong by R.A.C. Ferreira and A.B. Malinowska in (see [7]) using a counterexample and doubts are stated about the validity of other Noether's type Theorem, in particular ([9],Theorem 32). However, the counterexample does not explain why and where the proof given in [10] does not work. In this paper, we make a detailed analysis...
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Novel microstrip low-pass filters with fractal defected ground structures
PublicationIn this study, three microstrip low-pass filters (LPFs) containing fractal-shaped defected ground structures have been designed and manufactured. To improve the performance of microstrip LPF, cascades of inductively coupled fractal resonators have been applied. Simultaneously, to achieve relatively constant microstrip impedance resulting in essentially low reflection losses, a modification of the strip geometry has been introduced....
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Dynamic mass measurement in checkweighers using a discrete time-variant low-pass filter
PublicationConveyor belt type checkweighers are complex mechanical systems consisting of a weighing sensor (strain gauge load cell, electrodynamically compensated load cell), packages (of different shapes, made of different materials) and a transport system (motors, gears, rollers). Disturbances generated by the vibrating parts of such a system are reflected in the signal power spectra in a form of strong spectral peaks, located usually in...
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Arithmetic Loophole in Bell's Theorem: Overlooked Threat to Entangled-State Quantum Cryptography
PublicationBell’s theorem is supposed to exclude all local hidden-variable models of quantum correlations. However,an explicit counterexample shows that a new class of local realistic models, based on generalized arith-metic and calculus, can exactly reconstruct rotationally symmetric quantum probabilities typical oftwo-electron singlet states. Observable probabilities are consistent with the usual arithmetic employedby macroscopic observers...
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Novel topology of compact coplanar waveguide resonant cell low-pass filter
PublicationIn this study, a novel pseudoelliptic function low-pass filter (LPF) constituted by a compact coplanar waveguide resonant cell has been designed and manufactured. The lumped-element seven-pole prototype has been adequately realized by using complementary perturbations located both in signal line and ground plane metallization. The fabricated uniplanar LPF offers a compact size of 5.6 x 9.8 mm2, return loss better than 26 dB over...
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Automatic Correction of Non-Anechoic Antenna Measurements using Low-Pass Filters
PublicationPrototype measurements belong to key steps in the development of antenna structures. They are normally performed in expensive facilities, such as anechoic chambers (ACs). Alternatively, antenna performance can be extracted (at a low cost) in non-anechoic conditions upon appropriate post-processing. Unfortunately, existing correction algorithms are difficult to set up and prone to failure, which limits their practical usefulness....
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Representativity of ISO test track surface based on controlled pass-by measurements
PublicationWithin the Polish-Norwegian research project ELANORE, a limited Round Robin Test has been performed on four ISO tracks in Northern Europe. The basic objective of the project is to improve the EU directive on labelling of tyres for noise and rolling resistance. This directive is based on the measurement procedures proscribed in the UNECE Reg.117. Measurements on 3 ISO tracks were performed in 2021 and presented at InterNoise 2022....
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Assessment of the technological reliability of a hybrid constructed wetland for wastewater treatment in a mountain eco-tourist farm in Poland
PublicationThe aim of the present study was to assess the technological reliability of a domestic hybrid wastewater treatment installation consisting of a classic three-chambered (volume 6 m3) septic tank, a vertical flow trickling bed filled with granules of a calcinated clay material (KERAMZYT), a special wetland bed constructed on a slope, and a permeable pond used as a receiver. The test treatment plant was located at a mountain eco-tourist...
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Shift invariant operators and a saturation theorem.
PublicationPraca jest kontynuacją wcześniejszych dwóch prac wydanych w Appl. Math. w latach 2001 i 2002. Główny wynik dotyczy wygładzania specjalnego ciągu zbieżnego słabo, tak iż dostajemy ciąg zbieżny w normie supremum.
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Bernstein-type theorem for ϕ-Laplacian
PublicationIn this paper we obtain a solution to the second-order boundary value problem of the form \frac{d}{dt}\varPhi'(\dot{u})=f(t,u,\dot{u}), t\in [0,1], u\colon \mathbb {R}\to \mathbb {R} with Sturm–Liouville boundary conditions, where \varPhi\colon \mathbb {R}\to \mathbb {R} is a strictly convex, differentiable function and f\colon[0,1]\times \mathbb {R}\times \mathbb {R}\to \mathbb {R} is continuous and satisfies a suitable growth...
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Rocky Mountain Geology
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MOUNTAIN RESEARCH AND DEVELOPMENT
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A Noether theorem for stochastic operators on Schatten classes
PublicationWe prove that a stochastic (Markov) operator S acting on a Schatten class C_1 satisfies the Noether condition S'(A) = A and S'(A^2) = A^2, where A is a Hermitian bounded linear operator on a complex Hilbert space H, if and only if, S(E(G)XE(G)) = E(G)S(X)E(G) holds true for every Borel subset G of the real line R, where E(G) denotes the orthogonal projection coming from the spectral resolution of A. Similar results are obtained...
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The method of measuring the energy pass-band of a communication receiver
PublicationPrzedstawiono metodę wyznaczania energetycznego pasma odbiornika radiokomunikacyjnego na podstawie charakterystyki gęstości widmowej mocy szumów własnych na wyjściu odbiornika. Podano numeryczny estymator tego pasma. Wyprowadzono zależności na złożoną niepewność standardową wyznaczania szerokości pasma energetycznego odbiornika.
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A 0.5 V Nanowatt Biquadratic Low-Pass Filter with Tunable Quality Factor for Electronic Cochlea Applications
PublicationA novel implementation of an analogue low-power, second-order, low-pass filter with tunable quality factor (Q) is presented and discussed. The filter feature is a relatively simple, buffer-based, circuit network consisting of eleven transistors operating in a subthreshold region. Q tuning is accomplished by injecting direct current into a network node, which changes the output resistance of the transistors and, as a result, modifies...
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Application of Mazur-Orlicz`s theorem in AMISE calculation
PublicationW pracy podano nowe wyprowadzenie formuły asymptotycznej błędu aproksymacji dla operatorów całkowych w przestrzeniach niezmienniczych na przesunięcia. Obliczono asymptotykę błędu średniokwakratowego dla estymatora gęstości.
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Effective residue-to-binary converter with the Chinese Remainder Theorem
PublicationKonwersja liczb z systemu resztowego do systemu binarnego jest podstawową operacją we wszystkich układach cyfrowego przetwarzania sygnałów, które wykorzystują system resztowy. W niniejszej pracy zaproponowano nową metodę konwersji opartą o chińskie twierdzenie o resztach dla modułów 5- i 6-bitowych. Specyficzną cechą nowej metody jest sposób obliczania tzw. współczynnika nadmiaru w formule chińskiego twierdzenia o resztach, co...
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The Hopf type theorem for equivariant gradient local maps
PublicationWe construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of equivariant gradient otopy classes and the direct sum of countably many copies of Z.
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Frequency-dependent coupling model for microwave band-pass filter
PublicationThe goal of this work was to create a circuit model which represents frequency-dependent coupling between microwave resonators. Our models are designed for in-line filters. The frequency-dependent coupling enables one to realize a transmission zero which is not possible in classical approach with frequency independent inverters. In addition, the proposed model allows us to observe out-of-band behavior, e.g. spurious resonance....
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The hydrochemistry of high-altitude lakes in selected mountain ranges of Central and Southern Europe
PublicationWyniki badań hydrochemicznych 29 jezior wysokogórskich dwóch (zróżnicowanych pod względem genetycznym i współcześnie przebiegających procesów morfogenetycznych) obszarów wysokogórskich Europy: Karpat oraz Rodopów, rozpatrywane są w odniesieniu do lokalnych warunków geologicznych, klimatycznych, hydrologicznych antropopresji. Zróżnicowanie koncentracji głównych jonów (Na, K, Mg, Ca, SO4 i HCO3) wykazuje silne skorelowanie z bezwzględną...
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Sustainable Development of Mountain Territories
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Influence of PWHT Parameters on the Mechanical Properties and Microstructural Behavior of Multi-Pass GTAW Joints of P92 Steel
PublicationThe 9% Cr steels were developed for ultra-supercritical (USC) power plants to meet the requirements of high operating temperature and pressure. These steels are produced to operate at high temperatures where impact toughness is not a concern; however, it becomes important for the welded joints to have good impact toughness at room temperature for manufacturing. The present work investigates the effect of the post-weld heat treatment...
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New aspects of the use of Optical Theorem in the analysis of microcavity lasers
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RNS reverse converter based on the new chinese remainder theorem.
PublicationPrzeanalizowano złożoność układu cyfrowego opartego na nowej odmianie chińskiego twierdzenia o resztach.
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Mazur-Orlicz theorem and asymptotic formula for the error in supreme norm.
PublicationObliczono formułę asymptotyczną błędu interpolacji dla normy supremum.
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Imitating Quantum Probabilities: Beyond Bell’s Theorem and Tsirelson Bounds
PublicationLocal hidden-variable model of singlet-state correlations discussed in M. Czachor, Acta Phys. Polon. A 139, 70, is shown to be a particular case of an infinite hierarchy of local hidden-variable models based on an infinite hierarchy of calculi. Violation of Bell-type inequalities can be interpreted as a `confusion of languages' problem, a result of mixing different but neighboring levels of the hierarchy. Mixing of non-neighboring...
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Rating mathematical models for first-pass of tracer in pCT lung studies
PublicationThis paper presents a comparison of model based on the Gauss function and the most commonly used Gamma-variate model in perfusion computed tomography (pCT) lung studies. It also verifies whether used model affects value of blood volume parameter. Three mean concentration-time curves were created from actual pCT measurements: arterial input function, blood vessels in lungs and lung parenchyma. On the basis of these mean curves we...
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Sensitivity performance of all pole canonical low pass GmC filters.
PublicationW pracy badano własności częstotliwościowe kanonicznych filtrów dolnoprzepustowych GmC bez zer transmisyjnych. Przedstawiono ogólną strukturę kanonicznego filtru dolnoprzepustowego i jej opis macierzowy. Wyprowadzono ogólne wzory określające funkcje wrażliwościowe filtru. Dokonano porównania struktur do 10-go rzędu włącznie dla aproksymacji Butterwortha, Czebyshewa i Bessela.
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Optical theorem helps understand thresholds of lasing in open semiconductor microcavities
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Optical Theorem Helps Understand Thresholds of Lasing in Microcavities With Active Regions
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Fast rns scaling of signed numbers based on the chinese remainder theorem
PublicationPrzedstawiono architekturę szybkiego skalera resztowego dla liczb ze znakiem dla modułów 5-bitowych opartego na chińskim twierdzeniu o resztach. W architekturze zastosowano wyznaczanie projekcji ortogonalnych przy użyciu funkcji logicznych 5 zmiennych, sumator kodulo m/k oraz wejściowy konwerter do systemu resztowego. Operacja modulo m/k jest wykonywana przy zastosowaniu drzewa 4-operandowych sumatorów modulo 2m/k i końcowego...
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Damping Amplification Caused by a Mechanism that Trans-pass Trough its singular Position
PublicationW artykule przedstawiono badania dotyczące drgania hybrydowego systemu składającego się z mechanizmu i układu ciągłego. Pomimo ich obecności w wielu codziennych doświadczeniach to w większości przypadków technicznych obecność drgań jest niepożądana. Jednym z podstawowych problemów jest tu długie utrzymywanie się i konieczność tłumienia drgań o niskiej częstotliwości. W artykule badana jest metoda tłumienia oparta na niewspółmierności...
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Monitoring of myocardium state during off-pump coronary artery by-pass grafting
PublicationW pracy przedstawiono technikę pomiarową do oceny procesów zachodzących podczas operacji przesłowania aortalno-wieńcowego wymagających zatrzymania przepływu krwi. Zaproponiwany system i metoda pomiarowa przewidziane są do wykorzystania podczas opercacji na tzw. bijącym sercu. Pokazano przykłady rejestrowanych sygnałów przydatnych do oceny stanu mieśnia serca oraz dokonano oceny właściwości pomiarowych zastosowanych technik.
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Probabilistic Approach to Precipitation-Runoff Relation in a Mountain Catchment: A Case Study of the Kłodzka Valley in Poland
PublicationOn the basis of daily precipitation and discharges recorded in 1974–2013 relations between precipitation and runoff in the Kłodzka Valley (KV) in south-western Poland were analyzed. The degree of synchronicity between them was determined using the bivariate Archimedean copulas. This study aims at identifying and then describe in a probabilistic way the precipitation and runoff relations in the area playing an important role...
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An improved high-speed residue-to-binary converter based on the chinese remainder theorem
Publicationw pracy zaprezentowano nowy szybki konwerter z systemu resztowego do systemu binarnego. Projekcje ortogonalne wyznaczane są przy użyciu funkcji logicznych pięciu zmiennych. Suma projekcji obliczana jest z zastosowaniem drzewa Wallace'a. Wektor sumy i wektor przeniesienia są dzielone na segmenty tak aby liczba reprezentowana łącznie przez obydwa segmenty o młodszych wagach nie przekraczała zakresu systemu resztowego,M. Bity segmentów...
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The Modifications of Haemoglobin, Erythropoietin Values and Running Performance While Training at Mountain vs. Hilltop vs. Seaside
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Nonlinear Distribution Pattern of Hibernating Bats in Caves along an Elevational Gradient in Mountain (Carpathians, Southern Poland)
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Co-occurrence probability of water balance elements in a mountain catchment on the example of the upper Nysa Kłodzka River
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ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
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FPGA realization of the high-speed residue-to-binary converter based on chinese remainder theorem
PublicationW pracy przedstawiono architekturę, realizację FPGA oraz symulację numeryczną na poziomie bitowym szybkiego konwertera z systemu resztowego do systemu binarnego dla modułów 5-bitowych opartego na chińskim twierdzeniu o resztach. Algorytm konwertera obejmuje obliczanie projekcji ortogonalnych poprzez odczyt pamięci oraz sumowanie modulo M realizowane dwustopniowo, pierwszy stopień oparty o sumatory CSA umożliwia redukcję do zakresu...
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FPGA realization of the high-speed residue-to-binary converter based on the Chinese Remainder Theorem
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Forced vibrations in a dynamic system that is damped by a mechanism that trans-pass through its singular position
PublicationIn the paper, vibrations of a hybrid multibody-continuous system are investigated. For all the mechanical devices, effective damping methods are crucial in the design process. To obtain it, installation of viscous dampers or elasto-viscous elements is dominant. In the paper, an alternative method is investigated. It is based on modal disparity. To describe the method briefly, when structural damping is present in continuous systems,...
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The Influence of the Depth of Cut in Single-Pass Grinding on the Microstructure and Properties of the C45 Steel Surface Layer
PublicationThe paper contains the results of a metallographic examination and nanoindentation test conducted for the medium carbon structural steel with low content of Mn, Si, Cu, Cr, and Ni after its grinding to a depth ranging from 2 μm to 20 μm, at constant cutting speed (peripheral speed) of vs = 25 ms−1 and constant feed rate of vft = 1 m/min. Applied grinding parameters did not cause the surface layer hardening, which could generate...
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RNS reverse high-speed converter with quasi-regular structure based on the Chinese Remainder Theorem
PublicationPrzedstawiono dwie nowe architektury szybkiego konwertera z systemuresztowego do systemu binarnego oparte o chińskie tw. o resztach. Zastosowano nowe struktury 4-operandowych sumatorów modulo 2M. Pierwsza ze struktur oparta jest o wstępne sumowanie najstarszych bitów wektorów sumy i przeniesienia na wyjściu sumatora CSA, natomiast druga o bezpośrednie wykrywanie przekroczenia 2M. Konwerter wykorzystujący drugą ze struktur charakteryzuje...
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Fifth-order low-pass CMOS OTA-C continuous-time filter with on-chip automatic tuning
PublicationW pracy przedstawiono budowę operacyjnego wzmacniacza transkonduktancyjnego (OTA) zasilanego napięciem stałym 2.8-4.5V wykonanego w technologii CMOS0.8um n-well. Wzmacniacz ten wykorzystano do budowy dolnoprzepustowego filtru czasu ciągłego typu OTA-C piątego rzędu. W układzie scalonym umieszczono także blok automatycznego dostrajania częstotliwości odcięcia filtru. Przedstawiono wyniki symulacji komputerowych (modele MOS BSIM3v3)...
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Design of mm-wave MIC frequency multiplayers and mixers using simple microstrip high-pass filters
PublicationPrzedyskutowano podstawowe wymagania dotyczące impedancji elementów półprzewodnikowych wykorzystywanych w mieszaczach i powielaczach częstotliwości projektowanych dla zakresu fal milimetrowych. Określono typy układów filtrujących niezbędnych w różnych częściach układów, podkreślając znaczenie filtrów górnoprzepustowych. Mikropaskowy filtr ze zwartym brzegiem został wykonany i zaimplementowany w mieszaczu pracującym w zakresie 20-40GHz.
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Microstrip line with short-circuited edge as a high-pass filter operating up to millimeter-wave frequencies
PublicationPrzedstawiono prosty planarny filtr górnoprzepustowy wykorzystujący linię mikropaskową ze zwartym brzegiem. Układy zaprojektowano w taki sposób, aby pasmo przepustowe rozpoczynało się w zakresie K lub Ka. Wykonano dwa prototypy: na podłożu w postaci warstwy dielektrycznej wykonanej z ceramiki alundowej oraz na podłożu organicznym o niskiej przenikalności elektrycznej. Wykazano dużą zgodność teoretycznych i pomierzonych charakterystyk...
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Derivation of the scaling laws used in geotechnical centrifuge modelling-application of dimensional analysis and Buckingham Π theorem
PublicationGeotechnical centrifuge modelling has been a world-wide used technology in physical tests. In this paper a derivation of scaling laws by dimensional analysis for the centrifugal modelling is presented. Basic principles of centrifuge modelling are described. Scaling laws for slow events like consolidation and fast events like dynamic loads are shown. The differences in scale factors for both processes are noticed. The aim of this...
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FPGA implementation of reverse residue conversion based on the new Chinese Remainder Theorem II- Part I
PublicationW pracy opisano implementację algorytmu konwersji z systemu resztowego do systemu binarnego opartą na nowej formie chińskiego twierdzenia o resztach określanego jako CRT II.Nowa forma CRT nie wymaga operacji modulo M , gdzie M jest zakresem liczbowym systemu resztowego, jednak wymagana jest pewna liczba mnożników. W środowisku FPGA jest zwykle dostępne są mnożniki, stąd mogą być one wykorzystane do realizacji konwertera. Głównym...
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Bandwidth-Controllable Third-Order Band Pass Filter Using Substrate Integrated Full- and Semi-Circular Cavities
PublicationThe article presents a novel circular substrate integrated waveguide (SIW) bandpass filter (BPF) with controllable bandwidth. The proposed BPF is configured using two microstrip feedlines, semi- circular SIW cavities, capacitive slots, and inductive vias. The circular cavity is bisected into two halves, with the two copies thereof being cascaded. Two bisected and cascaded structures obtained this way are subsequently connected...
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CHILDRENS GEOLOGY. 6, 7 AND 8 YEAR-OLD CHILDRENS UNDERSTANDING OF THE PHENOMENA OF VOLCANIC EXPLOSION, MOUNTAINS FORMATION AND ACCUMULATION OF SNOW ON MOUNTAIN PEAKS
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FPGA implementation of reverse residue conversion based on the new Chinese Remainder Theorem II- Part II,- Experimantal results
PublicationW pracy opisano realizację sprzętową konwertera z systemu resztowego do systemu binarnego. Konwerter jest oparty na nowej formie chińskiego twierdzenia o resztach CRT II. Teoretyczne aspekty takiej konwersji przedstawiono w części I. Implementację konwertera wykonano w środowisku Xilinx FPGA. Zaprezentowano ogólną architekturę konwertera, a także opisano realizację wybranych bloków. Podano ilość koniecznych zasobów sprzętowych...
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Eco mont-Journal on Protected Mountain Areas Research
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Journal of Mountain Science
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Marek Czachor prof. dr hab.
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International Workshops on First-Order Theorem Proving
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Jarosław Przewłócki prof. dr hab. inż.
PeopleJarosław Przewłócki jest profesorem na Wydziale Architektury Politechniki Gdańskiej, zastępca kierownika Katedry Technicznych Podstaw Projektowania Architektonicznego. Podstawowym kierunkiem jego działalności naukowej są badania zjawisk losowych i zastosowanie metod probabilistycznych oraz teorii niezawodności w budownictwie, a w szczególności w geotechnice. Autor i współautor około stu publikacji naukowych, w tym szeregu książek...
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An investigation on residual stress and fatigue life assessment of T-shape welded joints
PublicationThis paper aims to quantitatively evaluate the residual stress and fatigue life of T-type welded joints with a multi-pass weld in different direction. The main research objectives of the experimental test were to test the residual stress by changing direction along with multiple wielding passes and determine the fatigue life of the welded joints. The result shows that compressive residual stress increases in the sample gradually...
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International Conference on Theorem Proving with Analytic Tableaux and Related Methods
Conferences -
Conference on Interactive Theorem Proving (previously TPHOLs, changed in 2009)
Conferences -
Functional delay fractional equations
PublicationIn this paper, we discuss functional delay fractional equations. A Banach fixed point theorem is applied to obtain the existence (uniqueness) theorem. We also discuss such problems when a delay argument has a form α(t) = αt, 0 < α < 1, by Rusing the method of successive approximations. Some existence results are also formulated in this case. An example illustrates the main result.
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A note on simple bifurcation of equilibrium forms of an elastic rod on a deformable foundation
PublicationWe study bifurcation of equilibrium states of an elastic rod on a two-parameter Winkler foundation. In the article "Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation" [Nonlinear Anal., Real World Appl. 39 (2018) 451-463] the existence of simple bifurcation points was proved by the use of the Crandall-Rabinowitz theorem. In this paper we want to present an alternative proof of this fact based...
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Fundamental properties of solutions to fractional-order Maxwell's equations
PublicationIn this paper, fundamental properties of solutions to fractional-order (FO) Maxwell's equations are analysed. As a starting point, FO Maxwell's equations are introduced in both time and frequency domains. Then, we introduce and prove the fundamental properties of electromagnetic field in FO electromagnetics, i.e. energy conservation, uniqueness of solutions, and reciprocity. Furthermore, the algorithm of the plane wave simulation...
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Janusz Smulko prof. dr hab. inż.
PeopleHe was born on April 25, 1964 in Kolno. He graduated in 1989 with honors from the Faculty of Electronics at Gdańsk University of Technology, specialising in measuring instruments. In 1989 he took second place in the Red Rose competition for the best student in the Pomerania Region. Since the beginning of his career ha has been associated with Gdańsk University of Technology: research assistant (1989-1996), Assistant Professor (1996-2012),...
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The Maslov index and the spectral flow—revisited
PublicationWe give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an associated path of self-adjoint first-order operators. We particularly pay attention to the continuity of the latter path of operators, where we consider the gap-metric on the set of all closed operators on a Hilbert space. Finally, we obtain from Cappell,...
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Justyna Zander dr inż.
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Conditions of spatiotemporal variability of the thickness of the ice cover on lakes in the Tatra Mountains
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Limits Theorems for Random Walks on Homeo(S1)
PublicationThe central limit theorem and law of the iterated logarithm for Markov chains corresponding to random walks on the space Homeo(S1) of circle homeomorphisms for centered Lipschitz functions and every starting point are proved.
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Planar Microwave Bragg Reflector Resonant Dielectric Sensor
PublicationIn this paper, a periodic structure is used to design a microwave Bragg reflector with the help of hexagonal lattice, which provides a 5 GHz wide stopband between the low-pass band with cut-off frequency 2.6 GHz and the bandpass response with start and stop frequency 7.8 GHz and 10.5 GHz, respectively. A defect in lattice allows passing a narrowband signal at 6 GHz which is found, from the dispersion relation, to be in the region...
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ENERGY ANALYSIS OF THE PROPULSION SHAFT FATIGUE PROCESS IN A ROTATING MECHANICAL SYSTEM PART III DIMENSIONAL ANALYSIS
PublicationThis article presents the third and last part of the problem of diagnosing the fatigue of marine propulsion shafts in terms of energy with the use of the action function, undertaken by the authors. Even the most perfect physical models of real objects, observed under laboratory conditions and developed based on the results of their research, cannot be useful in diagnostics without properly transferring the obtained results to the...
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Morse cohomology in a Hilbert space via the Conley index
PublicationThe main theorem of this paper states that Morse cohomology groups in a Hilbert space are isomorphic to the cohomological Conley index. It is also shown that calculating the cohomological Conley index does not require finite-dimensional approximations of the vector field. Further directions are discussed.
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Fractional equations of Volterra type involving a Riemann Liouville derivative
PublicationIn this paper, we discuss the existence of solutions of fractional equations of Volterra type with the Riemann Liouville derivative. Existence results are obtained by using a Banach fixed point theorem with weighted norms and by a monotone iterative method too. An example illustrates the results.
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Partial hyperbolicity and central shadowing
PublicationWe study shadowing property for a partially hyperbolic diffeomor- phism f. It is proved that if f is dynamically coherent then any pseudotrajec- tory can be shadowed by a pseudotrajectory with “jumps” along the central foliation. The proof is based on the Tikhonov-Shauder fixed point theorem.
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Analysis of the radiation dose in UV-disinfection flow reactors.
PublicationTheoretical considerations devoted to the variation of UV radiation doses in flow disinfection reactors are presented. The minimal time required by the fluid to pass the reactor was determined and combined with the radiation intensity. The active zones of the reactor were determined.
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Snow Cover Studies: a Review on the Intensity of Human Pressure
PublicationSnow cover should be treated as a highly dynamic medium. A variety of physical and chemical processes interact to alter its chemical composition and affect the metamorphism of its individual crystals and layers; this, in turn, has a direct influence on their mutual adhesion, and ultimately on the stability of the entire snow cover. The literature data here reported provide basic information on the forms of solid precipitation,...
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Reminiscencje z 18. Międzynarodowego Seminarium Obróbki Drewna w Vancouver cz.III. Największy na świecie producent gontów
PublicationPrzedstawiono kolejną część sprawozdania z pobytu na 18. International Wood Machining Seminar w Vancouver w Kanadzie. Ogólnie scharakteryzowano dwa zakłady, Small Teal Jones, mały tartak jak na warunki kanadyjskie, przerabiający 90000 m3 surowca oraz fabrykę Mitsui Home Inc. wytwarzającą panele ścian domów drewnianych, głównie na potrzeby rynku japońskiego. Podczas wycieczki poseminaryjnej naocznie zapoznano się z klęską ekologiczną...
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Magdalena Chmara dr inż.
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Comparative analysis of the theoretical models of ideal propulsor, ideal fluid brake, ideal screw propeller and ideal axial wind turbine
PublicationThe article presents a detailed discussion of four different fluid dynamics devices.These devices are presented with all relevant mathematical formulae regarding the forces, the power and the efficiency. It is demonstrated that application of the Betz theorem to axial wind turbines is not correct and it underestimates the maximujm achievable efficiency. This conclusion is supported by numerical calculations.
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Synthesis of coupled lossy resonator filters.
PublicationA technique for fast synthesis of coupling matrix low-pass prototypes of generalized. Chebyshev bandpass filters with lossy resonators is presented in this letter. The coupling matrix is found by solving a nonlinear least squares problem based on zeros and poles of filter's transfer functions.
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Positive solutions to boundary value problems for impulsive second-order differential equations
PublicationIn this paper, we discuss four-point boundary value problems for impulsive second-order differential equations. We apply the Krasnoselskii's fixed point theorem to obtain sufficient conditions under which the impulsive second-order differential equations have positive solutions. An example is added to illustrate theoretical results.
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Sławomir Milewski prof. dr hab. inż.
PeopleSławomir Milewski, born in 1955 in Puck, Poland, graduated in 1979 in Chemistry from the Faculty of Chemistry, Gdańsk University of Technology (GUT). In 1984 was employed at the Department of Pharmaceutical Technology and Biochemistry. In 1985 he got his PhD, in 1994 became a DSc (habilitation) and in 2002 got the professorship in chemical sciences. Currently he is a full professor and Head of the Department of Pharmaceutical Technology...
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Existence and uniqueness of solutions for single-population McKendrick-von Foerster models with renewal
PublicationWe study a McKendrick-von Foerster type equation with renewal. This model is represented by a single equation which describes one species which produces young individuals. The renewal condition is linear but takes into account some history of the population. This model addresses nonlocal interactions between individuals structured by age. The vast majority of size-structured models are also treatable. Our model generalizes a number...