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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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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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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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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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Mazur-Orlicz theorem and asymptotic formula for the error in supreme norm.
PublicationObliczono formułę asymptotyczną błędu interpolacji dla normy supremum.
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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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New aspects of the use of Optical Theorem in the analysis of microcavity lasers
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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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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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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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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...