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Search results for: flag manifold
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The Chow Ring of flag manifolds
Open Research DataSchubert calculus is the intersection theory of 19th century. Justifying this calculus is the content of the 15th problem of Hilbert. In the course to establish the foundation of algebraic geometry, Van der Vaerden and A. Weil attributed the problem to the determination of the chow ring of flag manifolds G/P, where G is a compact Lie group and P is...
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Complex Manifolds
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Smooth Orthogonal Projections on Riemannian Manifold
PublicationWe construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, S´er. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser (1992), and a similar decomposition when M is the sphere by Bownik and Dziedziul (Const....
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Parseval Wavelet Frames on Riemannian Manifold
PublicationWe 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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On the growth of the number of periodic points for smooth self maps of a compact manifold
PublicationDla ciągłego przekształcenia jednospójnej rozmaitości wymiaru co najmniej 3 w siebie, wykazujemy, że wzrost liczby punktów r-periodycznych w klasie homotopii może być nie szybszy niż liniowy, dla dowolnego, ustalonego r.
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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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Lefschetz periodic point free self-maps of compact manifolds
PublicationLet f be a self-map of a compact connected manifold M. We characterize Lefschetz periodic point free continuous self-maps of M for several classes of manifolds and generalize the results of Guirao and Llibre [J.L.G. Guirao, J. Llibre, On the Lefschetz periodic point free continuous self-maps on connected compact manifolds,
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Lefschetz periodic point free self-maps of compact manifolds
PublicationLet f be a self-map of a compact connected manifold M. We characterize Lefschetz periodic point free continuous self-maps of M for several classes of manifolds and generalize the results of Guirao and Llibre [J.L.G. Guirao, J. Llibre, On the Lefschetz periodic point free continuous self-maps on connected compact manifolds, Topology Appl. 158 (16) (2011) 2165-2169].
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Mitigation of the Flow Maldistribution in Minichannel and Minigap Heat Exchangers by Introducing Threshold in the Manifolds
PublicationIn the present paper, a detailed numerical investigation has been carried out to analyze the flow maldistribution in 50 parallel rectangular cross-section (1 mm depth and 1 mm width) minichannels and minigap section (1 mm depth and 99 mm width) with rectangular/trapezoidal manifolds in Z-type flow configuration. The author carried out numerical investigation with various mass flowrates, namely 0.05 kg/s, 0.1 kg/s and 0.2 kg/s which...
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The use of the static thermography in monitoring flap perfusion in breast reconstruction with TRAM flap
PublicationThis paper shows results of the static thermography for intraoperative and postoperative imaging of TRAM flap perfusion. The results were compared with the clinical examination of flap perfusion. The study was conducted on a group of 38 female patients who underwent breast reconstruction.
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INNOVATIVE RUN FLAT SYSTEMS
PublicationOne of the most essential threats to the mobility of wheeled vehicles is their relatively high sensitivity to tire damage. Tires can be damaged as a result at vehicle-targeting fire, after running on a mine or an improvised charge. The purpose of the article is to analyze the current technical solutions in wheeled vehicle tires, allowing for the unobstructed use of the vehicle despite the damage of one or several tires (RUN FLAT...
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Minimal number of periodic points for C^1 self-maps of compact simply-connected manifolds
PublicationNiech f będzie odwzorowaniem gładkiej zwartej i jednospójnej rozmaitości o wymiarze większym lub równym 3. W pracy zdefiniowany został topologiczny niezmiennik będący najlepszym dolnym oszacowaniem liczby punktów periodycznych w klasie gładkich odwzorowań homotopijnych z f.
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Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds
PublicationLet M be a smooth closed simply-connected 4-dimensional manifold, f be a smooth self-map of M with fast grow of Lefschetz numbers and r be a product of different primes. The authors calculate the invariant equal to the minimal number of r-periodic points in the smooth homotopy class of f.
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Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublicationLet M be a smooth compact and simply-connected manifold with simply-connected boundary ∂M, r be a fixed odd natural number. We consider f, a C1 self-map of M, preserving ∂M . Under the assumption that the dimension of M is at least 4, we define an invariant Dr(f;M,∂M) that is equal to the minimal number of r-periodic points for all maps preserving ∂M and C1-homotopic to f. As an application, we give necessary and sufficient...
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Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers
PublicationLet f be a smooth self-map of an m-dimensional (m >3) closed connected and simply-connected manifold such that the sequence of the Lefschetz num- bers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defned in combinatorial terms and is...
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Journal of Applied Logics (JAL-FLAP)
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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
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Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublicationLet $r$ be an odd natural number, $M$ a compact simply-connected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simply-connected. We consider $f$, a $C^1$ self-maps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241-258] the smooth Nielsen type periodic number $D_r(f;M,\partial M)$ was defined and proved to be equal to the minimal number of $r$-periodic points...
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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
PublicationFor a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m 4, we provide an algorithm for estimating the values of the topological invariant D^m_r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing D^m_r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013),...
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Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds
PublicationLet M be a closed smooth connected and simply connected manifold of dimension m at least 3, and let r be a fixed natural number. The topological invariant D^m_r [f], defined by the authors in [Forum Math. 21 (2009), 491-509], is equal to the minimal number of r-periodic points in the smooth homotopy class of f, a given self-map of M. In this paper, we present a general combinatorial scheme of computing D^m_r [f] for arbitrary dimension...
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Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers
PublicationLet f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math....
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Harmonic Analysis
Open Research DataWe construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, Sér. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser...
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Lapping of flat surfaces with two metallic tools.
PublicationPrzedstawiono opis docierania powierzchni płaskich docierakami aktywizowanymi w sposób swobodny i wymuszony oraz narzędziami dwumetalowymi i ściernometalowymi. Wyznaczono zużycie docieraków stalowo-żeliwnych oraz wydajność obróbki żeliwa sferoidalnego niestopowego i stali NC6.
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Problems of flat surface lapping : chapter 16
PublicationPrzedstawiono problemy docierania powierzchni płaskich w układach jednotarczowych. Omówiono analityczne i numeryczne modele kinematyki docierarek konwencjonalnych i niestandardowych, obróbkę docierakami aktywizowanymi w sposób swobodny i wymuszony, jednolitymi i dwumetalowymi. Zaprezentowano wyniki obróbki narzędziami ścierno-metalowymi elementów ceramicznych.
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Analysis of flat compensator lapping in an assembly process
PublicationPrzedstawiono sposób analizy docierania kompensatora płaskiego podczas montażu połączenia konstrukcyjnego. Wyznaczono czas główny obróbki i koszty operacji docierania jednotarczowego
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Influence of Flat Lapping Kinematics on Machinability of Ceramics
PublicationNew tools for flat grinding of ceramics are presented in the paper. Electroplated CBN tools (B64 and B107) were used in a modified single-disc lapping machine configuration. The results from experiments, such as the material removal rate and surface roughness parameters are presented and analyzed. Numerical simulations, based on the model for the shape error and tool wear estimation in machining with flat lapping kinematics, are...
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Research on the wear evenness of the tool in flat lapping
PublicationIn this paper, the dimensionless distribution of the material removal stock and the trajectories of abrasive grains cutting in single-sided lapping process are presented. They were numerically simulated based on the tribological model and kinematics equations. It can be observed that the trajectories geometry of single abrasive as well the velocities have a great influence on the final geometrical deviation. During machining, the...
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Correlation between shape errors in flat grinding
PublicationW pracy przedstawiono wyniki badań eksperymentalnych i symulacyjnych związanych z wpływem błędów kształtu narzędzia na błędy ksztaltu przedmiotu szlifowanego w układzie docierarki jednotarczowej. Szlifowanie realizowane było z wykorzystaniem specjalnych narzędzi z możliwością regulacji przekroju promieniowego.
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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
PublicationLet 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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Microgrinding of flat surfaces on single-disk lapping machine
PublicationW pracy przedstawiono wyniki badań mikroszlifowania z kinematyką docierania w układzie jednotarczowym z wykorzystaniem nowego narzędzia wykonanego z pastylek ściernych z ziarnem diamentowym (D3/2) i spoiwem żywicznym. Zakres pracy obejmował przeprowadzenie badań eksperymentalnych i modelowych związanych z analizą promienia krzywizny rys obróbkowych.
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Computer simulation of induction hardening of moving flat charge
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Microgrinding of flat surfaces on a single-disc lapping machine
PublicationW referacie przedstawiono wyniki badań eksperymentalnych mikroszlifowania z kinematyką docierania jednotarczowego. Przedstawiono propozycję narzędzia z wkładkami ściernymi z ziarnem diamentowym D3/2 i spoiwem żywicznym. Omówiono kinematykę docierania jednotarczowego i sposób oceny krzywizny rys obróbkowych.
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Microgrinding of flat surfaces on single-disc lapping machine
PublicationW pracy przedstawiono możliwości zastosowania specjalnych narzędzi do mikroszlifowania na docierarce jednotarczowej. Jedno z zastosowanych narzędzi posiada warstwę ścierniwa diamentowego (D64) nałożoną metodą galwaniczną. Drugie przetestowane narzędzie zbudowane zostało z diamentowych pastylek ściernych (D3/2). Przedstawiono analizę kinematyczną i wyniki ubytku materiałowego oraz osiągnięte parametry chropowatości.
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Machining of the flat surfaces with abrasive-metallic lapping tools.
PublicationPrzedstawiono konstrukcje narzędzi ścierno-metalowych do obróbki powierzchni płaskich na docierarkach jednotarczowych. Przeprowadzono badania wydajności i jakości powierzchni elementów ceramicznych o małych gabarytach.
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Modeling the application of steel slag in stabilizing expansive soil
PublicationThe objective of this study was to evaluate the suitability of steel slag as an additive to the engineering properties of weak clay soil. Different geotechnical laboratory tests were conducted on both stabilized and natural soils. Steel slag (SS) was added at a rate of 0, 5, 10, 15, 20, and 25% to the soil. Specific gravity, grain size analysis, Atterberg limit test, compaction test, free swell, California bearing ratio (CBR),...
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Recent Advances in Loop Heat Pipes with Flat Evaporator
PublicationThe focus of this review is to present the current advances in Loop Heat Pipes (LHP) with flat evaporators, which address the current challenges to the wide implementation of the technology. A recent advance in LHP is the design of flat-shaped evaporators, which is better suited to the geometry of discretely mounted electronics components (microprocessors) and therefore negate the need for an additional transfer surface (saddle)...
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Lapping flat surfaces with forced dosing of abrasive suspension
PublicationPrzedstawiono zbudowane stanowisko do badań wymuszonego dawkowania zawiesiny ściernej w procesie jednostronnego docierania powierzchni płaskich. Podano przyjęty program badań oraz sposób opracowania wyników realizowanych eksperymentów.
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Lapping flat surfaces with forced dosing of abrasive suspension
PublicationPrzedstawiono zbudowane stanowisko badawcze umożliwiające wymuszone dozowanie zawiesiny ściernej w operacji docierania jednotarczowego powierzchni płaskich. Podano program badań własnych oraz sposób opracowania otrzymanych wyników realizowanych eksperymentów.
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Analysis of Rolling Resistance of Tires With Run Flat Insert
PublicationRun flat properties are required for tires intended for special applications like military or rescue vehicles. Run-Flat inserts make possible to drive a car or truck, with certain restrictions, also when inflation pressure is very low or non-existing (after tire damage). Rolling resistance of tires rolling the inserts increases considerably in relation to the rolling resistance of properly inflated tires. This paper presents results...
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Wear of Electroplated Tools Used for Flat Grinding of Ceramics
PublicationTwo methods for the abrasive properties evaluation, based on the image processing, are presented in the paper. Image processing analysis was developed to evaluate quickly the abrasive properties as the tool wears down. The coefficient based on the image brightness was calculated and additional analysis was based on the number of grains located on the active surface of the tool before and after machining. The active surfaces of...
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Technological Problems in Lapping on Flat Surfaces of Ceramic Parts
PublicationThis paper will present the results of research on single-disc lapping of flat surfaces of small ceramic elements. Machining with the use of different tools such as metallic, two-metallic and abrasive-metallic will be analyzed. The basics and techniques of reinforcement of laps will be discussed. The results of the influence of parameters on the surface quality of ceramic conponents (sealing) for three treatments on lapping machines...
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Determining the conditions for temperature measurements during flat lapping
PublicationPrzedstawiono pomiary temperatury układu wykonawczego docierarki jednotarczowej ABRALAP 380. Badano wpływ liczby stosowanych pierścieni prowadzących przy docieraniu elementów ceramicznych mikroziarnami węglika krzemu. Analizowano przyrost temperatury układu w czasie do trzech godzin. W badaniach zastosowano kamerę termowizyjną V-20II firmy VIGO System S.A.
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Research on operational characteristics of tyres with run flat insert
PublicationThe paper describes results of research on heavy vehicle tyre with Run Flat VFI insert. The experiment has included the determination of heat generation, rolling resistanceand radial stifnessof two different tyre designes (textile and steel carcass). The results have been used for the purpose of ewalution of tyre operating characteristics. The study included research on non-inflated tyre properties. The purpose of the paper is...
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Simulation of induction hardening of flat surfaces of moving massive elements
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Advanced acoustic signal analysis used for wheel-flat detection
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Study of abrasive slurry dosage in flat surfaces lapping process
PublicationPrzedstawiono wyniki badań dozowania pasty i zawiesiny ściernej w procesach docierania powierzchni płaskich. Badano wpływ wielkości dawki ścierniwa na podstawowe parametry chropowatości powierzchni elementów miedzianych i ceramicznych. Docierano miedź betlenową MOOB oraz ceramikę Al2O3 i Al2O3-ZrO2 mikroziarnami węglika krzemu i węglika boru.
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Influence of abrasive slurry dosage on flat surface lapping effects
PublicationPrzedstawiono wyniki badań dawkowania zawiesiny ściernej w obróbce powierzchni płaskich na docierarce jednotarczowej. Analizowano wpływ dawki ścierniwa na wydajność i jakość obróbki elementów ceramicznych i miedzianych.
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Influence and development of new kinematic systems in flat surface lapping
PublicationThe face grinding and lapping technology is widely used in the field of the precise and ultraprecise manufacturing. It has become an indispensable technology in the manufacture of many parts. An absence of material restrictions allows machining both metal and non-metallic materials, including technical ceramics [1]. Nowadays there are mainly two kinematic systems in lapping machines [2]. The machining plane-parallel surfaces is...
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Flow of liquid in flat gaps of the satellite motor working mechanism
PublicationThe article describes the methodology and results of investigations of the flow of oil and HFA-E emulsion in flat gaps of the working mechanism of a satellite motor. The flow of liquid in those gaps is turbulent and not fully developed. The article presents two methods of modelling this flow. Method I makes use of the Darcy-Weisbach formula, while Method II bases on the assumption that in the variable-length gaps the flow is turbulent...
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Detonations in hydrogen-methane-air mixtures in semi confined flat channels
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