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Search results for: SMOOTH ORTHOGONAL PROJECTION SPHERE PARSEVAL FRAME
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Marcinkiewicz Averages of Smooth Orthogonal Projections on Sphere
PublicationWe construct a single smooth orthogonal projection with desired localization whose average under a group action yields the decomposition of the identity operator. For any full rank lattice \Gamma ⊂ R^d , a smooth projection is localized in a neighborhood of an arbitrary precompact fundamental domain R^d / \Gamma. We also show the existence of a highly localized smooth orthogonal projection, whose Marcinkiewicz average under the...
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Smooth orthogonal projections on sphere.
PublicationWe construct a decomposition of the identity operator on the sphere S^d as a sum of smooth orthogonal projections subordinate to an open cover of S^d. We give applications of our main result in the study of function spaces and Parseval frames on the sphere.
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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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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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The asymptotic formula for the error in orthogonal projection
PublicationW pracy podano formułę asymptotyczną błędu aproksymacji dla rzutów ortogonalnych w normie L^p.
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Comparison of the fracture toughness of pine wood determined on the basis of orthogonal linear cutting and frame sawing
PublicationIn this paper, the values of the fracture toughness of Scots pine determined by cutting tests are presented. The cutting tests were carried out using the samples of Scotch pine (Pinus sylvestris L.) from Pomeranian Region, Poland. These experiments were carried out on two research stands: orthogonal linear cutting tests were conducted using the microtome instrument and the frame saw PRW-15M was used for sawing tests. The values...
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Macromodeling techniques for accelerated finite element analysis
PublicationThis paper deals with the Model Order Reduction applied locally in the Finite Element Method (FEM) analysis. Due to the reduction process, blocks of FEM system matrices associated with selected subregions of the computational domain are projected onto the subspaces spanned by the vectors of suited orthogonal projection basis. In effect, large and sparse FEM matrices are replaced with small and dense ones, called macromodels. This...
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A Subspace-Splitting Moment-Matching Model-Order Reduction Technique for Fast Wideband FEM Simulations of Microwave Structures
PublicationThis article describes a novel model-order reduction (MOR) approach for efficient wide frequency band finite-element method (FEM) simulations of microwave components. It relies on the splitting of the system transfer function into two components: a singular one that accounts for the in-band system poles and a regular part that has no in-band poles. In order to perform this splitting during the reduction process, the projection...
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Applications of Immersive 3D Visualization Lab
PublicationThe paper presents Immersive 3D Visualization Lab (at the Faculty of Electronics, Telecommunications and Informatics at Gdańsk University of Technology in Poland) and its applications prepared after its launch in December 2014. The main device of the lab is a virtual reality cubic cave with six screen-walls, where a person can navigate in virtual space using different controllers. The most sophisticated controller is a freely rotating...
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Compressed Projection Bases for Model-Order Reduction of Multiport Microwave Components Using FEM
PublicationThis paper presents a projection basis compression technique for generating compact reduced-order models (ROM) in the FE analysis of microwave devices. In this approach redundancy is removed from the projection basis by means of the proper orthogonal decomposition technique applied to the projected system of linear equations. Compression allows for keeping the size of a reduced-order model as small as possible without compromising...
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Innovative Solutions for Immersive 3D Visualization Laboratory
PublicationThe paper presents results of the work concerning the technical specification of Immersive 3D Visualization Laboratory to be opened in late summer 2014 at the Faculty of Electronics, Telecommunications and Informatics at Gdańsk University of Technology in Poland. The person immersed in VR space will be placed in a transparent sphere with a diameter of over 10 feet, supported on rollers and equipped with a motion tracking system....
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Periodic points of latitudinal maps of the $m$-dimensional sphere
PublicationLet f be a smooth self-map of the m-dimensional sphere Sm. Under the assumption that f preserves latitudinal foliations with the fibres S1, we estimate from below the number of fixed points of the iterates of f. The paper generalizes the results obtained by Pugh and Shub and by Misiurewicz.
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Shub’s conjecture for smooth longitudinal maps of S^m
PublicationLet f be a smooth map of the m-dimensional sphere Sm to itself, preserving the longitudinal foliation. We estimate from below the number of fixed points of the iterates of f , reduce Shub’s conjecture for longitudinal maps to a lower dimensional classical version, and prove the conjecture in case m = 2 and in a weak form for m = 3.
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Scattering From a Cylindrical Object of Arbitrary Cross Section With the Use of Field Matching Method
PublicationA simple and intuitive solution to scattering problems in shielded and open structures is presented. The main idea of the analysis is based on the direct field matching technique involving the usage of projection of the fields at the boundary on a fixed set of orthogonal basis functions. Different convex shapes and various obstacle materials are considered to verify the validity of the method in open and closed structures. The...
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Macromodels for efficient FEM simulations of waveguides and resonators
PublicationThis paper introduces a novel technique for enhancing the efficiency of the finite element method (FEM) by incorporating special modules, called macromodels, into the standard eigenvalue formulation. The number of unknowns in the separated macromodel subdomain can be significantly reduced by orthogonal projection, using the efficient nodal order reduction algorithm. The idea of macromodels implementation is demonstrated on a simple...
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Propagation in the Open Cylindrical Guide of Arbitrary Cross Section With the Use of Field Matching Method
PublicationA simple solution to propagation problem in open waveguides and dielectric fibers of arbitrary convex cross section is presented. The idea of the analysis is based on the direct field matching technique involving the usage of the field projection at the boundary on a fixed set of orthogonal basis functions. A complex root tracing algorithm is utilized to find the propagation coefficients of the investigated guides. Different convex...
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Scattering and Propagation Analysis for the Multilayered Structures Based on Field Matching Technique
PublicationA semi-analytical method is employed to the analysis of scattering and guiding problems in multilayer dielectric structures. The approach allows to investigate objects with arbitrary convex cross section and is based on the direct field matching technique involving the usage of the field projection at the boundary on a fixed set of orthogonal basis functions. For the scattering problems the scattered field in the far zone is calculated...
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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An extended basis inexact shift–invert Lanczos for the efficient solution of large-scale generalized eigenproblems
PublicationThis paper proposes a technique, based on the Inexact Shift–Invert Lanczos (ISIL) method with Inexact Jacobi Orthogonal Component Correction (IJOCC) refinement, and a preconditioned conjugate-gradient (PCG) linear solver with multilevel preconditioner, for finding several eigenvalues for generalized symmetric eigenproblems. Several eigenvalues are found by constructing (with the ISIL process) an extended projection basis. Presented...
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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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Developing students' spatial skills and teaching the history of architecture through structural drawing
PublicationThe method of “structural drawing" is used in teaching history of architecture in the Architectural Faculty of Gdańsk University of Technology. It is addressed to students of the first semester of study – so to the architectural beginners. There are three main goals of the structural drawing method used in that educational course: (1) developing the students’ spatial skills; (2) training architectural drawing ability; (3) teaching...
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The Use of Photographs in the Teaching/Learning of Descriptive Geometry
PublicationThe article presents the concept of enriching the Descriptive Geometry course with photographs and several simplified real-life engineering tasks. The photographic images used for the exercises are tightly linked to engineering structures, the given specialization and the surrounding world. The photo image as a record of central projection of a real space can be useful for presentation and analysis of the properties of perspective....
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Efficient analysis of structures with rotatable elements using model order reduction
PublicationThis paper presents a novel full-wave technique which allows for a fast 3D finite element analysis of waveguide structures containing rotatable tuning elements of arbitrary shapes. Rotation of these elements changes the resonant frequencies of the structure, which can be used in the tuning process to obtain the S-characteristics desired for the device. For fast commutations of the response as the tuning elements are rotated, the...
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New hybrid quadrature schemes for weakly singular kernels applied to isogeometric boundary elements for 3D Stokes flow
PublicationThis work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for several partial differential equations including the Stokes equation for viscous flow and the Helmholtz equation for acoustics. The proposed quadrature schemes apply a Duffy transform-based quadrature...
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Efficient Usage of Dense GNSS Networks in Central Europe for the Visualization and Investigation of Ionospheric TEC Variations
PublicationThe technique of the orthogonal projection of ionosphere electronic content variations for mapping total electron content (TEC) allows us to visualize ionospheric irregularities. For the reconstruction of global ionospheric characteristics, numerous global navigation satellite system (GNSS) receivers located in different regions of the Earth are used as sensors. We used dense GNSS networks in central Europe to detect and investigate...
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Dead time effects compensation strategy by third harmonic injection for a five-phase inverter
PublicationThis paper proposes a method for compensation of dead-time effects for a fivephase inverter. In the proposed method an additional control subsystem was added to the field-oriented control (FOC) scheme in the coordinate system mapped to the third harmonic. The additional control loop operates in the fixed, orthogonal reference frame ( α - β coordinates) without the need for additional Park transformations. The purpose of this method...
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Performance analysis of data transmission in MC-CDMA radio interface with turbo codes
PublicationMulti-carrier code division multiple access (MC-CDMA) technique is a combination of two radio access techniques: CDMA and orthogonal frequency division multiplexing and has the advantages of both techniques. The paper presents the design of transmitter and receiver for MC-CDMA radio interface. It also presents encoders and decoders of turbo codes which were used in simulation of the MC-CDMA technique. Two turbo codes with 8-state...
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Rectangular Waveguide Filters Based on Deformed Dual-Mode Cavity Resonators
PublicationIn this paper, a novel design for rectangular waveguide filters with deformed dual-mode (DM) cavity resonators is demonstrated. The new resonant cavity shape is a result of applying shape deformation to the basic rectangular cavity to enable its dual-mode operation. Internal coupling between the two orthogonal cavity modes is realized by geometry deformation, eliminating the need for additional coupling elements. The designs are...
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Face Profile View Retrieval Using Time of Flight Camera Image Analysis
PublicationMethod for profile view retrieving of the human face is presented. The depth data from the 3D camera is taken as an input. The preprocessing is, besides of standard filtration, extended by the process of filling of the holes which are present in depth data. The keypoints, defined as the nose tip and the chin are detected in user’s face and tracked. The Kalman filtering is applied to smooth the coordinates of those points which...
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Horizontal velocity field derived from EPN and ASG-EUPOS satellite data on the example of south-western part of Poland
PublicationPresently the determination of the velocity field in the global reference frame is possible by using different space techniques and dense terrestrial networks from global to local and regional scales. However, the reliability of such determinations is strongly limited by the restricted number of unmodeled effects. Some of them are periodic (atmospheric or hydrological effects), some instantaneous (natural or man-made seismicity)...
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Testing OFDM Transmission Schemes for Shallow Water Acoustic Communications
PublicationLarge variability of communication properties of underwater acoustic channels, and especially strongly varying instantaneous conditions in shallow waters, is a tough challenge for the designers of underwater acoustics communication (UAC system. There is a need for developing adaptive signaling schemes that would dynamically optimize signal parameters in both physical and link layers of communication protocols. The orthogonal frequency...
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ROBOT TYPU QUADROCOPTER STEROWANY MIKROKONTROLERAMI O NIEWIELKIEJ MOCY OBLICZENIOWEJ
PublicationWspółczesna robotyka rozwija się bardzo dynamicznie. Coraz więcej osób prywatnych i inżynierów konstruuje różnego rodzaju pojazdy mobilne. Dlatego autorzy niniejszego referatu postawili sobie następującą tezę: możliwa jest budowa latającego robota mobilnego na bazie kontrolera o niskiej mocy obliczeniowej oraz prostego regulatora, i podjęli się jej udowodnienia.
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Study on deformed steel columns subjected to impact load due to soft-storey failure in buildings during earthquakes
PublicationThe so called soft-storey failure is one of the most typical types of damage induced in buildings as the result of earthquake excitation. It has been observed during ground motions that the failure of an upper soft storey of a structure results in large vertical impact load acting on the lower floors. If the resistance of the structural members of the lower storeys is not sufficient it may further lead to progressive collapse of...