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    Wyświetlanie 1-8 z 8
    Tytuł:
    A systematic approach for solving the great circle track problems based on vector algebra
    Autorzy:
    Chen, C. L.
    Powiązania:
    https://bibliotekanauki.pl/articles/260175.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Gdańska. Wydział Inżynierii Mechanicznej i Okrętownictwa
    Tematy:
    great circle
    vector algebra
    multiple products
    spherical trigonometry
    Opis:
    A systematic approach, based on multiple products of the vector algebra (S-VA), is proposed to derive the spherical triangle formulae for solving the great circle track (GCT) problems. Because the mathematical properties of the geometry and algebra are both embedded in the S-VA approach, derivations of the spherical triangle formulae become more understandable and more straightforward as compared with those approaches which use the complex linear combination of a vector basis. In addition, the S-VA approach can handle all given initial conditions for solving the GCT problems simpler, clearer and avoid redundant formulae existing in the conventional approaches. With the technique of transforming the Earth coordinates system of latitudes and longitudes into the Cartesian one and adopting the relative longitude concept, the concise governing equations of the S-VA approach can be easily and directly derived. Owing to the advantage of the S-VA approach, it makes the practical navigator quickly adjust to solve the GCT problems. Based on the S-VA approach, a program namely GCTPro_VA is developed for friendly use of the navigator. Several validation examples are provided to show the S-VA approach is simple and versatile to solve the GCT problems.
    Źródło:
    Polish Maritime Research; 2016, 2; 3-13
    1233-2585
    Pojawia się w:
    Polish Maritime Research
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Vector algebra for Steep Slope Model analysis
    Autorzy:
    Kolecka, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/295124.pdf
    Data publikacji:
    2012
    Wydawca:
    Stowarzyszenie Geomorfologów Polskich
    Tematy:
    vector algebra
    Steep Slope Model
    geographic information systems
    slope
    aspect
    Opis:
    Geographic Information Systems offer many algorithms that allow analysis of digital elevation models. They work with both GRID and TIN data, but they are limited to 2.5D models, where one planar (X,Y) position refers to only one vertical (Z) value. In mountainous regions, however, many steep, vertical and even overhung parts of rock walls and slopes occur. GRID and TIN models in a standard projection are not capable to deal with such a relief as they are not able to capture all complexity of steep slopes that can be observed from the terrestrial perspective. Such a perspective can be introduced into GIS via computer graphics software that allows 3D surface modelling by means of mesh, e.g. 3D triangular network. The paper presents a concept that implements 3D mesh in GIS and utilizes vector algebra to analyze such a surface. The idea is based on using normal vectors to compute slope and aspect of each triangle in a mesh. The computed values are saved as their attributes. Complete procedures are written in Python programming language and implemented into popular GIS software to work as a plug-in tool.
    Źródło:
    Landform Analysis; 2012, 21; 17-25
    1429-799X
    Pojawia się w:
    Landform Analysis
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Character analysis on linear elementary algebra with max-plus operation
    Autorzy:
    Kalfin, Kalfin
    Jufra, Jufra
    Muhtar, Norma
    Subiyanto, Subiyanto
    Supian, Sudradjat
    Powiązania:
    https://bibliotekanauki.pl/articles/1177763.pdf
    Data publikacji:
    2018
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Max-Plus Algebra
    eigenvalues and eigenvectors
    matrix
    vector space
    Opis:
    This paper discusses the further characteristic that exists in max-plus algebra by comparing the characteristics that exist in ordinary linear algebra. The steps taken are to examine what happens to linear algebra, then applied to max-plus algebra with respect to the existing operations. Characteristics of matrix operations and differences that occur in linear algebra and are met in max-plus algebra with max and plus operations. However, max-plus algebra does not satisfy the vector space characteristics.
    Źródło:
    World Scientific News; 2018, 100; 110-123
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Lie algebras of vector fields related to Riemannian foliations
    Autorzy:
    Rybicki, Tomasz
    Powiązania:
    https://bibliotekanauki.pl/articles/1311816.pdf
    Data publikacji:
    1993
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Riemannian foliation
    Lie algebra
    ideal
    isomorphism
    vector field
    generalized manifold
    stratification
    Opis:
    Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.
    Źródło:
    Annales Polonici Mathematici; 1993, 58, 2; 111-122
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the versal discriminant of $J_{k,0}$ singularities
    Autorzy:
    Jaworski, Piotr
    Powiązania:
    https://bibliotekanauki.pl/articles/1311249.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    versal deformation
    versal unfolding
    moduli
    liftable vector fields
    local algebra
    topological triviality
    Opis:
    It is well known that the versal deformations of nonsimple singularities depend on moduli. The first step in deeper understanding of this phenomenon is to determine the versal discriminant, which roughly speaking is an obstacle to analytic triviality of an unfolding or deformation along the moduli. The versal discriminant of the Pham singularity ($J_{3,0}$ in Arnold's classification) was thoroughly investigated by J. Damon and A. Galligo [2], [3], [4]. The goal of this paper is to continue their work and to describe the versal discriminant of a general $J_{k,0}$ singularity.
    Źródło:
    Annales Polonici Mathematici; 1996, 63, 1; 89-99
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Integral theorems for monogenic functions in an infinite-dimensional space with a commutative multiplication
    Twierdzenia całkowe dla funkcji monogenicznych w przestrzeni nieskończenie-wymiarowej z mnożeniem przemiennym
    Autorzy:
    Plaksa, Sergiy Anatoliyovych
    Shpakivskyi, Vitalii Stanislavovych
    Powiązania:
    https://bibliotekanauki.pl/articles/699868.pdf
    Data publikacji:
    2018
    Wydawca:
    Łódzkie Towarzystwo Naukowe
    Tematy:
    Laplace equation, spatial potentials, harmonic algebra, topological vector space, differentiable in the sense of Gateaux function, monogenic function, Cauchy- Riemann conditions
    równanie Laplace’a, potencjały przestrzenne, algebra harmoniczna, przestrzeń wektorowa topologiczna, różniczkowalność w sensie Gateaux, funkcja monogeniczna, warunki Cauchy’ego-Riemanna
    Opis:
    https://doi.org/10.26485/0459-6854/2018/68.2/2 Rozpatrujemy funkcje o wartościach w wektorowej przestrzeni topologicznej będącej rozszerzeniem pewnej nieskończenie-wymiarowej przemiennej algebry Banacha stowarzyszonej z trójwymiarowym równaniem Laplace’a. Uzyskujemy twierdzenia całkowe dla funkcji monogenicznych o wartościach we wspomnianej algebrze i we wspomnianej wektorowej przestrzeni topologicznej.
    https://doi.org/10.26485/0459-6854/2018/68.2/2 We consider monogenic functions taking values in a topological vector space being an expansion of a certain infinite-dimensional commutative Banach algebra associated with the three-dimensional Laplace equation. We establish also integral theorems for monogenic functions taking values in the mentioned algebra and the mentioned topological vector space.
    Źródło:
    Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations; 2018, 68, 2; 25-36
    1895-7838
    2450-9329
    Pojawia się w:
    Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Testing hypotheses about structure of parameters in models with block compound symmetric covariance structure
    Autorzy:
    Zmyślony, Roman
    Kozioł, Arkadiusz
    Powiązania:
    https://bibliotekanauki.pl/articles/1194457.pdf
    Data publikacji:
    2019-07-02
    Wydawca:
    Główny Urząd Statystyczny
    Tematy:
    coordinate-free approach
    Jordan algebra
    multivariate model
    block compound symmetric covariance structure
    best unbiased estimators
    testing structure of mean vector
    testing independence of block variables
    Opis:
    In this article we deal with testing the hypotheses of the so-called structured mean vector and the structure of a covariance matrix. For testing the above mentioned hypotheses Jordan algebra properties are used and tests based on best quadratic unbiased estimators (BQUE) are constructed. For convenience coordinate-free approach (see Kruskal (1968) and Drygas (1970)) is used as a tool for characterization of best unbiased estimators and testing hypotheses. To obtain the test for mean vector, linear function of mean vector with the standard inner product in null hypothesis is changed into equivalent hypothesis about some quadratic function of mean parameters (it is shown that both hypotheses are equivalent and testable). In both tests the idea of the positive and negative part of quadratic estimators is applied to get the test, statistics which have F distribution under the null hypothesis. Finally, power functions of the obtained tests are compared with other known tests like LRT or Roy test. For some set for parameters in the model the presented tests have greater power than the above mentioned tests. In the article we present new results of coordinate-free approach and an overview of existing results for estimation and testing hypotheses about BCS models.
    Źródło:
    Statistics in Transition new series; 2019, 20, 2; 139-153
    1234-7655
    Pojawia się w:
    Statistics in Transition new series
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Around Widders characterization of the Laplace transform of an element of $L^{∞}(ℝ^{+})$
    Autorzy:
    Kisyński, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/1207972.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    operators from $L_{ϰ}^{1}(ℝ^{+})$ into a Banach space
    complete monotonicity and positivity with respect to a cone
    one-parameter semigroups of operators
    vector measures
    Gelfand space
    Radon-Nikodym property
    representations of the convolution algebra $L_{ϰ}^{1}(ℝ^{+})$
    pseudoresolvents and their generators
    real inversion formulas for the Laplace transform
    Opis:
    Let ϰ be a positive, continuous, submultiplicative function on $ℝ^{+}$ such that $lim_{t→∞} e^{-ωt}t^{-α}ϰ(t) = a$ for some ω ∈ ℝ, α ∈ $\overline{ℝ^{+}}$ and $a ∈ ℝ^{+}$. For every λ ∈ (ω,∞) let $ϕ_{λ}(t) =e^{-λt}$ for $t ∈ ℝ^{+}$. Let $L^{1}_{ϰ}(ℝ^{+})$ be the space of functions Lebesgue integrable on $ℝ^{+}$ with weight $ϰ$, and let E be a Banach space. Consider the map $ϕ_{•}: (ω,∞) ∋ λ → ϕ_{λ} ∈ L_{ϰ}^{1}(ℝ^{+})$. Theorem 5.1 of the present paper characterizes the range of the linear map $T → Tϕ_{•}$ defined on $L(L_{ϰ}^{1}(ℝ^{+});E)$, generalizing a result established by B. Hennig and F. Neubrander for $ϰ(t)=e^{ωt}$. If ϰ ≡ 1 and E =ℝ then Theorem 5.1 reduces to D. V. Widder's characterization of the Laplace transform of a function in $L^{∞}(ℝ^{+})$. Some applications of Theorem 5.1 to the theory of one-parameter semigroups of operators are discussed. In particular a version of the Hille-Yosida generation theorem is deduced for $C_0$ semigroups $(S_t)_{t ∈ \overline{ℝ^{+}}}$ such that $sup_{t ∈ \overline{ℝ^{+}}} (ϰ(t))^{-1}∥ S_t∥ < ∞$.
    Źródło:
    Annales Polonici Mathematici; 2000, 74, 1; 161-200
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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