Wyniki wyszukiwania - Biblioteka Nauki

1

The inertia of unicyclic graphs and bicyclic graphs

100%

Liu Y.

Discussiones Mathematicae - General Algebra and Applications

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2013

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tom 33

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nr 1

109-115

EN

Let G be a graph with n vertices and ν(G) be the matching number of G. The inertia of a graph G, In(G) = (n₊,n₋,n₀) is an integer triple specifying the numbers of positive, negative and zero eigenvalues of the adjacency matrix A(G), respectively. Let η(G) = n₀ denote the nullity of G (the multiplicity of the eigenvalue zero of G). It is well known that if G is a tree, then η(G) = n - 2ν(G). Guo et al. [Ji-Ming Guo, Weigen Yan and Yeong-Nan Yeh. On the nullity and the matching number of unicyclic graphs, Linear Algebra and its Applications, 431 (2009), 1293-1301.] proved if G is a unicyclic graph, then η(G) equals n - 2ν(G) - 1, n-2ν(G) or n - 2ν(G) + 2. Barrett et al. determined the inertia sets for trees and graphs with cut vertices. In this paper, we give the nullity of bicyclic graphs 𝓑ₙ⁺⁺. Furthermore, we determine the inertia set in unicyclic graphs and 𝓑ₙ⁺⁺, respectively.

2

Sources of inertia in an expanding universe

100%

Prytz K.

Open Physics

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2015

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tom 13

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nr 1

EN

In a cosmological perspective, gravitational induction is explored as a source to mechanical inertia in line with Mach’s principle. Within the standard model of cosmos, considering the expansion of the universe and the necessity of retarded interactions, it is found that the assumed dynamics may account for a significant part of an object’s inertia.

3

Geometry and inertia of the human body - review of research

100%

Erdmann W. S.

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1999

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tom Vol. 1, nr 1

23-35

EN

The paper is devoted to such morphological quantities of the human body as (1) geometric, i.e., linear, planar, and spatial;(2) inertial, especially - mass, density, radius of center of mass, moment of inertia and its radius. Description of quantities was given, material used (live subjects, cadavers, models), and methods utilized: mechanical and electromechanical, optical, geometric (for inertia quantities), penetrating, calculation, modelling. The most important results were given, especially for inertial quantities.

4

Compensation of mechanical inertia in car power transmission systems

86%

Mamala J. , Jantos J. , Brol S.

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2007

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tom R. 46, nr SC1

259-266

EN

In order to secure energetic efficiency the combustion engine should operate with relatively high torque level. In the circumstances of small power demand; for instance, when the car is moving with low speed it is associated with low rotational speed of engine. In power transmission systems with constant power supply e.g. CVTs characterised by a large differentiation of kinematic transmission, the investigated issue plays an important role. In order to secure a prompt response of such transmission systems a variety of control strategies is proposed. Particular attention is devoted to transmission systems with zero inertia, which apply an supplementary power source (device applying inertia or electrical motor) to assist the engine in accelerating in the transition phase. Due to the large complexity of those systems an alternative construction is proposed, one which does not apply a hybrid drive. The compensation of mechanical inertia secured by a short-term engine supercharging. This supercharging is performed with the aid of compressed air chamber. This paper presents the design and control of this system and the technique of controlling it. On the basis of results of stand tests it was indicated among all that an abrupt temperature fall resultsin from iar expansion is effective in preventing knocking sounds in combustion.

5

Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials

86%

Karelin I. , Lerer L.

International Journal of Applied Mathematics and Computer Science

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2001

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tom 11

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nr 6

1285-1310

EN

It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of . The proof of these results depends heavily on a new inertia theorem for matrix polynomials which is also one of the main results in this paper.

6

Bezwładność mechaniczna układu napędowego w procesie przyspieszania

72%

Mamala J. , Jantos J.

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2008

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tom R. 105, z. 6-M

167-179

PL

W niniejszym artykule przeanalizowano konstrukcję układu doładowania silnika spalinowego o zapłonie iskrowym w celu kompensacji niedoboru siły napędowej na kołach samochodu oraz przedstawiono wyniki wstępnych badań.

EN

They analyzed in the paper structure of the system of charging the internal-combustion engine up about the spark ignition in the purpose for the compensation for the shortage of the driving force on wheels of the car and results of research were presented.

7

Matrix Quadratic Equations, Column/row Reduced Factorizations and an Inertia Theorem for Matrix Polynomials

72%

Karelin I. , Lerer L.

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2001

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tom Vol. 11, no 6

1285-1310

EN

It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial G(lambda) (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of G(lambda). The proof of these results depends heavily on a new inertia theorem for matrix polynomials which is also one of the main results in this paper.

8

Procesy analiz numerycznych płyt masywnych w strukturach 3D

72%

Krentowski J. , Szeląg R. , Tribiłło R.

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2006

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tom Z. 27

149-162

PL

Publikacja zawiera interpretację fizyczną i techniczną równowagi masy materiału konstrukcji, która usytuowana w kartezjańskiej przestrzeni inercji przejmuje siły grawitacji. Oczekiwanym rezultatem analizy są przemieszczenia i naprężenia wewnętrzne, które stosownie do warunków na powierzchni brył, kwalifikują zagadnienie jako problem statyczny lub dynamiczny. Uwzględniono proces analizy numerycznej dla warunków brzegowych stabilizujących masę. W takich kryteriach uogólniono klasyczną interpretację technicznie ortotropowych struktur w klasie modeli fizycznych 2D i opracowano algorytm wykorzystany do kształtowania elementów konstrukcji inżynierskich w klasie 3D.

EN

The papers contains physical and technical interpretation of equilibrum of mass of material construction which is situated in space of inertia the strength of gravitation. Dislocations and internal tensions are the expected result of analysis, which suitably to conditions on the surface of clods, qualify the matter to static or dynamic problems. The process of numeric analysis was considered for shore stabilising the mass conditions. In such criteria the classic interpretation of the technically orthotropic structures in the class of physical models 2D was generalizing and the algorithm used to formation of the elements of engeenering constructions in 3D class was has worked out.

9

On the gravitodynamics of moving bodies

72%

Mol A.

Open Physics

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2011

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tom 9

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nr 5

1151-1164

EN

In the present work we propose a generalization of Newton’s gravitational theory from the original works of Heaviside and Sciama, that takes into account both approaches, and accomplishes the same result in a simpler way than the standard cosmological approach. The established formulation describes the local gravitational field related to the observables and effectively implements the Mach’s principle in a quantitative form that retakes Dirac’s large number hypothesis. As a consequence of the equivalence principle and the application of this formulation to the observable universe, we obtain, as an immediate result, a value of Ω = 2. We construct a dynamic model for a galaxy without dark matter, which fits well with recent observational data, in terms of a variable effective inertial mass that reflects the present dynamic state of the universe and that replicates from first principles, the phenomenology proposed in MOND. The remarkable aspect of these results is the connection of the effect dubbed dark matter with the dark energy field, which makes it possible for us to interpret it as longitudinal gravitational waves.