Causal Character Research Articles

Projective Vector Fields on Semi-Riemannian Manifolds

This paper explores the properties of projective vector fields on semi-Riemannian manifolds. The main result establishes that if a projective vector field P on such a manifold is also a conformal vector field with potential function ψ and the vector field ζ dual to dψ does not change its causal character, then P is homothetic, or ζ is a light-like vector field. Additionally, it is shown that a complete Riemannian manifold admits a projective vector field that is also conformal and non-Killing if and only if it is locally Euclidean. The paper also presents other results related to the characterization of Killing and parallel vector fields using the Ricci curvature and the Hessian of the function given by the inner product of the vector field.

Ruled surfaces obtained by infinitesimal bendings of curves in Minkowski 3-space

In this paper, we define a ruled surface obtained by an infinitesimal bending of a curve in Minkowski [Formula: see text]-space. We also characterize such ruled surfaces according to causal characters of the curve. Furthermore, we find appropriate conditions of ruled surfaces obtained by infinitesimal bendings of curves to be (lightlike) developable, in particular, cylindrical or conical in Minkowski [Formula: see text]-space, with examples presented.

Sections of the light cone in Minkowski 4-space

The intersection of an affine hyperplane in L4 with the light cone C is called a conic section. In this paper, it is proved that the conic sections in L4 are either Riemannian spheres, hyperbolic spaces or horospheres, depending on the causal character of the hyperplane. Analogous results for affine sections of de Sitter and hyperbolic spaces in L4 are also presented at the end.

Entrepreneurial orientation and performance in nonprofit organizations: A meta‐analysis

AbstractThis meta‐analysis examines the state of research on the relationship between entrepreneurial orientation (EO) and performance in nonprofit organizations (NPOs). The evidence on this relationship in the business context is already well consolidated. Nonprofit research also elaborated review publications on EO. However, existing knowledge lacks an examination of the EO–performance relationship in NPOs. This study includes 25 publications in the correlation‐based meta‐analysis and finds that various performance goals are positively affected. Nonetheless, the results reveal several inconsistencies regarding conceptual and methodological approaches. A critical reflection on the complexity and differentiation of both constructs, problems of bias, and the causal character of the relationship addresses these issues.

Closed 1/2-elasticae in the hyperbolic plane

We study critical trajectories in the hyperbolic plane for the 1/2-Bernoulli's bending energy with length constraint. Critical trajectories with periodic curvature are classified into three different types according to the causal character of their momentum. We prove that closed trajectories arise only when the momentum is a time-like vector. Indeed, for suitable values of the Lagrange multiplier encoding the conservation of the length during the variation, we show the existence of countably many closed trajectories with time-like momentum, which depend on a pair of relatively prime natural numbers.

Double null data and the characteristic problem in general relativity

General hypersurfaces of any causal character can be studied abstractly using the hypersurface data formalism. In the null case, we write down all tangential components of the ambient Ricci tensor in terms of the abstract data. Using this formalism, we formulate and solve in a completely abstract way the characteristic Cauchy problem of the Einstein vacuum field equations. The initial data is detached from any spacetime notion, and it is fully diffeomorphism and gauge covariant. The results of this paper put the characteristic problem on a similar footing as the standard Cauchy problem in General Relativity.

Helicoidal surfaces in some conformally flat pseudo-spaces of dimensional three

We introduce the complete pseudo-Riemannian manifold [Formula: see text] with a conformally flat pseudo-metric satisfying Einstein’s equation. First, we get a theorem that associates the curvatures of a non-degenerate surface belonging to conformally equivalent spaces, say [Formula: see text] and [Formula: see text]. Next, we evaluate the existence of non-degenerate helicoidal surfaces in some conformally flat pseudo-spaces with pseudo-metrics corresponding to particular conformal factors (for example, a certain rotational symmetry with translational symmetry). We determine these conformal factors according to the causal characters of the axis of rotation. Right after, we get a two-parameter family of non-degenerate helicoidal surfaces with prescribed extrinsic curvature or mean curvature given by smooth functions, corresponding to both spacelike and timelike axes of rotation. As for the lightlike axis, we discuss some particular cases.

The Darboux trihedrons of timelike surfaces in the Lorentzian 3-space

The parameter curves [Formula: see text] and [Formula: see text] intersecting under the angle [Formula: see text] on a timelike surface and any curve [Formula: see text] passing through the same point with these curves have six different cases according to their causal characters. In this study, the Darboux trihedrons of these three curves and the Darboux instantaneous rotation vectors of these trihedrons are separately calculated for each of these six cases, and the relationships between these vectors are given. In addition, some theorems and results have been obtained on this surface. Besides, the special cases where the parameter curves [Formula: see text] and [Formula: see text] intersect perpendicularly are examined and these cases are compared with previous studies.

Timelike loxodromes on Lorentzian helicoidal surfaces in Minkowski n-space

In this paper, we examine timelike loxodromes on three kinds of Lorentzian helicoidal surfaces in Minkowski nn-space. First, we obtain the first order ordinary differential equations which determine timelike loxodromes on the Lorentzian helicoidal surfaces in En1E1n according to the causal characters of their meridian curves. Then, by finding general solutions, we get the explicit parametrizations of such timelike loxodromes. In particular, we investigate the timelike loxodromes on the three kinds of Lorentzian right helicoidal surfaces in En1E1n. Finally, we give an example to visualize the results.

Conformal actions on the Einstein universe

In this paper we study nontransitive irreducible and transitive reducible conformal actions on the Einstein universe Ein1,n−1. In either case, we give the explicit representation of the acting group in O(2,n). When the action is nontransitive and irreducible, we determine the dimension and the causal character of the induced orbits in the nullcone of R2,n and then in the Einstein universe. We prove that any such nontransitive action induces an open orbit in the Einstein universe and that the orbit space is finite.

On an Explicit Characterization of Spherical Curves in Dual Lorentzian 3-SpaceD13

In this study, we developed a mathematical framework for studying spherical and null curves in dual Lorentzian 3-spaceD13. Considering the causal character of the dual curve, sufficient and necessary conditions for spacelike curves to be dual Lorentzian spherical were given. Also, new sufficient and necessary conditions for non-null curves to be hyperbolic dual spherical were presented. Then, an insight on curves with null-principal normal is reported.

The Prevalence of Histopathological Features of Pneumonia in Goats with Symptomatic Caprine Arthritis-Encephalitis.

Chronic interstitial pneumonia (CIP) is a main pathology of sheep infected with small ruminant lentivirus (SRLV). Caprine arthritis-encephalitis (CAE) is caused by the same pathogen; however, the presence of CIP has been only occasionally reported in SRLV-infected goats. We carried out a cross-sectional study to determine the prevalence of histopathological lesions indicative of CIP in goats with symptomatic CAE, and to investigate whether CIP was associated with a higher prevalence of other types of pneumonia (purulent bronchopneumonia, fibrinous pleuropneumonia) or bacterial infections. Lung specimens and bronchial swabs were collected for histopathological and bacteriological examination, respectively, from 116 goats from a CAE-affected herd. All goats were euthanized due to severe clinical signs of CAE. The goats were seropositive for SRLV infection in two different ELISAs and the presence of SRLV antigen in the lung tissue was confirmed by immunohistochemistry. Histopathologically, pneumonia of any type was confirmed in 82 goats (70.7%) and CIP was present in 67 goats (57.8%). In most goats, the severity of the histopathological features of pneumonia was mild. Bacteria were detected in bronchial swabs from 73 goats (62.9%). CIP proved to be significantly positively linked to the occurrence of purulent bronchopneumonia (p < 0.001), fibrinous pleuropneumonia (p = 0.001), and of the infection of lungs with bacteria capable of causing pneumonia (p = 0.050). The causal character of these associations should be considered and warrants further investigation.

Associated curves of a Frenet curve in the dual Lorentzian space

In this work, we firstly introduce notions of principal directed curves and principal donor curves which are associated curves of a Frenet curve in the dual Lorentzian space D 3 1 D13 . We give some relations between the curvature and the torsion of a dual principal directed curve and the curvature and the torsion of a dual principal donor curve. We show that the dual principal directed curve of a dual general helix is a plane curve and obtain the equation of dual general helix by using position vector of plane curve. Then we show that the principal donor curve of a circle in $\mathbb{D}^{2}$ or a hyperbola in $\mathbb{D}_{1}^{2}$ and the principal directed curve of a slant helix in $\mathbb{D}_{1}^{3}$ are a helix and general helix, respectively. We explain with an example for the second case. Finally, according to causal character of the principal donor curve of principal directed rectifying curve in $\mathbb{D}_{1}^{3}$, we show this curve to correspond to any timelike or spacelike ruled surface in Minkowski 3−space R 3 1 R13 .

Geometric kinematics of persistent rigid motions in three-dimensional Minkowski space

This paper investigates whether Lorentz geometry can be systematically implemented to study the geometric kinematics of persistent rigid motions in three-dimensional Minkowski space. The notion of persistence of a one-parameter rigid motion is identified by the property that the instantaneous twist of the motion has a constant pitch. The main difference between three-dimensional Euclidean and Minkowski spaces is that the pitch of twists will take three different values in Minkowski space depending on the causal character of the curve on which the motions are based. Furthermore, based on the fundamentals of screw theory, the paper establishes necessary and sufficient criteria for modeling the persistence of some significant frame motions, including Frenet–Serret, adapted frame, and Bishop motions. Then, the axode surfaces of these special motions and their geometric concepts are defined. Finally, for a thorough treatment of special frame motions in three-dimensional Minkowski space, this paper reveals some illustrative examples of persistent rigid motions and axode surfaces.

Spacelike Surfaces with a Common Line of Curvature in Lorentz-Minkowski 3-Space

This paper aims to study spacelike surfaces from a given spacelike curve in Minkowski 3–space. Also, we investigate the necessary and sufficient conditions for the given space-like curve to be the line of curvature on the space-like surface. Depending on the causal character of the curve, the necessary and sufficient conditions for the given space-like curve to satisfy the line of curvature and the geodesic (resp. asymptotic) requirements are also analyzed. Furthermore, we give with illustration some computational examples in support of our main results.

On rectifying curves in Minkowski 3-space

In this study, we investigate the rectifying curve and its centrode by using a dilation of a unit speed curve on pseudo-sphere or pseudo-hyperbolic space. Firstly, considering a causal character of any curve, we study the connection between Serret-Frenet apparatus of the curve on pseudo-sphere or pseudo-hyperbolic space and its dilation. Then, we extend necessary conditions in order to make the centrode a rectifying curve. Also, we examine some properties of centrode which is a rectifying curve.

Nikolai Andreevich Chinakal: a Personality in Science Resume

The unique personality and scientific biography of Nikolai Andreevich Chinakal (1888–1979), a scientist in the field of mining, a Corresponding Member of the USSR Academy of Sciences make it relevant. He was the oldest among the members of the SB RAS and got his education before the October Revolution. He lived through change of epoch, turmoil of revolutions and wars, forced labour in a “sharaga”, scientific advances, technical failures and creative breakthroughs. This feature of his biography actualizes the ways of transiting a specialist from one social reality to another, where the profession determines the model of behavior. This transition required significant efforts since it was sometimes complicated by the historical context. The aim of the research is to study the mentality of the actor in science whose professional activity dominated over other social life imperatives. Importantly, Chinakal’s work was connected with two geographic regions known for their major coal basins: the Donetsk Coal Basin, or Donbass, and Kuznetsk Coal Basin, or Kuzbass. The author highlights the characteristic features of these regions and shows how they affected the engineering and organizational decisions made by the scientist. The methodology and research methods are based on the theory of biography, activity-oriented aspect of the life of the history actor that depended strongly on his occupation, B. Latour’s actor-network theory, systematic approach to studying the natural character of causality and network connections of the “scientist-science-object” structure examined in this work. N. A. Chinakal was actively involved in starting academic science in Siberia. For 28 years, he was a director of the Institute of Mining in the West-Siberian Branch of the USSR Academy of Sciences, which later became part of the Siberian Branch of the USSR Academy of Sciences. The authority and academic status of the director were of great importance for the institute staff. Equally important was the stability provided by Chinakal’s leadership. In our time, stability is very much in demand, although there is an imbalance of stability and instability, which is felt by the staff of the Institute of Mining. Keywords: science in Siberia, mining, Institute of Mining Siberian Branch, Russian Academy of Sciences, Nikolai Andreevich Chinakal, personality in science

On Constraint Manifolds of Lorentz Sphere

Abstract The expression of the structure equation of a mechanism is significant to present the last position of the mechanism. Moreover, in order to attain the constraint manifold of a chain, we need to constitute the structure equation. In this paper, we determine the structure equations and the constraint manifolds of a spherical open-chain in the Lorentz space. The structure equations of spherical open chain with reference to the causal character of the first link are obtained. Later, the constraint manifolds of the mechanism are determined by means of these equations. The geometric constructions corresponding to these manifolds are studied.

Envelopes of circles and spacelike curves in the Lorentz–Minkowski 3-space

Abstract The isotropy projection establishes a correspondence between curves in the Lorentz–Minkowski space 𝐄 1 3 {\mathbf{E}_{1}^{3}} and families of cycles in the Euclidean plane (i.e., curves in the Laguerre plane ℒ 2 {\mathcal{L}^{2}} ). In this paper, we shall give necessary and sufficient conditions for two given families of cycles to be related by a (extended) Laguerre transformation in terms of the well known Lorentzian invariants for smooth curves in 𝐄 1 3 {\mathbf{E}_{1}^{3}} . We shall discuss the causal character of the second derivative of unit speed spacelike curves in 𝐄 1 3 {\mathbf{E}_{1}^{3}} in terms of the geometry of the corresponding families of oriented circles and their envelopes. Several families of circles whose envelopes are well-known plane curves are investigated and their Laguerre invariants computed.

Some characterizations of non-null rectifying curves in dual Lorentzian 3-space $\mathbb{D}_{1}^{3}$

&lt;abstract&gt; &lt;p&gt;This paper gives several properties and characterization of non-null rectifying curves in dual Lorentzian 3-space $\mathbb{D% }_{1}^{3}$. In considering a causal character of a dual curve we give some parameterization of rectifying dual curves, and a dual differential equation of third order is constructed for every non-null dual curve. Then several well-known characterizations of spherical, normal and rectifying dual curves are consequences of this differential equation.&lt;/p&gt; &lt;/abstract&gt;