scholarly journals Necessary condition for the existence of a simple closed geodesic on a regular tetrahedron in the spherical space

2020 ◽  
pp. 9-14
Author(s):  
D.D. Sukhorebska ◽  
Keyword(s):  
Closed Geodesic ◽  
Necessary Condition ◽  
Regular Tetrahedron ◽  
Spherical Space ◽  
Intrinsic Geometry ◽  
The Third ◽  
Coprime Integers ◽  
Simple Closed Geodesic

In the spherical space the curvature of the tetrahedron’s faces equals 1, and the curvature of the whole tetrahedron is concentrated into its vertices and faces. The intrinsic geometry of this tetrahedron depends on the value α of faces angle, where π/3 < α ⩽ 2π/3. The simple (without points of self-intersection) closed geodesic has the type (p,q) on a tetrahedron, if this geodesic has p points on each of two opposite edges of the tetrahedron, q points on each of another two opposite edges, and (p+q) points on each edges of the third pair of opposite one. For any coprime integers (p,q), we present the number αp, q (π/3 < αp, q < 2π/3) such that, on a regular tetrahedron in the spherical space with the faces angle of value α > αp, q, there is no simple closed geodesic of type (p,q)

Analysis of error motions of axial locking-prevention hydrostatic spindle

2018 ◽  
Vol 233 (1) ◽  
pp. 3-17
Author(s):  
Penghai Zhang ◽  
Yaolong Chen
Keyword(s):  
Significant Influence ◽  
Harmonic Component ◽  
Necessary Condition ◽  
Third Harmonic ◽  
The Third ◽  
Fourth Harmonic ◽  
Radial Error ◽  
Tilt Error ◽  
Error Motion ◽  
Error Averaging

Hydrostatic spindles are widely used in precision optical grinder and lathe. Their high precision comes from the error averaging effect of oil film. The purpose of this paper is to give the quantitative analysis of the error averaging effect for a newly developed axial locking-prevention hydrostatic spindle. An approximate error motion model of the hydrostatic spindle is established to analyze the internal relationship between the geometric errors of the shaft and the error motions of the spindle including radial, tilt and axial error motions. The theoretical analysis shows that, the roundness errors of the two journals have a major impact on error motions while the coaxiality errors of two journals, the perpendicularity errors of front thrust plate and the coaxiality errors of the land of back thrust bearing, have no significant influences on error motions. The elliptical component of roundness errors of the two journals has significant influence on the axial error motion but no influence on the pure radial and tilt error motions, resulting into the fourth harmonic component of axial error motion. The trilobal component of roundness errors of the two journals has significant influence on the pure radial and tilt error motions but no influence on the axial error motion, resulting in the third harmonic component of pure radial and tilt error motions. The changes of recess pressures are not necessary condition for the error motions. Additionally, the experiment analysis shows that, the third harmonic component is the main part of the measured radial error motion and the third, fourth harmonic components are the main parts of the measured face error motion, which can be reasonably explained by the theory. The model proposed in this paper can be used to guide the precision design and optimization of hydrostatic spindle.

scholarly journals Solutions of the second and fourth Painlevé equations, I

1997 ◽  
Vol 148 ◽  
pp. 151-198 ◽  
Author(s):  
Hiroshi Umemura ◽  
Humihiko Watanabe
Keyword(s):  
Vector Field ◽  
Differential Equations ◽  
Painlevé Equations ◽  
Necessary Condition ◽  
Hamiltonian Vector Field ◽  
Rigorous Proof ◽  
Painleve Equations ◽  
Algebraic Differential Equations ◽  
The Third ◽  
Principal Ideals

AbstractA rigorous proof of the irreducibility of the second and fourth Painlevé equations is given by applying Umemura’s theory on algebraic differential equations ([26], [27], [28]) to the two equations. The proof consists of two parts: to determine a necessary condition for the parameters of the existence of principal ideals invariant under the Hamiltonian vector field; to determine the principal invariant ideals for a parameter where the principal invariant ideals exist. Our method is released from complicated calculation, and applicable to the proof of the irreducibility of the third, fifth and sixth equation (e.g. [32]).

Secularization and States of Modernity

1984 ◽  
Vol 36 (3) ◽  
pp. 362-382 ◽  
Author(s):  
Terrance G. Carroll
Keyword(s):  
Detailed Analysis ◽  
Third World ◽  
Necessary Condition ◽  
Modern State ◽  
The Third ◽  
Political Modernity ◽  
General Proposition ◽  
Significant Obstacle ◽  
The Third World ◽  
The Relationship

Extensive secularization is frequently held to be a necessary condition for political modernity. The author argues that the relationship between religion and the modern state is considerably more complex than this general proposition suggests. It is necessary to specify particular ideological models of the modern state, since these differ significantly from one another; and it is necessary to specify particular religions in their contemporary manifestations, since these also differ in important ways. A detailed analysis of this type suggests that there is no general incompatibility between the main religions of the third world and widely shared, nonideological features of political modernity. Specific religions are shown to be incompatible with some specific forms of the modern state, while presenting no significant obstacle to other models of political modernity.

The Argument from the Sense of Freedom, and a Desperate Compatibilism

2021 ◽  
pp. 27-38
Author(s):  
Andrew V. Mertsalov ◽  
Keyword(s):  
Free Will ◽  
Rational Choice ◽  
Necessary Condition ◽  
The Third ◽  
Defence Strategies

The argument from the sense of freedom, unlike many other libertarian arguments, doesn’t question the compatibility of free will and determinism, but is aimed against the belief that determinism is true. The endorsement of determinism undermines the sense of freedom and thereby excludes the possibility of rational choice. And since its possibility is a necessary condition for free will, the belief that determinism is true excludes it as well, the argument concludes. In the first part of the article, I outline how the sense of freedom can be understood and what are the reasons to admit its existence. For it is possible that the sense of freedom is misleading, in the second part I consider why we should think that it doesn’t deceive us, and what are the reasons against skepticism about it. In the third part, I formulate the argument from the sense of freedom; I also examine standard compatibilist defence strategies against such kind of arguments and demonstrate their inefficiency against the argument from the sense of freedom. In conclusion, I argue that the argument from the sense of freedom, supplemented by the antiseptic thesis, reveals vulnerabilities of all but the most desperate compatibilist theories.

The Compassion of Shared Spectatorship

2019 ◽  
pp. 87-136
Author(s):  
Celine Parreñas Shimizu
Keyword(s):  
Third World ◽  
The Philippines ◽  
The Other ◽  
Necessary Condition ◽  
The Third ◽  
The Spectator ◽  
The Third World

Through his filming of bodies in poverty and squalor, Brillante Mendoza prevents the traditional consumption of the third world as enjoyable, entertaining, and educational, and instead enables a multisensorial immersion in a bewildering pandemonium that remains tense and uncomfortable. In this, the filmmaker questions the basis of identification: they suffer like me is replaced by they suffer unlike me. Yet the films demand a feeling, what I call shared spectatorship, for it is a mode of identification predicated not on pleasure but on difference as the necessary condition for us to mark our own positions outside that suffering. We are not inside the shoes or the soul of the other, rather the movie shows us our distance through representations of proximity that emphasize difference. His films butcher the spectator because people are rampantly butchered in the Philippines—as a fact and not a fantasy that his films concoct.

Szaber Frenzy

2010 ◽  
pp. 173-203
Author(s):  
Marcin Zaremba
Keyword(s):  
Ethnic Difference ◽  
Necessary Condition ◽  
Power Structures ◽  
Culture Of Poverty ◽  
The Third ◽  
The Subject ◽  
Northern Territories ◽  
Post War

The subject of this article is war, and especially post-war, szaber – a phenomenon of mass looting of unattended property. The text is divided into three parts. In the first part, I attempt to explain theoretically the origin of szaber, indicating (among other things) its links with the culture of poverty and a necessary condition for the szaber to take place – a moment of chaos and a temporary decline of the power structures. In the second part, I formulate a hypothesis that ethnic difference was a necessary condition for szaber to emerge. I illustrate it with examples from September 1939, when first we faced a phenomenon of mass looting of unattended property. The article also deals with the pillage of the ghettos by Poles in 1942. The third part is devoted to the highest wave of looting, which took place mostly in the Regained Western and Northern Territories, immediately after the war. The text is constructed in such a way that at the end I return to the origin of the phenomenon, formulating a thesis that it created a certain szaber culture

Symmetry of topographs of Markoff forms

2020 ◽  
Vol 16 (07) ◽  
pp. 1573-1598
Author(s):  
Ryuji Abe ◽  
Iain R. Aitchison
Keyword(s):  
Half Plane ◽  
Quadratic Forms ◽  
Closed Geodesic ◽  
Infinite Path ◽  
A Value ◽  
Punctured Torus ◽  
Upper Half Plane ◽  
Simple Closed Geodesic ◽  
Indefinite Quadratic ◽  
Discrete Part

The Markoff spectrum is defined as the set of normalized values of arithmetic minima of indefinite quadratic forms. In the theory of the Markoff spectrum we observe various kinds of symmetry. Each of Conway’s topographs of quadratic forms which give values in the discrete part of the Markoff spectrum has a special infinite path consisting of edges. It has symmetry with respect to a translation along the path and countable central symmetries by which the path is invariant. We prove that these properties are obtained from the fact that the path is a discretization of a geodesic in the upper half-plane which corresponds to a value of the discrete part of the Markoff spectrum and projects to a simple closed geodesic on the once punctured torus with the highest degree of symmetry.

scholarly journals The significance of faith in the concept of integral knowledge of Vladimir Solovyov

2020 ◽  
Vol 36 (3) ◽  
pp. 460-472
Author(s):  
Teresa Obolevitch ◽  
Keyword(s):  
Cognitive Process ◽  
Dominant Role ◽  
Necessary Condition ◽  
Faith And Reason ◽  
The Third ◽  
Types Of Knowledge ◽  
Special Factor ◽  
Theology And Science ◽  
Integral Knowledge ◽  
Objective Existence

The article examines the role and place of faith in the concept of Vladimir Solovyov who is considered to be the creator of the first Russian philosophical system. The purpose of the article is to determine the epistemological and methodological significance of faith in Solovyov’s understanding as a special factor of cognition. In order to study this problem, a synthetic method of reconstruction of the thought of Solovyov as well as a method of philosophical analysis was used. First, Solovyov’s project of integral knowledge or free theosophy is presented, i. e. synthesis of philosophy, theology, and science. The suppositions of this concept are revealed and its polemical context is indicated, namely, Solovyov’s attempt to overcome the abstract or one-sided principles: reason, empirical experience, and faith in order to create an integral system that should unite all types of knowledge. In addition, philosophy as such corresponds to reason, science to experience, and theology to faith. The second part of the article is devoted to the epistemological aspects of faith in the concept of integral knowledge. It lies in the fact that each act of cognition begins with the assertion of the objective existence of its object, which Solovyov describes as faith in a broad sense of the word. Thus, faith has a universal significance as a necessary condition for the cognitive process. The third part of the article discusses the methodological aspect of faith as a key link in the system of integral knowledge. As a result, faith has a dominant role not only in theology, but in all spheres of knowledge, including philosophy and science. Thus, it is possible to conclude that there is no conflict between faith and reason; on the contrary, they complement each other. Solovyov’s position is still relevant nowadays.

Reconceptualizing the Organism

2018 ◽  
Author(s):  
Daniel J. Nicholson
Keyword(s):  
Alternative Conception ◽  
Living Systems ◽  
Necessary Condition ◽  
Equilibrium Thermodynamics ◽  
The Third ◽  
Biological Ontology ◽  
Flowing Stream ◽  
Non Equilibrium

This chapter draws on insights from non-equilibrium thermodynamics to demonstrate the ontological inadequacy of the machine conception of the organism. The thermodynamic character of living systems underlies the importance of metabolism and calls for the adoption of a processual view, exemplified by the Heraclitean metaphor of the stream of life. This alternative conception is explored in its various historical formulations, and the extent to which it captures the nature of living systems is examined. Next, the chapter considers the metaphysical implications of reconceptualizing the organism from complex machine to flowing stream. What do we learn when we reject the mechanical and embrace the processual? Three key lessons for biological ontology are identified. The first is that activity is a necessary condition for existence. The second is that persistence is grounded in the continuous self-maintenance of form. And the third is that order does not entail design.

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