Infinity Research Articles

The embodiment of mater’s archetype in song genre (on repertoire material by master students of Popular Music and Jazz Department)

The embodiment of mater’s archetype in song genre (on repertoire material by master students of Popular Music and Jazz Department)

Dynamic Process of Spontaneous Energy Radiation from Spinning Black Holes through Force-free Magnetic Field

Abstract Recent general relativistic magnetohydrodynamic (MHD) simulations have suggested that relativistic jets from active galactic nuclei are powered by the rotational energy of central black holes through magnetic fields. Some mechanisms for the extraction of rotational energy of black holes have been proposed, such as the Penrose process, the Blandford–Znajek mechanism, the MHD/magnetic Penrose process, and superradiance. Among them, the Blandford–Znajek mechanism is the most promising as an important process of the central engines of the high-energy phenomena. However, a distinctive dynamic process of this mechanism has not yet been demonstrated intuitively, whereas extraction via the Penrose process has a simple interpretation. In this study, we performed numerical simulations of 1D force-free magnetodynamics (FFMD) with respect to the emergence of the Blandford–Znajek mechanism at the equatorial plane of the rapidly spinning black hole. A radial monopole-like magnetic field is used as an initial condition. We found a numerical solution of the steady-state region spreading from the ergosphere to the infinity point like a “tsunami.” We can intuitively understand that this tsunami is caused and sustained by the degeneracy of the electromagnetic field of the perfect conducting plasma in the ergosphere. However, this degeneracy is not mathematically guaranteed in the time-dependent equations of FFMD. The degeneracy is given by an appropriate initial condition and is sustained by the condition at the “stretched horizon” of the black hole.

Paracatadioptric camera calibration based on properties of polar line of infinity point with respect to circle and line

Two linear calibration methods based on space-line projection properties for a paracatadioptric camera are presented. Considering the central catadioptric system, a straight line is projected into a circle on the viewing spherical surface for the first projection. The tangent lines in a group at antipode point pairs with respect to the circle are parallel, with the infinity point being the intersection point; therefore, the infinity line can be obtained from two groups of antipode point pairs. Further, the direction of the polar line of an infinity point with respect to the circle is orthogonal to the direction of its infinity point. Hence, on the imaging plane, images of the circular points or orthogonal vanishing points are used to determine the intrinsic parameters. On the basis of the properties of the antipodal point pairs and a least-squares fitting, a corresponding optimization algorithm for line image fitting is proposed. Experimental results demonstrate the robustness of the two calibration methods, that is, for images of the circular points and orthogonal vanishing points.

EXPLORING PRE-SERVICE MATHEMATICS TEACHERS’ UNDERSTANDINGS OF COUNTABILITY AND INFINITY IN WEBQUEST BASED LEARNING ENVIRONMENT

Infinity concept is difficult to understand because of its nature. Even if the concept of infinity doesn’t directly take part in mathematics curriculum, it takes place on many topics such as lines, planes, sets, irrational numbers, limit, differentiation, and integration. The present study examined pre-service mathematics teachers’ understandings of infinity and countability concepts in WebQuest based learning environment. Twenty-nine pre-service teachers participated at the study. Data were collected through a questionnaire developed by the researchers and semi-structured interviews. Qualitative data were analyzed by using phenomenology research method. The findings of this study revealed that pre-service teachers generally defined infinite sets as the sets whose elements continue infinitely. They inclined to define countable sets as bounded sets, finite sets, and the sets with known elements. Whereas most of the students stated countable finite sets and countable infinite sets were existent, they also expressed uncountable finite sets and uncountable infinite sets were non-existent. They used natural numbers set as an example for the countable infinite sets. This research presented some implications for teacher education programme in the light of obtained findings. Article visualizations:

Asymptotic analysis of the clamped-pinned elastica

Asymptotic solutions for the clamped-pinned elastica when the displacement of the pinned end is small (immediately after buckling) and when it approaches its limiting displacement (when the force in the rod tends to infinity) are presented. Simple leading order relationships describing the force as a function of the pinned end’s displacement are derived. Those approximate the force-displacement behaviour of the clamped-pinned elastica for small and limiting end displacements. All our results are valid for the clamped-pinned elastica in any mode.

¿Qué significa una ‘mentalidad universal’? La respuesta de san Josemaría

espanolEl hombre, un ser que vive en la superficie, se pregunta por el fundamento; aunque en particular busca la universalidad; si bien esta marcado por la finitud, esta abierto al infinito. En el ensayo se trata sobre el tema del acceso a lo universal, una cuestion que para la teologia tiene una maxima importancia y luego se aborda un analisis de un texto de san Josemaria Escriva, donde se alude a la necesidad que tienen los cristianos, en especial los intelectuales, de formarse una mentalidad universal. EnglishMan, a being who lives on the surface, asks himself about the foundation; although he is particular, he seeks universality; although marked by finitude, he is open to infinity. The essay deals with the issue of access to the universal world, a question that is most important for theology and then an analysis of a text of St. Josemaria Escriva is discussed, which refers to the need of Christians, especially the intellectuals, to form a universal mentality.

Imperfect collusion in an asymmetric duopoly

espanolUsando el coeficiente de cooperacion, analizamos el efecto de las asimetrias en costes en los acuerdos colusorios cuando las empresas son capaces de coordinarse en niveles de produccion distintos de aquel que maximiza el beneficio conjunto. En este contexto, primero investigamos en que medida son factibles los acuerdos colusorios. En segundo lugar, nos centramos en la sostenibilidad de la colusion en un juego repetido infinitos periodos. Se demuestra que, independientemente del grado de asimetria en costes, al menos cierto nivel de colusion siempre es sostenible. Finalmente, tambien se obtiene el grado de colusion endogeno para demostrar que la cooperacion tiene un limite superior determinado por la empresa mas ineficiente. EnglishUsing the coefficient of cooperation, we analyse the effect of cost asymmetries on collusive agreements when firms are able to coordinate on distinct output levels than the unrestricted joint profit maximization outcome. In this context, we first investigate the extent to which collusive agreements are feasible. Secondly, we focus on collusion sustainability in an infinitely repeated game. We show that, regardless of the degree of cost asymmetry, at least some collusion is always sustainable. Finally, the degree of collusion is also endogeneised to show that cooperation has an upper bound determined by the most inefficient firm.

Notes on Nonsculpture Sculpture: Figures of Sonic and Mirrored Infinity

Notes on Nonsculpture Sculpture: Figures of Sonic and Mirrored Infinity

Abstraction and Infinity by Paolo Mancosu

Abstraction and Infinity by Paolo Mancosu

Surface Green’s functions in finite plane elastostatics of harmonic materials

The closed-form representations of surface Green’s functions corresponding to the action of a concentrated force applied at the boundary of a region occupied by a particular class of compressible hyperelastic materials of harmonic type, has been derived. In our analysis, we consider both a bounded region in the form of a circular disk and an unbounded region with either an elliptical hole or a parabolic boundary.

The Infinity of the Text and the Limits of Interpretation

рецензія: Дзера О. Біблійна інтертекстуальність і переклад : англо-український контекст : [монографія] / Оксана Дзера. — Львів : ЛНУ імені Івана Франка, 2017. — 490 с.

The Infinitude of Solutions to the Diophantine Equation p3 + q = z3 when p, q are Primes

The Infinitude of Solutions to the Diophantine Equation p3 + q = z3 when p, q are Primes

„Nichts“ (Rosenzweig) ir „Il y a“ (Levinas) problema kaip asmens tapatumo koreliatyvumas

The relation between the abyss of death and the human identity is constitutive for the thought of the dialogical thinkers Rosenzweig and Levinas. For Rosenzweig, the Nothing is the end point of Kantian thinking. Death, as the existential experience of this nothingness, was the reality of everyman during the violent decades at the turn of the century. Rosenzweig took this nothingness as the starting point for rethinking and safeguarding human identity. Human identity is a dam against nothingness. But human identity is also open to alterity. In his early texts, Levinas makes a similar move. The there is is the starting point of human identity. Levinas develops a dialectical phenomenology starting from death. Human identity is interpreted as hypostasis. But in Totalite et Infi ni, an important shift takes place. The starting point is now found in human identity as desire. The there is comes to the centre as the flip side of the elementale and human identity is interpreted as separation. Keywords: Rosenzweig, Star of Redemption, Levinas, Totality and Infi nity, human identity, nothingness, there is, hypostasis, separation, Kant, Nietzsche, Meinecke, Schelling. DOI: http://dx.doi.org/10.15823/zz.2017.15

The Two Parallel Infinities – Bounded Infinity Is the Source of Existence of the Things

The Two Parallel Infinities – Bounded Infinity Is the Source of Existence of the Things

Global existence and asymptotics for quasi-linear one-dimensional Klein-Gordon equations with mildly decaying Cauchy data

Let u be a solution to a quasi-linear Klein-Gordon equation in one-space dimension, $\Box u + u = P (u, ∂_t u, ∂_x u; ∂_t ∂_x u, ∂^2_x u)$ , where P is a homogeneous polynomial of degree three, and with smooth Cauchy data of size $e → 0$. It is known that, under a suitable condition on the nonlinearity, the solution is global-in-time for compactly supported Cauchy data. We prove in this paper that the result holds even when data are not compactly supported but just decaying as $\langle x \rangle^ {−1}$ at infinity, combining the method of Klainerman vector fields with a semiclassical normal forms method introduced by Delort. Moreover, we get a one term asymptotic expansion for u when $t → +∞$.

Enhanced IMC synthesis for tracking control of magnetic levitation system

This paper presents an enhanced internal model control (EIMC) scheme for a time-delayed second order unstable process, which is subjected to exogenous disturbance and model variations. Even though the conventional internal model control (IMC) can provide an asymptotic tracking response with desired stability margins, the major limitation of conventional IMC is that it cannot be applied for an unstable system because a small exogenous disturbance can trigger the control signal to grow unbounded. Hence, modifying the conventional IMC structure to guarantee the internal stability, we present an EIMC scheme which can offer better trade-off between setpoint tracking and disturbance rejection characteristics. To improve the load disturbance rejection characteristics and attenuate the effect of sensor noise, we solve the selection of controller gains as an H∞ optimization problem. One of the key aspects of the EIMC scheme is that the robustness of the closed loop system can be tuned via a single tuning parameter. The performance of the EIMC scheme is experimentally assessed on a magnetic levitation plant for reference tracking application. Experimental results substantiate that the EIMC scheme can effectively counteract the inherent time delay in the model and offer precise tracking, even in the presence of exogenous disturbance. Moreover, by comparing the trajectory tracking performance of EIMC with that of the proportional integral velocity (PIV) controller through cumulative power spectral density (CPSD) of the tracking error, we show that the EIMC can offer better low frequency servo response with minimal vibrations.

The Ontological and Epistemological Dimensions of Infinity in Malebranche

The Ontological and Epistemological Dimensions of Infinity in Malebranche

Infinity and Redemption: Pascal and T. S. Eliot

Infinity and Redemption: Pascal and T. S. Eliot

“As all men are alike (tho’ infinitely various) So all Religions”. On the Philosophical and Religious Underpinnings of William Blake’s Cosmogony

Moving from the Christian religion to the Western occult tradition, Blake’s religious syncretism emerges from a deep symbolic and thematic plot. This article aims to analyse how this religious and philosophical traditions may have played on Blake’s thought and to what extent it is possible to envisage in his poetical system a transmigration of symbols both from Christian doctrine and the Cabalistic tradition. Particular attention will be given to the analysis of the Prophetic Books, in which Blake created a cosmogony inhabited by Oriental deities, druids, and Old Testament characters.

To infinity and beyond

To infinity and beyond