scholarly journals Rotational-monad metaphysics

2021 ◽  
Author(s):  
Roman Kremen
Keyword(s):  
Three Dimensional ◽  
Physical Space ◽  
Discrete Element ◽  
Physical Reality ◽  
Foundations Of Mathematics ◽  
Important Special Case ◽  
Infinite Dimensional ◽  
The One ◽  
Special Case ◽  
Mathematics And Physics

The article presents a metaphysical concept, in the main tesa of which the simplest discrete element of physical reality is constituted — designated as a protomonad — which forms the basis of spatial forms of materiality, including space itself as such. The genesis of the protomonad is clarified by a certain way interpreted rotation of the spiritual essence, which in itself does not have an extension, and both the indicated essence and its rotation have a metaphysical order, and the dimension of physical space finds a rational interpretation through the characteristics of metaphysical rotation. The semantic aspects of complex mathematical constructs are considered that convey the semantics of rotations, and quite reasonably proposed by some mathematicians as the unified foundations of mathematics and physics, where the properties of constructs act as a mathematically strict co-proof of the validity of the concept. The meaning of number is explained as a method of restriction on infinite pre-physical multiplicity, and finite natural multiplicities are the result of such restrictions; the most important special case is the three-dimensional spatial metric given in the experiment, which appears as a restriction of an infinite-dimensional metaphysical space. The so-called principle of genetic inheritance is formulated, which makes it possible to remove the dialectical opposition between the one and the multiple and illustrates the categories of time and space as dialectical oppositions.

ON THE DENSITY OF HAUSDORFF DIMENSIONS OF BOUNDED TYPE CONTINUED FRACTION SETS: THE TEXAN CONJECTURE

2004 ◽  
Vol 04 (01) ◽  
pp. 63-76 ◽  
Author(s):  
OLIVER JENKINSON
Keyword(s):  
Hausdorff Dimension ◽  
Finite Subset ◽  
Continued Fraction ◽  
Cantor Set ◽  
Computational Method ◽  
Accurate Approximation ◽  
Natural Numbers ◽  
Important Special Case ◽  
The One ◽  
Special Case

Given a non-empty finite subset A of the natural numbers, let EA denote the set of irrationals x∈[0,1] whose continued fraction digits lie in A. In general, EA is a Cantor set whose Hausdorff dimension dim (EA) is between 0 and 1. It is shown that the set [Formula: see text] intersects [0,1/2] densely. We then describe a method for accurately computing dimensions dim (EA), and employ it to investigate numerically the way in which [Formula: see text] intersects [1/2,1]. These computations tend to support the conjecture, first formulated independently by Hensley, and by Mauldin & Urbański, that [Formula: see text] is dense in [0,1]. In the important special case A={1,2}, we use our computational method to give an accurate approximation of dim (E{1,2}), improving on the one given in [18].

scholarly journals SHOCK FORMATION IN THE COMPRESSIBLE EULER EQUATIONS AND RELATED SYSTEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 149-172 ◽  
Author(s):  
GENG CHEN ◽  
ROBIN YOUNG ◽  
QINGTIAN ZHANG
Keyword(s):  
Euler Equations ◽  
Space Dimension ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Compressible Euler Equations ◽  
Shock Formation ◽  
Compressible Euler ◽  
Systems Of Conservation Laws ◽  
The One ◽  
Special Case

We prove shock formation results for the compressible Euler equations and related systems of conservation laws in one space dimension, or three dimensions with spherical symmetry. We establish an L∞ bound for C1 solutions of the one-dimensional (1D) Euler equations, and use this to improve recent shock formation results of the authors. We prove analogous shock formation results for 1D magnetohydrodynamics (MHD) with orthogonal magnetic field, and for compressible flow in a variable area duct, which has as a special case spherically symmetric three-dimensional (3D) flow on the exterior of a ball.

scholarly journals Three-dimensional model of track growth: Comparison with other models

2003 ◽  
Vol 18 (2) ◽  
pp. 24-30 ◽  
Author(s):  
Dragoslav Nikezic ◽  
Peter Yu ◽  
Dragana Kostic
Keyword(s):  
Surface Area ◽  
Growth Models ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Nuclear Track Detectors ◽  
The One ◽  
Special Case ◽  
Track Etch

Here, we present a three-dimensional model of track growth in nuclear track detectors. The equation for the track wall in three dimensions and the equation of the contour line of the track opening have been derived for all types of tracks (i. e., tracks with sharp tips and tracks with rounded tips). The expression for the surface area of the track opening has also been found. The equations become the well-known expressions for minor and major axes for the special case of constant track etch rates. Computations of track parameters based on our model have been compared with the track growth models given by Somogyi and Szalay and the one given by Fews and Henshaw. Good agreements have been found among these three independent models.

Stably continuous frames

1988 ◽  
Vol 104 (1) ◽  
pp. 7-19 ◽  
Author(s):  
B. Banaschewski ◽  
G. C. L. Brummer
Keyword(s):  
Lattice Theory ◽  
The Other ◽  
Hausdorff Spaces ◽  
Important Special Case ◽  
Compact Spaces ◽  
The One ◽  
Continuous Frames ◽  
Special Case

In the lattice theory that underlies topology, that is, in the study of frames, a class of frames arising naturally is that of the stably continuous frames (see §0 for definitions). On the one hand, they correspond to the most reasonable not necessarily Hausdorff compact spaces, and on the other, they are precisely the retracts of coherent frames. Moreover, an important special case of stably continuous frames are the compact regular frames which correspond to compact Hausdorff spaces.

scholarly journals Approximation of discontinuous functions of three variables by discontinuous interpolation splines

2021 ◽  
pp. 99-104
Author(s):  
Iuliia Pershyna
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Computed Tomography ◽  
Internal Structure ◽  
Approximation Method ◽  
Three Dimensional ◽  
Discontinuous Functions ◽  
The One ◽  
Dimensional Object ◽  
Special Case

In this paper, discontinuous interpolation splines of three variables are constructed and a method for reconstructing of the discontinuous internal structure of a three-dimensional body by constructed splines is proposed. It is believed that a three-dimensional object, which is described by a function of three variables with discontinuities of the first kind on a given grid of nodes, is completely covered by a system of parallelepipeds. The experimental data are the one-sided value of the discontinuous function in a given grid of nodes. In the article, theorems on interpolation properties and the error of the constructed discontinuous structures are formulated and proved. Moreover, the constructed discontinuous interpolation splines include, as a special case, classical continuous splines. The developed approximation method can be applied in three-dimensional mathematical modeling of discontinuous processes, including in computed tomography.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Sea Urchins and Circuses: The Modernist Natural Histories of Jean Painlevé and Alexander Calder

2018 ◽  
Vol 13 (2) ◽  
pp. 187-211
Author(s):  
Patricia E. Chu
Keyword(s):  
New Media ◽  
Sea Urchins ◽  
Life Sciences ◽  
Three Dimensional ◽  
Machine Age ◽  
Avant Garde ◽  
History Of ◽  
And Performance ◽  
The One ◽  
Natural Historian

The Paris avant-garde milieu from which both Cirque Calder/Calder's Circus and Painlevé’s early films emerged was a cultural intersection of art and the twentieth-century life sciences. In turning to the style of current scientific journals, the Paris surrealists can be understood as engaging the (life) sciences not simply as a provider of normative categories of materiality to be dismissed, but as a companion in apprehending the “reality” of a world beneath the surface just as real as the one visible to the naked eye. I will focus in this essay on two modernist practices in new media in the context of the history of the life sciences: Jean Painlevé’s (1902–1989) science films and Alexander Calder's (1898–1976) work in three-dimensional moving art and performance—the Circus. In analyzing Painlevé’s work, I discuss it as exemplary of a moment when life sciences and avant-garde technical methods and philosophies created each other rather than being classified as separate categories of epistemological work. In moving from Painlevé’s films to Alexander Calder's Circus, Painlevé’s cinematography remains at the forefront; I use his film of one of Calder's performances of the Circus, a collaboration the men had taken two decades to complete. Painlevé’s depiction allows us to see the elements of Calder's work that mark it as akin to Painlevé’s own interest in a modern experimental organicism as central to the so-called machine-age. Calder's work can be understood as similarly developing an avant-garde practice along the line between the bestiary of the natural historian and the bestiary of the modern life scientist.

scholarly journals Acoustic Cell Patterning in Hydrogel for Three-Dimensional Cell Network Formation

Micromachines ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 3
Author(s):  
Kyo-in Koo ◽  
Andreas Lenshof ◽  
Le Thi Huong ◽  
Thomas Laurell
Keyword(s):  
Network Formation ◽  
Umbilical Vein ◽  
Three Dimensional ◽  
Extrusion Process ◽  
Fibroblast Cells ◽  
Glass Capillary ◽  
Cell Network ◽  
Significant Difference ◽  
The One ◽  
Umbilical Vein Endothelial Cells

In the field of engineered organ and drug development, three-dimensional network-structured tissue has been a long-sought goal. This paper presents a direct hydrogel extrusion process exposed to an ultrasound standing wave that aligns fibroblast cells to form a network structure. The frequency-shifted (2 MHz to 4 MHz) ultrasound actuation of a 400-micrometer square-shaped glass capillary that was continuously perfused by fibroblast cells suspended in sodium alginate generated a hydrogel string, with the fibroblasts aligned in single or quadruple streams. In the transition from the one-cell stream to the four-cell streams, the aligned fibroblast cells were continuously interconnected in the form of a branch and a junction. The ultrasound-exposed fibroblast cells displayed over 95% viability up to day 10 in culture medium without any significant difference from the unexposed fibroblast cells. This acoustofluidic method will be further applied to create a vascularized network by replacing fibroblast cells with human umbilical vein endothelial cells.

scholarly journals H-plane horn antenna with enhanced directivity using conformal transformation optics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hossein Eskandari ◽  
Juan Luis Albadalejo-Lijarcio ◽  
Oskar Zetterstrom ◽  
Tomáš Tyc ◽  
Oscar Quevedo-Teruel
Keyword(s):  
Conformal Transformation ◽  
Phase Error ◽  
Three Dimensional ◽  
Physical Space ◽  
Horn Antenna ◽  
High Gain ◽  
Transformation Optics ◽  
Graded Index ◽  
Low Profile ◽  
Dielectric Lens

AbstractConformal transformation optics is employed to enhance an H-plane horn’s directivity by designing a graded-index all-dielectric lens. The transformation is applied so that the phase error at the aperture is gradually eliminated inside the lens, leading to a low-profile high-gain lens antenna. The physical space shape is modified such that singular index values are avoided, and the optical path inside the lens is rescaled to eliminate superluminal regions. A prototype of the lens is fabricated using three-dimensional printing. The measurement results show that the realized gain of an H-plane horn antenna can be improved by 1.5–2.4 dB compared to a reference H-plane horn.

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