scholarly journals COVID-19 Angst

2021 ◽  
Vol 17 (1-2) ◽  
Author(s):  
FRITZ ILONGO
Keyword(s):  
Space Time ◽  
Reference Points ◽  
Social Psychological ◽  
The Matrix

The COVID-19 pandemic has disrupted traditional physical, social, psychological reference points and perspectives, through immediate lockdown, discontinuity of supply, exacerbation of demand and the generation of fear, uncertainty and panic. The latter scenarios could be reframed and reviewed through a creative and poetic lens as the matrix for creative reinterpretation by highlighting the impacts of COVID-19 on space, time, mind, consciousness, emotions, thinking, and behaviour, as seen through ‘space implosion,’ ‘the matrix of creativity,’ ‘I and I,’ ‘technological kinship’ and ‘time explosion.’

scholarly journals EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (31) ◽  
pp. 5765-5785 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Space Time ◽  
Gauge Fields ◽  
Poincaré Group ◽  
Matrix Representations ◽  
Poincare Group ◽  
Yang Mills ◽  
The Matrix ◽  
Transversal Plane

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

Video conferencing software selection based on hybrid MCDM and cumulative prospect theory under a major epidemic

2021 ◽  
pp. 1-18
Author(s):  
Jie Xu ◽  
Jian Lv ◽  
Hong-Tai Yang ◽  
Yan-Lai Li
Keyword(s):  
Prospect Theory ◽  
Weighting Function ◽  
Video Conferencing ◽  
Cumulative Prospect Theory ◽  
Reference Points ◽  
Software Selection ◽  
Interval Numbers ◽  
The Matrix ◽  
Selection Decision ◽  
Gains And Losses

The video conferencing software is regarded as a significant tool for social distancing and getting incorporations up and going. Due to the indeterminacy of epidemic evolution and the multiple criteria, this paper proposes a video conferencing software selection method based on hybrid multi-criteria decision making (HMCDM) under risk and cumulative prospect theory (CPT), in which the criteria values are expressed in various mathematical forms (e.g., real numbers, interval numbers, and linguistic terms) and can be changed with natural states of the epidemic. Initially, the detailed description of video conferencing software selection problem under an epidemic are given. Subsequently, a whole procedure for video conferencing software selection is conducted, the approaches for processing and normalizing the multi-format evaluation values are presented. Furthermore, the expectations provided by DMs under different natural states of the epidemic are considered as the corresponding reference points (RP). Based on this, the matrix of gains and losses is constructed. Then, the prospect values of all criteria and the perceived probabilities of natural states are calculated according to the value function and the weighting function in CPT respectively. Finally, the proposed method is illustrated by an empirical case study, and the comparison analysis and the sensitivity analysis for the loss aversion parameter are conducted to prove the effectiveness and robustness. The results show that considering the psychological characteristics of DMs in selection decision is beneficial to avoid the unacceptable and potential loss risks. This study could provide a useful guideline for managers who intend to select appropriate video conferencing software.

scholarly journals An Efficient Method for Forming Parabolic Curves and Surfaces

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 592
Author(s):  
Yuliy Lyachek
Keyword(s):  
Mathematical Description ◽  
Reference Points ◽  
Coordinate Systems ◽  
Parabolic Curve ◽  
Curves And Surfaces ◽  
Parabolic Interpolation ◽  
Second Derivatives ◽  
The Matrix ◽  
Positive Effect ◽  
Continuity Analysis

A new method for the formation of parabolic curves and surfaces is proposed. It does not impose restrictions on the relative positions in space of the sequence of reference points relative to each other, meaning it compares favorably with other prototypes. The disadvantages of the Overhauser and Brever–Anderson methods are noted. The method allows one to effectively form and edit curves and surfaces when changing the coordinates of any given point. This positive effect is achieved due to the appropriate choice of local coordinate systems for the mathematical description of each parabola, which together define a composite interpolation curve or surface. The paper provides a detailed mathematical description of the method of parabolic interpolation of curves and surfaces based on the use of matrix calculations. Analytical descriptions of a composite parabolic curve and its first and second derivatives are given, and continuity analysis of these factors is carried out. For the matrix of points of the defining polyhedron, expressions are presented that describe the corresponding surfaces, as well as the unit normal at any point. The comparative table of the required number of pseudo-codes for calculating the coordinates of one point for constructing a parabolic curve for the three methods is given.

scholarly journals Mathematical model of methane driven by hydraulic fracturing in gassy coal seams

2020 ◽  
Vol 38 (3-4) ◽  
pp. 127-147
Author(s):  
Weiyong Lu ◽  
Bingxiang Huang
Keyword(s):  
Mathematical Model ◽  
Hydraulic Fracturing ◽  
Pore Pressure ◽  
Hydraulic Fracture ◽  
Water Saturation ◽  
Reduction Rate ◽  
Space Time ◽  
Matrix Block ◽  
The Matrix ◽  
Pore Pressure Gradient

During hydraulic fracturing in gassy coal, methane is driven by hydraulic fracturing. However, its mathematical model has not been established yet. Based on the theory of ‘dual-porosity and dual-permeability’ fluid seepage, a mathematical model is established, with the cleat structure, main hydraulic fracture and methane driven by hydraulic fracturing considered simultaneously. With the help of the COMSOL Multiphysics software, the numerical solution of the mathematical model is obtained. In addition, the space–time rules of water and methane saturation, pore pressure and its gradient are obtained. It is concluded that (1) along the direction of the methane driven by hydraulic fracturing, the pore pressure at the cleat demonstrates a trend of first decreasing and later increasing. The pore pressure gradient exhibits certain regional characteristics along the direction of the methane driven by hydraulic fracturing. (2) Along the direction of the methane driven by hydraulic fracturing, the water saturation exhibits a decreasing trend; however, near the cleat or hydraulic fracture, the water saturation first increases and later decreases. The water saturation in the central region of the coal matrix block is smaller than that of its surrounding region, while the saturation of water in the entire matrix block is greater than that in the cleat or hydraulic fracture surrounding the matrix block. The water saturation at the same space point increases gradually with the time progression. The space–time distribution rules of methane saturation are contrary to those of the water saturation. (3) The free methane driven by hydraulic fracturing includes the original free methane and the free methane desorbed from the adsorption methane. The reduction rate of the adsorption methane is larger than that of free methane.

Nichtlineare Spinorgleichungen und affiner Zusammenhang

1964 ◽  
Vol 19 (7-8) ◽  
pp. 825-827
Author(s):  
G. Braunss
Keyword(s):  
Lorentz Transformation ◽  
Space Time ◽  
Linear Term ◽  
Pauli Equation ◽  
Non Linear ◽  
The Matrix ◽  
Lorentz Condition ◽  
Electro Magnetic ◽  
Point To Point

It is shown that the non-linear term of the HEisENBERG-PAULi-equation can be interpreted as torsion of space-time in the following way. The wavefuinction is subjected to a (non-rigid) LORENTZ-transformation varying from point to point: ψ = Sψ'. If the matrix S=S(x) is chosen so that it satisfies the equation γλ(∂S/∂xλ) S-1+l2γλγ5 ψ̅ γλγ5ψ=0, than the non-linear term of the H.-P.-equation vanishes in the system x'; i. e.with (∂xλ/∂xμ′) γμ=S-1 γλ S one has 0=γλ(∂ψ/∂xλ) +l2γλγ5 ψ ψ̅ γλ γ5 ψ ≡ S γμ (∂ψ'/∂xμ′). This result holds also in the case where the H.-P.-equation contains still a term with γλ ψ̅ γλ ψ and/or γλ Αλ (Aλ = electro-magnetic potential), provided Aλ satisfies the LoRENTz-condition ∂Aλ/∂xλ=0. The proof is a follows: Taking a representation of S in the DIRAC-ring, the equation which determines S splits into 8 equations. Between these equations there exist 2 identities (which correspond to the PAULI—GuRSEY-transformation resp. LoRENTz-condition); so one finally has 6 equations for the determination of the 6 parameters of S.

Kairos, Chronos and Chaos

2003 ◽  
Vol 36 (2) ◽  
pp. 202-217 ◽  
Author(s):  
Jeff Roberts
Keyword(s):  
Group Analysis ◽  
Space Time ◽  
Ancient Greek ◽  
Time And Space ◽  
The Matrix ◽  
Nature Of Time ◽  
Self Organizing

This paper explores the ancient Greek quasi-mystical concepts of Chronos and then Kairos, particularly in relation to group analysis and individual analytic psychotherapy. It concludes with some thoughts on the nature of time and space and introduces Chaos, a third Greek concept, with a consideration of the chaotic patterns of movement in space-time which are, it seems, self-organizing and have led to the emergence from the matrix of space-time of matter, life and ultimately mind.

scholarly journals Octonions, trace dynamics and noncommutative geometry—A case for unification in spontaneous quantum gravity

2020 ◽  
Vol 75 (12) ◽  
pp. 1051-1062
Author(s):  
Tejinder P. Singh
Keyword(s):  
Standard Model ◽  
Noncommutative Geometry ◽  
Degrees Of Freedom ◽  
Planck Scale ◽  
Space Time ◽  
Yang Mills ◽  
The Standard Model ◽  
The Matrix ◽  
Definition Of ◽  
Matrix Dynamics

AbstractWe have recently proposed a new matrix dynamics at the Planck scale, building on the theory of trace dynamics and Connes noncommutative geometry program. This is a Lagrangian dynamics in which the matrix degrees of freedom are made from Grassmann numbers, and the Lagrangian is trace of a matrix polynomial. Matrices made from even grade elements of the Grassmann algebra are called bosonic, and those made from odd grade elements are called fermionic—together they describe an ‘aikyon’. The Lagrangian of the theory is invariant under global unitary transformations and describes gravity and Yang–Mills fields coupled to fermions. In the present article, we provide a basic definition of spin angular momentum in this matrix dynamics and introduce a bosonic(fermionic) configuration variable conjugate to the spin of a boson(fermion). We then show that at energies below Planck scale, where the matrix dynamics reduces to quantum theory, fermions have half-integer spin (in multiples of Planck’s constant), and bosons have integral spin. We also show that this definition of spin agrees with the conventional understanding of spin in relativistic quantum mechanics. Consequently, we obtain an elementary proof for the spin-statistics connection. We then motivate why an octonionic space is the natural space in which an aikyon evolves. The group of automorphisms in this space is the exceptional Lie group G2 which has 14 generators [could they stand for the 12 vector bosons and two degrees of freedom of the graviton?]. The aikyon also resembles a closed string, and it has been suggested in the literature that 10-D string theory can be represented as a 2-D string in the 8-D octonionic space. From the work of Cohl Furey and others it is known that the Dixon algebra made from the four division algebras [real numbers, complex numbers, quaternions and octonions] can possibly describe the symmetries of the standard model. In the present paper we outline how in our work the Dixon algebra arises naturally and could lead to a unification of gravity with the standard model. From this matrix dynamics, local quantum field theory arises as a low energy limit of this Planck scale dynamics of aikyons, and classical general relativity arises as a consequence of spontaneous localisation of a large number of entangled aikyons. We propose that classical curved space–time and Yang–Mills fields arise from an effective gauging which results from the collection of symmetry groups of the spontaneously localised fermions. Our work suggests that we live in an eight-dimensional octonionic universe, four of these dimensions constitute space–time and the other four constitute the octonionic internal directions on which the standard model forces live.

scholarly journals Dimensional oxidization on coset space

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Koichi Harada ◽  
Pei-Ming Ho ◽  
Yutaka Matsuo ◽  
Akimi Watanabe
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Symmetry Algebra ◽  
Scalar Fields ◽  
Space Time ◽  
Coset Space ◽  
Infinite Dimensional ◽  
Gauge Algebra ◽  
The Matrix ◽  
Chern Simons

Abstract In the matrix model approaches of string/M theories, one starts from a generic symmetry gl(∞) to reproduce the space-time manifold. In this paper, we consider the generalization in which the space-time manifold emerges from a gauge symmetry algebra which is not necessarily gl(∞). We focus on the second nontrivial example after the toroidal compactification, the coset space G/H, and propose a specific infinite-dimensional symmetry which realizes the geometry. It consists of the gauge-algebra valued functions on the coset and Lorentzian generator pairs associated with the isometry. We show that the 0-dimensional gauge theory with the mass and Chern-Simons terms gives the gauge theory on the coset with scalar fields associated with H.

scholarly journals Irreducibility of some unitary representations of the poincaré group with respect to the Poincaré subsemigroup, II

1982 ◽  
Vol 87 ◽  
pp. 147-174 ◽  
Author(s):  
Hitoshi Kaneta
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Unitary Representations ◽  
Poincaré Group ◽  
Poincare Group ◽  
3 Dimensional ◽  
The Matrix ◽  
Dimensional Space Time

Let P+(3) and P+(3) be the 3-dimensional space-time Poincaré group and the Poincaré subsemigroup, that is, P(3) = R3 × sSU(1, 1) and P+(3) = V+(3)=SSU(1, 1) where The multiplication is defined by the formula (x, g)(x′, g′) = (x + g*−1x′g−1, gg′) for x, x′ ∈ R3 and g, g′ ∈ SU(l, 1). Here x = (x0, x1, x2) is identified with the matrix

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