Search results for: symmetry singularity

Authors: Leonard Kabeya Mukeba Yakasham

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The theoretical machinery from singularity theory introduced by Glolubitsky, Stewart, and Schaeffer, to study equivariant bifurcation problem is completed and expanded wile generalized to the multiparameter context. In this setting the finite deterinancy theorem or normal forms, the stability of equivariant bifurcation problem, and the structural stability of universal unfolding are discussed. With Yakam Matrix the solutions are limited for some partial differential equations stochastic nonlinear of the open questions in singularity artificial intelligence for future.

Keywords: equivariant bifurcation, symmetry singularity, equivariant jets and transversality; normal forms, universal unfolding instability, structural stability, artificial intelligence, pdens, yakam matrix

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Authors: Teoman Ozer, Ozlem Orhan

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This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.

Keywords: λ-symmetry, μ-symmetry, classification, invariant solution

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Authors: Francisco Lobo

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Kant’s household theory of human dignity as a common feature of all rational beings is the starting point of any intellectual endeavor to unravel the implications of this normative notion. Yet, it is incomplete, as it neglects considering the importance of the singularity or uniqueness of the individual. In a first, deconstructive stage, this paper describes the Kantian account of human dignity as one among many conceptions of human dignity. It reads carefully into the original wording used by Kant in German and its English translations, as well as the works of modern commentators, to identify its shortcomings. In a second, constructive stage, it then draws on the theories of Aristotle, Alexis de Tocqueville, John Stuart Mill, and Hannah Arendt to try and enhance the Kantian conception, in the sense that these authors give major importance to the singularity of the individual. The Kantian theory can be perfected by including elements from the works of these authors, while at the same time being mindful of the dangers entailed in focusing too much on singularity. The conclusion of this paper is that the Kantian conception of human dignity can be enhanced if it acknowledges that not only morality has dignity, but also the irreplaceable human individual to the extent that she is a narrative, original creature with the potential to act morally.

Keywords: commonality, dignity, Kant, singularity

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Authors: Seung-Yeon Kim

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The Ising model, consisting magnetic spins, is the simplest system showing phase transitions and critical phenomena at finite temperatures. The Ising model has played a central role in our understanding of phase transitions and critical phenomena. Also, the Ising model explains the gas-liquid phase transitions accurately. However, the Ising model in a nonzero magnetic field has been one of the most intriguing and outstanding unsolved problems. We study analytically the partition function zeros in the complex magnetic-field plane and the Yang-Lee edge singularity of the infinite-range Ising model in an external magnetic field. In addition, we compare the Yang-Lee edge singularity of the infinite-range Ising model with that of the square-lattice Ising model in an external magnetic field.

Keywords: Ising ferromagnet, magnetic field, partition function zeros, Yang-Lee edge singularity

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Authors: Amir Hadi Ziaie

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In the present work, we revisit the collapse process of a spherically symmetric homogeneous scalar field (in FRW background) minimally coupled to gravity, when the phase-space deformations are taken into account. Such a deformation is mathematically introduced as a particular type of noncommutativity between the canonical momenta of the scale factor and of the scalar field. In the absence of such deformation, the collapse culminates in a spacetime singularity. However, when the phase-space is deformed, we find that the singularity is removed by a non-singular bounce, beyond which the collapsing cloud re-expands to infinity. More precisely, for negative values of the deformation parameter, we identify the appearance of a negative pressure, which decelerates the collapse to finally avoid the singularity formation. While in the un-deformed case, the horizon curve monotonically decreases to finally cover the singularity, in the deformed case the horizon has a minimum value that this value depends on deformation parameter and initial configuration of the collapse. Such a setting predicts a threshold mass for black hole formation in stellar collapse and manifests the role of non-commutative geometry in physics and especially in stellar collapse and supernova explosion.

Keywords: gravitational collapse, non-commutative geometry, spacetime singularity, black hole physics

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Authors: Michele Sinico

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The present research investigates the effect of symmetry on the perception of happiness and boredom in design products. Three experiments were carried out in order to verify the degree of the visual expressive value on different models of bookcases, wall clocks, and chairs. 60 participants directly indicated the degree of happiness and boredom using 7-point rating scales. The findings show that the participants acknowledged a different value of expressive quality in the different product models. Results show also that symmetry is not a significant constraint for an emotional design project.

Keywords: product experience, emotional design, symmetry, expressive qualities

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Authors: Tushnik Sarkar, Mofazzal H. Khondekar, Subrata Banerjee

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This paper investigates the nature of the fluctuation of the daily average Solar wind speed time series collected over a period of 2492 days, from 1^st January, 1997 to 28^th October, 2003. The degree of self-similarity and scalability of the Solar Wind Speed signal has been explored to characterise the signal fluctuation. Multi-fractal Detrended Fluctuation Analysis (MFDFA) method has been implemented on the signal which is under investigation to perform this task. Furthermore, the singularity spectra of the signals have been also obtained to gauge the extent of the multifractality of the time series signal.

Keywords: detrended fluctuation analysis, generalized hurst exponent, holder exponents, multifractal exponent, multifractal spectrum, singularity spectrum, time series analysis

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Authors: Amir Hadi Ziaie, Mostafa Hashemi, Shahram Jalalzadeh

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It is now known that the end state of the collapse process of a dense star under its own gravity is the formation of a spacetime singularity. This is the spacetime event where the energy density and spacetime curvature diverge, and the classical general relativity breaks down. As we know, a realistic star is composed of fermions so that their spin effects could alter the final fate of the collapse scenario. The underlying theory within which the inclusion of spin effects can be worked out is the Einstein-Cartan theory. In this theory, the spacetime torsion which is defined as a geometrical quantity, is related to an intrinsic angular momentum of fermions (spin). In this work, we study the collapse process of a homogeneous spin fluid in such a framework and show that taking into account the spin effects of the collapsing cloud could prevent the formation of spacetime singularity.

Keywords: gravitational collapse, einstein-cartan theory, spacetime singularity, black hole physics

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Authors: Krish Jhurani

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The research paper presents an in-depth analysis of symmetry properties in linear algebraic systems under the operation of non-canonical scalar multiplication structures, specifically semirings, and near-rings. The objective is to unveil the profound alterations that occur in traditional linear algebraic structures when we replace conventional field multiplication with these non-canonical operations. In the methodology, we first establish the theoretical foundations of non-canonical scalar multiplication, followed by a meticulous investigation into the resulting symmetry properties, focusing on eigenvectors, eigenspaces, and invariant subspaces. The methodology involves a combination of rigorous mathematical proofs and derivations, supplemented by illustrative examples that exhibit these discovered symmetry properties in tangible mathematical scenarios. The core findings uncover unique symmetry attributes. For linear algebraic systems with semiring scalar multiplication, we reveal eigenvectors and eigenvalues. Systems operating under near-ring scalar multiplication disclose unique invariant subspaces. These discoveries drastically broaden the traditional landscape of symmetry properties in linear algebraic systems. With the application of these findings, potential practical implications span across various fields such as physics, coding theory, and cryptography. They could enhance error detection and correction codes, devise more secure cryptographic algorithms, and even influence theoretical physics. This expansion of applicability accentuates the significance of the presented research. The research paper thus contributes to the mathematical community by bringing forth perspectives on linear algebraic systems and their symmetry properties through the lens of non-canonical scalar multiplication, coupled with an exploration of practical applications.

Keywords: eigenspaces, eigenvectors, invariant subspaces, near-rings, non-canonical scalar multiplication, semirings, symmetry properties

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Authors: M. Kamel El-Sayed

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The process of determining the degree of membership for an element to an uncertain concept has been found in many ways, using equivalence and symmetry relations in information systems. In the case of similarity, these methods did not take into account the degree of symmetry between elements. In this paper, we use a new definition for finding the membership based on the degree of symmetry. We provide an example to clarify the suggested methods and compare it with previous methods. This method opens the door to more accurate decisions in information systems.

Keywords: information system, uncertain concept, membership function, similarity relation, degree of similarity

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Authors: Gayatri Ghosh

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In this work, a flavour theory of a neutrino mass model based on A_4 symmetry is considered to explain the phenomenology of neutrino mixing. The spontaneous symmetry breaking of A_4 symmetry in this model leads to tribimaximal mixing in the neutrino sector at a leading order. We consider the effect of Z_2 × Z_2 invariant perturbations in neutrino sector and find the allowed region of correction terms in the perturbation matrix that is consistent with 3σ ranges of the experimental values of the mixing angles. We study the entanglement of this formalism on the other phenomenological observables, such as δ_CP phase, the neutrino oscillation probability P(νµ → νe), the effective Majorana mass |mee| and |meff νe |. A Z_2 × Z_2 invariant perturbations in this model is introduced in the neutrino sector which leads to testable predictions of θ_13 and CP violation. By changing the magnitudes of perturbations in neutrino sector, one can generate viable values of δ_CP and neutrino oscillation parameters. Next we investigate the feasibility of charged lepton flavour violation in type-I seesaw models with leptonic flavour symmetries at high energy that leads to tribimaximal neutrino mixing. We consider an effective theory with an A_4 × Z_2 × Z_2 symmetry, which after spontaneous symmetry breaking at high scale which is much higher than the electroweak scale leads to charged lepton flavour violation processes once the heavy Majorana neutrino mass degeneracy is lifted either by renormalization group effects or by a soft breaking of the A_4 symmetry. In this context the implications for charged lepton flavour violation processes like µ → eγ, τ → eγ, τ → µγ are discussed.

Keywords: Z2 × Z2 invariant perturbations, CLFV, delta CP phase, tribimaximal neutrino mixing

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Authors: Mihriban Hacisalihoğlu Karadeniz, Figen Bozkuş, Tuğba Baran, Ümit Akar

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Creating the correct symmetry of conceptual knowledge about students, conceptual information about the symmetry of the instructors is important. However, teachers’, the students should be aware of the existing misconceptions and be able to develop strategies to correct these misconceptions. In this study, the purpose, the prospective teachers’, the students’ explanations for corrections of misconceptions and misconceptions were asked to be introduced. The working group during the 2012-2013 academic year, Kocaeli University Faculty of Education Mathematics Education consists of studying at the twenty-six prospective teachers. The study adopted a qualitative approach. The data prepared by the researchers were obtained with an open-ended test. As a result of analysis of the data, prospective with teaching the concept of symmetry observed in more developed practical solutions. These solutions are focused on the method, students utilization mirrors, paper folding, such as using a square piece of registration of events. Prospective teachers’ who think this way, students observed that overlooked the creation of conceptual knowledge.

Keywords: symmetry concepts, misconceptions, elementary mathematics, prospective teachers-students

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Authors: Jeremy Attard, Jordan François, Serge Lazzarini, Thierry Masson

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Gauge theories are the natural background for describing geometrically fundamental interactions using principal and associated fiber bundles as dynamical entities. The central notion of these theories is their local gauge symmetry implemented by the local action of a Lie group H. There exist several methods used to reduce the symmetry of a gauge theory, like gauge fixing, bundle reduction theorem or spontaneous symmetry breaking mechanism (SSBM). This paper is a presentation of another method of gauge symmetry reduction, distinct from those three. Given a symmetry group H acting on a fiber bundle and its naturally associated fields (Ehresmann (or Cartan) connection, curvature, matter fields, etc.) there sometimes exists a way to erase (in whole or in part) the H-action by just reconfiguring these fields, i.e. by making a mere change of field variables in order to get new (‘composite‘) fields on which H (in whole or in part) does not act anymore. Two examples: the re-interpretation of the BEHGHK (Higgs) mechanism, on the one hand, and the top-down construction of Tractor and Penrose's Twistor spaces and connections in the framework of conformal Cartan geometry, one the other, will be discussed. They have, of course, nothing to do with each other but the dressing field method can be applied on both to get a new insight. In the first example, it turns out, indeed, that generation of masses in the Standard Model can be separated from the symmetry breaking, the latter being a mere change of field variables, i.e. a dressing. This offers an interpretation in opposition with the one usually found in textbooks. In the second case, the dressing field method applied to the conformal Cartan geometry offer a way of understanding the deep geometric nature of the so-called Tractors and Twistors. The dressing field method, distinct from a gauge transformation (even if it can have apparently the same form), is a systematic way of finding and erasing artificial symmetries of a theory, by a mere change of field variables which redistributes the degrees of freedom of the theories.

Keywords: BEHGHK (Higgs) mechanism, conformal gravity, gauge theory, spontaneous symmetry breaking, symmetry reduction, twistors and tractors

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Authors: Nabil Beroual, Tewfik Sari

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We consider the Gause-type predator-prey system in the case where the response function is not smooth at the origin. We discuss the conditions under which this system has exactly one stable limit cycle or has a positive stable equilibrium point, and we describe the basin of attraction of the stable limit cycle and the stable equilibrium point, respectively. Our results correct previous results of the existing literature.

Keywords: predator-prey model, response function, singularity, basin of attraction, limit cycle

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Authors: Ayami Umemura

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The purpose of this paper is to examine the meaning of verbalization in clinical practice using the keywords silence and singularity. A patient's experience of illness and treatment is singular, irreplaceable, and irreproducible and ultimately cannot be compared with that of others. In his book Difference and Repetition, Gilles Deleuze positioned irreplaceable singularity as the opposite concept of particularity as a generalizable and substitutable property and matched the former with universality. He also said that singularity could not be represented because of its irreplaceable nature. Representation or verbalization is a procedure that converts an irreplaceable, idiosyncratic reality into something that can be substituted. Considering the act of verbalizing medical diagnosis based on this, it can be said that diagnosis is the practice of decontextualizing and generalizing the suffering embedded in the patient's irreplaceable life history as a disease. This paper examines the above with the key concept of the practice of "non-verbalization" in traditional medical practices in Sri Lanka. In the practice of Sri Lankan traditional medicine and the inheritance of medical knowledge and care techniques, there is a tendency to avoid verbalizing specific matters or stating them aloud. Specifically, the following should be avoided. The healer informs the patient of the name of the disease, mentions the name of the herb used in front of the patient, explains the patient's condition to the healer, and referring the names of poisonous animals, such as poisonous snakes that have been damaged. And so on. Furthermore, when passing on medical knowledge and skills, it is also possible to avoid verbalizing knowledge of medicinal herbs and medical treatment methods and explaining them verbally. In addition to the local belief that the soul of language in Sri Lanka is deeply involved in this background, Sri Lankan traditional medicine has a unique view of the human body and personality that is rooted in the singularity that appears in the relationship with the movement of celestial bodies and the supernatural realm. It can be pointed out that it is premised on the view. In other words, the “silence” in Sri Lankan indigenous medicine is the reason for emphasizing specificity. Furthermore, we can say that "non-verbalization" is a practice aimed at healing. Based on these discussions, this paper will focus on the unique relationships between practitioners and patients that become invisible due to verbalization, which is overlooked by clinical medicine, where informed consent, ensuring transparency, and audit culture is dominant. We will examine the experience of treatment and aim to relativize clinical medicine, which is based on audit cultures.

Keywords: audit cultures, indigenous medicine, singularity, verbalization

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Authors: Maba Boniface Matadi

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This paper analyses the model of Malaria endemic from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the nonlinear model. Furthermore, corresponding determining equations were constructed, and new symmetries were found. As a result, the findings of the study demonstrate of the integrability of the model to present an invariant solution for the Malaria model.

Keywords: group theory, lie symmetry, invariant solutions, malaria

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Authors: Gulcan Ozerim, Gunay Anlas

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In shape memory alloys, upon loading, stress increases around crack tip and a martensitic phase transformation occurs in early stages. In many studies the stress distribution in the vicinity of the crack tip is represented by using linear elastic fracture mechanics (LEFM) although the pseudo-elastic behavior results in a nonlinear stress-strain relation. In this study, the HRR singularity (Hutchinson, Rice and Rosengren), that uses Rice’s path independent J-integral, is tried to formulate the stress distribution around the crack tip. In HRR approach, the Ramberg-Osgood model for the stress-strain relation of power-law hardening materials is used to represent the elastic-plastic behavior. Although it is recoverable, the inelastic portion of the deformation in martensitic transformation (up to the end of transformation) resembles to that of plastic deformation. To determine the constants of the Ramberg-Osgood equation, the material’s response is simulated in ABAQUS using a UMAT based on ZM (Zaki-Moumni) thermo-mechanically coupled model, and the stress-strain curve of the material is plotted. An edge cracked shape memory alloy (Nitinol) plate is loaded quasi-statically under mode I and modeled using ABAQUS; the opening stress values ahead of the cracked tip are calculated. The stresses are also evaluated using the asymptotic equations of both LEFM and HRR. The results show that in the transformation zone around the crack tip, the stress values are much better represented when the HRR singularity is used although the J-integral does not show path independent behavior. For the nodes very close to the crack tip, the HRR singularity is not valid due to the non-proportional loading effect and high-stress values that go beyond the transformation finish stress.

Keywords: crack, HRR singularity, shape memory alloys, stress distribution

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Authors: Manuel Urueña Palomo

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In this paper, we introduce the study of a new solution to gravitational singularities by violating the energy conditions of the Penrose Hawking singularity theorems. We consider that a shift to negative energies, and thus, to negative masses, takes place at the event horizon of a black hole, justified by the original, singular and exact Schwarzschild solution. These negative energies are supported by relativistic particle physics considering the negative energy solutions of the Dirac equation, which states that a time transformation shifts to a negative energy particle. In either general relativity or full Newtonian mechanics, these negative masses are predicted to be repulsive. It is demonstrated that the model fits actual observations, and could possibly clarify the size of observed and unexplained supermassive black holes, when considering the inflation that would take place inside the event horizon where massive particles interact antigravitationally. An approximated solution of the model proposed could be simulated in order to compare it with these observations.

Keywords: black holes, CPT symmetry, negative mass, time transformation

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Authors: Alpana Tiwari, N. K. Gaur

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We have incorporated the translational rotational (TR) coupling effects in the framework of three body force shell model (TSM) to develop an extended TSM (ETSM). The dynamical matrix of ETSM has been applied to compute the phonon frequencies of orientationally disordered mixed crystal (ND4Br)x(KBr)1-x in (q00), (qq0) and (qqq) symmetry directions for compositions 0.10≤x≤0.50 at T=300K.These frequencies are plotted as a function of wave vector k. An unusual acoustic mode softening is found along symmetry directions (q00) and (qq0) as a result of translation-rotation coupling.

Keywords: orientational glass, phonons, TR-coupling, lattice dynamics

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Authors: Shyam Sunder Gupta

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Written scriptures are created out of Words of God, revealed or inspired. This process of conversion, from revealed Words to written scriptures, happens after a long gap of time and with the involvement of a large number of persons, and unintentionally, scientific and other types of errors get into scriptures; otherwise, scriptures are, in reality, truly scientific. Description of Chronology of life in the womb (Fetal Development), Rotation of Universe, spherical shape of the earth, evolution process of non-living matter and living species, classification of species by nature of birth, etc., most convincing prove that scriptures are truly scientific. In fact, there are many facts for which, to date, science has not found answers but are available in scriptures, like the creation of singularity from which the Big Bang took place and the Universe got created innumerable universes, and the most fundamental particle Param-anu. These findings demonstrate that scriptures contain scientific knowledge that predates scientific discoveries.

Keywords: Big Bang, evolution, Param-anu, scientific, scriptures, singularity, universe

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Authors: Saleh Elawgali

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In order to present the effect of the dynamic eccentricity on the stator currents of squirrel cage induction machines, the current spectrums of a 550 kW induction motor was calculated for the cases of full symmetry and dynamic eccentricity. The calculations presented in this paper are based on the Poly-Harmonic Model accounting for static and dynamic eccentricity, stator and rotor slotting, parallel branches as well as cage asymmetry. The calculations were followed by Fourier analysis of the stator currents in steady state operation. The paper presents the stator current spectrums for full symmetry and dynamic eccentricity cases, and demonstrates the harmonics present in each case. The effect of dynamic eccentricity is demonstrating via comparing the current spectrums related to dynamic eccentricity cases with the full symmetry one.

Keywords: current spectrum, dynamic eccentricity, harmonics, Induction machine, slot harmonic zone.

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Authors: Wen-Chung Chiang, Lun-Jou Lo, Hsiu-Hsia Lin

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This study aimed to improve the evaluation of facial symmetry, which is crucial for planning and assessing outcomes in orthognathic surgery (OGS). Facial symmetry plays a key role in both aesthetic and functional aspects of OGS, making its accurate evaluation essential for optimal surgical results. To address the limitations of traditional methods, a different approach was developed, combining three-dimensional (3D) facial contour mapping with hyperdimensional (HD) computing to enhance precision and efficiency in symmetry assessments. The study was conducted at Chang Gung Memorial Hospital, where data were collected from 2018 to 2023 using 3D cone beam computed tomography (CBCT), a highly detailed imaging technique. A large and comprehensive dataset was compiled, consisting of 150 normal individuals and 2,800 patients, totaling 5,750 preoperative and postoperative facial images. These data were critical for training a machine learning model designed to analyze and quantify facial symmetry. The machine learning model was trained to process 3D contour data from the CBCT images, with HD computing employed to power the facial symmetry quantification system. This combination of technologies allowed for an objective and detailed analysis of facial features, surpassing the accuracy and reliability of traditional symmetry assessments, which often rely on subjective visual evaluations by clinicians. In addition to developing the system, the researchers conducted a retrospective review of 3D CBCT data from 300 patients who had undergone OGS. The patients’ facial images were analyzed both before and after surgery to assess the clinical utility of the proposed system. The results showed that the facial symmetry algorithm achieved an overall accuracy of 82.5%, indicating its robustness in real-world clinical applications. Postoperative analysis revealed a significant improvement in facial symmetry, with an average score increase of 51%. The mean symmetry score rose from 2.53 preoperatively to 3.89 postoperatively, demonstrating the system's effectiveness in quantifying improvements after OGS. These results underscore the system's potential for providing valuable feedback to surgeons and aiding in the refinement of surgical techniques. The study also led to the development of a web-based system that automates facial symmetry assessment. This system integrates HD computing and 3D contour mapping into a user-friendly platform that allows for rapid and accurate evaluations. Clinicians can easily access this system to perform detailed symmetry assessments, making it a practical tool for clinical settings. Additionally, the system facilitates better communication between clinicians and patients by providing objective, easy-to-understand symmetry scores, which can help patients visualize the expected outcomes of their surgery. In conclusion, this study introduced a valuable and highly effective approach to facial symmetry evaluation in OGS, combining 3D contour mapping, HD computing, and machine learning. The resulting system achieved high accuracy and offers a streamlined, automated solution for clinical use. The development of the web-based platform further enhances its practicality, making it a valuable tool for improving surgical outcomes and patient satisfaction in orthognathic surgery.

Keywords: facial symmetry, orthognathic surgery, facial contour mapping, hyperdimensional computing

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Authors: Saurabh Basu, Sudin Ganguly

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Conductance in graphene nanoribbons (GNR) in presence of magnetic (for example, Iron) and non-magnetic (for example, Gold) adatoms are explored theoretically within a Kane-Mele model for their possible spintronic applications and topologically non-trivial properties. In our work, we have considered the magnetic adatoms to induce a Rashba spin-orbit coupling (RSOC) and an exchange bias field, while the non-magnetic ones induce an RSOC and an intrinsic spin-orbit (SO) coupling. Even though RSOC is present in both, they, however, represent very different physical situations, where the magnetic adatoms do not preserve the time reversal symmetry, while the non-magnetic case does. This has important implications on the topological properties. For example, the non-magnetic adatoms, for moderately strong values of SO, the GNR denotes a quantum spin Hall insulator as evident from a 2e²/h plateau in the longitudinal conductance and presence of distinct conducting edge states with an insulating bulk. Since the edge states are protected by time reversal symmetry, the magnetic adatoms in GNR yield trivial insulators and do not possess any non-trivial topological property. However, they have greater utility than the non-magnetic adatoms from the point of view of spintronic applications. Owing to the broken spatial symmetry induced by the presence of adatoms of either type, all the x, y and z components of the spin-polarized conductance become non-zero (only the y-component survives in pristine Graphene owing to a mirror symmetry present there) and hence become suitable for spintronic applications. However, the values of the spin polarized conductances are at least two orders of magnitude larger in the case of magnetic adatoms than their non-magnetic counterpart, thereby ensuring more efficient spintronic applications. Further the applications are tunable by altering the adatom densities.

Keywords: magnetic and non-magnetic adatoms, quantum spin hall phase, spintronic applications, spin polarized conductance, time reversal symmetry

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Authors: Hubert Klar

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High double excitation of two-electron atoms has been investigated using hyperpherical coordinates within a modified adiabatic expansion technique. This modification creates a novel fictitious force leading to a spontaneous exchange symmetry breaking at high double excitation. The Pauli principle must therefore be regarded as approximation valid only at low excitation energy. Threshold electron scattering from high Rydberg states shows an unexpected time reversal symmetry breaking. At threshold for double escape we discover a broad (few eV) Cooper pair.

Keywords: correlation, resonances, threshold ionization, Cooper pair

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Authors: I. Pina, M. Painho

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Increased knowledge about the nature of place and the conditions under which space becomes place is a key factor for better urban planning and place-making. Although there is a broad consensus on the relevance of this knowledge, difficulties remain in relating the theoretical framework about place and urban management. Issues related to representation of places are among the greatest obstacles to overcome this gap. With this critical discussion, based on literature review, we intended to explore, in a common framework for geographical analysis, the potential of stories to spell out place meanings, bringing together qualitative text analysis and text mining in order to capture and represent the singularity contained in each person's life history, and the patterns of social processes that shape places. The development of this reasoning is based on the extensive geographical thought about place, and in the theoretical advances in the field of Geographic Information Science (GISc).

Keywords: discourse analysis, geographic information science place, place-making, stories

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Authors: Mahmoud Reza Hosseini

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The universe is in a continuous expansion process, resulting in the reduction of its density and temperature. Also, by extrapolating back from its current state, the universe at its early times has been studied known as the big bang theory. According to this theory, moments after creation, the universe was an extremely hot and dense environment. However, its rapid expansion due to nuclear fusion led to a reduction in its temperature and density. This is evidenced through the cosmic microwave background and the universe structure at a large scale. However, extrapolating back further from this early state reaches singularity which cannot be explained by modern physics and the big bang theory is no longer valid. In addition, one can expect a nonuniform energy distribution across the universe from a sudden expansion. However, highly accurate measurements reveal an equal temperature mapping across the universe which is contradictory to the big bang principles. To resolve this issue, it is believed that cosmic inflation occurred at the very early stages of the birth of the universe According to the cosmic inflation theory, the elements which formed the universe underwent a phase of exponential growth due to the existence of a large cosmological constant. The inflation phase allows the uniform distribution of energy so that an equal maximum temperature could be achieved across the early universe. Also, the evidence of quantum fluctuations of this stage provides a means for studying the types of imperfections the universe would begin with. Although well-established theories such as cosmic inflation and the big bang together provide a comprehensive picture of the early universe and how it evolved into its current state, they are unable to address the singularity paradox at the time of universe creation. Therefore, a practical model capable of describing how the universe was initiated is needed. This research series aims at addressing the singularity issue by introducing an energy conversion mechanism. This is accomplished by establishing a state of energy called a “neutral state”, with an energy level which is referred to as “base energy” capable of converting into other states. Although it follows the same principles, the unique quanta state of the base energy allows it to be distinguishable from other states and have a uniform distribution at the ground level. Although the concept of base energy can be utilized to address the singularity issue, to establish a complete picture, the origin of the base energy should be also identified. This matter is the subject of the first study in the series “A Conceptual Study for Investigating the Creation of Energy and Understanding the Properties of Nothing” which is discussed in detail. Therefore, the proposed concept in this research series provides a road map for enhancing our understating of the universe's creation from nothing and its evolution and discusses the possibility of base energy as one of the main building blocks of this universe.

Keywords: big bang, cosmic inflation, birth of universe, energy creation

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Authors: Anas Ibrahim Yahaya, Christophe Soligo

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A substantial body of literature has reported on facial symmetry and asymmetry and their role in human mate choice. However, major gaps persist, with nearly all data originating from the WEIRD (Western, Educated, Industrialised, Rich and Developed) populations, and results remaining largely equivocal when compared across studies. This study is aimed at quantifying facial asymmetry from the 3D faces of the Hausa of northern Nigeria and also aimed at determining their (Hausa) perceptions and judgements of standardised facial images with different levels of asymmetry using questionnaires. Data were analysed using R-studio software and results indicated that individuals with lower levels of facial asymmetry (near facial symmetry) were perceived as more attractive, more suitable as marriage partners and more caring, whereas individuals with higher levels of facial asymmetry were perceived as more aggressive. The study conclusively asserts that all faces are asymmetric including the most beautiful ones, and the preference of less asymmetric faces was not just dependent on single facial trait, but rather on multiple facial traits; thus the study supports that physical attractiveness is not just an arbitrary social construct, but at least in part a cue to general health and possibly related to environmental context.

Keywords: face, asymmetry, symmetry, Hausa, preference

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Authors: Rinku Maji, Joydeep Chakrabortty, Stephen F. King

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The grand unified theory (GUT) rationales the arbitrariness of the standard model (SM) and explains many enigmas of nature at the outset of a single gauge group. The GUTs predict the proton decay and, the spontaneous symmetry breaking (SSB) of the higher symmetry group may lead to the formation of topological defects, which are indispensable in the context of the cosmological observations. The Super-Kamiokande (Super-K) experiment sets sacrosanct bounds on the partial lifetime (τ) of the proton decay for different channels, e.g., τ(p → e+ π0) > 1.6×10³⁴ years which is the most relevant channel to test the viability of the nonsupersymmetric GUTs. The GUTs based on the gauge groups SO(10) and E(6) are broken to the SM spontaneously through one and two intermediate gauge symmetries with the manifestation of the left-right symmetry at least at a single intermediate stage and the proton lifetime for these breaking chains has been computed. The impact of the threshold corrections, as a consequence of integrating out the heavy fields at the breaking scale alter the running of the gauge couplings, which eventually, are found to keep many GUTs off the Super-K bound. The possible topological defects arising in the course of SSB at different breaking scales for all breaking chains have been studied.

Keywords: grand unified theories, proton decay, threshold correction, topological defects

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Authors: David C. Ni

Abstract:

The current efforts for Grand Unification Theory (GUT) can be classified into General Relativity, Quantum Mechanics, String Theory and the related formalisms. In the geometric approaches for extending General Relativity, the efforts are establishing global and local invariance embedded into metric formalisms, thereby additional dimensions are constructed for unifying canonical formulations, such as Hamiltonian and Lagrangian formulations. The approaches of extending Quantum Mechanics adopt symmetry principle to formulate algebra-group theories, which evolved from Maxwell formulation to Yang-Mills non-abelian gauge formulation, and thereafter manifested the Standard model. This thread of efforts has been constructing super-symmetry for mapping fermion and boson as well as gluon and graviton. The efforts of String theory currently have been evolving to so-called gauge/gravity correspondence, particularly the equivalence between type IIB string theory compactified on AdS5 × S5 and N = 4 supersymmetric Yang-Mills theory. Other efforts are also adopting cross-breeding approaches of above three formalisms as well as competing formalisms, nevertheless, the related symmetries, dualities, and correspondences are outlined as principles and techniques even these terminologies are defined diversely and often generally coined as duality. In this paper, we firstly classify these dualities from the perspective of physics. Then examine the hierarchical structure of classes from mathematical perspective referring to Coleman-Mandula theorem, Hidden Local Symmetry, Groupoid-Categorization and others. Based on Fundamental Theorems of Algebra, we argue that rather imposing effective constraints on different algebras and the related extensions, which are mainly constructed by self-breeding or self-mapping methodologies for sustaining invariance, we propose a new addition, momentum-angular momentum duality at the level of electromagnetic duality, for rationalizing the duality algebras, and then characterize this duality numerically with attempt for addressing some unsolved problems in physics and astrophysics.

Keywords: general relativity, quantum mechanics, string theory, duality, symmetry, correspondence, algebra, momentum-angular-momentum

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Authors: Kirill Trapezon, Alexandr Trapezon

Abstract:

A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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