Type Of Symmetry Research Articles

Single-chirality nanotube synthesis by guided evolutionary selection.

Bringing to fruition the tantalizing properties, foreseen since the discovery of carbon nanotubes, has been hindered by the challenge to produce a desired helical symmetry type, single chirality. Despite progress in postsynthesis separation or somewhat sporadic success in selective growth, obtaining one chiral type at will remains elusive. The kinetics analysis here shows how a local yet moving reaction zone (the gas feedstock or elevated temperature) can entice the tubes to follow, so that, remotely akin to proverbial Lamarck giraffes, only the fastest survive. Reversing the reaction to dissolution would further eliminate the too fast-reactive types so that a desired chirality is singled out in production.

On the Matrix Method for Solving Heat Conduction Problems in a Multilayer Medium in the Presence of Phase Transitions

This paper is devoted to the applicability of the matrix method for solving the heat equation for multilayer media in the case where a phase transition is possible in some layer. We consider only stationary processes in the absence of internal heat sources. We propose a general method for layer systems with translation, axial, or central symmetry based on the technique of generalized Bers powers. Using this method, we perform calculations for one substance, when after a phase transition, the system becomes a two-layer system. We consider the dependence of the coordinate of the phase-transition point on the external temperature and compare results obtained for media with types of symmetry indicated above. A temperature field is constructed for multilayer media with various types of symmetry when a phase transition has occurred in a certain layer.

Structure particularities and first, second order Raman spectra of LiNbO3:Tb near the concentration threshold

Defective structure particularities have been studied in pure non-stoichiometric (Li/Nb≠1) lithium niobate (NSLN) crystals and LiNbO3:Tb (2.24 wt%) crystal. NSLN Raman spectra contain low-intensity extra bands in the area 100-1000 cm−1 at different scattering geometries. The bands are not provided by the selection rules for LN. The bands are caused by static disorder in cation sublattice of crystals. Besides, we have established additional bands in the area 1300-2000 cm−1 of a LiNbO3:Tb (2.24 wt%) crystal Raman spectrum. The bands correspond to overtone states of crystal lattice polar fundamental modes. Second-order Raman spectrum of LiNbO3:Tb contains bands with frequencies higher than that of overtones of the highest-frequency fundamental polar modes with А1(Z) and Е(X,Y) symmetry type. The particularities are manifestation of bonded states of polar modes – bipolaritons; they convert in two entangled photons or in a bonded state – biphoton at an exit from the crystal.

Hilbert spaces and low-lying zeros of L-functions

Generalizing previous work of Iwaniec, Luo, and Sarnak (2000), we use information from one-level density theorems to estimate the proportion of non-vanishing of L-functions in a family at a low-lying height on the critical line (measured by the analytic conductor). To solve the Fourier optimization problems that arise, we provide a unified framework based on the theory of reproducing kernel Hilbert spaces of entire functions (there is one such space associated to each symmetry type). Explicit expressions for the reproducing kernels are given. We also revisit the problem of estimating the height of the first low-lying zero in a family, considered by Hughes and Rudnick (2003) and Bernard (2015). We solve the associated Fourier optimization problem in this setting by establishing a connection to the theory of de Branges spaces of entire functions and using the explicit reproducing kernels. In an appendix, we study the related problem of determining the sharp embeddings between the Hilbert spaces associated to the five symmetry types and the classical Paley-Wiener space.

GRASP: The Future?

The theoretical foundations of relativistic electronic structure theory within quantum electrodynamics (QED) and the computational basis of the atomic structure code GRASP are briefly surveyed. A class of four-component basis set is introduced, which we denote the CKG-spinor set, that enforces the charge-conjugation symmetry of the Dirac equation. This formalism has been implemented using the Gaussian function technology that is routinely used in computational quantum chemistry, including in our relativistic molecular structure code, BERTHA. We demonstrate that, unlike the kinetically matched two-component basis sets that are widely employed in relativistic quantum chemistry, the CKG-spinor basis is able to reproduce the well-known eigenvalue spectrum of point-nuclear hydrogenic systems to high accuracy for all atomic symmetry types. Calculations are reported of third- and higher-order vacuum polarization effects in hydrogenic systems using the CKG-spinor set. These results reveal that Gaussian basis set expansions are able to calculate accurately these QED effects without recourse to the apparatus of regularization and in agreement with existing methods. An approach to the evaluation of the electron self-energy is outlined that extends our earlier work using partial-wave expansions in QED. Combined with the treatment of vacuum polarization effects described in this article, these basis set methods suggest the development of a comprehensive ab initio approach to the calculation of radiative and QED effects in future versions of the GRASP code.

Identification of higher symmetry in triclinic stiffness tensor: Application to high pressure dependence of elastic anisotropy in deep underground structures

We present an approach of identifying anisotropy axes and the type of symmetry from ultrasonic measurements of 21 elastic constants of the complete stiffness tensor characterizing anisotropic materials. The approach is applied to examine anisotropic elasticity of two crystalline rock samples from two underground research laboratories : (1) the migmatized gneiss from Bukov in the Czech Republic; and (2) the Aare Granite from Grimsel in Switzerland. The full stiffness matrix is measured at selected pressure levels from 0.1 to 100 MPa. We demonstrate that the Bukov migmatized gneiss is orthorhombic , whereas the Grimsel granite is transversely isotropic under atmospheric pressure. The degree of anisotropy of both rocks decreases with applied confining pressure due to closing of preferentially oriented cracks. While the Grimsel granite is very sensitive to pressure and becomes almost isotropic at high pressures, a great portion of anisotropy in the Bukov migmatized gneiss remains even under high pressures due to its texture. The dependence of Young's and shear moduli with pressure emphasizes the importance of taking the pressure into account for underground projects.

The theory of continuous distributions of composite defects

This work undertakes the analysis of continuous media that carry simultaneously two different material or geometric structures in the same material substrate. Even when these two structures are individually perfectly uniform and homogeneous, their combination may result in a non-uniform assembly. Thus, in contradistinction to the classical interpretation of material defectivity as a manifestation of material inhomogeneity, the lack of uniformity of a composite is physically interpreted as the presence of a different kind of continuously distributed material defects. Various quantitative measures of misalignment and lack of uniformity are proposed associated with solid constituents of different symmetry types. Finally, from a more formal point of view, the use of double groupoids and their associated double Lie algebroids is suggested as the natural setting for further developments of the theory.

Средства художественной выразительности в стихотворении Бо Цзюйи «Чувства, вызванные созерцанием луны»

The study aims to determine the percentage of parallel fragments in Bai Juyi’s poem “Feelings on Watching the Moon” out of the total number of characters. For this purpose, the researcher will consider fragments characterised by both local and global parallelism as parallel fragments. The study is novel in that it is the first in Russian academic literature to carry out such an analysis of the parallelism of this work that is based on analysing all the lines of the poem at the level of phrases. As a result of the study, it has been shown that the poem under consideration is characterised by vertical and horizontal, local and global symmetry, with horizontal and vertical symmetry complementing each other. None of these types of symmetry is dominant. Parallel fragments make up 87.5% of the total number of characters in the poem. Parallelism is complemented by four metaphors, one symbol and expressive-emotive vocabulary.

Symmetry classification of scalar autonomous Ito stochastic differential equations with simple noise

It is known that knowledge of a symmetry of a scalar Ito stochastic differential equations leads, thanks to the Kozlov substitution, to its integration. In the present paper we provide a classification of scalar autonomous Ito stochastic differential equations with simple noise possessing symmetries; here "simple noise" means the noise coefficient is of the form $\s (x,t) = s x^k$, with $s$ and $k$ real constants. Such equations can be taken to a standard form via a well known transformation; for such standard forms we also provide the integration of the symmetric equations. Our work extends previous classifications in that it also consider recently introduced types of symmetries, in particular standard random symmetries, not considered in those.

Review force general conjectural modeling transforms formalism physics

This review article discusses recent advance formalisms trying to resolve inconsistencies of algorithmic grand unified physics. Logical conjectures starting with considering universe as a matrix of existential points and developing knowhow mechanics to configure algorithms to quantify quantum physical discontinuum dissipative process mechanism is emphasized. This projects algorithmic generalized transforms to model fundamentally force out of first definitional principle that will consider infinitum multiverses that encompasses universes allowing information leaking. These aspects may explain why none of the universal constants, especially Planck’s constant, speed of light, universal gravitational constant, fine structure constant, as well as others may not be constant after all!! Hereafter, emphasis will be on observable that are theoretically and/or theoretically testable measurable observations. Realizing that a real astrophysical parameter may be only signal/noise matrix, step by via step algorithms are developed from first principles of physical mathematics especially matrices, properties, rules, mathematical conceptuality, and physical attributable entity simple common-sense approach. Types of symmetries, intensity matrix versus density matrix, hidden causality, functor, functional algebra function point absolute microblackhole gage gravity force PHYSICS transforms superluminous plenum vacuum quanta with quantum sub-quantum hod-PDP micromechanics have been analyzed extensively with grand unifiable algorithm equating formalisms.

A new symmetry for large deviation functions of time-integrated dynamical variables

A new type of symmetry in the large deviation function of a time-integrated current is introduced. This current is different from the fluctuating entropy production for which the large deviation function is symmetric in the content of the fluctuation theorem. The origin of this symmetry, similar to that of the Gallavotti-Cohen-Evans-Morriss symmetry, is related to time-reversal. The symmetry is more unveiled when one performs an appropriate grouping of stochastic trajectories in the space of microscopic configurations. It turns out that the characteristic polynomial of the modified generator of this current is not symmetric; however, its minimum eigenvalue is symmetric.

Influence of Symmetry Theory on Understanding the Qur'anic Ayas

Symmetry theory is a well-known mathematical theory, which has been applied to physics and chemistry as well as other scientific disciplines. Here, we apply the symmetry theory to language in general and to the Holy Quran in specific. We argue that there is ample evidence for this theory in language such as the X-bar theory, parallelism and the mirror image derivation across languages. We show that there are vertical as well as horizontal types of symmetry, some of which have a line of symmetry while others have a virtual point. The data is analyzed from a semantic angle with some reference to syntax. We focus on symmetry at the Aya (verse) level. The paper found that symmetry can help interpret Ayas of similar wording or similar structures. It also found that symmetry theory presents a solution for the either-or-pause Ayas. Further, it showed how symmetry theory help solve ellipsis in the Holy Quran. Finally, the paper revealed that there are symmetry-less sentences that communicate propositions without the need for a symmetrical image. Keywords: Symmetry Theory, the Holy Quran, X’ Theory, Semantics, Discourse Analysis.

Educational Case Studies for Pilot Engineer 4.0 Programme: Monitoring and Control of Discrete-Event Systems Using OPC UA and Cloud Applications

The current trend in industry is the digitalisation of production processes using modern information and communication technologies, a trend that falls under the fourth industrial revolution, Industry 4.0. Applications that link the world of information technologies (IT) and operational technologies (OT) are in particular demand. On the basis of information from practice, it can be stated that there is a shortage of specialists in the labour market for the interconnection of PLCs with information and communication technologies (cloud, web, mobile applications, etc.) in Slovakia and neighbouring countries. However, this problem is beginning to affect other countries in Europe as well. The main objective of the work was to prepare case studies suitable for educational purposes, which would address the modelling and control of a virtual discrete-event system using a PLC program and its subsequent interfacing to a cloud application. Within the scope of the work, three case studies were prepared to demonstrate the control of discrete-event system using different programming systems and their communication with the developed cloud applications. These applications are to be used for data monitoring and emergency intervention of the discrete-event system. The characteristics of the prepared case studies, which combine operational and informational technologies, predestines them for use in the sphere of education of engineers for digitalisation of production processes. They can also be helpful in research on the creation of digital twins, which represent a type of symmetry between real and virtual systems.

Floral symmetry: the geometry of plant reproduction.

The flower is an astonishing innovation that arose during plant evolution allowing flowering plants — also known as angiosperms — to dominate life on earth in a relatively short period of geological time. Flowers are formed from secondary meristems by co-ordinated differentiation of flower organs, such as sepals, petals, stamens, and carpels. The position, number and morphology of these flower organs impose a geometrical pattern — or symmetry type — within the flower which is a trait tightly connected to successful reproduction.During evolution, flower symmetry switched from the ancestral poly-symmetric (radial symmetry) to the mono-symmetric (bilateral symmetry) type multiple times, including numerous reversals, with these events linked to co-evolution with pollinators and reproductive strategies.In this review, we introduce the diversity of flower symmetry, trace its evolution in angiosperms, and highlight the conserved genetic basis underpinning symmetry control in flowers. Finally, we discuss the importance of building upon the concept of flower symmetry by looking at the mechanisms orchestrating symmetry within individual flower organs and summarise the current scenario on symmetry patterning of the female reproductive organ, the gynoecium, the ultimate flower structure presiding over fertilisation and seed production.

A class of 5D Hamiltonian conservative hyperchaotic systems with symmetry and multistability

Conservative chaos systems have been investigated owing to their special advantages. Taking symmetry as a starting point, this study proposes a class of five-dimensional(5D) conservative hyperchaotic systems by constructing a generalized Hamiltonian conservative system. The proposed systems can have different types of coordinate-transformation and time-reversal symmetries. Also, the constructed systems are conservative in both volume and energy. The constructed systems are analyzed, and their conservative and chaotic properties are verified by relevant analysis methods, including the equilibrium points, phase diagram, Lyapunov exponent diagram, bifurcation diagram, and two-parameter Lyapunov exponent diagram. An interesting phenomenon, namely that the proposed systems have multistable features when the initial values are changed, is observed. Furthermore, a detailed multistable characteristic analysis of two systems is performed, and it is found that the two systems have different numbers of coexisting orbits under the same energy. And, this type of system can also exhibit the coexistence of infinite orbits of different energies. Finally, the National Institute of Standards and Technology tests confirmed that the proposed systems can produce sequences with strong pseudo-randomness, and the simulation circuit is built in Multisim software to verify the simulation results of some dynamic characteristics of the system.

Phase control of localization in the nonlinear two-mode system from harmonic mixing driving: Perturbative analysis and symmetry consideration

In this paper, we present a rigorous analysis of symmetry and underlying physics of the nonlinear two-mode system driven by a harmonic mixing field, by means of multiple scale asymptotic analysis method. The effective description in the framework of the second-order perturbative theory provides an accurate picture for understanding the Floquet eigenspectrum and dynamical features of the nonlinear two-mode system, showing full agreement with the prediction of symmetry considerations. We find that two types of symmetries play significant role in the dynamical features of this model, the mechanism behind which can be interpreted in terms of the effective description. The results are of relevance for the phase control of the atomic localization in Bose–Einstein condensates or switch of the optical signals in nonlinear mediums.

Low-lying zeros in families of elliptic curve L-functions over function fields

We investigate the low-lying zeros in families of L-functions attached to quadratic and cubic twists of elliptic curves defined over Fq(T). In particular, we present precise expressions for the expected values of traces of high powers of the Frobenius class in these families with a focus on the lower order behavior. As an application we obtain results on one-level densities and we verify that these elliptic curve families have orthogonal symmetry type. In the quadratic twist families our results refine previous work of Comeau-Lapointe. Moreover, in this case we find a lower order term in the one-level density reminiscent of the deviation term found by Rudnick in the hyperelliptic ensemble. On the other hand, our investigation is the first to treat these questions in families of cubic twists of elliptic curves and in this case it turns out to be more complicated to isolate lower order terms due to a larger degree of cancellation among lower order contributions.

Rotational symmetry detection in 3D using reflectional symmetry candidates and quaternion-based rotation parameterization

The property of symmetry in 3D objects is helpful in various applications such as object alignment, compression, symmetrical editing or reconstruction of incomplete objects. However, its robust and efficient detection is a challenging task. The two most commonly occurring types of symmetry are probably reflectional and rotational symmetry. While reflectional symmetry detection methods are quite plentiful, this does not seem to be the case with rotational symmetry detection. In this paper a use of approximate reflectional symmetries to derive plausible approximate rotational symmetries is proposed that can be integrated with multiple different approaches for reflectional symmetry detection. One such specific approach, based on maximizing a given symmetry measure, is chosen and combined with this idea. A modification of the maximization step for rotations is further proposed using a simple, yet efficient, quaternion-based parameterization of the rotation transformation which seems novel in the field of symmetry detection. The results confirm that this combination provides a robust and efficient solution for finding rotational symmetry in a 3D point set and can handle approximate symmetry, noisy input or even partial data.

Temperature sensing using bulk and nanoparticles of Ca0.79Er0.01Yb0.2MoO4 phosphor

Optical temperature sensing is widely realized by using upconversion (UC) emission in lanthanide-doped phosphors. There are various parameters that are responsible for UC intensity of the phosphor like particle shape and size, type of symmetry that exist at the site position, distribution of lanthanide ions in the phosphor, and so on. However, a comparative study of the bulk and nanostructure on the temperature sensing ability of such phosphor is rare. In the present work, we have taken Ca0.79Er0.01Yb0.2MoO4 phosphors as a model system and synthesized its bulk (via solid-state reaction method, named SCEY) and nanostructures (via solution combustion route, named CCEY). We further studied their phase, crystal structure, phonon frequency, optical excitation, and emission (upconversion & downshifting) properties. Finally, the optical temperature sensing behavior of SCEY and CCEY, in the range 305 K–573 K, have been compared. The maximum relative sensitivity of the phosphor SCEY and CCEY are 0.0061 K−1 at 305 K and 0.0094 K−1 at 299 K, respectively, while, the maximum absolute sensitivities are 0.0150 K−1 at 348 K, and 0.0170 K−1 at 398 K, respectively. We thus conclude that the temperature sensing ability of nanoparticle-based Ca0.79Er0.01Yb0.2MoO4 phosphor is better compared to its bulk phosphor.

Families of symmetries and the hydrogen atom

We study a new type of symmetry for the hydrogen atom involving algebraic families of groups parametrized by the energy value in the time-independent Schrödinger equation. We construct an algebraic family of Harish-Chandra modules from the solutions of the Schrödinger equation, and we characterize this family. We show that the subspaces of physical states may be obtained from our algebraic family using a Jantzen filtration, and we relate our algebraic methods with spectral theory and scattering theory using the limiting absorption principle.