Center Of Symmetry Research Articles

Metric invariants of a second-order hypersurface in an n-dimensional Euclidean space

The article is devoted to the classical problem of analytic geometry in n-dimensional Euclidean space: finding the canonical equation of a quadric. The canonical equation is determined by the invariants of the second-order surface equation. Invariants are quantities that do not change under an affine change of space coordinates. S. L. Pevsner found a convenient system of the following invariants: q is the rank of the extended matrix of the system for determining the center of symmetry of the surface; the roots of the characteristic polynomial of the matrix of quadratic terms of the surface equation, i. e. the eigenvalues of this matrix; K_q is the coefficient of the variable λ to the power of n − q in a polynomial equal to the determinant of the n + 1 order matrix obtained by a certain rule from the original surface equation. All the coefficients of the canonical equations of quadrics are expressed through eigenvalues of the matrix of quadratic terms and the coefficient K_q. Pevsner’s result is proved in a new way. Elementary properties of determinants are used in the proof. This algorithm for finding the canonical equation of a quadric is a very convenient algorithm for computer graphics.

Tail bounds for empirically standardized sums

Exponential tail bounds for sums play an important role in statistics, but the example of the t-statistic shows that the exponential tail decay may be lost when population parameters need to be estimated from the data. However, it turns out that if Studentizing is accompanied by estimating the location parameter in a suitable way, then the t-statistic regains the exponential tail behavior. Motivated by this example, the paper analyzes other ways of empirically standardizing sums and establishes tail bounds that are sub-Gaussian or even closer to normal for the following settings: Standardization with Studentized contrasts for normal observations, standardization with the log likelihood ratio statistic for observations from an exponential family, and standardization via self-normalization for observations from a symmetric distribution with unknown center of symmetry. The latter standardization gives rise to a novel scan statistic for heteroscedastic data whose asymptotic power is analyzed in the case where the observations have a log-concave distribution.

Synthesis and Structure of Polymeric Copper(I) Compound with Single-Stranded Dihelicate Units involving Multiring Nitrogen-Heterocyclic Ligand

The polymeric copper(I) complex [Cu2(L)I2] (1) containing a new biologically relevant heterocyclic bis-bidentate ligand viz. 3,3′-dipyridine-2-yl-[1.1′]bi[imidazo[1,5-a]pyridineyl] (L) was synthesized and characterized by single-crystal X-ray diffraction analysis. The molecule lacks molecular center of symmetry where coordination environments around both Cu(1) and Cu(2) are distorted tetrahedral (Cu···Cu# separation of 3.5 Å). Compound in its solid-state structure shows π-π non-covalent interactions as well as Carene-H---anion non-classical hydrogen bonding interactions that play dominant roles in shaping the extended structure of the molecule.

Controllable characteristics of interface states in one-dimensional inverted symmetric photonic structures

Using the transfer matrix method, the tunable characteristics of the interface state generated by one-dimensional photonic structure with inversion symmetry are studied, and the samples are prepared by electron beam evaporation technology for experimental verification. According to the different inversion symmetry centers of unit cell, the inverted symmetric layered photonic structures are divided into two types i.e. PCI and PCII. The calculation results show that for the combined structure composed of PCI and PCII, there is an interface state at a characteristic frequency where the sum of the imaginary parts of the surface impedance of PCI and PCII is equal to zero, and this frequency of the interface state is independent of the number of unit cells. On this basis, if a PCI structure is added to form PCI + PCII + PCI photonic structure, two interface states will be generated in the same band gap, and changing the unit cell number in each or part of of individual PCI and PCII structures, the frequencies of two interface states can be regulated. The experimental results show that the regulation of interface state by controlling unit cell number is feasible, which provides a more flexible idea for designing the extremely narrow-band filters and multi-channel filters to meet different application requirements.

Paramagnetic centers in chromium-doped Na-=SUB=-5-=/SUB=-AlF-=SUB=-2-=/SUB=-(PO-=SUB=-4-=/SUB=-)-=SUB=-2-=/SUB=- single crystal

The paramagnetic resonance of Na5AlF2(PO4)2 single crystals with chromium impurity was studied. The Cr3+ centers have been found to replace the triclinic Al3+ positions. In the local coordinate system, the spectra of these centers were described by the spin Hamiltonian of rhombic symmetry. In addition, vanadium centers and unidentified triclinic symmetry centers have been observed. Keywords: impurity ions, aluminum fluoride phosphate, paramagnetic resonance.

Electron Diffraction Study of the Space Group Variation in the Al–Mn–Pt T-Phase

Binary high temperature “Al3Mn” (T-phase) and its extensions in ternary systems were the subjects of numerous crystallographic investigations. The results were ambiguous regarding the existence or lack of the center of symmetry: both Pna21 and Pnam space groups were reported. Our research on the Al–Mn–Pt T-phase allowed concluding that inside a continuous homogeneity region, the structure of the Al-rich T-phase (e.g., Al78Mn17.5Pt4.5) belongs to the non-centrosymmetric Pna21 space group, while the structure of the Al-poor T-phase (such as Al71.3Mn25.1Pt3.6) is centrosymmetric, i.e., Pnam. Following metallurgical and crystallographic considerations, the change in the symmetry was explained.

Impact of geomechanical heterogeneity on multiple hydraulic fracture propagation

Abstract To extract more gas from shale gas reservoirs, the spacing among hydraulic fractures should be made smaller, resulting in a significant stress shadow effect. Most studies regarding the stress shadow effect are based on the assumption of homogeneity in rock properties. However, strong heterogeneity has been observed in shale reservoirs, and the results obtained with homogeneous models can be different from practical situations. A series of case studies have been conducted in this work to understand the effects of mechanical heterogeneity on multiple fracture propagation. Fracture propagation was simulated using the extended finite element method. A sequential Gaussian simulation was performed to generate a heterogeneous distribution of geomechanical properties. According to the simulation results, the difficulty of fracture propagation is negatively correlated with the Young's modulus and Poisson's ratio, and positively correlated with tensile strength. When each of the multiple fractures propagates in a homogeneous area with different mechanical properties, the final geometry of the fracture is similar to homogeneous conditions. When the rock parameter is a random field or heterogeneity perpendicular to the propagation direction of fracture, the fracture will no longer take the wellbore as the center of symmetry. Based on the analysis of fracture propagation in random fields, a small variance of elastic parameters can result in asymmetrical propagation of multiple fractures. Moreover, the asymmetrical propagation of hydraulic fractures is more sensitive to the heterogeneity of Poisson's ratio than Young's modulus. This study emphasises the importance of considering geomechanical heterogeneity and provides some meaningful suggestions regarding hydraulic fracturing designs.

Численное решение задачи о сжатии газа при заданном законе воздействия

Выполнено численное моделирование одномерных течений политропного газа, описывающее сжатие покоящегося газа с плотностью 1 в покоящийся газ, сжатый до значения 10. Описываемое сжатие происходит без ударных волн эффективным с точки зрения энерговложения способом, так как энергия тратится только на сжатие газа, но не на его разгон Controlled thermonuclear fusion (CTF) is an almost unlimited source of energy and scientists have been studying it for several decades. This requires an efficient and stable compression of diyterium-tritium fuel to a very high density. This work addresses shockless one-dimensional (plane, cylindrical and spherical symmetry cases) “compression from rest to rest”, when gas from the initial resting state under the influence of an impenetrable piston is shocklessly transferred to a resting homogeneous state, but compressed by 10000 times. This compression is energetically most advantageous, because work is spent only on the compression, but not on the gas acceleration. Earlier [10] this problem was solved in the opposite direction of time change. In this case, a density jump occurs on the piston which was taken into account in calculations [3] at the final moment of compression. The numerical solution of this problem in the opposite direction of time variation allows calculating the trajectory of the compressing piston in the form of a set of points ( t,r ) at which the gas velocity and density are determined. In this paper, the problem of shockless “compression from rest to rest” is numerically solved in the forward direction of time change if the compressing piston trajectory is known. The compression piston moves along a monotonous trajectory away from the axis or center of symmetry. It is important, when calculating in forward direction of time change, no internal characteristics are initially entered. They, like all gas flow in the calculation area, are determined in the process of direct calculation. This indicates that the trajectory of compressing piston is the recommendation for appropriate physical experiments

All are aromatic: A 3D globally aromatic cage containing five types of 2D aromatic macrocycles

All are aromatic: A 3D globally aromatic cage containing five types of 2D aromatic macrocycles

Multi-Target Recognition of Bananas and Automatic Positioning for the Inflorescence Axis Cutting Point

Multi-target recognition and positioning using robots in orchards is a challenging task in modern precision agriculture owing to the presence of complex noise disturbance, including wind disturbance, changing illumination, and branch and leaf shading. To obtain the target information for a bud-cutting robotic operation, we employed a modified deep learning algorithm for the fast and precise recognition of banana fruits, inflorescence axes, and flower buds. Thus, the cutting point on the inflorescence axis was identified using an edge detection algorithm and geometric calculation. We proposed a modified YOLOv3 model based on clustering optimization and clarified the influence of front-lighting and backlighting on the model. Image segmentation and denoising were performed to obtain the edge images of the flower buds and inflorescence axes. The spatial geometry model was constructed on this basis. The center of symmetry and centroid were calculated for the edges of the flower buds. The equation for the position of the inflorescence axis was established, and the cutting point was determined. Experimental results showed that the modified YOLOv3 model based on clustering optimization showed excellent performance with good balance between speed and precision both under front-lighting and backlighting conditions. The total pixel positioning error between the calculated and manually determined optimal cutting point in the flower bud was 4 and 5 pixels under the front-lighting and backlighting conditions, respectively. The percentage of images that met the positioning requirements was 93 and 90%, respectively. The results indicate that the new method can satisfy the real-time operating requirements for the banana bud-cutting robot.

Rare-earth induced nonlinear structural evolutions in fluorite solid solution crystals

The modification of chemical composition to improve desired material parameters is an effective method in materials science and engineering. In this work, Ca1-xSrxF2 solid solution is chosen as the subject. Nd3+ and Y3+ ions are used as dopants. We have found that spectral properties of Nd3+:Ca1-xSrxF2 and Nd3+,Y3+:Ca1-xSrxF2 crystals vary nonlinearly with the ‘x’. The X-ray diffraction (XRD) patterns and the density functional theory (DFT) calculations on Ca1-xSrxF2 solid solutions have ruled out the influence of matrix crystals on spectral properties. The rare-earth monomer centers of C4v or C3v symmetry, and the high order clusters are modeled. The calculated results show, that thermodynamic stabilities of the centers vary nonlinearly. Temperature-dependent dielectric losses and the results of projected density of states (pDOS) calculations also show nonlinear dependency. The nonlinearly evolved local structures from cubic to square antiprism sublattice cause the nonlinear variation of spectral properties. The methodology of rare-earth induced nonlinear structural evolutions is then proposed, which is useful for exploring new materials.

Semiclassical constant-density spheres in a regularized Polyakov approximation

We provide an exhaustive analysis of the complete set of solutions of the equations of stellar equilibrium under semiclassical effects. As classical matter we use a perfect fluid of constant density; as the semiclassical source we use the renormalized stress-energy tensor (RSET) of a minimally coupled massless scalar field in the Boulware vacuum (the only vacuum consistent with asymptotic flatness and staticity). For the RSET we use a regularized version of the Polyakov approximation. We present a complete catalogue of the semiclassical self-consistent solutions which incorporates regular as well as singular solutions, showing that the semiclassical corrections are highly relevant in scenarios of high compactness. Semiclassical corrections allow the existence of ultra-compact equilibrium configurations which have bounded pressures and masses up to a central core of Planckian radius, precisely where the regularized Polyakov approximation is not accurate. Our analysis strongly suggests the absence of a Buchdahl limit in semiclasical gravity, while indicating that the regularized Polyakov approximation used here must be improved to describe equilibrium configurations of arbitrary compactness that remain regular at the center of spherical symmetry.

New numerical framework for the generalized Baumgarte-Shapiro-Shibata-Nakamura formulation: The vacuum case for spherical symmetry

Here we report a developed high performance and simplified version of the code denominated RIO, which can be easily extended, for the generalized BSSN formulation. We implement a code which is regular at the center of symmetry, without use a special procedure for regularization, as usual. We get exponential convergence for constraints. The numerical algorithm is based on the Galerkin-Collocation method developed successfully for diverse physical scenarios by the Numerical Relativity Group at UERJ. For the sake of clarity in presentation, we consider here the most simple case to display the most salient features of the procedure. Thus, we focus on the definite tests of the new numerical framework. The timing and performance of the code show that we can reach a better accuracy close to the machine precision, for the Hamiltonian and momentum constraints. RIO will be an open source code; currently is under continuous development to consider more general and realistic problems.

Prediction of optical polarization and high-field hyperfine structure via a parametrized crystal-field model for low-symmetry centers in Er3+ -doped Y2SiO5

We report on the development and application of a parametrized crystal-field model for both ${\mathrm{C}}_{1}$ symmetry centers in trivalent erbium-doped ${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$. High-resolution Zeeman and temperature dependent absorption spectroscopy was performed to acquire the necessary experimental data. The obtained data, in addition to the ground $(^{4}\mathrm{I}_{15/2}{\mathrm{Z}}_{1})$ state and exited $(^{4}\mathrm{I}_{13/2}{\mathrm{Y}}_{1})$ state Zeeman and hyperfine structure, were simultaneously fitted in order to refine an existing crystal-field interpretation of the ${\mathrm{Er}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ system. We demonstrate that it is possible to account for the electronic, magnetic, and hyperfine structure of the full $4{f}^{11}$ configuration of ${\mathrm{Er}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ and further, that it is possible to predict both optical polarization behavior and high magnetic field hyperfine structure of transitions in the $1.5\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$ telecommunications band.

Real time display with the ferrolens of homogeneous magnetic fields

In our previous published research we have studied the applications of the ferrolens for the observation and qualitative analysis of non-homogeneous magnetic fields. Latest developments over the last few years of the ferrolens increased multifold the sensitivity of this device allowing it to display magnetic fields as low as 10mT in strength and therefore it is possible now to observe also the homogeneous (i.e. straight parallel magnetic flux lines of uniform density in space) magnetic field existing inside air solenoids and between N-S poles of two attracting separated permanent magnets. We present and analyze herein these novel observations of homogeneous magnetic fields with the ferrolens and as a potential new application of this device. The ferrolens can now display the projected magnetic field on air from a distance without needing to be in physical contact with the field source. Experiments were carried out to demonstrate these new capabilities of the ferrolens as a nanomagnetic flux viewer, real-time physical device and scientific qualitative tool. We compare the geometry of magnetic fields of condensed matter ferromagnets with that of magnetic fields inside electrical air solenoids. Specifically, the homogeneous field between two N-S attracting magnets at a distance as well as inside air solenoids and Helmholtz coils and also the non-homogeneous total field of single dipole permanent magnets were observed using a latest generation very sensitive ferrolens. The unique feature of this magneto optic fluid thin film physical device is that it can display discrete magnetic flux lines of the macroscopic field. Also we show how the ferrolens can be used to detect qualitatively the symmetry center of a non ideal homogeneous magnetic field.

Insight into structural description of novel 1,4-Diacetyl-3,6-bis(phenylmethyl)-2,5-piperazinedione: synthesis, NMR, IR, Raman, X-ray, Hirshfeld surface, DFT and docking on breast cancer resistance protein

In this work, novel 1,4-diacetyl-3,6-bis(phenylmethyl)-2,5-piperazinedione (2) is prepared exclusively as the (R,S)-stereoisomer evidenced and confirmed by X-ray diffraction analysis. In addition, spectroscopic (NMR, IR, Raman) analyses were used to characterize the new compound. 2 crystallizes in the Pbca orthorhombic space group, with a symmetry center located at the centroid of the diketopiperazine ring. The structure of 2 is compact with the two phenyl rings folded over and under the diketopiperazine ring, conferring thereby a unique S shape to the molecule. The crystal structure is stabilized by intramolecular interactions, whereas the crystal packing is stabilized by intermolecular H-bond and C−H···π interactions. The different intermolecular interactions were confirmed using Hirshfeld surface analysis and molecular fingerprint. Molecular 2D fingerprint that quantify the different interactions highlights that H···H (58.2%), H···O/O···H (24.8%) and C···H/H···C (14.2%) account for 97.2% of all contacts. The topology of the interaction energy in the crystal structure is obtained and described. The Cremer and Pople puckering parameters indicate that the diketopiperazine ring adopts a flattened chair conformation with Θ = 0.00 ° and Q = 0.2233 (11) Å. Moreover, a computational investigation revealed that the optimized structure of 2 using DFT calculation shows excellent agreement with the experimental data. As potential pharmacological active molecule, the molecular docking on breast cancer resistance protein (BCRP) reveals that 2 could interacts with the binding domain residues Phe728, Tyr949, Ser975 and Val978 and could be consider as promising BCRP inhibitor.

Cores of 1/2< 110 >-type dislocations in the CrMnFeCoNi high-entropy alloy investigated by STEM, the center of symmetry and the Nye tensor mapping techniques

Cores of 1/2< 110 >-type dislocations in the CrMnFeCoNi high-entropy alloy investigated by STEM, the center of symmetry and the Nye tensor mapping techniques

Novel study on the electron density distribution projection maps calculated via the discrete cosine transform

It is already known that a curve estimated via the discrete cosine transform (DCT) always passes through all the measured points without using imaginary numbers in the DCT coefficients, unlike the discrete Fourier transform. Moreover, owing to its character, the DCT can be used instead of the nonlinear least-squares method to express various theoretical curves. Because the DCT is a kind of Fourier transform, there is a possibility that the DCT could be employed to draw electron density distribution maps of crystals. If so, the probability that the DCT could be used to investigate the internal structure of materials by analysing the theoretical curves would increase. This article reports an attempt to draw the electron density distribution maps of the Mg3BN3 low-pressure phase [Mg3BN3(L)] by using the DCT in order to confirm the utility of the DCT for analysing the internal structure of materials. It is found that the DCT can provide mirror-symmetric electron density distribution projection maps and a modified DCT can be used to calculate whole standard electron density distribution projection maps for the surface plane of the unit cell. Moreover, a real crystal structure that has a centre of symmetry can be determined by the DCT by transforming a 1/4 part of the mirror-symmetric electron density distribution projection map.

Centers of spatial and time inversion symmetry in magnetoelectric crystalline materials

Centers of spatial and time inversion symmetry in magnetoelectric crystalline materials

Antimicrobial activities of cadmium (II) and nickel (II) complexes containing pyridine ring: Investigation of crystallographic, spectroscopic, Hirshfeld surface analysis, and TD/DFT calculations

AbstractTwo complexes [Cd(L)2(NO3)2] (1) and [Ni(L)2(OH)2][Ni(L)2(CH3OH)2](NO3)2·CH3OH (2) (L = 2‐[2‐pyridyl]‐4‐methyl‐1,2‐dihydroquinazolin 3‐oxide) were gained via complexation an amount of the new ligand L with different nitrate salts. The obtained complexes were characterized by elemental analysis, spectroscopy, and X‐ray crystallographic. In the crystal structure, centrosymmetric 1 adopted slightly distorted octahedral geometry. On the other hand, the independent unit of 2 contained two half Ni (II) complex located on a center of symmetry, differing for the axial ligand, two uncoordinated nitrate ions, and one lattice methanol molecule. Both the crystal structures formed a 3‐D supramolecular architecture through different interactions (H‐bonds, π···π, etc). X‐ray crystallography revealed that complexes 1 and 2 had 2:1 ligand‐to‐metal ratios. Most strikingly, 1 performed different fluorescence behaviors in diverse solvents, whereas 2 exhibited fluorescence quenching. When 1 was dissolution in N,N‐dimethylformamide (DMF) solvent system, it has better fluorescence properties. The geometry optimization and HOMOs and LUMOs energies of both complexes were calculated by density functional theory (DFT) methods, and the nucleophilic and electrophilic attack sites were confirmed with electrostatic potential (ESP) calculations. Preliminary investigation of antimicrobial activities of all compounds against Gram‐negative bacteria (Escherichia coli) and Gram‐positive bacteria (Bacillus subtilis) was reported. Additionally, CrystalExplorer program was used to quantify the noncovalent interactions in complexes 1 and 2 through Hirshfeld surface analysis.