Center Of Symmetry Research Articles

ВИКОРИСТАННЯ ФУНКЦІЙ ГАУСА ДЛЯ АПРОКСИМАЦІЇ БІОЛОГІЧНИХ СИГНАЛІВ

Purpose. Currently, the method of mathematical analysis of various biological signals is increasingly used in medicine. Most of them are random and quasi-periodic processes, which greatly complicates the possibility of using an automated data processing process. Signals of this type include respiratory noises, phonocardiographic and electrocardiographic signals. The shape of the waves of the ECG signal is quite accurately described by asymmetric Gaussian pulses. It is possible to achieve the required approximation accuracy by introducing additional pulses to describe the diagnostically important inhomogeneities of the signal. In the previous work of the authors the simple algorithm of coefficients selection of asymmetric functions in the form of the Labview virtual device is realized. But for the cases of superposition of waves of different polarity and non-standard pulse shapes, the result of applying this algorithm gives a significant error. Methodology. In the analysis of waves of negative polarity, the presence of a positive burst, even a small value, leads to a complete disregard for the negative wave. To eliminate this shortcoming, it is necessary to determine the maximum and minimum values of the amplitudes of the samples in this area and compare their absolute values. A larger value will determine the polarity of the wave coming to the virtual instrument for analysis. The next complication is the presence of a wide flat wave top with an offset maximum value by extreme samples. This is a significant shift in the symmetry of the wave and, as a consequence, incorrect determination of parameters for a wide part of the pulse. To eliminate this shortcoming, it is proposed to determine all the influential extremes, and shift the center of symmetry to the middle of the flat top of the wave. In the case where the wave has a significant violation of symmetry, it is possible that the virtual device determines the midpoints and amplitudes of the left to right parts with a significant deviation from the actual peak value. To prevent the vertices of the Gaussian functions from shifting relative to the real maximum it was proposed to mirror the data sets corresponding to the left and right parts of the wave. Results. In this article, the algorithm of the virtual device operation for automatic determination of the parameters of the approximate asymmetric Gaussian curves in the Labview software environment is improved. It is planned to use approximation by Gaussian impulses to synthesize standard leads from reduced sets of ECG signal leads. According to preliminary studies, a surface of approximation coefficients has been created, which allows synthesizing a cardiac signal for an arbitrary derivation. Originality. Algorithm for approximating biological signals by asymmetric Gaussian functions is improved. In this case, a more confident approximation of waves was obtained in the presence of: bursts of opposite polarity; wide flat top of the wave when the maximum value is shifted to extreme samples; significant violation of the symmetry of the waves; narrow fragments of waves. Practical value. A virtual device was created to approximate signals (including ECG signal leads, respiratory noises and phonocardiosignals) using asymmetric Gaussian functions. The analysis of certain coefficients will make it possible to use them as average criteria for the diagnosis of the corresponding diseases, which requires further research. References 10, figures 11.

Entropy based designing and analysis of a compact single layer double negative metamaterial with oblique incidents

The underlying study investigates a novel fuzzy cross entropy based methodology for enhancing the designing and analysis of a compact single layer double negative metamaterial with varying oblique incidents. Materials having a refractive index greater than unity may slow down the propagation of waves in comparison to the vacuum. A material with zero refractive index can boost the speed and wavelength of the wave to infinity. Nevertheless, metamaterials with a negative index of refraction have the necessary capability for controlling the wave velocity, although, mimicking zero index property in materials is quite difficult in real practices. Based on experimental observations and data visualizations, the lower bound of each measured indiscriminative index of refraction is extracted at various oblique incidents and then rehabilitated into the form of normalized and idealized fuzzy index sets (FISs). Thereafter, the proposed fuzzy cross entropy measure is deployed for identifying the most negative indiscriminative refractive index along with the desired wave velocity, intended to obtain the best incident angle and desired transition frequency. The experimental results suggest that the structure is behaving as a double negative metamaterial for all the azimuth angles with transition frequency fluctuating near to 7 GHz with different negative levels. The lowest transition frequency for the designed structure is observed at 0°azimuthal and increases thereafter with augmenting incident angle up to 90°. Although, the observed transition frequency decreases thereafter with further augmentation of incident angle (from 90°to 180°) and exhibits approximate symmetry in terms of transition frequency with the center of symmetry at 90°. Subsequently, the minimum (maximum) fuzzy cross entropy value between normalized and idealized fuzzy index sets is deployed to obtain the highest (lowest) wave velocity, which is observed at 135°(157.5°) azimuthal angle. The underlying fuzzy cross entropy-based methodology is capable of handling double negative metamaterial with oblique incidents and can effectively be applied for achieving the desired wave velocity as well as indiscriminative refractive index, depending upon the application requirements.

Agreement of Fixation Disparity Curve between Two Different Instruments.

Fixation disparity tests with various characteristics of fusional stimulus are very important for assessment of decompensated heterophoria. The results suggest that there was no reasonable agreement between the fixation disparity curve's parameters of the modified near Mallett unit and the Sheedy disparometer. The purpose of this study was to determine the agreement of the fixation disparity curve parameters between the modified near Mallett unit and the Sheedy disparometer in patients with decompensated near heterophoria. A total of 147 young adults (mean age, 22.7 ± 4.8 years) participated in this cross-sectional study. After applying the exclusion criteria, the statistical analysis was done on the data of 134 individuals. All participants underwent preliminary optometric examinations including the measurement of uncorrected and best-corrected visual acuity, objective and subjective refraction, and unilateral and alternating cover tests. The fixation disparity was evaluated using the modified near Mallett unit and the Sheedy disparometer at 40 cm, and forced-vergence fixation disparity curves were generated. There were statistically significant differences in the fixation disparity curve parameters (except the center of symmetry) between the two devices. The median fixation disparity measured by the Sheedy disparometer was more positive compared with the modified near Mallett unit (toward more esodisparity or less exodisparity). The median associated phoria measured by the Sheedy disparometer was more positive compared with the Mallett unit. Also, the slope of the curve obtained by the Mallett unit was steeper. The wide limits of agreement indicated the poor agreement of all fixation disparity curve parameters between the two instruments.

On the possibility of creating a magnetic field with a given degree of spatial inhomogeneity

Proposed here is a method for constructing systems of circular thin Helmholtz coils (conic coils), which makes it possible to obtain a magnetic field with any degree of inhomogeneity by doubling the number of coils. A functional relationship is obtained between the currents of the coils and their distances to the center, which allows zeroing all derivatives in the expansion of the magnetic field in a series in spatial variables in the center of the system to a derivative of arbitrary order. An analytical expression is obtained for the magnitude of the magnetic field of the systems along the axis of symmetry. All the systems considered here have the same parity (oddness) of the projections of the magnetic field with respect to spatial variables and equal inhomogeneity in all directions in the center of symmetry.

Comparison of Spatio-Temporal Parameter and Symmetry during Gait between Healthy Elderly and Young People

Background Previous studies have examined the gait patterns of healthy elderly people who are able to walk without musculoskeletal pain, but results have been conflicting. Systemic diseases such as diabetes, depression, and hypertension, as well as musculoskeletal system dysfunction, can induce gait deterioration. Purpose The purpose of the current study was to compare velocity, cadence, step width, stride length, center of pressure (COP) and symmetry between healthy young and elderly people who had not been diagnosed with depression, hypertension, dementia, diabetes, or osteoarthritis. Study design Cross-sectional study Methods Twenty-four healthy elderly and twenty healthy young people participated in this study. A force distribution plate was used to obtain data on spatiotemporal parameters, COP, and gait symmetry. The groups were compared using independent <italic>t</italic>-tests. Results There was no significant difference in walking velocity, step width, stride length, symmetry of step length, foot rotation, length of gait, single support line, or lateral symmetry between the elderly and young groups (<italic>p</italic>&gt;0.05). However, the elderly group showed higher cadence and larger anterior–posterior sway than the young group (mean difference=8.98 steps/min, <italic>p</italic>&lt;0.01; and mean difference=5.88 mm, <italic>p</italic>=0.04, respectively). Conclusions The gait patterns of healthy elderly people without depression, hypertension, dementia, diabetes, or musculoskeletal were similar in terms of spatiotemporal parameters and symmetry to those of healthy young people, except for cadence and anterior–posterior sway. Based on these findings, clinicians should inform elderly people about the importance of maintaining fitness to prevent deterioration of gait.

Structure and Properties of Ln2MoO6 Oxymolybdates (Ln = La, Pr, Nd) Doped with Magnesium

The literature data and the results obtained by the authors on the study of the structure and properties of a series of polycrystalline and single-crystal samples of pure and Mg-doped oxymolybdates Ln2MoO6 (Ln = La, Pr, Nd) are analyzed. Presumably, the high-temperature phase I41/acd of Nd2MoO6 single crystals is retained at room temperature. The reason for the loss of the center of symmetry in the structures of La2MoO6 and Pr2MoO6 and the transition to the space group I4¯c2 is the displacement of oxygen atoms along the twofold diagonal axes. In all structures, Mg cations are localized near the positions of the Mo atoms, and the splitting of the positions of the atoms of rare-earth elements is found. Thermogravimetric studies, as well as infrared spectroscopy data for hydrated samples of Ln2MoO6 (Ln = La, Pr, Nd), pure and with an impurity of Mg, confirm their hygroscopic properties.

Upconversion Thermometry Using Yb3+/Er3+ Co-Doped KY3F10 Nanoparticles

We report high-sensitivity luminescence thermometry using Yb3+/Er3+ co-doped KY3F10 core and core–shell upconverting nanoparticles. The highest thermal sensitivities of 1.510 ± 0.015%·K–1 (300 K) and 1.245 ± 0.013%·K–1 (316 K) and temperature uncertainty of 0.11 K were achieved by tuning the excitation wavelength to 975 nm to be in-resonant with optical transitions of the Yb3+ ion. The high-resolution Yb3+ excitation spectra were recorded by observing the Er3+, 4S3/2, 4F9/2 → 4I15/2 upconversion fluorescence, with the highest fluorescence yield obtained at 10 254 cm–1 (975 nm) for both nanoparticles. This coincides with the ground-state absorption maximum at 297 K. However, at 10 K, the Yb3+ upconversion excitation spectra also exhibit excited-state absorption peaks. The Yb3+ absorption spectra for the core and core–shell nanoparticles are dominated by single-ion centers (of C4v symmetry). Resonant excitation of the core and core–shell nanoparticles is observed to yield a 5-fold enhancement in Er3+ upconversion fluorescence intensity in comparison to excitation at 980 nm, increasing the fluorescence intensity ratio and the thermal sensitivity of a KY3F10 nanothermometer operating at the physiological temperatures.

Influence of laser wavelength on surface enhanced Raman spectroscopy using Mn based nano-particles produced by laser ablation synthesis in 4,4′ Bipyridine solution (LASiS)

In this work surface Raman spectroscopy of Mn based nano-particles produced by laser ablation technique in 4,4′ Bipyridine (Bipy: C10H8N2) aqueous environment is studied using three Raman spectroscopes with different laser wavelengths of 532, 632.8 and 785 nm. Transmission electron microscopy (TEM), X-ray diffraction (XRD), UV–visible spectroscopy (UV-Vis), dynamic light scattering (DLS) and Fourier transformations infra-red spectroscopy (FTIR) produced the characteristics of the obtained samples. Results of TEM and DLS showed that spherical Mn based nano-particles with a diameter of 40 nm and nano-rods with different lengths were produced. A value of − 23.61 mV for zeta potential and a mobility of − 1.84 × 10−8 m2s−1V−1 showed the instability of the produced nano-particles in the solution which can be stabilized by ultrasonic treatment of the solution. The absorption spectra showed two peaks at 400 and 422 nanometer wavelengths that may be assigned as transverse and longitudinal plasmonic oscillations of the nano-rod particles, respectively. The most intense peak in the XRD pattern of nano-particles in Bipy solution was assigned as MnO2(131) and no Mn peak was observed. Raman and FTIR analyses should not result in similar data for molecules with center of symmetry. This is confirmed in the results of this work for Bipy as such molecule. High enhancement of the Raman peaks of Bipy was achieved using all three different laser wavelengths. The influence of laser wavelength on different main Raman shifts of Bipy is discussed and related to the correlation between the laser wavelength and size of the nano-particles. In particular, and consistent with this and previous results some combined Raman shifts are also observed using 632.8 nm laser wavelength.

C * -simplicity of HNN extensions and groups acting on trees

The first author is supported by a PhD stipend from the Danish National Research Foundation (DNRF) through the Centre for Symmetry and Deformation at University of Copenhagen.

2-(2,4-Di-chloro-phen-oxy)-N'-[2-(2,4-di-chloro-phen-oxy)acet-yl]acetohydrazide.

The complete mol-ecule of the title compound, C16H12Cl4N2O4, is generated by a crystallographic centre of symmetry. In the crystal, N-H⋯O hydrogen bonds link the mol-ecules into [010] chains featuring R 2 2(10) loops. The chains are cross-linked by short Cl⋯N contacts [3.224 (2) Å].

Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients

Black-box techniques have been applied with outstanding results to classify, in a supervised manner, the movement patterns of Alzheimer’s patients according to their stage of the disease. However, these techniques do not provide information on the difference of the patterns among the stages. We make use of functional data analysis to provide insight on the nature of these differences. In particular, we calculate the center of symmetry of the underlying distribution at each stage and use it to compute the functional depth of the movements of each patient. This results in an ordering of the data to which we apply nonparametric permutation tests to check on the differences in the distribution, median and deviance from the median. We consistently obtain that the movement pattern at each stage is significantly different to that of the prior and posterior stage in terms of the deviance from the median applied to the depth. The approach is validated by simulation.

The effect of impurity position and doping concentration on the binding energies and total optical absorption coefficients in a $${\delta }$$-doped quantum well

In this present work, for different impurity position and ionized doping concentrations, we have theoretically investigated the linear, third-order nonlinear, and total optical absorption coefficients corresponding to the $$(1\rightarrow 2)$$ intersubband transitions between the ground and first-excited conduction band states in a single $$\delta $$ -doped GaAs well, with and without the presence of a donor impurity. Impurity binding energies were calculated using the effective-mass and parabolic band approximations within a variational scheme. The linear, third-order nonlinear, and total optical absorption coefficients for the intersubband transitions are calculated within the compact density matrix approach. The obtained results show that adding an impurity positioned at the symmetry center of the well, as well as the increase in the ionized donor concentrations, shifts the total optical absorption coefficients to higher photon energies. However, the off-center positions of impurities together with the varying ionized donor concentrations lead to blue or red shifts in relation to the values of binding energies. The results in this study may be useful for the design and applications of the devices based on the $$\delta $$ -doped structures.

Evaluation of the presence of a central fusion lock effect on fixation disparity curve parameters in symptomatic and asymptomatic subjects

ABSTRACT Clinical relevance: Several parameters are likely to affect the magnitude of fixation disparity (FD) and FD curve characteristics. Presence of a central fusion lock may have an important effect on clinical testing of FD and interpretation of its results. Background: The aim of this study was to evaluate FD curve parameters using the modified near Mallett unit (with a central fusion lock) and the Sheedy disparometer (without a central fusion lock) in symptomatic and asymptomatic subjects. Methods: This cross-sectional study was conducted in 147 patients with a mean age of 22.5 years who presented to the optometry clinic of Paramedical College of Mashhad University of Medical Sciences. The symptoms were recorded in a questionnaire for each patient. FD was measured using the modified near Mallett unit and Sheedy disparometer and FD curves were generated using the AutoCAD 2005 software. Results: There was a significant difference in the FD, associated phoria, and slope measurements between the two devices (all p values < 0.05). Significant difference was found in the mean FD between symptomatic and asymptomatic subjects using the modified near Mallett unit (p < 0.0001) and Sheey disparometer (p = 0.007). In symptomatic subjects, the mean slope was steeper for the modified near Mallett unit compared to the Sheedy disparometer (p = 0.001). Although the mean centre of symmetry was more negative in the modified near Mallett unit versus the Sheedy disparometer, the difference between the instruments was not significant in symptomatic (p = 0.477) and asymptomatic (p = 0.257) participants. Conclusion: There are differences in the FD curve parameters between the modified near Mallett unit and Sheedy disparometer. Slope is a proper criterion for differentiating asymptomatic subjects from symptomatic individuals. The modified near Mallett unit is a more precise tool for assessment of non-compensated heterophoria compared to the Sheedy disparometer.

Threefold helical assembly via hy-droxy hydrogen bonds: the 2:1 co-crystal of bi-cyclo-[3.3.0]octane-endo-3,endo-7-diol and bi-cyclo-[3.3.0]octane-endo-3,exo-7-diol.

Reduction of bi-cyclo-[3.3.0]octane-3,7-dione yields a mixture of the endo-3,endo-7-diol and endo-3, exo-7-diol (C8H14O2) isomers (5 and 6). These form (5)2·(6) co-crystals in the monoclinic P21/n space group (with Z = 6, Z' = 1.5) rather than undergoing separation by means of fractional recrystallization or column chromatography. The mol-ecule of 5 occupies a general position, whereas the mol-ecule of 6 is disordered over two orientations across a centre of symmetry with occupancies of 0.463 (2) and 0.037 (2). Individual diol hy-droxy groups associate around a pseudo-threefold screw axis by means of hydrogen bonding. The second hy-droxy group of each diol behaves in a similar manner, generating a three-dimensional hydrogen-bonded network structure. This hydrogen-bond connectivity is identical to that present in three known helical tubuland diol-hydro-quinone co-crystals, and the new crystal structure is even more similar to two homologous aliphatic diol co-crystals.

Crystal structure of a methanol solvate of a macrocycle bearing two flexible side-arms.

Di-tert-butyl N,N'-{[13,15,28,30,31,33-hexa-ethyl-3,10,18,25,32,34-hexa-aza-penta-cyclo-[25.3.1.15,8.112,16.120,23]tetra-triaconta-1(31),3,5,7,9,12(33),13,15,18,20,22,24,27,29-tetra-deca-ene-14,29-di-yl]bis-(methyl-ene)}dicarbamate methanol disolvate, C52H72N8O4·2CH3OH, was found to crystallize in the space group P21/c with one half of the macrocycle (host) and one mol-ecule of solvent (guest) in the asymmetric unit of the cell, i.e. the host mol-ecule is located on a crystallographic symmetry center. Within the 1:2 host-guest complex, the solvent mol-ecules are accommodated in the host cavity and held in their positions by O-H⋯N and N-H⋯O bonds, thus forming ring synthons of graph set R 2 2(7). The connection of the 1:2 host-guest complexes is accomplished by C-H⋯O, C-H⋯N and C-H⋯π inter-actions, which create a three-dimensional supra-molecular network.

Schiff’s base with center of symmetry as an effective corrosion inhibitor for mild steel in acid medium: Electrochemical & simulation studies

Green and efficient corrosion inhibitors have received widespread attention from various disciplines due to their wide application in petrochemical and other fields. However, because of its inability to fully understand the corrosion inhibition mechanism, the understanding of corrosion inhibition performance is limited. In this work, we synthesized a Schiff base (1, 2−1H-Benzoimidazol-2-yl)-(1, 2-diphenyl-ethylidene)-amine) (BDEA) with centre of symmetry structure by 2-aminobenzimidazole and benzyl. The central symmetric distribution of the heteroatoms has a higher coordination effect, thus, the adsorption performance has been outstanding. Characterization of synthesized compound was done using Fourier transform infrared spectroscopy (FTIR) and nuclear magnetic resonance (NMR) analysis. The corrosion inhibition property of the synthesized Schiff base on X80 steel was determined using potentiodynamic polarization, electrochemical impedance spectroscopy (EIS), and scanning electrochemical microscopy (SECM) analysis in 1 M HCl medium. Surface analyses of the alloy samples were performed using atomic force microscopy (AFM) analysis and contact angle measurement. BDEA can effectively protect X80 steel corrosion in 1 M HCl medium and the maximum efficiency obtained was 94.26 %. The surface analysis further proved that morphology of the metal surface was more protected in the presence of BDEA. In addition, the production of the reaction between BDEA and Fe3+ were studied by UV–vis spectrum analysis, and the mechanism was deliberated. The study of SECM showed that BDEA could adsorb both active and non-active regions on the metal surface at the same time. DFT studies suggested that the inhibition efficiency of its neutral as well as protonated form followed the order of η(protonated form) >η(neutral form) using DFT-based quantum chemical calculations. Besides, the degradation of BDEA showed that temperature had a significant effect on the degradation rate of BDEA using total organic carbon (TOC) analysis. Thermogravimetric analysis (TGA) indicated BDEA had admirable thermal stability. The influence of molecular behavior on corrosion inhibition performance is revealed from the perspective of structural characteristics. This work provides strong evidence for revealing the effect of structure on corrosion inhibition mechanism.

Further boundary conditions in heat conduction problems in multilayer structures

This paper presents an approximate analytical solution of the heat conduction problem for a two-layer plate under symmetric boundary conditions of the first kind. The solution was determined on the basis of the property of the parabolic heat transfer equation associated with an infinite velocity of heat propagation, by determining the accessory unknown function and accessory boundary conditions in the integral heat balance method.Local coordinate systems are given in order to obtain the simplest possible coordinate system satisfying the matching conditions and boundary conditions for each separate layer. An accessory unknown function is the temperature change over time in the center of symmetry. The use of this function in the heat balance integral method allows for reduction in the solution of the initial partial differential equation to the integration of an ordinary differential equation with respect to the additional unknown function.Further boundary conditions are defined in such a way that their satisfaction by an unknown solution is equivalent to the satisfaction of the equations at the boundary points. Studies have shown that the equation fulfillment at the boundaries leads to their fulfillment within the regions.

Hyperbolically symmetric static fluids: A general study

We carry on a comprehensive study on static fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. The energy density appears to be necessarily negative, which suggests that any possible application of this kind of fluids requires extreme physical conditions where quantum effects are expected to play an important role. Also, it is found that the fluid distribution cannot fill the region close to the center of symmetry. Such a region may be represented by a vacuum cavity around the center. A suitable definition of mass function, as well as the Tolman mass are explicitly calculated. While the former is positive defined, the latter is negative in most cases, revealing the repulsive nature of gravitational interaction. A general approach to obtain exact solutions is presented and some exact analytical solutions are exhibited.

Novograblenovite from Radlin, Upper Silesia, Poland and its relation to ‘redikortsevite’

AbstractThe paper presents detailed mineralogical and structural characteristics of novograblenovite that occurs abundantly on a burning coal dump at Radlin, Upper Silesia, Poland. Our results indicate that NH4MgCl3⋅6H2O is the proper formula of this mineral. The thermal behaviour of novograblenovite shows a two-step dehydration at 155 and 193°C and sublimation of NH4Cl at 341°C. A Raman spectrum, obtained for the first time, reveals the normal modes of H2O and NH4+ vibrations. The crystal structure of novograblenovite was refined on the basis of high quality X-ray diffraction data. The final discrepancy factor wR2 was 0.0567 for 94 parameters and 1464 independent reflections. The structure has a monoclinic C2/c space group symmetry with the following unit cell parameters: a = 9.2709(3) Å, b = 9.5361(2) Å, c = 13.2741(4) Å and β = 90.054(3)°. We were able to specify the architecture of the disordered NH4+ cation located at the symmetry centre. This led to reasonable parameters for the H-bonding formed by this cation. In carnallite the K+ cations occupy an identical space to the ammonium ion in novograblenovite, but when embedded into the latter crystal structure it is bound less tightly. Voids occupy 14% of the space in the novograblenovite crystal structure. Novograblenovite is exactly the same phase as the ‘redikortsevite’ described previously from Chelabinsk coal dumps and this informally introduced name should be abandoned.

Testing symmetry based on the extropy of record values

In this paper, we first present the symmetric property of the extropy of record values and some characterisations of exponential distributions. Then a new test for symmetry of the continuous distribution is proposed based on a characterisation result. Our proposed test has an advantage that we do not need to estimate the centre of symmetry. Moreover, for a wide variety of alternative asymmetric distributions, Monte Carlo simulation shows that our test performs better than the competitor tests. Finally, two real data sets are used to illustrate the applicability of the proposed test by monitoring p-values of our test and its competitors.