Symmetrical Triangle Research Articles

Ultrafast Imaging of Jahn-Teller Distortion and the Correlated Proton Migration in Photoionized Cyclopropane.

The Jahn-Teller (JT) distortion is one of the fundamental processes in molecules and condensed phase matters. For photoionized organic molecules with high symmetry, the JT effect leads to geometric instability in certain electron configurations and thus has a significant effect on the subsequent isomerization and proton migration processes. Utilizing the femtosecond pump-probe Coulomb explosion method, we probe the isomerization dynamics process of a monovalent cyclopropane cation (C3H6+) caused by proton migration and reveal the relationship between proton migration and JT distortion. We found that the C3H6+ cation evolves from the D3h symmetric equilateral triangle geometry either to the acute triangle via two elongated C-C bonds (JT1) or to the obtuse triangle via a single elongated C-C bond (JT2). The JT1 pathway does not involve proton migration, while the JT2 pathway drives proton migration and can be mapped into the indirect dissociation channel of Coulomb explosion. The time-resolved experiment indicates that the delay time between those two JT pathways can be as large as ∼600 fs. After the JT distortion, the cyclopropane cation undergoes a subsequent structural evolution, which brings a greater variety of dissociation channels.

Synthetic Aperture Ladar Motion Compensation Method Based on Symmetric Triangle Linear Frequency Modulation Continuous Wave Segmented Interference

Synthetic Aperture Ladar (SAL) is a sensor that combines laser detection technology with synthetic aperture technology to achieve ultra-high-resolution imaging. Due to its extremely short wavelength, SAL is more sensitive to motion errors. The micrometer-level motion will affect the target’s azimuth focus. This article proposes an SAL motion compensation method based on Symmetric Triangular Linear Frequency Modulation Continuous Wave (STLFMCW) segmented interference, utilizing the characteristics of a triangular wave, to solve the problem of target azimuth defocusing. This article first establishes an STLFMCW echo signal model based on the SAL system under the influence of motion errors. Secondly, the radial velocity gradient along the azimuth direction is extracted using the triangular-wave-positive and -negative frequency modulation signals segmented interference method. Then, for the initial phase wrapping problem, the frequency spectral cross-correlation method is used to accurately estimate the initial radial velocity error. The radial velocity gradient is integrated along the azimuth to obtain the platform motion trajectory. Finally, the compensation functions are constructed to complete the echo Range Cell Migration (RCM) correction and residual phase compensation, resulting in a focused SAL image. This article verifies the practical effect of this method in eliminating motion errors using only one-period STLFMCW signal through simulation and real experiments. The quantitative results show that compared with the traditional method, the proposed method reduces the azimuth Peak Sidelobe Ratio (PSLR) by 8dB and the Integrated Sidelobe Ratio (ISLR) by 9 dB. This method has significant improvements and is of great significance for high-resolution FMCW SAL imaging.

Automated Maximum Torque per Ampere Identification for Synchronous Reluctance Machines with Limited Flux Linkage Information

The synchronous reluctance machine is well-known for its highly nonlinear magnetic saturation and cross-saturation characteristics. For high performance and high-efficiency control, the flux-linkage maps and maximum torque per ampere table are of paramount importance. This study proposes a novel automated online searching method for obtaining accurate flux-linkage and maximum torque per ampere Identification. A limited 6 × 2 dq-axis flux-linkage look-up table is acquired by applying symmetric triangle pulses during the self-commissioning stage. Then, three three-dimensional modified linear cubic spline interpolation methods are applied to extend the flux-linkage map. The proposed golden section searching method can be easily implemented to realize higher maximum torque per ampere accuracy after 11 iterations with a standard drive, which is a proven faster solution with reduced memory sources occupied. The proposed algorithm is verified and tested on a 15-kW SynRM drive. Furthermore, the iterative and execution times are evaluated.

Design of control algorithms for false information dissemination in smart city social media based on symmetric triangle interval

Design of control algorithms for false information dissemination in smart city social media based on symmetric triangle interval

Formation of pyramidal structures through mixing gold and platinum atoms: the AuxPty2+ clusters with x + y = 10.

The geometric and electronic structures of a small series of mixed gold and platinum AuxPty2+ clusters, with x + y = 10, were investigated using quantum chemical methods. A consistent tetrahedral pyramid structure emerges, displaying two patterns of structural growth by a notable critical point at y = 5. This affects the clusters' electron population, chemical bonding, and stability. For the Pt-doped Au clusters with y values from 2 to 5, the bonds enable Pt atoms to assemble into symmetric line, triangle, quadrangle, and tetragonal pyramidal Pty blocks, respectively. For the Au-doped Pt clusters, with larger values of y > 5, the structures are more relaxed and the d electrons of Pt atoms become delocalized over more centers, leading to lower symmetry structures. A certain aromaticity arising from delocalization of d electrons over the multi-center framework in the doped Pt clusters contributes to their stability, with Pt102+ at y = 10 exhibiting the highest stability. While the ground electronic state of the neutral platinum atom [Xe]. 4f145d96s1 leads to a triplet state (3D3), the total magnetic moments of AuxPty2+ are large increasing steadily from 0 to 10 μB and primarily located on Pt atoms, corresponding to the increase of the number of Pt atoms from 0 to 10 and significantly enhancing the magnetic moments. An admixture of both Au and Pt atoms thus emerges as an elegant way of keeping a small pyramidal structure but bringing in a high and controllable magnetic moment.

IONIC CONDUCTIVITY OF POLYVINYL ALCOHOL-BASED GEL ELECTROLYTE CONTAINING DIETHYL CARBONATE PLASTICIZER FOR SUPERCAPACITOR APPLICATION

In this study, diethyl carbonate (DEC) as a plasticizer have been added to the gel electrolytes (GEs) system to influence the conductivity and storage performance of supercapacitor. The GE was prepared through a stirring method consisting of ethylene carbonate (EC), propylene carbonate (PC), potassium iodide (KI), polyvinyl alcohol (PVA) and dimethyl sulfoxide (DMSO). Consecutively, 5 wt. % DEC as a plasticizer was added for all samples. The GE preparation started with stirring all materials and heated until a homogenous gel was formed. The prepared GEs have been characterized with electrochemical impedance spectroscopy (EIS), which utilized to study the ionic conductivity of them. Sample with 15 wt. % of DEC in GE has the ionic conductivity of ~6 x 10-3 Scm-1. This study shows that by adding DEC will cause the ionic conductivity improved which is suggested that this DEC enhanced the ion’s mobility in the GEs’ structures. In cyclic voltammetry, the gel electrolyte with 15 wt.% DEC attain the highest specific capacitance of 55.56 Fg-1 (scan rate of 10 mV s-1). The charge-discharge curve of gel electrolyte acquires a shark fin-like shape which is alike with an ideal supercapacitor symmetric triangle shape. To summarize, the development of high conductivity GE may provide the path for high-performance supercapacitor.

Synthesis And Characterization Of Carbon-Chitosan Composite Electrodes Based On Biomass Carbon Activated Using The Microwave Method

In this research, the synthesis and characterization of chitosan modified carbon composites based on biomass carbon has been carried out using the microwave method. Chemically activated carbon with 2.5% H3PO4 activator was stirred using a magnetic stirrer for 1 hour and allowed to stand for 24 hours. The carbon was then physically reactivated using a microwave for 20 minutes with a power variation of 800, 1000 and 1200 watts and a Scanning Electron Microscopy (SEM) test was carried out. After the SEM test, chitosan modified carbon was synthesized with a composition ratio of 1:1, 2:1 and 3:1 and the specific capacitance was measured using Galvanostatic Charge-Discharge (GCD) testing. The SEM test results analyzed using ImageJ software-based image processing methods show that the value of sphericity, pore size and carbon porosity decreases with increasing microwave power used. The optimum conditions based on the value of Sphericity, pore size and porosity were obtained at a variation of 800 watts of microwave power with values ​​of 0.952, 0.832 m, and 25.87%, respectively, which were included in the macropore size (>50 nm). Because the higher the power used, the smaller the pore area and porosity. The electrode-specific capacitance values ​​were 3.4 x 10-1 F/g, 24.02 F/g, and 1.3 x 10-1 F/g, respectively. Electrodes with a ratio of 2:1 have the largest capacitance value, because they can be charged by an electric charge. The longer the charge-discharge process, the greater the capacitance value, so the curve will approach a more symmetrical isosceles triangle shape.

An Efficient Method for Solving Second-Order Fuzzy Order Fuzzy Initial Value Problems

In this paper, we present an accurate numerical approach based on the reproducing kernel method (RKM) for solving second-order fuzzy initial value problems (FIVP) with symmetry coefficients such as symmetric triangles and symmetric trapezoids. Finding the exact solution of FIVP is not an easy task since the definition will produce a complicated optimization problem. To overcome this difficulty, a numerical method is developed to solve this type of problems. We start by introducing the necessary definitions and theorems about the fuzzy logic. Then, we derived the kernels for two Hilbert spaces. The RKM is derived for the second-order IVP in the Boolean sense, and then we generalize it for the fuzzy sense. Numerical and theoretical results will be given to obtain the accuracy of the developed technique. We solved four linear and non-linear fuzzy IVPs numerically using the proposed method, and we compute the error in each case to show the efficiency of the method. The absolute error was very small in the four examples.

Symmetric binary Steinhaus triangles and parity-regular Steinhaus graphs

A binary Steinhaus triangle is a triangle of zeroes and ones that points down and with the same local rule as the Pascal triangle modulo 2. A binary Steinhaus triangle is said to be rotationally symmetric, horizontally symmetric or dihedrally symmetric if it is invariant under the 120 degrees rotation, the horizontal reflection or both, respectively. The first part of this paper is devoted to the study of linear subspaces of rotationally symmetric, horizontally symmetric and dihedrally symmetric binary Steinhaus triangles. We obtain simple explicit bases for each of them by using elementary properties of the binomial coefficients. A Steinhaus graph is a simple graph with an adjacency matrix whose upper-triangular part is a binary Steinhaus triangle. A Steinhaus graph is said to be even or odd if all its vertex degrees are even or odd, respectively. One of the main results of this paper is the existence of an isomorphism between the linear subspace of even Steinhaus graphs and a certain linear subspace of dihedrally symmetric binary Steinhaus triangles. This permits us to give, in the second part of this paper, an explicit basis for even Steinhaus graphs and for the vector space of parity-regular Steinhaus graphs; i.e., the linear subspace of Steinhaus graphs that are even or odd. Finally, in the last part of this paper, we consider the generalized Pascal triangles, that are triangles of zeroes and ones, that point up now, and always with the same local rule as the Pascal triangle modulo 2. New simple bases for each linear subspace of symmetric generalized Pascal triangles are deduced from the results of the first part.

Strategic Triangles and Balancing in World Politics

Trilateral diplomacy is a common format of interaction in international relations, which forms various configurations of the balance of power within the framework of triangles. The concept of a “triangle” is characterized by ambivalence, has a variety of characteristics and principles of formation.The article provides an overview of the theoretical discourse on strategic triangles, as well as of practical examples of trilateral diplomacy of the past and present day. The main characteristics of strategic triangles and the features of changes in their configuration are identified (the case of USA–PRC–USSR triangle). Classification of both symmetric and asymmetric triangles (unicenter and bicenter) are given, the concept of buffer states, as well as regional conflicts with the participation of a great power as a defender, are presented.The most influential countries at the global and regional levels, forming geopolitical triangles, are identified basing on the Composite Index of National Capability (CINC). The concept of pivot states is analyzed permitting to indicate relatively small but geopolitically important countries, forming triangles together with influential states.The main strategic triangles of the modern world order are analyzed, presenting mostly countries of Asia (China, Japan, India), Russian Federation, USA and EU. The main trends of global competition based on geopolitical triangles in the XXI-st century are identified.

Thirugnana Sambandhar - A Mathematician

India has been the Land of notable poets whose exemplary works are world renowned. One such great poet is Thirugnana Sambandhar. He is a saint, poet, philosopher, composer who belongs to 7th Century. He was born in Seerkaazhi of Tamilnadu. He had coined many Special Geometrical poetic structures like Thiru ezhukkootrirukkai (poem with mathematical Triangular Pattern), Maalai Maatru (a poem with palindromic Structure), Mozhi Maatru (a poem in which the meaning of the poem can be observed by a systematic Chane of words), Gomuthri (Flow of the poem in such a way it forms a wave line), Chakramaatru (a poem which is constructed in a circular form ). By the above mentioned amazing structure He has no parallels in the worlds poetry Thirugnana Sambandhar is the epitome of Tamil Literature has penned down many such extraordinary poems. A Mathematician is one who uses an extensive knowledge of Mathematics in their work. Mathematicians are concerned with numbers, data, quantity, structure, space,models and change. Here in this poetic form Thiruezhukkootrirukkai Thirugnana Sambandhar had used numbers in a brilliant way to form a Triangle. This is called “Chitrakavi” in Tamil. By analyzing the whole poem we will get a geometrical structure. In this Thiruezhukkootrirukkai Thirugnana Sambandhar has constructed the words in such a way to form a symmetrical triangle. These triangle is arranged in a perfect mathematical calculation. This can be analysed through the law of binomial co- efficient. This is analysed and proved in this paper. Thirugnana Sambandhar belongs to 7th Century whereas the Scientist and Mathematician Pascal who discovered the law of Bi-nomial co-efficient belongs to 17th century. Other than this Mathematical diagram of triangle this poem has Palindromic numbers which add more beauty to this structure which is also a mathematical calculation. By constructing this amazing poetic structure Thirugnana Sambandhar proves beyond doubt that he is a “Mathematician” of India of the 7th Century itself who had applied the law of triangle earlier.

A Four-Layer Odd Function Symmetrical Dual-Polarization Equilateral Right Triangle Slot Printed Broadband Directional Antenna for Wireless Lab Measurement Applications

A four-layer odd function symmetrical dual-polarization coplanar waveguide- (CPW-) fed equilateral right triangle slot printed broadband directional antenna for wireless lab measurement applications is presented. The proposed antenna consists of two stacked perpendicular odd function symmetrical equilateral right triangle slot antenna structures with two stacked reflector ground planes. It is miniaturized, simple, and easy to be fabricated. The measured results demonstrate that the proposed antenna can achieve wide impedance bandwidth that is almost 520% for |S11| and |S22|; VSWR ≦ 3 which has implemented the operating band from 1.37 to 7.12 GHz for Global Positioning System (GPS, 1.575 GHz), Wireless Local Area Networks band (2.4 GHz and 5.8 GHz), 6 GHz unlicensed spectrum (5.925 GHz∼7.125 GHz), Long Term Evolution Upper Band (LTE, 1710–2690 MHz), and sub-6 5 G band (3.5 GHz and 4.7 GHz) applications. The measured in-band isolation performance between the two input ports |S12| ≦ −17 dB is significantly achieved, and meanwhile, the antenna radiation pattern, peak gain, and efficiency of the proposed antenna are measured as well. In the end, the radiation pattern data are compared and analyzed with simulation results.

MIM waveguide structure consisting of two triangle stubs, side-coupled with an eight-like resonant cavity

Herein, a Fano resonance based optical sensor with high sensitivity is proposed. The sensor comprises a metal–insulator–metal (MIM) waveguide with two symmetric triangle stubs, side-coupled with a square ring resonator with a stub (SRS). Utilizing the 2D finite element algorithm, the transmission characteristics of the MIM waveguide structure are systematically explored. This analysis reveals that the coupling effect between the MIM waveguide and the SRS leads to the appearance of Fano resonance. After using a polydimethylsiloxane (PDMS)-sealed resonator, an outstanding temperature sensitivity of −20.3 nm/∘C is obtained. In addition, the influence of the width of the MIM waveguide, the coupling distance, the distance between two symmetric triangle stubs and the geometric parameters of the resonator on the Fano resonance line is also studied in detail. Optimizing these structural parameters results in a peak refractive index (RI) sensitivity of 6000 nm/RIU, and the figure of merit (FOM) is 17RIU−1. These results not only help to narrow the gap with the optical fiber sensor, but also pave the way for the design and application of ultra-high sensitive RI sensor and temperature sensor.

Dynamics of vowel acoustic space indicators in patients with long-term hearing loss

To characterize VAS of adult Russian speakers with long-term HL using newly developed acoustic indicators. Recordings of sustained Russian cardinal vowels /a/, /i/, /u/ of 10 women and 10 men with long-term HL were acoustically analyzed. For each participant, two first formants of each vowel were measured and log-transformed (logF1, logF2). VAS was transformed into right triangles, their /u/ corners were moved to the origin, and their legs were aligned with axes. VAS was almost symmetrical, equal and have a maximum size in the control group consisted of subjects without hearing impairment while these of long-term HL group VAS size tended to have reduced and VAS stretched along one axis. Our study showed that a new VAS normalization approach can distinguish at least three groups of people with long-term HL. There are those with vowel triangles stretched along logF1-axis, with vowel triangles stretched along logF2-axis, and with symmetrical vowel triangles. Causes of the VAS differences require further investigation.

Research on time-division analog multiplier for 50ppm reference electrical energy meter

Time-division analog multiplier is the measurement core of reference electrical energy meter. The measurement accuracy of time-division analog multiplier is improved by using signal conversion and phase lock technologies and symmetrical triangle wave generator. Signal conversion and phase-locked technology will be measured signal and triangle wave generator of time division multiplier correlation processing, to achieve triangle wave generator of time division power multiplier and measured signal full cycle synchronization. A symmetrical triangle wave generator with reference level accuracy is developed, which makes the measurement accuracy of time-division analog multiplier reached 20ppm and meet the measurement requirements of 50ppm reference electrical energy meter.

A simulation study of first-order autoregressive to evaluate the performance of measurement error based symmetry triangular fuzzy number

<span>Data collected by various data collection methods are often exposed to uncertainties that may affect the information presented by quantitative results. This also causes the forecasted model developed to be less precise because of the uncertainty contained in the input data used. Hence, preparing the data by means of handling inherent uncertainties is necessary to avoid the developed forecasting model to be less accurate. Traditional autoregressive (AR) model uses precise values and deals with the uncertainty normally in forecasting model. Fewer researches are focused on data preparation in time-series autoregressive for handling the uncertainties in data. Hence, this paper proposes a procedure to perform data preparation to handle uncertainty. The fuzzy data preparation involves the construction of fuzzy symmetric triangle numbers using percentage error and standard deviation method. The proposed approach is evaluated by using the simulation method for first-order autoregressive, AR (1) model in terms of forecasting accuracy performance. Simulation result demonstrates that the proposed approach obtains smaller error in forecasting and hence achieving better forecasting accuracy and dealing with uncertainty in the analysis.</span>

Symmetric triangle quadrature rules for arbitrary functions

Despite extensive research on symmetric polynomial quadrature rules for triangles, as well as approaches to their calculation, few studies have focused on non-polynomial functions, particularly on their integration using symmetric triangle rules. In this paper, we present two approaches to computing symmetric triangle rules for singular integrands by developing rules that can integrate arbitrary functions. The first approach is well suited for a moderate amount of points and retains much of the efficiency of polynomial quadrature rules. The second approach better addresses large amounts of points, though it is less efficient than the first approach. We demonstrate the effectiveness of both approaches on singular integrands, which can often yield relative errors two orders of magnitude less than those from polynomial quadrature rules.

A Novel Motion Compensation Approach Based on Symmetric Triangle Wave Interferometry for UAV SAR Imagery

The combination of synthetic aperture radar (SAR) with unmanned aerial vehicles (UAVs) is attractive for acquiring high-resolution images without the restrictions of time and weather. However, because UAVs are lightweight and small in size, the UAV SAR system is very sensitive to turbulence, resulting in serious trajectory deviations and remaining residual motion errors (RMEs), such as residual range cell migration (RCM) and aperture phase errors (APEs). In this paper, a novel motion compensation (MoCo) strategy is developed based on the symmetric triangle linear frequency modulated continuous wave (STLFMCW) signal. The STLFMCW signal model is first presented, which reveals the relevance between the positive-negative frequency modulations and motion errors. The residual RCMs and relative phase errors are estimated directly through the phase differential interferometry of up-ramp and down-ramp chirp signals, instead of the traditional approach of relying on the range-shift gradient of adjacent range profiles. The proposed approach is independent of conventional prominent point processing (PPP) and calculates the range deviation to avoid the accumulation of errors, thereby achieving high precision and efficiency. Experiments based on simulated and measured data sets validate the proposed approach.

A linear piezoelectric actuator with the parasitic motion of equilateral triangle flexure mechanism

A parasitic type piezoelectric actuator with an equilateral triangle flexure mechanism is proposed and investigated to achieve large-stroke linear motion. Right-circular flexure hinges with different thicknesses (t1 and t2) are utilized in the design of the equilateral triangle flexure mechanism which is able to generate parasitic motion. The working principle is analyzed and illustrated by the theoretical simulation and finite element method (FEM) simulation. A prototype is manufactured to study the performance of proposed parasitic type actuator, together with an experimental system. Experiments indicate that the maximum stepping displacement is ΔL = 9.00 μm in the case that input voltage Ue = 150 V; the minimum stepping displacement ΔL = 0.24 μm is achieved under Ue = 60 V; the maximum speed is Vs = 180 μm s−1; the largest output force is F = 106.3 g under that input frequency f = 1 Hz and Ue = 100 V. This study demonstrates the feasibility of symmetrical triangle flexure mechanisms in the design of parasitic type piezoelectric actuators with large working stroke.

Fano Resonance in a MIM Waveguide with Two Triangle Stubs Coupled with a Split-Ring Nanocavity for Sensing Application.

Herein, a compact refractive index nanosensor comprising a metal- insulator- metal (MIM) waveguide with symmetric two triangle stubs coupled with a circular split-ring resonance cavity (CSRRC) is theoretically presented. An analysis of the propagation characteristics of the designed structure is discussed employing the finite element method (FEM). The calculation results revealed that a Fano resonance outline emerged, which results from an interaction between the continuous broadband state of the waveguide with two symmetric triangle stubs and the discrete narrowband state of the CSRRC. The influence of geometric parameters on sensing properties was studied in detail. The maximum sensitivity reached 1500 nm/RIU with a high figure of merit of 65.2. The presented structure has great applications for on-chip plasmonic nanosensors.