Symmetric Square Research Articles

Broadband all-metal reflective-mode geometric metasurfaces for visible multi‐functional wavefront manipulation

Visible light manipulation has become a well-explored subject over recent years owing to its fascinating prospect in the optical communication field. Nevertheless, the limitations imposed by materials inherent in natural hamper the progress of the optical devices. Here, a broadband reflective-mode all-metal geometric metasurface (GMS) capable of high-efficient circular polarization (CP) conversion and applicable for multi-functional wavefront manipulation was proposed and investigated numerically in visible region. The proposed all-metal GMS is comprised of the periodically arranged gold dumbbell-shaped (DBS) nanostructure with symmetrical square notch adhered on the gold substrate. Simulation results demonstrate that the cross-polarized reflection amplitude of the all-metal GMS for normal incident CP light is practically higher than 85% from 310 THz to 500 THz, and the full 2π phase shift in this frequency range can be acquired by varying oriented angle of the DBS nanostructure. As proofs of multi-functional wavefront manipulation devices, beam deflectors, reflective planar focusing metalens and vortex beam generators were constructed and demonstrated numerically with the all-metal DBS nanostructure based on geometric phase principle. Overall, the proposed GMS carries with it considerable advantages of compaction and high efficiency, thus possessing infinite potential in optical devices.

An explicit formula for the second moment of Maass form symmetric square $L$-functions

An explicit formula for the second moment of Maass form symmetric square $L$-functions

Research on mapping recognition of arc welding molten pool characterisation and penetration state based on embedded system

AbstractIn order to explore the mapping recognition of arc welding molten pool characterisation and penetration state, according to the idea of embedded system construction, this article adopts the idea of software and hardware co‐design to find the zero‐crossing point of the second derivative in welding image edge detection, and give a threshold. When the absolute value of the first‐order derivative exceeds the threshold and has a different sign with the first‐order derivative of the previous edge, it is judged as a valid edge. The welding current adopts a symmetrical pulsed AC square wave, and the proportion of heat flow input is high. At the base current, the arc light is darker, so a clear image is obtained. This article designs a simulation experiment to verify the effect of the embedded system in this article. From the experimental research, it can be known that the embedded system constructed in this article can play a certain role in the mapping recognition of the arc welding molten pool characterisation and penetration state.

On higher moments of Dirichlet coefficients attached to symmetric square L-functions over certain sparse sequence

On higher moments of Dirichlet coefficients attached to symmetric square L-functions over certain sparse sequence

Computational aspects of experimental designs in multiple-group mixed models

We extend the equivariance and invariance conditions for construction of optimal designs to multiple-group mixed models and, hence, derive the support of optimal designs for first- and second-order models on a symmetric square. Moreover, we provide a tool for computation of D- and L-efficient exact designs in multiple-group mixed models by adapting the algorithm of Harman et al. (Appl Stoch Models Bus Ind, 32:3–17, 2016). We show that this algorithm can be used both for size-constrained problems and also in settings that require multiple resource constraints on the design, such as cost constraints or marginal constraints.

Homological mirror symmetry for the symmetric squares of punctured spheres

For an appropriate choice of a Z-grading structure, we prove that the wrapped Fukaya category of the symmetric square of a (k+3)-punctured sphere, i.e. the Weinstein manifold given as the complement of (k+3) generic lines in CP2 is quasi-equivalent to the derived category of coherent sheaves on a singular surface Z2,k constructed as the boundary of a toric Landau-Ginzburg model (X2,k,w2,k). We do this by first constructing a quasi-equivalence between certain categorical resolutions of both sides and then localizing. We also provide a general homological mirror symmetry conjecture concerning all the higher symmetric powers of punctured spheres. The corresponding toric LG-models (Xn,k,wn,k) are constructed from the combinatorics of curves on the punctured sphere and are related to small toric resolutions of the singularity x1…xn+1=v1…vk.

A Hybrid Five-Level Modular Multilevel Converter With High Efficiency and Small Energy Storage Requirements for HVDC Transmission

This article presents a hybrid five-level converter (H5LC) with cascaded full-bridge submodules (FBSMs) for high voltage direct current (HVdc) transmission. A five-level converter operates at a fundamental switching frequency to generate symmetric five-level square wave output voltages which are shaped into smooth sinusoidal voltages by the ac-side FBSMs. Using a proposed third-order harmonic voltage injection scheme, the FBSMs’ total blocking voltage is limited to one-eighth of the dc-side voltage, reducing the H5LC's losses, footprint, and capital costs. dc pole-to-pole fault blocking is enabled using a bypass branch consisting of bidirectional thyristor valves and fast mechanical switches to suppress the ac-side fault contribution within half a fundamental cycle. Full-scale HVdc simulation studies show the H5LC's ability to control real and reactive powers and additionally, its dc fault resilience. A lab-scale hardware implementation of an H5LC with 30 FBSMs is presented to verify its operating principle. In contrast to the half-bridge submodule based modular multilevel converter, the H5LC has improved efficiency, fewer semiconductor devices, and significantly reduced energy storage requirements.

On the Hermitian momentum of Wigner-Dunkl quantum mechanics

In this paper the Hermitian momentum operator on the usual Hilbert space is constructed for the Wigner-Dunkl quantum mechanics utilizing a symmetric Dunkl derivative. The inverse of the derivative is shown to exhibit different realization on the subspaces of even and odd functions. The continuity conditions at finite discontinuities of symmetric potential is investigated. As an example, the finite symmetric square well is discussed in detail.

Local Langlands correspondence for the twisted exterior and symmetric square $$\epsilon $$-factors of $$\text {GL}_n$$

Local Langlands correspondence for the twisted exterior and symmetric square $$\epsilon $$-factors of $$\text {GL}_n$$

An asymmetric-square-wave voltage injection method for online inductance identification of PMSM under sensorless control

In this paper, an online inductance identification method for PMSM, which is embedded into the flux-estimation-based sensorless control, is proposed. By injecting a periodic voltage where a larger negative voltage lasts one switching cycle, and a smaller positive voltage lasts several switching cycles, the extra voltage equation is established. Then, the q-axis current can be decomposed to an asymmetric triangular wave component and a low frequency component. Using the triangular wave current and the voltage equation, an inductance identification algorithm is designed. Since the injected positive voltage can be smaller, this method overcomes the difficulty that the symmetric square wave voltage cannot be injected at high-speed range, thus expanding the application of the inductance identification. And since the triangular wave current can be accurately extracted, the interference caused by back-EMF is eliminated. The simulation results demonstrate the effectiveness of the method.

Spectral decomposition formula and moments of symmetric square $L$-functions

We prove a spectral decomposition formula for averages of Zagier $L$-series in terms of moments of symmetric square $L$-functions associated to Maass and holomorphic cusp forms of levels $4$, $16$, $64$.

Spectral decomposition formula and moments of symmetric square $L$-functions

Доказана формула спектрального разложения для средних значений $L$-рядов Загье в терминах моментов $L$-функций симметрического квадрата, ассоциированных с формами Маасса и голоморфными параболическими формами уровней $4$, $16$, $64$. Библиография: 18 наименований.

НОВЫЕ ФОРМУЛЫ РАСЧЕТА ИНДУКТИВНОСТИ ПЛАНАРНЫХ СИММЕТРИЧНЫХ КАТУШЕК ИНДУКТИВНОСТИ КВАДРАТНОЙ ФОРМЫ

The paper presents new analytical formulas for calculating the inductance of planar symmetrical square inductors. The formulas are obtained by using the modified method of inductors layout decomposition. The inductors layout is divided into parts (inner incomplete turn, full turns, leads) and the total inductances of each part and the mutual inductances between the parts are calculated. Comparison with the results of 3D finite element modeling in ADS CAD showed that the proposed formulas have an error of no more than 2% for inductance value from 100 pH to 10 nH.

Electric‐Field Enhancement of Electron Emission Rates for Deep‐Level Traps in n‐type GaN

Results of a deep‐level transient spectroscopy (DLTS) study of trapping states in Ni/Au Schottky diodes made on Si‐doped GaN layers grown by metal–organic vapor‐phase epitaxy (MOVPE) on highly conductive n‐type Ammono‐GaN substrates are reported. In all as‐grown samples, the DLTS signals due to traps with the activation energies for electron emission (Eem) of about 0.26 and 0.60 eV (referred to as E1 and E3 traps, respectively) have been detected. It is found that the electric field (E) significantly enhances the electron emission rate (eem) for the E1 trap, while for the E3 trap the eem(E) dependence is not very strong. The eem(E) dependence for the E1 trap is found to be characteristic of attractive traps with spherically symmetric square well potential with a radius of about 2.9 ± 0.25 nm. The eem(E) dependence for the E3 trap is accounted for by a phonon‐assisted tunneling mechanism. The zero‐E Eem values for both traps are determined. Correlations between the concentrations of the E1 and E3 traps and concentrations of impurities (H, C, Si, O, Mg, and Fe) determined by secondary ion mass spectrometry in the samples are investigated. Charge states and origins of the E1 and E3 traps are discussed.

Severi varieties on blow‐ups of the symmetric square of an elliptic curve

AbstractWe prove that certain Severi varieties of nodal curves of positive genus on general blow‐ups of the twofold symmetric product of a general elliptic curve are nonempty and smooth of the expected dimension. This result, besides its intrinsic value, is an important preliminary step for the proof of nonemptiness of Severi varieties on general Enriques surfaces.

Parametric Multispectral Mappings and Comparative Genomics

This article describes new algorithms that allow for viewing genetic sequences in the form of their multispectral images. We presented examples of the construction of such mappings with a demonstration of the practical problems of comparative genomics. New DNA visualization tools seem promising, thanks to their informativeness and representativeness. The research illustrates how a novel sort of multispectral mapping, based on decomposition in several parametric spaces, can be created for comparative genetics. This appears to be a crucial step in the investigation of the genetic coding phenomenon and in practical activities, such as forensics, genetic testing, genealogical analysis, etc. The article gives examples of multispectral parametric sets for various types of coordinate systems. We build mappings using binary sub-alphabets of purine/pyrimidine and keto/amino. We presented 2D and 3D renderings in different characteristic spaces: structural, integral, cyclic, spherical, and third-order spherical. This research is based on the method previously developed by the author for visualizing genetic information based on new molecular genetic algorithms. One of the types of mappings, namely two-dimensional, is an object of discrete geometry, a symmetrical square matrix of high dimension. The fundamental properties of symmetry, which are traced on these mappings, allow us to speak about the close connection between the phenomenon of genetic coding and symmetry when using the developed mathematical apparatus for representing large volumes of complexly organized molecular genetic information.

Dimensionless numbers on columnar structured electrodes in hydrogen/oxygen polymer electrolyte fuel cells

Platinum columnar growth was found on anode and cathode catalysts after 6 months of operation in hydrogen/oxygen cells (1 A cm−2) from original smooth microspheres layers with loads ca. 1 mg cm−2. The application of symmetric and asymmetric large frequency square wave potential programs in strong sulphuric acid solutions for catalyst preparation showed those effects. For columnar electrodes, current and potential distributions are not those expected for smooth surfaces and constitute the main reason of a mismatching between theory and experimental data. The employ of exact analytical solutions arising from mass/charge balances are a better way to envisage electrochemical profiles instead of numerical solutions. Columnar catalysts can be parameterized by a trochoid curvilinear profile knowing the radius and pass (from ex situ STM images) rendering values ca. ½ for both parameters. Polarization and power density curves were also mimicked from the obtained current and cell potential distributions for the rough columnar surfaces. Finally, Wagner, Damkoehler and Graetz numbers that typify the electrochemical reactor were developed applying these parametric equations using local variations of tangential and normal velocities, from which a general dimensionless equation was obtained.

Development of Microstrip Decimeter Antennas with Circular Polarization

Modern design variants of microstrip antennas with circular polarization are considered, in which circular polarization is created using single-point and two-point power supply. To manufacture the studied antenna model with circular polarization, the simplest form of the antenna was chosen; the one with a radiator in the form of a continuous circle, which is powered by a two-point scheme. With regard to use in intra-object telemetry systems, the frequency of operation range of 640 ... 650 MHz was chosen. Two options for a two-point power supply of such an antenna were studied - with the help of a symmetrical and asymmetric square strip bridge. Calculation, coordination and tuning simulation of power divider variants were performed. As a result, the manufactured layout of the first antenna design turned out to be three-layered, the second - two-layered. The technique for creating antennas includes an estimated calculation of geometric dimensions, which was further refined using computer simulation in the CST Microwave Studio program. Frequency tuning of the completed antenna layouts is carried out using adjusting teeth along the contour of the round radiator. The study of the created antenna layouts showed better manufacturability and stability of the characteristics of a two-layer structure compared to a three-layer one. Therefore, a two-layer round antenna with a point-to-point power supply was chosen for production. It is designed for telemetric radio channels inside enclosed spaces. The measurements performed showed that the manufactured antenna operates in right-hand circular polarization with an ellipticity factor of 1.2 dB. The standing wave ratio in the operating frequency band of 640…650 MHz did not exceed 1.32, the gain was at least 5 dBi, the width of the radiation patterns in two planes was 95 and 93 angular degrees, respectively. The antenna provides for an operation mode as a transceiver, since the decoupling of the receiving and transmitting paths is carried out due to different polarization, for which it is necessary to connect the second input of the power divider instead of a balanced resistor to the receiving device.

An asymptotic expansion for a Lambert series associated to the symmetric square L-function

Hafner and Stopple proved a conjecture of Zagier that the inverse Mellin transform of the symmetric square [Formula: see text]-function associated to the Ramanujan tau function has an asymptotic expansion in terms of the nontrivial zeros of the Riemann zeta function [Formula: see text]. Later, Chakraborty et al. extended this phenomenon for any Hecke eigenform over the full modular group. In this paper, we study an asymptotic expansion of the Lambert series [Formula: see text] where [Formula: see text] is the [Formula: see text]th Fourier coefficient of a Hecke eigenform [Formula: see text] of weight [Formula: see text] over the full modular group.

The Derived Hecke Algebra for Dihedral Weight One Forms

We study the action of the derived Hecke algebra in the setting of dihedral weight one forms and prove a conjecture of the second- and fourth- named authors relating this action to certain Stark units associated to the symmetric square L-function. The proof exploits the theta correspondence between various Hecke modules as well as the ideas of Merel and Lecouturier on higher Eisenstein elements.