Symmetric Square Research Articles

The distribution of Fourier coefficients of symmetric square L-functions over arithmetic progressions

The distribution of Fourier coefficients of symmetric square L-functions over arithmetic progressions

Study on the Influence of the Cell Structure on the Pressure Drop of Gasoline Particulate Filter

The cell structure of a gasoline particulate filter (GPF) is made up of thousands of individual cells. Although the symmetric square cell structure of the GPF is commonly used internationally, several cell designs have been proposed to reduce the pressure drop in the GPF trapping process. The aim of this paper was to use AVL-Fire software to establish GPF models of different cell structures, mainly including the symmetric square cell structure, asymmetric square cell structure, and symmetric hexagonal cell structure, and analyze the GPF pressure drop characteristics of different cell structures according to the carrier structural parameters and altitude. The results show that compared with the pressure drop of the symmetric square cell structure, the pressure drop of the asymmetric cell structure with inlet/outlet side length ratios ranging from 1.1 to 1.4 is decreased by 4.61%, 9.07%, 12.19%, and 13.22%, respectively, and the pressure drop of the symmetric hexagonal cell structure is decreased by 33.17%. Both asymmetric and symmetric hexagonal cell structure GPFs can decrease the pressure drop during trapping by increasing the cell density. From 200 CPSI to 300 CPSI, the pressure drop of the asymmetric cell structure with inlet/outlet side length ratios ranging from 1.1 to 1.4 is decreased by 20.43%, 20.53%, 20.39%, and 18.56%, respectively, and the pressure drop of the symmetric hexagonal cell structure is decreased by 18.70%. The pressure drop values of GPFs with asymmetric and symmetric hexagonal cell structures show an increasing trend with an increasing filter wall thickness and inlet/outlet plug length. The pressure drop values of GPFs with asymmetric and symmetric hexagonal cell structures show an increasing trend with an increasing altitude, and the larger the inlet/outlet ratio, the more significant the increase in the pressure drop.

Enhancing defect detection in solid materials using low-duty cycle square wave lock-in thermography: a time-efficient and quantitative approach

Lock-in thermography has been used to detect material defects but has faced challenges in quantitatively identifying defects. Traditional methods with a sine wave or symmetrical square wave heat source require time-consuming frequency adjustments with multiple experiments. This study introduces a novel technique using a heat source of a low-duty cycle square wave in lock-in thermography. This harmonic-rich heat source provides information on the blind frequency and the depth of defects, significantly reducing testing time. This method was validated by finite element simulations, which generated phase maps and phase difference-frequency curves at multiple frequencies that located defects. The study explored the correlation between thermal diffusion length at the blind frequency and defect depth and the impact of transverse thermal diffusion on depth measurement. The findings indicate that phase maps at the optimal frequency are most suitable for measuring defect edges. This approach offers a promising, time-efficient, and quantitative solution for defect detection.

Silicon-based ultra-broadband mid-IR and LWIR near-perfect metamaterial absorber

Ultra-broadband metamaterial absorbers (UBMAs) that are compatible with CMOS technology for use in the mid-infrared and long-wave infrared regions are crucial for a variety of applications, including radiative cooling, thermal photovoltaic, and thermal imaging. In this regard, we propose, in this work, a design of an UBMA based on the heavily doped silicon (D-Si) and silicon carbide (SiC). The 3D finite-difference time-domain method is used, mainly, to numerically calculate the optical characteristics of the proposed UBMA. The absorber, which is made up of a periodic array of symmetrical multilayered square rings of D-Si and SiC, achieves high absorption with an average absorption of 95% over a wavelength range of 2.5–22 µm. This broad range of wavelength absorption is attained, encompassing the mid-, long-wave, and partial far-infrared regions. In addition to the materials' inherent absorption, the stimulation of magnetic polaritons, surface plasmon polaritons, localized surface plasmon resonance, and cavity resonance are responsible for the nearly perfect broadband absorption. Under normal incidence, the proposed UBMA is polarization-independent due to the symmetrical design of the absorber. Furthermore, the impact of the incidence angle on the absorption of transverse electric and transverse magnetic waves is examined.

Perfect absorber based on symmetric square silicon grating with polarization and angular stability using particle swarm optimization algorithm

Perfect absorber based on symmetric square silicon grating with polarization and angular stability using particle swarm optimization algorithm

Toward a three-dimensional counterpart of Cruse’s theorem

Completing partial latin squares is NP-complete. Motivated by Ryser’s theorem for latin rectangles, in 1974, Cruse found conditions that ensure a partial symmetric latin square of order m m can be embedded in a symmetric latin square of order n n . Loosely speaking, this results asserts that an n n -coloring of the edges of the complete m m -vertex graph K m K_m can be embedded in a one-factorization of K n K_n if and only if n n is even and the number of edges of each color is at least m − n / 2 m-n/2 . We establish necessary and sufficient conditions under which an edge-coloring of the complete λ \lambda -fold m m -vertex 3-graph λ K m 3 \lambda K_m^3 can be embedded in a one-factorization of λ K n 3 \lambda K_n^3 . In particular, we prove the first known Ryser type theorem for hypergraphs by showing that if n ≡ 0 ( m o d 3 ) n\equiv 0\ (\mathrm {mod}\ 3) , any edge-coloring of λ K m 3 \lambda K_m^3 where the number of triples of each color is at least m / 2 − n / 6 m/2-n/6 , can be embedded in a one-factorization of λ K n 3 \lambda K_n^3 . Finally we prove an Evans type result by showing that if n ≡ 0 ( m o d 3 ) n\equiv 0\ (\mathrm {mod}\ 3) and n ≥ 3 m n\geq 3m , then any q q -coloring of the edges of any F ⊆ λ K m 3 F\subseteq \lambda K_m^3 can be embedded in a one-factorization of λ K n 3 \lambda K_n^3 as long as q ≤ λ ( n − 1 2 ) − λ ( m 3 ) / ⌊ m / 3 ⌋ q\leq \lambda \binom {n-1}{2}-\lambda \binom {m}{3}/\left \lfloor m/3\right \rfloor .

A low-frequency ultrathin metamaterial absorber using magnetic material

In this paper, an ultra-thin metamaterial absorber (UMA) in the S-band is designed. The overall structure adopts a three-layer design. The top layer is a magnetic material, and the middle layer of the UMA is composed of a centrally symmetrical open square ring (four edges are opened) and a circular pattern placed at the center, which is etched on the FR4 dielectric substrate by printed circuit board technology. The absorptivity of the absorber is more than 90% in 1.73–4.04 GHz under normal incidence, and the fractional bandwidth is 80.1%. The total thickness of the absorber is about 3.4 mm, corresponding to 0.02 λL at the lowest operating frequency. Moreover, it also has good polarization insensitivity and wide-angle incident characteristics. The absorption mechanism of the UMA is analyzed from the aspects of power loss density and surface current. Finally, a sample was fabricated and measured. The measured results are in good agreement with the simulation results, which verifies the effectiveness of the design method.

Multiplicity-free Representations of Algebraic Groups

Let K K be an algebraically closed field of characteristic zero, and let G G be a connected reductive algebraic group over K K . We address the problem of classifying triples ( G , H , V ) (G,H,V) , where H H is a proper connected subgroup of G G , and V V is a finite-dimensional irreducible G G -module such that the restriction of V V to H H is multiplicity-free – that is, each of its composition factors appears with multiplicity 1. A great deal of classical work, going back to Dynkin, Howe, Kac, Stembridge, Weyl and others, and also more recent work of the authors, can be set in this context. In this paper we determine all such triples in the case where H H and G G are both simple algebraic groups of type A A , and H H is embedded irreducibly in G G . While there are a number of interesting familes of such triples ( G , H , V ) (G,H,V) , the possibilities for the highest weights of the representations defining the embeddings H > G H>G and G > G L ( V ) G>GL(V) are very restricted. For example, apart from two exceptional cases, both weights can only have support on at most two fundamental weights; and in many of the examples, one or other of the weights corresponds to the alternating or symmetric square of the natural module for either G G or H H .

On Swan exponents of symmetric and exterior square Galois representations

On Swan exponents of symmetric and exterior square Galois representations

An Approximate Solution to the Transcendental Equation Problem of the Finite Square Well Potential in Quantum Mechanics

Abstract: In this paper, we present an approach that gives a formal and an approximate solution for a special class of transcendental equations. This solution is in the form of an infinite series generated by a Taylor reversion process. To showcase this technique, we have chosen the transcendental equation that describes the energy levels of a particle moving in a symmetrical finite square well potential in quantum mechanics. The cases for very deep, very shallow, and the intermediate-sized wells are discussed separately. Our results, when compared with the numerical findings, show the validity of our approach and its potential future application to other similar physics and engineering problems. Keywords: Transcendental equations, Taylor reversion, Algebraic approximation, Finite square well, Bound energy.

Fourier Transform from the Symmetric Square Representation of PGL2 and SL2

Abstract Let $G$ be a connected reductive group over $\overline{{\mathbb{F}}}_{q}$ and let $\rho ^{\vee }:G^{\vee }\rightarrow \mathrm{GL}_{n}$ be an algebraic representation of the dual group $G^{\vee }$. Assuming that $G$ and $\rho ^{\vee }$ are defined over ${\mathbb{F}}_{q}$, Braverman and Kazhdan defined an operator on the space ${{\mathcal{C}}}(G({\mathbb{F}}_{q}))$ of complex valued functions on $G({\mathbb{F}}_{q})$. In this paper we are interested in the case where $G$ is either $\mathrm{SL}_{2}$ or $\mathrm{PGL}_{2}$ and $\rho ^{\vee }$ is the symmetric square representation of $G^{\vee }$. We construct a natural $G\times G$-equivariant embedding $G\hookrightarrow{{\mathcal{G}}}={{\mathcal{G}}}_{\rho }$ and an involutive operator (Fourier transform) ${{\mathcal{F}}}^{{{\mathcal{G}}}}$ on the space of functions ${{\mathcal{C}}}({{\mathcal{G}}}({\mathbb{F}}_{q}))$ that extends Braverman-Kazhdan’s operator.

Highlighting of the impact of periodic operations on the performance of methanol steam reforming process for pure hydrogen generation

In this paper, we focus to highlighting the positive role of periodic operation which can be played for performance improvement of a hydrogen separator reactor integrating a palladium membrane. For this subject, a mathematical approach describing the pure hydrogen production and its pumping during methanol steam reforming process is developed to simulate the effect of the reactor inlet feed and of sweeping gas on reactor performance. The main findings show that the reactor responses exhibit a periodic phenomenon. So, in order to achieve a yield improvement higher than that obtained under the steady state conditions, it is necessary to intensify the process by using a periodic operation. Therefore, when the reactor is simultaneously forced by running the feed composition in the reaction side and by the sweeping gas in the permeate side using a symmetric square function, the magnitude of improvement of methanol conversion and pure hydrogen recovery are higher than that achieved at steady state operation. This is due to the dual effect synergistic, which is could be brought by the potential periodic mode of the inputs coupling.

Rational points on symmetric squares of constant algebraic curves over function fields

Rational points on symmetric squares of constant algebraic curves over function fields

Gap coupled symmetric square split ring high EMR resonator-based metamaterial for S-, C-, and X-bands wireless applications: Simulation and experiment

This article describes a metamaterial (MTM) based on a symmetric square ring resonator (SSRR) that exhibits epsilon negative (ENG) and near-zero index (NZI) properties. A 0.035 mm thick copper resonator is used to construct the proposed asymmetric MTM structure, designed on a 1.5 mm thick FR-4 substrate for microwave applications. The MTM structure attained optimum resonance at frequencies corresponding to the microwave frequency range of the S, C, and X bands, 2.88 GHz, 4.78 GHz, and 10.9 GHz, respectively. The near-zero index characteristics are realized in the frequency ranges 2.22–3.17 GHz, 4.52–5.10 GHz, and 9.63–11.36 GHz, while the ENG characteristics are realized in the frequency ranges 2.1–3.2 GHz, 4.57–5 GHz, and 9.7–11.4 GHz. The electrical dimensions of the structure are 0.139λ × 0.139λ × 0.014λ, corresponding to an estimated wavelength of 2.88 GHz. The effective medium ratio (EMR), which for this construction is 7.194, indicates the compactness of the design structure. Using CST 2019 simulation software, the proposed structure is designed and developed before its construction and performance evaluation. The circuit was validated by comparing the S21 response using the Advanced Design System (ADS) software. The response of S21 from the proposed MTM structure was almost identical when it was tested through simulation (using CST and ADS software) or actual measurements. The compact size, substantial electromagnetic response (ER), negative permittivity, almost zero permeability, and refractive index of this MTM make it perfect for wireless applications in S-, C-, and X-bands.

Double-sided asymmetric method for automated fetal heart rate baseline calculation.

The fetal heart rate (FHR) signal is used to assess the well-being of a fetus during labor. Manual interpretation of the FHR is subject to high inter- and intra-observer variability, leading to inconsistent clinical decision-making. The baseline of the FHR signal is crucial for its interpretation. An automated method for baseline determination may reduce interpretation variability. Based on this claim, we present the Auto-Regressed Double-Sided Improved Asymmetric Least Squares (ARDSIAsLS) method as a baseline calculation algorithm designed to imitate expert obstetrician baseline determination. As the FHR signal is prone to a high rate of missing data, a step of gap interpolation in a physiological manner was implemented in the algorithm. The baseline of the interpolated signal was determined using a weighted algorithm of two improved asymmetric least squares smoothing models and an improved symmetric least squares smoothing model. The algorithm was validated against a ground truth determined from annotations of six expert obstetricians. FHR baseline calculation performance of the ARDSIAsLS method yielded a mean absolute error of 2.54bpm, a max absolute error of 5.22bpm, and a root mean square error of 2.89bpm. In a comparison between the algorithm and 11 previously published methods, the algorithm outperformed them all. Notably, the algorithm was non-inferior to expert annotations. Automating the baseline FHR determination process may help reduce practitioner discordance and aid decision-making in the delivery room.

A dynamic energy budget model for black rockfish Sebastes schlegelii: Parameterization and application in marine ranching areas, Yellow Sea, China

Marine ranching has become a powerful tool for coastal habitat restoration, ecosystem conservation and stock enhancement. With increasing development of marine ranching in recent years, it has attracted wide attentions for fishery management and sustainability. The stock of black rockfish Sebastes schlegelii has undergone a serious decline due to overfishing in the past few decades, but has considerably recovered recently in marine ranching areas along the coasts of the Northwest Pacific. Appropriate management of the species is essential for marine ranching development. In this study, a dynamic energy budget (DEB) model of S. schlegelii was developed and applied in the Xixiakou, Changdao and Qiansandao marine ranching areas, Yellow Sea, China. The effects of food availability and water temperature on its growth and reproduction were quantified. The model was parameterised following the AmP procedure, which resulted in mean relative error of 0.123 and symmetric mean square errors of 0.134. The application of the model has showed that the model could reproduce the growth trajectories of both length and weight at each of the three marine ranching areas without site-specific calibration. The growth rates of S. schlegelii showed that Qiansandao > Changdao > Xixiakou in both length and weight. Temperature and food availability are the main contribution to the variations of growth amongst sites. In Qiansandao, the fast growth and maturation of the species correspond to relative high water temperature and sufficient food availability. Food availability limited growth and reproduction of S. schlegelii in Xixiakou, which indicated that the stock density in the areas might be close to the carrying capacity. The earlier maturation was a result of higher temperature and more food supply in Qiansandao than in Changdao and Xixiakou. Fishing and recapture in marine ranching areas should be adjusted to flexibly avoid spawning periods. The presented model is applicable to other marine ranching areas and coastal habitats. It provides an important component of ecosystem management approaches to estimate the ecological carrying capacities. This study provides information about the stock enhancement potential of coastal environments and a powerful tool for sustainable coastal fisheries management.

A novel featurization methodology using JaGen algorithm for time series forecasting with deep learning techniques

Accurate time series forecasting is crucial in various fields, including finance, economics, healthcare, transportation, and energy. Recently, deep learning methods have gained significant attention in time series forecasting. Despite their ability to model complex and nonlinear data patterns, their performance may be degraded when there is not sufficient input data. To address this issue, in this study, we propose a methodology that performs feature-based representation through time series featurization and adds the relevant features as an auxiliary input to deep learning models. Specifically, after conducting the featurization step, as another contribution, we develop a novel combined feature selection algorithm called JAYA-Genetic (JaGen) and employ it as the feature selection technique. The JaGen algorithm takes advantage of both the JAYA and Genetic algorithms to make balance between exploring and exploitation processes. To assess the efficacy of the suggested methodology, two deep learning models, a convolutional network and a multi-head attention mechanism are used. According to the findings of experiments carried out on ten Covid-19 datasets, two product demand time series datasets, and two public time series datasets, the derived models outperform their regular counterparts and current models in terms of performance metrics like symmetric mean absolute percentage error (SMAPE) and root mean square error (RMSE).

A Reissner–Mindlin plate formulation using symmetric Hu-Zhang elements via polytopal transformations

In this work we develop new finite element discretisations of the shear-deformable Reissner–Mindlin plate problem based on the Hellinger–Reissner principle of symmetric stresses. Specifically, we use conforming Hu-Zhang elements to discretise the bending moments in the space of symmetric square integrable fields with a square integrable divergence M∈HZ⊂Hsym(Div). The latter results in highly accurate approximations of the bending moments M and in the rotation field being in the Lebesgue space ϕ∈[L2]2, such that the Kirchhoff–Love constraint can be satisfied for t→0. In order to preserve optimal convergence rates across all variables for the case t→0, we present an extension of the formulation using Raviart–Thomas elements for the shear stress q∈RT⊂H(div).We prove existence and uniqueness in the continuous setting and rely on exact complexes for inheritance of well-posedness in the discrete setting.This work introduces an efficient construction of the Hu-Zhang base functions on the reference element via the polytopal template methodology and Legendre polynomials, making it applicable to hp-FEM. The base functions on the reference element are then mapped to the physical element using novel polytopal transformations, which are suitable also for curved geometries.The robustness of the formulations and the construction of the Hu-Zhang element are tested for shear-locking, curved geometries and an L-shaped domain with a singularity in the bending moments M. Further, we compare the performance of the novel formulations with the primal-, MITC- and recently introduced TDNNS methods.

Design of Microwave Electromagnetic Sensor for Liquid Characterization

The design, fabrication, and testing of a highly sensitive GHz sensor for real-time measurement of engine oil quality are presented in this paper. The proposed microwave sensor is constructed on symmetric square slots structures, to improve the performance of the sensor. By using the resonant perturbation theory, the change in the max E field of test samples, produce the frequency shift. The footprint of the designed sensor is (0.5523λeff × 0.0920λeff) where λeff is the effective wavelength value calculated at the operating frequency of 5.52GHz. The oil sample adulteration analysis is done by immersion of a dielectric probe up to a reference level of 20 mm. Thus, the dielectric behavior of the sensor is estimated with an average sensitivity of 1.7. The performance of the microwave sensor is evaluated by submerging it in different engine oil samples, thereby resulting in frequency shifts from 5.53 to lower values. The result obtained from it indicated that the sensor has a quality factor of 54.55 and a FoM of 19.17. Thus, the proposed GHz sensor due to its good sensitivity, FoM, and quality factor is the eminent solution for the automobile industry.

Totally symmetric quasigroups of order 16

AbstractWe present the number of totally symmetric quasigroups (equivalently, totally symmetric Latin squares) of order 16, as well as the number of isomorphism classes of such objects. Totally symmetric quasigroups of orders up to and including 16 that are (respectively) medial, idempotent, and unipotent are also enumerated.