Symmetric Square Research Articles

Non-Symmetric Spatial-Temporal Network for Bus Origin–Destination Demand Prediction

Urban public transport has become a preferred choice for alleviating traffic congestion. The bus passenger OD (origin–destination) demand prediction based on bus operational data is the key technology to realize urban intelligent transportation system. However, most of the existing bus OD demand prediction methods only considered regional passengers. The problem of the OD demand prediction based on historical OD matrices of bus lines is still not easy to implement, exceptionally, which is suitable for most of the urban bus lines. This paper presents a non-symmetric spatial-temporal network (NSTN) based on convolutional neural network (CNN) and convolutional long short-term memory (ConvLSTM) network to predict bus OD. NSTN contains the station spatial component (SSC) module and the spatial-temporal component (STC) module. SSC consists of two CNNs to learn the OD features and the DO (destination-origin) features, respectively. To make the prediction shift to the OD features, the non-symmetric input is designed. STC extracts spatial-temporal features based on ConvLSTM. Compared with other methods, NSTN has the best performance measured by symmetric mean absolute percentage error (SMAPE) and root mean square error (RMSE), where its SMAPE falls by 4.3 percentage points to 16.4 percentage points and RMSE falls by 23.1 percentage points to 69.9 percentage points. Experimental results on other bus lines show that NSTN has strong generalization ability.

Thermodynamic perturbation theory coefficients for ellipsoidal molecules

Perturbation theory has been the center of the development of the new generation of equations of state. First- and second-order perturbation theories are very common, but require approximations for obtaining an analytical form. Recently, a new equation of state has been proposed in which the reference fluid is based on the hard Gaussian overlap approach, and the perturbed potential is defined as a spherically symmetric square well. In such an approach, the first- and second-order coefficients were considered the same as the ones applied for a system in which the reference term is spherical. Using Monte Carlo simulations, we investigated the validity of such an approximation by calculating the first- and second-order coefficients of the high-temperature expansion series of the Helmholtz free energy. With our findings, this approximation seems to be quite reasonable for a certain range of anisotropies. We also present a calculation of the perturbed molar Helmholtz free energy using Monte Carlo simulations, which could in principle be used for improving the equation of state.

Multi-objective uncertain optimization with an ellipsoid-based model of a centrally symmetrical square tube with diaphragms for subways

Multi-objective uncertain optimization with an ellipsoid-based model of a centrally symmetrical square tube with diaphragms for subways

On regular set systems containing regular subsystems

Let X,Y be finite sets, r,s,h,λ∈N with s≥r,X⊊Y. By λXh we mean the collection of all h-subsets of X where each subset occurs λ times. A coloring (partition) of λXh is r-regular if each element of X is in exactly r subsets of each color. A one-regular color class is a perfect matching. We are interested in necessary and sufficient conditions under which an r-regular coloring of λXh can be embedded into an s-regular coloring of λYh. Using algebraic techniques involving glueing together orbits of a suitably chosen cyclic group, the first author and Newman solved the case when λ=1,r=s,gcd(|X|,|Y|,h)=gcd(|Y|,h). Using purely combinatorial techniques, we nearly settle the case h=4.It is worth noting that completing partial symmetric latin squares is closely related to the case λ=r=s=1,h=2 which was solved by Cruse.

Lateral Motion Control Invariance Helicopter on the Roll Angle. Analytical Synthesis

For the linearized fourth-order model of the isolated lateral motion of a single-rotor helicopter as a MIMO system containing two inputs, the control is analytically synthesized, which ensures the invariance of the roll angle motion in the presence of disturbances in the control channels, as well as the required placement of the poles of the closed-loop system, given any specific values from the area of their stability. The approach to the synthesis of invariant control consists in finding a matrix of feedback coefficients of a linear system that satisfies the invariance conditions, which are a system of power matrix equations of a certain design. The synthesis is based on the application of theor ems based on the use of the regularization condition of the matrix equation and the invariance conditions under disturbances in the control channels, as well as theorems that make it possible to place the poles of the MIMO system using the original decomposition of the control object. Regularization of a matrix equation is understood as a solution to the problem of providing a given set of singular values for an inverted symmetric square matrix. The invariance of the MIMO system is considered with respect to unmeasured disturbances inthe control channels. The use of such an approach to the synthesis of invariant control made it possible to obtain an analytical solution that is versatile and can be applied in various flight modes of single-rotor helicopters with different dynamic properties. The results of the numerical synthesis of the lateral motion of a singlerotor helicopter using the obtained laws of invariant control, which confirm the reliability of the analytical expressions, areshown.

On Fourier Coefficients of the Symmetric Square L-Function at Piatetski-Shapiro Prime Twins

Let Pc(x)={p≤x|p,[pc]areprimes},c∈R+∖N and λsym2f(n) be the n-th Fourier coefficient associated with the symmetric square L-function L(s,sym2f). For any A>0, we prove that the mean value of λsym2f(n) over Pc(x) is ≪xlog−A−2x for almost all c∈ε,(5+3)/8−ε in the sense of Lebesgue measure. Furthermore, it holds for all c∈(0,1) under the Riemann Hypothesis. Furthermore, we obtain that asymptotic formula for λf2(n) over Pc(x) is ∑p,qprimep≤x,q=[pc]λf2(p)=xclog2x(1+o(1)), for almost all c∈ε,(5+3)/8−ε, where λf(n) is the normalized n-th Fourier coefficient associated with a holomorphic cusp form f for the full modular group.

Decomposition of exterior and symmetric squares in characteristic two

Let V be a finite-dimensional vector space over a field of characteristic two. As the main result of this paper, for every nilpotent element e∈sl(V), we describe the Jordan normal form of e on the sl(V)-modules ∧2(V) and S2(V). In the case where e is a regular nilpotent element, we are able to give a closed formula.We also consider the closely related problem of describing, for every unipotent element u∈SL(V), the Jordan normal form of u on ∧2(V) and S2(V). A recursive formula for the Jordan block sizes of u on ∧2(V) was given by Gow and Laffey [J. Group Theory 9 (2006), 659–672]. We show that their proof can be adapted to give a similar formula for the Jordan block sizes of u on S2(V).

Design of a triple band notched polarization independent compact FSS at UWB frequency range

The design of a compact triple band notched Frequency Selective surface (FSS) at Ultra-Wide-Band (UWB) frequency range is presented. To make the proposed FSS polarization insensitive, on the upper part of the substrate a single metallic square loop (SL) and four identical rotational symmetric square split ring resonators (SSRR1) are placed, whereas at the bottom part another four identical rotational symmetric SSRR loops (SSRR2) are printed. Here each SSRR is rotated in 90°clockwise direction over a single layered FR4 substrate. Triple band notches are obtained at WiMAX and Satellite communication downlink C-band (3.3-4.2 GHz), WLAN (5.1-5.9 GHz) and Satellite communication X-band (7.2-8.4 GHz) for both TE and TM polarizations. Angular stability is achieved until 70° and attenuation of more than 25 dB is observed at resonance. The passband is obtained at 4.37 and 6.22 GHz. The proposed structure separates the closely spaced frequency bands by a ratio of 1.44 and 1.39 at the stop band and 1.42 at the pass band. The dimensions of the proposed FSS unit cell are 0.13λ0 × 0.13λ0 × 0.020 λ0, where λ0 represents the free space wavelength at the lowest resonance frequency. Good agreement between modeled and measured results is obtained.

Non-vanishing of Maass form symmetric square L-functions

We prove asymptotic formulas for the twisted first and second moments of Maass form symmetric square L-functions at the central point. As an application, we establish effective lower bounds on the proportion of non-zero central L-values in short intervals.

Symmetric square shaped metamaterial structure with quintuple resonance frequencies for S, C, X and Ku band applications

This study explores the effect of symmetrical square shaped metamaterial design for microwave frequency applications. The latest technology demands of advanced performance and research studies of metamaterial integration in the related bands are increasing tremendously. Therefore, this motivates us to explore the metamaterial design structure that has a high possibility to be applied in more than two resonance bands using a compact design structure. This study emphasis on a compact 14 × 14 mm2 and 1.524 mm thick substrate material known as Rogers RT6002. Seven distinct square shaped metamaterial (SQM) rings were constructed on the substrate material to achieve the goal of this research study. Besides that, the investigations of the metamaterial electromagnetic properties and effective medium parameters were carried out by utilising the Computer Simulation Technology Microwave Studio (CST) software. According to the numerical simulation results, the proposed SQM unit cell manifested quintuple resonance frequencies precisely at 3.384 (S band), 5.436, 7.002 (C band), 11.664 (X band), and 17.838 GHz (Ku band). Meanwhile, for the validation process, the comparison between the simulation and measurement results was analysed and data showed that the first and third resonance frequencies were increased by 0.336 and 0.139 GHz, respectively while other frequencies were reduced by 0.186, 0.081, and 0.709 GHz in sequential order. The numerical simulation of the metamaterial design was conducted in a High Frequency Structure Simulator (HFSS) to further validate the results. Furthermore, the proposed SQM manifested left handed characteristics at the second to fifth resonance bands. In a nutshell, the SQM successfully achieves the objectives of this research work and can be applied to multi band applications.

Monolithic Patch-Antenna THz Lasers with Extremely Low Beam Divergence and Polarization Control

Arrays of patch antennas have impacted modern telecommunications in the RF range significantly, owing to their versatility in tailoring the properties of the emitted radiation such as beam width and polarization, along with their ease of fabrication. At higher frequencies, in the terahertz (THz) range, there is a pressing need for a similar monolithic platform to realize and enable the advanced functionalities available in the RF technology. This platform would benefit a wide variety of fields such as astronomy, spectroscopy, wireless communications, and imaging. Here, we demonstrate THz lasers made of arrays of 10 × 10 patch antenna microcavities that provide up to 25 mW output power with robust single mode frequency and spatial mode. This device architecture leads to an unprecedented beam divergence, better than 2° × 2°, which depends only on the number of resonators. This allows to functionalize the device while preserving a high quality far-field pattern. By interconnecting the symmetric square microcavities with narrow plasmonic wires along one direction, we introduce an asymmetry into the originally degenerate and cross-polarized TM01 and TM10 modes, leading to a precise control of the resonant frequency detuning between the TM modes. This feature allows devices to be designed that radiate with any coherent polarization states from linear to circular. Large-scale full-wave simulations of the emission from entire arrays support our experimental results. Our platform provides a solution to finally achieve monolithic terahertz emitters with advanced integrated functionalities such as active beam steering and polarization control.

Single-layer ultra-wide stop-band frequency selective surface using interconnected square rings

In this paper, a miniaturized ultra-wide stop-band frequency selective surface (FSS) with angular stability and polarization insensitivity is presented. The FSS is composed of four symmetric square loops connected to each other using a small metallic strip. The proposed FSS shows good band rejection over the entire ultra-wideband (UWB), where <−10 dB and <−20 dB fractional bandwidths (FBW) are 143.71% (2.8–17.1 GHz) and 73.68% (6–13 GHz), respectively. The structure was made of a single side single layer FR4, which has one of the smallest size (0.074λ0 × 0.074λ0 × 0.014λ0) in this class of FSS.

Interpretable Topic Extraction and Word Embedding Learning Using Non-Negative Tensor DEDICOM

Unsupervised topic extraction is a vital step in automatically extracting concise contentual information from large text corpora. Existing topic extraction methods lack the capability of linking relations between these topics which would further help text understanding. Therefore we propose utilizing the Decomposition into Directional Components (DEDICOM) algorithm which provides a uniquely interpretable matrix factorization for symmetric and asymmetric square matrices and tensors. We constrain DEDICOM to row-stochasticity and non-negativity in order to factorize pointwise mutual information matrices and tensors of text corpora. We identify latent topic clusters and their relations within the vocabulary and simultaneously learn interpretable word embeddings. Further, we introduce multiple methods based on alternating gradient descent to efficiently train constrained DEDICOM algorithms. We evaluate the qualitative topic modeling and word embedding performance of our proposed methods on several datasets, including a novel New York Times news dataset, and demonstrate how the DEDICOM algorithm provides deeper text analysis than competing matrix factorization approaches.

The second moment of symmetric square L-functions over Gaussian integers

We prove a new upper bound on the second moment of Maass form symmetric square L-functions defined over Gaussian integers. Combining this estimate with the recent result of Balog–Biro–Cherubini–Laaksonen, we improve the error term in the prime geodesic theorem for the Picard manifold.

Iwasawa theory for symmetric squares of non-$p$-ordinary eigenforms

Let f be a normalized cuspidal eigen-newform of level coprime to p with a_p(f)=0 . We formulate both integral signed Iwasawa main conjectures and analytic Iwasawa main conjectures attached to the symmetric square motive of f twisted by an auxiliary Dirichlet character. We show that the Beilinson-Flach elements attached to the symmetric square motive factorize into integral signed Beilinson-Flach elements, giving evidence towards the existence of a rank-two Euler system predicted by Perrin-Riou. We use these integral elements to prove one inclusion in the integral and analytic Iwasawa main conjectures.

Uniform bounds for the number of rational points on symmetric squares of curves with low Mordell–Weil rank

A central problem in Diophantine geometry is to uniformly bound the number of $K$-rational points on a smooth curve $X/K$ in terms of $K$ and its genus $g$. A recent paper by Stoll proved uniform bounds for the number of $K$-rational points on a hyperelliptic curve $X$ provided that the rank of the Jacobian of $X$ is at most $g - 3$. Katz, Rabinoff and Zureick-Brown generalized his result to arbitrary curves satisfying the same rank condition. In this paper, we prove conditional uniform bounds on the number of rational points on the symmetric square of $X$ outside its algebraic special set, provided that the rank of the Jacobian is at most $g-4$. We also find rank-favorable uniform bounds (that is, bounds depending on the rank of the Jacobian) in the hyperelliptic case.

The third-power moment of the Riesz mean error term of symmetric square $ L $-function

<abstract> Let $ f(z) $ be a holomorphic Hecke eigenform of weight $ k $ with respect to the full modular group $ SL(2, Z) $, and let $ \Delta_{\rho}(x; sym^{2}f) $ be the error term of the Riesz mean of the symmetric square $ L $-function $ L(s, sym^{2}f) $. In this paper, using a Voronoï type formula for $ \Delta_{\rho}(x; sym^{2}f) $, we consider the third-power moment of $ \Delta_{\rho}(x; sym^{2}f) $ and derive the asymptotic formula for <p class="disp_formula">$ \int_{1}^{T}\Delta_{\rho}^{3}(x;sym^{2}f)dx. $ </abstract>

A Thermopile Device with Sub-Wavelength Hole Arrays by CMOS-MEMS Technology.

A thermopile device with sub-wavelength hole array (SHA) is numerically and experimentally investigated. The infrared absorbance (IRA) effect of SHAs in active area of the thermopile device is clearly analyzed by the finite-difference time-domain (FDTD) method. The prototypes are manufactured by the 0.35 μm 2P4M complementary metal-oxide-semiconductor micro-electro-mechanical-systems (CMOS-MEMS) process in Taiwan semiconductor manufacturing company (TSMC). The measurement results of those prototypes are similar to their simulation results. Based on the simulation technology, more sub-wavelength hole structural effects for IRA of such thermopile device are discussed. It is found from simulation results that the results of SHAs arranged in a hexagonal shape are significantly better than the results of SHAs arranged in a square and the infrared absorption efficiencies (IAEs) of specific asymmetric rectangle and elliptical hole structure arrays are higher than the relatively symmetric square and circular hole structure arrays. The overall best results are respectively up to 3.532 and 3.573 times higher than that without sub-wavelength structure at the target temperature of 60 °C when the minimum structure line width limit of the process is ignored. Obviously, the IRA can be enhanced when the SHAs are considered in active area of the thermopile device and the structural optimization of the SHAs is absolutely necessary.

Power Moments of the Riesz Mean Error Term of Symmetric Square L-Function in Short Intervals

Let f(z) be a holomorphic Hecke eigenform of weight k with respect to SL(2,Z) and let L(s,sym2f)=∑n=1∞cnn−s,ℜs&gt;1 denote the symmetric square L-function of f. In this paper, we consider the Riesz mean of the form Dρ(x;sym2f)=L(0,sym2f)Γ(ρ+1)xρ+Δρ(x;sym2f) and derive the asymptotic formulas for ∫T−HT+HΔρk(x;sym2f)dx, when k≥3.

PERAMALAN HARGA SAHAM DENGAN METODE LOGISTIC SMOOTH TRANSITION AUTOREGRESSIVE (LSTAR) (Studi Kasus pada Harga Saham Mingguan PT. Bank Mandiri Tbk Periode 03 Januari 2011 sampai 24 Desember 2018)

Series such as financial and economic data do not always form a linear model, so a nonlinear model is needed. One of the popular nonlinear models is the Smooth Transition Autoregressive (STAR). STAR has two possible suitable transition function such as logistic and exponential that need to be test to find the appropriate transition function. The purpose of writing this thesis is to determine the LSTAR model, then use the model to predict the stock price of PT Bank Mandiri. This study uses the data of the weekly stock price of PT Bank Mandiri from the period of January 3, 2011 to December 24, 2018 as insample data and the period of January 1, 2019 to December 30, 2019 as outsample data. The research procedure begins with modeling the data with the Autoregressive (AR) process, testing the linearity of the data, modeling with LSTAR, forecasting, and finally evaluating the results of forecasting. Evaluating the results of the forecasting of the weekly share price of PT Bank Mandiri with the STAR model results in the best nonlinear model LSTAR (1,1). This model produces an highly accurate forecasting result with a value of symmetric Mean Square Error (sMAPE) to be 5.12%.Keywords: Nonlinear, Time Series, STAR, LSTAR.