Polynomial Coefficients Research Articles

Seismic data extrapolation based on multi-scale dynamic time warping

Seismic data reconstruction can provide high-density sampling and regular input data for inversion and imaging, playing a crucial role in seismic data processing. In seismic data reconstruction, a common scenario involves a significant distance between the source and the first receiver, which makes it unattainable to acquire near-offset data. A new workflow for seismic data extrapolation is proposed to address this issue, which is based on a multi-scale dynamic time warping (MS-DTW) algorithm. MS-DTW can accurately calculate the time-shift between two time series and is a robust method for predicting time-offset (t−x) domain data. Using the time-shift calculated by the MS-DTW as the basic input, predict the two-way traveltime (TWT) of other traces based on the TWT of the reference trace. Perform autoregressive polynomial fitting on TWT and extrapolate TWT based on the fitted polynomial coefficients. Extract amplitude information from the TWT curve, fit the amplitude curve, and extrapolate the amplitude using polynomial coefficients. The proposed workflow does not necessitate data conversion to other domains and does not require prior knowledge of underground geological information. It applies to both isotropic and anisotropic media. The effectiveness of the workflow was verified through synthetic data and field data. The results show that compared with the method of predictive painting based on local slope, this approach can accurately predict missing near-offset seismic signals and demonstrates good robustness to noise.

Complete Solutions for the Approximate Synthesis of Spherical Four-Bar Function Generators

Abstract Kinematic synthesis to meet an approximate motion specification naturally forms a constrained optimization problem. Instead of using local methods, we conduct global design searches by direct computation of all critical points. The idea is not new, but performed at scale is only possible through modern polynomial homotopy continuation solvers. Such a complete computation finds all minima, including the global, which allows for a full exploration of the design space, whereas local solvers can only find the minimum nearest to an initial guess. We form equality-constrained objective functions that pertain to the synthesis of spherical four-bar linkages for approximate function generation. We consider the general case where all mechanism dimensions may vary and a more specific case that enables the placement of ground pivots. The former optimization problem is shown to permit 268 sets of critical points, and the latter permits 61 sets. Critical points are classified as saddles or minima through a post-process eigenanalysis of the projected Hessian. The discretization points are contained within the coefficients of the stationarity polynomials, so the algebraic structure of the synthesis equations remains invariant to the number of points. The results of our computational work were used to design a mechanism that coordinates the folding wings. We also use this method to parameterize mechanism dimensions for a family of hyperbolic curves.

Extremal Bicyclic Graphs with Respect to Permanental Sums and Hosoya Indices

Graph polynomials is one of the important research directions in mathematical chemistry. The coefficients of some graph polynomials, such as matching polynomial and permanental polynomial, are related to structural properties of graphs. The Hosoya index of a graph is the sum of the absolute value of all coefficients for the matching polynomial. And the permanental sum of a graph is the sum of the absolute value of all coefficients of the permanental polynomial. In this paper, we characterize the second to sixth minimal Hosoya indices of all bicyclic graphs. Furthermore, using the results, the second to sixth minimal permanental sums of all bicyclic graphs are also characterized.

A neural network‐based error correction in the first‐stage residue of pipelined analog to digital converters

SummaryAn analog background calibration approach is presented for the full calibration of pipeline analog‐to‐digital converters (ADCs). A well‐trained neural network acts close to the ideal 1.5‐bit stage, and its residue is compared with the real 1.5‐bit stage including gain error and amplifier nonlinearities. The detected error is used to compensate for the imperfect residue using four calibration polynomial coefficients. The corrected residue enters the second stage of the pipeline ADC and follows a normal path to achieve high resolution. The introduced structure is verified in a 12‐bit pipelined ADC composed of 11 stages; the first 10 stages have a 1.5‐bit structure, while the last stage is a 2‐bit flash. The sampling frequency is 100 MHz, and 10% non‐ideal factors (5% for each of the nonlinear and gain errors and 10% for the aggregated error) are considered for the first stage, while the input is 19.5 MHz sinusoidal waveform. A random noise is applied to the input to limit the effective number of bits (ENOB) to almost 11.8. The evaluation parameters of the ADC are extracted, signal‐to‐noise and distortion ratio increases from 39.14 to 72.91 dB, spurious free dynamic range improves from 40.94 to 79.69 dB, and the ENOB enhances from 6.2 to 11.82. The presented mechanism shows an acceptable accuracy in the high‐speed and high‐resolution ADCs.

Independence polynomials of graphs with given cover number or dominate number

For a graph [Formula: see text], let [Formula: see text] be the number of independent sets of size [Formula: see text] in [Formula: see text]. The independence polynomial [Formula: see text] has been the focus of considerable research. In this paper, using the coefficients of independence polynomials, we order graphs with some given parameters. We first determine the extremal graph whose all coefficients of [Formula: see text] are the largest (respectively, smallest) among all connected graphs (respectively, bipartite graphs) with given vertex cover number. Then we also derive the extremal graph whose all coefficients of [Formula: see text] are the largest among all connected graphs (respectively, bipartite graphs) with given vertex dominate number.

Preliminary Analysis of Beam Position Monitor Accuracy

The beam position is the most important reference basis for the operation of synchrotron radiation light sources, particularly for commissioning the first-turn injection of fourth-generation light sources. To improve the accuracy of the beam position measurement, we analyzed methods for calculating the beam position, and a finite element calculation and the stretched wire calibration system were used to demonstrate the procedure. We proved the relationship between the coverage range, fitting order, scanning step size, and accuracy both theoretically and experimentally, which can provide a basis for selecting the appropriate fitting order for different operation stages of the accelerator. It was proved that the accuracy of beam position calculations using simplified polynomial coefficients is comparable to those without a simplified one, which can save resources for reading electronic processing. The testing results of a batch of beam position monitors (BPMs) were in good agreement with the finite element calculation results, and the small difference between the manufactured BPMs also proved that quality control was performed well, and it benefited from button sorting.

Topological Deformations of Manifolds by Algebraic Compositions in Polynomial Rings

The interactions between topology and algebraic geometry expose various interesting properties. This paper proposes the deformations of topological n-manifolds over the automorphic polynomial ring maps and associated isomorphic imbedding of locally flat submanifolds within the n-manifolds. The manifold deformations include topologically homeomorphic bending of submanifolds at multiple directions under algebraic operations. This paper introduces the concept of a topological equivalence class of manifolds and the associated equivalent class of polynomials in a real ring. The concepts of algebraic compositions in a real polynomial ring and the resulting topological properties (homeomorphism, isomorphism and deformation) of manifolds under algebraic compositions are introduced. It is shown that a set of ideals in a polynomial ring generates manifolds retaining topological isomorphism under algebraic compositions. The numerical simulations are presented in this paper to illustrate the interplay of topological properties and the respective real algebraic sets generated by polynomials in a ring within affine 3-spaces. It is shown that the coefficients of polynomials generated by a periodic smooth function can induce mirror symmetry in manifolds. The proposed formulations do not consider the simplectic class of manifolds and associated quantizable deformations. However, the proposed formulations preserve the properties of Nash representations of real algebraic manifolds including Nash isomorphism.

Wolfes model aka G2/I6-rational integrable model: g(2), g(3) hidden algebras and quartic polynomial algebra of integrals

One-dimensional 3-body Wolfes model with 2- and 3-body interactions also known as G2/I6-rational integrable model of the Hamiltonian reduction is exactly-solvable and superintegrable. Its Hamiltonian H and two integrals I1,I2, which can be written as algebraic differential operators in two variables (with polynomial coefficients) of the 2nd and 6th orders, respectively, are represented as non-linear combinations of g(2) or g(3) (hidden) algebra generators in a minimal manner. By using a specially designed MAPLE-18 code to deal with algebraic operators it is found that (H,I1,I2,I12≡[I1,I2]) are the four generating elements of the quartic polynomial algebra of integrals. This algebra is embedded into the universal enveloping algebra g(3). In turn, 3-body/A2-rational Calogero model is characterized by cubic polynomial algebra of integrals, it is mentioned briefly.

Connecting descent and peak polynomials

A permutation $\sigma=\sigma_1 \sigma_2 \cdots \sigma_n$ has a descent at $i$ if $\sigma_i>\sigma_{i+1}$. A descent $i$ is called a peak if $i>1$ and $i-1$ is not a descent. The size of the set of all permutations of $n$ with a given descent set is a polynomials in $n$, called the descent polynomial. Similarly, the size of the set of all permutations of $n$ with a given peak set, adjusted by a power of $2$ gives a polynomial in $n$, called the peak polynomial. In this work we give a unitary expansion of descent polynomials in terms of peak polynomials. Then we use this expansion to give an interpretation of the coefficients of the peak polynomial in a binomial basis, thus giving a constructive proof of the peak polynomial positivity conjecture.

Perceptions of a reduced nicotine policy and predictors of policy support: A nationally representative U.S. survey

BackgroundThe U.S. Food and Drug Administration is considering a policy to reduce nicotine in cigarettes to non-addictive levels. Although current evidence supports the public-health benefits of a reduced-nicotine policy, almost half of people who smoke (∼ 40%) do not support the policy. This study estimates the factors most strongly associated with support or opposition toward the policy, including tobacco use status, perceived effects of a reduced nicotine policy, trust in the FDA, and psychological distress. The study aims to inform messaging campaigns and policy makers. MethodsData were collected in 2021 with nationally representative samples of U.S. adults (n = 1763). After receiving information about the reduced nicotine policy, participants indicated their beliefs and support for or opposition to the policy, along with other individual difference characteristics. Univariate population parameters and multinomial logistic regression coefficients were estimated. ResultsIn adjusted models, people who formerly or never smoked were less likely to oppose the policy compared to those who currently smoke; people with higher psychological distress and those who believe the policy will promote switching to e-cigarettes were more likely to oppose the policy. In addition, people were more likely to support the policy if they believed it would make quitting easier or that the FDA is trustworthy. ConclusionsEducational campaigns about reduced nicotine policy should expect higher impact by targeting prevalent perceptions and those more strongly associated with policy sentiment. In anticipation of the policy rollout, there may be a critical window to shape public opinion.

Diverse characterizations of Q-Dunkl classical orthogonal polynomials

In this paper, we present four characterizations of q-Dunkl-classical orthogonal polynomials. The first one is a T θ , q -distributional equation of Pearson type fulfilled by its associated form, where T θ , q is the q-Dunkl operator. The second is a second order linear T θ , q -difference equation. The third is a first order linear T θ , q -difference equation with polynomial coefficients satisfied by the corresponding Stieltjes function. The fourth is the so-called structure relation fulfilled by q-Dunkl-classical polynomials. Moreover, we provide an example of a non-symmetric sequence of T θ , q -classical orthogonal polynomials.

Spectral quasi-clustering estimates for certain semiregular systems

We show a quasi-clustering result for a subclass of the class of Semiregular Metric Globally Elliptic Systems (SMGES) including certain quantum optics models (such as Jaynes-Cummings and its generalizations) which describe light-matter interaction. More precisely, we show that for the class of systems with polynomial coefficients we consider, the spectrum concentrates within the union of intervals (not necessarily disjoint, but at most intersecting in an a priori finite number) centered at a sequence determined in terms of invariants of the (total) symbol and width decreasing as the centers go to infinity.

Nonvanishing of second coefficients of Hecke polynomials

Let Tm(N,2k) be the mth Hecke operator on the space S(N,2k) of cuspforms of weight 2k and level N. This paper shows that in all but finitely many cases, which we list, the second coefficient of the characteristic polynomial of T2(N,2k) does not vanish when 2 and N are coprime.

The Impact of GCP Chip Distribution on Kompsat-3A RPC Bias Compensation

The vast potential of high-resolution satellite images, including Kompsat-3A, has been demonstrated across diverse applications, such as mapping and disaster monitoring. However, these images can only be utilized as reliable GIS (geographic information system) data when they possess precise geographical information. To achieve this, sensor model information, represented by RPCs (rational polynomial coefficients), requires bias compensation through GCPs (ground control points). Though having a substantial number of well-distributed GCPs across satellite images is ideal, the acquisition process is often restricted due to cost and inaccessibility. The uniform distribution of GCP chips is not guaranteed, necessitating an investigation into the impact of GCP distribution on the bias compensation process, which is the focus of this study. Experiments were meticulously conducted using Kompsat-3A data using dense GCP information. The dense GCP information was automatically generated from aerial orthoimages through a three-step process. Firstly, the GCP chips were extracted from the aerial images, focusing on feature points. Secondly, these chips were projected onto the target Kompsat-3A data to align them accurately. Lastly, precise satellite image coordinates of the chips were obtained through image matching between the chips and the target Kompsat-3A image. The dense GCPs enabled detailed bias analysis that exhibited skewness in most Kompsat-3A data. This necessitates the implementation of an affine model for proper bias compensation over the entire image space. Next, the study delved into the influence of GCP distribution on RPC bias compensation. To this end, each target satellite image space was divided into nine zones, with the dense GCPs assigned accordingly. The accuracy of bias compensation was analyzed across nine experimental cases, ranging from GCPs occupying only one zone to GCPs covering all nine zones. It was observed that GCPs covering at least four or five zones should be utilized for reliable RPC bias compensation of Kompsat-3A, especially when aiming for a high level of accuracy with an RMSE of one pixel. Finally, it was concluded that GCPs covering three zones yielded satisfactory results as a minimum GCP requirement, but this was contingent upon their distribution not following a straight zone pattern.

Accurate diabatization based on combined-hyperbolic-inverse-power-representation: 1,2 2A' states of BeH2.

A diabatic potential energy matrix (DPEM) for the two lowest states of BeH2+ has been constructed using the combined-hyperbolic-inverse-power-representation (CHIPR) method. By imposing symmetry constraints on the coefficients of polynomials, the complete nuclear permutation inversion symmetry is correctly preserved in the CHIPR functional form. The symmetrized CHIPR functional form is then used in the diabatization by ansatz procedure. The abinitio energies are reproduced with satisfactory accuracy. In addition, the CHIPR-based DPEM also reproduces the local topology of a conical intersection. Future work will focus on a complete four-state diabatic representation with emphasis on the long-range interactions and spin-orbit couplings, which will enable accurate quantum scattering calculations for the Be+(2P) + H2 → BeH+(X1Σ+) + H(2S) reaction.

Zeros of meromorphic functions of the form [formula omitted]

We study zeros distribution for meromorphic functions of the form ∑ncn(z−tn)2, where ∑n|cn||tn|2<∞. We prove an analog of a well-known theorem of Keldysh and discuss a relation between zero-free functions of this form and second order differential equations with polynomial coefficients.

Laboratory study of aberration calculation in underwater turbulence using Shack-Hartmann wavefront sensor and Zernike polynomials

This paper presents a laboratory study of the aberrations calculation in underwater turbulence using the Shack-Hartmann wavefront sensor. The wavefront decomposition method and Zernike polynomials determine the aberration parameters. In our experimental setup, the turbulent phase screen generator is located in two locations: near the transmitter and therefore far from the receiver, and near the receiver and consequently far from the transmitter. Additionally, we investigate the impact of aperture diameter on turbulence-induced aberrations in the optical receiver system. However, it is essential to note that the coefficients of Zernike polynomials obtained using this method are subject to errors caused by receiver sensor noise and correlation between the polynomials. To address this, we first calculate the coefficients in different arrangements and then correct measurement errors arising from sensor noise and polynomial coefficient correlation.

Genetic analysis of test-day milk yield in sheep recorded at two governmental breeding and multiplication centers in Ethiopia

ABSTRACT One aim was to compare four classes of ewes for test-day milk yield (TDMY). The classes are the local Menz breed, the Awassi breed, and their main crossbreds (50 and 75%). Another aim was to estimate variance components to facilitate the prediction of breeding values and their accuracy. A total of 1040 TDMY records of 211 ewes were used. A univariate repeatability model with Legendre polynomial coefficients were used to model lactation curves. The 100% Awassi ewes produced significantly (p < 0.05) more milk than the other studied ewe groups within 120 Days in milk (DIM). The Local ewes produced significantly less than the other groups. Estimates of heritability (h 2) and repeatability (r) of TDMY were 0.10 ± 0.08 and 0.15 ± 0.03, respectively. The genetic variance indicated for TDMY could give a genetic gain in the dissemination program if recorded for all ewes at the two centres.

GPU Acceleration for SAR Satellite Image Ortho-Rectification

Synthetic Aperture Radar (SAR) satellite image ortho-rectification requires pixel-level calculations, which are time-consuming. Moreover, for SAR images with large overlapping areas, the processing time for ortho-rectification increases linearly, significantly reducing the efficiency of SAR satellite image mosaic. This paper thoroughly analyzes two geometric positioning models for SAR images. In order to address the high computation time of pixel-by-pixel ortho-rectification in SAR satellite images, a GPU-accelerated pixel-by-pixel correction method based on a rational polynomial coefficients (RPCs) model is proposed, which improves the efficiency of SAR satellite image ortho-rectification. Furthermore, in order to solve the problem of linearly increasing processing time for the ortho-rectification of multiple SAR images in large overlapping areas, a multi-GPU collaborative acceleration strategy for the ortho-rectification of multiple SAR images in large overlapping areas is proposed, achieving efficient ortho-rectification processing of multiple SAR image data in large overlapping areas. By conducting ortho-rectification experiments on 20 high-resolution SAR images from the Gaofen-3 satellite, the feasibility and efficiency of the multi-GPU collaborative acceleration processing algorithm are verified.

Fourier series for the multidimensional-matrix functions of the vector variable

In the article, the theory of the Fourier series on the orthogonal multidimensional-matrix (mdm) polynomials is developed. The known results from the theory of the orthogonal polynomials of the vector variable and the Fourier series are given and the new results are presented. In particular, the known results of the Fourier series theory are extended to the case of the mdm functions, what allows us to solve more general approximation problems. The general case of the approximation of the mdm function of the vector argument by the Fourier series on the orthogonal mdm polynomials is realized programmatically as the program function and its efficiency is confirmed. The analytical expressions for the coefficients of the second degree orthogonal polynomials and Fourier series for possible analytical studies are obtained.