First-order Terms Research Articles

Improved difference model applied in the Fourier-transform-based integration method based on Taylor theory.

The two-dimensional Fourier-transform-based integration algorithm is widely used in shape or wavefront reconstruction from gradients. However, its reconstruction accuracy is limited by the truncation error of the difference model. The truncation error is affected by the distribution of the sampling points. It increases when the sampling points are unevenly distributed and arranged irregularly. For improving, a novel way to calculate the difference is proposed based on Taylor expansion theory of binary functions. The first-order partial derivative terms are used to estimate the second- and third-order partial derivative terms for reducing the truncation error. The proposed difference model is applied to Fourier-transform-based integration. The reconstruction results show that it can get better results when the sampling points are irregularly distributed.

A Direct-Decoupling Closed-Loop Control Method for Roll-to-Roll Web Printing Systems

The roll-to-roll (R2R) web printing system is a complex coupling system, in which tension fluctuation is caused by upstream register control, thus results in downstream register errors. Therefore, it is indispensable to compensate for the couplings in order to improve the register precision in R2R printing systems. However, existing control methods do not realize complete decoupling due to their indirect calculation of compensations for the register errors. In this article, a mechanical model is set up to represent the direct relationship between the downstream register errors and all their upstream register controls. According to the model, compensation is calculated on the basis of the Lyapunov stability theorem to converge the register errors to zero. Then, a direct-decoupling closed-loop control method with first-order compensation terms, i.e., the direct-decoupling proportional derivative control (DDPD), is proposed to completely compensate for the couplings between all upstream register controls and downstream register errors. In addition, the first-order expression of the compensation makes it easy to implement in industrial applications. An industrial example indicates that the proposed control method eliminates the couplings and maintains the range of register errors within ±0.06 mm. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article proposes a control strategy for the roll-to-roll (R2R) printing system, particularly for printing systems with electronic line shafts. Few existing studies have been done in detailedly analyzing the upstream register controls and the downstream register errors. This article establishes a mechanical model of printing registration and gives a systematic analysis of the complete relationship between upstream register controls and downstream register errors and then proposes a control strategy based on the Lyapunov stability analysis. The proposed method can be extended to other similar R2R systems. Simulation and industrial examples show that the control method is more feasible and effective compared with the existing methods. In future work, we will study a control method combined with the mechanical model and data model in different R2R systems.

A Complete Uniform Asymptotic Expansion of the Sommerfeld Integral of an Impedance Plane for Imperfectly Homogeneous Half-Space

The Sommerfeld integral for an impedance plane has played an important role in many electromagnetic applications. A direct numerical computation may not be efficient and cannot provide a robust and accurate result especially for highly conductive media and/or antennas located near the surface. Two complete asymptotic series are formulated for the integral, which is a power series of the reciprocal of the distance between the source and observation point. The asymptotic series are nonuniform, so the application of the series is limited and is not accurate for the aforementioned cases. Hence, in this article, a new uniform asymptotic expansion of the integral is derived, which is represented in terms of repeated integrals of the complementary error function. The representation is very similar to the conventional uniform expansion of the integral. However, the formulated expansion is a complete power series of the reciprocal of the distance, while the conventional series contains only the first-order term. For a far-field region, the proposed expansion is mathematically shown to reduce the known complete nonuniform expansion for the first few terms of the expansion. For some scenarios that include near-earth propagation and/or highly conductive media, the proposed formulation is numerically verified and its mathematical properties are examined.

Critical Fujita Exponent for the Porous Medium Equation in ${\mathbb R}^{{N}}$ with hole

We study the large time behavior of solutions to the Neumann Problem of the porous medium equation. It is shown that the critical Fujita exponent is determined not only by the spatial dimension and the nonlinear exponent, but also by the coefficient $k$ of the first-order term.

Design Architecture for Continuous-Time Control of Dual Active Bridge Converter

The dual active bridge (DAB) is one of the useful interfaces for the bidirectional power exchange between two buses with galvanic isolation. In this article, a design framework is given in the analog domain that completely fulfills the operational features of a DAB under phase angle modulation. This is a cost-effective solution with configurable control parameters and easy to implement using well-established semiconductor integrated circuit (IC). Moreover, it provides an efficient way to study the behavior of power converters. A closed-loop control for bidirectional power exchange is established. For that, a control-to-output current transfer function is derived analytically considering the dc and first-order harmonic terms and verified experimentally. A small scale laboratory prototype of DAB is set up for the validation of the concept. It is shown that the design architecture has the facility for supervisory control that is useful for battery charging/discharging, microgrid application, etc.

BRITE-Constellation photometry of π5 Orionis, an ellipsoidal SPB variable

ABSTRACT Results of an analysis of the BRITE-Constellation photometry of the SB1 system and ellipsoidal variable π5 Ori (B2 III) are presented. In addition to the orbital light-variation, which can be represented as a five-term Fourier cosine series with the frequencies forb, 2forb, 3forb, 4forb, and 6forb, where forb is the system’s orbital frequency, the star shows five low-amplitude but highly significant sinusoidal variations with frequencies fi (i = 2, .., 5, 7) in the range from 0.16 to 0.92 d−1. With an accuracy better than 1σ, the latter frequencies obey the following relations: f2 − f4 = 2forb, f7 − f3 = 2forb, f5 = f3 − f4 = f7 − f2. We interpret the first two relations as evidence that two high-order ℓ = 1, m = 0 gravity modes are self-excited in the system’s tidally distorted primary component. The star is thus an ellipsoidal SPB variable. The last relations arise from the existence of the first-order differential combination term between the two modes. Fundamental parameters, derived from photometric data in the literature and the Hipparcos parallax, indicate that the primary component is close to the terminal stages of its main-sequence (MS) evolution. Extensive Wilson–Devinney modelling leads to the conclusion that best fits of the theoretical to observed light curves are obtained for the effective temperature and mass consistent with the primary’s position in the HR diagram and suggests that the secondary is in an early MS evolutionary stage.

Association between vertebral bone mineral density, myocardial perfusion, and long-term cardiovascular outcomes: A sex-specific analysis

BackgroundSexual dimorphism in the manifestation of coronary artery disease (CAD) has unleashed a call to reconsider cardiovascular risk assessment. Alterations of bone mineral density (BMD) have been associated with congestive heart failure and appear to be modified by sex. However, the sex-specific association between BMD, myocardial perfusion, and cardiovascular outcomes is currently unknown. MethodsA total number of 491 patients (65.9 ± 10.7 years, 32.4% women) underwent 13N-ammonia positron emission tomography/computed tomography for evaluation of CAD, and were tracked for major adverse cardiac events (MACEs). ResultsEvent-free survival (median follow-up time of 4.3 ± 2.0 years) was significantly reduced in patients with low (≤ 100 Hounsfield units) compared to those with higher BMD (log-rank P = .037). Accordingly, reduced BMD was chosen as significant predictor of MACE in a fully adjusted proportional hazards regression model (P = .015). Further, a first-order interaction term consisting of sex and BMD was statistically significant (P = .007). BMD was significantly lower in patients with abnormal myocardial perfusion or impaired left ventricular ejection fraction (P < .05). This difference, however, was noticed in men, but not in women. ConclusionsThe association between low BMD and cardiovascular disease is sex dependent. Our data suggest that quantification of BMD during myocardial perfusion imaging for evaluation of CAD may be particularly useful in men.

Evolution of orbits about comets with arbitrary comae

Spacecraft and natural objects orbiting an active comet are perturbed by gas drag from the coma. These gases expand radially at about 0.5 km/s, much faster than orbital velocities that are on the order of meters per second. The coma has complex gas distributions and is difficult to model. Accelerations from gas drag can be on the same order of gravity and are currently poorly understood. Semi-analytical solutions for the evolution of the Keplerian orbital elements of a spacecraft orbiting a comet using simplified drag and coma models are derived using a Fourier series expansion in the argument of latitude. It is found that the mean element evolution is only dependent on the zeroth- and first-order terms of the Fourier series expansion. For an arbitrary, inverse-square, radial, perturbing force, there are no frozen orbits; however, the argument of pericenter has a stable equilibrium and an unstable equilibrium and the angular momentum vector of the orbit is constant. Furthermore, the radius of the orbit at two specific angles relative to the ascending node is preserved. The evolution of the orbit is governed by the argument of pericenter, resulting in orientations that raise and lower the radius of pericenter and implying safe and unsafe orbit orientations for spacecraft operations.

Simulation of light scattering by two nano-sized circular cylinders using NS-FDTD method and interference analysis

Scattering problem by one cylinder whose radius is comparable to incident wavelength can be solved by Mie theorem. Due to complicated multiple scattering, scattering characteristics by two adjacent cylinders cannot be easily expounded. In this paper, high-accuracy non-standard finite-difference time domain (NS-FDTD) method is utilized to simulate electromagnetic field scattered by two nano-sized circular cylinders. Scattering intensities calculated by the NS-FDTD method demonstrate distinct polarization-dependence feature which can be explained by interference analyses including first-order and second-order scattering. The interference analyses indicate that the two-cylinder scattering problem in the transverse magnetic mode can be approximately solved by one-cylinder Mie scattering solution superposed with a first-order interference term, whereas both first-order and second-order interference should be considered into the superposition term in the transverse electric mode.

Maximum Principles for k-Hessian Equations with Lower Order Terms on Unbounded Domains

Our primary objective in this paper is to study a class of k-Hessian equations with zero-order and first-order terms in unbounded domains. Among others, we derive Phragmen–Lindelof and Liouville type results. The zero-order terms involved are required to satisfy Keller–Osserman type conditions.

Consistency of Term &lt;i&gt;star&lt;/i&gt;: a Statistical Analysis of the Productive Types of System Relations with Related Terminological Units

The article is devoted to the study of the term as a system unit in its interconnections with contiguous linguistic facts on the example of semantic relations existing in the term star in the field of scientific knowledge “astrophysics”. The study is based on an analysis of the systemic correlation of units in the field of astrophysics. The authors focus on terms representing various categories of concepts in accordance with the nature of the referents they represent. The most and least productive semantic relations are established and analyzed with related first-order terms presented in the definition and second-order terms, the relations with which are represented in the texts of scientific publications outside of the definitions. The categorical pertaining of related terms with which the term star has a systemic relationship is also determined in the study. Using a statistical analysis of a selection of terms in the field of “astrophysics”, we found that the most productive semantic relationships for them are relationships such as generic, attribution, and “part-whole”.

Formalizing the dependency pair criterion for innermost termination

• Dependency pairs criterion and verification of termination of rewriting systems. • Automating termination of rewriting and functional programs. • Formalization of termination of first-order term rewriting systems. • Innermost reduction and termination of rewriting. • Formally proving the soundness of rewriting with the PVS proof assistant. Rewriting is a framework for reasoning about functional programming. The dependency pair criterion is a well-known mechanism to analyze termination of term rewriting systems. Functional specifications with an operational semantics based on evaluation are related, in the rewriting framework, to the innermost reduction relation. This paper presents a PVS formalization of the dependency pair criterion for the innermost reduction relation: a term rewriting system is innermost terminating if and only if it is terminating by the dependency pair criterion. The paper also discusses the application of this criterion to check termination of functional specifications.

Discrete effects on the forcing term for the lattice Boltzmann modeling of steady hydrodynamics

This work concerns with the clean inclusion of the forcing term in the lattice Boltzmann method (LBM) for the modeling of non-uniform body forces in steady hydrodynamics. The study is conducted for the two-relaxation-time (TRT) scheme. Here, we consider a simple, but yet sufficiently generic, flow configuration driven by a spatially varying body force based on which we derive the analytical solution of the forced LBM-TRT and compare two force strategies set by first- and second-order expansions. This procedure exactly establishes the macroscopic system satisfied by each force formulation at discrete level. The obtained theoretical results are further verified in two distinct benchmark channel flow problems. Overall, this study shows that the spatial discrete effects posed by the LBM modeling of the force term may come in through two sources. The first one is a defect inherent to LBM, arising from the non-local spatial discretization of the forcing term, and given by the discrete Laplacian of the body force. While it corrupts the discrete momentum balance with a non-linear viscosity dependent term in the single-relaxation-time schemes, this inconsistency is avoided with the TRT scheme, through its free-tunable relaxation degree of freedom Λ. The other error source is unique to the use of second-order force expansions, where its non-zero second-order velocity moment interferes with the discrete momentum balance through a spurious first-order derivative term, leading to several forms of inconsistency in the LBM steady solution. For simulations under the convective scaling it makes the LBM scheme a numerical representation of a differential system distinct from the physical one, whereas under the diffusive scaling it leads to viscosity-dependent numerical errors, which corrupt the otherwise consistent structure of TRT steady-state solutions. In contrast, the defects reported herein are absent with the first-order force expansion scheme operated within the scope of the LBM-TRT model for steady hydrodynamics.

Coupled Surface–Subsurface Flow Modelling Using the GeRa Software

Mathematical model and numerical methods for the solution of coupled surface–subsurface flow in GeRa software is presented. Coupling of surface runoff and subsurface flow models is accomplished using first-order exchange term. The arising nonlinear solver convergence issues are addressed in the article. In order to overcome these issues, approaches for handling the surface–subsurface flux expression are introduced. The proposed numerical model is verified and validated using benchmarks with reference solutions obtained in different codes as well as experimental results.

Satellite-Imagery Geometric Accuracy Improvement Based on Direct Correction of Dominant Coefficients

An important and difficult point in the application of satellite imagery is refining the positioning model and improving the geometric accuracy. In this study, we focus on improvement in geometric accuracy and develop a new rational function model (&lt;small&gt;RFM&lt;/small&gt;) refinement method. First, we derive the conversion relationship between the rigorous sensor model and the &lt;small&gt;RFM&lt;/small&gt;, based on which we illustrate the approximate meaning of the zero-order and first-order terms of the rational polynomial coefficients (&lt;small&gt;RPCs&lt;/small&gt;). Second, the correlation problem between &lt;small&gt;RPCs&lt;/small&gt; and the influence of individual &lt;small&gt;RPCs&lt;/small&gt; on geometric positioning accuracy are analyzed and verified. The dominant coefficients that determine geolocation are then identified. Finally, a new &lt;small&gt;RFM&lt;/small&gt; refinement method based on direct correction of the dominant coefficients is proposed and validated. The experiments, conducted with &lt;small&gt;ZY3-02&lt;/small&gt; satellite imagery, indicate that the proposed method can effectively improve the geometric accuracy of satellite images.

Borders as opposed to so-called geography: which should be used to classify isolated ventricular septal defects?

Ventricular septal defects can be classified according to their borders or according to the fashion in which they open to the right ventricle, so-called geography. As yet, there is no consensus as to how they should be classified. In an attempt to achieve agreement, the International Society for Nomenclature of Congenital and Paediatric Heart Disease, in 2018, proposed a system incorporating both approaches. We have assessed the subjectivity of their suggested terms hoping to determine their suitability in the desired universal system for classification. We examined 212 specimens held in the archive of Birmingham Women's and Children's Hospital. Each defect was described by 3 independent examiners on the basis of borders and their relationship to the landmarks of the right ventricle. The interobserver agreement was then calculated using Fleiss' method. Calculations to assess interobserver agreement showed that the examiners were more likely to agree on the borders of the defects than their so-called geography (κ = 0.804 vs κ = 0.518). The landmarks of the right ventricle proved to be highly variable such that the application of 'geographic' terms to hearts with perimembranous defects proved particularly challenging. Interobserver agreement is lower when using terms based on 'geography' as opposed to borders. Whilst providing important morphological detail, the terms based on right ventricular landmarks are highly subjective. They should not be prioritized in a universal system of classification. Instead, the defects can be classified simply by using 'perimembranous', 'muscular', or 'doubly committed and juxta-arterial' as first-order terms.

The inverse problem of two-state quantum systems with non-adiabatic static linear coupling

We consider the inverse problem of determining the coupling coefficients in a two-state Schrödinger system. We prove a Lipschitz stability inequality for the zeroth- and first-order coupling terms by finitely many partial lateral measurements of the solution to the coupled Schrödinger equations.

Exchange-Correlation Energy Densities and Response Potentials: Connection between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond.

We analyze in depth two widely used definitions (from the theory of conditional probability amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn–Sham density functional theory. We introduce a local form of the coupling-constant-dependent Hohenberg–Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.

Quantum Algebraic Description of the Pairing Correlations in a Single-j Nuclear Shell

Pairing in a single-j shell is described in terms of two Q-oscillators, one describing the J=0 fermion pairs and the other corresponding to the J≠0 pairs, the deformation parameter Τ = lnQ being related to the inverse of the size of the shell. Using these two oscillators an SUQ(2) algebra is constructed, while a pairing Hamiltonian giving the correct energy eigenvalues up to terms of first order in the small parameter can be written in terms of the Casimir operators of the algebras appearing in the UQ(2) &gt; UQ(1) chain, thus exhibiting a quantum algebraic dynamical symmetry. The additional terms introduced by the Q-oscillator are found to improve the agreement with the experimental data for the neutron pair separation energies of the Sn isotopes, with no extra parameter introduced.

Simultaneous Retrieval of the Size and Refractive Index of Suspended Droplets in a Linear Quadrupole Electrodynamic Balance.

Single-particle trapping is an effective strategy to explore the physical and optical properties of aerosol with high precision. Laser-based methods are commonly used to probe the size, optical properties, and composition of nonlight-absorbing droplets in optical and electrodynamic traps. However, these methods cannot be applied to droplets containing photoactive chromophores, and thus, single-particle methods have been restricted to only a subset of atmospherically relevant particle compositions. In this work, we explore the application of a broadband light scattering approach, Mie resonance spectroscopy, to simultaneously probe the size and the refractive index (RI) of droplets in a linear quadrupole electrodynamic balance. We examine the evaporation of poly(ethylene glycol)s and compare the calculated vapor pressures with literature values to benchmark the size accuracy without prior constraint on the RI. We then explore the hygroscopic growth and deliquescence of sodium chloride droplets, measuring RI at the deliquescence relative humidity and demonstrating agreement to literature values. These data allow the wavelength dependence of the RI of aqueous NaCl to be determined using a first-order Cauchy equation, and we effectively reproduce literature data from multiple techniques. We finally discuss measurements from a light-absorbing aqueous droplet containing humic acid and interpret the spectra via the imaginary component of the RI. The approach described here allows the radius of nonabsorbing droplets to be determined within 0.1%, the refractive index within 0.2%, and the first-order term in the Cauchy dispersion equation within ∼5%.