Coefficients A2 Research Articles

Fekete–Szegö Inequalities for a New Subclass of Bi-Univalent Functions Associated with Gegenbauer Polynomials

We introduce and investigate in this paper a new subclass of bi-univalent functions associated with the Gegenbauer polynomials which satisfy subordination conditions defined in a symmetric domain, which is the open unit disc. For this new subclass, we obtain estimates for the Taylor–Maclaurin coefficients a2,a3 and the Fekete–Szegö inequality a3−μa22.

An Application of Miller–Ross-Type Poisson Distribution on Certain Subclasses of Bi-Univalent Functions Subordinate to Gegenbauer Polynomials

The Miller–Ross-type Poisson distribution is an important model for plenty of real-world applications. In the present analysis, we study and introduce a new class of bi-univalent functions defined by means of Gegenbauer polynomials with a Miller–Ross-type Poisson distribution series. For functions in each of these bi-univalent function classes, we have derived and explored estimates of the Taylor coefficients a2 and a3 and Fekete-Szegö functional problems for functions belonging to these new subclasses.

Coefficient Estimates for the Functions with Respect to Symmetric Conjugate Points Connected with the Combination Binomial Series and Babalola Operator and Lucas Polynomials

By using Lucas polynomials, we define a new subclass of analytic bi-univalent functions, class Σ, in the open unit disc with respect to symmetric conjugate points connected with the combination Binomial series and Babalola operator. The bounds on the initial coefficients a2 and a3 for the functions in this new subclass of Σ are investigated. Moreover, we obtain an estimation for the Fekete–Szego problem for the function subclass defined in this paper. Relevant connections of these results are presented here as corollaries.

Yamaguchi -Noshiro Type Bi-Univalent Functions Associated with Sălăgean-Erdély–Kober Operator

We defined two new subclasses of analytic bi-univalent function class Σ, in the open unit disk related with the Sălăgean–Erdély–Kober operator. The bounds on initial coefficients |a2|,|a3| and |a4| for the functions in these new subclasses of Σ are investigated. Using the estimates of coefficients a2,a3, we also discuss the Fekete-Szegö inequality results for the function classes defined in this paper. Relevant connections of these results, presented here as corollaries, are new and not studied in association with Sălăgean-Erdély–Kober operator for the subclasses defined earlier.

Dissolution and Solubility of the Calcite–Otavite Solid Solutions [(Ca1−xCdx)CO3] at 25 °C

A complete series of the calcite–otavite solid solutions [(Ca1−xCdx)CO3] were prepared, and their dissolution processes lasting nine months were experimentally investigated. For the dissolution in the N2-degassed water, the Ca concentrations of the aqueous phases increased up to the steady states after 5040 h of dissolution, and the Cd concentrations of the aqueous phases increased up to the highest values and then decreased gradually to the steady states of 0.017–6.476 μmol/L after 5040 h of dissolution. For the dissolution in the CO2-saturated water, the Ca and Cd concentrations of the aqueous phases increased up to the peak values and then decreased gradually to the steady states of 0.94–0.46 mmol/L and 0.046–9.643 μmol/L after 5040 h of dissolution, respectively. For the dissolution in the N2-degassed water at 25 °C, the mean solubility products (log Ksp) and the Gibbs free energies of formation (ΔGfθ) were estimated to be −8.45–−8.42 and −1129.65–−1129.48 kJ/mol for calcite [CaCO3] and −11.62–−11.79 and −671.81–−672.78 kJ/mol for otavite [CdCO3], respectively. Generally, the log Ksp values decreased non-linearly, and the ΔGfθ values increased linearly with the increasing Cd/(Ca+Cd) mole ratio (XCd) of the (Ca1−xCdx)CO3 solid solutions. In the Lippmann diagrams constructed for the sub-regular (Ca1−xCdx)CO3 solid solutions with the estimated Guggenheim coefficients a0 = −0.84 and a1 = −3.80 for the dissolution in the N2-degassed water or a0 = −1.12 and a1 = −3.83 for the dissolution in the CO2-saturated water, the (Ca1−xCdx)CO3 solid solutions dissolved incongruently, moved progressively up to the quasi-equilibrium curves for otavite and then along the quasi-equilibrium curve from right to left, approached the solutus curve and finally reached the minimum stoichiometric saturation curve for calcite. The considerably Cd-poor aqueous phases were finally in equilibrium with the CdCO3-rich solid phases.

Novel and robust auxiliary indicators to ankle-brachial index using multi-site pulse arrival time and detrended fluctuation analysis for peripheral arterial disease assessment

The ankle-brachial index (ABI) test is a common tool used for screening peripheral arterial disease (PAD), but its accuracy has been doubted especially in patients with incompressible arteries attributed to calcification. Advanced wearable sensing technologies have potential to offer novel solutions for PAD assessment. This study investigated several novel indicators using the Detrended Fluctuation Analysis (DFA) on beat-to-beat RR interval (RRI) and pulse arrival time (PAT) from the four limbs of 7 young healthy and 7 elderly PAD subjects in supine and sitting postures. The auxiliary value of these indicators in addition to ABI for PAD assessment was also studied using a binary logistic regression model. The results showed that the short-scale DFA coefficients (α1) of RRI, α1 of PATs of fingers and α1_ratio of PAT (the ratio of α1 of PAT between the ipsilateral finger and toe) in supine posture, were significantly different between the PAD and healthy groups (1.26 ± 0.24 vs 0.76 ± 0.21, 1.03 ± 0.30 vs 0.68 ± 0.19, and 0.84 ± 0.20 vs 1.42 ± 0.47, respectively, p < 0.05), and the α1 of RRI and α1_ratio of PAT were not significantly influenced by postural change. Moreover, using ABI together with the supine α1_ratio of PAT was more sensitive in detecting PAD (sensitivity = 92.9%) than ABI alone (78.6%) with the same specificity of 100%. The short-scale DFA coefficients of multi-site PAT in supine posture, which can be measured by wearable devices, is an auxiliary to ABI for detecting PAD.

An Avant-Garde Construction for Subclasses of Analytic Bi-Univalent Functions

The zero-truncated Poisson distribution is an important and appropriate model for many real-world applications. Here, we exploit the zero-truncated Poisson distribution probabilities to construct a new subclass of analytic bi-univalent functions involving Gegenbauer polynomials. For functions in the constructed class, we explore estimates of Taylor–Maclaurin coefficients a2 and a3, and next, we solve the Fekete–Szegő functional problem. A number of new interesting results are presented to follow upon specializing the parameters involved in our main results.

Subclasses of Bi-Univalent Functions Connected with Integral Operator Based upon Lucas Polynomial

In the contemporary paper, we introduce new subclasses of analytic and bi-univalent functions involving integral operator based upon Lucas polynomial. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients a2 and a3 for functions in these subclasses and obtain Fekete-Szegö problem for these subclasses.

The number of solutions of diagonal cubic equations over finite fields

Let Fq be a finite field of q=pk elements. For any z∈Fq, let An(z) and Bn(z) denote the number of solutions of the equations x13+x23+⋯+xn3=z and x13+x23+⋯+xn3+zxn+13=0 respectively. Recently, using the generator of Fq⁎, Hong and Zhu gave the generating functions ∑n=1∞An(z)xn and ∑n=1∞Bn(z)xn. In this paper, we give the generating functions ∑n=1∞An(z)xn and ∑n=1∞Bn(z)xn immediately by the coefficient z. Moreover, we gave the formulas of the number of solutions of equation a1x13+a2x23+a3x33=0 and our formulas are immediately determined by the coefficients a1,a2 and a3. These extend and improve earlier results.

Exploiting the Pascal Distribution Series and Gegenbauer Polynomials to Construct and Study a New Subclass of Analytic Bi-Univalent Functions

In the present analysis, we aim to construct a new subclass of analytic bi-univalent functions defined on symmetric domain by means of the Pascal distribution series and Gegenbauer polynomials. Thereafter, we provide estimates of Taylor–Maclaurin coefficients a2 and a3 for functions in the aforementioned class, and next, we solve the Fekete–Szegö functional problem. Moreover, some interesting findings for new subclasses of analytic bi-univalent functions will emerge by reducing the parameters in our main results.

Optical forces and optical force categorizations on small magnetodielectric particles in the framework of generalized Lorenz-Mie theory

A previous study has been devoted to the case of optical forces exerted on Rayleigh particles in the framework of generalized Lorenz-Mie theory (GLMT). This study is here extended to the case of small magnetodielectric particles which are characterized by their electric and magnetic Mie coefficients a1 and b1 respectively. A partition of optical forces between incident-scattered mixed terms and recoil terms has been established in GLMT since more than three decades. This partition is here complemented by another partition between gradient, scattering and non-standard forces. The relationship between these non-standard forces and curl forces exhibited in the framework of a dipole theory is emphasized. The case of Rayleigh particles (more generally of electric dipolar particles) previously published in the GLMT-framework is recovered as a special case of the case of small magnetodielectric particles discussed in the present paper. The case of illumination by plane waves furthermore provides complementary insights on the behavior of non-standard forces.

Bounds for Two New Subclasses of Bi-Univalent Functions Associated with Legendre Polynomials

In this article, two new subclasses of the bi-univalent function class σ related with Legendre polynomials are presented. Additionally, the first two Taylor–Maclaurin coefficients a2 and a3 for the functions belonging to these new subclasses are estimated.

Genetic evaluation of lactation persistency in the Gyr breed by using a two-trait random regression model

Context Lactation persistency (LP) is an economically important characteristic to include in the selection objectives of the Gyr breed. Two persistency measures were tested to establish their contribution to the genetic evaluation of milk production in this genotype. The second measure of persistency studied would be the more appropriate measure to use in the genetic evaluation of lactation persistency. Aim The aim of this work was to study LP in Gyr cows by using a random regression model (RRM) in two-trait analysis. Methods Test-day milk yields (TDMY) of the first two lactations of Gyr cows were analysed. RRM was performed by Bayesian inference using the GIBBS3F90 program. Fourth-order Legendre polynomials were used to describe the random additive genetic and permanent environmental effects of the animal. The fixed effects included in the model were contemporary group and, as covariates, age of cow at calving and the regression function according to the TDMY class of lactation as the average trajectories of lactation curve, distinguished by calving order. Two persistency measures (PSi, i.e. PS1 and PS2) were used in the analyses. Rank correlations were calculated between the predicted breeding values for PSi, 305-day lactation milk yield (MY305), and the regression coefficients a0 and a1, to determine the percentage of matching animals between rankings when different selection intensities are applied on the basis of the ranking for MY305. Key results The heritability estimates for PS1, PS2 and for MY305 were 0.19, 0.12 and 0.41 respectively, in the first lactation, and 0.43, 0.27 and 0.38 in the second lactation. The genetic correlation between MY305 and PS1 was negative and of low magnitude. The rank correlation between breeding values for PSi, obtained for bulls with at least five daughters with production records, was higher than 0.80 in the two lactation periods. Conclusions The results indicated that PS2 is the more suitable of the two persistency measures used in this work, for inclusion in genetic evaluations of lactation persistency in Brazilian Gyr cows. Implications PS2 must be included as a selection criteria in a breeding program for the Gyr breed.

Geometry-dependent two-photon absorption followed by free-carrier absorption in AlGaAs waveguides

Nonlinear absorption can limit the efficiency of nonlinear optical devices. However, it can also be exploited for optical limiting or switching applications. Thus, characterization of nonlinear absorption in photonic devices is imperative for designing useful devices. This work uses the nonlinear transmittance technique to measure the two-photon absorption coefficients ( α 2 ) of AlGaAs waveguides in strip-loaded, nanowire, and half-core geometries in the wavelength range from 1480 to 1560 nm. The highest α 2 values of 2.4, 2.3, and 1.1 c m / G W were measured at 1480 nm for 0.8-µm-wide half-core, 0.6-µm-wide nanowire, and 0.9-µm-wide strip-loaded waveguides, respectively, with α 2 decreasing with increasing wavelength. The free-carrier absorption cross section was also estimated from the nonlinear transmittance data to be around 2.2 × 10 − 16 c m 2 for all three geometries. Our results contribute to a better understanding of the nonlinear absorption in heterostructure waveguides of different cross-sectional geometries. We discuss how the electric field distribution in the different layers of a heterostructure can lead to geometry-dependent effective two-photon absorption coefficients. More specifically, we pinpoint the third-order nonlinear confinement factor as a design parameter to estimate the strength of the effective nonlinear absorption, in addition to tailoring the bandgap energy by varying the material composition.

Some Results of New Subclasses for Bi-Univalent Functions Using Quasi-Subordination

In this paper, we introduce new subclasses RΣ,b,cμ,αλ,δ,τ,Φ and KΣ,b,cμ,αλ,δ,η,Φ of bi-univalent functions in the open unit disk U by using quasi-subordination conditions and determine estimates of the coefficients a2 and a3 for functions of these subclasses. We discuss the improved results for the associated classes involving many of the new and well-known consequences. We notice that there is symmetry in the results obtained for the new subclasses RΣ,b,cμ,αλ,δ,τ,Φ and KΣ,b,cμ,αλ,δ,η,Φ, as there is a symmetry for the estimations of the coefficients a2 and a3 for all the subclasses defind in our this paper.

Drell-Yan angular lepton distributions at small x from TMD factorization.

The Drell-Yan process is studied in the framework of TMD factorization in the Sudakov region s » Q2 » {q}_{perp}^2 corresponding to recent LHC experiments with Q2 of order of mass of Z-boson and transverse momentum of DY pair ∼ few tens GeV. The DY hadronic tensors are expressed in terms of quark and quark-gluon TMDs with frac{1}{Q^2} and frac{1}{N_c^2} accuracy. It is demonstrated that in the leading order in Nc the higher-twist quark-quark-gluon TMDs reduce to leading-twist TMDs due to QCD equation of motion. The resulting hadronic tensors depend on two leading-twist TMDs: f1 responsible for total DY cross section, and Boer-Mulders function {h}_1^{perp } . The corresponding qualitative and semi-quantitative predictions seem to agree with LHC data on five angular coefficients A0− A4 of DY pair production. The remaining three coefficients A5− A7 are determined by quark-quark-gluon TMDs multiplied by extra frac{1}{N_c} so they appear to be relatively small in accordance with LHC results.

Working process of steam turbine and establishment of start-up model

In the research of steam turbine rotor, start-up optimization is a very key research problem. A series of start-up optimization research can greatly improve the start-up efficiency of steam turbine and the safety performance of the unit. The start-up optimization of steam turbine is inseparable from the analysis of the start-up process of steam turbine and the mathematical model of the startup process of steam turbine unit, because the optimization of steam turbine unit can be regarded as a function to find the optimal solution. This paper analyzes the start-up process of 300 MW steam turbine, analyzes the start-up process of steam turbine unit through the data used in the actual power plant, and gives the mathematical model of cold start-up of steam turbine according to the start-up process of steam turbine, so as to further study the start-up optimization of steam turbine. Finally, the optimization model is determined by several key parameters, which are three weight coefficients α1,α2,α3, the actual damage value Di and damage limit value Dlim, and the start-up time ti and total start-up time t0 of each stage.

New in situ aerosol hyperspectral optical measurements over 300–700 nm – Part 1: Spectral Aerosol Extinction (SpEx) instrument field validation during the KORUS-OC cruise

Abstract. In situ observations of spectrally resolved aerosol extinction coefficients (300–700 nm at ∼ 0.8 nm resolution) from the May–June 2016 Korea–United States Ocean Color (KORUS-OC) oceanographic field campaign are reported. Measurements were made with the custom-built Spectral Aerosol Extinction (SpEx) instrument that previously has been characterized only using laboratory-generated aerosols of known size and composition. Here, the performance of SpEx under realistic operating conditions in the field was assessed by comparison to extinction coefficients derived from commercial instruments that measured scattering and filter-based absorption coefficients at three discrete visible wavelengths. Good agreement was found between these two sets of extinction coefficients with slopes near unity for all three wavelengths within the SpEx measurement error (± 5 Mm−1). The meteorological conditions encountered during the cruise fostered diverse ambient aerosol populations with varying sizes and composition at concentrations spanning 2 orders of magnitude. The sampling inlet had a 50 % size cut of 1.3 µm diameter particles such that the in situ aerosol sampling suite deployed aboard ship measured fine-mode aerosols only. The extensive hyperspectral extinction data set acquired revealed that nearly all measured spectra exhibited curvature in logarithmic space, such that Ångström exponent (α) power law fits could lead to large errors compared to measured values. This problem was particularly acute for α values calculated over only visible wavelengths and then extrapolated to the UV, highlighting the need for measurements in this wavelength range. Second-order polynomial fits to the logarithmically transformed data provided a much better fit to the measured spectra than the linear fits of power laws. Building on previous studies that used total column aerosol optical depth observations to examine the information content of spectral curvature, the relationship between α and the second-order polynomial fit coefficients (a1 and a2) was found to depend on the wavelength range of the spectral measurement such that any given α maps into a line in (a1, a2) coefficient space with a slope of −2LN(λch), where λch is defined as the single wavelength that characterizes the wavelength range of the measured spectrum (i.e., the “characteristic wavelength”). Since the curvature coefficient values depend on λch, it must be taken into account when comparing values from spectra obtained from measurement techniques with different λch. Previously published work has shown that different bimodal size distributions of aerosols can exhibit the same α yet have differing spectral curvature with different (a1, a2). This implies that (a1, a2) contain more information about size distributions than α alone. Aerosol size distributions were not measured during KORUS-OC, and the data reported here were limited to the fine fraction, but the (a1, a2) maps obtained from the SpEx data set are consistent with the expectation that (a1, a2) may contain more information than α – a result that will be explored further with future SpEx and size distribution data sets.

New in situ aerosol hyperspectral optical measurements over 300–700 nm – Part 2: Extinction, total absorption, water- and methanol-soluble absorption observed during the KORUS-OC cruise

Abstract. This two-part study explores hyperspectral (300–700 nm) aerosol optical measurements obtained from in situ sampling methods employed during the May–June 2016 Korea–United States Ocean Color (KORUS-OC) cruise conducted in concert with the broader air quality campaign (KORUS-AQ). Part 1 focused on the hyperspectral measurement of extinction coefficients (σext) using the recently developed in situ Spectral Aerosol Extinction (SpEx) instrument and showed that second-order polynomials provided a better fit to the measured spectra than power law fits. Two dimensional mapping of the second-order polynomial coefficients (a1, a2) was used to explore the information content of the spectra. Part 2 expands on that work by applying a similar analytical approach to filter-based measurements of aerosol hyperspectral total absorption (σabs) and soluble absorption from filters extracted with either deionized water (σDI-abs) or methanol (σMeOH-abs). As was found for σext, second-order polynomials provided a better fit to all three absorption spectra sets. Averaging the measured σext from Part 1 over the filter sampling intervals in this work, hyperspectral single-scattering albedo (ω) was calculated. Water-soluble aerosol composition from the DI extracts was used to examine relationships with the various measured optical properties. In particular, both σDI-abs(365 nm) and σMeOH-abs(365 nm) were found to be best correlated with oxalate (C2O42-), but elevated soluble absorption was found from two chemically and optically distinct populations of aerosols. The more photochemically aged aerosols of those two groups exhibited partial spectra (i.e., the longer wavelengths of the spectral range were below detection) while the less-aged aerosol of the other group exhibited complete spectra across the wavelength range. The chromophores of these groups may have derived from different sources and/or atmospheric processes, such that photochemical age may have been only one factor contributing to the differences in the observed spectra. The differences in the spectral properties of these groups was evident in (a1, a2) maps. The results of the two-dimensional mapping shown in Parts 1 and 2 suggest that this spectral characterization may offer new methods to relate in situ aerosol optical properties to their chemical and microphysical characteristics. However, a key finding of this work is that mathematical functions (whether power laws or second-order polynomials) extrapolated from a few wavelengths or a subrange of wavelengths fail to reproduce the measured spectra over the full 300–700 nm wavelength range. Further, the σabs and ω spectra exhibited distinctive spectral features across the UV and visible wavelength range that simple functions and extrapolations cannot reproduce. These results show that in situ hyperspectral measurements provide valuable new data that can be probed for additional information relating in situ aerosol optical properties to the underlying physicochemical properties of ambient aerosols. It is anticipated that future studies examining in situ aerosol hyperspectral properties will not only improve our ability to use optical data to characterize aerosol physicochemical properties, but that such in situ tools will be needed to validate hyperspectral remote sensors planned for space-based observing platforms.

Analytic solution to the generalized delay diffusion equation with uncertain inputs in the random Lebesgue sense

In this paper, we deal with the randomized generalized diffusion equation with delay: ut(t, x) = a2uxx(t, x) + b2uxx(t − τ, x), t &gt; τ, 0 ≤ x ≤ l; , t ≥ 0; , 0 ≤ t ≤ τ, 0 ≤ x ≤ l. Here, τ &gt; 0 and l &gt; 0 are constant. The coefficients a2 and b2 are nonnegative random variables, and the initial condition φ(t, x) and the solution u(t, x) are random fields. The separation of variables method develops a formal series solution. We prove that the series satisfies the delay diffusion problem in the random Lebesgue sense rigorously. By truncating the series, the expectation and the variance of the random‐field solution can be approximated.