Excited-state dynamics of open quantum systems is analyzed by the hierarchical equations of motion (HEOM) or the thermalized time-evolving density operator with orthogonal polynomials algorithm (T-TEDOPA) method when a discrete abinitio linear vibronic model is parameterized by continuous temperature-dependent spectral densities leading to crossed correlation functions, i.e., correlated fluctuations of the energy gap collective modes. We focus on a conical intersection involving two collective modes tuning the energy of each excited state, and we revisit the transformation of the initial correlated tuning baths to de-correlated shared baths in order to reduce the computational resources. While a completely frequency-dependent transformation poses problems for HEOM, we find that in some particular cases, an optimal approximate frequency-independent transformation may be derived. On the contrary, T-TEDOPA is very efficient and allows us to use this frequency-dependent transformation at the price of managing long-range couplings in the tensor chain. An illustrative application is shown by using the linear vibronic coupling model of a planar symmetrical (phenylethynyl)benzene dimer.

Elliptic orthogonal polynomials and OPRL

Genetic parameter estimates and genetic trends for cow longevity indicators in Holstein cattle based on different culling reasons and random regression models.

The effect of increasing levels of coconut oil (CO: 0, 100, 200, and 300 g/kg of supplement DM) on productive performance, feed intake, rumen fermentation, microbiota, and gene expression was evaluated in 24 calves (Bos indicus × Bos taurus; 180 ± 10 kg BW) on rotational grazing (Cynodon dactylon) in a completely randomized design (n = 6) for 112 days. Supplement intake (offer–refusal) and forage intake (external marker: chromium) were measured. On day 112, rumen fluid (fermentation profile, protozoa, and metagenomic analysis: 16S rRNA V3-V4) and total blood (DNA microarray: M22k) were collected. Genomic analyses were performed by comparing the control vs. the group with the best productive response. For statistical analysis, SAS PROC GLM (initial weight as a covariate), orthogonal polynomials, the Tukey test, and Spearman correlation were used, considering significant effects (p ≤ 0.05) and trend (p ≤ 0.1). The inclusion of 200 g CO/kg supplement DM showed the best average daily gain (p = 0.018; +0.139 kg/d) with the highest retained energy (p = 0.02; +0.631 Mcal/d) versus the control group. In the rumen, propionate increased (p ≤ 0.05), while protozoa decreased (p < 0.0001) and the methanogenic archaea tended to decrease (Methanobacteriaceae −44%, p = 0.08; Thermoplasmatales −35%, p = 0.06). At the transcriptional level, 19 hub genes were modulated by CO, suggesting a lower intracellular signaling (cAMP-PKA-CREB) associated with a lower stress condition and better energy metabolism regulation. In conclusion, 200 g CO/kg supplement DM is a viable strategy for improving the productive performance of livestock in tropical systems.

Recurrence relations and the Christoffel–Darboux formula for a special class of elliptic orthogonal polynomials

The aim of this paper is to study the symmetrized form associated with a \(H_q\)-Laguerre-Hahn form, where \(H_q\) is the \(q\)-derivative operator. Given a \(H_q\)-Laguerre-Hahn form \(u\) of class \(s\), it is shown that its symmetrized form \(w\) is \(H_{\sqrt{q}}\)-Laguerre Hahn of class \(\tilde{s}\leq 2s+3\). We give the \(\sqrt{q}\)-Riccati equation satisfied by the Stieltjes formal series \(S(w)\) as well as a complete discussion of the class \(\tilde{s}\). As an application of this work, we generate two examples of symmetric \(H_{\sqrt{q}}\)-Laguerre-Hahn orthogonal polynomials of class two and three.

We study the monic orthogonal polynomials with respect to a perturbed Gaussian weight -1,\\enspace N, t>0. \\] ]]> w ( x ) = | x | α e − N ( x 2 2 + t x 4 4 ) , α > − 1 , N , t > 0. Using the ladder operator approach and the modified compatibility conditions, we show that the recurrence coefficients β n ( t ) are related to a particular discrete Painlevé equation. Differentiating the orthogonality relation, one obtains a second order ordinary differential equation about β n ( t ) . As n → ∞ , the asymptotic expansion of β n ( t ) is obtained with the aid of Dyson's Coulomb fluid approach. We also consider the Hankel determinant generated by our weight. The logarithmic derivative of the Hankel determinant can be expressed in terms of β n ( t ) . Through suitable transformation, the second order linear ordinary differential equation, satisfied by the orthogonal polynomials P n ( x ) , can be turn to a biconfluent Heun equation.

We consider the divided-difference operator D ω , the q-derivative one H q and the algebraic equation x 2 u = λxv , λ ∈ C ∖ { 0 } , in the regular case for the forms u and v. We study the D ω -semiclassical character and the variation of the class s ~ of u (respectively the H q -semiclassical case) where v is a symmetric D ω -semiclassical form of class s (respectively a symmetric H q -semiclassical form of class s). Some illustrative examples are highlighted in the two cases and integral representations or discrete one's are obtained.

Nonadiabatic effects arising from conical intersections between excited states play a crucial role in the optical properties of a wide range of chromophores and must be accounted for in first-principles modeling of spectral lineshapes. In this work, we investigate the importance of nonadiabatic effects in the absorption spectra of indole and cyanoindole derivatives by contrasting three modeling approaches. In the Gaussian-Condon and Gaussian-non-Condon theory formalisms, the linear response function is computed from excitation energy fluctuations of independent adiabatic excited states sampled along molecular dynamics trajectories, with the latter approach additionally including transition dipole moment fluctuations to account for Herzberg-Teller-type effects. In contrast, the tensor-network-based thermalized time-evolving density-matrix with orthogonal polynomials (T-TEDOPA) approach allows for numerically exact quantum dynamics simulations of explicitly coupled diabatic excited states. We find that only the explicit coupling of the two lowest-lying excited states, La and Lb, within the T-TEDOPA approach yields accurate absorption spectra for all systems, while an adiabatic treatment underestimates spectral contributions from excitations into states with highly mixed electronic character. We further elucidate the role of polar solvent stabilization of the charge-transfer character La state by comparing indole in vacuum and in water, showing that solvent effects significantly shape the ultrafast population transfer between excited states and contribute to differences in the experimental absorption lineshapes. Finally, we discuss the influence of cyano substituent position on the optical properties of cyanoindole derivatives through changes in the energy ordering of La and Lb, their relative transition dipole moments, and the stabilization of the charge-transfer state in a polar solvent.

Effects of dietary standardized ileal digestible crude protein levels on growth performance, meat quality, and Cecal microbiota of Arbor Acres broilers

The purpose of our paper is to provide a family of bilinear orthogonal expansions all based upon the same general pattern that is valid for a wide class of special functions. Our first family involves Jacobi, Laguerre, and Hermite polynomials. We give a discrete analogue of these bilinear expansions, the three families of classical orthogonal polynomials being replaced by zonal spherical functions associated with regular distance graphs. Such expansions playing a key role in the field of mathematical statistics, we show how our results apply to this field. We provide generalizations of the well-known Cramér–von Mises and Watson’s statistics, based upon an interpretation of their kernel in terms of the circular Laplacian. The product formula, well-known for zonal functions on Lie groups, is stated for distance-regular graphs, providing an elegant tool for proofs. Examples involving Hahn, q-Hahn, and Krawtchouk polynomials are given.

Ordinary differential equations are crucial in modeling complex phenomena in fluid mechanics, structural engineering, and damping systems. However, obtaining analytical solutions remains challenging due to inherent nonlinearities and intricate boundary conditions. This paper proposes a Perturbed Chebyshev Finite Difference Method (PCFDM) specifically designed to solve third-order ordinary differential equations (ODEs). The proposed framework integrates Chebyshev basis polynomials with a Legendre-based perturbation terms to enhance the approximation space and minimize truncation errors. Numerical experiments on third-order boundary value problems associated with draining and coating flows reveal that the PCFDM significantly outperforms conventional finite difference method (FDM) in terms of accuracy and computational efficiency. The results confirm that the integration of orthogonal polynomial and perturbation provides a flexible and reliable approach for solving high-order differential equations.

Genetic analyses of udder conformation traits and daily milk yield measured by robotic milking systems using repeatability and random regression models in American Holstein cattle.

In this article, we develop an approximate technique for solving a fractional advection-diffusion equation with a generalized Caputo derivative via a finite difference scheme. This technique employed the properties of shifted ultraspherical polynomials, which combine the finite difference scheme for the temporal discretization derivative and express the approximate solution in terms of shifted ultraspherical polynomials. The convergence and the stability of the proposed technique are proved. Numerical examples are considered, and the obtained results are compared with the analytical results and those obtained in the literature to establish the accuracy of the technique. The proposed techniques, based on the generalized Caputo derivative and the properties of shifted ultraspherical polynomials, produce robust results and encompass those obtained using several other families of orthogonal polynomials as demonstrated in the results of the examples considered.

This report presents estimates of any dietary supplement use in the past 30 days and number of dietary supplements taken among youth ages 0-19 years and among adults age 20 and older in the United States during August 2021-August 2023 as well as trends in use from 2013-2014 through August 2021-August 2023. National Health and Nutrition Examination Survey (NHANES) 30-day dietary supplement use questionnaire data were assessed. Analyses accounted for the complex survey design including nonresponse, noncoverage, and differential probability of selection. Variance estimates were computed using Taylor series linearization. Statistical comparisons were performed using linear regression for increasing or decreasing trends or using t tests for comparisons between groups. Trend tests over time were performed using orthogonal polynomial regression with linear and quadratic terms and accounting for the unequal duration and spacing of time between each survey cycle. During August 2021-August 2023, 35.7% of youth ages 0-19 years and 60.2% of adults age 20 and older used a dietary supplement in the past 30 days. Two or more dietary supplements were used by 11.3% of youth and 38.7% of adults. Use of two or more dietary supplements increased among youth and adults from 2013-2014 through August 2021-August 2023. Use of any dietary supplement also increased among adults.

An electrostatic model for the roots of discrete classical orthogonal polynomials

Intestinal health of broiler chickens fed red seaweed (Chondracanthus chamissoi) under dexamethasone-induced stress

Uniformly Stable Orthogonal Polynomial Weighted Finite Elements for Degenerate Elliptic Problems

This study investigated the interaction between dietary crude protein (CP) reduction and supplemental raw potato starch (RPS) on growth performance, nutrient digestibility, cecal short-chain fatty acids (SCFA) profiles, and cecal microbiota in broiler chickens. On day 7, birds were allocated to a 2 × 3 factorial arrangement in a randomized complete block design with eight replicates (22 birds per pen). Six dietary treatments comprised three CP levels (standard diet or reductions of 15 or 30 g/kg CP) and two RPS inclusion levels (20 or 40 g/kg) during both grower (day 7-21) and finisher (day 21-35) stages. The main effects of RPS level, as well as the linear and quadratic effects of dietary CP and their interactions, were evaluated using orthogonal polynomial contrasts. An interaction (P < 0.05) between RPS level and the quadratic effect of dietary CP levels was observed for weight gain and feed intake during the experimental period. Birds fed 20 g/kg RPS showed linear reductions in weight gain (WG) and feed intake (FI) as dietary CP decreased, whereas those fed 40 g/kg RPS showed a quadratic response, with the highest performance at the intermediate CP level. Cecal concentrations of acetate, butyrate, straight-chain fatty acids, and total SCFA on day 35 showed interactions (P < 0.05) between RPS level and dietary CP, following trends similar to growth performance. Isobutyrate and branched-chain fatty acids exhibited an interaction (P < 0.05) between RPS level and linear CP reduction, with linear decreases observed in birds fed 40 g/kg RPS but not in those fed 20 g/kg RPS. Irrespective of RPS level, decreasing dietary CP reduced the abundance of protein-fermenting microbes and enriched fiber-fermenting microbes (P < 0.05). Correlation analysis showed that straight-chain fatty acids were positively correlated with WG and negatively correlated with feed conversion ratio, whereas branched-chain fatty acids were negatively correlated with WG and FI. In conclusion, growth performance responses to reduced-protein diets in broilers can be modulated by dietary RPS inclusion level through shifts in cecal microbiota and fermentation patterns.

Second–order difference equation for quasi–orthogonal polynomials related to Hahn difference operator