Assessment of the Rice Panicle Initiation by Using NDVI-Based Vegetation Indexes

The assessment of rice panicle initiation is crucial for the management of nitrogen fertilizer application that affects yield and quality of grain. The occurrence of panicle initiation could be determined via either green ring, internode-elongation, or a 1–2 mm panicle, and was observed through manual dissection. The quadratic polynomial regression model was used to construct the model of the trend of normalized difference vegetation index-based vegetation indexes (NDVI-based VIs) between pre-tillering and panicle differentiation stages. The slope of the quadratic polynomial regression model tended to be alleviated in the period in which the panicle initiation stage should occur. The results indicated that the trend of the NDVI-based VIs was correlated with panicle initiation. NDVI-based VIs could be a useful indicator to remotely assess panicle initiation.

Qualitative Theory of Two-Dimensional Polynomial Dynamical Systems

A qualitative theory of two-dimensional quadratic-polynomial integrable dynamical systems (DSs) is constructed on the basis of a discriminant criterion elaborated in the paper. This criterion enables one to pick up a single parameter that makes it possible to identify all feasible solution classes as well as the DS critical and singular points and solutions. The integrability of the considered DS family is established. Nine specific solution classes are identified. In each class, clear types of symmetry are determined and visualized and it is discussed how transformations between the solution classes create new types of symmetries. Visualization is performed as series of phase portraits revealing all possible catastrophic scenarios that result from the transition between the solution classes.

Optimal Control of a 5-Link Biped Using Quadratic Polynomial Model of Two-Point Boundary Value Problem

To walk over constrained environments, bipedal robots must meet concise control objectives of speed and foot placement. The decisions made at the current step need to factor in their effects over a time horizon. Such step-to-step control is formulated as a two-point boundary value problem (2-BVP). As the dimensionality of the biped increases, it becomes increasingly difficult to solve this 2-BVP in real-time. The common method to use a simple linearized model for real-time planning followed by mapping on the high dimensional model cannot capture the nonlinearities and leads to potentially poor performance for fast walking speeds. In this paper, we present a framework for real-time control based on using partial feedback linearization (PFL) for model reduction, followed by a data-driven approach to find a quadratic polynomial model for the 2-BVP. This simple step-to-step model along with constraints is then used to formulate and solve a quadratically constrained quadratic program to generate real-time control commands. We demonstrate the efficacy of the approach in simulation on a 5-link biped following a reference velocity profile and on a terrain with ditches. A video is here: https://youtu.be/-UL-wkv4XF8.

On Polynomial Solutions of Pell’s Equation

Polynomial Pell’s equation is x 2 − D y 2 = ± 1 , where D is a quadratic polynomial with integer coefficients and the solutions X , Y must be quadratic polynomials with integer coefficients. Let D = a 2 x 2 + a 1 x + a 0 be a polynomial in Z x . In this paper, some quadratic polynomial solutions are given for the equation x 2 − D y 2 = ± 1 which are significant from computational point of view.

The Pintz–Steiger–Szemerédi estimate for intersective quadratic polynomials in function fields

Let [Formula: see text] be the polynomial ring over the finite field [Formula: see text] of [Formula: see text] elements. For a natural number [Formula: see text] let [Formula: see text] be the set of all polynomials in [Formula: see text] of degree less than [Formula: see text] Let [Formula: see text] be a quadratic polynomial over [Formula: see text] Suppose that [Formula: see text] is intersective, that is, which satisfies [Formula: see text] for any [Formula: see text] with [Formula: see text] where [Formula: see text] denotes the difference set of [Formula: see text] Let [Formula: see text] Suppose that [Formula: see text] and that the characteristic of [Formula: see text] is not divisible by 2. It is proved that [Formula: see text] for any [Formula: see text] where [Formula: see text] is a constant depending only on [Formula: see text] and [Formula: see text]

Release flux of heavy metals from river sediments at different flow rates

This paper simulates sediment motion under different hydrodynamic conditions, aiming to investigate the release flux of heavy metals in river sediments. During the lab experiments, carried out in a circular rectangular flume device, water velocity in the flume was altered by controlling the gate switch, and the flow rate was controlled from 0 to 1 m/s. Sediment from the Le'an River and chlorine-removed tap water were used as experimental sediment and water, respectively. Through analyses of Cu, Zn, Cd, and Pb concentration in water at different flow rates, the relationship between the release flux (y) of Cu, Zn, Cd, and Pb and the flow rate (x) was established with a fitting error of less than 15%. In order to judge the reliability of the conclusions, experimental results were verified outdoors. The results showed when the sediment particle size is between 0 and 250 μm, within 1 hour, a quadratic polynomial correlation between the release flux of Cu, Cd, and Pb from river sediments and water velocity when the water pH is 5–9 and the flow rate is 0–65 cm/s; when the water pH is 5–9, the flow rate is 0–35 cm/s, the release flux of Zn from river sediments was shown to have a quadratic polynomial relationship with water velocity. The error between the calculated and measured values of heavy metals released from sediment in the Le'an River were within 5–30%. Our results can provide a theoretical reference for the control and treatment of heavy metal pollution in rivers and further improve corresponding water quality models.

Response surface design for removal of Cr(VI) by hydrogel-supported sulfidated nano zero-valent iron (S-nZVI@H)

In this study, a new sulfidated nanoscale zero valent iron (S-nZVI) supported on hydrogel (S-nZVI@H) was successfully synthesized for the removal of Cr(VI) from groundwater. The surface morphology, dispersion phenomenon and functional groups of novel S-nZVI@H were characterized by scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR). Box-Behnken design (BBD) optimization technology based on response surface methodology (RSM) is applied to demonstrate the influence of the interaction of S-nZVI@H dose, initial Cr(VI) concentration, contact time, and initial pH with the Cr(VI) removal efficiency. The AVOVA results (F = 118.73, P < 0.0001, R2 = 0.9916) show that the quadratic polynomial model is significant enough to reflect the close relationship between the experimental and predicted values. The predicted optimum removal conditions are determined to be as follows: S-nZVI@H dose 9.46 g/L, initial Cr(VI) concentration 30 mg/L, contact time 40.7 min and initial pH 5.27, and the S-nZVI@H dose is the key factor affecting the removal of Cr(VI). The predicted value (99.76%) of Cr (VI) removal efficiency is in good agreement with the experimental value (97.75%), which verifies the validity of the quadratic polynomial model. This demonstrates that RSM with appropriate BBD can be considerably utilized to optimize the design of experiments for removal of Cr(VI).