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We employ the corrected Gaia Early Data Release 3 (EDR3) photometric data and spectroscopic data from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) DR7 to assemble a sample of approximately 0.25 million FGK dwarf photometric standard stars for the 12 J-PLUS filters using the Stellar Color Regression (SCR) method. We then independently validated the J-PLUS DR3 photometry, and uncovered significant systematic errors: up to 15 mmag in the results of Stellar Locus (SL) method, and up to 10 mmag mainly caused by magnitude-, color-, and extinction-dependent errors of the Gaia XP spectra with the Gaia BP/RP (XP) Synthetic Photometry (XPSP) method. We have also further developed the XPSP method using the corrected Gaia XP spectra by Huang et al. (2023) and applied it to the J-PLUS DR3 photometry. This resulted in an agreement of 1-5 mmag with the SCR method, and a two-fold improvement in the J-PLUS zero-point precision. Finally, the zero-point calibration for around 91% of the tiles within the LAMOST observation footprint is determined through the SCR method, with the remaining approximately 9% of tiles outside this footprint relying on the improved XPSP method. The re-calibrated J-PLUS DR3 photometric data establishes a solid data foundation for conducting research that depends on high-precision photometric calibration., Comment: ApJS accepted; 21 papes; 20 figures, see main results in Figures 5 and 12

A Deterministic affine quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the value function is differentiable and therefore satisfies the corresponding Hamilton-Jacobi-Bellman equation in the classical sense. Moreover, the so-called quasi-Riccati equation is derived and any optimal control admits a state feedback representation., Comment: 30 pages