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We present the results of our ALMA $\lesssim$0.5 kpc-resolution densemolecular line (HCN and HCO$^{+}$ J=2-1, J=3-2, and J=4-3) observations of 12nearby (ultra)luminous infrared galaxies ([U]LIRGs). After matching beam sizesof all molecular line data to the same values in all (U)LIRGs, we derivemolecular line flux ratios, by extracting spectra in the central 0.5, 1, 2 kpccircular regions, and 0.5-1 and 1-2 kpc annular regions. Based on non-LTE modelcalculations, we quantitatively confirm that the innermost ($\lesssim$0.5 kpc)molecular gas is very dense ($\gtrsim$10$^{5}$ cm$^{-3}$) and warm($\gtrsim$300 K) in ULIRGs, and that in one LIRG is also modestly dense(10$^{4-5}$ cm$^{-3}$) and warm ($\sim$100 K). We then investigate the spatialvariation of the HCN-to-HCO$^{+}$ flux ratios and high-J to low-J flux ratiosof HCN and HCO$^{+}$. A subtle sign of decreasing trend of these ratios fromthe innermost ($\lesssim$0.5 kpc) to outer nuclear (0.5-2 kpc) region isdiscernible in a significant fraction of the observed ULIRGs. For twoAGN-hosting ULIRGs which display the trend most clearly, we find based on aBayesian approach that the HCN-to-HCO$^{+}$ abundance ratio and gas kinetictemperature systematically increase from the outer nuclear to the innermostregion. We suggest that this trend comes from potential AGN effects, because nosuch spatial variation is found in a starburst-dominated LIRG.

ALMA 0.5 kpc Resolution Spatially Resolved Investigations of Nuclear  Dense Molecular Gas Properties in Nearby Ultraluminous Infrared Galaxies  Based on HCN and HCO$^{+}$ Three Transition Line Data