We present the results of the asteroseismic analysis of the red-giant star KIC 4351319 ( TYC 3124-914-1 ) , observed for 30 days in short-cadence mode with the Kepler satellite .
The analysis has allowed us to determine the large and small frequency separations , \Delta \nu _ { 0 } = 24.6 \pm 0.2 \mu Hz and \delta \nu _ { 02 } = 2.2 \pm 0.3 \mu Hz respectively , and the frequency of maximum oscillation power , \nu _ { max } = 386.5 \pm 4.0 \mu Hz . The high signal-to-noise ratio of the observations allowed us to identify 25 independent pulsation modes whose frequencies range approximately from 300 to 500 \mu Hz .

The observed oscillation frequencies together with the accurate determination of the atmospheric parameters ( effective temperature , gravity and metallicity ) , provided by additional ground-based spectroscopic observations , enabled us to theoretically interpret the observed oscillation spectrum . KIC 4351319 appears to oscillate with a well defined solar-type p-modes pattern due to radial acoustic modes and non-radial nearly pure p modes .
In addition , several non-radial mixed modes have been identified . Theoretical models well reproduce the observed oscillation frequencies and indicate that this star , located at the base of the ascending red-giant branch , is in the hydrogen-shell burning phase , with a mass of \sim 1.3 { M } _ { \odot } , a radius of \sim 3.4 R _ { \odot } and an age of \sim 5.6 Gyr .
The main parameters of this star have been determined with an unprecedent level of precision for a red-giant star , with uncertainties of 2 \% for mass , 7 \% for age , 1 \% for radius , and 4 \% for luminosity .