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Let 0 < γ1 < ⋯ ≤ γk ≤ ⋯ be the sequence of imaginary parts of nontrivial zeros of the Riemann zetafunction. In [R. Macaitienė and D. Šiaučiūnas, Joint universality of Hurwitz zeta-functions and nontrivial zeros of the Riemann zeta-function, Lith. Math. J., 59(1):81–95, 2019] a joint universality theorem on the approximation of analytic functions by shifts of the Hurwitz zeta-functions ζ(s + ihγk, α1), ..., ζ(s + ihγk, αr) has been obtained. In the paper, we prove universality theorems for the compositions F(ζ(s + ihγk, α1), ..., ζ(s + ihγk, αr)) for some classes of operators in the r-dimensional space of analytic functions. [ABSTRACT FROM AUTHOR]

Breast cancer is the most common cause of mortality due to cancer for women both in Lithuania and worldwide. Chances of survival after diagnosis differ significantly depending on the stage of disease at the time of diagnosis. Extended term periods are required to estimate survival of, e.g., 15–20 years. Moreover, since mortality of the average population changes with time, estimates of survival of cancer patients derived after a long period of observation can become outdated and can be no longer used to estimate survival of patients who were diagnosed later. Therefore, it can be useful to construct analytic functions that describe survival probabilities. Shorter periods of observation can be enough for such construction. We used the data collected by the Lithuanian Cancer Registry for our analysis. We estimated the chances of survival for up to 5 years after patients were diagnosed with breast cancer in Lithuania. Then we found analytic survival functions which best fit the observed data. At the end of this paper, we provided some examples for applications and directions for further research. We used mainly the Kaplan–Meier method for our study. [ABSTRACT FROM AUTHOR]