The evolutionary ayntheaio rnethod is applied to calculate Mgl+MgH λ 5150 and TiO λ 7150 absorption features of integrated spectra and integrated UBV colours of a stellar system. These calculations are used to investigate star formation rate in nuclei of some spiral galaxies. The (IMg, B-V) diagram is shown to be a goo discriminator between metallicity and star formation effects. Star formation rates, metallicities and initial mass function slopes are obtained for the nuclei of 8 spiral galaxies. Star formation rates in nuclei correlate with rotation velocities of galaxies. Dynamical friction of gas clouds system in a galactic stellar disk is the possible cause of that correlation.
This paper deals with the determination of global star formation rates (SPRs) from radlo free-free and submm/FIR dust emission. Masslve, hot and luminous stars interact with the surrounding
interstellar matter (ISM) lonlzing the gas and heating the dust. O star formation rates (OSFR) in the galactic disk are estimated with observed Lyman continuum photon production rates. Extrapolation to lower mass stars with a constant inltial mass function (IMF) yields, however, too high total SFRs. Furthermore, the lock-up rate, i.e. the rate at whlch gas transformed into stars is permanently locked up in low mass and dead stars, can not reproduce the present-day mass distribution of the galactic disk. Agreement between Lyc photon production rate and time integrated lockup rate can be reached by introducing bimodal star formation in the galactic disk. Thls means that induced star formation in main spiral arms produces only masslve stars ≥3mq. while spontaneous star formation in the interarm region produces stars in the total mass range ≥0.1 mq.
Estimates of SFR based on Lyc photon production rates can not easily be applied to external galaxies because of the difficulty to separate radio synchroton and free-free emission. It is found that slmilar problems are encountered in separating the emission from warm dust (heated by OB stars) and cold dust (heated by the general Interstellar radiation field). The relation between IR luminoslťy and star formation actlvity of galaxies is much more complex than previously assumed.
Let $G$ be a multigraph. The star number ${\mathrm s}(G)$ of $G$ is the minimum number of stars needed to decompose the edges of $G$. The star arboricity ${\mathrm sa}(G)$ of $G$ is the minimum number of star forests needed to decompose the edges of $G$. As usual $\lambda K_n$ denote the $\lambda $-fold complete graph on $n$ vertices (i.e., the multigraph on $n$ vertices such that there are $\lambda $ edges between every pair of vertices). In this paper, we prove that for $n \ge 2$ \[ \begin{aligned} {\mathrm s}(\lambda K_n)&= \left\rbrace \begin{array}{ll}\frac{1}{2}\lambda n&\text{if}\ \lambda \ \text{is even}, \frac{1}{2}(\lambda +1)n-1&\text{if}\ \lambda \ \text{is odd,} \end{array}\right. {\vspace{2.0pt}} {\mathrm sa}(\lambda K_n)&= \left\rbrace \begin{array}{ll}\lceil \frac{1}{2}\lambda n \rceil &\text{if}\ \lambda \ \text{is odd},\ n = 2, 3 \ \text{or}\ \lambda \ \text{is even}, \lceil \frac{1}{2}\lambda n \rceil +1 &\text{if}\ \lambda \ \text{is odd},\ n\ge 4. \end{array}\right. \end{aligned} \qquad \mathrm{(1,2)}\].