In this paper, we first give two new definitions for q-analytic functions. We also define a line q-integral. Finally, using these q-integrals obtain version of complex q-Green's formula.

Consider a sequence of n independent observations from a population of increasing size αi, i = 1,2,... and an absolutely continuous initial distribution function. The distribution of the kth record value is represented as a countable mixture, with mixing the distribution of the kth record time and mixed the distribution of the nth order statistic. Precisely, the distribution function and (pow...

1. Examples Example 1.1. The field extension Q(√ 2, √ 3)/Q is Galois of degree 4, so its Galois group has order 4. The elements of the Galois group are determined by their values on √ 2 and √ 3. The Q-conjugates of √ 2 and √ 3 are ± √ 2 and ± √ 3, so we get at most four possible automorphisms in the Galois group. See Table 1. Since the Galois group has order 4, these 4 possible assignments of v...

We consider autonomous holonomic dynamical systems defined by equations of the form $\ddot{q}^{a}=-\Gamma_{bc}^{a}(q) \dot{q}^{b}\dot{q}^{c}$ $-Q^{a}(q)$, where $\Gamma^{a}_{bc}(q)$ are coefficients a symmetric (possibly non-metrical) connection and $-Q^{a}(q)$ generalized forces. prove theorem which for these determines time-dependent first integrals (FIs) any order in systematic way, using `s...