On the value distribution of a differential monomial and some normality criteria

The aim of this paper is to study the zero distribution of the differential polynomial $\displaystyle af^{q_{0}}(f')^{q_{1}}...(f^{(k)})^{q_{k}}-\varphi,$where $f$ is a transcendental meromorphic function and $a=a(z)(\not\equiv 0,\infty)$ and $\varphi(\not\equiv 0,\infty)$ are small functions of $f$. Moreover, using this value distribution result, we prove the following normality criterion for family of analytic functions:\\ {\it Let $\mathscr{F}$ be a family of analytic functions on a domain $D$ and let $k \geq1$, $q_{0}\geq 2$, $q_{i} \geq 0$ $(i=1,2,\ldots,k-1)$, $q_{k}\geq 1$ be positive integers. If for each $f\in \mathscr{F}$: i.\ $f$ has only zeros of multiplicity at least $k$,\ ii.\ $\displaystyle f^{q_{0}}(f')^{q_{1}}\ldots(f^{(k)})^{q_{k}}\not=1$,then $\mathscr{F}$ is normal on domain $D$.

Indirect Inference Estimation of Spatial Autoregressions

The ordinary least squares (OLS) estimator for spatial autoregressions may be consistent as pointed out by Lee (2002), provided that each spatial unit is influenced aggregately by a significant portion of the total units. This paper presents a unified asymptotic distribution result of the properly recentered OLS estimator and proposes a new estimator that is based on the indirect inference (II) procedure. The resulting estimator can always be used regardless of the degree of aggregate influence on each spatial unit from other units and is consistent and asymptotically normal. The new estimator does not rely on distributional assumptions and is robust to unknown heteroscedasticity. Its good finite-sample performance, in comparison with existing estimators that are also robust to heteroscedasticity, is demonstrated by a Monte Carlo study.

Pengaruh Iklim Kerja, Kompensasi, dan Kompetensi terhadap Produktivitas Kerja pada STMIK Dharma Putra

Compensation is everything that will be received by a person as remuneration for the work she/he has done, either directly or indirectly. Assessment of labor productivity is almost always automatically associated with the rules and regulations of individual salary increases and bonus distribution. Result of the analysis indicates work environment played a very important role for the improvement of labor productivity with r2 = 0.933 (93.3%), and t 8.158 and t table 0.30. Result of the hypothesis testing of the effect of compensation onemployee and lecturer productivity (r2=0.933 or 93.3 % with t 3.729 and t table of 0.30) means compensation had a very strong influence. Result of the hypothesis testing of the effect of competence on employee and lecturerproductivity shows r2= 0.933 or by 93.3%, with t 4.014 and t table 0.30. Result of the analysis shows the correlation between work environment and labor productivity is equal to 0.769, means it had a fairly high correlation. The correlation between compensation and labor productivity by 0.482 is moderate. The correlation between competence and labor productivity by 0509 is moderate. The determination determination is equal to 0.933 means that employee and lecturer productivity was influenced by work environment, compensation, and competency in the amount of 0.933 (93.3%); while the 6.7% remaining was influenced by other variables outside the research. The regression function resulted from the analysis is Y = -0.026 + 0.548 X1 + 0.260 X2 + 0.281 X3.

q-ADDITIVE FUNCTIONS ON POLYNOMIAL SEQUENCES

The present paper deals with functions acting only on the digits of an q-ary expansion. In particular, let n be a positive integer, then we denote by [Formula: see text] its q-ary expansion. We call a function f strictly q-additive if it acts only on the digits of a representation, i.e. [Formula: see text] The goal is to prove that if p is a polynomial having at least one coefficient with bounded continued fraction expansion, then [Formula: see text] This result is motivated by the asymptotic distribution result of Bassily and Kátai and a similar result of Peter.

PHYSICS OF RANDOMNESS AND REGULARITIES FOR CITIES, LANGUAGES, AND THEIR LIFETIMES AND FAMILY TREES

Time evolution of the cities and languages is considered in terms of multiplicative noise1 and fragmentation2 processes; where power law (Pareto-Zipf law)3 and slightly asymmetric log-normal (Gauss)4 distribution result for the size distribution of the cities and for that of the languages, respectively. The cities and the languages are treated differently (and as connected; for example, the languages split in terms of splitting the cities, etc.) and thus two distributions are obtained in the same computation at the same time. Evolutions of lifetimes and families for the cities and the languages are also studied. We suggest that the regularities may be evolving out of randomness, in terms of the relevant processes.

A distribution result for slices of sums of squares

Asymptotically, the solutions of Waring’s problem follow a limit law of which we are able to compute explicitly the limit density. In the special cases of sums of 3 and 4 squares where such a result is not possible, we establish a distribution result for slices of at least h0(n) consecutive integers ending at n, that is integers from n−h0(n)+1 to n, where h0(n) = nε for 4 squares and h0(n) = n¼+ε for 3 squares (ε > 0). We then deduce from this study the asymptotic behaviour of some kind of Riemann sums with an arithmetic constraint for which we point out an application related to the study of Schrödinger equation.