Oscillation Criteria for First Order Linear Difference Equations with Several Delay Arguments

The difference equation with delayed arguments ∆u(k) + Σpₗ(k) u(τₗ(k)) = 0, is considered, where ∆u(k) = u(k + 1) − u(k), pₗ : N → R, τₗ : N → N, lim k→+∞ τₗ (k) = +∞, i = 1, ..., m. In the paper sufficient conditions are established for all proper solutions of the above equation to be oscillatory.The difference equation with delayed arguments ∆u(k) + Σpₗ(k) u(τₗ(k)) = 0, is considered, where ∆u(k) = u(k + 1) − u(k), pₗ : N → R, τₗ : N → N, lim k→+∞ τₗ (k) = +∞, i = 1, ..., m. In the paper sufficient conditions are established for all proper solutions of the above equation to be oscillatory. Розглянуто рiзницеве рiвняння з запiзненнями в аргументах ∆u(k) + Σpₗ(k) u(τₗ(k)) = 0, де u(k) = u(k + 1) − u(k), pₗ : N → R, τₗ : N → N, lim k→+∞ τₗ (k) = +∞, i = 1, ..., m. Знайдено достатнi умови для того, щоб всi правильнi розв’язки рiвняння були осцилюючими

The Asymptotic value of the Locating-Chromatic number of nn-ary Tree

In 2013, Welyyanti et al. proved that $\chi_L(T(n,k))\leq n+k-1$ for all positive integers $n,k\geq2$. In this paper we prove that for any fixed integer $k\geq2$, almost all $n$-ary Tree $T(n,k)$ satisfy $\chi_L(T(n,k))=n+k-1$, moreover $\lim\limits_{n\to \infty} \chi_L(T(n,k))-n=k-1$.Comment: 4 Pages, 1 figur

Analisis Yuridis Pengurusan Harta Kekayaan Anak Angkat di Bawah Umur pada Wni Keturunan Tionghoa (Studi Kasus Putusan Mahkamah Agung Nomor : 2161 K/pdt/2011)

Child adoption can be considered as a legal act which assigns a child from his biological parents to the other parents who will be responsible for his care and education; the adoptive parents have to bring him up in their own surrounding according to the Ruling of the District Court. The research used judicial normative with descriptive analytic approach. The result of the research showed that the legal guardian, Amini Nurdin, filed a complaint to the defendant I, Lim Agek alias Agek and the defendant II, Lim Asiong alias Asiong. The Supreme Court of the Republic of Indonesia vacated the Rulings of Pakanbaru District Court and of Pakanbaru Appellate Court and stated that the defendant I, Lim Agek alias Agek and the Defendant II, Lim Asiong alias Asiong had performed breach of contract or default and required both of them to return the three ingots of pure gold owned by the three under-aged adopted children to their legitimate guardian, Amini Nurdin, based on the Court\u27s Ruling

Euler's Limit -- Revisited

The aim of this short note is that if $\{ a_{n}\}$ and $\{ b_{n}\}$ are two sequences of positive real numbers such that $a_{n}\to +\infty$ and $b_n$ satisfying the asymptotic formula $b_n\sim k\cdot a_{n}$, where $k>0$, then $\lim\limits_{n\to\infty}\left(1+\frac{1}{a_{n}}\right)^{b_{n}}= e^{k}$.Comment: 1 pag