Equation for condensed matter phase transitions

Concludes combined equation for the pressure drop in the apparatus with stationary and fluidized granular layer, and the resulting recursive equation is used to calculate phase transitions of matter, from the atomic granularity of matter to granular (particulate) material.

Pengaruh Dwelling Time pada Penerimaan Pajak Impor di Indonesia

High dwelling time in Indonesia has been in the spotlight of President since his visit to the Port of Tanjung Priok in 2014. This could bring impact on international trade, one of which is indicated by import tax revenue. The value of import in Indonesia which continues to fall has brought impact to lower country revenue from import tax. The objective of this study is to analyze the effect of dwelling time on import tax revenue in Indonesia. The results from recursive equation system of Error Correction Model (ECM) by using data during January 2014 to November 2016 show that lower dwelling time will increase import tax revenue in Indonesia. ------------------------------------ Lamanya dwelling time menjadi sorotan Presiden RI sejak kunjungannya ke Pelabuhan Tanjung Priok tahun 2014 silam. Hal ini dapat berdampak pada perdagangan internasional, salah satunya diukur dari penerimaan pajak impor. Nilai impor Indonesia yang terus turun berdampak pada rendahnya penerimaan negara dari pajak impor. Penelitian ini bertujuan menganalisis pengaruh dwelling time pada penerimaan pajak impor di Indonesia. Berdasarkan hasil estimasi sistem persamaan rekursif Error Correction Model (ECM) dengan data periode Januari 2014–November 2016 diketahui bahwa dwelling time yang lebih rendah akan meningkatkan penerimaan pajak impor di Indonesia.

Fast Calculation Methods for Reliability of Connected-(r,s)-out-of-(m,n):F Lattice System in Special Cases

A connected-(r,s)-out-of-(m,n):F lattice system consists of components arranged as an (m,n) matrix, and fails if and only if the system has an (r,s) sub-matrix where all components fail. Though the previous study has proposed the recursive equation for computing the system reliability, it takes much time to compute the reliability. For one-dimensional systems, a matrix formula was provided based on the existing recursive equation when the system consists of independent and identically distributed components. The numerical experiments showed that the matrix formula was more efficient than the recursive equation. In contrast, for two-dimensional systems, the recursive equation is comparatively complex, so that it is difficult to drive a matrix formula directly from the recursive equation. In this study, we derive general forms of matrices for computing the reliability of the connected-(r,s)-out-of-(m,n):F lattice system consisting of independent and identically distributed components in the case of and . We compare our proposed method with the recursive equation in order to verify the effectiveness of the proposed method using numerical experiments.

Normal Limiting Distribution of the Size of Binary Interval Trees

The limiting distribution of the size of binary interval tree is investigated. Our illustration is based on the contraction method, and it is quite different from the case in one-sided binary interval tree. First, we build a distributional recursive equation of the size. Then, we draw the expectation, the variance, and some high order moments. Finally, it is shown that the size (with suitable standardization) approaches the standard normal random variable in the Zolotarev metric space.

Rational Divide-and-Conquer Relations

A rational divide-and-conquer relation, which is a natural generalization of the classical divide-and-conquer relation, is a recursive equation of the form f(bn)=R(f(n),f(n),…,f(b−1)n)+g(n), where b is a positive integer ≥2; R a rational function in b−1 variables and g a given function. Closed-form solutions of certain rational divide-and-conquer relations which can be used to characterize the trigonometric cotangent-tangent and the hyperbolic cotangent-tangent function solutions are derived and their global behaviors are investigated.

Characteristic Points of Recursive Systems

Characteristic points have been a primary tool in the study of a generating function defined by a single recursive equation. We investigate the proper way to adapt this tool when working with multi-equation recursive systems. Given an irreducible non-negative power series system with $m$ equations, let $\rho$ be the radius of convergence of the solution power series and let $\pmb{\tau}$ be the values of the solution series evaluated at $\rho$. The main results of the paper include: (a) the set of characteristic points form an antichain in ${\mathbb R}^{m+1}$, (b) given a characteristic point $(a,\mathbf{b})$, (i) the spectral radius of the Jacobian of $\pmb \gamma$ at $(a, \mathbf{b})$ is $\ge 1$, and (ii) it is $=1$ iff $(a,\mathbf{b}) = (\rho,\pmb{\tau})$, (c) if $(\rho,\pmb{\tau})$ is a characteristic point, then (i) $\rho$ is the largest $a$ for $(a,\mathbf{b})$ a characteristic point, and (ii) a characteristic point $(a,\mathbf{b})$ with $a=\rho$ is the extreme point $(\rho,\pmb{\tau})$.