The oscillator is an electronic circuit that is widely used in electronic devices. One of the mathematical models that describe the oscillator problem is the conservative nonlinear oscillator equation. In this study, the conservative nonlinear oscillator equation is discussed in the form of  where  and  are odd functions. The purpose of this study is to find a solution to the conservative nonlinear oscillator equation and to know the simulation of the obtained solution. The method used to find the solution to the equation is the homotopy perturbation method which is a combination of the homotopy and perturbation methods. The search for a solution to the conservative nonlinear oscillator equation using the homotopy perturbation method is also modified by the Lindstedt-Poincare method to deal with secular terms. The simulation results show that the greater the value of , the smaller the angular frequency produced and the fewer waves formed.

Land values in NJOP used as a basis for taxing land are often different from land values in the Land Value Zone (ZNT). The difference in land values contained in the NJOP and ZNT causes uncertainty about local tax revenue and creates injustice for the government and the community. Based on this, an analysis of Assesment Sales Ratio (ASR) is used to determine the determination of land values in NJOP with ZNT against the standard size determined by the International Association of Assessing Officers (IAAO). The results of the ASR analysis show that the determination of NJOP in Pamijahan Village, Plumbon District, Cirebon Regency is outside the standard range set by the IAAO, which is 0.90 to 1.10 (90% -110%). This can be seen from the results of the measurement of central tendency, which is a mean of 10.53%, a median of 0.1037, and a weighted mean of 6.136%. The comparisons between components of the measurement results of the central tendency indicate the occurrence of regressivity or downtrend. The Assessment Ratio in Pamijahan Village, Plumbon District, Cirebon Regency also did not show good uniformity, as indicated by a COD value of 0.66% and a COV value of 70.02% which were outside the standard set by IAAO i.e. the minimum and maximum values for COD and COV are 5% and 20%, respectively.

The accuracy of survey results depends on sample size. So far, in determining the sample size of the stratified random sampling method, researchers still use manual calculations. Because of that, this research aims to create a sample size determination program of  the stratified random sampling method using C++ and PHP programming languages. This research begins with the study of literacy, creating flowcharts and pseudocode algorithms, writing program syntax, and implementing data on the number of civil servants in each UPK in Banyumas Regency. By entering a 95% confidence level, the error limit that can be tolerated is 5, and the strata cost of each is 1, the minimum sample size is 60 with the 1st and 2nd strata sample sizes is 45 and 15. The program is expected to help researchers to determine sample size more easily. So far, the program also minimizes errors in calculations because a warning will appear when an error occurs.

We discuss the properties of the fundamental solution of multidimensional anomalous diffusion equation such as symmetric, decay, nonnegative, normality, and bounded in mathematical analysis approach.

In this article, we discuss the semigroup-like property of Mittag-Leffler function which is used to solve the initial value problem of an ordinary differential equation involving Caputo fractional derivative.