A Lepskiĭ-type stopping rule for the covariance estimation of multi-dimensional Lévy processes

We suppose that a Lévy process is observed at discrete time points. Starting from an asymptotically minimax family of estimators for the continuous part of the Lévy Khinchine characteristics, i.e., the covariance, we derive a data-driven parameter choice for the frequency of estimating the covariance. We investigate a Lepskiĭ-type stopping rule for the adaptive procedure. Consequently, we use a balancing principle for the best possible data-driven parameter. The adaptive estimator achieves almost the optimal rate. Numerical experiments with the proposed selection rule are also presented.

New Clause in Bank Credit Agreement in Relation to Consumer Protection Act (Study on PT. Bank Negara Indonesia, Tbk. Denpasar Branch)

Credit agreement in standard form which is being made unilaterally by the bank until present is still becoming a special legal issue in agreement field of civil law. In addition, viewed from the side of the agreement it is also against consumer protection law as set in Consumer Protection Act. Problem formulation of is divided into namely regarding the existence of standard clause in bank agreement if associated with Article 18 of Consumer Protection Act and legal consequence of standard clause in credit agreement associated with consumer protection. This study aims to identify the presence of standard clause in banking agreement if related with Article 18 of Consumer Protection Act and legal consequence to the standard clause in credit contract is associated with consumer protection. The research is a juridical empirical. The location is on PT. Bank Negara Indonesia in Denpasar city. The author is guided by laws and regulations related with public fact, that is first problem formulation is analyzed from balancing principle and next the second problem formulation is from consumer protection theory. The result shows that the implementation of the provision tends to protect the bank as businesses. Moreover, the legal consequence of Bank BNI’s credit contract which does not meet the provision will result in null and void.

New Clause in Bank Credit Agreement in Relation to Consumer Protection Act (Study on PT. Bank Negara Indonesia, Tbk. Denpasar Branch)

Credit agreement in standard form which is being made unilaterally by the bank until present is still becoming a special legal issue in agreement field of civil law. In addition, viewed from the side of the agreement it is also against consumer protection law as set in Consumer Protection Act. Problem formulation of is divided into namely regarding the existence of standard clause in bank agreement if associated with Article 18 of Consumer Protection Act and legal consequence of standard clause in credit agreement associated with consumer protection. This study aims to identify the presence of standard clause in banking agreement if related with Article 18 of Consumer Protection Act and legal consequence to the standard clause in credit contract is associated with consumer protection. The research is a juridical empirical. The location is on PT. Bank Negara Indonesia in Denpasar city. The author is guided by laws and regulations related with public fact, that is first problem formulation is analyzed from balancing principle and next the second problem formulation is from consumer protection theory. The result shows that the implementation of the provision tends to protect the bank as businesses. Moreover, the legal consequence of Bank BNI’s credit contract which does not meet the provision will result in null and void.

Soliton Solutions of Mathematical Physics Models Using the Exponential Function Technique

This paper is based on finding the exact solutions for Burger’s equation, Zakharov-Kuznetsov (ZK) equation and Kortewegde vries (KdV) equation by utilizing exponential function method that depends on the series of exponential functions. The exponential function method utilizes the homogeneous balancing principle to find the solutions of nonlinear equations. This method is simple, wide-reaching and helpful for finding the exact solution of nonlinear conformable PDEs.

Rotor Balancing Via an Enhanced Automatic Dynamic Balancer With Inductively Coupled Shunt Circuit

Despite the elegant nature of the automatic balancing principle for passive imbalance vibration control, the co-existence of undesired whirling limit-cycles is a major impediment to the more widespread application of automatic dynamic balancing devices also called automatic dynamic balancer (ADB) in industry. To enlarge the region of stable perfect balancing and to eliminate whirling limit-cycles, we develop an innovative enhanced ADB system. This new idea harnesses the automatic balancing principle via moving permanent magnet balancer masses which are inductively coupled to a parallel resistor–inductor–capacitor (RLC) circuit. It is found that the circuit parameters can be adjusted properly to suppress the whirling limit-cycle to enlarge the perfect balancing region. We start from a Lagrangian description of the system and get nonlinear autonomous equations-of-motion. We then solve two dominant steady-state solutions for the enhanced ADB system. One solution is for the perfect balancing equilibrium points (EPs), which can be solved analytically. While the other solution is for the whirling limit-cycle which is solved via a harmonic balance method. The stability of these solutions is then evaluated through eigenvalue analysis and Floquet theory. The newly involved electrical parameters, such as coupling coefficient, equivalent capacitance, and equivalent resistance, are designed via an arc-length continuation method to destabilize the limit-cycle solutions to then guarantee stable rotor balancing.

An Improved Skewness Balancing Filtering Algorithm Based on Thin Plate Spline Interpolation

Most filtering algorithms suffer from complex parameter settings or threshold adjusting. To solve this problem, this paper proposes an improved skewness balancing filtering algorithm based on thin plate spline (TPS) interpolation. The proposed algorithm filters the nonground points in an iterative manner. A reference surface that reflects the fluctuation of the terrain is generated using the TPS interpolation method. Accordingly, the elevation difference from each point to the surface can be calculated. By applying the skewness balancing principle to these elevation differences, nonground points can be removed automatically. To verify the validity and robustness of the proposed method, the datasets provided by the International Society for Photogrammetry and Remote Sensing (ISPRS) were adopted. The experimental results show that this presented method can adapt to complex environments and achieve a higher filtering accuracy than the traditional skewness balancing algorithm. Moreover, in comparison with the other eight filtering methods tested by the ISPRS and four improved filtering methods proposed recently, the proposed method achieved an average total error of 5.39%, which is smaller than that of most of these other methods.