Abstract This paper examines the capacitance properties of capacitors operating under alternating current up to 200 KHz, utilizing an LCR meter from the firm “R @ SH” (Germany, Munich). Considering the dielectric material’s frequency-dependent behavior, predictions regarding the alteration in the dielectric constant at elevated frequencies were calculated. The analysis led to a determination regarding the suitability of different capacitor models... This paper examines the capacitance properties of capacitors operating under alternating current up to 200 KHz, utilizing an LCR meter from the firm “R @ SH” (Germany, Munich). Considering the dielectric material’s frequency-dependent behavior, predictions regarding the alteration in the dielectric constant at elevated frequencies were calculated. The analysis led to a determination regarding the suitability of different capacitor models for the specified frequency range. Read More Read Less

Abstract A memory-efficient algorithm is developed and implemented to address the reverse issue of determining the variable density within a curvilinear layer from gravitational information. This algorithm is structured around the stabilized bi-conjugated gradient approach. By approximating the SLAE matrix with a Toeplitz-block-Toeplitz structure, the modification dramatically lowers the need for memory. The parallel versions of the algorithm were created for... A memory-efficient algorithm is developed and implemented to address the reverse issue of determining the variable density within a curvilinear layer from gravitational information. This algorithm is structured around the stabilized bi-conjugated gradient approach. By approximating the SLAE matrix with a Toeplitz-block-Toeplitz structure, the modification dramatically lowers the need for memory. The parallel versions of the algorithm were created for the Uran supercomputer, utilizing a combination of MPI+OpenMP technology. The practicality of this algorithm was demonstrated through its successful application to a model problem featuring synthetic data. Read More Read Less

Abstract A diagram of a polynomial of the nth degree in the real number line helps us identify all the real solutions. The number of real solutions can range from 0 to n. The remaining solutions are complex and not directly shown by the diagram. In the article, besides the diagram of the fundamental polynomial, two additional diagrams are created, which... A diagram of a polynomial of the nth degree in the real number line helps us identify all the real solutions. The number of real solutions can range from 0 to n. The remaining solutions are complex and not directly shown by the diagram. In the article, besides the diagram of the fundamental polynomial, two additional diagrams are created, which enable us to depict all complex solutions on the same real number line. The use of this approach is thoroughly explored for solving a cubic polynomial. In this scenario, the approach exhibits unique characteristics compared to polynomials of different degrees. Considering well-known formulas for the solutions of polynomials of degrees 3 and 4, the additional diagrams of the approach provide precise formulas for polynomials of order n up to 10. Read More Read Less

Abstract This paper discusses the methods for creating coherence maps for processing SAR image pairs. It outlines the acceptable range of coherence values for the averaging window. Based on these findings, the paper also introduces a method for enhancing map coherence. The SAR interferogram calculation using this enhanced method is carried out. The paper demonstrates an improvement in accuracy compared to... This paper discusses the methods for creating coherence maps for processing SAR image pairs. It outlines the acceptable range of coherence values for the averaging window. Based on these findings, the paper also introduces a method for enhancing map coherence. The SAR interferogram calculation using this enhanced method is carried out. The paper demonstrates an improvement in accuracy compared to traditional techniques. Read More Read Less