Asymmetric circular graph with Hosoya index and negative continued fractions

It has been known that the Hosoya index of caterpillar graph can be calculated as the numerator of the simple continued fraction. Recently in [MATCH Commun. Math. Comput. Chem. 2020, 84 (2), 399-428], the author introduces a more general graph called caterpillar-bond graph and shows that its Hosoya index can be calculated as the numerator of the general continued fraction. In this paper, we show how the Hosoya index of the graph with non-uniform ring structure can be calculated from the negative continued fraction. We also give the relation between some radial graphs and multidimensional continued fractions in the sense of the Hosoya index.

MATHEMATICAL MODELLING OF VIBRATIONS OF NON-UNIFORM RING-SHAPED ULTRASONIC WAVEGUIDES

The article describes technique for modelling of ultrasonic vibrations amplifiers, which are implemented in the form of non-uniform ring-shaped waveguides, based on application of harmonic balance method. Bending vibrations of the waveguide are described by means of non-uniform integral and differential equations equivalent to Euler–Bernoulli equations in order to simplify calculation of amplitude-frequency characteristics of vibrations, particularly, to exclude the need of working with singular matrices. Using harmonic balance method, equations of vibrations are reduced to overdetermined non-uniform linear system of algebraic equations, which least-squares solution is determined by means of pseudo-inverse matrix. On the basis of analysis of numerical example possibility of existence of variable-sign and constant-sign vibration modes of the waveguide is shown and it is determined that for realization of amplifying function it is necessary to use waveguide at constant-sign vibration mode. The constant-sign vibration modes are combinations of bending defor-mation and extensional deformation of central line of the waveguide and they are detected due to accounting extensibility of the central line in equations of vibrations. Validity of the obtained results is confirmed by comparing them to the results of modelling by means of finite element method.

Design and Fabrication of Non-Uniform Spacing Multiple Floating Field Limiting Rings for 6500V 4H-SiC JBS Diodes

Designed for 6500V 4H-SiC JBS diodes, a highly-efficient termination structure of a non-uniform multiple floating field limiting rings (MFFLR) featuring with a non-uniform ring spacing and a multiple region division is studied and purposed. For each region, ring spacing is modulated independently by a multiplication factor and a linear increment factor. The non-uniform MFFLR structure is simulated and optimized for a better electric field distribution and a higher breakdown voltage. Based on the simulation results, 4H-SiC JBS diodes with the optimized non-uniform termination designs are fabricated. Experimental results show that the SiC JBS diode with optimized non-uniform MFFLR termination structure can achieve a breakdown voltage of up to 7800 V, and its termination efficiency is about 94% of an ideal parallel-plane junction’s. Our results demonstrate that the optimized non-uniform MFFLR termination structure is capable for SiC JBS diodes with breakdown voltage of 6500V and above. Our results can provide a valuable design methodology of edge termination structures for other high-voltage SiC devices.

Vibro-Acoustics Characteristics of Non-Uniform Ring Stiffened Cylindrical Shells Using Wave Propagation Approach

Based on Donnell’s thin shell theory and basic equations, the wave propagation method is discussed here in detail, which is used to investigate the vibration and sound radiation characteristics of non-uniform ring stiffened cylindrical shells under various boundary conditions. The structure damp effects of cylindrical shells are investigated and the ring ribs were considered very narrow, and the rib forces are considered in radial direction. The conclusion are drawn that with the structural loss factor changing large, the whole pressure level are changed little, but the peak of resonance are slacking down obviously; The shell’s resonance frequency can be changed with irregular ring stiffened cylindrical shell .The work will give some guidelines for noise reduction of this kind of shell.