A Three-Pole Substrate Integrated Waveguide Bandpass Filter Using New Coupling Scheme

A novel three-pole substrate integrated waveguide (SIW) bandpass filter (BPF) using new coupling scheme is proposed in this paper. Two high order degenerate modes (TE102 and TE201) of a square SIW cavity and a dominant mode (TE101) of a rectangular SIW cavity are coupled to form a three-pole SIW BPF. The coupling scheme of the structure is given and analyzed. Due to the coupling between two cavities, as well as the coupling between source and load, three transmission zeros are created in the stopband of the filter. The proposed three-pole SIW BPF is designed and fabricated. Good agreement between simulated and measured results verifies the validity of the design methodology well

An alternative approach to determining average distance in a class of scale-free modular networks

Various real-life networks of current interest are simultaneously scale-free and modular. Here we study analytically the average distance in a class of deterministically growing scale-free modular networks. By virtue of the recursive relations derived from the self-similar structure of the networks, we compute rigorously this important quantity, obtaining an explicit closed-form solution, which recovers the previous result and is corroborated by extensive numerical calculations. The obtained exact expression shows that the average distance scales logarithmically with the number of nodes in the networks, indicating an existence of small-world behavior. We present that this small-world phenomenon comes from the peculiar architecture of the network family.Comment: Submitted for publicactio

An Optimal Support Function related to the Strong Openness Property

In the present article, we obtain an optimal support function of weighted $L^2$ integrations on superlevel sets of weights of multiplier ideal sheaves, which implies the strong openness property of multiplier ideal sheaves.Comment: 23 pages, some typos are correcte

Zhou valuations and jumping numbers

In this article, we prove that for any Zhou valuation $\nu$, there exists a graded sequence of ideals $\mathfrak{a}_{\bullet}$ and a nonzero ideal $\mathfrak{q}$ such that $\nu$ $\mathscr{A}-$computes the jumping number $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{a}_{\bullet})$, and that for the subadditive sequence $\mathfrak{b}^{\varphi}_{\bullet}$ related to a plurisubharmonic function $\varphi$, there exists a Zhou valuation which $\mathscr{A}-$computes $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{b}^{\varphi}_{\bullet})$, where the ``$\mathscr{A}-$compute'' coincides with the ``compute'' in Jonsson-Musta\c{t}\u{a}'s Conjecture when the Zhou valuation $\nu$ is quasimonomial. We also give a characterization for a valuation being a Zhou valuation.Comment: 19 pages, all comments are welcome

A generalization of the conjugate Hardy H2H^2 spaces

In this article, we consider a generalization of the conjugate Hardy $H^2$ spaces, and give some properties of the minimal norm of the generalization and some relations between the norm of the generalization and the minimal $L^2$ integrals. As applications, we give some monotonicity results for the conjugate Hardy $H^2$ kernels and the Bergman kernels on planar regions, and some relations between the conjugate Hardy $H^2$ kernels and the Bergman kernels on planar regions.Comment: 22 pages, all comments are welcome