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In literature, synthesis of cascaded lossless commensurate lines have been realized via some iterative methods. So to be able to obtain the value of an element which is not the first one, the designer has to obtain all the values ...
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In literature, synthesis of cascaded lossless commensurate lines have been realized via some iterative methods. So to be able to obtain the value of an element which is not the first one, the designer has to obtain all the values of the elements connected before the desired one. But in this paper, explicit synthesis formulae of the networks containing cascaded lossless commensurate lines up to three have been derived analytically, and all the element values can be calculated independently.
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We study the quasi-isometric rigidity of a large family of finitely generated groups that split as graphs of groups with virtually free vertex groups and two-ended edge groups. Let G be a group that is one-ended, hyperbolic relati...
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We study the quasi-isometric rigidity of a large family of finitely generated groups that split as graphs of groups with virtually free vertex groups and two-ended edge groups. Let G be a group that is one-ended, hyperbolic relative to virtually abelian subgroups, and has JSJ decomposition over two-ended subgroups containing only virtually free vertex groups that are not quadratically hanging. Our main result is that any group quasi-isometric to G is abstractly commensurable to G. In particular, our result applies to certain "generic" HNN extensions of a free group over cyclic subgroups.
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In the steady-state of lossless circuits, resonance can be obtained using the Laplace transform. We focus on commensurate transmission line circuits constructed using eight unit elements as an example and determine the resonance, ...
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In the steady-state of lossless circuits, resonance can be obtained using the Laplace transform. We focus on commensurate transmission line circuits constructed using eight unit elements as an example and determine the resonance, transient response, and nonstationary response of the circuits using a z-transform. In old quantum theory, light quanta are assumed to satisfy the heat conduction equation. When considering the response of light quanta as a physical phenomenon from the viewpoint of circuit theory, we can interpret that the heat conduction equation describes the propagation of waves on a lossy distributed RC transmission line, in which light quanta repeatedly collide with each other. We demonstrate that light quanta are different from photons, which are interpreted as satisfying the Maxwell's equations and propagating on a lossless transmission line.
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In this paper, an alternative approach is presented, to design equalizers (or matching networks) with commensurate (or equal length) transmission lines. The new method automatically yields the matching network topology with charac...
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In this paper, an alternative approach is presented, to design equalizers (or matching networks) with commensurate (or equal length) transmission lines. The new method automatically yields the matching network topology with characteristic impedances of the commensurate lines. In the implementation process of the new technique tirst, the driving point impedance data of the matching network is generated by tracing a pre-selected transducer power gain shape, without optimization. Then, it is modelled as a realizable bounded-real input reflection coefficient in Richard domain, which in turn yields the desired equalizer topology with line characteristic impedances. This process results in an excellent initial design for the commercially available computer aided design (CAD) packages to generate final circuit layout for fabrication. An example is given to illustrate the utilization of the new method. It is expected that the proposed design technique is employed as a front-end, to commercially available computer aided design (CAD) packages which generate the actual equalizer circuit layout with physical dimensions for mass production.
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For commensurate transmission line circuits constructed using a unit element, transient responses as well as resonance as a steady-state response can be obtained. Such circuits can be analyzed using the z-transform, and transient ...
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For commensurate transmission line circuits constructed using a unit element, transient responses as well as resonance as a steady-state response can be obtained. Such circuits can be analyzed using the z-transform, and transient responses that vary with time can be obtained. In addition, unit elements are symmetrical and lossless circuit elements. If the phase of a unit element is nπ and the internal resistance of the power source is equal to the load resistance, resonance occurs. Resonance also occurs if the phase of a unit element is nπ + π/2 and the product of the internal resistance and the load resistance is equal to the square of the characteristic resistance of the unit element.
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摘要 :AbstractGroups acting properly and discontinuously on the Cartesian product$$\mathbb {H}^{2}\times \mathbb {H}^{2}$$of two hyperbolic planes are termedhyperabelianby Picard. The automorphism group$$\mathrm {Aut}f$$of a q...
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AbstractGroups acting properly and discontinuously on the Cartesian product$$\mathbb {H}^{2}\times \mathbb {H}^{2}$$of two hyperbolic planes are termedhyperabelianby Picard. The automorphism group$$\mathrm {Aut}f$$of a quaternary integral quadratic formfof index 2 is an example of a hyperabelian group. Hence the quotient orbifold$$Q_{f}$$of the action of$$\mathrm {Aut}f$$on$$\mathbb {H}^{2}\times \mathbb {H}^{2}$$is a 4-dimensional arithmetic orbifold, endowed with a natural$$\mathbb {H}^{2}\times \mathbb {H}^{2}$$-geometry. Plücker coordinates are used to understand$$Q_{f}$$. A real automorphismUof收起
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A system of vortices in a quasi-two-dimensional HTSC plate with periodic pinning is considered. The magnetization curves are calculated by the Monte Carlo method for different values of an external magnetic field and different tem...
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A system of vortices in a quasi-two-dimensional HTSC plate with periodic pinning is considered. The magnetization curves are calculated by the Monte Carlo method for different values of an external magnetic field and different temperatures. It is shown that the vortex system with periodic pinning may crystallize with an increase in temperature. (C) 2002 MAIK "Nauka / Interperiodica". [References: 13]
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Active networks whose only state elements are commensurate transmission lines are analysed using topological methods. The state equations of these networks are derived in explicit form and four output equations are derived, depend...
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Active networks whose only state elements are commensurate transmission lines are analysed using topological methods. The state equations of these networks are derived in explicit form and four output equations are derived, depending on the choice of the output vector. No restrictions on the topology of the networks are required for the existence of these forms. An example of the applications of the results is given.
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Synthesis of vertical heterostructures that include atomically thin layers of materials with topologically nontrivial energy bands is desirable for exploring exotic quantum states. Here, the authors report on atomic‐layer‐by‐la...
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Synthesis of vertical heterostructures that include atomically thin layers of materials with topologically nontrivial energy bands is desirable for exploring exotic quantum states. Here, the authors report on atomic‐layer‐by‐layer deposition of magnesium on copper(111) surface by molecular beam epitaxy, monitored in situ by low‐energy electron microscopy and diffraction, and modeled by ab initio theory. It is found that a 2D MgCu2 intermetallic compound forms during initial Mg deposition and persists till a full monolayer of Mg is formed. Deposition of additional Mg triggers a phase transition from the commensurate MgCu2 to an incommensurate Mg2Cu layer and enables growth of the second layer of Mg. Ab initio calculations indicate non‐trivial topology of the electron bands in the interfacial Mg2Cu layer and the existence of Dirac nodal lines near the Fermi level. The new 2D Mg2Cu material emerges as a promising platform to study new topological states of matter.
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Exact synthesis of compact and wide-band filters with stub-loaded multiple-mode resonators is investigated in this letter. The multi-mode behavior and characteristics of the proposed filter structure are studied by conventional na...
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Exact synthesis of compact and wide-band filters with stub-loaded multiple-mode resonators is investigated in this letter. The multi-mode behavior and characteristics of the proposed filter structure are studied by conventional natural modes analysis. To develop the complete synthesis procedure, a bandpass prototype in the $S$-plane is used for good spurious suppression and size reduction. Approximation of the driving point impedance then proceeds, with the help of transformed variable. Network elements are then extracted by using Richards' theorem. The method is demonstrated by a design example of a third-order bandpass filter. Although six elements are used in this design, the total length is only one third of the wavelength at its center frequency. The experiment results justify the proposed procedure.
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