Abstract-Numerical computations of frequency domain field problems or elliptical partial differential equations may be based on differential equations or integral equations. The new concept of field computation presented in this paper is based on the postulate of the existence of linear equations of the discretized nodal values of the fields, different from the conventional equations, but leading to the same solutions. The postulated equations are local and invariant to excitation. It is shown how the equations can be determined by a sequence of "measures." The measured equations are particularly useful at the mesh boundary, where the finite difference methods fail. The measured equations do not assume the physical condition of absorption, so they are also applicable to concave boundaries. Using the measured equations, we can terminate the finite difference mesh very close to the physical boundary and still obtain robust solutions. It will definitely make a great impact on the way we apply finite difference and finite element methods in many problems. Computational results using the measured equations of invariance in two and three dimensions are presented.

Background and objectives To improve the nutritional value and flavor of traditional Chinese noodles, Hericium erinaceus powder (HEP) was incorporated into Chinese noodles. The effects of HEP on the digestion, gelatinization of starch, and quality characteristics of Chinese noodles were analyzed. Findings The results showed that adding HEP could significantly reduce starch digestion rate and digestion extent in noodle, and the antioxidant capacity and gelatinization temperature were also positively related to the amount of HEP. The water absorption and cooking loss of noodles were improved by HEP, and noodle color was also impacted, showing increased L*, a* and b* values. Incorporation of HEP apparently affected texture profile analysis of noodles, resulting in increased hardness, gumminess, and chewiness. When <6% of HEP was incorporated, noodle quality was not dramatically changed, although starch digestibility was significantly inhibited. More HEP could further reduce starch digestion and increase antioxidant capacity; however, noodle quality might be deteriorated. Conclusions In our study, it found that incorporation up to a 6% of HEP into the noodles yielded an acceptable product with improved nutraceutical properties. Significance and novelty The results provided guidance for the development of functional noodles and facilitated the comprehensive application of HEP.

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The power-aware SI (Signal Integrity) simulation takes into account the effect of the power supply noise. It is one of the key issues in the high-speed multi-level package system design. The multi-level package co-design requires a corresponding accurate modeling approach to include all signal, crosstalk and power noise effects to support the poweraware SI simulation.A general co-design approach to multi-level package modeling base on individual single-level package full-wave S-parameter modeling including signal and power/ground ports defined at chip-package and package-board vertical contact arrays is proposed in this paper with three features. Firstly, it includes not only the signal ports, but also the power and ground ports to support the power-aware SI simulations. Secondly, a port in the single-level model by this approach is seamlessly connectable to the corresponding port in another model by virtually connecting not only the port signal terminals, but also the port reference terminals. Thirdly, it combines package DC simulation and high-frequency fullwave simulation to guarantee wide band accuracy.A simple test case of a module-board-module with 20 ports on each module, and 20 ports on the board is used to verify the proposed method by both AC and nonlinear transient simulations.Another simple test case shows that the models by this approach can be used to fully model the transmission line structure in package even in the case of any transmission line referencing.

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