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We establish some relative volume comparison theorems for extremal volume forms of Finsler manifolds under suitable curvature bounds. As their applications, we obtain some results on curvature and topology of Finsler manifolds. Our results remove the usual assumption on S-curvature that is needed in the literature. [ABSTRACT FROM AUTHOR]

Analysis on the modified phase reversal structure of electro-optic modulators. Bandwidth of integrated electro-optic modulators; Electrode structure; Mathematical analysis using Newton's iteration method; Frequency response of electro-optic modulator; Half-wave voltage and the bandwidth to the half-wave voltage (BVR) ratio; Optimization of the overlap integral for each section of a phase reversal modulator; Conclusions.

Low-temperature scanning gate microscopy (LT-SGM) studies of graphene allow one to obtain important spatial information regarding coherent transport such as weak localization (WL) and universal conductance fluctuations. Although fascinating LT-SGM results on pristine graphene prepared by mechanical exfoliation have been reported in the literature, there appears to be a dearth of LT-SGM results on chemical vapor deposition (CVD)-grown graphene whose large scale and flexible substrate transferability make it an ideal candidate for coherent electronic applications. To this end, we have performed LT-SGM studies on CVD-grown graphene wide constriction (0.8 μm), which can be readily prepared by cost-effective optical lithography fully compatible with those in wafer foundry, in the WL regime. We find that the movable local gate can sensitively modulate the total conductance of the CVD graphene constriction possibly due to the intrinsic grain boundaries and merged domains, a great advantage for applications in coherent electronics. Moreover, such a conductance modulation by LT-SGM provides an additional, approximately magnetic-field-independent probe for studying coherent transport such as WL in graphene and spatial conductance variation. [ABSTRACT FROM AUTHOR]