Let G be a k-regular connected graph of order at least six. If G has girth three, its 3-restricted edge connectivity λ3(G) ≤3k-6. The equality holds when G is a cubic or 4-regular connected vertex-transitive graph w...Let G be a k-regular connected graph of order at least six. If G has girth three, its 3-restricted edge connectivity λ3(G) ≤3k-6. The equality holds when G is a cubic or 4-regular connected vertex-transitive graph with the only exception that G is a 4-regular graph with λ3(G) = 4. Furthermore, λ3(G) = 4 if and only if G contains K4 as its subgraph.展开更多
设G=(V,E)是一个连通图,边集S(?)E是一个3-限制性边割,如果G-S是不连通的并且G-S的每个分支至少有三个点.图G的3-限制性边连通度λ_3(G)是G中最小的一个3-限制性边割的基数.图G是λ_3(G)连通的,如果3-限制性边割存在.G是λ_3-最优的,如...设G=(V,E)是一个连通图,边集S(?)E是一个3-限制性边割,如果G-S是不连通的并且G-S的每个分支至少有三个点.图G的3-限制性边连通度λ_3(G)是G中最小的一个3-限制性边割的基数.图G是λ_3(G)连通的,如果3-限制性边割存在.G是λ_3-最优的,如果λ_3(G)=ξ_3(G),其中ξ_3(G)=min{|[U,(?)]|:U(?)V,|U|=3 and G[U]是连通的).G[U]表示V的子集U的导出子图,(?)=V\U表示U的补.[U,(?)]是一条边的一个端点在U中另一个端点在(?)中的边的集合.本文给出了不含三角形的图是λ_3-最优的一些充分条件.展开更多
Piezoelectric properties and related figures of merit are studied in novel 1-3-type composites based on ferroelectric domain-engineered lead-free single crystal with the relatively large longitudinal piezoelectric coe...Piezoelectric properties and related figures of merit are studied in novel 1-3-type composites based on ferroelectric domain-engineered lead-free single crystal with the relatively large longitudinal piezoelectric coefficient d_(33).Relationships between the piezoelectric properties and the set of figures of merit are analyzed for the 1-3 and 1-3-0 composites that contain the same single-crystal and polymer components.For a composite characterized by 1-3-0 connectivity,an influence of a porous piezo-passive matrix on the figures of merit and their volume-fraction behavior is considered additionally.A large anisotropy of figures of merit is observed in the 1-3-0 composite with specific porous matrices.A diagram is put forward to show volume-fraction regions of the large anisotropy of figures of merit of the studied 1-3-0 composite.Due to large figures of merit and their considerable anisotropy,the studied lead-free composites can be applied in piezoelectric energy-harvesting systems,sensors,transducers,and so on.展开更多
In the present work,piezoelectric composite films made of Polyaniline(PAni)coated Lead Zirconate Titanate(PZT)particles immersed into polyvinylidene fluoride(PVDF)matrix were characterized by mechanical tests,and the ...In the present work,piezoelectric composite films made of Polyaniline(PAni)coated Lead Zirconate Titanate(PZT)particles immersed into polyvinylidene fluoride(PVDF)matrix were characterized by mechanical tests,and the connectivity of the com-posite sample was determined using dielectric measurements and applying the Poon–Shin model.The composite was considered a binary system with coated PZT particles as one phase and the polymer matrix the other one.To support the result obtained from theoretical analysis,scanning electron microscopy of the composites were done.It was observed a decrease up to 85%on the mechanical resistance when the ceramic volume fraction increases from 0%to 40%.Furthermore,the composite film no longer can be considered with 0–3 connectivity when the ceramic content is 30 vol.%or over.展开更多
文摘Let G be a k-regular connected graph of order at least six. If G has girth three, its 3-restricted edge connectivity λ3(G) ≤3k-6. The equality holds when G is a cubic or 4-regular connected vertex-transitive graph with the only exception that G is a 4-regular graph with λ3(G) = 4. Furthermore, λ3(G) = 4 if and only if G contains K4 as its subgraph.
基金supported by NSFC (No.10671165)XJEDU (No.2004G05).
文摘设G=(V,E)是一个连通图,边集S(?)E是一个3-限制性边割,如果G-S是不连通的并且G-S的每个分支至少有三个点.图G的3-限制性边连通度λ_3(G)是G中最小的一个3-限制性边割的基数.图G是λ_3(G)连通的,如果3-限制性边割存在.G是λ_3-最优的,如果λ_3(G)=ξ_3(G),其中ξ_3(G)=min{|[U,(?)]|:U(?)V,|U|=3 and G[U]是连通的).G[U]表示V的子集U的导出子图,(?)=V\U表示U的补.[U,(?)]是一条边的一个端点在U中另一个端点在(?)中的边的集合.本文给出了不含三角形的图是λ_3-最优的一些充分条件.
基金The authors are grateful to Prof.Dr.I.A.Parinov and Prof.Dr.A.E.Panich(Southern Federal University,Russia),and Prof.Dr.C.R.Bowen(University of Bath,UK)for their interest in the field of modern piezo-active materials and applications.Research was financially supported by Southern Federal University,grant No.VnGr-07/2020-04-IM(Ministry of Science and Higher Education of the Russian Federation).
文摘Piezoelectric properties and related figures of merit are studied in novel 1-3-type composites based on ferroelectric domain-engineered lead-free single crystal with the relatively large longitudinal piezoelectric coefficient d_(33).Relationships between the piezoelectric properties and the set of figures of merit are analyzed for the 1-3 and 1-3-0 composites that contain the same single-crystal and polymer components.For a composite characterized by 1-3-0 connectivity,an influence of a porous piezo-passive matrix on the figures of merit and their volume-fraction behavior is considered additionally.A large anisotropy of figures of merit is observed in the 1-3-0 composite with specific porous matrices.A diagram is put forward to show volume-fraction regions of the large anisotropy of figures of merit of the studied 1-3-0 composite.Due to large figures of merit and their considerable anisotropy,the studied lead-free composites can be applied in piezoelectric energy-harvesting systems,sensors,transducers,and so on.
文摘In the present work,piezoelectric composite films made of Polyaniline(PAni)coated Lead Zirconate Titanate(PZT)particles immersed into polyvinylidene fluoride(PVDF)matrix were characterized by mechanical tests,and the connectivity of the com-posite sample was determined using dielectric measurements and applying the Poon–Shin model.The composite was considered a binary system with coated PZT particles as one phase and the polymer matrix the other one.To support the result obtained from theoretical analysis,scanning electron microscopy of the composites were done.It was observed a decrease up to 85%on the mechanical resistance when the ceramic volume fraction increases from 0%to 40%.Furthermore,the composite film no longer can be considered with 0–3 connectivity when the ceramic content is 30 vol.%or over.
