Abthors introduce the notation of generalized geometric constructions in Rm generated by a directed graph G and by a sequence of similarity ratios which are labelled with the edges of this graph. In this paper, it is ...Abthors introduce the notation of generalized geometric constructions in Rm generated by a directed graph G and by a sequence of similarity ratios which are labelled with the edges of this graph. In this paper, it is obtained the Hausdorff dimension and measure of this construction object for some cases.展开更多
Letτbe a generalized Thue-Morse substitution on a two-letter alphabet{a,b}:τ(a)=ambm,τ(b)=bmam for the integer m≥2.Letξbe a sequence in{a,b}Z that is generated byτ.We study the one-dimensional Schr?dinger operat...Letτbe a generalized Thue-Morse substitution on a two-letter alphabet{a,b}:τ(a)=ambm,τ(b)=bmam for the integer m≥2.Letξbe a sequence in{a,b}Z that is generated byτ.We study the one-dimensional Schr?dinger operator Hm,λon l2(Z)with a potential given by v(n)=λVξ(n),whereλ>0 is the coupling and Vξ(n)=1(Vξ(n)=-1)ifξ(n)=a(ξ(n)=b).LetΛ2=2,and for m>2,letΛm=m if m≡0 mod 4;letΛm=m-3 if m≡1 mod 4;letΛm=m-2if m≡2 mod 4;letΛm=m-1 if m≡3 mod 4.We show that the Hausdorff dimension of the spectrumσ(Hm,λ)satisfies that dimHσ(Hm,λ)>logΛm/(log 64m+4).It is interesting to see that dimHσσ(Hm,λ)tends to 1 as m tends to infinity.展开更多
Let S = Pi(i=1)(infinity){0, 1, ..., r - 1} and (R) over bar the general Sierpinski carpet, Let mu be the induced probability measure on (R) over bar of <(mu)over tilde> on S by phi, where phi is the natural sur...Let S = Pi(i=1)(infinity){0, 1, ..., r - 1} and (R) over bar the general Sierpinski carpet, Let mu be the induced probability measure on (R) over bar of <(mu)over tilde> on S by phi, where phi is the natural surjection from S onto (R) over bar and <(mu)over tilde> is the infinite product probability measure corresponding to probability vector (b(0), ..., b(r-1)) with b(i) = a(i)(logn) (m-1)/m(alpha). Authors show that dim(H) mu = (C) under bar(L)(mu) = (C) over bar(L)(mu) = (C) under bar(mu) = (C) over bar C(mu) = alpha.展开更多
Let R be a ring. We define a dimension, called P-cotorsion dimension, for modules and rings. The aim of this article is to investigate P-cotorsion dimensions of modules and rings and the relations between P-cotorsion ...Let R be a ring. We define a dimension, called P-cotorsion dimension, for modules and rings. The aim of this article is to investigate P-cotorsion dimensions of modules and rings and the relations between P-cotorsion dimension and other homological dimensions. This dimension has nice properties when the ring in consideration is generalized morphic.展开更多
We introduce generalized excellent extension of ring R in [4]. If S is a generalized excellent extension of R, we prove that (1) wgldim S≤ wgldim R and glodim S≤ gldim R; (2) the relations between rings R and rings S.
As a proper setting to study Gorenstein projective and injective dimensions of modules via vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced, which is a non-trivial generali...As a proper setting to study Gorenstein projective and injective dimensions of modules via vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced, which is a non-trivial generalization of Gorenstein rings. Moreover, a new proof for Bennis and Mahdou's equality of global Gorenstein dimension is given.展开更多
The giant magneto-impedance（GMI）effect of amorphous wire was analyzed theoretically.The amorphous wire had strong GMI effect in the stimulation of sharp pulse of 680kHz and18 mV.A pulse generator was designed to pro...The giant magneto-impedance（GMI）effect of amorphous wire was analyzed theoretically.The amorphous wire had strong GMI effect in the stimulation of sharp pulse of 680kHz and18 mV.A pulse generator was designed to provide high frequency pulse to a magnetic impedance（MI）element.The induced voltage on the pickup coil wound on the amorphous wire was sampled and held with a detect circuit using analog switch.A stable magnetic sensor was constructed.A three-dimension micro magnetic field detector was designed with a central controller MSP430F449.High stability and sensitivity were obtained in the MI sensor with the detect circuit.Experiment results showed that the resolution of the detector was 1nT in the full scale of±2 Oe and the detector worked stably from the room temperature to about 80℃.A small ferromagnetic target was detected by the three-dimension detector in laboratory environment without magnetic shielding.The target moving direction was ascertained with the wave shape of axis parallel in that direction.展开更多
为解决在三维空间状态下零件无法自动标注尺寸的问题,提出一种采用基于模型的定义(Model Based Definition,MBD)技术的零件三维尺寸自动标注方法。首先根据工艺和拓扑相关的表面(Technologically and Topologically Related Surfaces,TT...为解决在三维空间状态下零件无法自动标注尺寸的问题,提出一种采用基于模型的定义(Model Based Definition,MBD)技术的零件三维尺寸自动标注方法。首先根据工艺和拓扑相关的表面(Technologically and Topologically Related Surfaces,TTRS)理论的功能表面分类和边界表示(Boundary Representation,B-Rep)方法,提取出零件的所有拓扑表面,并消除重复多余的表面;然后将提取出的零件表面进行分类,并提取出对应的几何元素;根据其需要标注的定形和定位尺寸制定规则,进而去除冗余元素,构建标注元素集合;最后对CATIA进行二次开发实现零件尺寸的自动标注功能,完成尺寸信息模型的构建。展开更多
文摘Abthors introduce the notation of generalized geometric constructions in Rm generated by a directed graph G and by a sequence of similarity ratios which are labelled with the edges of this graph. In this paper, it is obtained the Hausdorff dimension and measure of this construction object for some cases.
基金supported by the National Natural ScienceFoundation of China(11871098)。
文摘Letτbe a generalized Thue-Morse substitution on a two-letter alphabet{a,b}:τ(a)=ambm,τ(b)=bmam for the integer m≥2.Letξbe a sequence in{a,b}Z that is generated byτ.We study the one-dimensional Schr?dinger operator Hm,λon l2(Z)with a potential given by v(n)=λVξ(n),whereλ>0 is the coupling and Vξ(n)=1(Vξ(n)=-1)ifξ(n)=a(ξ(n)=b).LetΛ2=2,and for m>2,letΛm=m if m≡0 mod 4;letΛm=m-3 if m≡1 mod 4;letΛm=m-2if m≡2 mod 4;letΛm=m-1 if m≡3 mod 4.We show that the Hausdorff dimension of the spectrumσ(Hm,λ)satisfies that dimHσ(Hm,λ)>logΛm/(log 64m+4).It is interesting to see that dimHσσ(Hm,λ)tends to 1 as m tends to infinity.
文摘Let S = Pi(i=1)(infinity){0, 1, ..., r - 1} and (R) over bar the general Sierpinski carpet, Let mu be the induced probability measure on (R) over bar of <(mu)over tilde> on S by phi, where phi is the natural surjection from S onto (R) over bar and <(mu)over tilde> is the infinite product probability measure corresponding to probability vector (b(0), ..., b(r-1)) with b(i) = a(i)(logn) (m-1)/m(alpha). Authors show that dim(H) mu = (C) under bar(L)(mu) = (C) over bar(L)(mu) = (C) under bar(mu) = (C) over bar C(mu) = alpha.
基金supported by Collegial Natural Science Research Program of Education Department of Jiangsu Province (07KJD110043)
文摘Let R be a ring. We define a dimension, called P-cotorsion dimension, for modules and rings. The aim of this article is to investigate P-cotorsion dimensions of modules and rings and the relations between P-cotorsion dimension and other homological dimensions. This dimension has nice properties when the ring in consideration is generalized morphic.
文摘We introduce generalized excellent extension of ring R in [4]. If S is a generalized excellent extension of R, we prove that (1) wgldim S≤ wgldim R and glodim S≤ gldim R; (2) the relations between rings R and rings S.
基金Supported by the National Natural Science Foundation of China（11401476） Supported by the Project for Universities of Gansu Province（2015A-019）
文摘As a proper setting to study Gorenstein projective and injective dimensions of modules via vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced, which is a non-trivial generalization of Gorenstein rings. Moreover, a new proof for Bennis and Mahdou's equality of global Gorenstein dimension is given.
基金Supported by the National Natural Science Foundation of China(60874100)
文摘The giant magneto-impedance（GMI）effect of amorphous wire was analyzed theoretically.The amorphous wire had strong GMI effect in the stimulation of sharp pulse of 680kHz and18 mV.A pulse generator was designed to provide high frequency pulse to a magnetic impedance（MI）element.The induced voltage on the pickup coil wound on the amorphous wire was sampled and held with a detect circuit using analog switch.A stable magnetic sensor was constructed.A three-dimension micro magnetic field detector was designed with a central controller MSP430F449.High stability and sensitivity were obtained in the MI sensor with the detect circuit.Experiment results showed that the resolution of the detector was 1nT in the full scale of±2 Oe and the detector worked stably from the room temperature to about 80℃.A small ferromagnetic target was detected by the three-dimension detector in laboratory environment without magnetic shielding.The target moving direction was ascertained with the wave shape of axis parallel in that direction.
文摘为解决在三维空间状态下零件无法自动标注尺寸的问题,提出一种采用基于模型的定义(Model Based Definition,MBD)技术的零件三维尺寸自动标注方法。首先根据工艺和拓扑相关的表面(Technologically and Topologically Related Surfaces,TTRS)理论的功能表面分类和边界表示(Boundary Representation,B-Rep)方法,提取出零件的所有拓扑表面,并消除重复多余的表面;然后将提取出的零件表面进行分类,并提取出对应的几何元素;根据其需要标注的定形和定位尺寸制定规则,进而去除冗余元素,构建标注元素集合;最后对CATIA进行二次开发实现零件尺寸的自动标注功能,完成尺寸信息模型的构建。
