Flip-chip-type high-T c gradiometer for biomagnetic measurements in unshielded environment

A flip-chip-type gradiometer has been constructed with a 10 mm × 5 mm planar DCSQUID gradiometer fabricated on a SrTiO₃ bicrystal substrate and a flux transformer made from a YBCO*/YBCO/CeO₂/YSZ multilayer on ?50.8 mm Si wafer. The coupling coefficient between the flux transformer and the planar gradiometer is 0.18. The transformer increases effectively the resolution of the gradiometer. A magnetic field gradient resolution of 73 fT.cm^?1Hz^?1/2 in the white region and 596 fT.cm^?1Hz^?1/2 at 1 Hz has been obtained. High quality magnetocardiogram signals have been successfully measured by using this flip-chip-type gradiometer in an unshielded environment.     

Flip-chip-type high-Tc gradiometer for biomagnetic measurements in unshielded environment

A flip-chip-type gradiometer has been constructed with a 10 mm × 5 mm planar DCSQUID gradiometer fabricated on a SrTiO₃ bicrystal substrate and a flux transformer made from a YBCO*/YBCO/CeO₂/YSZ multilayer on ϕ50.8 mm Si wafer. The coupling coefficient between the flux transformer and the planar gradiometer is 0.18. The transformer increases effectively the resolution of the gradiometer. A magnetic field gradient resolution of 73 fT.cm⁻¹Hz^−1/2 in the white region and 596 fT.cm⁻¹Hz^−1/2 at 1 Hz has been obtained. High quality magnetocardiogram signals have been successfully measured by using this flip-chip-type gradiometer in an unshielded environment.     

High-T c superconducting thin film/GaAs MESFET hybrid microwave oscillator

A high-T _c superconducting (HTSC) thin film/GaAs MESFET hybrid microwave oscillator operated at 10.6 GHz has been designed, fabricated and characterized. Microstrip line structures were used throughout the circuit with superconducting thin film YBa₂Cu₃O_7-δ(YBCO) as the conductor material. The YBCO thin films were deposited on 15 mm×10 mm×0.5 mm LaAlO₃ substrates. The oscillator was common-source, series feedback type using a GaAs-MESFET (NE72084) as the active device and a superconducting microstrip resonator as the frequency stabilizing element. By improving the unloaded quality factorQ ₀ of the superconducting microstrip resonator and adjusting the coupling coefficient between the resonator and the gate of the MESFET, the phase noise of the oscillator was decreased. At 77 K, the phase noise of the oscillator at 10 kHz offset from carrier was −87 dBc/Hz. Project supported by the National Center for Research and Development on Superconductivity of China.     

求解二维Euler方程的旋转通量混合格式

为提高求解二维Euler方程数值结果的分辨率,提出了一种旋转通量混合格式.该算法采用旋转通量法的类一维处理思想,通量函数选用满足热力学第二定律的熵稳定数值通量和具有良好鲁棒性的HLL数值通量耦合的混合格式,时间方向采用三阶强稳定Runge-Kutta方法进行推进.该旋转通量混合格式具有结构简单、分辨率高的优点,数值结果表明了该算法的良好特性.     

关于Aluthge变换的数值域

设A是作用在希耳伯特空间H上的有界线性算子,如果A=V A是算子A的极分解,则定义A~=A 12V A 21和A~(*)=A*21V A*21分别为算子A的Aluthge变换A~和*-Aluthge变换A~(*).记A~和A~(*)的数值域分别为W(A~)和W(A~(*)).证明了W(A~)=W(A~(*)),即肯定了吴提出的一个猜想.     

连续时间下非参数回归模型的误差密度估计的渐近均方误差

本文研究了连续时间下非参数回归的误差官度估计的收敛速度，给出了一定条件下误差密度的估计量^fT(x)的均方收敛速度，详细说明了以下重要结果：E[^fT(x)-f(x)]^2＝O(T^-1/4)其中f(x)表示误差过程｛et,t≥0｝的未知密度。     

Preparation of Y-Ba-Cu-O film on metal substrate with buffer layers deposited by ion beam assisted deposition

Ion beam assisted pulsed laser deposition of biaxially aligned yttria-stabilized zirconia (YSZ) was used to produce a buffer layer for YBCO film on polycrystalline metallic substrate. The YSZ layers were biaxially aligned with (001) axis normal to the substrate. The minimum FWHM of (111) phi-scan of the YSZ was 19°, and the minimum FWHM of the rocking curve of YSZ was 4.5°. Highly c-axis oriented biaxially aligned YBCO thin films were epitaxially grown by laser ablation on these layers, with J_C(77K, 0T) = 2.1 × 10⁵ A/cm², . Project supported by the National Center for R&D on Superconductivity of China.     

Distance Integral Complete Multipartite Graphs with s=5, 6

Let D(G) = (dij )n×n denote the distance matrix of a connected graph G with order n, where dij is equal to the distance between vertices vi and vj in G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In 2014, Yang and Wang gave a su?cient and necessary condition for complete r-partite graphs Kp1,p2,··· ,pr =Ka1·p1,a2·p2,··· ,as···ps to be distance integral and obtained such distance integral graphs with s = 1, 2, 3, 4. However distance integral complete multipartite graphs Ka1·p1,a2·p2,··· ,as·ps with s>4 have not been found. In this paper, we find and construct some infinite classes of these distance integral graphs Ka1·p1,a2·p2,··· ,as·ps with s = 5, 6. The problem of the existence of such distance integral graphs Ka1·p1,a2·p2,··· ,as·ps with arbitrarily large number s remains open.     

High quality YBCO superconductive thin films fabricated by laser molecular beam epitaxy

High quality YBa₂.Cu₃O_{6 +x}(YBCO) superconductive thin films have been fabricated on the SrTiO₃(100) substrate using laser molecular beam epitaxy (laser-MBE). The active oxygen source was used, which made the necessary ambient oxygen pressure be 2–3 orders lower than that in pulsed laser deposition (PLD). T_c0 is 85–87 K, and J_c, 1.0 × 10⁶ A/cm². Atomic force microscopy (AFM) measurements show that no obvious particulates can be observed and the root mean square roughness is 7.8 nm. High stability DC superconducting quantum interference devices (DC-SQUID) was fabricated using this YBCO thin film.     

Maximal planar graphs of diameter two

A maximal planar graph is a simple planar graph in which every face is a triangle. We show here that such graphs with maximum degree Δ and diameter two have no more than 3/2Δ + 1 vertices. We also show that there exist maximal planar graphs with diameter two and exactly [3/2Δ + 1] vertices.     

Improvements on the density of maximal 1‐planar graphs

A graph is 1‐planar if it can be drawn in the plane such that each edge is crossed at most once. A graph, together with a 1‐planar drawing is called 1‐plane. A graph is maximal 1‐planar (1‐plane), if we cannot add any missing edge so that the resulting graph is still 1‐planar (1‐plane). Brandenburg et al. showed that there are maximal 1‐planar graphs with only edges and maximal 1‐plane graphs with only edges. On the other hand, they showed that a maximal 1‐planar graph has at least edges, and a maximal 1‐plane graph has at least edges. We improve both lower bounds to .     

求解二维浅水波方程的旋转混合格式北大核心CSCD

针对二维浅水波方程数值求解问题,构造了一种旋转通量混合格式.空间方向上,该算法利用浅水波方程通量函数的旋转不变性,在单元界面法线方向及单元界面切线方向上采用可消除红斑现象的HLL与满足热力学第二定律的熵稳定加权混合数值通量函数,时间方向上采用三阶强稳定Runge-Kutta法.数值结果表明,该混合格式对于二维浅水波方程数值求解具有分辨率高的良好特性.     

求解二维浅水波方程的移动网格旋转通量法

为提高求解二维浅水波方程数值算法的分辨率,拟构造求解该方程的新算法:基于移动网格法,选用熵稳定数值通量函数,利用旋转不变性得到混合数值通量.该算法中,浅水波方程的数值求解和依据解的特性进行自适应疏密分布的网格计算过程交错进行.利用变分原理进行网格重构,新网格上的物理量采用二阶精度的守恒型插值公式计算,最终采用三阶强稳定Runge-Kutta法与满足热力学第二定律的熵稳定格式实现浅水波方程的数值求解.数值结果表明,新算法具有良好的间断捕捉能力,分辨率高.     

On the two-dimensional orthogonal drawing of series-parallel graphs

It has been known that every planar 4-graph has a 2-bend 2-D orthogonal drawing, with the only exception being the octahedron, every planar 3-graph has a 1-bend 2-D orthogonal drawing with the only exception being K₄, and every outerplanar 3-graph with no triangles has a 0-bend 2-D orthogonal drawing. We show in this paper that every series-parallel 4-graph has a 1-bend 2-D orthogonal drawing.     

On the Growth of Solutions of a Class of Higher Order Linear Differential Equations

In this paper, we investigate the growth of solutions of the differential equations f(k)+Ak?1(z)f(k?1)+· · ·+A0(z)f =0, where Aj(z)(j=0, · · · , k?1) are entire functions. When there exists some coe?cient As(z)(s ∈ {1, · · · , k?1}) being a nonzero solution of f00+P(z)f =0, where P(z) is a polynomial with degree n(≥1) and A0(z) satisfiesσ(A0)≤1/2 or its Taylor expansion is Fabry gap, we obtain that every nonzero solution of such equations is of infinite order.     

初等算子与Putnam-Fuglede定理

本文证明若A =(A1 ,A2 ,… )和B =(B1 ,B2 ,… )是Hilber空间H上的交换的正常算子列 ,满足条件 ∑∞j=1A j Aj=I和 ∑∞j=1B jBj =I.则对H上任何有界线性算子X ,由 ∑∞j=1AjXBj =X 可推得 :等式AjX =XBj和A jX =XB j 对所有的j成立     

Effect of Flux Evaluation Methods on the Resolution and Robustness of the Two-Step Finite-Difference WENO Scheme

The resolution and the robustness of the weighted essentially non-oscillatory (WENO) scheme and two-step finite-difference WENO (TSFDWENO) schemes are compared by strictly using the same flux evaluation method and smoothness indicators. TSFDWENO schemes are defined to include a family of weighted compact nonlinear scheme (WCNS) and an alternative WENO scheme. Comparison results indicate that WCNS has a higher resolution than the WENO scheme, while the WENO scheme is more robust than WCNS. Additionally, various flux evaluation methods are combined with TSFDWENO schemes, and they are evaluated. Then, the effects of the flux evaluation methods on the resolution and robustness of the scheme are investigated, and the results show that the robustness and the resolution can be significantly altered by changing the flux evaluation method. This study reveals the advantage of being able to use various flux evaluation methods in the TSFDWENO scheme as well as the fair comparison of the WENO schemes and WCNS. On the other hand, these effects are marginalized when changing the interpolation and differencing method. Such knowledge can be important when selecting schemes for actual simulation and developing guidelines for scheme improvement.     

Extending matchings in planar graphs V

A graph G on at least 2n + 2 vertices in n-extendable if every set of n independent edges extends to (i.e., is a subset of) a perfect matching in G. It is known that no planar graph is 3-extendable. In the present paper we continue to study 2-extendability in the plane. Suppose independent edges e₁ and e₂ are such that the removal of their endvertices leaves at least one odd component C_o. The subgraph G[V(C_o) V(e₁) V(e₂)] is called a generalized butterfly (or gbutterfly). Clearly, a 2-extendable graph can contain no gbutterfly. The converse, however, is false.

We improve upon a previous result by proving that if G is 4-connected, locally connected and planar with an even number of vertices and has no gbutterfly, it is 2-extendable. Sharpness with respect to the various hypotheses of this result is discussed.     

完全多部图的无符号Laplacian特征多项式(英文)

For a simple graph G,let matrix Q（G）=D（G） + A（G） be it’s signless Laplacian matrix and Q G （λ）=det（λI Q） it’s signless Laplacian characteristic polynomial,where D（G） denotes the diagonal matrix of vertex degrees of G,A（G） denotes its adjacency matrix of G.If all eigenvalues of Q G （λ） are integral,then the graph G is called Q-integral.In this paper,we obtain that the signless Laplacian characteristic polynomials of the complete multi-partite graphs G=K（n₁,n₂,···,n_t）.We prove that the complete t-partite graphs K（n,n,···,n）t are Q-integral and give a necessary and sufficient condition for the complete multipartite graphs K（m,···,m）s（n,···,n）t to be Q-integral.We also obtain that the signless Laplacian characteristic polynomials of the complete multipartite graphs K（m,···,m,）s1（n,···,n,）s2（l,···,l）s3.