Bifurcations in a Leslie–Gower model with constant and proportional prey refuge at high and low density

Assuming that the prey refuge is proportional to the prey density if its population size is below a critical threshold, or constant if its size is above the threshold, this paper proposes, and qualitatively analyzes, a Leslie–Gower predator–prey model assuming alternative feeding and harvesting in predators, and a Holling II function as the predator functional response. From the results of the mathematical analysis to the predator–prey models with proportional or constant prey refuge, the proposed model retains the same bifurcation cases obtained for each model analyzed. However, appropriate alterations of the parameters representing the critical threshold of prey population size and harvest in predators allows the formation of at least one limit cycle, stable or unstable, that lives in both vector fields of the proposed model.     

The effect of gradient sampling schemes on diffusion metrics derived from probabilistic analysis and tract-based spatial statistics

Purpose

The purpose was to systematically evaluate the effect of diffusion gradient encoding scheme on estimated fractional anisotropy (FA), mean diffusivity (MD) and the voxel-wise probability of identifying crossing fibers in the brain.

Materials and Methods

Eight healthy volunteers (mean age 26.5±1.3 years, 5 males, 3 females) were imaged using a Spin-Echo Echo-Planar-Imaging sequence acquired with two signal averages [number of signals averaged (NSA)], 127 diffusion directions, and b-values of 750 s/mm² and 1500 s/mm². The number of diffusion gradient directions (N_d) was reduced from the original value whilst maintaining a homogeneous gradient distribution enabling direct comparison of subsampled data sets with N_d=15, 28, 43, 84, 112 and 127. FA and MD maps were generated and analyzed using tract-based spatial statistics. Effect of N_d on estimated FA and MD was tested with voxel-wise statistics in 13 regions of interest. The number of voxels supporting two fiber populations (NV²) at different N_d values was estimated using Bayesian estimation of diffusion parameters.

Results

Low FA values decreased significantly with increasing N_d and with increasing NSA. MD was only marginally sensitive to N_d and NSA. NV₂ increased significantly with N_d but not with NSA. Thus, we conclude that accurate estimation of standard diffusion metrics FA and MD is mainly dependent on the signal-to-noise ratio (SNR), whereas the ability to differentiate multiple fiber populations requires a high diffusion sampling density.     

Orientation of Nd and Mn magnetic moments in a CMR Nd0.72Ba0.28MnO3 by X-ray magnetic circular dichroism

X-ray absorption and X-ray magnetic circular dichroism at Mn L_2,3- and Nd M_4,5-edges of a twinned Nd_0.72Ba_0.28MnO₃ single crystal have been performed versus temperature (between 10 and 300 K) and applied magnetic field (between 0 and 6.5 T). The results show that neodymium cations order below 70 K with the magnetic moments antiparallel to the manganese subnetwork in weak applied magnetic field (<1.5 T). For higher magnetic field, the neodymium moments turn parallel to the manganese ones showing that the antiferromagnetic exchange coupling between both subnetworks is weak. The presence of a metal–insulator transition below 70 K in the studied single crystal correlated to the magnetic ordering of neodymium cations can be understood on the basis of the cation mismatch introduced by barium substitution.     

比波谱导数和零交点法测定混合物含量

Ｐｂ２＋、Ｃｄ２＋、Ｈｇ２＋在ｐＨ６．５的硼砂－盐酸缓冲溶液中,与四（４－三甲铵基苯基）卟啉（ＴＡＰＰ）生成稳定配合物,采用ＫＩ和低聚度聚乙烯醇（ＰＶＡ）增敏、增溶,Ｐｂ２＋、Ｃｄ２＋、Ｈｇ２＋的εｍａｘ分别为ε４８１．５（４．９×１０５Ｌ·ｍｏｌ－１·ｃｍ－１）、ε４５７（７．９×１０５Ｌ·ｍｏｌ－１·ｃｍ－１）、ε４４４．５（８．１×１０４Ｌ·ｍｏｌ－１·ｃｍ－１）。在三吸收峰相互重叠的情形下,利用比波谱导数和零交点法,同时测定它们的含量,Ｐｂ２＋、Ｃｄ２＋、Ｈｇ２＋的检出限分别达４μｇ／Ｌ、２μｇ／Ｌ和１０μｇ／Ｌ。方法计算简便、快速。     

On the k-planar local crossing number

Given a fixed positive integer $k$, the $k$-planar local crossing number of a graph $G$, denoted by ${\text{<mi mathsize="small" is="true">LCR</mi>}}_k\left(G\right)$, is the minimum positive integer $L$ such that $G$ can be decomposed into $k$ subgraphs, each of which can be drawn in a plane such that no edge is crossed more than $L$ times. In this note, we show that under certain natural restrictions, the ratio ${\text{<mi mathsize="small" is="true">LCR</mi>}}_k\left(G\right)∕{\text{<mi mathsize="small" is="true">LCR</mi>}}_1\left(G\right)$ is of order $1∕k^2$, which is analogous to the result of Pach et al. (2018) for the $k$-planar crossing number ${\text{<mi mathsize="small" is="true">CR</mi>}}_k\left(G\right)$ (defined as the minimum positive integer $C$ for which there is a $k$-planar drawing of $G$ with $C$ total edge crossings). As a corollary of our proof we show that, under similar restrictions, one may obtain a $k$-planar drawing of $G$ with both the total number of edge crossings as well as the maximum number of times any edge is crossed essentially matching the best known bounds. Our proof relies on the crossing number inequality and several probabilistic tools such as concentration of measure and the Lovász local lemma.     

Crossing minimization in weighted bipartite graphs

Given a bipartite graph G=(L₀,L₁,E) and a fixed ordering of the nodes in L₀, the problem of finding an ordering of the nodes in L₁ that minimizes the number of crossings has received much attention in literature. The problem is NP-complete in general and several practically efficient heuristics and polynomial-time algorithms with a constant approximation ratio have been suggested. We generalize the problem and consider the version where the edges have nonnegative weights. Although this problem is more general and finds specific applications in automatic graph layout problems similar to those of the unweighted case, it has not received as much attention. We provide a new technique that efficiently approximates a solution to this more general problem within a constant approximation ratio of 3. In addition we provide appropriate generalizations of some common heuristics usually employed for the unweighted case and compare their performances.     

An analysis of some linear graph layout heuristics

The worst-case performances of some heuristics for the fixed linear crossing number problem (FLCNP) are analyzed. FLCNP is similar to the 2-page book crossing number problem in which the vertices of a graph are optimally placed on a horizontal “node line” in the plane, each edge is drawn as an arc in one half-plane (page), and the objective is to minimize the number of edge crossings. In FLCNP, the order of the vertices along the node line is predetermined and fixed. FLCNP belongs to the class of NP-hard optimization problems Masuda et al., 1990. In this paper we show that for each of the heuristics described, there exist classes of n-vertex, m-edge graphs which force it to obtain a number of crossings which is a function of n or m when the optimal number is a small constant. This leaves open the problem of finding a heuristic with a constant error bound for the problem.     

SEMI-ANALYTICAL SOLUTION FOR FREE VIBRATION OF THICK FUNCTIONALLY GRADED PLATES RESTED ON ELASTIC FOUNDATION WITH ELASTICALLY RESTRAINED EDGE

This paper deals with free vibration analysis of functionally graded thick circular plates resting on the Pasternak elastic foundation with edges elastically restrained against translation and rotation.Governing equations are obtained based on the first order shear deformation theory(FSDT) with the assumption that the mechanical properties of plate materials vary continuously in the thickness direction.A semi-analytical approach named differential transform method is adopted to transform the differential governing equations into algebraic recurrence equations.And eigenvalue equation for free vibration analysis is solved for arbitrary boundary conditions.Comparison between the obtained results and the results from analytical method confirms an excellent accuracy of the present approach.Afterwards,comprehensive studies on the FG plates rested on elastic foundation are presented.The effects of parameters,such as thickness-to-radius,material distribution,foundation stiffness parameters,different combinations of constraints at edges on the frequency,mode shape and modal stress are also investigated.     

纯平荫罩振动固有频率的研究

在高清晰度电视(HDTV)用的纯平彩色显像管中，由于荫罩的振动从而导致图像色纯度的降低．首先讨论了纯平荫罩振动的固有频率各种分析方法，然后应用弹性力学的基本理论，在建立薄膜横向振动基本方程的基础上，分析了纯平荫罩在四边简支条件下振动的固有频率和振型问题，得出了纯平荫罩振动频率的精确解，实例应用表明，在四边简支条件下的计算结果与实验结果基本一致，说明该方法确定纯平荫罩的振动固有频率是可行的、有效的，所得结果为减小荫罩振动进而对其结构参数进行优化设计提供了依据。     

Exact solution of the thick laminated open cylindrical shells with four clamped edges

ＥＸＡＣＴＳＯＬＵＴＩＯＮＯＦＴＨＥＴＨＩＣＫＬＡＭＩＮＡＴＥＤＯＰＥＮＣＹＬＩＮＤＲＩＣＡＬＳＨＥＬＬＳＷＩＴＨＦＯＵＲＣＬＡＭＰＥＤＥＤＧＥＳＦａｎＪｉａ－ｒａｎｇ（范家让）（ＨｅｆｅｉＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ）ＨｅｆｅｉＤｉ...