关于p－拉普拉斯方程径向解的一点注记

本文研究方程ｄｉｖ（｜ｕ｜ｐ－２ｕ）＋｜ｘ｜ｌ｜ｕ｜τ－１ｕ＝０，ｘ∈Ｂ的Ｄｉｒｉｃｈｌｅｔ边值问题ｕ｜Ｂ＝０的径向解。应用山路引理，我们将文［１］的结果（ｐ＝２时）推广到一般情形，证明上述问题有一非平凡的径向解。     

基于高光谱数据季相特征的山地草甸植被分类识别

新疆天山北坡山地草甸是天山山区草地生产力最高的草地类型,草地退化情况较为严重。对草地植被进行分类与识别,监测草地生态系统本底状况,可以快速、准确、有效的评价草地退化动态与程度,是进行生态重建的关键。为了探索适合草地植被的分类方法,选择天山北坡中段山地草甸植被作为研究对象,利用高光谱成像光谱仪（SOC710VP）获取了典型植被多季相（4个关键生育期）的原始反射光谱数据,通过多项式卷积平滑（S-G）及最小噪声分离（MNF）变换对光谱数据进行平滑去噪及降维处理,分别采用支持向量机（SVM）、BP人工神经网络（BP-ANN）及波谱角填图（SAM）三种方法建立分类模型,并对分类结果进行了对比分析。结果表明：使用S-G滤波及MNF变换预处理方法可以有效的对草地植被高光谱数据进行降维除噪,获得较平滑的光谱曲线,减少了数据的冗余程度并缩短了分类时间。不同季相山地草甸植被的“绿峰”、“红谷”及“红边”等参数差异较大,在植被生长旺盛期（4月—5月）的光谱曲线特征比黄枯期的光谱曲线特征更容易区分,这个时期分类精度较高。SVM分类模型在返青期（4月）和分蘖（枝）期（5月）总体分类精度均超过了90%,Kappa系数也超过了0.9;利用SVM方法进行分类时,在植物生长旺盛期（4月—5月）Polynomial核函数分类精度较高,植物成熟期（6月—9月）径向基核（RBF）函数分类精度较高。BP-ANN在分蘖（枝）期分类精度较高,总体分类精度为91.07%,Kappa系数为0.89,其他时期分类效果一般,虽然在MNF变换降维后能极大的缩短数据处理时间,但分类时间还是较SVM时间要长。SAM分类速度最快,但在各生育期的分类精度都较低,最高值为分蘖（枝）期的总体分类精度77.80%,Kappa系数为0.73。因此,利用Polynomial核函数的SVM分类模型适合对山地草甸植被进行分类识别,分类结果类别完整,准确度高,误分、错分现象相对较少,相比BP-ANN及SAM等高光谱数据分类方法具有较大的优势。     

Asymptotic behavior of the potential and existence of a periodic solution for a second order differential equation

We establish the existence of a 2π-periodic solution for a second order semilinear equation in terms of the asymptotic behavior of the potential of the nonlinearity. Our condition includes the case in which the nonlinearity is asymptotically linear with slopes at infinity of the jumping nonlinearity between the positive axes and the first Fucik spectrum curve (see [S. Fucik (1976 Fucik, S. 1976. Boundary value problems with jumping nonlinearities. Casopis Pest. Mat., 101: 69–87.  [Google Scholar]). Boundary value problems with jumping nonlinearities. Casopis Pest. Mat., 101, 69–87.]). Our results extend those of [L. Fernandez and F. Zanolin (1988 Fernandez, L. and Zanolin, F. 1988. Periodic solutions of a second order differential equation with one-sided growth restriction on the restoning term. Arch. Math., 51: 151–163.  [Google Scholar]). Periodic solutions of a second order differential equation with one-sided growth restriction on the restoning term. Arch. Math., 51, 151–163.].     

New periodic solutions for a class of singular Hamiltonian systems

In this paper, we apply a variant of the famous Mountain Pass Lemmas of Ambrosetti-Rabinowitz and Ambrosetti-Coti Zelati with (PSC)c type condition of Palais-Smale-Cerami to study the existence of new periodic solutions with a prescribed energy for symmetrical singular second order Hamiltonian conservative systems with weak force type potentials.     

具有小受迫项的哈密顿系统的同宿轨道

By Brezis-Nirenberg type Mountain Pass Theorem, the research has focused on the existence of nontrivial homoclinic orbits for a class of second order Hamiltonian systems with non-Ambrosetti-Rabinowitz type superquadratic potentials and small forced terms.     

基于Hyperion高光谱数据的温带森林不同冠层结构的光谱特征分析

冠层是植被进行生态过程的主要层次,森林冠层结构影响冠层生化组分的遥感反演,因此对其光谱特征的分析有助于提高冠层生化组分反演的精度。以长白山温带阔叶红松林为研究对象,利用Hyperion高光谱数据提取不同林冠反射率,运用连续统去除和光谱一阶微分法进行光谱变换,定量分析森林冠层的光谱特征。通过计算样方阔叶树种优势度(BFDI),以及一系列光谱指数(NIR,NDVI,EVI,NDNI,SPRI*NDVI和SPRI*EVI),探讨冠层结构组成对其光谱特征及光谱指数的影响。结果表明：(1)相比阔叶林冠层,针阔混交林、美人松林和樟子松林冠层光谱的红边有左移趋势,斜率明显下降,蓝边、黄边斜率特征也相应减弱,近红外波段反射率明显下降,可见光波段的归一化反射率有上升趋势,表明不同林冠,尤其针叶林与阔叶林林冠之间的光谱特征差异明显。(2)BFDI对冠层NIR反射率和三边斜率有明显的影响,与光谱指数显著相关(P<0.01),表明BFDI影响森林光谱指数。BFDI与NDVI,EVI,SPRI*EVI,NIR,SPRI*NDVI,NDNI的R2分别达到0.90,0.83,0.83,0.81,0.68,0.59,揭示了BFDI对于冠层绿度、叶面积指数、植被生产力以及冠层叶氮浓度等植被参数存在一定影响。研究表明,利用星载高光谱数据结合地面样方调查可以很好地阐明林冠结构组成对于光谱特征的影响,也对优化植被冠层生化组分和森林生态系统生产力的遥感反演具有借鉴意义。     

天山北坡融雪期雪层含水率地物光谱特征研究

积雪含水率是雪层中液态水的含量,也是积雪出流、产流的关键指标,对积雪含水率的研究对春季融雪产流及融雪型洪水有现实意义。借助美国ASD地物光谱仪和Snow Folk积雪特性仪获取原始数据,并利用SPSS19.0和Excel等统计软件对数据进行分析、处理,并利用这些数据进行制图、数据综合,建立雪表层的地物光谱特征预测模型。结果表明：积雪的光谱特征曲线由于在可见光和近红外由于吸收呈现出若干波谷;地物光谱特征与积雪表层含水率存在负相关关系,且随着波长的增加这种负相关关系变化明显,并在可见光和近红外形成三个相关关系的极小值;构建雪层含水率的地物光谱反射率模型,可见光范围内,在350 nm时的模型精度较高,能够达到75.9%,预测值和实测值拟合程度高,在近红外波段内,1 204 nm建模的模拟精度最高。     

Remarks on homoclinic solutions for semilinear fourth-order ordinary differential equations without periodicity

This paper mainly discusses the existence of nontrivial homoclinic solutions for nonperiodic semilinear fourth-order ordinary differential equation
u^（4）＋pu″＋a（x）u-b（x）u^2=c（x）u^3=3
arising in the study of pattern formation by means of Mountain Pass Lemma.     

On a class of degenerate and singular elliptic systems in bounded domains

This paper deals with the nonexistence and multiplicity of nonnegative, nontrivial solutions to a class of degenerate and singular elliptic systems of the form

where Ω is a bounded domain with smooth boundary ∂Ω in , N2, and , , h_i (i=1,2) are allowed to have “essential” zeroes at some points in Ω, (F_u,F_v)=F, and λ is a positive parameter. Our proofs rely essentially on the critical point theory tools combined with a variant of the Caffarelli–Kohn–Nirenberg inequality in [P. Caldiroli, R. Musina, On a variational degenerate elliptic problem, NoDEA Nonlinear Differential Equations Appl. 7 (2000) 189–199].