Multi-way dual Cheeger constants and spectral bounds of graphs

We introduce a set of multi-way dual Cheeger constants and prove universal higher-order dual Cheeger inequalities for eigenvalues of normalized Laplace operators on weighted finite graphs. Our proof proposes a new spectral clustering phenomenon deduced from metrics on real projective spaces. We further extend those results to a general reversible Markov operator and find applications in characterizing its essential spectrum.     

Small Data Scattering for the One-Dimensional Nonlinear Dirac Equation with Power Nonlinearity

We study scattering problems for the one-dimensional nonlinear Dirac equation (?_t + α?_x + iβ)Φ = λ|Φ|^p?1Φ. We prove that if p > 3 (resp. p > 3 + 1/6), then the wave operator (resp. the scattering operator) is well-defined on some 0-neighborhood of a weighted Sobolev space. In order to prove these results, we use linear operators D(t)xD(?t) and t?_x + x?_t ? α/2, where {D(t)}_t∈? is the free Dirac evolution group. For the reader's convenience, in an appendix we list and prove fundamental properties of D(t)xD(?t) and t?_x + x?_t ? α/2.     

Variational Solution of Stochastic Schrödinger Equations With Power-Type Nonlinearity

We investigate a Schrödinger problem with multiplicative Gaussian noise term and power-type nonlinearity on a bounded one-dimensional domain. In order to prove the existence and uniqueness of the variational solution, a further process will be introduced which allows to transform the stochastic nonlinear Schrödinger problem into a pathwise one. Galerkin approximations and compact embedding results are used.     

Chemical composition variations,allelopathic, and antioxidant activities of Symphyotrichum squamatum (Spreng.) Nesom essential oils growing in heterogeneous habitats

The present study aimed to analyze the chemical composition of Symphyotrichum squamatum EOs growing in two different habitats to explore the ecological implication on the EOs production and evaluate their antioxidant and allelopathic potentialities. The EOs from the aerial parts collected from coastal Mediterranean belt and inland abandoned habitats in the Nile Delta of Egypt, were extracted and analyzed using gas chromatography-mass spectrometry. Sixty compounds were characterized as overall constituents of EOs from both samples. Sesquiterpenes were the main component and represented by 69.77% and 88.68% from coastal and inland sample, respectively. The coastal sample attained a relatively high content of monoterpenes compared to the inland sample. Major compounds from the EOs of the coastal habitat sample, were humulene epoxide, (-)-spathulenol, (-)-caryophyllene oxide, germacrene D, and α-humulene representing 59.72%. However, β-pinene, germacrene D, α-humulene, α-muurolene, humulene epoxide, (-)-caryophyllene oxide, and β-cadinene were the major compounds of EOs of the inland habitat sample, representing 63.70%. The correlation analysis revealed more correlation between the Egyptian inland S. squamatum and the Japanese ecospecies. However, the Egyptian coastal S. squamatum and Turkish ecospecies were more correlated to each other. The present data suggested that chemotypes of S. squamatum maintain their typical pattern despite ecological or climatic differences. The EOs of S. squamatum showed moderate antioxidant activity, wherein coastal and inland EOs have an IC₅₀ value of 382.53 and 559.63 μL L⁻¹, respectively. Also, the EOs from both habitats showed moderate allelopathic activity against the noxious weed Bidens pilosa. However, the activity of the coastal sample was more than inland one and could be attributed to the content of the major compounds, especially the oxygenated terpenes.     

Phytochemical profiling and antimicrobial activity of ginger (Zingiber officinale) essential oils against important phytopathogens

The objectives of this study were to profile ginger essential oils (EOs) phytochemical constituents and antimicrobial activity against important phytopathogens. Ginger EOs was extracted using a modified Clevenger-type apparatus by hydro-distillation then followed by GCMS and headspace analysis of its phytochemical constituents. The phytoconstituents identified were monoterpenes and sesquiterpene hydrocarbons. Food poisoned and disc diffusion techniques were applied to determine the percentage inhibition of fungal mycelial and bacterial growth respectively. The EOs produced mycelial growth inhibition in all the test fungal pathogens after five days of incubation. The MIC and MFC of the EOs on the tested fungi were in the range of 1 μl/ml and 5–6 μl/ml, respectively. The bacterial growth of all the tested isolates was also affected by EOs at 100–500 µl/ml, from weak to strong antibacterial activity. The EOs affected the Xanthomonas oryzae pv. oryzae-strain A isolate most at a higher concentration of 400–500 μl/ml with mean inhibition of 20.66 mm and 22.66 mm respectively, which are found to be effective. The MIC values on the bacterial pathogens were at100 μl/ml. The inhibition zone of positive control (streptomycin) at 15 µg/disc was 25.00 mm and appeared to be efficient. Metabolomics analysis to concurrently quantify variability among multiple compounds in the data sets and identify such compounds responsible for the X. oryzae pv. oryzae-strain-A inhibition were determined. The cross-validated PLS model has shown a strong correlation between ginger EOs and bioactivity. The action of ginger EOs on the cell structure was fully identified using SEM by observing the changes in morphology and integrity of X. oryzae pv. oryzae-strain-A cells. The DMSO treatment (control) showed a normal rod shape cell, while treatment with the ginger EOs showed irregular shape with sunken surfaces, and treatment with antibiotics display abnormal growth of the cells. These findings can, therefore, propose that the ginger EOs could be used as a new antimicrobial agent in suppressing the growth of phytopathogens and as possible new alternatives to synthetic fungicides and bactericides.     

Correlation between chemical composition and radical scavenging activity of 10 commercial essential oils: Impact of microencapsulation on functional properties of essential oils

A comparative study was carried out on the essential oils of 10 aromatic plants that are extensively used in Egypt for their distinctive aroma and functional properties. Each essential oil (EO) was characterized by means of gas chromatography-mass spectrometry (GC–MS) analysis and evaluated for its radical scavenging activity by 2,2-diphenyl-1-picrylhydrazyl (DPPH) and 2,2-azinobis (2-ethyl-benzolhiaxoline-6-sulfonic acid)(ABTS) assays. The phenolic content of the 10 EOs was in the descending order: clove > thyme > majoram > basil > anise > chamomile > cinnamon > dill > ginger > rosemary. The radical scavenging activity of the EOs was correlated to the presence of phenolic compounds, such as eugenol, thymol, carvacrol and trans-anethol, or the synergism between the antioxidant activity of nonphenolic compounds such as terpinene-4-ol, α-terpinene, curcumene and chamazulene. Clove essential oil exhibited the highest oil content and radical scavenging activity so it was encapsulated, separately, in three coating materials. Sodium alginate showed the highest retention, encapsulation efficiency and loading capacity of clove EO. Microencapsulation in sodium alginate and chitosan improved the antioxidant activity and phenolic content of the encapsulated clove EO compared with carboxymethyl cellulose. The results support the possibility of using the encapsulated EOs as natural and easy handle antioxidants.     

Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients

The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix. The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities, including transcendental ones, in which the discretization process is as simple as that in solving linear problems, and only common two-term connection coefficients are needed. All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method, which does not require numerical integration in the resulting nonlinear discrete system. The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers. The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids, and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids. In addition, Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method, including the initial guess far from real solutions.

     

负五阶非线性下预啁啾高斯光脉冲的啁啾和频谱

为探究光纤负五阶非线性和光脉冲预啁啾对高斯光脉冲频率啁啾和频谱的综合影响,在忽略光纤色散的情况下,利用包含三五阶非线性的扩展非线性薛定谔方程,计算和分析了啁啾高斯脉冲的频谱和总啁啾。结果表明,脉冲无预啁啾时,负五阶非线性的存在可使脉冲频率啁啾的形状由单“S”形变为双“S”形,并使脉冲的中心附近由正啁啾变为负啁啾。此外,负五阶非线性的存在使预啁啾对脉冲频谱的影响发生了较大的变化。预啁啾与非线性所致啁啾叠加后对脉冲频谱的谱峰数目影响较小,而对能量在各个谱峰上的分布影响较大,在某些最大非线性相移下,甚至会出现总啁啾减小使谱峰值数目增加的情况。该研究对光开关、光脉冲压缩以及光纤通信系统等领域的深入发展具有一定的指导意义。     

带有凹凸非线性项的Klein-Gordon-Maxwell系统解的存在性和多重性

研究一类Klein-Gordon-Maxwell系统解的存在性和多重性.当非线性项是凹凸非线性项时,利用变分方法获得了系统解的存在性和多重性结果,并完善了此系统解的存在性的已有结果.     

超临界CO2萃取与水蒸气蒸馏法研究泽兰中挥发性有机物

以超临界CO2萃取法(SFE)提取中药泽兰中的挥发性有机物,经气相色谱-质谱联用(GC-MS)分析,人工解析质谱图及计算机谱库检索相结合进行化学成分结构鉴定,用面积归一化法计算各组分的相对含量。SFE法提取的产率为0.78%,共鉴定75种挥发性化合物,主要成分为植醇、石竹烯氧化物、十六酸、亚油酸、葎草烯等,比文献报道的该挥发油成分多且含量差异较大,其中松香芹醇、蒲勒烯、马鞭烯酮、香芹酮、十六酸、亚油酸、葎草烯、十六酸乙酯、亚麻酸等多种成分未见报道。与水蒸气蒸馏法(SD)提取的泽兰挥发油进行比较,后者提取的产率为0.12%,从中鉴定出50种化合物,主要成分为石竹烯氧化物、柠檬烯、α-蒎烯、葎草烯、月桂烯等。SFE与SD得到的成分仅有31种相同,其它各不相同。