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.     

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.     

假蒟挥发油化学成分气质联用分析研究

采用常规水蒸气蒸馏法提取出假岛精油,经气相色谱-质谱联机分析,分出60多个峰,鉴定出67种化合物,它们主要是2,4,5-三甲氧基-1-丙烯基苯3．20％）,顺-石竹烯（13．33％）,1,2-二甲氧基-4-（1-丙烯基）苯（12．63％）,细辛（9．94％）,4-甲氧基-6-（2-丙烯基）-1,3-苯并二恶茂（5．71％）,δ-杜松烯（3．03％）etc,占总峰面积的67．84％。     

湘西金银花挥发油化学成分研究

采用ＧＣ／ＭＳ／ＤＳ联用仪对湘西金角花挥发油中的化学成分进行了研究。并鉴定出４０种组分。其主要成分为：芳樟醇、环氧芳樟醇、α－萜品醇、顺－３－已 烯醇、顺芷酸－３、己烯酯、香叶醇、氧化芳樟醇、法尼醇、顺－苯酮、法尼烯、大根香叶烯、橙花醇等。其中芳樟醇含量最高,约占精油总量的２０％。     

振型归一化对梁结构柔度曲率损伤指标的影响

结构柔度矩阵需由质量矩阵归一化振型获得,而质量矩阵归一化振型难以直接测得,限制了柔度曲率类损伤指标的应用。为分析振型归一化方法对梁结构柔度曲率类损伤指标的影响,根据梁结构的刚度、弯矩和位移曲率的关系,建立了均布荷载作用下结构损伤前后位移曲率与损伤程度的理论表达式,实现定量分析均匀荷载面曲率结构损伤程度。提出P-范数振型归一化方法,通过均匀荷载面曲率指标推导了振型质量矩阵归一化系数差x_α与损伤程度的关系。以三跨连续梁算例对理论进行了验证,结果表明,损伤程度定量指标效果良好,不同P-范数振型归一化方法下,损伤程度的偏差可由2x_α估算;2-范数振型归一化方法的损伤识别结果与质量矩阵振型归一化结果最接近,故当无法获得质量矩阵归一化振型时,可采用2-范数归一化振型代替。     

THE EIGENVALUE PERTURBATION BOUND FOR ARBITRARY MATRICES

In this paper we present some new absolute and relative perturbation bounds for theeigenvalue for arbitrary matrices, which improves some recent results. The eigenvalueinclusion region is also discussed.     

Gowers norms and pseudorandom measures of subsets

Let $A \subset {{\Bbb Z}_N}$, and ${f_A}(s) = \left\{ {\begin{array}{*{20}{l}}{1 - \frac{{|A|}}{N},}&{{\rm{for}}\;s \in A,}\\{ - \frac{{|A|}}{N},}&{{\rm{for}}\;s \notin A.}\end{array}} \right.$ We define the pseudorandom measure of order k of the subset A as follows, P_k(A, N) = $\begin{array}{*{20}{c}}{\max }\\D\end{array}$|$\mathop \Sigma \limits_{n \in {\mathbb{Z}_N}}$f_A(n + c₁)f_A(n + c₂) … f_A(n + c_k)|, where the maximum is taken over all D = (c₁, c₂, . . . , c_k) ∈ ${\mathbb{Z}^k}$ with 0 ≤ c₁ < c₂ < … < c_k ≤ N - 1. The subset A ⊂ ${{\mathbb{Z}_N}}$ is considered as a pseudorandom subset of degree k if P_k(A, N) is “small” in terms of N. We establish a link between the Gowers norm and our pseudorandom measure, and show that “good” pseudorandom subsets must have “small” Gowers norm. We give an example to suggest that subsets with “small” Gowers norm may have large pseudorandom measure. Finally, we prove that the pseudorandom subset of degree L(k) contains an arithmetic progression of length k, where L(k) = 2·lcm(2, 4, . . . , 2|$\frac{k}{2}$|), for k ≥ 4, and lcm(a₁, a₂, . . . , a_l) denotes the least common multiple of a₁, a₂, . . . , a_l.