Construction of Multivariate Tight Framelet Packets Associated with Dilation Matrix

In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles.We also prove how to construct various tight frames for L2(Rd) by replac-ing some mother framelets.     

扩张环上的$\Sigma$-相伴素理想

作为对相伴素理想与幂零相伴素理想的推广,我们在本文中引进了$\Sigma$-相伴素理想的定义,探讨了$\Sigma$-相伴素理想的基本性质,证明了Ore扩张环$R[x;\alpha,\delta]$、斜洛朗多项式环$R[x,x^{-1};\alpha]$及斜幂级数环$R[[x;\alpha]]$的$\Sigma$-相伴素理想都分别可以用环$R$的$\Sigma$-相伴素理想来刻画,从而将相伴素理想与幂零相伴素理想的一些已有结论推广到更一般的情形.     

半格分次弱Hopf代数的$G$-Cleft扩张

本文首先将Clifford幺半群代数分解为交叉积的半格直和,然后将这个结果通过$H$-$G$-cleft扩张推广到所谓的$G$-交叉积上.     

Investigation of the complexation of essential oil components with cyclodextrins

The formation of inclusion complexes of six essential oil (EO) components (β-caryophyllene, cis-ocimene, trans-ocimene, sabinene hydrate (thujanol), γ-terpinene and α-terpineol) with six cyclodextrins (CDs) (α-CD, β-CD, γ-CD, HP-β-CD, RAMEB and CRYSMEB) was investigated by using static headspace-gas chromatography and UV–visible spectroscopy. Retention studies showed that CDs could efficiently reduce the volatility of EO components except for β-caryophyllene with α-CD. In this case, no inclusion complex was detected while for other compounds the formation of 1:1 inclusion complexes was observed. Results revealed that the inclusion stability mainly depends on geometric complementarity between encapsulated molecule and CD's cavity. Molecular modelling was used to investigate the complementarities between host and guest. Thus, CDs could efficiently be regarded as promising encapsulants for EO components leading to improve their application in cosmetic, pharmaceutical and agriculture fields.     

Synthesis and characterization of biodegradable polyesteramides constructed mainly by alternating diesterdiamide units from N,N′-bis(2-hydroxyethyl)-adipamide and diacids

Two kinds of aliphatic alternating polyesteramide prepolymers were prepared through melt polycondensation from N,N’-bis(2-hydroxyethyl)-adipamide and adipic acid or sebacic acid. Chain extension of them was conducted with 2,2′-(1,4-phenylene)-bis(2-oxazoline) and adipoyl biscaprolactamate as combined chain extenders. The chain extended polyesteramides (ExtPEAs) were characterized by IR, 1 H-NMR, differential scanning calorimetry, thermogravimetric analysis, wide angle X-ray scattering, tensile test and enzymatic degradation. The results showed that the ExtPEA(4,m)s were mainly constituted with the diester adipamide alternating units. ExtPEA(4,4) and ExtPEA(4,8) had Tm of 83.8℃ and 85.8℃ and initial decomposition temperature above 310.0℃. They crystallized similarly as Nylon-66 did and were flexible thermoplastic materials with tensile strength up to 25.64 MPa and strain at break up to 737%.     

The isometric extension problem between unit spheres of two separable Banach spaces

In this article, we use some analytic and geometric characters of the smooth points in a sphere to study the isometric extension problem in the separable or reflexive real Banach spaces. We obtain that under some condition the answer to this problem is affirmative.     

Chemical Composition and Antioxidant Activity of Essential Oils from Eugenia patrisii Vahl,E. punicifolia (Kunth) DC., and Myrcia tomentosa (Aubl.) DC., Leaf of Family Myrtaceae

Essential oils (EOs) were extracted from Eugenia patrisii, E. punicifolia, and Myrcia tomentosa, specimens A and B, using hydrodistillation. Gas chromatography coupled with mass spectrometry (GC/MS) was used to identify the volatile constituents present, and the antioxidant capacity of EOs was determined using diphenylpicryl-hydrazyl (DPPH) and trolox equivalent antioxidant capacity (TEAC) assays. For E. patrisii, germacrene D (20.03%), bicyclogermacrene (11.82%), and (E)-caryophyllene (11.04%) were identified as the major constituents of the EOs extracted from specimen A, whereas specimen B primarily comprised γ-elemene (25.89%), germacrene B (8.11%), and (E)-caryophyllene (10.76%). The EOs of E. punicifolia specimen A contained β-Elemene (25.12%), (E)-caryophyllene (13.11%), and bicyclogermacrene (9.88%), while specimen B was composed of (E)-caryophyllene (11.47%), bicyclogermacrene (5.86%), β-pinene (5.86%), and γ-muurolene (5.55%). The specimen A of M. tomentosa was characterized by γ-elemene (12.52%), germacrene D (11.45%), and (E)-caryophyllene (10.22%), while specimen B contained spathulenol (40.70%), α-zingiberene (9.58%), and γ-elemene (6.89%). Additionally, the chemical composition of the EOs was qualitatively and quantitatively affected by the collection period. Furthermore, the EOs of the studied specimens, especially specimen A of E. punicifolia, showed a greater antioxidant activity in DPPH rather than TEAC, as represented by a significantly high inhibition percentage (408.0%).     

Chemical Profiling,Toxicity and Anti-Inflammatory Activities of Essential Oils from Three Grapefruit Cultivars from KwaZulu-Natal in South Africa

The medicinal potential and volatile composition of different parts of three cultivars of grapefruit (Citrus paradisi) were evaluated for their toxicity and anti-inflammatory activities. Fresh leaf and fruit peel were separately isolated by hydrodistillation for 4 h. The essential oils were subjected to GC/GC-MS analysis for chemical profile. Toxicity of the essential oils in mice were evaluated using Lorke’s method, while an anti-inflammatory assay was performed in a rat model using egg albumin-induced oedema. The oils obtained were light yellow in colour, and odour varied from strong citrus smell to mild. Percentage yield of fresh peel oil (0.34–0.57%) was greater than the fresh leaf oil yield (0.21–0.34%). D-limonene (86.70–89.90%) was the major compound identified in the leaf oil, while β-phellandrene (90.00–91.01%) dominated the peel oil. At a dosage level of 5000 mg/kg, none of the oils showed mortality in mice. An anti-inflammatory bioassay revealed that all the oils caused a significant (p < 0.05–0.01) reduction in oedema size when compared to the negative control group throughout the 5 h post induction assessment period. The study reveals that the oils are non-toxic and demonstrate significant anti-inflammatory activity. Our findings suggest that the leaf and peel oils obtained from waste parts of grapefruit plants can be useful as flavouring agents, as well as anti-inflammatory agents.     

The Chemical Compositions,and Antibacterial and Antioxidant Activities of Four Types of Citrus Essential Oils

Nanfeng mandarins (Citrus reticulata Blanco cv. Kinokuni), Xunwu mandarins (Citrus reticulata Blanco), Yangshuo kumquats (Citrus japonica Thunb) and physiologically dropped navel oranges (Citrus sinensis Osbeck cv. Newhall) were used as materials to extract peel essential oils (EOs) via hydrodistillation. The chemical composition, and antibacterial and antioxidant activities of the EOs were investigated. GC-MS analysis showed that monoterpene hydrocarbons were the major components and limonene was the predominate compound for all citrus EOs. The antibacterial testing of EOs against five different bacteria (Bacillus subtilis, Staphylococcus aureus, Escherichia coli, Pseudomonas aeruginosa and Salmonella typhimurium) was carried out using the filter paper method and the broth microdilution method. Kumquat EO had the best inhibitory effect on B. subtilis, E. coli and S. typhimurium with MIC (minimum inhibitory concentration) values of 1.56, 1.56 and 6.25 µL/mL, respectively. All citrus EOs showed the antioxidant activity of scavenging DPPH and ABTS free radicals in a dose-dependent manner. Nanfeng mandarin EO presented the best antioxidant activity, with IC₅₀ values of 15.20 mg/mL for the DPPH assay and 0.80 mg/mL for the ABTS assay. The results also showed that the antibacterial activities of EOs might not be related to their antioxidant activities.     

Isolation of Volatile Compounds with Repellent Properties against Aedes albopictus (Diptera: Culicidae) Using CPC Technology

The present work describes the use of Centrifugal Partition Chromatography (CPC) for the bio-guided isolation of repellent active volatile compounds from essential oils. Five essential oils (EOs) obtained from three Pinus and two Juniperus species were initially analyzed by gas chromatography–mass spectrometry (GC/MS) and evaluated for their repellent properties against Aedes albopictus. The essential oil from needles of P. pinea (PPI) presented the higher activity, showing 82.4% repellency at a dose of 0.2 μL/cm². The above EO, together with the EO from the fruits of J. oxycedrus subsp. deltoides (JOX), were further analyzed by CPC using the biphasic system n-Heptane/ACN/BuOH in ratio 1.6/1.6/0.2 (v/v/v). The analysis of PPI essential oil resulted in the recovery of (−)-limonene, guaiol and simple mixtures of (−)-limonene/β-pheladrene, while the fractionation of JOX EO led to the recovery of β-myrcene, germacrene-D, and mixtures of α-pinene/β-pinene (ratio 70/30) and α-pinene/germacrene D (ratio 65/45). All isolated compounds and recovered mixtures were tested for their repellent activity. From them, (−)-limonene, guaiol, germacrene-D as well the mixtures of (−)-limonene/β-pheladrene presented significant repellent activity (>97% repellency) against Ae. albopictus. The present methodology could be a valuable tool in the effort to develop potent mosquito repellents which are environmentally friendly.