On designated-weight Boolean functions with highest algebraic immunity

Algebraic immunity has been considered as one of cryptographically significant properties for Boolean functions. In this paper, we study ∑d-1 i=0 (ni)-weight Boolean functions with algebraic immunity achiev-ing the minimum of d and n - d + 1, which is highest for the functions. We present a simpler sufficient and necessary condition for these functions to achieve highest algebraic immunity. In addition, we prove that their algebraic degrees are not less than the maximum of d and n - d + 1, and for d = n1 +2 their nonlinearities equalthe minimum of ∑d-1 i=0 (ni) and ∑ d-1 i=0 (ni). Lastly, we identify two classes of such functions, one having algebraic degree of n or n-1.     

序Banach空间非混合单调二元算子不动点的存在唯一性及应用

利用锥理论和Banach压缩映象原理在更一般的条件下建立了序Banach空间中一类非混合单调二元算子不动点的存在唯一性定理,并应用到Banach空间中二阶非线性Volterra型微分-积分方程初值问题,改进并推广了已有的一些结果.     

Contact Finite Determinacy of Relative Map Germs

The strong contact finite determinacy of relative map germs is studied by means of classical singularity theory. We first give the definition of a strong relative contact equivalence （or KS,T equivalence） and then prove two theorems which can be used to distinguish the contact finite determinacy of relative map germs, that is, f is finite determined relative to KS,T if and only if there exists a positive integer k, such that M^5（n）ε（S;n）p ∩→ TKs,T（f）.     

Mathematical analysis of an eco-epidemiological predator–prey model with stage-structure and latency

In this paper, an eco-epidemiological predator–prey model with stage structure for the prey and a time delay describing the latent period of the disease is investigated. By analyzing corresponding characteristic equations, the local stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the endemic equilibrium is addressed. The existence of Hopf bifurcations at the endemic equilibrium is established. By using Lyapunov functionals and LaSalle’s invariance principle, sufficient conditions are obtained for the global asymptotic stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the endemic equilibrium of the model.     

4-卤-5-(4-甲基-2H-1-苯并-2-吡喃酮-7-氧基)-2-取代-3(2H)-哒嗪酮衍生物的合成和生物活性研究

通过4,5-二氯(溴)-3(2H)-哒嗪酮与7-羟基-4-甲基香豆素在CH3CN/K2CO3体系下的缩合反应,将具有生物活性的哒嗪酮环引入到苯并吡喃酮结构中,设计、合成了9个含哒嗪酮环的香豆素类化合物,其中8个为新化合物.所有化合物的结构均经NMR,MS和元素分析确证.初步生物活性测试结果表明:化合物4-氯-5-(4-甲基-2H-1-苯并吡喃-2-酮-7-氧基)-2-(4-硝基苯基)-3(2H)-哒嗪酮对黄瓜根部具有一定的抑制作用.     

Oxadisilole fused triptycene and extended triptycene: precursors of triptycyne and extended triptycyne

With benzobisoxadisilole 1 as a 1,4-benzdiyne equivalent, oxadisilole fused triptycene 5 and extended triptycene 6 were synthesized. Triptycenes 5 and 6 are new precursors of triptycyne 7 and extended triptycyne 8 respectively via the phenyliodination/fluoride induced elimination protocol. Using these two arynes, a series of triptycene derivatives were synthesized.     

Solution‐Processed Bulk Heterojunction Photovoltaic Cells from Gradient π‐Conjugated Thienylene Vinylene Dendrimers

A series of gradient π‐conjugated dendrimers and their corresponding models based on 5,5,10,10,15,15‐hexahexyltruxene moieties as nodes and oligo(thienylene vinylene) (OTVs) units with different lengths as branching arms are synthesized in good yields through Wittig–Horner reactions. All new compounds are fully characterized by ¹H and ¹³C NMR spectroscopy, elemental analysis, and MALDI‐TOF MS or ESI‐MS. Investigation of their photophysical properties reveals that the gradient dendritic scaffold not only results in a higher molar absorption coefficient and broader absorption region than those of their corresponding model compounds, but also improves the PL quantum yields relative to the corresponding OTVs. The suitable HOMO and LUMO levels as well as excellent film forming properties make these molecules potential candidates for organic solar cells. Solution‐processed bulk heterojunction solar cells using these dendrimers as donor and [6,6]‐phenyl‐C₆₁ butyric acid methyl ester as acceptor are prepared and tested. The power conversion efficiency of the devices based on G0-4-2 is 0.40 % under illumination of air mass 1.5 and 100 mW cm^?2. This is the highest record value for OTV‐based materials to date. Although the absorption band of dendrimer G0-4-2 is much narrower than that of poly(3‐hexylthienylene vinylene) (P3HTV), the efficiency of its solar cell device is almost twice that of the device based on P3HTV. This result shows clearly the advantage of gradient dendritic structures as active materials for photovoltaic cells.     

Benzothiadiazole Containing D‐π‐A Conjugated Compounds for Dye‐Sensitized Solar Cells: Synthesis,Properties, and Photovoltaic Performances

Two D ‐π‐A conjugated molecules, BzTCA and BzTMCA , were developed through facile synthetic approaches for dye‐sensitized solar cells. The investigation of the photophysical properties of BzTCA and BzTMCA both in dilute solutions and in thin films indicates that their absorption exhibits a wide coverage of the solar spectrum. The absorption features for BzTCA and BzTMCA commence at about 710 nm in solution, and at about 800 nm in the solid state. The absorption maxima (λ_max) for both BzTCA and BzTMCA on TiO₂ film are almost the same as those in dilute solution. Their HOMOs and LUMOs were found to partly overlap at the center of these dyes, which guarantees appreciable interactions between the donors and acceptors. The investigation of the performance of dye‐sensitized solar cells fabricated from BzTCA and BzTMCA indicated that the power‐conversion efficiencies are 6.04 % and 4.68 %, respectively, which could be comparable with the normal sensitizer N3. BzTMCA showed lower incident photon‐to‐electron conversion efficiency (IPCE) and J_sc values relative to BzTCA , which is probably because of the weaker driving force of dye regeneration and electron injection process of BzTMCA . The IPCE responsive area reached nearly 800 nm, which provides great potential for further improvement of the photocurrent density and power‐conversion efficiency. Our investigations demonstrate that both dyes BzTCA and BzTMCA could be promising candidates for dye‐sensitized solar cells.     

A new sesquiterpene and other constituents from Saussurea lappa root

Five sesquiterpenes, dehydrocostus lactone (1), santamarine (5), beta-cyclocostunolide (6), 4alpha-hydroxy-4beta-methyldihydrocostol (7) and 10alpha-hydroxyl-artemisinic acid (9), along with four other compounds, beta-sitosterol (2), daucosterol (3), 5-hydroxymethyl-furaldehyde (4), and trans-syingin (8), were isolated and identified from the roots of Saussurea lappa (Compositae). Based on previous reports and our study, sesquiterpene derivatives are common and characteristic constituents of the genus Saussurea. Among the nine compounds obtained, 9 is a new sesquiterpene. It is an artemisinic acid derivative, whose structural skeleton has not been reported for Saussurea species before, but artemisinic acid is a common compound in another Compositae species, Artemisia annua. Dehydrocostus lactone (1) is present in high-content and is a possible bioprecursor of 10alpha-hydroxyartemisinic acid (9).     

碳/氧化物复合物中碳层对氧化物相变的影响

碳/氧化铝(氧化钛)复合物具有独特的物理化学性质,在吸附和催化过程中有广泛应用.复合物中碳层对氧化物的相变有重要影响.在高温下通氧气焙烧碳/γ-Al2O3复合物可使γ-Al2O3迅速转变为α-Al2O3;而在惰性气氛中,碳层可显著抑制氧化铝的相变与烧结.碳/氧化钛体系中,碳层可明显提高氧化钛在惰性气氛中的热稳定性,在800℃以下碳层能有效阻止锐钛矿相向金红石相的转变;在含氧气氛中控制焙烧条件可将碳层完全除去而基本不影响氧化钛的物相组成及织构.因此,碳层可作为一种特殊的表面修饰剂,既可在高温下抑制氧化物的相变,又可避免在氧化物中引入掺杂元素.