New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type

We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained.     

Ultrasound-assisted immersion freezing reduces the structure and gel property deterioration of myofibrillar protein from chicken breast

The effects of air freezing (AF), immersion freezing (IF) and ultrasound-assisted immersion freezing (UF) at different power levels (125, 165, 205 and 245 W) on the structure and gel properties of the myofibrillar protein (MP) of chicken breast were investigated. UF at 165 W (UF-165) had no obvious negative impact on the primary structure of the MP and effectively reduced the change in the secondary and tertiary structure. In addition, UF-165 significantly reduced the losses in the elastic modulus (G′), gel strength, and gel water holding capacity (P < 0.05). According to low field nuclear magnetic resonance analysis, the T₂₁ and T₂₂ of the UF-165 MP gels were shorter than those of the AF and IF samples, which meant that the UF-165 reduced the mobility of the immobilized water and free water in MP gel. A scanning electron microscopy analysis showed that the appropriate ultrasonic power promoted the formation of a compact and homogeneous protein gel network. These results suggested that the appropriate ultrasonic power maintained the MP structure and reduced the loss of gel quality.     

Characterization and linear-time detection of minimal obstructions to concave-round graphs and the circular-ones property

A graph is concave-round if its vertices can be circularly enumerated so that the closed neighborhood of each vertex is an interval in the enumeration. In this study, we give a minimal forbidden induced subgraph characterization for the class of concave-round graphs, solving a problem posed by Bang-Jensen, Huang, and Yeo [SIAM J. Discrete Math., 13 (2000), pp. 179–193]. In addition, we show that it is possible to find one such forbidden induced subgraph in linear time in any given graph that is not concave-round. As part of the analysis, we obtain characterizations by minimal forbidden submatrices for the circular-ones property for rows and for the circular-ones property for rows and columns and show that, also for both variants of the property, one of the corresponding forbidden submatrices can be found (if present) in any given matrix in linear time. We make some final remarks regarding connections to some classes of circular-arc graphs.     

Theoretical study on the catalytic properties of single-atom catalyst stabilised on silicon-doped graphene sheets

ABSTRACT

The stable configurations, electronic structures and catalytic activities of single-atom metal catalyst anchored silicon-doped graphene sheets (3Si-graphene-M, M?=?Ni and Pd) are investigated by using density functional theory calculations. Firstly, the adsorption stability and electronic property of different gas reactants (O₂, CO, 2CO, CO/O₂) on 3Si-graphene-M substrates are comparably analysed. It is found that the coadsorption of O₂/CO or 2CO molecules is more stable than that of the isolated O₂ or CO molecule. Meanwhile, the adsorbed species on 3Si-graphene-Ni sheet are more stable than those on the 3Si-graphene-Pd sheet. Secondly, the possible CO oxidation reactions on the 3Si-graphene-M are investigated through Eley–Rideal (ER), Langmuir–Hinshelwood (LH) and new termolecular Eley–Rideal (TER) mechanisms. Compared with the LH and TER mechanisms, the interaction between 2CO and O₂ molecules (O₂?+?CO → CO₃, CO₃?+?CO → 2CO₂) through ER reactions (< 0.2?eV) are an energetically more favourable. These results provide important reference for understanding the catalytic mechanism for CO oxidation on graphene-based catalyst.     

Certain fractional calculus and integral transform results of incomplete ℵ-functions with applications

In this paper, we study certain interesting and useful properties of incomplete $\aleph$-functions. The incomplete $\aleph$-function is an extension of the $\aleph$-function. We find several useful classical integral transforms of these functions. Further, we examine the fractional calculus with the incomplete $\aleph$-functions and point out several special cases. Finally, we give the applications of incomplete $\aleph$-functions in detecting glucose supply in human blood.     

受限亚音速气流中倒置悬臂壁板静气弹稳定性的理论及实验研究

板壳结构在航空航天、高速列车、能量采集等诸多工程领域已经得到了广泛应用. 将悬臂壁板倒置于轴向气流中并在壁板周围流场中设置刚性壁面可有效地调控壁板的失稳速度, 是俘能器优化设计的重要措施之一. 但针对刚性壁面作用下亚音速气流中倒置悬臂壁板的失稳机制仍需要开展深入研究. 本文以受限亚音速气流中倒置的二维悬臂壁板为对象, 以理论分析及风洞实验为手段, 研究了单侧刚性壁面效应对倒置悬臂壁板静态失稳特性的影响规律. 在理论分析中, 首先应用镜像函数法来处理壁面约束条件, 基于算子理论研究获得了以Possio积分方程为表征的壁板气动力, 壁面效应实际表征为一包含移位Tricomi算子的复合算子; 然后将壁板失稳方程的求解问题转化为定区间上的函数逼近问题; 最后, 依据Wererstrass定理并利用最小二乘法求解该最优函数, 以获得系统的失稳临界参数. 在试验研究中依据压杆稳定原理设计了壁板静态失稳的测试方法并完成了风洞实验. 理论分析结果表明, 壁板会发生发散(静气动弹性)失稳, 临界动压随壁板与壁面间距的增加而增大并最终趋于稳定(无壁面情况); 通过理论与风洞实验结果的对比分析, 验证了本文气动力及理论分析的适用性及准确性. 针对倒置悬臂壁板结构的气动弹性失稳问题, 本文提出的方法不涉及系统方程的离散及特征值求解问题, 而是将其转化为了定区间上的函数逼近问题进行求解, 这为弹性结构静气动弹性失稳问题的研究提供了一个可行的新思路.      

Free radical polymerization of caffeine‐containing methacrylate monomers

The incorporation of acrylic functionality into caffeine enables the preparation of a vast array of novel thermoplastics and thermosets. A two‐step derivatization provided a novel caffeine‐containing methacrylate monomer capable of free radical polymerization. Copolymers of 2‐ethylhexyl methacrylate and caffeine methacrylate (CMA) allowed for a systematic study of the effect of covalently bound caffeine on polymer properties. ¹H NMR and UV‐vis spectroscopy confirmed caffeine incorporation at 5 and 13 mol %, and SEC revealed the formation of high molecular weight (co)polymers (>40,000 g/mol). CMA incorporation resulted in a multistep degradation profile with initial mass loss closely correlating to caffeine content. Differential scanning calorimetry, rheological, and thermomechanical analysis demonstrated that relatively low levels of CMA increased the glass transition temperature, resulting in higher moduli and elucidating the benefits of incorporating caffeine into polymers. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2829–2837     

On the low-temperature anomalies of specific heat in disordered carbon nanotubes

The low-temperature behavior of the specific heat in disordered nanotubes strongly depends on structure changes and is not explained by the phonon contribution. Expression for electronic specific heat is carried out taking into account the multiple elastic electron scattering on impurities and structural inhomogeneities of short-range order type. The calculated electronic specific heat depends on diameter of nanotube, concentration of impurities, parameters of short-range order (structural heterogeneity) and describes the peculiarities of low-temperature behavior of specific heat observed in disordered CNT.     

Microstructure evolution and mechanical property of pulsed laser welded Ni-based superalloy

For evaluating the microstructure evolution and mechanical property of Ni-based Hastelloy C-276 weld joint by the pulsed laser welding, the influence of pulsed laser welding on the microstructure and mechanical property of the weld joint is investigated by the analysis of the microstructure morphology, microhardness, phase structure and tensile property. The results indicate that, in the fusion zone three sections are divided on the basis of the patterns of grain structures. In the weld joint, the element segregation is found, but the trend of brittle phase׳s formation is weakened. The weld microhardness presents just a little higher than that of base metal, and there is no obvious the softened heat affected zone. Meanwhile in the weld joint, the phase structure is still the face-center cubic with the tiny shift of peak positions and widened Full Width at Half-Maximum. The yield strength of weld joint is the same as that of base metal, and the tensile strength is nearly 90% of that of base metal. The decreased tensile strength is mainly attributed to the dislocation piling-up.     

Fabrication and microstructural characterization of functionally graded porous acrylonitrile butadiene styrene and the effect of cellular morphology on creep behavior

The ability to control material properties in space and time for functionally graded viscoelastic materials makes them an asset where they can be adapted to different design requirements. The continuous microstructure makes them advantageous over conventional composite materials. Functionally graded porous structures have the added advantage over conventional functionally graded materials of offering a significant weight reduction compared to a minor drop in strength. Functionally graded porous structures of acrylonitrile butadiene styrene (ABS) had been fabricated with a solid‐state constrained foaming process. Correlating the microstructure to material properties requires a deterministic analysis of the cellular structure. This is accomplished by analyzing the scanning electron microscopy images with a locally adaptive image threshold technique based on variational energy minimization. This characterization technique of the cellular morphology is analyst independent and works very well for porous structures. Inferences are drawn from the effect of processing on microstructure and then correlated to creep strain and creep compliance. Creep is strongly correlated to porosity and pore sizes but more associated to the size than to porosity. The results show the potential of controlling the cellular morphology and hence tailoring creep strain/compliance of ABS to some desired values. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 795–803