Convex hull of powers of a complex number,trinomial equations and the Farey sequence

The color of a complex number is defined as the number of vertices of the convex hull of powers of that number. This induces a coloring of the unit disk. The structure of the set of points where the color changes is investigated here. It is observed that there is a connection between this fractal set and some family of trinomial equations. Three algorithms for coloring the unit disk are described, the last one (related to the Farey sequence) arising out of a conjecture. This conjecture is formulated and proved in this presentation.     

Photochemistry of β, γ-unsaturated ketones-V: The direct irradiation of some γ-phenyl β, γ-enones

The photochemistry of some members of the two series of γ-phenyl substituted acyclic β, γ-unsaturated ketones 1 and 2 upon direct irradiation with γ 310nm has been investigated, viz 1c–1h and 2b+2c.The alkyl substituted (E)-5-phenyl-4-penten-2-ones 1c–1h yield the corresponding 1,3-acyl shift products and (Z)-isomers, and 1g and 1h in addition two decarbonylated products. 2b only yields the (Z)-isomer and some benzaldehyde, but 2c yields the 1,3-acyl shift product, the ODPM product, three hydrocarbons formed by disproportionation of the allyl radical, and some benzaldehyde. The β-phenyl β, γ-UK 3a proved to be photostable. The 1,3-acyl shift products of 1c–1h result mainly from the singlet excited state in a cage radical process. The exclusive formation of the (E)-configuration of the 1,3-acyl shift product is explained in terms of conformational preference of the intermediate allyl radical. It is proposed that the formation of the (Z)-isomer proceeds from ¹T(π -π^*) which is populated according to

. Evidence is presented which supports the proposed mechanism.The β,γ-UK 2b containing a benzoyl moiety leads to a higher degree of (E)-(Z) isomerization than the corresponding 1d which has an acetyl moiety.The triplet energies of (E)- and (Z)-1h are 56 and ca 70 kcal/mol respectively.     

266nm脉冲激光光解基质隔离的cis-(NO)2

NO的氧化是大气化学研究的重要课题．CIS－（NO）。是一氧化氮氧化过程的中间体，对其在低温基质条件下的形成和氧化过程研究前文风已作了报导．H。WhiffS等门曾用中压汞灯作为光解光源（220－320urn），研究了ets－（NO）。在Ar低温基质中的光解，产物为N。O和NZO3．CIS－（NO     

A new 4-D non-equilibrium fractional-order chaotic system and its circuit implementation

A new 4-D fractional-order chaotic system without equilibrium point is proposed in this paper. There is no chaotic behavior for its corresponding integer-order system. By computer simulations, we find complex dynamical behaviors in this system, and obtain that the lowest order for exhibiting a chaotic attractor is 3.2. We also design an electronic circuit to realize this 4-D fractional-order chaotic system and present some experiment results.     

Some Remarks on One-dimensional Functions and Their Riemann–Liouville Fractional Calculus

A one-dimensional continuous function of unbounded variation on [0,1] has been constructed.The length of its graph is infnite,while part of this function displays fractal features.The Box dimension of its Riemann–Liouville fractional integral has been calculated.     

CuI/l-proline catalyzed click reaction in glycerol for the synthesis of 1,2,3-triazoles

Despite the apparent simplicity of the copper(I) iodide catalyzed CuAAC reaction, the conversion of the catalytic species, i.e. Cu(I) to thermodynamically more stable Cu(II), via aerial oxidation or disproportionation is a major issue. To stabilize the Cu(I) species, the reaction is ideally carried out under an inert atmosphere in the presence of additives such as alcohols, amines, thiols, and aldehydes. Herein, we report the first CuI catalyzed click reaction without an inert atmosphere by employing the CuI/l-proline system in glycerol. The method showed remarkable stability towards sensitive functional groups such as acetonides and 1,2,4-trioxanes.     

On the symmetry of three identical interacting particles in a one-dimensional box

We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group D_3d$D_{3d}$. Group theory greatly facilitates the application of perturbation theory and the Rayleigh–Ritz variational method. A great advantage is that every irreducible representation can be treated separately. Group theory enables us to predict the connection between the states for the small box length and large box length regimes of the system. We discuss the crossings and avoided crossings of the energy levels as well as other interesting features of the spectrum of the system.     

Synthesis,design of experiments and optimization of heterogeneous Fenton-like degradation of tartrazine by MgFe2O4 nano-catalyst

In this work, magnesium ferrites nanoparticles (MgFe₂O₄ NPs) were successfully fabricated by sol-gel auto-combustion (SGAC) method and were used in heterogeneous Fenton-like degradation of tartrazine. The obtained products were characterized using XRD, FTIR, SEM and EDX. XRD studies confirmed that the synthesized MgFe₂O₄ NPs had a cubic spinel structure. The average crystallite size was evaluated using the Debyee Scherrer formula and found to be in the range 16.18–28.55 nm. In FTIR spectra, two primary absorption bands at 571 cm^?1 and 415 cm^?1 were observed. The spinel ferrites are characterized by these bands and the EDX confirms the presence of the desired elements Mg, Fe, and O. The influences of operating parameters were examined using the Box Behnken statistical design (BD), including magnesium ferrite dosage (0.04–0.12 g/L), tartrazine concentration (30–50 mg/L) and H₂O₂ concentration (3.53–7.06 mM). Using analysis of variance, a significant quadratic model was created. Optimum conditions were magnesium ferrite dosage of 0.092 g/L, tartrazine concentration of 30.21 mg/L and H₂O₂ concentration of 6.66 mM, respectively. The predicted degradation efficiency within the optimum conditions as established by the suggested model was 98.4%. Confirmatory tests were carried out and the degradation efficiency of 98.9% was observed, which was in good agreement with the model's prediction. After five recuperation and reapplications, the catalyst's degradation efficiency remains stable. These findings indicate that a heterogeneous Fenton-like process utilizing MgFe₂O₄ is effective in advanced wastewater treatment.     

基于kinect和unity的虚拟手抓取碰撞检测算法

针对目前碰撞检测算法效率低精度差的问题,提出了一种改进的层次方向包围盒（OBB）算法。首先通过位置关系判断虚拟手是否在物体包围球的邻近区域,然后用OBB和八叉树算法进行详细的碰撞检测,最后利用离散点到虚拟手简化面的矢量计算法实现精确的碰撞检测。实验结果表明,随着三维物体基元数目的增多,这种由粗略到精确递进的检测方式极大的提高了碰撞检测的效率和精度,具有可行性。该算法适用于任何复杂场景中刚体结构模型的碰撞检测,在运行时候不存在滞后情况,显示流畅,而且碰撞检测精度高,完全能够满足虚拟环境实时性和精确性的要求。     

Fragmentation of fuel pellets during transport via a belt conveyor: A design of experiment study

This work investigates the proportion of generated fines in a pilot-scale experiment using a belt conveyor and commercial fuel pellets. For this, a belt conveyor with a length of 3.1 m was used and operated at varying conditions: speeds, percentages of material loading on the belt, two combinations of the inclination angle of the belt and the falling height, and a different number of handling steps. We considered a design of experiments approach based on response surface methodology to investigate the effect of different conditions on the potential of fines generation. Moreover, a comparison between the results of the belt conveyor and three common benchmark experimental approaches (tumbling box, rotary impact tester, and mechanical compression test) was made. Results show that the number of handling steps and the combined effect of drop height and inclination angle directly affected the fines generation. However, the tested belt speed range and the level of loading were of lower significance. A polynomial quadratic model was derived based on the regression analysis and showed a high accuracy to predict the proportion of fines. Moreover, the tumbling box method showed good potential to predict the proportion of fines in a belt conveyor when transported several times.