Theoretical and Experimental Study of the Diffraction Intensity of Gradient Refractive-Index Lenses

We develop the wave-optics approach for calculating the diffraction distribution of gradient refractiveindex lenses and observing the diffraction pattern of gradient refractive-index lenses in the experiments. The results of our calculation are in good agreement with the experimental results obtained. We show that the diffraction can be regarded as a method to check the quality of the refractive-index distributions of gradient refractive-index lenses.     

The Dynamics of Power laws: Fitness and Aging in Preferential Attachment Trees

Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. The multiplicative fitness moderates the rate at which children are born, while the aging is integrable, so that individuals receives a finite number of children in their lifetime. We show the existence of a limiting degree distribution for such processes. In the preferential attachment case, where fitness and aging are absent, this limiting degree distribution is known to have power-law tails. We show that the limiting degree distribution has exponential tails for bounded fitnesses in the presence of integrable aging, while the power-law tail is restored when integrable aging is combined with fitness with unbounded support with at most exponential tails. In the absence of integrable aging, such processes are explosive.     

A remark on analytic Fredholm alternative

We apply a recent result of Borichev–Golinskii–Kupin on the Blaschke-type conditions for zeros of analytic functions on the complex plane with a cut along the positive semi-axis to the problem of the eigenvalues distribution of the Fredholm-type analytic operator-valued functions.     

Synthesis,characterization and molecular docking studies of thiouracil derivatives as potent thymidylate synthase inhibitors and potential anticancer agents

Thymidylate synthase (TS), one of folate-dependent enzymes, is a key and well-recognized target for anticancer agents. In this study, a series of 6-aryl-5-cyano thiouracil derivatives were designed and synthesized in accordance with essential pharmacophoric features of known TS inhibitors. Nineteen compounds were screened in vitro for their anti-proliferative activities toward HePG-2, MCF-7, HCT-116, and PC-3 cell lines. Compounds \(\mathbf{21}_{\mathbf{c}}\), \(\mathbf{21}_{\mathbf{d}}\), and 24 exhibited high anti-proliferative activity, comparable to that of 5-fluorouracil. Additionally, ten compounds with potent anti-proliferative activities were further evaluated for their ability to inhibit TS enzyme. Six compounds (\(\mathbf{21}_{\mathbf{b}}\), \(\mathbf{21}_{\mathbf{c}}\), \(\mathbf{21}_{\mathbf{d}}\), 22, 23 and 24) demonstrated potent dose-related TS inhibition with \(\hbox {IC}_{50}\) values ranging from 1.57 to \(3.89\,\upmu \hbox {M}\). The in vitro TS activity results were consistent with those of the cytotoxicity assay where the most potent anti-proliferative compounds of the series showed good TS inhibitory activity comparable to that of 5-fluorouracil. Furthermore, molecular docking studies were carried out to investigate the binding pattern of the designed compounds with the prospective target, TS (PDB-code: 1JU6).     

Generation of an arbitrary chirped microwave waveform with high time-bandwidth product for increasing range resolution of RADAR by using photonic technique

An approach for photonic generation of an arbitrary chirped microwave waveform with an increased time-bandwidth product (TBWP) is proposed and experimentally demonstrated. In the proposed model, light from the mode locked laser is splitted into two parts by using 1 × 2 power splitter: one is sent to linearly chirped fiber Bragg grating (LCFBG) through circulator and the other is time delayed by fiber delay line. The optical pulse in upper arm is time stretched by the LCFBG. Meanwhile, the optical pulse in lower arm experiences a time delay and then stretched by the dispersive single mode fiber. Temporal interference pattern is generated with an increasing or decreasing free spectral range by combination of two time-stretched optical pulses. Finally, the temporal interference pattern which is obtained at the output of optical coupler is transformed into an arbitrary chirped microwave waveform by using a photo-detector. The main advantage of this proposed model is high TBWP in the range of 750–1000 which ultimately results in an increased range resolution of radio detection and ranging.     

High-lying excited states in <Superscript>10</Superscript>Be from the <Superscript>9</Superscript>Be(<Superscript>9</Superscript>Be,<Superscript>10</Superscript>Be)<Superscript>8</Superscript>Be reaction

A transfer-reaction experiment of ⁹Be(⁹Be, ¹⁰Be)⁸Be was performed at a beam energy of 45 MeV. Excited states in ¹⁰Be up to 18.80 MeV are produced using missing mass and invariant mass methods. Most of the observed high-lying resonant states, reconstructed from the α + ⁶He and t + ⁷Li decay channels, agree with the previously reported results. In addition, two new resonances at 15.6 and 18.8 MeV are identified from the present measurement. The 18.55 MeV state is found to decay into both the t + ⁷Li_g.s. and t + ⁷Li* (0.478 MeV) channels, with a relative branching ratio of 0.93 ± 0.33. Further theoretical investigations are encouraged to interpret this new information on cluster structure in neutron-rich light nuclei.     

Enhancement of electrochemical properties of Ca<Subscript>3</Subscript>Co<Subscript>4</Subscript>O<Subscript>9</Subscript> as anode materials for lithium-ion batteries by transition metal doping

Misfit-layered calcium cobaltites (Ca₃Co₄O₉, Ca₃Co_3.9Fe_0.1O₉, and Ca₃Co_3.9Mn_0.1O₉), as anode materials for lithium-ion batteries, were synthesized by a simple hydro-decomposition method. All synthesized samples do not show any impurity phase. They exhibited plate-like particle with the particle size of 1–2 μm. The specific capacities of doped samples showed higher electrochemical performance compared to the undoped sample. After charge/discharge of 50 cycles, the specific capacities of Ca₃Co₄O₉, Ca₃Co_3.9Fe_0.1O₉, and Ca₃Co_3.9Mn_0.1O₉ were 343, 562, and 581 mAh g^?1, respectively. The doped samples showed an increase of over 60% compared to the undoped sample. The cyclic voltammetry profile of the doped samples showed the enhanced reactivity corresponding to their improved electrochemical performance. The capacity improvement of doped samples resulted from the metal oxide/Li conversion reactions, volume change, and high reactivity.     

A piperidinium-based ester-functionalized ionic liquid as electrolytes in Li/LiFePO<Subscript>4</Subscript> batteries

A new functionalized ionic liquid (IL) based on cyclic quaternary ammonium cations with ester group and bis(trifluoromethanesulfonyl)imide ([TFSI]^?) anion, namely, N-methyl-N-methoxycarbonylpiperidinium bis(trifluoromethanesulfonyl)imide ([MMOCPip][TFSI]), was synthesized and characterized. Physical and electrochemical properties, including Li-ion transference number, ionic conductivity, and electrochemical stability, were investigated. The electrochemical window of [MMOCPip][TFSI] was 6 V, which was wide enough to be used as a common electrolyte material. The Li-ion transference number of this IL electrolyte containing 0.1 M LiTFSI was 0.56. The half-cell tests indicated that the [MMOCPip][TFSI] obviously improved the cyclability of a Li/LiFePO₄ cell. For the Li/LiFePO₄ half-cells, after 20 cycles at room temperature at 0.1 C, the discharge capacity was 109.7 mAh g^?1 with 98.7% capacity retention in the [MMOCPip][TFSI]/0.1 M LiTFSI electrolyte. The good electrochemical performance demonstrated that the [MMOCPip][TFSI] could be used as electrolyte for lithium-ion batteries.     

On adaptive modified projective synchronization of a supply chain management system

In this paper, the synchronization problem of a chaotic supply chain management system is studied. A novel adaptive modified projective synchronization method is introduced to control the behaviour of the leader supply chain system by a follower chaotic system and to adjust the leader system parameters until the measurable errors of the system parameters converge to zero. The stability evaluation and convergence analysis are carried out by the Lyapanov stability theorem. The proposed synchronization and antisynchronization techniques are studied for identical supply chain chaotic systems. Finally, some numerical simulations are presented to verify the effectiveness of the theoretical discussions.     

基于Jiles-Atherton理论的铁磁材料塑性变形磁化模型修正

Jiles-Atherton(J-A)模型在磁化建模领域应用广泛,但不同文献给出的J-A模型并不一致,致使采用不同表达式建立的塑性变形磁化模型存在多种版本,其正确性难以甄别.通过对无磁滞磁化方程、能量守恒方程和等效磁场强度方程的梳理与比较,发现原有模型中存在将磁化强度和无磁滞磁化强度混用、将不可逆磁化能量等效于全部的磁化能量、等效磁场强度中应力磁化项界定不清等问题.在此基础上,对上述方程进行了修正,推导了基于J-A模型的塑性变形磁化修正模型.将修正模型计算结果与原模型计算结果、相关文献中的试验结果进行对比,结果表明:与原有计算模型相比,修正模型计算结果的饱和磁化强度和剩余磁化强度随塑性变形增加而减小,矫顽力随塑性变形增大而增大,达到饱和磁化强度时的外磁场强度随塑性变形增大而增大的趋势有所减弱,更符合试验结果,可更准确地反映塑性变形对材料磁化的影响.