The First Principle Study on the Rectification of Molecular Junctions Based on the Alkyl-chain-modified Phenyl Benzothiophene Derivative

Using density functional theory（DFT） combined with nonequilibrium Green＇s function investigates the electron-transport properties of several molecular junctions based on the PBTDT-CH=NH molecule, which is modified by one to four alkyl groups forming PBTDT-（CH2）nCH=NH. The electronic structures of the isolated molecules（thiol-ended PBTDT-（CH2）nCH=N） have been investigated before the electron-transport calculations are performed. The asymmetric current-voltage characteristics have been obtained for the molecular junctions. Rectifying performance of Au/S-PBTDT-CH=N-S/Au molecular junction can be regulated by introducing alkyl chain. The N3 molecular junction exhibits the best rectifying effect. Its maximum rectifying ratio is 878, which is 80 times more than that of the molecular junction based on the original N molecular junction. The current-voltage（I-V） curves of all the sandwich systems in this work are illustrated by transmission spectra and molecular projection density analysis.

CONSIDER SAINT-VENANT'S PRINCIPLE BY MEANS OF CHAIN MODEL

A precise background theory of computational mechanics is formed. Saint_Venant's principle is discussed in chain model by means of this precise theory. The classical continued fraction is developed into operator continued fraction to be the constrictive formulation of the chain model. The decay of effect of a self_equilibrated system of forces in chain model is decided by the convergence of operator continued fraction, so the reasonable part of Saint_Venant's principle is described as the convergence of operator continued fraction. In case of divergence the effect of a self_equilibrated system of forces may be non_zero at even infinite distant sections, so Saint_Venant's principle is not a common principle.

CHARACTERISTIC GRAIN SIZE: PART Ⅱ MEASURING PRINCIPLES

The principles for measuring characteristic grain sizes of materials, such as fully-dense single phase materials, porous materials and materials with isolated second phase particles, are developed on the basis of its definition associated closely with the surface area per unit volume, Sv, of grain. The focus of the measuring principles of the characteristic grain size is put on determining Sv of grains. Unlike the measurement of average grain size commonly used, G, correcting factors such as grain shape and grain size distribution factors, will not be applied to the determination of the characteristic grain size, Gc, due to its unique geometric meaning and the measure precision of Sv being guaranteed by quantitative stereological technique and gas adsorption method. The measurement of Gc can be directly carried out on the polished and etched cross section of materials, similar to the measuremernt of the average grain size using the Heyn intercept method.

Energetics and electronic structure of a single copper atomic chain wrapped in a carbon nanotube:a first-principles study

In the generalized gradient approximation, the energy and electronic structure are investigated for a single copper atomic chain wrapped in （4, 4）, （5, 5） and （6, 6） armchair carbon nanotubes by using the first-principles projector-augmented wave potential within the framework of density functional theory. The results show that the （4, 4） and （5, 5） tubes are too narrow to wrap a Cu chain, but the （6, 6） tube is nearly ideal to wrap a Cu chain on its centre axis. Wider tubes are anticipated to wrap more than one Cu chain spontaneously with forces amounting to a fraction of a nanonewton. Although the tube-chain interaction decreases with the increase of the tube diameter of （4, 4）, （5, 5） and （6, 6） successively, the charge density of the Cu@（6, 6） combined system still does not show complete superposition of that of the pristine （6, 6） tube and Cu chain. Successively reducing the restrictions of （4, 4）, （5, 5） and （6, 6） tubes on the Cu chain leads to a reduction in shift of the highest peak of the Cu chain towards lower energies, that is from -0.5177 eV of the isolated Cu chain to -1.36785 eV, -0.668 eV and -0.588 eV for the Cu@（4, 4）, Cu@（5, 5） and Cu@（6, 6） systems, respectively. In reverse, the strong metallic character of the Cu chain also enhances the metallic character of the combined systems so that the broader pseudogaps of the pristine carbon nanotubes around the Fermi level change into the narrow pseudogaps of the combined systems.

Type Synthesis of Fully-Decoupled 3R2T Parallel Mechanisms Based on Driven-Chain Principle

To avoid the existence of nonlinear and strong coupling in parallel mechanisms,it is necessary to address special care to the type synthesis of mechanisms,especially for the type synthesis of fully-decoupled parallel mechanisms. Based on the screw theory and the driven-chain principle,a methodology of structural synthesis for fully-decoupled three-rotational( 3R) and two-translational( 2T)parallel mechanisms was proposed by analyzing the characteristics of the input-output relations for fully-decoupled parallel mechanisms.Firstly,according to the desired kinematic characteristics of fullydecoupled parallel mechanisms,a method was presented by virtue of screw theory to synthesize the desired forms for both the direct and the inverse Jacobian matrices. Secondly,according to the feature of the direct and the inverse Jacobian matrices,the effective screws,the actuated screws and the mobile un-actuated screws of each leg were established based on the reciprocal screw theory and all possible topology structures fulfilling the requirements were obtained.Finally,the desired fully-decoupled parallel mechanisms could be synthesized by using the structural synthesis rule and structural synthesis of fully-decoupled 3R2 T parallel mechanisms could be obtained exploiting the abovementioned methodology. Furthermore,the Jacobian matrix of a synthesized 3R2 T parallel mechanism was deduced to demonstrate the decoupling feature of the parallel mechanism,which also validated the correctness of the methodology of the type synthesis for fully-decoupled 3R2 T parallel mechanisms.

Classical Electromagnetic Fields of Moving Charges as a Vehicle to Probe the Connection between the Elementary Charge and Heisenberg’s Uncertainty Principle

The radiation fields generated when a charged particle is incident on or moving away from a perfectly conducting plane are obtained. These fields are known in the literature as transition radiation. The field equations derived thus are used to evaluate the energy, momentum and the action associated with the radiation. The results show that for a charged particle moving with speed ν, the longitudinal momentum associated with the transition radiation is approximately equal to ΔU/c for values of ?1- ν/c smaller than about 10-3 where ΔU is the total radiated energy dissipated during the interaction and cis the speed of light in free space. The action of the radiation, defined as the product of the total energy dissipated and the duration of the emission, increases as 1- ν/c decreases and, for an electron, it becomes equal to h/4π when ν = c - νm where νm is the speed pertinent to the lowest possible momentum associated with a particle confined inside the universe and?h is the Planck constant. Combining these results with Heisenberg’s uncertainty principle, an expression that predicts the value of the elementary charge is derived.

Dissociations of O_2 molecules on ultrathin Pb(111) films:first-principles plane wave calculations

Using first-principles calculations, we systematically study the dissociations of 02 molecules on different ultrathin Pb（lll） films. According to our previous work revealing the molecular adsorption precursor states for O2, we further explore why there are two nearly degenerate adsorption states on Pb（lll） ultrathin films, but no precursor adsorption states existing at all on Mg（0001） and Al（lll） surfaces. The reason is concluded to be the different surface electronic structures. For the O2 dissociation, we consider both the reaction channels from gas-like and molecularly adsorbed O2 molecules. We find that the energy barrier for O2 dissociation from the molecular adsorption precursor states is always smaller than that from O2 gas. The most energetically favorable dissociation process is found to be the same on different Pb（lll） fihns, and the energy barriers are found to be influenced by the quantum size effects of Pb（lll） films.

The Invariance Principle for p-■Chain

There are two parts in this paper. In the first part we construct the Markov chain in random environment（MCRE）, the skew product Markov chain and p-θ^→ chain from a random transition matrix and a two-dimensional probability distribution, and in the second part we prove that the invarianee principle for p-θ^→ chain, a more complex non-homogeneous Markov chain, is true under some reasonable conditions. This result is more powerful.

Understanding formation mechanism of ZnO diatomic chain and multi-shell structure using physical mechanics:Molecular dynamics and first-principle simulations

In this paper,the possibility of the monatomic chain (MC) formation for ZnO material was studied by molecular dynamics (MD) simulation.The process of MC formation and the effects of temperature,strain rate and size were studied extensively.The tensile process can be divided to be five stages and the ZnO diatomic chain (DC) can be found.The MD results show that most atoms in MC came from the original surface of ZnO nanowires (NWs).Temperature and strain rate are two important factors affecting the process,and both high temperature and low strain rate in a certain range would be beneficial to the formation of DC.Moreover,the effects of strain rate and temperature could attribute to the Arrhenius model and the energy release mechanism.Furthermore,multi-shell structure was found for the samples under tensile strain and the layer-layer distance was about 3.Our studies based on density functional theory showed that the most stable structure of ZnO DC was confirmed to be linear,and the I-V curve was also got using ATK.

Effects of Particle Size and Chain Length on Flotation and Adsorption of Quaternary Ammonium Salts onto Kaolinite

Effects of particle size and chain length on flotation of quaternary ammonium salts (QAS) onto kaolinite have been investigated by mico-flotation tests. The two kinds of quaternary ammonium salts [RN(CH3)3] with different chain lengths, dodecyltrimethylammonium chloride (DTAC) and cetyltrimethylammonium chloride (CTAC) were used as collectors for kaolinite in different particle size fractions (0.075–0.01 mm, 0.045–0.075 mm, 0–0.045 mm). The anomalous flotation behavior of kaolinite have been further explained based on crystal structure considerations by adsorption tests and molecular dynamics (MD) simulation. The results show that the flotation recovery of kaolinite in all different particle size fractions decreases with an increase in pH when DTAC and CTAC are used as collectors. As the concentration of collectors increases, the flotation recovery increases. The longer the carbon chain of QAS is, the higher the recoveries of coarse kaolinite (0.075–0.01 mm and 0.045–0.075 mm) are. But the flotation recovery of the finest kaolinite (0–0.045 mm) decreases with chain lengths of QAS collectors increasing, which is consistent with the flotation results of unsifted kaolinite (0–0.075 mm). It is explained by the froth stability related to the residual concentration of QAS collector. In lower residual concentration, the froth stability becomes worse. Within the range of flotation collector concentration, it's easy of CTAC to be completely adsorbed by kaolinite in the particle size fraction (0–0.045 mm), which led to lower flotation recovery. Moreover, it is interesting that the particle size of kaolinite is coarser, the flotation recovery is higher. The anomalous flotation behavior of kaolinite is rationalized based on crystal structure considerations. The results of MD simulations show that the (001) kaolinite surface has the strongest interaction with DTAC, compared with the (001), (010) and (110) surfaces. On the other hand, when particle size of kaolinite is altered, the number of basal planes and edge planes is changed. It is observed that the finer kaolinite particles size become, the greater relative surface area of edges is, and the more the number of edges is. It means that fine kaolinite particles have more edges to adsorb less cationic colletors than that of coarse kaolinite particles, which is responsible for the poorer floatability of fine kaolinite.

Study on Factors Influencing the Reliability of the Organization Management Chain of the Large and Medium-Sized Project in the Construction Period

On the basis of analyzing the reliability of the organization’ management chain of the large and medium- sized project in the construction period, the paper studies the factors influencing the reliability of the organi-zation management chain, which, corresponding to four elements of management chain – “Management Loop”, “Management Link”, “Management Chain”, and “Management Network”, can be summarized as project main body, interface management, connection sequence and management model. The paper then re-searches on the specific influencing factors from the above-mentioned four aspects.

Firm Size, Innovation and Vertical Integration Incentives： The Case of Food Supply Chain

This study aims to investigate and explore the relationship between vertical integration and the firm＇s innovativeness in food supply chain. For doing so, a two-stage least-squares model was used. It encompassed instrumental variables that attempt to describe the effective determinants of firm＇s vertical integration willingness. Results based on data concerning a set of 130 food-manufacturing firms, highlighted that vertical integration of a firm is strongly affected by internal incentives such as innovation rate and firm size. Moreover, it is simultaneously influenced by the economies of scale and some structure incentives. To conclude, results indicate globally that important and statistically significant differences exist across the studied firms and the small effective ones which acquire a high level of vertical integration.

Size Effect on the Raman Spectra and Electronic Structure of the Glycine-alanine Oligopeptide Chains

A theoretical study on oligopeptide chains of glycine-alanine by density functional theory（DFT） is given in this paper. Raman spectra of the oligopeptide chains are examined. The geometric structures, frontier orbital, energy gap, atomic charge distribution, density of states and chemical activity of the side chain are studied at the B3LYP/6-31G（d） level. Results show that, with the number of residues increasing, vibrations of typical functional groups present Raman frequency shift, and the energy gap is gradually reduced. The HOMO and LUMO focus on the amino and carboxyl at the ends of oligopeptides. It is helpful for oligopeptides to self-assemble into chains. In addition, different residues（glycine or alanine） at the ends of chains result in the even-odd effect of orbital energy in the growth process. The size effects of physical and chemical properties only exist when the oligopeptides are shorter, and the phenomenon disappeared as the chain continues to grow.

Application of Stork Optimization Algorithm for Solving Sustainable Lot Size Optimization

The efficiency of businesses is often hindered by the challenges encountered in traditional Supply Chain Manage-ment(SCM),which is characterized by elevated risks due to inadequate accountability and transparency.To address these challenges and improve operations in green manufacturing,optimization algorithms play a crucial role in supporting decision-making processes.In this study,we propose a solution to the green lot size optimization issue by leveraging bio-inspired algorithms,notably the Stork Optimization Algorithm(SOA).The SOA draws inspiration from the hunting and winter migration strategies employed by storks in nature.The theoretical framework of SOA is elaborated and mathematically modeled through two distinct phases:exploration,based on migration simulation,and exploitation,based on hunting strategy simulation.To tackle the green lot size optimization issue,our methodology involved gathering real-world data,which was then transformed into a simplified function with multiple constraints aimed at optimizing total costs and minimizing CO_(2) emissions.This function served as input for the SOA model.Subsequently,the SOA model was applied to identify the optimal lot size that strikes a balance between cost-effectiveness and sustainability.Through extensive experimentation,we compared the performance of SOA with twelve established metaheuristic algorithms,consistently demonstrating that SOA outperformed the others.This study’s contribution lies in providing an effective solution to the sustainable lot-size optimization dilemma,thereby reducing environmental impact and enhancing supply chain efficiency.The simulation findings underscore that SOA consistently achieves superior outcomes compared to existing optimization methodologies,making it a promising approach for green manufacturing and sustainable supply chain management.

Comparison principle and stability criteria for stochastic differential delay equations with Markovian switching

In the present paper we first obtain the comparison principle for the nonlinear stochastic differentialdelay equations with Markovian switching. Later, using this comparison principle, we obtain some stabilitycriteria, including stability in probability, asymptotic stability in probability, stability in the pth mean, asymptoticstability in the pth mean and the pth moment exponential stability of such equations. Finally, an example isgiven to illustrate the effectiveness of our results.

On the optimal harvesting of size-structured population dynamics

This work is concerned with a kind of optimal control problem for a size-structured biological population model.Well-posedness of the state system and an adjoint system are proved by means of Banach＇s fixed point theorem.Existence and uniqueness of optimal control are shown by functional analytical approach.Optimality conditions describing the optimal strategy are established via tangent and normal cones technique.The results are of the first ones for this novel structure.

Optimal harvesting for an age-dependent n-dimensional food chain model

This paper is concerned with optimal harvesting policy for an age-dependent n-dimensional food chain model. The existence and uniqueness of non-negative solution of the system are proved using the fixed point theorem. By Mazur＇s theorem, the existence of optimal control strategy is demonstrated and optimality conditions derived by means of normal cone.

具有size结构的捕食种群系统的最优收获策略

分析了一类捕食者种群带有Size结构的捕食-被捕食系统的最优收获问题.利用不动点定理证明了状态系统及其共轭系统非负解的存在唯一性、解对控制变量的连续依赖性.应用切锥法锥技巧导出了最优性条件,借助Ekeland变分原理讨论了最优收获策略的存在唯一性,推广了年龄结构种群模型中的相应结论.

一类具有Size结构的竞争种群系统的最优输入率控制

本文分析一类具有Size结构的竞争种群系统的最优输入率控制问题.首先利用特征线法给出解对控制变量的连续依赖性定理,又利用共轭系统和Ekeland变分原理证明最优控制的存在唯一性,并借助于法锥概念得到最优控制的必要性条件.

Surface,Size and Thermal Effects in Alkali Metal with Core-Electron Binding-Energy Shifts

Consistency between density functional theory calculations and X-ray photoelectron spectroscopy measurements confirms our predications on the undercoordination-induced local bond relaxation and core level shift of alkali metal,which determine the surface,size and thermal properties of materials.Zone-resolved photoelectron spectroscopyanalysis method and bond order-length-strength theory can be utilized to quantify the physical parameters regarding bonding identities and electronic property of metal surfaces,which allows for the study of the core-electron binding-energy shifts in alkali metals.By employing these methods and first principle calculation in this work,we can obtain the information of bond and atomic cohesive energy of under-coordinated atoms at the alkali metal surface.In addition,the effect of size and temperature towards the binding-energy in the surface region can be seen from the view point of Hamiltonian perturbation by atomic relaxation with atomic bonding.