FUNCTIONAL REPRESENTATION OF THE NEGATIVE AKNS HIERARCHY

This paper is devoted to the negative flows of the AKNS hierarchy. The main result of this work is the functional representation of the extended AKNS hierarchy, composed of both positive (classical) and negative flows. We derive a finite set of functional equations, constructed by means of the Miwa's shifts, which contains all equations of the hierarchy. Using the obtained functional representation we convert the nonlocal equations of the negative subhierarchy into local systems of higher order, derive the generating function of the conservation laws and the N-dark-soliton solutions for the extended AKNS hierarchy. As an additional result we obtain the functional representation of the Landau–Lifshitz hierarchy.     

Solutions of the nonlocal(2+1)-D breaking solitons hierarchy and the negative order AKNS hierarchy

The(2+1)-dimensional nonlocal breaking solitons AKNS hierarchy and the nonlocal negative order AKNS hierarchy are presented.Solutions in double Wronskian form of these two hierarchies are derived by means of a reduction technique from those of the unreduced hierarchies.The advantage of our method is that we start from the known solutions of the unreduced bilinear equations,and obtain solitons and multiple-pole solutions for the variety of classical and nonlocal reductions.Dynamical behaviors of some obtained solutions are illustrated.It is remarkable that for some real nonlocal equations,amplitudes of solutions are related to the independent variables that are reversed in the real nonlocal reductions.     

Breather Dynamics of the Sine-Gordon Equation

This paper studies the adiabatic dynamics of the breather soliton of the sine-Gordon equation. The integrals of motion are found and then used in soliton perturbation theory to derive the differential equation governing the soliton velocity. Time-dependent functions arise and their properties are studied. These functions are found to be bounded and periodic and affect the soliton velocity. The soliton velocity is numerically plotted against time for different combinations of initial velocities and perturbation terms.     

Continuous Correspondence of Conservation Laws of the Semi-discrete AKNS System

In this paper we investigate the semi-discrete Ablowitz–Kaup–Newell–Segur (sdAKNS) hierarchy, and specifically their Lax pairs and infinitely many conservation laws, as well as the corresponding continuum limits. The infinitely many conserved densities derived from the Ablowitz-Ladik spectral problem are trivial, in the sense that all of them are shown to reduce to the first conserved density of the AKNS hierarchy in the continuum limit. We derive new and nontrivial infinitely many conservation laws for the sdAKNS hierarchy, and also the explicit combinatorial relations between the known conservation laws and our new ones. By performing a uniform continuum limit, the new conservation laws of the sdAKNS system are then matched with their counterparts of the continuous AKNS system.     

Scalar–tensor representation of f(R) gravity and Birkhoff's theorem

Birkhoff's theorem is discussed in the frame of f(R) gravity by using its scalar–tensor representation. Modified gravity has become very popular in recent times as it is able to reproduce the unification of inflation and late‐time acceleration with no need of a dark energy component or an inflation field. Here, another aspect of modified f(R) gravity is studied, specifically the range of validity of Birkhoff's theorem, compared with another alternative to general relativity, the well‐known Brans–Dicke theory. As a novelty, here both theories are studied using a conformal transformation and writing the actions in the Einstein frame, where spherically symmetric solutions are studied using perturbation techniques. The differences between both theories are analyzed as well as the validity of the theorem within the Jordan and Einstein frames, where interesting results are obtained.     

Charge recombination mechanism to explain the negative capacitance in dye-sensitized solar cells

Negative capacitance(NC) in dye-sensitized solar cells(DSCs) has been confirmed experimentally. In this work, the recombination behavior of carriers in DSC with semiconductor interface as a carrier's transport layer is explored theoretically in detail. Analytical results indicate that the recombination behavior of carriers could contribute to the NC of DSCs under small signal perturbation. Using this recombination capacitance we propose a novel equivalent circuit to completely explain the negative terminal capacitance. Further analysis based on the recombination complex impedance show that the NC is inversely proportional to frequency. In addition, analytical recombination resistance is composed by the alternating current(AC) recombination resistance(Rrac) and the direct current(DC) recombination resistance(Rrdc), which are caused by small-signal perturbation and the DC bias voltage, respectively. Both of two parts will decrease with increasing bias voltage.     

Symmetries and conservation laws of the damped harmonic oscillator

We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the variational or Noether symmetries of the damped harmonic oscillator representing it by an explicitly time-dependent Lagrangian and found that a five-parameter group of transformations leaves the action integral invariant. Amongst the associated conserved quantities only two are found to be functionally independent. These two conserved quantities determine the solution of the problem and correspond to a two-parameter Abelian subgroup.      

Low-bias negative differential resistance in combined nanostructure of two zigzag-edged trigonal graphenes

Using the density functional theory combined with the non-equilibrium Green's function method, we have investigated the electron transport properties of combined nanostructures of two zigzag-edged trigonal graphenes linked by their vertex carbon atoms bridged between two gold electrodes. The results show that obvious negative differential resistance behavior can be obtained at low bias (0.3 V) in such combined systems. The observed low-bias negative differential resistance behavior is analyzed by the bias-dependent transmission spectra, projected density of states, and voltage drop.     

Majorana's stellar representation for the quantum geometric tensor of symmetric states

Majorana's stellar representation provides an intuitive picture in which quantum states in high-dimensional Hilbert space can be observed using the trajectory of Majorana stars. We consider the Majorana's stellar representation of the quantum geometric tensor for a spin state up to spin-3/2. The real and imaginary parts of the quantum geometric tensor, corresponding to the quantum metric tensor and Berry curvature, are therefore obtained in terms of the Majorana stars. Moreover, we work out the expressions of quantum geometric tensor for arbitrary spin in some important cases. Our results will benefit the comprehension of the quantum geometric tensor and provide interesting relations between the quantum geometric tensor and Majorana's stars.     

Auxiliary Field Functional Integral Representation of the Many-Body Evolution Operator

Finding an appropriate functional integral representation of the many-body evolution operator is a crucial task for performing efficient calculations of fermionic systems within the auxiliary field approach. In this paper we derive a new field representation of the imaginary-time evolution operator using the method of Gaussian equivalent representation of Efimov and Ganbold (1991, Physica Status Solidi 168, 165). The goal is to obtain a functional integral representation, in which the main divergences caused by the tadpole Feynman diagrams are efficiently eliminated. These diagrams provide the main contributions to the ground state of the system under consideration, and therefore it is important to take them into account adequately, especially at lower temperatures. In addition, we show that the well-known mean field representation of the imaginary-time evolution operator is only the limiting case of the Gaussian equivalent representation in the small time-step regime.     

双负介质对光子晶体透射能带谱的简并效应研究

利用传输矩阵法理论,通过数值计算模拟的方法,研究双负介质对一维光子晶体透射能带谱的影响。结果表明:当C介质由双正介质变成双负介质时,光子晶体(CBAABC)n的禁带、能带和光子晶体(AB)m(CBAABC)n(BA)m的透射峰均出现明显的简并现象,即前者相邻多禁带和多能带结构简并为较宽的单禁带和单能带结构,后者的透射峰由2n+1条简并成2n-1条;当双负介质C的光学厚度负值减小时,光子晶体(AB)m(CBAABC)n(BA)m的透射峰向禁带中心靠拢,出现简并趋势。双负介质对光子晶体透射能带谱的简并效应,为光子晶体设计光学滤波器件、光学开关等提供参考。     

Comparative Study of the Ratio Spectra Derivative Spectrophotometry,Derivative Spectrophotometry and Vierordt's Method Appued to the Analysis of Lisinopril and Hydrochlorothiazide in Tablets

Abstract

Three new spectrophotometric methods are described for the determination of lisinopril and hydrochlorothiazide in their binary mixturer: First derivative spectrophotometry ratio spectra derivative and Vierordt's method. The procedures do not require any prior separation. In the derivative spectrophotometry, the dA/dλ values in the first derivative spectra of the mixture were measured at 269.6 nm for lisinopril and at 279.8 nm for hydrochlorothiazide. The calibration graphs were linear in the range 25.56–129.50 μg.ml^?1 for lisinopril and 10.60–139.80 μg.ml^?1 for hydrochlorothiazide. In ratio spectra derivative spectrophotometry, the calibration graphs for 15.68–129.50 μg.ml^?1 lisinopril and for 5.98–139.80 μg.ml^?1 hydrochlorothiazide were obtained by measuring the signals at 253.7 nm and 243.6 nm for lisinopril and at 280.1 nm and 270.8 nm for hydrochlorothiazide. In Vierordt's method, A¹ ₁ (1 %, 1 cm) values of lisinopril and hydrochlorothiazide were determined at 259.8 nm and 272.7 nm in the zero-order spectra. The quantity of both compounds were calculated by using the A¹ ₁ (1 %, 1cm) values. The methods were successfully applied to a pharmaceutical formulation for determination of both active compounds.     

On the Nature of Functional Differentiation: The Role of Self-Organization with Constraints

The focus of this article is the self-organization of neural systems under constraints. In 2016, we proposed a theory for self-organization with constraints to clarify the neural mechanism of functional differentiation. As a typical application of the theory, we developed evolutionary reservoir computers that exhibit functional differentiation of neurons. Regarding the self-organized structure of neural systems, Warren McCulloch described the neural networks of the brain as being “heterarchical”, rather than hierarchical, in structure. Unlike the fixed boundary conditions in conventional self-organization theory, where stationary phenomena are the target for study, the neural networks of the brain change their functional structure via synaptic learning and neural differentiation to exhibit specific functions, thereby adapting to nonstationary environmental changes. Thus, the neural network structure is altered dynamically among possible network structures. We refer to such changes as a dynamic heterarchy. Through the dynamic changes of the network structure under constraints, such as physical, chemical, and informational factors, which act on the whole system, neural systems realize functional differentiation or functional parcellation. Based on the computation results of our model for functional differentiation, we propose hypotheses on the neuronal mechanism of functional differentiation. Finally, using the Kolmogorov–Arnold–Sprecher superposition theorem, which can be realized by a layered deep neural network, we propose a possible scenario of functional (including cell) differentiation.     

硼氮原子取代掺杂对分子器件负微分电阻效应的影响

利用基于非平衡格林函数和密度泛函理论相结合的第一性原理计算方法,研究了硼氮原子取代掺杂对三并苯分子电子输运性质的影响.计算结果表明,三并苯分子器件的电流在特定偏压区间内随电压的增加而减小呈现出负微分电阻效应,电流的峰谷之比高达5.12.用硼原子或者氮原子取代分子的中心原子后,器件0.8V以内的电流明显增加,但是负微分电阻效应减弱,相应的电流峰谷比分别降至3.83和3.61.分析认为,输运系数在特定偏压下的移动是器件负微分电阻效应的主要成因.核外电子数的差异导致硼氮原子掺杂取代可以使器件轨道及其透射峰分别向高能方向或者低能方向移动从而有效地调控了器件的低偏压下的电子传输能力和负微分电阻效应.     

On the Computations of Gas-Solid Mixture Two-Phase Flow

This paper presents high-resolution computations of a two-phase gas-solid mixture using a well-defined mathematical model. The HLL Riemann solver is applied to solve the Riemann problem for the model equations. This solution is then employed in the construction of upwind Godunov methods to solve the general initial-boundary value problem for the two-phase gas-solid mixture. Several representative test cases have been carried out and numerical solutions are provided in comparison with existing numerical results. To demonstrate the robustness, effectiveness and capability of these methods, the model results are compared with reference solutions. In addition to that, these results are compared with the results of other simulations carried out for the same set of test cases using other numerical methods available in the literature. The diverse comparisons demonstrate that both the model equations and the numerical methods are clear in mathematical and physical concepts for two-phase fluid flow problems.     

Precanonical quantization of Yang-Mills fields and the functional Schrödinger representation

Precanonical quantization of pure Yang-Mills fields, which is based on the covariant De Donder-Weyl (DW) Hamiltonian formulation, and its connection with the functional Schrödinger representation in the temporal gauge are discussed. The mass gap problem is related to the finite-dimensional spectral problem for a generalized Clifford-valued magnetic Schrödinger operator which represents the DW Hamiltonian operator.     

Quantum transport of the single metallocene molecule

The Quantum transport of three single metallocene molecule is investigated by performing theoretical calculations using the non-equilibrium Green's function method combined with density functional theory. We find that the three metallocen molecules structure become stretched along the transport direction, the distance between two C_p rings longer than the other theory and experiment results. The lager conductance is found in nickelocene molecule, the main transmission channel is the electron coupling between molecule and the electrodes is through the Ni d_xz and d_yz orbitals and the s, d_xz, d_yz of gold. This is also confirmed by the highest occupied molecular orbital resonance at Fermi level. In addition, negative differential resistance effect is found in the ferrocene, cobaltocene molecules, this is also closely related with the evolution of the transmission spectrum under applied bias.