严复《英文汉解》中“条顿”考证

“条顿”是严复著译中经常出现的词语,在《原富》《群学肄言》《社会通诠》《法意》及《英文汉解》中,均有提到。在目前已出版的严复全集、严复文集及严复学术资料选编中,大多收录有《英文汉解》一文,严复在该文中提到了“条顿”的英文表达方式。长期以来,《英文汉解》中的“条顿”一直被拼写为“Tentonic”,而经查证,“Tentonic”在字典中是不存在的,应该是后人在辑录时把其中的字母“u”误看作“n”录入了,正确表述应为“Teutonic”。

Degradation of polyvinyl-alcohol wastewater by Fenton’s reagent: Condition optimization and enhanced biodegradability

The pretreatment of refractory polyvinyl-alcohol （PVA） wastewater with low value of CODcr by Fenton＇s reagent was investigated to enhance the biodegradabilily. The effects of operating conditions such as pH of the solution, Fe2＋ dosage, H2O2 dosage, reaction time and initial PVA concentration on the removal efficiency of CODCr were discussed. It is demonstrated that the optimum value of pH for removal of CODcr is 5 and the most suitable dosages of H2O2 （2%） and FeSO4 （10 mg/L） are 5% and 8.0%, respectively. When the initial CODcr value of the PVA water is 760 mg/L, the favorable reaction time is 110 min. Under these optimum conditions, the removal ratio of CODcr is 58.6% 61.4%, and the value of biodegradability （CODB/CODcr） increases markedly from 8.9% 9.7% to 62.6% 68.3%.

Neighborhood Conditions for Claw-Free Graphs

Two new sufficient conditions for hamiltonian claw free graphs are given. Some known results become corollaries of the conclusion, the conditions of theorem are the best possible in a sense.

Experimentally Determining Bloch Parameters of Hamiltonian for Single-Qubit Systems

By considering the identification problem of unknown but fixed Hamiltonian H = S0σ0 ＋∑i=x,y,z Siσi where σi （i = x, y, z） are pauli matrices and σ0=I, we explore the feasibility and limitation of empirically determining the Hamiltonian parameters for quantum systems under experimental conditions imposed by projective measurements and initialization procedures. It may be unsurprising to physicists that one can not obtain the knowledge of So no matter what kind of projective measurements and initialization are permitted, but the observation draws our attention to the importance of the parameter identifiability under different experimental condition. It has also been revealed that one can obtain the knowledge of ｜Sz｜ and Sx^2＋Sy^2 at most when only the projective measurement {｜0/（0｜, ｜1/（1｜} is permitted to perform on and initialize the qubit. Further more, we demonstrated that it is feasible to distinguish ｜Sx｜, ｜Sy｜, and ｜Sz｜ even without any a priori information about Hamiltonian if at least two kinds of projective measurement or initialization procedures are permitted. It should be emphasized that both projective measurements and initialization procedures play an important role in quantum system identification.

Completeness of Eigenfunction Systems for Off-Diagonal Infinite-Dimensional Hamiltonian Operators

For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.

A Dirac Type Condition for Heavy Cycles in Weighted Graphs

In this paper we give a Dirac type condition for heavy cycles in a 3-connected weighted graph, reading that if d^w（v）≥ d for all v ∈ V（G）／{x} and w（uz） = w（vz）, when uz, vz ∈ E（G） and uv ∈/ E（G）. Then G contains either an （x, y）-cycle of weight at least 2d or a Hamilton cycle.

Kantorovich’s theorem for Newton’s method on Lie groups

The convergence criterion of Newton’s method to find the zeros of a map f from a Lie group to its corresponding Lie algebra is established under the assumption that f satisfies the classical Lipschitz condition, and that the radius of convergence ball is also obtained. Furthermore, the radii of the uniqueness balls of the zeros of f are estimated. Owren and Welfert (2000) stated that if the initial point is close sufficiently to a zero of f, then Newton’s method on Lie group converges to the zero; while this paper provides a Kantorovich’s criterion for the convergence of Newton’s method, not requiring the existence of a zero as a priori.

Studies on quasi-Newton methods in timedomain multiscale full waveform inversion

The time-domain multiscale full waveform inversion(FWI)mitigates the influence of the local minima problem in nonlinear inversion via sequential inversion using different frequency components of seismic data.The quasi-Newton methods avoid direct computation of the inverse Hessian matrix,which reduces the amount of computation and storage requirement.A combination of the two methods can improve inversion accuracy and efficiency.However,the quasi-Newton methods in time-domain multiscale FWI still cannot completely solve the problem where the inversion is trapped in local minima.We first analyze the reasons why the quasi-Newton Davidon–Fletcher–Powell and Broyden–Fletcher–Goldfarb–Shanno methods likely fall into the local minima using numerical experiments.During seismic-wave propagation,the amplitude decreases with the geometric diffusion,resulting in the concentration of the gradient of the velocity model in the shallow part,and the deep velocity cannot be corrected.Thus,the inversion falls into the local minima.To solve this problem,we introduce a virtual-source precondition to remove the influence of geometric diffusion.Thus,the model velocities in the deep and shallow parts can be simultaneously completely corrected,and the inversion can more stably converge to the global minimum.After the virtual-source precondition is implemented,the problem in which the quasi-Newton methods likely fall into the local minima is solved.However,problems remain,such as incorrect search direction after a certain number of iterations and failure of the objective function to further decrease.Therefore,we further modify the process of timedomain multiscale FWI based on virtual-source preconditioned quasi-Newton methods by resetting the inverse of the approximate Hessian matrix.Thus,the validity of the search direction of the quasi-Newton methods is guaranteed.Numerical tests show that the modified quasi-Newton methods can obtain more reasonable inversion results,and they converge faster and entail lesser computational resources than the gradient method.

An implicit symmetry constraint of the modified Korteweg-de Vries (mKdV) equation

In this paper, an implicit symmetry constraint is calculated and its associated binary nonlinearization of the Lax pairs and the adjoint Lax pairs is carried out for the modified Korteweg-de Vries (mKdV) equation. After introducing two new inde-pendent variables, we find that under the implicit symmetry constraint, the spatial part and the temporal part of the mKdV equation are decomposed into two finite-dimensional systems. Furthermore we prove that the obtained finite-dimensional systems are Hamiltonian systems and completely integrable in the Liouville sense.

Time domain system identification of unknown initial conditions

System identification is a method for using measured data to create or improve a mathematical model of the object being tested. From the measured data however, noise is noticed at the beginning of the response. One solution to avoid this noise problem is to skip the noisy data and then use the initial conditions as active parameters, to be found by using the system identification process. This paper describes the development of the equations for setting up the initial conditions as active parameters. The simulated data and response data from actual shear buildings were used to prove the accuracy of both the algorithm and the computer program, which include the initial conditions as active parameters. The numerical and experimental model analysis showed that the value of mass, stiffness and frequency were very reasonable and that the computed acceleration and measured acceleration matched very well.

Symmetry of the Point Spectrum of Upper Triangular Infinite Dimensional Hamiltonian Operators

In this paper, by using characterization of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H, a necessary and sufficient condition is obtained on the symmetry of σP（A） and σ1/P（-A^＊） with respect to the imaginary axis. Then the symmetry of the point spectrum of H is given, and several examples are presented to illustrate the results.

EDGE CONDITION FOR A HAMILTONIAN BIPARTITE GRAPH TO BE BIPANCYCLIC

Let G be a hamiltonian, bipartite graph on 2n vertices, where n > 3. It isshown that if e(G) > n(n ― 1)/2 + 2 then G contains cycles of every possible even length. Thisimproves a result of Entringer and Schmeichel.

Existence of solutions for sub-linear or super-linear operator equations

We investigate solutions to superlinear or sublinear operator equations and obtain some abstract existence results by minimax methods. These results apply to superlinear or sublinear Hamiltonian systems satisfying several boundary value conditions including Sturm-Liouville boundary value conditions and generalized periodic boundary value conditions, and yield some new theorems concerning existence of solutions or nontrivial solutions. In particular, some famous results about periodic solutions to superlinear or sublinear Hamiltonian systems by Rabinowitz or Benci and Rabinowitz are special cases of the theorems.

A new kind of optimal second-order symplectic scheme for seismic wave simulations

Here we introduce generalized momentum and coordinate to transform seismic wave displacement equations into Hamiltonian system.We define the Lie operators associated with kinetic and potential energy,and construct a new kind of second order symplectic scheme,which is extremely suitable for high efficient and long-term seismic wave simulations.Three sets of optimal coefficients are obtained based on the principle of minimum truncation error.We investigate the stability conditions for elastic wave simulation in homogeneous media.These newly developed symplectic schemes are compared with common symplectic schemes to verify the high precision and efficiency in theory and numerical experiments.One of the schemes presented here is compared with the classical Newmark algorithm and third order symplectic scheme to test the long-term computational ability.The scheme gets the same synthetic surface seismic records and single channel record as third order symplectic scheme in the seismic modeling in the heterogeneous model.

On symplectic self-adjointness of Hamiltonian operator matrices

Symplectic self-adjointness of Hamiltonian operator matrices is studied, which is important to symplectic elasticity and optimal control. For the cases of diagonal domain and off-diagonal domain, necessary and sufficient conditions are shown. The proofs use Frobenius-Schur factorizations of unbounded operator matrices.Under additional assumptions, sufficient conditions based on perturbation method are obtained. The theory is applied to a problem in symplectic elasticity.

Dynamic simulation based on Jacobian-free Newton-GMRES methods with adaptive preconditioner for power systems

Dynamic simulation is one of the most complex and important computations for power systems researches.Traditional solutions based on normal Newton iterations almost all depend on evaluations of Jacobian matrixes,which increases the programming complexity of and limits the parallelizability of the whole simulation.In this paper,a new adaptive preconditioned Jacobian-free Newton-GMRES(m)method is proposed to be applied to dynamic simulations of power systems.This new method has totally Jacobian-free characteristics,which saves calculations and storages of Jacobian matrixes and features strong parallelizability.Moreover,several speedup strategies are introduced to enhance efficiency and parallelizability of overall computations.Numerical tests are carried out on IEEE standard test systems and results show that in series computing environment,simulations based on the proposed method have comparable speed to those based on classical Newton-Raphson methods.