“同均三宫”的传统调性空间对中国当代音乐创作的启示

由黄翔鹏首次提出的“同均三宫”理论将中国传统乐学理论研究引入了一个全新的境界。这一理论使得中国传统音乐的调性范围进一步拓宽,也给当代音乐创作提供了更大的调性空间。文章以“同均三宫”理论中的调性思维为对象,探讨其对中国当代音乐创作的影响和启发。

论环境审美中的悲剧空间设计

本文论述了环境审美中,悲剧空间的审美和历史文化意义;从悲剧的审美特性出发,阐述了如何运用空间调性间的呼应或对比、空间形态上的矛盾修辞、以及空间序列中的失落与疏离,来构建悲剧空间的方法;并进而分析了在悲剧空间的塑造之中,对废墟以及残缺留白之中“悲剧场”的引用。

增减调式的理论与应用

从传统大小调体系到全音调式体系的确立,历经了一段艰苦的历史演变过程。增、减调式的出现正处于传统的大小调体系向全音调式体系过渡的转型时期。它在丰富调式色彩、扩展调性空间以及在和声结构与旋律结构的重组等方面都起到了重要作用。

IMPROVEMENT OF MATRIX REPRESENTATION METHOD IN NORMAL FORM THEORY

In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.

Anti-periodic solutions to a class of second-order evolution equations

In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.

A review on spatial self-phase modulation of two-dimensional materials

Self-diffraction appears when the strong laser goes through two-dimensional material suspension,and this spatial self-phase modulation(SPPM)phenomenon can be used to measure nonlinear optical parameters and achieve optical switch.At present,the mechanism of SPPM is still ambiguous.The debate mainly focuses on whether the phenomenon is caused by the nonlinear refractive index of the two-dimensional material or the thermal effect of the laser.The lack of theory limits the dimension of the phase modulation to the radius of the diffraction ring and the vertical imbalance.Therefore,it is urgent to establish a unified and universal SSPM theoretical system of two-dimensional material.

A Preliminary Evaluation of Global and East Asian Cloud Radiative Effects in Reanalyses

Cloud radiative effects （CREs） at the top of the atmosphere （TOA） in three reanalysis datasets （the Eur- opean Center for Medium-Range Weather Forecasts In- terim Reanalysis （ERA-Interim）, the Japanese 55-yr Re- analysis Project （JRA-55）, and the Modem-Era Retro- spective Analysis for Research and Applications （MERRA）） are evaluated using recent satellite-based observations. The reanalyses can basically capture the spatial pattern of the annual mean shortwave CRE, but the global mean longwave CRE in ERA-interim and JRA55 is weaker than observed, leading to overestimations of the net CRE. Moreover, distinct CRE biases of the reanalyses occur in the Intertropical Convergence Zone （ITCZ）, coastal Pa- cific and Atlantic regions, and East Asia. Quantitative examination further indicates that the spatial correlations of CREs and TOA upward radiation fluxes with corre- sponding observations in ERA-Interim are better than in the other two reanalyses. Although MERRA has certain abilities in producing the magnitudes of global mean CREs, its performance in terms of spatial correlations in winter and summer are worse than for the other two re- analyses. The ability of JRA55 in reflecting CREs lies between the other two datasets. Compared to the global mean results, the spatial correlations of shortwave CRE in East Asia decrease and the biases of regional mean CREs increase in the three reanalyses. This implies that, cur- rently, it is still difficult to reproduce East Asian CREs based on these reanalyses. Relatively, ERA-Interim de- scribes the seasonal variation of East Asian CREs well, albeit weaker than observed. The present study also sug- gests that in-depth exploration of the ability of reanalysis data to describe aspects relating to cloud properties and rad- iation is needed usin~ more comprehensive observations.

Solution and Coupled Minimal-Maximal Quasi-Solutions of Nonlinear Non-monotone Operator Equations in Banach Spaces

Abstrac In this paper, we discuss the existence of the solution and coupled minimal and maximal quasi-solutions for nonlinear non-monotone operator equation x = A(x, x), improved and generalized many relevant results.

CONSTRUCTIONS OF THREE-TRANSMIT-ANTENNA SPACE-TIME CODES

In this paper, we give design methods for three-transmit-antenna space-time codes which have reasonable parameters. A few examples are given to show that some unitary space-time codes constructed with our methods are better than the previously best-known ones.

Exact Solutions of the Two-Dimensional Cubic-Quintic Nonlinear Schrdinger Equation with Spatially Modulated Nonlinearities

Applying the similarity transformation, we construct the exact vortex solutions for topological charge S≥1 and the approximate fundamental soliton solutions for S = 0 of the two-dimensional cubic-quintic nonlinear Schrodinger equation with spatially modulated nonlinearities and harmonic potential. The linear stability analysis and numerical simulation are used to exam the stability of these solutions. In different profiles of cubic-quintic nonlinearities, some stable solutions for S 〉 0 and the lowest radial quantum number n = 1 are found. However, the solutions for n ≥ 2 are all unstable.

Sharpness of some properties of weighted modulation spaces

We obtain some optimal properties on weighted modulation spaces. We find the necessary and sufficient conditions for product inequalities, convolution inequalities and embedding on weighted modulation spaces. Especially, we establish the analogue of the sharp Sobolev embedding theorem on weighted modulation spaces.

Weak Orlicz spaces:Some basic properties and their applications to harmonic analysis

We study some basic properties of weak Orlicz spaces and their applications to harmonic analysis.We first discuss the absolute continuity of the quasi-norm and its normality,then prove the boundedness of several maximal operators.We also establish a kind of Marcinkiewicz-type interpolation theorem between weak Orlicz spaces.As applications,the weak type analogues of several classical inequalities in harmonic analysis is obtained.

Non-integer power estimate in modulation spaces and its applications

We give a method to estimate non-integer power function|u|~ku in modulation space which is an open question in the study of modulation space.As an application,we can study Cauchy problem for the nonlinear Klein-Gordon equation with nonlinear term|u|~ku in modulation space,where k is not an integer.Moreover,we also study the global solution with small initial value for the Klein-Gordon-Hartree equation.The results show some advantages of modulation space both in high and low regularity cases.

Modulation space estimates for damped fractional wave equation

Instead of the L^p estimates,we study the modulation space estimates for the solution to the damped wave equation.Decay properties for both the linear and semilinear equations are obtained.The estimates in modulation space differ in many aspects from those in L^p space.

CHAOS AND ORDER OF INVERSE LIMIT SPACE FOR A GRAPH MAP

With the method of inverse limit, the author obtains several criteria of chaos of piecewise monotone continuous maps on finite graphs.

ANTI-PERIODIC SOLUTIONS FOR FIRST AND SECOND ORDER NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES

In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presented. The equations contain nonlinear monotone operators and a nonmonotone perturbation. Moreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of secondorder nonlinear evolution equations is verified. Our abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.

Vortex and Gaussian Solitons of (3+1)-Dimensional Spatially Modulated Cubic-Quintic-Septimal Nonlinear Schrdinger Equation with External Potential

Based on the variable separation principle and the similarity transformation, vortex soliton solution of a （3＋1）-dimensional cubie-quintic-septimal nonlinear Schrodinger equation with spatially modulated nonlinearity under the external potential are obtained in the spatially modulated cubic-quintic-septimal nonlinear media. If the topological charge m = 0 and m ≠0, Gaussian solitons and vortex solitons can be constructed respectively. The shapes of vortex soliton possess similar structures when the value of l - m is same. Moreover, all phases of vortex solitons exist m-jump with the change of every jump as 2π/m-jumps, and thus totally realize the azimuthal change of 21r around their cores.

The time discretization in classes of integro-differential equations with completely monotonic kernels:Weighted asymptotic stability

We study discretization in classes of integro-differential equationswhere the functions aj（t）, 1 ≤ j ≤n, are completely monotonic on （0, ∞） and locally integrable, but not constant. The equations are discretized using the backward Euler method in combination with order one convolution quadrature for the memory term. The stability properties of the discretization are derived in the weighted 11 （p; 0, ∞） norm, where p is a given weight function. Applications to the weighted l^1 stability of the numerical solutions of a related equation in Hilbert space are given.

Unveiling the charge density wave inhomogeneity and pseudogap state in 1T-TiSe_2

By using scanning tunneling microscopy(STM)/spectroscopy(STS), we systematically characterize the electronic structure of lightly doped 1 T-TiSe_2, and demonstrate the existence of the electronic inhomogeneity and the pseudogap state. It is found that the intercalation induced lattice distortion impacts the local band structure and reduce the size of the charge density wave(CDW) gap with the persisted 2 × 2 spatial modulation. On the other hand, the delocalized doping electrons promote the formation of pseudogap. Domination by either of the two effects results in the separation of two characteristic regions in real space, exhibiting rather different electronic structures. Further doping electrons to the surface confirms that the pseudogap may be the precursor for the superconducting gap. This study suggests that the competition of local lattice distortion and the delocalized doping effect contribute to the complicated relationship between charge density wave and superconductivity for intercalated 1 T-TiSe_2.

COHOMOLOGY VANISHING IN HILBERT SPACES

The authors give two cohomology vanishing theorems for domains, which are not pseudoconvex, and characterize the holomorphy of domains with smooth boundaries in separable Hilbert spaces through cohomology vanishing.