静不定问题的力的补充方程——解析表达通式

只要给出内力表达式就能建立力的补充方程,方法是:内力与内力的变分之积被相应的刚度相除,再将上述表达式在相应的区域内积分,最后求和,即得力的补充方程(组)。

微分法计算定位误差的分析与探讨

针对设计专用机床夹具定位误差的计算,重点讨论了用微分法计算定位误差应注意的事项,并从数学角度对微分、增量以及增量对定位误差的影响进行了解释,最终得出了用微分法计算定位误差的全微分表达通式.

波浪的非线性频散关系

在概括和总结现有非线性频散关系的基础上,给出了非线性频散关系的通式形式及其显式表达式。通过与原频散关系的比较可知显式形式具有很高的精度,与隐式形式吻合很好。利用频散关系的显式形式,结合含非线性项的缓坡方程,得到考虑非线性弥散影响的波浪变形模型。模型中对采用非线性频散关系和修正的非线性频散关系的计算结果进行了比较。结果表明,用新的频散关系的显式表达式得到的模型更加精确、合理。

Preserving Coherence of Coherent State Studied via Weyl-Wigner Correspondence

By means of the Weyl correspondence and the explicit normally ordered expression of the Wigner operatorwe convert the time evolution equation of coherent states,governed by some Hamiltonian operators,into seeking forconsistent solution of a set of evolution equtions of classical variables which can meet the requirment that an initialcoherent state remains coherent all the time.

Analytic expression of the chirped sampled function used to produce the equal chirp in the specific reflection channel in uniform period fiber Bragg gratings

The general analytic expression of the chirped sampled function is derived based on coupled mode theory. This function can be used to describe how to use uniform period fiber Bragg grating to produce the equal chirp at will in the specific reflection channel. As an example,the exact sampled function expression that produces a linear chirped at the +4 channel is given. The simulation results by using the transfer-matrix show that the theory is correct.

Derivation of Multiverse from Universal Wave Function Interpretation of String Theory

The multiverse is a hypothesis created to solve certain problems in cosmology. Currently, this scheme is still largely ad hoc, rather than derived from fundamental laws and principles. Because of this, the predictive power of this theory is rather limited. Furthermore, there are concerns that this theory will make it impossible to calculate some measured quantities, such as the masses of quarks and the electron. In this paper, we will show that a new development in string theory, the universal wave function interpretation of string theory, provides a way to derive the mathematical expression of the multiverse. We will demonstrate that the Weyl invariance existing in string theory indicates that our observed universe is a projection from a hologram. We will present how the laws of physics can be derived from this fact. Furthermore, we suggest it may also provide a way to calculate the masses of fundamental particles such as quarks and the electron.

Transcriptome profiling of the developing postnatal mouse testis using next-generation sequencing

Mammalian testis development is a complex and highly sophisticated process. To study the dynamic change of normal testis development at the transcriptional level, we investigated mouse testes at three postnatal ages: 6 days postnatal, 4 weeks old, and 10 weeks old, representing infant (PN1), juvenile (PN2), and adult (PN3) stages, respectively. Using ultra high-throughput RNA sequencing (RNA-seq) technology, we obtained 211 million reads with a length of 35 bp. We identified 18837 genes that were expressed in mouse testes, and found that genes expressed at the highest level were involved in spermatogenesis. The gene expression pattern in PN1 was distinct from that in PN2 and PN3, which indicates that spermatogenesis has commenced in PN2. We analyzed a large number of genes related to spermatogenesis and somatic development of the testis, which play important roles at different developmental stages. We also found that the MAPK, Hedgehog, and Wnt signaling pathways were significantly involved at different developmental stages. These findings further our understanding of the molecular mechanisms that regulate testis development. Our study also demonstrates significant advantages of RNA-seq technology for studying transcriptome during development.

Tight-binding models for ultracold atoms in optical lattices：general formulation and applications

Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.

Quantum Fisher Information for Density Matrices with Arbitrary Ranks

We provide a new expression of the quantum Fisher information(QFI) for a general system.Utilizing this expression,the QFI for a non-full rank density matrix is only determined by its support.This expression can bring convenience for an infinite-dimensional density matrix with a finite support.Besides,a matrix representation of the QFI is also given.

Tunable time delay in active fiber Bragg grating coupler

Slowing down velocity and controlling time delay of optical pulses in fiber have many potential applications in optical com-munication systems,and a number of theoretical and experimental studies have been done.In this paper,the transmission spectrum and reflective spectrum of active fiber Bragg grating(FBG)couplers are studied,and the analytic expressions of dispersion and time delay are obtained.By changing the detuning and gain coefficient,different dispersions and time delays in active fiber Bragg grating coupler are obtained.The results show that different detunings and gain coefficients can result in various time delays,and thus tunable time delay could be achieved by changing signal frequency or gain coefficient.