Naturally ordered regular semigroups with an inverse monoid transversal

The notion of an inverse transversal of a regular semigroup is well-known. Here we investigate naturally ordered regular semigroups that have an inverse transversal. Such semigroups are necessarily locally inverse and the inverse transversal is a quasi-ideal. After considering various general properties that relate the imposed order to the natural order, we highlight the situation in which the inverse transversal is a monoid. The regularity of Green’s relations is also characterised. Finally, we determine the structure of a naturally ordered regular semigroup with an inverse monoid transversal.     

Influence of transverse magnetic field on thermocapillary flow in liquid bridge

For exploring the optimizing convection control technique by external magnetic field in floating zone crystal growth of semiconductor under microgravity, thermocapillary flow in a floating half‐zone model is simulated numerically, and the influences of both the transversal uniform magnetic field and the magnetic field generated by transversal four coils on thermocapillary flow are investigated. The results indicate that the transversal uniform magnetic field is likely to break the axisymmetrical structure of thermocapillary flow, which is unfavorable to the growth of high‐quality crystal; under the magnetic field generated by transversal four coils, both the mean and the maximum velocities increase with the increment of the distance between coils or the decrement of coil radius; and the convection tends to be more axisymmetrical with increasing coil radius. Compared to the transversal uniform magnetic field, the magnetic field generated by transversal four coils of appropriate radius and relative distance may not only suppress convection, but also enhance the axisymmetry of convection at the same time, and finally, the better convection control can be achieved. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transversal reverse transformation of anomalous hollow beams in strongly isotropic nonlocal media

Based on the nonlocal nonlinear Schr6dinger equation, the propagation properties of anomalous hollow beams in strongly isotropic nonlocal media are investigated. The analytical expressions of the beam propagation, the on-axis intensity and the beam width are obt.ained. The results show that the evolution of the beam is periodical and the input power is the most important parameter. The input power determines the variation of the period. Furthermore, it is found that there exists a critical input power in the x direction and in the y direction separately when the initial beam widths in the two transversal directions are unequal. The beam width remains invariant in the corresponding transversal direction when the input power equals the critical power in one of the transversal directions. Selecting a properinput power, the beam can be broadened or compressed in the two transversal directions at the same time, In particular, the beam can be broadened （compressed） in one transversal direction, whereas in the other transversal direction, it is compressed （broadened）, i.e., the transversal reverse transformation.     

Latin squares with restricted transversals

We prove that for all odd m ≥ 3 there exists a latin square of order 3 m that contains an ( m ? 1 ) × m latin subrectangle consisting of entries not in any transversal. We prove that for all even n ≥ 10 there exists a latin square of order n in which there is at least one transversal, but all transversals coincide on a single entry. A corollary is a new proof of the existence of a latin square without an orthogonal mate, for all odd orders n ≥ 11 . Finally, we report on an extensive computational study of transversal‐free entries and sets of disjoint transversals in the latin squares of order n ? 9 . In particular, we count the number of species of each order that possess an orthogonal mate. © 2011 Wiley Periodicals, Inc. J Combin Designs 20:124‐141, 2012     

Divisibility of multilinear mappings with applications to affine differential geometry

For real finite-dimensional vector spaces V, W we call a bilinear symmetric mapping h?:?V?×?V?→?W non-degenerate if the components of h with respect to a certain basis are linearly independent and non-degenerate. We say that a symmetric trilinear mapping C?:?V?×?V?×?V?→?W is divisible by h if there exists a linear form α such that C(v,?v,?v)?=?α(v)h(v,?v) for every v?∈?V. In affine differential geometry of affine immersions h is the second fundamental form and C – the cubic form of the immersion. The immersion has pointwise planar normal sections if h(v,?v)?∧?C(v,?v,?v)?=?0 for every tangent vector v. We prove that it implies that C is divisible by h if h is non-degenerate and the codimension is greater than two. For immersions with Wiehe's or Sasaki's choice of transversal bundles divisibility of C by h implies vanishing of C.     

热声换热器的工作机制及换热特性研究

基于弱非线性热声理论,对热声换热器的换热特性进行了理论研究.获得了平行平板通道内二阶周期平均热流的解析解,并指出存在临界声导率比的模|Ya|_(cr)~I,使得二阶周期平均热流为零.当实际声导率比的模大于|Ya|_(cr)~I时,振荡流体从外热源吸热,为吸热器;当实际声导率比的模小于|Ya|_(cr)~I时,振荡流体向外放热,为放热器.获得了平行平板通道内二阶周期平均温度的解析解.计算分析了工作流体的物性参数、流动参数以及声导率比对二阶周期平均温度分布的影响,为进一步考察换热系数提供了依据。     

Concerning eight mutually orthogonal latin squares

In this article, we provide a direct construction for 8 mutually orthogonal latin squares (MOLS)(48). Using this design together with one of Wilson's recursive constructions produces 8 new MOLS(v) for 88 other values of v. We also mention a few other new sets of 8 and 12 MOLS obtained recursively. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 255–261, 2007     

带两洞的不完全自正交拉丁方的存在性

讨论不完全自正交拉丁方ISOLS(v;3,3)的存在性问题.证明当v≥12,v{13,14,15,16,17,18,19,20,21,22,23,24,25,27,28,29,30,31,33,35,36}时,存在ISOLS(v;3,3).     

Stability of a Laser-diode-pumped Cr4+:YAG Passively Q-switched Nd3+:YAG Laser

In this paper, the stability of a laser-diode-pumped Cr4+:YAG passively Nd3+:YAG Q-switched laser and the influence of the transversal mode structure on the stability are investigated. With the laser operating in TEM00 mode, the pulse energy fluctuation and the repetition rate fluctuation as functions of the repetition rate are measured, and semi-quantitatively and qualitatively analyzed, respectively.     

一种非简谐的微振动模型

研究了一类特殊的非简谐运动———对称双弹性振子的横振动,得到了在微振动条件下的严格解,发现其运动周期与振幅的大小成反比,其波形对于简谐波的形变系数较小,且与振幅的大小无关.