Convenient One Pot Synthesis and Antibacterial Evaluation of Some New Mannich Bases Carrying 1,2,4‐Triazolyl Moiety

A series of Mannich bases were synthesized by a three‐component Mannich reaction. The newly synthesized compounds were well characterized by elemental analyses, IR, NMR and mass spectroscopic studies. The potential antibacterial effects of the synthesized compounds were investigated using standard bacterial strains: Gram‐positive and Gram‐negative bacteria. Interestingly, all the synthesized compounds were observed to be promising leads, possessing moderate to significant inhibitory activity as compared to standard.     

Magnetoelectric Energy in Electrodynamics: Magnetoelectricity,Bi(an)isotropy,and Magnetoelectric Meta-Atoms

Magnetoelectricity denotes the relationship between electric polarization and magnetization. In materials with an intrinsic magnetoelectric (ME) effect, the energy density comprises the polarization, magnetization, and ME energy densities. These three components of energy define local (subwavelength) characteristics of electromagnetic (EM) responses in multiferroic materials. In a subwavelength domain, coupling between the electric and magnetic dipole oscillations forms the ME field structures that are characterized by the violation of both spatial and temporal symmetry. Unlike multiferroics, bi(an)isotropic metamaterials are associated with an EM response characterized only by spatial symmetry breaking. This also applies to chiral materials. Since no “intrinsic magnetoelectricity” is assumed in such structures, any concepts about the stored ME energy are not applicable. This clearly points to the effect of nonlocality. That is why the basic concepts of bi(an)isotropy can only be analyzed by the EM far-field characteristics. In this paper, it is argued that in the implementation of local (subwavelength) ME meta-atoms and systems for near-field probing of chirality, the concept on ME energy is crucial. Real ME energy can occur when ME fields in a singular subwavelength domain are characterized by a violation of both the symmetry of time reversal and spatial reflection.     

Integrable couplings,bi‐integrable couplings and their Hamiltonian structures of the Giachetti–Johnson soliton hierarchy

On the basis of zero curvature equations from semi‐direct sums of Lie algebras, we construct integrable couplings of the Giachetti–Johnson hierarchy of soliton equations. We also establish Hamiltonian structures of the resulting integrable couplings by the variational identity. Moreover, we obtain bi‐integrable couplings of the Giachetti–Johnson hierarchy and their Hamiltonian structures by applying a class of non‐semisimple matrix loop algebras consisting of triangular block matrices. Copyright © 2014 John Wiley & Sons, Ltd.     

Least‐squares solutions of matrix inverse problem for bi‐symmetric matrices with a submatrix constraint

An n × n real matrix A = (a_ij)_{n × n} is called bi‐symmetric matrix if A is both symmetric and per‐symmetric, that is, a_ij = a_ji and a_ij = a_n+1?1,n+1?i (i, j = 1, 2,..., n). This paper is mainly concerned with finding the least‐squares bi‐symmetric solutions of matrix inverse problem AX = B with a submatrix constraint, where X and B are given matrices of suitable sizes. Moreover, in the corresponding solution set, the analytical expression of the optimal approximation solution to a given matrix A^* is derived. A direct method for finding the optimal approximation solution is described in detail, and three numerical examples are provided to show the validity of our algorithm. Copyright © 2007 John Wiley & Sons, Ltd.     

Defocusing as a means of light removal from an amplifying medium

Defocusing as a means of light removal from an amplifying medium is studied. The wave propagation in a simple layer and in an Epstein layer is considered. It is shown that defocusing leads to additional nonsaturatable, nonresonante losses. When defocusing is optimum, it is profitable to operate in the saturation regime with no limitations on the length of the active medium. Defocusing naturally leads to a single-mode regime and to a high directivity of the output radiation. Experiment showed that defocusing is present in the superluminescence of a dye excited by a narrow knife-shaped pumping beam. The properties of defocusing layers and fibers are, in some respects, familiar to those of unstable resonators.     

On Steiner Versions of (bi)Connectivity in Network Problems

The notions of connectivity and biconnectivity can be generalized in the Steiner sense, i.e., they are restricted to a given subset of the vertices of a graph. We illustrate this generalization on two problems. The first problem is the bottleneck biconnected subgraph problem, the second one is the so-called bipartition problem. The adapted algorithms to solve the Steiner versions of these problems exploit depth-first search to attain respectively a running time of O(|E|+|V|log|V|) and O(|E|+|V|) with E denoting the set of edges and V the set of vertices of the given graph.Final version received: October 15, 2003     

高测速双频激光干涉仪

现代机械工业的发展使得数控机床和三坐标测量机等的运行速度已经达到 10 0 0 mm/ s,而目前商用外差干涉仪的测量速度不能满足这一要求。为此研制了一种基于 5 MHz频差双反射膜激光器的高测速干涉仪。通过实验对干涉仪的测量速度进行了验证。实验证明 ,该种干涉仪可以对速度为 10 0 0 mm/ s的运动物体进行位移和速度测量     

In situ observation of the pressure-induced mesophase for 4′-n-hexadecyloxy-3′-nitrobiphenyl-4-carboxylic acid

In situ observation of the optical texture, and X-ray patterns of the pressure-induced mesophase seen for 4′-n-hexadecyloxy-3′-nitrobiphenyl-4-carboxylic acid (ANBC-16) was performed under hydrostatic pressures up to 100MPa using a polarizing optical microscope equipped with a high pressure hot stage and a wide angle X-ray diffractometer equipped with a high pressure vessel respectively. It was found that the pressure-induced mesophase (hereafter refered to as ‘X’) appeared at pressures above 60 MPa, and exhibits a birefringent broken-fan or a sand-like texture that remain unaltered in the SmC phase. The POM-transmitted light intensity curve measured on heating clearly showed the Cr₄ → Cr₁ → SmC → ‘X’ → SmA → I transition sequence at 80 MPa. The optical texture and the POM-transmitted light intensity measured during a pressure cycle at 185°C showed a reversible change between the cubic and ‘X’ phases. The WAXD pattern of the ‘X’ phase showed a spot-like pattern, suggesting no layered structure for this phase, and also revealed a substantial decrease in the d-spacing of the low angle reflection at 80 and 100 MPa, compared with the d-spacings of the (0 0 1) reflection of the SmC phase and also the (2 1 1) reflection of the cubic phase. It is concluded from these data that the ‘X’ phase is a birefringent hexagonal columnar phase.     

SIMPLE METHOD FOR THE SYNTHESIS OF STANNOLE DIANION

Reduction of 1-t-butyl-1,2,3,4,5-pentaphenylstannole by lithium gave the stannole dianion. Reduction of the bi(1,1-stannole) having a t-butyl group on the tin by lithium also gave the stannole dianion, the formation of which was evidenced by spectral analysis and chemical trapping reaction.