Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

An approach to characterization of the agricultural self-propelled machines stability

This paper presents an analytical algorithm with appropriate software specified for the approximation of the allowed critical slope of the solid flat terrain that guarantees static and/or dynamic stability of the specified self-propelled agricultural machines and their aggregates. This algorithm assumes machine as a rigid body, having 3 or 4 contact points (defined by wheels or crawlers), under uniform motion at different constant velocities and radii of curvature trajectories. Using this algorithm, based on the principles of theoretical mechanics combined with 3D analytical geometry, the computer program SSPM (stability of the self-propelled agricultural machines) has been coded. This software is intended to facilitate the analysis, comparison and optimization of different configurations of self-propelled agricultural machines in operation on horizontal and sloped flat terrains at constant velocities and radii of trajectory with respect to their static and dynamic stability. It calculates critical pitch and roll angles of the self-propelled machine and the maximum allowed slope of the flat terrain under the given conditions. The algorithm and the appropriate SSPM software were experimentally verified using the platform and low-scale tractor model. Average difference between calculated and experimental critical values of roll and pitch angles were about 4°     

Regularity and Rigidity for Nonlocal Curvatures in Conformal Geometry

In this paper, we will explore the geometric effects of conformally covariant operators and the induced nonlinear curvature equations in certain nonlocal nature. Mainly, we will prove some regularity and rigidity results for the distributional solutions to those equations.     

Synthesis,Characterization and Evaluation of the Antibacterial and Antitumor Activity of HalogenatedSalen Copper (II) Complexes derived from Camphoric Acid

Platinum metal complexes are the most common chemotherapeutics currently used in cancer treatment. However, the frequent adverse effects, as well as acquired resistance by tumor cells, urge the development of effective alternatives. In the recent past, copper complexes with Schiff base ligands have emerged as good alternatives, showing interesting results. Accordingly, and in continuation of previous studies in this area, three new camphoric acid-derived halogenated salen ligands and their corresponding Cu (II) complexes were synthesized and their antitumor activity was evaluated in order to determine the influence of the type and number of halogens present (Br, Cl). The in vitro cytotoxic activity was screened against colorectal WiDr and LS1034 and against breast MCF-7 and HCC1806 cancer cell lines. The results proved the halogenated complexes to be very efficient, the tetrachlorinated Cu (II) complex being the most promising, presenting IC₅₀ of 0.63–1.09 μM for the cell lines studied. The complex also shows selectivity to colorectal cancer cells compared to non-tumor colon cells. It is worth highlighting that the tetrachlorinated Cu (II) complex, our most efficient complex, shows a significantly more powerful antitumor effect than the reference drugs currently used in conventional chemotherapy. The halogenated salen and corresponding complexes were also screened for their antimicrobial activity against four bacterial species-Staphylococcus aureus, Enterococcus faecalis, Escherichia coli and Pseudomonas aeruginosa-and four fungal species-Candida albicans, Candida glabrata, Aspergillus fumigatus and Alternaria alternata. The compounds were found to exhibit moderate to strong antibacterial activity against the bacterial strains studied. NMR studies and theoretical calculations provided some insight into the structure of the ligands and copper complexes. Considering the results presented herein, our work validates the potential use of copper-based chemotherapeutics as alternatives for cancer treatment.     

三层流体中斜入射波作用下半无限板的水弹性响应

解析地研究了在三层流体中斜入射波浪与半无限弹性板的相互作用引起的波散射和板的水弹性响应. 三层流体在界面处的密度发生阶跃, 各层为一常数. 假设流体不可压缩、无黏、流体运动无旋. 在线性势流理论框架下, 使用本征函数展开法和内积式给出波板相互作用的半解析解. 根据色散关系分析, 得到了表面波模态和界面波模态入射时的临界入射角. 随着物理参数的变化, 临界角将随之发生变化. 临界角决定了当由开阔水域向板覆盖水域传播的表面波或界面波的存在性: (1)板覆盖水域入射界面上, 透射波能否存在; (2)入射界面之上界面中, 板覆盖水域中的透射波以及开阔水域中的反射波能否存在. 当下界面波入射时并且入射角足够大时, 开阔水域中的下界面波模态是整个流体域中唯一存在的模态.      

Oxotitanium(IV) complexes of some bis‐unsymmetric Schiff bases: Synthesis,structural elucidation and biomedical applications

A number of oxotitanium(IV) complexes of the type TiOL with bis‐unsymmetric dibasic tetradentate Schiff base (LH₂) containing ONNO donor atoms have been synthesized. Mono‐Schiff base (OPD‐HNP) was prepared by the condensation of 1:3 molar ratio of 2‐hydroxy‐1‐naphthaldehyde (HNP) with o‐phenylenediamine (OPD). Dibasic unsymmetric tetradentate diamine Schiff bases were prepared by the reaction of OPD‐HNP with 2‐hydroxyacetophenone, 2‐hydroxypropeophenone, benzoylacetone, acetylacetone and ethylacetoacetate. Further, titanylacetylacetonate was reacted with these ligands to obtain their metal complexes. On the basis of analytical and physiochemical data, the formation of complexes as TiOL was suggested having square pyramidal geometry. Quantum mechanical approach also confirmed this geometry. The assessment of the synthesized ligands and their complexes showed that some behave as good inhibitors of mycelial growth against selected phytopathogic fungi but weak inhibitors against some selected bacteria. A few of them also showed antioxidant properties.     

Minimal kernels of Dirac operators along maps

Let M be a closed spin manifold and let N be a closed manifold. For maps and Riemannian metrics g on M and h on N, we consider the Dirac operator of the twisted Dirac bundle . To this Dirac operator one can associate an index in . If M is 2‐dimensional, one gets a lower bound for the dimension of the kernel of out of this index. We investigate the question whether this lower bound is obtained for generic tupels .