Spectral conditions for a graph to be Hamilton-connected

In this paper we establish some spectral conditions for a graph to be Hamilton-connected in terms of the spectral radius of the adjacency matrix or the signless Laplacian of the graph or its complement. For the existence of Hamiltonian paths or cycles in a graph, we also give a sufficient condition by the signless Laplacian spectral radius

{3,3′-Bis[(anthracen-9-yl)meth­yl]-1,1′-[(ethane-1,2-diyldi­oxy)bis­(ethane-1,2-di­yl)]bis­(imidazol-2-yl­idene)}mercury(II) bis­(hexa­fluoridophosphate) acetonitrile disolvate

In the title compound, [Hg(C42H38N4O2)](PF6)2·2CH3CN, the HgII cation lies on a twofold axis which is also the inter­nal symmetry element of the complete cationic complex. The HgII cation is coordinated by two symmetry-related C(carbene) atoms [Hg—C = 2.058 (9) Å] in a nearly linear geometry, with a C—Hg—C angle of 175.8 (5)°. There are weak inter­molecular C—H⋯F inter­actions in the crystal packing between an F atom of a hexa­fluoridophosphate anion and a –CH2– group of the bis-N-heterocyclic carbene ligand

Active RIS Aided ISAC Systems: Beamforming Design and Performance Analysis

This paper considers an active reconfigurable intelligent surface (RIS)-aided integrated sensing and communication (ISAC) system. We aim to maximize radar signal-to-interference-plus-noise-ratio (SINR) by jointly optimizing the beamforming matrix at the dual-function radar-communication (DFRC) base station (BS) and the reflecting coefficients at the active RIS subject to the quality of service (QoS) constraints of communication users (UE) and the transmit power constraints of active RIS and DFRC BS. To tackle the optimization problem, the majorization-minimization (MM) algorithm is applied to address the nonconvex radar SINR objective function, and the resulting quartic problem is solved by developing an semidefinite relaxation (SDR)-based approach. Moreover, we derive the scaling order of the radar SINR with a large number of reflecting elements. Next, the transmit power allocation problem and the deployment strategy of the active RIS are studied with a moderate number of reflecting elements. Finally, we validate the potential of the active RIS in ISAC systems compared to passive RIS. Additionally, we deliberate on several open problems that remain for future research.Comment: 17 pages,11 figures, accepted by IEEE TCOM.The manuscript has been revised to correct several typographical error

Tris(2-ethyl-1H-imidazole-κN 3)(terephthalato-κO)zinc(II)

The title compound, [Zn(C8H4O4)(C5H8N2)3], has a neutral monomeric structure in which one terephthalate dianion and three 2-ethyl-1H-imidazole ligands coordinate to the ZnII ion in a distorted tetra­hedral geometry. The methyl group of one of the ethyl groups is disordered over two positions with occupancies of 0.66 (2) and 0.34 (2). In the crystal structure, mol­ecules are linked into a three-dimensional hydrogen-bonded network by inter­molecular N—H⋯O interactions involving the uncoordinated carboxyl­ate O atoms

Percutaneous closure of a post-traumatic ventricular septal defect with a patent ductus arteriosus occluder

OBJECTIVE: Ventricular septal defects resulting from post-traumatic cardiac injury are very rare. Percutaneous closure has emerged as a method for treating this disorder. We wish to report our experience in three patients who underwent percutaneous closure of a post-traumatic ventricular septal defect with a patent ductus arteriosus occluder. METHODS: We treated three patients with post-traumatic ventricular septal defects caused by stab wounds with knives. After the heart wound was repaired, patient examinations revealed ventricular septal defects with pulmonary/systemic flow ratios (Qp/Qs) of over 1.7. The post-traumatic ventricular septal defects were closed percutaneously with a patent ductus arteriosus occluder (Lifetech Scientific (Shenzhen) Co., LTD, Guangdong, China) utilizing standard techniques. RESULTS: Post-operative transthoracic echocardiography revealed no residual left-to-right shunt and indicated normal ventricular function. In addition, 320-slice computerized tomography showed that the occluder was well placed and exhibited normal morphology. CONCLUSION: Our experiences indicate that closure of a post-traumatic ventricular septal defect using a patent ductus arteriosus occluder is feasible, safe, and effective