Foliations of Isonergy Surfaces and Singularities of Curves

It is well known that changes in the Liouville foliations of the isoenergy surfaces of an integrable system imply that the bifurcation set has singularities at the corresponding energy level. We formulate certain genericity assumptions for two degrees of freedom integrable systems and we prove the opposite statement: the essential critical points of the bifurcation set appear only if the Liouville foliations of the isoenergy surfaces change at the corresponding energy levels. Along the proof, we give full classification of the structure of the isoenergy surfaces near the critical set under our genericity assumptions and we give their complete list using Fomenko graphs. This may be viewed as a step towards completing the Smale program for relating the energy surfaces foliation structure to singularities of the momentum mappings for non-degenerate integrable two degrees of freedom systems.Comment: 30 pages, 19 figure

Design of Wideband Printed Antenna Array in Corner Reflector with Cosecant Square-Shaped Beam Pattern

The paper presents a wideband printed antenna array with a cosecant square-shaped beam pattern. The array is with four symmetrical pentagonal dipoles as radiating elements operating at the second resonance. The apex of the corner reflector is at a distance λ0/2 from antenna array. Orchard Elliott’s methods and genetic algorithm are used for synthesizing the proposed antenna. A symmetrical tapered feed network of impedance transformers enables a required distribution. Simulated and measured results show that proposed antenna model has a 15 dBi gain and side lobe suppression around 20 dB in E-plane at the frequency of 10 GHz

Polymeric Copper(II) Complexes with a Newly Synthesized Biphenyldicarboxylic Acid Schiff Base Ligand—Synthesis, Structural and Thermal Characterization

The newly synthesized biphenyldicarboxylic acid Schiff base and its complexes with Cu(II) were synthesized, and their spectroscopic and structural analysis was performed. The reaction of the ligand and copper(II) acetate in different solvents resulted in the formation of two solvatomorphic complexes, one with MeOH, and the other with DMF molecules, in the crystal lattice. The differences in the results of the thermal analysis could be explained by the different polarities of the solvents present. SC-XRD analysis revealed that the ligand is coordinated as a dianion, in a pentadentate manner, through two phenoxide oxygen atoms, two azomethine nitrogen atoms, and with the oxygen atom of one carboxylate functioning as a bridge that connects the monomeric units. The coordination polyhedron was described with several parameters obtained from different methods of calculation. The presence of different solvents in the crystal structure results in differences in the H-bond networks, and an overall different crystal packing of the structural units in the obtained complexes

Polymeric Copper(II) Complexes with a Newly Synthesized Biphenyldicarboxylic Acid Schiff Base Ligand—Synthesis, Structural and Thermal Characterization

The newly synthesized biphenyldicarboxylic acid Schiff base and its complexes with Cu(II) were synthesized, and their spectroscopic and structural analysis was performed. The reaction of the ligand and copper(II) acetate in different solvents resulted in the formation of two solvatomorphic complexes, one with MeOH, and the other with DMF molecules, in the crystal lattice. The differences in the results of the thermal analysis could be explained by the different polarities of the solvents present. SC-XRD analysis revealed that the ligand is coordinated as a dianion, in a pentadentate manner, through two phenoxide oxygen atoms, two azomethine nitrogen atoms, and with the oxygen atom of one carboxylate functioning as a bridge that connects the monomeric units. The coordination polyhedron was described with several parameters obtained from different methods of calculation. The presence of different solvents in the crystal structure results in differences in the H-bond networks, and an overall different crystal packing of the structural units in the obtained complexes

Synthesis, Characterization, and Impact of Water on the Stability of Postmodified Schiff Base Containing Metal–Organic Frameworks

In this study, the synthesis of a Schiff base containing metal–organic frameworks (MOFs) of the UiO-67 family has been investigated. MOFs featuring free amine groups were successfully synthesized under mild solvothermal conditions using 2-amino-[1,1′-biphenyl]-4,4′-dicarboxylic acid and 2,2′-diamino-[1,1′-biphenyl]-4,4′-dicarboxylic acid as bridging ligands, resulting in MOFs with amine groups covalently linked to the bridging ligands. Both types of functionalized MOFs were post-synthetically modified with 4-formylbenzonitrile that resulted in imine formation. All the obtained compounds were characterized by PXRD, TGA, DTA, BET, NMR, and FTIR spectroscopy, while stability in water was monitored with SEM, EDS, and UV–VIS spectroscopy

Synthesis, Characterization, and Impact of Water on the Stability of Postmodified Schiff Base Containing Metal–Organic Frameworks

In this study, the synthesis of a Schiff base containing metal–organic frameworks (MOFs) of the UiO-67 family has been investigated. MOFs featuring free amine groups were successfully synthesized under mild solvothermal conditions using 2-amino-[1,1′-biphenyl]-4,4′-dicarboxylic acid and 2,2′-diamino-[1,1′-biphenyl]-4,4′-dicarboxylic acid as bridging ligands, resulting in MOFs with amine groups covalently linked to the bridging ligands. Both types of functionalized MOFs were post-synthetically modified with 4-formylbenzonitrile that resulted in imine formation. All the obtained compounds were characterized by PXRD, TGA, DTA, BET, NMR, and FTIR spectroscopy, while stability in water was monitored with SEM, EDS, and UV–VIS spectroscopy