Smith meets Smith: Smith normal form of Smith matrix

In 1861, Henry John Stephen Smith [H.J.S. Smith, On systems of linear indeterminate equations and congruences, Philos. Trans. Royal Soc. London. 151 (1861), pp. 293–326] published famous results concerning solving systems of linear equations. The research on Smith normal form and its applications started and continues. In 1876, Smith [H.J.S. Smith, On the value of a certain arithmetical determinant, Proc. London Math. Soc. 7 (1875/76), pp. 208–212] calculated the determinant of the n?×?n matrix ((i,?j)), having the greatest common divisor (GCD) of i and j as its ij entry. Since that, many results concerning the determinants and related topics of GCD matrices, LCM matrices, meet matrices and join matrices have been published in the literature. In this article these two important research branches developed by Smith, in 1861 and in 1876, meet for the first time. The main purpose of this article is to determine the Smith normal form of the Smith matrix ((i,?j)). We do this: we determine the Smith normal form of GCD matrices defined on factor closed sets.     

Mono‐ and Bis(imidazolidinium ethynyl) Cations and Reduction of the Latter To Give an Extended Bis‐1,4‐([3]Cumulene)‐p‐carboquinoid System

An extended π‐system containing two [3]cumulene fragments separated by a p‐carboquinoid and stabilized by two capping N‐heterocyclic carbenes (NHCs) has been prepared. Mono‐ and bis(imidazolidinium ethynyl) cations have also been synthesized from the reaction of an NHC with phenylethynyl bromide or 1,4‐bis(bromoethynyl)benzene. Cyclic voltammetry coupled with synthetic and structural studies showed that the dication is readily reduced to a neutral, singlet bis‐1,4‐([3]cumulene)‐p‐carboquinoid as a result of the π‐accepting properties of the capping NHCs.     

Regioselective syntheses, structural characterization, and electron ionization mass spectrometric behavior of regioisomeric 2,3-disubstituted 2-imino-1,3-thiazolidin-4-ones

The regioselective syntheses of 3-alkyl(aryl)-2-(anthracen-9'-ylimino)-1,3-thiazolidin-4-ones (2) and 2-alkyl(aryl)imino-3-(anthracen-9'-yl)-1,3-thiazolidin-4-ones (3) from N-(anthracen-9-yl)-N'-alkyl(aryl)thioureas were accomplished effectively using methyl bromoacetate and bromoacetyl bromide, respectively. Detailed structural characteristics were confirmed mainly by NMR techniques. The mass spectrometric behavior of the resulting sets of compounds of known structures was shown to be characteristic for each set. Some interesting fragmentation pathways involving the transfer and rearrangements of various moieties were also revealed, as well as regioisomerization for particular substituent-specific fragmentations.     

Locked conformations for proline pyrrolidine ring: synthesis and conformational analysis of cis- and trans-4-tert-butylprolines

The motional restrictions of the proline pyrrolidine ring allow this secondary amine amino acid to act as a turn inducer in many peptides and proteins. The pyrrolidine ring is known to exhibit two predominant pucker modes (i.e., C-4 (Cgamma) exo and endo envelope conformers whose ratio can be controlled by proper substituents in the ring). In nature, the exo puckered 4(R)-hydroxy-l-proline plays a crucial role as a building block in collagen and collagen-like structures. It has been previously concluded that the electronegativity of the 4-cis-substituent increases the endo puckering while the electronegativity of the 4-trans-substituent favors the exo puckering. Here, we have introduced a sterically demanding tert-butyl group at C-4 in trans- and cis-configurations. In the case of trans-substitution, the induced puckering effect on the pyrrolidine ring was studied with X-ray crystallography and 1H NMR spectral simulations. Both cis- and trans-4-tert-butyl groups strongly favor pseudoequatorial orientation, thereby causing opposite puckering effects for the pyrrolidine ring, cis-exo and trans-endo for l-prolines, in contrast to the effects observed in the case of electronegative C-4 substituents. The syntheses and structural analysis are presented for the conformationally constrained 4-tert-butylprolines. The prolines were synthesized from 4-hydroxy-l-proline, substitution with t-BuCuSPhLi being the key transformation. This reaction gave N-Boc-trans-4-tert-butyl-l-proline tert-butyl ester in 94% ee and 57% de. Enantioselectivity was increased to 99.2% ee by crystallization of N-Boc-trans-4-tert-butyl-l-proline in the final step of the synthesis.     

Controlling warpage of molded package for inkjet manufacturing

A system consisting of four silicon dies and several discrete components was encapsulated with epoxy mold material and the package was used for the evaluation of inkjet manufacturing in electronics. Experimental samples showed that the molding process induces thermo-mechanical stresses that warp the package after the mold resin is cured at elevated temperature. The molding process was modeled using the finite element method (FEM), and different package structures were simulated to see how those affect the final warpage of the package. Material properties of the mold material were measured and used in the FE model. The viscoelastic behavior of mold material was modeled with a sum of Prony series terms and a time-temperature shift factor was used to include the temperature effect. To verify the modeling assumptions, the surface profile of an experimental package was measured with an optical profilometer and the measurements were compared with the simulated profile. A good correlation was found between the measured and simulated profile of the package. The simulations with different package structures showed that e.g. an additional film placed on top of the mold resin reduces significantly the warpage of the package.     

On eigenvalues of meet and join matrices associated with incidence functions

Let (P,?,∧) be a locally finite meet semilattice. Let

     

Modification of polypropylene surfaces with micropits and hierarchical micropits/nanodepressions

Micropit surfaces and hierarchically structured micropit/nanodepression surfaces were fabricated in polypropylene by injection moulding. The first step in the process was the microstructuring of aluminium foils with a micro-working robot to obtain a pattern of micropits. Dimensions of the micropits could be controlled by adjusting the working parameters of the robot. The microstructured faces of some of the foils were anodized to aluminium oxide giving a surface in which both micropits and the smooth areas between were covered with nanopores. Mould inserts for the injection moulding were obtained by cold mounting of an epoxy resin mixture on the foils. After the epoxy resin had hardened, the foils were etched away. Dimensions of the micropillars and micropillars/nanobumps on the epoxy related to the dimensions of the structures on the foils. Finally, structures were replicated in polypropylene as micropits and hierarchical micropits/nanodepressions by injection moulding. The dimensions of these hollow structures corresponded well with those of the epoxy pillars and the original micropits.Static and dynamic contact angles on the micropit-structured polypropylene surfaces were elevated from the slightly hydrophobic values of smooth polypropylene. With hierarchical micropit/nanodepression structures, the contact angles approached the superhydrophobic limit of 150°. The work demonstrates an inexpensive and reproducible technique to fabricate hollow structures of various dimensions and scales on polypropylene and modify the surface properties of the polymer.