On nadir points of multiobjective integer programming problems

In this study, we consider the nadir points of multiobjective integer programming problems. We introduce new properties that restrict the possible locations of the nondominated points necessary for computing the nadir points. Based on these properties, we reduce the search space and propose an exact algorithm for finding the nadir point of multiobjective integer programming problems. We present an illustrative example on a three objective knapsack problem. We conduct computational experiments and compare the performances of two recent algorithms and the proposed algorithm.     

Periodic analogues of Dedekind sums and transformation formulas of Eisenstein series

Let \(\bar{p}(n)\) denote the number of overpartitions of n. Fortin et al. and Hirschhorn and Sellers established some congruences modulo powers of 2 for \(\bar{p}(n)\). Recently, Xia and Yao found several congruences modulo powers of 2 and 3. In particular, they proved that \(\bar{p}(96n+12)\equiv 0 \ (\mathrm{mod}\ 9)\) and \(\bar{p}(24n+19)\equiv 0\ (\mathrm{mod\ }27)\). In this paper, we generalize the two congruences and establish several new infinite families of congruences modulo 9 and 27 for \(\bar{p}(n)\). Furthermore, we prove some strange congruences modulo 9 and 27 for \(\bar{p}(n)\) by employing some results due to Cooper et al. For example, we prove that for \(k\ge 0\), \(\bar{p}(4^{k+1})\equiv 2^{k+3}+6(-1)^k\ (\mathrm{mod} \ 27) \) and \(\bar{p}\left( 7^{2k}\right) \equiv 2-2k\ (\mathrm{mod}\ 9)\). We also present two conjectures on congruences for \(\bar{p}(n)\).     

Adsorption Mechanisms of 6-Chloro-3-Hydroxy-2-Pyrazinecarboxamide on Pristine,Si- and Al-Doped C<Subscript>60</Subscript> Fullerenes: A DFT Study

Fullerenes have been of research interest and they have been particularly studied for their possible applications as drug delivery vehicles. In the present research, the optimized molecular geometries, electronic properties and the possible interaction mechanisms between C₆₀, Si- or Al-doped C₆₀ and 6-chloro-3-hydroxy-2-pyrazinecarboxamide were investigated using quantum mechanical calculations. The calculated binding energies to the Si- and Al-doped fullerenes suggest that doping of fullerene nanocage enhances the interaction mechanism and alters the chemical and electronic properties. The results and parameters found in this research reveal further insight into drug delivery systems.     

Antimicrobial activities and absorption properties of disazo dyes containing imidazole and pyrazole moieties

The newly synthesized thirteen disazo dyes containing imidazole and pyrazole cycles (3a-3m) were carried out by diazotization reaction of 5-amino-4-arylazo-3-methyl-1H-pyrazoles (2a-2m) and coupling reaction with 1-methyl imidazole. Structures of synthesized azo dyes were characterized by UV–Vis, FT-IR, ¹H-NMR, elemental analysis and their solvatochromic properties were studied in DMSO, DMF, methanol, acetic acid and chloroform. In addition, the antimicrobial activities of dyes against twelve pathogenic bacteria were examined in detail and all dyes showed antimicrobial activity against different bacterial strains.     

Experimental study on the 3D‐printed plastic parts and predicting the mechanical properties using artificial neural networks

This study investigates the mechanical properties of 3D‐printed plastic parts fabricated using Fused Deposition Modeling (FDM). For this purpose, a 3D printer named KASAME was designed and built by the researchers. The test samples were fabricated using polylactic acid (PLA). The experiments were conducted using three melt temperatures (190°C, 205°C, and 220°C), four layer thickness values (0.06 mm, 0.10 mm, 0.19 mm, and 0.35 mm), and three raster pattern orientations (+45°/?45° [the crisscross pattern], horizontal and vertical). Tensile strength tests were performed to determine tensile strength values of the samples and fracture surfaces were also analyzed. Using artificial neural networks, a mathematical model for the tensile test results was generated corresponding to the raster pattern employed in 3D fabrication. Tensile strength tests indicated that melt temperature, layer thickness, and raster pattern orientation had a significant effect on the tensile strengths of the samples. According to the result of the experiment, the maximum average tensile strength values were observed for the samples fabricated using the crisscross raster pattern. The analysis of variance (ANOVA) table shows the raster pattern (PCR) value of 48.68% was obtained with the highest degree of influence. With respect to R ², the best performing artificial neural network model, with test and training values of 0.999199 and 0.999997, respectively, was observed to be the crisscross raster pattern. Copyright © 2016 John Wiley & Sons, Ltd.     

Synthesis,crystal structure,thermal decomposition,and XPS studies of homo and heterotrinuclear Cu(II)–Cu(II)–Cu(II) and Cu(II)–Ni(II)–Cu(II) complexes obtained from salpn type ligands

In this study, a mononuclear CuL complex was prepared by the use of bis-N,N′-(salicylidene)-1, 3-propanediamine (LH₂) and Cu²⁺ ion. NiCl₂ and NiBr₂ salt were treated with this complex in dioxanewater medium and two new complexes [(CuL)₂NiCl₂(H₂O)₂] and [(CuL)₂NiBr₂(H₂O)₂)] with Cu(II)–Ni(II)–Cu(II) nucleus structure were obtained. In addition to this bis-N,N′-(2-hydroxybenzyl)-1,3-diaminopropane (L^HH₂) was prepared by the reduction of LH₂ with NaBH₄ in MeOH medium. The treatment of this reduced complex with Cu²⁺ ion resulted a complex [(CuL^H)₂CuCl₂] with a structure of Cu(II)–Cu(II)–Cu(II). The complexes prepared were characterized by the use of elemental analysis, IR spectroscopy, thermogravimetric and X-ray diffraction methods. The crystal structures of [(CuL)₂NiBr₂(H₂O)₂] (СIF file CCDC 1448402) and [(CuL^H)₂CuCl₂] (СIF file CCDC 1448401) complexes were elucidated. It was found that halogen ions are coordinated to terminal Cu²⁺ ions which are in a distorted square pyramid coordination sphere. It was determined that the central Cu(II), which joins terminal square pyramidal Cu(II), was coordinated only by the phenolic oxygens of the ligand while the central Ni(II) was coordinated by two phenolic oxygens of the organic ligand and two water molecules. These complexes were investigated by XPS and it was found that the terminal and central Cu²⁺ ions were different in Cu(II)–Cu(II)–Cu(II) complex. Also, the thermal degradation of the CuLH complex unit was observed to exothermic in contrast to the expectations.

     

Novel mixed-ligand complexes of coumarilate/<Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>′-diethylnicotinamide with some transition metals

Coordination complexes of transition metal cations (Co^II, Ni^II, Cu^II and Zn^II) containing coumarilate and N,N′-diethylnicotinamide were synthesized. The structural characterization and thermal behaviour analysis of novel samples synthesized were conducted through elemental analysis, magnetic susceptibility, solid-state UV–Vis, direct and injection probe mass spectra, FTIR spectra, thermoanalytic TG-DTG/DTA and single crystal X-ray diffraction methods. The structural details of single crystals of [Co(dena)₂(H₂O)₄](coum)₂ (I) and [Cu(coum)₂(dena)₂(H₂O)₂] (III) complexes were resolved completely. Moreover, the results of analysis obtained for [Ni(coum)₂(dena)₂(H₂O)₂] (II) and [Zn(dena)₂(H₂O)₄](coum)₂ (IV) complexes were interpreted considering the samples with crystal structures defined and made assumptions about the structural details. It was determined that the complex of Co^II metal cation has salt-type structure and the coordination number of metal is accomplished to six as the sum of 4 mol of water and also 2 mol of N,N′-diethylnicotinamide ligands in trans position located within the coordination sphere. It was observed that 2 mol of coumarilate anions are located outside the coordination sphere and have stabilized to the charge (2+) of metal. The Cu^II complex has totally molecular structure, and the coordination sphere of metal cation was 6 as the sum of 2 mol of water, 2 mol of N,N′-diethylnicotinamide and 2 mol of monoanionic monodentate coumarilate ligands. All ligands have been located in –trans position. The geometry of both complex structures is distorted octahedral. It is assumed that the Ni^II complex structure is isostructural with Cu^II complex structure and also does Zn^II complex with Co^II structure. It was determined that the decomposition products obtained from thermal analysis are the oxides of related metal cations.     

The behavior of solutions of second order delay differential equations

In this paper, we study the behavior of solutions of second order delay differential equation

y^″(t)=p₁y^′(t)+p₂y^′(t−τ)+q₁y(t)+q₂y(t−τ),     

A generalization of a theorem of A. Grothendieck

In this article we characterize the quasi‐barrelledness of the projective tensor product of a coechelon space of type one k ¹(A) with a Fréchet space, including homological conditions as exactness properties of the corresponding tensor product functor k ¹(A) ·: ? → ??, acting from the category of Fréchet spaces to the category of linear spaces, resp. the vanishing of its first right derivative Tor¹_π (k ¹(A),.). This generalizes and extends a classical theorem of A. Grothendieck ([13, Chap. II, §4, No. 3, Theorem 15]). Further we present an analogous theorem for complete coechelon spaces of type zero and the injective tensor product and results concerning the stronger property of barrelledness. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Brieskorn manifolds as contact branched covers of spheres

We show that Brieskorn manifolds with their standard contact structures are contact branched coverings of spheres. This covering maps a contact open book decomposition of the Brieskorn manifold onto a Milnor open book of the sphere.