A note on certain modular constructions of pseudorandom binary sequences with composite moduli

J. Rivat and A. Sárközy extended two large families of pseudorandom binary sequences to the case of composite moduli m, where m is the product of two different primes not far apart. In this paper we continue the study in this direction. We shall improve the estimates for the correlation measure of the sequences.     

An investigation of the self-assembly of neutral, interlaced, triple-stranded molecular braids

The synthesis and structures of six compounds prepared in two different systems have been explored with the purpose of isolating coordination polymers with interlaced triple-stranded molecular braid architectures. The dinuclear paddle-wheel units of [Cu(2)(maa)(4)2 H(2)O] can be rationally tuned to form three classes of isomorphous compounds, namely [Cu(2)(maa)(4)(bpp)] (1) (bpp=1,3-bis(4-pyridyl)propane, Hmaa=2-methylacrylic acid), [Cu(3)(maa)(6)(bpp)(2)] (2), and[Cu(4)(maa)(8)(bpp)(4)(H(2)O)(2)]2 H(2)O (3), with a bridging bpp ligand, at controlled ligand-to-metal molar ratios, and lead to three coordination polymers having similar one-dimensional characteristics but different mono- and dinuclear nodes. Compound 1, with a bpp:[Cu(2)(maa)(4)2 H(2)O] stoichiometry of 1:1, contains a zigzag chain containing dinuclear nodes, whereas polymer 2, with a bpp:[Cu(2)(maa)(4)2 H(2)O] stoichiometry of 1.5:1, also adopts the topology of a zigzag chain but with both mono- and dinuclear nodes. Compound 3, with a bpp:[Cu(2)(maa)(4)2 H(2)O] stoichiometry of 2:1, contains a neutral, interlaced, triple-stranded molecular braid, which is interwoven by three single-stranded meso-helical chains that contain only a mononuclear node. With the three aromatic chelating terminal ligands 2,2':6',2'-terpyridine (tpy), 1,10-phenanthroline (phen), and di(2-pyridyl)amine (dpa) we have also prepared three neutral complexes containing the linear, rigid bridging ligand biphenyl-4,4'-dicarboxylate (bpdc), namely [Cd(bpdc)(tpy)]H(2)O (4), [Cu(bpdc)(phen)(2)]4.25 H(2)O (5), and [Cu(bpdc)(dpa)] (6). An infinite meso-helix is formed initially in 4, and then three of these chains assemble into a triple-stranded braid similar to that of 3. Complexes 5 and 6 have a mononuclear and a looped dinuclear structure, respectively. Compounds 3 and 4 are unusual examples of triple-stranded molecular braid coordination frameworks based on different types of co-ligands.     

Synthesis, crystal structure and thermochemical behaviour of a barium complex [Ba(5-OH-BDC)(H2O)3] [5-OH-H2BDC = 5-hydroxyisophtalic acid]

A novel complex [Ba(5-OH-BDC)(H₂O)₃] [5-OH-H₂BDC = 5-hydroxyisophtalic acid] was synthesized and characterized by X-ray crystallography. The complex is Monoclinic P2₁/c, a = 11.1069(4), b = 14.8192(6), c = 6.5005(2) Å, β = 103.465(3)° and Z = 4, which exhibits a three-dimensional framework formed by linkage of adjacent two-dimensional (6, 3) layers via intermolecular hydrogen bonds. The title complex has been studied by IR spectrum and TG-DTG. The constant-volume combustion energy of the complex, Δ_cU, was determined as being (−3210.45 ± 1.41) kJ mol⁻¹ by a precise rotating-bomb calorimeter at 298.15 K. The standard enthalpy of combustion, , and the standard enthalpy of formation, , were calculated as being (−3207.97 ± 1.41) and (−1922.80 ± 1.76) kJ mol⁻¹, respectively. A calculation model for determining the specific heat capacity of the complex with an improved RD496-III microcalorimeter is also derived. The specific heat capacity of the complex was (6158.387 ± 0.187) J mol⁻¹ K⁻¹.     

Determination of metformin based on amplification of its voltammetric response by a combination of molecular wire and carbon nanotubes

Molecular wires containing copper(II) (CuMW), in the form of the coordination polymer (Cu(II)₄(bpp)₄(maa)₈(H₂O)₂).2H₂O (bpp=1,3-bis(4-pyridyl)propane, maa=2-methylacrylic acid), and multiwalled carbon nanotubes (CNT) have been combined to prepare a paste electrode (CuMW/CNT/PE). The voltammetric response of the CuMW/CNT/PE to metformin (MET) was significantly greater than that of electrodes prepared from other materials, because of both the surface effect of CuMW and CNT and coordination of MET with the Cu(II) ion in the CuMW. A novel voltammetric method for determination of MET is proposed. In pH 7.2 Britton–Robinson buffer, using single sweep voltammetry, the second-order derivative peak current for oxidation of MET at 0.97 V (relative to SCE) increased linearly with MET concentration in the range 9.0 × 10⁻⁷–5.0 × 10⁻⁵ mol L⁻¹ and the detection limit was 6.5 × 10⁻⁷ mol L⁻¹. Figure When a combination of molecular wires containing copper(II) (CuMW) and multiwalled carbon nanotubes (CNT) was used to prepare a paste electrode (CuMW/CNT/PE) the voltammetric response to metformin (curve c) was significantly higher than that at a carbon/PE (curve a) or a CNT/PE (curve b), because of the amplification effect of CNT and CuMW. A novel voltammetric method is proposed for determination of MET     

Enhanced photoactivity of CuPp-TiO2 photocatalysts under visible light irradiation

Three novel porphyrins, 5,10,15-tri-phenyl-20-[4-(3-phenoxy)-propoxy]phenyl porphyrin, 5,15-di-phenyl-10,20-di-[4-(3-phenoxy)-propoxy]phenyl porphyrin and 5-phenyl-10,15,20-tri- [4-(3-phenoxy)-propoxy]phenyl porphyrin, and their corresponding copper(II) complexes were synthesized and characterized spectroscopically. The photocatalytic effects of TiO₂ samples impregnated with copper(II) porphyrins was investigated by photodegradation of 4-nitrophenol (4-NP) in aqueous solution under visible light. The photocatalysts were characterized by means of scanning electron microscopy (SEM), X-ray diffraction (XRD), UV-vis spectra and FT-IR spectra. The results indicated that CuPps were successfully loaded and interacted with the surface of TiO₂ microsphere, which is crucial to enhance the activity of the catalytic composite under visible light.     

Molecular structure,quantum chemical investigation,and thermal behavior of (DNAZ-CO)<Subscript>2</Subscript>

Bis-(3,3-dinitroazetidinyl)-oxamide ((DNAZ-CO)₂) is an acyl derivative of 3,3-dinitroazetidine (DNAZ). It is prepared and its crystal structure is determined. The crystal is orthorhombic, Fdd2 space group, a = 13.136(14) Å, b = 19.48(3) Å, c = 10.326(14) Å, V = 2642 (6) ų, Z = 8. A density functional theory (DFT) method of the Amsterdam Density Functional (ADF) package is used to calculate the geometry, frequencies, and properties. The optimized geometry, frontier orbital energy, and main atomic orbital percentage are obtained. The thermal behavior is studied under a non-isothermal condition by DSC and TG/DTG methods. The apparent activation energy (E _a) and pre-exponential factor (A) of the exothermic decomposition reaction of (DNAZ-CO)₂ are 164.10 kJmol^?1 and 10^13.38 s^?1 respectively. The critical temperature of thermal explosion is 272.20°C. The values of ΔS ^≠, ΔH ^≠, and ΔG ^≠ of this reaction are 6.44 Jmol^?1·K^?1, 163.76 kJmol^?1 and 160.34 kJmol^?1 respectively.     

Molecular structure and thermal behavior of N-Benzoyl-3,3-dinitroazetidine

N-Benzoyl-3,3-dinitroazetidine (BDNAZ) has been synthesized and characterized by elemental analysis, FT-IR spectroscopy, ¹H NMR and X-ray single crystal diffraction technique. BDNAZ crystallizes in the monoclinic space group P2₁/c. Its thermal behavior was studied under a non-isothermal condition by DSC and TG/DTG methods, the value of E _a and A of the exothermic decomposition reaction of BDNAZ are 143.19 kJ mol^?1 and 10^14.34 s^?1, respectively. The specific heat capacity of BDNAZ was determined with a continuous C _p mode of micro-calorimeter and theoretical calculation. The adiabatic time-to-explosion was evaluated as 109.9?C124.4 s.     

Generalized Knopp identities for homogeneous Hardy sums and Cochrane-Hardy sums

Let q, h, a, b be integers with q > 0. The classical and the homogeneous Dedekind sums are defined by $$s(h,q) = \sum\limits_{j = 1}^q {\left( {\left( {{j \over q}} \right)} \right)\left( {\left( {{{hj} \over q}} \right)} \right),{\rm{ }}s(a,b,q) = \sum\limits_{j = 1}^q {\left( {\left( {{{aj} \over q}} \right)} \right)\left( {\left( {{{bj} \over q}} \right)} \right),} } $$ respectively, where $((x)) = \left\{ \begin{gathered} x - [x] - \tfrac{1} {2},if x is not an integer; \hfill \\ 0,if x is an integer. \hfill \\ \end{gathered} \right. $ The Knopp identities for the classical and the homogeneous Dedekind sum were the following: $$\sum\limits_{d|n} {\sum\limits_{r = 1}^d {s\left( {{n \over d}a + rq,dq} \right) = \sigma (n)s(a,q),} } $$ $$\sum\limits_{d|n} {\sum\limits_{{r_1} = 1}^d {\sum\limits_{{r_2} = 1}^d s \left( {{n \over d}a + {r_1}q,{n \over d}b + {r_2}q,dq} \right) = n\sigma (n)s(a,b,q),} } $$ where σ(n) =Σ _d|n d. In this paper generalized homogeneous Hardy sums and Cochrane-Hardy sums are defined, and their arithmetic properties are studied. Generalized Knopp identities for homogeneous Hardy sums and Cochrane-Hardy sums are given.     

Thermochemistry of ammonium based ionic liquids: Tetra-alkyl ammonium nitrates – Experiments and computations

In this work data of the molar enthalpies of formation of the ionic liquids [R₄N][NO₃] were measured by means of combustion calorimetry. The thermal behavior of [R₄N][NO₃] was studied using differential scanning calorimetry. First-principles calculations of the enthalpy of formation in the gaseous phase have been performed for the ionic species using the G3(MP2) theory. Enthalpies of formation of aqueous tetra-alkyl ammonium ions ${\mathrm{\Delta }}_{\text{f}}{H}_{\text{m}}^{°}$ ([R₄N]⁺_(aq)) derived in this work are useful for prediction thermochemical properties of the ammonium based ionic liquids.