Simple pictorial mathematics problems for children: locating sources of cognitive load and how to reduce it

ZDM – Mathematics Education - Pictorial representations are often used to help children understand the situation described in a given number-sentence scheme. These static pictorial problems...     

A supramolecular structure of bis(1,3-diphenyl-1,3-propanedionato-O,O′) (1,10-phenanthroline-N,N′)cobalt(II) based on C–H…O, C–H…π and π…π interactions

The compound bis(1,3-diphenyl-1,3-propanedionato-O,O′) (1,10-phenanthroline-N, N′)cobalt(II) (Co(DBM)₂(1,10-phe)) was investigated as a potential host component for functional inclusion materials. The molecules of the complex in the crystal (a=21.015(5) ?, b=17.456(5) ?, c=9.503(3) ?, β=107.04(2)°, s.g. C 2/c) are centrosymmetric and assemble by way of C–H···O and C–H···π hydrogen bonds as well as π···π stacking interactions to provide a supramolecular ladder-like motif that is accompanied by a variant of the six phenyl-embrace synthon.     

Intramolecular N−H...O hydrogen bonding,quinoid effect,and partial π-electron delocalization in N-aryl Schiff bases of 2-hydroxy-1-naphthaldehyde: the crystal structures of planar N-(α-naphthyl)- and N-(β-naphthyl)-2-oxy-1-naphthaldimine

The structures of N-(-naphthyl)-2-oxy-1-naphthaldimine1 and N-(-naphthyl)-2-oxy-1-naphthaldimine2 have been investigated by X-ray analysis and by spectroscopic methods. Crystals of1 are monoclinic, space groupPn, with cell dimensionsa=10.823(3),b=5.826(2),c=11.899 (3) Å, and =99.66(3)°. Compound2 crystallizes in the orthorhombic space groupPca2₁ witha=17.564(3),b=6.314(2), andc=13.663(4) Å. The IR spectra exhibited neither N–H nor O–H stretching frequencies. The existence of theintramolecular hydrogen bonding of N–H...O type was predicted by spectroscopic experiment but unequivocally established by diffraction experiment in both cases1 and2. The molecules1 and2 are significantly planar with considerable quinoid effect at the 2-oxy-naphthaldimine moiety. Although essentially planar, both molecules1 and2 show the delocalization of -electrons only in the central part of the molecules including C=N imino group with pendent ring carbon atoms.Intermolecular attractions in the crystals belong to weak van der Waals interactions-between discrete planar molecules spatially arranged into the expectedherringbone motif in the solid state.     

Syntheses of alpha- and beta-C-glucopyranosyl serines from a common intermediate

A versatile synthesis leading to either C-linked alpha- or beta-glucopyranosyl serines is presented from a common, advanced synthetic intermediate. Cyclization of the penultimate carbinol onto the alkene and methanolysis of the lactone yields selectively the alpha-linkage. A transposition of these last steps leads to the beta-linked isomer selectively.     

Stereoselective synthesis of 3,3-diarylacrylonitriles as tubulin polymerization inhibitors

A series of 3,3-diarylacrylonitriles were synthesized stereoselectively as tubulin polymerization inhibitors for potential use in cancer chemotherapy. This synthetic route features stannylcupration and palladium-catalyzed Stille cross-coupling chemistry, allowing both E and Z isomers of 3,3-diarylacrylonitriles to be prepared in a very short sequence of reactions.     

Composite planar electrode for sensing electrochemical oxygen demand

This work reports on the development of a graphite-polystyrene composite electrode of planar configuration, containing silver(II) oxide and copper(II) oxide catalysts (AgO-CuO), for the measurement of electrochemical oxygen demand (EOD). Optimisation studies of the composite composition as well as conditions for its processing on planar substrates and generation of an appropriate electrochemical active area resulted in the scalable fabrication of robust composite electrodes. These were evaluated with glucose as target analyte. They showed competitive low limits of detection in a linear concentration range from 5 mg L⁻¹ to 1400 mg L⁻¹ of O₂. Besides, they were stable for at least one year. The determination of EOD in wastewater samples coming from production lines of parenteral food and winemaking was successfully carried out.     

A Ramanujan-type congruence modulo 5 for 4-colored generalized Frobenius partitions

In his 1984 AMS Memoir, Andrews introduced the \(k\)-colored generalized Frobenius partition function \(c\phi _k(n)\) which denotes the number of generalized Frobenius partitions of \(n\) with \(k\) colors. Recently, Baruah and Sarmah, Lin, and Sellers established several Ramanujan-type congruences for \(c\phi _4(n)\). In this paper, employing some theta identities due to Ramanujan, the \((p, k)\)-parametrization of theta functions given by Alaca, Alaca, and Williams, and some results of Baruah and Sarmah, we prove that \(c\phi _4(20n+11)\equiv 0\ (\mathrm{mod}\ 5)\).     

A wider convergence area for the MSTMAOR iteration methods for LCP

In this paper, based on the Hermitian and skew-Hermitian splitting, we give a generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method to solve singular complex symmetric linear systems, this method has two parameters. We give the semi-convergent conditions, and some numerical experiments are given to illustrate the efficiency of this method.