On the number of cycles of length 4 in a maximal planar graph

Let p and C₄ (G) be the number of vertices and the number of 4-cycles of a maximal planar graph G, respectively. Hakimi and Schmeichel characterized those graphs G for which C₄ (G) = 1/2(p² + 3p - 22). This characterization is correct if p ≥ 9. However, for p = 7 or 8, there is exactly one other graph which violates the theorem in the sense that the upper bound of C₄ (G) is also attained.     

Computations with viscoplastic and viscoelastoplastic fluids

This numerical study focuses on regularised Bingham-type and viscoelastoplastic fluids, performing simulations for 4:1:4 contraction?Cexpansion flow with a hybrid finite element?Cfinite volume subcell scheme. The work explores the viscoplastic regime, via the Bingham?CPapanastasiou model, and extends this into the viscoelastoplastic regime through the Papanastasiou?COldroyd model. Our findings reveal the significant impact that elevation has in yield stress parameters, and in sharpening of the stress singularity from that of the Oldroyd/Newtonian models to the ideal Bingham form. Such aspects are covered in field response via vortex behaviour, pressure-drops, stress field structures and yielded?Cunyielded zones. With rising yield stress parameters, vortex trends reflect suppression in both upstream and downstream vortices. Viscoelastoplasticity, with its additional elasticity properties, tends to disturb upstream?Cdownstream vortex symmetry balance, with knock-on effects according to solvent-fraction and level of elasticity. Yield fronts are traced with increasing yield stress influences, revealing locations where relatively unyielded material aggregates. Analysis of pressure drop data reveals significant increases in the viscoplastic Bingham?CPapanastasiou case, O (12%) above the equivalent Newtonian fluid, that are reduced to 8% total contribution increase in the viscoelastoplastic Papanastasiou?COldroyd case. This may be argued to be a consequence of strengthening in first normal stress effects.     

Behavoir of Trapped Bromothymol Blue into Sol-Gel Matrix in Presence of CTAB

Encapsulation of bromothymol blue (BTB) into a polysiloxane network was prepared using sol-gel method without using a catalyst. The co-entrappment of the bromothymol blue (BTB) and surfactant cetyltrimethyl ammonium bromide (CTAB) was used to modify the properties of the sol-gel matrixes which may provide a highly porous materials and made the polysiloxane network an excellent host for sensing molecules. Monolithic disks of trapped BTB were obtained with no leaching. Polarized light microscopy shows that a almost unique particle sizes distributions were formed. The immobilized BTB shows a response for various pH solutions, the feature of absorption spectra of the immobilized BTB was almost the same as that of the solutions.     

Trägerfixierte Organometallkomplexe. IV. Strukturuntersuchungen an neutralen und kationischen (Ether-phosphan)palladium(II)-Komplexen

Supported Organometallic Complexes. IV. Structural Investigations on Neutral and Cationic (Ether-phosphane)palladium(II) Complexes . Reaction of the (ether-phosphane) ligands PhP(R)CH₂—D ( 2a?c ) [D=CH₂OCH₃: R=Ph ( a ), (CH₂)₃Si(OCH₃)₃ ( b ), (CH₂)₃SiO_3/2 ( b ′); D= R=(CH₂)₃Si(OCH₃)₃ ( c ), (CH₂)₃SiO_3/2 ( c ′)] with Cl₂Pd(COD) ( 1 ) results in the formation of Cl₂Pd(P — O)₂ ( 3a?c ). Cleavage of Cl^? from 3 with AgSbF₆ yields the cationic, monochelated complexes [ClPd(P — O)(P ∩ O)]⁺ ( 4 a—c ) (P — O: η¹-P-coordinated; P ∩ O: η²-O ∩ P-coordinated). 4 a crystallizes in the monoclinic space group P2₁/c with the lattice constants a=1 062,4(2), b=1 912,2(4) und c=1 635,5(3) pm, β=101,22(3)° and Z=4 (R=0,0341; R_w=0,033). With water 3 b, c and 4 b, c are subjected to polycondensation to give the supported complexes 3 b′, c′, 4 b′, c ′. The structure 3 b′, c′, 4 b′, c ′ is investigated by comparison of their ³¹P CP MAS data with the ³¹P{¹H} NMR spectra of their soluble precursors 3 b, c, 4 b, c . ¹³C CP MAS NMR spectra of 3 b′, c ′ and 4 b′, c ′ indicate η¹-P- and η²-O ∩ P-coordination of the ligands. The polysiloxane network of 4 b ′ was inspected by contact time variation of the ²⁹Si CP MAS NMR spectra and it appeared that 77% of the Si—O units are crosslinked, corresponding to a ratio T₄:T₃:T₁=67:100:10.     

Optimization of Maceration Conditions for Improving the Extraction of Phenolic Compounds and Antioxidant Effects of Momordica Charantia L. Leaves Through Response Surface Methodology (RSM) and Artificial Neural Networks (ANNs)

The main goals of this research were the chemical and biological characterization of the bitter melon (Momordica charantia) isolate obtained by traditional (maceration) extraction, as well as optimization of this process using response surface methodology (RSM) and artificial neural networks (ANNs). Experiments were performed using Box–Behnken experimental design on three levels and three variables: extraction temperature (20?°C, 40?°C, and 60?°C), solvent concentration (30%, 50%, and 70%) and extraction time (30, 60, and 90?min). The measurements consisted of 15 randomized runs with 3 replicates in a central point. The antioxidant activity of obtained extracts was determined by the 1,1-diphenyl-2-picrylhydrazyl (DPPH), cupric ion reducing antioxidant capacity (CUPRAC) and ferric reducing antioxidant power (FRAP) assays while chemical characterization was done in terms of the total phenolic content (TPC). The methodology shows positive influence of solvent concentration on all four observed outputs, while temperature showed a negative impact. RSM showed that the optimal extraction conditions were 20?°C, 70% methanol, and an extraction time of 52.2?min. Under these conditions, the TPCs were 20.66 milligrams of gallic acid equivalents (mg GAE/g extract), DPPH 30.22 milligrams of trolox equivalents (mg TE/g extract), CUPRAC 67.78 milligrams of trolox equivalents (mg TE/g extract), and FRAP 45.48 milligrams of trolox equivalents (mg TE/g extract). The neural network coupled with genetic algorithms (ANN-GA) was also used to optimize the conditions for each of the outputs separately. It is anticipated that results reported herein will establish baseline data and also demonstrate that that the present model can be applied in the food and pharmaceutical industries.