Rings of bonds in graphs

It is shown that every strict maximal ring of bonds of size greater than 3 is even.     

Kinetics of wetting of a compacted powder by aqueous solutions of surface active agents

Summary The capillary rise of aqueous solutions of anionic wetting agents into a compacted powder of an organic chromium complex is discussed on the basis of the Washburn-Rideal equation expanded to account for the porous structure parameters.At the porosity 1 —/6, corresponding to the loosest packing of monodisperse spheres the penetration rate is found to be mostly governed by the effective tensions operative at the moving three phase line of contact in case no deflocculation intervenes.

---

Zusammenfassung Der Kapillaraufstieg wässeriger Lösungen anionischer Netzmittel in gepreßtem Pulver eines organischen Chrom-Komplexes wird durch die erweiterte Gleichung vonWashburn-Rideal wiedergegeben, in der die Parameter der porösen Struktur mit einbezogen werden.Bei der Porosität 1 —/6, die der lockersten Anordnung gleichförmiger Kugeln entspricht, wird die Eindringgeschwindigkeit meistens durch die an der sich bewegenden Dreiphasengrenze wirkenden Grenzflächenspannungen bestimmt, wenn keine Peptisation eintritt.

---

---

Paper presented at the XII Intern. Congr. Fat Research, Milan, September 1974.     

Synthesis of ylideplatinum(II) complexes via α-functionalised alkylplatinum(II) intermediates and some comparative data on palladium(II) complexes; X-ray structure of trans-[Pt(CH2PEt3)I(PEt3)2]I

The reaction of [Pt(PEt₃)₃] with CH₂I₂ affords trans-[Pt(CH₂PEt₃)I(PEt₃)₂]I and is believed to proceed via the α-functionalised alkyl cis-[Pt(CH₂I)I(PEt₃)₂], because similar ylides are obtained from cis- or trans-[PT(CH₂X)(PPh₃)₂X] (XCl, Br, or I) with PR₃ (PEt₃, PBu₃ⁿ, PMePh₂, PEtPh₂, or PPh₃); cis-[Pd(CH₂I)-I(PPh₃)₂] does not react with excess PPh₃, but with PEt₃ yields trans-[Pd(CH₂PEt₃)I(PPh₃)₂]I; the X-ray structure of trans-[Pt(CH₂PEt₃)I(PEt₃)₂]I (current R = 0.045) shows PtP(1) 2.332(7), PtP(2) 2.341(8), PtC 2.08(2), and PtI 2.666(2) Å, and angles (a) C(1)PtI, P(1), P(2): 176.9(8), 91.6(6), 93.4(6), (b) IPtP(1), P(2): 87.1(2), 88.5(2), and (c) P(1)P(2), 166.8(3), and (d) PtC(1)P(3), 118(1)°.     

Scanning XPS; low kinetic energy source scanning: some design considerations

Summary The logistics of electron-beam scanning in two special applications in surface-analysis are discussed, particularly with a view to multitechnique surface-analysis. For electron-beam charge-neutralisation it is necessary first to produce an x,y-positionable beam at low (a few eV) kinetic energies, with a significant space-charge, and submillimetre focus. These performance requirements seem at first sight to be at odds with the requirement for multitechnique surface-analysis, namely that the solid-angle subtended by each technique be kept to a minimum. Here both the high space-charge, and the small, positionable focus requirements indicate a larger solid-angle is required. Similarly, in scanning small-area (imaging) XPS, a requirement arises for keeping the solid-angle to a modest value, whilst not compromising the large-collection-angle electron-spectroscopy techniques, on a component hemispherical-sector electron energy analyser. Tested solutions for either case, satisfying all criteria, are presented.     

An assessment of the resolution limitation due to radiation-damage in X-ray diffraction microscopy

X-ray diffraction microscopy (XDM) is a new form of X-ray imaging that is being practiced at several third-generation synchrotron-radiation X-ray facilities. Nine years have elapsed since the technique was first introduced and it has made rapid progress in demonstrating high-resolution three-dimensional imaging and promises few-nanometer resolution with much larger samples than can be imaged in the transmission electron microscope. Both life- and materials-science applications of XDM are intended, and it is expected that the principal limitation to resolution will be radiation damage for life science and the coherent power of available X-ray sources for material science. In this paper we address the question of the role of radiation damage. We use a statistical analysis based on the so-called “dose fractionation theorem” of Hegerl and Hoppe to calculate the dose needed to make an image of a single life-science sample by XDM with a given resolution. We find that the needed dose scales with the inverse fourth power of the resolution and present experimental evidence to support this finding. To determine the maximum tolerable dose we have assembled a number of data taken from the literature plus some measurements of our own which cover ranges of resolution that are not well covered otherwise. The conclusion of this study is that, based on the natural contrast between protein and water and “Rose-criterion” image quality, one should be able to image a frozen-hydrated biological sample using XDM at a resolution of about 10 nm.     

Covering hypercubes by isometric paths

An isometric path is merely any shortest path between two vertices. If the vertices of the hypercube Q_n are represented by the set of 0–1 vectors of length n, an isometric path is obtained by changing the coordinates of a vector one at a time, never changing the same coordinate more than once. The minimum number of isometric paths required to cover the vertices of Q_n is at least 2ⁿ/(n+1). We show that when n+1 is a power of 2, the lower bound is in fact the minimum. In doing so, we construct a family of disjoint isometric paths which can be used to find an upper bound for additional classes of hypercubes.     

Quantitative characterization of nanoparticle agglomeration within biological media

The electronics industry is one of the world??s fastest growing manufacturing industries. However, e-waste has become a serious pollution problem. This study reports the recovery of e-waste for preparing valuable MCM-48 and ordered mesoporous carbon for the first time. Specifically, this study adopts an alkali-extracted method to obtain sodium silicate precursors from electronic packaging resin ash. The influence of synthesis variables such as gelation pH, neutral/cationic surfactant ratio, hydrothermal treatment temperature, and calcination temperature on the mesophase of MCM-48 materials is investigated. Experimental results confirm that well-ordered cubic MCM-48 materials were synthesized in strongly acidic and strongly basic media. The resulting mesoporous silica had a high surface area of 1,317?m²/g, mean pore size of about 3.0?nm, and a high purity of 99.87?wt%. Ordered mesoporous carbon with high surface area (1,715?m²/g) and uniform pore size of CMK-1 type was successfully prepared by impregnating MCM-48 template using the resin waste. The carbon structure was sensitive to the sulfuric acid concentration and carbonization temperature. Converting e-waste into MCM-48 materials not only eliminates the disposal problem of e-waste, but also transforms industrial waste into a useful nanomaterial.     

The Rohlin property for shifts of finite type

We show that an automorphism of a unital AF C^*-algebra with a certain approximate Rohlin property has the Rohlin property. This generalizes a result of Kishimoto. Using this we show that the shift automorphism on the bilateral C^*-algebra associated with an aperiodic irreducible shift of finite type has the Rohlin property.