Local and itinerant Magnetism AND Crystal structure of RRh2Ge2 and RRu2Ge2 (r = rare earth)

The compounds RRh₂Ge₂; and RRu₂Ge₂ were synthesized X-ray studies show that they have the expected ThCr₂Si₂; tetragonal-type structure Magnetization studies at 1 8–300 K, ¹⁵¹Eu Mossbauer studies at 4 l, 77 and 300 K and the crystallography studies show the following- All RRh₂Ge₂; like RRh₂Si₂; exhibit two magnetic phase transitions, one corresponding to the antiferromagnetic ordering of the local rare earth moments. T_N = 8–90 K, the other corresponding to the itinerant electron ordering of the Rh sublattice. T_M = 3–9 K The heavy rare earths in RRu₂G₂; order antiferromagnetically and undergo a spin-flop transition in a relatively low magnetic field, <10 kOe The light elements in RRu₂Ge₂; order in a ferromagnetic, somewhat unclear structure NdRu₂Ge₂, like NdRu₂Si₂, exhibits two peaks in the magnetization curves Again, the lower may correspond to itinerant electron ordenng or, alternatively, to spin reorientation of the rare earth sublattice Eu in both EuRh₂Ge₂ and EuRu₂Ge₂ is divalent, whereas Ce in both CeRh₂Ge₂ and CeRu₂Ge₂ is trivalent For all rare earths the ordenng transition in RRh₂Ge₂ is higher than in RRu₂Ge₂. This fact can be associated with the smaller R-R distances in RRh₂Ge₂ and/ or due to the stronger magnetic character of the Rh 4d conduction electrons Companson of the magnetic properties and ¹⁵¹Eu hyperfine interactions of Eu²⁺Rh₂Ge₂, Eu²⁺Ru₂Ge₂, Eu²⁺Rh₂Si₂ and Eu³⁺Ru₂Si₂ with all the other systems leads to the conclusion that the conduction electrons play the dominant role in determining the magnetic properties of these systems Crystal-field effects are also of considerable importance, since the Mossbauer studies yield for the second-order crystal-field parameter A⁰₂〈r²_4f〉 the huge values +385 and +282 K for EuRu₂Ge₂; and EuRh₂Ge₂, respectively The easy axis of magnetization in the Eu compounds is in the basal plane The large second-order crystal field predicts well the direction of the easy axis for all other rare earths No superconductivity has been observed in any of the compounds, down to 1 8 K A companson of the magnetic properties of the germanides with those of the silicides shows great similanties, the differences being accounted for by the different unit cell sizes and c/a ratios.     

From Fermat to Wiles: Fermat''s Last Theorem Becomes a Theorem

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From Fermat to Wiles: Fermat's Last Theorem Becomes a Theorem

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Theoretical and practical aspects of acid-base determinants by spectrophotometric flow-injection analysis

A simple mathematical treatment is applied to the instantaneous acid-base equilibria prevailing at the peak maxima when reagents containing acid-base indicators are used for spectrophotometric flow-injection determinations of acids and bases. Equations are derived relating the absorbance, the fraction of the relevant acidic or basic form of the indicator and the rate of change of either form with the initial concentration of the analyte and other parameters that influence these determinations. Based on these relationships, criteria are set for the choice of reagent/indicator combinations likely to yield linear absorbance/concentration dependence for general and special cases. These considerations simplified the design of experimental work. Suitable conditions are described for the determination of hydrochloric, phosphoric and acetic acids and for sodium hydroxide and ethanolamine. Very weak acids and bases and concentrations lower than 0.01 N were not investigated, because they were not predicted to conform with the criteria for linearity presented. Least-squares treatment of the data obtained indicated a relative standard deviation of 0.5% from linear behavior, for favorable cases, over a reasonably wide concentrations range. Short-term standard deviations were 0.8% or better; long-term deviations, over several hours, were 1–2%. Highest throughput of samples examined was 144 h^?1.     

Finiteness of the discrete spectrum of some block Toeplitz operators

Sufficient conditions are given for the finiteness of the discrete spectrum of the block Toeplitz operatorT _A generated in the spaceH ₂ ⁿ by self-adjoint matrix functionA(t)(|t|=1). These results are obtained by means of theorems concerning the spectrum of a perturbed self-adjoint operators.     

Stereochemical assignment by mass spectrometry : Double bond geometrical isomers of 3,5-dialkylcyclohexylidene acetic acid esters and 3-alkyl-2-alkenoates

Mass spectrometry is the best physical method for the configurational assignment of E- and Z-3,5-dialkylcyclohexylidene acetic acid esters 1 and E- and Z-3-alkyl-2-alkenoates 2. The homoallylic cleavage resulting in the loss of the C-3 and C-5 alkyl groups from 1 and of the two δ-alkyls from 2 is a stereospecific process: the loss of the group which is adjacent to the carbonyl is significantly preferred. The stereospecificity of this fragmentation is interpreted in terms of a hidden hydrogen transfer preceding the carbon-carbon bond cleavage.     

Binding neutral guests to concave surfaces of molecular hosts. Rigid structural model for complexation between two lipophilic entities

The 1:2 compound formed between a new cavitand C₄₀H₄₈Si₄O₈ [chemical name: 5,10;12,17;19,24;26,3-tetrakis(dimethylsiladioxa)-1,8,15,22-tetramethyl[1₄]metacyclophane] and CS₂ (M _r =921.42) provided a suitable structural model for a rigid inclusion complex between uncharged lipophilic molecules. The detailed structure of this compound has been determined by single crystal X-ray diffraction at 128 K (Crystal data:a=11.233,b=20.018,c=10.069 Å, =90.84^o,Z=2, space groupP2₁/m). Anisotropic refinement converged atR=0.040 for 3768 reflections above the intensity threshold, leading to positional and thermal parameters of a relatively high precision. The cavitand has an enforced cavity appropriately sized to include only slim linear guests. The crystallographic analysis revealed a 1:1 molecular inclusion complex with CS₂, the guest species being almost entirely encapsulated within the basket-shaped cavity of the host. The complex is stabilized by dispersion forces. All the guest atoms lie within van der Waals distances from the surrounding sections of the host and are well ordered. The second CS₂ molecule is located in the crystal lattice between molecules of the complex and is slightly disordered. Mirror plane symmetry characterizes the entire structure. Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82032 (22 pages).     

Interrelation between hydration and interheadgroup interaction in phospholipids

The stability and the ionic conductivity of biological membranes and of lipid bilayers depend on their hydration. A small number of water molecules adhere strongly to the different residues of the lipid headgroups and are oriented by them. An additional number of water molecules adhere more weakly, preserving their freedom of rotation, but are essential for bestowing the thermodynamic properties of hydrated bilayers and of biological membranes. Around six water molecules are attached so strongly to the headgroups of different phospholipids (PL) that they are rendered unfreezable, or their freezing is extended over such a wide range of temperatures that it cannot be detected by differential scanning calorimetry (DSC). If cholesterol is added to the PL above the concentration at which phase separation of the cholesterol phase occurs, the number of unfreezable water molecules per PL increases, indicating that the PL molecules on the border line between the two phases attach nearly twice as many water molecules as those in the middle of the phase. The orientation of about seven or eight water molecules attached to PL headgroups (seven to phosphatidyl serine (PS)) can be detected by polarized FTIR. The dichroic ratio of the successively adhering water molecules to the headgroup of PS fluctuates between 2.6 and 2.9, with the cumulative value of about 2.8 for the seven water molecules adhering to the headgroup of PS. In addition, in this case, the number of water molecules oriented by PL molecule residues on the border line of the two phases is much larger ( approximately 13 for PS). Interaction between two opposite negatively charged layers containing PS approaching each other may lead, after correlated electrostatic attraction, to change in the conformation of the headgroups with concomitant dehydration. This process is enhanced by Ca(+) and by Li(+), but it may also occur with Na(+) and K(+) as counter-ions if the layers are mutually aligned. This process may be important in the fusion mechanism of biological membranes, and its molecular modeling has been carried out.     

Individual cell migration analysis using fiber-optic bundles

In this paper we describe a novel optical fiber-based technology for analyzing cell migration. Cells were labeled with a membrane-bound fluorescent dye and distributed onto a polished optical fiber bundle. When a cell passes over one of the individual fibers in the bundle, the membrane-bound dye causes a large intensity increase, which stays for a given residence time until the cell departs from the fiber. Residence time increases significantly upon exposure to an antimigratory drug, indicating a decrease in cell migration. This approach provides a simple migration assay and does not require sophisticated tracking software. By using optical fiber bundles containing smaller individual fibers with higher spatial resolution, this approach was employed to develop a migration assay based on subcellular imaging. The subcellular imaging platform allows for rapid analysis of migratory potential, reducing experimental time from several hours in a standard assay to 5 min using this technology.Electronic Supplementary Material Supplementary material is available for this article at