Conjugate-point conditions for variational problems with delayed argument

A variational problem with delayed argument is investigated. The existing necessary conditions are first reviewed. New results, two conjugate-point conditions, are then derived for this problem. The method of proof is similar to that used by Bliss for the classical problem. An example shows that the two conditions are not equivalent, and that the first-order necessary conditions, the strengthened Legendre conditions, and the conjugate-point conditions do not in general constitute a set of sufficient conditions for the delay problem. It is shown that a special case, referred to as the separated-integrand problem, leads to considerable simplification of the results for the general problem.     

Investigation of the ε phase in the Fe–Al system by high-temperature neutron diffraction

In the central part of the Fe–Al system between about 58 and 65 at.% Al, a high-temperature phase denoted as ε occurs with a hitherto unknown crystallographic structure. The phase is stable between 1231°C and 1095°C. In order to study the crystallographic structure of the ε phase, in situ high-temperature neutron time-of-flight diffraction experiments have been performed at the HIPPO instrument at the Los Alamos Neutron Science Center (LANSCE). The ε phase was found to have the formula Fe₅Al₈ with a body-centred cubic structure of the Hume–Rothery Cu₅Zn₈ type (I $\bar{4}3In the central part of the Fe–Al system between about 58 and 65 at.% Al, a high-temperature phase denoted as ε occurs with a hitherto unknown crystallographic structure. The phase is stable between 1231°C and 1095°C. In order to study the crystallographic structure of the ε phase, in situ high-temperature neutron time-of-flight diffraction experiments have been performed at the HIPPO instrument at the Los Alamos Neutron Science Center (LANSCE). The ε phase was found to have the formula Fe₅Al₈ with a body-centred cubic structure of the Hume–Rothery Cu₅Zn₈ type (I[`4]3\bar{4}3m (No. 217), Z=4, cI52) and 52 atoms in the unit cell. Its lattice parameter is a=8.9756(2) ? at 1120°C, which is 3.02 times that of cubic FeAl (B2) at the same temperature. We report here the evolution of the crystallographic parameters over the temperature range between 1080°C and 1120°C.     

Performance of a Single-Family Heat Pump at Different Working Conditions Using Small Quantity of Propane as Refrigerant

The performance of a domestic heat pump that uses a low quantity of propane as refrigerant has been experimentally investigated. The heat pump consists of two minichannel aluminium heat exchangers, a scroll compressor, and an electronic expansion valve. It was charged with the minimum amount of refrigerant propane required for the stable operation of the heat pump without permitting refrigerant vapor into the expansion valve at incoming heat source fluid temperature to the evaporator of +10°C. The inlet temperature of the heat source fluid passing through the evaporator was varied from +10°C to ?10°C while holding the condensing temperature constant at 35°C, 40°C, 50°C, and 60°C, respectively. The minimum refrigerant charges required at above-tested condensing temperatures were found to decrease when the condensing temperature increased and were recorded as 230 g, 224 g, 215 g, and 205 g, respectively. The results confirm that a heat pump with 5 kW capacity can be designed with less than 200 g charge of refrigerant propane in the system. Due to the high solubility of propane in compressor lubrication oil, the amount of refrigerant which may escape rapidly in case of accident or leakage is less than 150 g.     

Abrikosov-to-Josephson vortex lattice crossover in heavy fermion CeCoIn5

We present torque magnetization measurements on the quasi-2D heavy fermion superconductor CeCoIn₅ at temperatures down to 20 mK and magnetic fields up to 18?T. At orientations with the magnetic field perpendicular to the conducting planes, a prominent vortex lattice peak effect is present at around 0.5H _c2. The peak effect gradually disappears upon rotating the field into the plane parallel orientation. We interpret the absence of the peak effect for the plane parallel case as a transformation of the Abrikosov lattice into a Josephson vortex state, favored by the Pauli paramagnetic limit in CeCoIn₅ together with the unusually large condensation energy. Additionally, we do not observe flux avalanches as found in organic superconductors and suggest that the complete absence of vortex activity in the plane parallel field orientation is crucial for the formation of Fulde–Ferrell–Larkin–Ovchinnikov superconductivity in CeCoIn₅.     

XPS and resistive studies on thin films of a copper(II)‐based coordination polymer deposited on functionalized interdigital electrodes

A symmetrical 2‐thiopyrimidine based molecule with an expanded π‐electron system is synthesized and used to form a self‐assembled monolayer (SAM) on gold surfaces. Utilizing chemical vapor deposition a monolayer of (3‐mercaptopropyl)triethoxysilane is formed on silicon dioxide substrates. Both of these SAM coated substrates are characterized by X‐ray photoelectron spectroscopy and the growth of a coordination polymer built up from 5,5′‐(ethyne‐1,2‐diyl)bis(2‐hydroxyacetophenone) and copper(II) on dual SAM coated transducers is studied. After the deposition procedure on interdigital electrodes the electrical properties of the polymer are investigated performing resistive measurements. A significant change of the resistance, which depends on the surrounding atmosphere, proves the sensing behavior of the synthesized coordination polymer. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 335–344     

Tunable carbon monoxide overtone laser sideband system for precision spectroscopy from 2.6 to 4.1 microm

We report a source of tunable laser radiation for high-precision molecular spectroscopy in the 2.6- 4.1-microm spectral region. Laser light from a CO overtone laser is mixed with microwaves, generating tunable sidebands of ~1 mW of power. We achieve very high absolute frequency accuracy by frequency-offset locking the CO laser to a CO(2) laser secondary frequency standard. The uncertainty of the laser frequency is less than 30 kHz (Dnu/nu=3x10(-10)) , and the laser linewidth is of the order of 100 kHz. This tunable and ultrastable laser system is suitable for very accurate molecular spectroscopy and metrology in a most interesting wavelength region. We demonstrate an application of the system to saturated-absorption spectroscopy of a rovibrational transition of carbonyl sulfide.     

Tris(triphenylphosphine)rhodium cyano and triphenylcyanoborate complexes: Structures and a DFT study

The structures of [Rh(CN)(PPh₃)₃](EtOH) (1), [Rh(NCBPh₃)(PPh₃)₃] (2), and [Rh(CNBPh₃)(PPh₃)₃] (3) are reported together with a density functional theory (DFT) study of the model compounds [Rh(NCBH₃)(PH₃)₃] and [Rh(CNBH₃)(PH₃)₃]. Compound 1 crystallizes in space group Pc with a = 10.4798(15) Å, b = 12.5410(18) Å, c = 19.974(3) Å and = 112.215(6)°; compound 2 crystallizes in space group with a = 12.929(2) Å, b = 14.362(2) Å, c = 17.575(3) Å and = 92.544(3)°, = 90.214(3)°, = 113.831(3)°; compound 3 crystallizes in space group with a = 12.915(2), b = 14.296(2), c = 17.664(3) Å and = 92.469(3)°, = 90.088(3)°, = 113.768(3)°. All three complexes show slight tetrahedral distortion from ideal square planar geometry (largest for 1). Differences in the reactivity and stability of 2 and 3 are interpreted according to the results of a density functional theory study.     

A new synthesis of lysophosphatidylcholines and related derivatives. Use of p-toluenesulfonate for hydroxyl group protection

A new stereoselective synthesis of lysophosphatidylcholines is reported. The synthesis is based upon (1) the use of 3-p-toluenesulfonyl-sn-glycerol to provide the stereocenter for construction of the optically active lysophospholipid molecule, (2) tetrahydropyranylation of the secondary alcohol function to achieve orthogonal protection of the sn-2- and sn-3-glycerol positions, and (3) elaboration of the phosphodiester headgroup using a 2-chloro-1,3,2-dioxaphospholane/trimethylamine sequence. In the course of developing the synthesis it has been discovered that methoxyacetate displacement of the sn-3-p-toluenesulfonate yields a reactive methoxyacetyl ester, which in turn can be selectively cleaved with methanol/tert-butylamine, while the ester group at the sn-1-position remains unaffected. The sequence has been shown to be suitable for preparation of spectroscopically labeled lysophosphatidylcholines. One of these compounds was readily converted to a double-labeled mixed-chain phosphatidylcholine applicable for real-time fluorescence resonance energy transfer (FRET) assay of lipolytic enzymes. In addition, the work led to new synthetic strategies based on chemoselective manipulation of the tosyl group in the presence of other base-labile groups such as FMOC derivatives that are often used for the protection of amino and hydroxyl groups in syntheses.