Generation of macroscopic superpositions of quantum states by linear coupling to a bath

We demonstrate through an exactly solvable model that collective coupling to any thermal bath induces effectively nonlinear couplings in a quantum many-body (multispin) system. The resulting evolution can drive an uncorrelated large-spin system with high probability into a macroscopic quantum-superposition state. We discuss possible experimental realizations.     

Criteria for validity of the maximum modulus principle for solutions of linear parabolic systems

We consider systems of partial differential equations of the first order int and of order 2s in thex variables, which are uniformly parabolic in the sense of Petrovskii. We show that the classical maximum modulus principle is not valid inR ⁿ×(0,T] fors≥2. For second order systems we obtain necessary and, separately, sufficient conditions for the classical maximum modulus principle, to hold in the layerR ⁿ×(0,T] and in the cylinder μ×(0,T], where μ is a bounded subdomain ofR ⁿ. If the coefficients of the system do not depend ont, these conditions coincide. The necessary and sufficient condition in this case is that the principal part of the system is scalar and that the coefficients of the system satisfy a certain algebraic inequality. We show by an example that the scalar character of the principal part of the system everywhere in the domain is not necessary for validity of the classical maximum modulus principle when the coefficients depend both onx andt. The research of the first author was supported by the Ministry of Absorption, State of Israel.     

Mathematical programming applied to cement-plant and quarry operations

A large linear-programming model is developed that describes cement operations from the quarry to the market. Separate optimization of clinker composition and quarry scheduling leads to inconsistencies, thereby creating a need for simultaneous optimization. By including both problems and their interfaces in the mode, simultaneous optimization is accomplished. Other factors included in the model are equipment acquisition and assignment, hauling distances and capacities, plant capacities, market prices and demands, and operational costs. Optimization objectives are maximization of net present value, life of mine, or production. Time periods are organized so that long-range profits guide short-range scheduling. Computer implementation of the model is also discussed.     

Pyrimidines. 8. chlorination of 6-methyluracil with phosphorus oxychloride in the presence of trialkyamines

The effect of the tertiary amines triethyl, tri-n-propyl, and tri-n-butylamines on the chlorination of 6-methyluracil by phosphorus oxychloride was studied. A comparison with the reaction of preformed 2,4-dichloro-6-methylpyrimidine and triethylamine in toluene was made. The reaction in phosphorus oxychloride in the presence of triethylamine afforded low yields of 2-diethylamino derivative after short heating periods and high yields of the 2,4-bis(diethylamino) derivative after 188 hours of boiling. Heating the preformed 2,4-dichloro-6-methylpyrimidine in toluene in the presence of triethylamine yielded primarily the 2-diethylaminopyrimidine along with a small amount of the 4-diethylamino isomer. After 188 hours, the product mixture was composed of 87% 2-diethylamino and 13% of 4-diethylamino isomers. Although substituent orientation was essentially the same, the yields of products seem to have been influenced by the dielectric constants of the solvents. Tri-n-propylamine in phosphorus oxychloride yielded solely the dichloropyrimidine, even after 188 hours of boiling, and is recommended as the amine of choice in such chlorination reactions. Tri-n-butylamine was the same after 48 hours, but 4% of 4-di-n-butylaminopyrimidine was found after 188 hours of heating.     

Gas chromatography-mass spectrometry with supersonic molecular beams

Gas chromatography-mass spectrometry (GC-MS) with supersonic molecular beams (SMBs) (also named Supersonic GC-MS) is based on GC and MS interface with SMBs and on the electron ionization (EI) of vibrationally cold analytes in the SMBs (cold EI) in a fly-through ion source. This ion source is inherently inert and further characterized by fast response and vacuum background filtration capability. The same ion source offers three modes of ionization including cold EI, classical EI and cluster chemical ionization (CI). Cold EI, as a main mode, provides enhanced molecular ions combined with an effective library sample identification, which is supplemented and complemented by a powerful isotope abundance analysis method and software. The range of low-volatility and thermally labile compounds amenable for analysis is significantly increased owing to the use of the contact-free, fly-through ion source and the ability to lower sample elution temperatures through the use of high column carrier gas flow rates. Effective, fast GC-MS is enabled particularly owing to the possible use of high column flow rates and improved system selectivity in view of the enhancement of the molecular ion. This fast GC-MS with SMB can be further improved via the added selectivity of MS-MS, which by itself benefits from the enhancement of the molecular ion, the most suitable parent ion for MS-MS. Supersonic GC-MS is characterized by low limits of detection (LOD), and its sensitivity is superior to that of standard GC-MS, particularly for samples that are hard for analysis. The GC separation of the Supersonic GC-MS can be improved with pulsed flow modulation (PFM) GC x GC-MS. Electron ionization LC-MS with SMB can also be combined with the Supersonic GC-MS, with fast and easy switching between these two modes of operation.     

Pulsed flow modulation comprehensive two-dimensional gas chromatography

Pulsed flow modulation (PFM) is based on higher flow rate time compression of the first GC column effluent, which prior to the injection into the second column is stored for a few seconds in a standard fused silica wide bore transfer line. We constructed the PFM device with two standard 1/16 in. brass compression fittings with the insertion of the two columns inside the wide bore 0.53 mm i.d. fused silica storage transfer line for the elimination of dead volumes. This simple arrangement provides a combination of flexibility in the length of the sample storage transfer line hence comprehensive two-dimensional gas chromatography (GC x GC) cycle time, inert sample path and full elimination of cooling gas consumption. A record short second column injection time of 20 ms is demonstrated. Practical injection times are the sample collection time (such as 4s) divided by the second to first column flow rate ratio (such as 20/0.7), which is typically around 150 ms. Due to the low cost of the device it can also be considered for use with non comprehensive time segmented GC x GC to remove a few accidental coelutions. PFM-GCxGC excels with high second column capacity due to the use of 0.32 mm i.d. columns with high flow rates as the second dimension GC x GC column. As a result, PFM-GCxGC can have up to two orders of magnitude higher second column sample capacity and linear dynamic range for improved reduction of adverse matrix interference effects due to column overloading.     

Outer approximation methods for solving variational inequalities in Hilbert space

In this paper, we study variational inequalities in a real Hilbert space, which are governed by a strongly monotone and Lipschitz continuous operator F over a closed and convex set C. We assume that the set C can be outerly approximated by the fixed point sets of a sequence of certain quasi-nonexpansive operators called cutters. We propose an iterative method, the main idea of which is to project at each step onto a particular half-space constructed using the input data. Our approach is based on a method presented by Fukushima in 1986, which has recently been extended by several authors. In the present paper, we establish strong convergence in Hilbert space. We emphasize that to the best of our knowledge, Fukushima’s method has so far been considered only in the Euclidean setting with different conditions on F. We provide several examples for the case where C is the common fixed point set of a finite number of cutters with numerical illustrations of our theoretical results.     

Experimental constraints on the spin and parity of the Lambdac(2880)+

We report the results of several studies of the Lambda(c)(+)pi(+)pi(-)X final state in continuum e(+)e(-) annihilation data collected by the Belle detector. An analysis of angular distributions in Lambda(c)(2880)(+)-->Sigma(c)(2455)(0,++)pi(+,-) decays strongly favors a Lambda(c)(2880)(+) spin assignment of 5/2 over 3/2 or 1/2. We find evidence for Lambda(c)(2880)(+)-->Sigma(c)(2520)(0,++)pi(+,-) decay and measure the ratio of Lambda(c)(2880)(+) partial widths Gamma(Sigma(c)(2520)pi)/Gamma(Sigma(c)(2455)pi)=0.225+/-0.062+/-0.025. This value favors the Lambda(c)(2880)(+) spin-parity assignment of 5/2(+) over 5/2(-). We also report the first observation of Lambda(c)(2940)(+)-->Sigma(c)(2455)(0,++)pi(+,-) decay and measure Lambda(c)(2880)(+) and Lambda(c)(2940)(+) mass and width parameters. These studies are based on a 553 fb(-1) data sample collected at or near the Upsilon(4S) resonance at the KEKB collider.     

Electron ionization LC‐MS with supersonic molecular beams—the new concept,benefits and applications

A new type of electron ionization LC‐MS with supersonic molecular beams (EI‐LC‐MS with SMB) is described. This system and its operational methods are based on pneumatic spray formation of the LC liquid flow in a heated spray vaporization chamber, full sample thermal vaporization and subsequent electron ionization of vibrationally cold molecules in supersonic molecular beams. The vaporized sample compounds are transferred into a supersonic nozzle via a flow restrictor capillary. Consequently, while the pneumatic spray is formed and vaporized at above atmospheric pressure the supersonic nozzle backing pressure is about 0.15 Bar for the formation of supersonic molecular beams with vibrationally cold sample molecules without cluster formation with the solvent vapor. The sample compounds are ionized in a fly‐though EI ion source as vibrationally cold molecules in the SMB, resulting in ‘Cold EI’ (EI of vibrationally cold molecules) mass spectra that exhibit the standard EI fragments combined with enhanced molecular ions. We evaluated the EI‐LC‐MS with SMB system and demonstrated its effectiveness in NIST library sample identification which is complemented with the availability of enhanced molecular ions. The EI‐LC‐MS with SMB system is characterized by linear response of five orders of magnitude and uniform compound independent response including for non‐polar compounds. This feature improves sample quantitation that can be approximated without compound specific calibration. Cold EI, like EI, is free from ion suppression and/or enhancement effects (that plague ESI and/or APCI) which facilitate faster LC separation because full separation is not essential. The absence of ion suppression effects enables the exploration of fast flow injection MS‐MS as an alternative to lengthy LC‐MS analysis. These features are demonstrated in a few examples, and the analysis of the main ingredients of Cannabis on a few Cannabis flower extracts is demonstrated. Finally, the advantages of EI‐LC‐MS with SMB are listed and discussed. Copyright © 2015 John Wiley & Sons, Ltd.