The fluorescence quenching rate constant for the distance-dependent quenching processes in the presence of diffusion

It is shown that the fluorescence quenching constant is given by the Laplace transform of the time-dependent bimolecular rate constant k(t). The dependence of the quenching rate constant on the transformation parameter can be obtained from measurements of the fluorescence decay functions and a Stern-Volmer-type analysis in the Laplace domain. The advantages of this type of investigation of the quenching rate function are demonstrated by a numerical calculation for the distance-dependentquenching process in     

An empirical force field. II. Crystalline alkanes

The EFF'93 force field is used to study crystalline alkanes. In addition to detailed molecular geometries, the sublimation enthalpy, heat capacity, and lattice vibrations for a number of saturated hydrocarbons are reported and compared with experiment. © 1995 by John Wiley & Sons, Inc.     

Determination of calcium in silicate rocks by potentiometric titration with ethyleneglycol-bis-(2-Aminoethylether)tetraacetic acid and a calcium-selective electrode

The method reported for the determination of calcium in silicate rocks involves titration with ethyleneglycol-bis(2-aminoethylether)tetraacetic acid (EGTA) to a potentiometric end-point. A Crytur calcium-selective electrode is used; the selectivity constants (K_ca,x) are less than 10^-3 for Mg, Ba, Sr, K and Na. The method can be used for calcium contents of 2% or higher (and exceptionally for lower contents), in the presence of up to 60% Mg, 33% AI, 17% Fe, 5% Ba, 5% Ti, and 2.5% Mn. Al, Fe and Ti are masked with sulphosalicylic acid, barium is precipitated as its sulphate, and manganese is bound as its cyanide complex. If the magnesium content is less than that of calcium, EDTA can be used as titrant, magnesium being masked with acetylacetone.     

Hydrogen bond studies: 80. A deuteron magnetic resonance and infrared spectroscopic study of the water molecule in lithium formate monohydrate,LiHCOO · H2O

A deuteron magnetic resonance and infrared study of the water molecules in lithium formate monohydrate, LiHCOO · H₂O, has been made. The quadrupole coupling constants (e²qQ/h) and asymmetry parameters (η) were found to be 198.7±0.4 and 231.3±0.6 kHz, and 0.060±0.005 and 0.097±0.003, respectively, at 25 ° C.An interpretation is given of the infrared spectra in the OH-stretching region in terms of intra- and intermolecular couplings of the water molecules. It is found that the water molecules are vibrationally distorted by their environments such that the OH-stretching modes consist of independent stretchings of the two O-H bonds.     

Studies on the photooxidation mechanism of polymers. IV. Effect of ultraviolet light (2537 Å) on solid PVC particles suspended in different liquids

The photolysis of virgin PVC powder suspended in water, methanol, n-hexane, aqueous NH₄OH (30 wt-%), and 0.1 wt-% iodine in methanol and also as dry powder was studied. The mechanism of photolysis of PVC powder has been investigated by using ESR spectroscopy, conductivity titration, gel-permeation chromatography (GPC), and absorption spectroscopy. Photolysis of PVC has been found to occur by a free-radical mechanism. ESR spectroscopy permits a partial identification of several different types of free radicals in PVC such as alkyl, polyenyl, and peroxy radicals. An interpretation is proposed of the mechanism of formation of conjugated polyene structures, and also a new explanation of the crosslinking mechanism, in which transfer of unpaired electrons to double bonds occurs, is suggested. It has also been found that conjugated double bonds can photosensitize free-radical formation as a result of increased ultraviolet absorption due to polyene structures.     

Asymptotic and exponential decay in mean square for delay geometric Brownian motion

Applications of Mathematics - We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions of the geometric Brownian motion with delay. The conditions...     

A heuristic method for dispatching repair men

A company has to provide service to its customers. A service consists of a visit to the customer plus the spending of some given time at the scene. The future customer demand is not known but the probability distribution for the demand may be known. When a customer call comes in, the company must immediately specify a time window within which the start of service will be provided. The problem is for a fixed service level to determine an optimal strategy of route design and time window setting so that the total distance travelled is minimized over the time horizon given. A heuristic method BARTOC (Booking Algorithm for Routing and Timing Of Customers) to solve the problem mentioned above is suggested. BARTOC is based on a cluster-first route-second approach. Some computational results are presented. The results indicate that BARTOC produces high quality solutions.Peter Matthiesen, Inc.Dano Chemo, Inc.     

Kneser-type oscillation criteria for self-adjoint two-term differential equations

It is proved that the even-order equationy ⁽²ⁿ⁾ +p(t)y=0 is (n,n) oscillatory at if

Intersection Dimensions of Graph Classes

The intersection dimension of a graphG with respect to a classA of graphs is the minimumk such thatG is the intersection of at mostk graphs on vertex setV(G) each of which belongs toA. We consider the question when the intersection dimension of a certain family of graphs is bounded or unbounded. Our main results are (1) ifA is hereditary, i.e., closed on induced subgraphs, then the intersection dimension of all graphs with respect toA is unbounded, and (2) the intersection dimension of planar graphs with respect to the class of permutation graphs is bounded. We also give a simple argument based on [Ben-Arroyo Hartman, I., Newman, I., Ziv, R.:On grid intersection graphs, Discrete Math.87 (1991) 41-52] why the boxicity (i.e., the intersection dimension with respect to the class of interval graphs) of planar graphs is bounded. Further we study the relationships between intersection dimensions with respect to different classes of graphs.     

Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions

The ground state energy of an atom of nuclear chargeZe in a magnetic fieldB is exactly evaluated to leading order asZ in the following three regions:BZ ^4/3,BZ ^4/3 andZ ^4/3BZ³. In each case this is accomplished by a modified Thomas-Fermi (TF) type theory. We also analyze these TF theories in detail, one of their consequences being the nonintuitive fact that atoms are spherical (to leading order) despite the leading order change in energy due to theB field. This paper complements and completes our earlier analysis [1], which was primarily devoted to the regionsBZ ³ andBZ³ in which a semiclassical TF analysis is numerically and conceptually wrong. There are two main mathematical results in this paper, needed for the proof of the exactitude of the TF theories. One is a generalization of the Lieb-Thirring inequality for sums of eigenvalues to include magnetic fields. The second is a semiclassical asymptotic formula for sums of eigenvalues that isuniform in the fieldB.Work partially supported by U.S. National Science Foundation grant PHY90-19433 A02Work partially supported by U.S. National Science Foundation grant DMS 92-03829Work partially supported by the Heraeus Stiftung and the Research Fund of the University of Iceland.