Collisional energy dependence of peptide ion fragmentation

The energy dependence of fragmentation in a collision cell was measured for 2400 protonated peptide ions derived from the digestion of 24 proteins. The collision voltage at which the sum of the fragment ion abundances was equal to the remaining parent ion (V _1/2) was the principal measure of fragmentation effectiveness. Each class of peptides was characterized by a linear relation between V _1/2 and m/z whose slope depended on the peptide class and, with little adjustment, intersected the origin. Peptide ions where the number of protons is no greater than the number of arginine residues show the greatest slope, V _1/2/(m/z)=0.0472 (all slopes in units of V Da⁻¹ e). For peptides where the number of protons is greater than the number of arginines, but not greater than the total number of basic residues, the slope decreases to 0.0414 for singly charged ions, 0.0382 for doubly charged, 0.0346 for triply charged, and 0.0308 for more highly charged ions. With one mobile proton, the slope is about 0.029 for singly and doubly charged ions and slightly lower for more highly charged ions. With two or more mobile protons the slope is 0.0207. By removing m/z dependence, the deviation of V _1/2 from a line provides a relative measure of the ease of fragmentation of an ion in each class. This information can guide the selection of optimal conditions for tandem mass spectrometry studies in collision cells for selected peptide ions as well as aid in comparing the reactivity of ions differing in m/z and charge state.     

Basin attractors for various methods for multiple roots

There are several methods for approximating the multiple zeros of a nonlinear function when the multiplicity is known. The methods are classified by the order, informational efficiency and efficiency index. Here we consider other criteria, namely the basin of attraction of the method and its dependence on the order. We discuss all known methods of orders two to four and present the basin of attraction for several examples.     

Aeroacoustics of the swinging corrugated tube: voice of the Dragon

When one swings a short corrugated pipe segment around one's head, it produces a musically interesting whistling sound. As a musical toy it is called a "Hummer" and as a musical instrument, the "Voice of the Dragon." The fluid dynamics aspects of the instrument are addressed, corresponding to the sound generation mechanism. Velocity profile measurements reveal that the turbulent velocity profile developed in a corrugated pipe differs notably from the one of a smooth pipe. This velocity profile appears to have a crucial effect both on the non-dimensional whistling frequency (Strouhal number) and on the amplitude of the pressure fluctuations. Using a numerical model based on incompressible flow simulations and vortex sound theory, excellent predictions of the whistling Strouhal numbers are achieved. The model does not provide an accurate prediction of the amplitude. In the second part of the paper the sound radiation from a Hummer is discussed. The acoustic measurements obtained in a semi-anechoic chamber are compared with a theoretical radiation model. Globally the instrument behaves as a rotating (Leslie) horn. The effects of Doppler shift, wall reflections, bending of the tube, non-constant rotational speed on the observed frequency, and amplitude are discussed.     

Rate constants for some reactions of inorganic radicals with inorganic ions. Temperature and solvent dependence

Rate constants for several reactions of inorganic radicals with inorganic anions in aqueous and aqueous/acetonitrile solutions have been measured as a function of temperature by laser flash photolysis. The reactions studied were (1) Cl₂^? + N₃^?, (2) Br₂^? + N₃^?, (3) Cl₂^? + SCN^?, (4) Br₂^? + SCN^?, (5) SO₄^? + Cl^?, (6) SO₄^? + CO₃^2?, and (7) N₃? + I^?. The rate constants were corrected for ionic strength and ranged from 10⁶ to 10⁹ L mol^?1 s^?1. The Arrhenius activation energies varied from 2 to 12 kJ mol^?1 for the first 4 reactions, were higher for reaction 6, and negative for reaction 5. The pre-exponential factors also varied considerably with log A ranging from 5 to 14. The values of k₂₉₈ decreased in most cases by more than an order of magnitude upon increasing the acetonitrile (ACN) fraction from 0 to 70%. For most reactions, this decrease in k₂₉₈ was due to changes in log A with little regularity in the small changes observed in E_a. For reaction 7, k₂₉₈ was practically unchanged due to compensating effects of the changes in E_a and log A with ACN mol fraction, giving an isokinetic relationship. An isokinetic relationship was also observed in the case of reaction 6; E_a and log A change in parallel while changing ACN mol fraction. Reaction 3 (Cl₂^? + SCN^?) was also studied in water/t-butanol and water/acetic acid mixtures. Linear correlation was found between log k and the dielectric constant of the medium for water/ACN and water/t-BuOH but the lines for the two solvent mixtures had different slopes, suggesting specific solvation effects in addition to the primary solvent polarity effects. With water/acetic acid, k decreased and then increased upon addition of acetic acid. © 1993 John Wiley & Sons, Inc.     

Graphs with Few 3‐Cliques and 3‐Anticliques are 3‐Universal

For given integers we ask whether every large graph with a sufficiently small number of k‐cliques and k‐anticliques must contain an induced copy of every l‐vertex graph. Here we prove this claim for with a sharp bound. A similar phenomenon is established as well for tournaments with .     

On High-Dimensional Acyclic Tournaments

We study a high-dimensional analog for the notion of an acyclic (aka transitive) tournament. We give upper and lower bounds on the number of $d$ -dimensional $n$ -vertex acyclic tournaments. In addition, we prove that every $n$ -vertex $d$ -dimensional tournament contains an acyclic subtournament of $\Omega (\log ^{1/d}n)$ vertices and the bound is tight. This statement for tournaments (i.e., the case $d=1$ ) is a well-known fact. We indicate a connection between acyclic high-dimensional tournaments and Ramsey numbers of hypergraphs. We investigate as well the inter-relations among various other notions of acyclicity in high-dimensional tournaments. These include combinatorial, geometric and topological concepts.