Ionization Cross Sections of Gas Molecules for Plasma Chemistry

Using the recently tested formula of Gryzinski electron impact ionization cross sections for several molecules are calculated. The additivity rule and the statistical approach by Fitch and Sauter are discussed. With new experimental ionization cross sections it is possible to derive the regression coefficients also for P, As, B, and Si, which are presented together with the previously obtained values as a function of the atomic number. It appears to be possible to obtain coefficients for other atoms by interpolation. First attemps to determine regression coefficients also for 20 and 35 eV electron energy are discussed.     

Structure of mercaptobiphenyl monolayers on mercury

The molecular-scale structure and phase behavior of single-component Langmuir films of 4'-methyl-4-mercaptobiphenyl (MMB) and 4'-perfluoromethyl-4-mercaptobiphenyl (FMMB) on mercury were studied using surface tensiometry, grazing incidence X-ray diffraction, and X-ray reflectivity. At low coverages, a condensed but in-plane disordered single layer of surface-parallel molecules is found for both compounds. At high coverages, both compounds exhibit in-plane-ordered phases of standing-up molecules. For MMB, the biphenyl core dominates the structure, yielding a centered-rectangular unit cell with an area A(x) of 21.8 A(2)/molecule, with molecules tilted by approximately 14 degrees from the surface normal in the nearest-neighbor direction, and a coherence length xi of >1000 A for the crystalline domains. For FMMB, the perfluoromethyl group dominates the structure, yielding a hexagonal unit cell with untilted molecules, an area A(x) of 24.2 A(2)/molecule, and a much smaller xi of approximately 110 A. The structure is discussed in comparison with self-assembled monolayers of MMB on crystalline Au(111) and similar-length alkanethiolate SAMs on Au(111) and on mercury. The differences in the structure are discussed and traced to the differences in the substrate's surface structure, and in the molecular cross section and rigidity.     

An alternate proof of Cohn's four squares theorem

While various techniques have been used to demonstrate the classical four squares theorem for the rational integers, the method of modular forms of two variables has been the standard way of dealing with sums of squares problems for integers in quadratic fields. The case of representations by sums of four squares in was resolved by Götzky, while those of and were resolved by Cohn. These efforts utilized modular forms. In previous work, the author was able to demonstrate Götzky's theorem by means of the geometry of numbers. Here Cohn's theorem on representation by the sum of four squares for is proven by a combination of geometry of numbers and quaternionic techniques.     

The case for large-size mutations

There are no laws of physics or chemistry that forbid large mutations. Therefore, the "size" of a random mutation should fit the mathematics of a Poisson point process: The number of mutations (N), versus mutation size (MS), should obey an exponential relationship. Three examples are examined: A simple 15-mutation sequence; actual experimental data involving a sequence of 56,611 random action potentials (rather than mutations); and a synthetic sequence of 65,535 random mutations. In the latter example, with an average MS of 2.22 units, the largest MS is a 25-unit giant that would be associated with major changes.     

Congenitally corrected transposition of the great arteries (L-TGA) with situs inversus totalis in adulthood: findings with magnetic resonance imaging

Diagnosis of congenitally corrected transposition of the great arteries (L-TGA) with situs inversus totalis in two adult patients was made by magnetic resonance imaging (MRI). Visualization of the complete anatomy and quantification of ventricular function was possible. Relevant concomitant disease such as perimembraneous ventricular septal defect, atrial secundum septal defect, tricuspid regurgitation, valvular pulmonic stenosis, and pulmonary artery dilatation were clearly depicted by MRI using standard spin-echo and gradient-echo techniques. Findings were confirmed by cardiac catheterization in both patients. In this rare and complex congenital cardiac anomaly, MRI is an excellent imaging modality as echocardiography may be difficult to interpret due to restricted imaging windows. MRI may help in the decision about the necessity to undergo further invasive evaluation and may help to make cardiac catheterization a straightforward procedure.     

Conformational analysis of methylphenidate: comparison of molecular orbital and molecular mechanics methods

Summary Methylphenidate (MP) binds to the cocaine binding site on the dopamine transporter and inhibits reuptake of dopamine, but does not appear to have the same abuse potential as cocaine. This study, part of a comprehensive effort to identify a drug treatment for cocaine abuse, investigates the effect of choice of calculation technique and of solvent model on the conformational potential energy surface (PES) of MP and a rigid methylphenidate (RMP) analogue which exhibits the same dopamine transporter binding affinity as MP. Conformational analysis was carried out by the AM1 and AM1/SM5.4 semiempirical molecular orbital methods, a molecular mechanics method (Tripos force field with the dielectric set equal to that of vacuum or water) and the HF/6-31G* molecular orbital method in vacuum phase. Although all three methods differ somewhat in the local details of the PES, the general trends are the same for neutral and protonated MP. In vacuum phase, protonation has a distinctive effect in decreasing the regions of space available to the local conformational minima. Solvent has little effect on the PES of the neutral molecule and tends to stabilize the protonated species. The random search (RS) conformational analysis technique using the Tripos force field was found to be capable of locating the minima found by the molecular orbital methods using systematic grid search. This suggests that the RS/Tripos force field/vacuum phase protocol is a reasonable choice for locating the local minima of MP. However, the Tripos force field gave significantly larger phenyl ring rotational barriers than the molecular orbital methods for MP and RMP. For both the neutral and protonated cases, all three methods found the phenyl ring rotational barriers for the RMP conformers/invertamers (denoted as cte, tte, and cta) to be: cte, tte> MP > cta. Solvation has negligible effect on the phenyl ring rotational barrier of RMP. The B3LYP/6-31G* density functional method was used to calculate the phenyl ring rotational barrier for neutral MP and gave results very similar to those of the HF/6-31G* method.     

Approximating weak Chebyshev subspaces by Chebyshev subspaces

We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties.     

Short proofs of the universality of certain diagonal quadratic forms

In a paper of Kim, Chan, and Rhagavan, the universal ternary classical quadratic forms over quadratic fields of positive discriminant were discovered. Here a proof of the universality of some of these quadratic forms is given using a technique of Liouville. Another quadratic form over the field of discriminant 8 is shown universal by a different elementary approach. Received: 30 October 2007     

Climbing Mount Scalable: Physical Resource Requirements for a Scalable Quantum Computer

The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources places a fundamental constraint on the systems that are suitable for scalable quantum computation. To be scalable, the effective number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an equivalent qubit-based quantum computer.