Invariants of linear maps on matrix algebras

Let L be a linear map on the space of n×n matrices over a field. We determine the structure of the maps L that preserve commutativity. We also determine the structure of all linear maps on complex matrices that preserve the higher numerical range. The main tool is the Fundamental Theorem of Projective Geometry.     

Isotope effects in the EPR spectrum of a tin-vacancy pair in silicon

The S = 1 EPR spectrum for a tin-vacancy pair in silicon reveals easily detected isotope shifts in the fine structure splitting D for the various nuclear isotopes of tin (σD/D = + 1.0 × 10^?4 per unit mass) as well as well as those for the six near neighbor silicon atoms (σD/D = ?0.67 × 10^?4 per unit mass). These are attributed to the different vibrational amplitudes vs isotopic mass.     

Excited state properties of 5H-dibenzo(a,d) cycloheptene

A number of photophysical properties of 5H-dibenzo(a,d) cycloheptene have been measured including the emission and triplet-triplet absorption spectra. The quantum yields and decay parameters for the triplet state of this molecule as a function of temperature have also been measured. The results are discussed and compared to those of molecules.     

Mechanism of amine catalyzed isomerization of itaconic anhydride to citraconic anhydride: Citraconamic acid formation

The amine catalyzed isomerization of itaconic to citraconic anhydride has been investigated. Studies show that the rate of isomerization is dependent on the base strength and solvent media. Triethylamine causes complete isomerization within 5 min at room temperature in acetone or chloroform solvent, whereas aromatic tertiary amines such as pyridine and N,N-dimethylaniline require time perods as long as 23h at room temperature for almost complete isomerization. In the presence of aniline no isomerization occures even under acetone reflux conditions over a 24 h period. For the preparation of citraconamic acids from itaconic anhydrides and aliphatic diamines nuclear magnetic resonance and infrared spectroscopic evidence is presented to support the reaction path of initial isomerization of itaconic anhydride to citraconic anhydride followed by amine attack on the anhydride to form the corresponding cis-citraconamic acids. The mechanism of isomerization of itaconic to citraconic acids is proposed.     

Four-photon resonant multiphoton ionization spectroscopy

Resonant multiphoton lonization (MPI) has been found to the red of the lowest energy three-photon resonant MPI band of butadiene. The signal arises from four-photon resonant MPI with an estimated cross section of 10^?115-2-10^?118 cm⁸ s³. The observed resonance is deduced to arise from a succession of one-photon allowed transitions.     

Characterization of pure high-grade DCIS on magnetic resonance imaging using the evolving breast MR lexicon terminology: can it be differentiated from pure invasive disease?

Magnetic resonance imaging (MRI) is now a recognized method of imaging the breast. Unfortunately, there is lack of standardization in the MRI terminology used to characterize the appearance of breast lesions. Moreover, cases of mixed histologies are often imaged. We retrospectively identified cases of pure high-grade ductal carcinoma in situ (DCIS) using the recently introduced breast MRI lexicon and characterized the lesions in order to try and identify features that might distinguish high-grade DCIS from invasive disease. Five-year review of our institution's database revealed 637 patients underwent gadolinium-enhanced breast MRI examination. Twenty patients had histologically proven pure high-grade DCIS. After excluding patients with previous chemotherapy or inadequate MRI examination, 13 patients were analyzed and compared to the 13 most recent cases of pure invasive breast carcinoma. The morphological and dynamic features were then compared. High-grade DCIS cases were significantly more likely to show focal branching pattern (P=.03) and to have an irregular contour (P=.03), compared with invasive disease. Although of marginal statistical significance, DCIS lesions are more likely to have a lower morphological score than invasive carcinoma (P=.06), whilst the latter is more likely to show ring enhancement (P=.07). Use of breast MRI for staging at our institution shows that pure DCIS and pure invasive cancers are both rare entities. Despite the relatively limited numbers, we identified features that would help to differentiate high-grade DCIS from invasive carcinoma on MRI.     

A comparison of T2*-weighted magnitude and phase imaging for measuring the arterial input function in the rat aorta following intravenous injection of gadolinium contrast agent

The arterial input function (AIF) is important for quantitative MR imaging perfusion experiments employing Gd contrast agents. This study compared the accuracy of T(2)*-weighted magnitude and phase imaging for noninvasive measurement of the AIF in the rat aorta. Twenty-eight in vivo experiments were performed involving simultaneous arterial blood sampling and MR imaging following Gd injection. In vitro experiments were also performed to confirm the in vivo results. At 1.89 T and TE=3 ms, the relationship between changes in 1/T(2)* in blood (estimated from MR signal magnitude) and Gd concentration ([Gd]) was measured to be approximately 19 s(-1) mM(-1), while that between phase and [Gd] was approximately 0.19 rad mM(-1). Both of these values are consistent with previously published results. The in vivo phase data had approximately half as much scatter with respect to [Gd] than the in vivo magnitude data (r(2)=.34 vs. r(2)=.17, respectively). This is likely due to the fact that the estimated change in 1/T(2)* is more sensitive than the phase to a variety of factors such as partial volume effects and T(1) weighting. Therefore, this study indicates that phase imaging may be a preferred method for measuring the AIF in the rat aorta compared to T(2)*-weighted magnitude imaging.     

TDDFT study of one- and two-photon absorption properties: donor-pi-acceptor chromophores

We report a comprehensive time-dependent density functional theory (TDDFT) study of one-photon and two-photon absorption (OPA and TPA, respectively) spectra for donor-pi-acceptor molecules. The calculated excitation energies were generally shown to be in good agreement with experiment, particularly when compared to results from measurements carried out in a nonpolar solvent, although the oscillator strengths were overestimated in some cases. Calculated TPA cross sections applying the two-state approximation were shown to be highly dependent on the form of the line-shape function used. Although a good agreement with experimental TPA spectra was generally observed, the wide range in the experimentally measured values and lack of systematic experimental data on solvent effects limited a detailed comparison as yet.     

Improved measurement of the form factors in the decay lambda+c-->lambda + nue

Using the CLEO detector at the Cornell Electron Storage Ring, we have studied the distribution of kinematic variables in the decay lambda(+)(c)lambda--> e(+)nu(e). By performing a four-dimensional maximum likelihood fit, we determine the form factor ratio, R= f(2)/f(1) = -0.31 +/- 0.05(stat) +/- 0.04(syst), the pole mass, M(pole) = [2.21 +/- 0.08(stat) +/- 0.14(syst)] GeV/c(2), and the decay asymmetry parameter of the lambda(+)(c), alpha (lambda(c)) = -0.86 +/-0.03(stat) +/- 0.02(syst), for q(2) = 0.67 (GeV/c(2))(2). We compare the angular distributions of the lambda(+)(c) and lambda(-)(c) and find no evidence for CP violation: A(lambda(c)) = (alpha(lambda(c)) + alpha (lambda(c)))/(alpha(lambda(c))-alpha(lambda(c))) = 0.00 +/- 0.03(stat) +/- 0.01(syst) +/- 0.02, where the third error is from the uncertainty in the world average of the CP-violating parameter, A(lambda), for ppi(-).     

Speech intelligibility and spatial release from masking in young children

Children between the ages of 4 and 7 and adults were tested in free field on speech intelligibility using a four-alternative forced choice paradigm with spondees. Target speech was presented from front (0 degrees); speech or modulated speech-shaped-noise competitors were either in front or on the right (90 degrees). Speech reception thresholds were measured adaptively using a three-down/one-up algorithm. The primary difference between children and adults was seen in elevated thresholds in children in quiet and in all masked conditions. For both age groups, masking was greater with the speech-noise versus speech competitor and with two versus one competitor(s). Masking was also greater when the competitors were located in front compared with the right. The amount of masking did not differ across the two age groups. Spatial release from masking was similar in the two age groups, except for in the one-speech condition, when it was greater in children than adults. These findings suggest that, similar to adults, young children are able to utilize spatial and/or head shadow cues to segregate sounds in noisy environments. The potential utility of the measures used here for studying hearing-impaired children is also discussed.