Computation of Rotation Matrices Making Lined‐Up to the Local Cartesian Coordinates

Rotation matrices were expressed in terms of Gaunt coefficients and complex spherical harmonics. The rotation matrices were calculated using two different ways. In the first, Gaunt coefficients and normalized complex spherical harmonics were directly calculated using binomial coefficients; in the second, Gaunt coefficients and complex spherical harmonics were recursively calculated. The methods were compared with respect to accuracy and computation time (CPU) for low and very high quantum numbers.     

Linear and Nonlinear Optical Properties in Spherical Quantum Dots

We calculate the energy eigenvalues and the sate functions of one-electron Quantum Dot （QD） by using a combination of Quantum Genetic Algorithm （QGA） and Hartre-Fock-Roothaan （HFR） method. The linear and the third-order nonlinear optical absorption coefficients for the 1s-1p, 1p-1d, and 1d-1f transitions are examined as a function of the incident photon energy for three different values of the stoichiometric ratio. The results show that the stoichiometric ratio, impurity, relaxation time, and dot size have great influence on the optical absorption coefficients of QDs.     

Using close range photogrammetry to measure the position of inaccessible geological features

Experimental Techniques - In this study, the tectonic Timras doline geological maps were successfully obtained using digital close range photogrammetric techniques. This method is more reliable,...     

Exact propagators for some degenerate hyperbolic operators

Exact propagators are obtained for the degenerate second order hyperbolic operators ∂² _t -t ^2l Δ _x , l=1,2,..., by analytic continuation from the degenerate elliptic operators ∂² _t +t ^2l Δ _x . The partial Fourier transforms are also obtained in closed form, leading to integral transform formulas for certain combinations of Bessel functions and modified Bessel functions.     

An unsolvable hypoelliptic differential operator

It is proved that the differential operatorD ₁ +ix ₁ D ₂ ² is hypoelliptic everywhere, but is not locally solvable in any open set which intersects the linex ₁=0. Thus, this operator is not contained in the usual classes of hypoelliptic differential operators. The proofs involve certain properties of the characteristic Cauchy problem for the backward heat operator.     

Existence of a utility in infinite dimensional partially ordered spaces

An example is given of a preference order on a space of denumerable algebraic dimension that has no utility, and necessary and sufficient conditions for the existence of utilities in various linear spaces are given. Research partially supported by the U.S. Office of Naval Research under contract No. N 62558-3586.     

Diffusion-weighted magnetic resonance imaging in differentiation of postobstructive consolidation from central lung carcinoma

Purpose

To prospectively evaluate diffusion-weighted (DW) magnetic resonance (MR) imaging for differentiation of postobstructive consolidation from centrally located lung carcinomas by using apparent diffusion coefficients (ADCs).

Materials and Methods

An institutional review board approved this study; informed consent was obtained from patients. Forty-nine consecutive patients (3 women, 46 men; mean age, 63.6 years; age range, 42–85 years) with lung carcinoma underwent DW MR imaging. Forty patients had central and nine patients had peripheral lung carcinomas. ADC of each lung carcinoma was calculated from DW MR images obtained with two different b values (0, 1000 s/mm²).In the final study group including 27 patients with central lung carcinoma accompanying distal lung consolidation (mean age, 67.2 years; 3 women, 24 men), ADCs of lung carcinomas were statistically compared among cytologic/histologic types and accompanying postobstructive consolidations. Unpaired t test was used for measurable variables with normal distribution, and Kruskal–Wallis variance analysis and Mann–Whitney U tests were used for the measurable variables without normal distribution.

Results

There was no significant difference between mean ADC values of all types of carcinomas (P=.302) and also between mean ADC values of central (1.91 ± 0.7×10⁻³ mm²/s) and peripheral carcinomas (1.58 ± 0. 6×10⁻³ mm²/s) (P=.224). The mean ADC value for the masses of central lung carcinoma with postobstructive consolidations was 1.83 ± 0.75×10⁻³ mm²/s, and for consolidation was 2.50 ± 0.76×10⁻³ mm²/s. ADC of central carcinoma masses was significantly lower than that of postobstructive consolidations (P=.003).

Conclusions

ADC values of central lung carcinoma masses appear to be lower than accompanying postobstructive consolidations. ADC values could be considered useful as a differentiating parameter among central lung carcinomas and accompanying postobstructive consolidations.     

Computation of the oscillator strength and absorption coefficients for the intersubband transitions of the spherical quantum dot

The electronic structure and optical properties of one-electron Quantum Dot (QD) with and without an on-center impurity were investigated by assuming a spherically symmetric confining potential of finite depth. The energy eigenvalues and the state functions of QD were calculated by using a combination of Quantum Genetic Algorithm (QGA) and Hartree–Fock Roothan (HFR) method. We have calculated the binding energy for the states 1s,1p,1d,1f, oscillator strengths, the linear and third-order nonlinear optical absorption coefficients as a function of the incident photon energy and incident optical intensity for the 1s–1p, 1p–1d and 1d–1f transitions. The existence of the impurity has great influence on the optical absorption spectra and the oscillator strengths. Also we found that the magnitudes of the total absorption coefficients of the spherical QD increase for transitions between higher states.     

Computation of two‐center Coulomb integrals over Slater‐type orbitals using elliptical coordinates

A general analytic formula is obtained for the two‐center Coulomb integrals over Slater‐type orbitals in elliptical coordinates. Finite series expansions are used in the evaluation of the radial part of the integrals. The analytic formula is expressed in terms of a product of the well‐known auxiliary functions A_k(p) and B_k(p) and incomplete gamma functions. Recursive relations for the computer evaluation of these functions are given as well. The recursive relations are stable and our computer results are in good agreement with the benchmark values given in the literature. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003