An approximation algorithm for finding long paths in Hamiltonian graphs

In this paper we present a polynomial-time algorithm that finds paths of length Ω((logn/loglogn)²) in undirected Hamiltonian graphs, improving the previous best of Ω(logn).     

Synthesis and characterization of soluble polyimides containing trifluoromethyl groups in their backbone

A series of polyimides were synthesized from 2,2‐Bis(3,4‐dicarboxyphenyl)hexafluoropropane, 2,2‐bis(3‐amino‐4‐hydroxyphenyl)‐hexafluoropropane, and 4,4′‐oxydianiline by chemical imidization. The effects of the diamine ratios on the properties of the films were evaluated through the study of their thermal, electrical, and morphological properties. All the polymers exhibited better solubility in most of the organic solvents and hence were easily processable. Polyimides with more 2,2‐bis(3‐amino‐4‐hydroxyphenyl)‐hexafluoropropane exhibited better solubility and a low refractive index, which is highly desired for microelectronic applications. The dielectric constant and birefringence were strongly dependent on the fluorine content. With an increase in the fluorine substitution, both the dielectric constant and birefringence decreased. All the polymers exhibited high thermal stability (>400 °C). The absence of crystalline melting in differential scanning calorimetry and broad wide‐angle X‐ray diffraction patterns revealed the amorphous nature of the polymers, which was due to the presence of bulky CF₃ groups and hinged ether linkages of the diamine component. The residual stress values decreased with an increase in the 4,4′‐oxydianiline content, and the results were in agreement with the dielectric constant. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4303–4312, 2004     

A real algorithm for the Hermitian eigenvalue decomposition

Modifying complex plane rotations, we derive a new Jacobi-type algorithm for the Hermitian eigendecomposition, which uses only real arithmetic. When the fast-scaled rotations are incorporated, the new algorithm brings a substantial reduction in computational costs. The new method has the same convergence properties and parallelism as the symmetric Jacobi algorithm. Computational test results show that it produces accurate eigenvalues and eigenvectors and achieves great reduction in computational time.The work of this author was supported in part by the National Science Foundation grant CCR-8813493 and by the University of Minnesota Army High Performance Computing Research Center contract DAAL 03-89-C-0038.The work of this author was supported in part by the University of Minnesota Army High Performance Computing Research Center contract DAAL 03-89-C-0038.     

Auditory evoked responses: A tool to assess the fetal neurological activity

An intact auditory system at birth is requisite for the successful accomplishment of many developmental skills. Evoked responses to auditory stimuli have been used as a sensitive test to determine the functional status of the adult and neonatal brain. It has been established that fetuses can hear in utero and respond to external acoustic stimuli. We present an overview of the transmission of sound through the maternal abdomen to the fetal ear and the recordings of an auditory evoked response obtained from the fetus using a non-invasive magnetoencephalography technique. The investigation of cortical activity of the fetus in response to auditory stimulation can help understand and track the neurological development of the fetus.     

Anomalous elastic behaviour of Bi-Pb-Ag composites

Bi-Pb and Bi-Pb-Ag superconducting composites have been prepared by the solid state reaction method. After the usual characterization, ultrasonic longitudinal velocity and attenuation studies have been undertaken over a temperature range 80–300 K by the pulse transmission technique. In contrast to normal solids, the ultrasonic velocities of both the samples in the temperature range 200-100 K are found to decrease with decreasing temperature (softening), followed by a velocity maximum. The samples are also found to exhibit longitudinal attenuation peaks at TEMPERATURES = 260, 160 and 120 K. An attempt has also been made to verify whether the Wachtman's equations can theoretically explain the low-temperature behaviour of the Young's modulus of these materials. A qualitative explanation for both the phenomena of softening of velocity as well as the occurrence of attenuation peaks is given.     

Synthesis of 3‐(substituted)‐2,4,8,15‐tetroxa‐3‐phosphadispiro[5.2.5]hexadecane‐3‐oxides

Novel 3‐(substituted)‐2,4,8,15‐tetroxa‐3‐phosphadispiro[5.2.5]hexadecane‐3‐oxides (3‐12) have been synthesized by cyclization of 1,5‐dioxaspiro[5.5]undecande‐3,3‐dimethanol (1) with various substituted aryl phosphorus dichloridates (2) in dry toluene‐THF in the presence of triethylamine at 40‐60 ^oC. Their molecular structures were determined by ir, nmr and mass spectral studies and were screened for antifungal activity against Curvularia lunata and Aspergillus niger, and antibacterial activity on Staphylococcus aureus and Escherichia coli. Most of them possess significant activity.     

Photophysical studies on binding of curcumin to bovine serum albumins

The excited-state photophysical properties of curcumin in the presence of bovine serum albumin (BSA) have been studied. The absorption and fluorescence changes in curcumin on binding to BSA have been followed at varying concentrations of either curcumin or BSA to determine the binding constant, which has been found to be approximately 10(4) to 10(5) M(-1). Stopped-flow kinetics studies suggested at least two distinct kinetic steps for the binding of curcumin to BSA. The photophysical properties of the singlet-excited state of the curcumin-BSA complex have also been studied. Whereas the absorption spectrum of curcumin is redshifted, the fluorescence spectrum of curcumin was blueshifted in the presence of BSA. The fluorescence quantum yield of curcumin on complexing with BSA was approximately 0.05. Steady-state fluorescence anisotropy studies showed a significant increase in the anisotropy value of 0.37 in BSA-bound curcumin. The fluorescence decay of the curcumin-BSA complex followed a biexponential decay with fluorescence lifetimes of 413 ps (33%) and 120 ps (67%). On the basis of these complementary results, it has been concluded that curcumin shows very high binding to BSA, probably at the hydrophobic cavities inside the protein.     

Thiocarboxylato Complexes of Biscyclopentadienyl and Bisindenyl Titanium (IV)

Reactions of biscyclopentadienyl (and bisindenyl) titanium (IV) dichlorides with sodium salts of various thiocarboxylic acids in tetrahydrofuran medium, yield the complexes of the general formula (D) ²Ti(SCOR) ² where D is cyclopentadienyl or indenyl group and R? H, CH₃, C₂H₅, C⁴H⁵ or p-C⁴H⁴CH³ group. The foul smelling complexes are monomeric in nature. The IR spectra, thermal stabilities and Some physical characteristics of these complexes have been studied.