On sequential labelings of graphs

A valuation on a simple graph G is an assignment of labels to the vertices of G which induces an assignment of labels to the edges of G. β-valuations, also called graceful labelings, and α-valuations, a subclass of graceful labelings, have an extensive literature; harmonious labelings have been introduced recently by Graham and Sloane. This paper introduces sequential labelings, a subclass of harmonious labelings, and shows that any tree admitting an α-valuation also admits a sequential labeling and hence is harmonious. Constructions are given for new families of graceful and sequential graphs, generalizing some earlier results. Finally, a conjecture of Frucht is shown to be wrong by exhibiting several graceful labelings of wheels in which the center label is larger than previously thought possible.     

A unified view of imaging the elastic properties of tissue

A number of different approaches have been developed to estimate and image the elastic properties of tissue. The biomechanical properties of tissues are vitally linked to function and pathology, but cannot be directly assessed by conventional ultrasound, MRI, CT, or nuclear imaging. Research developments have introduced new approaches, using either MRI or ultrasound to image the tissue response to some stimulus. A wide range of stimuli has been evaluated, including heat, water jets, vibration shear waves, compression, and quasistatic compression, using single or multiple steps or low-frequency (<10 Hz) cyclic excitation. These may seem to be greatly dissimilar, and appear to produce distinctly different types of information and images. However, our purpose in this tutorial is to review the major classes of excitation stimuli, and then to demonstrate that they produce responses that fall within a common spectrum of elastic behavior. Within this spectrum, the major classes of excitation include step compression, cyclic quasistatic compression, harmonic shear wave excitation, and transient shear wave excitation. The information they reveal about the unknown elastic distribution within an imaging region of interest are shown to be fundamentally related because the tissue responses are governed by the same equation. Examples use simple geometry to emphasize the common nature of the approaches.     

On nonoscillatory solutions of differential inclusions

This paper introduces a nonoscillatory theory for differential inclusions based on fixed point theory for multivalued maps.

     

Simple ABCD matrix treatment for transversely varying saturable gain

We have developed an ABCD matrix that, for the first time to our knowledge, accurately describes the transformation of a Gaussian beam by a medium with transversely varying saturable gain. In contrast with the conventional ABCD matrix, the newly developed matrix is shown to be in excellent agreement with a full beam propagation code over a wide parameter range. Accurate treatment of transversely varying saturable gain in laser resonators is important for the optimization of end-pumped lasers, particularly for efficient diode-pumped solid-state and Kerr-lens mode-locked systems.     

Synthesis and spectroscopic properties of furyl-phenyl-acrylates and naphthofurans and their interaction with ct- DNA

A series of novel substituted derivatives related to furyl-phenyl-acrylates and naphthofurans, was synthesized and characterized by UV/Vis and fluorescence spectroscopy. Acyclic compounds can undergo photochemical dehydrocyclization by visible light irradiation in order to obtain their cyclic derivatives. The interactions of the prepared compounds with calf thymus DNA was investigated by means of electronic absorption and fluorescence spectra. It is intriguing that addition of ct-DNA induced a fluorescence increase of acyclic derivatives, exactly the opposite of the strong fluorescence quenching observed for cyclic derivatives 10 and 12. Compound 11 showed decreasing fluorescence intensity for lower concentrations of ct-DNA, while increasing of fluorescence is observed for high excess of added ct-DNA.