Usually this theorem is proved by using continued fractions; see Theorem 193 in [2]. S. Hartman [3] has restricted the approximating numbers f to those fractions, where u and v belong to fixed residue classes a and b with respect to some modulus s. He proved the following: For any irrational number £, any s > 1, and integers a and b, there are infinitely many integers u and v > 0 satisfying 2s (1)

Under general hypotheses on the target set S and the dynamics of the system, we show that the minimal time function TS(·) is a proximal solution to the Hamilton–Jacobi equation. Uniqueness results are obtained with two different kinds of boundary conditions. A new propagation result is proven, and as an application, we give necessary and sufficient conditions for TS(·) to be Lipschitz continuou...

2 One of the key medical methods for detection and characterization of pathologies is the assessment of tissue stiffness by palpation. The importance of clinical assessment of tissue stiffness has been known since ancient times: In Pharonic Egypt, more than 5000 years ago, physicians practiced palpation of body parts to determine tissue stiffness. They knew that a hard mass within an organ was ...

AIM Arterial wall elasticity including the circumferential and longitudinal modulus is a measure of sub-clinical cardiovascular disease; the circumferential modulus is increased in acute ischemic stroke (AIS). There are still no reports of non-invasive measurement of longitudinal elastic modulus of arterial wall and its prospect of clinical application. In this study, the longitudinal elastic m...

Nanoindentation of cellulose diacetate-graft-poly(lactide)s (CDA-g-PLLAs) synthesized by ring opening graft copolymerization of L-lactide in bulk onto the residual hydroxyl positions on CDA were conducted to investigate the effect of the molecular composition and thermal aging on mechanical properties and creep behavior. Continuous stiffness measurement (CSM) technique was used to obtained hard...

We demonstrate that a microfabricated bump array can concentrate genomic-length DNA molecules efficiently at continuous, high flow velocities, up to 40 μm/s, if the single-molecule DNA globule has a sufficiently large shear modulus. Increase in the shear modulus is accomplished by compacting the DNA molecules to minimal coil size using polyethylene glycol (PEG) derived depletion forces. We map ...

During the past decade the southern pine industry has adopted technology for kilndrying dimension lumber at temperatures above the boiling point of water. Does exposure to such temperatures diminish the mechanical properties of southern pine? Previous research (Koch 1971) has indicated that when dried 21 hours at 240 F (100 F wet-bulb temperature) with crosscirculation air velocity of 1,(XX) £p...

The high strain rate compressive behaviour of a Silicone elastomer: Sylgard 184® is presented. Experiments were performed over strain rates between 3000 and 15,000 s -1 , and temperatures between -40 and +73 oC, corresponding to environmental conditions in many industrial applications. An Ogden strain energy density function was fit to the data, and the strain rate and temperature dependence of...

We present S-A-N-Sand elastic plateau modulus data obtained from semi-dilute wormlike micellar solutions, with small amounts of salt added. The spectra of these solutions are reminiscent of polyelectrolyte send-dilute solutions. The plateau modulus, which is related to the correlation length of the fluctuations in strain, is increased by the addition ofsalt. The primary result is that the elect...

Mechanical modelling using the level-cut Gaussian random field approach has been employed to simulate effect of radiation induced amorphization on Young´s modulus, Poisson´s ratio and hardness zircon (ZrSiO4). A good agreement with previous nanoindentation experiments achieved. Two percolation transitions occur at ~16% ~84% amorphous volume fraction, leading deviations from linearity in evoluti...