This paper develops a theoretical foundation for the undercut-proof equilibrium (see Shy, 1996, 2002; Morgan and Shy, 2013). In a general spatial setting, the set of undercut-proof prices is equivalent the core of a non-transferable utility cooperative-game, played on the set of outcomes that are feasible in Bertrand competition. The result depends critically on two conditions: First, firms mus...

We present a systematic investigation of the dynamic properties of silicon nitride cantilevers in air. The thermal noise spectra of cantilevers have been measured using a home-made optical deflection setup. Torsional and flexural resonances up to the seventh mode are observed. The dependence of resonance frequencies on the dimensions and mode number is studied in detail. It is found that underc...

The undercut procedure was presented by Brams et al. [3] as a procedure for identifying an envy-free allocation when agents have preferences over sets of objects. They assumed that agents have strict preferences over objects and their preferences are extended over to sets of objects via the responsive set extension. We point out some shortcomings of the undercut procedure. We then simplify the ...

The undercut procedure was presented by Brams, Kilgour and Klamler (2012) as a procedure for identifying an envyfree allocation when agents have preferences over sets of objects. They assumed that agents have strict preferences over objects and their preferences are extended over to sets of objects via the responsive set extension. We point out some shortcomings of the undercut procedure. We th...

We present an approach for controlling the undercut and the minimal overhang angle in density based topology optimization, which are useful for reducing support structures in additive manufacturing. We cast both the undercut control and the minimal overhang angle control that are inherently constraints on the boundary shape into a domain integral of Heaviside projected density gradient. Such a ...

In this paper, the stress intensity factor (SIF) expression for defected butt welds containing undercut and inclined lack of penetration (LOP) subject to far-field tensile stress is derived. Some of the standards such as ISO 5817 and BS EN 25817 have specified allowable limits for the length of the undercut and LOP defects and for the height of the weld. In addition, EN 29692 standard has deter...

In the mature brain, the K(+)/Cl- cotransporter KCC2 is important in maintaining low [Cl-]i, resulting in hyperpolarizing GABA responses. Decreases in KCC2 after neuronal injuries result in increases in [Cl-]i and enhanced neuronal excitability due to depolarizing GABA responses. We used the gramicidin perforated-patch technique to measure E(Cl) ( approximately E(GABA)) in layer V pyramidal neu...

Posttraumatic epilepsy (PTE) usually develops in a small percentage of patients of traumatic brain injury after a varying latent period. Modeling this chronic neurological condition in rodents is time consuming and inefficient, which constitutes a significant obstacle in studying its mechanism and discovering novel therapeutics for its prevention and treatment. Partially isolated neocortex, or ...

Reduced synaptic inhibition is an important factor contributing to posttraumatic epileptogenesis. Axonal sprouting and enhanced excitatory synaptic connectivity onto rodent layer V pyramidal (Pyr) neurons occur in epileptogenic partially isolated (undercut) neocortex. To determine if enhanced excitation also affects inhibitory circuits, we used laser scanning photostimulation of caged glutamate...

This study tested the hypothesis that early functional alterations in neuronal synchrony in the partially deafferented cortex may lead to spontaneously occurring electrographic seizures. In vivo experiments with partial deafferentation of cat suprasylvian gyrus after extensive undercut of the white matter were conducted using multi-site EEG, extracellular unit and intracellular recordings. The ...