The ‘midpoint’ approximation to the integral $$\int_0^1 f $$ is $${M_n}\left( \right) = {1 \over n}\sum\limits_{r 1}^n \left( {{{2r - 1} {2n}}} \right)$$ .

OBJECTIVE To study changes in midpoint lumbar disc heights in an asymptomatic Jordanian sample relative to age, sex, lumbar level and midvertebral heights. METHODS A total of 153 asymptomatic patients (87 males, age range 20-65 years; mean 43+/-12.1 and 66 females, age range 22-68 years; mean 47+/-13.7) were selected during the study period. All underwent midsagittal magnetic resonance imagin...

The category variability effect refers to that people tend to classify the midpoint item between two categories as the category more variable. This effect is regarded as evidence against the exemplar model, such as GCM (Generalized Context Model) and favoring the rule model, such as GRT (i.e., the decision bound model). Although this effect has been found in conceptual category learning, it is ...

We have measured the redox potentials for the flavin cofactor of native Old Yellow Enzyme and for a series of chemically modified flavin derivatives bound to the apoprotein. These flavin derivatives have midpoint potentials ranging from -120 to -300 mV in free solution. For the native enzyme, the midpoint potential of the first one-electron couple EFMNox + e- in equilibrium EFMN-. is E1 = -245 ...

This paper presents a detailed description of the computer implementation of a generalized midpoint algorithm for integration of constitutive relations for von Mises’ hardening material. A nonlinear scalar equation for determination of the plastic multiplier is derived. The solution of this equation for a hardening material, by the Newton-Raphson method, usually converges in threefour iteration...

Rightward deviation on bisection of a horizontal line is well described in patients with right brain injury and left hemineglect. Because of the observation that hemineglect patients may bisect very short lines to the left of the true midpoint (the so-called crossover effect), additional models have been proposed to incorporate this finding into existing theories of hemineglect. We investigated...

In this paper, the dynamic responses of cracked beams under different moving forces, including moving load, moving mass, moving oscillator, and four-degrees-of-freedom moving system, are investigated. Structural elements such as beams are designed to withstand the predicted loads, but unfortunately, they are always exposed to unpredictable damage such as cracks. Several factors may cause these ...