The Supreme Court’s affirmative action decisions in Grutter v. Bollinger and Gratz v. Bollinger changed the meaning of “narrow tailoring.” While the narrow tailoring requirement has always had multiple dimensions, a central meaning has been that the government must use the smallest racial preference needed to achieve its compelling interest. We might have expected, therefore, that if the Court ...

We demonstrate a flexible-bandwidth network testbed with a real-time, adaptive control plane that adjusts modulation format and spectrum-positioning to maintain quality of service (QoS) and high spectral efficiency. Here, low-speed supervisory channels and field-programmable gate arrays (FPGAs) enabled real-time impairment detection of high-speed flexible bandwidth channels (flexpaths). Using p...

This study evaluates how people represent “even if” conditionals when they have to integrate them with previous “if then” conditionals and also make an inference. The terms in the premises were ordered to facilitate their integration (Figure 1: If A then B; Even if B C). In half the cases, the “even if” conditional was expressed with a negation instead of an affirmation (If A then B; Even if no...

Inverse Young inequality asserts that if $nu >1$, then $|zw|ge nu|z|^{frac{1}{nu}}+(1-nu)|w|^{frac{1}{1-nu}}$, for all complex numbers $z$ and $w$, and equality holds if and only if $|z|^{frac{1}{nu}}=|w|^{frac{1}{1-nu}}$. In this paper the complex representation of quaternion matrices is applied to establish the inverse Young inequality for matrices of quaternions. Moreover, a necessary and ...

In this paper we study almost uniserial rings and modules. An R−module M is called almost uniserial if any two nonisomorphic submodules are linearly ordered by inclusion. A ring R is an almost left uniserial ring if R_R is almost uniserial. We give some necessary and sufficient condition for an Artinian ring to be almost left uniserial.

in this article, we study the artin-rees property in  c(x), in the  rings of fractions of  c(x) and in the factor rings of c(x) . we show that c(x)/(f) is an artin-rees ring if and only if  z(f)  is an open p-space. a necessary and sufficient condition for the local rings of  c(x)   to be artin-rees rings is that each prime ideal in  c(x)  becomes minimal and it turns out that every local ring ...