The result of Theorem 4.1 prompts us to consider the following general refinements of the Erdös-Mordell inequality in the form: sum R_{1}gefrac{2sum k_{1}(r_{1}+R_{1})}{sum k_{1}}ge2sum r_{1}, (5.1) where (k_{1}), (k_{2}), (k_{3}) are positive real numbers.
Hence, (1.3) is different from the Cauchy-Schwarz inequality in the above direct sum.
Most of this increase (59%) was due to cardiovascular diseases that is, (increase in absolute educational inequalities for cardiovascular disease)/(increase in sum of cause specific absolute educational inequalities)=285/479 (the sum 479 does not total 483 because separate regressions were run for each cause of death) and lung cancer (21%).
We establish a general form of sum-difference inequality in two variables, which includes both more than two distinct nonlinear sums without an assumption of monotonicity and a nonconstant term outside the sums.
By substituting the vector of optimal transmit power ( {mathbf{P}}^=left{{p}_1^(t),{p}_2^(t),cdots, {p}_N^(t)right} ) into the interference power constraint inequality in (6), we can obtain: sum limits_{iin mathcal{N}}{p}_i^(t){G}_{left i,bright)}le {varpi}_{mathrm{PBS}}.
This result is proven directly in [3], Theorem 1, using Jensen's operator inequality on the sum of the operators.
The fourth lemma is a norm inequality for the sum of two operators, which can be found in [14].
A matrix inequality in terms of the row sums of a matrix has been applied to the configurational design of a flotation network.
A lot of what he thinks is going wrong with inequality in cities like London is summed up for him in the stonework of the Sutton estate mansion blocks.
In sum, the difference between strong economic growth and current inequality trends versus weak economic growth and falling inequality is one billion people (see figure 1 .Figure 1.
In sum, the confluence of increasing diversity and income inequality makes Sweden a particularly relevant place to investigate the relationship between ethnic enclaves and health.
