Prove that if the functions g:[a,b] --> R and h:[a,b] --> R are continuous, with h(x)\geq0 for all x in [a,b] then there is a point c in (a,b) such that...
Mathematically, the p-value is calculated using integral calculus from the area under the probability distribution curve for all values of statistics that are at least as far from the reference value as the observed value is, relative to the total area under the probability distribution curve. Sta...
Integral range optimizations The compiler now generates optimized code for more instances ofstart..finishandstart..step..finishexpressions. Previously, these were only optimized when the type wasint/int32and the step was a constant1or-1. Other integral types and different step values used an ineff...
Let , , , be as in that theorem. It will be convenient to normalise the weights by to make their mean value comparable to . From Theorem 1 and summation by parts we have whenever does not consist entirely of ones. We now take a closer look at what happens when does consist entirely...
and formally differentiating under the integral sign, we obtain the Biot-Savart law This law is of fundamental importance in the study of incompressible fluid equations, such as the Euler equations since on applying the curl operator one obtains the vorticity equation and then by substituting ...
Learn how to write a mathematical proof. Understand why proofs are important in mathematics and see their definition and parts through math proof examples. Related to this Question What does proof by induction mean? Use the Mathematical Induction to prove that 1 + 2 + 3 + ... + n...
Communication in the context of service adoption does NOT mean sending an email to your employees and making sure they know the help desk extension number! If that's the extent of your communications plan, your change plan will encounter severe difficulties. Omni-directional marketing means simultan...
Soft skills either can’t be acquired or are notoriously hard to acquire through traditional education. They are, however, transferable. What does it mean? In short, you have transferable skills regardless of your job. For example, if you’re a great communicator, you’ll remain one after ch...
one can eventually get the to behave like an Archimedean character for some that is not too large (polynomial size in ), and then one can use relatively standard (but technically a bit lengthy) “major arc” techiques based on various integral estimates for zeta and functions to conclude. ...
Continuous integration (CI) and continuous delivery (CD) are integral components of modern software development, but what exactly do these terms mean, and how do they differ? Let’s dive into the key concepts of CI, CD, and an additional approach known as continuous deployment (theotherCD) ...