Use Kiosk Mode, Align Form Fields and eSign

This integral can be easily solved using Feynman parametrization trick, and hence avoiding completely complex analysis. To do so, we write the integral in the following form:[math]\text{I}(a)= \int_0^{\infty} \frac{\cos(ax)}{x^2+1}\mathrm dx \,\,\,\,\,\,\,\, a>0\tag*{}[/math]We now differentiate under the integral sign using Leibniz rule:[math]\begin{align} \text{I}’(a)&= - \int_0^{\infty}\frac{x \sin(ax)}{x^2+1}\mathrm dx\\&=- \int_0^{\infty} \frac{x^2 \sin(ax)}{x(x^2+1)}\mathrm dx \\ &= - \int_0^{\infty} \frac{x^2 \sin(ax)+ \sin(ax) - \sin(ax)}{x(x^2+1)}\mathrm dx \\&= - \int_0^{\infty} \frac{\sin(ax)}{x} \mathrm dx + \int_0^{\infty} \frac{ \sin(ax)}{x(x^2+1)}\mathrm dx\\ \text{I}’(a)&= - \frac{\pi}{2}\text{sgn}(a) + \int_0^{\infty} \frac{ \sin(ax)}{x(x^2+1)}\mathrm dx\\ \text{I}’’(a)&= \int_0^{\infty} \frac{\cos(ax)}{x^2+1} \mathrm dx \\ &= \text{I}(a)\end{align}\tag*{}[/math]hence we get the following linear and homogeneous second order differential equation[math]\text{I}’’(a)- \text{I}(a)= 0\tag*{}[/math]whose solution is:[math]\text{I}(a)= c_1 e^{a} + c_2 e^{-a}\tag*{}[/math]Now we have to find the coefficients using these equations:[math]\begin{align}\text{I}(a=0)&=c_1+c_2 = \frac{\pi}{2}\\\text{I}’(a=0)&=c_1-c_2 = -\frac{\pi}{2}\end{align}\tag*{}[/math]hence[math]c_1=0, c_2=\frac{\pi}{2}\tag*{}[/math]So we finally end up with[math]\boxed{\boxed{ \text{I}(a=1)= \frac{\pi}{2} e^{-1} = \frac{\pi}{2 e}}}\tag*{}[/math]Quantum Gravity: ESSENTIALS OF LOOP QUANTUM GRAVITY, Toni Sementana - Amazon.comQFT: An Intuitive Approach to Quantum Field Theory, Toni Sementana - Amazon.com

You shouldn’t think of the Lagrangian as being always kinetic minus potential energy. What we have here is a “generalized potential”, that is, [math]L = T - U[/math] where [math]U[/math] depends on velocity. A generalized potential should not be interpreted as the true potential energy of the particle.In fact, the total energy of an interacting system of point charges and currents can be written in two equivalent forms:\begin{align}E &= T + \frac{\epsilon_0}{2} \int E^2 \, \mathrm{d}^3 x + \frac{1}{2\mu_0} \int B^2 \, \mathrm{d}^3 x \\&= T + \frac{1}{2} \sum q \phi + \frac{1}{2} \sum qv \cdot A\end{align}The former attribu...

7 Ways to Increase Your Form Field Conversion Rate (by Up to 672%)Pop quiz: How do you generate leads?Answer: By placing a high-converting lead generation form in a landing page.From there, you begin to nurture the leads—persuading them to buy your product. A SalesForce study found that “companies that excel at lead nurturing generate 50 percent more sales-ready leads at 33 percent lower cost.”The gateway between your site and the visitor is the lead generation form, also known as the lead gen form. As you already know, a lead gen form that’s placed on a landing page with offers visitors ca...

I’ll stretch the meaning of the question a little bit and tell the story of the “mathematical development landmarks”: each of the following represents a new, key concept along the journey of discovery, a new tool added to our abstract reasoning kit. I find it fascinating how we are sequentially enlightened while learning mathematics.I’m only superficially acquainted with many of the topics and ideas mentioned, but as a beginner self-learner, I think I can provide some insight as to why these concepts feel mysterious and open up doors. So let’s get started!Warning: This is going to be a long...

What is an intuitive way of explaining how the "Green's function" works?When I think about Green's functions, I like to think about the archetypal example, Poisson's equation for gravity. The Green's function of the Laplacian in the three-dimensional case is just the Newtonian gravitational potential of a point source. The gravitational field of an arbitrary distribution of matter can be expressed as the sum (or integral) of a large number of point sources. This is possible because (Newtonian) gravity is linear: the sum of the gravitational fields of two masses is the gravitational field of the sum of two masses.Generally, then, if you know the solution in the ...

Lead generation forms are forms on your website which web visitors fill in with their details (name, email, etc) to access an offer (e.g. a free piece of content) or an event (e.g. book a demo, arrange a meeting, etc).These are lead generation forms because once an individual person fills it out they become a “lead”: i.e. a potential buyer who is potentially interested in your product or service.If you want to create a high-perfoming lead generation form, a lead gen form that’s placed on a landing page with offers visitors can’t resist always performs well.But how do you ensure that your le...

OK. There are already a lot of questions about Noether's (first) theorem, so first make sure you're not looking for the answer to one of them:What is the significance of Noether's theorem?What is Noether's theorem stated for the layman?What is an intuitive explanation for Noether's Theorem?What is it that makes Noether's Theorem so beautiful?Second, I should point out that Noether's signNow itself, "Invariant Variation Problems", qualifies as an answer to this question: an exposition of Noether's theorem in mathematical notation with accompanying explanation in English. You can find the signNow...

We (i.e. Kwanzoo) know both Bizo and Demandbase reasonably well, since all 3 companies (Bizo is now a division of LinkedIn) service the same customers (B2B marketers at mid-to-large enterprises) with their retargeting, display advertising and account-based marketing (ABM) needs.We have all been trying to innovate in a very dynamic space over the past 4+ years. So anything I say here is with a lot of respect for my compatriots and the leadership at Bizo and Demandbase. I will try to be accurate, but apologies in advance, if either Bizo or Demandbase have made some further innovation(s) or ...Is there any way to get a user's email address through LinkedIn?A few tips:The simplest way is to look through profile information by using combo ctrl+F OR command+F and typing '@' in the appeared field at the right top corner and then pressing Enter. If there's an email address it will be highlighted with a different color. The success rate is arou...

There are plenty of tensors which are purely symmetric and plenty which are purely asymmetric! I’m new to the subject, but I can think of a symmetric tensor off the top of my head.This is the stress tensor - given a rigid body, you can think of it as a tensor field, i.e. a tensor is assigned to each point in the body. We can analyze the stress at a point by considering a tiny cube, or “volume element”, and measuring the stress on each face of the element.We only need to consider three faces of the cube since the stress on the other three faces are just the negatives of the stress on the first three faces - this comes from the fact that the stress on the bottom of the cube is equal and opposite to the stress on the top of the cube below it by Newton’s 3rd, and the stress hasn’t changed much from cube-to-cube if we consider infinitesimal cubes.The stress on any face is a 3-vector that can be separated into three components, one of which is perpendicular to the face and results in tensile-compressive forces, and two of which are parallel to the face and result in shear forces.I’m not going to show you why this is a tensor, but I will show you why it is symmetric. Imagine an imaginary line through the center of the cube in the [math]x_1[/math] direction. In order for the cube to be in equilibrium, the sum of the torques about that axis must be zero. If we look at our diagram, only two components contribute to the torque - [math]\sigma_{23}[/math] and [math]\sigma_{32}[/math] - the other components are either parallel to the axis or intersect the axis. Also, the stresses on the opposite three faces make the problem worse since, if we were to draw them, they would double the torque, not cancel it.Thus, the sum of torques across the top three faces must be zero. This means that [math]\sigma_{23}=\sigma_{32}[/math], since they oppose each other. Similarly, [math]\sigma_{12}=\sigma_{21}[/math] and [math]\sigma_{13}=\sigma_{31}[/math].