Best Bed Frame Topper for Back Pain

I broke two steel frames in different ways, but both were used for commuting under heavy loads.The bottom line is, steel (or any metal) fatigues; but in both of these cases it was helped along by my own abuse - both were learning experiences for me

1. Do my glasses have to make my eyes look soooo tiny?

If you have a thick Rx, I would suggest going with a high index lens - the highest we can get in the states is a 1.74 but I think they go to 1.80 in other countries. (There are some health restrictions around even thinner glasses and potential to shatter and hurt your eye.) Good news for you - plastic frames are more in style now than metal frames, and this will help to hide some of the thickness. You can also go with an anti-glare coating, which could reduce the obviousness that you are wearing glasses. You can get both of these things online at Replacement Lens Express - they do not accept Insurance up-front, but you should be able to take your submit your receipt and get reimbursed fully. Even if you want to get frames locally, you can send in your frames to have them put in the high quality thin lenses - I will put the link to their 1.74 high index lens page below. Do not stress either way you go - lots of people need glasses! You are not alone :)

2. Energy required to accelerate from different reference frames

In special relativity the transition from one frame to another is given by the Lorentz boosts. This is not quite the same as an acceleration, but a transformation that relates observations on one frame with another. We can think of an acceleration as being a succession of infinitesimal Lorentz boosts that map one frame to another.The infinitesimal distance in flat spacetime $ds$ for a particle is given by $$ ds^2 = c^2dt^2 - dx^2 - dy^2 - dx^2 $$ where this distance $ds - cdtau$, for $tau$ the time as measured by a clock on the frame of the particle. Let us consider the motion of this particle in the $x$ direction. Now divide through by $ds^2$ to get $$ 1 = left(fracdtdtau

ight)^2 - frac1c^2left(fracdxdtau

ight)^2. $$ We can write this according to four-velocity $U_t = fracdtdtau$, $U_x = fracdxdtau$ $$ 1 = U_t^2 - U_x^2. $$ Now take the derivative of this with respect to $tau$ so that $$ 0 = left(fracdU_tdtau

ight)U_t - frac1c^2left(fracdU_xdtau

ight)U_x. $$ This leads to the interesting observation that in spacetime the four-acceleration is perpendicular to the four-velocity. This system of equations leads to a solution for the four-velocity $$ U_t = cosh(gtau),U_x = csinh(gtau), $$ for $g$ the acceleration. We can see that the equation defines a hyperbola in $t, x$ coordinates. For large $tau$ that the hyperbola is approximately $U_t^2 = U_x^2$, and it is not hard to get these in the $t, x$ coordinates. We can also see that the coordinate based velocity is $$ fracdxdt = fracU_xU_t = ctanh(gt), $$ which indicates this particle asymptotes to the speed of light as $tau

ightarrowinfty$.When it comes to energy we appeal to the four-momentum interval in special relativity $$ m^2 = E^2 - p^2 $$ where $E = mU_t$ and $p = mU_x$ are energy and spatial momentum respectively. Using the properties of hyperbolic trigonometric functions this can be seen. We can see right off that energy is given by a hyperbolic cosine function that diverges enormously as $tau

ightarrowinfty$.

3. Will Lenscrafters adjust my frames for free?

Most eyeglass shops will adjust glasses for free whether you bought them there or not. They want you as a customer for that next pair

4. I have a HTML Frames problem..?

Unless you have to use frames, I would switch to CSS and perhaps even a 960 grid. Your problem lies in the fact that you've only got one frame in your page and you need at least 2 frames. Check the w3c.org for more information on HTML layout. They've got lots of great information there.

5. See two frames in Photoshop at once

There's a free plugin called AnimDessin Plugin available through the Adobe Add-Ons that will help you with all of this. Better frame control and onion skinning