Cross Cap
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Capped Rate Mortgages: The Questions You Have Answered
Capped rate mortgages are in a lot of ways a cross between a variable or tracker rate mortgage and a fixed rate mortgage. They act like fixed rate mortgages in that they can not climb above a particular level - here is the cap. And they are generally the same as variable rate mortgages for the reason that your repayments can change on a month to month basis in line with the Bank of England’s base rate, so any falls in the base rate should see comparable falls in your mortgage rate. Some lenders now put a floor (or collar) on how low your mortgage rate can go but at any rate you'll be protected in case the base rate rises over a particular level. Your rate of interest will climb with the base rate however only up to a certain level. Once it reaches the ceiling, or cap, your repayments will stay the same.
The positives and negatives of capped rate mortgages
The important pro, in some ways, is getting the best of all possible worlds - fixed and variable. If interest rates go above the cap on your contract you will be protected and when rates fall you will probably} benefit.
You will pay a premium for having the best of both worlds. There are not that a lot of these deals around so they aren't that competitively priced. On the whole you will pay a higher rate than the equivalent fixed rate mortgage and you also could lose out if interest rates go below the “collar” set in your arrangement. Lenders are constantly analysing the markets as well as the economy. Most likely they won't put the cap much below the maximum they expect interest rates to reach anyway and if that was the case you wouldn’t have much to gain from the cap.
Bear in mind nonetheless that mortgage offers do change from lender to lender and from day to day so always speak to an expert mortgage consultant who can help you identify the most suitable mortgage loan to match your requirements.
If you are looking for a new mortgage or want to remortgage it makes sense to talk to a mortgage adviser who can talk you through all the different options. Just make sure they are FSA approved. Alternatively visit http://www.findmortgagedeals.co.uk and fill in our one minute mortgage form and an appropriate adviser will contact you.
What is a cross cap;explain?
In mathematics, a cross-cap is a two-dimensional surface that is topologically equivalent (i.e. homeomorphic) to a Möbius strip. The term ‘cross-cap’, however, often implies that the surface has been deformed so that its boundary is an ordinary circle.
A cross-cap that has been closed up by gluing a disc to its boundary is an immersion of the real projective plane. Two cross-caps glued together at their boundaries form a Klein bottle. An important theorem of topology, the classification theorem for surfaces, states that all two-dimensional compact manifolds without boundary are homeomorphic to spheres with some number of ‘handles’ and at most two cross-caps.
A cross-cap can also refer synonymously to the closed surface obtained by gluing a disk to a cross-cap. This surface can be represented parametrically by the following equations:
X(u,v) = r , (1 + cos v) , cos u,
Y(u,v) = r , (1 + cos v) , sin u,
Z(u,v) = - hbox{tanh} left(u - pi right) , r , sin v,
where both u and v range from 0 to 2π. These equations are similar to those of a torus. Figure 1 shows a closed cross-cap.
A cross-cap has a plane of symmetry which passes through its line segment of double points. In Figure 1 the cross-cap is seen from above its plane of symmetry z = 0, but it would look the same if seen from below.
A cross-cap can be sliced open along its plane of symmetry, while making sure not to cut along any of its double points. The result is shown in Figure 2
Once this exception is made, it will be seen that the sliced cross-cap is homeomorphic to a self-intersecting disk, as shown in Figure 3.
The self-intersecting disk is homeomorphic to an ordinary disk. The parametric equations of the self-intersecting disk are:
X(u,v) = r , v , cos 2 u,
Y(u,v) = r , v , sin 2 u,
Z(u,v) = r , v , cos u,
where u ranges from 0 to 2π and v ranges from 0 to 1.
Projecting the self-intersecting disk onto the plane of symmetry (z = 0 in the parametrization given earlier) which passes only through the double points, the result is an ordinary disk which repeats itself (doubles up on itself).
The plane z = 0 cuts the self-intersecting disk into a pair of disks which are mirror reflections of each other. The disks have centers at the origin.
Now consider the rims of the disks (with v = 1). The points on the rim of the self-intersecting disk come in pairs which are reflections of each other with respect to the plane z = 0.
A cross-cap is formed by identifying these pairs of points, making them equivalent to each other. This means that a point with parameters (u,1) and coordinates (r , cos 2 u, r , sin 2 u, r , cos u) is identified with the point (u + π,1) whose coordinates are (r , cos 2 u, r , sin 2 u, - r , cos u) . But this means that pairs of opposite points on the rim of the (equivalent) ordinary disk are identified with each other; this is how a real projective plane is formed out of a disk. Therefore the surface shown in Figure 1 (cross-cap with disk) is topologically equivalent to the real projective plane RP2.
Rand Paul’s Pro-Polluter Bill Shot Down by Senate (Green Options)
All but one of the Senate Democrats - and even seven Republicans - defeated a
bill on Thursday that would have blocked the EPA from slashing power plant air
pollution that blows downwind to other states and causes lung and heart
problems. Rand Paul, a Kentucky Republican and Tea Party favorite, proposed a
bill to [...]Related posts:
1. Rand Paul Tries to Stop EPA's Ozone Cap and Trade
2. Senate GOP Pushing Energy Bill Socialism?
3. CBO Scores Senate Climate Bill - Will Save $21 Billion in First 10 Years
shinshi doumei cross cap 4
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