> parties dominate the political scene, as is the case in the US and

> as has been the case for a long time in the UK.

It isn’t reasonable, as the FPTP system locks tends to lock in the two-party dominance – ie. it is a circular argument.

]]>*Thanks — corrected now.*

S’_k = kS_(k-1) + constant

Actually the constant = (-1)^k * B(k), B(k) is the kth Bernoulli Number

B(0) = 1, B(1) = -1/2, B(2) = 1/6…

Even if you do not Bernoulli Numbers, you may use simple substitution to wok out the “constant)

using simple integration and substitution, you can then work out all kth power sums.

For example,

S0 = n, S1 = (n^2)/2 + cn (integration of S0)

put n = 1, S1(1) = 1 = (1^2)/2 + c, c= 1/2

hence, S1 = (n^2)/2 + n/2

2*S1 = (n^2) + n

integrate 2*S1 = (n^3)/3 + (n^2)/2

hence S2 = (n^3)/3 + (n^2)/2 + cn

put n = 1, c = 1/6

S2 = (n^3)/3 + (n^2)/2 + n/6 = n(n+1)(2n+1)/6

S3, S4… can be worked out similarly.

]]>1) K forces (for all x A(x)) –> Q

2) but K does not force exists x (A(x) –> Q)

The intuitive reason behind it is that

for all x A(x) or exists x not A(x)

is not constructive or in computability sense, it is not decidable.

If we think the implication in A –> B as a universal machine that construct a proof of B by getting a proof of A as input (BHK interpretation),

A –> B

and

not A or B

are not alike.

So, by knowing the set X, we can not construct or compute a real number ‘b’ in X such that

|b| diam(X)<= 2

Anyway, I find it very curious and interesting.

]]>https://web.math.princeton.edu/~gunning/bk.ps. ]]>

One of the reasons that the negotiations in the UK had such disappointing results was a view that there was no realistic plan B. But the Germans have shown us that there’s a pretty good one: just manage somehow until Elsevier caves in.

It will be very interesting to see whether Elsevier tries to get the Germans to pay for this access that has been restored. If I were a German negotiator, then one of the first things I would say is, “We didn’t ask for this, so we’re not paying for it.” My guess is that Elsevier has taken this action because it is *very* dangerous for them if it becomes widely known that a whole country can manage just fine when access to ScienceDirect was cut off — a bit inconvenient yes, but by no means a disaster.

German scientists regain access to Elsevier journals

Publisher restores access as negotiations for a nationwide licence continue. ]]>

The law relating to pensions gives trustees wide discretion in choice of discount rate. They do NOT have to use FRS17.

It is highly questionable whether USS is in deficit or if it is by how much. Have a look at this article which questions the whole methodology for valuing pension schemes:

Also have a look at this article by a firm of actuaries who believe in DB pensions instead of doom mongers like you:

The point is that pensions are in better shape if valued on an ongoing basis than if valued using short term risk and expectations of closing.

Mathematicians have a lot to answer for by ignoring the economics that underlies pensions. Sometimes they talk as if the world is going to cease. The economy is going to continue to make profits from which pension funds can benefit and the universities that are members of USS are going to continue in existence on an ongoing basis.

]]>Is the USS going to be around to pay my pension in 10 years time or I am going to be in line for food banks??

God help us from another financial meltdown…it is coming… ]]>

In your post you write “Cambridge, for example, has paid over £750,000 this year in article processing charges, from a grant provided for the purpose”.

Is this on top of the £1,161,571 that they are spending per year, according to the FOI data? If there is off-setting going on, do we know how much?

Richard

]]>