In this paper we prove identities involving the classical Jacobi theta functions of the form ∑c(i1, i2, i3, i4)θ1(z|τ)1 θ2(z|τ)2 θ3(z|τ)3 θ4(z|τ)4 = 0 with c(i1, i2, i3, i4) ∈ K[Θ], where K is a computable field and Θ := { θ 1 (0|τ) : k ∈ N } ∪ { θ j (0|τ) : k ∈ N and j = 2,3,4 } . We give two algorithms that solve this problem. The second algorithm is simpler and works in a restricted input cl...

Bornmann and Leydesdorff (in press) proposed methods based on Web-of-Science data to identify field-specific excellence in cities where highly-cited papers were published more frequently than can be expected. Top performers in output are cities in which authors are located who publish a number of highly-cited papers that is statistically significantly higher than can be expected for these citie...

Quantitative assessment of left ventricular function was performed by single plane cineangiography in I3 patients with ischaemic heart disease without clinical heart failure. As compared with normal controls, 7 of I3 patients had a reduced ejection fraction and 'normalized' ejection rate, suggesting impaired left ventricular function. These patients could not be differentiated clinically in any...

For the composition ideas and technologies of the REWERSE working group I3 to be successful, it is vital to understand how the collaborating groups within the network view its work. It is important to understand, and take into consideration, the requirements of the collaborating working groups wrt. their languages and applications, which I3 is to support with composition technology. To this end...

Bornmann and Leydesdorff (2011) proposed methods based on Web of Science data to identify field-specific excellence in cities where highly cited papers were published more frequently than can be expected. Top performers in output are cities in which authors are located who publish a number of highly cited papers that is statistically significantly higher than can be expected for these cities. U...

where detξ denotes the determinant of ξ, and (C4) W (PξQ) = W (ξ) for all ξ ∈ M and all P,Q ∈ SO(3) for N = 3, with SO(3) := {Q ∈ M : QQ = QQ = I3 and detQ = 1}, where I3 denotes the identity matrix in M 3×3 and Q is the transposed matrix of Q. (In fact, (C4) is an additional condition which is not related to (2). However, it means that W is frame-indifferent, i.e., W (Pξ) = W (ξ) for all ξ ∈ M...

A dynamic two-sided matching market is considered. We examine two existing notions of stability—the core and recursive core—for this multi-period market and argue that they both have limitations. We define two new notions of stability and label them, self-sustaining stability and strict self-sustaining stability. Both concepts can be viewed as the recursive core with more stringent conditions f...

Remark 1. One may wonder why Impagliazzo’s hard core lemma (see the previous lecture for the lemma statement) is not enough to get a 12 −2 −δn-hard function starting with a 2−δn-hard function. The difficulty lies in the fact that the hard core lemma only tells about the existence of a hard core set such that on that set f is 1 2 − 2 −δn -hard. We do not know how to sample from that hard core se...

Kant is well known for his restrictive conception of proper science. In the present paper I will try to explain why Kant adopted this conception. I will identify three core conditions which Kant thinks a proper science must satisfy: systematicity, objective grounding, and apodictic certainty. These conditions conform to conditions codified in the Classical Model of Science. Kant’s infamous clai...