We prove that a large class of leading order string solutions which generalize both the plane-wave and fundamental string backgrounds are, in fact, exact solutions to all orders in α′. These include, in particular, the traveling waves along the fundamental string. The key features of these solutions are a null symmetry and a chiral coupling of the string to the background. Using dimensional red...

We propose a simple technique for verifying probabilistic models whose transition probabilities are parametric. The key is to replace parametric transitions by nondeterministic choices of extremal values. Analysing the resulting parameter-free model using off-the-shelf means yields (refinable) lower and upper bounds on probabilities of regions in the parameter space. The technique outperforms t...

It is shown that every cyclic split system S defined on an n-set with #S > 2kn− (2k+1 2 ) for some k ≤ n−1 2 always contains a subset of k+1 pairwise incompatible splits provided one has min(k, n−(2k+1)) ≤ 3. In addition, some related old and new conjectures are also discussed.

The problem of the title is to construct an analytic k × k matrixvalued function in the unit disc with a number of prescribed derivatives at 0 and with spectral radius bounded by 1. We show that the problem can be reduced to an interpolation problem for the symmetrized polydisc Gk, and thereby show that, in the case of derivatives of orders 0 and 1 being prescribed, the problem is equivalent to...

We prove several results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph theory and Ramsey theory, have been collected together because in each case the relevant proofs are quite short.

In this paper we classify all extremal and -extremal binary self-dual codes of length 38. There are exactly 2744 extremal self-dual codes, two -extremal codes, and 1730 -extremal codes. We obtain our results from the use of a recursive algorithm used in the recent classification of all extremal self-dual codes of length 36, and from a generalization of this recursive algorithm for the shadow. T...

A compact hyperbolic surface of genus g is said to be extremal if it admits an extremal disc, a disc of the largest radius determined only by g. We discuss how many extremal discs are embedded in non-orientable extremal surfaces of genus 6. This is the final genus in our interest because it is already known for g = 3, 4, 5, or g > 6. We show that non-orientable extremal surfaces of genus 6 admi...

Abstract—In this paper we classify all extremal and s-extremal binary self-dual codes of length 38. There are exactly 2744 extremal [38, 19, 8] self-dual codes, two s-extremal [38, 19, 6] codes, and 1730 s-extremal [38, 19, 8] codes. We obtain our results from the use of a recursive algorithm used in the recent classification of all extremal self-dual codes of length 36, and from a generalizati...

‎For a simple graph $G$‎, ‎the signless Laplacian Estrada index is defined as $SLEE(G)=sum^{n}_{i=1}e^{q^{}_i}$‎, ‎where $q^{}_1‎, ‎q^{}_2‎, ‎dots‎, ‎q^{}_n$ are the eigenvalues of the signless Laplacian matrix of $G$‎. ‎In this paper‎, ‎we first characterize the unicyclic graphs with the first two largest and smallest $SLEE$'s and then determine the unique unicyclic graph with maximum $SLEE$ a...