Electric communication during courtship and spawning in two sibling species of dwarf stonebasher from southern Africa, Pollimyrus castelnaui and P. marianne (Mormyridae, Teleostei): evidence for a non species-specific communication code?

The fixed part of the electrocommunication signal, the electric organ discharge (EOD) waveform, is well differentiated in the two vicariant dwarf stonebasher species, Pollimyrus castelnaui and P. marianne. However, differentiation regarding the variable, situation-dependent part, i.e., inter-discharge interval (IDI) patterns, has never been studied in a pair of sibling species of mormyrid fish. We here compare the electrical signalling that accompanies different motor behaviours (such as resting and swimming, territorial agonistic interactions, courtship and spawning) in the two species. Double pulse patterns of regularly alternating short IDIs of 8-11 ms and long ones of 16-100 ms accompanied threat displays in both species. In three pairs of P. marianne and five pairs of P. castelnaui, courtship was characterised by nest building, territory patrolling and acoustic displays (advertisment calls) that were accompanied by long discharge breaks in the male and highly regular IDIs around 50 ms in the female of both species. Nest-tending males showed IDI sequences consisting of regularly alternating double pulse patterns, similar to threat displays. During spawning both sexes generated stereotyped IDI sequences of a low discharge rate. All IDI patterns occurring in one species were also found in the other, and no species-specifity was identified at that level. Playback experiments contrasting conspecific and heterospecific IDI sequences (that had been recorded from nocturnally swimming fish) revealed preferences in none of the six experimental subjects. Double pulse patterns, high discharge rate displays (HD) and regularisations of the IDI sequence accompanying specific behaviours occurred in similar form in both dwarf stonebasher species of the present study. Therefore, we conclude that in the speciation of P. castelnaui and P. marianne the fixed part of the EOD, its waveform, was under more differential selection pressure than its variable part, the patterns of IDI

Maximal Slicing for Puncture Evolutions of Schwarzschild and Reissner-Nordstr\"om Black Holes

We prove by explicit construction that there exists a maximal slicing of the Schwarzschild spacetime such that the lapse has zero gradient at the puncture. This boundary condition has been observed to hold in numerical evolutions, but in the past it was not clear whether the numerically obtained maximal slices exist analytically. We show that our analytical result agrees with numerical simulation. Given the analytical form for the lapse, we can derive that at late times the value of the lapse at the event horizon approaches the value ${3/16}\sqrt{3} \approx 0.3248$, justifying the numerical estimate of 0.3 that has been used for black hole excision in numerical simulations. We present our results for the non-extremal Reissner-Nordstr\"om metric, generalizing previous constructions of maximal slices.Comment: 21 pages, 9 figures, published version with changes to Sec. VI

On an Interpolation Problem for J-Potapov Functions

Let, J, be an m-by-m-signature matrix and let D be the open unit disk in the complex plane. Denote by P{J,0}(D) the class of all meromorphic m-by-m-matrix-valued functions, f, in D which are holomorphic at 0 and take J-contractive values at all points of D at which f is holomorphic. The central theme of this paper is the study of the following interpolation problem: Let n be a nonnegative integer, and let A_0, A_1, ..., A_n be a sequence of complex m-by-m-matrices. Describe the set of all matrix-valued functions, f, belonging to the class P{J,0}(D), such that the first n+1 Taylor coefficients of f coincide with A_0, A_1, ..., A_n. In particular, we characterize the case that this set is non-empty. In this paper, we will solve this problem in the most general case. Moreover, in the non-degenerate case we will give a description of the corresponding Weyl matrix balls. Furthermore, we will investigate the limit behaviour of the Weyl matrix balls associated with the functions belonging to some particular subclass of P{J,0}(D).Comment: 44 page

An Application of the Schur Complement to Truncated Matricial Power Moment Problems

The main goal of this paper is to reconsider a phenomenon which was treated in earlier work of the authors' on several truncated matricial moment problems. Using a special kind of Schur complement we obtain a more transparent insight into the nature of this phenomenon. In particular, a concrete general principle to describe it is obtained. This unifies an important aspect connected with truncated matricial moment problems

On the structure of Hausdorff moment sequences of complex matrices

The paper treats several aspects of the truncated matricial $[\alpha,\beta]$-Hausdorff type moment problems. It is shown that each $[\alpha,\beta]$-Hausdorff moment sequence has a particular intrinsic structure. More precisely, each element of this sequence varies within a closed bounded matricial interval. The case that the corresponding moment coincides with one of the endpoints of the interval plays a particular important role. This leads to distinguished molecular solutions of the truncated matricial $[\alpha,\beta]$-Hausdorff moment problem, which satisfy some extremality properties. The proofs are mainly of algebraic character. The use of the parallel sum of matrices is an essential tool in the proofs.Comment: 53 pages, LaTeX; corrected typos, added missing notation