Parity of transversals of Latin squares

We introduce a notion of parity for transversals, and use it to show that in Latin squares of order $2 \bmod 4$, the number of transversals is a multiple of 4. We also demonstrate a number of relationships (mostly congruences modulo 4) involving $E_1,\dots, E_n$, where $E_i$ is the number of diagonals of a given Latin square that contain exactly $i$ different symbols. Let $A(i\mid j)$ denote the matrix obtained by deleting row $i$ and column $j$ from a parent matrix $A$. Define $t_{ij}$ to be the number of transversals in $L(i\mid j)$, for some fixed Latin square $L$. We show that $t_{ab}\equiv t_{cd}\bmod2$ for all $a,b,c,d$ and $L$. Also, if $L$ has odd order then the number of transversals of $L$ equals $t_{ab}$ mod 2. We conjecture that $t_{ac} + t_{bc} + t_{ad} + t_{bd} \equiv 0 \bmod 4$ for all $a,b,c,d$. In the course of our investigations we prove several results that could be of interest in other contexts. For example, we show that the number of perfect matchings in a $k$-regular bipartite graph on $2n$ vertices is divisible by $4$ when $n$ is odd and $k\equiv0\bmod 4$. We also show that $${\rm per}\, A(a \mid c)+{\rm per}\, A(b \mid c)+{\rm per}\, A(a \mid d)+{\rm per}\, A(b \mid d) \equiv 0 \bmod 4$$ for all $a,b,c,d$, when $A$ is an integer matrix of odd order with all row and columns sums equal to $k\equiv2\bmod4$

Children's acquisition of science terms: does fast mapping work?

About the book: This proceedings contains 99 selected papers from the 8th Conference of the International Association for the Study of Child Language (IASCL) held in Donostia-San Sebastián in the Spanish Basque Country in July 1999. The proceedings includes the plenary addresses by Jean-Paul Bronckart, Brian MacWhinney, and Miquel Siguan. The other 96 papers are organized into sections on bilingualism, discourse, phonology, language disorders, lexicon, morphology, syntax, and signed languages. Several of these sections include symposia with introductions as well as individual papers

The final two redshifts for radio sources from the equatorial BRL sample

Best, Rottgering and Lehnert (1999, 2000a) defined a new sample of powerful radio sources from the Molonglo Reference Catalogue, for which redshifts were compiled or measured for 177 of the 178 objects. For the final object, MRC1059-010 (3C249), the host galaxy is here identified using near-infrared imaging, and the redshift is determined from VLT spectroscopy. For one other object in the sample, MRC0320+053 (4C05.14), the literature redshift has been questioned: new spectroscopic observations of this object are presented, deriving a corrected redshift. With these two results, the spectroscopic completeness of this sample is now 100%. New redshifts are also presented for PKS0742+10 from the Wall & Peacock 2.7 GHz catalogue, and PKS1336+003 from the Parkes Selected Regions. PKS0742+10 shows a strong neutral hydrogen absorption feature in its Lyman-alpha emission profile.Comment: 4 pages. LaTeX. Accepted for publication in MNRA

The International Urban Energy Balance Comparison Project: Initial Results from Phase 2.

Many urban land surface schemes have been developed, incorporating different assumptions about the features of, and processes occurring at, the surface. Here, the first results from Phase 2 of an international comparison are presented. Evaluation is based on analysis of the last 12 months of a 15 month dataset. In general, the schemes have best overall capability to model net all-wave radiation. The models that perform well for one flux do not necessarily perform well for other fluxes. Generally there is better performance for net all wave radiation than sensible heat flux. The degree of complexity included in the models is outlined, and impacts on model performance are discussed in terms of the data made available to modellers at four successive stages

A jet-cloud interaction in 3C34 at redshift z = 0.69

We report the detection of a strong jet-cloud interaction at a distance of 120 kpc from the nucleus of the radio galaxy 3C34, which has redshift z=0.69. Hubble Space Telescope images of the radio galaxy show a long narrow region of blue emission orientated along the radio axis and directed towards a radio hotspot. The William Herschel Telescope has been used to provide long-slit spectroscopic data of this object, and infrared observations made with the United Kingdom InfraRed Telescope have enabled its spectral energy distribution to be modelled. We propose that the aligned emission is associated with a region of massive star-formation, induced by the passage of the radio jet through a galaxy within the cluster surrounding 3C34. A star-formation rate of about 100 solar masses per year is required, similar to the values necessary to produce the alignment effect in high-redshift radio galaxies. The consequences of this result for models of star formation in distant radio galaxies are discussed.Comment: 12 pages including 11 figures, LaTeX. To appear in MNRA