In this note we compute the (uni)versal deformation of two types of mod 3 Galois representations ρ̄ : Gal(Q3/Q3)→ GL2(F3). In the cases considered the (uni)versal ring is not formally smooth over a ring of Witt vectors. The main result is that this ring is an integral domain. This has applications to the local Langlands conjecture. The computations are based on [Bö] but made more explicit.

In this paper, we show that one can associate a pseudoregulus with every scattered linear set of rank 3n in PG(2n − 1, q3). We construct a scattered linear set having a given pseudoregulus as associated pseudoregulus and prove that there are q − 1 different scattered linear sets that have the same associated pseudoregulus. Finally, we give a characterisation of reguli and pseudoreguli in PG(3, ...

Protein structure prediction has always been an important research area in biochemistry. In particular, the prediction of protein secondary structure has been a well-studied research topic. The experimental methods currently used to determine protein structure are accurate, yet costly both in terms of equipment and time. Despite the recent breakthrough of combining multiple sequence alignment i...

We construct N-soliton solutions to the equation called Q3 in the recent Adler-Bobenko-Suris classification. An essential ingredient in the construction is the relationship of (Q3) δ=0 to the equation proposed by Nijhoff, Quispel and Capel in 1983 (the NQC equation). This latter equation has two extra parameters, and depending on their sign choices we get a 4-to-1 relationship from NQC to (Q3) ...

We investigate the homology of a congruence subgroup Γ SL3(Z) with coefficients in Steinberg modules St(Q3) and St(E3), where E is real quadratic field are Q. By Borel-Serre duality, H0(Γ,St(Q3)) isomorphic to H3(Γ,Q). Taking image connecting homomorphism H1(Γ,St(E3)/St(Q3))→H0(Γ,St(Q3)), followed by isomorphism, we obtain naturally defined Hecke-stable subspace H(Γ,E) conjecture that independe...

In PG(2, q3), let π be a subplane of order q that is tangent to `∞. The tangent splash of π is defined to be the set of q2 + 1 points on `∞ that lie on a line of π. This article investigates properties of the tangent splash. We show that all tangent splashes are projectively equivalent, investigate sublines contained in a tangent splash, and consider the structure of a tangent splash in the Bru...

To generate transgenic mice that express Cre-recombinase exclusively in the megakaryocytic lineage, we modified a mouse bacterial artificial chromosome (BAC) clone by homologous recombination and replaced the first exon of the platelet factor 4 (Pf4), also called CXCL4, with a codon-improved Cre cDNA. Several strains expressing the transgene were obtained and one strain, Q3, was studied in deta...

It is important to preprocess high-throughput data generated from microarray or mass spectrometry experiments in order to obtain a successful analysis. Outlier detection is an important preprocessing step. For outlier detection, upper and lower fences (Q3+1.5IQR and Q1 − 1.5IQR) of the differences are often used in statistics, where Q1=lower 25% quantile, Q3=upper 25% quantile, and IQR = Q3 − Q...

Let Uβ be the special Buekenhout-Metz unital in PG(2, q 2) formed by a union of q conics, where q = pe is an odd prime power. It can be shown that the dimension of the binary code of the corresponding unital design Uβ is less than or equal to q3 + 1− q. Baker and Wantz conjectured that equality holds. We prove that the aforementioned dimension is greater than or equal to q3(1− 1 p ) + q 2 p .