A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. Let dr be the least integer such that for all n > dr there exist r pairwise orthogonal diagonal Latin squares of order n. In a previous paper Wallis and Zhu gave several bounds on the dr. In this paper we shall present some constructions of pairwise orthogonal diagonal Latin squares and conseq...

We show that a knowledge of diagonal partons at a low scale is sufficient to determine the off-diagonal (or skewed) distributions at a higher scale, to a good degree of accuracy. We quantify this observation by presenting results for the evolution of off-diagonal distributions from a variety of different inputs.

In many countries of moderate to high seismicity, reinforced concrete (RC) core walls are used as lateral bracing systems in midto high-rise buildings where they typically accommodate lift shafts or stair cases. Unlike planar walls which provide horizontal strength and stiffness mainly in the in-plane direction of the wall, core walls provide bidirectional strength and stiffness. This feature c...

A matrix D is diagonal if all its off-diagonal entries are zero. If D is diagonal, then its eigenvalues are the diagonal entries, and the characteristic polynomial of D is fD(x) = ∏i=1(x−dii), where dii is the (i, i) diagonal entry of D. A matrix A is diagonalisable if there is an invertible matrix Q such that QAQ−1 is diagonal. Note that A and QAQ−1 always have the same eigenvalues and the sam...

Abstract This study investigates the seismic performance of a composite structure comprising cold-formed steel and high-strength concrete. Four short shear walls composed concrete, namely, one specimen without diagonal bracing, with angle-steel two lattice were designed for testing their low cyclic loading. The cracking load, ultimate displacement, maximum horizontal bearing capacity, failure p...

We shall show that any two quadrangulations on the sphere with n vertices can be transformed into each other by at most 6n− 32 diagonal slides and rotations, up to homeomorphism, if n ≥ 9.

A considerable number of studies for VIV under the uniform flow have been performed. However, research on VIV under shear flow is scarce. An experiment for VIV under the shear flow with the same shear parameter at the two different Reynolds numbers was conducted in a deep-water offshore basin. Various measurements were obtained by the fiber bragg grating strain sensors. Experimental data were a...

PURPOSE We propose an absolute quantitation method for metabolites with strongly coupled spin systems using localized 2-dimensional (2D) constant-time correlation spectroscopy (CT-COSY). We also develop two methods for improving the quality of in vivo CT-COSY spectra. METHODS We substituted an image selected in vivo spectroscopy (ISIS) pulse for a 180° slice pulse in the CT-COSY module to dec...