OBJECTIVE Missing data are a pervasive problem, often leading to bias in complete records analysis (CRA). Multiple imputation (MI) via chained equations is one solution, but its use in the presence of interactions is not straightforward. STUDY DESIGN AND SETTING We simulated data with outcome Y dependent on binary explanatory variables X and Z and their interaction XZ. Six scenarios were simu...

It is well known that some of the most basic properties of words, like the commutativity (xy = yx) and the conjugacy (xz = zy), can be expressed as solutions of word equations. An important problem is to decide whether or not a given equation on words has a solution. For instance, the equation xmyn = zp has only periodic solutions in a free monoid, that is, if xmyn = zp holds with integers m,n,...

In the present work, we have obtained the equation of state for neutron star matter considering the in uence of the ferromagnetic and antiferromagnetic spin state. We have also investigated the structure of neutron stars. According to our results, the spin asymmetry stiens the equation of state and leads to high mass for the neutron star.

We present a complete description of $2$-dimensional equations that arise as symmetry reductions fourf $3$-dimensional Lax-integrable equations: (1) the universal hierarchy equation~$u_{yy}=u_zu_{xy}-u_yu_{xz}$; (2) 3D rdDym equation $u_{ty}=u_xu_{xy}-u_yu_{xx}$; (3) The basic Veronese web $u_{ty}=u_tu_{xy}-u_yu_{tx}$; (4) Pavlov's $u_{yy}=u_{tx}+u_yu_{xx}-u_xu_{xy}$.

We study totally real number fields that admit a universal quadratic form whose coefficients are rational integers. show Q(5) is the only such field, and among of degrees 3, 4, 5, 7 which have principal codifferent ideal, one Q(ζ7+ζ7−1), over x2+y2+z2+w2+xy+xz+xw universal. Moreover, we prove an upper bound for Pythagoras numbers orders in depends on degree field.