ŁOJASIEWICZ INEQUALITY ON NON-COMPACT DOMAINS AND SINGULARITIES AT INFINITY

We give a version of the Łojasiewicz inequality for the real polynomials on non-compact domains. The inequality takes in account not only distance to a fiber, but also distance to a polar set. It improves the recent results of [D. S. Tiep, H. H. Vui and N. T. Thao, Łojasiewicz inequality for polynomial functions on non-compact domains, Int. J. Math.23(4) (2012), Article ID: 1250033, 28 pp., doi:10.1142/S0129167X12500334], since we consider a distance to a smaller set. Then we use this new version of the inequality to obtain a sufficient condition for the existence of a vanishing component at infinity for real polynomials in several variables.

Igbo adjectives as morphophonologized relatives

Igbo adjectives are semantically, syntactically and morphophonologically derived. Underlyingly, they are relatives that are phonologized into a suppietive form. For this reason they cannot occur in predicative position, unlike adjectives in English. They are in two sets: the relative, polar set, which can be emphasized and further suppleted, and the non-relative, antipodal or taxonomic set, which cannot be emphasized, except perhaps by way of ideophonic periphrasis. Non-emphatic adjectives are also often ambiguous because of their inevitable incorporation of two copulas, one stative and neutral, the other active and cognate. One implication of all this is that 'Adj' is not a primitive syntactic category in Igbo and as such is not needed for its formal description. Another is that on the basis of formal behavioural criteria, a proper census of true adjectives in Igbo can now be taken.