Let I be a homogeneous ideal in polynomial ring over field. $$I^{(n)}$$ the n-th symbolic power of I. Motivated by results about ordinary powers I, we study asymptotic behavior regularity function $${{\,\mathrm{reg}\,}}(I^{(n)})$$ and maximal generating degree $$\omega (I^{(n)})$$ , when is monomial ideal. It known that both functions are eventually quasi-linear. We show that, addition, sequenc...

Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x 1 ,. .. , x n ] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi's theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and He...

Let R be a polynomial ring over a field of dimension n. Let m be the maximal homogeneous ideal of R. Let I be a complete intersection homogeneous ideal of R minimally generated by polynomials of degrees d1, d2, . . . , dn. F. S. Macaulay showed that for all integers i = 0, 1, . . . , δ + 1, I : m = I + m where δ = d1 + d2 + . . .+ dn − n. We provide a modern proof of a generalization of this re...

The notions of $${{\mathcal {N}}}$$ -ideal types $$(\in , \in )$$ and \! \vee \, {q})$$ soft $${\mathcal N}_{\in }$$ -set, {N}}}_{q}$$ {N}}}_{\in {q}}$$ -subalgebra in BCK/BCI-algebra are introduced, several properties investigated. Characterizations N}$$ discussed.

Due to its constantly growing incidence, obesity is an increasingly serious social and medical problem. Available data on the use of novel oral anticoagulants in morbidly obese and obese patients are very limited. However, we tried to summarize the available knowledge on the use of anticoagulants in this subpopulation of patients in everyday clinical practice. Studies on the clinical use of ant...

OBJECTIVE To evaluate the current and ideal body weight perceptions of schoolchildren in relation to their actual body weight and socio-economic status (SES). DESIGN Baseline evaluation of schoolchildren from January 2008 to April 2008 as part of a 3-year longitudinal study. SETTING City and non-city locations, Karnataka State, South India. SUBJECTS Schoolchildren (n 1877) aged between 8 ...

Although the burgeoning discipline of welfare economics is based on essentially utilititarian principles, the foundations of utilitarianism have received little attention in recent years. This paper seeks to reopen the debate by drawing a distinction between Harsanyi’s two defences of utilitarianism, labeling the first a teleological or ideal-observer theory, and the second a nonteleological th...

Two studies assessed the goodness of fit of ideal, quasi-, and noncircumplex models of interpersonal traits. Study 1 (N = 132) represents a secondary data analysis using J.S. Wiggins's {1979) original Interpersonal Adjectives Scales (IAS) and reported by J.S. Wiggins, J.H. Steiger, and L. Gaelick (1981). Study 2 (N = 401) represents a primary data analysis using Wiggins's revised IAS (J.S. Wigg...