Ferroelectric properties of a triphenylene derivative with polar functional groups in the crystalline state
نویسندگان
چکیده
منابع مشابه
extensions of some polynomial inequalities to the polar derivative
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15 صفحه اولOn the polar derivative of a polynomial
For a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, Dewan et al [K. K. Dewan, N. Singh and A. Mir, Extension of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). In this paper we improve and extend the above inequality. Our result generalizes certai...
متن کاملInequalities for the polar derivative of a polynomial with $S$-fold zeros at the origin
Let $p(z)$ be a polynomial of degree $n$ and for a complex number $alpha$, let $D_{alpha}p(z)=np(z)+(alpha-z)p'(z)$ denote the polar derivative of the polynomial p(z) with respect to $alpha$. Dewan et al proved that if $p(z)$ has all its zeros in $|z| leq k, (kleq 1),$ with $s$-fold zeros at the origin then for every $alphainmathbb{C}$ with $|alpha|geq k$, begin{align*} max_{|z|=...
متن کاملon the polar derivative of a polynomial
for a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, dewan et al [k. k. dewan, n. singh and a. mir, extension of some polynomial inequalities to the polar derivative, j. math. anal. appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). in this paper we improve and extend the above inequality. our result generalizes certai...
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ژورنال
عنوان ژورنال: Physical Review B
سال: 2004
ISSN: 1098-0121,1550-235X
DOI: 10.1103/physrevb.69.212201