Given a formal power series f(z) ∈ C[[z]] we define, for any positive integer r, its rth Witt transform, W (r) f , by W (r) f (z) = 1 r ∑ d|r μ(d)f(z d)r/d, where μ denotes the Möbius function. The Witt transform generalizes the necklace polynomials, M(α;n), that occur in the cyclotomic identity 1 1− αy = ∞

In this note we present rth-order kernel density derivative estimators using canonical higher-order kernels. These canonical rescalings uncouple the choice of kernel and scale factor. This approach is useful for selection of the order of the kernel in a data-driven procedure as well as for visual comparison of kernel estimates. 1991 Mathematics Subject Classification 62G07.

Esaki, Takanori, Hideyo Suzuki, Michelle Cook, Kazuaki Shimoji, Sheue-Yann Cheng, Louis Sokoloff, and Jacques Nunez. Cardiac glucose utilization in mice with mutated and -thyroid hormone receptors. Am J Physiol Endocrinol Metab 287: E1149–E1153, 2004. First published August 10, 2004; doi:10.1152/ajpendo.00078. 2004.—Abnormal thyroid function is usually associated with altered cardiac function. ...

Sebagai ibukota Kabupaten Banyumas, pertumbungan dan perkembangan Kota Purwokerto cukup pesat dalam beberapa dekade terakhir. Pengalihan fungsi lahan menjadi permukiman bangunan untuk lain salah satu akibat dari adanya pembangunan di Purwokerto. Pertambahan jumlah penduduk juga mengakibatkan pengalihan semakin tinggi. Hal ini menyebabkan terjadinya penurunan ketersediaan Ruang Terbuka Hijau (RT...

CONTEXT Maternal hypothyroidism and hyperthyroidism have deleterious effects on the outcome of pregnancy. While the effects of thyroid hormone (TH) deprivation on the fetus, independently from that on the mother, can be studied in infants with congenital hypothyroidism, this is not the case in those with fetal thyrotoxicosis. OBJECTIVE To study the effects of TH excess on fetuses carried by m...

Bone development is extremely sensitive to alterations in thyroid status. Recently, we analyzed the skeletal phenotypes of mice with the dominant negative resistance to thyroid hormone (RTH) mutation PV targeted to either the thyroid hormone receptor (TR) alpha1 or beta gene. This perspective summarizes our findings to date and explores the wider implications for thyroid status and T3 target ge...

The rth Faber polynomial of the Laurent series f(t) = t + f0 + f1/t + f2/t + · · · is the unique polynomial Fr(u) of degree r in u such that Fr(f) = tr + negative powers of t. We apply Faber polynomials, which were originally used to study univalent functions, to lattice path enumeration.

We present generalisations of several MacWilliams type identities, including those by Kløve and Shiromoto, and of the theorems of Greene and Barg that describe how the Tutte polynomial of the vector matroid of a linear code determines the rth support weight enumerators of the code. One of our main tools is a generalisation of a decomposition theorem due to Brylawski.

The weight of a code is the number of coordinate positions where no codeword is zero. The rth minimum weight dr is the least weight of an r-dimensional subcode. Wei and Yang conjectured a formula for the minimum weights of some product codes. The conjecture is proved in two di erent ways, each with interesting side-results.

A necessary and sufficient condit ion is presented for the normalized asymptotic rth power distortion of a mismatched multidimensional quantizer to converge to a certtin opt imum constant known as Bennett’s integral. The dimensionality of our results is al lowed to approach infinity in order to make some universal source coding compar isons to quantization theory.