The differential spectrum of a ternary power mapping

Postponed access: the file will be available after 2022-03-06A function f(x)from the finite field GF(pn)to itself is said to be differentially δ-uniform when the maximum number of solutions x ∈GF(pn)of f(x +a) −f(x) =bfor any a ∈GF(pn)∗and b ∈GF(pn)is equal to δ. Let p =3and d =3n−3. When n >1is odd, the power mapping f(x) =xdover GF(3n)was proved to be differentially 2-uniform by Helleseth, Rong and Sandberg in 1999. Fo r even n, they showed that the differential uniformity Δfof f(x)satisfies 1 ≤Δf≤5. In this paper, we present more precise results on the differential property of this power mapping. Fo r d =3n−3with even n >2, we show that the power mapping xdover GF(3n)is differentially 4-uniform when n ≡2 (mod 4) and is differentially 5-uniform when n ≡0 (mod 4). Furthermore, we determine the differential spectrum of xdfor any integer n >1.acceptedVersio

The Differential Spectrum of the Power Mapping xpn−3

Let n be a positive integer and p a prime. The power mapping xpn−3 over Fpn has desirable differential properties, and its differential spectra for p=2,3 have been determined. In this paper, for any odd prime p , by investigating certain quadratic character sums and some equations over Fpn , we determine the differential spectrum of xpn−3 with a unified approach. The obtained result shows that for any given odd prime p , the differential spectrum can be expressed explicitly in terms of n . Compared with previous results, a special elliptic curve over Fp plays an important role in our computation for the general case p≥5.acceptedVersio

Editor\u27s Notes, Chiba Medical Journal 90-1

Multiple sequence alignment of deduced amino acid sequences of 25 wheat annexin genes with rice annexin OsAnn2 (Os05g31760) obtained by ClustalW. (PDF 212 kb

Sphingosine Kinase 1 Regulates the Akt/FOXO3a/Bim Pathway and Contributes to Apoptosis Resistance in Glioma Cells

The aim of this study was to investigate the mechanism through which Sphingosine kinase-1 (SPHK1) exerts its anti-apoptosis activity in glioma cancer cells. We here report that dysregulation of SPHK1 alters the sensitivity of glioma to apoptosis both in vitro and in vivo. Further mechanistic study examined the expression of Bcl-2 family members, including Bcl-2, Mcl-1, Bax and Bim, in SPHK1-overexpressing glioma cells and revealed that only pro-apoptotic Bim was downregulated by SPHK1. Moreover, the transcriptional level of Bim was also altered by SPHK1 in glioma cells. We next confirmed the correlation between SPHK1 and Bim expression in primary glioma specimens. Importantly, increasing SPHK1 expression in glioma cells markedly elevated Akt activity and phosphorylated inactivation of FOXO3a, which led to downregulation of Bim. A pharmacological approach showed that these effects of SPHK1 were dependent on phosphatidylinositol 3-kinase (PI3K). Furthermore, effects of SPHK1 on Akt/FOXO3a/Bim pathway could be reversed by SPHK1 specific RNA interference or SPHK1 inhibitor. Collectively, our results indicate that regulation of the Akt/FOXO3a/Bim pathway may be a novel mechanism by which SPHK1 protects glioma cells from apoptosis, thereby involved in glioma tumorigenesis