A note on the (h,q)-Zeta type function with weight alpha

The objective of this paper is to derive symmetric property of (h,q)-Zeta function with weight alpha. By using this property, we give some interesting identities for (h,q)-Genocchi polynomials with weight alpha. As a result, our applications possess a number of interesting property which we state in this paper.Comment: 7 page

A note on q-Bernstein polynomials

In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.Comment: 13 page

New identities involving q-Euler polynomials of higher order

In this paper we give new identities involving q-Euler polynomials of higher order.Comment: 11 page

Identities involving values of Bernstein, q-Bernoulli and q-Euler polynomials

In this paper we give some relation involving values of q-Bernoulli, q-Euler and Bernstein polynomials. From these relations, we obtain some interesting identities on the q-Bernoulli, q-Euler and Bernstein polynomials.Comment: 12 page

Quantitative Analysis of BTF3, HINT1, NDRG1 and ODC1 Protein Over-Expression in Human Prostate Cancer Tissue

Prostate carcinoma is the most common cancer in men with few, quantifiable, biomarkers. Prostate cancer biomarker discovery has been hampered due to subjective analysis of protein expression in tissue sections. An unbiased, quantitative immunohistochemical approach provided here, for the diagnosis and stratification of prostate cancer could overcome this problem. Antibodies against four proteins BTF3, HINT1, NDRG1 and ODC1 were used in a prostate tissue array (> 500 individual tissue cores from 82 patients, 41 case pairs matched with one patient in each pair had biochemical recurrence). Protein expression, quantified in an unbiased manner using an automated analysis protocol in ImageJ software, was increased in malignant vs non-malignant prostate (by 2-2.5 fold, p<0.0001). Operating characteristics indicate sensitivity in the range of 0.68 to 0.74; combination of markers in a logistic regression model demonstrates further improvement in diagnostic power. Triple-labeled immunofluorescence (BTF3, HINT1 and NDRG1) in tissue array showed a significant (p<0.02) change in co-localization coefficients for BTF3 and NDRG1 co-expression in biochemical relapse vs non-relapse cancer epithelium. BTF3, HINT1, NDRG1 and ODC1 could be developed as epithelial specific biomarkers for tissue based diagnosis and stratification of prostate cancer

Commutator subgroups of the extended Hecke groups Hˉ(λq)\bar{H}(\lambda_q)

summary:Hecke groups $H(\lambda _q)$ are the discrete subgroups of ${\mathrm PSL}(2,\mathbb{R})$ generated by $S(z)=-(z+\lambda _q)^{-1}$ and $T(z)=-\frac{1}{z}$. The commutator subgroup of $H$($\lambda _q)$, denoted by $H^{\prime }(\lambda _q)$, is studied in [2]. It was shown that $H^{\prime }(\lambda _q)$ is a free group of rank $q-1$. Here the extended Hecke groups $\bar{H}(\lambda _q)$, obtained by adjoining $R_1(z)=1/\bar{z}$ to the generators of $H(\lambda _q)$, are considered. The commutator subgroup of $\bar{H}(\lambda _q)$ is shown to be a free product of two finite cyclic groups. Also it is interesting to note that while in the $H(\lambda _q)$ case, the index of $H^{\prime }(\lambda _q)$ is changed by $q$, in the case of $\bar{H}(\lambda _q)$, this number is either 4 for $q$ odd or 8 for $q$ even