We provide a proof of conjecture made by Richard McIntosh in 1996 on the values Franel integrals, $$\int_0^1((ax))((bx))((cx))((ex))\,dx,$$ where $((x))$ is first periodic Bernoulli function. Secondly, we extend our ideas to prove similar theorem for $$\int_0^1((a_1x))((a_2x))\cdots ((a_{n}x))\,dx.$$ Lastly, further generalization which replaced any particular function with odd index.

The treatment efficacy of advanced breast cancer is still not promising. This study aimed to compare the efficacy and safety of docetaxel/S-1 (DS1) versus docetaxel/capecitabine (DX) as the first-line treatment for advanced breast cancer.From June 2008 to June 2013, 22 patients with advanced breast cancer were treated with the DS1 regimen. Another 26 age- and disease status-matched patients tre...

The intracellular penetration and activity of DX-619 in human polymorphonuclear leukocytes have been evaluated. DX-619 reached intracellular concentrations 10 times higher than the extracellular concentrations reached. Uptake was rapid, reversible, nonsaturable, and affected by environmental temperature, some metabolic inhibitors, and a soluble membrane activator. DX-619 showed intracellular ac...

In the Hilbert space $H:=L_2(\mathbb{R})$, we consider impedance Sturm--Liouville operator $T:H\to H$ generated by differential expression $ -p\frac{d}{dx}{\frac1{p^2}}\frac{d}{dx}p$, where function $p:\mathbb{R}\to\mathbb{R}_+$ is of bounded variation on $\mathbb{R}$ and $\inf_{x\in\mathbb{R}} p(x)>0$. Existence transformation for $T$ its properties are studied.
 paper, suggest an effi...

Limits and rate of convergence for the distribution of search cost under the move-to-front rule. I 2 (t) = Z log(t) 1 e ?x x (log(t=x)) d dx + Z t log t e ?x x (log(t=x)) d dx def = I 21 (t) + I 22 (t) (7.66) Here, the asymptotic behavior of I 21 (t) is determined by I 21 (t) (log(t)) d Z log(t) 1 e ?x x dx (log(t)) d Z 1 1 e ?x x dx; (7.67) and I 21 (t) (log(t= log(t))) d Z log(t) 1 e ?x x dx ...

A multiscale, non-parametric, Bayesian framework for identification of model parameters Motivation Bayesian Paradigm Nonparametric prior Inference Numerical Results Prediction Motivation T (0) = T 0 q(1) = q 0 l = 1 c(x) =?    d dx −c(x) dT dx = 0 T (0) = T 0 q(1) = −c(x) dT dx x=1 = q 0 (1) 2 / 56 A multiscale, non-parametric, Bayesian framework for identification of model parameters Motiva...

For $$p \in (1,N)$$ and $$\Omega \subseteq {\mathbb {R}}^N$$ open, the Beppo-Levi space $${\mathcal {D}}^{1,p}_0(\Omega )$$ is completion of $$C_c^{\infty }(\Omega with respect to norm $$\left[ \int _{\Omega }|\nabla u|^p dx \right] ^ \frac{1}{p}.$$ Using p-capacity, we define a then identify Banach function {H}}(\Omega set all g in $$L^1_{loc}(\Omega that admits following Hardy–Sobolev ty...

BACKGROUND The safe use in biomedicine of semiconductor nanoparticles, also known as quantum dots (QDs), requires a detailed understanding of the biocompatibility and toxicity of QDs in human beings. The biological characteristics and physicochemical properties of QDs entail new challenges regarding the management of potential adverse health effects following exposure. At certain concentrations...

Surface codes are quantum error correcting typically defined on a 2D array of qubits. A [dx, dz] surface code design is being introduced, where dx(dz) represents the distance for bit (phase) correction, motivated by fact that severity flip and phase errors in physical system asymmetric. We present pseudo-threshold threshold values proposed asymmetric channels presence various degrees asymmetry ...

INTRODUCTION The use of chemotherapy in node-negative, (O)Estrogen Receptor (ER)-positive breast cancer has changed significantly since the introduction of Oncotype DX to determine systemic recurrence risk based on tumour genomic signature. AIMS This study aims to METHODS A cohort study was undertaken, including consecutive patients with early node-negative, ER-positive breast cancer diagno...