We study the field theories for pinned elastic systems at equilibrium and at depinning. Their beta functions differ to two loops by novel "anomalous" terms. At equilibrium we find a roughness zeta = 0.208 298 04 epsilon + 0.006 858 epsilon(2) (random bond), zeta = epsilon/3 (random field). At depinning we prove two-loop renormalizability and that random field attracts shorter range disorder. We...

Let $\mathbb{S} \subset \mathbb{C}$ be the circle in plane, and let $\Omega\colon \mathbb{S} \to \mathbb{S}$ an odd bi-Lipschitz map with constant $1+\delta\_\Omega$, where $\delta\_\Omega\geq 0$ is small. Assume also that $\Omega$ twice continuously differentiable. Motivated by a question raised Mattila Preiss, we prove following: If Radon measure $\mu$ has positive lower density finite upper ...

We prove that the spaces $\operatorname{tot}\big(\Gamma(\Lambda^\bullet A^\vee \otimes_R\mathcal{T}_{\operatorname{poly}}^{\bullet}\big)$ and A^\vee)\otimes_R\mathcal{D}_{\operatorname{poly}}^{\bullet}\big)$ associated with a Lie pair $(L,A)$ each carry an $L_\infty$ algebra structure canonical up to isomorphism identity map as linear part. These two serve, respectively, replacements for of for...

You work with a circuit’s transfer function all the time in this course and make extensive use of the logarithmic scale: you are asked to Bode-plot a system’s frequency response in your homework assignments, lab reports, or maybe exams using Matlab, Agilent VEE, or even with bare hands, where the horizontal axis reads Frequency (log-scale). Good or bad, you will continue to see such plots here ...

The simetry of voltages, among other parameters, in to real power networks, is essential for ensuring optimum performances of the electrical systems and a standard quality of the energy. To control this, there are specific electric and electronic relays, which are hardware programmed to survey the symmetrical components of currents and voltages. The paper describe a software method to control t...

To study the expression of globin genes in human cells, human epsilon-globin genes were transferred into a K562 cell line, Bos, which synthesizes very low amounts of epsilon-globin mRNA. A plasmid (pSV2neo-epsilon) containing a complete epsilon-globin gene and 2 kilobases (kb) of 5' flanking DNA as well as a neomycin-resistance gene and a simian virus 40 origin of replication was transfected in...