The catalytic core of Escherichia coli DNA polymerase III holoenzyme contains three subunits: alpha, epsilon, and theta. The alpha subunit contains the polymerase, and the epsilon subunit contains the exonucleolytic proofreading function. The small (8-kDa) theta subunit binds only to epsilon. Its function is not well understood, although it was shown to exert a small stabilizing effect on the e...

We construct a function on the orbifold fundamental group of the moduli space of smooth theta divisors, which we call the Meyer function for smooth theta divisors. In the construction, we use the adiabatic limits of the η-invariants of the mapping torus of theta divisors. We shall prove that the Meyer function for smooth theta divisors cobounds the signature cocycle, and we determine the values...

Given a supercritical branching random walk $$\{Z_n\}_{n\ge 0}$$ on $${\mathbb {R}}$$ , let $$Z_n(A)$$ be the number of particles located in set $$A\subset {\mathbb at generation n. It is known from Biggins (J Appl Probab 14:630–636, 1977) that under some mild conditions, for $$\theta \in [0,1)$$ $$n^{-1}\log Z_n([\theta x^* n,\infty ))$$ converges almost surely to $$\log \left( {E}}[Z_1({\math...

Dilation theory is a paradigm for studying operators by way of exhibiting an operator as compression another which in some sense well behaved. For example, every contraction can be dilated to (i.e., of) unitary operator, and on this simple fact penetrating non-normal has been developed. In the first part survey, I will leisurely review key classical results dilation single or several commuting ...

Let $(X, \tau)$ and $(Y, \sigma)$ be topological spaces in which no separation axioms are assumed, unless explicitly stated if $\mathcal{I}$ is an ideal on $X$.Given a multifunction $F\colon (X, \tau)\rightarrow (Y, \sigma)$, $\alpha,\beta$ operators \tau)$, $\theta,\delta$ proper $X$. We introduce study upper lower $(\alpha, \beta,\theta,\delta,\mathcal{I})$-continuous multifunctions.A said to...

We investigate the quasinormal modes (QNMs) of scalar field coupled to Einstein's tensor in non-commutative geometry inspired black hole spacetime. It is found that lapse function metric can be represented by a Kummer's confluent hypergeometric function, which effectively solve problem numerical results QNMs are sensitive model parameters and make values more reliable. careful analysis QNM freq...

It is well known that the convergence rate of the expectation-maximization (EM) algorithm can be faster than those of convention first-order iterative algorithms when the overlap in the given mixture is small. But this argument has not been mathematically proved yet. This article studies this problem asymptotically in the setting of gaussian mixtures under the theoretical framework of Xu and Jo...

In this study, the second harmonic generation (SHG) response to polarization and subsequent data analysis is used to discriminate, in the same image, different SHG source architectures with pixel resolution. This is demonstrated in a mammalian tissue containing both skeletal muscle and fibrilar collagen. The SHG intensity variation with the input polarization (PSHG) is fitted pixel by pixel in ...

We develop an exact simple random variate generator for the theta distribution, which occurs as the limit distribution of the height of nearly all models of uniform random trees. Even though the density is only known as an infinite sum of functions, our algorithm does not require any summation. The properties of the theta distribution with distribution function F(x)= ~ (1-2j2x2)e-J2x2 j~-(x3 oo...

In the present explorative experimental study, we examined the diversity of electroencephalographic (EEG) short-term spectral patterns (SPs) within a broad frequency band (1.5-30Hz) for healthy adult subjects during closed eyes and open eyes resting conditions. The types of EEG SPs were assessed by counting all identical SPs with peaks in the same frequency bins from the pools of SPs, which wer...