This is the first paper in a two-part series containing some results on dimension estimates for $C^1$ iterated function systems and repellers. In this part, we prove that the upper box-counting dimension of the attractor of any $C^1$ iterated function system (IFS) on ${\Bbb R}^d$ is bounded above by its singularity dimension, and the upper packing dimension of any ergodic invariant measure associated with this IFS is bounded above by its Lyapunov dimension. Similar results are obtained for the repellers for $C^1$ expanding maps on Riemannian manifolds.

This is the second part of our study on the dimension theory of $C^1$ iterated function systems (IFSs) and repellers on $\mathbb {R}^d$. In the first part [D.-J. Feng and K. Simon. Dimension estimates for $C^1$ iterated function systems and repellers. Part I. Preprint, 2020, arXiv:2007.15320], we proved that the upper box-counting dimension of the attractor of every $C^1$ IFS on ${\Bbb R}^d$ is bounded above by its singularity dimension, and the upper packing dimension of every ergodic invariant measure associated with this IFS is bounded above by its Lyapunov dimension. Here we introduce a generalized transversality condition (GTC) for parameterized families of $C^1$ IFSs, and show that if the GTC is satisfied, then the dimensions of the IFS attractor and of the ergodic invariant measures are given by these upper bounds for almost every (in an appropriate sense) parameter. Moreover, we verify the GTC for some parameterized families of $C^1$ IFSs on ${\Bbb R}^d$.

Let $\mathbf{M}=(M_{1},\ldots ,M_{k})$ be a tuple of real $d\times d$ matrices. Under certain irreducibility assumptions, we give checkable criteria for deciding whether $\mathbf{M}$ possesses the following property: there exist two constants $\unicode[STIX]{x1D706}\in \mathbb{R}$ and $C>0$ such that for any $n\in \mathbb{N}$ and any $i_{1},\ldots ,i_{n}\in \{1,\ldots ,k\}$, either $M_{i_{1}}\cdots M_{i_{n}}=\mathbf{0}$ or $C^{-1}e^{\unicode[STIX]{x1D706}n}\leq \Vert M_{i_{1}}\cdots M_{i_{n}}\Vert \leq Ce^{\unicode[STIX]{x1D706}n}$, where $\Vert \cdot \Vert$ is a matrix norm. The proof is based on symbolic dynamics and the thermodynamic formalism for matrix products. As applications, we are able to check the absolute continuity of a class of overlapping self-similar measures on $\mathbb{R}$, the absolute continuity of certain self-affine measures in $\mathbb{R}^{d}$ and the dimensional regularity of a class of sofic affine-invariant sets in the plane.

The present study aimed to investigate the effect of maternal malnutrition on offspring glucose tolerance and the epigenetic mechanisms involved. In total, twelve primiparous Landrace×Yorkshire gilts were fed rations providing either 100 % (control (CON)) or 75 % (undernutrition (UN)) nutritional requirements according to the National Research Council recommendations, throughout gestation. Muscle samples of offspring were collected at birth (dpn1), weaning (dpn28) and adulthood (dpn189). Compared with CON pigs, UN pigs showed lower serum glucose concentrations at birth, but showed higher serum glucose and insulin concentrations as well as increased area under the blood glucose curve during intravenous glucose tolerance test at dpn189 (P<0·05). Compared with CON pigs, GLUT-4 gene and protein expressions were decreased at dpn1 and dpn189 in the muscle of UN pigs, which was accompanied by increased methylation at the GLUT4 promoter (P<0·05). These alterations in methylation concurred with increased mRNA levels of DNA methyltransferase (DNMT) 1 at dpn1 and dpn28, DNMT3a at dpn189 and DNMT3b at dpn1 in UN pigs compared with CON pigs (P<0·05). Interestingly, although the average methylation levels at the muscle GLUT4 promoter were decreased at dpn189 compared with dpn1 in pigs exposed to a poor maternal diet (P<0·05), the methylation differences in individual CpG sites were more pronounced with age. Our results indicate that in utero undernutrition persists to silence muscle GLUT4 likely through DNA methylation during the ageing process, which may lead to the amplification of age-associated glucose intolerance.

A study of 7,388 consecutive patients after hepatic resection between 2011 and 2012 identified hepatolithiasis, cirrhosis, and intraoperative blood transfusion as the only independent risk factors of both incisional and organ/space surgical site infection (SSI). Patients with these conditions should be cared for with caution to lower SSI rates.

We study the decay of μ(B(x,r)∩C)/μ(B(x,r)) as r ↓ 0 for different kinds of measures μ on ℝn and various cones C around x. As an application, we provide sufficient conditions that imply that the local dimensions can be calculated via cones almost everywhere.

The paper is devoted to the study of the multifractal structure of disintegrations of Gibbs measures and conditional (random) Birkhoff averages. Our approach is based on the relativized thermodynamic formalism, convex analysis and, especially, the delicate constructions of Moran-like subsets of level sets.

To identify Porcine haemagglutinating encephalomyelitis virus (HEV) 67N receptor in porcine kidney (PK) cell membranes, the S1 protein of HEV was expressed in Pichia pastoris and purified by Ni2+ affinity chromatograph. Polyclonal antibodies to HEV were prepared by immunizing rabbits by injecting the purified S1 protein four times. After SDS–polyacrylamide gel electrophoresis (SDS–PAGE), the PK cell membrane proteins were transferred on to nitrocellulose membrane. A virus overlay protein binding assay (VOPBA) was performed using the recombinant S1 protein to identify the protein binding receptor, HEV-S1. The result showed that HEV-S1 protein bound to one band (about 90 kDa) in PK cell membranes. This result is very important for the study of the pathogenic mechanism of HEV.

We prove that for any self-conformal measures, without any separation conditions, the multifractal formalism partially holds. The result follows by establishing certain Gibbs properties for self-conformal measures.

For a given expanding d-fold covering transformation of the one-dimensional torus, the notion of weak Gibbs measure is defined by a natural generalization of the classical Gibbs property. For these measures, we prove that the singularity spectrum and the $L^q$-spectrum form a Legendre transform pair. The main difficulty comes from the possible existence of first-order phase transition points, that is, points where the $L^q$-spectrum is not differentiable. We give examples of weak Gibbs measure with phase transition, including the so-called Erdös measure.

Let $\mu$ be the self-similar measure for a linear function system $S_jx=\rho x+b_j$ ($j=1,2,\ldots,m$) on the real line with the probability weight $\{p_j\}_{j=1}^m$. Under the condition that $\{S_j\}_{j=1}^m$ satisfies the finite type condition, the $L^q$-spectrum $\tau(q)$ of $\mu$ is shown to be differentiable on $(0,\infty)$; as an application, $\mu$ is exact dimensional and satisfies the multifractal formalism.

Let ([sum ]A, T) be a topologically mixing subshift of finite type on an alphabet consisting of m symbols and let Φ:[sum ]A → Rd be a continuous function. Denote by σΦ(x) the ergodic limit limn→∞n−1 [sum ]n−1j=0 Φ(Tjx) when the limit exists. Possible ergodic limits are just mean values ∫ Φdμ for all T-invariant measures. For any possible ergodic limit α, the following variational formula is proved:

[formula here]

where hμ denotes the entropy of μ and htop denotes topological entropy. It is also proved that unless all points have the same ergodic limit, then the set of points whose ergodic limit does not exist has the same topological entropy as the whole space [sum ]A

Let K be a compact subset of ℝn, 0[les ]s[les ]n. Let Ps0, [Pscr]s denote s-dimensional packing premeasure and measure, respectively. We discuss in this paper the relation between Ps0 and [Pscr]s. We prove: if Ps0(K)<∞, then [Pscr]s(K) = Ps0(K); and if Ps0(K) = ∞, then for any ε>0, there exists a compact subset F of K such that [Pscr]s(F) = Ps0(F) and [Pscr]s(F)[ges ][Pscr]s(K)−ε.

For modern management and full resource sharing among libraries and scientific departments both in Chinese and worldwide observatories, we established the computer system of library management and information retrieval during the period 1984-1987.

The system is composed of ten component sub-systems:

• 1. Book ordering system. This system can produce orders for books and periodicals, balance accounts, produce statistics as well as claims for outstanding book orders.

• 2. Book cataloguing system. This system can catalogue books under certain rules while appending new records of books to the databases. It can also produce catalogue cards and produce written reports about the new books.

• 3. Book retrieval system has the ability to search for a specific book in several ways.

• 4. Book lending or circulation system. This system is a complete circulation system; including book lending, renewals, waiting lists, and recall of borrowed books.

• 5. Periodical management system. This system is in charge of processing of periodicals and magazines in the library, including cataloguing, management, and lending.

• 6. Scientific information retrieval system. One can retrieve scientific information by keywords or in many other ways.

• 7. Internal material booking system. It can make orders of internal materials, claims for materials outstanding and make exchanges with other observatories and institutions both in or outside the country.

• 8. Internal material management system. It can do the work that is analogous to that done with books and periodicals.

• 9. Information relationship system. It handles exchanges of information between institutions. Computer system of library management ... at Shaanxl 183

• 10. Scientific information network management system. It manages affairs within a certain information network.