THERMODYNAMIC FORMALISM FOR SUBADDITIVE SEQUENCE OF DISCONTINUOUS FUNCTIONS

The topological pressure for subadditive sequence of discontinuous functions is defined on any invariant subset having a nested family of subsets in the compact metric space. Two subadditive variational principles associated with two different relatively weak conditions are developed for the defined topological pressure. As an application, we give an example on systems with nonzero Lyapunov exponents.

OVERCONVERGENCE AND ZEROS OF SEQUENCES OF RATIONAL FUNCTIONS

In the present paper we consider sequences of rational functions with a bounded number or free poles con- verging uniformly with a maximum geometric rate to a holomorphic function on a regular set,and we examine the limiting distribution of the Zeros and its relations with the phenomenon of overconvergence.Our results further extend the well known classical theory of overconvergence and the zeros of sections of Taylor series.

On some difference sequence spaces defined by a sequence of Orlicz functions

The idea of difference sequence spaces was introduced in （Klzmaz, 1981） and this concept was generalized in （Et and Colak, 1995）. In this paper we define some difference sequence spaces by a sequence of Orlicz functions and establish some inclusion relations.

Two Sequences of Operator Monotone Functions and Strictly Chaotic Order

In this paper we introduce two sequences of operator functions and their dualfunctions： fk（t） = （flogt）k-（t-1）k/log^k＋2t （k = 1,2,...）, gk（t） = （t-1）k-logkt /log^k＋1t （k = 1,2,...） and fk（t）tklog^k＋1t/（tlogt）k-（t-1）^k（k=1,2…）,gk（t）=t^klog^k＋1t/（t-1）^k-log^kt（k=1,2…）defined onWe find that they are all operator monotone functions with respect to the strictly chaoticorder and some ordinary orders among positive invertible operators. Indeed, we extend theresults of the operator monotone function tlogt-t＋1/log^2t which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics[1].

A SEQUENCE SPACE DEFINED BY ORLICZ FUNCTIONS

In this paper we define a sequence space using Orlicz functions. We give certain properties and inclusion relations between known sequence spaces and new sequence space.

PN code generator based on generalized Bent function for SW/SFH System

Generalized Bent function and generalized Bent function sequences are introduced in this paper.The main performance or these sequences used as SW/SFH(Short Wave/Slow Frequency Hopping) code are studied. And the hardware circuit and the soflware program flow chart of the SW/SFH PN code generator are also given,which is based on generalized Bent function sequence generator by using a single chip mlcrocomputer.

Normal family and the sequence of omitted functions

Let {fn} be a sequence of meromorphic functions on a plane domain D, whose zeros and poles have multiplicity at least 3. Let {hn} be a sequence of meromorphic functions on D, whose poles are multiple, such that {hn} converges locally uniformly in the spherical metric to a function h which is meromorphic and zero-free on D.If fn≠hn, then {fn} is normal on D.

Normality Concerning the Sequence of Functions

Let {fn} be a sequence of functions meromorphic in a domain D, let {hn} be a sequence of holomorphic functions in D, such that hn（z） x h（z）, where h（z） 0 is holomorphic in D, and let k be a positive integer. If for each n ∈ N＋, fn（z） ≠ 0 and fn（k）（z） - hn（z） has at most k distinct zeros （ignoring multiplicity） in D, then {fn} is normal in D.

Genome-wide mining, characterization, and development of microsatellite markers in Marsupenaeus japonicus by genome survey sequencing

The kuruma prawn, Marsupenaeus japonicus, is one of the most cultivated and consumed species of shrimp. However, very few molecular genetic/genomic resources are publically available for it. Thus, the characterization and distribution of simple sequence repeats(SSRs) remains ambiguous and the use of SSR markers in genomic studies and marker-assisted selection is limited. The goal of this study is to characterize and develop genome-wide SSR markers in M. japonicus by genome survey sequencing for application in comparative genomics and breeding. A total of 326 945 perfect SSRs were identified, among which dinucleotide repeats were the most frequent class(44.08%), followed by mononucleotides(29.67%), trinucleotides(18.96%), tetranucleotides(5.66%), hexanucleotides(1.07%), and pentanucleotides(0.56%). In total, 151 541 SSR loci primers were successfully designed. A subset of 30 SSR primer pairs were synthesized and tested in 42 individuals from a wild population, of which 27 loci(90.0%) were successfully amplified with specific products and 24(80.0%) were polymorphic. For the amplified polymorphic loci, the alleles ranged from 5 to 17(with an average of 9.63), and the average PIC value was 0.796. A total of 58 256 SSR-containing sequences had significant Gene Ontology annotation; these are good functional molecular marker candidates for association studies and comparative genomic analysis. The newly identified SSRs significantly contribute to the M. japonicus genomic resources and will facilitate a number of genetic and genomic studies, including high density linkage mapping, genome-wide association analysis, marker-aided selection, comparative genomics analysis, population genetics, and evolution.

Fundamental Trackability Problems for Iterative Learning Control

Generally, the classic iterative learning control(ILC)methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory,whereas they ignore a fundamental problem of ILC: whether the specified trajectory is trackable, or equivalently, whether there exist some inputs for the repetitive systems under consideration to generate the specified trajectory? The current paper contributes to dealing with this problem. Not only is a concept of trackability introduced formally for any specified trajectory in ILC, but also some related trackability criteria are established. Further, the relation between the trackability and the perfect tracking tasks for ILC is bridged, based on which a new convergence analysis approach is developed for ILC by leveraging properties of a functional Cauchy sequence(FCS). Simulation examples are given to verify the effectiveness of the presented trackability criteria and FCS-induced convergence analysis method for ILC.

Studies on Kinetics of Chlorination Reaction of Polyethylene

Through kinetic method, the reaction mechanism and the rate equations of chlorination of polyethylene are suggested in this paper. The rate of chlorination is second order with respect to the concentration of methylene remained and chlorine, respectively. Apparent changes in crystallinity during chlorination processes were determinated by differential scanning calorimetry(DSC). The mathematical model relating crystallinety with kinetic parameters and function of sequence length distribution are derived.

The Spectrum Sequences of Periodic Frame Multiresolution Analysis

The periodic multiresolution analysis （PMRA） and the periodic frame multiresolution analysis （PFMRA） provide a general recipe for the construction of periodic wavelets and periodic wavelet frames, respectively. This paper addresses PFMRAs by the introduction of the notion of spectrum sequence. In terms of spectrum sequences, the scaling function sequences generating a normalized PFMRA are characterized; a characterization of the spectrum sequences of PFMRAs is obtained, which provides a method to construct PFMRAs since its proof is constructive; a necessary and sufficient condition for a PFMRA to admit a single wavelet frame sequence is obtained; a necessary and sufficient condition for a PFMRA to be contained in a given PMRA is also obtained. What is more, it is proved that an arbitrary PFMRA must be contained in some PMRA. In the meanwhile, some examples are provided to illustrate the general theory.

On the Seneta Sequences

In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc.

Characterization of Periodic Multiresolution Analysis and an Application

In this paper, we study the properties of periodic multiresolution analysis, and present a complete characterization of the scaling function sequence, which enables us to construct a new scaling function sequence from a given one. An application of the main results is given at the end.

The critical case for a Berestycki-Lions theorem

We consider the existence of the ground states solutions to the following Schrodinger equation -△u ＋ V（x）u = f（u）, u ∈ H1（RN）, where N ） 3 and f has critical growth. We generalize an earlier theorem due to Berestycki and Lions about tile subcritical case to the current critical case.