The aim of the present paper is to investigate the existence of solutions to functional differential inclusions with infinite delay in Banach spaces. A relevant set of phase space axioms is proposed. The main tools used in this paper are certain fixed point theorems based on the setcontraction theory.
The characterization of long-range correlations and fractal properties of DNA sequences has proved to be adifficult though rewarding task mainly due to the mosaic character of DNA consisting of many patches of various lengthswith different nucleotide constitutions.In this paper we investigate statistical correlations among different positions in DNAsequences using the two-dimensional DNA walk.The root-mean-square fluctuation F(l)is described by a power law.Theautocorrelation function C(l),which is used to measure the linear dependence and periodicity,exists a power law ofC(l)-l^(-μ).We also calculate the mean-square distancealong the DNA chain,and it may be expressed as-l^(?)with 2>γ>1.Our investigations can provide some insights into long-range correlations in DNA sequences.
In protein molecules each residue has a different ability to form contacts.In this paper,we calculated the number of contacts per residue and investigated the distribution of residue-residue contacts from 495 globular protein molecules using Contacts of Structural Units(CSU)software.It was found that the probability P(n)of amino acid residues having n pairs of contacts in all contacts fits Gaussian distribution very well.The distribution function of residue-residue contacts can be expressed as:P(n)=P_0+aexp[-b(n-n_c)~2].In our calculation,P_0=-0.06,α=11.4,b=-0.04 and n_c=9.0.According to distribution function,we found that those hydrophobic(H)residues including Leu,Val,Ile,Met,Phe,Tyr,Cys,and Trp residues have large values of the most probable number of contact n_c,and hydrophilic(P)residues including Ala,Gly,Thr, His,Glu,Gln,Asp,Asn,Lys,Ser,Arg,and Pro residues have the small ones.We also compare with Fauchere-Pliska hydrophobicity scale(FPH)and the most probable number of contact n_c for 20 amino acid residues,and find that there exists a linear relationship between Fauchere-Pliska hydrophobicity scale(FPH)and the most probable number of contact n_c, and it is expressed as:n_c=a+b×FPH,here α=8.87,and b=1.15.It is important to further explain protein folding and its stability from residue-residue contacts.
This paper investigates the maximal and minimal solutions of periodic boundary value problems for second order integro-differential equations in Banach spaces by establishing a comparison result and using the monotone iterative method.
