The present paper deals with the eighth order periodic boundary value problem of the following form, u⁽⁸⁾(t)=f(t,u(t),u⁽⁴⁾(t)), u⁽ⁱ⁾(0)=u⁽ⁱ⁾(2π), i=0,1,…,7.where f(t,u,v) is a Caratheodory function.It is proved that if there exist upper and lower solutions to the periodic boundary value problem, represented by β(t) and α(t) respectively, and β (t)≤α(t), then the monotone sequences of functions ｛β_j｝ and ｛α_j｝, β_j≤α_j, can be constructed so that the sequences converge uniformly on ［0,2π］ to the extremal solutions of the problem and hence the solutions to the problem is obtained.

The segmenting method, which is established in this treatise, is composed of three kinds of segmenting methods in some kind of priori ty, so that a very good segmenting method is got. In other treatises only one kind method is used, and that method is not very effective under some special condition that is useless.

The present paper deals with the existence and the uniqueness of periodic solutions to the following integro-differential equations: u_1t-J*u₁+u₁+f(u₁,u ₂)=0, u_2t-DΔu₂+g(u₁,u₂)=0,where D>0 is constant.

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The present paper proves the following result : Let R be a 2-torsion free prime ring, let J be a Jordan ideal and a subring of R. If φ: R→R is an automorphism satisfying φ(u²)=φ(u)² for all u∈J, then φ(uv)=φ(u)φ(v) or φ(uv)=φ(v)φ(u) f or all u,v∈J.

In this paper, the second equivalence theorem of eigenvalue method for solving sparse polynomial equations is proved. The correspondence relation between eigenvalues and the solution of the equations is given.

In this paper, the properties of n-dimensional Minkowski space are discussed by using Clifford algebra. The reversed Schwarz inequalities, the Hyperbolic Euler Formula of n-dimensional Minkowski space and its Lorentz transformation are given.

The sufficient and necessary condition for the existence of monotone increasing solutions of a class functional equation are discussed by using Arzela-Ascoli theorem. The existence of continuous solutions and cont inuation of solutions are studied by using Schauder fixed pointed theorem and some sufficient conditions are obtained.

An iterative method is presented for the modification of structural stiffness. The present method is a preconditioned conjugate gradient-based technique and is intended to utilize the existing stiffness matrix fac torization developed for the initial design. It can preserve the ease of impleme ntation and improve significantly the quality of the results. In particular, the method can adaptively monitor the accuracy of approximate solutions. The method is suitable for general finite element systems. The computational cost is significantly reduced. It has been validated by numerical examples that the proposed reanalysis method can achieve excellent approximate results for large changes in cross-sections and in structural geometry.

The present paper deals with the advances and some important results about the studies on the cellular automata, expecially the artific ial life and its character and the problems caused by the self-reproduction of a cellular automata.

This paper deals with the replacement repair and reconfiguration by means of the theory of model-based diagnosis, presents the concepts of replacement repair and reconfiguration for the system being diagnosed. The effects of component replacement upon the observed values of the system being diagnosed are used to characterize the repair and reconfiguration, etc.

The Kleinberg HITS algorithm is an eigenvector method for identifying authoritative or influential articles under given hyperlink information. That such an algorithm should give reliable or consistent answers is surely a desideratum. On the basis of the fact that the algorithm can give stable rankings under small perturbations to the linkage patterns, the paper presents a new algorithm: Sub-space HITS method, and deals with their performance empirically with Web hyperlink data.

Action calculi have been introduced as a framework for representing the models of interactive behaviours. Aiming at molecular forms of action calculi, and the data flow analysis method for a single action based on t he structural tree of molecular grammar and the implementation of the algorithms. The present paper provides a way to further studying the features and application of action calculi.

The problems of over-constraint and under-constraint have been solved by using dependency graph based on the freedom analysis method. The dependency graph contains the dependency information between the variables in the solving problem. When the system detects contradictory overconstraint or underconstraint, it will show some message to the user, so that the user can deal with it.

Fuzzy logic and its reasoning based on triangular norms are presented the properties and the method of triangular norms are introduced, and the conjunction is evaluated by means of t-norm and the implication by means of residuum, at the same time, biimplication, equality relation and the semantic of fuzzy sets are discussed too. The paper presents an explanation of vague environments by equality relation and several examples.

Nanocrystalline composite oxide BaFe₁₂O₁₉ was synthesized via a citrate method. The composite was characterized by means of X-ray powder diffraction and infrared spectral analysis. Nanocrystalline composite oxide BaFe₁₂O₁₉ and the traditional micro wave absorbing mat erial, iron powder were dispersed into the macromolecule polymer uniformly and respectively. Microwave-absorbing coatings with a two-layer structure were obt ained by smearing the mixture of the composite dispersed in the macromolecule polymer, and the mixture of the iron powder dispersed in the macromolecule polymer alternatively on the iron plate until the total thickness being only 1 mm, in this case, a big reflection loss over broadband is realizable. The possible microwave absorptive mechanisms of nanocrystalline material are also discussed on the basis of the experiments.

The B_s→K transition form factor was studied by means of light cone QCD sum rule in the whole kinematically accessible range. We chose a new correlation to eliminate the effect from the twist-3 function, thus, we can extract the CKM matrix element |V_ub| precisely.

By means of the combination of Monte Carlo model of fast electron and ions (N^＋_２，N^＋) in a plasma, the axial distribution of the creation rate of the atomic ions for bo th N^＋_２-N_２ and e^－-N _２ dissociations under different discharge conditions in nitrogen glow discharge and the distribution of the energy for bombarding the cathode were investigated. It was found that the creation rate of the atomic ions increased wit h inc reasing the voltage or the gas pressure, but decreased with increasing gas temp e rature. Ions N^＋_２ are mainly produced by N^＋_２-N_２ dissociation in front of the cathode at a higher voltage.

The transition behavior of the properties of a Hopfield model with random asymmetric interactions was theoretically investigated. The results show that when the memory loading level is greater than its critical value, a new kind of transition of the networks occurs. The results also show that in the neighborhood of the critical point of the memory loading level, the retrieval band appears again after it has merged with the band composed of the spurious stable states.

A generalized Ginzburg-Landau-Devonashire (GLD) free energy is represented to study the behavior of ferroelectric thin film with a imperfect surface layer. The effect of the imperfect surface layer on the hystere sis loop makes the hysteresis loop deviate from central symmetry (on point E=0， P=0).

X-ray method was used to investigate the effect of retrogression time on δ′ precipitation in an Al-9.74%Li alloy treated by retrog ression. The investigation results show that the hardness clearly drops in short retrogression time due to the dissolution of δ′ particles. A weak peak value of hardness was achieved and gradually dropped due to the δ′ particles repreci pitation and coarsening because of increasing retrogression time.

The Cu/Fe multilayer on Si substrate was prepared by the magnetron sputtering method. The samples have been studied by X-ray photoelectron spectroscopy (XPS). With the sputtering depth increasing, the alloying forms on the interface of Cu/Fe.

The adsorption of three kinds of heavy metals Mn, Cd and Pb by extracellular polymers was investigated. The extracellular polymers were obtained from superiority bacteria in Changchun South Lake. The results show that both the Langmuir and the Freundlich isotherm equations could describe the course of the adsorption of the three metals on the extracellular polymers. The existence of Mn in extracellular polymers affected the adsorption of Pb more seriously than that of Cd.

An atomic colouring number (f_i) defined on the basis of the syst ematic n omenclature principle of organic compounds and the structure characteristics of bonding atoms has excellent selectivity for non-hydrogen atoms in alkanes and alkyl derivative molecules. On the basis of adjacency matrix, two novel connec tivity indexes (^mQ and its converse index ^mQ^ ) are constructed from f_i. The boiling points (Ｔ_b, K) of 85 alkanes can be expressed by means of ^０Q1Qand δ_max (the largest point valence of carbon atom): ln(714-Ｔ_b)=－0.1472 ^０Q－0.0041¹Q+0.0089δ_max+6.5164， R=0.998　9； A satisfactory function for 72 aliphatic aldehydes and alkanones is established, i.e.： ln(693-Ｔ_b)=－0.2267^{1< /sup> Q－0.00671Q+0.0301δ_max+6.1425， R=0.999　0. The boiling points for above mentioned 157 organic compounds are expressed as： ln(690-Ｔ_b)=－0.0320０Q+ 0.0005 1Q+0.0195δ_max+6.1590， R=0.99 7　6. Their correlativities are more ideal than those by the literature method s. It is concluded that the indices bear good structure selectivity and property rel ativity. For this new method the calculation is convenient and the result is accurate.}

Orthogonal design was used to explore the optimum organic nitrogen sources for lentinus edodes fermentation and the best ratio of the three nitrogen sources in the medium is that bean powder is 1, yeast extract paste 1.5, tryptone 0.2. The results also indicate that bean powder is the best nitrogen source for lentinus edodes fermentation. Subsequently, lentinus edodes was cultured in the optimum medium for 130 h and the concentration of lentinen in the fermentation medium could reach the climax of 25.1 mg/mL. lentinen was crudely extracted from the liquid medium by alcohol precipitation, then deproteinized by the Sevag method from the polysacchrides and the deproteinized lentinen was purified by gel filtration with Sephadex G-75 to obtain two components of lentinen.

A three-step continuous extraction method was used to study the bioavailability of heavy metals including Cu, Pb, Zn and Cd in seven samples of sludges collected in Hejiagou River in Harbin. The impact of heavy metals on the environment is discussed based on the available metals, mobile plus mobilisable, in the sludge from Hejiagou, and the resulted information is expected to give a suggestion for the treatment of the sludge if discharged.

The velvet antler polypeptide was extracted and purified by gel filtration, ion exchange chromatography and HPLC, which showed a single peak in HPLC chromatography and a single band in SDS-PAGE. The molecular weight measured by MALDI/TOF/MS spectrum is 3 095.1. The polypeptide consists mostly of Ala, Phe, Lys, Gly, but no Cys. The N-terminal amino acid of the polypeptide was detected by FDNB method to be Val. The experiment of pharmaceutical activity indicated that the polypeptide could obviously stimulate proliferation of the epithelial cells and BRL cells.

Promethazine hydrochloride and chloropromazine hydrochloride were determined by oscillopolarographic titration with sodium tetraphenylborate(Na-TPB) as titrant. TPB gives a sharp oscillopolarographic incision in 0~5 mol/L NaAc-HAc(pH=5.4), which can be used to indicate the end point of the titration. The characteristics of the method are simple, quick and exact. The results are satisfactory.

The structural fragmentation of three cephalosporins in electrospray ionization conditions was studied by electrospray ionization quadrupole time-of-flight mass spectrometry in positive mode. Some common fragmentation pathways were found to be closely related to the substituent of the 7-aminocephalosporin nucle us. The product ion experiments turned out to be an essential technique to draw the fragmentation patterns of compounds. The results suggest that electrospray ionization quadrupole time-of-flight mass spectrometry is an ideal instrument to investigate the fragmentation pathways of drugs.

The NMR spectra were used for elucidating the structure of nateglinide , N-［(trans-4-isopropylcyclohexyl)-carbonyl］-D-phenylalanine, which is used as an oral hypoglycemic drug. By means of DEPT,¹Ｈ-¹Ｈ CO SY and ^1３C-¹Ｈ HETCOR techni ques, the proton and¹³Ｃ spectra of nateglinide were assigned co mpletely.

The present paper focuses on the metabolism of antioxidant T501 in the transformer oil caused by Mycoplana and the relationship among the quantity of Mycoplana, the majo r components of the oil (such as alkane, cyclanes and aromatic hydrocarbon) and dielectric loss. The experiment result indicates that Mycoplana could grow taking antioxidant T501（2，6-ditertiary-butyl-pcresol） as the sole carbon and energy sources. With the quantity of Mycoplana put into the oil inc reasing gradually, the content of T501 became more and more lower, at the same time, the contents of alkane, cyclanes and aromatic hydrocarbon in the transformer oil also became more and more lower, which led to the increasing of dielectric loss.