Mallat algorithm established the one to one mapping between orthogonal wavelets and N length discrete coefficient series, while RAS FWT discovers the similar one to one mapping between orthogonal wavelets and N/2 length discrete angle series.

When the membership functions (represented with fuzzy set) of fuzzy terms are continuous functions, a one to one mapping between the universe of discouse of fuzzy terms in antecedent of rule and that in consequent of rule is given, and a method of interpolation fuzzy reasoning based on fuzzy sets in this case is given also.

When the membership functions (represented with Vague sets ) of fuzzyterms are continuous functions, one to one mapping between the universe of discourse of fuzzy terms in antecedent of rule and that in consequent of rule is given. The method of approximate reasoning based on vague sets is presented in this case.

When the membership functions (represented by vague sets) of fuzzy terms are continuous functions, we give a one to one mapping between the universe of discourse of fuzzy terms in the antecedent of the rule and that in the consequent of the rule. In this way, we are able to find a method of interpolation fuzzy reasoning based on vague sets.

In the data persistence tier, the author uses Hibernate framework based on O/R Mapping, this framework provides light persistence framework in J2EE platform, the one to one mapping relation and the object-oriented query language and the recovery mechanism.

When the membership functions of fuzzy set are discrete functions, after given one to one mapping between the universe of discourse of fuzzy terms in antecedent of rule and that in consequent of rule, a method of linear interpolation about membership functions of fuzzy set for antecedent of rule and fact, making them become continuous functions. A method of interpolation fuzzy reasoning based on fuzzy sets in this case is given.

When the membership functions of Vague sets are discrete functions, after the above one to one mapping mentioned is given, a method of linear interpolation about true/false membership functions of Vague sets for antecedent of rule and fact. is put forward, making them become continuous functions. And a method of approximate reasoning based on vague sets in this case is provided.

The results already known show that if the constitutive relations of the elements included in the circuits are strictly increasing and one to one mapping (single value), then the circuits will have unique steady state under certain conditions.

Additionally, the introduction of multiplicative edge weights allows us to directly represent the so-called complement edges which are used in OBDDs, thus providing a one to one mapping of all OBDDs to FEVBDDs.

Let Φ be a conformal one to one mapping of the unit disc with Φ (1)=1.

Let P={Pθ: θ∈Θ} be an exponential family of probability distributions with θ the canonical parameter and consider the one to one mapping ?: Pθ→θ.

With sign, as with speech, there is a highly overlearned one-to-one mapping between the perceptual and productive forms.

We have restricted this paper to cover sets of data and identifiers with a one-to-one mapping.

Although it has already been enunciated that the stress-strain relations in elasticityor the constitutive relations in continuous media must be independent of the observer,the rigorous mathematical definition of an observer and the general theory of a changeof observers was not available until 1964 when Noll first gave it.The fundamental the-orem defines the most general form of a one-to-one mapping of time-space onto itself sothat the distances,the time intervals,and the temporal order are...

Although it has already been enunciated that the stress-strain relations in elasticityor the constitutive relations in continuous media must be independent of the observer,the rigorous mathematical definition of an observer and the general theory of a changeof observers was not available until 1964 when Noll first gave it.The fundamental the-orem defines the most general form of a one-to-one mapping of time-space onto itself sothat the distances,the time intervals,and the temporal order are preserved.In thispaper,a further discussion about the correspondence between the change of observersand the point transformation of the four-dimensional space-time is given,and by meansof the metric formulation a new proof of Noll's theorem is presented.

This paper presents a method for conformal mapping of a two-connected region onto an annulus The principle of the method is to find a holomorphic function, the real part of which should be a harmonic function satisfying certain boundary conditions. The key for solving the problem is to determine the inner radius of annulus, According to the theory of complex functions we shall determine it from the condition that the line integral predicted along multiple closed paths should be zero. It is then easy to...

This paper presents a method for conformal mapping of a two-connected region onto an annulus The principle of the method is to find a holomorphic function, the real part of which should be a harmonic function satisfying certain boundary conditions. The key for solving the problem is to determine the inner radius of annulus, According to the theory of complex functions we shall determine it from the condition that the line integral predicted along multiple closed paths should be zero. It is then easy to see that the imaginary part can directly be obtained with the aid of Cauchy-Riemann equations The unknown integral constants can also be derived by using the one-to-one mapping of previous region onto annulus. Without loss of generality. the method may be used to conformally map other two-connected regions onto an annulus.

This paper is the crystallization of the long-term observation made by the author on the electromagnetic forewarning form seismic focus. The author selects the lowest frequency band (0.1-10Hz) as his obser- vation frequency, uses self-made high-effect aerial and the improved alternate aerial and the receiving-recording instruments; and as a result he has received in the four years more than 150 seismic forewarnings of different distances and magnitudes. The result of the said observation indicates: 1. There...

This paper is the crystallization of the long-term observation made by the author on the electromagnetic forewarning form seismic focus. The author selects the lowest frequency band (0.1-10Hz) as his obser- vation frequency, uses self-made high-effect aerial and the improved alternate aerial and the receiving-recording instruments; and as a result he has received in the four years more than 150 seismic forewarnings of different distances and magnitudes. The result of the said observation indicates: 1. There exists definite relation bewteen the appearance of forewar- ning and the occurring of earthquake: 2. Uuder the condition of certain magnitude-distance, there is a one -to-one mapping relation bewteen the forewarning and the earthquake; 3. The forewarning wave-pattern differs along with the difference of the location of seismic foci.