An Improvement of Herbrand's Theorem and Its Application to Model Generation Theorem Proving

This paper presents an improvement of Herbrand's theorem.We propose a method for specifying a subuniverse of the Herbrand universe of a clause set S for each argument of predicate symbols and function symbols in S.We prove that a clause set S is unsatisfiable if and only if there is a finite unsatisfiable set of ground instances of clauses of S that are derived by only instantiating each variable,which appears as an argument of predicate symbols or function symbols,in S over its corresponding argument's sub-universe of the Herbrand universe of S.Because such sub-universes are usually smaller(sometimes considerably)than the Herbrand universe of S,the number of ground instances may decrease considerably in many cases.We present an algorithm for automatically deriving the sub-universes for arguments in a given clause set,and show the correctness of our improvement.Moreover,we introduce an application of our approach to model generation theorem proving for non-range-restricted problems,show the range-restriction transformation algorithm based on our improvement and provide examples on benchmark problems to demonstrate the power of our approach.

Complete Real Solution of the Five-orientation Motion Generation Problem for a Spherical Four-bar Linkage

For a spherical four-bar linkage,the maximum number of the spherical RR dyad（R：revolute joint）of five-orientation motion generation can be at most 6.However,complete real solution of this problem has seldom been studied.In order to obtain six real RR dyads,based on Strum＇s theorem,the relationships between the design parameters are derived from a 6th-degree univariate polynomial equation that is deduced from the constraint equations of the spherical RR dyad by using Dixon resultant method.Moreover,the Grashof condition and the circuit defect condition are taken into account.Given the relationships between the design parameters and the aforementioned two conditions,two objective functions are constructed and optimized by the adaptive genetic algorithm（AGA）.Two examples with six real spherical RR dyads are obtained by optimization,and the results verify the feasibility of the proposed method.The paper provides a method to synthesize the complete real solution of the five-orientation motion generation,which is also applicable to the problem that deduces to a univariate polynomial equation and requires the generation of as many as real roots.

α-times Integrated Cosine Operator Functions with Growth ω

For a continuous,increasing functionω:[0,∞)→C of finite exponential type,we establish a Hille-Yosida type theorem for strongly continuous α-times(α>0)integrated cosine operator functions with O(ω).It includes the corresponding results for n-times integrated cosine operator functions that are polynomially bounded and exponentially bounded.

STRONGLY CONTINUOUS INTEGRATED COSINE OPERATOR FUNCTIONS WITH GROWTHω

For a continuous increasing function ω ： [0, ∞） → （0, ∞） of finite exponetial type, we establish a Hille-Yosida type theorem for strongly continuous integrated cosine operator functions with O（ω）. It includes the well-known polynomially bounded and exponentially bounded cases.

Metric of the gravitational field outside the neutron star

We have obtained the solution of the Einstein equation and the electric-magnetic field outside the neutron star, and at the same time, we investigated their asymptotic properties.