修正的Gdel系统的子代数中F(S)的分划及升级算法

将修正的Gdel逻辑系统中广义矛盾式理论推广,讨论了修正的Gdel逻辑系统中一类子代数上的广义矛盾式理论,进而在相应的子代数上给出了公式集F(S)的一种分划。     

修正的G(o)del逻辑系统中子代数的广义重言式理论

将修正的G(o)6del逻辑系统中的广义重言式理论进行推广,讨论其序稠密子代数的广义重言式理论,并利用可达广义重言式概念和α-矛盾式概念在G-的序稠密子代数中给出F(S)关于┓同余的一个分划.     

修正的Gdel逻辑系统中子代数的广义重言式理论

将修正的Gdel逻辑系统中的广义重言式理论进行推广,讨论其序稠密子代数的广义重言式理论,并利用可达广义重言式概念和α-矛盾式概念在G的序稠密子代数中给出F(S)关于┐同余的一个分划.     

Gdel逻辑系统中1/2-子代数上的广义重言式理论

将Gdel逻辑系统中的广义重言式理论进行推广,讨论了逻辑系统-G中具有1/2聚点的三类无限子代数上的广义重言式理论,并利用可达广义重言式的概念在-G的三类子代数中给出F(S)关于同余的一个分划。     

Gödel系统中一类子代数上的广义重言式理论

将Gödel逻辑系统中的广义重言式理论进行推广,讨论了一类无限子代数上的广义重言式理论,并利用可达广义重言式的概念在G的标准子代数E0中给出F(S)关于G同余的一个分划。     

修正的Gödel逻辑系统中子代数的广义重言式理论

将修正的Gödel逻辑系统中的广义重言式理论进行推广,讨论其序稠密子代数的广义重言式理论,并利用可达广义重言式概念和α-矛盾式概念在G的序稠密子代数中给出F（S）关于┐同余的一个分划.     

Gödel逻辑系统中1/2-子代数上的广义重言式理论

将Gödel逻辑系统中的广义重言式理论进行推广，讨论了逻辑系统G中具有1/2聚点的三类无限子代数上的广义重言式理论，并利用可达广义重言式的概念在G的三类子代数中给出F（S）关于¬同余的一个分划。     

修正的RDP逻辑系统中子代数的广义重言式理论

讨论了修正的RDP逻辑系统中序稠密子代数的广义重言式理论,并利用可达广义重言式概念和[α-]矛盾式概念在[RDP]的序稠密子代数中给出[F(S)]关于[～]同余的一个分划。     

修正的n值G(o)del逻辑系统的随机化

利用赋值集的随机化方法,在修正的n值G(o)del逻辑系统中提出了公式的随机真度和随机距离的概念,建立了随机度量空间.指出当取均匀概率时,随机真度就转化为计量逻辑学中的真度,建立了更一般的随机逻辑度量空间.     

Gdel区间值逻辑系统的广义拟重言式

吴洪博博士将王国俊教授在R0逻辑系统中的广义重言式理论推广到Gdel逻辑系统中,通过定义两个同构映射,得到其逻辑系统F(S)的一个分划。将这一理论推广到区间值模糊命题逻辑系统中,定义了两个新的区间同构映射,最终得到区间值逻辑系统F(S)的一个分划。     

平原区河道流速分布规律及其在横向声学多普勒流量测验系统中的应用

横向声学多普勒流速仪(H-ADCP)因其测验的自动高效和信息传输的快捷在流量测验中得到广泛应用。针对现状代表流速选取存在水文物理含义不明的缺点,根据垂线流速分布理论模型,并结合实测垂线流速资料,提出了平原区不同类型河道流速分布拟合模型,并实际引用。应用结果表明：基于幂指数函数和一元多项式函数拟合的流速分布模型能够用于H-ADCP层流速到垂线流速的转化,率定的单断关系精度可靠,可为H-ADCP测流系统流速率定单断关系提供新的方法。     

The numerical solution of the time-dependent matrix equation A(t)V(t) + WA(t) = G(t)

A rapidly convergent iterative method for the solution of matrix equations of the form

A(t)V(t) + WA (t) = G(t)

is outlined. Such matrix equations arise in the study of parabolic systems and in the application of Lyapunov methods in the stability analysis of linear time-invariant systems. The desired solution at each time step is obtained by solving a comparatively small ordered matrix equation of the form

AV + WA=G rather than resorting to the conventional systems of linear algebraic equations with a composite coefficient matrix of order mn × mn.     

Zeros of f(z) = (az-b)npm (cz-d)n

The zeros off(z) = (az - b)^{n} pm (cz - d)^{n}are found to lie on a circle of radius|(ad - cb)/(|a|^{2} - |c|^{2})|with its center atz = (a^{ast}b - c^{ast}d)/(|a|^{2} - |c|^{2}), wherea, b, c, anddare complex numbers andnis assumed real. When|a| = |c|the locus of the zeros is a straight line perpendicular to the line joining the pointsb/aandb/cand intersecting it atz = 0.5(b/a + d/c). The zeros are found analytically and constructed geometrically.     

On comparingLL(k) andLR(k) grammars

A new and rigorous proof of the well-known fact thatLL(k) grammars areLR(k) grammars is provided. The proof is elementary in the sense that it is directly based on relations defining leftmost and rightmost derivations and no additional formalism is needed.     

Parallel construction of SLR (1) and LALR (1) parsers

The generation of an LR parser consists of constructing a parse table, with one row per state (in a push-down automaton), and one column per terminal symbol. Traditionally, this is carried out row by row, with the computation of one row depending (potentially) on all the others. We present a technique for carrying out the lookahead computation of SLR (1) and LALR (1) parsers in a completely parallel fashion. Our technique performs the computation by column, rather than by row. We show that the computation is totally independent for each column, making it ideal for parallelization. The speedup factor of the technique is min (N, T), whereN is the number of processors andT is the number of terminal symbols in the user's grammar.     

Relational analysis of (co)inductive predicates, (co)algebraic datatypes, and (co)recursive functions

We present techniques for applying a finite relational model finder to logical specifications that involve high-level definitional principles such as (co)inductive predicates, (co)algebraic datatypes, and (co)recursive functions. In contrast to previous work, which focused on algebraic datatypes and restricted occurrences of unbounded quantifiers in formulas, we can handle arbitrary formulas by means of a three-valued Kleene logic. The techniques form the basis of the counterexample generator Nitpick for Isabelle/HOL. As case studies, we consider formulas about an inductively defined context-free grammar, a functional implementation of AA trees, and a coalgebraic list datatype.     

Programs for generating Clebsch-Gordan coefficients of SU(3) in SU(2) and SO(3) bases

Computer codes are developed to calculate Clebsch-Gordan coefficients of SU(3) in both SU(2)- and SO(3)-coupled bases. The efficiency of this code derives from the use of vector coherent state theory to evaluate the required coefficients directly without recursion relations. The approach extends to other compact semi-simple Lie groups. The codes are given in subroutine form so that users can incorporate the codes into other programs.

Program summary

Title of program: SU3CGVCSCatalogue identifier: ADTNProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTNProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: Persons requesting the program must sign the standard CPC non-profit use licenseComputers for which the program is designed and others on which it is operable: SGI Origin 2000, HP Apollo 9000, Sun, IBM SP, PentiumOperating systems under which the program has been tested: IRIX 6.5, HP UX 10.01, SunOS, AIX, LinuxProgramming language used: FORTRAN 77Memory required to execute with typical data: On the HP system, it requires about 732 KBytes.Disk space used for output: 2100+2460 bytesNo. of bits in a word: 32 bit integer and 64 bit floating point numbers.No. of processors used: 1Has the code been vectorized: NoNo. of bytes in distributed program, including test data, etc.: 26 309No. of lines in distributed program, including test data, etc.: 3969Distribution format: tar gzip fileNature of physical problem: The group SU(3) and its Lie algebra have important applications, for example, in elementary particle physics, nuclear physics, and quantum optics [1-3]. The code presented is particularly relevant for the last two fields. Clebsch-Gordan (CG) coefficients are required whenever the symmetries of many-body systems are used for the evaluation of matrix elements of tensor operators. Moreover, the construction of CG coefficients for SU(3) serves as a nontrivial prototype for larger compact semi-simple Lie algebras and even for non semi-simple Lie algebras. It is the simplest Lie algebra to have multiplicity in its outer products and a non-canonical subalgebra, i.e., SO(3).Method of solution: Vector coherent state theory is first used to construct bases for the products of two irreducible representations (irreps) [4]. The bases are SU(2)-coupled so that SU(2)-reduced CG (or isoscalar factors) can be constructed naturally. The CG coefficients in the SO(3) bases are constructed subsequently from the overlaps between the SU(2) and SO(3) bases.Restriction on the complexity of the problem: The programs are limited by computer memory and the maximum size of variable arrays. As dimension overflow conditions are possible, they are flagged and can be fixed by following the directions given as part of the error message.Typical running time: The calculation time for a single SU(3) CG coefficient is very different for SU(2) and SO(3) bases. It varies between 7.3-54.1 ns in SGI Origin 2000, 0.81-5.48 ms in HP Apollo 9000, or 0.055-0.373 ms in Intel Pentium 4 for SU(2) bases while it is between 0.027-0.255 s in Intel Pentium 4 for SO(3) bases.Unusual features of the program: Intrinsic bit functions: and, or, and shift, called iand, ior, and ishft, respectively, in FORTRAN, are used for packing and unpacking the labels for the irreps. Intrinsic logical btest is used to test the bit for the phase factor.References:[1] Y. Ne'eman, Nucl. Phys. 26 (1961) 222;  M. Gell-Man, Y. Ne'eman, The Eightfold Way, Benjamin, New York, 1964.[2] J.P. Elliott, Proc. Roy. Soc. A 245 (1958) 128, 562.[3] M. Reck, A. Zeilinger, H.J. Bernstein, P. Bertani, Phys. Rev. Lett. 73 (1994) 58;  B.C. Sanders, H. de Guise, D.J. Rowe, A. Mann, J. Phys. A 32 (1999) 7111.[4] D.J. Rowe, C. Bahri, J. Math. Phys. 41 (2000) 6544.