1. We see how algebraic laws allow us to give a precise and succinct description of each operator.

2. We then obtain n - 2 linear algebraic equations for the n - 2 unknowns pi.

3. The algebraic approach to programming language semantics has several features to recommend it.

4. Algebraic laws alone only allow us to prove one occam program equal to another.

5. The matrix theory is presented in classical algebraic form with no recourse to the notions and nomenclature of vector space theory.

6. Latin abbreviations, algebraic symbols, contractions of words and personal inventions can all be used.

7. Somewhat more satisfactory would be to consider the algebraic numbers those complex numbers which are solutions of algebraic equations with integer coefficients.

8. The algebraic laws thus yield an algebraic semantics for occam that is isomorphic to our chosen denotational semantics.

9. This paper studies algebraic modeling of discrete time series.

10. Approximation solution of the algebraic eigenvalue problem.

11. Write an algebraic expression for each verbal expression.

12. Optimum bias is expressed through a simple algebraic equation.

13. This is an algebraic equation(), deduced from experimental results.

14. A very fast algebraic compiler.

15. The algebraic number more or the transcendental number?

16. Turbulence is enclosed with algebraic Baldwin - Lomax model.

17. An algebraic and a bijective proof is presented.

18. Choose and solve algebraic Baldwin - Lomax turbulent model.

19. Fully Automatic Test Algebraic Language?

20. Jules Own Version of the International Algebraic Language?

20. Wish you can benefit from our online sentence dictionary and make progress every day!

21. The algebraic multigrid method can avoid those defects.

22. Purely algebraic methods for computing the sensitivity of linear algebraic system have been proven to be simple and effective in the frequency domain.

23. The subject was set upon firm foundations around 1930 by Emmy Noether and van der Waerden using an abstract algebraic approach.

24. The underlying assumption of the project is that certain computer-based experiences can help pupils bridge the gap between arithmetical and algebraic thinking.

25. This does not present the same barrier to pupils use of algebraic ideas within computer programming environments.

26. In algebra they developed a concept of polynomials and pioneered an algebraic geometry that has traditionally been ascribed to Descartes.

27. First, consider the problem of finding integer solutions of systems of algebraic equations with integer coefficients.

28. The problem of solving large deflection plate by the variational method is changed into that of solving systems of cubic algebraic equations with multi-unknown quantities.

29. The third type im-proper integral can be written as the algebraic sum of the first and second type integrals.

30. It is firstly pointed out that unknown input appearing in measurement can be eliminated by a simple algebraic transformation.

31. Since the coefficient of the new polynomial is too complicate to calculate directly, we introduce a linear operator and study the algebraic properties of it.

32. The existence of congruence relation between them was proved by constructing the corresponding algebraic system respectively.

33. Moreover, multivariate splines also have certain relations with pure mathematics, such as, abstract algebra, algebraic geometry combinatorics and so forth.

34. This paper analyzes the general protection mechanisms for ASON and provides for each of them an algebraic formula for the availability analysis.

35. This unconstrained optimization problem may be transformed into nonlinear algebraic system of equations.

36. Ritt-Wu's method of characteristic sets is an effective method to solve algebraic equations by computer, while one cannot get the multiplicity of an isolated solution by this method so far.

37. In the past, there were many methods or handling the acidity such as algebraic method and logarithmic graph method.

38. The conditions of one family of planar quintic polynomial differential system which(possesses) a quintic algebraic invariant curve are presented.

39. A conjugate gradient iterative procedure was used to solve the algebraic problems arising from those two approximate schemes.

40. This paper discusses algebraic specification technology and its automatic transformation into PROLOG.

41. A new algebraic method of balancing redox reaction formulas is introduced.

42. I still can not perform the calculation in this algebraic expression.

43. The research for the means has a long history, the classical means include algebraic mean, geometric mean and harmonic mean etc.

44. It'shows the effectiveness and practicability of the approach to prove algebraic identities with combinatorial analysis.

45. Potentials may be summed by the law of algebraic addition.

46. The integral group rings of finite abelian groups are of great importance in algebraic k - theory.

47. This paper intends to expound some important definitions and conclusions in real variable function by using algebraic operation, thus making a new approach to the use of computers in this field.

48. In this paper, the theory of constructing PES of polyatomic molecules by dynamic Lie algebraic method is presented, and its application in different molecular systems is introduced.

49. An algebraic method is proposed for the forward displacement analysis of the dodecahedral variable geometry truss manipulators.

50. An algebraic expression is one or more algebraic terms in a phrase.

51. To find this angle, we first work out general algebraic expression for the range.

52. Character 2:The algebraic sum of the moments of the forces of a couple about any point in its plane of action is independent of the location of that point and is equal to the moment of the couple.

53. Especially, this method offers an efficient parallel algorithm for solving tridiagonal linear systems of algebraic equations on multiprocessors (MIMD).

54. It is the purpose of this paper to investigate the torsion theory for this algebraic system of much more extensive and to give it some characterizations makeing use of the method of lattice theory.

55. Diophantine equation is an important subject in number theory and closely connected with algebraic number theory, combinatorics, algebraic geometry and computer science etc.

56. As a consequence of the above result , we have that implicative semilattices form an algebraic variety.

57. The system with unknown input is translated into an equivalent system without unknown input by a simple algebraic transformation.

58. And first to derive the transformation matrix D by using "Linear algebraic method". And then obtain an incidence submatrix A.

59. This paper , firstly introduces the elliptic curve in finite field and algebraic law of its point group, gives the order of the group.

60. Elliptic Curve Cryptosystem(ECC) is a kind of public-key cryptosystem based on algebraic curve.

61. The algebraic sum of the product of any point on a closed curve and the distance from this point's normal line to a fix point is zero.

62. For commutative algebra, algebraic geometry, and singularity theory, the SINGULAR computer algebra system provides a large variety of algorithms in the package kernel as well as shared libraries.

63. Its clarity in algebraic and analytical operations far outweighs any drawbacks.

64. The algebraic system, on the other hand, makes up for the loss of elasticity and animation by being immediately "constructible."

65. The second step deals with nonlinearity by solving nonlinear algebraic equations and satisfies constraint by desaturation.

66. The radial magnetic pressure of axisymmetric coil can be calculated by algebraic analysis.

67. Based on the relation between the hamming weight and the algebraic degree of Boolean functions, we get a sufficiency condition about Boolean functions without low degree annihilator.

68. A process algebraic approach to the modelling of information flow security is explained.

69. Mathematical equations, from simple algebraic ones to the more challenging differential equations, have allowed us to summarize an enormous amount of physical phenomena into a simple format.

70. It has developed from two sources : algebraic geometry and algebraic member theory.

71. This paper contains two parts:1. Algebraic operations of quaternion are defined by utilizing the knowledge in vector algebra and the fundamental properties of algebra of quaternions are derived.

72. This algebraic notation of the image allows the entire image, or just a portion of the image, to be recreated at any time by evaluating the algebraic description over the range of interest.

73. In this paper we discuss the algebraic expression of involutory perspective in three-dimensional projective space.

74. Then the relation net is an algebra of the algebraic specification.

75. Finally the computational problem of such deformation is reduced to solve a set of nonlinear algebraic equations related to the strained configuration of the radial tire.

76. In this paper, we present a new interpolation formula of algebraic multigrid (AM G ).

77. The properties of the proper algebraic boundary point sets of the sets in topological linear spaces were discussed.

78. The interconnection and damping assignment passivity-based control (IDA-PBC) methodology is extended to solve the regulation problem of affine nonlinear differential algebraic system.

79. In the nineteenth century, the system of algebraic knowledge is enormous, which contains the permutation group, matrix, algebraic number theory, algebraic geometry and other branches.

80. These extensions lead to generalized Gaussian quadrature formulas which have high algebraic precision.

80. Wish you can benefit from our online sentence dictionary and make progress day by day!

81. Through the medium of walsh transform, the logical differential equation can be transformed into algebraic equation.

82. The algebraic immunity is a criteria on evaluating the property of the Boolean function recently.

83. An algorithm for computing the geodesic line between the two points of an algebraic surface was presented.

84. By using algebraic techniques, Some inequalities related to the degree sequence of a graph are established, and the corresponding extremal graphs are also determined.

85. In this paper, we introduce the concept of fuzzifying groups based on many valued logic and investigate some algebraic properties of normal subgroups, coset and homomorphism.

86. This method is accomplished with calculation grids generated by an algebraic transformation, and thus it can be easily applied to the design analysis of centrifugal impellers.

87. The symplectic geometric algorithm and the Ronge-Kutta algorithm are examined from the viewpoint of the algebraic dynamical algorithm.

88. The algebraic sum of the through variables associated with the edges to any vertex is zero.

89. The two mode coupling in analogy with the motion of the pendulum is proposed by an algebraic approach, which is based on an algebraic classical Hamiltonian on the coset sphere.

90. The principle of differential algebraic method is applied to calculate arbitrary high order aberrations of electrostatic electron lens systems.

91. Based on energy theory, a simple critical force calculation for pressed beam with variable cross sections is derived. It reduces the complex integration algorithm into a simple algebraic operation.

92. A radical is an indicated root of an algebraic or arithmetic expression.

93. This paper mainly discusses the formulation and the numerical methods of real symmetrical matrix inverse algebraic eigenvalue.

94. In essence, the goal here is to create a small language that allows users to type in relatively simple algebraic expressions that this code will evaluate and produce a result.

95. This general solution consists of either the combinations of trigonometric and hyperbolic functions, or algebraic polynomials.

96. As an algebraic system, Lie triple systems arise upon consideration of certain sub-spaces of Riemannian manifolds, the totally geodesic submanifolds.

97. Then, the origin of an algebraic loop is discussed and there solutions to algebraic loops are compared.

98. By using the orthogonality condition of augmented eigenvector of multibody system, the algebraic equation group with unknowns of structure parameter is formed.

99. Topics covered range from computational complexity, algebraic geometry, dynamics, through to number theory and quantum groups.

100. Algebraic Decision Diagram ( ADD ) is a symbolic method utilized to represent Boolean function.

101. Indicate how each of the following algebraic identities might be established geometrically.

102. For this program, we can construct any compactly supported biorthogonal wavelets . And the algebraic structure of this filter bank can be shown by the program.

103. The simulation results indicate that the algebraic loop can be eliminated by adding a delayed module in the feedback channel, but the simulation precision and speed of the system will be reduced.

104. The algebraic sum of the through variables associated with the edges incident to any vertex is zero.

105. The concepts of indecomposable matrices and fully indecomposable matrices over a distributive lattice L are introduced, and some algebraic properties of them are obtained.

106. According to algebraic property that a direct sum of Galois fields is isomorphic to a finite ring, the linear block code for multiplexing systems is proposed.

107. However, these problems cannot be solved by means of the traditional binary algebraic system.

108. But recently some people presented a new algebraic diagonalization method.

109. Then a similar intergrid transfer operator is given for the spaces of velocity, and the W-cycle multigrid method is presented for solving the algebraic equations.

110. Based on the max-plus algebraic model, referring to automata theory and lattice theory, by the definitions of conjunctive and disjunctive functions[http:///algebraic.html], a supervisory controller was put forward.

111. The energy eigenvalues and the squeezed state solutions are obtained by making use of algebraic diagonalization.

112. The underlying algebraic structures are composite Galois fields GF (( 2~ n ) ~ m ) in a standard base representation.

113. In this paper, we introduce the concepts of fuzzifying infix codes and fuzzifying outfix codes on free monoid and discuss their elementary algebraic properties.

114. This course involves mathematic logic, theory of set, algebraic system and the theory of graph.

115. But there is no general principle to find initial or terminal algebraic specification for a given abstract data type.

116. In the derivation of dynamic models of rectifying columns, the energy balance equations are generally assumed to be quasistatic. As a result, they are often simplified as algebraic equations.

117. In this paper, we shall introduce the notion of fuzzy code, fuzzy prefix code, and maximal prefix code, and discuss their algebraic character and algebraic properties.

118. The key to power distribution system is to ignore transient process in this sub-system and to draw the network equivalent circuit diagram, therefore its node voltage equation is algebraic equation.

119. In this article, we showed the algebraic structure of syntactic categories based on monoid and defined categorial equation whose solutions are described by consistency and correlation .

120. Through constructing a novel dioid, a linear max-plus algebraic model was derived for HTEG, then a partial order was deduced based on the model.

121. This paper presents a non-uniform and part-searching-area algebraic codebook based on Algebraic Code Excited Linear Preiction(ACELP) speech coding algorithm.

122. Some more advanced algebraic topology may also be useful as might some knowledge of category theory.

123. By using the lowering dimensionality expansions, we construct boundary type cubature formulas with the algebraic precision for integrals.

124. CG - ADDM algorithm is the effective combination of CG algorithm and ADDM ( Algebraic Domain Decomposition Method ) .

125. It is based on the concept of indefinite admittance matrix, and uses an algebraic method of symbolic code in the generation of symbolic network functions.

126. When wrapped out, these internal-integrated models could form the open-loop co-simulation so as to avoid the algebraic loop.

127. A modified algebraic multigrid(AMG) method for queueing networks is presented.

128. The minimal path sets (MPS) are achieved by Boolean algebraic simplification calculation. The authors put forward the analyzing result of the structural significance of the basic event.

129. It is a kind of method which combinates differential analysis and algebraic attack.

130. However, Diophantus' solution is strictly algebraic, unlike the quasigeometric Babylonian solution.

131. Governing equation discrete, solving of the conjugated algebraic equation set and SIMPLE method are also discussed in this paper.

132. An efficient numerical algorithm for a differential - algebraic system model of reactive distillation is given.

133. An algebraic expression showing that a quantity is greater than or less than another quantity.

134. In the whole computing process, it utilizes an interval with rational endpoints to represent the exact algebraic number and avoid floating-point computation.

135. The ABS algorithm for nonlinear algebraic systems is generalized. The local convergence and quadratic convergence of the generalized algorithm have also been proved.

136. Then the mathematical description of operation relativity is given systematically from algebraic specification, Gantt chart expression and type conversion.

137. The control of a specific flip - flop which stores the algebraic sign of numbers.

138. The notion of pointer mapping algebraic system is proposed. On the basis of this, it analyzes how to construct pointer mapping sets and describes the detailed testing steps.

139. On the basis of software architecture, category theory and algebraic specification are combined together to provide precise semantics for architecture models and their mapping relations in this paper.

140. It successfully replaces the solving of complicated differential equations in the kineto-elastodynamic(KED) analysis with the solving of a set of algebraic equations, saving a lot of computing time.

140. try its best to gather and create good sentences.

141. Algebraic transformation of geometric problem makes the algorithm a original approach.

142. The Baldwin - Lomax algebraic model is used for turbulence simulation.

143. A unifying method for constructing the solutions to the Yang-Baxter equation by using the computer algebraic system Mathematica is presented.

144. Likewise, monadic Boolean algebras supply the algebraic semantics for S5.

145. Based on experimental data, dynamic torques of turbine and pump are shown as algebraic equations, and dynamic torsional damping of the hydraulic torque converter is estimated.

146. An algebraic expression is a combination of constants and variables.

147. This paper researches a class of singular biological economic model using the theories of differential - algebraic equations.

148. The second step deals with nonlinearity by solving a nonlinear algebraic equation (group) and satisfies constraint by desaturation.

149. Three century Diophantine one of the outstanding contribution that Greece algebra simplify, simplify algebraic created.

150. Double angle formula can transform the circular function equation to a biquadratic algebraic equation, and the analysis solution can be solved by extract equation directly.

151. The implementation of algebraic specification is a key for algebraic specification to support rapid prototype technology.

152. The scheme resulting from this method is linear in the sense that it requires only to solve a single linear algebraic system at each time step.

153. ITU-T G729 protocol is a kind of speech compression coding technology based on Conjugate Structure Algebraic Code Excited Linear Prediction(CS-ACELP) algorithm.

154. He also worked on functions that changed celestial mechanics, helped pioneer algebraic topology and co-discovered the special theory of relativity.

155. TRACING OF SINGULARITY INDUCED BIFURCATION IN POWER SYSTEM DIFFERENTIAL ALGEBRAIC EQUATION MODEL AND ITS THEORETICAL ANALYSIS.

156. With algebraic multi - grid method ( AMG ), linear system of equations are solved.

157. The paper describes the methods of the class-level testing for object-oriented software based on algebraic specification, and constructs a frame for semi-automatic testing frame.

158. In analogy to algebraic data type theory, this paper proposed the mathematical model of objects, object types and abstract object types.

159. Baldwin - Lomax algebraic turbulent model is corrected to adapt the feature of the base flow.

160. It mainly introduces basic concepts and basic methods in logic, set theory, algebraic system and graph theory.

161. A new attack — algebraic att - acks is studied in this paper.

162. A modified Baldwin - Lomax algebraic turbulent model and wall function law are also adopted in the prediction.

163. The meter reading will be the algebraic sum of all these sources.

164. The expansions obtained in this paper are simple and easy to be transformed into the expansions at AND, OR and NOT algebraic system.

165. The paper summarized the common linear and nonlinear mathematics model in the research of mechanism science, focusing on the comment on the methods to solve nonlinear algebraic system of equations.

166. The algebraic method described the appearance of weld, welding spatter loss coefficient and slag detachability of weld is put forward and applied to the development of flux cored wires.

167. Our approach is to combine object-oriented paradigm with formal methods in software engineering, especially abstract data type theory, and algebraic specification of systems.

168. PARI is a fast-running C library of symbolic functions for factorization, algebraic number theory, elliptic curves, matrices, and transcendental functions.

169. To the inverse problem of the system of linear algebraic equations, tiauthor gives a symmetric matrix solution and the expression of its general solution.

170. It takes neither differential equation nor Laplace transformation. Instead , some algebraic Methods: Will do.

170. try its best to collect and build good sentences.

171. By translating this real cubic system into a complex planar system, an applicable linear algebraic recursion formula of the equator and the first 6 quantities of the equator are given.

172. And - Or - Not algebraic system is a traditional Boolean algebraic system.

173. In the algebra system to solve some linear algebraic problems are in convenient.

174. The turbulent flow in a straight channel was numerically simulated with LES of algebraic modelling.

175. Rydberg energy levels and oscillator strength of endohedrally confined H atom have been calculated by using a nonlinear algebraic mapping technique and B-spline method.

176. Operational semantics and algebraic laws are very useful in practice.

177. They are studied for their global properties by the methods of algebra and algebraic topology and form a natural domain for the global analysis of differential equations.

178. The algebraic system uses the method of algebra to study the properties and characteristics of various things in the world.

179. A class of piecewise - linear capacitor is a single operational amplifier based on the algebraic n - port theory.

180. Compound discharge of the chink is the vectorial sum of shearing discharge and pressure differential discharge, but compound loss power is the algebraic sum.

181. The pity is that the first auxiliary directrix after modification is generally expressed in an algebraic form, because of the complexity of the vectorial expression.

182. The reason we are doing all these algebraic manipulation is we can parallelize this method in the following way.

183. Algebraic specification of ADT is an important source of black - box testing.

184. More likely, though, traffic traversing networks would become a locally undecipherable algebraic stream.

185. Finally, the problems can be reduced to solving a low order system of algebraic equations like the initial parameter algorithm.

186. I find this latter CSE especially cool, as I've seen real programmers miss this sort of algebraic simplification in real code.

187. Another result is presented a topological formula for any 2-order algebraic cofactor in passive network node admittance matrixes.

188. At last, based on a mathematical tool: algebraic system, this paper gives definition of spatial data cube.

189. In this paper, we give the upper and lower bounds of the largest quasi-Laplace eigenvalue of a connected graph by algebraic method.

190. This paper proposes a piecewise geometric approach to parametrize a kind of quartic implicit algebraic surface.

191. Further, it blends the given convex trihedral angle by algebraic splines and then proves that the blending surfaces obtained by the method have the property of convex preservation.

192. The algebraic properties of the operator exclusive-or are characterized by the ACUN theory.

193. Based on the analysis result, the fault tree of oil tank is established. The minimal path sets (MPS) are achieved by Boolean algebraic simplification calculation.

194. This paper discusses how to use the method of algebraic specification in specifying software systems.

195. A max plus algebraic approach was put forward to study the minimum initial marking (MIM) problem of hybrid timed event graph (HTEG).

196. The capability of the solver is greatly enhanced through the use of the Multiblock and Algebraic Multigrid techniques to solve realistic problems with complex physics over complex geometries.

197. Heron also translated much of the Greek geometrical algebra into arithmetic and algebraic processes.

198. The coupled boundary integral equations and their reduced forms are deduced for hybrid mode problems, and these equations are discreted into a system of linear algebraic equations by moment method.

199. The algebraic regularity of monopole eigenfunctions in various dynamical0 (2, 1) basis shows the symmetry in radial phase space.

200. The solar irradiance can be predicted with the algebraic sum of the irradiance of each frequency range forecasted by the established network model.

201. In the calibration of the system[ ], a plan based on the principle of cross ratio invariance in algebraic projective geometry was used to calibrate the coded light planes.

202. This paper discussed the theorem of the average arithmetic geometric mean of algebraic polynomials systematically, then derived and analyzed the original geometric programming (GP) briefly.

203. Use the labels to translate the verbal model into an algebraic equation.

204. Self - contained, the book examines situations where explicit algebraic analogues of theorems of number theory are available.

205. All of gene effects for the final characters were found to be algebraic sum of the respective parameters for net growths at different development stages.

206. Signals are expressed by using a generalized basis. Convolutional operation is converted to formal algebraic operation.

207. The moment of the resultant of a general coplanar force system about any center is equal to the algebraic sum of the moments of the forces about that center.

208. In numerical mathematics, it is interesting and of importance to study the theory of algebraic functions and its applications.

209. Also, it is proved that many algebraic number fields of finite degree are not elementarily equivalent to the above-mentioned ultraproducts.

210. A radical is an indicated root of an algebraic expression.

211. In this paper, we prove that a Boolean algebra is equivalent to an algebraic system with a single binary partial operation.

212. The paper presents a linear algebraic solution of the dynamic disturbance decoupling problem for a generalized discrete time nonlinear system.

213. Its real value depends on the moral sign attached to it, just as strictly as that of a mathematical quantity depends on the algebraic sign attached to it.

214. The thesis presents a new test case automated generation method based on algebraic specification of ADT.

215. The algebraic system defined on the points of an elliptic curve can be used to construct various cryptographic schemes.

216. So the sum of spinor can be simply replaced by the spin average calculation by using grassmann variables algebraic simplified sum spin coupling sum and reduce the computational complexity.

217. The computer algebra system CASS1 is designed by algebraic simplification method.

218. The discrete algebraic equation systems are solved using CGS method with incomplete LU preconditioner.

219. Based on the analysis of the basic algorithms for the ECC, the computer algebraic model and the software architecture are established, thus lay a solid foundation for the algorithm optimization.

220. This paper solves some non-routine mathematical problems by using Taylor series with the help of computer algebraic system MAPLE.

221. Some algebraic laws of Timed RSL are presented, which can be proved from the denotational semantics, and be used in program transformation and optimization.

222. AAA, an algebraic specification language based on the abstract data type, is introduced first.

223. This paper discusses one new kind of algebraic operation on series and its character.

224. Filter back projection ( FBP ) algorithm, local reconstruction algorithm ( Local RA ) and modified algebraic reconstruction technique are researched.

225. Algebraic was derived constraint for shape recognition, and was use to shape recognition.

226. Then by the principle of superposition and solving two sets of algebraic equations, the interaction between the point force and the point charge was uncoupled.