In addition, utilizing properties of the Levi-Civita symbol, the program can derive types of multi-term vector identities that are not recognized by reduction, subsequently applying these to simplify large expressions. In a companion paper (Burby et al., 2013), we employ VEST in the automation...
In this case study, a Support Vector Classifier function has been developed in Mathematica. Starting with a brief summary of the support vector classification method, a step by step implementation of the classification algorithm is presented. Using this function, two test problems -- learning a ...
A translation is a displacement of a vector by the addition of a nonzero vector. Illustration ■ Translation of vectors in ℝ2 translation[vector_] := vector + {3, 4} translation[{5, 6}] {8, 10} ■ Translation of vectors in ℝ3 translation[vector_] :=vector + {a, b, c} tr...
In addition, Section 4 will explore conformal projective vector fields. Conformal vector fields are crucial. They are significant elements in the study of the geometry of various types of manifolds. A smooth vector field P on a semi-Riemannian manifold (𝑁,ℎ)(N,h) is termed a conformal ...
In addition, it is possible to take the representation tensor product to get another representation. All of these versions of tensor product can be understood as module tensor products. The trick is to find the right way to think of these spaces as modules. ...
In particular, scalar and vector currents contain terms of the form AaµRiRj , AaµAb,ν Acν , (2.26) which at two loops give the diagrams shown in figures 2a and 2b. However, in Feynman gauge these diagrams vanish. In addition, the ghost-current shown in figure 1d does not ...
ActaMathematicaSinica, EnglishSeries ⑥Springer-VerlagBerlinHeidelberg& TheEditorial0师ceofAMS2014 OnDoubleVectorBundles zhuoCHEN Departmento/Mathematics,TsinghuaUniversity,Beijing100084,P.R.China E-mail:zehen@math.tsinghn.edu.cn ZhangJuLIU DepartmentofMathematicsandLMAM,PekingUniversity,Beijing100871,P.R.Chi...
In addition several methods are reviewed and compared. 1001 被引用 · 1 笔记 引用 The university of Florida sparse matrix collection Timothy A. DavisYifan Hu ACM Transactions on Mathematical Software Nov 2011 We describe the University of Florida Sparse Matrix Collection, a large and actively ...
The lysis systems that have been applied in germs mainly include: the lysis system based on regulated delayed peptidoglycan synthesis, the lysis system based on the regulation of bacteriophage lysis protein and the lysis system based on the toxin-antitoxin system. In addition, a potential lysis ...
Then the set S ¼ fz 2 C : kzk ¼ 1g [ f0g inherits the hyperfield structure from T C: The hyperoperation addition is as follows: z1 ÅS z2 ¼ z1 Å z2 \ S ¼ & fc 2 C :c2 S; Sz1z2 g; if z1 þ z2 6¼ 0; otherwise; for all z1; z2 2 S: ...