STUDY B-SPLINE OF SIXTH ORDER AND THEIR LINEAR COMBINATION

We present a complete and minimal catalogue of MSSM gauge invariant monomials. That is, the catalogue of Gherghetta, Kolda and Martin is elaborated to include generational structure for all monomials. Any gauge invariant operator can be built as a linear combination of elements of the catalogue lifted to nonnegative integer powers. And the removal of any one of the monomials would deprive the catalogue of this feature. It contains 712 monomials, plus 3 generations of right-handed neutrinos if one extends the model to the νMSSM. We note that νMSSM flat directions can all be lifted by the sixth-order superpotential compared to the ninth-order needed in MSSM.

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Application of Techniques of Homotopy Types to Sixth Order Boundary Value Problems and Comparing the Results with Cubic B-Spline Collocation Method

Journal of Advanced Physics ◽

10.1166/jap.2018.1457 ◽

2018 ◽

Vol 7 (4) ◽

pp. 510-517

Author(s):

Muhammad Naeem ◽

Sher Muhammad ◽

Syed Asif Hussain ◽

Mohammad Ishaq ◽

Syed Inayat Ali Shah

Keyword(s):

Boundary Value Problems ◽

Collocation Method ◽

Boundary Value ◽

Sixth Order ◽

Spline Collocation ◽

B Spline ◽

Spline Collocation Method ◽

Homotopy Types

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Numerical solution of sixth order boundary value problems with sixth degree B-spline functions

Applied Mathematics and Computation ◽

10.1016/j.amc.2006.08.068 ◽

2007 ◽

Vol 186 (2) ◽

pp. 992-999 ◽

Cited By ~ 12

Author(s):

G.B. Loghmani ◽

M. Ahmadinia

Keyword(s):

Numerical Solution ◽

Boundary Value Problems ◽

Boundary Value ◽

Sixth Order ◽

Spline Functions ◽

B Spline

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An optimal sixth‐order quartic B‐spline collocation method for solving Bratu‐type and Lane‐Emden–type problems

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.5537 ◽

2019 ◽

Vol 42 (8) ◽

pp. 2613-2630 ◽

Cited By ~ 11

Author(s):

Pradip Roul ◽

Kiran Thula ◽

VMK Prasad Goura

Keyword(s):

Collocation Method ◽

Sixth Order ◽

Spline Collocation ◽

B Spline ◽

Spline Collocation Method

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An Example of Two-Dimensional Interpolation Using a Linear Combination of Bicubic B-Splines

International Journal of Electronics and Telecommunications ◽

10.2478/v10177-011-0039-2 ◽

2011 ◽

Vol 57 (3) ◽

pp. 293-299

Author(s):

Stanisław Rosłoniec

Keyword(s):

Linear Combination ◽

Short Description ◽

Two Dimensional ◽

Interpolation Algorithm ◽

Rectangular Grid ◽

B Spline ◽

One Dimensional ◽

The Real ◽

B Splines

An Example of Two-Dimensional Interpolation Using a Linear Combination of Bicubic B-Splines The paper describes how a linear combination of bicubic B-splines can be effectively used in a two-dimensional interpolation. It is assumed that values of a function to be interpolated are evaluated at the uniformly located nodes of a corresponding rectangular grid. All formulae of importance have been derived step by step and are presented in a form convenient for computer implementations. To ensure clarity of considerations a short description of one-dimensional B-spline is also given in Appendix 1. The usefulness of the presented interpolation algorithm has been confirmed by the real engineering example of applications.

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