“…See Eq. (7) in [1] and the discussion following that equation. This observation implies the preceding methods are potentially more fertile than methods that are based on applied operational calculus [2,3].…”
Section: Discussionmentioning
confidence: 98%
“…1. The coordinates of vertices A, B, C, and D are (-1,-1), (1,-1), (-1,1), and (1,1) respectively. The distance between any vertex and its two nearest neighbors is two units.…”
Section: A Cubic Equation For Four Positive Numbers In a Rectangular mentioning
confidence: 99%
“…Several years ago, a new equation appeared for the interpolation of four positive, bilinear numbers in rectangular array. The new equation is also exact on the squares of the original bilinear numbers [1].…”
Four numbers in a rectangular array can be interpolated by the bilinear equation. If the numbers are positive, they can be interpolated by a new bi-cubic equation. The array can be interpolated by eight new fourth-degree equations. The positive squareroots of the fourth-degree equations are new bi-quadratic equations that are applicable to the analysis of the same four-point arrays. The new equations are suitable for the analysis of two-parameter laboratory experiments. Mathematics Subject Classification: 65D05, 65D07, 65D17
“…See Eq. (7) in [1] and the discussion following that equation. This observation implies the preceding methods are potentially more fertile than methods that are based on applied operational calculus [2,3].…”
Section: Discussionmentioning
confidence: 98%
“…1. The coordinates of vertices A, B, C, and D are (-1,-1), (1,-1), (-1,1), and (1,1) respectively. The distance between any vertex and its two nearest neighbors is two units.…”
Section: A Cubic Equation For Four Positive Numbers In a Rectangular mentioning
confidence: 99%
“…Several years ago, a new equation appeared for the interpolation of four positive, bilinear numbers in rectangular array. The new equation is also exact on the squares of the original bilinear numbers [1].…”
Four numbers in a rectangular array can be interpolated by the bilinear equation. If the numbers are positive, they can be interpolated by a new bi-cubic equation. The array can be interpolated by eight new fourth-degree equations. The positive squareroots of the fourth-degree equations are new bi-quadratic equations that are applicable to the analysis of the same four-point arrays. The new equations are suitable for the analysis of two-parameter laboratory experiments. Mathematics Subject Classification: 65D05, 65D07, 65D17
“…Operational methods [2] permit the developments of many unexpected results. The representations of four-and five-point rectangles, and eight-and nine-point rectangular prisms by quadratic, cubic, exponential, and trigonometric equations are among the developments [1][2][3][4][5]. Eq.…”
“…The bilinear equation is the standard method for interpolating surfaces described by four data in a rectangular array. A quadratic equation for this design was illus-trated several years ago [1]. It was first derived by operational methods [2].…”
Four-point rectangles can be interpolated by bilinear equations, by quadratic equations, and by cubic equations. A new cubic equation for the four-point rectangle is illustrated by numerical examples.
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