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Full-Text Articles in Physical Sciences and Mathematics
About A Non-Standard Interpolation Problem, Daniel Alpay, Alain Yger
About A Non-Standard Interpolation Problem, Daniel Alpay, Alain Yger
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using algebraic methods, and motivated by the one variable case, we study a multipoint interpolation problem in the setting of several complex variables. The duality realized by the residue generator associated with an underlying Gorenstein algebra, using the Lagrange interpolation polynomial, plays a key role in the arguments.
Interpolating Between Hilbert–Samuel And Hilbert–Kunz Multiplicity, William D. Taylor
Interpolating Between Hilbert–Samuel And Hilbert–Kunz Multiplicity, William D. Taylor
Mathematical Sciences Faculty Research
We define a function, called s-multiplicity, that interpolates between Hilbert–Samuel multiplicity and Hilbert–Kunz multiplicity by comparing powers of ideals to the Frobenius powers of ideals. The function is continuous in s, and its value is equal to Hilbert–Samuel multiplicity for small values of s and is equal to Hilbert–Kunz multiplicity for large values of s. We prove that it has an Associativity Formula generalizing the Associativity Formulas for Hilbert–Samuel and Hilbert–Kunz multiplicity. We also define a family of closures such that if two ideals have the same s-closure then they have the same s-multiplicity, and the converse holds under mild …
Organic Agricultural Analysis: Efficiency Of Common Practices, Bradley Biega
Organic Agricultural Analysis: Efficiency Of Common Practices, Bradley Biega
Undergraduate Journal of Mathematical Modeling: One + Two
To analyze the efficiency of common watering practices in an organic agriculture setting we use Sweetwater Organic Farm’s conventional methods for irrigation and land allotment as well as some algebra and calculus technique. Sweetwater’s operation is limited to their largest growing field. A mathematical model is built to determine the current efficiency of the rotary head sprinkler system. Then the efficiency of this system is compared to a new drip line system. Several variables like soil porosity, absorption rates, and areas where no plants are located, are taken into consideration. Our results show that the current irrigation in place wastes …