Trivariate spline quasi-interpolants based on simplex splines and polar forms

Identification schemes based on multivariate polynomials have been receiving attraction in different areas due to the quantum secure property. Identification is one of the most important elements for the IoT to achieve communication between objects, gather and share information with each other. Thus, identification schemes which are post-quantum secure are significant for Internet-of-Things (IoT) devices. Various polar forms of multivariate quadratic and cubic polynomial systems have been proposed for these identification schemes. There is a need to define polar form for multivariate dth degree polynomials, where d ≥ 4 . In this paper, we propose a solution to this need by defining constructions for multivariate polynomials of degree d ≥ 4 . We give a generic framework to construct the identification scheme for IoT and RFID applications. In addition, we compare identification schemes and curve-based cryptoGPS which is currently used in RFID applications.

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Back Page: My Favorite Lesson: Arctic Search and Destroy

Mathematics Teacher ◽

10.5951/mathteacher.108.1.0080 ◽

2014 ◽

Vol 108 (1) ◽

pp. 80

Author(s):

Cindy Kroon

Keyword(s):

Common Core ◽

Common Core State Standards ◽

State Standards ◽

Polar Coordinate System ◽

Complex Numbers ◽

Core State ◽

Rectangular Coordinates ◽

Polar Coordinate ◽

The Common ◽

Polar Forms

“You sunk my battleship!”Many of us have fond memories of the Milton Bradley game Battleship®. Using rectangular coordinates to identify and sink an opponent's ships remains a classic childhood pastime. A similar activity can be used to help students as they learn to plot positions in the polar coordinate system. The Common Core State Standards for Mathematics (CCSSM) suggest that students “[r]epresent complex numbers on the complex plane in rectangular and polar form, and explain why the rectangular and polar forms of a given complex number represent the same number” (CCSSM Standard N-CN.4).

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Null Spaces of Differential Operators, Polar Forms, and Splines

Journal of Approximation Theory ◽

10.1006/jath.1996.0056 ◽

1996 ◽

Vol 86 (1) ◽

pp. 81-107 ◽

Cited By ~ 10

Author(s):

Dan Gonsor ◽

Marian Neamtu

Keyword(s):

Differential Operators ◽

Polar Forms

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On discrete simplex splines and subdivision

Journal of Approximation Theory ◽

10.1016/0021-9045(92)90066-w ◽

1992 ◽

Vol 70 (3) ◽

pp. 358-374 ◽

Cited By ~ 2

Author(s):

Marian Neamtu

Keyword(s):

Simplex Splines

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Comprehension and production of comparatives and superlatives

Journal of Child Language ◽

10.1017/s0305000900002518 ◽

1979 ◽

Vol 6 (3) ◽

pp. 511-527 ◽

Cited By ~ 14

Author(s):

Thomas L. Layton ◽

Sheldon L. Stick

Keyword(s):

Task Analysis ◽

Lexical Unit ◽

Comprehension Task ◽

Polar Forms

ABSTRACTTen objects were used to assess comprehension, production, and imitation of comparative and superlative suffixes in 100 children ranging in age from 2; 6 to 4; 6. The results indicated that comprehension of both suffix forms was similar at each of five age levels studied; although incrementally better comprehension scores occurred with succeeding ages. Virtually all subjects were successful in imitating forms missed during the comprehension task. Analysis revealed that the -er suffix was produced more often than the -est suffix, at the youngest age (2; 6): at succeeding age levels this difference was reversed. Big was the primary lexical unit selected by the subjects for positive and negative polar forms connoting size; little was the second most frequently used adjective form.

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