On the Remainders Obtained in Finding the Greatest Common Divisor of Two Polynomials

In 1917 Pell (1) and Gordon used sylvester2, Sylvester’s little known and hardly ever used matrix of 1853, to compute(2) the coefficients of a Sturmian remainder — obtained in applying in Q[x], Sturm’s algorithm on two polynomials f, g ∈ Z[x] of degree n — in terms of the determinants (3) of the corresponding submatrices of sylvester2. Thus, they solved a problem that had eluded both J. J. Sylvester, in 1853, and E. B. Van Vleck, in 1900. (4) In this paper we extend the work by Pell and Gordon and show how to compute (2) the coefficients of an Euclidean remainder — obtained in finding in Q[x], the greatest common divisor of f, g ∈ Z[x] of degree n — in terms of the determinants (5) of the corresponding submatrices of sylvester1, Sylvester’s widely known and used matrix of 1840. (1) See the link http://en.wikipedia.org/wiki/Anna_Johnson_Pell_Wheeler for her biography (2) Both for complete and incomplete sequences, as defined in the sequel. (3) Also known as modified subresultants. (4) Using determinants Sylvester and Van Vleck were able to compute the coefficients of Sturmian remainders only for the case of complete sequences. (5) Also known as (proper) subresultants.

Lp extremal polynomials. Results and perspectives

2000 Mathematics Subject Classification: 30C40, 30D50, 30E10, 30E15, 42C05.

Approximation Properties of Schurer-Stancu Type Polynomials

MSC 2010: 41A25, 41A35

On Thom Polynomials for A4(−) via Schur Functions

2000 Mathematics Subject Classification: 05E05, 14N10, 57R45.

Smale's Conjecture on Mean Values of Polynomials and Electrostatics

2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.

Some Coefficient Estimates for Polynomials on the Unit Interval

2000 Mathematics Subject Classification: 26C05, 26C10, 30A12, 30D15, 42A05, 42C05.

Predegree Polynomials of Plane Configurations in Projective Space

2000 Mathematics Subject Classification: 14N10, 14C17.

Letter to the Editor. Remarks on Some Inequalities for Polynomials

MSC 2010: 30A10, 30C10, 30C80, 30D15, 41A17.

Even and Old Overdetermined Strata for Degree 6 Hyperbolic Polynomials

2000 Mathematics Subject Classification: 12D10.

Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials

MSC 2010: 30C10, 32A30, 30G35

Integral Representations of Functional Series with Members Containing Jacobi Polynomials

MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10

Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.

Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32

Development of a multivariable online monitoring system for the thermoforming process

The thermoforming industry has been relatively slow to embrace modern measurement technologies. As a result researchers have struggled to develop accurate thermoforming simulations as some of the key aspects of the process remain poorly understood. For the first time, this work reports the development of a prototype multivariable instrumentation system for use in thermoforming. The system contains sensors for plug force, plug displacement, air pressure and temperature, plug temperature, and sheet temperature. Initially, it was developed to fit the tooling on a laboratory thermoforming machine, but later its performance was validated by installing it on a similar industrial tool. Throughout its development, providing access for the various sensors and their cabling was the most challenging task. In testing, all of the sensors performed well and the data collected has given a powerful insight into the operation of the process. In particular, it has shown that both the air and plug temperatures stabilize at more than 80C during the continuous thermoforming of amorphous polyethylene terephthalate (aPET) sheet at 110C. The work also highlighted significant differences in the timing and magnitude of the cavity pressures reached in the two thermoforming machines. The prototype system has considerable potential for further development. 

Application of multivariable control using artificial neural networks in a debutanizer distillation column

LOPES, Jose Soares Batista et al. Application of multivariable control using artificial neural networks in a debutanizer distillation column.In: INTERNATIONAL CONGRESS OF MECHANICAL ENGINEERING - COBEM, 19, 5-9 nov. 2007, Brasilia. Anais... Brasilia, 2007