There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

2004아테네 올림픽대회출전 한국레슬링 대표선수의 무산소성 운동능력 및 등속성 근력

Now more than ever, Gravitation and Spacetime, Second Edition, by Hans C. Ohanian and new coauthor Remo Ruffini, deserves John Wheeler's praise as "the best book on the market today of 500 pages or less on gravitation and general relativity." Gravitation and Spacetime has been thoroughly updated with the most exciting finds and hottest theoretical topics in general relativity and cosmology. Highlights of the revision include the rise and fall of the fifth force, principles and applications of gravitational lensing, COBE's spectacular confirmation of the blackbody spectrum of the cosmic thermal radiation, theories of dark matter and inflation, and the early universe as a testing ground for particle physicists' unification theories, and much, much more. The ideal choice for a graduate-level introduction to general relativity, Gravitation and Spacetime is also suitable for an advanced undergaduate course.

Gravitation and spacetime.

2003-예방원년, 소아과 의사의 역할

1 S-polynomials eliminating the leading term Buchberger's criterion and algorithm 2 Wavelet Design construct wavelet filters 3 Proof of the Buchberger Criterion two lemmas proof of the Buchberger criterion termination and elimination

Gröbner Bases와 응용

We present a new method for implicitization of parametric curves, surfaces and hypersurfaces usingessen tially numerical linear algebra. The method is applicable for polynomial, rational as well as trigonometric parametric representations. The method can also handle monoparametric families of parametric curves, surfaces and hypersurfaces with a small additional amount of human interaction. We illustrate the method with a number of examples. The efficiency of the method compares well with the other available methods for implicitization.

Numerical Implicitization of Parametric Hypersurfaces with Linear Algebra

A new algorithm is presented for factoring bivariate approximate polynomials over C[x, y] Given a particular polynomial, the method constructs a nearby composite polynomial, if one exists, and its irreducible factors Subject to a conjecture, the time to produce the factors is polynomial in the degree of the problem This method has been implemented in Maple, and has been demonstrated to be efficient and numerically robust

/pdf/towards-factoring-bivariate-approximate-polynomials-1n0jj1z864.pdf

Towards factoring bivariate approximate polynomials

In this paper, we propose a new semi-numerical algorithmic method for factoring multivariate polynomials absolutely. It is based on algebraic and geometric properties after reduction to the bivariate case in a generic system of coordinates. The method combines 4 tools: zero-sum relations at triplets of points, partial information on monodromy action, Newton interpolation on a structured grid, and a homotopy method. The algorithm relies on a probabilistic approach and uses numerical computations to propose a candidate factorization (with probability almost one) which is later validated.

/pdf/a-geometric-numeric-algorithm-for-absolute-factorization-of-1o5hzs212y.pdf

A geometric-numeric algorithm for absolute factorization of multivariate polynomials

A collection of complex sequences of length $$v$$ v is complementary if the sum of their periodic autocorrelation function values at all non-zero shifts is constant. For a complex sequence $$A = [a_0,a_1,\ldots ,a_{v-1}]$$ A = [ a 0 , a 1 , ... , a v - 1 ] of length $$v = dm$$ v = d m we define the $$m$$ m -compressed sequence $$A^{(d)}$$ A ( d ) of length $$d$$ d whose terms are the sums $$a_i + a_{i+d} + \cdots + a_{i+(m-1)d}$$ a i + a i + d + ? + a i + ( m - 1 ) d . We prove that the $$m$$ m -compression of a complementary collection of sequences is also complementary. The compression procedure can be used to simplify the construction of complementary $$\{\pm 1\}$$ { ± 1 } -sequences of composite length. In particular, we construct several supplementary difference sets $$(v;r,s;\lambda )$$ ( v ; r , s ; ? ) with $$v$$ v even and $$\lambda = (r+s)-v/2$$ ? = ( r + s ) - v / 2 , given here for the first time. There are 15 normalized parameter sets $$(v;r,s;\lambda )$$ ( v ; r , s ; ? ) with $$v\le 50$$ v ≤ 50 for which the existence question was open. We resolve all but one of these cases.

Compression of periodic complementary sequences and applications

We apply computational algebra methods to the construction of Hadamard matrices with two circulant cores, given by Fletcher, Gysin and Seberry. We introduce the concept of Hadamard ideal, to systematize the application of computational algebra methods for this construction. We use the Hadamard ideal formalism to perform exhaustive search constructions of Hadamard matrices with two circulant cores for the twelve orders 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52. The total number of such Hadamard matrices is proportional to the square of the parameter. We use the Hadamard ideal formalism to compute the proportionality constants for the twelve orders listed above. Finally, we use the Hadamard ideal formalism to improve the lower bounds for the number of inequivalent Hadamard matrices for the seven orders 44, 48, 52, 56, 60, 64, 68.

/pdf/hadamard-ideals-and-hadamard-matrices-with-two-circulant-23j7ftcxk9.pdf

Ilias S. Kotsireas

Papers

Numerical Implicitization of Parametric Hypersurfaces with Linear Algebra

Towards factoring bivariate approximate polynomials

A geometric-numeric algorithm for absolute factorization of multivariate polynomials

Compression of periodic complementary sequences and applications

Hadamard ideals and Hadamard matrices with two circulant cores