188,654 research outputs found
Hyperbolic hypersurfaces in P^n of Fermat-Waring type
No full text5 pagesInternational audienceIn this note we show that there are algebraic families of hyperbolic, Fermat-Waring type hypersurfaces in P^n of degree 4(n-1)^2, for all dimensions n>1. Moreover, there are hyperbolic Fermat-Waring hypersurfaces in P^n of degree 4n^2-2n+1 possessing complete hyperbolic, hyperbolically embedded complements.S 0002-9939(01)06417-6Article electronically published on December 27, 200
Waring identifiable subspaces over finite fields
Get PDFWaring's problem, of expressing an integer as the sum of powers, has a very
long history going back to the 17th century, and the problem has been studied
in many different contexts. In this paper we introduce the notion of a Waring
subspace and a Waring identifiable subspace with respect to a projective
algebraic variety . When is the Veronese variety,
these subspaces play a fundamental role in the theory of symmetric tensors and
are related to the Waring decomposition and Waring identifiability of symmetric
tensors (homogeneous polynomials). We give several constructions and
classification results of Waring identifiable subspaces with respect to the
Veronese variety in and in
, and include some applications to the theory
of linear systems of quadrics in
Fixed-Parameter Debordering of Waring Rank
Get PDFBorder complexity measures are defined via limits (or topological closures), so that any function which can approximated arbitrarily closely by low complexity functions itself has low border complexity. Debordering is the task of proving an upper bound on some non-border complexity measure in terms of a border complexity measure, thus getting rid of limits.
Debordering is at the heart of understanding the difference between Valiant’s determinant vs permanent conjecture, and Mulmuley and Sohoni’s variation which uses border determinantal complexity. The debordering of matrix multiplication tensors by Bini played a pivotal role in the development of efficient matrix multiplication algorithms. Consequently, debordering finds applications in both establishing computational complexity lower bounds and facilitating algorithm design. Currently, very few debordering results are known.
In this work, we study the question of debordering the border Waring rank of polynomials. Waring and border Waring rank are very well studied measures in the context of invariant theory, algebraic geometry, and matrix multiplication algorithms. For the first time, we obtain a Waring rank upper bound that is exponential in the border Waring rank and only linear in the degree. All previous known results were exponential in the degree. For polynomials with constant border Waring rank, our results imply an upper bound on the Waring rank linear in degree, which previously was only known for polynomials with border Waring rank at most 5
A note on empirical sample distribution of journal impact factors in major discipline groups
Get PDFWhat type of statistical distribution do the Journal Impact Factors follow? In the past, researchers have hypothesized various types of statistical distributions underlying the generation mechanism of journal impact factors. These are: lognormal, normal, approximately normal, Weibull, negative exponential, combination of exponentials, Poisson, Generalized inverse Gaussian-Poisson, negative binomial, generalized Waring, gamma, etc. It is pertinent to note that the major characteristics of JIF data lay in the asymmetry and non-mesokurticity. The present study, frequently encounters Burr-XII, inverse Burr-III (Dagum), Johnson SU, and a few other distributions closely related to Burr distributions to best fit the JIF data in subject groups such as biology, chemistry, economics, engineering, physics, psychology and social sciences.Journal impact factor; JIF; theoretical probability distribution; Burr; Dagum; Generalized extreme value; generalized gamma; Inverse Gaussian; Johnson SU; Johnson SB; Kumaraswamy; Log-logistic; lognonmal; log-Pearson; Weibull; Generalized normal; Hypersecant; Beta; empirical distribution; sample
On real Waring decompositions of real binary forms
Get PDFThe Waring Problem over polynomial rings asks how to decompose a homogeneous polynomial p of degree d as a finite sum of d-th powers of linear forms. In this work we give an algorithm to obtain a real Waring decomposition of any given real binary form p of length at most its degree. In fact, we construct a semialgebraic family of Waring decompositions for p. Some examples are shown to highlight the difference between the real and the complex case.Ministerio de Ciencia e Innovación (MICINN)Universidad Complutense de MadridFac. de Ciencias MatemáticasInstituto de Matemática Interdisciplinar (IMI)FALSEunpu
A note on the computation of an actuarial Waring formula in the finite-exchangeable case
Get PDFWe present in this paper the actuarial Waring formula, which is used in several fields, like life-insurance or credit risk. In a particular framework where considered random variables are exchangeable, we show that some problems can occur when using this formula. We propose alternative recursions in order to improve the complexity of the calculations, and to cope with the numerical instability of the formula.
Waring decompositions of special ternary forms with different Hilbert functions
No full textWe prove the existence of ternary forms admitting apolar sets of points of cardinality equal to the Waring rank, but having different Hilbert function and different regularity. This is done exploiting liaison theory and Cayley-Bacharach properties for sets of points in the projective plane
On Waring numbers of henselian rings
Get PDFLet be a positive integer. Let be a henselian local ring with residue field of th level . We give some upper and lower bounds for the th Waring number in terms of and . In large number of cases we are able to compute . Similar results for the th Waring number of the total ring of fractions of are obtained. We then provide applications. In particular we compute and for and any prime .34 pages, final version, to appear in Mathematik
Waring Rank and Apolarity of Some Symmetric Polynomials
Get PDFWe examine lower bounds for the Waring rank for certain types of symmetric polynomials. The first are Schur polynomials, a symmetric polynomial indexed by integer partitions. We prove some results about the Waring rank of certain types of Schur polynomials, based on their integer partition. We also make some observations about the Waring rank in general for Schur polynomials, based on the shape of their Semistandard Young Tableaux. The second type of polynomials we refer to as a Power of a Fermat-type polynomial, or a PFT polynomial. This is a Fermat type (or power sum) polynomial over n variables with degree p taken to some power k. We prove this polynomial is not compressed when p \u3e k and k \u3e 2, and conjecture the result is true in general for all p. The proof takes the following form: the degree k + 1 annihilator ideal is examined and identified, and form of Rank-Nullity is applied, which provides a formula for the size of the degree k + 1 subspace of non-zero partial derivatives for that polynomial. Then we verify that this subspace is linearly independent, which gives us the dimension of the space of Derivs, and thus a lower bound for the Waring rank of that polynomial
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