نتایج جستجو برای: rational function
تعداد نتایج: 1270425 فیلتر نتایج به سال:
The integral of a rational function proposed as a question in Mathematics Stack Exchange is evaluated. The integrand has a polynomial of degree 4 as denominator. A natural extension to degree 8 is shown to vanish.
We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The proposed method treats D-, E-, A-, and Φp-optimal designs in a unified manner, and generates a polynomial whose zeros are the support points of the optimal appr...
Theories of how people learn relationships between continuous variables have tended to focus on two possibilities: one, that people are estimating explicit functions, or two that they are performing associative learning supported by similarity. We provide a rational analysis of function learning, drawing on work on regression in machine learning and statistics. Using the equivalence of Bayesian...
A smooth surface interpolation scheme for positive and convex data has been developed. This scheme has been extended from the rational quadratic spline function of Sarfraz [11] to a rational bi-quadratic spline function. Simple data dependent constraints are derived on the free parameters in the description of rational bi-quadratic spline function to preserve the shape of 3D positive and convex...
Of 144 patients with suspected pancreatic disease in whom a 75Se-selenomethionine scan was performed, endoscopic retrograde pancreatography (ERP) was successful in 108 (75%). The final diagnosis is known in 100 patients and has been compared with scan and ERP findings. A normal scan reliably indicated a normal pancreas, but the scan was falsely abnormal in 30%. ERP distinguished between carcino...
Abramov’s algorithm enables us to decide whether a univariate rational function can be written as a difference of another rational function, which has been a fundamental algorithm for rational summation. In 2014, Chen and Singer have generalized Abramov’s algorithm to the case of rational functions in two (q-)discrete variables. In this paper we solve the remaining three mixed cases, which comp...
Computer algebra systems (CAS) usually support computation with exact or approximate rational functions stored as ratios of polynomials in “expanded form” with explicit coefficients. We examine the consequences of using a partial-fraction type of form in which all rational functions are expressed as a polynomial plus a sum of terms each of which has a denominator consisting of a monic univariat...
My talk will be based on paper " Synthesis of two-dimensional loss-less m-ports with prescribed scattering matrix " by A. Kummert.
Let G be a split reductive group over a finite field Fq. Let F = Fq(t) and let A denote the adèles of F . We show that every double coset in G(F)\G(A)/K has a representative in a maximal split torus of G. Here K is the set of integral adèlic points of G. When G ranges over general linear groups this is equivalent to the assertion that any algebraic vector bundle over the projective line is isom...
Let m, n be nonnegative integers and a<m+n) be a set of m + n + 1 real in~lation points (not necessarily distinct). Let Rm.n = P m.n / Qm.n be the unique rational function with degPm.n ::; m, deg Qm,n :$n, that in~lates e'" in the points of a<nr+n). Ifm = mv, n = nv with mv + nv --+ 00, and mv /nv --+ A as v --+ 00, and the sets a<nr+n) are uniformly bounded, we show that Pm.n(z) --+ ~/(l+)'), ...
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