Let A = K[x1, . . . , xn] denote the polynomial ring in n variables over a field K. We will classify all the Gotzmann ideals of A with at most n generators. In addition, we will study Hilbert functions H for which all homogeneous ideals of A with the Hilbert function H have the same graded Betti numbers. These Hilbert functions will be called inflexible Hilbert functions. We introduce the notio...

We describe the eventual behaviour of the Hilbert function of a set of distinct points in Pn1 × · · · × Pnk . As a consequence of this result, we show that the Hilbert function of a set of points in Pn1 × · · · × Pnk can be determined by computing the Hilbert function at only a finite number of values. Our result extends the result that the Hilbert function of a set of points in Pn stabilizes a...

in this paper some new applications of empirical mode decomposition (emd) and hilbert spectrum in seismic ground-roll attenuation, random noise attenuation and spectral decomposition are introduced. hilbert spectrum is a time-frequency representation for hilbert-huang transform which is obtained by combination of instantaneous frequency (if) concept and intrinsic mode function of empirical mode...

We show that the Hilbert scheme, that parametrizes all ideals with the same Hilbert function over a Clements-Lindtröm ring W, is connected. More precisely, we prove that every graded ideal is connected by a sequence of deformations to the lex-plus-powers ideal with the same Hilbert function. Our result is an analogue of Hartshorne’s theorem that Grothendieck’s Hilbert scheme is connected; howev...

Let $T$ be a bounded linear operator on a Hilbert space $mathscr{H}$. We say that $T$ has the hyponormal property if there exists a function $f$, continuous on an appropriate set so that $f(|T|)geq f(|T^ast|)$. We investigate the properties of such operators considering certain classes of functions on which our definition is constructed. For such a function $f$ we introduce the $f$-Aluthge tran...

we investigate a class of fourth-order differential operators with eigenparameter dependent boundary conditions and transmission conditions. a self-adjoint linear operator a is defined in a suitable hilbert space h such that the eigenvalues of such a problem coincide with those of a . we discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions. finally, we obtain th...