This paper analyzes non-ideal step down matrix converter (MC) under the control strategy proposed by Venturini [l] using circuit W transformation (CWT) technique [2]. The non-ideal step down MC consists of L. C and switches where L and C act as current and voltage sources, respectively. Closed form solutions for the voltage gain and the input phase angle are obtained from the W transformed equi...

Let N be a complete, orientable, finite-volume, one-cusped hyperbolic 3-manifold with an ideal triangulation. Using combinatorics of the ideal triangulation of N we construct a plane curve in C×C which contains the squares of eigenvalues of PSL(2,C) representations of the meridian and longitude. We show that the defining polynomial of this curve is related to the PSL(2,C) A-polynomial and has p...

A lattice diagram is a finite set L = {(p1, q1), . . . , (pn, qn)} of lattice cells in the positive quadrant. The corresponding lattice diagram determinant is ∆L(Xn;Yn) = det ‖ x pj i y qj i ‖. The space ML is the space spanned by all partial derivatives of ∆L(Xn;Yn). We denote by M 0 L the Y -free component of ML. For μ a partition of n + 1, we denote by μ/ij the diagram obtained by removing t...

A right ideal is a language L over an alphabet Σ that satisfies L = LΣ∗. We show that there exists a stream (sequence) (Rn | n > 3) of regular right ideal languages, where Rn has n left quotients and is most complex under the following measures of complexity: the state complexities of the left quotients, the number of atoms (intersections of complemented and uncomplemented left quotients), the ...

Let I be a homogeneous ideal in a polynomial ring P over a field. By Macaulay’s Theorem, there exists a lexicographic ideal L = Lex(I) with the same Hilbert function as I. Peeva has proved that the Betti numbers of P/I can be obtained from the graded Betti numbers of P/L by a suitable sequence of consecutive cancellations. We extend this result to any ideal I in a regular local ring (R,n) by pa...

Let T denote the full Toeplitz algebra on the Bergman space of the unit ball Bn. For each subset G of L ∞, let CI(G) denote the closed two-sided ideal of T generated by all TfTg − TgTf with f, g ∈ G. It is known that CI(C(Bn)) = K the ideal of compact operators and CI(C(Bn)) = T. Despite these “extremal cases”, T does contain other non-trivial ideals. This paper gives a construction of a class ...

Our main subject is to study the action of the Hecke operators Tl on the Jacobian J of the modular curve X0(N). We consider the Hecke algebra T, i.e. the subring of End(J) generated by the Tl and the involution ω and define the Eisenstein ideal I ⊂ T as the ideal generated by 1 +ω and 1 + l−Tl, l prime 6= N . The Eisenstein quotient of J is the quotient J̃ := J/aJ where a denotes the kernel of t...

We present several explicit constructions of hyperelliptic function fields whose Jacobian or ideal class group has large 3-rank. Our focus is on finding examples for which the genus and the base field are as small as possible. Most of our methods are adapted from analogous techniques used for generating quadratic number fields whose ideal class groups have high 3-rank, but one method, applicabl...

We shall prove the following analogue of a theorem of Kronecker's : Let J be a difference field containing an element t which is distinct from its transforms of any order. Every perfect ideal in the ring 7\yu ' ' ' y y<n\ has a basis consisting of n + 1 difference polynomials. The corresponding theorem for differential polynomials was proved by J. F. Ritt. We shall follow in all but details a b...