The stability of axisymmetric plasmas confined by closed poloidal magnetic field lines is considered. The results are relevant to plasmas in the dipolar fields of stars and planets, as well as the Levitated Dipole Experiment, multipoles, Z pinches and field reversed configurations. The ideal MHD energy principle is employed to study the stability of pressure driven shear Alfvén modes. A point d...

Let εD = v+u √ D be the fundamental unit of Z[ √ D] with Z being the ordinary integers, or maximal order, in the rational field Q. We prove that for any square-free integer D > 1, with D not dividing u, there exists a prime fD such that the relative class number HD(fD) = hf2 DD/hD = 1, where hD is the ideal class number of Z[ √ D] and hf2 DD is the ideal class number of Z[fD √ D], the order of ...

shown in Fig. 2 and like the circuits of [I], realise an FI of value .Z-2 = Z,Z2 / Z 3 without requiring any passive component matching conditions. Changing the connections a,-b,, arbz to a,-b,, a, b, facilitates the realisation of negative FIs from the same circuits. A variety of single-resistance-tunable floating elements (such as ideal floating inductance, ideal resistively-variable floating...

The standard security definition of unconditional secure function evaluation, which is based on the ideal/real model paradigm, has the disadvantage of being overly complicated to work with in practice. On the other hand, simpler ad-hoc definitions tailored to special scenarios have often been flawed. Motivated by this unsatisfactory situation, we give an information-theoretic security definitio...

denote the ring of integer-valued polynomials on D with respect to the subset E (for ease of notation, if E = D, then set Int(D,D) = Int(D)). Gilmer’s work in this area (with the assistance of various co-authors) was truly groundbreaking and led to numerous extensions and generalizations by authors such as J. L. Chabert, P. J. Cahen, D. McQuillan and A. Loper. In this paper, we will review Gilm...

We construct a model with an indecisive precipitous ideal and a model with a precipitous ideal with a non precipitous normal ideal below it. Such kind of examples were previously given by M. Foreman [1] and R. Laver [4] respectively. The present examples differ in two ways: firstthey use only a measurable cardinal and secondthe ideals are over a cardinal. Also a precipitous ideal without a norm...

We consider two-class linear classification in a high-dimensional, low-sample size setting. Only a small fraction of the features are useful, the useful features are unknown to us, and each useful feature contributes weakly to the classification decision – this setting was called the rare/weak model (RW Model) in [11]. We select features by thresholding feature z-scores. The threshold is set by...

The method (theory plus algorithms) of Gröbner bases provides a uniform approach to solving a wide range of problems expressed in terms of sets of multivariate polynomials. x y 2y z z 0 y 2 x 2 z x z 0 z 2 y 2 x x 0 Example: kinematic equations of a robot. algebraic geometry, commutative algebra, polynomial ideal theory invariant theory automated geometrical theorem proving Groebner-Bases.nb 1

Let Z be a finite set of double points in P 1 × P 1 and suppose further that X, the support of Z, is arithmetically Cohen-Macaulay (ACM). We present an algorithm, which depends only upon a combinatorial description of X, for the bigraded Betti numbers of I Z , the defining ideal of Z. We then relate the total Betti numbers of I Z to the shifts in the graded resolution, thus answering a special ...

This paper deals with a question regarding tight closure in characteristic zero which we now review. Let R be a commutative ring of prime characteristic p and let I ⊆ R be an ideal. Recall that for e ≥ 0, the e-th Frobenius power of I, denoted I [p e], is the ideal of R generated by all p-th powers of elements in I. We say that f ∈ I∗, the tight closure of I, if there exists a c not in any mini...