On the rationalization of a sum of surds

A program to rationalize the equations ∑⁵_i = 1√y_i = 0 and ∑⁶_i = 1√y_i= 0 is described; here y_i are indeterminates. Complete answers are given for these two cases, and for the elementary cases where the sum consists of three or four terms. The rationalization utilizes a family of algorithms treating the algebra of symmetric functions. This is the first step in the construction of a comprehensive computer package—SYMPACK—designed to carry out all useful manipulations of the five basic symmetric functions. The contents of this package, as currently envisaged, is given in outline.     

The value of MRI in evaluating perirectal and pelvic disease

MRI of the perirectal region is facilitated by the superb soft tissue contrast, multiplanar imaging capability, lack of respiratory motion artifact and absence of clip artifact which can hamper visualization by CT scan. MRI provides distinct advantages over CT scanning without the need for ionizing radiation or the injection of intravenous contrast material. This study reviews the findings in 18 consecutive patients with a variety of perirectal pathologies including rectal carcinoma (3), gynecologic neoplasm (8), sacral lesions (2), pelvic arteriovenous malformations (2), inflammatory bowel disease (2), and a pelvic kidney (1). In the perirectal region, MR was useful to show normal tissue planes, benign processes which can mimic neoplasm, intrapelvic extension of malignancy and adenopathy.     

MRI in staging of endometrial and cervical carcinoma

MRI of 54 patients with endometrial and cervical carcinoma was performed on a 0.6-T superconducting magnet. In 18 of 24 cases of surgically proved endometrial carcinoma, MRI accurately showed the depth of myometrial invasion. MRI was superior to CT scan for defining the primary site and extent of the tumor in 14 of 24 cases. Of 25 patients with cervical carcinoma studied, MRI was superior to CT scan in 15 of 19 cases with CT correlation for localizing the primary site. MRI showed parametrial extension and invasion of surrounding structures but is probably less reliable than CT scan for detection of adenopathy because of false positive findings from volume averaging with bowel.     

Measurement of the mass of110Pd and114Pd using the (14C,16O) reaction

A measurement of the mass excess of¹¹⁰Pd and¹¹⁴Pd has been made by detecting emergent¹⁶O ions in aQ3D magnetic spectrometer using the¹¹²Cd(¹⁴C,¹⁶O)¹¹⁰Pd and¹¹⁶Cd(¹⁴C,¹⁶O)¹¹⁴Pd reactions at 60 MeV. The results are compared with theoretical predictions.     

Ratchet driven by quasimonochromatic noise

The currents generated by noise-induced activation processes in a periodic potential are investigated analytically, by digital simulation and by performing analog experiments. The noise is taken to be quasimonochromatic and the potential to be a smoothed sawtooth. Two analytic approaches are studied. The first involves a perturbative expansion in inverse powers of the frequency characterizing quasimonochromatic noise and the second is a direct numerical integration of the deterministic differential equations obtained in the limit of weak noise. These results, together with the digital and analog experiments, show that the system does indeed give rise, in general, to a net transport of particles. All techniques also show that a current reversal exists for a particular value of the noise parameters.     

Production of vector and tensor mesons in proton-proton collisions at\sqrt s = 52.5 GeV

Inclusive production of ?⁰,f, andg ⁰ mesons and ofK _s ⁰ ,K ^*0 (892), ? andK ^*0(1430)mesons has been measured at <y>～2.6 and <p _T >～1.1 GeV/c in proton-proton interactions at \(\sqrt s = 52.5\) GeV. The negative particle from the two-body decays of these resonances were identified by a threshold Cerenkov counter and used for triggering. Starting from the measured differential cross section, total inclusive cross sections for the vector and tensor mesons were determined using various parametrizations for they andp _T dependence of the differential cross section. The experimental results are discussed in the framework of production models based on the parton picture. The strangeness suppresion factor λ=(0.30±0.10) due toSU(3) symmetry breaking of the quark sea is derived.     

Numerical studies on the anderson localization problem

The electron localization is studied for Anderson's tight-binding model with diagonal and off-diagonal disorder for a very large square lattice (10,000 sites) and diamond lattice (27,000 sites). The numerical investigations are based on the Lanczos recursion method. The convergence of the recursion coefficientsa _n ,b _n is discussed with regard to the electron localization.From Anderson's criterion and an exact real space renormalization method the energy of the localization edge is found as a function of the degree of disorder. Also the dependence of the spatial decay rate of localized wave functions on the energy and the degree of disorder is evaluated. Near the Anderson transition, where all states become localized, we get two critical exponentsv _E andv _W , which lead us to the tentative suggestion of multicritical scaling laws for this transition.     

Convex fuzzy random variables

A theory of fuzzy random variables is developed that applies to situations involving both randomness and fuzziness. The use of membership functions that are quasi-concave play an important role in the theory. The expectation of a fuzzy random variable is a fuzzy variable (fuzzy set). The usual linearity properties of probabilistic expectation carry over to fuzzy random variables. A special case of a fuzzy Law of Large Number is proven.     

Tame combing and almost convexity conditions

We give the first examples of groups which admit a tame combing with linear radial tameness function with respect to any choice of finite presentation, but which are not minimally almost convex on a standard generating set. Namely, we explicitly construct such combings for Thompson??s group F and the Baumslag?CSolitar groups BS(1, p) with p ??? 3. In order to make this construction for Thompson??s group F, we significantly expand the understanding of the Cayley complex of this group with respect to the standard finite presentation. In particular we describe a quasigeodesic set of normal forms and combinatorially classify the arrangements of 2-cells adjacent to edges that do not lie on normal form paths.