Relatively hyperbolic groups, rapid decay algebras, and a generalization of the Bass conjecture

By deploying dense subalgebras of $\ell^1(G)$ we generalize the Bass conjecture in terms of Connes' cyclic homology theory. In particular, we propose a stronger version of the $\ell^1$-Bass Conjecture. We prove that hyperbolic groups relative to finitely many subgroups, each of which posses the polynomial conjugacy-bound property and nilpotent periodicity property, satisfy the $\ell^1$-Stronger-Bass Conjecture. Moreover, we determine the conjugacy-bound for relatively hyperbolic groups and compute the cyclic cohomology of the $\ell^1$-algebra of any discrete group.Comment: 32 pages, 2 figures; added an appendix also by C. Ogl

Analysis of a Magnetically Trapped Atom Clock

We consider optimization of a rubidium atom clock that uses magnetically trapped Bose condensed atoms in a highly elongated trap, and determine the optimal conditions for minimum Allan variance of the clock using microwave Ramsey fringe spectroscopy. Elimination of magnetic field shifts and collisional shifts are considered. The effects of spin-dipolar relaxation are addressed in the optimization of the clock. We find that for the interstate interaction strength equal to or larger than the intrastate interaction strengths, a modulational instability results in phase separation and symmetry breaking of the two-component condensate composed of the ground and excited hyperfine clock levels, and this mechanism limits the clock accuracy.Comment: 11 pages, 6 figures. Accepted for publication in Phys. Rev.

Analyzing the test process using structural coverage

A large, commercially developed FORTRAN program was modified to produce structural coverage metrics. The modified program was executed on a set of functionally generated acceptance tests and a large sample of operational usage cases. The resulting structural coverage metrics are combined with fault and error data to evaluate structural coverage. It was shown that in the software environment the functionally generated tests seem to be a good approximation of operational use. The relative proportions of the exercised statement subclasses change as the structural coverage of the program increases. A method was also proposed for evaluating if two sets of input data exercise a program in a similar manner. Evidence was provided that implies that in this environment, faults revealed in a procedure are independent of the number of times the procedure is executed and that it may be reasonable to use procedure coverage in software models that use statement coverage. Finally, the evidence suggests that it may be possible to use structural coverage to aid in the management of the acceptance test processed

Piecewise-linear pseudodiagrams

There are 2^n possible resolutions of a smooth pseudodiagram with n precrossings. If we consider piecewise-linear (PL) pseudodiagrams and resolutions that themselves are PL, certain resolutions of the pseudodiagram may not exist in three-space. We investigate this situation and its impact on the weighted resolution set of PL pseudodiagrams as well as introduce a concept specific to PL pseudodiagrams, the forcing number. Our main result classifies the PL shadows whose weighted resolution sets differ from the weighted resolution set that would exist in the smooth case.Comment: 7 pages, 8 figures; V2 fixes a minor typo in both statement of Cor. 2.8 and in its proo

Truth and Probability

Contains two other essays as well: Further Considerations & Last Papers: Probability and Partial Belief.

ARROWSMITH-P: A prototype expert system for software engineering management

Although the field of software engineering is relatively new, it can benefit from the use of expert systems. Two prototype expert systems were developed to aid in software engineering management. Given the values for certain metrics, these systems will provide interpretations which explain any abnormal patterns of these values during the development of a software project. The two systems, which solve the same problem, were built using different methods, rule-based deduction and frame-based abduction. A comparison was done to see which method was better suited to the needs of this field. It was found that both systems performed moderately well, but the rule-based deduction system using simple rules provided more complete solutions than did the frame-based abduction system

Projective techniques: Are they a victim of clashing paradigms?

This paper reviews the concept and historical development of projective techniques. It considers why, given the importance of their psychoanalytical foundations to the underlying paradigms of management theory, they have been generally marginalised as a mainstream business and management research tool. Projective techniques are defined and their historical origins delineated. This is followed by an overview of projective ‘types’. Some of the general advantages and current issues associated with employing projective techniques are also presented. Thereafter a discussion of the reasons projective techniques have not been widely adopted by positivist academic management researchers is made. We put forward the central argument that since many of the challenges facing management research are due to the restrictions introduced by bounded rationality, projective techniques offer a possible alternative to traditional mixed methods.Projective Techniques; Management Research;

Concentrated mass effects on the flutter of a composite advanced turboprop model

The effects on bending-torsion flutter due to the addition of a concentrated mass to an advanced turboprop model blade with rigid hub are studied. Specifically the effects of the magnitude and location of added mass on the natural frequencies, mode shapes, critical interblade phase angle, and flutter Mach number are analytically investigated. The flutter of a propfan model is shown to be sensitive to the change in mass distribution. Static unbalance effects, like those for fixed wings, were shown to occur as the concentrated mass was moved from the leading edge to the trailing edge with the exception of one mass location. Mass balancing is also inferred to be a feasible method for increasing the flutter speed