Recurrence Formulas for Fully Exponentially Correlated Four-Body Wavefunctions

Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (>= -1) of all the interparticle distances r_ij, multiplied by an exponential containing an arbitrary linear combination of all the r_ij. These integrals are generalizations of those encountered using Hylleraas basis functions, and include all that are needed to make energy computations on the Li atom and other four-body systems with a fully exponentially correlated Slater-type basis of arbitrary quantum numbers. The only quantities needed to start the recursion are the basic four-body integral first evaluated by Fromm and Hill, plus some easily evaluated three-body "boundary" integrals. The computational labor in constructing integral sets for practical computations is less than when the integrals are generated using explicit formulas obtained by differentiating the basic integral with respect to its parameters. Computations are facilitated by using a symbolic algebra program (MAPLE) to compute array index pointers and present syntactically correct FORTRAN source code as output; in this way it is possible to obtain error-free high-speed evaluations with minimal effort. The work can be checked by verifying sum rules the integrals must satisfy.Comment: 10 pages, no figures, accepted by Phys. Rev. A (January 2009

Graphs with the Same Detour Matrix

The detour matrix (DD) of a graph has for its (i,j) entry the length of the longest path between vertices i and j. The sum of all entries above the main diagonal gives the detour index dd. Distinct graphs that have the same detour index have been reported in the literature. We examined such graphs and others that we have found and report on some of their regularities. We noticed that many graphs have not only the same detour index but also the same detour matrix. We considered in particular graphs for which the elements of the detour matrix are maximal. Such graphs are called saturated graphs. The detour matrix of a saturated graph is the same as that of the complete graph having the same number or vertices

Graphs with the Same Detour Matrix

The detour matrix (DD) of a graph has for its (i,j) entry the length of the longest path between vertices i and j. The sum of all entries above the main diagonal gives the detour index dd. Distinct graphs that have the same detour index have been reported in the literature. We examined such graphs and others that we have found and report on some of their regularities. We noticed that many graphs have not only the same detour index but also the same detour matrix. We considered in particular graphs for which the elements of the detour matrix are maximal. Such graphs are called saturated graphs. The detour matrix of a saturated graph is the same as that of the complete graph having the same number or vertices

Ecophysiological Responses of C3 Forbs and C4 Grasses to Drought and Rain on a Tallgrass Prairie in Northeastern Kansas

This is the publisher's official version, also available electronically at: http://www.jstor.org/stable/2995208.Ecophysiological responses to drought and a 3-cm rain were measured in seven C3 forb and five C4 grass species on a tallgrass prairie in northeastern Kansas. In general, midday leaf water potentials and conductances increased after rain to a greater extent in the C3 forbs, although exceptions occurred. In particular, the deeply rooted Silphium laciniatum showed little or no change in water potential and three of the five grass species exhibited no change in conductance. Although the above differences in species and life-form responses were noted, few of the species exhibited signs of severe stress at the height of the drought, emphasizing the degree to which both C3 forbs and C4 grasses are adapted to occasional severe droughts in the prairies of North America

Differences in unpleasantness induced by experimental pressure pain between patients with fibromyalgia and healthy controls

Pain possesses both sensory and affective dimensions, which are highly correlated yet distinct. Comparison of these dimensions within experimental pain settings has resulted in the construct of relative unpleasantness. Relative unpleasantness is defined as the amount of affective unpleasantness elicited for a given sensory magnitude. The aim of this study was to determine the relationship between affective and sensory components of evoked pain in subjects with fibromyalgia (FM) and healthy controls. Here we show that patients with FM unexpectedly display less relative unpleasantness than healthy controls in response to random noxious pressure stimuli. Relative unpleasantness was not correlated with distress, anxiety, or depression, which were pronounced in the FM group. Clinical pain in patients with FM was perceived to be more unpleasant than the evoked pain stimuli. These results are consistent with the concept that chronic pain may reduce the relative unpleasantness of evoked pain sensations

The LHCb trigger and data acquisition system

The LHCb experiment is the most recently approved of the 4 experiments under construction at CERNs LHC accelerator. It is a special purpose experiment designed to precisely measure the CP violation parameters in the B-B system. Triggering poses special problems since the interesting events containing B-mesons are immersed in a large background of inelastic p-p reactions. We therefore decided to implement a 4 level triggering scheme. The LHCb Data Acquisition (DAQ) system will have to cope with an average trigger rate of ~40 kHz, after two levels of hardware triggers, and an average event size of ~100 kB. Thus an event-building network which can sustain an average bandwidth of 4 GB/s is required. A powerful software trigger farm will have to be installed to reduce the rate from the 40 kHz to ~100 Hz of events written to permanent storage. In this paper we outline the general architecture of the Trigger and DAQ system and the readout protocols we plan to implement. First results of simulations of the behavior of the event- building network implementations under the expected traffic patterns are presented. (8 refs)

Differences in unpleasantness induced by experimental pressure pain between patients with fibromyalgia and healthy controls

Pain possesses both sensory and affective dimensions, which are highly correlated yet distinct. Comparison of these dimensions within experimental pain settings has resulted in the construct of relative unpleasantness. Relative unpleasantness is defined as the amount of affective unpleasantness elicited for a given sensory magnitude. The aim of this study was to determine the relationship between affective and sensory components of evoked pain in subjects with fibromyalgia (FM) and healthy controls. Here we show that patients with FM unexpectedly display less relative unpleasantness than healthy controls in response to random noxious pressure stimuli. Relative unpleasantness was not correlated with distress, anxiety, or depression, which were pronounced in the FM group. Clinical pain in patients with FM was perceived to be more unpleasant than the evoked pain stimuli. These results are consistent with the concept that chronic pain may reduce the relative unpleasantness of evoked pain sensations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90166/1/j.ejpain.2004.09.001.pd

Even Galois Representations and the Fontaine--Mazur conjecture II

We prove, under mild hypotheses, that there are no irreducible two-dimensional_even_ Galois representations of \Gal(\Qbar/\Q) which are de Rham with distinct Hodge--Tate weights. This removes the "ordinary" hypothesis required in previous work of the author. We construct examples of irreducible two-dimensional residual representations that have no characteristic zero geometric (= de Rham) deformations.Comment: Updated to take into account suggestions of the referee; the main theorems remain unchange

Slow group velocity and Cherenkov radiation

We theoretically study the effect of ultraslow group velocities on the emission of Vavilov-Cherenkov radiation in a coherently driven medium. We show that in this case the aperture of the group cone on which the intensity of the radiation peaks is much smaller than that of the usual wave cone associated with the Cherenkov coherence condition. We show that such a singular behaviour may be observed in a coherently driven ultracold atomic gas.Comment: 4 pages, 4 figure