A Theorem on Homeomorphic Convergence and Some Applications

Borsuk [ 3 ] has given interesting conditions under which a certain function space is separable (see Theorem 3. 1 ). We give a proof for Borsuk\u27s Theorem here and we show how it can be used to establish a useful theorem on homeomorphic convergence. We illustrate the utility of the theorem on homeomorphic convergence by stating and proving several of its consequences. For example we show that the plane (E2) does not contain uncount­ably many pairwise disjoint contina each of which contains a simple triod (Corollary 4. 1 ). We prove that in an uncountable collection G of pairwise disjoint simple closed curves in E2 almost all elements of G must be converged to homeomorphically from both sides by sequences of elements of G (see Theorem 4. 3 ). The same technique allows us to prove the nonexistence of uncountably many pairwise dis -joint wild 2 -spheres in E3. Another interesting consequence of Borsuk\u27s Theorem is Theorem 3. 4 which shows that in each set G consisting of uncountably many com­pact subsets of a metric space, some element of G is an element of convergence. Proofs for this theorem do not often appear in the literature, and, as far as the author knows, the proof given here does not appear in the literature. We wish to emphasize that all the proofs given in this report were constructed by the author without reference to the literature, in fact the author was unaware of the references until after the proofs were given. We given reference at the end of the paper where proofs in the literature can be compared with the proofs given here. We wish to emphasize that all the proofs given in this report were constructed by the author without reference to the literature, in fact the author was unaware of the references until after the proofs were given. We given reference at the end of the paper where proofs in the literature can be compared with the proofs given here

Maize Production Impacts on Groundwater Quality

The cumulative effects of management practices on nitrate-nitrogen (NO3-N) leaching and ground water quality are frequently difficult to document because of the time required for expression and the diversity of interacting process involved. This work reports results of a N and water management program initiated by the Central Platte Natural Resource District (CPNRD) in Nebraska. Cultural pratices recommended by the (CPNRD) in Nebraska. Cultural practices recommended by the CPNRD and reported by producers for the 1988 growing season, representing approximately 3900 fields covering 84 210 ha of irrigated corn (Zea mays L.) indicated NO3-N contamination of groundwater was influenced by yield goals and fertilizer N application rates. Groundwater NO2-N concentrations were positively correlated with residual N in the surface 0.9 m of soil prior to the growing season, reflecting the effects of past N and water management practices. Yield goals in 1988 averaged 9% higher than the average 10.0 Mg ha-1 corn yield attained, which accounts for an average of about 20 kg N ha-1 in excess of the average N recommendation. By comparison, in a 1980 to 1984 study from an area within the CPNRD, yield goals in 1988 accounted for 42% of the average excess N application rate of 48 kg ha-1 (based on University of Nebraska recommendations). A large portion of average excess N application is attributed to producers in 14% of the area who applied \u3e100 kg N ha-1 more than the recommended rates. Fertilizer N applied showed little relationship to fertilizer N recommended. Better education and more stringent measures may be required to address the select group of producers who fail to follow CPNRD recommendations

Enlightening cyclists:an evaluation study of a bicycle light communication system aimed to support older cyclists in traffic interactions

In the Netherlands, older cyclists run an increased risk of bicyclecrashes. Critical factors are low-speed interactions, stopping, (dis)mounting,and potentially misjudging riding speeds. A Bicycle Light CommunicationSystem (BLCS) was therefore developed that displayed riding speed, braking,and turning intentions. In an experiment, 21 older and 20 younger cyclistsobserved BLCS-signals of a lead cyclist and estimated speeds of anapproaching cyclist, with and without BLCS. Interviews were conducted toassess general opinions on BLCS and its influence on cycling behaviour. In a small follow-up study, twelve older cyclists used a BLCS-bicycle oneweek to explore first user-impressions. The majority evaluated the BLCSpositively, mainly the turning indicator and brake light components, eventhough interpreting the speed signals was difficult. Although the first userimpressions revealed that the direction indicator does not influence selfreported balance (positively or negatively), the majority reported that theywould like to use a BLCS themselves

Changes in nasal airflow and heat transfer correlate with symptom improvement after surgery for nasal obstruction

Surgeries to correct nasal airway obstruction (NAO) often have less than desirable outcomes, partly due to the absence of an objective tool to select the most appropriate surgical approach for each patient. Computational fluid dynamics (CFD) models can be used to investigate nasal airflow, but variables need to be identified that can detect surgical changes and correlate with patient symptoms. CFD models were constructed from pre- and post-surgery computed tomography scans for 10 NAO patients showing no evidence of nasal cycling. Steady-state inspiratory airflow, nasal resistance, wall shear stress, and heat flux were computed for the main nasal cavity from nostrils to posterior nasal septum both bilaterally and unilaterally. Paired t-tests indicated that all CFD variables were significantly changed by surgery when calculated on the most obstructed side, and that airflow, nasal resistance, and heat flux were significantly changed bilaterally as well. Moderate linear correlations with patient-reported symptoms were found for airflow, heat flux, unilateral allocation of airflow, and unilateral nasal resistance as a fraction of bilateral nasal resistance when calculated on the most obstructed nasal side, suggesting that these variables may be useful for evaluating the efficacy of nasal surgery objectively. Similarity in the strengths of these correlations suggests that patient-reported symptoms may represent a constellation of effects and that these variables should be tracked concurrently during future virtual surgery planning

Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone

In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For {\it arbitrary} self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector space, the endomorphism encoding the self-adjoint extension chosen. For particular examples, like the Friedrich's extension, the answer is easily extracted from the general result. In combination with \cite{BKD}, a closed expression for the determinant of an arbitrary self-adjoint extension of the full Laplace-type operator on the generalized cone can be obtained.Comment: 27 pages, 2 figures; to appear in Manuscripta Mathematic

CPsuperH2.3: an Updated Tool for Phenomenology in the MSSM with Explicit CP Violation

We describe the Fortran code CPsuperH2.3, which incorporates the following updates compared with its predecessor CPsuperH2.0. It implements improved calculations of the Higgs-boson masses and mixing including stau contributions and finite threshold effects on the tau-lepton Yukawa coupling. It incorporates the LEP limits on the processes e^+ e^- to H_i Z, H_i H_j and the CMS limits on H_i to tau^+ tau^- obtained from 4.6/fb of data at a centre-of-mass energy of 7 TeV. It also includes the decay mode H_i to Z gamma and the Schiff-moment contributions to the electric dipole moments of Mercury and Radium225, with several calculational options for the case of Mercury. These additions make CPsuperH2.3 a suitable tool for analyzing possible CP-violating effects in the MSSM in the era of the LHC and a new generation of EDM experimentsComment: 31 pages, 10 eps figures, 7 tables; H to Z gamma and SM BRs included; To appear in CPC; Typos in Eq.(A.2) corrected;The program may be obtained from http://www.hep.man.ac.uk/u/jslee/CPsuperH.html, or by contacting the first author at [email protected]; A comment added after Eq.(15) and a typo in Eq.(A.4) correcte

Electromagnetic form factors of light vector mesons

The electromagnetic form factors G_E(q^2), G_M(q^2), and G_Q(q^2), charge radii, magnetic and quadrupole moments, and decay widths of the light vector mesons rho^+, K^{*+} and K^{*0} are calculated in a Lorentz-covariant, Dyson-Schwinger equation based model using algebraic quark propagators that incorporate confinement, asymptotic freedom, and dynamical chiral symmetry breaking, and vector meson Bethe-Salpeter amplitudes closely related to the pseudoscalar amplitudes obtained from phenomenological studies of pi and K mesons. Calculated static properties of vector mesons include the charge radii and magnetic moments: r_{rho+} = 0.61 fm, r_{K*+} = 0.54 fm, and r^2_{K*0} = -0.048 fm^2; mu_{rho+} = 2.69, mu_{K*+} = 2.37, and mu_{K*0} = -0.40. The calculated static limits of the rho-meson form factors are similar to those obtained from light-front quantum mechanical calculations, but begin to differ above q^2 = 1 GeV^2 due to the dynamical evolution of the quark propagators in our approach.Comment: 8 pages of RevTeX, 5 eps figure

Multiwalled carbon nanotube: Luttinger liquid or not?

We have measured IV-curves of multiwalled carbon nanotubes using end contacts. At low voltages, the tunneling conductance obeys non-Ohmic power law, which is predicted both by the Luttinger liquid and the environment-quantum-fluctuation theories. However, at higher voltages we observe a crossover to Ohm's law with a Coulomb-blockade offset, which agrees with the environment-quantum-fluctuation theory, but cannot be explained by the Luttinger-liquid theory. From the high-voltage tunneling conductance we determine the transmission line parameters of the nanotubes.Comment: RevTeX, 4 pages, 2 EPS-figures, submitted to Phys. Rev. Let