Representations of U(1,q) and Constructive Quaternion Tensor Products

The representation theory of the group U(1,q) is discussed in detail because of its possible application in a quaternion version of the Salam-Weinberg theory. As a consequence, from purely group theoretical arguments we demonstrate that the eigenvalues must be right-eigenvalues and that the only consistent scalar products are the complex ones. We also define an explicit quaternion tensor product which leads to a set of additional group representations for integer ``spin''.Comment: 28 pages, Latex, Dipartimento di Fisica, Universita di Lecce INFN-Sezione di Lecc

Timelapse

We discuss the existence in an arbitrary frame of a finite time for the transformation of an initial quantum state into another e.g. in a decay. This leads to the introduction of a timelapse $\tilde{\tau}$ in analogy with the lifetime of a particle. An argument based upon the Heisenberg uncertainty principle suggests the value of $\tilde{\tau}=1 / M_0$. Consequences for the exponential decay formula and the modifications that $\tilde{\tau}$ introduces into the Breit-Wigner mass formula are described.Comment: 5 pages [2 figs], ReV-Te

Survival law in a potential model

The radial equation of a simple potential model has long been known to yield an exponential decay law in lowest order (Breit-Wigner) approximation. We demonstrate that if the calculation is extended to fourth order the decay law exhibits the quantum Zeno effect. This model has further been studied numerically to characterize the extra exponential time parameter which compliments the lifetime. We also investigate the inverse Zeno effect.Comment: 16 pages, 2 tables, 3 figures, AMS-Te

Quaternionic Electroweak Theory and CKM Matrix

We find in our quaternionic version of the electroweak theory an apparently hopeless problem: In going from complex to quaternions, the calculation of the real-valued parameters of the CKM matrix drastically changes. We aim to explain this quaternionic puzzle.Comment: 8, Revtex, Int. J. Theor. Phys. (to be published

Remarks upon the mass oscillation formulas

The standard formula for mass oscillations is often based upon the approximation $t \approx L$ and the hypotheses that neutrinos have been produced with a definite momentum $p$ or, alternatively, with definite energy $E$. This represents an inconsistent scenario and gives an unjustified reduction by a factor of two in the mass oscillation formulas. Such an ambiguity has been a matter of speculations and mistakes in discussing flavour oscillations. We present a series of results and show how the problem of the factor two in the oscillation length is not a consequence of gedanken experiments, i.e. oscillations in time. The common velocity scenario yields the maximum simplicity.Comment: 9 pages, AMS-Te

Phase 1 User Instruction Manual. A Geological Formation - Drill String Dynamic Interaction Finite Element Program (Geodyn)

User instructions for the GEODYN Interactive Finite Element Computer Program are presented. The program is capable of performing the analysis of the three-dimensional transient dynamic response of a Polycrystalline Diamond Compact Bit - Bit Sub arising from the intermittent contact of the bit with the downhole rock formations. The program accommodates non-linear, time dependent, loading and boundary conditions

Chemical signature of colorectal cancer: case–control study for profiling the breath print

Background: Effective screening for colorectal cancer can reduce mortality by early detection of tumours and colonic polyps. An altered pattern of volatile organic compounds (VOCs) in exhaled breath has been proposed as a potential non-invasive diagnostic tool for detection of cancer. The aim of this study was to evaluate the reliability of breath-testing for colorectal cancer screening and early diagnosis using an advanced breath sampler. Methods: The exhaled breath of patients with colorectal cancer and non-cancer controls with negative findings on colonoscopy was collected using the ReCIVA® Breath Sampler. This portable device is able to capture the alveolar breath fraction without environmental contamination. VOCs were desorbed thermally and analysed by gas chromatography–mass spectrometry. The discriminatory ability of VOCs in detecting colorectal cancer was evaluated by receiver operating characteristic (ROC) curve analysis for each VOC, followed by cross-validation by the leave-one-out method, and by applying stepwise logistic regression analysis. Results: The study included 83 patients with colorectal cancer and 90 non-cancer controls. Fourteen VOCs were found to have significant discriminatory ability in detecting patients with colorectal cancer. The model with the diagnosis of cancer versus no cancer resulted in a statistically significant likelihood of discrimination of 173⋅45 (P <0⋅001), with an area under the ROC curve of 0⋅979. Cross-validation of the model resulted in a true predictive value for colorectal cancer of 93 per cent overall. Reliability of the breath analysis was maintained irrespective of cancer stage. Conclusion: This study demonstrated that analysis of exhaled VOCs can discriminate patients with colorectal cancer from those without. This finding may eventually lead to the creation of a smart online sensory device, capable of providing a binary answer (cancer/no cancer) and directing to further screening