Soliton response to transient trap variations

The response of bright and dark solitons to rapid variations in an expulsive longitudinal trap is investigated. We concentrate on the effect of transient changes in the trap frequency in the form of temporal delta kicks and the hyperbolic cotangent functions. Exact expressions are obtained for the soliton profiles. This is accomplished using the fact that a suitable linear Schrodinger stationary state solution in time can be effectively combined with the solutions of non-linear Schrodinger equation, for obtaining solutions of the Gross-Pitaevskii equation with time dependent scattering length in a harmonic trap. Interestingly, there is rapid pulse amplification in certain scenarios

Delta-Function Potential with a Complex Coupling

We explore the Hamiltonian operator H=-d^2/dx^2 + z \delta(x) where x is real, \delta(x) is the Dirac delta function, and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a (real) spectral singularity at E=-z^2/4. For \Re(z)<0, H has an eigenvalue at E=-z^2/4. For the case that \Re(z)>0, H has a real, positive, continuous spectrum that is free from spectral singularities. For this latter case, we construct an associated biorthonormal system and use it to perform a perturbative calculation of a positive-definite inner product that renders H self-adjoint. This allows us to address the intriguing question of the nonlocal aspects of the equivalent Hermitian Hamiltonian for the system. In particular, we compute the energy expectation values for various Gaussian wave packets to show that the non-Hermiticity effect diminishes rapidly outside an effective interaction region.Comment: Published version, 14 pages, 2 figure

SMT-Solving Induction Proofs of Inequalities

This paper accompanies a new dataset of non-linear real arithmetic problems for the SMT-LIB benchmark collection. The problems come from an automated proof procedure of Gerhold–Kauers, which is well suited for solution by SMT. The problems of this type have not been tackled by SMT-solvers before. We describe the proof technique and give one new such proof to illustrate it. We then describe the dataset and the results of benchmarking. The benchmarks on the new dataset are quite different to the existing ones. The benchmarking also brings forward some interesting debate on the use/inclusion of rational functions and algebraic numbers in the SMT-LIB

SMT-Solving Induction Proofs of Inequalities

This paper accompanies a new dataset of non-linear real arithmetic problems for the SMT-LIB benchmark collection. The problems come from an automated proof procedure of Gerhold--Kauers, which is well suited for solution by SMT. The problems of this type have not been tackled by SMT-solvers before. We describe the proof technique and give one new such proof to illustrate it. We then describe the dataset and the results of benchmarking. The benchmarks on the new dataset are quite different to the existing ones. The benchmarking also brings forward some interesting debate on the use/inclusion of rational functions and algebraic numbers in the SMT-LIB.Comment: Presented at the 2022 SC-Square Worksho

A Poly-algorithmic Approach to Quantifier Elimination

Cylindrical Algebraic Decomposition (CAD) was the first practical means for doing real quantifier elimination (QE), and is still a major method, with many improvements since Collins' original method. Nevertheless, its complexity is inherently doubly exponential in the number of variables. Where applicable, virtual term substitution (VTS) is more effective, turning a QE problem in $n$ variables to one in $n-1$ variables in one application, and so on. Hence there is scope for hybrid methods: doing VTS where possible then using CAD. This paper describes such a poly-algorithmic implementation, based on the second author's Ph.D. thesis. The version of CAD used is based on a new implementation of Lazard's recently-justified method, with some improvements to handle equational constraints

Lazard-style CAD and Equational Constraints

McCallum-style Cylindrical Algebra Decomposition (CAD) is a major improvement on the original Collins version, and has had many subsequent advances, notably for total or partial equational constraints. But it suffers from a problem with nullification. The recently-justified Lazard-style CAD does not have this problem. However, transporting the equational constraints work to Lazard-style does reintroduce nullification issues. This paper explains the problem, and the solutions to it, based on the second author's Ph.D. thesis and the Brown--McCallum improvement to Lazard. With a single equational constraint, we can gain the same improvements in Lazard-style as in McCallum-style CAD . Moreover, our approach does not fail where McCallum would due to nullification. Unsurprisingly, it does not achieve the same level of improvement as it does in the non-nullified cases. We also consider the case of multiple equational constraints.Comment: 9 page

Monovarietal extra-virgin olive oil classification: a fusion of human sensory attributes and an electronic tongue

Olive oil quality grading is traditionally assessed by human sensory evaluation of positive and negative attributes (olfactory, gustatory, and final olfactorygustatory sensations). However, it is not guaranteed that trained panelist can correctly classify monovarietal extra-virgin olive oils according to olive cultivar. In this work, the potential application of human (sensory panelists) and artificial (electronic tongue) sensory evaluation of olive oils was studied aiming to discriminate eight single-cultivar extra-virgin olive oils. Linear discriminant, partial least square discriminant, and sparse partial least square discriminant analyses were evaluated. The best predictive classification was obtained using linear discriminant analysis with simulated annealing selection algorithm. A low-level data fusion approach (18 electronic tongue signals and nine sensory attributes) enabled 100 % leave-one-out cross-validation correct classification, improving the discrimination capability of the individual use of sensor profiles or sensory attributes (70 and 57 % leave-one-out correct classifications, respectively). So, human sensory evaluation and electronic tongue analysis may be used as complementary tools allowing successful monovarietal olive oil discrimination.This work was co-financed by FCT/MEC and FEDER under Program PT2020 (Project UID/EQU/50020/2013); by Fundacao para a Ciencia e Tecnologia under the strategic funding of UID/BIO/04469/2013 unit; and by Project POCTEP through Project RED/AGROTEC-Experimentation network and transfer for development of agricultural and agro industrial sectors between Spain and Portugal

Effects of Vitamin D levels on asthma control and severity in pre-school children

OBJECTIVE: Prevalence of asthma and Vitamin D deficiency has been increasing and leading to significant morbidities. This study aimed to compare the Vitamin D levels in the pre-school children with asthma and in healthy controls and to assess the relationship between Vitamin D levels and asthma clinical parameters and control. PATIENTS AND METHODS: Vi tamin D [25(OH)D3] levels were measured in 102 preschool children, aged 1-4 years with asthma and 102 healthy controls in winter. The patients with asthma were grouped according to serum Vitamin D levels as sufficient, insufficient and deficient. Asthma control was classified according to the Global Initiative for Asthma (GINA) guidelines and the Test for Respiratory and Asthma Control in Kids (TRACK) in 1-4 years-old children. RESULTS: Serum Vitamin D levels were 22.64 (9.96) ng/ml in the asthma group and 32.11 (14.74) ng/ml in the control group (p = 0.001). Total number of exacerbations during the previous year were significantly lower in the Vitamin D sufficient group, compared to the deficient and insufficient groups (p = 0.03). Frequency of patients with controlled asthma was higher in the sufficient group compared to the deficient and insufficient groups (p = 0.001 and p = 0.001, respectively). There was a positive correlation between serum Vitamin D levels and asthma control. CONCLUSIONS: The frequency of Vitamin D deficiency and insufficiency was higher in children with asthma, compared to the controls. Therefore, we suggest that lower levels of Vitamin D are associated with poor asthma control and increased asthma severity