121 research outputs found

    SMT-Solving Induction Proofs of Inequalities

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    SMT-Solving Induction Proofs of Inequalities

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    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

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    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 nn variables to one in n1n-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

    Surgical Treatment of Peripheral Aneurysms in Patients with Behcet’s Disease

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    AbstractIntroductionOur aim was to report our experience with 23 patients presenting with 32 peripheral aneurysms secondary to Behcet’s disease (BD) and their outcome after vascular surgery.MethodsThe study was retrospective in nature. Except for those presenting with aneurysm rupture, patients underwent surgery after treatment of acute inflammatory lesions. All aneurysms appeared to be pseudo-aneurysms. Graft interposition with polytetrafluoroethylene or saphenous vein was most commonly employed. Postoperatively, all patients were put on immunosuppressive and antiplatelet therapy. Follow-up was done every 6–12 months, complications recorded and managed appropriately.ResultsAll the patients were males. The mean age at diagnosis of a peripheral aneurysm was 41.0 ± 9 years. There were 17 (53%) femoral, 8 (25%) popliteal, two carotid, two external iliac, two brachial and one internal iliac aneurysms. Fourteen (61%) patients had a single peripheral aneurysm while nine had two. Surgery was performed for all initially presenting 23 aneurysms. Six patients with multiple peripheral aneurysms had surgery for their second asymptomatic aneurysm. The mean follow-up period was 84 ± 62 months. Of 29 aneurysms operated on, 7 (24%) anastomotic pseudo-aneurysms and 11 (38%) graft occlusions developed. Five (22%) patients underwent major lower extremity amputations. Six (26%) mortalities were recorded.ConclusionSurgery for peripheral aneurysms in BD is warranted in many instances. Results of operation can be improved by prolonged monitoring. However, despite all efforts, peripheral aneurysm involvement in BD worsens the prognosis

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

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    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

    Soliton response to transient trap variations

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    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

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    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

    Non-Hermitian Hamiltonians with a Real Spectrum and Their Physical Applications

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    We present an evaluation of some recent attempts at understanding the role of pseudo-Hermitian and PT-symmetric Hamiltonians in modeling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in the study of complex scattering potentials.Comment: 9 pages, contributed to Homi Bhabha Centenary Conference on Non-Hermitian Hamiltonians in Quantum Physics (8th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics), held in Mumbai, January 13-16, 200

    "I should live and finish it": A qualitative inquiry into Turkish women's menopause experience

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    <p>Abstract</p> <p>Background</p> <p>While bio-medically, menopause could be treated as an illness, from a psychosocial and cultural perspective it could be seen as a "natural" process without requiring medication unless severe symptoms are present.</p> <p>Our objective is to explore the perceptions of Turkish women regarding menopause and Hormone Therapy (HT) to provide health care workers with an insight into the needs and expectations of postmenopausal women.</p> <p>Methods</p> <p>A qualitative inquiry through semi-structured, in-depth interviews was used to explore the study questions. We used a purposive sampling and included an equal number of participants who complained about the climacteric symptoms and those who visited the outpatient department for a problem other than climacteric symptoms but when asked declared that they had been experiencing climacteric symptoms. The interview questions focused on two areas; 1) knowledge, experiences, attitudes and beliefs about menopause and; 2) menopause-related experiences and ways to cope with menopause and perception of HT.</p> <p>Results</p> <p>Most of the participants defined menopause as a natural transition process that one should go through. Cleanliness, maturity, comfort of not having a period and positive changes in health behaviour were the concepts positively attributed to menopause, whereas hot flushes, getting old and difficulties in relationships were the negatives. Osteoporosis was an important concern for most of the participants. To deal with the symptoms, the non-pharmacological options were mostly favoured.</p> <p>Conclusion</p> <p>To our knowledge, this is the first qualitative study which focuses on Turkish women's menopausal experiences. Menopause was thought to be a natural process which was characterised by positive and negative features. Understanding these features and their implications in these women's lives may assist healthcare workers in helping their clients with menopause.</p
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