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- Sasane, Sara Maad, et al.
(author)
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A FRIENDLY APPROACH TO COMPLEX ANALYSIS : 2nd edition
- 2023. - 2nd
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Book (peer-reviewed)abstract
- The book constitutes a basic, concise, yet rigorous first course in complex analysis, for undergraduate students who have studied multivariable calculus and linear algebra. The textbook should be particularly useful for students of joint programmes with mathematics, as well as engineering students seeking rigour. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series. Each section contains several problems, which are not drill exercises, but are meant to reinforce the fundamental concepts. Detailed solutions to all the 243 exercises appear at the end of the book, making the book ideal for self-study. There are many figures illustrating the text. The second edition corrects errors from the first edition, and includes 89 new exercises, some of which cover auxiliary topics that were omitted in the first edition. Two new appendices have been added, one containing a detailed rigorous proof of the Cauchy Integral Theorem, and another providing background in real analysis needed to make the book self-contained.
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- Aspenberg, Magnus, et al.
(author)
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Hygiene may attenuate selection for antibiotic resistance by changing microbial community structure
- 2023
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In: Evolution, Medicine and Public Health. - : Oxford University Press (OUP). - 2050-6201. ; 11:1
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Journal article (peer-reviewed)abstract
- Good hygiene, in both health care and the community, is central to containing the rise of antibiotic resistance, as well as to infection control more generally. But despite the well-known importance, the ecological mechanisms by which hygiene (or other transmission control measures) affect the evolution of resistance remain to be elucidated. Using metacommunity ecology theory, we here propose that hygiene attenuates the effect of antibiotic selection pressure. Specifically, we predict that hygiene limits the scope for antibiotics to induce competitive release of resistant bacteria within treated hosts, and that this is due to an effect of hygiene on the distribution of resistant and sensitive strains in the host population. We show this in a mathematical model of bacterial metacommunity dynamics, and test the results against data on antibiotic resistance, antibiotic treatment, and the use of alcohol-based hand rub in long-term care facilities. The data are consistent with hand rub use attenuating the resistance promoting effect of antibiotic treatment. Our results underscore the importance of hygiene, and point to a concrete way to weaken the link between antibiotic use and increasing resistance.
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- Maad Sasane, Sara
(author)
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Monotone Smoothing Splines with Bounds
- 2020
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In: Acta Applicandae Mathematicae. - : Springer Science and Business Media LLC. - 0167-8019 .- 1572-9036. ; 169:1, s. 613-627
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Journal article (peer-reviewed)abstract
- The problem of monotone smoothing splines with bounds is formulated as a constrained minimization problem of the calculus of variations. Existence and uniqueness of solutions of this problem is proved, as well as the equivalence of it to a finite dimensional but nonlinear optimization problem. A new algorithm for computing the solution which is a spline curve, using a branch and bound technique, is presented. The method is applied to examples in neuroscience and for fitting cumulative distribution functions from data.
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- Sasane, Sara Maad, et al.
(author)
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Perturbations of embedded eigenvalues for self-adjoint ODE systems
- 2023
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In: Arkiv for Matematik. - 0004-2080. ; 61:1, s. 177-202
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Journal article (peer-reviewed)abstract
- We consider a perturbation problem for embedded eigenvalues of a self-adjoint differential operator in L2(R;Rn). In particular, we study the set of all small perturbations in an appropriate Banach space for which the embedded eigenvalue remains embedded in the continuous spectrum. We show that this set of small perturbations forms a smooth manifold and we specify its co-dimension. Our methods involve the use of exponential dichotomies, their roughness property and Lyapunov-Schmidt reduction.
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