222 research outputs found

    Lower bounds for Mahler measure that depend on the number of monomials

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    We prove a new lower bound for the Mahler measure of a polynomial in one and in several variables that depends on the complex coefficients, and the number of monomials. In one variable our result generalizes a classical inequality of Mahler. In MM variables our result depends on ZM\mathbb{Z}^M as an ordered group, and in general our lower bound depends on the choice of ordering

    Independent relative units of low height

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    We prove inequalities that compare the relative regulator of an extension of number fields with a product of heights of multiplicatively independent relative units

    Some extremal functions in Fourier analysis, III

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    We obtain the best approximation in L1(R)L^1(\R), by entire functions of exponential type, for a class of even functions that includes eλxe^{-\lambda|x|}, where λ>0\lambda >0, logx\log |x| and xα|x|^{\alpha}, where 1<α<1-1 < \alpha < 1. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.Comment: 26 pages. Submitte

    Lattice-point enumerators of ellipsoids

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    Minkowski's second theorem on successive minima asserts that the volume of a 0-symmetric convex body K over the covolume of a lattice \Lambda can be bounded above by a quantity involving all the successive minima of K with respect to \Lambda. We will prove here that the number of lattice points inside K can also accept an upper bound of roughly the same size, in the special case where K is an ellipsoid. Whether this is also true for all K unconditionally is an open problem, but there is reasonable hope that the inductive approach used for ellipsoids could be extended to all cases.Comment: 9 page

    The study protocol of the Norwegian randomized controlled trial of electroconvulsive therapy in treatment resistant depression in bipolar disorder

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    <p>Abstract</p> <p>Background</p> <p>The treatment of depressive phases of bipolar disorder is challenging. The effects of the commonly used antidepressants in bipolar depression are questionable. Electroconvulsive therapy is generally considered to be the most effective treatment even if there are no randomized controlled trials of electroconvulsive therapy in bipolar depression. The safety of electroconvulsive therapy is well documented, but there are some controversies as to the cognitive side effects. The aim of this study is to compare the effects and side effects of electroconvulsive therapy to pharmacological treatment in treatment resistant bipolar depression. Cognitive changes and quality of life during the treatment will be assessed.</p> <p>Methods/Design</p> <p>A prospective, randomised controlled, multi-centre six- week acute treatment trial with seven clinical assessments. Follow up visit at 26 weeks or until remission (max 52 weeks). A neuropsychological test battery designed to be sensitive to changes in cognitive function will be used. Setting: Nine study centres across Norway, all acute psychiatric departments. Sample: n = 132 patients, aged 18 and over, who fulfil criteria for treatment resistant depression in bipolar disorder, Montgomery Åsberg Depression Rating Scale Score of at least 25 at baseline. Intervention: Intervention group: 3 sessions per week for up to 6 weeks, total up to 18 sessions. Control group: algorithm-based pharmacological treatment as usual.</p> <p>Discussion</p> <p>This study is the first randomized controlled trial that aims to investigate whether electroconvulsive therapy is better than pharmacological treatment as usual in treatment resistant bipolar depression. Possible long lasting cognitive side effects will be evaluated. The study is investigator initiated, without support from industry.</p> <p>Trial registration</p> <p>NCT00664976</p

    Short-term prediction of threatening and violent behaviour in an Acute Psychiatric Intensive Care Unit based on patient and environment characteristics

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    <p>Abstract</p> <p>Background</p> <p>The aims of the present study were to investigate clinically relevant patient and environment-related predictive factors for threats and violent incidents the first three days in a PICU population based on evaluations done at admittance.</p> <p>Methods</p> <p>In 2000 and 2001 all 118 consecutive patients were assessed at admittance to a Psychiatric Intensive Care Unit (PICU). Patient-related conditions as actuarial data from present admission, global clinical evaluations by physician at admittance and clinical nurses first day, a single rating with an observer rated scale scoring behaviours that predict short-term violence in psychiatric inpatients (The Brøset Violence Checklist (BVC)) at admittance, and environment-related conditions as use of segregation or not were related to the outcome measure Staff Observation Aggression Scale-Revised (SOAS-R). A multiple logistic regression analysis with SOAS-R as outcome variable was performed.</p> <p>Results</p> <p>The global clinical evaluations and the BVC were effective and more suitable than actuarial data in predicting short-term aggression. The use of segregation reduced the number of SOAS-R incidents.</p> <p>Conclusions</p> <p>In a naturalistic group of patients in a PICU segregation of patients lowers the number of aggressive and threatening incidents. Prediction should be based on clinical global judgment, and instruments designed to predict short-term aggression in psychiatric inpatients.</p> <p>Trial registrations</p> <p><a href="http://www.clinicaltrials.gov/ct2/show/NCT00184119">NCT00184119</a>/<a href="http://www.clinicaltrials.gov/ct2/show/NCT00184132">NCT00184132</a></p

    Bandlimited approximations to the truncated Gaussian and applications

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    In this paper we extend the theory of optimal approximations of functions f:RRf: \R \to \R in the L1(R)L^1(\R)-metric by entire functions of prescribed exponential type (bandlimited functions). We solve this problem for the truncated and the odd Gaussians using explicit integral representations and fine properties of truncated theta functions obtained via the maximum principle for the heat operator. As applications, we recover most of the previously known examples in the literature and further extend the class of truncated and odd functions for which this extremal problem can be solved, by integration on the free parameter and the use of tempered distribution arguments. This is the counterpart of the work \cite{CLV}, where the case of even functions is treated.Comment: to appear in Const. Appro

    On the error term in Weyl's law for the Heisenberg manifolds (II)

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    In this paper we study the mean square of the error term in the Weyl's law of an irrational (2l+1)(2l+1)-dimensional Heisenberg manifold . An asymptotic formula is established
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