Closed-Form Density of States and Localization Length for a Non-Hermitian Disordered System

We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat eigenvalue problem corresponding to the attractive non-linear Schroedinger equation with a Gaussian random pulse as initial value function. Using an extension of the Thouless formula to non-Hermitian random operators, we calculate the corresponding average density of states. We analyze two cases, one with circularly symmetric complex Gaussian pulses and the other with real Gaussian pulses. We discuss the implications in the context of the information transmission through non-linear optical fibers.Comment: 5 pages, 1 figur

Darboux transformations with tetrahedral reduction group and related integrable systems

In this paper, we derive new two-component integrable differential difference and partial difference systems by applying a Lax-Darboux scheme to an operator formed from a

Cosymmetries and Nijenhuis recursion operators for difference equations

In this paper we discuss the concept of cosymmetries and co--recursion operators for difference equations and present a co--recursion operator for the Viallet equation. We also discover a new type of factorisation for the recursion operators of difference equations. This factorisation enables us to give an elegant proof that the recursion operator given in arXiv:1004.5346 is indeed a recursion operator for the Viallet equation. Moreover, we show that this operator is Nijenhuis and thus generates infinitely many commuting local symmetries. This recursion operator and its factorisation into Hamiltonian and symplectic operators can be applied to Yamilov's discretisation of the Krichever-Novikov equation

Geometrical characteristics of magnetospheric energetic ion time series: evidence for low dimensional chaos

International audienceIn the first part of the paper we study the geometrical characteristics of the magnetospheric ions' time series in the reconstructed phase space by using the SVD extended chaotic analysis, and we test the strong null hypothesis supposing that the ions' time series is caused by a linear stochastic process perturbed by a static nonlinear distortion. The SVD reconstructed spectrum of the ions' signal reveals a strong component of high dimensional, external coloured noise, as well as an internal low dimensional nonlinear deterministic component. Also, the stochastic Lorenz system produced by coloured noise perturbation of the deterministic Lorenz system was used as an archetype model in comparison with the dynamics of the magnetrospheric ions

Satisfaction with aspects of labour as a factor of motivation and the integration of young industrial workers

Статья посвящена вопросам мотивации и интеграции молодых работников на промышленных предприятиях, а также их удовлетворенности аспектами трудовой деятельности. Авторы, опираясь на работы уральских ученых, анализируют результаты опроса 300 молодых работников предприятий Свердловской области.The article is devoted to motivation and integration of young workers in industrial enterprises, as well as their satisfaction with aspects of the work. The Authors, building on work of the Ural scientists analyze the results of a survey of 300 young workers of enterprises of the Sverdlovsk region

Exponential Log-Periodic Antenna Design Using Improved Particle Swarm Optimization with Velocity Mutation

An improved particle swarm optimization (PSO) method applied to the design of a new wideband log-periodic antenna (LPA) geometry is introduced. This new PSO variant, called PSO with velocity mutation (PSOvm), induces mutation on the velocities of those particles that cannot improve their position. The proposed LPA consists of wire dipoles with lengths and distances varied according to an exponential rule, which is defined by two specific parameters called length factor and spacing factor. The LPA is optimized for operation in 790-6000MHz frequency range, in order to cover the most usual wireless services in practice, and also to provide in this range the highest possible forward gain, gain flatness below 2dB, secondary lobe level below –20dB with respect to the main lobe peak, and standing wave ratio below 2. To demonstrate its superiority in terms of performance, PSOvm is compared to well-known optimization methods. The comparison is performed by applying all the methods on several test functions and also on the LPA optimization problem defined by the above-mentioned requirements. Furthermore, the radiation characteristics of the PSOvm-based LPA give prominence to the effectiveness of the proposed exponential geometry compared to the traditional Carrel’s geometry

Viscosupplementation for knee osteoarthritis: systematic review and meta-analysis

Objective: To evaluate the effectiveness and safety of viscosupplementation for pain and function in patients with knee osteoarthritis. Design: Systematic review and meta-analysis of randomised trials. Data sources Searches were conducted of Medline, Embase, and the Cochrane Central Register of Controlled Trials (CENTRAL) databases from inception to 11 September 2021. Unpublished trials were identified from the grey literature and trial registries. Eligibility criteria for study selection: Randomised trials comparing viscosupplementation with placebo or no intervention for knee osteoarthritis treatment. Main outcome measures: The prespecified primary outcome was pain intensity. Secondary outcomes were function and serious adverse events. Pain and function were analysed as standardised mean differences (SMDs). The prespecified minimal clinically important between group difference was −0.37 SMD. Serious adverse events were analysed as relative risks. Methods: Two reviewers independently extracted relevant data and assessed the risk of bias of trials using the Cochrane risk of bias tool. The predefined main analysis was based only on large, placebo controlled trials with ≥100 participants per group. Summary results were obtained through a random effects meta-analysis model. Cumulative meta-analysis and trial sequential analysis under a random effects model were also performed. Results: 169 trials provided data on 21 163 randomised participants. Evidence of small study effects and publication biases was observed for pain and function (Egger’s tests with P<0.001 and asymmetric funnel plots). Twenty four large, placebo controlled trials (8997 randomised participants) included in the main analysis of pain indicated that viscosupplementation was associated with a small reduction in pain intensity compared with placebo (SMD −0.08, 95% confidence interval −0.15 to −0.02), with the lower bound of the 95% confidence interval excluding the minimal clinically important between group difference. This effect corresponds to a difference in pain scores of −2.0 mm (95% confidence interval −3.8 to −0.5 mm) on a 100 mm visual analogue scale. Trial sequential analysis for pain indicated that since 2009 there has been conclusive evidence of clinical equivalence between viscosupplementation and placebo. Similar conclusions were obtained for function. Based on 15 large, placebo controlled trials on 6462 randomised participants, viscosupplementation was associated with a statistically significant higher risk of serious adverse events than placebo (relative risk 1.49, 95% confidence interval 1.12 to 1.98). Conclusion: Strong conclusive evidence indicates that viscosupplementation leads to a small reduction in knee osteoarthritis pain compared with placebo, but the difference is less than the minimal clinically important between group difference. Strong conclusive evidence indicates that viscosupplementation is also associated with an increased risk of serious adverse events compared with placebo. The findings do not support broad use of viscosupplementation for the treatment of knee osteoarthritis