Generalized Sobolev Spaces of Exponential Type Associated with the Dunkl Operators

2000 Mathematics Subject Classification: 35E45

Automorphisms of the Planar Tree Power Series Algebra and the Non-Associative Logarithm

2000 Mathematics Subject Classification: 17A50, 05C05.

Singular Solutions with Exponential Growth for the (3+1)-D Wave Equation

Недю И. Попиванов, Тодор П. Попов, Рудолф Шерер - Разглеждат се четиримерни гранични задачи за нехомогенното вълново уравнение. Те са предложени от М. Протер като многомерни аналози на задачата на Дарбу в равнината. Известно е, че единственото обобщено решение може да има силна степенна особеност само в една гранична точка. Тази сингулярност е изолирана във върха на характеристичния конус и не се разпространява по конуса. Друг аспект на проблема е, че задачата не е фредхолмова, тъй като има безкрайномерно коядро. Предишни резултати сочат, че решението може да има най-много експоненциален ръст, но оставят открит въпроса дали наистина съществуват такива решения. Показваме, че отговора на този въпрос е положителен и строим обобщено решение на задачата на Протер с експоноциална особеност.

Densities with Spherical Level Sets in the Gauss-exponential Domain

2000 Mathematics Subject Classification: 60F05, 60B10.

Characterizations of Exponential Distribution via Conditional Expectations of Record Values

2000 Mathematics Subject Classification: 62G30, 62E10.

Exponential approximation in the norms and semi-norms

The deviations of some entire functions of exponential type from real-valued functions and their derivatives are estimated. As approximation metrics we use the Lp-norms and power variations on R. Theorems presented here correspond to the Ganelius and Popov results concerning the one-sided trigonometric approximation of periodic functions (see [4, 5 and 8]). Some related facts were announced in [2, 3, 6 and 7].

Characterizations of Exponential Distribution Based on Sample of Size Three

2010 Mathematics Subject Classification: 62G30, 62E10.

Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates

2000 Mathematics Subject Classification: 35B40, 35L15.

O paradoxo da superdifusão de uma caminhada aleatória com memória exponencial

The random walk models with temporal correlation (i.e. memory) are of interest in the study of anomalous diffusion phenomena. The random walk and its generalizations are of prominent place in the characterization of various physical, chemical and biological phenomena. The temporal correlation is an essential feature in anomalous diffusion models. These temporal long-range correlation models can be called non-Markovian models, otherwise, the short-range time correlation counterparts are Markovian ones. Within this context, we reviewed the existing models with temporal correlation, i.e. entire memory, the elephant walk model, or partial memory, alzheimer walk model and walk model with a gaussian memory with profile. It is noticed that these models shows superdiffusion with a Hurst exponent H > 1/2. We study in this work a superdiffusive random walk model with exponentially decaying memory. This seems to be a self-contradictory statement, since it is well known that random walks with exponentially decaying temporal correlations can be approximated arbitrarily well by Markov processes and that central limit theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes. The solution to the apparent paradox is that the model is genuinely non-Markovian, due to a time-dependent decay constant associated with the exponential behavior. In the end, we discuss ideas for future investigations.

Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire

Acknowledgements This study was possible by partial financial support from the following Brazilian government agencies: CNPq, CAPES, and FAPESP (2011/19296-1 and 2015/07311-7). We also wish thank Newton Fund and COFAP.

[N]pT ensemble and finite-size-scaling study of the critical isostructural transition in the generalized exponential model of index 4.

First-order transitions of system where both lattice site occupancy and lattice spacing fluctuate, such as cluster crystals, cannot be efficiently studied by traditional simulation methods, which necessarily fix one of these two degrees of freedom. The difficulty, however, can be surmounted by the generalized [N]pT ensemble [J. Chem. Phys. 136, 214106 (2012)]. Here we show that histogram reweighting and the [N]pT ensemble can be used to study an isostructural transition between cluster crystals of different occupancy in the generalized exponential model of index 4 (GEM-4). Extending this scheme to finite-size scaling studies also allows us to accurately determine the critical point parameters and to verify that it belongs to the Ising universality class.

Non-conventional advertising formats in television versus spots: An analysis based on the generated recall

Advertising investment and audience figures indicate that television continues to lead as a mass advertising medium. However, its effectiveness is questioned due to problems such as zapping, saturation and audience fragmentation. This has favoured the development of non-conventional advertising formats. This study provides empirical evidence for the theoretical development. This investigation analyzes the recall generated by four non-conventional advertising formats in a real environment: short programme (branded content), television sponsorship, internal and external telepromotion versus the more conventional spot. The methodology employed has integrated secondary data with primary data from computer assisted telephone interviewing (CATI) were performed ad-hoc on a sample of 2000 individuals, aged 16 to 65, representative of the total television audience. Our findings show that non-conventional advertising formats are more effective at a cognitive level, as they generate higher levels of both unaided and aided recall, in all analyzed formats when compared to the spot.

Effectiveness of Community versus Hospital Eye Service follow-up for patients with neovascular age-related macular degeneration with quiescent disease (ECHoES): a virtual non-inferiority trial

OBJECTIVES: To compare the ability of ophthalmologists versus optometrists to correctly classify retinal lesions due to neovascular age-related macular degeneration (nAMD).

DESIGN: Randomised balanced incomplete block trial. Optometrists in the community and ophthalmologists in the Hospital Eye Service classified lesions from vignettes comprising clinical information, colour fundus photographs and optical coherence tomographic images. Participants' classifications were validated against experts' classifications (reference standard).

SETTING: Internet-based application.

PARTICIPANTS: Ophthalmologists with experience in the age-related macular degeneration service; fully qualified optometrists not participating in nAMD shared care.

INTERVENTIONS: The trial emulated a conventional trial comparing optometrists' and ophthalmologists' decision-making, but vignettes, not patients, were assessed. Therefore, there were no interventions and the trial was virtual. Participants received training before assessing vignettes.

MAIN OUTCOME MEASURES: Primary outcome-correct classification of the activity status of a lesion based on a vignette, compared with a reference standard. Secondary outcomes-potentially sight-threatening errors, judgements about specific lesion components and participants' confidence in their decisions.

RESULTS: In total, 155 participants registered for the trial; 96 (48 in each group) completed all assessments and formed the analysis population. Optometrists and ophthalmologists achieved 1702/2016 (84.4%) and 1722/2016 (85.4%) correct classifications, respectively (OR 0.91, 95% CI 0.66 to 1.25; p=0.543). Optometrists' decision-making was non-inferior to ophthalmologists' with respect to the prespecified limit of 10% absolute difference (0.298 on the odds scale). Optometrists and ophthalmologists made similar numbers of sight-threatening errors (57/994 (5.7%) vs 62/994 (6.2%), OR 0.93, 95% CI 0.55 to 1.57; p=0.789). Ophthalmologists assessed lesion components as present less often than optometrists and were more confident about their classifications than optometrists.

CONCLUSIONS: Optometrists' ability to make nAMD retreatment decisions from vignettes is not inferior to ophthalmologists' ability. Shared care with optometrists monitoring quiescent nAMD lesions has the potential to reduce workload in hospitals.

TRIAL REGISTRATION NUMBER: ISRCTN07479761; pre-results registration.