Пределы векторных мер в пространствах Фреше

(uk) Розв’язане питання про те, які міри в просторах Фреше можуть бути зображені як границі аналітичних векторних мір в топологіях збіжності за варіацією, відносно напівваріації та збіжності на системі вимірних множин.(en) It is solved a problem: Which measures in Frechet spaces could be represented as limits of analytic vector measures in topologies of variational convergence, semi-variational convergence and convergence on every measurable set

Performance evaluation of non-thermal plasma on particulate matter, ozone and CO2 correlation for diesel exhaust emission reduction

This study is seeking to investigate the effect of non-thermal plasma technology in the abatement of particulate matter (PM) from the actual diesel exhaust. Ozone (O3) strongly promotes PM oxidation, the main product of which is carbon dioxide (CO2). PM oxidation into the less harmful product (CO2) is the main objective whiles the correlation between PM, O3 and CO2 is considered. A dielectric barrier discharge reactor has been designed with pulsed power technology to produce plasma inside the diesel exhaust. To characterise the system under varied conditions, a range of applied voltages from 11 kVPP to 21kVPP at repetition rates of 2.5, 5, 7.5 and 10 kHz, have been experimentally investigated. The results show that by increasing the applied voltage and repetition rate, higher discharge power and CO2 dissociation can be achieved. The PM removal efficiency of more than 50% has been obtained during the experiments and high concentrations of ozone on the order of a few hundreds of ppm have been observed at high discharge powers. Furthermore, O3, CO2 and PM concentrations at different plasma states have been analysed for time dependence. Based on this analysis, an inverse relationship between ozone concentration and PM removal has been found and the role of ozone in PM removal in plasma treatment of diesel exhaust has been highlighted

Experimental Study on the Optimization of Dielectric Barrier Discharge Reactor for NOx Treatment

In this paper, a comprehensive study of a DBD reactor is conducted to investigate the optimum operating conditions of the reactor for NOx treatment. For each parameter, the objective is to find the maximum NOx removal efficiency with the minimum consumed power. Different effective parameters of the reactor i.e. electrode length and diameter, electrode and dielectric materials as well as parameters of power generator, i.e. voltage and frequency, are investigated. The results show that for this configuration, the electrode with 20 cm length and 10 mm diameter has the best performance. Aluminum as the inside electrode material and quartz as the dielectric material are selected. Furthermore, the optimum value for the pulse frequency is 16.6 kHz. For the mentioned optimum conditions, the NOx removal efficiency achieved is equal to almost 82% at the input power of 486 W. Furthermore, the highest achieved NOx removal is almost 92% at the input power of 864 W. The results of this paper can be used to reduce the energy consumption of NTP systems to acceptable levels

Generation of (synthetic) influent data for performing wastewater treatment modelling studies

The success of many modelling studies strongly depends on the availability of sufficiently long influent time series - the main disturbance of a typical wastewater treatment plant (WWTP) - representing the inherent natural variability at the plant inlet as accurately as possible. This is an important point since most modelling projects suffer from a lack of realistic data representing the influent wastewater dynamics. The objective of this paper is to show the advantages of creating synthetic data when performing modelling studies for WWTPs. This study reviews the different principles that influent generators can be based on, in order to create realistic influent time series. In addition, the paper summarizes the variables that those models can describe: influent flow rate, temperature and traditional/emerging pollution compounds, weather conditions (dry/wet) as well as their temporal resolution (from minutes to years). The importance of calibration/validation is addressed and the authors critically analyse the pros and cons of manual versus automatic and frequentistic vs Bayesian methods. The presentation will focus on potential engineering applications of influent generators, illustrating the different model concepts with case studies. The authors have significant experience using these types of tools and have worked on interesting case studies that they will share with the audience. Discussion with experts at the WWTmod seminar shall facilitate identifying critical knowledge gaps in current WWTP influent disturbance models. Finally, the outcome of these discussions will be used to define specific tasks that should be tackled in the near future to achieve more general acceptance and use of WWTP influent generators

Autism genetic database (AGD): a comprehensive database including autism susceptibility gene-CNVs integrated with known noncoding RNAs and fragile sites

Background: Autism is a highly heritable complex neurodevelopmental disorder, therefore identifying its genetic basis has been challenging. To date, numerous susceptibility genes and chromosomal abnormalities have been reported in association with autism, but most discoveries either fail to be replicated or account for a small effect. Thus, in most cases the underlying causative genetic mechanisms are not fully understood. In the present work, the Autism Genetic Database (AGD) was developed as a literature-driven, web-based, and easy to access database designed with the aim of creating a comprehensive repository for all the currently reported genes and genomic copy number variations (CNVs) associated with autism in order to further facilitate the assessment of these autism susceptibility genetic factors. Description: AGD is a relational database that organizes data resulting from exhaustive literature searches for reported susceptibility genes and CNVs associated with autism. Furthermore, genomic information about human fragile sites and noncoding RNAs was also downloaded and parsed from miRBase, snoRNA-LBME-db, piRNABank, and the MIT/ICBP siRNA database. A web client genome browser enables viewing of the features while a web client query tool provides access to more specific information for the features. When applicable, links to external databases including GenBank, PubMed, miRBase, snoRNA-LBME-db, piRNABank, and the MIT siRNA database are provided. Conclusion: AGD comprises a comprehensive list of susceptibility genes and copy number variations reported to-date in association with autism, as well as all known human noncoding RNA genes and fragile sites. Such a unique and inclusive autism genetic database will facilitate the evaluation of autism susceptibility factors in relation to known human noncoding RNAs and fragile sites, impacting on human diseases. As a result, this new autism database offers a valuable tool for the research community to evaluate genetic findings for this complex multifactorial disorder in an integrated format. AGD provides a genome browser and a web based query client for conveniently selecting features of interest. Access to AGD is freely available at http://wren.bcf.ku.edu/ webcite

Intersecting geodesics on the modular surface

We introduce the \textit{modular intersection kernel}, and we use it to study how geodesics intersect on the full modular surface $\mathbb{X}=PSL_2\left(\mathbb{Z}\right) \backslash \mathbb{H}$. Let $C_d$ be the union of closed geodesics with discriminant $d$ and let $\beta\subset \mathbb{X}$ be a compact geodesic segment. As an application of Duke's theorem to the modular intersection kernel, we prove that $\{\left(p,\theta_p\right)~:~p\in \beta \cap C_d\}$ becomes equidistributed with respect to $\sin \theta ds d\theta$ on $\beta \times [0,\pi]$ with a power saving rate as $d \to +\infty$. Here $\theta_p$ is the angle of intersection between $\beta$ and $C_d$ at $p$. This settles the main conjectures introduced by Rickards \cite{rick}. We prove a similar result for the distribution of angles of intersections between $C_{d_1}$ and $C_{d_2}$ with a power-saving rate in $d_1$ and $d_2$ as $d_1+d_2 \to \infty$. Previous works on the corresponding problem for compact surfaces do not apply to $\mathbb{X}$, because of the singular behavior of the modular intersection kernel near the cusp. We analyze the singular behavior of the modular intersection kernel by approximating it by general (not necessarily spherical) point-pair invariants on $PSL_2\left(\mathbb{Z}\right) \backslash PSL_2\left(\mathbb{R}\right)$ and then by studying their full spectral expansion.Comment: Fixed a few errors in the proof. Revised to improve the readability. 25 page

Limiting distributions of conjugate algebraic integers

Let $\Sigma \subset \mathbb{C}$ be a compact subset of the complex plane, and $\mu$ be a probability distribution on $\Sigma$. We give necessary and sufficient conditions for $\mu$ to be the weak* limit of a sequence of uniform probability measures on a complete set of conjugate algebraic integers lying eventually in any open set containing $\Sigma$. Given $n\geq 0$, any probability measure $\mu$ satisfying our necessary conditions, and any open set $D$ containing $\Sigma$, we develop and implement a polynomial time algorithm in $n$ that returns an integral monic irreducible polynomial of degree $n$ such that all of its roots are inside $D$ and their root distributions converge weakly to $\mu$ as $n\to \infty$. We also prove our theorem for $\Sigma\subset \mathbb{R}$ and open sets inside $\mathbb{R}$ that recovers Smith's main theorem \cite{Smith} as special case. Given any finite field $\mathbb{F}_q$ and any integer $n$, our algorithm returns infinitely many abelian varieties over $\mathbb{F}_q$ which are not isogenous to the Jacobian of any curve over $\mathbb{F}_{q^n}$

Metabolic health profile in young adults with Prader–Willi syndrome: results of a 2-year randomized, placebo-controlled, crossover GH trial

Context: Patients with Prader–Willi syndrome (PWS) have an increased fat mass and decreased lean body mass. GH-treated young adults with PWS who have attained adult height benefit from continuation of growth hormone (GH) treatment, as GH maintained their improved body composition, whereas fat mass increased during the placebo period. Adults with PWS are predisposed to T2DM and cardiovascular disease. Whether GH affects metabolic health profile of this patient group is unknown. Objective: To investigate the effects of GH vs placebo on metabolic health, in young adults with PWS who were GH-treated for many years during childhood and had attained adult height (AH). Method: A 2-year, randomized, double-blind, placebo-controlled crossover study with stratification for gender and BMI in 27 young adults with PWS. Intervention with GH (0·67 mg/m2/day) and placebo, both for 1-year duration. Results: Compared to placebo, GH treatment resulted in similar glucose and insulin levels during oral glucose tolerance test. Only fasting glucose and insulin were slightly higher during GH vs placebo (+0·2 mmol/l and +18·4 pmol/l), although both remained within normal ranges in both phases. Blood pressure and lipid profile were similar after GH vs placebo. At baseline (AH) and during GH, no patients had metabolic syndrome, while 1 developed it during placebo treatment. Conclusions: Growth hormone treatment has no adverse effects on metabolic health profile. Thus, GH-treated young adults with PWS who have attained AH benefit from continuation of GH treatment without safety concerns regarding metabolic health

A quantitative converse of Fekete's theorem

Given a compact subset $\Sigma \subset \mathbb{R}$ (or $\mathbb{C}$) with logarithmic capacity greater than zero, we construct an explicit family of probability measures supported on $\Sigma$ such that their closure is all the possible weak limit measures of complete sets of conjugate algebraic integers lying inside $\Sigma$. We give an asymptotic formula for the number of algebraic integers with given degree and prescribed distribution. We exploit the algorithmic nature of our approach to give a family of upper bounds that converges to the smallest limiting trace-to-degree ratio of totally positive algebraic integers and improve the best previously known upper bound on the Schur-Siegel-Smyth trace problem to 1.8216.Comment: arXiv admin note: text overlap with arXiv:2302.0287