Perturbation of Burkholder's martingale transform and Monge--Amp\`ere equation

Let $\{d_k\}_{k \geq 0}$ be a complex martingale difference in $L^p[0,1],$ where $1<p<\infty,$ and \{\e_k\}_{k \geq 0} a sequence in $\{\pm 1\}.$ We obtain the following generalization of Burkholder's famous result. If $\tau \in [-\frac 12, \frac 12]$ and $n \in \Z_+$ then |\sum_{k=0}^n{(\{c} \e_k \tau) d_k}|_{L^p([0,1], \C^2)} \leq ((p^*-1)^2 + \tau^2)^{\frac 12}|\sum_{k=0}^n{d_k}|_{L^p([0,1], \C)}, where $((p^*-1)^2 + \tau^2)^{\frac 12}$ is sharp and $p^*-1 = \max\{p-1, \frac 1{p-1}\}.$ For $2\leq p<\infty$ the result is also true with sharp constant for $\tau \in \R.$Comment: 45 pages, 13 figure

Tutorials: Resource Instruction for Distance Learners

Academic librarians, devoted to providing resources and services for learners, find both opportunity and challenge in the continuing growth of online programs in higher education. The technology tools available for online courses are also available to librarians seeking to support those courses with research and information literacy skills instruction. Researchers have delineated factors necessary for achieving defined learning outcomes with online tutorials. These factors include assignment relevance, faculty collaboration, and student interaction. A fourth issue emerges as equally critical; there must be a single iteration of the tutorial, posted in a unique online location, and subject to dynamic revision. There are cost-effective ways to serve online learners that meet all four criteria

Історія релігії та церкви в Україні в давні часи та добу середньовіччя

Мета курсу полягає у всебічному висвітленні проблеми становлення та розвитку релігійного та церковного життя в Україні від найдавніших часів до початку визвольної війни українського народу під проводом Богдана Хмельницького. У зв’язку з цим він спирається на знання студентів із нормативного курсу «Давня та середньовічна історія України». Завдання: опрацювати основну джерельну базу та історіографію з даної дисципліни; проаналізувати основні етапи становлення та розвитку релігії та церкви на теренах України; простежити еволюцію релігійних поглядів українського населення та визначити основні чинники, які вплинули на цей процес; дослідити діяльність основних релігійних осередків, що діяли на території України у зазначений період

Містика і реальність: сутність комуністичної епохи крізь призму творчості Івана Багряного

There are two directions of investigation in this article: 1) to determine special features of style in the I. Bagr anuj’s writings; 2) у to elucidate substance and content of the era of communism

Response: Commentary: Probing Genomic Aspects of the Multi-Host Pathogen Clostridium perfringens Reveals Significant Pangenome Diversity, and a Diverse Array of Virulence Factors

Official Student Newspaper Issue is 20 pages long

Суб’єктний склад сурогатного материнства

У статті вивчаються питання суб’єктного складу програми сурогатного материнства. Досліджуються думки вітчизняних та зарубіжних вчених-юристів щодо цього питання. Проводиться аналіз закордонного законодавства, що регулює сурогатне материнство

Kankakee River Basin in Illinois: hydraulics, hydrology, river geometry, and sand bars interim report

This interim report summarizes the work completed within the first nine months of the project. This report summarizes all of the existing streamflow records for Illinois and for two stations from Indiana, lists the available literature, and describes the field trip to the site. Analyses of the bed and bank material samples collected during the field trip also are included. Maps of the bank lines from the Route 30 Bridge in Indiana to the confluence of the Kankakee River with the Des Plaines River have been completed and will be available with the final report. Bank conditions of the entire main stem of the Kankakee River from the Route 30 Bridge in Indiana to its confluence with the Des Plaines River are also summarized. This includes general bank conditions, shoreline stability, erosion sites and severity, pumping stations, log and tree jams, and other features. Additional work on the surveying of the river and sand bar geometries is now being done. A final report will be prepared that summarizes all of the existing and newly collected data on hydraulics, hydrology, sediment transport, bed and bank material distributions, and sedimentation patterns

Centrifuge testing of a bridge pier on a rocking isolated foundation supported on unconnected piles

Volume conduction models can help in acquiring knowledge about the distribution of the electric field induced by transcranial magnetic stimulation. One aspect of a detailed model is an accurate description of the cortical surface geometry. Since its estimation is difficult, it is important to know how accurate the geometry has to be represented. Previous studies only looked at the differences caused by neglecting the complete boundary between cerebrospinal fluid (CSF) and grey matter (Thielscher et al 2011 NeuroImage 54 234-43, Bijsterbosch et al 2012 Med. Biol. Eng. Comput. 50 671-81), or by resizing the whole brain (Wagner et al 2008 Exp. Brain Res. 186 539-50). However, due to the high conductive properties of the CSF, it can be expected that alterations in sulcus width can already have a significant effect on the distribution of the electric field. To answer this question, the sulcus width of a highly realistic head model, based on T1-, T2- and diffusion-weighted magnetic resonance images, was altered systematically. This study shows that alterations in the sulcus width do not cause large differences in the majority of the electric field values. However, considerable overestimation of sulcus width produces an overestimation of the calculated field strength, also at locations distant from the target location

Improbable nationalists? Social democracy and national independence in Georgia 1918-1921

The Democratic Republic of Georgia (1918-1921) had the world’s first ever elected social-democratic government. However, despite attempts then and later to present it as an exemplar of democratic socialism, the main tasks its leaders faced, in the context of post-imperial revolutionary chaos, were those of nation-building and consolidation. This necessarily led the state into conflict with its neighbours and national minorities, and to adopt a series of measures and compromises which both undermined the socialist aspects of the regime and fostered nationalism and even chauvinism, against the intentions and ideology of its rulers. This in turn weakened the regime, facilitating its eventual overthrow by the Red Army

CRISPR-Cas9 ribonucleoprotein-mediated co-editing and counterselection in the rice blast fungus

The rice blast fungus Magnaporthe oryzae is the most serious pathogen of cultivated rice and a significant threat to global food security. To accelerate targeted mutation and specific genome editing in this species, we have developed a rapid plasmid-free CRISPR-Cas9-based genome editing method. We show that stable expression of Cas9 is highly toxic to M. oryzae. However efficient gene editing can be achieved by transient introduction of purified Cas9 pre-complexed to RNA guides to form ribonucleoproteins (RNPs). When used in combination with oligonucleotide or PCR-generated donor DNAs, generation of strains with specific base pair edits, in-locus gene replacements, or multiple gene edits, is very rapid and straightforward. We demonstrate a co-editing strategy for the creation of single nucleotide changes at specific loci. Additionally, we report a novel counterselection strategy which allows creation of precisely edited fungal strains that contain no foreign DNA and are completely isogenic to the wild type. Together, these developments represent a scalable improvement in the precision and speed of genetic manipulation in M. oryzae and are likely to be broadly applicable to other fungal species