The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations

Недю Попиванов, Цветан Христов - Изследвани са някои тримерни аналози на задачата на Дарбу в равнината. През 1952 М. Протер формулира нови тримерни гранични задачи както за клас слабо хиперболични уравнения, така и за някои хиперболично-елиптични уравнения. За разлика от коректността на двумерната задача на Дарбу, новите задачи са некоректни. За слабо хиперболични уравнения, съдържащи младши членове, ние намираме достатъчни условия както за съществуване и единственост на обобщени решения с изолирана степенна особеност, така и за единственост на квази-регулярни решения на задачата на Протер.

Singular Solutions of Protter’s Problem for a Class of 3-D Hyperbolic Equations

Недю Иванов Попиванов, Алексей Йорданов Николов - През 1952 г. М. Протър формулира нови гранични задачи за вълновото уравнение, които са тримерни аналози на задачите на Дарбу в равнината. Задачите са разгледани в тримерна област, ограничена от две характеристични конуса и равнина. Сега, след като са минали повече от 50 години, е добре известно, че за безброй гладки функции в дясната страна на уравнението тези задачи нямат класически решения, а обобщеното решение има силна степенна особеност във върха на характеристичния конус, която е изолирана и не се разпространява по конуса. Тук ние разглеждаме трета гранична задача за вълновото уравнение с младши членове и дясна страна във формата на тригонометричен полином. Дадена е по-нова от досега известната априорна оценка за максимално възможната особеност на решенията на тази задача. Оказва се, че при по-общото уравнение с младши членове възможната сингулярност е от същия ред като при чисто вълновото уравнение.

Application of the D-Fullness Technique for Breakdown Point Study of the Trimmed Likelihood Estimator to a Generalized Logistic Model

2000 Mathematics Subject Classification: 62J12, 62F35

Eigen-Adaptation and Distributed Representation of 2-D Phase, Energy, Scale and Orientation in Spatial Vision

Distributed representations (DR) of cortical channels are pervasive in models of spatio-temporal vision. A central idea that underpins current innovations of DR stems from the extension of 1-D phase into 2-D images. Neurophysiological evidence, however, provides tenuous support for a quadrature representation in the visual cortex, since even phase visual units are associated with broader orientation tuning than odd phase visual units (J.Neurophys.,88,455–463, 2002). We demonstrate that the application of the steering theorems to a 2-D definition of phase afforded by the Riesz Transform (IEEE Trans. Sig. Proc., 49, 3136–3144), to include a Scale Transform, allows one to smoothly interpolate across 2-D phase and pass from circularly symmetric to orientation tuned visual units, and from more narrowly tuned odd symmetric units to even ones. Steering across 2-D phase and scale can be orthogonalized via a linearizing transformation. Using the tiltafter effect as an example, we argue that effects of visual adaptation can be better explained by via an orthogonal rather than channel specific representation of visual units. This is because of the ability to explicitly account for isotropic and cross-orientation adaptation effect from the orthogonal representation from which both direct and indirect tilt after-effects can be explained.

Az értékesítés és a marketing kapcsolatának piaci tájékozód��sban betöltött szerepe és meghatározó tényezői (Role of the sales and marketing relationship in market orientation and its determining factors)

A szerző kutatásában azt vizsgálja, hogy az értékesítés területén dolgozó munkatársak piaci megfigyeléseit milyen mértékben képesek beépíteni a marketingvezetők a menedzsmentmunkába. Az értékesítési munkatársak piaci megfigyelései mindig naprakészek, ráad��sul jelentősebb ráford��tás nélkül hozzáférhetők. A marketing- és a sales munkatársak közötti hagyományosan konfliktusokkal terhelt kapcsolat miatt azonban a vállalatok sokszor mégsem aknázzák ki a piaci tájékozód��snak ezt a lehetőségét. A nagyvállalati mintán empirikusan tesztelt modell szerint a menedzserek azon képessége, hogy felhasználják a vállalaton belül rendelkezésre álló információkat, alapvetően nem egyéni, hanem szervezeti képesség. Azok a menedzserek, akik olyan cégeknél dolgoznak, ahol a vállalati továbbképzések során más részlegek munkájába is bekapcsolódhatnak, nagyobb mértékben támaszkodnak a munkatársak piaci megfigyeléseire d��ntéseik meghozatala során. _____ The author examines in her research that to what extent marketing leaders can build market experience of sales employees into the management activity. Because of the traditionally problematic relationship between marketing and sales employees, companies do not exploit this opportunity of market orientation. According to the model tested on a big corporation sample, the capacity of managers to use information available within the company is basically not an individual but organisational capacity.

Design and synthesis of S-ribosylhomocysteine analogues

Bacteria are known to release a large variety of small molecules known as autoinducers (AI) which effect quorum sensing (QS) initiation. The interruption of QS effects bacterial communication, growth and virulence. ^ Three novel classes of S-ribosylhomocysteine (SRH) analogues as potential inhibitors of S-ribosylhomocysteinase (LuxS enzyme) and AI-2 modulators of QS were developed. The synthesis of 2-deoxy-2-bromo-SRH analogues was attempted by coupling of the corresponding 2-bromo-2-deoxypentafuranosyl precursors with the homocysteinate anion. The displacement of the bromide from C2 rather than the expected substitution of the mesylate from C5 was observed. The synthesis of 4-C-alkyl/aryl-S-ribosylhomocysteine analogues involved the following steps: (i) conversion of the D-ribose to the ribitol-4-ulose; (ii) diastereoselective addition of various alkyl or aryl or vinyl Grignard reagents to 4-ketone intermediate; (iii) oxidation of the primary hydroxyl group at C1 followed by the intramolecular ring closure to the corresponding 4-C-alkyl/aryl-substituted ribono-1,4-lactones; (iv) displacement of the activated 5-hydroxyl group with the protected homocysteinate. Treatment of the 4-C-alkyl/aryl-substituted SRH analogues with lithium triethylborohydride effected reduction of the ribonolactone to the ribose (hemiacetal) and subsequent global deprotection with trifluoroacetic acid provided 4-C-alkyl/aryl-SRHs. ^ The 4-[thia]-SRH were prepared from the 1-deoxy-4-thioribose through the coupling of the &agr;-fluoro thioethers (thioribosyl fluorides) with homocysteinate anion. The 4-[thia]-SRH analogues showed concentration dependent effect on the growth on las (50% inhibitory effect at 200 µg/mL). The most active was 1-deoxy-4-[thia]-SRH analogue with sufur atom in the ring oxidized to sulfoxide decreasing las gene activity to approximately 35% without affecting rhl gene. Neither of the tested compounds had effect on bioluminescence nor on total growth of V. harveyi, but had however slight inhibition of the QS.^

The H I chronicles of LITTLE THINGS blue compact dwarf galaxies

Star formation occurs when the gas (mostly atomic hydrogen; H I) in a galaxy becomes disturbed, forming regions of high density gas, which then collapses to form stars. In dwarf galaxies it is still uncertain which processes contribute to star formation and how much they contribute to star formation. Blue compact dwarf (BCD) galaxies are low mass, low shear, gas rich galaxies that have high star formation rates when compared to other dwarf galaxies. What triggers the dense burst of star formation in BCDs but not other dwarfs is not well understood. It is often suggested that BCDs may have their starburst triggered by gravitational interactions with other galaxies, dwarf-dwarf galaxy mergers, or consumption of intergalactic gas. However, there are BCDs that appear isolated with respect to other galaxies, making an external disturbance unlikely.^ Here, I study six apparently isolated BCDs from the LITTLE THINGS sample in an attempt to understand what has triggered their burst of star formation. LITTLE THINGS is an H I survey of 41 dwarf galaxies. Each galaxy has high angular and velocity resolution H I data from the Very Large Array (VLA) telescope and ancillary stellar data. I use these data to study the detailed morphology and kinematics of each galaxy, looking for signatures of starburst triggers. In addition to the VLA data, I have collected Green Bank Telescope data for the six BCDs. These high sensitivity, low resolution data are used to search the surrounding area of each galaxy for extended emission and possible nearby companion galaxies.^ The VLA data show evidence that each BCD has likely experienced some form of external disturbance despite their apparent isolation. These external disturbances potentially seen in the sample include: ongoing/advanced dwarf-dwarf mergers, an interaction with an unknown external object, and external gas consumption. The GBT data result in no nearby, separate H I companions at the sensitivity of the data. These data therefore suggest that even though these BCDs appear isolated, they have not been evolving in isolation. It is possible that these external disturbances may have triggered the starbursts that defines them as BCDs.^

The determinants of R&D investment: A survey of the empirical research

This paper offers an extensive survey and a critical discussion of the empirical literature on the driving factors of R&D. These factors are subsumed under five broad types. The paper first summarises the key predictions from theory regarding each type's R&D effect. It then examines for which factors differences in the theoretical predictions can also be found in empirical studies, and for which factors the empirical evidence is more unanimous. As the focus is on the empirical literature, methodological issues are also highlighted. The major factor types identified in the literature are, individual firm or industry characteristics, particularly internal finance and sales; competition in product markets; R&D tax credits and subsidies; location and resource related factors, such as spillovers from university research within close geographic proximity, membership of a research joint venture and cooperation with research centres, and the human capital embodied in knowledge workers; and spillovers from foreign R&D. Although on balance there is a consensus regarding the R&D effects of most factors, there is also variation in results. Recent work suggests that accounting for non-linearities is one area of research that may explain and encompass contradictory findings.

Innovation in the pharmaceutical industry: New estimates of R&D costs.

The research and development costs of 106 randomly selected new drugs were obtained from a survey of 10 pharmaceutical firms. These data were used to estimate the average pre-tax cost of new drug and biologics development. The costs of compounds abandoned during testing were linked to the costs of compounds that obtained marketing approval. The estimated average out-of-pocket cost per approved new compound is $1395 million (2013 dollars). Capitalizing out-of-pocket costs to the point of marketing approval at a real discount rate of 10.5% yields a total pre-approval cost estimate of $2558 million (2013 dollars). When compared to the results of the previous study in this series, total capitalized costs were shown to have increased at an annual rate of 8.5% above general price inflation. Adding an estimate of post-approval R&D costs increases the cost estimate to $2870 million (2013 dollars).