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A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics
We consider the ordinary differential equation
x2u′′=axu′+bu−c(u′−1)2,x∈(0,x0),
with
a∈R,b∈R
, c>0 and the singular initial condition u(0)=0, which in financial economics describes optimal disposal of an asset in a market with liquidity effects. It is shown in the paper that if a+b0 then there are infinitely many continuous solutions with indistinguishable asymptotics near 0. Moreover, it is proved that in the latter case there is precisely one solution u corresponding to the choice x 0=∞ which is such that 0≤u(x)≤x for all x>0, and that this solution is strictly increasing and concave
ÚČINNOSŤ DEZINFEKČNÉHO PRÍPRAVKU DUSEPT NA G- A G+ BAKTÉRIE TEPELNE OŠETRENÉHO MLIEKA
We were evaluating the effectiveness of disinfecting appliance Dusept on mixture of G+ and G- bacteria and on
the micro-organisms of heat-treated milk by three methods. By using the qualitative method effective action of
2% reagent was found on mixture of G+ and G- bacteria. By the qualitative method with carrier the 2% reagent
was also effective on the mixture of G+ and G- bacteria, 1% and 0,1% reagents were not effective. The 2%
reagent was not effective on the micro-organisms of milk on a carrier. The 2% solution was effective when
applying the quantitative method by 20 minutes actuation on bacteria contained in milk.V experimente sme hodnotili účinnosť dezinfekčného prípravku na báze chlóru tromi metódami na zmes G+
a G- baktérií a na mikroorganizmy obsiahnuté v pasterizovanom mlieku. Pri použití kvalitatívnej platňovej
metódy bolo účinné pôsobenie 2 %-ného roztoku na zmes G+ a G- baktérií. Pri kvalitatívnej metóde s použitím
skleneného nosiča bol 2 %-ný roztok taktiež účinný na zmes G+ a G- , 1 %-ný a 0,1 %-ný roztok nebol účinný.
Pre mikroorganizmy mlieka na nosiči 2 %-ný roztok bol neúčinný. Pri kvantitatívnej metóde bol 2 %-ný
roztok po 20 minútovom pôsobení na baktérie obsiahnuté v mlieku účinný
Measurement of Moisture Storage Parameters of Building Materials
The moisture storage parameters of three different building materials: calcium silicate, ceramic brick and autoclaved aerated concrete, are determined in the hygroscopic range and overhygroscopic range. Measured sorption isotherms and moisture retention curves are then combined into moisture storage functions using the Kelvin equation. A comparison of measured results with global characteristics of the pore space obtained by mercury intrusion porosimetry shows a reasonable agreement; the median pore radii by volume are well within the interval given by the beginning and the end of the characteristic steep parts of the moisture retention curves
Obrada čelika P2-04BCH kutno kanalnom ekstruzijom (KKE)
The article presents results of investigation of structure and properties of low-carbon steel grade P2-04BCH after application of ECAE at temperature of approx. 290C. The ECAE method leads to significant improvement of strength of investigated material. Investigation of structure was made by combination of TEM and FEG SEM together with EBSD. It was proven the ECAE method enables obtaining of ultra fine-grained ferritic structure formed by recrystallised grains with very low density of dislocations and with a small portion of spheroidised carbides, which occurred usually on the boundaries of ferritic grains.Članak prikazuje rezultate istraživanja strukture i svojstava niskougljičnog čelika kvalitete P2-04BCH nakon kanalno kutne ekstruzije (KKE) pri temperaturi od oko 290°C. Zabilježen je značajan porast čvrstoće materijala. Struktura je ispitana kombinacijom transmisijskog elektronskog mikroskopa (TEM), skenirajućeg elektronskog mikroskopa s emisijom polja (FEG SEM) te elektronskom difrakcijom (EBSD). Dokazano je da se jednakokanalnom kutnom ekstruzijom postiže izuzetno sitnozrnata feritna struktura rekristalizacijom zrna, uz vrlo nisku gustoću dislokacija i mali udio sferičnih karbida s rasporedom, obično na granicama feritnih zrna
Pendulum Energy Harvester with Amplifier
This paper presents a new principle of inductive vibration power harvester. Harvester is a pendulum that uses energy capacitor which is the mass. The mass is connected to the pendulum via a gearbox to achieve greater movement of the pendulum that generates an electromagnetic voltage. The harvester is developed at a very low frequency (1-10 Hz) which uses the rectified magnetic fluxes. Magnets are statically placed in the harvester case, and relative motion is carried out by the coil. Magnets are static, and the coil moves due to the weight ratio of magnets which the steel leads of the magnetic flux and the coil itself. This paper is focused on a harvester with a mechanical amplifier with the proposed technique is brings the plow harvester access with an auxiliary force. The experimental results indicate that the optimal results of the harvester with an accumulator for the resonant zone are 3.75 Hz, 7 Hz, and 10 Hz
Measuring the Process Parameters of the IBAD Method
Chromium nitride films are known as good protective layers for against both corrosion and wear. These coatings have been studied in detail during recent years. Their protective capability strongly depends on the deposition conditions. A modern method for preparing chromium nitride is the IBAD (Ion Beam Assisted Deposition) method. The main parameter determining the composition and properties of the films prepared by the IBAD method is the arrival ratio of impinging nitrogen ions to chromium atoms. In order to calibrate the ion beam XY-mechanical scanner with a Faraday cup, a detector was designed and constructed. By mathematical processing of the data, the flux of the nitrogen atoms was found. To obtain the flux of the chromium atoms the RBS and Talystep methods were used. Now, on the basis of this data, we can perform CrNx, coatings with controlled composition and properties
Near-Optimal Scheduling for LTL with Future Discounting
We study the search problem for optimal schedulers for the linear temporal
logic (LTL) with future discounting. The logic, introduced by Almagor, Boker
and Kupferman, is a quantitative variant of LTL in which an event in the far
future has only discounted contribution to a truth value (that is a real number
in the unit interval [0, 1]). The precise problem we study---it naturally
arises e.g. in search for a scheduler that recovers from an internal error
state as soon as possible---is the following: given a Kripke frame, a formula
and a number in [0, 1] called a margin, find a path of the Kripke frame that is
optimal with respect to the formula up to the prescribed margin (a truly
optimal path may not exist). We present an algorithm for the problem; it works
even in the extended setting with propositional quality operators, a setting
where (threshold) model-checking is known to be undecidable
Diversification and limited information in the Kelly game
Financial markets, with their vast range of different investment
opportunities, can be seen as a system of many different simultaneous games
with diverse and often unknown levels of risk and reward. We introduce
generalizations to the classic Kelly investment game [Kelly (1956)] that
incorporates these features, and use them to investigate the influence of
diversification and limited information on Kelly-optimal portfolios. In
particular we present approximate formulas for optimizing diversified
portfolios and exact results for optimal investment in unknown games where the
only available information is past outcomes.Comment: 11 pages, 4 figure
Reset thresholds of automata with two cycle lengths
We present several series of synchronizing automata with multiple parameters,
generalizing previously known results. Let p and q be two arbitrary co-prime
positive integers, q > p. We describe reset thresholds of the colorings of
primitive digraphs with exactly one cycle of length p and one cycle of length
q. Also, we study reset thresholds of the colorings of primitive digraphs with
exactly one cycle of length q and two cycles of length p.Comment: 11 pages, 5 figures, submitted to CIAA 201
On edge intersection graphs of paths with 2 bends
An EPG-representation of a graph G is a collection of paths in a grid, each corresponding to a single vertex of G, so that two vertices are adjacent if and only if their corresponding paths share infinitely many points. In this paper we focus on graphs admitting EPG-representations by paths with at most 2 bends. We show hardness of the recognition problem for this class of graphs, along with some subclasses. We also initiate the study of graphs representable by unaligned polylines, and by polylines, whose every segment is parallel to one of prescribed slopes. We show hardness of recognition and explore the trade-off between the number of bends and the number of slopes. © Springer-Verlag GmbH Germany 2016
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