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Search Results: 1 - 10 of 19799 matches for " Alexander Zaporozhets "
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Kartographisch-semiotische Aktivit ten an der National Aviation University in Kyiw [Cartographic-semiotic activities at the National Aviation University in Kyiv]
Alexander Zaporozhets,Alexander Wolodtschenko
Meta-Carto-Semiotics , 2010,
Abstract:
Mean width of regular polytopes and expected maxima of correlated Gaussian variables
Zakhar Kabluchko,Alexander E. Litvak,Dmitry Zaporozhets
Mathematics , 2015,
Abstract: An old conjecture states that among all simplices inscribed in the unit sphere the regular one has the maximal mean width. An equivalent formulation is that for any centered Gaussian vector $(\xi_1,\dots,\xi_n)$ satisfying $\mathbb E\xi_1^2= \dots =\mathbb E\xi_n^2=1$ one has $$ \mathbb E\,\max\{\xi_1,\dots,\xi_n\}\leq\sqrt{\frac{n}{n-1}}\, \mathbb E\,\max\{\eta_1,\dots,\eta_n\}, $$ where $\eta_1,\eta_2,\dots,$ are independent standard Gaussian variables. Using this probabilistic interpretation we derive an asymptotic version of the conjecture. We also show that the mean width of the regular simplex with $2n$ vertices is remarkably close to the mean width of the regular crosspolytope with the same number of vertices. Interpreted probabilistically, our result states that $$ 1\leq\frac{\mathbb E\,\max\{|\eta_1|,\dots,|\eta_n|\}}{\mathbb E\,\max\{\eta_1,\dots,\eta_{2n}\}} \leq\min\left\{\sqrt{\frac{2n}{2n-1}}, \, 1+\frac{C}{n\, \log n} \right\}, $$ where $C>0$ is an absolute constant. We also compute the higher moments of the projection length $W$ of the regular cube, simplex and crosspolytope onto a line with random direction, thus proving several formulas conjectured by S. Finch. Finally, we prove distributional limit theorems for the length of random projection as the dimension goes to $\infty$. In the case of the $n$-dimensional unit cube $Q_n$, we prove that $$ W_{Q_n} - \sqrt{\frac{2n}{\pi}} \overset{d}{\underset{n\to\infty}\longrightarrow} {\mathcal{N}} \left(0, \frac{\pi-3}{\pi}\right), $$ whereas for the simplex and the crosspolytope the limiting distributions are related to the Gumbel double exponential law.
Parametric investigation of acoustic radiation by a beam under load and actuator forces Параметрическое исследование акустического излучения балкой под нагрузкой и актуаторами типа силы ПАРАМЕТРИЧНЕ ДОСЛ ДЖЕННЯ АКУСТИЧНОГО ВИПРОМ НЮВАННЯ БАЛКОЮ П Д НАВАНТАЖЕННЯМ ТА АКТУАТОРАМИ ТИПУ СИЛИ
Alexander Zaporozhets,Vadim Tokarev,Werner Hufenbach,Olaf Taeger
Proceedings of National Aviation University , 2005,
Abstract: The objective of this paper is to investigate the parametric characteristics of oscillating beam using an analytical theory of beam vibration. Analytical investigation of the bending oscillations of a finite elastic beam is considered for criteria based on minimal acoustic radiation. The solution of the task is defined by solving of Helmholtz equation and inhomogeneous differential equation for beam bending vibration with harmonic time dependence. For calculation of the acoustic field a model of a plane piston, which is set in an infinite rigid baffle, is used. Исследованы параметрические характеристики колебаний балки с использованием аналитической теории вибрации балки. Аналитическое исследование изгибных колебаний эластичной балки конечных размеров рассмотрено для критерия, определяющего минимальное акустическое излучение. Решение задачи определено для уравнения Гельмгольца и неоднородного дифференциального уравнения гармонических изгибных колебаний балки. Для расчета акустического поля использована модель поршня, установленного на бесконечный экран. Досл джено параметричн характеристики коливань балки з використанням анал тично теор в брац балки. Анал тичне досл дження згинальних коливань еластично балки к нцевих розм р в розглянуто для критер ю, що визнача м н мальне акустичне випром нювання. Розв’язок задач визначено для р вняння Гельмгольца неоднор дного диференц йного р вняння гармон чних згинальних коливань балки. Для обчислення акустичного поля застосовано модель поршня, установленого на неск нченний екран.
Simple and Rapid Determination of Diuretics by Luminescent Method  [PDF]
Iuna Tsyrulneva, Olga Zaporozhets
Pharmacology & Pharmacy (PP) , 2013, DOI: 10.4236/pp.2013.47075
Abstract: Diuretics are drugs widely used in treatment of heart failure and hypertension and as doping agents in sports. Wrong prescription and excessive abuse can lead to negative side effects. Despite the effectiveness of methods usually used for the determination of diuretics (gas or liquid chromatography, capillary electrophoresis), they do not always provide necessary sensitivity. Moreover, sample preparation increases time of analysis. A rapid and sensitive luminescent method for determination of 5 diuretics (amiloride, bendroflumethiazide, bumetanide, furosemide, triamterene) in aqueous solutions and amiloride and triamterene in human urine is described. Intrinsic luminescent properties of protolytic forms of diuretics were studied in order to provide highly sensitive analysis. Investigation of interfering influence of diuretics was carried out to provide selective determination of triamterene, bumetanide and furosemide in aqueous mixtures of diuretics. Influence of urine at luminescent properties of diuretics was studied. The possibility of determination of triamterene and amiloride in human urine as individual substances and in mixture was proved. Simple and rapid technique for their determination in human urine was elaborated. The techniques elaborated for determination of triamterene in presence of other diuretics and furosemide in presence of commensurate amount of bumetanide allow enhancing specifity of analysis. Sufficient selectivity and sensitivity were reached in determination of amiloride and triamterene in human urine. The reduction of time of analysis due to avoiding sample preparation merits the techniques proposed.
Determination of 8 Diuretics and Probenecid in Human Urine by Gas Chromatography-Mass Spectrometry: Confirmation Procedure  [PDF]
Olga Zaporozhets, Iuna Tsyrulneva, Mykola Ischenko
American Journal of Analytical Chemistry (AJAC) , 2012, DOI: 10.4236/ajac.2012.34044
Abstract: A fast and sensitive method for determination of 8 diuretics (acetazolamide, bendroflumethiazide, bumetanide, chlorthalidone, furosemide, hydrochlorothiazide, metolazone, triamterene) and masking agent (probenecid) in human urine using gas-chromatography with mass spectrometric detection is described. The extraction of the substances as function of the nature of organic solvent, mixing time and pH of aqueous phase was studied. The tandem mass spectrometry was used to increase selectivity of diuretics determination due to elimination of background interferences. Fragmentation reactions were studied for each compound and their collision energies were optimized to obtain the best selectivity. The results of method’s validation demonstrate its suitability in routine analysis for confirmation purposes.
Урахування впливу експлуатац йних чинник в при визначенн р вн в ав ац йного шуму в окол аеропорту ACCOUNTING FOR INFLUENCE OF THE OPERATIONAL FACTORS IN AIRCRAFT NOISE CALCULATIONS AROUND THE AIRPORTS Учет влияния эксплуатационных факторов при определении уровней авиационного шума в окрестностях аэропорта
Oleksandr Zaporozhets,Gregory Golembievsky
Proceedings of National Aviation University , 2006,
Abstract: Розглянуто основн в дм нност м ж укра нським методом розрахунку ав ац йного шуму поточним методом, що рекоменду ться вропейською конференц ю цив льно ав ац . Показано вплив експлуатац йних фактор в на випром нювання розповсюдження шуму. Basic differences between Ukrainian method for aircraft noise calculation and current ECAC proposal are considered in the article: they include the influence of operational factors on noise radiation and propagation. Рассмотрены основные отличия между украинским методом расчета авиационного шума и текущим методом, рекомендуется Европейской конференцией гражданской авиации. Показано влияние эксплуатационных факторов на излучение и распространение шума.
Roots of random polynomials whose coefficients have logarithmic tails
Zakhar Kabluchko,Dmitry Zaporozhets
Mathematics , 2011, DOI: 10.1214/12-AOP764
Abstract: It has been shown by Ibragimov and Zaporozhets [In Prokhorov and Contemporary Probability Theory (2013) Springer] that the complex roots of a random polynomial $G_n(z)=\sum_{k=0}^n\xi_kz^k$ with i.i.d. coefficients $\xi_0,\ldots,\xi_n$ concentrate a.s. near the unit circle as $n\to\infty$ if and only if ${\mathbb{E}\log_+}|\xi_0|<\infty$. We study the transition from concentration to deconcentration of roots by considering coefficients with tails behaving like $L({\log}|t|)({\log}|t|)^{-\alpha}$ as $t\to\infty$, where $\alpha\geq0$, and $L$ is a slowly varying function. Under this assumption, the structure of complex and real roots of $G_n$ is described in terms of the least concave majorant of the Poisson point process on $[0,1]\times (0,\infty)$ with intensity $\alpha v^{-(\alpha+1)}\,du\,dv$.
Asymptotic distribution of complex zeros of random analytic functions
Zakhar Kabluchko,Dmitry Zaporozhets
Mathematics , 2014, DOI: 10.1214/13-AOP847
Abstract: Let $\xi_0,\xi_1,\ldots$ be independent identically distributed complex- valued random variables such that $\mathbb{E}\log(1+|\xi _0|)<\infty$. We consider random analytic functions of the form \[\mathbf{G}_n(z)=\sum_{k=0}^{\infty}\xi_kf_{k,n}z^k,\] where $f_{k,n}$ are deterministic complex coefficients. Let $\mu_n$ be the random measure counting the complex zeros of $\mathbf{G}_n$ according to their multiplicities. Assuming essentially that $-\frac{1}{n}\log f_{[tn],n}\to u(t)$ as $n\to\infty$, where $u(t)$ is some function, we show that the measure $\frac{1}{n}\mu_n$ converges in probability to some deterministic measure $\mu$ which is characterized in terms of the Legendre-Fenchel transform of $u$. The limiting measure $\mu$ does not depend on the distribution of the $\xi_k$'s. This result is applied to several ensembles of random analytic functions including the ensembles corresponding to the three two-dimensional geometries of constant curvature. As another application, we prove a random polynomial analogue of the circular law for random matrices.
Universality for zeros of random analytic functions
Zakhar Kabluchko,Dmitry Zaporozhets
Mathematics , 2012,
Abstract: Let $\xi_0,\xi_1,...$ be independent identically distributed (i.i.d.) random variables such that $\E \log (1+|\xi_0|)<\infty$. We consider random analytic functions of the form $$ G_n(z)=\sum_{k=0}^{\infty} \xi_k f_{k,n} z^k, $$ where $f_{k,n}$ are deterministic complex coefficients. Let $\nu_n$ be the random measure assigning the same weight $1/n$ to each complex zero of $G_n$. Assuming essentially that $-\frac 1n \log f_{[tn], n}\to u(t)$ as $n\to\infty$, where $u(t)$ is some function, we show that the measure $\nu_n$ converges weakly to some deterministic measure which is characterized in terms of the Legendre--Fenchel transform of $u$. The limiting measure is universal, that is it does not depend on the distribution of the $\xi_k$'s. This result is applied to several ensembles of random analytic functions including the ensembles corresponding to the three two-dimensional geometries of constant curvature. As another application, we prove a random polynomial analogue of the circular law for random matrices.
Intrinsic volumes of Sobolev balls with applications to Brownian convex hulls
Zakhar Kabluchko,Dmitry Zaporozhets
Mathematics , 2014,
Abstract: A formula due to Sudakov relates the first intrinsic volume of a convex set in a Hilbert space to the maximum of the isonormal Gaussian process over this set. Using this formula we compute the first intrinsic volumes of infinite-dimensional convex compact sets including unit balls with respect to Sobolev-type seminorms and ellipsoids in the Hilbert space. We relate the distribution of the random one-dimensional projections of these sets to the distributions $S_1,S_2,C_1,C_2$ studied by Biane, Pitman, Yor [Bull.\ AMS 38 (2001)]. We show that the $k$-th intrinsic volume of the set of all functions on $[0,1]$ which have Lipschitz constant bounded by $1$ and which vanish at $0$ (respectively, which have vanishing integral) is given by $$ V_k = \frac{\pi^{k/2}}{\Gamma\left(\frac 32 k +1 \right)}, \text{ respectively } V_k = \frac{\pi^{(k+1)/2}}{2\Gamma\left(\frac 32 k +\frac 32\right)}. $$ This is related to the results of Gao and Vitale [Discrete Comput. Geom. 26 (2001), Elect. Comm. Probab. 8 (2003)] who considered a similar question for functions with a restriction on the total variation instead of the Lipschitz constant. Using the results of Gao and Vitale we give a new proof of the formula for the expected volume of the convex hull of the $d$-dimensional Brownian motion which is due to Eldan [Elect. J. Probab., to appear]. Additionally, we prove an analogue of Eldan's result for the Brownian bridge. Similarly, we show that the results on the intrinsic volumes of the Lipschitz balls can be translated into formulae for the expected volumes of zonoids (Aumann integrals) generated by the Brownian motion and the Brownian bridge. Also, these results have discrete versions for Gaussian random walks and bridges. Our proofs exploit Sudakov's and Tsirelson's theorems which establish a connection between the intrinsic volumes and the isonormal Gaussian process.
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