Approximate controllability of the wave equation with mixed boundary conditions

We consider initial boundary-value problem for acoustic equation in the time space cylinder Ω×(0, 2T) with unknown variable speed of sound, zero initial data, and mixed boundary conditions. We assume that (Neumann) controls are located at some part Σ × [0, T], Σ ⊂ ∂Ω of the lateral surface of the cylinder Ω × (0, T). The domain of observation is Σ × [0, 2T], and the pressure on another part (∂Ω\Σ) × [0, 2T]) is assumed to be zero for any control. We prove the approximate boundary controllability for functions from the subspace V ⊂ H¹(Ω) whose traces have vanished on Σ provided that the observation time is 2T more than two acoustic radii of the domain Ω. We give an explicit procedure for solving Boundary Control Problem (BCP) for smooth harmonic functions from V (i.e., we are looking for a boundary control f which generates a wave uf such that uf (., T) approximates any prescribed harmonic function from V ). Moreover, using the Friedrichs–Poincar´e inequality, we obtain a conditional estimate for this BCP. Note that, for solving BCP for these harmonic functions, we do not need the knowledge of the speed of sound

Infinite dimensional integrals beyond Monte Carlo methods: yet another approach to normalized infinite dimensional integrals

An approach to (normalized) infinite dimensional integrals, including normalized oscillatory integrals, through a sequence of evaluations in the spirit of the Monte Carlo method for probability measures is proposed. in this approach the normalization through the partition function is included in the definition. For suitable sequences of evaluations, the ("classical") expectation values of cylinder functions are recoveredComment: Submitted as a communication in the ICMSQUARE conference, september 201

Characterization of chitin and its complexes extracted from natural raw sources

It is known that the main source of chitin and chitosan are shells of shrimp and other sea crustaceans. Alternative row sources of chitin, chitosan and its complexes are the lowest plants - mushrooms and insects. Also industrial wastes, especially from brewing of beer and manufacture of wine and ethanol can be used for extracting chitosan-containing products. The present research is aimed to the extraction of chitin and its complexes from alternative row sources, such as insects (cockroaches Pariplaneta Americana linnaeus and bees Apis mellifera lineaus), mushrooms (Amanita phalloides and Lactarius subdulius), waste banana wine (Kovibar and Urwibutso Inc.) and beer products (Bralirwa Inc., traditional sorghum) characteristic for Rwanda and their characterization using FTIR spectroscopy and elementary analysis. In chitin and its complexes extraction from all used raw sources, conditions for deproteinization were: 8% NaOH at 95 °C for 1 h and demineralization involved treatment with 6.7 % HCl at room temperature. Chitin and its complexes in the extracted samples were identified by FTIR spectroscopy using reference sample of Aspegillus Niger mushrooms. The presence of chitin parts causes the absorption band at 1650, 1552 and 1376 cm-1, which correspond to vibrations of amide groups amide I amide II and amide III, respectively. Using elemental analysis, the ratios of chitin and glucan parts were estimated and the percentage of chitin composition of all species was determined. For most of raw sources a fraction of chitin part was greater than that of glucan part. The chitin content of the samples studied ranged between 0.7-0.8 % of DM (dried mass) for wine (beer) waste products and 38% of dried mass (DM) for cockroaches. © 2016 Author(s).2014/239, 4.1626.2014/KRussian Foundation for Basic Research, RFBR: 14-03-00898Government Council on Grants, Russian FederationThis work was supported by the Russian Foundation for Basic Research (Grant 14-03-00898), the Program 211 of the Government of the Russian Federation No 02.A03.21.0006 and the State Tasks of the Ministry of Education (Russian Federation) No. 4.1626.2014/K and No. 2014/239 and the local Grant of University of Rwanda "Chitosancontaining materials of multifunctional application for needs of Rwanda". The authors are thankful to J.P. Intwali (Rwanda), E.V. Habumugisha (Rwanda), Ch. Ukundineza (Rwanda) and D. Niyoyita (Rwanda) for capturing insects and gathering mushrooms and their initial preparation for chitin extraction

Local monotonicity of Riemannian and Finsler volume with respect to boundary distances

We show that the volume of a simple Riemannian metric on $D^n$ is locally monotone with respect to its boundary distance function. Namely if $g$ is a simple metric on $D^n$ and $g'$ is sufficiently close to $g$ and induces boundary distances greater or equal to those of $g$, then $vol(D^n,g')\ge vol(D^n,g)$. Furthermore, the same holds for Finsler metrics and the Holmes--Thompson definition of volume. As an application, we give a new proof of the injectivity of the geodesic ray transform for a simple Finsler metric.Comment: 13 pages, v3: minor corrections and clarifications, to appear in Geometriae Dedicat

Filling minimality of Finslerian 2-discs

We prove that every Riemannian metric on the 2-disc such that all its geodesics are minimal, is a minimal filling of its boundary (within the class of fillings homeomorphic to the disc). This improves an earlier result of the author by removing the assumption that the boundary is convex. More generally, we prove this result for Finsler metrics with area defined as the two-dimensional Holmes-Thompson volume. This implies a generalization of Pu's isosystolic inequality to Finsler metrics, both for Holmes-Thompson and Busemann definitions of Finsler area.Comment: 16 pages, v2: improved introduction and formattin

On Alternative Supermatrix Reduction

We consider a nonstandard odd reduction of supermatrices (as compared with the standard even one) which arises in connection with possible extension of manifold structure group reductions. The study was initiated by consideration of the generalized noninvertible superconformal-like transformations. The features of even- and odd-reduced supermatrices are investigated on a par. They can be unified into some kind of "sandwich" semigroups. Also we define a special module over even- and odd-reduced supermatrix sets, and the generalized Cayley-Hamilton theorem is proved for them. It is shown that the odd-reduced supermatrices represent semigroup bands and Rees matrix semigroups over a unit group.Comment: 22 pages, Standard LaTeX with AmS font

Space Biology and Medicine

Volume IV is devoted to examining the medical and associated organizational measures used to maintain the health of space crews and to support their performance before, during, and after space flight. These measures, collectively known as the medical flight support system, are important contributors to the safety and success of space flight. The contributions of space hardware and the spacecraft environment to flight safety and mission success are covered in previous volumes of the Space Biology and Medicine series. In Volume IV, we address means of improving the reliability of people who are required to function in the unfamiliar environment of space flight as well as the importance of those who support the crew. Please note that the extensive collaboration between Russian and American teams for this volume of work resulted in a timeframe of publication longer than originally anticipated. Therefore, new research or insights may have emerged since the authors composed their chapters and references. This volume includes a list of authors' names and addresses should readers seek specifics on new information. At least three groups of factors act to perturb human physiological homeostasis during space flight. All have significant influence on health, psychological, and emotional status, tolerance, and work capacity. The first and most important of these factors is weightlessness, the most specific and radical change in the ambient environment; it causes a variety of functional and structural changes in human physiology. The second group of factors precludes the constraints associated with living in the sealed, confined environment of spacecraft. Although these factors are not unique to space flight, the limitations they entail in terms of an uncomfortable environment can diminish the well-being and performance of crewmembers in space. The third group of factors includes the occupational and social factors associated with the difficult, critical nature of the crewmembers' work: the risks involved in space flight, changes in circadian rhythms, and intragroup interactions. The physical and emotional stress and fatigue that develop under these conditions also can disturb human health and performance. In addition to these factors, the risk also exists that crewmembers will develop various illnesses during flight. The risk of illness is no less during space flight than on Earth, and may actually be greater for some classes of diseases

Grafting of (3-chloropropyl)-trimethoxy silane on halloysite nanotubes surface

Modified halloysite nanotubes (HNTs-Cl) were synthesized by a coupling reaction with (3-chloropropyl) trimethoxysilane (CPTMS). The incorporation of chloro-silane onto HNTs surface creates HNTs-Cl, which has great chemical activity and is considered a good candidate as an active site that reacts with other active molecules in order to create new materials with great applications in chemical engineering and nanotechnology. The value of this work lies in the fact that improving the degree of grafting of chloro-silane onto the HNT’s surface has been accomplished by incorporation of HNTs with CPTMS under different experimental conditions. Many parameters, such as the dispersing media, the molar ratio of HNTs/CPTMS/H2O, refluxing time, and the type of catalyst were studied. The greatest degree of grafting was accomplished by using toluene as a medium for the grafting process, with a molar ratio of HNTs/CPTMS/H2O of 1:1:3, and a refluxing time of 4 h. The addition of 7.169 mmol of triethylamine (Et3N) and 25.97 mmol of ammonium hydroxide (NH4OH) led to an increase in the degree of grafting of CPTMS onto the HNT’s surface

Noise auto-correlation spectroscopy with coherent Raman scattering

Ultrafast lasers have become one of the most powerful tools in coherent nonlinear optical spectroscopy. Short pulses enable direct observation of fast molecular dynamics, whereas broad spectral bandwidth offers ways of controlling nonlinear optical processes by means of quantum interferences. Special care is usually taken to preserve the coherence of laser pulses as it determines the accuracy of a spectroscopic measurement. Here we present a new approach to coherent Raman spectroscopy based on deliberately introduced noise, which increases the spectral resolution, robustness and efficiency. We probe laser induced molecular vibrations using a broadband laser pulse with intentionally randomized amplitude and phase. The vibrational resonances result in and are identified through the appearance of intensity correlations in the noisy spectrum of coherently scattered photons. Spectral resolution is neither limited by the pulse bandwidth, nor sensitive to the quality of the temporal and spectral profile of the pulses. This is particularly attractive for the applications in microscopy, biological imaging and remote sensing, where dispersion and scattering properties of the medium often undermine the applicability of ultrafast lasers. The proposed method combines the efficiency and resolution of a coherent process with the robustness of incoherent light. As we demonstrate here, it can be implemented by simply destroying the coherence of a laser pulse, and without any elaborate temporal scanning or spectral shaping commonly required by the frequency-resolved spectroscopic methods with ultrashort pulses.Comment: To appear in Nature Physic

Theory and computation of directional nematic phase ordering

A computational study of morphological instabilities of a two-dimensional nematic front under directional growth was performed using a Landau-de Gennes type quadrupolar tensor order parameter model for the first-order isotropic/nematic transition of 5CB (pentyl-cyanobiphenyl). A previously derived energy balance, taking anisotropy into account, was utilized to account for latent heat and an imposed morphological gradient in the time-dependent model. Simulations were performed using an initially homeotropic isotropic/nematic interface. Thermal instabilities in both the linear and non-linear regimes were observed and compared to past experimental and theoretical observations. A sharp-interface model for the study of linear morphological instabilities, taking into account additional complexity resulting from liquid crystalline order, was derived. Results from the sharp-interface model were compared to those from full two-dimensional simulation identifying the specific limitations of simplified sharp-interface models for this liquid crystal system. In the nonlinear regime, secondary instabilities were observed to result in the formation of defects, interfacial heterogeneities, and bulk texture dynamics.Comment: first revisio