Search

Abstract: A new technique is proposed for analyzing the convergence of a projection difference scheme as applied to the initial value problem for a linear parabolic operator-differential equation. The technique is based on discrete analogues of weighted estimates reflecting the smoothing property of solutions to the differential problem for t > 0. Under certain conditions on the right-hand side, a new convergence rate estimate of order O($$ \sqrt \tau $$ + h) is obtained in a weighted energy norm without making any a priori assumptions on the additional smoothness of weak solutions. The technique leads to a natural projection difference approximation of the problem of controlling nonsmooth initial data. The convergence rate estimate obtained for the approximating control problems is of the same order O($$ \sqrt \tau $$ + h) as for the projection difference scheme.

Abstract: The productivity of the nitrogen mineralization in the A0 (0–2 cm), A1 (2–3 cm), and A2 (3–13 cm) horizons of a soddy-podzolic soil was measured in a wood-sorrel-whortleberry birch forest (7Birch3Asp, 80 years, the second stand quality class, tree canopy density 0.7, Yaroslavl oblast) using the sample incubation method; the measurements were performed from May till October in eight replicates for each horizon. In 2007, 5.85 ± 0.73 g N/m2 were mineralized in the soil. In the litter, 2.01 ± 0.23 g N/m2 were mineralized, whereas 0.35 ± 0.03 and 3.49 ± 0.72 g N/m2 were mineralized in the A1 and A2 horizons, respectively. In 2008, 3.34 ± 0.25 g N/m2 were mineralized in the A0 and A1 horizons, of which 2.44 ± 0.23 g N/m2 were in the former. Ammonification prevailed in all the horizons. The contribution of nitrification was assessed as 1.6 and 0.3% of the process’s productivity in 2007 and 2008, respectively. The Corg and Norg pools decreased in the litter by 407 g C/m2 and 13.7g N/m2 (or 33%) from May to October. Of this carbon amount, 67% is spent for humification and the organic mass preservation and 33% was transformed to carbonic acid. The nitrogen expenses for the synthesis of humus acids are equal to 70 and 30%; it is spent equally for the mineralization of the element and its immobilization by microorganisms. In the A0 and A1 horizons, the seasonal trends of the ammonification correlated with the carbon dioxide emission from these horizons in the year of 2008 with r = 0.75 atp = 0.09 and r = 0.82 atp = 0.04 for both horizons, respectively.

Abstract: The mineralization of nitrogen in forest soils, one of the processes that provides forest ecosystems with nitrogen, has practically not been studied in Russia. A variant of the method used for the measurement of the nitrogen mineralization in forest soils is proposed, and a description of its field and laboratory stages is given. At the field stage, as the ammonium concentrations are determined in the soil horizons, eight soil samples free of plants and plant roots are recommended to be exposed in a uniform forest area in order to provide a 10% error of the average. The results obtained in a laboratory by the traditional method of measuring the ammonium content in litter extracts may be overstated by 5 times (on the average, by 1.7 times) as compared to the results obtained by the diffusion-isothermic method proposed. The source of errors in the former method is the specific features of Nessler’s reagent, which forms colored complexes with metals and organic compounds. In addition, extracts from loamy soils often grow turbid and opalescent at the addition of Nessler’s reagent, which makes the measurement of the optical density impossible. A highly sensitive and well-reproducible method is recommended for the reduction of nitrates to nitrites in a column with coppered cadmium. The methods proposed are simple and reliable and do not require the expensive autoanalyzers that are used abroad.

Abstract: The mean seasonal rates of the ammonia nitrogen emission from a soddy-podzolic soil under an oxalis-bilberry birch forest in Yaroslavl oblast were measured from May to October in 2005 and 2006 and comprised 27 ± 14 and 25 ± 11 μg N/m2 per day, which corresponded to 44 ± 23 and 32 ± 15 g N/ha, respectively. The maximum rates of the emission had a positive correlation with the soil temperature (r = 0.77 and 0.82, respectively) and a negative correlation with the soil water content (r = 0.3 and 0.54). The coefficients of the multiple correlation between these parameters were 0.82 and 0.84, respectively (at p = 0.16). The mean seasonal rate of the ammonia nitrogen emission from a soddy-podzolic soil under an herbaceous meadow in 2006 reached 155 ± 80 μg N/m2 per day, or 160 ± 80 g N/ha. The rates of the ammonia emission during the growing season correlated with the soil temperature (r = 0.81 at p = 0.03). A method for measuring the ammonia emission from soils was proposed.

Abstract: The problem of transverse vibrations of a thin elastic plate is considered. It is proved that the differential operators of the boundary value problem are regularly elliptic, and weak solutions are estimated. For a previously developed difference method, the solution to the difference problem is proved to converge strongly to a weak solution of the original differential problem and the rate of convergence is estimated.

A systematic computational analysis of the ability of aromatic carbon-bound fluorine to participate in hydrogen bonding and electrostatic interactions has been completed. The interaction energies between the most common fluoroaromatics used in medicinal chemistry and both water, the prototypical hydrogen bond donor, and several cations have been calculated at different levels of theory (HF, MP2, DFT). Our results show that aromatic fluorine can participate in significant hydrogen bonds and can also interact with charged molecules.

Abstract: We consider the initial boundary-value problem for the quasilinear diffusion equation ∂ t u+u − DΔu = K(x, y)(1 + γ(u + ϕ(x, y))) describing the dynamics of optical systems with controlled feedback wave intensity modulation K(x, y) in the presence of incoming-wave phase perturbations ϕ(x, y). The control problem for the parameter K(x, y) is formulated with the objective of smoothing out the spatial nonhomogeneities of the total output phase u(x, y, T) + ϕ(x, y). We prove existence and uniqueness theorems for the generalized solutions of the direct and conjugate problems, solvability theorems for the optimization problems, and Frechet-differentiability of the objective functional. A formula for the functional gradient is derived and the efficiency of the gradient projection method is demonstrated numerically.

We consider the optimization of the two-dimensional transformation $$g\left( x \right):\bar \Omega \to \bar \Omega $$ of the spatial arguments of the sought function in the mixed initial boundary-value problem for the functional-differential diffusion equation $$\partial _t u + u - D\Delta u = F_g \left( u \right)$$ where the right-hand side is defined by the generalized superposition $$F\left( s \right) \in C^2 \left( {\bar R} \right)$$ , and the argument transformation g(x) in the form of the functional $$\left\langle {F_g \left( u \right),\varphi } \right\rangle = \int\limits_{\bar \Omega } {F\left( {u\left( {x,t} \right)} \right)} \varphi \left( {g\left( x \right)} \right)dx$$ defined on the space of continuous test functions ϕ ∈ $${\bar \Omega }$$ . The quality of optimization is evaluated by the integral functional $$J\left( g \right) = \int\limits_{Q_T } {\rho \left( {x,t} \right)\left| {u\left( {x,t;g} \right) - u_1 \left( {x,t} \right)} \right|^2 dxdt,Q_T = } \bar \Omega \times \left[ {0,T} \right].$$ The minimizing sequence for the minimization problem J(g) → infGon the set G= g∈ L2(Q): g( $${\bar \Omega }$$ ) ⊂ $${\bar \Omega }$$ } of pointwise-bounded transformations is constructed by the gradient projection method combined with special projection-difference approximations of the direct and the conjugate initial boundary-value problems, which allow for possible irreversibility of the argument transformation and its generalized specification. Numerical optimization results are discussed using two examples of localized objective functions u1(x, t).

A comparative analysis is presented of the accuracy possibilities of competitive systems for measuring linear and angular displacements constructed using various schemes. A scheme is presented and a description is given of the principle of operation of a system which possesses fundamentally higher accuracy possibilities. This system is shown to be of universal application.

We consider a mixed initial boundary-value problem for the nonlinear parabolic functional-differential equation. The functional part of the equation depends on a generalized superposition of the sought solution and a transformation of the one-dimensional spatial argument. An approximate projection difference scheme is proposed for a wide class of measurable (including non-invertible) transformations. An O(τ + h1 + γ) bound is obtained for the rate of convergence in the L2(Q) norm to the generalized solutions of the original problem without prior assumptions about invertibility of the transformation, smoothness of the solution, or compatibility of grid increments.

We consider an initial-boundary-value problem for the nonlinear Schrödinger equation in the complexvalued functionE=E(x,z):(1) $$\partial _z E + i\Delta E + i\alpha \left| E \right|^p E + \beta \left| E \right|^q E = 0, q > p \geqslant 0, \beta > 0,$$ (2) $$\left. E \right|_{z = 0} = E_0 \in H^2 (\Omega ) \cap H_0^1 (\Omega ), \left. E \right|_{\partial \Omega } = 0, \Omega \subset R^2 , \partial \Omega \in C^2 .$$ We investigate the behavior of the solution of problem (1)–(2) as β→0 and its closeness to the solution of the degenerate equation (β=0). Given the consistency conditionq(β)=p+εln(1/β), 0<ɛ≤ɛ0, we establish boundedness of the norm $$\left\| E \right\|_{C([0,z_0 ]):H_0^1 (\Omega ))} + \left\| {\partial _z E} \right\|_{C([0,z_0 ]);L^2 (\Omega ))} $$ for every finitez0>0 as β→0. For α≤0 and a fixedq, we prove uniform (in β) boundness of solutions of problem (1)–(2) on some interval [0,Z] and their convergence as β→0 to the solution of the degenerate problem (β=0) in the normC([0,Z];L2(Ω)).

We consider the diagnostics of nonequilibrium gaseous media in a spatially one-dimensional formulation with the measurement sensors placed in various flow cross-sections. The variational method minimizes the discrepancy functional over the system of initial parameters allowing for the reliability, of the observations. A technique is developed for deriving the functional gradient, which depends on the path components of the Cauchy problem calculated at various points. The gradient is shown to be Lipschitz-continuous in control and the iterative gradient projection method converges to the set of stationary points of the functional.

We derive conservation laws for so-called generalized nonlinear Schrödinger equation (GNLSE), which describes a propagation of super-short femtosecond pulse in a medium with cubic nonlinear response in the framework of slowly-evolving-wave approximation (SEWA). We take into account the beam diffraction, the pulse spreading due to second order dispersion, the pulse self-steepening, as well as mixed derivatives of the pulse envelope. Such nonlinear interaction of the laser pulse with a medium is widely investigated by many authors because various substances manifest a cubic nonlinear response of medium in various laser systems. However, until present time the conservation laws (integrals of motion) of the GNLSE are absent. For their deriving we propose a novel transform of the GNLSE. It results in an equation containing neither the derivative of a term describing the nonlinear response of medium nor mixed derivatives of a complex amplitude. In new variables, the femtosecond pulse propagation is described by three equations containing only the linear differential operators. Using this transform, the conservation laws for a problem under consideration are found out. We claim that for avoiding a non-physical modulation instability of a laser pulse propagation it is necessary to satisfy to a spectral invariant at the frequency, which is singular one in the Fourier space. This frequency is inherent to the GNLSE. The conservation laws allow developing the conservative finite-difference schemes that preserve difference analogs of these laws. [ABSTRACT FROM AUTHOR]