On weak solutions of linear coercive integral equations in spacesL 2(X; ℋ k )

Пусть (X,A, μ) - полное про странство с σ-конечно й мерой, и пусть \(\overline {\mu \times \mu } \) . - замык ание меры μ×μ. Пусть далееg: X×X→C - квадратично интегрируемая функц ия по мере \(\overline {\mu \times \mu } \) . Рассматривается лин ейное интегральное у равнение (слабого) типа (1) (1) $$u(t) + A(\mathop \smallint \limits_x g(t,s)u(s)d\mu ) = f(t)\Pi .B.B\,X,$$ гдеА - максимальное р асширение L _k ^′ (в простр анстве ХëрмандераH ₁=B₂к) соотв ествующего линейного (псевдодиф ференциального) опер атораL: S→S; иS обозначает класс Щварца функций Rⁿ→-C. Уст анавливается сущест вование (слабых) решений (1) при н екотором условии коэрпитивно сти на оператор (2) (2) $$(L\Psi )(t) = \Psi (t) + \int\limits_x {g(t,s)L(\Psi (s))d\mu ,} $$ где Ψ принадлежит про странстувуD(Х, S) всех конечно-значных функ ций изX→S. Далее, изучается обобщенна я обратимость максим ального расширения оператора L. Наконец, пр иводится некоторое алгебраическое усло вие, обеспечивающее коэрцитивность L.     

On semi-fredholm properties of a boundary value problem inR + n

The paper considers a boundary value problem with the help of the smallest closed extensionL ^∼ :H _k →H _{k 0}×B _{h 1}×...×B _{h N} of a linear operatorL :C ₍₀₎ ^∞ (R ₊ ⁿ ) →L(R ₊ ⁿ )×L(R ⁿ⁻¹)×...×L(R ⁿ⁻¹). Here the spacesH _k (the spaces ℬ _h ) are appropriate subspaces ofD′(R ₊ ⁿ ) (ofD′(R ⁿ⁻¹), resp.),L(R ₊ ⁿ ) andC ₍₀₎ ^∞ (R ₊ ⁿ )) denotes the linear space of smooth functionsR ⁿ →C, which are restrictions onR ₊ ⁿ of a function from the Schwartz classL (fromC ₀ ^∞ , resp.),L(R ⁿ⁻¹) is the Schwartz class of functionsR ⁿ⁻¹ →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L ^∼) and for the uniqueness of solutionsL ^∼ U=F are expressed. In addition, ana priori estimate for the corresponding boundary value problem is established.     

A three‐dimensional finite element model for the control of certain non‐linear bioreactors

This paper deals with the dynamics of non‐linear distributed parameter fixed‐bed bioreactors. The model consists of a pair of non‐linear partial differential (evolution) equations. The true spatially three‐dimensional situation is considered instead of the usual one‐dimensional approximation. This enables one to take into account the effects of flow profiles and the true location of the measurement transducer. The (output) evolution of the corresponding open‐loop control system is simulated. Furthermore, the associated closed‐loop system with respect to the relevant output function is considered. Especially, the asymptotic output tracking is found to be successful by applying the usual process based on the state feedback linearization. Copyright © 2000 John Wiley & Sons, Ltd.     

Probing surface plasmons by bare V-shaped tips: modeling by geometrical optics and rigorous diffraction theory

Optical Review - We consider probing inhomogeneous waves in the near fields of metallic nanostructures with the aid of a dielectric V-shaped wedge connected to a waveguide. A geometrical model...     

Coherence-polarization mixing in resonance gratings

We show, using rigorous diffraction theory, that resonance gratings can be used to transfer partial spatial correlation to partial polarization even if the incident light beam is fully polarized. The phenomenon is based on the fact that either of the two orthogonal polarization components can be coupled into the leaky waveguide mode, leading to a strong phase delay, while the other one is reflected without being coupled into the grating. Numerical demonstrations are based on a Gaussian Schell-model beam and a grating analysis performed by rigorous Fourier modal method.     

On realizations related to Weyl operators

The paper deals with the minimal and the maximal realizations (L ^w )^~ and (L ^w ):L ₂L ₂ of linear operators of Weyl type

Comparing the quality and predictiveness between 3D QSAR models obtained from manual and automated alignment

A set of 113 flexible cyclic urea inhibitors of human immunodeficiency virus protease (HIV-1 PR) was used to compare the quality and predictive power of CoMFA and CoMSIA models for manually or automatically aligned inhibitor set. Inhibitors that were aligned automatically with molecular docking were in agreement with information obtained from existing X-ray structures. Both alignment methods produced statistically significant CoMFA and CoMSIA models, with the best q(2) value being 0.649 and the best predictive r(2) being 0.754. The manual alignment gave statistically higher values, whereas the automated alignment gave more robust models for predicting the activities of an external inhibitor set. Both models utilized similar amino acids in the HIV-1 PR active site, supporting the idea that hydrogen bonds form between an inhibitor and the backbone carbonyl oxygens of Gly48 and Gly48' and also the backbone NH group of Asp30, Gly48, Asp29', and Gly48' of the enzyme. These results suggest that an automated inhibitor alignment can yield predictive 3D QSAR models that are well comparable to manual methods. Thus, an automated alignment method in creating 3D QSAR models is encouragable when a well-characterized structure of the target protein is available.     

An Optimization-Based Approach to the Multiple Static Delivery Technique in Radiation Therapy

The paper considers the intensity modulated radiation therapy (inverse) treatment planning. An approach to determine the trajectories of the leaves of the multileaf collimator (MLC) in order to produce the prescribed intensity distribution is developed. The paper concentrates on the multiple static delivery technique. A mathematical model for calculating the intensity distribution with the help of locations of the leafheads of subsequent subfields is constructed. Furthermore, an optimization model in which the decision variables are the locations of leafheads is developed. The relevant constraints are considered as well. The optimization problem is a large dimensional constrained nonlinear global extremum problem. It is solved by the LGO (Lipschitz (Continuous) Global Optimizer) program system. Comparisons with other optimization method (Hooke–Jeeves iteration) are included. Numerical experiments are presented to confirm the functionality of the method.     

Modeling incoherent reflections from rough room surfaces with image sources

Reflections at rough surfaces change the temporal structure of the reflected signal. This paper shows how to incorporate this temporal behavior in geometric room acoustics modeling. Specifically, a beam tracer is used for calculating the image sources and reflection paths. The roughness of the surfaces is taken into account in post-processing. A single reflection is assumed to distribute the energy according to an exponential function in time based on Biot's rough surface modeling theory. Multiple reflections are modeled with convolutions of exponential functions which are approximated as gamma functions.