Robust Contour Tracking Model Using a Variational Level-Set Algorithm

In this work, we provide a novel variational level-set based object contour tracking approach. Thus, a mathematically rigorous variant of the Chan-Vese algorithm for image segmentation via geometric active contour model is proposed here. With respect to the original contour detection algorithm, the level set function ?(t) defining the evolving contour S _t  = {x; ?(t, x) = 0} is iteratively computed from a nonlinear parabolic boundary value problem that is well posed in the space of functions with bounded variations. We provide a robust mathematical justification of the proposed level-set model.     

Nonlinear PDE Model for Image Restoration Using Second-Order Hyperbolic Equations

In this article we consider a novel nonlinear PDE-based image denoising technique. The proposed restoration model uses second-order hyperbolic diffusion equations. It represents an improved nonlinear version of a linear hyperbolic PDE model developed recently by the author, providing more effective noise removal results while preserving the edges and other image features. A rigorous mathematical investigation is performed on this new differential model and its well-posedness is treated. Next, a consistent finite-difference numerical approximation scheme is proposed for this nonlinear diffusion-based approach. Our successful image denoising experiments and method comparisons are also described.     

The Generator of the Transition Semigroup Corresponding to a Stochastic Variational Inequality

One proves that the generator of the transition semigroup of a stochastic differential equation with boundary reflection on a convex set K is the realization of a second order elliptic operator on K with zero oblique derivative boundary conditions. Several implications to parabolic problems with oblique derivative are also derived.     

Feedback Stabilization for a Reaction-Diffusion System with Nonlocal Reaction Term

We consider a two-component reaction-diffusion system with a nonlocal reaction term. A necessary condition and a sufficient condition for the internal stabilizability to zero of one of the two components of the solution while preserving the nonnegativity of both components have been established in [6 S. Ani?a , W.-E. Fitzgibbon , and M. Langlais ( 2009 ). Global existence and internal stabilization for a class of predator-prey systems posed on non coincident spatial domains . Discrete Cont. Dynam. Syst. B 11 : 805 – 822 .[Crossref], [Web of Science ®] , [Google Scholar]]. In case of stabilizability, a feedback stabilizing control of harvesting type has been indicated. The rate of stabilization (for the indicated feedback control) is given by the principal eigenvalue of a certain non-selfadjoint operator. A large principal eigenvalue leads to a fast stabilization. The first main goal of this article is to approximate this principal eigenvalue. This is done in two steps. First, we investigate the large-time behavior of the solution to a logistic population dynamics with migration, and next we derive as a consequence a method to approximate the principal eigenvalue. The other main goal is to derive a conceptual iterative algorithm to improve the position of the support of the control in order to get a faster stabilization. Our results apply to prey-predator systems.     

Effect of the amine type on thermal stability of modified mesoporous silica used for CO2 adsorption

In this study, the preparation by grafting of amino-functionalized SBA-15 molecular sieves was carried out. Amino-functionalized molecular sieves were synthesized using a silane coupling agent and different types of amination reagents which react with modified SBA-15. These composites were characterized by FT-IR spectroscopy, X-ray diffraction at low angles, nitrogen physisorption at 77 K, and evaluated by the adsorption of CO₂ and its temperature-programmed desorption—TPD. Thermal stability was investigated by TGA and DTA methods. In the view of a possible use of these amino-functionalized molecular sieves as sorbents for CO₂ removal, their adsorption–desorption properties towards CO₂ were also investigated by the TPD method. The mass loss of amino-functionalized molecular sieves above 215 °C was due to the oxidation and decomposition of amino propyl functional groups. This means that these composites could be used for adsorption of CO₂ at temperatures below 215 °C. The adsorption of CO₂ and its temperature programmed desorption using thermogravimetry were studied for amino-functionalized molecular sieves at 60 °C. The evolved gases during the adsorption–desorption of CO₂ on amino-functionalized molecular sieves were identified by online mass spectrometry coupled with thermogravimetry. CO₂ adsorption isotherms of functionalized samples at 60 °C showed that both the adsorption capacity (mg CO₂/g adsorbent) and the efficiency of amino groups (mol CO₂/mol NH₂) depend on the type of amination reagents and the amount of organic compound used.

     

Periodic solutions to nonlinear one dimensional wave equation with -dependent coefficients

This paper deals with -periodicity and regularity of solutions to the one dimensional nonlinear wave equation with -dependent coefficients

     

Cohomological q-convexity versus local q-completeness with corners

We show that if (D, π) is an unramified Riemann domain over a distinguished complex manifold X such that D is cohomologically q-convex, then π is locally q-complete with corners. We call X distinguished if for every point x of X there is a holomorphic line bundle $\cal L$ on X (which may depend on x) so that the global sections $\Gamma (X \cal L)$ of $\cal L$ generate its 1-jets at x. Examples of distinguished complex manifolds include all complex submanifolds of C^m × Pⁿ; in particular all Stein or projectively algebraic manifolds.     

Tris(triphenylphosphine)rhodium cyano and triphenylcyanoborate complexes: Structures and a DFT study

The structures of [Rh(CN)(PPh₃)₃](EtOH) (1), [Rh(NCBPh₃)(PPh₃)₃] (2), and [Rh(CNBPh₃)(PPh₃)₃] (3) are reported together with a density functional theory (DFT) study of the model compounds [Rh(NCBH₃)(PH₃)₃] and [Rh(CNBH₃)(PH₃)₃]. Compound 1 crystallizes in space group Pc with a = 10.4798(15) Å, b = 12.5410(18) Å, c = 19.974(3) Å and = 112.215(6)°; compound 2 crystallizes in space group with a = 12.929(2) Å, b = 14.362(2) Å, c = 17.575(3) Å and = 92.544(3)°, = 90.214(3)°, = 113.831(3)°; compound 3 crystallizes in space group with a = 12.915(2), b = 14.296(2), c = 17.664(3) Å and = 92.469(3)°, = 90.088(3)°, = 113.768(3)°. All three complexes show slight tetrahedral distortion from ideal square planar geometry (largest for 1). Differences in the reactivity and stability of 2 and 3 are interpreted according to the results of a density functional theory study.     

High-pressure vapor–liquid and vapor–liquid–liquid equilibria in the carbon dioxide + 1-heptanol system

Vapor–liquid equilibria (VLE) and vapor–liquid–liquid equilibria (VLLE) data for the carbon dioxide + 1-heptanol system were measured at 293.15, 303.15, 313.15, 333.15 and 353.15 K. Phase behavior measurements were made in a high-pressure visual cell with variable volume, based on the static-analytic method. The pressure range under investigation was between 0.58 and 14.02 MPa. The Soave–Redlich–Kwong (SRK)-EOS coupled with Huron–Vidal (HV) mixing rules and a reduced UNIQUAC model, was used in a semi-predictive approach, in order to represent the complex phase behavior (critical curve, LLV line, isothermal VLE, LLE, and VLLE) of the system. The topology of phase behavior is qualitatively correct predicted.     

1-Adamantanethiolate monolayer displacement kinetics follow a universal form

Alkanethiol molecules in solution displace 1-adamantanethiolate self-assembled monolayers on Au{111}, ultimately leading to complete molecular exchange. Specifically, here, fast insertion of n-dodecanethiolate at defects in the original 1-adamantanethiolate monolayer nucleates an island growth phase, which is followed by slow ordering of the n-dodecanethiolate domains into a denser and more crystalline form. Langmuir-based kinetics, which describe alkanethiolate adsorption on bare Au{111}, fail to model this displacement reaction. Instead, a Johnson-Mehl-Avrami-Kolmogorov model of perimeter-dependent island growth yields good agreement with kinetic data obtained by Fourier transform infrared spectrometry over 100-fold variation in n-dodecanethiol concentration. Rescaling the growth rate at each concentration collapses all the data onto a single universal curve, suggesting that displacement is a scale-free process. The rate of displacement varies as the square-root of the n-dodecanethiol concentration across the 0.01-1.0 mM range studied.