We investigate the large-time behavior of the value functions of the optimal control problems on the n-dimensional torus which appear in the dynamic programming for the system whose states are governed by random changes. From the point of view of the study on partial differential equations, it is equivalent to consider viscosity solutions of quasi-monotone weakly coupled systems of Hamilton–Jacobi equations. The large-time behavior of viscosity solutions of this problem has been recently studied by the authors and Camilli, Ley, Loreti, and Nguyen for some special cases, independently, but the general cases remain widely open. We establish a convergence result to asymptotic solutions as time goes to infinity under rather general assumptions by using dynamical properties of value functions. 相似文献
In an attempt to examine the random version of the spectral theorem, the notion of random spectral measures and generalized random spectral measures are introduced and investigated. It is shown that each generalized random spectral measure on $(\mathbb C ,\mathcal{B}(\mathbb C ))$ admits a modification which is a random spectral measure. 相似文献
In this paper, we introduce and study some low computational cost numerical methods for finding a solution of a variational inequality problem over the solution set of an equilibrium problem in a real Hilbert space. The strong convergence of the iterative sequences generated by the proposed algorithms is obtained by combining viscosity-type approximations with projected subgradient techniques. First a general scheme is proposed, and afterwards two practical realizations of it are studied depending on the characteristics of the feasible set. When this set is described by convex inequalities, the projections onto the feasible set are replaced by projections onto half-spaces with the consequence that most iterates are outside the feasible domain. On the other hand, when the projections onto the feasible set can be easily computed, the method generates feasible points and can be considered as a generalization of Maingé’s method to equilibrium problem constraints. In both cases, the strong convergence of the sequences generated by the proposed algorithms is proven. 相似文献
In this paper, we establish some quotient calculus rules in terms of contingent derivatives for the two extended-real-valued functions defined on a Banach space and study a nonsmooth multiobjective fractional programming problem with set, generalized inequality and equality constraints. We define a new parametric problem associated with these problem and introduce some concepts for the (local) weak minimizers to such problems. Some primal and dual necessary optimality conditions in terms of contingent derivatives for the local weak minimizers are provided. Under suitable assumptions, sufficient optimality conditions for the local weak minimizers which are very close to necessary optimality conditions are obtained. An application of the result for establishing three parametric, Mond–Weir and Wolfe dual problems and several various duality theorems for the same is presented. Some examples are also given for our findings.
In most diseases, the clinical need for serum/plasma markers has never been so crucial, not only for diagnosis, but also for the selection of the most efficient therapies, as well as exclusion of ineffective or toxic treatment. Due to the high sample complexity, prefractionation is essential for exploring the deep proteome and finding specific markers.In this study, three different sample preparation methods (i.e., highly abundant protein precipitation, restricted access materials (RAM) combined with IMAC chromatography and peptide ligand affinity beads) were investigated in order to select the best fractionation step for further differential proteomic experiments focusing on the LMW proteome (MW inferior to 40,000 Da). Indeed, the aim was not to cover the entire plasma/serum proteome, but to enrich potentially interesting tissue leakage proteins. These three methods were evaluated on their reproducibility, on the SELDI-TOF-MS peptide/protein peaks generated after fractionation and on the information supplied.The studied methods appeared to give complementary information and presented good reproducibility (below 20%). Peptide ligand affinity beads were found to provide efficient depletion of HMW proteins and peak enrichment in protein/peptide profiles. 相似文献
An alternative approach for fabricating a protein array at nanoscale is suggested with a capability of characterization and/or
localization of multiple components on a nanoarray. Fluorescent micro- and nanobeads each conjugated with different antibodies
are assembled by size-dependent self-assembly (SDSA) onto nanometer wells that were created on a polymethyl methacrylate (PMMA)
substrate by electron beam lithography (EBL). Antibody-conjugated beads of different diameters are added serially and electrostatically
attached to corresponding wells through electrostatic attraction between the charged beads (confirmed by zeta potential analysis)
and exposed p-doped silicon substrate underneath the PMMA layer. This SDSA method is enhanced by vibrated-wire-guide manipulation
of droplets on the PMMA surface containing nanometer wells. Saturation rates of antibody-conjugated beads to the nanometer
patterns are up to 97% under one component and 58–70% under two components nanoarrays. High-density arrays (up to 40,000 wells)
could be fabricated, which can also be multi-component. Target detection utilizes fluorescence resonance energy transfer (FRET)
from fluorescent beads to fluorescent-tagged secondary antibodies to Octamer-4 (Oct4), which eliminates the need for multiple
steps of rinsing. The 100 nm green beads are covalently conjugated with anti-Oct4 to capture Oct4 peptides (39 kDa); where
the secondary anti-Oct4 and F(ab)2 fragment of anti-gIgG tagged with phycoerythrin are then added to function as an indicator of Oct4 detection. FRET signals
are detected through confocal microscopes, and further confirmed by Fluorolog3 spectrofluorometer. The success rates of detecting
Oct4 are 32% and 14% of the beads in right place under one and two component nanoarrays, respectively. Ratiometric FRET is
used to quantify the amount of Oct4 peptides per each bead, which is estimated about 2 molecules per bead. 相似文献