Second-Order Necessary Optimality Conditions for Some State-Constrained Control Problems of Semilinear Elliptic Equations

In this paper we are concerned with some optimal control problems governed by semilinear elliptic equations. The case of a boundary control is studied. We consider pointwise constraints on the control and a finite number of equality and inequality constraints on the state. The goal is to derive first- and second-order optimality conditions satisfied by locally optimal solutions of the problem. Accepted 6 May 1997     

On K‐Theory of Simplicial Rings and Degreewise Constructions

We give a measure of the difference between Waldhausen's definition of the Ktheory of a simplicial ring and the definition we obtain by extending Quillen's definition degreewise. This has computational advantages as the degreewise Ktheory sometimes is simpler to work with.     

A finite element model of localized deformation in frictional materials taking a strong discontinuity approach

A finite element model of localized deformation in frictional materials taking a strong discontinuity approach is presented. A rate-independent, non-associated, strain-softening Drucker–Prager plasticity model is formulated in the context of strong discontinuities and implemented along with an enhanced quadrilateral element within the framework of an assumed enhanced strain finite element method. For simple model problems such as uniform compression, the strong discontinuity approach has been shown to lead to mesh-independent finite element solutions when localized deformation is present. In this paper, a finite element analysis of localized deformation occurring in a more complex model problem of slope stability is conducted in a nearly mesh-independent manner. The effect of dilatancy on the orientation of slip lines is demonstrated for the slope stability problem.     

Formal Power Series and Some Theorems of J. F. Rittin Arbitrary Characteristic

 We study composition of power series and polynomials over algebraically closed fields of arbitrary characteristic. The so-called Boettcher function of a power series is introduced and investigated. It is the principal aim of this paper to prove some results going back to J. F. Ritt in this general setting. In particular, we determine the pairs of permutable polynomials and characterize polynomials which satisfy a certain rational functional equation and polynomials which have a common iterate. Received 12 February 1998; in revised form 20 April 1998     

Construction of universal modal worlds based on hyperset theory

Knowledge modal formulas are interpreted by a universal modal world in the hypersets universe [A]. This remedies the limitation of the interpretation of knowledge formulas by a tower of modal worlds in the well founded universe [F], where each world can interpret only a portion of knowledge modal formulas. Received: 21 August 1995     

A controlled boundary theorem for Hilbert cube manifolds

In this paper a boundary theorem for Hilbert cube manifolds is established,where it is required that the boundary be put on the manifold with arbitrarily small control in a given compact metric parameter space.     

L-spaces and S-spaces in P(ω)

We show that CH implies that $\text{P}\text{(ω)}$, when equipped with the Vietoris topology, has a subspace which is an L-space and a subspace which is an S-space. This is an immediate consequence of the following purely combinatorial result: CH implies the existence of an ω₁-sequence 〈x_α: α < ω₁〉 in $\text{P}\text{(ω)}$ such that (1) if α<β<ω₁, then $\text{X}{}_{\mathrm{\beta }}\text{?}{}^1\text{X}{}_{\mathrm{\alpha }}$; (2) if I ?ω₁ is unaccountable, then there are distinct α, β ∈ I with X_β ?X_α.     

Explicit constructions of graphs without short cycles and low density codes

We give an explicit construction of regular graphs of degree 2r withn vertices and girth ≧c logn/logr. We use Cayley graphs of factor groups of free subgroups of the modular group. An application to low density codes is given.     

Tumor‐Targeting W18O49 Nanoparticles for Dual‐Modality Imaging and Guided Heat‐Shock‐Response‐Inhibited Photothermal Therapy in Gastric Cancer

Photothermal therapy (PTT) is an emerging noninvasive and precise localized therapeutic modality; however, it is deeply limited by its poor tumor accumulation, inadequate photothermal conversion efficiency, and the thermoresistance of cancer cells. Aimed at these shortcomings, tumor‐targeting nanoparticles (iRGD‐W₁₈O₄₉‐17AAG) comprising carboxyl‐group‐functionalized W₁₈O₄₉ nanoparticles, integrin‐targeting peptide iRGD, and HSP90‐inhibitor 17AAG are developed. The W₁₈O₄₉ nanoparticles act as excellent PTT carriers and computed tomography (CT) imaging contrast agents. The ring type polypeptide iRGD promotes the accumulation of nanoparticles in the tumour and further penetration into cancer cells. The introduction of 17AAG can inhibit the heat‐shock response and overcome the thermoresistance, thus increasing the curative effect of PTT and reducing the chance of tumor recurrence. The W₁₈O₄₉ nanoparticles can also be used to monitor and guide the phototherapeutic through CT and near‐infrared fluorescence imaging after modification with Cy5.5. In addition, superior biosafety is also indicated in both preliminary in vitro and in vivo assessments. The potential of iRGD‐W₁₈O₄₉‐17AAG in tumor targeting, dual modality imaging‐guided and remarkable enhanced PTT of gastric cancer with ignorable side effect both in vitro and in vivo, which may be further applied in clinic, is highlighted.