Carleson embeddings for Sobolev spaces via heat equation

Let u(t,x) be the solution of the heat equation (∂_t-Δ_x)u(t,x)=0 on subject to u(0,x)=f(x) on Rⁿ. The main goal of this paper is to characterize such a nonnegative measure μ on that f(x)?u(t²,x) induces a bounded embedding from the Sobolev space , p∈[1,n) into the Lebesgue space , q∈(0,∞).     

Levitin-Polyak well-posedness of variational inequalities

In this paper we consider the Levitin-Polyak well-posedness of variational inequalities. We derive a characterization of the Levitin-Polyak well-posedness by considering the size of Levitin-Polyak approximating solution sets of variational inequalities. We also show that the Levitin-Polyak well-posedness of variational inequalities is closely related to the Levitin-Polyak well-posedness of minimization problems and fixed point problems. Finally, we prove that under suitable conditions, the Levitin-Polyak well-posedness of a variational inequality is equivalent to the uniqueness and existence of its solution.     

Well-posed equilibrium problems

In this paper we introduce some notions of well-posedness for scalar equilibrium problems in complete metric spaces or in Banach spaces. As equilibrium problem is a common extension of optimization, saddle point and variational inequality problems, our definitions originates from the well-posedness concepts already introduced for these problems.We give sufficient conditions for two different kinds of well-posedness and show by means of counterexamples that these have no relationship in the general case. However, together with some additional assumptions, we show via Ekeland’s principle for bifunctions a link between them.Finally we discuss a parametric form of the equilibrium problem and introduce a well-posedness concept for it, which unifies the two different notions of well-posedness introduced in the first part.     

Dirichlet principle using computers

In this article we shall give practical and numerical solutions of the Laplace equation on multidimensional spaces and show the numerical experiments by using computers. Our method is based on the Dirichlet principle by combinations with generalized inverses, Tikhonov's regularization and the theory of reproducing kernels.     

Gallai–Edmonds structure theorem for weighted matching polynomial

In this paper, we prove the Gallai–Edmonds structure theorem for weighted matching polynomials. Our result implies the Parter–Wiener theorem and its recent generalization about the existence of principal submatrices of a Hermitian matrix whose graph is a tree.     

Prime ends for domains in metric spaces

In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Carathéodory and Näkki. Modulus ends and prime ends, defined by means of the p$p$-modulus of curve families, are also discussed and related to the prime ends. We provide characterizations of singleton prime ends and relate them to the notion of accessibility of boundary points, and introduce a topology on the prime end boundary. We also study relations between the prime end boundary and the Mazurkiewicz boundary. Generalizing the notion of John domains, we introduce almost John domains, and we investigate prime ends in the settings of John domains, almost John domains and domains which are finitely connected at the boundary.     

Effect of an aliphatic spacer group on the adsorption mechanism on the colloidal silver surface of L‐proline phosphonodipeptides

A comparative study of molecular structures of five L ‐proline (L ‐Pro) phosphonodipeptides: L ‐Pro‐NH‐C(Me,Me)‐PO₃H₂ (P1), L ‐Pro‐NH‐C(Me,iPr)‐PO₃H₂ (P2), L ‐Pro‐L ‐NH‐CH(iBu)‐PO₃H₂ (P3), L ‐Pro‐L ‐NH‐CH(PA)‐PO₃H₂ (P4) and L ‐Pro‐L ‐NH‐CH(BA)‐PO₃H₂ (P5) has been carried out using Raman and absorption infrared techniques of molecular spectroscopy. The interpretation of the obtained spectra has been supported by density functional theory calculations (DFT) at the B3LYP; 6–31 + + G** level using Gaussian 2003 software. The surface‐enhanced Raman scattering (SERS) on Ag‐sol in aqueous solutions of these phosphonopeptides has also been investigated. The surface geometry of these molecules on a silver colloidal surface has been determined by observing the position and relative intensity changes of the Pro ring, amide, phosphonate and so‐called spacer (−R) groups vibrations of the enhanced bands in their SERS spectra. Results show that P4 and P5 adsorb onto the silver as anionic molecules mainly via the amide bond (∼1630, ∼1533, ∼1248, ∼800 and ∼565 cm⁻¹), Pro ring (∼956, ∼907 and ∼876 cm⁻¹) and carboxylate group (∼1395 and ∼909 cm⁻¹). Coadsorption of the imine nitrogen atom and PO group with the silver surface, possibly by formation of a weaker interaction with the metal, is also suggested by the enhancement of the bands at 1158 and 1248 cm⁻¹. P1, P2 and P3 show two orientations of their main chain on the silver surface resulting from different interactions of the  C CH₃,  NH and  CONH fragments with this surface. Bonding to the Ag surface occurs mainly through the imino atom (1166 cm⁻¹) for P2, while for P1 and P3 it occurs via the methyl group(s) (1194–1208 cm⁻¹). The amide group functionality (CONH) is practically not involved in the adsorption process for P1 and P2, whereas the C_s P bonds do assist in the adsorption. Copyright © 2008 John Wiley & Sons, Ltd.     

Theoretical Studies on the Fe-M Interactions and 31P NMR in Fe(CO)3(EtPhPpy)2MX2 (X=NCS, SCN, Cl; M=Zn, Cd, Hg)

采用密度泛函理论PBE0方法,计算了单核配合物[Fe(CO)3(EtPhPpy)2] (1)、双核配合物[Fe(CO)3(EtPhPpy)2M(NCS)2] (2:M=Zn,3: M=Cd,4: M=Hg) 和[Fe(CO)3(EtPhPpy)2CdX2] (5:X=Cl,6: X=SCN)的几何构型和电子结构,研究了Fe-M相互作用及其对31P化学位移的影响. 结果表明：配合物的稳定性(S)为S(2)>S(3)>S(4),S(3)≈S(6)>S(5).在[Fe(CO)3(EtPhPpy)2CdX2]体系中,含[SCN]-配合物的稳定性大于含Cl-的. Fe-M相互作用的强度(I )顺序为I (2)≈I (3)31P化学位移比单核配合物的小.     

Synthesis of 29H,31H-phthalocyanine and chloro (29H,31H-phthalocyaninato) aluminum derivatives showed anti-cancer and anti-bacterial actions

Continuous administration of most chemotherapeutic drugs can induce different types of side effects. There has been growing interest in exploring an alternative approach to synthesizing compounds that are most effective and have fewer side effects. We synthesized 29H,31H-Phthalocyanine, and Chloro (29H,31H- phthalocyaninato) aluminum at low temperatures using lithium in the present study with diisopropylamide as the nucleophile. The physical characteristics of 29H,31H-Phthalocyanine, and Chloro (29H,31H- phthalocyaninato) aluminum were confirmed by FT-IR method, XRD, SEM, and the impact of these compounds on human colorectal carcinoma (HCT-116) and human cervical cells (HeLa) was examined. Treatment with 29H,31H-Phthalocyanine significantly decreased cancer cell growth and proliferation, as determined by MTT and DAPI staining analysis. In contrast, Chloro (29H,31H- phthalocyaninato) aluminum treatment did not show any inhibitory action on colon or cervical cancer cells. We also calculated the inhibitory concentration (IC50) of 29H,31H-Phthalocyanine, which was 30 µg/ml (HCT-116) and 33 µg/ml (HeLa cells). The antibacterial effectiveness of 29H,31H-Phthalocyanine, and chloro (29H,31H- phthalocyaninato) aluminum was studied using Enterococcus faecalis (E. faecalis). The CFU (colony frequency unit) assay confirmed significant activity against the test bacterium after treatment with 29H,31H-Phthalocyanine. However, no activity was seen upon treatment with chloro (29H,31H- phthalocyaninato) aluminum against E. faecalis.