Substitution of [Pt(terpy)H2O]2+ and [Pt(bpma)H2O]2+ with thiols in acidic aqueous solution. terpy = 2,2′:6′2″-terpyridine; bpma = bis(2-pyridylmethyl)amine

The substitution behaviour of [Pt(terpy)H₂O]²⁺ and [Pt(bpma)H₂O]²⁺, where terpy is 2,2:62-terpyridine and bpma is bis(2-pyridylmethyl)amine, was studied as a function of entering thiol concentration and temperature. The reactions between the Pt-complexes and DL-penicillamine, L-cysteine and glutathione were carried out in a 0.10 mol dm^–3 aqueous HClO₄ medium using stopped-flow and conventional u.v.–vis spectrophotometry. The observed pseudo-first-order rate constants for the substitutions are given by k _obs = k ₂[thiol] + k _–2. The k _–2 term represents the reverse solvolysis. This was found to be zero for Pt^II(terpy) which was the most reactive complex. The second-order rate constants, k ₂, for the three thiols varied between 0.107 ± 0.001 and 0.517 ± 0.025 M^–1 s^–1 for Pt^II(bpma) and 10.7 ± 0.7–711.9 ± 18.3 M^–1 S^–1 for Pt^II(terpy), whereas glutathione was found to be the strongest nucleophile. An analysis of the activation parameters, H and S , clearly shows that the substitution process is associative in nature.     

Kinetic and mechanistic study on the reactions of [Pt(bpma)(H2O)]2+ and [Pd(bpma)(H2O)]2+ with some nucleophiles. Crystal structure of [Pd(bpma)(py)](ClO4)2

Substitution reactions of the complexes [Pd(bpma)(H2O)]2+ and [Pt(bpma)(H2O)]2+, where bpma = bis(2-pyridylmethyl)amine, with TU, DMTU and TMTU for both complexes and Cl-, Br-, I- and SCN- for the platinum complex, were studied in aqueous 0.10 M NaClO4 at pH 2.5 using a variable-temperature stopped-flow spectrophotometer. The pKa value for the coordinated water molecule in [Pd(bpma)(H2O)]2+ (6.67) is a unit higher than that of [Pt(bpma)(H2O)]2+. The observed pseudo-first-order rate constants k(obs) (s(-1)) obeyed the equation k(obs) = k2[Nu] (Nu = nucleophile). The second-order rate constants indicate that the Pd(II) complex is a factor of 10(3) more reactive than Pt(II) complex. The nucleophile reactivity attributed to the steric hindrance in case of TMTU and the inductive effect for DMTU was found to be DMTU > TU > TMTU for [Pt(bpma)(H2O)]2+ and DMTU approximately TU > TMTU for [Pd(bpma)(H2O)]2+. The trend for ionic nucleophile was I- > SCN- > Br- > Cl-, an order linked to their polarizability and the softness or hardness of the metal. Activation parameters were determined for all reactions and the negative entropies of activation (Delta S++) support an associative ligand substitution mechanism. The X-ray crystal structure of [Pd(bpma)(py)](ClO4)2 was determined; it belongs to the triclinic space group P1 and has one formula unit in the unit cell. The unit cell dimensions are a = 8.522(2), b = 8.627(2), c = 16.730(4) A; alpha = 89.20(2), beta = 81.03(2), gamma = 60.61(2) degrees ; V = 1055.7(5) A3. The structure was solved using direct methods in WinGX's implementation of SHELXS-97 and refined to R = 0.054. The coordination geometry of [Pd(bpma)(py)]2+ is distorted square-planar. The Pd-N(central) bond distance, 1.996(3) A, is shorter than the other two Pd-N distances, 2.017(3) and 2.019(3) A. The Pd-N(pyridine) distance is 2.037(3) A.     

Judiciously 3‐partitioning 3‐uniform hypergraphs

Bollobás, Reed, and Thomason proved every 3‐uniform hypergraph ? with m edges has a vertex‐partition V()=V₁?V₂?V₃ such that each part meets at least edges, later improved to 0.6m by Halsegrave and improved asymptotically to 0.65m+o(m) by Ma and Yu. We improve this asymptotic bound to , which is best possible up to the error term, resolving a special case of a conjecture of Bollobás and Scott.     

Existence of a Steady Flow of Stokes Fluid Past a Linear Elastic Structure Using Fictitious Domain

We use fictitious domain method with penalization for the Stokes equation in order to obtain approximate solutions in a fixed larger domain including the domain occupied by the structure. The coefficients of the fluid problem, excepting the penalizing term, are independent of the deformation of the structure. It is easy to check the inf-sup condition and the coercivity of the Stokes problem in the fixed domain. Subtracting the structure equations from the fictitious fluid equations in the structure domain, we obtain a weak formulation in a fixed domain, where the continuity of the stress at the interface does not appear explicitly. Existence of a solution is proved when the structure displacement is generated by a finite number of modes.     

A Property of Sobolev Spaces and Existence in Optimal Design

Abstract. We prove that for bounded open sets Ω with continuous boundary, Sobolev spaces of type W ₀ ^l,p (Ω ) are characterized by the zero extension outside of Ω . Combining this with a compactness result for domains of class C, we obtain a general existence theorem for shape optimization problems governed by nonlinear nonhomogenous Dirichlet boundary value problems of arbitrary order, in arbitrary dimension and with general cost functionals.     

The second main theorem of hypersurfaces in the projective space

We deal with a holomorphic map from the complex plane ${\mathbb{C}}$ to the n-dimensional complex projective space ${\mathbb{P}^{n}(\mathbb{C})}$ and prove the Nevanlinna Second Main Theorem for some families of non-linear hypersurfaces in ${\mathbb{P}^{n}(\mathbb{C})}$ . This Second Main Theorem implies the defect relation. If the degree of the hypersurfaces are sufficiently large, the defect of the map is smaller than one. This means that holomorphic maps which omit the irreducible hypersurface of large degree is algebraically degenerate. To prove the Second Main Theorem, we use a meromorphic partial projective connection which is totally geodesic with respect to these hypersurfaces. A meromorphic partial projective connection is a family of locally defined meromorphic connections such which work as an entirely defined meromorphic connection under the Wronskian operator. By resolving the singularity and pulling back a meromorphic partial projective connection, we also prove the Second Main Theorem for singular hypersurfaces in ${\mathbb{P}^{n}(\mathbb{C})}$ , and prove the Second Main Theorem for smooth hypersurfaces in ${\mathbb{P}^{2}(\mathbb{C})}$ which are not normal crossing.     

A Property of Sobolev Spaces and Existence in Optimal Design

   Abstract. We prove that for bounded open sets Ω with continuous boundary, Sobolev spaces of type W ₀ ^l,p (Ω ) are characterized by the zero extension outside of Ω . Combining this with a compactness result for domains of class C, we obtain a general existence theorem for shape optimization problems governed by nonlinear nonhomogenous Dirichlet boundary value problems of arbitrary order, in arbitrary dimension and with general cost functionals.