Flow by mean curvature inside a moving ambient space

We show some computations related to the motion by mean curvature flow of a submanifold inside an ambient Riemannian manifold evolving by Ricci or backward Ricci flow. Special emphasis is given to the possible generalization of Huisken’s monotonicity formula and its connection with the validity of some Li–Yau–Hamilton differential Harnack-type inequalities in a moving Riemannian manifold.     

The impact of two-product joint lifecycles on capacity planning of remanufacturing networks

Capacity planning in the reverse channel of closed-loop supply chains (CLSCs) involves complex issues due to the different lifecycles of product offerings in combination with the variability regarding product usage time, quality level of used products and return patterns. (Georgiadis, P., Vlachos, D., Tagaras, G., 2006. The impact of product lifecycle on capacity planning of closed-loop supply chains with remanufacturing. Production and Operations Management 15; 514–527) developed a system dynamics (SD) model to study a CLSC with remanufacturing for a single product which incorporates a dynamic capacity modeling approach. We extend this SD model for two sequential product-types under two alternative scenarios regarding the market preferences over the product-types; in the first scenario, the market is considered showing no preferences, while in the second scenario, the demand over a product-type can be satisfied only by providing units of the specific type. We study how the joint lifecycles of two product-types, entry time of the second product-type to the market and used product return patterns affect the optimal policies regarding expansion and contraction of collection and remanufacturing capacities. The results of extensive numerical investigation are tested for their statistical significance using analysis of variance (ANOVA). In the first scenario, the results show that the system performs best when the two lifecycles form a trapezoid pattern for total demand while in the second scenario, when the two lifecycles form a triangular pattern.     

A Reduced Space Branch and Bound Algorithm for Global optimization

A general class of branch and bound algorithms forsolving a wide class of nonlinear programs with branching only in asubset of the problem variables is presented. By reducing the dimension of thesearch space, this technique may dramatically reduce the number ofiterations and time required for convergence to tolerancewhile retaining proven exact convergence in the infinite limit. Thispresentation includes specifications of the class of nonlinearprograms, a statement of a class of branch and bound algorithms, aconvergence proof, and motivating examples with results.     

Brillouin spectra of mixed alkali glasses: xCs2O(1−x)Na2O5SiO2

The Brillouin spectra of a series of mixed alkali glasses, of the composition _xCs₂O(1?x)Na₂O5SiO₂, have been measured and analyzed. Significant nonlinearities are found for the variation of the isothermal compressibility [K_T,0(T_f)] and Landau-Placzeck ratio, with a minimum observed in each as a function of x, while the longitudinal and transverse sound velocities and related elastic constants, C₁₁, C₄₄ and Young's modulus, E, vary monotonically (nearly linearly) with x. The results are interpreted in connection with related ultrasonic data and the effect of varying composition on the mechanical properties of mixed alkali glasses.     

Synthesis and characterization of novel oxotechnetium (99Tc and 99mTc) and oxorhenium complexes from the 2,2'-bipyridine (NN)/thiol (S) mixed-ligand system

The synthesis and characterization of oxotechnetium and oxorhenium mixed-ligand complexes of the general formula MO[NN][S](3) (M = (99)Tc and Re), where NN represents the bidentate ligand 2,2'-bipyridine and S represents a monodentate thiophenol, is reported. The complexes were prepared by ligand exchange reactions using (99)Tc-gluconate and ReOCl(3)(PPh(3))(2) as precursors for the oxotechnetium and oxorhenium complexes, respectively. Compound 1 (M = (99)Tc, S = 4-methylthiophenol) crystallizes in the monoclinic space group P2(1)/a, a = 23.12(1) A, b = 14.349(6) A, c = 8.801(4) A, beta = 94.81(2) degrees, V = 2918(2) A(3), Z = 4. Compound 3 (M = Re, S = 4-methylthiophenol) crystallizes in the monoclinic space group P2(1)/a, a = 23.018(9) A, b = 14.421(5) A, c = 8.775(3) A, beta = 94.78(1) degrees, V = 2903(2) A(3), Z = 4. Compound 4 (M = Re, S = 4-methoxythiophenol) crystallizes in the orthorhombic space group Pbca, a = 16.32(1) A, b = 24.55(2) A, c = 16.94(1) A, V = 6788(9) A(3), Z = 8. In all cases, the coordination geometry around the metal is distorted octahedral with the equatorial plane being defined by the three sulfur atoms of the thiophenols and one nitrogen atom of 2,2'-bipyridine, while the apical positions are occupied by the second nitrogen atom of 2,2'-bipyridine and the oxygen of the M=O core. The complexes are stable, neutral, and lipophilic. Complete (1)H and (13)C NMR assignments are reported for all complexes. The analogous oxotechnetium complexes have been also synthesized at tracer level ((99m)Tc) by mixing the 2,2'-bipyridine and the corresponding thiol with Na(99m)TcO(4) generator eluate using NaBH(4) as reducing agent. Their structure was established by chromatographic comparison with authentic oxotechnetium and oxorhenium complexes using high performance liquid chromatography techniques.     

A new scalable synthesis of entecavir

A new synthesis of entecavir from d-glucose in an average total yield of 3.5% was achieved via an intramolecular nitrile oxide cycloaddition (INOC) reaction and a Peterson olefination as key-steps. The present process was designed for industrial application, using widely available raw materials, simple and cheap reagents and avoiding low reaction temperatures, which are very common in the synthetic approaches towards similarly complex structures.     

Is the nature of magnetic order in copper-oxides and in iron-pnictides different?

We use the results of first-principles electronic structure calculations and a strong coupling perturbation approach, together with general theoretical arguments, to illustrate the differences in super-exchange interactions between the copper-oxides and iron-pnictides. We provide a possible explanation for the two magnetic ground states within the same theoretical foundation. Contrary to the emerging view that magnetic order in the iron-pnictides is of itinerant nature, we argue that the observed magnetic moment is small because of frustration introduced by the electrons of the Fe orbitals as they compete to impose their preferred magnetic ordering.     

Parametric global optimisation for bilevel programming

We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower’s) problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables of the outer (leader’s) problem. By inserting the obtained rational reaction sets in the upper level problem the overall problem is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global optimisation strategy.     

On the global solution of multi-parametric mixed integer linear programming problems

This paper deals with the global solution of the general multi-parametric mixed integer linear programming problem with uncertainty in the entries of the constraint matrix, the right-hand side vector, and in the coefficients of the objective function. To derive the piecewise affine globally optimal solution, the steps of a multi-parametric branch-and-bound procedure are outlined, where McCormick-type relaxations of bilinear terms are employed to construct suitable multi-parametric under- and overestimating problems. The alternative of embedding novel piecewise affine relaxations of bilinear terms in the proposed algorithmic procedure is also discussed.