On Duality Theorems for Nonsmooth Lipschitz Optimization Problems

A nonsmooth Lipschitz vector optimization problem (VP) is considered. Using the Fritz John type necessary optimality conditions for (VP), we formulate the Mond–Weir dual problem (VD) and establish duality theorems for (VP) and (VD) under (strict) pseudoinvexity assumptions on the functions. Our duality theorems do not require a constraint qualification.     

Alternative Second-Order Conditions in Constrained Optimization

New formulations are given for the second-order necessary conditions in parameter optimization with equality constraints. The new conditions are shown to be equivalent to previously known conditions by using the properties of projection matrices. The various conditions require different computational tools. As one of the obtained conditions requires standard computational tools (i.e., matrix inversion and eigenvalue computation), it might be useful in applications (e.g., real-time optimization schemes), when these standard tools are already in use.     

Microwave-assisted Cannizzaro reaction—Optimisation of reaction conditions

The microwave-assisted Cannizzaro reaction was studied in order to develop fully reproducible synthetic protocols for transformation of aldehydes to carboxylic acid and alcohols. Optimised were the following process parameters: power, temperature, and time. Aromatic, heteroaromatic and aliphatic aldehydes were used in the studies. It was found that furfural, thiophene-2-carbaldehyde, pyridinecarboxaldehyde and aromatic aldehydes react under mild conditions, while 1-methyl-pyrrole-2-carboxaldehyde derivatives and aliphatic aldehydes require more drastic reaction conditions and a longer exposure time to microwave radiation.     

An Improved Synthesis of α,β Methylenic Cyclic Ketones

This communication describes a convenient two steps procedure for the preparation of α,β methylenic cyclic ketones from arylmethyl ketones involving a preformed Mannich reagent.     

Dependence of the Constant of the Mark‐Houwink Equation under Theta Conditions on the Bulk of Substituents for Hydrocarbon Polymers

The logarithm of the constant K _θ in the Mark‐Houwink equation under theta conditions was found to be proportional to the molar volume of the substituent groups in the case of vinyl‐ and vinylidene‐type hydrocarbon polymers. This simple empirical relation can be used to estimate K _θ for such polymers.     

Nano Fe3O4 as magnetically recyclable catalyst for the synthesis of α-aminophosphonates in solvent-free conditions

The three component, one-pot synthesis of α-aminophosphonates has been achieved using super magnetic nano iron oxide at 50 °C under solvent-free conditions in excellent yields. The major advantages of the present method are high yields, short reaction times, magnetically recyclable catalyst, and solvent-free reaction conditions.     

Thec logc contribution to the electrolyte conductance and Onsager's reciprocal relation

The differential equations and the boundary conditions for the nonequilibrium binary distribution function of an unsymmetrical binary electrolyte are derived from the Ebeling-Falkenhagen continuity equation. The connection between the Onsager reciprocal relation and the binary distribution functions is shown. Further, Feistel's result for thec logc contribution to the conductance is extended to unsymmetrical binary electrolytes. The reason for the difference between Feistel's and Chen'sc logc term is explained, and the significance of Onsager's reciprocal relation for the calculation ofc logc and higher-concentration contributions of the conductance is discussed.     

Sample capacity in open tubular and micro-packed columns for GC

Equations have been derived from which the maximum sample size which may be loaded on a column without significantly affecting the performance may be calculated. It is shown that micro-packed columns can handle a sample which is as much as forty times larger than that which can be loaded onto wall-coated open tubular columns with comparable conditions.     

Numerical study of a well boat operating at a fish farm in current

Dynamic response of a well boat operating at a fish farm in current is investigated numerically. An objective is to determine the operational conditions of the well boat. In terms of the fish farm, a realistic set-up (with single cage) is considered, including a floating collar, an elastic sinker tube, a flexible-closed net cage and a complex mooring system. A time-domain solution is used to find the steady configuration and response. Transverse viscous current loads are estimated using the cross-flow principle. The drag coefficients are obtained empirically by considering cross-sectional details, free surface and three-dimensional (3D) flow effects. The drag force is experimentally validated. The effect of the ship wake on the net loading is also assessed.The most critical scenario with the well boat placed at the weather side of the fish farm is analyzed in detail. Critical response variables for operational limits are the maximum anchor-line tensions and floater stresses. Numerical results show that the anchor loads will increase more than 40% in small current velocities and up to 90% in high current velocities due to the viscous current loads on the boat. There is also a strong increase of the floating collar deformations and stresses when the well boat is in contact with the floating collar.A sensitivity analysis has been carried out to identify the physical parameters affecting the anchor loads and the maximum stress in the floating collar. From our studies, the anchor loads are more sensitive to current direction, bottom weight system, sinker tube depth and mooring line properties (pretension load, anchor chain weight, etc.) and less sensitive to other parameters such as floating collar stiffness and cross-sectional drag coefficients of the well boat. The shading effect of the well boat on the fish-farm inflow has been examined and appeared not negligible with 4% to 10% reduction of the anchor loads for the studied current conditions. The maximum stress in the floating collar is sensitive to well-boat loads related parameters (current direction, cross-sectional drag coefficient) and pretension load in the anchor line; not so sensitive to net loading related parameters such as sinker tube depth and sinker tube weight.Lastly, the operational conditions of the well boat at the fish farm were discussed. Numerical results show that the maximum stresses in the floating collar should be of major concern. The loads in the mooring lines are moderate compared with the corresponding breaking limits.