Zero weights and non-zero slacks:different solution to the same problem

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Rough-terrain groundspeed measurement:a radar-based commercial solution

Off-highway motive plant equipment is costly in capital outlay and maintenance. To reduce these overheads and increase site safety and workrate, a technique of assessing and limiting the velocity of such equipment is required. Due to the extreme environmental conditions met on such sites, conventional velocity measurement techniques are inappropriate. Ogden Electronics Limited were formed specifically to manufacture a motive plant safety system incorporating a speed sensor and sanction unit; to date, the only such commercial unit available. However, problems plague the reliability, accuracy and mass production of this unit. This project assesses the company's exisiting product, and in conjunction with an appreciation of the company history and structure, concludes that this unit is unsuited to its intended application. Means of improving the measurement accuracy and longevity of this unit, commensurate with the company's limited resources and experience, are proposed, both for immediate retrofit and for longer term use. This information is presented in the form of a number of internal reports for the company. The off-highway environment is examined; and in conjunction with an evaluation of means of obtaining a returned signal, comparisons of processing techniques, and on-site gathering of previously unavailable data, preliminary designs for an alternative product are drafted. Theoretical aspects are covered by a literature review of ground-pointing radar, vehicular radar, and velocity measuring systems. This review establishes and collates the body of knowledge in areas previously considered unrelated. Based upon this work, a new design is proposed which is suitable for incorporation into the existing company product range. Following production engineering of the design, five units were constructed, tested and evaluated on-site. After extended field trials, this design has shown itself to possess greater accuracy, reliability and versatility than the existing sensor, at a lower unit cost.

Explicit Solution of Bitsadze-Samarskii Problem

Иван Димовски, Юлиан Цанков - В статията е намерено точно решение на задачата на Бицадзе-Самрски (1) за уравнението на Лаплас, като е използвано операционно смятане основано на некласическа двумернa конволюция. На това точно решение може да се гледа като начин за сумиране на нехармоничния ред по синуси на решението, получен по метода на Фурие.

Cationic Bovine Serum Albumin (CBA) conjugated Poly Lactic-co-Glycolic Acid (PLGA) nanoparticles for extended delivery of methotrexate into brain tumor

Current treatment strategies for the treatment of brain tumor have been hindered primarily by the presence of highly lipophilic insurmountable blood-brain barrier (BBB). The purpose of current research was to investigate the efficiency of engineered biocompatible polymeric nanoparticles (NPs) as drug delivery vehicle to bypass the BBB and enhance biopharmaceutical attributes of anti-metabolite methotrexate (MTX) encapsulated NPs. The NPs were prepared by solvent diffusion method using cationic bovine serum albumin (CBA), and characterized for physicochemical parameters such as particle size, polydispersity index, and zeta-potential; while the surface modification was confirmed by FTIR, and NMR spectroscopy. Developed NPs exhibited zestful relocation of FITC tagged NPs across BBB in albino rats. Further, hemolytic studies confirmed them to be non-toxic and biocompatible as compared to free MTX. In vitro cytotoxicity assay of our engineered NPs on HNGC1 tumor cells proved superior uptake in tumor cells; and elicited potent cytotoxic effect as compared to plain NPs and free MTX solution. The outcomes of the study evidently indicate the prospective of CBA conjugated poly (D,L-lactide-co-glycolide) (PLGA) NPs loaded with MTX in brain cancer bomber with amplified capability to circumvent BBB.

Hybrid formulation solution for stress analysis of curved pipes with welded bending joints

A method is presented for evaluating the stress intensity factor of part-through cracks in a thin pipe elbow. A hybrid formulation solution is used to evaluate the stress field close to the crack area. The stress field values are then inputted into a previously developed method published in the literature to evaluate the stress intensity factor in cylindrical shells. Results from cylindrical shells with part-through cracks are extended to double-curvature pipe configurations that contain the same kind of flaw.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

Peripherally η1-Platinated Organometallic Porphyrins as Building Blocks for Multiporphyrin Arrays

The modification of peripherally metalated meso-η1-platiniometalloporphyrins, such as trans-[PtBr(NiDAPP)(PPh3)2] (H2DAPP = 5-phenyl-10,20-bis(3‘,5‘-di-tert-butylphenyl)porphyrin), leads to the analogous platinum(II) nitrato and triflato electrophiles in almost quantitative yields. Self-assembly reactions of these meso-platinioporphyrin tectons with pyridine, 4,4‘-bipyridine, or various meso-4-pyridylporphyrins in chloroform generate new multicomponent organometallic porphyrin arrays containing up to five porphyrin units. These new types of supramolecular arrays are formed exclusively in high yields and are stable in solution or in the solid state for extended periods. They were characterized by multinuclear NMR and UV−visible spectroscopy as well as high-resolution electrospray ionization mass spectrometry.