A flexible approach to ranking with an application to MBA Programs

We develop a model for flexibly ranking multi-dimensional alternatives/units into preference classes via Mixed Integer Programming. We consider a linear aggregation model, but allow the criterion weights to vary within pre-specified ranges. This allows the individual alternatives/units to play to their strengths. We illustrate the use of the model by considering the Financial Times Global MBA Program rankings and discuss the implications. We argue that in many applications neither the data nor the weights or the aggregation model itself is precise enough to warrant a complete ranking, providing an argument for sorting or what we call flexible ranking.     

Monotone optimal replacement policies for a Markovian deteriorating system in a controllable environment

We consider the optimal replacement of a periodically inspected system under Markov deterioration that operates in a controlled environment. Provided are sufficient conditions that characterize an optimal control-limit replacement policy with respect to the system’s condition and its environment. The structure of the optimal policy is illustrated by a numerical example.     

Generalized Hyperbolic Octonion Formulation for the Fields of Massive Dyons and Gravito-Dyons

The close analogy between electromagnetic theory and linear gravity is discussed by the hyperbolic (split) octonion formalism. Using the similarities between the relevant field equations of massive dyons in electromagnetic theory and gravito-dyons in linear gravity, a new mathematical model is proposed to formulate these fields in a compact and simple form. The generalized wave equation including both massive dyon and monopole terms is derived. Similarly, the most generalized form of hyperbolic octonionic Klein–Gordon equation is obtained for the hypothetical particle carrying simultaneously both electromagnetic and gravitational charges (masses).     

Spectral,electron microscopic and chemical investigations of gamma-induced purple color zonings in amethyst crystals from the Dursunbey-Balıkesir region of Turkey

Amethyst crystals on matrix specimens from the Dursunbey-Bal?kesir region in Turkey have five representative purple color zonings: dark purple, light purple, lilac, orchid, and violet. The purple color zonings have been analyzed with optical absorption spectra in the visible wavelength region, chemical full trace element analyses (inductively coupled plasma-atomic emission spectroscopy and inductively coupled plasma-mass spectroscopy), and scanning electron microscopic images with high magnification. It can be proposed that the production of the purple color in amethyst crystals is due to three dominant absorption bands centered at 375, 530, and 675 nm, respectively. In addition, the purple color zonings are also due to four minor absorption bands centered at 435, 480, 620, and 760 nm. X-ray diffraction graphics of the investigated amethyst crystals indicate that these crystals are composed of a nearly pure alpha-quartz phase and do not include any moganite silica phase and/or other mineral implications. Trace element analyses of the amethyst crystals show five representative purple color zonings, suggesting that the absorption bands can be mainly attributed to extrinsic defects (chemical impurities). However, another important factor that influences all structural defects in amethyst is likely to be the gamma irradiation that exists during amethyst crystallization and its inclusion in host materials. This gamma irradiation originates from the large underlying intrusive granitoid body in the region of amethyst formation. Irradiation modifies the valence values of the impurity elements in the amethyst crystals. It is observed that the violet-colored amethyst crystals have the most stable and the least reversible coloration when exposed to strong light sources. This situation can be related to the higher impurity content of Fe (2.50 ppm), Co (3.1 ppm), Ni (38 ppm), Cu (17.9 ppm), Zn (10 ppm), Zr (3.9 ppm), and Mo (21.8 ppm).     

Radioactivity concentrations in topsoil samples from the Thrace region of Turkey and assessment of radiological hazard

The activity concentrations of gamma emitting radionuclides were measured in surface soil samples from the Thrace region. ²³²Th, ²³⁸U, ²²⁶Ra, ⁴⁰K and ¹³⁷Cs activities and physico-chemical parameters of the soil samples were determined in samples collected from 73 sampling stations. Radionuclide concentrations measured were compared with those found in the samples from other locations of Turkey and from different countries. The average activity concentrations of ²³²Th, ²³⁸U, ²²⁶Ra, ⁴⁰K and ¹³⁷Cs were found to be 24.71 ± 8.79, 22.30 ± 7.93, 32.09±12.44, 509.00±160.05, 32.74±29.24 Bq kg^?1, respectively. The mean value of the annual effective dose equivalent from the outdoor terrestrial gamma radiation was calculated as 57.2 μ Sv.     

Electron paramagnetic resonance and FT-IR spectroscopic studies of DL-2-aminoadipic acid and ammonium acetate powders

Exposure of powder forms of DL-2-aminoadipic acid and ammonium acetate to gamma radiation results in the formation of free radicals detected by the electron paramagnetic resonance spectroscopy at room temperature. In these compounds, the observed paramagnetic species were attributed to the HOOCCH₂CH₂CH₂CHCOOH and CH₂COONH₄ radicals, respectively. The g values and the hyperfine coupling constants of the unpaired electron with the environmental protons were determined for these two radicals. In work, the observed paramagnetic species were found to be stable at room temperature for more than two months. Also, these compounds were characterised by FT-IR and UV–VIS. Their thermal stabilities were determined by TGA and DTA measurements. Thermal analyses were shown to be unstable of the HOOCCH₂CH₂CH₂CH(NH₂)COOH and CH₃COONH₄ against thermo-oxidative decomposition.     

He's homotopy perturbation method for solving the shock wave equation

In this article, we discuss the analytic solution of the fully developed shock waves. The homotopy perturbation method is used to solve the shock wave equation, which describes the flow of gases. Unlike the various numerical techniques, which are usually valid for short period of time, the solution of the presented equation is analytic for 0 < t < ∞. The results presented converge very rapidly, indicating that the method is reliable and accurate.     

On Finite Factorization Rings

Let R be a commutative ring with identity. R is a finite factorization ring (FFR) if every nonzero nonunit of R has only a finite number of factorizations up to order and associates. In this article, we give a characterization of R for R[X] and R[[X]] to be an FFR.     

Split Fibonacci Quaternions

Starting from ideas given by Horadam in [5] , in this paper, we will define the split Fibonacci quaternion, the split Lucas quaternion and the split generalized Fibonacci quaternion. We used the well-known identities related to the Fibonacci and Lucas numbers to obtain the relations between the split Fibonacci, split Lucas and the split generalized Fibonacci quaternions. Moreover, we give Binet formulas and Cassini identities for these quaternions.