Extension of VIKOR method for decision making problem with interval numbers

The VIKOR method was developed for multi-criteria optimization of complex systems. It determines the compromise ranking list and the compromise solution obtained with the initial (given) weights. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria. It introduces the multi-criteria ranking index based on the particular measure of “closeness” to the “ideal” solution. The aim of this paper is to extend the VIKOR method for decision making problems with interval number. The extended VIKOR method’s ranking is obtained through comparison of interval numbers and for doing the comparisons between intervals, we introduce α as optimism level of decision maker. Finally, a numerical example illustrates and clarifies the main results developed in this paper.     

Micro-Raman observation on the HPO4(2-) association structures in an individual dipotassium hydrogen phosphate (K2HPO4) droplet

A single K(2)HPO(4) droplet with size of ～50 μm on a Teflon substrate was forced to enter into the supersaturated state by decreasing the relative humidity (RH), allowing accurate control over the concentration of the solute within a droplet of a nanogram. The K(2)HPO(4) solutions from dilute (0.1-1.0 mol·L(-1) bulk) to concentrated state (a droplet from RH 98.2% to 25.1%) were studied through micro-Raman spectroscopy in the spectral region of about 200-4000 cm(-1). The area ratio between the water stretching band to the sum of the ν(1)-PO(3), ν(2)-POH, and ν(4)-PO(3) bands of the HPO(4)(2-) at various RHs was used to describe the dehydration behavior of a microsized single K(2)HPO(4) droplet in dehumidifying process. The peak position of the v(1)-PO(3) band for the 1 mol·L(-1) bulk solution appeared at 991 cm(-1) and moved to 986 cm(-1) at 98.2% RH, to 978 cm(-1) at 70.2% RH, and then to 964 cm(-1) at 30.0% RH for a droplet, accompanying an increase of the full width at half-height (fwhh) of this peak from 16.3 to 17.2, 22.2, and then to 24.2 cm(-1), indicating transition of the HPO(4)(2-) anions from monomers to dimers/trimers/oligomers and then to polyanions with chain structures in the K(2)HPO(4) solutions. After 25.1% RH, the solid was proved to be K(2)HPO(4)·3H(2)O according to the Raman spectral features. Furthermore, the O-H stretching envelope of a K(2)HPO(4) droplet showed that the intensity ratios of the strong hydrogen bonding component (3255 cm(-1)) to the weak one (3417 cm(-1)) and the cage-like water (2925 cm(-1)) to the weak one (3417 cm(-1)) were sensitive to the HPO(4)(2-) association structures, which can be used to understand the effects of dimers/trimers/oligomers and chain structures of the HPO(4)(2-) associations on the hydrogen bonding of water molecules.     

Rhizonin A from Burkholderia sp. KCTC11096 and its growth promoting role in lettuce seed germination

We isolated and identified a gibberellin-producing Burkholderia sp. KCTC 11096 from agricultural field soils. The culture filtrate of plant growth promoting rhizobacteria (PGPR) significantly increased the germination and growth of lettuce and Chinese cabbage seeds. The ethyl acetate extract of the PGPR culture showed significantly higher rate of lettuce seed germination and growth as compared to the distilled water treated control. The ethyl acetate fraction of the Burkholderia sp. was subjected to bioassay-guided isolation and we obtained for the first time from a Burkholderia sp. the plant growth promoting compound rhizonin A (1), which was characterized through NMR and MS techniques. Application of various concentrations of 1 significantly promoted the lettuce seed germination as compared to control.     

Gold nanothorns-macroporous silicon hybrid structure: a simple and ultrasensitive platform for SERS

We synthesised a novel gold-on-porous silicon hybrid material that exhibits a highly sensitive and reproducible surface-enhanced Raman spectroscopy (SERS) response. The material was fabricated simply by reducing gold chloride with hydrofluoric acid on the surface of macro-porous silicon (macro-PSi). The material consists of thorn-shaped gold nanocrystals with characteristic shapes and sizes on the surface of macro-PSi.     

Assessing epithelial cell nuclear morphology by using azimuthal light scattering spectroscopy

We describe azimuthal light scattering spectroscopy (phi/LSS), a novel technique for assessing epithelial-cell nuclear morphology. The difference between the spectra measured at azimuthal angles phi = 0 degrees and phi = 90 degrees preferentially isolates the single backscattering contribution due to large (approximately 10 microm) structures such as epithelial cell nuclei by discriminating against scattering from smaller organelles and diffusive background. We demonstrate the feasibility of using phi/LSS for cancer detection by showing that spectra from cancerous colon tissue exhibit significantly greater azimuthal asymmetry than spectra from normal colonic tissues.     

Dense coating of surface mounted CuBTC Metal-Organic Framework nanostructures on silk fibers, prepared by layer-by-layer method under ultrasound irradiation with antibacterial activity

The growth of Cu₃(BTC)₂ (BTC = 1,3,5-benzenetricarboxylate), also known as CuBTC and HKUST-1, Metal-Organic Framework (MOF) nanostructures on silk fibers were achieved by layer-by-layer technique in alternating bath of Cu(OAc)₂·2H₂O and H₃BTC solutions under ultrasound irradiation. The effect of pH, reaction time, ultrasound irradiation and sequential dipping steps in growth of the CuBTC Metal-Organic Framework nanostructures has been studied. These systems depicted a decrease in the size accompanying a decrease in the sequential dipping steps. In addition, dense coating of silk fibers with CuBTC MOF results in decrease the emission intensity of silk fibers. The silk fibers containing CuBTC Metal-Organic Framework exhibited high antibacterial activity against Escherichia coli and Staphylococcus aureus. The samples were characterized with powder X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR) spectra and scanning electron microscopy (SEM). XRD analyses indicated that the prepared CuBTC MOF nanostructures on silk fibers were crystalline.     

Spatio-temporal dynamics of security investments in an interdependent risk environment

In a globalised world where risks spread through contagion, the decision of an entity to invest in securing its premises from stochastic risks no longer depends solely on its own actions but also on the actions of other interacting entities in the system. This phenomenon is commonly seen in many domains including airline, logistics and computer security and is referred to as Interdependent Security (IDS). An IDS game models this decision problem from a game-theoretic perspective and deals with the behavioural dynamics of risk-reduction investments in such settings. This paper enhances this model and investigates the spatio-temporal aspects of the IDS games. The spatio-temporal dynamics are studied using simple replicator dynamics on a variety of network structures and for various security cost tradeoffs that lead to different Nash equilibria in an IDS game. The simulation results show that the neighbourhood configuration has a greater effect on the IDS game dynamics than network structure. An in-depth empirical analysis of game dynamics is carried out on regular graphs, which leads to the articulation of necessary and sufficient conditions for dominance in IDS games under spatial constraints.     

Role of Interaction in Enhancing the Epistemic Utility of 3D Mathematical Visualizations

Many epistemic activities, such as spatial reasoning, sense-making, problem solving, and learning, are information-based. In the context of epistemic activities involving mathematical information, learners often use interactive 3D mathematical visualizations (MVs). However, performing such activities is not always easy. Although it is generally accepted that making these visualizations interactive can improve their utility, it is still not clear what role interaction plays in such activities. Interacting with MVs can be viewed as performing low-level epistemic actions on them. In this paper, an epistemic action signifies an external action that modifies a given MV in a way that renders learners’ mental processing of the visualization easier, faster, and more reliable. Several, combined epistemic actions then, when performed together, support broader, higher-level epistemic activities. The purpose of this paper is to examine the role that interaction plays in supporting learners to perform epistemic activities, specifically spatial reasoning involving 3D MVs. In particular, this research investigates how the provision of multiple interactions affects the utility of 3D MVs and what the usage patterns of these interactions are. To this end, an empirical study requiring learners to perform spatial reasoning tasks with 3D lattice structures was conducted. The study compared one experimental group with two control groups. The experimental group worked with a visualization tool which provided participants with multiple ways of interacting with the 3D lattices. One control group worked with a second version of the visualization tool which only provided one interaction. Another control group worked with 3D physical models of the visualized lattices. The results of the study indicate that providing learners with multiple interactions can significantly affect and improve performance of spatial reasoning with 3D MVs. Among other findings and conclusions, this research suggests that one of the central roles of interaction is allowing learners to perform low-level epistemic actions on MVs in order to carry out higher-level cognitive and epistemic activities. The results of this study have implications for how other 3D mathematical visualization tools should be designed.     

A Non-Parametric Approach to Model Evaluation

All existing tests and criteria for model evaluation are based on the sum of squared residuals. These measures do not evaluate the performance of a model in predicting turning points in the variable of interest. Here, three tests are proposed to evaluate models on the basis of their ability to predict turning points and to give an unbiased prediction of the relative order of magnitude of changes. Five models are evaluated using the proposed tests. Results indicate that the tests expose facets of models that R² and sum of squared residuals are unable to highlight. Hence, the tests are suggested to complement existing model evaluation techniques.     

New quasi-exactly solvable Hamiltonians in two dimensions

Quasi-exactly solvable Schrödinger operators have the remarkable property that a part of their spectrum can be computed by algebraic methods. Such operators lie in the enveloping algebra of a finite-dimensional Lie algebra of first order differential operators—the hidden symmetry algebra. In this paper we develop some general techniques for constructing quasi-exactly solvable operators. Our methods are applied to provide a wide variety of new explicit two-dimensional examples (on both flat and curved spaces) of quasi-exactly solvable Hamiltonians, corresponding to both semisimple and more general classes of Lie algebras.Supported in Part by DGICYT Grant PS 89-0011.Supported in Part by an NSERC Grant.Supported in Part by NSF Grant DMS 92-04192.