On a maximum eigenvalue of 3rd order pairwise comparison matrices in AHP and convergence of Newton\u27s method

In this short note, we apply the Newton\u27s method to the characteristic polynomial of the 3rd order pairwise comparison matrices.We show the convergence of the series generated from the initial value 3, to the maximum eigenvalue

On convergence of Newton\u27s method for the characteristic equation of 4th order pairwise comparison matrix in AHP

In this article, we apply Newton\u27s method to the characteristic polynomial of 4th order pairwise comparison matrices. We will see that convergent limit of the sequence generated by the iteration of Newton\u27s method depends on the choice of an initial value. We seek the viability of possible choice of the initial value corresponding to the consistency of the pairwise comparison

On a Maximum Eigenvalue of Third‑Order Pairwise Comparison Matrix in Analytic Hierarchy Process and Convergence of Newton’s Method

Nowadays, the analytic hierarchy process is an established method of multiple criteria decision making in the field of Operations Research. Pairwise comparison matrix plays a crucial role in the analytic hierarchy process. The principal (maximum magnitude) eigenvalue of the pairwise comparison matrix can be utilized for measuring the consistency of the decision maker\u27s judgment. The simple transformation of the maximum magnitude eigenvalue is known to be Saaty\u27s consistency index. In this short note, we shed light on the characteristic polynomial of a pairwise comparison matrix of third order. We will show that the only real-number root of the characteristic equation is the maximum magnitude eigenvalue of the third-order pairwise comparison matrix. The unique real-number root appears in the area where it is greater than 3, which is equal to the order of the matrix. By applying usual Newton\u27s method to the characteristic polynomial of the third-order pairwise comparison matrix, we see that the sequence generated from the initial value of 3 always converges to the maximum magnitude eigenvalue

Practice of Excel in the Classroom of Operations Research at Japanese Local Universities

In this article, we report practices of operations research subject which are given in Japanese local universities. The subjects are two. Portfolio optimization and the analytic hierarchy process.They both maintain prominence in Japan because of the academic and educationl activities of Professors Konno and Tone. We will see hereafter the compatibility with Microsoft Excel, the most popular spreadsheet application, and add-in tool Solver

Supersaturated state of diazepam injection following dilution with infusion fluid

BackgroundSignificant precipitation produced by the dilution of diazepam (DZP) injection with an infusion fluid is a great concern for the clinical practice. In this study, the precipitation behavior under different conditions was investigated.MethodFor the sample preparation, DZP injections (Horizon injection and Cercine injection) were diluted with various infusion fluids (Saline, 5% glucose infusion fluid and Soldem 3A) at designated dilution ratios ranging from 1× to 40× (5 mg/mL to 0.125 mg/mL). In addition, to measure the solubility of DZP in the samples, the saturated solutions of DZP were prepared. The DZP concentrations in the samples were measured by high-performance liquid chromatography (HPLC). This study also investigated the precipitate using various analytical methods: infrared microscopy, 1H-NMR, differential scanning calorimetry, and powder X-ray deflection.ResultsFirst, the compatibility of injection with infusion fluids was investigated. Significant precipitation occurred at dilution ratios ranging from 2× to 20×. No significant effects of formulations and infusion fluids on the compatibility were observed. The solubility of DZP was then further investigated. The concentration of DZP dissolved in the admixtures was higher than the solubility. This indicated that DZP existed in a supersaturated state in the infusion fluid admixtures. In the next phase of this study, the precipitate was investigated using various analytical methods. Results showed that the precipitate in infusion fluid admixtures was mostly composed of DZP, but also contained small amounts of the ingredients of DZP injection, such as benzoic acid and benzyl alcohol.ConclusionsThis study clarified details of the precipitation occurring after dilution of DZP injection with infusion fluids. It is worth noting that DZP in an infusion admixture existed in a supersaturated state. These findings offer important insight into the clinical practice of DZP injection

Direct measurement of spectral shape of Cherenkov light using cosmic muons

The spectral pulse shape of Cherenkov lights was directly measured by using cosmic muons. The observed decay times for early and late timing were 5.0 and 5.2ns, respectively. They were actually shorter than the time of scintillation lights which were also measured as 9.3ns and 9.2ns, respectively. However we could not see the difference of the rise time between scintillation and Cherenkov lights. This was due to the slow response of our DAQ equipment, photomultiplier and FADC digitize

Precise pulse shape measurement of Cherenkov light using sub-MeV electrons from Sr-90/Y-90 beta source

The precise spectral pulse shape from Cherenkov lights was directly measured by using sub-MeV electrons from 90Sr/90Y beta source. The observed shape was clearly different from the shape of scintillation light. The pulse rise and fall （decay） time for Cherenkov light were 0.8 ns and 2.5 ns, respectively. They were actually shorter than those times of scintillation light which were also measured by 1.6 ns and 6.5 ns, respectively. This clear Thisclearclear difference of rise time will be used for the pulse shape discrimination in order to select PMTs which receive Cherenkov lights, and the topological information due to Cherenkov light will be used for the reduction of backgrounds from 208Tl beta decay which should be major backgrounds observed around Q-value （3.35MeV）of 96Zr neutrinoless double beta decay

Highly Stretchable Stress-Strain Sensor from Elastomer Nanocomposites with Movable Cross-links and Ketjenblack

Practical applications like very thin stress-strain sensors require high strength, stretchability, and conductivity, simultaneously. One of the approaches is improving the toughness of the stress-strain sensing materials. Polymeric materials with movable cross-links in which the polymer chain penetrates the cavity of cyclodextrin (CD) demonstrate enhanced strength and stretchability, simultaneously. We designed two approaches that utilize elastomer nanocomposites with movable cross-links and carbon filler (ketjenblack, KB). One approach is mixing SC (a single movable cross-network material), a linear polymer (poly(ethyl acrylate), PEA), and KB to obtain their composite. The electrical resistance increases proportionally with tensile strain, leading to the application of this composite as a stress- strain sensor. The responses of this material are stable for over 100 loading and unloading cycles. The other approach is a composite made with KB and a movable cross-network elastomer for knitting dissimilar polymers (KP), where movable cross-links connect the CD-modified polystyrene (PSCD) and PEA. The obtained composite acts as a highly sensitive stress-strain sensor that exhibits an exponential increase in resistance with increasing tensile strain due to the polymer dethreading from the CD rings. The designed preparations of highly repeatable or highly responsive stress-strain sensors with good mechanical properties can help broaden their application in electrical devices

Development of pulse shape discrimination for Cherenkov lights in liquid scintillator

With a liquid scintillation used for ZICOS experiment, we measured pulse shapes in case of several radio isotopes, 60Co, 137Cs, 133Ba, and 57Co. Taking FADC timing at 60 nsec for the peak position, FADC spectra from 58.5 nsec to 80 nsec were almost same shape for each RI, however, before 58.5 nsec, we have found that those were different shape. Especially, in case of 57Co, the energy is lower than Cherenkov threshold, so that the spectra should not include Cherenkov light. Using those spectra between 57.0 nsec and 58.0 nsec（3 bins）, we calculated simply χ2 and it was clearly discriminated that χ2 ≥ 0.1 should be include Cherenkov lights. This was also confirmed by Compton electrons with fixed energy and fixed direction. Obtained detection inefficiency of Cherenkov lights was observed by 21.4 ± 9.6 %. According to Compton edge events which have almost same direction as the incident γ and backgrounds events which should have isotropic direction, the detection inefficiency were 10.4 ± 0.5 % and 49.1 ± 1.4 %, respectively. They were quite different values and the inefficiency of both fixed energy and Compton edge events were statistically same. This is a direct evidence that Cherenkov lights should keep their topology even if they are emitted by around 1 MeV electron