New operations over hesitant fuzzy sets

Hesitant fuzzy sets are considered to be the way to characterize vague phenomenon. Their study has opened a new area of research and applications. Set operations on them lead to a number of properties of these sets which are not evident in classical (crisp) sets make the area mathematically also very productive. Since these sets are defined in terms of functions and set of functions, which is not the case when the sets are crisp, it is possible to define several set operations. Such a study enriches the use of these sets. In this paper, four new operations are envisaged, defined and taken up to study a score of new identities on hesitant fuzzy sets.     

Computer-assisted bijectification of Franel's recurrence

We show how to automatically translate algebraic proofs into bijective proofs. As an example, we bijectify Franel's recurrence relation on the sum of the cubes of the binomial coefficients.     

Spectral Investigations of Solvatochromism and Preferential Solvation on 1,4-Dihydroxy-2,3-Dimethyl-9,10-Anthraquinone

Solvatochromic and preferential solvation of 1,4-dihydroxy-2,3-dimethyl-9,10-anthraquinone (DHDMAQ) have been investigated using optical absorption and fluorescence emission techniques. Optical absorption spectra of DHDMAQ in different solvents show the intra molecular charge transfer band in the region 400–550nm. The observed blue shift with solvent polarity indicates the delocalisation of the excited state, owing to reduction in quasiaromaticity of the chelate rings formed by intra molecular hydrogen bonds, due to electrostatic or hydrogen bonding interaction. This is also confirmed by the observed low oscillator strength and the transition dipole moment. The observed quantum yield of DHDMAQ in different solvents is due to the inter molecular hydrogen bond in the excited state in addition to the intra molecular hydrogen bond. It also reveals from the low oscillator strength, which indicates that the radiative decay is low. Excited state dipole moment of DHDMAQ is calculated by solvatochromic data and it shows a lower value than ground state dipole moment. The preferential solvation parameter shows that in dimethyl formamide (DMF) + ethanol mixture, the DHDMAQ is preferentially solvated by ethanol in DMF rich region and by DMF in ethanol rich region. In the case of DMF + dichloromethane mixture DHDMAQ is preferentially solvated by DMF.     

Determination of Fucose Concentration in a Lectin-Based Displacement Microfluidic Assay

We compare three different methods to quantify the monosaccharide fucose in solutions using the displacement of a large glycoprotein, lactoferrin. Two microfluidic analysis methods, namely fluorescence detection of (labeled) lactoferrin as it is displaced by unlabeled fucose and the displacement of (unlabeled) lactoferrin in SPR, provide fast responses and continuous data during the experiment, theoretically providing significant information regarding the interaction kinetics between the saccharide groups and binding sites. For comparison, we also performed a static displacement ELISA. The stationary binding site in all cases was immobilized S2-AAL, a monovalent polypeptide based on Aleuria aurantia lectin. Although all three assays showed a similar dynamic range, the microfluidic assays with fluorescent or SPR detection show an advantage in short analysis times. Furthermore, the microfluidic displacement assays provide a possibility to develop a one-step analytical platform.

     

Monaural level discrimination under dichotic conditions

The ability to make judgments about the stimulus at one ear when a stimulus is simultaneously presented to the other ear was tested. Specifically, subjects discriminated the level of a 600 Hz target tone presented at the left ear while an identical-frequency distractor was simultaneously presented at the other ear. When there was no distractor, threshold was 0.7 dB. Threshold increased to 1.1 dB when a distractor with a fixed phase and level was introduced contra-aurally to the target. Further increases in threshold were observed when an across-presentation variability was introduced into the distractor phase (threshold of 1.6 dB) or level (threshold of 5.8 dB). When both the distractor level and phase varied, the largest threshold of 7.3 dB was obtained. These increases in threshold cannot be predicted by common binaural models, which assume that a target stimulus at one ear can be processed without interference from the stimulus at the nontarget ear. The measured thresholds are consistent with a model that utilizes two binaural dimensions that roughly correspond to the loudness and the position of a fused binaural image. The results show that, with binaurally fused tonal stimuli, subjects are unable to listen to one ear.     

Magnetocaloric effect in high-energy ball-milled Gd5Si2Ge2 and Gd5Si2Ge2/Fe nanopowders

Evolution of structure and magnetocaloric properties in ball-milled Gd₅Si₂Ge₂ and Gd₅Si₂Ge₂/0.1 wt% Fe nanostructured powders were investigated. The high-energy ball-milled powders were composed of very fine grains (70–80 nm). Magnetization decreased with milling time due to decrease in the grain size and randomization of the magnetic moments at the surface. The magnetic entropy change (ΔS_M) was calculated from the isothermal magnetization curves and a maximum value of 0.45 J/kg K was obtained for 32 h milled Gd₅Si₂Ge₂ alloy powder for a magnetic field change of 2 T while it was still low in Fe-contained alloy powders. The thermo-magnetic measurements revealed that the milled powders display distribution of magnetic transitions, which is desirable for practical magnetic refrigerant to cover a wide temperature span.     

Nondestructive characterization of musical pillars of Mahamandapam of Vitthala Temple at Hampi, India

This paper presents the first scientific investigation on the musical pillars of the Vitthala Temple at Hampi, India. The solid stone columns in these pillars produce audible sound, when struck with a finger. Systematic investigations on the acoustic characteristics of the musical pillars of mahamandapam (great stage) of the Vitthala Temple have been carried out. The 11 most popular pillars that produce sounds of specific musical instruments are considered for the investigations. The sound produced from these 11 most popular musical pillars was recorded systematically and different nondestructive testing techniques such as low frequency ultrasonic testing, impact echo testing, and in situ metallography were employed on the musical columns of these pillars. The peak frequencies in the amplitude spectrum of the sound produced from various columns in these pillars are correlated with the dimensional measurements and ultrasonic velocity determined using impact echo technique. The peak frequencies obtained experimentally have been found to have excellent correlation with the calculated flexural frequencies based on the dimensional measurements and ultrasonic velocities of the columns.     

Effect of spatial uncertainty of masker on masked detection for nonspeech stimuli

Research on informational masking for nonspeech stimuli has focused on the effects of spectral uncertainty in the masker. In this letter, results are presented from some preliminary probe experiments in which the spectrum of the masker is held fixed but the spatial properties of the masker are randomized. In addition, in some tests, the overall level of the stimulus is randomized. These experiments differ from previous experiments that have measured the effect of spatial uncertainty on masking in that the only attributes (aside from level) that distinguish the target from the masker are the spatial attributes; in all of the tests, the target and masker were statistically identical, statistically independent, narrowband noise signals. In general, the results indicate that detection performance is degraded by spatial uncertainty in the masker but that compared both to the effects of spectral uncertainty and to the effects of overall-level uncertainty, the effects of spatial uncertainty are relatively small.