Novel applications of bipolar fuzzy graphs to decision making problems

Zhang introduced the concept of bipolar fuzzy sets as a generalization of fuzzy sets. Bipolar fuzzy sets have shown advantages in solving decision making problems than fuzzy sets. In this research paper, we study several different types of domination, including equitable domination, k-domination and restrained domination in bipolar fuzzy graphs. We present novel applications of bipolar fuzzy graphs to decision making problems. We also present an algorithm for computing dominating number in our applications.     

Families of multiresolution and wavelet spaces with optimal properties

Under suitable conditions, if the scaling functions ?₁ and ?₂ generate the multiresolutions V _(j)(?₁) and V _(j)(?₂), then their convolution ?₁*?₂also generates a multiresolution V _(j)(?₁*?₂) More over, if p is an appropriate convolution operator from l ₂ into itself and if ? is a scaling function generating the multiresolution V _(j)(?),then p*?is a scaling function generating the same multiresolution V _(j)(?)=V _(j)(p*?). Using these two properties, we group the scaling and wavelet functions into equivalent classes and consider various equivalent basis functions of the associated function spaces We use the n-fold convolution product to construct sequences of multiresolution and wavelet spaces V _(j)(?ⁿ) and W _(j)(?ⁿ) with increasing regularity. We discuss the link between multiresolution analysis and Shannon's sampling theory. We then show that the interpolating and orthogonal pre- and post-filters associated with the multiresolution sequence V ₍₀₎(?ⁿ)asymptotically converge to the ideal lowpass filter of Shannon. We also prove that the filters associated with the sequence of wavelet spaces W ₍₀₎(?ⁿ)convergeto the ideal bandpass filter. Finally, we construct the basic wavelet sequences ψ ^b _nand show that they tend to Gabor functions. Thisprovides wavelets that are nearly time-frequency optimal. The theory is illustrated with the example of polynomial splines.     

Study of the Antioxidant and Anti-Inflammatory Properties of the Biological Extracts of Psophocarpus tetragonolobus Using Two Extraction Methods

Psophocarpus tetragonolobus has long been used in traditional medicine and cuisine. In this study, Psophocarpus tetragonolobus extracts were isolated by maceration and ultrasound-assisted extraction and were evaluated for their antioxidant and anti-inflammatory effects in lipopolysaccharide (LPS)-stimulated RAW264.7 macrophages. The obtained results show that both extracts (maceration and ultrasound) were rich in bioactive molecules and exerted substantial antioxidant and anti-inflammatory effects. The P. tetragonolobus extracts’ treatment in LPS-stimulated RAW264.7 macrophages resulted in a significant downregulation of the expressions of tumor necrosis factor-α (TNF-α), interleukin-6 (IL-6), and IL-1β mRNA. In addition, the P. tetragonolobus extracts’ treatment attenuated inducible nitric oxide synthase (iNOS) and cyclooxygenase-2 (COX-2) protein expression. Our observations indicate that there is no significant difference between the two studied extracts of P. tetragonolobus in terms of biological properties (specifically, antioxidant and anti-inflammatory effects. Regardless of the extraction method, P. tetragonolobus could be used for treating diseases related to oxidative stress and inflammatory reactions.     

Exact iterative reconstruction algorithm for multivariate irregularly sampled functions in spline-like spaces: The -Theory

We prove that the exact reconstruction of a function from its samples on any ``sufficiently dense" sampling set can be obtained, as long as is known to belong to a large class of spline-like spaces in . Moreover, the reconstruction can be implemented using fast algorithms. Since a limiting case is the space of bandlimited functions, our result generalizes the classical Shannon-Whittaker sampling theorem on regular sampling and the Paley-Wiener theorem on non-uniform sampling.

     

A pyrazole-based orthogonal ferromagnetically coupled [2 × 2] homoleptic square Cu4 grid: Magnetostructural correlations

The synthesis and structure of a pyrazole-based orthogonal ferromagnetically coupled tetracopper(II) 2 × 2 homoleptic grid complex [Cu₄(PzOAPyz)₄(ClO₄)₂](ClO₄)₂ · 6H₂O (1), formed by the reaction between the ditopic ligand PzOAPyz and Cu(ClO₄)₂ · 6H₂O, are described. The ligand contains terminal pyrazole and pyrazine residues bound to a central flexible diazine subunit (N–N) as well as one potentially bridging alkoxo group. The two adjacent metal centers are linked by an alkoxo oxygen forming essentially a square Cu₄(μ-O₄) cluster. In the Cu₄(μ-O₄) core, out of the four copper centers, two copper centers are penta-coordinated and the remaining two are hexa-coordinated. In each case of hexa-coordination, the sixth position is occupied by one of the oxygen atoms of a coordinated perchlorate ion. Complex 1 has been characterized structurally and magnetically. Although the large Cu–O–Cu bridge angles (137–138°) and short Cu–Cu distances (3.964–3.970 Å) are suitable for the transmission of the expected antiferromagnetic coupling, the square-based Cu₄(μ-O₄) cluster exhibits an intramolecular ferromagnetic exchange (J = 7.47 cm⁻¹) between the metal centers with an S = 2 magnetic ground state associated with the quasi orthogonal arrangement of the magnetic orbitals (d_x2-y2${\text{d}}_{x^2-y^2}$). The exchange pathway parameters have been evaluated from density functional calculations.     

Investigation of 500 keV Si ion induced surface structuring of Ni and Ti for enhancement of field emission properties

The present paper reports the investigation of surface morphology, elemental composition, phase changes and field emission properties of Si ion irradiated nickel (Ni) and titanium (Ti). The Ni and Ti targets have been irradiated with 500 keV Si ions generated by Pelletron accelerator at various fluences ranging from 6.9 × 10¹³ to 77.1 × 10¹³ ions/cm². Stopping range of ions in matter analysis revealed higher values of electronic stopping and sputtering yield for Ni as compared with Ti. For both irradiated metals, electronic energy loss dominant over the nuclear stopping. The growth of induced surface structures have been analysed by using field emission scanning electron microscopy (FESEM) analysis. In case of Ni, as the ion fluence increases from 6.9 × 10¹³ to 65.8 × 10¹³ ions/cm², the formation of spherical particulates, agglomers and sputtering is observed. Although in the case of Ti, with the increase of Si ion fluence from 11.6 × 10¹³ to 77.1 × 10¹³ ions/cm², the formation of irregular-shaped particulates along with crater and sputtered channels is observed. X-ray diffraction (XRD) analysis shows that no new phase is identified. However, a significant increase in peak intensity is observed with increasing ion fluence. The variation in crystallite size and dislocation line density is also observed as a function of Si ion fluence. Fourier transform infrared spectroscopy analysis shows that no bands are formed after the Si ion irradiation. Field emission properties of ion-structured Ni and Ti are well correlated with the growth of surface structures observed by SEM and dislocation line density evaluated by XRD analysis.     

Non-racemic (scalemic) planar-chiral five-membered metallacycles: routes, means, and pitfalls in their synthesis and characterization

This critical review provides a systematic classification of the synthetic routes to planar-chiral five-membered metallacycles into several routes, namely C-H bond activation, oxidative addition, transmetallation and optical resolution. As a characteristic of these bulk compounds is that they are synthesized as binary mixtures of enantiomers in proportions varying from the racemate to enantiopure, a review of absolute-configuration determination of the title planar-chiral scalemates is presented. This review is of interest to organic and organometallic synthetic chemists involved in asymmetric synthesis (97 references).     

Synthesis of two new linear trinuclear Cu(II) complexes: mechanism of magnetic coupling through hybrid B3LYP functional and CShM studies

Two new Cu(II) linear trinuclear Schiff base complexes, [Cu3(L)2(CH3COO)2] (1) and [Cu3(L)2(CF3COO)2] (2), have been prepared using a symmetrical Schiff base ligand H2L [where H2L = N,N'-bis(2-hydroxyacetophenone)propylenediimine]. Both of the complexes have been characterized by elemental analyses, Fourier transform IR, UV/vis, and electron paramagnetic resonance spectroscopy. Single-crystal X-ray structures show that the adjacent Cu(II) ions are linked by double phenoxo bridges and a mu(2)-eta(1):eta(1) carboxylato bridge. In each complex, the central copper atom is located in an inversion center with distorted octahedral coordination geometry, while the terminal copper atoms have square-pyramidal geometry. Cryomagnetic susceptibility measurements over a wide range of temperature exhibit a distinct antiferromagnetic interaction of J = -36.5 and -72.3 cm(-1) for 1 and 2, respectively. Density functional theory calculations (B3LYP functional) and continuous-shape measurement (CShM) studies have been performed on the trinuclear unit to provide a qualitative theoretical interpretation of the antiferromagnetic behavior shown by the complexes.     

Low temperature pyrolysis of carboxymethylcellulose

Unlike the common high temperature pyrolysis of carboxymethylcellulose (CMC) targeting activated carbon, this study investigates the pyrolytic behaviour of plain CMC at low temperatures ranging between 260 and 300 °C. Preliminary experiments were conducted using differential scanning calorimetry to define the temperature range necessary for the process. Low-temperature pyrolysis was then simulated using thermogravimetric analysis under inert atmosphere. Investigations reveal that a minimum holding temperature of 260 °C is required for an isothermal process, at which pyrolysis is terminated after around 26 min. Increasing exposure temperature reduces pyrolysis time. Within the range of the investigated sample and CMC particle size, no significant effects could be measured regarding the decomposition behaviour. The resulting char was further analysed using X-ray diffraction and Fourier transform infrared spectroscopy. Visual inspection was conducted using scanning electron microscopy. Upon pyrolysis, originally longitudinally shaped CMC was found to be converted into spherical particles of functionalised amorphous carbon with an average particle size of 41 µm.