n-Colour self-inverse compositions

MacMahon’s definition of self-inverse composition is extended ton-colour self-inverse composition. This introduces four new sequences which satisfy the same recurrence relation with different initial conditions like the famous Fibonacci and Lucas sequences. For these new sequences explicit formulas, recurrence relations, generating functions and a summation formula are obtained. Two new binomial identities with combinatorial meaning are also given.     

Quantum imaging with incoherent photons

We propose a technique to obtain subwavelength resolution in quantum imaging with potentially 100% contrast using incoherent light. Our method requires neither path-entangled number states nor multiphoton absorption. The scheme makes use of N photons spontaneously emitted by N atoms and registered by N detectors. It is shown that for coincident detection at particular detector positions a resolution of lambda/N can be achieved.     

Generation of symmetric Dicke states of remote qubits with linear optics

We propose a method for generating all symmetric Dicke states, either in the long-lived internal levels of N massive particles or in the polarization degrees of freedom of photonic qubits, using linear optical tools only. By means of a suitable multiphoton detection technique, erasing Welcher-Weg information, our proposed scheme allows the generation and measurement of an important class of entangled multiqubit states.     

Cytotoxic agents for KB and SiHa cells from n-hexane fraction of Cissampelos pareira and its chemical composition

Eleven constituents were characterised by gas chromatography–mass spectrometry analysis, and five molecules were isolated using column chromatography. The in vitro study of the extract and isolated molecules against KB and SiHa cell lines revealed oleanolic acid (1) and oleic acid (2) as potent cytotoxic molecules with potential anticancer activity. The IC₅₀ values of n-hexane extract (CPHF), oleanolic acid (1) and oleic acid (2) were >300, 56.08 and 70.7 μg/mL (μM), respectively, against KB cell lines and >300, 47.24 and 80.2 μg/mL (μM), respectively, against SiHa cell lines.     

Self‐Organization of Gold Nanoparticle Assemblies with 3D Spatial Order and Their External Stimuli Responsiveness

Gold nanoparticles (AuNP) with pyridyl end‐capped polystyrenes (PS‐4VP) as “quasi‐monodentate” ligands self‐assemble into ordered PS‐4VP/AuNP nanostructures with 3D hexagonal spatial order in the dried solid state. The key for the formation of these ordered structures is the modulation of the ratio AuNP versus ligands, which proves the importance of ligand design and quantity for the preparation of novel ordered polymer/metal nanoparticle conjugates. Although the assemblies of PS‐4VP/AuNP in dispersion lack in high dimensional order, strong plasmonic interactions are observed due to close contact of AuNP. Applying temperature as an external stimulus allows the reversible distortion of plasmonic interactions within the AuNP nanocomposite structures, which can be observed directly by naked eye. The modulation of the macroscopic optical properties accompanied by this structural distortion of plasmonic interaction opens up very interesting sensoric applications.

     

$$\mathcal {H}^+$$-multivalued contractions and their application to homotopy theory

Kikkawa and Suzuki (Nonlinear Anal 69:2942–2949, 2008) and Kikkawa and Suzuki (Fixed Point Theory Appl, 2008, Art. ID 649749) proved some fixed point results that are generalizations of Kannan’s, Nadler’s and Suzuki’s fixed point theorems. Here, we present fixed point results of this kind for multivalued mappings in the setting of \(\mathcal {H}^+\)-metric spaces. The theorems provided allow upgrading of some known results which is shown by examples. Moreover, we give a homotopy result as an application of our main theorem.     

Modified classification of non-self-adjoint second-order difference equations

This paper is concerned with the classification of non-self-adjoint second-order difference equations. The relationship between the number of summable solutions of non-self-adjoint difference equations and that of the discrete linear Hamiltonian system is discussed. A classification for non-self-adjoint second-order difference equations is established, which is independent of the choice of the rotated half plane and the fixed point.     

Effect of nanoclay and barium sulfate nanoparticles on the thermal and morphological properties of polyvinylidene fluoride nanocomposites

The thermal, morphological and optical studies of BaSO₄ and MMT (nanoclay) embedded in PVDF were investigated. Nanocomposites samples of PVDF–BaSO₄–MMT were prepared by varying the loadings (1–4 mass%) in case of BaSO₄ and MMT nanomaterials, respectively. Polyvinylidene fluoride–barium sulfate-montmorillonite (PVDF–BaSO₄–MMT) nanocomposites were prepared by solvent-mixing technique. Nanoparticles were synthesized by in situ deposition technique with the help of nonionic polymeric surfactant, and the particle size of nanoparticles was recognized by scanning electron microscopy (SEM) analysis which confirms that the particle has diameter of 80–90 nm. As prepared, nanocomposites films (thickness, 25 μm) were characterized by Fourier transform infrared microscopy (FTIR), SEM and electron diffraction spectroscopy (EDS). FTIR shows that all the chemical constituents were present in the nanocomposites, whereas SEM analysis suggested that the nanofillers dispersed well in polymer matrix and EDS showed the elemental composition of nanocomposite samples. Thermal properties of nanocomposites were studied by using TG/DTA/DTG. TG/DTA studies showed decomposition temperature of pure PVDF is 473.5 °C. The decomposition temperature (T _d) of nanocomposites was increased by 93 °C in case of nanocomposites with addition of both BaSO₄ and MMT nanomaterials. The difference in the thermal degradation temperature was found to be 1.2% higher in case of addition of BaSO₄ nanoparticle as compared to nanoclay. The obtained transparent nanocomposite films were characterized by using UV–Vis spectrophotometer which shows that transparencies of nanocomposites are maintained in visible region, the intensity of absorption band in UV region is increased with the addition of BaSO₄ nanoparticles, while in case of addition of nanoclay the UV region does not show drastic changes. Addition of both nanoparticle and nanoclay shows higher absorption in comparison with the individual samples. But further, doubling the amount of nanoparticle and nanoclay shows decrease in UV absorption. Overall, the results of thermal studies show that the incorporation of BaSO₄ and MMT could significantly improve the thermal properties of nanocomposites.     

An innovative extensional viscometer for low-viscosity and low-elasticity liquids

A spinline-type extensional viscometer is described in which an innovative method of tensile stress measurement is employed. A limited amount of liquid flows through a vertical capillary at a constant flow rate under the influence of a constant pressure head. The drainage time decreases when the liquid stream leaving the capillary is stretched by the application of vacuum. These drainage times are measured in a manner similar to that used for intrinsic viscosity measurements. The measured difference in drainage times, with and without stretching, is trivially related to the extensional stress at the capillary exit, and this provides a very simple method of accurately determining fluid stretching forces having a magnitude as low as 10^-4 N; stresses at other axial locations in the stretched liquid jet are obtained by means of a force balance in the usual manner. The validity of the proposed technique is demonstrated by obtaining the expected results for a Newtonian oil having a shear viscosity of 56.2 mPa-s. Also presented are preliminary data on polyethylene oxide-in-water solutions having an even lower shear viscosity.