A note on an approximate lagrange multiplier rule

In this note we show that for a large class of optimization problems, the Lagrange multiplier rule can be derived from the approximate multiplier rule.     

Incorporating one-way substitution policy into the newsboy problem with imprecise customer demand

This paper presents an approach for solving an inventory model for single-period products with maximizing its expected profit in a fuzzy environment, in which the retailer has the opportunity for substitution. Though various structures of substitution arise in real life, in this study we consider the fuzzy model for two-item with one-way substitution policy. This one-way substitutability is reasonable when the products can be stored according to certain attribute levels such as quality, brand or package size. Again, to describe uncertainty usually probability density functions are being used. However, there are many situations in real world that utilize knowledge-based information to describe the uncertainty. The objective of this study is to provide an analysis of single-period inventory model in a fuzzy environment that enables us to compute the expected resultant profit under substitution. An efficient numerical search procedure is provided to identify the optimal order quantities, in which the utilization of imprecise demand and the use of one-way substitution policy increase the average expected profit. The benefit of product substitution is illustrated through numerical example.     

Composites of hydrophilic polymers and organic nanocrystals enable enhanced robustness

We describe a new family of composite materials, polymer/organic nanocrystal (ONC) hybrids. These were prepared from soluble ONCs based on perylene diimides (PDI) and water‐soluble polymers (sodium alginate and polyvinyl alcohol). Polymer/ONC films were characterized by optical spectroscopy, electron microscopy, and tensile strength studies. The films show enhanced chemical and mechanical stability due to synergy between the constituents. The hybrid films are stable in both water and organic solvents, unlike the individual components. The ONCs we employed possess nonlinear optical activity (second harmonic generation, SHG); they showed improved photostability (stable SHG under laser light) in the hybrids. Tensile strength enhancement (as high as twofold in the film having just 2.4% ONCs by weight) was observed as revealed by mechanical measurements. Hybrids with aligned ONCs were also prepared using simple extrusion via syringe needle followed by gelation. Employing ONCs in polymeric hybrid materials enables facile fabrication in aqueous media, synergy, chemical, mechanical, and photostability as well as useful photofunction (SHG), introducing a versatile class of composite materials.     

An overview on the recent developments in polyaniline‐based supercapacitors

With the ever‐increasing depletion of nonrenewable fossil fuel reserve, greater attention has been directed towards renewable energy storage devices. One of the most important of such devices is the supercapacitor, which exhibits high specific capacitance. Polyaniline (PAni) is a versatile conducting polymer, which has demonstrated excellent electrochemical properties along with good stability and ease of synthesis. Therefore, PAni has been extensively used in the fabrication of supercapacitors. In the last few decades, researchers have studied the effect of morphology, developed during the synthesis of PAni, on its electrochemical properties. It is known that the electrical conductivity and the electrochemical properties of PAni get influenced by the level and type of dopant used, the method of synthesis adopted, and the surface area and porosity possessed. However, it has been realized that supercapacitors based on PAni suffer from short cycle life. This led to development of PAni composites with carbon‐based materials and transition metal oxides. In this review, focus has been laid on the achieved performance levels of the recently developed PAni‐based supercapacitors. In addition, an attempt has been made to study the fundamental aspects of the conductivity and the electrochemical properties of PAni and their effect on the supercapacitor performance. Moreover, several new interesting applications of PAni‐based supercapacitors have also been included in this review.     

Review on augmentation in photocatalytic activity of CoFe2O4 via heterojunction formation for photocatalysis of organic pollutants in water

In previous years, cobalt ferrite has gained huge consideration in the field of semiconductor photocatalysis for waste water treatment. Cobalt ferrite and its derivatives own tunable magnetic properties which results in higher absorption capability in comparison with other photocatalyst semiconductors. In the current review, a brief overview of CoFe₂O₄ as a semiconductor photocatalyst is presented and ferromagnetic behaviour of CoFe₂O₄ is also discussed. Few drawbacks such as agglomeration, photocorrosion and recombination rate of electrons-holes are also discussed. For the enhancement of photocatalytic action of cobalt ferrite, the role of cobalt ferrite with type I, type II, direct Z-scheme, solid state Z-scheme heterojunctions, Schottky and p-n heterojunctions based on different heterostructures were also discussed. In conclusive outlook formation of cobalt ferrite based heterojunctions is best approach for the enhancement of photocatalytic performance. This is because heterojunction formation enhanced the rate of charge separation and thus reduced the electron–hole recombination. Herein, this review highlights the CoFe₂O₄ based heterojunctions for the photodegradation of noxious organic pollutants in water. Furthermore, the future expectations and challenges in exploiting CoFe₂O₄ nanocomposites for water treatment, also discussed in precise conclusion of this review.     

Dark Energy Accretion onto Van der Waal's Black Hole

We consider the most general static spherically symmetric black hole metric. The accretion of the fluid flow around the Van der Waal's black hole is investigated and we calculate the fluid's four-velocity, the critical point and the speed of sound during the accretion process. We also analyze the nature of the universe's density and the mass of the black hole during accretion of the fluid flow. The density of the fluid flow is also taken into account. We observe that the mass is related to redshift. We compare the accreting power of the Van der Waal's black hole with Schwarzschild black hole for different accreting fluid.     

Unraveling the Homologation Reaction Sequence of the Zeolite‐Catalyzed Ethanol‐to‐Hydrocarbons Process

Although industrialized, the mechanism for catalytic upgrading of bioethanol over solid‐acid catalysts (that is, the ethanol‐to‐hydrocarbons (ETH) reaction) has not yet been fully resolved. Moreover, mechanistic understanding of the ETH reaction relies heavily on its well‐known “sister‐reaction” the methanol‐to‐hydrocarbons (MTH) process. However, the MTH process possesses a C₁‐entity reactant and cannot, therefore, shed any light on the homologation reaction sequence. The reaction and deactivation mechanism of the zeolite H‐ZSM‐5‐catalyzed ETH process was elucidated using a combination of complementary solid‐state NMR and operando UV/Vis diffuse reflectance spectroscopy, coupled with on‐line mass spectrometry. This approach establishes the existence of a homologation reaction sequence through analysis of the pattern of the identified reactive and deactivated species. Furthermore, and in contrast to the MTH process, the deficiency of any olefinic‐hydrocarbon pool species (that is, the olefin cycle) during the ETH process is also noted.     

Self-organized nanostructure formation on the graphite surface induced by helium ion irradiation

The effects of helium ion irradiation on the graphite surface are studied by employing a plasma focus device. The device emits helium ion pulse having energies in the range of a few keV to a few MeV and flux on the order of 10²⁵ m^?2?s^?1 at 60 mm axial position from the anode tip. The field emission scanning electron microscopy confirms the formation of multi-modal spherical and elongated agglomerated structures on irradiated samples surface with increase in agglomerate size with increasing number of irradiation shots. The transient annealing in each irradiation was not enough to cause the Oswald ripening or sintering of particles into bigger particle or crystal size but only resulted in clustering. The atomic force micrographs reveal an increase in average surface roughness with increasing ion irradiation. The Raman study demonstrates increase in disordered D peak along with reduced crystallite size ($L_a$) with increasing number of irradiation shots.     

A Flat-Gain Double-Pass Amplifier with New Hafnia-Bismuth-Erbium Codoped Fiber

An efficient and compact double-pass optical fiber amplifier is demonstrated using a newly developed hafnia bismuth erbium co-doped fiber(HBEDF) as a gain medium. The HBEDF is fabricated using a modified chemical vapor deposition in conjunction with solution doping. The fiber has an erbium ion concentration of 12500 ppm.At the optimum length of 0.5 m, the HBEDF amplifier(HBEDFA) achieves a flat gain of 26 d B with a gain variation of less than 1.5 d B within a wavelength region from 1530 to 1560 nm when the input signal and pump power are fixed at-30 d Bm and 140 m W, respectively. On the other hand, at the input signal power of-10 d Bm,the HBEDFA also achieves a flat gain of 14.2 d B with a gain variation of less than 2.5 d B within a wide wavelength region from 1525 to 1570 nm. Compared with the conventional zirconia erbium co-doped fiber based amplifier,the proposed HBEDFA obtains a more efficient gain and lower noise figure. For an input signal of-30 d Bm, the gain improvements of 6.2 d B and 4.8 d B are obtained at 1525 nm and 1540 nm, respectively.