Numerical scheme and analytical solutions to the stochastic nonlinear advection diffusion dynamical model

In this study, we give the numerical scheme to the stochastic nonlinear advection diffusion equation. This models is considered with white noise (or random process) having same intensity by changing frequencies. Furthermore, the stability and consistency of proposed scheme are also discussed. Moreover, it is concerned about the analytical solutions, the Riccati equation mapping method is adopted. The different families of single (shock and singular) and mixed (complex solitary-shock, shock-singular, and double-singular) form solutions are obtained with the different choices of free parameters. The graphical behavior of solutions is also depicted in 3D and corresponding contours.

Highly dispersive optical soliton perturbation with cubic–quintic–septic law via two methods

The main consideration of this paper is to discuss cubic optical solitons in a polarization-preserving fiber modeled by nonlinear Schrödinger equation (NLSE). We extract the solutions in the forms of hyperbolic, trigonometric including a class of solitary wave solutions like dark, bright–dark, singular, singular periodic, multiple-optical soliton and mixed complex soliton solutions. A recently developed integration tool known as new extended direct algebraic method (NEDAM) is applied to analyze the governing model. Moreover, the studied equation is discussed with two types of nonlinearity. The constraint conditions are explicitly presented for the resulting solutions. The accomplished results show that the applied computational system is direct, productive, reliable and can be carried out in more complicated phenomena.

The Influence of Cayenne Pepper on the Human Gastrointestinal Microbiota and Intestinal Inflammation Among Overweight or Obese Adults

Objectives To identify the impact of cayenne pepper on the diversity of the gut microbiome and inflammatory biomarkers in the stool of adults with overweight or obesity. Methods 31 individuals participated. All participants had a BMI > 25. Most participants were female (64.5%) and averaged 28 ± 8 years of age. Participants consumed two 250 mL servings of tomato juice or tomato juice plus 1.9 grams (0.8 g per dose) of cayenne pepper each day for one week before crossing over to the other study arm. The study design allowed participants to continue eating a mixed, complex diet but sources of capsaicin, the pungent component of cayenne, were to be avoided. Stool samples were collected in the home at the end of each treatment period. DNA was extracted from the stools, 16S rRNA libraries were made, and libraries were sequenced using an Illumina MiSeq. Sequences were processed using mothur, and data were analyzed in R using the vegan package. Results The spice intervention did not increase the richness of gut microbiota nor alter the overall gut microbiota composition at the genus level. However, at the single taxa at the genus level, participants who consumed tomato juice without cayenne had higher abundances of Prevotella and Bacteroides in their stool. Cayenne treatment did not affect either lipocalin or calprotectin levels in the stool. Calprotectin and lipocalin concentrations were positively correlated with each other, but only when participants were consuming cayenne pepper. Neither lipocalin nor calprotectin levels in stool of participants were related to gut microbiota richness or composition. Conclusions There was no detectable impact of the spice treatment on gut microbiota composition or intestinal inflammation in adults with overweight or obesity at the time of treatment. Though these results were unanticipated, given prior results in animal models, these results suggest that research in free-living humans must continue as treatments that are only effective under tightly controlled conditions will be of little use to most individuals. Funding Sources Academy of Nutrition and Dietetics Foundation/McCormick Science Institute as well as by startup funds provided by MSU and the MSU Department of Food Science and Human Nutrition.

Mixed metal oxide pigments

Mixed metal oxide (MMO) pigments, also knowns as complex inorganic color pigments (CICPs), are an important class of inorganic pigments. They are representatives of the blue, green, yellow, brown, and black pigments. These pigments are called mixed complex because they contain two or more different metals in the composition. Their main advantages are high opacity, heat stability, useful infrared properties, light- and weather fastness, and chemical resistance. MMOs are solid solutions of metal oxides, which are homogenously distributed in their crystal lattices. They are based on different types of crystal structures, such as rutile, spinel, inverse spinel, hematite, priderite, and pseudobrookite. Other products belonging to the CICPs besides the rutile and spinel type MMOs are pigments based on zirconium silicate (zircon, ZrSiO4). Such compositions belong to the class of ceramic pigments (color stains for glazes).

Optical solitons and other soluions for Radhakrishnan–Kundu–Lakshmanan equation in birefringent fibers by an efficient computational technique

In this article, we are interested to discuss the exact optical soiltons and other solutions in birefringent fibers modeled by Radhakrishnan-Kundu-Lakshmanan equation in two component form for vector solitons. We extract the solutions in the form of hyperbolic, trigonometric and exponential functions including solitary wave solutions like multiple-optical soliton, mixed complex soliton solutions. The strategy that is used to explain the dynamics of soliton is known as generalized exponential rational function method. Moreover, singular periodic wave solutions are recovered and the constraint conditions for the existence of soliton solutions are also reported. Besides, the physical action of the solution attained are recorded in terms of 3D, 2D and contour plots for distinct parameters. The achieved outcomes show that the applied computational strategy is direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. The primary benefit of this technique is to develop a significant relationships between NLPDEs and others simple NLODEs and we have succeeded in a single move to get and organize various types of new solutions. The obtained outcomes show that the applied method is concise, direct, elementary and can be imposed in more complex phenomena with the assistant of symbolic computations

MIXED COMPLEX COMPOUNDS OF PALMITATE, OLEATE CALCIUM WITH ACETAMIDE, NICOTINAMIDE AND THIOCARBAMIDE

The purpose of the study was the synthesis and study of the structure of mixed complexes of palmitate, calcium oleate with acetamide, nicotinamide and thiocarbamide. The mixed coordination compounds of palmitate and calcium oleate were synthesized. The composition, individuality, thermal behavior, methods of coordinating the palmitate and oleate fragments, acetamide, nicotinamide and thiocarbamide molecules have been established. Comparison of the diffraction patterns of calcium palmitate and oleate, free ligand molecules and synthesized compounds showed the mismatch of the diffractograms, conseqently that the synthesized complexes have an individual crystal lattice different from the starting materials. The method of coordination of amide molecules, the environment of the central ion, are proved by IR spectroscopy. Acetamide molecules are coordinated with the central atom through an oxygen atom, thiocarbamide and nicotinamide

Color-tunable white-light of binary tris-β-diketonate-(Dy3+, Gd3+ ) complexes’ blend under single wavelength excitation

Based on the Dy³⁺-centered yellow-light and the ligands-based blue-light of the iso-structural two complexes [Ln(acac)3(5-Br-2,2′-bpy)] (Ln³⁺ = Dy³⁺ (2) or Gd³⁺ (3); Hacac = acetylacetone, 5-Br-2,2′-bpy = 5-bromo-2,2′-bipyridine), respectively, the stoichiometric fluorescence titrations of their tris-β-diketonate-(Dy³⁺, Gd³⁺x)-mixed complex, show that it is capable of the smooth color-tuning (yellow- to white- and to blue-light) under single wavelength excitation. Moreover, through the dichromatic integration, the binary tris-β-diketonate-(Dy³⁺, Gd³⁺x) complex exhibits the straightforward white-light in solid-state.