Abstract In this article, the perturbed Gerdjikov-Ivanov equation, describing the dynamics of propagation of solitons, is studied. The balanced modified extended tanh-function and the non-balanced Riccati-Bernoulli Sub-ODE methods are used for the first time to obtain the new optical solitons of this equation. The obtained results give an accurate interpretation of the propagation of solitons. We performed a comparison between our results and those in the literature. The efficiency of these methods for constructing the exact solutions has been demonstrated. It is shown that these different techniques reduce the large number of calculations.

Abstract In this paper, we propose the method of functional variable for finding soliton solutions of two practical problems arising in electronics, namely, the conformable time-conformable Generalized Zakharov-Kuznetsov equation (GZKE) and the conformable time-conformable Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahoney equation (GZK-BBM). The soliton solutions are expressed by two types of functions which are hyperbolic and trigonometric functions.

Abstract The investigation of the Ginzburg-Landau equation (GLE) has been done to find out and investigate new chirped bright, dark periodic and singular function solutions. For this purpose, we have used the traveling wave hypothesis and the chirp component. From there it was pointed out the constraint relation to the different arbitrary parameters of the GLE. Thereafter, we have employed the improved sub-ODE method to handle the nonlinear ordinary differential equation (NODE). In the paper, the virtue of the used analytical method has been highlighted via new chirped solitary waves. Besides, to emphasize the confrontation between the nonlinearity and dispersion terms, we have investigated the steady state of the newly obtained results. It has been obtained the Modulation instability (MI) gain spectra under the effect of the power incident and the transverse wave number. In our knowledge, these results are new compared to Refs. [28-34], and are going to be helpful to explain physical phenomena.

Abstract This paper studies solitary wave solutions in two-core optical fibers with coupling-coefficient dispersion and intermodal dispersion. To construct bright, dark and W-shape bright solitons, the couple of nonlinear equations describing the pulses propagation along the two-core fiber have been reduced to one equivalent equation. By adopting the traveling-waves hypothesis, exact analytical solutions of the generalized nonlinear equation (GNSE) were obtained by using three relevant mathematical methods, namely, the auxiliary equation method, the modified auxiliary equation method and the sine-Gordon expansion approach. Lastly, the behavior of the soliton solutions was discussed and some contours of the plot evolution of the bright, W-shape bright and dark solitons are obtained.

The concept of virtual cellular manufacturing system (VCMS) is finding acceptance among researchers as an extension to group technology. In fact, in order to realize benefits of cellular manufacturing system in the functional layout, the VCMS creates provisional groups of resources (machines, parts and workers) in the production planning and control system. This paper develops a mathematical model to design the VCMS under a dynamic environment with a more integrated approach where production planning, system reconfiguration and workforce requirements decisions are incorporated. The advantages of the proposed model are as follows: considering the operations sequence, alternative process plans for part types, machine time-capacity, worker time-capacity, cross-training, lot splitting, maximal cell size, balanced workload for cells and workers. An efficient linear programming embedded particle swarm optimization algorithm is used to solve the proposed model. The algorithm searches over the 0-1 integer variables and for each 0-1 integer solution visited; corresponding values of integer variables are determined by solving a linear programming sub-problem using the simplex algorithm. Numerical examples show that the proposed method is efficient and effective in searching for near optimal solutions.

El concepto de sistema de manufactura celular virtual (SMCV) está siendo aceptado entre los investigadores como una extensión de la tecnología de grupos. De hecho, para hacer realidad los beneficios del sistema de manufactura celular en el diseño funcional, el SMCV crea grupos provisionales de recursos (máquinas, partes y trabajadores) en la planificación de la producción y el sistema de control. En el presente trabajo se describe el desarrollo de un modelo matemático para diseñar el SMCV en el marco de un entorno dinámico con un enfoque más integrado en donde se incorporan la planificación de la producción, la reconfiguración del sistema y las decisiones relacionadas con los requisitos de la fuerza de trabajo. Las ventajas del modelo propuesto son las siguientes: considera la secuencia de operaciones, planes de proceso alternativos según los tipos de partes, tiempo de trabajo de la máquina, tiempo de trabajo del trabajador, capacitación mixta, división del trabajo, tamaño máximo de la célula y carga de trabajo balanceada para las células y trabajadores. Para resolver el modelo propuesto se usa un algoritmo eficiente de optimización por enjambre de partículas embebidas de programación lineal. El algoritmo busca en las variables enteras 0-1 y cada variable entera 0-1 visitada; los valores correspondientes de las variables enteras se determinan resolviendo una parte de un problema de programación lineal por medio del algoritmo simple. Mediante ejemplos numéricos se demuestra que el método propuesto es eficiente y efectivo en la búsqueda de soluciones casi óptimas.

Análise das partes aéreas de Chrozophora tinctoria (Euphorbiaceae) através de HPLC preparativa com coluna de fase reversa produziu cinco glicosídeos de flavonóides, quercetina 3-O-rutinosídeo (1, rutina), acacetina 7-O-rutinosídeo (2), apigenina 7-O-b-D-[(6-p-cumaroil)]-glicopiranosídeo (3), apigenina 7-O-b-D-glicopiranosídeo (4) e apigenina 7-O-b-D-[-(3,4-diidroxibenzoil)]-glicopiranosídeo (chamado crozoforina, 5), sendo o último um novo produto natural. As estruturas dessas substâncias foram inequivocamente elucidadas por análise de espectrofotometria de UV com o uso de reagentes de deslocamento, ESIMS, e técnicas de RMN 1D e 2D. A atividade de captura de radicais livres do extrato metanólico (RC50 = 2,24 x 10-1 mg/mL) bem como das substâncias isoladas (1-5) (RC50 = 4,38 x 10-3, 2,26 x 10-2, 7,69 x 10-4, 8,71 x 10-3 e 3,19 x 10-4 mg/mL, respectivamente) foram analisados pelo método DPPH.

Preparative reversed-phase HPLC analysis of the methanol extract of the aerial parts of Chrozophora tinctoria (Euphorbiaceae) yielded five flavonoid glycosides, quercetin 3-O-rutinoside (1, rutin), acacetin 7-O-rutinoside (2), apigenin 7-O-b-D-[(6-p-coumaroyl)]-glucopyranoside (3), apigenin 7-O- b-D-glucopyranoside (4) and apigenin 7-O-b-D-[6-(3,4-dihydroxybenzoyl)]-glucopyranoside (named, chrozophorin, 5), the last one being a new natural product. The structures of these compounds were elucidated unambiguously by UV spectroscopic analyses using shift reagents, ESIMS, and 1D and 2D NMR spectroscopic techniques. The free-radical scavenging activity of the methanol extract (RC50 = 2.24 x 10-1 mg/mL) as well as the isolated compounds (1-5) (RC50 = 4.38 x 10-3, 2.26 x 10-2, 7.69 x 10-4, 8.71 x 10-3 and 3.19 x 10-4 mg/mL, respectively) were assessed by the DPPH assay.