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Lie symmetry analysis (LSA) is one of the most common, effective, and estimation-free methods to find the symmetries and solutions of the differential equations (DEs) by following an algorithm. This analysis leads to reduce the order of partial differential equations (PDEs). Many physical problems are converted into non-linear DEs and these DEs or system of DEs are then solved with several methods such as similarity methods, Lie Bäcklund transformation, and Lie group of transformations. LSA is suitable for providing the conservation laws corresponding to Lie point symmetries or Lie Bäcklund symmetries. Short pulse equation (SPE) is a non-linear PDE, used in optical fibers, computer graphics, and physical systems and has been generalized in many directions. We will find the symmetries and a class of solutions depending on one-parameter (ε) obtained from Lie symmetry groups. Then we will construct the optimal system for the Lie algebra and invariant solutions (called similarity solutions) from Lie subalgebras of generalized SPE.

Aquaculture has been expanding in Malaysia due to the increased demand for fish products. In addition, aquaculture faces challenges in maintaining feed suitability in support of the global growth of fish production. Therefore, improvements in diet formulation are necessary to achieve the optimal requirements and attain a desirable growth efficiency and health performance in fish. Seven weeks of study were conducted to compare the equal amounts of different fatty acids (2%) (oleic acid, stearic acid, palmitic acid, and behenic acid) on the survival, the growth, and the immune response of hybrid grouper (Epinephelus fuscoguttatus × Epinephelus lanceolatus) against V. vulnificus. After six weeks of the feeding trial, fish were challenged with V. vulnificus for 30 min before continuing on the same feeding regime for the next seven days (post-bacterial challenge). Fish supplemented with dietary oleic acid showed significantly (p < 0.05) enhanced immune responses, i.e., lysozyme, respiratory burst, and phagocytic activities compared to the control diet group for both pre-and post-bacterial challenges. Following the Vibrio challenge, no significant effects of supplemented fatty acid diets on survival rate were observed, although dietary oleic acid demonstrated the highest 63.3% survival rate compared to only 43.3% of the control diet group. In addition, there were no significant effects (p > 0.05) on specific growth rate (SGR), white blood cell (WBC), and red blood cell (RBC) counts among all experimental diets. The results from this study suggest that among the tested dietary fatty acids, the oleic acid diet showed promising results in the form of elevated immune responses and increased disease resistance of the hybrid grouper fingerlings challenged with V. vulnificus.

The potential of activated carbon as a cheap bioadsorbent prepared from Reptonia buxifolia seeds, for the removal of Pb(II) from wastewater was investigated. The morphology and structure of the prepared activated carbon was characterized using different techniques. Adsorption phenomenon was studied by varying the metal ion concentration, contact time, temperature, and pH, in a batch process. The SEM results showed that the thermal treatment significantly altered the topography of synthesized activated carbon due to formation of numerous pores on the surface of the adsorbent. At equilibrium, the Langmuir model gave a better fit to the adsorption isotherm results than the Freundlich model. Kinetics data indicate that equilibrium is established within the first 60 min. The results showed that activated carbon obtained from seeds of R. buxifolia have the potential to be used as alternative economical biosorbent for the removal of heavy metals from wastewater.

In this paper, we examine q-Bernstein-Bézier surfaces in Minkowski space- R13 with q as the shape parameter. These surfaces, a generalization of Bézier surfaces, have applications in mathematics, computer-aided geometric design, and computer graphics for the surface formation and modeling. We analyze the timelike and spacelike cases of q-Bernstein-Bézier surfaces using known boundary control points. The mean curvature and Gaussian curvature of these q-Bernstein-Bézier surfaces are computed by finding the respective fundamental coefficients. We also investigate the shape operator dependency for timelike and spacelike q-Bernstein-Bézier surfaces in Minkowski space- R13 , and provide biquadratic and bicubic q-Bernstein-Bézier surfaces as illustrative examples for different values of the shape controlling parameter q. [ABSTRACT FROM AUTHOR]

The purpose of this study is to highlight the shallow water wave patterns along the ocean shore or in lakes with the higher-order Boussinesq–Burgers system possessing a fractional derivative operator. A generic fractional transformation is used, which turns the proposed model into an nonlinear ordinary differential equations (NLODEs) system. For the construction of new solitons of the mentioned coupled system, the auxiliary equation technique is employed. This approach produced numerous soliton solutions such as bright, singular and w-shaped solitons of the aforesaid model successfully. These results are expressed graphically to exemplify their physical appearance with the help of soft computations in Mathematica. All the solutions yielded by this method are novel and have not been derived yet. [ABSTRACT FROM AUTHOR]

The idea of this paper is to look some anisotropic star models in a metric f(R)$f(R)$ approach, where R is the Ricci scalar. The Karmarkar and Tolman system is used to analyze the physics of some spherically symmetric stars using two independent computational gravitational theories. The behavior of structural factors is evaluated using diagrams, and the feasibility of compact objects is investigated using boundary conditions for the involved constants. The investigation in the profiles of the effective energy/matter states, the equilibrium phases, and the Tolman‐Oppenheimer‐Volkoff models and stability analysis is performed for various realistic candidates of stars. Under a few important cosmological backgrounds, the assessment of our graphics may offer assistance in the search of the realistic and viable f(R)$f(R)$ gravitational models. [ABSTRACT FROM AUTHOR]

A Coons patch is characterized by a finite set of boundary curves, which are dependent on the choice of blending functions. For a bicubically blended Coons patch (BBCP), the Hermite cubic polynomials (interpolants) are used as blending functions. A BBCP comprises information about its four corner points, including the curvature represented by eight tangent vectors, as well as the twisting behavior determined by the four twist vectors at these corner points. The interior shape of the BBCP depends not only on the tangent vectors at the corner points but on the twist vectors as well. The alteration in the twist vectors at the corner points can change the interior shape of the BBCP even for the same arrangement of tangent vectors at these corner points. In this study, we aim to determine the optimal twist vectors that would make the surface an extremal of the minimal energy functional. To achieve this, we obtain the constraints on the optimal twist vectors (MPDs) of the BBCP for the specified corner points by computing the extremal of the Dirichlet and quasi-harmonic functionals over the entire surface with respect to the twist vectors. These twist vectors can then be used to construct various quasi-minimal and quasi-harmonic BBCP s by varying corner points and tangent vectors. The optimization techniques involve minimizing a functional subject to certain constraints. The methods used to optimize twist vectors of BBCP s can have potential applications in various fields. They can be applied to fuzzy optimal control problems, allowing us to find the solution of complex and uncertain systems with fuzzy constraints. They provide us an opportunity to incorporate symmetry considerations for the partial differential equations associated with minimal surface equations, an outcome of zero-mean curvature for such surfaces. By exploring and utilizing the underlying symmetries, the optimization strategies can be further enhanced in terms of robustness and adaptability. [ABSTRACT FROM AUTHOR]

Road Traffic and Transportation Regulations are a condition of traffic that takes place regularly in accordance with the rights and obligations of each Road User. In this modern era, it is not difficult to do something related to transportation, with an online-based mobile application, it can make it easier for people to access online-based motorcycle taxis. This paper discusses how to implement Article 283 of Law Number 22 of 2009 concerning Road Traffic and Transportation in the City of Gorontalo. This study uses empirical legal research methods which are conducted by collecting data through observation and interviews. The results of this study indicate that the application of Article 283 of Law Number 22 of 2009 to online motorcycle taxi drivers who use mobile phones in Gorontalo City is still not effective. It can be seen from the widespread use of mobile phones while driving on the road, the Gorontalo Police Traffic Unit has taken action and also socialized several motorists who use mobile phones while driving, but this is still being done by online motorcycle taxi drivers. [ABSTRACT FROM AUTHOR]