Numerical Methods for Fractional-Order Fornberg-Whitham Equations in the Sense of Atangana-Baleanu Derivative

In this paper, we investigate the numerical solution of the Fornberg-Whitham equations with the help of two powerful techniques: the modified decomposition technique and the modified variational iteration technique involving fractional-order derivatives with Mittag-Leffler kernel. To confirm and illustrate the accuracy of the proposed approach, we evaluated in terms of fractional order the projected models. Furthermore, the physical attitude of the results obtained has been acquired for the fractional-order different value graphs. The results demonstrated that the future method is easy to implement, highly methodical, and very effective in analyzing the behavior of complicated fractional-order linear and nonlinear differential equations existing in the related areas of applied science.

Physical Implementability of Linear Maps and Its Application in Error Mitigation

Completely positive and trace-preserving maps characterize physically implementable quantum operations. On the other hand, general linear maps, such as positive but not completely positive maps, which can not be physically implemented, are fundamental ingredients in quantum information, both in theoretical and practical perspectives. This raises the question of how well one can simulate or approximate the action of a general linear map by physically implementable operations. In this work, we introduce a systematic framework to resolve this task using the quasiprobability decomposition technique. We decompose a target linear map into a linear combination of physically implementable operations and introduce the physical implementability measure as the least amount of negative portion that the quasiprobability must pertain, which directly quantifies the cost of simulating a given map using physically implementable quantum operations. We show this measure is efficiently computable by semidefinite programs and prove several properties of this measure, such as faithfulness, additivity, and unitary invariance. We derive lower and upper bounds in terms of the Choi operator's trace norm and obtain analytic expressions for several linear maps of practical interests. Furthermore, we endow this measure with an operational meaning within the quantum error mitigation scenario: it establishes the lower bound of the sampling cost achievable via the quasiprobability decomposition technique. In particular, for parallel quantum noises, we show that global error mitigation has no advantage over local error mitigation.

The Numerical Investigation of Fractional-Order Zakharov–Kuznetsov Equations

In this article, a modified method called the Elzaki decomposition method has been applied to analyze time-fractional Zakharov–Kuznetsov equations. In this method, the Adomian decomposition technique and Elzaki transformation are combined. Two problems are investigated to show and validate the efficiency of the suggested method. It is also shown that the solutions achieved from the current producer are in good contact with the exact solutions to show with the help of graphs and table. It is observed that the suggested technique is to be reliable, efficient, and straightforward to implement for many related models of engineering and science.

Kajian pengaruh kondisi dekomposisi analisis logam tembaga dalam sedimen di pelabuhan ikan Sendang Biru secara SSA

Cu that is absorbed in marine sediments can accumulate in the food chain even in small concentrations. Cu analysis in these sediments can be used to analyze water pollution due to human activities. The purpose of this study was to determine the level of Cu in decomposed sediments with variation of solvent concentration, variation of decomposition time, and variation of solvent volume and then compare the result of Cu analysis decomposed using HNO3 solvent under effective condition with aqua regia solvent. The method of analysis used is decomposition technique of sediment sample by using reflux and then analyzed with AAS.. Cu yang terserap dalam sedimen laut dapat berakumulasi dalam rantai makanan meskipun dalam konsentrasi kecil. Analisis Cu dalam sedimen ini dapat digunakan untuk menganalisis pencemaran perairan akibat aktivitas manusia. Tujuan penelitian ini adalah menentukan kadar Cu dalam sedimen yang didekomposisi dengan variasi konsentrasi pelarut, variasi waktu dekomposisi, dan variasi volume pelarut dan membandingkan hasil analisis Cu yang didekomposisi menggunakan pelarut HNO3 pada kondisi efektif dengan pelarut akuaregia. Metode analisis yang digunakan yaitu teknik dekomposisi sampel sedimen dengan menggunakan refluks dan dianalisis dengan SSA.