Mawhin’s Continuation Technique for a Nonlinear BVP of Variable Order at Resonance via Piecewise Constant Functions

In this paper, we establish the existence of solutions to a nonlinear boundary value problem (BVP) of variable order at resonance. The main theorem in this study is proved with the help of generalized intervals and piecewise constant functions, in which we convert the mentioned Caputo BVP of fractional variable order to an equivalent standard Caputo BVP at resonance of constant order. In fact, to use the Mawhin’s continuation technique, we have to transform the variable order BVP into a constant order BVP. We prove the existence of solutions based on the existing notions in the coincidence degree theory and Mawhin’s continuation theorem (MCTH). Finally, an example is provided according to the given variable order BVP to show the correctness of results.

Calculations of Complex Chemical Reaction Equilibria using Free Energy Minimization and Arc-Length Continuation

In the present paper, we determine the chemical equilibrium compositions for two combustion reactions involving either hydrazine or propane at fixed high pressure and temperature values using several computational approaches. Then, we compute the chemical equilibria for reacting systems under a multitude of temperature and pressure conditions and various initial system compositions. These sensitivity analyses are based on a combination of the method of Lagrangian multipliers and the arc-length continuation technique. Indeed, three industrially relevant case studies are elucidated: (1) the synthesis of ammonia using the Haber process, (2) the gasification of a typical biomass surrogate: glucose using steam and (3) the gasification of cellulose using steam. For all the above reacting systems, our results are benchmarked against their counterparts obtained either from the ubiquitous process simulator: ASPEN-Plus® or from data available in the open literature.

Inverse Source Problem for a Multiterm Time-Fractional Diffusion Equation with Nonhomogeneous Boundary Condition

This paper is devoted to identify a space-dependent source function in a multiterm time-fractional diffusion equation with nonhomogeneous boundary condition from a part of noisy boundary data. The well-posedness of a weak solution for the corresponding direct problem is proved by the variational method. We firstly investigate the uniqueness of an inverse initial problem by the analytic continuation technique and the Laplace transformation. Then, the uniqueness of the inverse source problem is derived by employing the fractional Duhamel principle. The inverse problem is solved by the Levenberg-Marquardt regularization method, and an approximate source function is found. Numerical examples are provided to show the effectiveness of the proposed method in one- and two-dimensional cases.

KESANTUNAN BERBAHASA PADA PERIBAHASA INDONESIA BERMAKNA SINDIRAN: KAJIAN PRAGMATIK

Immoral problems at the form of sarkasme which is identical with behavior insinuate in have leanguage, pushing research qualitative this to identify form proverb of Indonesian have a meaning of insinuation, to descirbe his context and meaning, and also obedient to describe of suavity principles hanve language at proverb of Indonesian have a meaning of insinuation. The target reached to pass method correct reading with descriptive approach qualitative. Source of data in this research refer at proverb dictionary in application of offline Fifth KBBI Edition and also dictionary print Proverb and Poetry Indonesia as other source. Proverb data have a meaning of insinuation mustered to pass documentation technique, continuation technique correct reading free entangle to speak, and technique note. Authenticity of data gathered data, to be strived with testing credibility through range of time in lengthening of peroeption, durability of fokus aa make up of assidinity, and triangulation of is source of data. Here in after analyse data done with technique link to conpare to equalize and link to compare to differentiate which is mustered in method correspond extralingual. This research yield proverb from have a meaning of insinuation pursuant to classification theory of majas marginally, among others form oposition of contradiction type, coherent of repetation type, retoris, and climax, and also comparison of supposing type of word, symbolic, and comparison of diction. Third of the form both of the same aim to the strengthen insinuation meaning in proverb. Besides, yielded also proverb meaning and context have a meaning of insinuation influenced by relation at the opposite of its of him which share to assist interpretation of used association. Context and the meaning constitute obediently of suavity principles have language of Leech at proverb of insinuation, proven of teared meaning which implied by figurative language, at the same time become marker of principal bowing to interest as elementary principle which obeyed by proverb of insinuation. Proven other obedient at humility principle, wise, and praise.

Radiative correction to the Casimir energy for Lorentz-violating scalar field in d + 1 dimensions

The renormalization program in every renormalized theory should run consistently with the type of boundary condition imposed on quantum fields. To maintain this consistency, the counterterms usually appear in the position-dependent form. In this study, using such counterterms, we calculated the radiative correction to the Casimir energy for massive and massless Lorentz-violating scalar field constrained with Dirichlet boundary condition between two parallel plates in [Formula: see text] spatial dimensions. In the calculation procedure, to remove infinities appearing in the vacuum energies, the box subtraction scheme (BSS) supplemented by the cutoff regularization technique and analytic continuation technique was employed. Normally, in the BSS, two similar configurations are defined and their vacuum energies are subtracted from each other in the appropriate limits. Our final results regarding all spatial dimensions were convergent and consistent with the expected physical basis. We further plotted the Casimir energy density for the time-like and space-like Lorentz-violating systems in a number of odd and even dimensions; multiple aspects of the obtained results were ultimately discussed.

Inversion of the Initial Value for a Time-Fractional Diffusion-Wave Equation by Boundary Data

In this study, we consider an inverse problem of recovering the initial value for a multi-dimensional time-fractional diffusion-wave equation. By using some additional boundary measured data, the uniqueness of the inverse initial value problem is proven by the Laplace transformation and the analytic continuation technique. The inverse problem is formulated to solve a Tikhonov-type optimization problem by using a finite-dimensional approximation. We test four numerical examples in one-dimensional and two-dimensional cases for verifying the effectiveness of the proposed algorithm.

A Continuation Procedure for the Quasi-Static Analysis of Materially and Geometrically Nonlinear Structural Problems

Discussed is the implementation of a continuation technique for the analysis of nonlinear structural problems, which is capable of accounting for geometric and dissipative requirements. The strategy can be applied for solving quasi-static problems, where nonlinearities can be due to geometric or material response. The main advantage of the proposed approach relies in its robustness, which can be exploited for tracing the equilibrium paths for problems characterized by complex responses involving the onset and propagation of cracks. A set of examples is presented and discussed. For problems involving combined material and geometric nonlinearties, the results illustrate the advantages of the proposed hybrid continuation technique in terms of efficiency and robustness. Specifically, less iterations are usually required with respect to similar procedures based on purely geometric constraints. Furthermore, bifurcation plots can be easily traced, furnishing the analyst a powerful tool for investigating the nonlinear response of the structure at hand.

Vibration of composite thin-walled beams with variable open cross section by a high order implicit algorithm

In this work, we study the forced nonlinear vibrations with large amplitude and large torsion of composite thinwalled beams with open variable cross sections under external dynamic loads using a high order implicit algorithm. The used algorithm is based on the temporal and spatial discretizations, the homtopoy transformation, Taylor series expansion and the continuation technique. A 3D beam element with two nodes and seven degrees of freedom per node is adopted. The obtained results are compared with those computed by the industriel Abaqus code.