Optical closed form soliton structures for the Kuralay-II equation in nonlinear optical complex media. [PDF]
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Determining Olefin Content of Gasoline by Adaptive Partial Least Squares Regression Combined with Near-Infrared Spectroscopy. [PDF]
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Deep learning model for screening causes of activated partial thromboplastin time prolongation using clot waveform analysis at multiple wavelengths. [PDF]
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Moiré-Induced Electronic Reconstruction in van der Waals Heterobilayer PtSe<sub>2</sub>/PtTe<sub>2</sub>. [PDF]
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Partial Derivatives and Applications
2021This chapter collects problems on partial derivatives and their applications, the Jacobian and the Hessian matrices, differential operators, the chain rule, homogeneous functions and Euler’s identity, Taylor’s formula for functions of two variables, as well as extrema of functions of several variables.
Alina Sîntămărian, Ovidiu Furdui
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For the fundamental solutions of heat-type equations of order n we give a general stochastic representation in terms of damped oscillations with generalized gamma distributed parameters. By composing the pseudo-process X-m related to the higher-order heat-type equation with positively skewed stable r.v.'s T-1/3(j), j = 1, 2, . . . , n we obtain genuine
ORSINGHER, Enzo, D'OVIDIO, MIRKO
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Partial stabilities and partial derivations of -variable functions
Nonlinear Analysis: Theory, Methods & Applications, 2010The authors introduce the notion of the partial derivations of an \(n\)-variable function from a normed algebra \({\mathcal{A}}_1 \times {\mathcal{A}}_1 \times \cdots \times {\mathcal{A}}_n\) into a Banach algebra \({\mathcal{B}}\). Using this notion, they prove the Hyers-Ulam-Rassias stability for the partial derivations.
Chu H.-Y., Ku S.-H., Park J.-S.
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Partial Derivatives. Applications
1985A function f is a mapping which takes each element of the domain D into an element of the range S. We write f: D → S. If the domain D consists of ordered pairs of numbers, then we have a function on R e or a function of two variables.
Murray H. Protter, Charles B. Morrey
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