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Page 1
Fractional generalized Cauchy process.
Uchiyama Y, Kadoya T, Konno H. Uchiyama Y, et al. Phys Rev E. 2019 Mar;99(3-1):032119. doi: 10.1103/PhysRevE.99.032119. Phys Rev E. 2019. PMID: 30999522
This paper presents a fractional generalized Cauchy process (FGCP) with an additive and a multiplicative Gaussian white noise for describing subordinated anomalous fluctuations. The FGCP displays intermittent dynamics on random time durations, whose analytical representati …
This paper presents a fractional generalized Cauchy process (FGCP) with an additive and a multiplicative Gaussian white noise for des …
Application of the Cauchy integral formula as a tool of analytic continuation for the resummation of divergent perturbation series.
Mihálka ZÉ, Szabados Á, Surján PR. Mihálka ZÉ, et al. J Chem Phys. 2019 Jan 21;150(3):031101. doi: 10.1063/1.5083191. J Chem Phys. 2019. PMID: 30660152
Previous attempts to the resummation of divergent power series by means of analytic continuation are improved applying the Cauchy integral formula for complex functions. The idea is tested on divergent Moller-Plesset perturbation expansions of the electron co …
Previous attempts to the resummation of divergent power series by means of analytic continuation are improved applying the Cauchy …
On an Approximate Solution of the Cauchy Problem for Systems of Equations of Elliptic Type of the First Order.
Juraev DA, Shokri A, Marian D. Juraev DA, et al. Entropy (Basel). 2022 Jul 13;24(7):968. doi: 10.3390/e24070968. Entropy (Basel). 2022. PMID: 35885190 Free PMC article.
The focus of this paper is on regularization formulas for solutions to the Cauchy problem. The question of the existence of a solution to the problem is not considered-it is assumed a priori. At the same time, it should be noted that any regularization formula …
The focus of this paper is on regularization formulas for solutions to the Cauchy problem. The question of the existence of a …
Time-dependent propagators for stochastic models of gene expression: an analytical method.
Veerman F, Marr C, Popović N. Veerman F, et al. J Math Biol. 2018 Aug;77(2):261-312. doi: 10.1007/s00285-017-1196-4. Epub 2017 Dec 15. J Math Biol. 2018. PMID: 29247320 Free PMC article.
The requisite procedure consists of three steps: a probability-generating function is introduced which transforms the CME into (a system of) partial differential equations (PDEs); application of the method of characteristics then yields (a system of) ordinary differential equatio …
The requisite procedure consists of three steps: a probability-generating function is introduced which transforms the CME into (a system of) …
Cauchy problem of the generalized Zakharov type system in [Formula: see text].
You S, Ning X. You S, et al. J Inequal Appl. 2017;2017(1):32. doi: 10.1186/s13660-017-1306-2. Epub 2017 Feb 1. J Inequal Appl. 2017. PMID: 28216987 Free PMC article.
We prove the existence and uniqueness of global smooth solutions to the initial value problem in the Sobolev space through making a priori integral estimates and the Galerkin method....
We prove the existence and uniqueness of global smooth solutions to the initial value problem in the Sobolev space through making a priori …
Some Useful Integral Representations for Information-Theoretic Analyses.
Merhav N, Sason I. Merhav N, et al. Entropy (Basel). 2020 Jun 26;22(6):707. doi: 10.3390/e22060707. Entropy (Basel). 2020. PMID: 33286479 Free PMC article.
This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for quantities tha …
This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored …
Kramers problem: numerical Wiener-Hopf-like model characteristics.
Ezin AN, Samgin AL. Ezin AN, et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Nov;82(5 Pt 2):056703. doi: 10.1103/PhysRevE.82.056703. Epub 2010 Nov 3. Phys Rev E Stat Nonlin Soft Matter Phys. 2010. PMID: 21230615
In contrast to the Melnikov approach, which implements factorization through a Cauchy-theorem-based formulation, we employ the Wiener-Levy theorem to reduce the Kramers problem to a Wiener-Hopf sum equation written in terms of Toeplitz matrices. ...For certain conditions, …
In contrast to the Melnikov approach, which implements factorization through a Cauchy-theorem-based formulation, we employ the Wiener …
Magnetic resonance elastography in nonlinear viscoelastic materials under load.
Capilnasiu A, Hadjicharalambous M, Fovargue D, Patel D, Holub O, Bilston L, Screen H, Sinkus R, Nordsletten D. Capilnasiu A, et al. Biomech Model Mechanobiol. 2019 Feb;18(1):111-135. doi: 10.1007/s10237-018-1072-1. Epub 2018 Aug 27. Biomech Model Mechanobiol. 2019. PMID: 30151814 Free PMC article.
In this paper, it is shown how combined knowledge of a material's rheology and loading state can be used to eliminate loading bias and enable interpretation of intrinsic (unloaded) stiffness properties. Equations are derived utilising perturbation theory and Cauchy's …
In this paper, it is shown how combined knowledge of a material's rheology and loading state can be used to eliminate loading bias and enabl …
Generalizing the Boltzmann equation in complex phase space.
Zadehgol A. Zadehgol A. Phys Rev E. 2016 Aug;94(2-1):023316. doi: 10.1103/PhysRevE.94.023316. Epub 2016 Aug 25. Phys Rev E. 2016. PMID: 27627421
The virtual particles, in the present work, are concentrated on virtual "branes" which surround the computational nodes. Employing the Cauchy integral formula, it is shown that certain variations of the "branes," in the complex phase space, do not affect the …
The virtual particles, in the present work, are concentrated on virtual "branes" which surround the computational nodes. Employing the Ca …
A possible analogy between contours in mathematics--as exemplified by Cauchy's integral formula--and contours in the arts.
Gerr S. Gerr S. Perception. 1982;11(4):483-90. doi: 10.1068/p110483. Perception. 1982. PMID: 7182805
The analogy is seen to depend on the fact that both methods use definite values along a contour to imply a totality of values within the contour; thus, the use of a part to suggest the whole, by way of a hypothetical 'gestalt-like integration' in the case of the art contou …
The analogy is seen to depend on the fact that both methods use definite values along a contour to imply a totality of values within the con …
21 results