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Journal articles on the topic '1-Laplace'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

Xuan, Haiyan, Lixin Song, Muhammad Amin, and Yongxia Shi. "Quasi-maximum likelihood estimator of Laplace (1, 1) for GARCH models." Open Mathematics 15, no. 1 (December 29, 2017): 1539–48. http://dx.doi.org/10.1515/math-2017-0131.

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Abstract This paper studies the quasi-maximum likelihood estimator (QMLE) for the generalized autoregressive conditional heteroscedastic (GARCH) model based on the Laplace (1,1) residuals. The QMLE is proposed to the parameter vector of the GARCH model with the Laplace (1,1) firstly. Under some certain conditions, the strong consistency and asymptotic normality of QMLE are then established. In what follows, a real example with Laplace and normal distribution is analyzed to evaluate the performance of the QMLE and some comparison results on the performance are given. In the end the proofs of some theorem are presented.

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2

CHANG, KUNG CHING. "THE SPECTRUM OF THE 1-LAPLACE OPERATOR." Communications in Contemporary Mathematics 11, no. 05 (October 2009): 865–94. http://dx.doi.org/10.1142/s0219199709003570.

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The eigenfunction of the 1-Laplace operator is defined to be a critical point in the sense of the strong slope for a nonsmooth constraint variational problem. We completely write down all these eigenfunctions for the 1-Laplace operator on intervals.

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3

Littig, Samuel, and Friedemann Schuricht. "Perturbation results involving the 1-Laplace operator." Advances in Calculus of Variations 12, no. 3 (July 1, 2019): 277–302. http://dx.doi.org/10.1515/acv-2017-0006.

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AbstractWe consider perturbed eigenvalue problems of the 1-Laplace operator and verify the existence of a sequence of solutions. It is shown that the eigenvalues of the perturbed problem converge to the corresponding eigenvalue of the unperturbed problem as the perturbation becomes small. The results rely on nonsmooth critical point theory based on the weak slope.

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4

Aravkin, Aleksandr Y., Bradley M. Bell, James V. Burke, and Gianluigi Pillonetto. "An $\ell _{1}$-Laplace Robust Kalman Smoother." IEEE Transactions on Automatic Control 56, no. 12 (December 2011): 2898–911. http://dx.doi.org/10.1109/tac.2011.2141430.

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5

Dyer. "Inverse laplace transformation of rational functions. 1." IEEE Instrumentation and Measurement Magazine 9, no. 6 (October 2006): 13–15. http://dx.doi.org/10.1109/mim.2006.1708344.

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6

Yavuz, Mehmet, and Necati Ozdemir. "Numerical inverse Laplace homotopy technique for fractional heat equations." Thermal Science 22, Suppl. 1 (2018): 185–94. http://dx.doi.org/10.2298/tsci170804285y.

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In this paper, we have aimed the numerical inverse Laplace homotopy technique for solving some interesting 1-D time-fractional heat equations. This method is based on the Laplace homotopy perturbation method, which is combined form of the Laplace transform and the homotopy perturbation method. Firstly, we have applied to the fractional 1-D PDE by using He?s polynomials. Then we have used Laplace transform method and discussed how to solve these PDE by using Laplace homotopy perturbation method. We have declared that the proposed model is very efficient and powerful technique in finding approximate solutions to the fractional PDE.

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7

Kahsay, Hafte Amsalu, Adnan Khan, Sajjad Khan, and Kahsay Godifey Wubneh. "Fractional Operators Associated with the ք -Extended Mathieu Series by Using Laplace Transform." Advances in Mathematical Physics 2021 (June 8, 2021): 1–7. http://dx.doi.org/10.1155/2021/5523509.

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In this paper, our leading objective is to relate the fractional integral operator known as P δ -transform with the ք -extended Mathieu series. We show that the P δ -transform turns to the classical Laplace transform; then, we get the integral relating the Laplace transform stated in corollaries. As corollaries and consequences, many interesting outcomes are exposed to follow from our main results. Also, in this paper, we have converted the P δ -transform into a classical Laplace transform by changing the variable ln δ − 1 s + 1 / δ − 1 ⟶ s ; then, we get the integral involving the Laplace transform.

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8

Ovchintsev, M. P., and E. G. Sitnikova. "Eigenfunction of the Laplace operator in +1-dimentional simplex." Vestnik MGSU, no. 11 (November 2014): 68–73. http://dx.doi.org/10.22227/1997-0935.2014.11.68-73.

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9

KRUGLIKOV, BORIS. "LAPLACE TRANSFORMATION OF LIE CLASS ω = 1 OVERDETERMINED SYSTEMS." Journal of Nonlinear Mathematical Physics 18, no. 4 (January 2011): 583–611. http://dx.doi.org/10.1142/s1402925111001805.

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10

Pashaei, Ronak, Mohammad Sadegh Asgari, and Amir Pishkoo. "Conformable Derivatives in Laplace Equation and Fractional Fourier Series Solution." International Annals of Science 9, no. 1 (November 7, 2019): 1–7. http://dx.doi.org/10.21467/ias.9.1.1-7.

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In this paper the solution of conformable Laplace equation, \frac{\partial^{\alpha}u(x,y)}{\partial x^{\alpha}}+ \frac{\partial^{\alpha}u(x,y)}{\partial y^{\alpha}}=0, where 1 < α ≤ 2 has been deduced by using fractional fourier series and separation of variables method. For special cases α =2 (Laplace's equation), α=1.9, and α=1.8 conformable fractional fourier coefficients have been calculated. To calculate coefficients, integrals are of type "conformable fractional integral".

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11

KAWOHL, BERND, and FRIEDEMANN SCHURICHT. "DIRICHLET PROBLEMS FOR THE 1-LAPLACE OPERATOR, INCLUDING THE EIGENVALUE PROBLEM." Communications in Contemporary Mathematics 09, no. 04 (August 2007): 515–43. http://dx.doi.org/10.1142/s0219199707002514.

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We consider a number of problems that are associated with the 1-Laplace operator Div (Du/|Du|), the formal limit of the p-Laplace operator for p → 1, by investigating the underlying variational problem. Since corresponding solutions typically belong to BV and not to [Formula: see text], we have to study minimizers of functionals containing the total variation. In particular we look for constrained minimizers subject to a prescribed [Formula: see text]-norm which can be considered as an eigenvalue problem for the 1-Laplace operator. These variational problems are neither smooth nor convex. We discuss the meaning of Dirichlet boundary conditions and prove existence of minimizers. The lack of smoothness, both of the functional to be minimized and the side constraint, requires special care in the derivation of the associated Euler–Lagrange equation as necessary condition for minimizers. Here the degenerate expression Du/|Du| has to be replaced by a suitable vector field [Formula: see text] to give meaning to the highly singular 1-Laplace operator. For minimizers of a large class of problems containing the eigenvalue problem, we obtain the surprising and remarkable fact that in general infinitely many Euler–Lagrange equations have to be satisfied.

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12

Grinfeld, Pavel, and Gilbert Strang. "Laplace eigenvalues on regular polygons: A series in 1/N." Journal of Mathematical Analysis and Applications 385, no. 1 (January 2012): 135–49. http://dx.doi.org/10.1016/j.jmaa.2011.06.035.

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13

Shirakawa, Ken. "Asymptotic convergence ofp-Laplace equationswith constraint asp tends to 1." Mathematical Methods in the Applied Sciences 25, no. 9 (2002): 771–93. http://dx.doi.org/10.1002/mma.314.

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14

Zhao, Lin. "Monotonicity and symmetry of positive solution for 1-Laplace equation." AIMS Mathematics 6, no. 6 (2021): 6255–77. http://dx.doi.org/10.3934/math.2021367.

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15

Chen, Jing-Bo. "Dispersion analysis of an average-derivative optimal scheme for Laplace-domain scalar wave equation." GEOPHYSICS 79, no. 2 (March 1, 2014): T37—T42. http://dx.doi.org/10.1190/geo2013-0230.1.

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Laplace-domain modeling is an important foundation of Laplace-domain full-waveform inversion. However, dispersion analysis for Laplace-domain numerical schemes has not been completely established. This hampers the construction and optimization of Laplace-domain modeling schemes. By defining a pseudowavelength as a scaled skin depth, I establish a method for Laplace-domain numerical dispersion analysis that is parallel to its frequency-domain counterpart. This method is then applied to an average-derivative nine-point scheme for Laplace-domain scalar wave equation. Within the relative error of 1%, the Laplace-domain average-derivative optimal scheme requires four grid points per smallest pseudowavelength, whereas the classic five-point scheme requires 13 grid points per smallest pseudowavelength for general directional sampling intervals. The average-derivative optimal scheme is more accurate than the classic five-point scheme for the same sampling intervals. By using much smaller sampling intervals, the classic five-point scheme can approach the accuracy of the average-derivative optimal scheme, but the corresponding cost is much higher in terms of storage requirement and computational time.

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16

KHAIRUN NISA, RAHMI, ZULAKMAL ZULAKMAL, and MUHAFZAN MUHAFZAN. "SOLUSI PERSAMAAN DIFERENSIAL FRAKSIONAL NONHOMOGEN." Jurnal Matematika UNAND 10, no. 2 (April 29, 2021): 202. http://dx.doi.org/10.25077/jmu.10.2.202-209.2021.

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. Dalam makalah ini diselesaikan persamaan diferensial fraksional nonhomogen untuk α ∈ (0, 1) dengan turunan tipe Caputo menggunakan metode transformasi Laplace. Beberapa contoh yang mengilustrasikan teorema utama disajikan.Kata Kunci: Persamaan Diferensial Fraksional Nonhomogen, Turunan Tipe Caputo, Transformasi Laplace.

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17

De Micheli, Enrico. "On the Connection between Spherical Laplace Transform and Non-Euclidean Fourier Analysis." Mathematics 8, no. 2 (February 20, 2020): 287. http://dx.doi.org/10.3390/math8020287.

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We prove that, if the coefficients of a Fourier–Legendre expansion satisfy a suitable Hausdorff-type condition, then the series converges to a function which admits a holomorphic extension to a cut-plane. Next, we introduce a Laplace-type transform (the so-called Spherical Laplace Transform) of the jump function across the cut. The main result of this paper is to establish the connection between the Spherical Laplace Transform and the Non-Euclidean Fourier Transform in the sense of Helgason. In this way, we find a connection between the unitary representation of SO ( 3 ) and the principal series of the unitary representation of SU ( 1 , 1 ) .

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18

Scricciolo, Catia. "Bayes and maximum likelihood for $$L^1$$ L 1 -Wasserstein deconvolution of Laplace mixtures." Statistical Methods & Applications 27, no. 2 (September 15, 2017): 333–62. http://dx.doi.org/10.1007/s10260-017-0400-4.

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19

Alzaid, Abdulhamid, Jee Soo Kim, and Frank Proschan. "Laplace ordering and its applications." Journal of Applied Probability 28, no. 1 (March 1991): 116–30. http://dx.doi.org/10.2307/3214745.

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Two arbitrary life distributions F and G can be ordered with respect to their Laplace transforms. We say is Laplace-smaller than for all s > 0. Interpretations of this ordering concept in reliability, operations research, and economics are described. General preservation properties are presented. Using these preservation results we derive useful inequalities and discuss their applications to M/G/1 queues, time series, coherent systems, shock models and cumulative damage models.

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20

Alzaid, Abdulhamid, Jee Soo Kim, and Frank Proschan. "Laplace ordering and its applications." Journal of Applied Probability 28, no. 01 (March 1991): 116–30. http://dx.doi.org/10.1017/s0021900200039474.

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Two arbitrary life distributions F and G can be ordered with respect to their Laplace transforms. We say is Laplace-smaller than for all s > 0. Interpretations of this ordering concept in reliability, operations research, and economics are described. General preservation properties are presented. Using these preservation results we derive useful inequalities and discuss their applications to M/G/1 queues, time series, coherent systems, shock models and cumulative damage models.

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21

Abate, Joseph, and Ward Whitt. "Transient behavior of the M/M/1 queue via Laplace transforms." Advances in Applied Probability 20, no. 01 (March 1988): 145–78. http://dx.doi.org/10.1017/s0001867800017985.

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This paper shows how the Laplace transform analysis of Bailey (1954), (1957) can be continued to yield additional insights about the time-dependent behavior of the queue-length process in theM/M/1 model. A transform factorization is established that leads to a decomposition of the first moment as a function of time into two monotone components. This factorization facilitates developing approximations for the moments and determining their asymptotic behavior as. All descriptions of the transient behavior are expressed in terms of basic building blocks such as the first-passage-time distributions. The analysis is facilitated by appropriate scaling of space and time so that regulated or reflected Brownian motion (RBM) appears as the special case in which the traffic intensity ρ equals the critical value 1. An operational calculus is developed for obtainingM/M/1 results directly from corresponding RBM results as well as vice versa. The analysis thus provides useful insight about RBM approximations for queues.

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22

Milbers, Zoja, and Friedemann Schuricht. "Existence of a sequence of eigensolutions for the 1-Laplace operator." Journal of the London Mathematical Society 82, no. 1 (May 31, 2010): 74–88. http://dx.doi.org/10.1112/jlms/jdq012.

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23

Abate, Joseph, and Ward Whitt. "Transient behavior of the M/M/1 queue via Laplace transforms." Advances in Applied Probability 20, no. 1 (March 1988): 145–78. http://dx.doi.org/10.2307/1427274.

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This paper shows how the Laplace transform analysis of Bailey (1954), (1957) can be continued to yield additional insights about the time-dependent behavior of the queue-length process in the M/M/1 model. A transform factorization is established that leads to a decomposition of the first moment as a function of time into two monotone components. This factorization facilitates developing approximations for the moments and determining their asymptotic behavior as . All descriptions of the transient behavior are expressed in terms of basic building blocks such as the first-passage-time distributions. The analysis is facilitated by appropriate scaling of space and time so that regulated or reflected Brownian motion (RBM) appears as the special case in which the traffic intensity ρ equals the critical value 1. An operational calculus is developed for obtaining M/M/1 results directly from corresponding RBM results as well as vice versa. The analysis thus provides useful insight about RBM approximations for queues.

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24

Scheven, Christoph, and Thomas Schmidt. "BV supersolutions to equations of 1-Laplace and minimal surface type." Journal of Differential Equations 261, no. 3 (August 2016): 1904–32. http://dx.doi.org/10.1016/j.jde.2016.04.015.

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25

Segura de León, Sergio, and Claudete M. Webler. "Global existence and uniqueness for the inhomogeneous 1-Laplace evolution equation." Nonlinear Differential Equations and Applications NoDEA 22, no. 5 (April 4, 2015): 1213–46. http://dx.doi.org/10.1007/s00030-015-0320-7.

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26

Wang, Fu Wei, and Bing Wei Mao. "Fluid Model Driven by an M/M/1 Queue with Set-Up and Close-Down Period." Applied Mechanics and Materials 513-517 (February 2014): 3377–80. http://dx.doi.org/10.4028/www.scientific.net/amm.513-517.3377.

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The fluid model driven by an M/M/1 queue with set-up and close-down period is studied. The Laplace transform of the joint stationary distribution of the fluid model is of matrix geometric structure. With matrix geometric solution method, the Laplace-Stieltjes transformation of the stationary distribution of the buffer content is obtained, as well as the mean buffer content. Finally, with some numerical examples, the effect of the parameters on mean buffer content is presented.

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27

Wang, Xiongrui, Ruofeng Rao, and Shouming Zhong. "LMI Approach to Stability Analysis of Cohen-Grossberg Neural Networks withp-Laplace Diffusion." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/523812.

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The nonlinearp-Laplace diffusion (p>1) was considered in the Cohen-Grossberg neural network (CGNN), and a new linear matrix inequalities (LMI) criterion is obtained, which ensures the equilibrium of CGNN is stochastically exponentially stable. Note that, ifp=2,p-Laplace diffusion is just the conventional Laplace diffusion in many previous literatures. And it is worth mentioning that even ifp=2, the new criterion improves some recent ones due to computational efficiency. In addition, the resulting criterion has advantages over some previous ones in that both the impulsive assumption and diffusion simulation are more natural than those of some recent literatures.

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28

Bekollé, David, and Aline Bonami. "Hausdorff-Young inequalities for functions in Bergman spaces on tube domains." Proceedings of the Edinburgh Mathematical Society 41, no. 3 (October 1998): 553–66. http://dx.doi.org/10.1017/s001309150001988x.

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We prove that the functions of the Bergman spaces Ap on tube domains may be written as Laplace transforms of functions when 1 ≤ p ≤ 2. We give in this context a generalization of the Hausdorff–Young inequality with the exact constant, and deduce from the case p = 2 the expression of the Bergman kernel as a Laplace transform.

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29

Bertsimas, Dimitris J., Julian Keilson, Daisuke Nakazato, and Hongtao Zhang. "Transient and busy period analysis of the GIG/1 Queue as a Hilbert factorization problem." Journal of Applied Probability 28, no. 4 (December 1991): 873–85. http://dx.doi.org/10.2307/3214690.

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In this paper we find the waiting time distribution in the transient domain and the busy period distribution of the GI G/1 queue. We formulate the problem as a two-dimensional Lindley process and then transform it to a Hilbert factorization problem. We achieve the solution of the factorization problem for the GI/R/1, R/G/1 queues, where R is the class of distributions with rational Laplace transforms. We obtain simple closed-form expressions for the Laplace transforms of the waiting time distribution and the busy period distribution. Furthermore, we find closed-form formulae for the first two moments of the distributions involved.

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30

Bertsimas, Dimitris J., Julian Keilson, Daisuke Nakazato, and Hongtao Zhang. "Transient and busy period analysis of the GI G/1 Queue as a Hilbert factorization problem." Journal of Applied Probability 28, no. 04 (December 1991): 873–85. http://dx.doi.org/10.1017/s0021900200042789.

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In this paper we find the waiting time distribution in the transient domain and the busy period distribution of the GI G/1 queue. We formulate the problem as a two-dimensional Lindley process and then transform it to a Hilbert factorization problem. We achieve the solution of the factorization problem for the GI/R/1, R/G/1 queues, where R is the class of distributions with rational Laplace transforms. We obtain simple closed-form expressions for the Laplace transforms of the waiting time distribution and the busy period distribution. Furthermore, we find closed-form formulae for the first two moments of the distributions involved.

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31

ELMOATAZ, A., X. DESQUESNES, and M. TOUTAIN. "On the game p-Laplacian on weighted graphs with applications in image processing and data clustering." European Journal of Applied Mathematics 28, no. 6 (July 3, 2017): 922–48. http://dx.doi.org/10.1017/s0956792517000122.

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Game-theoretic p-Laplacian or normalized p-Laplacian operator is a version of classical variational p-Laplacian which was introduced recently in connection with stochastic games called Tug-of-War with noise (Peres et al. 2008, Tug-of-war with noise: A game-theoretic view of the p-laplacian. Duke Mathematical Journal145(1), 91–120). In this paper, we propose an adaptation and generalization of this operator on weighted graphs for 1 ≤ p ≤ ∞. This adaptation leads to a partial difference operator which is a combination between 1-Laplace, infinity-Laplace and 2-Laplace operators on graphs. Then we consider the Dirichlet problem associated to this operator and we prove the uniqueness and existence of the solution. We show that the solution leads to an iterative non-local average operator on graphs. Finally, we propose to use this operator as a unified framework for interpolation problems in signal processing on graphs, such as image processing and machine learning.

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32

Baccelli, Francois, and William A. Massey. "A sample path analysis of the M/M/1 queue." Journal of Applied Probability 26, no. 2 (June 1989): 418–22. http://dx.doi.org/10.2307/3214049.

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The exact solution for the transient distribution of the queue length and busy period of the M/M/1 queue in terms of modified Bessel functions has been proved in a variety of ways. Methods of the past range from spectral analysis (Lederman and Reuter (1954)), combinatorial arguments (Champernowne (1956)), to generating functions coupled with Laplace transforms (Clarke (1956)). In this paper, we present a novel approach that ties the computation of these transient distributions directly to the random sample path behavior of the M/M/1 queue. The use of Laplace transforms is minimized, and the use of generating functions is eliminated completely. This is a method that could prove to be useful in developing a similar transient analysis for queueing networks.

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33

Baccelli, Francois, and William A. Massey. "A sample path analysis of the M/M/1 queue." Journal of Applied Probability 26, no. 02 (June 1989): 418–22. http://dx.doi.org/10.1017/s002190020002742x.

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The exact solution for the transient distribution of the queue length and busy period of the M/M/1 queue in terms of modified Bessel functions has been proved in a variety of ways. Methods of the past range from spectral analysis (Lederman and Reuter (1954)), combinatorial arguments (Champernowne (1956)), to generating functions coupled with Laplace transforms (Clarke (1956)). In this paper, we present a novel approach that ties the computation of these transient distributions directly to the random sample path behavior of the M/M/1 queue. The use of Laplace transforms is minimized, and the use of generating functions is eliminated completely. This is a method that could prove to be useful in developing a similar transient analysis for queueing networks.

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34

OLIVIER, D., and G. VALENT. "MULTIPLICATIVE RENORMALIZABILITY AND THE LAPLACE-BELTRAMI OPERATOR." International Journal of Modern Physics A 06, no. 06 (March 10, 1991): 955–76. http://dx.doi.org/10.1142/s0217751x91000526.

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For some rank 1 non-linear σ models we prove that a necessary and sufficient condition of multiplicative renormalizability for composite fields is that they should be eigenfunctions of the coset Laplace-Beltrami operator. These eigenfunctions span the irreducible representation space of the isometry group and may be finite- or infinite-dimensional. The zero mode of the Laplace-Beltrami operator plays a particular role since it is not renormalized at all.

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35

SZAREK, TOMASZ Z. "MULTIPLIERS OF LAPLACE TRANSFORM TYPE IN CERTAIN DUNKL AND LAGUERRE SETTINGS." Bulletin of the Australian Mathematical Society 85, no. 2 (December 15, 2011): 177–90. http://dx.doi.org/10.1017/s0004972711003078.

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AbstractWe investigate Laplace type and Laplace–Stieltjes type multipliers in the d-dimensional setting of the Dunkl harmonic oscillator with the associated group of reflections isomorphic to ℤd2 and in the related context of Laguerre function expansions of convolution type. We use Calderón–Zygmund theory to prove that these multiplier operators are bounded on weighted Lp, 1<p<∞, and from L1 to weak L1.

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36

Schuricht, Friedemann. "An alternative derivation of the eigenvalue equation for the 1-Laplace operator." Archiv der Mathematik 87, no. 6 (December 2006): 572–77. http://dx.doi.org/10.1007/s00013-006-1827-2.

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37

Brown, Gavin, Feng Dai, and Ferenc Móricz. "Strong approximation by Fourier--Laplace series on the unit sphere Sn-1." Acta Mathematica Hungarica 102, no. 1/2 (2004): 91–116. http://dx.doi.org/10.1023/b:amhu.0000023210.94136.89.

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38

Li, Zhouxin, and Ruishu Liu. "Existence and concentration behavior of solutions to 1-Laplace equations on RN." Journal of Differential Equations 272 (January 2021): 399–432. http://dx.doi.org/10.1016/j.jde.2020.09.041.

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39

Bai, Zhanbing, Xiangqian Liang, and Weiming Li. "Positive solutions for some 1-dimensional boundary value problems of Laplace-type." Applied Mathematics-A Journal of Chinese Universities 22, no. 1 (March 2007): 13–20. http://dx.doi.org/10.1007/s11766-007-0003-1.

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40

Filobello-Nino, Uriel, Hector Vazquez-Leal, Agustin Herrera-May, Roberto Ambrosio-Lazaro, Victor Jimenez-Fernandez, Mario Sandoval-Hernandez, Oscar Alvarez-Gasca, and Beatriz Palma-Grayeb. "The study of heat transfer phenomena by using modified homotopy perturbation method coupled by Laplace transform." Thermal Science 24, no. 2 Part B (2020): 1105–15. http://dx.doi.org/10.2298/tsci180108204f.

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In this paper, we present modified homotopy perturbation method coupled by Laplace transform to solve non-linear problems. As case study modified homotopy perturbation method coupled by Laplace transform is employed in order to obtain an approximate solution for the non-linear differential equation that describes the steady-state of a heat 1-D flow. The comparison between approximate and exact solutions shows the practical potentiality of the method.

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41

Chill, Ralph, and Mahamadi Warma. "Dirichlet and Neumann boundary conditions for the p-Laplace operator: what is in between?" Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 5 (September 20, 2012): 975–1002. http://dx.doi.org/10.1017/s030821051100028x.

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Let p ∈ (1, ∞) and let Ω ⊆ ℝN be a bounded domain with Lipschitz continuous boundary. We characterize on L2(Ω) all order-preserving semigroups that are generated by convex, lower semicontinuous, local functionals and are sandwiched between the semigroups generated by the p-Laplace operator with Dirichlet and Neumann boundary conditions. We show that every such semigroup is generated by the p-Laplace operator with Robin-type boundary conditions.

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42

Milovanović, Gradimir V., Rakesh K. Parmar, and Arjun K. Rathie. "Certain Laplace transforms of convolution type integrals involving product of two special pFp functions." Demonstratio Mathematica 51, no. 1 (October 1, 2018): 264–76. http://dx.doi.org/10.1515/dema-2018-0025.

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Abstract Recently the authors obtained several Laplace transforms of convolution type integrals involving Kummer’s function 1F1 [Appl. Anal. Discrete Math., 2018, 12(1), 257-272]. In this paper, the authors aim at presenting several new and interesting Laplace transforms of convolution type integrals involving product of two special generalized hypergeometric functions pFp by employing classical summation theorems for the series 2F1, 3F2, 4F3 and 5F4 available in the literature.

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43

del Teso, Félix, David Gómez-Castro, and Juan Luis Vázquez. "Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas." Fractional Calculus and Applied Analysis 24, no. 4 (August 1, 2021): 966–1002. http://dx.doi.org/10.1515/fca-2021-0042.

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Abstract We introduce three representation formulas for the fractional p-Laplace operator in the whole range of parameters 0 < s < 1 and 1 < p < ∞. Note that for p ≠ 2 this a nonlinear operator. The first representation is based on a splitting procedure that combines a renormalized nonlinearity with the linear heat semigroup. The second adapts the nonlinearity to the Caffarelli-Silvestre linear extension technique. The third one is the corresponding nonlinear version of the Balakrishnan formula. We also discuss the correct choice of the constant of the fractional p-Laplace operator in order to have continuous dependence as p → 2 and s → 0+, 1−. A number of consequences and proposals are derived. Thus, we propose a natural spectral-type operator in domains, different from the standard restriction of the fractional p-Laplace operator acting on the whole space. We also propose numerical schemes, a new definition of the fractional p-Laplacian on manifolds, as well as alternative characterizations of the W s, p (ℝ n ) seminorms.

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44

Rao, G. L. N., and L. Debnath. "A generalized Meijer transformation." International Journal of Mathematics and Mathematical Sciences 8, no. 2 (1985): 359–65. http://dx.doi.org/10.1155/s0161171285000370.

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In a series of papers [1-6], Kratzel studies a generalized version of the classical Meijer transformation with the Kernel function(st)νη(q,ν+1; (st)q). This transformation is referred to as GM transformation which reduces to the classical Meijer transform whenq=1. He also discussed a second generalization of the Meijer transform involving the Kernel functionλν(n)(x)which reduces to the Meijer function whenn=2and the Laplace transform whenn=1. This is called the Meijer-Laplace (or ML) transformation. This paper is concerned with a study of both GM and ML transforms in the distributional sense. Several properties of these transformations including inversion, uniqueness, and analyticity are discussed in some detail.

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45

Torres del Castillo, G. F., and K. C. Gutiérrez-Herrera. "Double and dual numbers. SU(2) groups, two-component spinors and generating functions." Revista Mexicana de Física 66, no. 4 Jul-Aug (July 1, 2020): 418. http://dx.doi.org/10.31349/revmexfis.66.418.

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We explicitly show that the groups of $2 \times 2$ unitary matrices with determinant equal to 1 whose entries are double or dual numbers are homomorphic to ${\rm SO}(2,1)$ or to the group of rigid motions of the Euclidean plane, respectively, and we introduce the corresponding two-component spinors. We show that with the aid of the double numbers we can find generating functions for separable solutions of the Laplace equation in the $(2 + 1)$ Minkowski space, which contain special functions that also appear in the solution of the Laplace equation in the three-dimensional Euclidean space, in spheroidal and toroidal coordinates.

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46

Iakovlev, Serguei. "Inverse Laplace Transforms Encountered in Hyperbolic Problems of Non-Stationary Fluid-Structure Interaction." Canadian Mathematical Bulletin 50, no. 4 (December 1, 2007): 547–66. http://dx.doi.org/10.4153/cmb-2007-053-1.

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AbstractThe paper offers a study of the inverse Laplace transforms of the functions where In is the modified Bessel function of the first kind and r is a parameter. The present study is a continuation of the author's previous work on the singular behavior of the special case of the functions in question, r=1. The general case of r ∈ [0, 1] is addressed, and it is shown that the inverse Laplace transforms for such r exhibit significantly more complex behavior than their predecessors, even though they still only have two different types of points of discontinuity: singularities and finite discontinuities. The functions studied originate from non-stationary fluid-structure interaction, and as such are of interest to researchers working in the area.

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SAWAYANAGI, HIROHUMI. "HAMILTONIAN BRST QUANTIZATION OF (1 + 1)-DIMENSIONAL MASSIVE VECTOR FIELDS." Modern Physics Letters A 11, no. 18 (June 14, 1996): 1509–22. http://dx.doi.org/10.1142/s0217732396001508.

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The Lagrangian of a (1 + 1)-dimensional massive vector field is quantized. Since it gives the system with second-class constraints, following Batalin and Fradkin, we introduce additional fields. Although the Stueckelberg field is usually introduced, we can use a pseudoscalar field instead. The duality between them is discussed. We show that the Stueckelberg mass term is equivalent to the Laplace transform of the Lagrangian of the gauged Wess-Zumino-Witten model.

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48

Chaudhry, M. Aslam. "Laplace transform of certain functions with applications." International Journal of Mathematics and Mathematical Sciences 23, no. 2 (2000): 99–102. http://dx.doi.org/10.1155/s0161171200001150.

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The Laplace transform of the functionstν(1+t)β,Reν>−1, is expressed in terms of Whittaker functions. This expression is exploited to evaluate infinite integrals involving products of Bessel functions, powers, exponentials, and Whittaker functions. Some special cases of the result are discussed. It is also demonstrated that the famous identity∫0∞sin (ax)/x dx=π/2is a special case of our main result.

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Betancor, Jorge J., Teresa Martínez, and Lourdes Rodríguez-Mesa. "Laplace Transform Type Multipliers for Hankel Transforms." Canadian Mathematical Bulletin 51, no. 4 (December 1, 2008): 487–96. http://dx.doi.org/10.4153/cmb-2008-049-3.

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AbstractIn this paper we establish that Hankel multipliers of Laplace transform type are bounded from Lp(w) into itself when 1 < p < ∞, and from L1(w) into L1,∞(w), provided that w is in the Muckenhoupt class Ap on ((0,∞), dx).

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50

Gunawan, Hendra. "Some weighted estimates for imaginary powers of Laplace operators." Bulletin of the Australian Mathematical Society 65, no. 1 (February 2002): 129–35. http://dx.doi.org/10.1017/s0004972700020141.

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We study the boundedness of singular integral operators that are imaginary powers of the Laplace operator in Rn, especially from weighted Hardy spaces to weighted Lebesgue spaces where 0 < p ≤ 1. In particular, we prove some estimates for these operators when 0 < p ≤ 1 and w is in the Muckenhoupt's class Aq, for some q > 1.

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