Search results for "Computational Mathematic"

On the Fučík spectrum of the p-Laplacian with no-flux boundary condition

2023

In this paper, we study the quasilinear elliptic problem \begin{align*} \begin{aligned} -\Delta_{p} u&= a\l(u^+\r)^{p-1}-b\l(u^-\r)^{p-1} \quad && \text{in } \Omega,\\ u & = \text{constant} &&\text{on } \partial\Omega,\\ 0&=\int_{\partial \Omega}\left|\nabla u\right|^{p-2}\nabla u\cdot \nu \,\diff \sigma,&& \end{aligned} \end{align*} where the operator is the $p$-Laplacian and the boundary condition is of type no-flux. In particular, we consider the Fu\v{c}\'{\i}k spectrum of the $p$-Laplacian with no-flux boundary condition which is defined as the set $\fucik$ of all pairs $(a,b)\in\R^2$ such that the problem above has a nontrivial solution. It turns out…

Interview: Kalyanmoy Deb Talks about Formation, Development and Challenges of the EMO Community, Important Positions in His Career, and Issues Faced …

2023

Kalyanmoy Deb was born in Udaipur, Tripura, the smallest state of India at the time, in 1963 [...]

𝒦-convergence as a new tool in numerical analysis

2019

Abstract We adapt the concept of $\mathscr{K}$-convergence of Young measures to the sequences of approximate solutions resulting from numerical schemes. We obtain new results on pointwise convergence of numerical solutions in the case when solutions of the limit continuous problem possess minimal regularity. We apply the abstract theory to a finite volume method for the isentropic Euler system describing the motion of a compressible inviscid fluid. The result can be seen as a nonlinear version of the fundamental Lax equivalence theorem.

A sufficient condition for the instability of theq-d algorithm

1959

Frequency-based ensemble forecasting model for time series forecasting

2022

AbstractThe M4 forecasting competition challenged the participants to forecast 100,000 time series with different frequencies: hourly, daily, weekly, monthly, quarterly, and yearly. These series come mainly from the economic, finance, demographics, and industrial areas. This paper describes the model used in the competition, which is a combination of statistical methods, namely auto-regressive integrated moving-average, exponential smoothing (ETS), bagged ETS, temporal hierarchical forecasting method, Box-Cox transformation, ARMA errors, Trend and Seasonal components (BATS), and Trigonometric seasonality BATS (TBATS). Forty-nine submissions were evaluated by the organizers and compared with…

Self-learning inductive inference machines

1991

Self-knowledge is a concept that is present in several philosophies. In this article, we consider the issue of whether or not a learning algorithm can in some sense possess self-knowledge. The question is answered affirmatively. Self-learning inductive inference algorithms are taken to be those that learn programs for their own algorithms, in addition to other functions. La connaissance de soi est un concept qui se retrouve dans plusieurs philosophies. Dans cet article, les auteurs s'interrogent a savoir si un algorithme d' apprentissage peut dans une certaine mesure posseder la connaissance de soi. lis apportent une reponse positive a cette question. Les algorithmes d'inference inductive a…

A direct impedance tomography algorithm for locating small inhomogeneities

2003

Impedance tomography seeks to recover the electrical conductivity distribution inside a body from measurements of current flows and voltages on its surface. In its most general form impedance tomography is quite ill-posed, but when additional a-priori information is admitted the situation changes dramatically. In this paper we consider the case where the goal is to find a number of small objects (inhomogeneities) inside an otherwise known conductor. Taking advantage of the smallness of the inhomogeneities, we can use asymptotic analysis to design a direct (i.e., non-iterative) reconstruction algorithm for the determination of their locations. The viability of this direct approach is documen…

Multistate active spaces from local CAS-SCF molecular orbitals: the photodissociation of HFCO as an example.

2005

A recently developed algorithm to generate localized molecular orbitals (LMO) is applied to the study of excited states along a photodissociation process. The LMOs allow for the selection of a consistent complete active space (CAS) for the simultaneous description of all the electronic states involved in a multistate process on the basis of simple chemical criteria. The local nature of the orbitals is used to label them in a unique way that does not depend on the molecular geometry. The selection of the electronic configurations of interest for the set of target states on only the basis of the dominant excitations required by the simplest configuration interaction (CI) descriptions for both…

Basis set and correlation effects in the calculation of accurate gas phase dimerization energies of two M+2 to give M2+4 (M = S, Se)

2000

The dimerization energies of two M2+ to give M42+ (M = S, Se) were calcd. They depend strongly on the size of the basis set and the correlation method used (ranging from 217 to 522 kJ/mol, M = S) and, therefore, a systematic study of basis set and correlation effects was performed [MP2, MP3, MP4(SDQ), CCSD, CCSD(T)]. The introduction of a second set of polarizing d-functions caused a significant redn. of the dimerization energies, but neither of the above limits is reached by the MPn (n = 2, 3, 4) theory, even with the largest basis sets [cc-pVQZ]. However, convergence was achieved by CCSD(T), compd. methods or hybrid HF/DFT calcns. employing flexible basis sets [e.g., CCSD(T)/cc-pV5Z, CBS-…

Vertical spectrum of the C2H 2+ system. An open shell (SC)2-CAS-SDCI study

2003

The open shell (SC)(2)-CAS-SDCI method along with a basis set of atomic natural orbitals (ANO) has been applied for calculating the main ionization potentials of acetylene, as well as the manifold of excited states of the different symmetries up to 32 eV. In this method, the single and double excitations of a CAS space are generated and the corresponding CI matrix is corrected by means of the (SC)(2) procedure that cancels the size-extensivity error and adds some high order contributions. The mean absolute error for the outer-valence X (2)Pi(u)(1pi(u) (-1)), A (2)Sigma(g) (+)(3sigma(g) (-1)), and B (2)Sigma(u) (+)(2sigma(u) (-1)) states, and the inner-valence C (2)Sigma(g) (+)(2sigma(g) (-1…