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article.listelement.badgeSpectrum of a qdeformed Schrödinger equation by means of the variational method(Mathematical Methods in the Applied Sciences, 202312)In this work, the qdeformed Schrödinger equations defined in different form of the q  Hamil tonian for qharmonic oscillator studied in [5] are considered with symmetric, asymmetric and nonpolynomial potentials. The spectrum of the qHamiltonian is obtained by using the Rayleigh Ritz variational method in which the discrete qHermite I polynomials are taken as the basis. As applications, qharmonic, purely qquartic and qquartic oscillators are examined in the class of symmetric polynomial potentials. Moreover, the qversion of Gaussian potential for an example of a nonpolynomial symmetric potential and a specific example of qversion of asymmetric dou ble well potential are presented. Numerous results are given for these potentials for several values of q. The limit relation as q → 1 − is discussed. The obtained results of ground and excitedstate energies of the purely qquartic oscillator and the accuracy of the groundstate energy levels are compared with the existing results. Also, the results are compared with the classical case appearing in the literature in the limiting case q → 1 −.

article.listelement.badgeGlobal energy preserving model reduction for multisymplectic PDEs(Applied Mathematics and Computation, 20230101)Many Hamiltonian systems can be recast in multisymplectic form. We develop a reducedorder model (ROM) for multisymplectic Hamiltonian partial differential equations (PDEs) that preserves the global energy. The fullorder solutions are obtained by finite difference discretization in space and the global energy preserving average vector field (AVF) method. The ROM is constructed in the same way as the fullorder model (FOM) applying proper orthogonal decomposition (POD) with the Galerkin projection. The reducedorder system has the same structure as the FOM, and preserves the discrete reduced global energy. Applying the discrete empirical interpolation method (DEIM), the reducedorder solutions are computed efficiently in the online stage. A priori error bound is derived for the DEIM approximation to the nonlinear Hamiltonian. The accuracy and computational efficiency of the ROMs are demonstrated for the Korteweg de Vries (KdV) equation, ZakharovKuznetzov (ZK) equation, and nonlinear Schrödinger (NLS) equation in multisymplectic form. Preservation of the reduced energies shows that the reducedorder solutions ensure the longterm stability of the solutions.

article.listelement.badgeOn the image of the Lupaş qanalogue of the Bernstein Operators(Bulletin of the Malaysian Mathematical Sciences Society, 202401)The Lupa\c{s} $q$analogue, $R_{n,q}$, is historically the first known $q$version of the Bernstein operator. It has been studied extensively in different aspects by a number of authors during the last decades. In this work, the following issues related to the image of the Lupa\c{s} $q$analogue are discussed: A new explicit formula for the moments has been derived, independence of the image $R_{n,q}$ from the parameter $q$ has been examined, the diagonalizability of operator $R_{n,q}$ has been proved and the fact that $R_{n,q}$ does not preserve modulus of continuity has been established.

article.listelement.badgeClassification of some quadrinomials over finite fields of odd characteristic(Finite Fields and Their Applications, 20230315)In this paper, we completely determine all necessary and su cient conditions such that the polynomial f (x) = x3+axq+2+bx2q+1+cx3q , where a, b, c ∈ F∗ q , is a permutation quadrinomial of Fq2 over any nite eld of odd characteristic. This quadrinomial has been studied rst in [25] by Tu, Zeng and Helleseth, later in [24] Tu, Liu and Zeng revisited these quadrinomials and they proposed a more comprehensive characterization of the coe cients that results with new permutation quadrinomials, where char(Fq ) = 2 and nally, in [16], Li, Qu, Li and Chen proved that the su cient condition given in [24] is also necessary and thus completed the solution in even characteristic case. In [6] Gupta studied the permutation properties of the polynomial x3 +axq+2 +bx2q+1 +cx3q , where char(Fq ) = 3, 5 and a, b, c ∈ F∗q and proposed some new classes of permutation quadrinomials of Fq2 . In particular, in this paper we classify all ermutation polynomials of Fq2 of the form f (x) = x3 + axq+2 + bx2q+1 + cx3q , where a, b, c ∈ F∗q , over all nite elds of odd characteristic and obtain several new classes of such permutation quadrinomials.

article.listelement.badgeComplete characterization of some permutation polynomials of the form xr(1 + axs1(q−1) + bxs2(q−1)) over Fq2(Cryptography and Communications, 20230418)We completely characterize all permutation trinomials of the form f (x) = x3(1+axq−1 + bx2(q−1)) over Fq2 , where a, b ∈ F∗q and all permutation trinomials of the form f (x) = x3(1+bx2(q−1) +cx3(q−1)) over Fq2 , where b, c ∈ F∗q in both even and odd characteristic cases.