@article{MTMT:34628993,
	title = {On the weak solutions for the MHD systems with controllable total energy and cross helicity},
	url = {https://m2.mtmt.hu/api/publication/34628993},
	author = {Miao, Changxing and Ye, Weikui},
	doi = {10.1016/j.matpur.2023.12.010},
	journal-iso = {J MATH PURE APPL},
	journal = {JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES},
	volume = {181},
	unique-id = {34628993},
	issn = {0021-7824},
	keywords = {Non-uniqueness; Weak solutions; Convex integral iteration; The MHD system; Cross helicity},
	year = {2024},
	eissn = {1776-3371},
	pages = {190-227}
}

@article{MTMT:34614073,
	title = {Geometric bounds for the magnetic Neumann eigenvalues in the plane},
	url = {https://m2.mtmt.hu/api/publication/34614073},
	author = {Colbois, Bruno and Lena, Corentin and Provenzano, Luigi and Savo, Alessandro},
	doi = {10.1016/j.matpur.2023.09.014},
	journal-iso = {J MATH PURE APPL},
	journal = {JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES},
	volume = {179},
	unique-id = {34614073},
	issn = {0021-7824},
	abstract = {We consider the eigenvalues of the magnetic Laplacian on a bounded domain Omega of R-2 with uniform magnetic field beta > 0 and magnetic Neumann boundary conditions. We find upper and lower bounds for the ground state energy lambda(1) and we provide semiclassical estimates in the spirit of Kroger for the first Riesz mean of the eigenvalues. We also discuss upper bounds for the first eigenvalue for non-constant magnetic fields beta = beta(x) on a simply connected domain in a Riemannian surface. In particular: we prove the upper bound lambda(1) < beta for a general plane domain for a constant magnetic field, and the upper bound lambda(1) < max(x is an element of Omega)(-)|beta(x)| for a variable magnetic field when omega is simply connected. For smooth domains, we prove a lower bound of lambda t depending only on the intensity of the magnetic field beta and the rolling radius of the domain. The estimates on the Riesz mean imply an upper bound for the averages of the first k eigenvalues which is sharp when k -> infinity and consists of the semiclassical limit 2 pi k/ |Omega| plus an oscillating term.We also construct several examples, showing the importance of the topology: in particular we show that an arbitrarily small tubular neighborhood of a generic simple closed curve has lowest eigenvalue bounded away from zero, contrary to the case of a simply connected domain of small area, for which lambda(1) is always small.(c) 2023 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).},
	keywords = {Upper and lower bounds; Magnetic Laplacian; Constant field; Neumann eigenvalues; Semiclassical estimates},
	year = {2023},
	eissn = {1776-3371},
	pages = {454-497}
}

@article{MTMT:34614069,
	title = {Bogoliubov excitation spectrum of trapped Bose gases in the Gross-Pitaevskii regime},
	url = {https://m2.mtmt.hu/api/publication/34614069},
	author = {Nam, Phan Thanh and Triay, Arnaud},
	doi = {10.1016/j.matpur.2023.06.002},
	journal-iso = {J MATH PURE APPL},
	journal = {JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES},
	volume = {176},
	unique-id = {34614069},
	issn = {0021-7824},
	abstract = {We consider an inhomogeneous system of N bosons in R3 confined by an external potential and interacting via a repulsive potential of the form N2V(N(x - y)). We prove that the low-energy excitation spectrum of the system is determined by the eigenvalues of an effective one-particle operator, which agrees with Bogoliubov's approximation. (c) 2023 Elsevier Masson SAS. All rights reserved.},
	keywords = {Excitation spectrum; Bose-Einstein condensation; Bogoliubov transformation; Many-body quantum mechanics},
	year = {2023},
	eissn = {1776-3371},
	pages = {18-101}
}

@article{MTMT:34458081,
	title = {A mechanism for detecting normally hyperbolic invariant tori in differential equations},
	url = {https://m2.mtmt.hu/api/publication/34458081},
	author = {Pereira, Pedro C. C. R. and Novaes, Douglas D. and Candido, Murilo R.},
	doi = {10.1016/j.matpur.2023.06.008},
	journal-iso = {J MATH PURE APPL},
	journal = {JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES},
	volume = {177},
	unique-id = {34458081},
	issn = {0021-7824},
	abstract = {Determining the existence of compact invariant manifolds is a central quest in the qualitative theory of differential equations. Singularities, periodic solutions, and invariant tori are examples of such invariant manifolds. A classical and useful result from the averaging theory relates the existence of isolated periodic solutions of non-autonomous periodic differential equations, given in a specific standard form, with the existence of simple singularities of the so-called guiding system, which is an autonomous differential equation given in terms of the first non-vanishing higher order averaged function. In this paper, we provide an analogous result for the existence of invariant tori. Namely, we show that a non-autonomous periodic differential equation, given in the standard form, has a normally hyperbolic invariant torus in the extended phase space provided that the guiding system has a hyperbolic limit cycle. We apply this result to show the existence of normally hyperbolic invariant tori in a family of jerk differential equations.& COPY; 2023 Elsevier Masson SAS. All rights reserved.},
	keywords = {manifolds; Invariant tori; averaging theory; Normally hyperbolic invariant; Method of continuation},
	year = {2023},
	eissn = {1776-3371},
	pages = {1-45}
}

@article{MTMT:34297245,
	title = {New regularity estimates for fully nonlinear elliptic equations},
	url = {https://m2.mtmt.hu/api/publication/34297245},
	author = {Nascimento, Thialita M. and Teixeira, Eduardo V.},
	doi = {10.1016/j.matpur.2022.12.008},
	journal-iso = {J MATH PURE APPL},
	journal = {JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES},
	volume = {171},
	unique-id = {34297245},
	issn = {0021-7824},
	abstract = {We establish new quantitative Hessian integrability estimates for viscosity supersolutions of fully nonlinear elliptic operators. As a corollary, we show that the optimal Hessian power integrability epsilon = epsilon(lambda,Lambda, n) in the celebrated W-2,W-epsilon-regularity estimate satisfies.[GRAPHICS].where n >= 3is the dimension and 0 < lambda< Lambda are the ellipticity constants. In particular,(Lambda/lambda)(n-1) epsilon(lambda,Lambda, n) blows-up, as n ->infinity; previous results yielded fast decay of such a quantity. The upper estimate improves the one obtained by Armstrong, Silvestre, and Smart in [1].},
	keywords = {Fully nonlinear elliptic PDEs; Viscosity supersolutions; Hessian integrability; Quantitative regularity estimates},
	year = {2023},
	eissn = {1776-3371},
	pages = {1-25}
}

@article{MTMT:34249588,
	title = {The Frisch-Parisi conjecture I: Prescribed multifractal behavior, and a partial solution},
	url = {https://m2.mtmt.hu/api/publication/34249588},
	author = {Barral, Julien and Seuret, Stephane},
	doi = {10.1016/j.matpur.2023.05.003},
	journal-iso = {J MATH PURE APPL},
	journal = {JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES},
	volume = {175},
	unique-id = {34249588},
	issn = {0021-7824},
	abstract = {In this work and its companion [1], we construct Baire function spaces in which typical elements share the same prescribed multifractal behavior and obey a multifractal formalism, providing a solution to the so-called Frisch-Parisi conjecture for functions, an inverse problem raised by S. Jaffard. In this first part, a family Ed of almost-doubling fully supported capacities on Rd with prescribed singularity spectra is constructed. With each & mu; & ISIN; Ed we associate a Baire function space B & mu;(Rd) (a generalisation of Holder-Zygmund spaces) in which typical functions share the same singularity spectrum as & mu;. This yields a partial solution to the conjecture. In [1], we introduce and study a family B = {B & mu;,p q (Rd)}& mu;EEd,(p,q)E[1,+oo]2 of heterogeneous Besov spaces that contains {B & mu;(Rd)}& mu;EEd and generalises in a natural direction the family of standard Besov spaces, and we solve the inverse problem exhaustively inside B. & COPY; 2023 Elsevier Masson SAS. All rights reserved.},
	keywords = {Wavelets; Hausdorff dimension; Multifractal formalism; Frechet spaces; Holder-Zygmund spaces},
	year = {2023},
	eissn = {1776-3371},
	pages = {76-108}
}

@article{MTMT:34245811,
	title = {Products and commutators of martingales in H1 and BMO},
	url = {https://m2.mtmt.hu/api/publication/34245811},
	author = {Bonami, Aline and Jiao, Yong and Xie, Guangheng and Yang, Dachun and Zhou, Dejian},
	doi = {10.1016/j.matpur.2023.10.001},
	journal-iso = {J MATH PURE APPL},
	journal = {JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES},
	unique-id = {34245811},
	issn = {0021-7824},
	year = {2023},
	eissn = {1776-3371}
}

@article{MTMT:34169240,
	title = {Weighted slice rank and a minimax correspondence to Strassen's spectra},
	url = {https://m2.mtmt.hu/api/publication/34169240},
	author = {Christandl, M. and Lysikov, V. and Zuiddam, J.},
	doi = {10.1016/j.matpur.2023.02.006},
	journal-iso = {J MATH PURE APPL},
	journal = {JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES},
	volume = {172},
	unique-id = {34169240},
	issn = {0021-7824},
	year = {2023},
	eissn = {1776-3371},
	pages = {299-329}
}

@article{MTMT:33969073,
	title = {CRISPR/Cas12a coupled with enzyme-DNA molecular switch photoelectrochemical assay for HIV nucleic acid},
	url = {https://m2.mtmt.hu/api/publication/33969073},
	author = {Qin, Lilin and Lou, Fangxu and Wang, Yan and Zhang, Yinhao and Liu, Shishi and Hun, Xu},
	doi = {10.1016/j.microc.2023.108713},
	journal-iso = {J MATH PURE APPL},
	journal = {JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES},
	volume = {169},
	unique-id = {33969073},
	issn = {0021-7824},
	abstract = {Molecular switches formed by enzyme-DNA hybrid compounds combined with CRISPR-Cas12a cis-cleavage used for photoelectrochemical nucleic acid assay was fabricated. A compound, molecular switch, consisting of Taq DNA polymerase, aptamer, block DNA and methylene blue labeled primer (primer-Mb) is formed. Block DNA is assembled on the surface of MBs (block DNA-MBs), and hybridized with the primer-Mb. In the presence of Human Immunodeficiency Virus (HIV) target, molecular switches are turned on by hybridization of the target with block DNA. The Taq DNA polymerase is released and activated. The activated Taq DNA polymerase elongates the primer via the template, block DNA, which attached onto Magnetic beads (MBs). A dsDNA with Mb (dsDNA-Mb) was formed. With the assistance of Cas12a, a amplified photoelectrochemical signal was obtained and the HIV target DNA was qualified. Under the best conditions, the limit of detection (LOD) can be as low as 0.3 fM. This photoelectrochemical assay extends the tool kit of molecular nanotechnology.},
	keywords = {methylene blue; MOLECULAR SWITCH; Photoelectrochemical sensing; CRISPR-Cas12a; Cis-cleavage},
	year = {2023},
	eissn = {1776-3371}
}

@article{MTMT:33909213,
	title = {Recurrence properties for linear dynamical systems: An approach via invariant measures},
	url = {https://m2.mtmt.hu/api/publication/33909213},
	author = {Grivaux, Sophie and Lopez-Martinez, Antoni},
	doi = {10.1016/j.matpur.2022.11.011},
	journal-iso = {J MATH PURE APPL},
	journal = {JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES},
	volume = {169},
	unique-id = {33909213},
	issn = {0021-7824},
	abstract = {We study different pointwise recurrence notions for linear dynamical systems from the Ergodic Theory point of view. We show that from any reiteratively recurrent vector x0, for an adjoint operator T on a separable dual Banach space X, one can construct a T-invariant probability measure which contains x0 in its support. This allows us to establish some equivalences, for these operators, between some strong pointwise recurrence notions which in general are completely distinguished. In particular, we show that (in our framework) reiterative recurrence coincides with frequent recurrence; for complex Hilbert spaces uniform recurrence coincides with the property of having a spanning family of unimodular eigenvectors; and the same happens for power-bounded operators on complex reflexive Banach spaces. These (surprising) properties are easily generalized to product and inverse dynamical systems, which implies some relations with the respective hypercyclicity notions. Finally we study how typical is an operator with a non-zero reiteratively recurrent vector in the sense of Baire category.(c) 2022 The Authors. Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).},
	keywords = {Recurrence; invariant measures; Linear dynamics; Frequently recurrent operators; Unimodular eigenvectors; Uniformly recurrent operators},
	year = {2023},
	eissn = {1776-3371},
	pages = {155-188}
}