Enhancing the Sustainment Warfighter Function in Constructive Training

Συγγραφείς: Oliver, Madison, Crocker, Abigail

Πηγή: 2026 IEEE International Systems Conference (SysCon) Systems Conference (SysCon), 2026 IEEE International. :1-8 Apr, 2026

Relation: 2026 IEEE International Systems Conference (SysCon)

Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities

Additional Titles: We prove exponential expressivity with stable ReLU Neural Networks (ReLU NNs) in $H^1(Ω)$ for weighted analytic function classes in certain polytopal domains $Ω$, in space dimension $d=2,3$. Functions in these classes are locally analytic on open subdomains $D\subset Ω$, but may exhibit isolated point singularities in the interior of $Ω$ or corner and edge singularities at the boundary $\partial Ω$. The exponential expression rate bounds proved here imply uniform exponential expressivity by ReLU NNs of solution families for several elliptic boundary and eigenvalue problems with analytic data. The exponential approximation rates are shown to hold in space dimension $d = 2$ on Lipschitz polygons with straight sides, and in space dimension $d=3$ on Fichera-type polyhedral domains with plane faces. The constructive proofs indicate in particular that NN depth and size increase poly-logarithmically with respect to the target NN approximation accuracy $\varepsilon>0$ in $H^1(Ω)$. The results cover in particular solution sets of linear, second order elliptic PDEs with analytic data and certain nonlinear elliptic eigenvalue problems with analytic nonlinearities and singular, weighted analytic potentials as arise in electron structure models. In the latter case, the functions correspond to electron densities that exhibit isolated point singularities at the positions of the nuclei. Our findings provide in particular mathematical foundation of recently reported, successful uses of deep neural networks in variational electron structure algorithms.

Συγγραφείς: Marcati, Carlo, Opschoor, Joost A. A., Petersen, Philipp C., Schwab, Christoph

Όροι ευρετηρίου: Numerical Analysis, Machine Learning, 35Q40, 41A25, 41A46, 65N30, text

Σύνδεσμος: http://arxiv.org/abs/2010.12217

On an approximative version of the notion of constructive analytic function

Συγγραφείς: Dantsin, E. Ya.

Πηγή: Journal of Soviet Mathematics. 14:1457-1463

Θεματικοί όροι: Other generalizations of analytic functions (including abstract-valued functions), Metric spaces, metrizability, constructive function theory, 0101 mathematics, Other constructive mathematics, constructive analytic function, constructive metric space, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/3702652
https://doi.org/10.1007/bf01693977

Approximate Taylor Theorem for Analytic Lipschitz Functions.

Συγγραφείς: Deterding, Stephen¹ (AUTHOR) deterding@marshall.edu

Πηγή: Constructive Approximation. May2026, p1-12. 12p.

Θεματικοί όροι: *Taylor's series, *Lipschitz spaces, *Analytic functions, *Mathematical complex analysis

Constructive Renormalization of the $2$-dimensional Grosse-Wulkenhaar Model

Additional Titles: We study a quartic matrix model with partition function $Z=\int d\ M\exp{\rm Tr}\ (-ΔM^2-\fracλ{4}M^4)$. The integral is over the space of Hermitian $(Λ+1)\times(Λ+1)$ matrices, the matrix $Δ$, which is not a multiple of the identity matrix, encodes the dynamics and $λ>0$ is a scalar coupling constant. We proved that the logarithm of the partition function is the Borel sum of the perturbation series, hence is a well defined analytic function of the coupling constant in certain analytic domain of $λ$, by using the multi-scale loop vertex expansions. All the non-planar graphs generated in the perturbation expansions have been taken care of on the same footing as the planar ones. This model is derived from the self-dual $ϕ^4$ theory on the 2 dimensional Moyal space, also called the 2 dimensional Grosse-Wulkenhaar model. This would also be the first fully constructed matrix model which is non-trivial and not solvable.

Συγγραφείς: Wang, Zhituo

Όροι ευρετηρίου: Mathematical Physics, High Energy Physics - Theory, Operator Algebras, Probability, text

Σύνδεσμος: http://arxiv.org/abs/1805.06365

The Weighted BMO Condition and a Constructive Description of Classes of Analytic Functions Satisfying this Condition

Συγγραφείς: Chikvinidze, L.^{aff1_w2aab2b8b3b1b7b1aab1b3b1Aa}

Πηγή: 3(3):217-232

Διαθεσιμότητα: https://www.degruyter.com/document/doi/10.1515/GMJ.1996.217/html

Constructive methods for linear and nonlinear boundary value problems for analytic functions : theory and applications / Vladimir V. Mityushev, Sergei V. Rogosin.

Συγγραφείς: Mitiuszew, Władimir (1958- ).

Συνεισφορές: Rogožin, Sergej Vasilʹevič (1952- ).

Πηγή: Bibliogr. s. 257-280. Indeks.

Σύνδεσμος πρόσβασης: http://katalog.nukat.edu.pl/lib/item?id=chamo:1167088&theme=nukat

Assessment of Online Environment and Digital Footprint Functions in Higher Education Analytics

Συγγραφείς: Pozdeeva, Elena, Shipunova, Olga (ORCID 0000-0001-8953-7434), Popova, Nina, Evseev, Vladimir, Evseeva, Lidiya, Romanenko, Inna, Mureyko, Larisa

Πηγή: Education Sciences. 2021 11.

Peer Reviewed: Y

Page Count: 11

Descriptors: Learning Analytics, Higher Education, Electronic Learning, Foreign Countries, Cognitive Mapping, Undergraduate Students, Student Attitudes, College Faculty, Teacher Attitudes

Γεωγραφικοί όροι: Russia

Uniformization and Constructive Analytic Continuation of Taylor Series

Συγγραφείς: Costin, Ovidiu, Dunne, Gerald V.

Πηγή: Commun. Math. Phys. 392, 863-906 (2022)

Θεματικοί όροι: Mathematics - Complex Variables, High Energy Physics - Theory, Mathematical Physics, Mathematics - Classical Analysis and ODEs

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2009.01962

Taylor and Laurent Series Expansions for α-conformable Fractional Analytic Functions.

Συγγραφείς: Alshanti, Waseem Ghazi, Hammad, Ma'mon Abu, Khalil, Roshdi

Πηγή: Palestine Journal of Mathematics; 2025, Vol. 14 Issue 4, p289-297, 9p

Θεματικοί όροι: Taylor's series, Laurent series, Mathematical analysis, Fractional calculus, Conformal mapping, Series expansion (Mathematics), Analytic functions

The Deck of Cards Method to Build Interpretable Fuzzy Sets in Decision-making.

Συγγραφείς: García-Zamora, Diego¹ (AUTHOR) dgzamora@ujaen.es, Dutta, Bapi² (AUTHOR) bdutta@ujaen.es, Figueira, José Rui³ (AUTHOR) figueira@tecnico.ulisboa.pt, Martínez, Luis² (AUTHOR) martin@ujaen.es

Πηγή: European Journal of Operational Research. Nov2024, Vol. 319 Issue 1, p246-262. 17p.

Θεματικοί όροι: *Data analytics, Membership functions (Fuzzy logic), Fuzzy sets, Fuzzy numbers, Semantics

On uniqueness properties of constructive analytic functions

Συγγραφείς: Manukyan, S. N.

Θεματικοί όροι: uniqueness property, Other constructive mathematics, constructive analytic function

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/4031686

On the Determinants for a Class of Analytic Function Using Sigmoid Beta‐Catas Operator.

Συγγραφείς: Fadipe-Joseph, Olubunmi A., Oluwaseyi, Olanike R., Opaleye, E. O., Ezeafulukwe, Uzoamaka A., Akeroyd, John R.

Πηγή: Journal of Function Spaces; 8/7/2025, Vol. 2025, p1-13, 13p

Θεματικοί όροι: Geometric function theory, Analytic functions, Differential operators, Hankel functions, Toeplitz matrices, Univalent functions, Logistic functions (Mathematics)

Numerical Computation of the Schwarz Function.

Συγγραφείς: Trefethen, Lloyd N.¹ (AUTHOR) trefethen@seas.harvard.edu

Πηγή: Constructive Approximation. Aug2026, Vol. 64 Issue 1, p3-14. 12p.

Θεματικοί όροι: *Schwarz function, *Algorithms, *Laplace's equation, *Partial differential equations, *Approximation error, *Set-valued maps, *Analytic functions

On an approximative version of the notion of constructive analytic function

Συγγραφείς: Dancin, E. Ja.

Θεματικοί όροι: Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Computability and recursion theory on ordinals, admissible sets, etc, Proof theory and constructive mathematics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/3537655

HAYMAN'S THEOREM FOR ANALYTIC FUNCTIONS IN A COMPLETE REINHARDT DOMAIN.

Συγγραφείς: SALO, T. M.

Πηγή: Matematychni Studii; 2025, Vol. 63 Issue 2, p129-135, 7p

Θεματικοί όροι: Analytic functions, Partial differential equations, Linear systems, Definitions

On the complexity of spectra of bounded analytic functions

Συγγραφείς: Timothy Hugh McNicholl, Brian Rudolph Zilli

Πηγή: Journal of Logic and Analysis. 17

Θεματικοί όροι: computable analysis, Convergence and divergence of infinite products, Constructive functional analysis, Blaschke products, Inner functions of one complex variable, Computation over the reals, computable analysis, complex analysis, Constructive and recursive analysis

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://logicandanalysis.org/index.php/jla/article/view/510

The Constructive Closure of the Riemann Hypothesis: A Unified Analytic Framework via the Nyman–Beurling–Baez–Duarte and ABF Correspondence

Συγγραφείς: CHOI, JONGMIN

Θεματικοί όροι: Zeta function, Explicit formula, Báez–Duarte, Nyman–Beurling, Functional equation, Weighted least squares, Nyman–Beurling criterion, Number theory, Möbius function, Riemann, Zero-free region, Hilbert kernel, Analytic number theory, Numerical analysis

A Constructive Analytic Closure of the Riemann Hypothesis via the NB/BD Framework (V4.3)

Συγγραφείς: CHOI, JONGMIN

Θεματικοί όροι: Zeta function, Nyman–Beurling criterion, Number theory, Möbius function, Explicit formula, Báez–Duarte, Nyman–Beurling, Zero-free region, Hilbert kernel, Analytic number theory, Functional equation, Weighted least squares, Numerical analysis

A Constructive Endpoint Closure Argument for the Riemann Hypothesis

Συγγραφείς: Ahmad, Sheikh farhan

Θεματικοί όροι: explicit formula, endpoint closure, Riemann xi-function, zero distribution, Riemann Hypothesis, critical line, Mathematical physics, analytic number theory, FOS: Mathematics, Riemann zeta function, dyadic positivity gap, Mathematics, Analysis, finite-band method