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Extending the works of Alladi and Sweeting and Woo, we state and prove the general higher order duality between prime ideals in number rings. We then use the second order duality to obtain the a new formula for the Chebotarev Density…

Number Theory · Mathematics 2026-02-02 Sroyon Sengupta

In this paper we investigate homogenization results for the principal eigenvalue problem associated to $1$-homogeneous, uniformly elliptic, second-order operators. Under rather general assumptions, we prove that the principal eigenpair…

Analysis of PDEs · Mathematics 2022-05-11 Gonzalo Dávila , Andrei Rodríguez-Paredes , Erwin Topp

We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, homogeneous kernels of such operators are also studied. The…

Functional Analysis · Mathematics 2021-12-08 Zhirayr Avetisyan , Alexey Karapetyants

Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…

Logic in Computer Science · Computer Science 2025-12-09 Vikraman Choudhury , Wind Wong

A notion of partial ideal for an operator algebra is a weakening the notion of ideal where the defining algebraic conditions are enforced only in the commutative subalgebras. We show that, in a von Neumann algebra, the ultraweakly closed…

Operator Algebras · Mathematics 2014-08-07 Nadish de Silva , Rui Soares Barbosa

Most zeroth-order optimization algorithms mimic a first-order algorithm but replace the gradient of the objective function with some gradient estimator that can be computed from a small number of function evaluations. This estimator is…

Optimization and Control · Mathematics 2026-01-12 Wouter Jongeneel , Man-Chung Yue , Daniel Kuhn

In this paper, we give a way to construct graded filtrations of graded modules. We then apply it to the Sally module, which describes a correction term of the Hilbert function. As a result, we obtain the inequality of the Hilbert…

Commutative Algebra · Mathematics 2021-10-11 Shinya Kumashiro

The ranges of a certain type of second order differential operator, on a Sobolev subspace of the Lebesgue space $L^2$ of the circle group, can be characterised by the vanishing of the Fourier coefficients at (generally) two integers that…

Classical Analysis and ODEs · Mathematics 2015-03-17 Rodney Nillsen

For a class of partially ordered means we introduce a notion of the (nontrivial) cancelling mean. A simple method is given which helps to determine cancelling means for well known classes of Holder and Stolarsky means.

Classical Analysis and ODEs · Mathematics 2013-01-18 Slavko Simic

The prevalent interpretation of G\"odel's Second Theorem states that a sufficiently adequate and consistent theory does not prove its consistency. It is however not entirely clear how to justify this informal reading, as the formulation of…

Logic · Mathematics 2020-08-13 Balthasar Grabmayr

We study the generalized eigenvalue problem on the whole space for a class of integro-differential elliptic operators. The nonlocal operator is over a finite measure, but this has no particular structure. Some of our results even hold for…

Analysis of PDEs · Mathematics 2022-11-24 Ari Arapostathis , Anup Biswas , Prasun Roychowdhury

In this note, we present an elementary proof for a well-known second-order sufficient optimality condition in nonlinear semidefinite optimization which does not rely on the enhanced theory of second-order tangents. Our approach builds on an…

Optimization and Control · Mathematics 2023-02-09 Patrick Mehlitz

This paper on the whole concerns with the duality of Mayer problem for k-th order differential inclusions, where k is an arbitrary natural number. Thus, this work for constructing the dual problems to differential inclusions of any order…

Optimization and Control · Mathematics 2019-06-20 Elimhan N. Mahmudov

We classify the propositional modal validities arising from the category of sets under its natural classes of morphisms. The resulting validities depend on the morphism class, the size of the world, and the permitted substitution instances.…

Logic · Mathematics 2026-04-29 Wojciech Aleksander Wołoszyn

A systematic construction of the Green's matrix for a second order, self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the…

Mathematical Physics · Physics 2011-01-06 Tahsin Cagri Sisman , Bayram Tekin

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating…

Classical Analysis and ODEs · Mathematics 2007-12-27 F. M. Mahomed , A. Qadir

The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…

Optimization and Control · Mathematics 2023-08-04 N. T. V. Hang , M. E. Sarabi

We describe the second order ODE's cubic in the first order derivative with 2-dimensional symmetry algebra. We show that there exist only eight different types of them. We also construct the easily verifiable Equivalence Criterion for every…

Classical Analysis and ODEs · Mathematics 2013-07-15 Vera V. Kartak

We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…

Logic in Computer Science · Computer Science 2025-09-11 Chad E. Brown , Cezary Kaliszyk , Martin Suda , Josef Urban

What does it mean for a machine learning model to be `fair', in terms which can be operationalised? Should fairness consist of ensuring everyone has an equal probability of obtaining some benefit, or should we aim instead to minimise the…

Computers and Society · Computer Science 2021-03-24 Reuben Binns