Related papers: The maximal linear extension theorem in second ord…

We prove a generalization of Maehara's lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig's interpolation property. As a…

Monadic Second-Order Logic (MSO) extends First-Order Logic (FO) with variables ranging over sets and quantifications over those variables. We introduce and study Monadic Tree Logic (MTL), a fragment of MSO interpreted on infinite-tree…

Multi-task learning (MTL) has emerged as a pivotal paradigm in machine learning by leveraging shared structures across multiple related tasks. Despite its empirical success, the development of likelihood-based efficiently solvable…

We show that the higher order linear differential equation possesses all solutions of infinite order under certain conditions by extending the work of authors about second order differential equation \cite{dsm2}.

To follow up on the results of [1], we propose a computationally efficient explicit cyclic decomposition of the maximal tori in the groups $SL_n(q)$ and $SU_n(q)$ and their projective images. We also derive some corollaries to simplify…

We show that a complete first-order theory $T$ is distal provided it has a model $M$ such that the theory of the Shelah expansion of $M$ is distal.

In continuous logic, there are plenty of examples of interesting stable metric structures. However, on the other side of the SOP line, there are only a few metric structures where order is relevant, and orders often appear in different…

We show that the linear map defined by multiplication with a general bi-homogeneous form between two bi-graduated pieces of the first cohomology of a nonsingular quadric in the projective space is of maximal rank. This is the first non…

Linear arrangements of graphs are a well-known type of graph labeling and are found in many important computational problems, such as the Minimum Linear Arrangement Problem ($\texttt{minLA}$). A linear arrangement is usually defined as a…

A complete extension theorem for linear codes over a module alphabet and the symmetrized weight composition is proved. It is shown that an extension property with respect to arbitrary weight function does not hold for module alphabets with…

Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are…

We prove that Higman's lemma is strictly stronger for better quasi orders than for well quasi orders, within the framework of reverse mathematics. In fact, we show a stronger result: the infinite Ramsey theorem (for tuples of all lengths)…

We prove a maximal restriction inequality for the Fourier transform, providing an answer to a question left open by M\"uller, Ricci and Wright. Our methods are similar to the ones in their article, with the addition of a suitable trick to…

A linear arrangement is a mapping $\pi$ from the $n$ vertices of a graph $G$ to $n$ distinct consecutive integers. Linear arrangements can be represented by drawing the vertices along a horizontal line and drawing the edges as semicircles…

We briefly survey recent results related to linear series on curves that are general in various moduli spaces, highlighting the interplay between algebraic geometry on a general curve and the combinatorics of its degenerations.…

The first two authors have shown [KK99,KK00] that the sum the exponent (and thus the number) of maximal repetitions of exponent at least 2 (also called runs) is linear in the length of the word. The exponent 2 in the definition of a run may…

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…

The degree of a projective subscheme has an upper bound in term of the codimension and the reduction number. If a projective variety has an almost maximal degree, that is, the degree equals to the upper bound minus one, then its Betti table…

We prove that finite partial orders with a linear extension form a Ramsey class. Our proof is based on the fact that class of acyclic graphs has the Ramsey property and uses the partite construction.

We present a counter-example to the statement that there is a linear reduction in both directionsbetween the largest common subtree and the smallest common supertrees. Moreover, we show that in general, even having of one of them, it is…