Research
Research
Research
Research
30,204+ open-access research outputs.
In this paper, we propose a scaled gradient modified non-monotone line search method for solving constrained minimization problems, and explore several specific properties of this method, namely, its …
In 1967 Hajnal and Juh{\'a}sz showed that the cardinality of a first-countable Hausdorff space with the countable chain condition has cardinality at most $\mathfrak{c}$, the cardinality of the real li…
We construct valuatively independent bases for the space of sections of an ample line bundle on a log Calabi--Yau pair over a discretely valued field and the space of regular functions on an affine CY…
J. Conway defined useful operations on the Class of combinatorial games and also introduced a notion of equivalence between games. Conway showed that, under his equivalence, games form a Group. Howeve…
This work studies numerical integration by the M\"obius-transformed trapezoidal rule, which combines the classical trapezoidal rule with a change of variables induced by a M\"obius transformation that…
On the flag variety $ \mathcal{F}l_s(E)$ associated to a vector bundle $E,$ , a sequence $s$ and a partition $a,$ there is a line bundle $\it Q^a_s$ on $ \mathcal{F}l_s(E).$ The aim of this pape…
We develop a harmonic gauge on the space of Riemannian metrics and study its role in the variational and flow-theoretic structure of geometric analysis. We prove that the harmonic gauge eliminates div…
In finance, portfolio management is a traditional yet difficult problem that has drawn attention from practitioners and researchers for many years. However, there are still difficult technological pro…
The bull is a graph consisting of a triangle and two pendant edges. The P_5 is the chordless path on five vertices. The house is the complement of a P_5. A graph is k-critical if it is k-chromatic but…
Motivated by an optimal-matching problem (Leighton-Shor) and the random-field Ising model (Aizenman-Wehr, Ding-Wirth), we consider a variational problem for graphs in $1+1$ dimension maximizing an act…
We extend Atiyah's holomorphic jet bundle formalism to holomorphic vector bundles over noncommutative algebras endowed with a bigraded differential calculus truncated at bidegree $(1,1)$; we refer to …
In this paper, we utilize our previous results on mod p monodromy of cyclic coverings of the projective line to realize a large series of groups of the form PSL(n, q) and PSU(n, q) as Galois groups ov…
In this paper, we prove a big monodromy theorem for the monodromy of cyclic coverings of projective line for cohomology with Fp-coefficients. This is a direct generalization of the results of Achter a…
Optimization of quadratic functions and the quotient of those are relevant in subspace and iterative optimization methods. In this paper, the calculation of the generalized operator norm and extremal …
We prove a refinement of Gromov's cowaist inequality in the case of Hermitian line bundles. Combined with the cowaist-systole estimates in recent work of Stryker, this gives sharp stable two-systolic …
Here, we investigate the solutions to equation \[f(f(-x)+x)=f(-f(x))+f(x),\qquad x\in\mathbb{R}\] that are prescribed on the non-positive half-line. We will refer to this prescribed function as the ge…
In 2014, Michal Lewicki and Andrzej Olbry\'s proved that if a real valued function $f$ defined on the real line satisfies the conditional functional equation \[ f(tx + (1-t)y) = t f(x) + (1-t) f(y),\q…
In this note we survey some of our results on the Lagrangian reduction of discrete-time mechanical systems (DMSs). It is intended as an introduction to the general ideas that we used in the reduction …
Let $C \subset \mathbb{P}^3$ be a canonical curve of genus $4$ over an algebraically closed field $k$ of characteristic zero. For a line $l \subset \mathbb{P}^3$, we consider the projection $\pi_l: C …
In this paper, we prove several rigidity results for complete noncompact manifolds with nonnegative intermediate curvatures. We show that when either $3\leq n\leq 5$, $1\leq m\leq n-1$, or $6\leq n\le…
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