Related papers: A proof of the Brill-Noether method from scratch

A variational approach is used to develop a robust numerical procedure for solving the nonlinear Poisson-Boltzmann equation. Following Maggs et al., we construct an appropriate constrained free energy functional, such that its…

In this paper, we are interested in a Neumann-type series for modified Bessel functions of the first kind which arises in the study of Dunkl operators associated with dihedral groups and as an instance of the Laguerre semigroup constructed…

Every beginning real analysis student learns the classic Heine-Borel theorem, that the interval [0,1] is compact. In this article, we present a proof of this result that doesn't involve the standard techniques such as constructing a…

In this paper we introduce a new algebraic method in tilings. Combining this method with Hilbert's Nullstellensatz we obtain a necessary condition for tiling $n$-space by translates of a cluster of cubes. Further, the polynomial method will…

Many proofs of the fundamental theorem of algebra rely on the fact that the minimum of the modulus of a complex polynomial over the complex plane is attained at some complex number. The proof then follows by arguing the minimum value is…

We study the Lie and Noether point symmetries of a class of systems of second-order differential equations with $n$ independent and $m$ dependent variables ($n\times m$ systems). We solve the symmetry conditions in a geometric way and…

We prove a non abelian Torelli type result for smooth projective curves by working in the derived category of some associated polarized Quot schemes and defining Brill-Noether loci and Abel-Jacobi maps on them.

Beginning from the formal resolution of Riemann Zeta function, by using the formula of inner product between two infinite-dimensional vectors in the complex space, the author proved the world's baffling problem -- Riemann hypothesis raised…

In 1998, Bremner conjectured that elliptic curves over the rationals having long sequences of distinct rational points whose $x$-coordinates are in arithmetic progression, have large rank. This was proved some years ago in a strong form as…

Given a space it is easy to obtain the system of geodesic equations on it. In this paper the inverse problem of reconstructing the space from the geodesic equations is addressed. A procedure is developed for obtaining the metric tensor from…

This paper offers a contemporary and comprehensive perspective on the classical algorithms utilized for the solution of minimum-time problem for linear systems (MTPLS). The use of unified notations supported by visual geometric…

We propose a generalization of Artin's definition of algebraic stack, which we call {\em geometric $n$-stack}. The main observation is that there is an inductive structure to the definition whereby the ingredients for the definition of…

In the sl\_n case, A. Berenstein and A. Zelevinsky studied the Sch\"{u}tzenberger involution in terms of Lusztig's canonical basis, [3]. We generalize their construction and formulas for any semisimple Lie algebra. We use for this the…

Let $X$ be a smooth projective variety of dimension $n$ and let $H$ be an ample line bundle on $X$. Let $M_{X,H}(r;c_1, ..., c_{s})$ be the moduli space of $H$-stable vector bundles $E$ on $X$ of rank $r$ and Chern classes $c_i(E)=c_i$ for…

In this work, we take a short recap of a formal framework of the Eddington-inspired Born-Infeld (EiBI) theory of gravity and derive the point-like Lagrangian for underlying theory based on the use of Noether gauge symmetries (NGS). We study…

In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…

Consider the sum of the first $N$ eigenspaces for the Laplacian on a Riemannian manifold. A basis for this space determines a map to Euclidean space and for $N$ sufficiently large the map is an embedding. In analogy with a fruitful idea of…

We investigate the power of graph isomorphism algorithms based on algebraic reasoning techniques like Gr\"obner basis computation. The idea of these algorithms is to encode two graphs into a system of equations that are satisfiable if and…

In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…

Translated from the Latin original "Novae demonstrationes circa resolutionem numerorum in quadrata" (1774). E445 in the Enestrom index. See Chapter III, section XI of Weil's "Number theory: an approach through history". Also, a very clear…