相关论文: Graphical patterns in quadratic residues

A visualization scheme for quantum many-body wavefunctions is described, which we have termed qubism. Its main property is its recursivity: increasing the number of qubits reflects in an increase in the image resolution. Thus, the plots are…

We survey some results on toric topology.

We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…

In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…

In this article, we study the distribution of large quadratic character sums. Based on the recent work of Lamzouri~\cite{La2022}, we obtain the structure results of quadratic characters with large character sums.

Some basic geometric properties of doubly twisted product immersions are established.

In this paper, we introduce the cyclic polygon plot, a representation based on a novel projection concept for multi-dimensional values. Cyclic polygon plots combine the typically competing requirements of quantitativeness, image-space…

This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…

Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.

Some boundedness properties of function spaces (considered as topological groups) are studied.

We consider the rational linear relations between real numbers whose squared trigonometric functions have rational values, angles we call ``geodetic''. We construct a convenient basis for the vector space over Q generated by these angles.…

In this paper, we derive the quadratic formula as a consequence of constructively proving the existence of standard and factored forms for general form real quadratic functions. Emphasis is put on connections to graphing of corresponding…

This will is an expository description of quadratic rational maps. Sections 2 through 6 are concerned with the geometry and topology of such maps. Sections 7--10 survey of some topics from the dynamics of quadratic rational maps. There are…

The conic sections, as well as the solids obtained by revolving these curves, and many of their surprising properties, were already studied by Greek mathematicians since at least the fourth century B.C. Some of these properties come to the…

A residue formula is given for the Verlinde formula, which allows one to calculate its coefficients as a polynomial in the level and connects it to the Riemann-Roch formula on the moduli space of vector bundles on a curve.

For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.

Two-, three- and four-dimensional representations of Penrose tilings of the plane are described. The vertices that occur in these representations lie on lattices. Symmetries and methods of visualizing these representations are discussed.…

This paper has a double goal, the first one is to make a slight survey of some theoretical results about the existence of positively invariant curves that allow to describe important properties of the set of bounded orbits and its boundary…

Various aspects of Supersymmetry in 1-dimensional systems are analyzed.

In this paper, we characterize the polynomiality of surfaces of revolution by means of the polynomiality of an associated plane curve. In addition, if the surface of revolution is polynomial, we provide formulas for computing a polynomial…