Search results for " Mathematical"
showing 10 items of 686 documents
Fast MATLAB assembly of FEM matrices in 2D and 3D: Edge elements
2014
We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. We apply this for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in discretizations of H(div) spaces and Nedelec elements in discretizations of H(curl) spaces. We explain vectorization ideas and comment on a freely available MATLAB code which is fast and scalable with respect to time.
A New Nonparametric Estimate of the Risk-Neutral Density with Applications to Variance Swaps
2021
We develop a new nonparametric approach for estimating the risk-neutral density of asset prices and reformulate its estimation into a double-constrained optimization problem. We evaluate our approach using the S\&P 500 market option prices from 1996 to 2015. A comprehensive cross-validation study shows that our approach outperforms the existing nonparametric quartic B-spline and cubic spline methods, as well as the parametric method based on the Normal Inverse Gaussian distribution. As an application, we use the proposed density estimator to price long-term variance swaps, and the model-implied prices match reasonably well with those of the variance future downloaded from the CBOE websi…
Lines on K3 quartic surfaces in characteristic 2
2016
We prove that a K3 quartic surface defined over a field of characteristic 2 can contain at most 68 lines. If it contains 68 lines, then it is projectively equivalent to a member of a 1-dimensional family found by Rams and Sch\"utt.
The prime graph on class sizes of a finite group has a bipartite complement
2020
Abstract Let G be a finite group, and let cs ( G ) denote the set of sizes of the conjugacy classes of G. The prime graph built on cs ( G ) , that we denote by Δ ( G ) , is the (simple undirected) graph whose vertices are the prime divisors of the numbers in cs ( G ) , and two distinct vertices p, q are adjacent if and only if pq divides some number in cs ( G ) . A rephrasing of the main theorem in [8] is that the complement Δ ‾ ( G ) of the graph Δ ( G ) does not contain any cycle of length 3. In this paper we generalize this result, showing that Δ ‾ ( G ) does not contain any cycle of odd length, i.e., it is a bipartite graph. In other words, the vertex set V ( G ) of Δ ( G ) is covered b…
Bounding the number of vertices in the degree graph of a finite group
2020
Abstract Let G be a finite group, and let cd ( G ) denote the set of degrees of the irreducible complex characters of G . The degree graph Δ ( G ) of G is defined as the simple undirected graph whose vertex set V ( G ) consists of the prime divisors of the numbers in cd ( G ) , two distinct vertices p and q being adjacent if and only if pq divides some number in cd ( G ) . In this note, we provide an upper bound on the size of V ( G ) in terms of the clique number ω ( G ) (i.e., the maximum size of a subset of V ( G ) inducing a complete subgraph) of Δ ( G ) . Namely, we show that | V ( G ) | ≤ max { 2 ω ( G ) + 1 , 3 ω ( G ) − 4 } . Examples are given in order to show that the bound is bes…
On sigma-subnormal subgroups of factorised finite groups
2020
Abstract Let σ = { σ i : i ∈ I } be a partition of the set P of all prime numbers. A subgroup X of a finite group G is called σ-subnormal in G if there is chain of subgroups X = X 0 ⊆ X 1 ⊆ ⋯ ⊆ X n = G with X i − 1 normal in X i or X i / C o r e X i ( X i − 1 ) is a σ i -group for some i ∈ I , 1 ≤ i ≤ n . In the special case that σ is the partition of P into sets containing exactly one prime each, the σ-subnormality reduces to the familiar case of subnormality. If a finite soluble group G = A B is factorised as the product of the subgroups A and B, and X is a subgroup of G such that X is σ-subnormal in 〈 X , X g 〉 for all g ∈ A ∪ B , we prove that X is σ-subnormal in G. This is an extension…
Degrees of rational characters of finite groups
2010
Abstract A classical theorem of John Thompson on character degrees states that if the degree of any complex irreducible character of a finite group G is 1 or divisible by a prime p, then G has a normal p-complement. In this paper, we consider fields of values of characters and prove some improvements of this result.
On irreducible products of characters
2021
Abstract We study the problem when the product of two non-linear Galois conjugate characters of a finite group is irreducible. We also prove new results on irreducible tensor products of cross-characteristic Brauer characters of quasisimple groups of Lie type.
Powers of conjugacy classes in a finite groups
2020
[EN] The aim of this paper is to show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper was to show several results about solvability concerning the case in which the power of a conjugacy class is a union of one or two conjugacy classes. Moreover, we show that the above conditions can be determined through the character table of the group.