Secreted proteins coded by parasitism genes expressed in esophageal gland cells mediate infection and parasitism of plants by root-knot nematodes. An essential parasitism gene, designated as 16D10, encodes a conserved root-knot nematode secretory peptide that stimulates root growth and functions as a ligand for a plant transcription factor. Plants were engineered to silence this parasitism gene...

We study the stationary solution to the recursion Xn+1 = γXn+ξn, where γ ∈ (0, 1) is a constant and ξn are Gaussian variables with random parameters. Specifically, we assume that ξn = μn + σnεn, where (ε)n∈Z is an i.i.d. sequence of standard normal variables and (μn, σn)n∈Z is a stationary and ergodic process independent of (εn)n∈Z, which serves as an exogenous dynamic environment for the model...

Let D be a domain with quotient field K and A a D-algebra. A polynomial with coefficients in K that maps every element of A to an element of A is called integer-valued on A. For commutative A we also consider integer-valued polynomials in several variables. For an arbitrary domain D and I an arbitrary ideal of D we show I -adic continuity of integer-valued polynomials on A. For Noetherian one-d...

The field of mathematics is known to be especially challenging from a bibliometric point of view. Its bibliographic metrics are especially sensitive to distortions and are heavily influenced by the subject and its popularity. Therefore, quantitative methods are prone to misrepresentations, and need to take subject information into account. In this paper we investigate how the mathematical bibli...

We consider Mn(R), the ring of n by n matrices on the real numbers where n ≥ 2. We find all of the natural numbers that are the degree of nilpotency of some nilpotent derivations on Mn(R). Mathematics Subject Classification: 16S50, 13N15, 16N40

In this paper, we observe the frog model, an infinite system of interacting random walks, on Z with an asymmetric underlying random walk. Under the assumption of transience with a fixed frog distribution, we construct an explicit formula for the moments of the lower bound of the model’s long-run range, as well as their asymptotic limits as the drift of the underlying random walk vanishes. We al...

Many prominent continuous-time stochastic volatility models exhibit certain functional relationships between price jumps and volatility jumps. We show that stochastic volatility models like the Ornstein-Uhlenbeck and other continous-time CARMA models as well as continous-time GARCH and EGARCH models all exhibit such functional relations. We investigate the asymptotic behaviour of certain functi...

We show that the set of Heisenberg polynomials furnishes a simple non-trivial example in the uniform treatment of Darboux’s method. MSC2010: 41A60; 33C15

Let C be a smooth projective curve in P1 × P1 of genus g 6= 4, and assume that it is birationally equivalent to a curve defined by a Laurent polynomial that is non-degenerate with respect to its Newton polygon ∆. Then we show that the convex hull ∆(1) of the interior lattice points of ∆ is a standard rectangle, up to a unimodular transformation. Our main auxiliary result, which we believe to be...

Schreyer has proved that the graded Betti numbers of a canonical tetragonal curve are determined by two integers b1 and b2, associated to the curve through a certain geometric construction. In this article we prove that in the case of a smooth projective tetragonal curve on a toric surface, these integers have easy interpretations in terms of the Newton polygon of its defining Laurent polynomia...