We investigate the solution set of the pseudoperiodic extension of the classical Lyndon and Schützenberger word equations. Consider u1 · · ·u` = v1 · · · vmw1 · · ·wn, where ui ∈ {u, θ(u)} for all 1 ≤ i ≤ `, vj ∈ {v, θ(v)} for all 1 ≤ j ≤ m, wk ∈ {w, θ(w)} for all 1 ≤ k ≤ n and u, v and w are variables, and θ is an antimorphic involution. A solution is called pseudoperiodic, if u, v, w ∈ {t, θ(...

Objective The purpose of this study is to examine oscillations in the activity of a BCM neuron, as the neuron adapts to an input. We want to explore how the various aspects of the oscillations (frequency, amplitude, etc...) depend on the parameters of the BCM model. 1 The Theory This study is to organize my thoughts on the subject, and to present the material in a way which highlights the main ...

This supplementary appendix contains additional materials for the paper “Robustness and Separation in Multidimensional Screening.” Section B contains proofs of auxiliary results not included in the main paper. Section C details how the generalized virtual values coincide with traditional (ironed) virtual values in the single-good monopoly problem. Theorems, equations, and sections in the main p...

and Applied Analysis 3 Theorem 2.3. Suppose that f : R ×Rd×Rd → ×Rd is continuous, a, b : R → R are continuous, strictly increasing functions satisfying a 0 b 0 0. Let constants M > 0 and q ∈ 0, 1 exist such that for n ∈ Z, a |x| ≤ V t, x ≤ b |x| , t ∈ R, x ∈ R, 2.3 V n 1, x n 1 ≤ qV n, x n , 2.4 V t, x t ≤ MV n, x n , for t ∈ n, n 1 . 2.5 Then the trivial solution of 1.1 is asymptotically stab...

Bounded linear types have proved to be useful for automated resource analysis and control in functional programming languages. In this paper we introduce a bounded linear typing discipline on a general notion of resource which can be modeled in a semiring. For this type system we provide both a general type-inference procedure, parameterized by the decision procedure of the semiring equational ...

is a module over the ring of all modular forms with respect to the group Γ2[4, 8]. We are interested in its structure. By Igusa, the ring of modular forms is generated by the ten classical theta constants θ[m]. The module M contains a submodule N which is generated by 45 Cohen-Rankin brackets {θ[m], θ[n]}. We determine defining relations for this submodule and compute its Hilbert function (Theo...

Sex differences in skews of vertebrate lifetime reproductive success are difficult to measure directly. Evolutionary histories of differential skew should be detectable in the genome. For example, male-biased skew should reduce variation in the biparentally inherited genome relative to the maternally inherited genome. We tested this approach in lek-breeding ruff (Class Aves, Philomachus pugnax)...

Starting from the pseudo-differential decomposition D = ( − Δ ) 1 2 H of Dirac operator ∑ j n e ∂ x in terms fractional order and Riesz–Hilbert type we will investigate fundamental solutions space-fractional equation Lévy–Feller t Φ α , ; θ exp i π involving Laplacian α, with 2m≤α < 2m + m ∈ ℕ), exponentiation as hypercomplex counterpart transform carrying skewness parameter θ, values range | ≤...

We 1 summarize previous VLBI observations of Sgr A* at millimeter wavelengths and present new results from VLBI observations at 86 GHz and at 215 GHz. At 86 GHz the measured closure phase is close to zero, consistent with a point-like or symmetric structure of 190±30 µas size. At 215 GHz we have (for the first time) detected Sgr A* with a signal-to-noise ratio of 6. This yields a tentative size...

Plant responses to drought stress vary depending on the severity of stress and the stage of drought progression. To improve the understanding of such responses, the leaf physiology, abscisic acid (ABA) concentration, and expression of genes associated with ABA metabolism and signalling were investigated in Petunia × hybrida. Plants were exposed to different specific substrate water contents (θ ...