Estimating moisture content variation in kiln dried Pacific coast hemlock

Kiln drying is admittedly a significant value-adding step in timber processing where the importance of predicting moisture within a dried batch cannot be overemphasized. This study predicts and characterizes the moisture variation in kiln-dried wood based on the initial and target moisture values using polynomial models. Four polynomial models are used to correlate initial and final moisture characteristics. First model is linear while the three others are nonlinear. The robustness of the three best models is analyzed and a closed formula is proposed to evaluate the final moisture coefficient of variation based on the target moisture and initial moisture coefficient of variation. Three models could successfully characterize the final moisture variation with the best one showing an R 2 > 96%. However, the first (linear) model is the most resilient and, thus recommended for estimating final moisture variation.

Labels distance in bucket recursive trees with variable capacities of buckets

The bucket recursive tree is a natural multivariate structure. In this paper, we apply a trivariate generating function approach for studying of the depth and distance quantities in this tree model with variable bucket capacities and give a closed formula for the probability distribution, the expectation and the variance. We show as j → ∞, lim-iting distributions are Gaussian. The results are obtained by presenting partial differential equations for moment generating functions and solving them.

Krull modules and completely integrally closed modules

Let [Formula: see text] be a torsion-free module over an integral domain [Formula: see text] with quotient field [Formula: see text]. We define a concept of completely integrally closed modules in order to study Krull modules. It is shown that a Krull module [Formula: see text] is a [Formula: see text]-multiplication module if and only if [Formula: see text] is a maximal [Formula: see text]-submodule and [Formula: see text] for every minimal prime ideal [Formula: see text] of [Formula: see text]. If [Formula: see text] is a finitely generated Krull module, then [Formula: see text] is a Krull module and [Formula: see text]-multiplication module. It is also shown that the following three conditions are equivalent: [Formula: see text] is completely integrally closed, [Formula: see text] is completely integrally closed, and [Formula: see text] is completely integrally closed.

On geodesically reversible Finsler manifolds

A Finsler manifold is said to be geodesically reversible if the reversed curve of any geodesic remains a geometrical geodesic. Well-known examples of geodesically reversible Finsler metrics are Randers metrics with closed [Formula: see text]-forms. Another family of well-known examples are projectively flat Finsler metrics on the [Formula: see text]-sphere that have constant positive curvature. In this paper, we prove some geometrical and dynamical characterizations of geodesically reversible Finsler metrics, and we prove several rigidity results about a family of the so-called Randers-type Finsler metrics. One of our results is as follows: let [Formula: see text] be a Riemannian–Finsler metric on a closed surface [Formula: see text], and [Formula: see text] be a small antisymmetric potential on [Formula: see text] that is a natural generalization of [Formula: see text]-form (see Sec. 1). If the Randers-type Finsler metric [Formula: see text] is geodesically reversible, and the geodesic flow of [Formula: see text] is topologically transitive, then we prove that [Formula: see text] must be a closed [Formula: see text]-form. We also prove that this rigidity result is not true for the family of projectively flat Finsler metrics on the [Formula: see text]-sphere of constant positive curvature.

Periodic solutions of Hilbert’s fourth problem

It is shown that a possibly irreversible [Formula: see text] Finsler metric on the torus, or on any other compact Euclidean space form, whose geodesics are straight lines is the sum of a flat metric and a closed [Formula: see text]-form. This is used to prove that if [Formula: see text] is a compact Riemannian symmetric space of rank greater than one and [Formula: see text] is a reversible [Formula: see text] Finsler metric on [Formula: see text] whose unparametrized geodesics coincide with those of [Formula: see text], then [Formula: see text] is a Finsler symmetric space.

Stereochemistry and chiroptical properties of bimetallic single helicates of hexapyrrole-α, ω-dicarbaldimines with high diastereoselectivity

Bimetallic complexes of hexapyrrole-[Formula: see text],[Formula: see text]-dicarbaldimines consisting of a pair of four-coordinate metal sites adopt a helical closed [Formula: see text]-symmetric form or sigmoidal open forms depending on whether the 2,2[Formula: see text]-bipyrrole subunit at the center of the hexapyrrole chain takes cis- or trans-conformation. X-ray crystallography of a bisNi complex having N-[([Formula: see text]-1-cyclohexylethyl]carbaldimine units at both ends of the hexapyrrole chain revealed a non-symmetric heterohelical open form where the metal coordination sites of opposite helical sense sit on opposite sides of the central 2,2[Formula: see text]-bipyrrole subunit. BisPd complexes preferred a closed [Formula: see text] form and a steric bulk at the 3,3[Formula: see text]-position of the 2,2[Formula: see text]-bipyrrole subunit improved the helical sense bias. A bisPd complex with N-[([Formula: see text]-1-cyclohexylethyl]carbaldimine units adopts a helical closed [Formula: see text] form exclusively with full bias for a [Formula: see text]-helical sense. These bimetallic single stranded helicates were reversibly oxidized to [Formula: see text]-cation radicals at 0.1[Formula: see text]0.3 V vs. a ferrocene/ferrocenium couple and spectroelectrochemistry revealed remarkable absorption and CD spectral changes in the Vis-NIR region.

String correlators on AdS3: three-point functions

We revisit the computation of string worldsheet correlators on Euclidean AdS3 with pure NS-NS background. We compute correlation functions with insertions of spectrally flowed operators. We explicitly solve all the known constraints of the model and for the first time conjecture a closed formula for three-point functions with arbitrary amount of spectral flow. We explain the relation of our results with previous computations in the literature and derive the fusion rules of the model. This paper is the first in a series with several installments.

The motivic Igusa zeta function of a space monomial curve with a plane semigroup

In this article, we compute the motivic Igusa zeta function of a space monomial curve that appears as the special fiber of an equisingular family whose generic fiber is a complex plane branch. To this end, we determine the irreducible components of the jet schemes of such a space monomial curve. This approach does not only yield a closed formula for the motivic zeta function, but also allows to determine its poles. We show that, while the family of the jet schemes of the fibers is not flat, the number of poles of the motivic zeta function associated with the space monomial curve is equal to the number of poles of the motivic zeta function associated with a generic curve in the family.

A Discrete Morse Perspective on Knot Projections and a Generalised Clock Theorem

We obtain a simple and complete characterisation of which matchings on the Tait graph of a knot diagram induce a discrete Morse function (dMf) on the two sphere, extending a construction due to Cohen. We show these dMfs are in bijection with certain rooted spanning forests in the Tait graph. We use this to count the number of such dMfs with a closed formula involving the graph Laplacian. We then simultaneously generalise Kauffman's Clock Theorem and Kenyon-Propp-Wilson's correspondence in two different directions; we first prove that the image of the correspondence induces a bijection on perfect dMfs, then we show that all perfect matchings, subject to an admissibility condition, are related by a finite sequence of click and clock moves. Finally, we study and compare the matching and discrete Morse complexes associated to the Tait graph, in terms of partial Kauffman states, and provide some computations.