What Ike brought about and took away: a hurricane and Doug Klein

What Ike brought about and took away: a hurricane and Doug Klei

Formal structure of periodic system of elements

For more than 150 years the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is. Herein, based on the relations of order and similarity, we report a formal mathematical structure for the periodic system, which corresponds to an ordered hypergraph. It is shown that the current periodic system of chemical elements is an instance of the general structure. The definition is used to devise a tailored periodic system of polarizability of single covalent bonds, where order relationships are quantified within subsets of similar bonds and among these classes. The generalised periodic system allows envisioning periodic systems in other disciplines of science and humanities

Natural Variation in Wood Properties of Alnus Acuminata H.B.K. Grown in Colombia

Ninety-nine Andean alder (Alnus acuminata H.B.K.) trees were sampled from eleven regions in Colombia and Venezuela to determine the pattern of wood property variation between regions, between altitude within regions, between trees, and within a tree. A 5-mm-diameter increment core was extracted from each tree at breast height. The core was used to evaluate wood density and the dynamic compliance coefficient in the longitudinal direction. Based on mean regional values, wood density varied from 314 kg/m3 to 409 kg/m3; and dynamic compliance coefficient varied from 91 x 10-6 MPa-1 to 136 x 10-6 MPa-1. Single-tree values ranged from 249 kg/m3 to 446 kg/m3 for wood density, and from 81 x 10-6 MPa-1 to 187 x 10-6 MPa-1 for the compliance coefficient, respectively. The analysis of variance indicated that both wood properties vary considerably between geographic locations, between trees, and within a tree. The wood density tends to increase linearly from pith to bark, although there were differences in the magnitude of increase between regions. Finally, tree characteristics (tree height and diameter at breast height) were not related to wood properties

LOS ELEMENTOS QUÍMICOS, SU MATEMÁTICA Y RELACIÓN CON EL SISTEMA PERIÓDICO

El sistema periódico de los elementos químicos visto como un conjunto de objetos definidos por sus propiedades físico-químicas, es susceptible de ser estudiado mediante matemática de conjuntos y topología general. En este trabajo hacemos una revisión de este estudio y resaltamos resultados como que la frontera matemática de los metales es un grupo de elementos semimetálicos y que los elementos alcalinos y gasesnobles son elementos que guardan pocas relaciones de similitud con el resto de los elementos

Ecuaciones operacionales y ecuaciones diferenciales

Sea E un espacio de Banach y sea T: E → E  un operador continuo. Para cada y  ∈ E defínase el operador(1)                       S (x)  = T(x) -  y  ;entonces x es una solución de  la ecuación(2)                       T(x)  =  ysi y solo si  x  es una solución de(3)                       S(x)  =  0Supongamos que la ecuación diferencial                        [Formula Matemática

Remarks on weakly continuous functions in banach spaces

Let E be a Banach space over the real.s and let E* be the dual space. Le t = (∝1 , …,  ∝n) be a finite sequence of non-negative integers and u = (u1, …,un) a finite sequence of elements in E*. The notation u∝ = u1 u1∝1  … u1∝1 … un∝n is standard and will used throughout. We will write  |∝| = ∝1 + … + ∝n .  Any real valued function in E of the form   P = ∑ (|∝|≤n) a∝ u∝ , a∝  a real number, is said to be a polynomial. Clearly, every polynomial is weakly continuous