Thermal and radical polymerization of anthracene acrylates and methacrylates

The thermal and radical-induced polymerizations of 9-anthrylmethyl acrylate ( I ), 9-anthrylmethyl methacrylate ( II ), 1′-(9-anthryl)ethyl acrylate ( III ), and 1′-(9-anthryl)ethyl methacrylate ( IV ) have been studied. It was found that the radical-induced polymerization takes place for the methacrylates only, while thermal polymerization leads to polymers for both types of monomers and takes place by Diels–Alder cycloaddition in the case of acrylates, and by both normal enchainment and Diels–Alder cycloaddition in the case of methacrylates.     

Safety of structural systems with correlated resistances

In this paper, the reliability of basic structural systems is examined. For elementary chain and ductile parallel systems, the effects of equal correlation between element strengths is established assuming normality. A special case involving a choice between statically determinate and indeterminate structural systems is examined and an ‘optimum’ design approach is presented. In this optimal solution, the correlation structure between elements is controlled so as to maximize the system reliability for given element safety. Reliability analysis is based on a two moment safety index.     

From the Cube to the Dyck and Klein Tessellations: Implications for the Structures of Zeolite-like Carbon and Boron Nitride Allotropes

Geometrical transformations can be described which have the effect of multiplying the numbers of vertices in a trivalent polyhedron by three, four, or seven. Tripling the cube by the so-called leapfrog transformation gives the truncated octahedron. Quadrupling the cube followed by identifying the square faces to give a genus 3 surface gives the Dyck surface of 12 octagons. Septupling the cube by the so-called capra transformation followed by identifying the square faces to give a genus 3 surface gives the Klein surface of 24 heptagons. These geometrical transformations relate to the construction of low-density zeolite-like structures for carbon and boron nitride allotropes based on a cubic lattice     

On the Number of Even Parts in All Partitions of $$\varvec{n}$$n into Distinct Parts

Annals of Combinatorics - A famous theorem of Euler asserts that there are as many partitions of n into distinct parts as there are partitions into odd parts. The even parts in partitions of n into...     

Binomial transforms and integer partitions into parts of <Emphasis Type="Italic">k</Emphasis> different magnitudes

A relationship between the general linear group of degree n over a finite field and the integer partitions of n into parts of k different magnitudes was investigated recently by the author. In this paper, we use a variation of the classical binomial transform to derive a new connection between partitions into parts of k different magnitudes and another finite classical group, namely the symplectic group Sp. New identities involving the number of partitions of n into parts of k different magnitudes are introduced in this context.     

A common fixed point theorem with applications to vector equilibrium problems

In this paper, using the Brouwer fixed point theorem, we establish a common fixed point theorem for a family of set-valued mappings. As applications of this result we obtain existence theorems for the solutions of two types of vector equilibrium problems, a Ky Fan-type minimax inequality and a generalization of a known result due to Iohvidov.     

An electro-viscoelastic frictional contact problem with damage

We consider a quasistatic frictional contact problem between a piezoelectric body and a foundation. The contact is modeled with normal compliance and friction is modeled with a general version of Coulomb's law of dry friction; the process is quasistatic and the material's behavior is described by an electro-viscoelastic constitutive law with damage. We derive a variational formulation for the model which is in the form of a system involving the displacement field, the electric potential field, and the damage field. Then we provide the existence of a unique weak solution to the model. The proof is based on arguments of evolutionary variational inequalities and fixed point.