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.     

Fatty Acid Ethyl Esters (FAEE): A New,Green and Renewable Solvent for the Extraction of Carotenoids from Tomato Waste Products

Currently there is a drive towards the minimisation and reclamation of valuable materials from the waste products of the food and beverage industry. This can be achieved through the extraction of residual nutraceuticals from such materials. Tomato pomace contains carotenoids and other chemicals which can be extracted directly into edible oils to improve the health-giving properties of such oils. We report here a novel green solvent, fatty acid ethyl esters (FAEE), which is significantly more effective than sunflower oil and hexane for the extraction of lycopene and beta-carotene from tomato skin waste. FAEE are a non-toxic renewable resource that is environmentally friendly and to our knowledge has never been used as a vegetal extraction fluid. The efficiency of FAEE extraction was significantly improved relative to both sunflower oil and hexane under ultrasound-assisted extraction (UAE) conditions. In addition, FAEE have the additional and significant advantage that once enriched with the extracted nutraceuticals can be used directly as a food additive.     

An intersection theorem for set-valued mappings

Given a nonempty convex set X in a locally convex Hausdorff topological vector space, a nonempty set Y and two set-valued mappings T: X ? X, S: Y ? X we prove that under suitable conditions one can find an x ∈ X which is simultaneously a fixed point for T and a common point for the family of values of S. Applying our intersection theorem, we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.