History-dependent subdifferential inclusions and hemivariational inequalities in contact mechanics

We consider a class of subdifferential inclusions involving a history-dependent term for which we provide an existence and uniqueness result. The proof is based on arguments on pseudomonotone operators and fixed point. Then we specialize this result in the study of a class of history-dependent hemivariational inequalities. Such kind of problems arises in a large number of mathematical models which describe quasistatic processes of contact between a deformable body and an obstacle, the so-called foundation. To provide an example we consider a viscoelastic problem in which the frictional contact is modeled with subdifferential boundary conditions. We prove that this problem leads to a history-dependent hemivariational inequality in which the unknown is the velocity field. Then we apply our abstract result in order to prove the unique weak solvability of the corresponding contact problem.     

Corrigendum to “on the restricted partition function”

The Ramanujan Journal - This article is a corrigendum to our paper (Cimpoea? and Nicolae in Ramanujan J 473:565–588, 2018).     

Combinatorial proofs of two theorems related to the number of even parts in all partitions of n into distinct parts

The Ramanujan Journal - Recently, Andrews and Merca considered the number of even parts in all partitions of n into distinct parts and obtained new combinatorial interpretations for this number....     

Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry

The aim of this paper is to study two problems in the framework of paracontact geometry of dimension \(3\) , namely, the class of parallel symmetric tensor fields of \((0, 2)\) -type and possible Lorentz Ricci solitons. We search for two types of Ricci solitons: the first when its potential vector field is exactly the characteristic vector field \(\xi \) of the paracontact structure and the second when the potential vector field is a paracontact-holomorphic one. For the former case we find all variants of Ricci solitons, expanding, steady and shrinking, and the fact that \(\xi \) is a conformal Killing vector field. A class of examples is completely discussed.     

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.     

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.     

Joint seminormality and Dirac operators

In this article, an approach to joint seminormality based on the theory of Dirac and Laplace operators on Dirac vector bundles is presented. To eachn-tuple of bounded linear operators on a complex Hilbert space we first associate a Dirac bundle furnished with a metric-preserving linear connection defined in terms of thatn-tuple. Employing standard spin geometry techniques we next get a Bochner type and two Bochner-Kodaira type identities in multivariable operator theory. Further, four different classes of jointly seminormal tuples are introduced by imposing semidefiniteness conditions on the remainders in the corresponding Bochner-Kodaira identities. Thus we create a setting in which the classical Bochner's method can be put into action. In effect, we derive some vanishing theorems regarding various spectral sets associated with commuting tuples. In the last part of this article we investigate a rather general concept of seminormality for self-adjoint tuples with an even or odd number of entries.     

Separation of chitosan oligomers by immobilized metal affinity chromatography

A novel approach for chitosan oligosaccharide (COS) separation by immobilized metal affinity chromatography (IMAC) based on the differences in the interactions of chelated copper (II) ions with various COS (dimers, trimers, tetramers) is described. Polyhydroxylic chromatographic supports (agarose CL-6B and silica) were functionalized with various chelating functions such as iminodiacetate (IDA), carboxymethyl-aspartate (CM-Asp) and tris(carboxymethyl)ethylenediamine (TED). The COS retention capacities of the columns were between 2 and 6 mg/cm(3), depending on the chelating group. The COS were separated and/or enriched up to 95% for dimer and trimer and 90% for the tetramer, with yields of 60-95%.