111 research outputs found
Remarks on the conjectures of Capparelli, Meurman, Primc and Primc
No full textIn a sequence of two papers, S. Capparelli, A. Meurman, A. Primc, M. Primc
(CMPP) and then M. Primc put forth three remarkable sets of conjectures,
stating that the generating functions of coloured integer partition in which
the parts satisfy restrictions on the multiplicities admit simple infinite
product forms. While CMPP related one set of conjectures to the principally
specialised characters of standard modules for the affine Lie algebra
, finding a Lie-algebraic interpretation for the remaining
two sets remained an open problem. In this paper, we use the work of Griffin,
Ono and the fourth author on Rogers-Ramanujan identities for affine Lie
algebras to solve this problem, relating the remaining two sets of conjectures
to non-standard specialisations of standard modules for
and . We also use their work to formulate conjectures
for the bivariate generating function of one-parameter families of CMPP
partitions in terms of Hall-Littlewood symmetric functions. We make a detailed
study of several further aspects of CMPP partitions, obtaining (i) functional
equations for bivariate generating functions which generalise the well-known
Rogers-Selberg equations, (ii) a partial level-rank duality in the
case, and (iii) (conjectural) identities of the
Rogers-Ramanujan type for .Comment: 37 page
New partition identities for odd W odd
No full textIn this note we conjecture Rogers-Ramanujan type colored partition identities for an array Nwodd with odd number of rows w such that the first and the last row consist of even positive integers. In a strange way this is different from the partition identities for the array Nw with odd number of rows w such that the first and the last row consist of odd positive integers - the partition identities conjectured by S. Capparelli, A. Meurman, A. Primc and the author and related to standard representations of the affine Lie algebra of type Cl(1) for w = 2l + 1. The conjecture is based on numerical evidence
Strategies for Improved Wettability of Polyetheretherketone (PEEK) Polymers by Non-Equilibrium Plasma Treatment
No full textPolyetheretherketone (PEEK) is the material of choice in several applications ranging from the automotive industry to medicine, but the surface properties are usually not adequate. A standard method for tailoring surface properties is the application of gaseous plasma. The surface finish depends enormously on the processing parameters. This article presents a review of strategies adapted for improved wettability and adhesion of PEEK. The kinetics of positively charged ions, neutral reactive plasma species, and vacuum ultraviolet radiation on the surface finish are analyzed, and synergies are stressed where appropriate. The reviewed articles are critically assessed regarding the plasma and surface kinetics, and the surface mechanisms are illustrated. The directions for obtaining optimal surface finish are provided together with the scientific explanation of the limitations of various approaches. Super-hydrophilic surface finish is achievable by treatment with a large dose of vacuum ultraviolet radiation in the presence of oxidizing gas. Bombardment with positively charged ions of kinetic energy between about 100 and 1000 eV also enable high wettability, but one should be aware of excessive heating when using the ions
Surface Modification of Polyamides by Gaseous Plasma—Review and Scientific Challenges
No full textA review of the most significant scientific achievements in the field of surface modification of polyamides by non-equilibrium plasma treatments is presented. Most authors employed atmospheric pressure discharges and reported improved wettability. The super-hydrophilic surface finish was only achieved using a low-pressure plasma reactor and prolonged treatment time, enabling both the nanostructuring and functionalization with polar functional groups. The average increase of the oxygen concentration as probed by XPS was about 10 at%, while the changes in nitrogen concentrations were marginal in almost all cases. The final static water contact angle decreased with the increasing treatment time, and the oxygen concentration decreased with the increasing discharge power. The need for plasma characterization for the interpretation of experimental results is stressed
Recent Advances in Surface Activation of Polytetrafluoroethylene (PTFE) by Gaseous Plasma Treatments
No full textFluorinated polymers are renowned for their chemical inertness and thus poor wettability and adhesion of various coatings. Apart from chemical methods employing somewhat toxic primers, gaseous plasma treatment is a popular method for the modification of surface properties. Different authors have used different plasmas, and the resultant surface finish spans between super-hydrophobic and super-hydrophilic character. Some authors also reported the hydrophobic recovery. The review of recent papers is presented and discussed. Correlations between plasma and/or discharge parameters and the surface finish are drawn and the most important conclusions are summarized. The concentration of oxygen in the surface film as probed by X-ray photoelectron spectroscopy is inversely dependent on the concentration of oxygen in gaseous plasma. The predominant mechanism leading to hydrophilic surface finish is bond scission by deep ultraviolet radiation rather than functionalization with reactive oxygen species
Hydrophilization of Polypropylene by Gaseous Plasma Treatments and Hydrophobic Recovery
No full textAlthough polypropylene (PP) is among the most widely used polymers with adequate chemical and mechanical properties, its poor wettability prevents adhesive joints needed for sticking with other materials, printing, etc. Plasma treatment, an established method for increasing wettability, is presented, and relevant literature is analyzed. A comparison of different reviewed articles shows little influence of the discharge parameters on PP wettability, and that the methods for achieving a super-hydrophilic surface of this polymer have yet to be developed. The peculiarities of PP prevent stable surface functionalization, although the formation of molecular fragments is the predominant effect of plasma treatments. The key conclusion after analyzing the reviewed literature is that the washing of PP following plasma treatment will cause a low level of wettability regardless of the peculiarities of the plasmas or discharges, including the treatment time, and all authors reported a water contact angle between about 75 and 80° after washing the plasma-treated PP. The hydrophobic recovery of washed plasma-treated PP was not addressed in any reviewed article
Two constructions of grading-restricted vertex (super)algebras
No full textWe give two constructions of grading-restricted vertex (super)algebras. We first give a new construction of a class of grading-restricted vertex (super)algebras originally obtained by Meurman and Primc using a different method. This construction is based on a new definition of vertex operators and a new method. Our second construction is a generalization of the author's construction of the moonshine module vertex operator algebra and a related vertex operator superalgebra. This construction needs properties of intertwining operators formulated and proved by the author. (C) 2016 Elsevier B.V. All rights reserved.SCI(E)[email protected]
Haemostatic Response of Polyethylene Terephthalate Treated by Oxygen and Nitrogen Plasma Afterglows
No full textSamples of polymer polyethylene terephthalate were coated with heparin and the haemostatic response has been determined by optical imaging of samples after incubation with fresh blood from a healthy donor. Prior to coating the samples were treated by neutral reactive particles of the oxygen or nitrogen plasma flowing afterglow. X-ray photoelectron spectroscopy analysis showed intensive functionalization of the polymer foils upon treatment with afterglows; however, the concentration of sulphur from heparin remained below the detection limit. The optical imaging showed densely distributed blood platelets in highly activated forms on untreated samples, whereas treatment with both afterglows revealed improved hemocompatibility. Best results were obtained for oxygen-functionalized polymer, whereas additional coating with heparin caused moderate loss of hemocompatibility, that was explained by deactivation of surface functional groups upon incubation with heparin
Plasma Treatment of Nanocellulose to Improve the Surface Properties
No full textNanocellulose is among the most promising materials for enhancing the mechanical properties of polymer composites. Broad application is, however, limited by inadequate surface properties. A standard technique for tailoring the surface composition and wettability of polymers is a brief treatment with non-equilibrium gaseous plasma, but it often fails when treating materials with a large surface-to-mass ratio, such as cellulose nanofibers. In this paper, the theoretical limitations are explained, the approaches reported by different groups are reviewed, and the results are interpreted. The treatment of dry nanocellulose is limited by the ability of uniform treatment, whereas the plasma treatment of nanocellulose dispersed in liquids is a slow process. The methods for enhancing the treatment efficiency for both dry and water-dispersed nanocellulose are explained
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