A complete list of conservation laws for non-integrable compacton equations of K(m,m)K(m,m) type

In 1993, P. Rosenau and J. M. Hyman introduced and studied Korteweg-de-Vries-like equations with nonlinear dispersion admitting compacton solutions, $u_t+D_x^3(u^n)+D_x(u^m)=0$, $m,n>1$, which are known as the $K(m,n)$ equations. In the present paper we consider a slightly generalized version of the $K(m,n)$ equations for $m=n$, namely, $u_t=aD_x^3(u^m)+bD_x(u^m)$, where $m,a,b$ are arbitrary real numbers. We describe all generalized symmetries and conservation laws thereof for $m\neq -2,-1/2,0,1$; for these four exceptional values of $m$ the equation in question is either completely integrable ($m=-2,-1/2$) or linear ($m=1$) or trivial ($m=0$). It turns out that for $m\neq -2,-1/2,0,1$ there are only three symmetries corresponding to $x$- and $t$-translations and scaling of $t$ and $u$, and four nontrivial conservation laws, one of which expresses the conservation of energy, and the other three are associated with the Casimir functionals of the Hamiltonian operator $\mathfrak{D}=aD_x^3+bD_x$ admitted by our equation. Our result, \textit{inter alia}, provides a rigorous proof of the fact that the K(2,2) equation has just four conservation laws found by P. Rosenau and J. M. Hyman

Virus Replication as a Phenotypic Version of Polynucleotide Evolution

In this paper we revisit and adapt to viral evolution an approach based on the theory of branching process advanced by Demetrius, Schuster and Sigmund ("Polynucleotide evolution and branching processes", Bull. Math. Biol. 46 (1985) 239-262), in their study of polynucleotide evolution. By taking into account beneficial effects we obtain a non-trivial multivariate generalization of their single-type branching process model. Perturbative techniques allows us to obtain analytical asymptotic expressions for the main global parameters of the model which lead to the following rigorous results: (i) a new criterion for "no sure extinction", (ii) a generalization and proof, for this particular class of models, of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930-2939), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in in four distinct "stages": extinction threshold, lethal mutagenesis, stationary "equilibrium" and transient. Finally, based on these quantitative results we are able to draw some qualitative conclusions.Comment: 23 pages, 1 figure, 2 tables. arXiv admin note: substantial text overlap with arXiv:1110.336

Functional characterization of two defensin isoforms of the hard tick Ixodes ricinus

<p>Abstract</p> <p>Background</p> <p>The immune system of ticks is stimulated to produce many pharmacologically active molecules during feeding and especially during pathogen invasion. The family of cationic peptides - defensins - represents a specific group of antimicrobial compounds with six conserved cysteine residues in a molecule.</p> <p>Results</p> <p>Two isoforms of the defensin gene <it>(def1 </it>and <it>def2</it>) were identified in the European tick <it>Ixodes ricinus</it>. Expression of both genes was induced in different tick organs by a blood feeding or pathogen injection. We have tested the ability of synthetic peptides def1 and def2 to inhibit the growth or directly kill several pathogens. The antimicrobial activities (expressed as minimal inhibition concentration and minimal bactericidal concentration values) against Gram positive bacteria were confirmed, while Gram negative bacteria, yeast, Tick Borne Encephalitis and West Nile Viruses were shown to be insensitive. In addition to antimicrobial activities, the hemolysis effect of def1 and def2 on human erythrocytes was also established.</p> <p>Conclusions</p> <p>Although there is nothing known about the realistic concentration of defensins in <it>I. ricinus </it>tick body, these results suggest that defensins play an important role in defence against different pathogens. Moreover this is a first report of a one amino acid substitution in a defensins molecule and its impact on antimicrobial activity.</p

Novel Bradykinin Analogues Modified in the N-Terminal Part of the Molecule with a Variety of Acyl Substituents

In the current work we present some pharmacological characteristics of ten new analogues of bradykinin (Arg–Pro–Pro–Gly–Phe–Ser–Pro–Phe–Arg) modified in the N-terminal part of the molecule with a variety of acyl substituents. Of the many acylating agents used previously with B2 receptor antagonists, the following residues were chosen: 1-adamantaneacetic acid (Aaa), 1-adamantanecarboxylic acid (Aca), 4-tert-butylbenzoic acid (t-Bba), 4-aminobenzoic acid (Aba), 12-aminododecanoic acid (Adc), succinic acid (Sua), 4-hydroxybenzoic acid, 4-hydroxy-3-methoxybenzoic acid, 3-(4-hydroxyphenyl)propionic acid and 6-hydroxy-2-naphthoic acid. Biological activity of the compounds was assessed in the in vivo rat blood pressure test and the in vitro rat uterus test. Surprisingly, N-terminal substitution of the bradykinin peptide chain itself with aforementioned groups resulted in antagonists of bradykinin in the pressor test and suppressed agonistic potency in the uterotonic test. These interesting findings need further studies as they can be helpful for designing more potent B2 receptor blockers

Linear feedback analysis of cardiovascular system using seismocardiogram

The paper deals with an analysis of relationship between heart rate described by a sequence of cardiac interbeat intervals and mechanical activity of heart represented by a sequence of systolic forces. Both the quantities were determined from seismocardiograms recorded from healthy subjects under two different experimental conditions. The method of the linear feedback baroreflex approach originally developed in [1], [2] and [3] was applied for the analysis. Different character of obtained results in comparison to those described in [1], [2] or [3], is explained by differences between frequency properties of the recorded sequences of the systolic forces and values of systolic blood pressure

Aerogels of Polypyrrole/Tannic Acid with Nanofibrillated Cellulose for the Removal of Hexavalent Chromium Ions

The preparation of conducting polymer aerogels is an effective strategy to produce innovative materials with enhanced physicochemical properties. Herein, polypyrrole (PPy) aerogels were oxidatively prepared in the presence of tannic acid (TA) with different concentrations (2.5, 5, and 10% mole ratio to pyrrole monomer) under freezing conditions. Nanofibrillated cellulose (NFC) was added during the PPy/TA synthesis to enhance mechanical stability. The effect of TA concentration on the aerogels’ morphology, conductivity, thermal stability, and adsorption capacity was investigated. The conductivity of 9.6 ± 1.7 S cm−1 was achieved for PPy/TA prepared with 2.5% TA, which decreased to 0.07 ± 0.01 S cm−1 when 10% TA was used. PPy/TA aerogels have shown high efficacy in removing Cr(VI) ions from aqueous solutions. Adsorption experiments revealed that all the aerogels follow pseudo-second-order kinetics. PPy/TA prepared with NFC has a maximum adsorption capacity of 549.5 mg g−1

Speedy bioceramics: Rapid densification of tricalcium phosphate by ultrafast high-temperature sintering

Due to unique osteogenic properties, tricalcium phosphate (TCP) has gained relevance in the field of bone repair. The development of novel and rapid sintering routes is of particular interest since TCP undergoes to hightemperature phase transitions and is widely employed in osteoconductive coatings on thermally-sensitive metal substrates. In the present work, TCP bioceramics was innovatively obtained by Ultrafast High-temperature Sintering (UHS). Ca-deficient hydroxyapatite nano-powder produced by mechanochemical synthesis of mussel shellderived calcium carbonate was used to prepare the green samples by uniaxial pressing. These were introduced within a graphite felt which was rapidly heated by an electrical current flow, reaching heating rates exceeding 1200 degrees C min-1. Dense (> 93%) ceramics were manufactured in less than 3 min using currents between 25 and 30 A. Both beta and alpha-TCP were detected in the sintered components with proportions depending on the applied current. Preliminary tests confirmed that the artifacts do not possess cytotoxic effects and possess mechanical properties similar to conventionally sintered materials. The overall results prove the applicability of UHS to bioceramics paving the way to new rapid processing routes for biomedical components.Web of Science127art. no. 11224