Raman study of PANI thin film during long time period in dependence on storage conditions

Conducting polymer polyaniline which is nowadays in forefront of the interest was in our study prepared in a form of thin films from anilinium sulfate by its chemical oxidation using ammonium peroxydisulfate. During the oxidation process, the polyaniline was deposited on glass slides and immersed into reaction mixture. Two sets of polyaniline thin films were prepared with different oxidation times (10, 20, 30, and 40 min). The first set was kept dry in desiccator and the second one was freely exposed to air moisture. Raman spectroscopy, nondestructive technique which is very sensitive to changes in structure of polymers, was used for the characterization of the protonation state of prepared polyaniline thin films. It was found that storage conditions affect the protonation state which in case of samples kept in desiccator is maintained without significant changes for longer time. Raman spectroscopy also revealed the dependence of protonation state on the oxidation time and 10 min proved as not sufficient for the creation of the protonation form of polyaniline.     

Generating sublocales by subsets and relations: a tangle of adjunctions

Generalizing the obvious representation of a subspace \({Y \subseteq X}\) as a sublocale in Ω(X) by the congruence \({\{(U, V ) | U\cap Y = V \cap Y\}}\), one obtains the congruence \({\{(a, b) |\mathfrak{o}(a) \cap S = \mathfrak{o}(b) \cap S\}}\), first with sublocales S of a frame L, which (as it is well known) produces back the sublocale S itself, and then with general subsets \({S\subseteq L}\). The relation of such S with the sublocale produced is studied (the result is not always the sublocale generated by S). Further, we discuss in general the associated adjunctions, in particular that between relations on L and subsets of L and view the aforementioned phenomena in this perspective.     

Existence of weak solutions to doubly degenerate diffusion equations

We prove existence of weak solutions to doubly degenerate diffusion equations

Left conjugacy closed loops of nilpotency class two

Every LCC loop Q with Inn Q abelian is nilpotent class two. A loop Q of nilpotency class two is LCC ? L(x, y) = L(y, x) for all x, y ∈ Q ? ?/Z(Mlt Q) is abelian ? [x, y, z] = [x,z,y] for all x, y, z ∈ Q ? [x, y, z] = [xy, z][x, z]^?1 for all x, y, z ∈ Q. All nilpotent LCC loops of order p² are described, and some of their multiplication groups are computed.     

Few associative triples,isotopisms and groups

Let Q be a quasigroup. For \(\alpha ,\beta \in S_Q\) let \(Q_{\alpha ,\beta }\) be the principal isotope \(x*y = \alpha (x)\beta (y)\). Put \(\mathbf a(Q)= |\{(x,y,z)\in Q^3;\) \(x(yz)) = (xy)z\}|\) and assume that \(|Q|=n\). Then \(\sum _{\alpha ,\beta }\mathbf a(Q_{\alpha ,\beta })/(n!)^2 = n^2(1+(n-1)^{-1})\), and for every \(\alpha \in S_Q\) there is \(\sum _\beta \mathbf a(Q_{\alpha ,\beta })/n! = n(n-1)^{-1}\sum _x(f_x^2-2f_x+n)\ge n^2\), where \(f_x=|\{y\in Q;\) \( y = \alpha (y)x\}|\). If G is a group and \(\alpha \) is an orthomorphism, then \(\mathbf a(G_{\alpha ,\beta })=n^2\) for every \(\beta \in S_Q\). A detailed case study of \(\mathbf a(G_{\alpha ,\beta })\) is made for the situation when \(G = \mathbb Z_{2d}\), and both \(\alpha \) and \(\beta \) are “natural” near-orthomorphisms. Asymptotically, \(\mathbf a(G_{\alpha ,\beta })>3n\) if G is an abelian group of order n. Computational results: \(\mathbf a(7) = 17\) and \(\mathbf a(8) \le 21\), where \(\mathbf a(n) = \min \{\mathbf a(Q);\) \( |Q|=n\}\). There are also determined minimum values for \(\mathbf a(G_{\alpha ,\beta })\), G a group of order \(\le 8\).     

Scale transformations in phase space and stretched states of a harmonic oscillator

We consider scale transformations (q, p) → (λq, λp) in phase space. They induce transformations of the Husimi functions H(q, p) defined in this space. We consider the Husimi functions for states that are arbitrary superpositions of n-particle states of a harmonic oscillator. We develop a method that allows finding so-called stretched states to which these superpositions transform under such a scale transformation. We study the properties of the stretched states and calculate their density matrices in explicit form. We establish that the density matrix structure can be described using negative binomial distributions. We find expressions for the energy and entropy of stretched states and calculate the means of the number-ofstates operator. We give the form of the Heisenberg and Robertson–Schrödinger uncertainty relations for stretched states.     

Zinc-phosphate nanoparticles with reversibly attached TNF-α analogs: an interesting concept for potential use in active immunotherapy

The authors’ intention was to prepare nanometer-sized zinc-phosphate nanoparticles that would be capable of binding histidine-rich TNF-α analogs onto their surface via a coordinative bond. Zinc-phosphate nanoparticles with a size of around 60 nm were prepared by a wet precipitation method and characterized using SEM, EDX, XRD, and DLS. First, BSA was bound as a testing protein, afterward two TNF-α analogs with decreased activity were bound to the described nanoparticles. The efficiency of binding and the existence of coordinative bond were confirmed with SDS-PAGE analysis. During binding, particle storage, and release experiments, the prepared TNF-α analogs retained their biological activity—hence the epitopes necessary for formation of antibodies stayed intact. The particle size did not change within a period of 2 weeks. No significant agglomeration was observed, the particles could be quickly dispersed in ultrasound. The present nanoparticles and the general approach of coordinative binding are widely applicable for natural and engineered histidine-rich proteins. The nanoparticles bearing appropriate TNF-α analogs could also be potentially used for active immunotherapy to tackle the chronic inflammatory diseases associated with pathogenically elevated levels of TNF-α.     

Optimization of cubic GaN/AlGaN quantum cascade structures for negative refraction in the THz spectral range

In this work we theoretically investigate a possibility to use cubic nitride based multi-layer periodic nanostructure as a semiconductor metamaterial. The structure design is based on an active region of a quantum cascade laser optimized to achieve optical gain in the Terahertz (THz) spectral range. In particular, we test the GaN/AlGaN quantum well configurations, which should exhibit important advantages compared to GaAs-based structures, namely room temperature operation without the assistance of magnetic field and lower doping densities. Our numerical rate-equations model is solved self-consistently and it takes into account electron-longitudinal optical phonon scattering between all the relevant states among the adjacent periods of the structure. A global optimization routine, specifically genetic algorithm is then used to generate new gain-optimized structures. This work confirms the advantages of cubic GaN designs over GaAs ones, namely feasibility of negative refraction at room temperature without the assistance of magnetic field while keeping the doping densities of the same order of magnitude.     

Algebraic domain decomposition solver for linear elasticity

We generalize the overlapping Schwarz domain decomposition method to problems of linear elasticity. The convergence rate independent of the mesh size, coarse-space size, Korn's constant and essential boundary conditions is proved here. Abstract convergence bounds developed here can be used for an analysis of the method applied to singular perturbations of other elliptic problems.