On locally linearly dependent operators and derivations

The first section of the paper deals with linear operators , , where and are vector spaces over an infinite field, such that for every , the vectors are linearly dependent modulo a fixed finite dimensional subspace of . In the second section, outer derivations of dense algebras of linear operators are discussed. The results of the first two sections of the paper are applied in the last section, where commuting pairs of continuous derivations of a Banach algebra such that is quasi-nilpotent for every are characterized.

     

External inversion,internal inversion,and reflection invariance

Having in mind that physical systems have different levels of structure we develop the concept of external, internal and total improper Lorentz transformation (space inversion and time reversal). A particle obtained from the ordinary one by the application of internal space inversion or time reversal is generally a different particle. From this point of view the intrinsic parity of a nuclear particle (elementary particle) is in fact the external intrinsic parity, if we take into account the internal structure of a particle. We show that non-conservation of the external parity does not necessarily imply noninvariance of nature under space inversion. The conventional theory of beta-decay can be corrected by including the internal degrees of freedom to become invariant under total space inversion, though not under the external one.     

Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings

The idea that spacetime has to be replaced by Clifford space (C-space) is explored. Quantum field theory (QFT) and string theory are generalized to C-space. It is shown how one can solve the cosmological constant problem and formulate string theory without central terms in the Virasoro algebra by exploiting the peculiar pseudo-Euclidean signature of C-space and the Jackiw definition of the vacuum state. As an introduction into the subject, a toy model of the harmonic oscillator in pseudo-Euclidean space is studied.     

Comment on the analysis of angle-dependent X-ray magnetic circular dichroism in systems with reduced dimensionality

The magnetic dipole term T appearing in the X-ray magnetic circular dichroism (XMCD) spin sum rule can be eliminated from the analysis within the spin sum rule by angle-dependent XMCD spectroscopy if the effects of spin–orbit coupling are small so that T_x+T_y+T_z≈0. It is shown by the ab initio electron theory for the extreme case of a low-dimensional system, i.e., for a free-standing monatomic Co wire that this relation is strongly violated, indicating that the determination of T by the angle-dependent XMCD is possibly not very reliable for low-dimensional magnetic systems.     

Polysulfobetaine films prepared by electrografting technique for reduction of biofouling on electroconductive surfaces

The sulfobetaine films were prepared on stainless steel and golden surfaces. In the first step, the poly(2-(dimethylamino)ethyl methacrylate) film was created by employing the electrografting polymerization technique. In the second step, this film was modified to polysulfobetaine, i.e. the polymer film bearing the zwitterionic groups. The presence of the electrografted film and its modification were determined by contact angle measurements, infrared spectroscopy in reflectance mode and X-ray photoelectron spectroscopy. The prepared films were homogeneous with the thickness from about 5 to 26 nm as determined by X-ray photoelectron spectroscopy. The atomic force microscopy measurements showed the increase of surface roughness upon the surface coating. In vitro tests using adherent RAT-2 fibroblast cells and fluorescently labelled bovine serum albumin proteins showed that prepared polysulfobetaine films can be used in applications requiring the resistance against cell attachment and biofouling.     

Specific O₂⁻ generation in corona discharge for ion mobility spectrometry

This study deals with O₂⁻ generation in corona discharge (CD) in point to plane geometry for single flow ion mobility spectrometry (IMS) with gas outlet located behind the ionization source. We have designed CD of special geometry in order to achieve the high O₂⁻ yield. Using this ion source we have achieved in zero air conditions that up to 74% all negative ions were O₂⁻ or O₂⁻(H₂O). It has been demonstrated that the non-electronegative nitrogen positively influences the efficiency of O₂⁻ generation in O₂/N₂ mixtures. The reduced ion mobility of 2.27 cm² V⁻¹ s⁻¹ has been measured for O₂⁻/O₂⁻(H₂O) ions in zero air. Additional ions detected in zero air (less than 200 ppb CO₂) using the mass spectrometric and IMS technique were, NO₂⁻, N₂O₂⁻ (2.37 cm² V⁻¹ s⁻¹), NO₃⁻, N₂O₃⁻ and N₂O₃⁻(H₂O). The CO₃⁻ and CO₄⁻ ions have been detected after the introduction of 5 ppm CO₂ into zero air.     

Paths through inverse limits

In Bani?, ?repnjak, Merhar and Milutinovi? (2010) [2] the authors proved that if a sequence of graphs of surjective upper semi-continuous set-valued functions fn:X→X² converges to the graph of a continuous single-valued function f:X→X, then the sequence of corresponding inverse limits obtained from fn converges to the inverse limit obtained from f. In this paper a more general result is presented in which surjectivity of fn is not required. The result is also generalized to the case of inverse sequences with non-constant sequences of bonding maps. Finally, these new theorems are applied to inverse limits with tent maps. Among other applications, it is shown that the inverse limits appearing in the Ingram conjecture (with a point added) form an arc.     

Single atom hot-spots at Au-Pd nanoalloys for electrocatalytic H2O2 production

A novel strategy to direct the oxygen reduction reaction to preferentially produce H(2)O(2) is formulated and evaluated. The approach combines the inertness of Au nanoparticles toward oxidation, with the improved O(2) sticking probability of isolated transition metal "guest" atoms embedded in the Au "host". DFT modeling was employed to screen for the best alloy candidates. Modeling indicates that isolated alloying atoms of Pd, Pt, or Rh placed within the Au surface should enhance the H(2)O(2) production relative to pure Au. Consequently, Au(1-x)Pd(x) nanoalloys with variable Pd content supported on Vulcan XC-72 were prepared to investigate the predicted selectivity toward H(2)O(2) production for Au alloyed with Pd. It is demonstrated that increasing the Pd concentration to 8% leads to an increase of the electrocatalytic H(2)O(2) production selectivity up to nearly 95%, when the nanoparticles are placed in an environment compatible with that of a proton exchange membrane. Further increase of Pd content leads to a drop in H(2)O(2) selectivity, to below 10% for x = 0.5. It is proposed that the enhancement in H(2)O(2) selectivity is caused by the presence of individual surface Pd atoms surrounded by gold, whereas surface ensembles of contiguous Pd atoms support H(2)O formation. The results are discussed in the context of exergonic electrocatalytic H(2)O(2) synthesis in Polymer Electrolyte Fuel Cells for the simultaneous cogeneration of chemicals and electricity, the latter a credit to production costs.     

Jordan Ideals Revisited

An alternative approach to the study of Jordan ideals in associative algebras is considered. The same method can be used when analogous questions in graded algebras are treated.