On Hidden Markov Processes with Infinite Excess Entropy

We investigate stationary hidden Markov processes for which mutual information between the past and the future is infinite. It is assumed that the number of observable states is finite and the number of hidden states is countably infinite. Under this assumption, we show that the block mutual information of a hidden Markov process is upper bounded by a power law determined by the tail index of the hidden state distribution. Moreover, we exhibit three examples of processes. The first example, considered previously, is nonergodic and the mutual information between the blocks is bounded by the logarithm of the block length. The second example is also nonergodic but the mutual information between the blocks obeys a power law. The third example obeys the power law and is ergodic.     

On a nonlinear boundary value problem modeling corneal shape

In this paper we present some results concerning a boundary value problem for a nonlinear ordinary differential equation that was used before in modeling the topography of human cornea. These results generalize previously obtained theorems on existence and uniqueness. We show that our equation has a unique solution for all parameters and conditions that can arise in physical situation. In the second part of the article we derive some new estimates and approximate solutions. Numerical calculations verify that these approximations are very accurate.     

Electroanalysis of Norepinephrine at Bare Gold Electrode Pure and Modified with Gold Nanoparticles and S‐Functionalized Self‐Assembled Layers in Aqueous Solution

Gold nanoparticles (Au‐NPs), cystamine (CA) and 3,3′‐dithiodipropionic acid (DTDPA) modified gold bare electrodes were applied in voltammetric sensors for simultaneous detection of norepinephrine (NEP), ascorbic (AA) and uric (UA) acids. A linear relationship between norepinephrine concentration and current response was obtained in the range of 0.1 μM to 600 μM M with the detection limit ≤0.091 μM for the electrodes modified at 2D template and in the range of 0.1 μM to 700 μM M with the detection limit ≤0.087 μM for the electrodes modified at 3D template The results have shown that using modified electrodes it is possible to perform electrochemical analysis of norepinephrine without interference of ascorbic and uric acids, whose presence is the major limitation in norepinephrine determination at a bare gold electrode. The modified SAMs electrodes show good selectivity, sensitivity, reproducibility and high stability.     

Saw-sedge <Emphasis Type="Italic">Cladium mariscus</Emphasis> as a functional low-cost adsorbent for effective removal of 2,4-dichlorophenoxyacetic acid from aqueous systems

For the first time in the published literature, a study is described concerning the use of the saw-sedge Cladium mariscus (C. mariscus) for adsorption of 2,4-dichlorophenoxyacetic acid (2,4-D) from aqueous systems. Among the experiments carried out, the elemental composition of C. mariscus was determined (C = 48.0 %, H = 7.1 %, N = 0.95 %, S = 0.4 %), FTIR spectroscopic analysis was performed to confirm the chemical structure of the adsorbent, and porous structure parameters were measured: BET surface area (A _BET  = 0.6 m²/g), total pore volume (V _p  = 0.001 cm³/g) and average pore size (S _p  = 6.6 nm). It was shown that the effectiveness of removal of 2,4-D from aqueous systems using C. mariscus depends on parameters of the process: contact time, system pH, mass of sorbent, and temperature. Maximum adsorption was attained for a solution at pH = 3. Further increase in the alkalinity of the tested systems led to a reduction in the effectiveness of the process. The kinetic of adsorption of 2,4-D by C. mariscus was also determined, and thermodynamic aspects were investigated. The experimental data obtained correspond to a pseudo-second-order kinetic model of type 1. Additionally the negative values obtained for ΔHº indicate that the process is exothermic, and the negative values of ΔGº show it to be spontaneous. As the temperature of the system increases the spontaneity of adsorption is reduced, in accordance with the exothermic nature of the process.     

High-Pressure Mechanistic Insight into Bioinorganic NO Chemistry

Pressure is one of the most important parameters controlling the kinetics of chemical reactions. The ability to combine high-pressure techniques with time-resolved spectroscopy has provided a powerful tool in the study of reaction mechanisms. This review is focused on the supporting role of high-pressure kinetic and spectroscopic methods in the exploration of nitric oxide bioinorganic chemistry. Nitric oxide and other reactive nitrogen species (RNS) are important biological mediators involved in both physiological and pathological processes. Understanding molecular mechanisms of their interactions with redox-active metal/non-metal centers in biological targets, such as cofactors, prosthetic groups, and proteins, is crucial for the improved therapy of various diseases. The present review is an attempt to demonstrate how the application of high-pressure kinetic and spectroscopic methods can add additional information, thus enabling the mechanistic interpretation of various NO bioinorganic reactions.     

Determination of microgram amounts of azide by gas chromatography

Azide ions (5–120 μg) are oxidized by cerium(IV) in an acidic medium. The nitrogen evolved is displaced by helium carrier and quantified by gas chromatography with a thermal conductivity detector. The relative standard deviation is <5%. Many sulphur anions, cyanide and some metal ions which form azide complexes do not interfere.     

Joint universality for dependent <Emphasis Type="Italic">L</Emphasis>-functions

We prove that, for arbitrary Dirichlet L-functions \(L(s;\chi _1),\ldots ,L(s;\chi _n)\) (including the case when \(\chi _j\) is equivalent to \(\chi _k\) for \(j\ne k\)), suitable shifts of type \(L(s+i\alpha _jt^{a_j}\log ^{b_j}t;\chi _j)\) can simultaneously approximate any given set of analytic functions on a simply connected compact subset of the right open half of the critical strip, provided the pairs \((a_j,b_j)\) are distinct and satisfy certain conditions. Moreover, we consider a discrete analogue of this problem where t runs over the set of positive integers.     

Mössbauer effect studies of electrochemically hydrogenated austenitic steels

Electrochemically hydrogenated ASTM 310 and ASTM 316 austenitic steels were investigated by means of⁵⁷Fe Mössbauer spectroscopy. Starting with non-hydrogenated materials, freshly hydrogenated ones and one-day room temperature aged hydrogenated samples were studied. The resultant spectra were analysed with a modified Hesse-Rübartsch method [1] adopted to the case of isomer shift distribution.