A sequent calculus for logic of knowledge and past time: Completeness and decidability

We consider logic of knowledge and past time. This logic involves the discrete-time linear temporal operators next, until, weak yesterday, and since. In addition, it contains an indexed set of unary modal operators agent i knows.We consider the semantic constraint of the unique initial states for this logic. For the logic, we present a sequent calculus with a restricted cut rule. We prove the soundness and completeness of the sequent calculus presented. We prove the decidability of provability in the considered calculus as well. So, this calculus can be used as a basis for automated theorem proving. The proof method for the completeness can be used to construct complete sequent calculi with a restricted cut rule for this logic with other semantical constraints as well. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 427–437, July–September, 2006.     

Probing the influence of an allylic methyl group in zearalenone analogues on binding to Hsp90

By the replacement of an acetate with propionate by means of organic synthesis, a range of zearalenone analogues were prepared that feature an allylic methyl group. For the synthesis of the aliphatic region of the analogues, we used an asymmetric alkylation to yield pentenol derivatives 16 and ent‐ 16 . By means of hydroboration the corresponding aldehydes were secured. These were coupled with 2‐pentynol derivate 23 by means of a Carreira acetylide addition. Further routine steps led to the sulfones 29 and 45 , respectively. After merging them with 2‐bromobenzaldehyde 9 in a Julia–Kocienski reaction, metalation, carboxylation, and protecting‐group manipulations gave the seco acids 35 and 49 . By means of lactonization under Mitsunobu (alcohol activation) or Trost–Kita conditions (carboxyl activation), all four possible macrocyclic ketone stereoisomers were accessible. In all, considering various protecting‐group decorations, 16 analogues were obtained and tested for cytotoxicity (L929 mouse fibroblast cell line). Whereas most of the analogues were less active than zearalenone (IC₅₀=9.4 μM ), the resorcinol derivatives were comparable, with one stereoisomer ( 40 b ) being slightly more active (IC₅₀=6.6 μM ). These results were also reflected in the binding assays to Hsp90 in which 40 b showed a dissociation constant (K_d) value of 130 nM .     

Density Functional Calculation of the Photoelectron Emission Spectra of BiSCl Crystal and Molecular Clusters

The photoelectron emission spectra of BiSCl crystal and molecular clusters have been calculated by the Density Functional Theory (DFT) method. Molecular clusters consists from 2 to 20 molecules in one double chain along z(c) axis. Total and partial density of states of BiSCl crystal and clusters have been weighted with atomic photoemission emission cross-section. The molecular clusters have been investigated including all normal modes of vibration. Theoretical results of BiSCl crystal and molecular clusters have been compared with experimental X-ray photoelectron emission spectra (XPS) of BiSI crystal.     

Quantification of the evolution of shape storage and recovery in thermally responsive shape memory polymers

This study demonstrates the relevance of strain and stress storage/recovery profiles for the thermomechanical behaviour of thermally responsive Shape Memory Polymers (SMPs). It is shown how these experimentally determined profiles may be used for the development, calibration and validation of continuum-based models describing the shape memory effect in polymeric materials. The presented methodology applies both to small and finite strain deformation problems under the assumption of constant strain and cooling/heating rates. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Large Deviations of Vector-Valued Additive Functions of a Markov Gaussian Field

We prove a local limit theorem for large deviations of the sums , where , is a Markov Gaussian random field, is a bounded vector-valued function, and . This paper generalizes the paper [13].     

Evaluation of novel sample identification approach based on chromatographic fingerprint set correlation homogeneity analysis

Instead of usual rationale for chromatographic fingerprint based sample identification which relies upon visual inspection or principal component analysis of raw or aligned chromatograms novel nonparametric statistical measure of fingerprint set homogeneity is proposed. Randomization test is applied for significance analysis of fingerprint set homogeneity while average maximum crosscorrelation is used as a merit function. Chromatogram sets generated by random selection from standard and unknown sample chromatogram collections are compared with respect to merit function values with set of chromatograms that represents standard and/or unknown sample. In that instance fingerprint homogeneity significance is represented by the fraction of random chromatogram sets that have higher merit values than the standard and/or unknown sample sets. A set of peptide maps corresponding to different haemoglobin variants has been selected for evaluation of proposed test. This approach is compared to chromatogram alignment based on correlation optimized warping coupled with principal component or cluster analysis. Proposed method is simple i.e. straightforward sample identification procedure which reliability has been evaluated here. Impact of this approach on peptide mapping validation and system suitability analysis is discussed.     

Simultaneous purification of sewage from Cd(II) and nonionic surfactant with cation exchanger

The sorption of nonionic surfactant (alkylmonoethers ALM-10), taking place simultaneously with the sorption of Cd(II) in H-form of polyacrylic cation exchangers KB-2 and KB-2-12P was investigated. Increasing the sorption of surfactant the decrease in both the stability of Cd(II) complex with cation exchanger and the equilibrium sorption of Cd(II) was observed. The isotherms of the sorption were measured; the coefficients of intraparticle diffusion (D) were calculated. The integration of the filter filled with polyacrylic cation exchanger into the system of sewage purification is suggested.     

Light Engineering and Silicon Diffractive Optics Assisted Nonparaxial Terahertz Imaging

The art of light engineering unveils a world of possibilities through the meticulous manipulation of photonic properties such as intensity, phase, and polarization. Precision control over these properties finds application in a variety of fields spanning communications, light–matter interactions, laser direct writing, and imaging. Terahertz (THz) range, nestled between microwaves and infrared light, stands out for its remarkable ability to propagate with minimal losses in numerous dielectric materials and compounds, making THz imaging a powerful tool for noninvasive control and inspection. In this study, a rational framework for the design and optimal assembly of nonparaxial THz imaging systems is established. The research is centered on lensless photonic systems composed solely of high-resistivity silicon-based nonparaxial elements such as the Fresnel zone plate, the Fibonacci lens, the Bessel axicon, and the Airy zone plate, all fabricated using laser ablation technology. Through a comprehensive examination through illumination engineering and scattered light collection from raster-scanned samples in a single-pixel detector scheme, the imaging systems are evaluated via diverse metrics including contrast, resolution, depth of field, and focus. These findings chart an exciting course toward the development of compact and user-friendly THz imaging systems where sensors and optical elements seamlessly integrate into a single chip.     

Magnetic-Field-Controlled Quantum Critical Points in the Triangular Antiferromagnetic Cs2CuCl4-xBrx Mixed System

The triangular antiferromagnetic Cs₂CuCl_4-xBr_x mixed system is studied by neutron single-crystal diffraction in magnetic field. It shows a rich magnetic phase diagram consisting of four regimes depending on the Br concentration and is characterized by different exchange coupling mechanisms. For the investigated compositions from regime I (0 < x ≤ 1.5), a critical magnetic field B_c is found for a Br concentration x = 0.8 at B_c = 8.10(1) T and for x = 1.1 at B_c = 7.73(1) T and from regime IV (3.2 < x < 4) for x = 3.3 at B_c = 0.99(3) T. For magnetic fields larger than the respective B_c, magnetic superlattice reflections of these compounds are not found. The incommensurate magnetic wave vector q = (0, 0.470, 0) appears below the ordering temperature T_N = 0.51(1) K for Cs₂CuCl_3.2Br_0.8, and q = (0, 0.418, 0) below T_N = 1.00(6) K for Cs₂CuCl_0.3Br_3.7. Neutron diffraction experiments at around 60 mK for x = 3.7 in a magnetic field show the critical magnetic field at B_c = 7.94(16) T and the formation of the second magnetic phase at around 8.5 T depending on the temperature. Inelastic neutron scattering experiments for the compound from regime III (2 < x ≤ 3.2) with x = 2.2 show dynamical correlations at a temperature around 50 mK giving evidence for a spin liquid phase.