Experimental Determination of Third Derivative of the Gibbs Free Energy, <Emphasis Type="Italic">G</Emphasis> II: Differential Pressure Perturbation Calorimetry

We have been evaluating third derivative quantities of the Gibbs free energy, G, by graphically differentiating the second derivatives that are accessible experimentally, and demonstrated their power in elucidating the mixing schemes in aqueous solutions. Here we determine directly one of the third derivatives of G, the partial molar entropy-volume cross fluctuation density of 2-butoxyethanol (BE) in the BE–H₂O system, ^SV δ _BE . The difference of the heats of compression were directly determined using two identical cells and applying the same pressure change to both cells concurrently. Both cells are filled with sample solutions having a small appropriate difference in mole fraction. The results indicated that this method is feasible with the prior knowledge of the thermal expansivity of the solution to within a few per cent accuracy. If the volumes of the two cells are identical within the order of 0.01%, the method provides the required results to within 0.1% without the thermal expansivity data. This success opens a possibility of evaluating the fourth derivative graphically, which is expected to provide much more detailed information about the molecular processes in aqueous solutions.     

Fischer decomposition in symplectic harmonic analysis

In the framework of quaternionic Clifford analysis in Euclidean space \(\mathbb {R}^{4p}\) , which constitutes a refinement of Euclidean and Hermitian Clifford analysis, the Fischer decomposition of the space of complex valued polynomials is obtained in terms of spaces of so-called (adjoint) symplectic spherical harmonics, which are irreducible modules for the symplectic group Sp \((p)\) . Its Howe dual partner is determined to be \(\mathfrak {sl}(2,\mathbb {C}) \oplus \mathfrak {sl}(2,\mathbb {C}) = \mathfrak {so}(4,\mathbb {C})\) .     

Effects of gadoxetic acid on liver elasticity measurement by using magnetic resonance elastography

The purpose of this study was to evaluate the effect of gadoxetic acid (Gd-EOB-DTPA) on measurements of liver stiffness by using magnetic resonance elastography (MRE). In this study, 104 consecutive patients (mean age, 67.7±9.4 years) underwent MRE using a 1.5-T MR scanner equipped with a cylindrical passive driver that was placed across the right chest wall for delivering vibrations. Axial gradient-echo images, which were automatically converted to elastograms that represented stiffness (kPa), were acquired using a continuous sinusoidal vibration of 60 Hz. Two raters independently placed a region of interest on the right lobe of the liver on the elastograms obtained before and after Gd-EOB-DTPA was administered. Liver stiffness was measured using these two elastograms and compared using a paired t test and correlation analysis. No significant difference was observed in liver stiffness before and after Gd-EOB-DTPA was administered (Rater 1, P=.1200; Rater 2, P=.3585). The correlation coefficients were 0.986 (Rater 1) and 0.984 (Rater 2), indicating excellent correlation between the stiffness values before and after Gd-EOB-DTPA was administered. Liver stiffness measured by MRE did not differ before and after Gd-EOB-DTPA was administered.     

Ricci-corrected derivatives and invariant differential operators

We introduce the notion of Ricci-corrected differentiation in parabolic geometry, which is a modification of covariant differentiation with better transformation properties. This enables us to simplify the explicit formulae for standard invariant operators given in [A. ?ap, J. Slovák, V. Sou?ek, Invariant operators on manifolds with almost hermitian symmetric structures, III. Standard operators, Differential Geom. Appl. 12 (2000) 51-84], and at the same time extend these formulae from the context of AHS structures (which include conformal and projective structures) to the more general class of all parabolic structures (including CR structures).     

The Generalized Dolbeault Complex in Two Clifford Variables

The Penrose transform is used to construct a complex starting with the Dirac operator in two Clifford variables. The corresponding relative BGG complex and its direct image is computed for cohomology with values in line bundles induced by representations in singular infinitesimal character. The limit of the induced spectral sequence is computed in cases connected with the Dirac operator in two Clifford variables. The work presented here is a part of the research project MSM 0021620839 and was supported also by the grants GAUK 447/2004 and GA ČR 201/05/2117.     

Graphs of finite mass which cannot be approximated in area by smooth graphs

In this note we shall show that there are obstructions of homotopic and not just of homological nature to the approximability in area of graphs of finite mass by graphs of smooth maps. We shall present a class of closed graphs with finite mass which cannot be approximated weakly and in area by smooth graphs. This work has been partially supported by the Ministero dell'Universitá e della Ricerca Scientifica, by C.N.R. contract n. 91.01343.CT01, and by the European Research Project GADGET     

Remarks on the lower semicontinuity of quasiconvex integrals

We prove lower semicontinuity of quasiconvex integrals with integrands controlled by the minors.This work has been partially supported by the Ministero dell'Università e della Ricerca Scientifica and by the European Research Project GADGET II     

Characterization of acoustic streaming and heating using synchronized infrared thermography and particle image velocimetry

Real-time measurements of acoustic streaming velocities and surface temperature fields using synchronized particle image velocimetry and infrared thermography are reported. Measurements were conducted using a 20 kHz Langevin type acoustic horn mounted vertically in a model sonochemical reactor of either degassed water or a glycerin-water mixture. These dissipative phenomena are found to be sensitive to small variations in the medium viscosity, and a correlation between the heat flux and vorticity was determined for unsteady convective heat transfer.     

Fundaments of Quaternionic Clifford Analysis I: Quaternionic Structure

Introducing a quaternionic structure on Euclidean space, the fundaments for quaternionic and symplectic Clifford analysis are studied in detail from the viewpoint of invariance for the symplectic group action.