On the regular convergence of multiple series of numbers and multiple integrals of locally integrable functions over ℝ̄ + m

We investigate the regular convergence of the m-multiple series (*) $$\sum\limits_{j_1 = 0}^\infty {\sum\limits_{j_2 = 0}^\infty \cdots \sum\limits_{j_m = 0}^\infty {c_{j_1 ,j_2 } , \ldots j_m } }$$ of complex numbers, where m ≥ 2 is a fixed integer. We prove Fubini’s theorem in the discrete setting as follows. If the multiple series (*) converges regularly, then its sum in Pringsheim’s sense can also be computed by successive summation. We introduce and investigate the regular convergence of the m-multiple integral (**) $$\int_0^\infty {\int_0^\infty { \cdots \int_0^\infty {f\left( {t_1 ,t_2 , \ldots ,t_m } \right)dt_1 } } } dt_2 \cdots dt_m ,$$ where f : ?? ₊ ^m → ? is a locally integrable function in Lebesgue’s sense over the closed nonnegative octant ?? ₊ ^m := [0,∞) ^m . Our main result is a generalized version of Fubini’s theorem on successive integration formulated in Theorem 4.1 as follows. If f ∈ L _loc ¹ (?? ₊ ^m ), the multiple integral (**) converges regularly, and m = p + q, where p and q are positive integers, then the finite limit $$\mathop {\lim }\limits_{v_{_{p + 1} } , \cdots ,v_m \to \infty } \int_{u_1 }^{v_1 } {\int_{u_2 }^{v_2 } { \cdots \int_0^{v_{p + 1} } { \cdots \int_0^{v_m } {f\left( {t_1 ,t_2 , \ldots t_m } \right)dt_1 dt_2 } \cdots dt_m = :J\left( {u_1 ,v_1 ;u_2 v_2 ; \ldots ;u_p ,v_p } \right)} , 0 \leqslant u_k \leqslant v_k < \infty } ,k = 1,2, \ldots p,}$$ exists uniformly in each of its variables, and the finite limit $$\mathop {\lim }\limits_{v_1 ,v_2 \cdots ,v_p \to \infty } J\left( {0,v_1 ;0,v_2 ; \ldots ;0,v_p } \right) = I$$ also exists, where I is the limit of the multiple integral (**) in Pringsheim’s sense. The main results of this paper were announced without proofs in the Comptes Rendus Sci. Paris (see [8] in the References).     

Experimental studies of flow boiling heat transfer by using nanofluids

Journal of Thermal Analysis and Calorimetry - Flow boiling heat transfer widely utilized in numerous industrial applications such as boiler tubes, evaporators and cooling of reactors in a nuclear...     

Perturbative and nonperturbative correspondences between compact and noncompact sigma-models

Compact (ferro- and antiferromagnetic) sigma-models and noncompact (hyperbolic) sigma-models are compared in a lattice formulation in dimensions d?2$d?2$. While the ferro- and antiferromagnetic models are essentially equivalent, the qualitative difference to the noncompact models is highlighted. The perturbative and the large N expansions are studied in both types of models and are argued to be asymptotic expansions on a finite lattice. An exact correspondence between the expansion coefficients of the compact and the noncompact models is established, for both expansions, valid to all orders on a finite lattice. The perturbative one involves flipping the sign of the coupling and remains valid in the termwise infinite volume limit. The large N correspondence concerns the functional dependence on the free propagator and holds directly only in finite volume.     

Copper-facilitated Suzuki-Miyaura coupling for the preparation of 1,3-dioxolane-protected 5-arylthiophene-2-carboxaldehydes

5-Formyl-2-thiopheneboronic acid is a widely used building block for the synthesis of diverse structures, however, due to a significant instability its transformation to 5-arylthiophene-2-carboxaldehydes by CC couplings could be performed only in low yields. Herein, as a solution, a convenient technique is described for the preparation of 1,3-dioxolane-protected 5-arylthiophene-2-carboxaldehydes via a one-pot borylation–copper(I) chloride co-catalyzed Suzuki-Miyaura coupling reaction. The utilization of the in situ prepared 2-thiopheneboronic ester derivative is allowed by the method developed. Elimination of the crucial, acidic liberation step of boronic acid species resulted in improved yields and purities. In addition, comparison of various aryl bromides is shown to demonstrate the high tolerance of the transformation to functional groups.     

Capillary electrophoretic determination of main components of natural dyes with MS detection

CE with UV-Vis and MS detections was investigated as a technique for detection of main components of selected natural dyes of plant and insect origin. The BGE giving the best separation of the investigated flavonoids and anthraquinoids, suitable for MS detection consisted of 40 mM ammonium acetate solution of pH 9.5 with 40% ACN. LODs obtained with MS detection were even one order of magnitude lower than the ones obtained with UV-Vis detection. Application of MS detection enabled determination of eleven dye compounds from three different chemical groups in 15 min. and proved to be more satisfactory than diode-array detection in the electrophoretic analysis of main classes of natural dyes both in terms of selectivity and sensitivity of analysis.     

4-Chloro-2-methoxybenzoates of heavy lanthanides(III) and yttrium(III)

4-Chloro-2-methoxybenzoates of heavy lanthanides(III) and yttrium(III) were obtained as mono-, di-, tri-or tetrahydrates with metal to ligand ratio of 1:3 and general formula Ln(C₈H₆ClO₃)₃·nH₂O, where n=1 for Ln=Er, n=2 for Ln=Tb, Dy, Tm, Y, n=3 for Ln=Ho and n=4 for Yb and Lu. The complexes were characterized by elemental analysis, FTIR spectra, TG, DTA and DSC curves, X-ray diffraction and magnetic measurements. The carboxylate group appears to be a symmetrical bidentate chelating ligand. All complexes are polycrystalline compounds. The values of enthalpy, ΔH, of the dehydration process for analysed complexes were also determined. The solubilities of heavy lanthanide(III) 4-chloro-2-methoxybenzoates in water at 293 K are of the order of 10⁻⁴ mol dm⁻³. The magnetic moments were determined over the range of 76–303 K. The results indicate that there is no influence of the ligand field of 4f electrons on lanthanide ions and the metal ligand bonding is mainly electrostatic in nature.     

Synthesis and application of monoterpene-based chiral aminodiols

Primary, secondary and tertiary aminodiols were synthetized regio- and stereoselectively from (−)-α-pinene 1 via α-pinene oxide 2, (−)-trans-pinocarveol 3 and key intermediate epoxy alcohol 4. N-Benzyl derivative 5 was transformed to spiro-fused oxazolidine 13 in a highly regioselective ring closure. Aminodiols and their derivatives 5-13 were applied as chiral catalysts in the enantioselective addition of diethylzinc to benzaldehyde, resulting in chiral 1-phenyl-1-propanol. The substituent effect on the nitrogen was studied in detail and the best enantioselectivity was observed in the case of N-methyl-N-benzyl-substituted derivative 8. The phenomenon was interpreted by using molecular modelling at an ab initio level.     

Application of capillary electrophoresis-inductively coupled plasma mass spectrometry to comparative studying of the reactivity of antitumor ruthenium(III) complexes differing in the nature of counter-ion toward human serum proteins

Varying the counter-ion is a highly supportive practice in tackling the problem of poor water-solubility of metal complexes of pharmaceutical importance. As a matter of fact, the relevant structural modification may alter the metabolic pathways and possibly the mode of action of a drug. To prove that this does not take place for one of the lead anticancer metal-based developmental compounds, indazolium trans-[RuCl(4)(1H-indazole)(2)] (KP1019), its reactivity toward human serum proteins was assessed under simulated physiological conditions and compared to that of a much more soluble analogue, sodium trans-[RuCl(4)(1H-indazole)(2)] (KP1339). For such kinetic assaying, capillary electrophoresis (CE) interfaced online with inductively coupled plasma mass spectrometry (ICP-MS) to specifically monitor changes in the metal speciation following the formation of ruthenium-protein adducts was applied. The rate constants of interaction with albumin and transferrin were determined at pharmacologically fitting drug-to-protein ratios as on average 0.0319+/-0.0021 min(-1) and 0.0931+/-0.0019 min(-1) (KP1019) and 0.0316+/-0.0018 min(-1) and 0.0935+/-0.0053 min(-1) (KP1339), respectively. The results of this brief study showed that changing from organic to inorganic counter-ion at the stage of formulation could commonly be recommended for improving ruthenium-based drug solubility and bioavailability.     

Ionic and pH effects on the osmotic properties and structure of polyelectrolyte gels

We investigate the effects of salt concentration and pH on neutralized poly(acrylic acid) (PAA) gels in near physiological salt solutions. Either adding calcium ions or decreasing the pH is found to induce reversible volume transitions but the nature of these transitions seems to be different. For example, the osmotic pressure exhibits a simple power law dependence on the concentration as the transition is approached in both systems, but the power law exponent n is substantially different in the two cases. On decreasing the pH the value of n gradually increases from 2.1 (at pH = 7) to 3.2 (at pH = 1). By contrast, n decreases with increasing calcium ion concentration from 2.1 (in 100 mM NaCl solution) to 1.6 (0.8 mM CaCl₂ in 100 mM NaCl solution). In both systems, a strong increase of the small-angle neutron scattering intensity (SANS) is observed near the volume transition. The SANS results reveal that calcium ions favor the formation of linearly aligned regions in PAA gels. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2803–2810, 2008