On a transport operator arising in growing cell populations II. Cauchy problem

This paper deals with Rotenberg's models of cell populations with general boundary conditions. It is shown, first, that the associated Cauchy problem is governed by a C₀‐semigroup. Second, we have proved that if the boundary operator is positive, the transport semigroup is irreducible. And finally, a spectral decomposition of the solution into an asymptotic term was derived. Copyright © 2004 John Wiley & Sons, Ltd.     

Development of the large increment method for elastic perfectly plastic analysis of plane frame structures under monotonic loading

The displacement-based finite element method dominates current practice for material nonlinear analysis of structures. However, there are several characteristics that may limit the effectiveness of this approach. In particular, for elastoplastic analysis, the displacement method relies upon a step-by-step incremental approach stemming from flow theory and also requires significant mesh refinement to resolve behavior in plastic zones. This leads to computational inefficiencies that, in turn, encourage the reconsideration of force-based approaches for elastoplastic problems.One of these force algorithms that has been recently developed is the large increment method. The main advantage of the flexibility-based large increment method (LIM) over the displacement method is that it separates the global equilibrium and compatibility equations from the local constitutive relations. Consequently, LIM can reach the solution in one large increment or in a few large steps, thus, avoiding the development of cumulative errors. This paper discusses the extension of the large increment methodology for the nonlinear analysis of plane frame structures controlled by an elastic, perfectly plastic material model. The discussion focuses on the power of LIM to handle these nonlinear problems, especially when plastic hinges form in the frame and ultimately as the structure approaches the collapse stage. Illustrative planar frame examples are presented and the results are compared with those obtained from a standard displacement method.     

<Emphasis Type="Italic">p</Emphasis>-Adic mathematical physics and B. Dragovich research

We present a brief review of some parts of p-adic mathematical physics related to the scientific work of Branko Dragovich on the occasion of his 70th birthday.     

Highly efficient synthesis of dicoumarols and xanthene derivatives in presence of Brønsted–Lewis acidic ionic liquids catalyst

A series of metal chloride-based acidic ionic liquids have been prepared and used as an efficient catalyst in one-pot multicomponent synthesis of biscoumarins and substituted xanthenes derivatives under solvent-free conditions. Among the acidic ionic liquids, N-methylpyrrolidonium zinc chloride (Hnmp/ZnCl₃)-based Brønsted–Lewis acidic ionic liquids were found to be an effective and recyclable catalyst for a one-pot synthesis of biscoumarins through the domino Knoevenagel–Michael reaction of a variety of aldehydes with 4-hydroxycoumarin in short reaction times. The reactions which occur under relatively mild conditions afforded the biscoumarin derivatives employing a very low loading of catalyst in satisfactory isolated yields and high purity after simple work-up. The Brønsted–Lewis acidic ionic liquid catalyst was reused four times without any variation in yield.     

One‐Pot Synthesis of New 1,5‐Disubstituted Tetrazoles Bearing 2,2‐Bis(trimethylsilyl)ethenyl Groups via The Ugi Four‐Component Condensation Reaction Catalyzed by MgBr2·2Et2O

A simple one‐pot Ugi four‐component condensation reaction has been developed for the synthesis of tetrazoles bearing 2,2‐bis(trimethylsilyl)ethenyl groups from the synthesized 4‐[2,2‐bis(trimethylsilyl) ethenyl]benzaldehyde ( 1 ), various amines, isocyanides, and trimethylsilylazide at room temperature, without solvent, and in the presence of catalytic amounts of MgBr₂·2Et₂O as catalyst.     

Structural studies of 3-chloro-N-(8′-quinolyl)×benzo[b]thiophene-2-carboxamide

3-Chloro-N-(8′-quinolyl)benzo[b]thiophene-2-carboxamide was synthesized from 3-chlorobenzo[b] thiophene -2-carboxyl chloride and 8-aminoquinoline in the presence of triethylamine. The single crystal X-ray structure determination confirmed the earlier proposed structure and also characterized by ¹HNMR, and Mass spectroscopy. Crystallographic study reveals that the structure crystallizes in monoclinic system, a = 14.878(4) ?, b = 8.4292(15) ?, c = 25.461(7) ?, β = 112.022(18)°, Z = 8, V = 2960.20(12) ?³ with space group C2/c (No. 15). In the structure packing, three kinds of interactions are responsible for the stability of the structure. Infinite two-dimensional stair-like layered chains are formed by relatively strong intermolecular hydrogen bonds [C14—H14...O1]. These parallel chains are connected by several π—π and CH—π interactions, alternatively. There are two such parallel chains with 70.53°, which are in contact by van der Waals interactions.     

Preconditioning of Axillary Buds in Thidiazuron-Supplemented Liquid Media Improves In Vitro Shoot Multiplication in <Emphasis Type="Italic">Nyctanthes arbor-tristis</Emphasis> L.

An efficient tissue culture technology has been designed for mass multiplication of Nyctanthes arbor-tristis L. by preculturing nodal explants in thidiazuron (TDZ)-supplemented liquid Murashige and Skoog (MS) media. Direct inoculation of nodal segments on semi-solid MS medium augmented with various concentrations of TDZ (0.1 to 0.9 μM) produced shoots but with low regeneration response and few shoots per explant. Hence, nodal explants were pretreated with greater concentrations of TDZ (5 to 100 μM) in liquid MS media for different durations (4, 8, 12, and 16 days) with the aim of improving shoot regeneration response from cultured explants. After pretreatment, explants were transferred to agar-solidified hormone-free MS medium. Best response in terms of percent regeneration (94%), number of shoots per explant (20.00 ± 1.15), and greatest shoot length (7.23 ± 0.83 cm) were obtained with nodal segments pretreated in75 μM TDZ for 8 days. Similarly, root induction was obtained from pulse-treated microshoots for 24 h with 200 μM indole-3-butyric acid (IBA) followed by their transfer to 1/2 MS medium which produced an average of 5.50 ± 0.92 roots per microshoot. The rooted plantlets were transplanted to soil with 80% success rate.     

Ultra Sensitive Quantification of Thiourea at Nanomolar Level by Catalytic‐Kinetic Differential Pulse Voltammetry

A new simple and highly selective and sensitive catalytic differential pulse voltammetry procedure for the determination of thiourea at nanomolar level is reported. Thiourea has a catalytic effect on the oxidation of Janus green by iodate in the hydrochloric acid medium. The potential was scanned in the negative direction and the differential pulse voltammograms were recorded. The variations of the peak current with hydrochloric acid concentration, oxidant, Janus green, pulse amplitude, pulse time and scan rate were optimized. Under the optimized conditions, the relationship between the peak current and concentration of thiourea was obtained. It is shown that the calibration curve is linear in the range of 0.01–6.00 µg/mL. The detection limit of the method was 0.005 µg/mL. The relative standard deviation for 6 replicate determinations of 0.01, 0.50 and 2.00 µg/mL is equal to 2.25%, 1.52% and 1.03%, respectively. The method was applied to the determination of thiourea in fruit juices with satisfactory results.     

Ambidentate coordination of dimethyl sulfoxide in rhodium(III) complexes

The two dimethyl sulfoxide solvated rhodium(III) compounds, [Rh(dmso-κO)(5)(dmso-κS)](CF(3)SO(3))(3) (1 & 1* at 298 K and 100 K, respectively) and [Rh(dmso-κO)(3)(dmso-κS)(2)Cl](CF(3)SO(3))(2) (2), crystallize with orthorhombic unit cells in the space group Pna2(1) (No. 33), Z = 4. In the [Rh(dmso)(6)](3+) complex with slightly distorted octahedral coordination geometry, the Rh-O bond distance is significantly longer with O trans to S, 2.143(6) ? (1) and 2.100(6) ? (1*), than the mean Rh-O bond distance with O trans to O, 2.019 ? (1) and 2.043 ? (1*). In the [RhCl(dmso)(5)](3+) complex, the mean Rh-O bond distance with O trans to S, 2.083 ?, is slightly longer than that for O trans to Cl, 2.067(4) ?, which is consistent with the trans influence DMSO-κS > Cl > DMSO-κO of the opposite ligands. Raman and IR absorption spectra were recorded and analyzed and a complete assignment of the vibrational bands was achieved with support by force field calculations. An increase in the Rh-O stretching vibrational frequency corresponded to a decreasing trans-influence from the opposite ligand. The Rh-O force constants obtained were correlated with the Rh-O bond lengths, also including previously obtained values for other M(dmso)(6)(3+) complexes with trivalent metal ions. An almost linear correlation was obtained for the MO stretching force constants vs. the reciprocal square of the MO bond lengths. The results show that the metal ion-oxygen bonding of dimethyl sulfoxide ligands is electrostatically dominated in those complexes and that the stretching force constants provide a useful measure of the relative trans-influence of the opposite ligands in hexa-coordinated Rh(III)-complexes.     

Spatial Wilson loops in a fully anisotropic model

Theoretical and Mathematical Physics - We study spatial Wilson loops for a fully anisotropic background metric supported by the Einstein action with a dilaton field and three Maxwell tensors. We...