Solutions to the Zakharov-Kuznetsov equation with higher order nonlinearity by mapping and ansatz methods

Solutions to the Zakharov-Kuznetsov equation with higher order nonlinearity are obtained using the mapping method. Several solutions are determined inclusing the cnoidal waves, shock waves, solitary waves, periodic singular waves and others. Finally, the ansatz method is applied to solve the equation with power law nonlinearity. It has been proved that the shock waves or topological solitons exist only for specific values of the power law parameter.     

Preparation of 3,3-disubstituted oxindoles by addition of malonates to 3-halo-3-oxindoles

A method for the synthesis of 3,3-disubstituted oxindole derivatives is described. This involves the base-mediated addition of malonate esters to 3-halo-3-alkyloxindoles. The addition is tolerant of a range of alkyl substituents at position 3 of the oxindole. Addition to an aryl chloro-oxindole is also described.     

Separable routing: A scheme for state-dependent routing of circuit switched telephone traffic

Separable routing is the first of a number of routing schemes for circuit switched telephone traffic invented at Bellcore. These routing schemes are state dependent, in the sense that, for each call attempt, a routing decision is made on the basis of the state of the network (defined in terms of the numbers of busy and idle trunks in the various trunk groups at the moment of the call attempt). In this paper, we describe separable routing and its mathematical background. Simulation results we have presented elsewhere show that the family of state-dependent routing schemes, of which separable routing is a member, is very attractive in terms of blocking rate, built-in network management features, and behavior in the presence of traffic forecast error.     

Synthesis and characterisation of urethane-methacrylates I

The paper describes the synthesis of urethane methacrylate resins by reaction of tolylene diisocyanate (TDI), butanol-1 (B) and 2-hydroxyethylmethacrylate (HEMA) by a two step procedure. Characterisation was done using FT-IR, FT-NMR, Mass Spectroscopy. The effect of temperature on the UV-curing behaviour was investigated by differential photocalorimetry. An activation energy of 8.4 kJ/mole was found in the temperature range of 50–100°C. Free radical polymerisation in presence of benzoyl peroxide was also investigated. The polymers were stable upto 200°C in N₂ atmosphere. A two step decomposition was observed in the temperature range of 200–500°C.

---

Zusammenfassung Vorliegende Arbeit beschreibt die Synthese von Urethan-methacrylat-Harzen durch die Reaktion von Toluylendiisocyanat (TDI), Butanol-1 (B) und 2-Hydroxyethylmethacrylat (HEMA) in einem zweistufigen Herstellungsverfahren. Charakterisiert wurden die Produkte mittels FT-IR, FT-NMR und Massenspektroskopie. Anhand von Differentialfotokalorimetrie wurde der Einfluß der Temperatur auf das UV-Aushärtungsverhalten untersucht. Im Temperaturbereich 50–100°C wurde eine Aktivierungsenergie von 8.4 kJ/mol gefunden. Weiterhin wurde auch die Radikalkettenpolimerisation in Gegenwart von Benzoylperoxid untersucht. In Stickstoffatmosphäre sind die Polymere bis 200°C stabil. Im Temperaturbereich 200–500°C wurde eine zweistufige Zersetzung beobachtet.

---

---

The Instrument system of E. I. DuPont de Nemours & Co. is acknowledged for differential photocalorimeter studies.     

The first polymorph in the family of nucleobases: a second form of cytosine

A new polymorph of cytosine, C₄H₅N₃O, is reported half a century after the report of its first known crystal structure [Barker & Marsh (1964). Acta Cryst. 17 , 1581–1587]. Cytosine thus provides the first polymorphic example in the category of parent nucleobases. The new form, denoted (Ib), was observed unexpectedly during an attempt to cocrystallize cytosine with catechol. Form (Ib) crystallizes in the orthorhombic centrosymmetric space group Pccn with two molecules in the asymmetric unit. The previously known form, denoted (Ia), crystallizes in the orthorhombic noncentrosymmetric space group P2₁2₁2₁. The cytosine molecule is planar in both forms. Hydrogen‐bonding interactions are also similar for both forms. Infinite one‐dimensional ribbons composed of cytosine base‐pair dimers in R₂²(8) arrangements are observed in both (Ia) and (Ib). However, the way that the ribbons are packed differs in (Ia) and (Ib). This appears to guide the centrosymmetric versus noncentrosymmetric space‐group selection through the formation of an inversion‐related motif in polymorph (Ib) and a helical propagation in polymorph (Ia). A few selected polymorphic systems have been gathered from the Cambridge Structural Database to understand possible structural features responsible for achiral molecules adopting centro‐ and noncentrosymmetric space groups.     

Four oxoindole‐linked α‐alkoxy‐β‐amino acid derivatives

Four structures of oxoindolyl α‐hydroxy‐β‐amino acid derivatives, namely, methyl 2‐{3‐[(tert‐butoxycarbonyl)amino]‐1‐methyl‐2‐oxoindolin‐3‐yl}‐2‐methoxy‐2‐phenylacetate, C₂₄H₂₈N₂O₆, (I), methyl 2‐{3‐[(tert‐butoxycarbonyl)amino]‐1‐methyl‐2‐oxoindolin‐3‐yl}‐2‐ethoxy‐2‐phenylacetate, C₂₅H₃₀N₂O₆, (II), methyl 2‐{3‐[(tert‐butoxycarbonyl)amino]‐1‐methyl‐2‐oxoindolin‐3‐yl}‐2‐[(4‐methoxybenzyl)oxy]‐2‐phenylacetate, C₃₁H₃₄N₂O₇, (III), and methyl 2‐[(anthracen‐9‐yl)methoxy]‐2‐{3‐[(tert‐butoxycarbonyl)amino]‐1‐methyl‐2‐oxoindolin‐3‐yl}‐2‐phenylacetate, C₃₈H₃₆N₂O₆, (IV), have been determined. The diastereoselectivity of the chemical reaction involving α‐diazoesters and isatin imines in the presence of benzyl alcohol is confirmed through the relative configuration of the two stereogenic centres. In esters (I) and (III), the amide group adopts an anti conformation, whereas the conformation is syn in esters (II) and (IV). Nevertheless, the amide group forms intramolecular N—H...O hydrogen bonds with the ester and ether O atoms in all four structures. The ether‐linked substituents are in the extended conformation in all four structures. Ester (II) is dominated by intermolecular N—H...O hydrogen‐bond interactions. In contrast, the remaining three structures are sustained by C—H...O hydrogen‐bond interactions.