On the asymptotic analysis of statistical multiplexers with hyper-bursty arrivals

We consider multiplexers in discrete time fed by the superposition of Ternary Markov Sources. Such sources are the natural extension of the Binary Markov Sources (BMS) recently used to model bursty arrivals in a high speed environment. Unlike BMS, we allow sources to have arbitrary (large) variance in the duration of their OFF (silence) or ON (burst) periods.This paper focuses mainly on the impact of large variability either in the ON or OFF period on the performance. Following some asymptotic analysis, simple results on the tail behavior of the number of cells queued in the multiplexer are given.Our results indicate that ignoring the variability in the ON period may grossly underestimate the cell buildup in the multiplexer queue for all levels of the utilization. Furthermore, the impact of large variability of the OFF period depends very much on the utilization of the system. For a lightly-loaded multiplexer (utilization below a given threshold), the impact of large variability of the OFF period is minimal. However, for a heavy-loaded multiplexer (utilization above the threshold) the impact of the large variability in the OFF period is similar to that of the ON period.     

Dediazoniation of Arenediazonium Ions. Part XXII. Reactions of 2, 6-Dialkyl-Substituted Benzenediazonium Ions in Super Acids,Acetonitrile and Acetone

Reactions of 2,4,6-trimethylbenzenediazonium ( 1 ), 2,6-diethylbenzenediazonium ( 2 ) and 2,6-diisopropylbenzenediazonium ( 3 ) tetrafluoroborates were studied in magic acid, SbF₅/SO₂ClF, acetonitrile and acetone by ¹H-NMR and by analysis of the dediazoniation products. The N_α-N_β rearrangement of β-N¹⁵-labelled tetrafluoroborates 1–3 was followed by ¹⁵N-NMR of the corresponding arylazonaphthols, as well as by MS analysis of the anilines obtained by reduction of the azo compounds. Diazonium salts 2 and 3 were synthesized for the first time and the steric effect of substituents at C(2) and C(6) on the reactions under study is discussed. All the results obtained can be rationalized by heterolytic dediazoniation of diazonium salts 1 – 3 and product formation from the corresponding aryl cations.     

Numerical solutions of distributed order fractional differential equations in the time domain using the Müntz–Legendre wavelets approach

In this paper, a numerical method is presented to obtain and analyze the behavior of numerical solutions of distributed order fractional differential equations of the general form in the time domain with the Caputo fractional derivative. The suggested method is based on the Müntz–Legendre wavelet approximation. We derive a new operational vector for the Riemann–Liouville fractional integral of the Müntz–Legendre wavelets by using the Laplace transform method. Applying this operational vector and collocation method in our approach, the problem can be reduced to a system of linear and nonlinear algebraic equations. The arising system can be solved by the Newton method. Discussion on the error bound and convergence analysis for the proposed method is presented. Finally, seven test problems are considered to compare our results with other well‐known methods used for solving these problems. The results in the tabulated tables highlighted that the proposed method is an efficient mathematical tool for analyzing distributed order fractional differential equations of the general form.     

Mass spectrometry of labile onium ions and carbocation salts. Study by desorption-ionization mass spectrometry: Fast atom bombardment,field desorption and 252Cf plasma desorption time-of-flight mass spectrometry

In contrast to the accepted notion that mass spectrometry is impractical as an analytical tool in condensed-phase preparative carbocation chemistry, it has been shown that desorption ionization techniques (fast atom bombard-ment, field desorption and²⁵²Cf plasma desorption time-of-flight mass spectrometry) provide rapid and reliable methods for relative molecular mass determination for a wide variety of highly unstable, fragile carbocation salts and onium ions. In addition, interesting fragment ions and cluster ions (two cations and one anion) are observed. Application of these methods to study several dication ether salts has also been demonstrated.     

A generalization of the construction of test problems for nonconvex optimization

In this paper we adopt and generalize the basic idea of the method presented in [3] and [4] to construct test problems that involve arbitrary, not necessarily quadratic, concave functions, for both Concave Minimization and Reverse Convex Programs     

Eco-friendly synthesis of 1,4-benzodiazepine-2,5-diones in the ionic liquid [bmim]Br

The green reaction of isatoic anhydrides with α-amino acids in presence of the ionic liquid 1-butyl-3-methylimidazolium bromide afforded 1,4-benzodiazepine-2,5-diones in excellent yields in absence of a catalyst. The reaction workup is simple and the ionic liquid was easily recovered from the reaction and reused. The methodology was quite general and a range of cyclic and acyclic α-amino acids were examined to produce 1,4-benzodiazepine-2,5-diones.     

Eco-friendly synthesis of 1,4-benzodiazepine-2,5-diones in the ionic liquid [<Emphasis Type="Italic">bmim</Emphasis>]Br

The green reaction of isatoic anhydrides with α-amino acids in presence of the ionic liquid 1-butyl-3-methylimidazolium bromide afforded 1,4-benzodiazepine-2,5-diones in excellent yields in absence of a catalyst. The reaction workup is simple and the ionic liquid was easily recovered from the reaction and reused. The methodology was quite general and a range of cyclic and acyclic α-amino acids were examined to produce 1,4-benzodiazepine-2,5-diones. Correspondence: Khosrow Jadidi, Department of Chemistry, Shahid Beheshti University, PO Box 1983963113, Tehran, Iran.     

New penta-ether as the internal donor in the MgCl2-supported Ziegler-Natta catalysts for propylene polymerization

The penta-ether compound was synthesized by the reaction of di(trimethylolpropane) with sodium hydride as the strong base and methyl iodide as the alkyl halide. This compound was characterized by NMR, FTIR, and GC techniques. The MgCl₂-supported titanium catalysts were incorporated with varying amounts of penta-ether compound as the internal donor and also the catalysts without the internal donor were synthesized. The synthesized catalysts and the conventional Ziegler- Natta catalyst were characterized. The titanium contents were determined by spectrophotometry, magnesium by complexometric titration and chloride by argentometric titration. The effects of the new internal donor on propylene polymerization with the prepared MgCl₂-supported Ziegler-Natta catalysts were investigated and then these results were compared to the results obtained using the conventional diisobutyl phthalate-besed-Ziegler-Natta catalyst. The highest crystallinity degree, melting temperature, and isotacticity of polypropylene were obtained using the catalyst with a penta-ether/Mg molar ratio equal to 0.21.     

Nickel(II) salophen-type complexes characterization and their thermodynamic studies with diorganotin(IV) dichlorides in chloroform

A u.v.–vis spectrophotometric study of the adduct formation of the nickel(II) Schiff base complexes,([NiL]) where L = [3-methoxysalophen, N,N′-bis(3-methoxysalicylidene)-1,2-phenylenediimine] (1), [4-methoxysalophen, N,N′-bis(4-methoxysalicylidene)-1,2-phenylenediimine] (2), [5-methoxysalophen, N,N′-bis(5-methoxysalicylidene)-1,2-phenylenediimine] (3) and [Salophen, [N,N′-bis(salicylaldehydo)-1,2-phenylenediimine] (4) as donors with R₂SnCl₂ (R = methyl, phenyl and n-butyl) as acceptors have been investigated in chloroform, as solvent. Adducts have been characterized by ¹H, ¹³C and ¹¹⁹Sn NMR, IR and electronic spectroscopy and CHN elemental microanalysis. The formation constants and the thermodynamic free energies were measured using u.v.–vis spectrophotometry titration for 1:1 adduct formation at various temperatures (T = 278 to 308 K). The trend of the adduct formation of the nickel Schiff base complexes with a given tin acceptor decreases as follows: