Many Sources Asymptotics for Networks with Small Buffers

In this paper, we obtain the overflow asymptotics in a network with small buffers when the resources are accessed by a large number of stationary independent sources. Under the assumption that the network is loop-free with respect to source–destination routes, we identify the precise large deviations rate functions for the buffer overflow at each node in terms of the external input characteristics. It is assumed that each type of source requires a Quality of Service (QoS) defined by bounds on the fraction of offered work lost. We then obtain the admissible region for sources which access the network based on these QoS requirements. When all the sources require the same QoS, we show that the admissible region asymptotically corresponds to that which is obtained by assuming that flows pass through each node unchanged.     

A note on the conservation law for continuous reflected processes and its application to queues with fluid inputs

In this note we provide a new derivation of a conservation law for stationary continuous reflected processes which arise in the context of fluid queueing models. This readily gives the so-called Little's law for fluid queues as a special case. We then apply the result to compute the Laplace transform of the stationary workload distribution for a queue with fluid ON-OFF inputs in terms of the Palm distribution associated with the beginning of ON periods. This revised version was published online in June 2006 with corrections to the Cover Date.     

Energy levels of λx 2k anharmonic oscillators using the quantum normal form

The ground state and first few excited energy levels of the generalized anharmonic oscillator defined by the HamiltonianH=–d ²/dx ²+x ²+x ^2k (k=3, 4,...) have been calculated by employing the method of quantum normal form, which is the quantum mechanical analogue of the classical Birkhoff-Gustavson normal form. The present energy eigenvalues are consistent with other tabulations of the energy levels.     

Ring-chain isomerism in conjugated guanylhydrazones: Experimental and theoretical study

Treatment of 1,3-diaryl-propene-2-one with aminoguanidine under acidic conditions for a short reaction period (1?h) delivers - in accordance with a literature report - the corresponding guanylhydrazones. However, when the reaction time was increased to 12?h, formation of the ring annulated product 4,5-dihydro-1H-pyrazole-1-carboximidamide was observed. This is the first case of ring-chain isomerism in conjugated guanylhydrazones. The acyclic conjugated guanylhydrazone and the corresponding annulated product (4,5-dihydro-1H-pyrazole-1-carboximidamide) could be clearly distinguished by means of UV and NMR spectroscopy. The formation of the ring isomer was further confirmed by single crystal XRD analysis. The time-dependent ¹H NMR study indicated the gradual transformation of the open-chain compound into the cyclic one. The mechanistic insights into the formation of these two products were explored using quantum chemical methods which revealed that the ring isomer is thermodynamically more stable than the open-chain isomer by 6–11?kcal/mol and the barrier for cyclization was found to be 31.37?kcal/mol.     

Pyranocarbazoles from Murraya koenigii (L.) Spreng. as antimicrobial agents

The bioassay guided fractionation of methanolic extract of Murraya koenigii (L.) Spreng. leaves resulted in the isolation of seven pyranocarbazoles. These were evaluated against four bacterial strains and ten Candida sp. including two matched pair of fluconazole sensitive/resistant clinical isolates. Out of seven, three i.e. Koenine (mk279), Koenigine (mk309) and Mahanine (mk347) exhibited significant antibacterial activity MIC90 3.12–12.5 μg/mL against bacterial strains Streptococcus aureus and Klebsiella pneumonia compared with standard drug Kanamycin MIC90 12.5 μg/mL. However, only mk309 was found active against variety of Candida species MIC90 12.5–100 μg/mL. It was observed that hydroxylation at C-6 and C-7 positions in the studied pyranocarbazoles activate the bioactivity. Simultaneously, decrease in Log P value compares with ?H and ?O?CH3 substituted derivatives. The study is focused on selective antifungal and antibacterial activity of pyranocarbazoles on bacterial strains S. aureus, K. pneumonia and variety of Candida species with structure activity relationship observations.     

Promising anticancer drug thapsigargin: A perspective toward the total synthesis

The guaianolide ring containing sesquiterpene thapsigargin is found in the roots and fruits of Mediterranean plant Thapsia garganica L. It is known for its activity as a potent antagonist for Ca²⁺-ATPase (sarco–endoplasmic reticulum Ca²⁺-ATPase) inhibition. Recently, a prodrug mipsagargin is being investigated to target the blood vessel of the cancer cells for the treatment of tumors. The limited natural supply (low isolation and only localized growth (Mediterranean area)) from the natural sources strongly urges for the development of chemical synthetic strategies to access these natural products. This review pertain the various strategies used so far in the thapsigargin’s synthesis, focusing on major contributions in the total synthesis till date.     

Limit theorems for monochromatic stars

Let T(K_1,r,G_n) be the number of monochromatic copies of the r‐star K_1,r in a uniformly random coloring of the vertices of the graph G_n. In this paper we provide a complete characterization of the limiting distribution of T(K_1,r,G_n), in the regime where is bounded, for any growing sequence of graphs G_n. The asymptotic distribution is a sum of mutually independent components, each term of which is a polynomial of a single Poisson random variable of degree at most r. Conversely, any limiting distribution of T(K_1,r,G_n) has a representation of this form. Examples and connections to the birthday problem are discussed.     

Similarities in electronic properties of organic charge-transfer solids and layered cobaltates

The apparently counterintuitive carrier concentration-dependent electronic properties of layered cobaltates have attracted wide interest. Here we point out that very similar carrier-concentration dependence has previously been noted in strongly correlated quasi-one dimensional (quasi-1D) organic charge-transfer solids. The normal states of both families can be understood, over the entire range of carrier concentration of interest, within the extended Hubbard Hamiltonian with significant intersite Coulomb interaction. As with the charge-transfer solids, superconductivity in the cobaltates appears to be limited to bandfilling of one-quarter. We point out further that there exist other families of correlated superconductors, such as spinels, where too strong correlations, geometric lattice frustration and bandfilling of one-quarter seem to be the essential features of the unconventional superconductors.     

X-ray,SEM, and DSC studies of ferroelectric Pb<Subscript>1−<Emphasis Type="Italic">X</Emphasis></Subscript>Ba<Subscript><Emphasis Type="Italic">X</Emphasis></Subscript>TiO<Subscript>3</Subscript> ceramics

The polycrystalline ferroelectric compounds of general formula Pb_1−X Ba _X TiO₃ with X = 0.00, 0.1, 0.2 and 0.5 were prepared by high temperature solid-state reaction technique using high purity oxides and carbonates. The compounds formation was confirmed by X-ray diffraction and all the X-ray peaks were indexed with tetragonal structure of space group P4mm. Morphology and particle size of the compounds were obtained using scanning electron microscopy. Ferroelectric phase transition, enthalpy change, and specific heat of the compounds were obtained using modulated differential scanning calorimetry. It was observed that the phase transition temperature decreased linearly with the increase of substitution concentration.