Scheduling data transfers in a network and the set scheduling problem

In this paper we consider the online ftp problem. The goal is to service a sequence of file transfer requests given bandwidth constraints of the underlying communication network. The main result of the paper is a technique that leads to algorithms that optimize several natural metrics, such as max-stretch, total flow time, max flow time, and total completion time. In particular, we show how to achieve optimum total flow time and optimum max-stretch if we increase the capacity of the underlying network by a logarithmic factor. We show that the resource augmentation is necessary by proving polynomial lower bounds on the max-stretch and total flow time for the case where online and offline algorithms are using same-capacity edges. Moreover, we also give polylogarithmic lower bounds on the resource augmentation factor necessary in order to keep the total flow time and max-stretch within a constant factor of optimum.     

Deciding confluence of certain term rewriting systems in polynomial time

We present a characterization of confluence for term rewriting systems, which is then refined for special classes of rewriting systems. The refined characterization is used to obtain a polynomial time algorithm for deciding the confluence of ground term rewrite systems. The same approach also shows the decidability of confluence for shallow and linear term rewriting systems. The decision procedure has a polynomial time complexity under the assumption that the maximum arity of a function symbol in the signature is a constant.     

Degree-regular triangulations of torus and Klein bottle

A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In [8], Lutz has classified all the weakly regular triangulations on at most 15 vertices. In [5], Datta and Nilakantan have classified all the degree-regular triangulations of closed surfaces on at most 11 vertices. In this article, we have proved that any degree-regular triangulation of the torus is weakly regular. We have shown that there exists ann-vertex degree-regular triangulation of the Klein bottle if and only if n is a composite number ≥ 9. We have constructed two distinctn-vertex weakly regular triangulations of the torus for eachn ≥ 12 and a (4m + 2)-vertex weakly regular triangulation of the Klein bottle for eachm ≥ 2. For 12 ≤n ≤ 15, we have classified all then-vertex degree-regular triangulations of the torus and the Klein bottle. There are exactly 19 such triangulations, 12 of which are triangulations of the torus and remaining 7 are triangulations of the Klein bottle. Among the last 7, only one is weakly regular.     

Constructing ‘hair’ for the three charge hole

It has been found that the states of the 2-charge extremal D1–D5 system are given by smooth geometries that have no singularity and no horizon individually, but a ‘horizon’ does arise after ‘coarse-graining’. To see how this concept extends to the 3-charge extremal system, we construct a perturbation on the D1–D5 geometry that carries one unit of momentum charge P. The perturbation is found to be regular everywhere and normalizable, so we conclude that at least this state of the 3-charge system behaves like the 2-charge states. The solution is constructed by matching (to several orders) solutions in the inner and outer regions of the geometry. We conjecture the general form of ‘hair’ expected for the 3-charge system, and the nature of the interior of black holes in general.     

A comparative adsorption study with different industrial wastes as adsorbents for the removal of cationic dyes from water

Four adsorbents have been prepared from industrial wastes obtained from the steel and fertilizer industries and investigated for their utility to remove cationic dyes. Studies have shown that the adsorbents prepared from blast furnace sludge, dust, and slag have poor porosity and low surface area, resulting in very low efficiency for the adsorption of dyes. On the other hand, carbonaceous adsorbent prepared from carbon slurry waste obtained from the fertilizer industry was found to show good porosity and appreciable surface area and consequently adsorbs dyes to an appreciable extent. The adsorption of two cationic dyes, viz., rhodamine B and Bismark Brown R on carbonaceous adsorbent conforms to Langmuir equation, is a first-order process and pore diffusion controlled. As the adsorption of dyes investigated was appreciable on carbonaceous adsorbent, its efficiency was evaluated by comparing the results with those obtained on a standard activated charcoal sample. It was found that prepared carbonaceous adsorbent exhibits dye removal efficiency that is about 80-90% of that observed with standard activated charcoal samples. Thus, it can be fruitfully used for the removal of dyes and is a suitable alternative to standard activated charcoal in view of its cheaper cost.     

Cross-axis synchronous flow-through coil planet centrifuge (type XLL). I. Design of the apparatus and studies on retention of stationary phase

The fourth prototype holds a pair of column holders in the lateral position at 15 cm from the center of the rotary shaft horizontally mounted on the rotary frame at 7.6 cm from the central axis of the apparatus. Using short coils of 2.6 mm I.D. PTFE (polytetrafluoroethylene) tubing with 7.6 cm and 24 cm helical diameters, retention of the stationary phase was measured in ten pairs of two-phase solvent systems under various experimental conditions. Satisfactory retention was obtained by choosing proper combinations of three factors, i.e., the direction of planetary motion, head-tail elution mode, and inward-outward elution mode. The polar butanol solvent systems showed excellent retention from 65 to 80% in the 7.6 cm helical diameter left-handed coil.     

Improved cross-axis synchronous flow-through coil planet centrifuge for performing counter-current chromatography. II. Studies on retention of stationary phase in short coils and preparative separations in multilayer coils

Performance of the apparatus was evaluated in terms of stationary phase retention, partition efficiency and sample loading capacity. Preliminary studies with short coils revealed high retention of the stationary phase under a proper combination of the head-tail elution and planetary motion. Preparative capability of the apparatus was successfully demonstrated on efficient multigram separations of 2,4-dinitrophenyl amino acids, indole auxins, and bacitracin in a pair of large multilayer coils with a total capacity of 1.5 l.