On generalizations of network design problems with degree bounds

Iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems. In this paper we extend the scope of the iterative relaxation method in two directions: (1) by handling more complex degree constraints in the minimum spanning tree problem (namely laminar crossing spanning tree), and (2) by incorporating ‘degree bounds’ in other combinatorial optimization problems such as matroid intersection and lattice polyhedra. We give new or improved approximation algorithms, hardness results, and integrality gaps for these problems. Our main result is a (1, b + O(log n))-approximation algorithm for the minimum crossing spanning tree (MCST) problem with laminar degree constraints. The laminar MCST problem is a natural generalization of the well-studied bounded-degree MST, and is a special case of general crossing spanning tree. We give an additive Ω(log ^c m) hardness of approximation for general MCST, even in the absence of costs (c > 0 is a fixed constant, and m is the number of degree constraints). This also leads to a multiplicative Ω(log ^c m) hardness of approximation for the robust k-median problem (Anthony et al. in Math Oper Res 35:79–101, 2010), improving over the previously known factor 2 hardness. We then consider the crossing contra-polymatroid intersection problem and obtain a (2, 2b + Δ ? 1)-approximation algorithm, where Δ is the maximum element frequency. This models for example the degree-bounded spanning-set intersection in two matroids. Finally, we introduce the crossing latticep olyhedron problem, and obtain a (1, b + 2Δ ? 1) approximation algorithm under certain condition. This result provides a unified framework and common generalization of various problems studied previously, such as degree bounded matroids.     

Stochastic decomposition in production inventory with service time

We study an (s, S) production inventory system where the processing of inventory requires a positive random amount of time. As a consequence a queue of demands is formed. Demand process is assumed to be Poisson, duration of each service and time required to add an item to the inventory when the production is on, are independent, non-identically distributed exponential random variables. We assume that no customer joins the queue when the inventory level is zero. This assumption leads to an explicit product form solution for the steady state probability vector, using a simple approach. This is despite the fact that there is a strong correlation between the lead-time (the time required to add an item into the inventory) and the number of customers waiting in the system. The technique is: combine the steady state vector of the classical M/M/1 queue and the steady state vector of a production inventory system where the service is instantaneous and no backlogs are allowed. Using a similar technique, the expected length of a production cycle is also obtained explicitly. The optimal values of S and the production switching on level s have been studied for a cost function involving the steady state system performance measures. Since we have obtained explicit expressions for the performance measures, analytic expressions have been derived for calculating the optimal values of S and s.     

Synthesis,characterization, and morphology of p‐toluene sulfonic acid‐doped polyaniline: A material for humidity sensing application

Polyaniline (PANI) doped with p‐toluene sulfonic acid was synthesized by chemical polymerization method using (NH₄)₂S₂O₈ as an oxidizing agent. This is a single step polymerization process for the direct synthesis of the conducting emeraldine salt (ES) phase, without the need of doping, dedoping, and redoping of the polymer. Presence of a free carrier tail at higher wavelength, characteristic of extended coil conformation along with a sharp polaronic peak is observed in the UV–vis spectrum of doped PANI in m‐cresol solvent. FT‐IR studies show the characteristic peaks of ES phase along with a sharp peak at 1120 cm^?1 representing vibration band of the dopant ion. Clumps of small fibers resulting in a sponge‐like structure was observed under scanning electron microscope. Thermal studies revealed a three‐step decomposition pattern. Conductivity is found to increase with an increase in the temperature showing “thermal activation behavior.” Decrease in resistance with increasing humidity is observed in a broad range of humidity. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2161–2169, 2005     

The Minimal Polynomial of Some Matrices Via Quaternions

This work provides explicit characterizations and formulae for the minimal polynomials of a wide variety of structured 4 × 4 matrices. These include symmetric, Hamiltonian and orthogonal matrices. Applications such as the complete determination of the Jordan structure of skew-Hamiltonian matrices and the computation of the Cayley transform are given. Some new classes of matrices are uncovered, whose behaviour insofar as minimal polynomials are concerned, is remarkably similar to those of skew-Hamiltonian and Hamiltonian matrices. The main technique is the invocation of the associative algebra isomorphism between the tensor product of the quaternions with themselves and the algebra of real 4 × 4 matrices. Extensions to higher dimensions via Clifford Algebras are discussed.     

Thickness-dependent orientation evolution in nickel thin films grown on yttria-stabilized zirconia single crystals

Microstructure evolution along with crystallographic orientation change as a function of film thickness was investigated in Ni thin films grown on (100) yttria-stabilized zirconia (YSZ) single crystal substrates. Texture development with two different orientation relationships, OR1: Ni {111}//YSZ {100} and OR2: Ni {100}//YSZ {100}, cube on cube orientation were identified by X-ray diffraction and transmission electron microscopy depending on the film thickness. The observed orientation transition reveals the existence of a critical thickness (～320?nm) favoring two different orientations in sputtered Ni films on YSZ (100) substrate.     

Random Fibonacci sequences and the number

For the familiar Fibonacci sequence (defined by , and for ), increases exponentially with at a rate given by the golden ratio . But for a simple modification with both additions and subtractions - the random Fibonacci sequences defined by , and for , , where each sign is independent and either or - with probability - it is not even obvious if should increase with . Our main result is that

with probability . Finding the number involves the theory of random matrix products, Stern-Brocot division of the real line, a fractal measure, a computer calculation, and a rounding error analysis to validate the computer calculation.

     

Optical properties of residual shallow donors in GaN epitaxial layers grown by horizontal LP-MOCVD

Received: 1 May 1998/Accepted: 23 June 1998     

Separation control by tangential blowing inside the bubble

 Experiments have been carried out investigating the effectiveness of steady tangential blowing (inside the separation bubble) to control an axisymmetric separated flow at low speeds. Turbulent boundary separation was induced on a contoured afterbody and the separated shear layer reattached on a narrow cylindrical sting. Measurements made consisted of model surface pressures, mean velocity, turbulent shear stress and kinetic energy profiles using a 2-component LDV system. The results explicitly demonstrate that blowing downstream of the separation location, but within the bubble, can be an effective means of separation control, considering both wall and wake flow reversals. Received: 16 October 1998/Accepted: 27 September 1999