Proper holomorphic mappings of balanced domains in C-n

We extend a well-known result, about the unit ball, by H. Alexander to a class of balanced domains in . Specifically: we prove that any proper holomorphic self-map of a certain type of balanced, finite-type domain in , is an automorphism. The main novelty of our proof is the use of a recent result of Opshtein on the behaviour of the iterates of holomorphic self-maps of a certain class of domains. We use Opshtein's theorem, together with the tools made available by finiteness of type, to deduce that the aforementioned map is unbranched. The monodromy theorem then delivers the result.

Simultaneous perturbation methods for adaptive labor staffing in service systems

We consider the problem of optimizing the workforce of a service system. Adapting the staffing levels in such systems is non-trivial due to large variations in workload and the large number of system parameters do not allow for a brute force search. Further, because these parameters change on a weekly basis, the optimization should not take longer than a few hours. Our aim is to find the optimum staffing levels from a discrete high-dimensional parameter set, that minimizes the long run average of the single-stage cost function, while adhering to the constraints relating to queue stability and service-level agreement (SLA) compliance. The single-stage cost function balances the conflicting objectives of utilizing workers better and attaining the target SLAs. We formulate this problem as a constrained parameterized Markov cost process parameterized by the (discrete) staffing levels. We propose novel simultaneous perturbation stochastic approximation (SPSA)-based algorithms for solving the above problem. The algorithms include both first-order as well as second-order methods and incorporate SPSA-based gradient/Hessian estimates for primal descent, while performing dual ascent for the Lagrange multipliers. Both algorithms are online and update the staffing levels in an incremental fashion. Further, they involve a certain generalized smooth projection operator, which is essential to project the continuous-valued worker parameter tuned by our algorithms onto the discrete set. The smoothness is necessary to ensure that the underlying transition dynamics of the constrained Markov cost process is itself smooth (as a function of the continuous-valued parameter): a critical requirement to prove the convergence of both algorithms. We validate our algorithms via performance simulations based on data from five real-life service systems. For the sake of comparison, we also implement a scatter search based algorithm using state-of-the-art optimization tool-kit OptQuest. From the experiments, we observe that both our algorithms converge empirically and consistently outperform OptQuest in most of the settings considered. This finding coupled with the computational advantage of our algorithms make them amenable for adaptive labor staffing in real-life service systems.

Two player game variant of the Erdos-Szekeres problem

The classical Erdos-Szekeres theorem states that a convex k-gon exists in every sufficiently large point set. This problem has been well studied and finding tight asymptotic bounds is considered a challenging open problem. Several variants of the Erdos-Szekeres problem have been posed and studied in the last two decades. The well studied variants include the empty convex k-gon problem, convex k-gon with specified number of interior points and the chromatic variant. In this paper, we introduce the following two player game variant of the Erdos-Szekeres problem: Consider a two player game where each player playing in alternate turns, place points in the plane. The objective of the game is to avoid the formation of the convex k-gon among the placed points. The game ends when a convex k-gon is formed and the player who placed the last point loses the game. In our paper we show a winning strategy for the player who plays second in the convex 5-gon game and the empty convex 5-gon game by considering convex layer configurations at each step. We prove that the game always ends in the 9th step by showing that the game reaches a specific set of configurations.

Nonvanishing of Koecher-Maass series attached to Siegel cusp forms

We prove a nonvanishing result for Koecher-Maass series attached to Siegel cusp forms of weight k and degree n in certain strips on the complex plane. When n = 2, we prove such a result for forms orthogonal to the space of the Saito-Kurokawa lifts `up to finitely many exceptions', in bounded regions. (C) 2015 Elsevier Inc. All rights reserved.

L-infinity norms of holomorphic modular forms in the case of compact quotient

We prove a sub-convex estimate for the sup-norm of L-2-normalized holomorphic modular forms of weight k on the upper half plane, with respect to the unit group of a quaternion division algebra over Q. More precisely we show that when the L-2 norm of an eigenfunction f is one, parallel to f parallel to(infinity) <<(epsilon) k(1/2-1/33+epsilon) for any epsilon > 0 and for all k sufficiently large.

Origin of nonlinearity and plausible turbulence by hydromagnetic transient growth in accretion disks: Faster growth rate than magnetorotational instability

We investigate the evolution of hydromagnetic perturbations in a small section of accretion disks. It is known that molecular viscosity is negligible in accretion disks. Hence, it has been argued that a mechanism, known as magnetorotational instability (MRI), is responsible for transporting matter in the presence of a weak magnetic field. However, there are some shortcomings, which question the effectiveness of MRI. Now the question arises, whether other hydromagnetic effects, e.g., transient growth (TG), can play an important role in bringing nonlinearity into the system, even at weak magnetic fields. In addition, it should be determined whether MRI or TG is primarily responsible for revealing nonlinearity in order to make the flow turbulent. Our results prove explicitly that the flows with a high Reynolds number (Re), which is the case for realistic astrophysical accretion disks, exhibit nonlinearity via TG of perturbation modes faster than that by modes producing MRI. For a fixed wave vector, MRI dominates over transient effects only at low Re, lower than the value expected to be in astrophysical accretion disks, and low magnetic fields. This calls into serious question the (overall) persuasiveness of MRI in astrophysical accretion disks.

Active Power Decoupling with Reduced Converter Stress for Single-Phase Power Conversion and Interfacing

Single-phase DC/AC power electronic converters suffer from pulsating power at double the line frequency. The commonest practice to handle the issue is to provide a huge electrolytic capacitor for smoothening out the ripple. But, the electrolytic capacitors having short end of lifetimes limit the overall lifetime of the converter. Another way of handling the ripple power is by active power decoupling (APD) using the storage devices and a set of semiconductor switches. Here, a novel topology has been proposed implementing APD. The topology claims the benefit of 1) reduced stress on converter switches 2) using smaller capacitance value thus alleviating use of electrolytic capacitor in turn improving the lifetime of the converter. The circuit consists of a third leg, a storage capacitor and a storage inductor. The analysis and the simulation results are shown to prove the effectiveness of the topology.

Risk-Sensitive Ergodic Control of Continuous Time Markov Processes With Denumerable State Space

In this article, we study risk-sensitive control problem with controlled continuous time Markov chain state dynamics. Using multiplicative dynamic programming principle along with the atomic structure of the state dynamics, we prove the existence and a characterization of optimal risk-sensitive control under geometric ergodicity of the state dynamics along with a smallness condition on the running cost.

On the Bounds of Certain Maximal Linear Codes in a Projective Space

The set of all subspaces of F-q(n) is denoted by P-q(n). The subspace distance d(S)(X, Y) = dim(X) + dim(Y)-2dim(X boolean AND Y) defined on P-q(n) turns it into a natural coding space for error correction in random network coding. A subset of P-q(n) is called a code and the subspaces that belong to the code are called codewords. Motivated by classical coding theory, a linear coding structure can be imposed on a subset of P-q(n). Braun et al. conjectured that the largest cardinality of a linear code, that contains F-q(n), is 2(n). In this paper, we prove this conjecture and characterize the maximal linear codes that contain F-q(n).

Effect of Chalcogens on Electronic and Photophysical Properties of Vinylene-Based Diketopyrrolopyrrole Copolymers

Three vinylene linked diketopyrrolopyrrole based donor acceptor (D-A) copolymers have been synthesized with phenyl, thienyl, and selenyl units as donors. Optical and electronic properties were investigated with UV-vis absorption spectroscopy, cyclic voltammetry, near edge X-ray absorption spectroscopy, organic field effect transistor (OFET) measurements, and density functional theory (DFT) calculations. Optical and electrochemical band gaps decrease in the order phenyl, thienyl, and selenyl. Only phenyl-based polymers are nonplanar, but the main contributor to the larger band gap is electronic, not structural effects. Thienyl and selenyl polymers exhibit ambipolar charge transport but with higher hole than electron mobility. Experimental and theoretical results predict the selenyl system to have the best transport properties, but OFET measurements prove the thienyl system to be superior with p-channel mobility as high as 0.1 cm(2) V-1 s(-1).

Separation index of graphs and stacked 2-spheres

In 1987, Kalai proved that stacked spheres of dimension d >= 3 are characterised by the fact that they attain equality in Barnette's celebrated Lower Bound Theorem. This result does not extend to dimension d = 2. In this article, we give a characterisation of stacked 2-spheres using what we call the separation index. Namely, we show that the separation index of a triangulated 2-sphere is maximal if and only if it is stacked. In addition, we prove that, amongst all n-vertex triangulated 2-spheres, the separation index is minimised by some n-vertex flag sphere for n >= 6. Furthermore, we apply this characterisation of stacked 2-spheres to settle the outstanding 3-dimensional case of the Lutz-Sulanke-Swartz conjecture that ``tight-neighbourly triangulated manifolds are tight''. For dimension d >= 4, the conjecture has already been proved by Effenberger following a result of Novik and Swartz. (C) 2015 Elsevier Inc. All rights reserved.

Simultaneous nonvanishing of Dirichlet L-functions and twists of Hecke-Maass L-functions

We prove that given a Hecke-Maass form f for SL(2, Z) and a sufficiently large prime q, there exists a primitive Dirichlet character chi of conductor q such that the L-values L(1/2, f circle times chi) and L(1/2, chi) do not vanish.

Mixed norm estimates for the Riesz transforms on the Heisenberg group

In this paper we prove weighted mixed norm estimates for Riesz transforms on the Heisenberg group and Riesz transforms associated to the special Hermite operator. From these results vector-valued inequalities for sequences of Riesz transforms associated to generalised Grushin operators and Laguerre operators are deduced.

SOME INFINITE SUMS IDENTITIES

We find the sum of series of the form Sigma(infinity)(i=1) f(i)/i(r) for some special functions f. The above series is a generalization of the Riemann zeta function. In particular, we take f as some values of Hurwitz zeta functions, harmonic numbers, and combination of both. These generalize some of the results given in Mezo's paper (2013). We use multiple zeta theory to prove all results. The series sums we have obtained are in terms of Bernoulli numbers and powers of pi.

Active Power Decoupling with Reduced Converter Stress for Single-Phase Power Conversion and Interfacing

Single-phase DC/AC power electronic converters suffer from pulsating power at double the line frequency. The commonest practice to handle the issue is to provide a huge electrolytic capacitor for smoothening out the ripple. But, the electrolytic capacitors having short end of lifetimes limit the overall lifetime of the converter. Another way of handling the ripple power is by active power decoupling (APD) using the storage devices and a set of semiconductor switches. Here, a novel topology has been proposed implementing APD. The topology claims the benefit of 1) reduced stress on converter switches 2) using smaller capacitance value thus alleviating use of electrolytic capacitor in turn improving the lifetime of the converter. The circuit consists of a third leg, a storage capacitor and a storage inductor. The analysis and the simulation results are shown to prove the effectiveness of the topology.