L2-Stability Of A Class Of Nonlinear-Systems

Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) δ > 0 ω ε (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 β 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt 1 − ε, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ε > 0, and , c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria

Empirical Studies on Labor Market Matching (summary section only)

This thesis analyzes how matching takes place at the Finnish labor market from three different angles. The Finnish labor market has undergone severe structural changes following the economic crisis in the early 1990s. The labor market has had problems adjusting from these changes and hence a high and persistent unemployment has followed. In this thesis I analyze if matching problems, and in particular if changes in matching, can explain some of this persistence. The thesis consists of three essays. In the first essay Finnish Evidence of Changes in the Labor Market Matching Process the matching process at the Finnish labor market is analyzed. The key finding is that the matching process has changed thoroughly between the booming 1980s and the post-crisis period. The importance of the number of unemployed, and in particular long-term unemployed, for the matching process has vanished. More unemployed do not increase matching as theory predicts but rather the opposite. In the second essay, The Aggregate Matching Function and Directed Search -Finnish Evidence, stock-flow matching as a potential micro foundation of the aggregate matching function is studied. In the essay I show that newly unemployed match mainly with the stock of vacancies while longer term unemployed match with the inflow of vacancies. When aggregating I still find evidence of the traditional aggregate matching function. This could explain the huge support the aggregate matching function has received despite its odd randomness assumption. The third essay, How do Registered Job Seekers really match? -Finnish occupational level Evidence, studies matching for nine occupational groups and finds that very different matching problems exist for different occupations. In this essay also misspecification stemming from non-corresponding variables is dealt with through the introduction of a completely new set of variables. The new outflow measure used is vacancies filled with registered job seekers and it is matched by the supply side measure registered job seekers.

A Novel Construction of Complex Orthogonal Designs with Maximal Rate and Low-PAPR

Space-time block codes based on orthogonal designs are used for wireless communications with multiple transmit antennas which can achieve full transmit diversity and have low decoding complexity. However, the rate of the square real/complex orthogonal designs tends to zero with increase in number of antennas, while it is possible to have a rate-1 real orthogonal design (ROD) for any number of antennas.In case of complex orthogonal designs (CODs), rate-1 codes exist only for 1 and 2 antennas. In general, For a transmit antennas, the maximal rate of a COD is 1/2 + l/n or 1/2 + 1/n+1 for n even or odd respectively. In this paper, we present a simple construction for maximal-rate CODs for any number of antennas from square CODs which resembles the construction of rate-1 RODs from square RODs. These designs are shown to be amenable for construction of a class of generalized CODs (called Coordinate-Interleaved Scaled CODs) with low peak-to-average power ratio (PAPR) having the same parameters as the maximal-rate codes. Simulation results indicate that these codes perform better than the existing maximal rate codes under peak power constraint while performing the same under average power constraint.

Electronic structure of square planar CuO46− clusters

The results of spin-polarized MSXagr calculations show that the ground state of the CuO 4 6– cluster is essentially non-magnetic in spite of odd number of electrons in the system for short Cu–O distances (1.90 Å) as found in the highT c superconductors. This arises due to the fact that the unpaired electron resides in a molecular orbital with primarily oxygen 3s character. The stability of this molecular orbital is found to be sensitive to the cluster geometry and thus, increase in Cu–O distance (as well as other changes affecting oxygen-oxygen distance) tend to favour a magnetic state. From these calculations we have also estimated the Coulomb correlation strength within the Cu 3d to be about 5.3 eV.

Atomic fountain of laser-cooled Yb atoms for precision measurements

We demonstrate launching of laser-cooled Yb atoms in a cold atomic fountain. Atoms in a collimated thermal beam are first cooled and captured in a magneto-optical trap (MOT) operating on the strongly allowed S-1(0) -> P-1(1) transition at 399 nm (blue line). They are then transferred to a MOT on the weakly allowed S-1(0) -> P-3(1) transition at 556 nm (green line). Cold atoms from the green MOT are launched against gravity at a velocity of around 2.5 m/s using a pair of green beams. We trap more than 107 atoms in the blue MOT and transfer up to 70% into the green MOT. The temperature for the odd isotope Yb-171 is similar to 1 mK in the blue MOT, and reduces by a factor of 40 in the green MOT.

Diproline Templates as Folding Nuclei in Designed Peptides. Conformational Analysis of Synthetic Peptide Helices Containing Amino Terminal Pro-Pro Segments

The effect of N-terminal diproline segments in nucleating helical folding in designed peptides has been studied in two model sequences Piv-Pro-Pro-Aib-Leu-Aib-Phe-OMe (1) and Boc-Aib-Pro-Pro-Aib-Val-Ala-Phe-OMe (2). The structure of 1 in crystals, determined by X-ray diffraction, reveals a helical (RR) conformation for the segment residues 2 to 5, stabilized by one 4 -> 1 hydrogen bond and two 5 -> 1 interactions. The N-terminus residue, Pro(1) adopts a polyproline II (P-II) conformation. NMR studies in three different solvent systems support a conformation similar to that observed in crystals. In the apolar solvent CDCl3, NOE data favor the population of both completely helical and partially unfolded structures. In the former, the Pro-Pro segment adopts an alpha(R)-alpha(R) conformation, whereas in the latter, a P-II-alpha(R) structure is established. The conformational equilibrium shifts in favor of the P-II-alpha(R) structure in solvents like methanol and DMSO. A significant population of the Pro(1)- Pro(2) cis conformer is also observed. The NMR results are consistent with the population of at least three conformational states about Pro- Pro segment: trans alpha(R)-alpha(R), trans P-II-alpha(R) and cis P-II-alpha(R). Of these, the two trans conformers are in rapid dynamic exchange on the NMR time scale, whereas the interconversion between cis and trans form is slow. Similar results are obtained with peptide 2. Analysis of 462 diproline segments in protein crystal structures reveals 25 examples of the alpha(R)-alpha(R) conformation followed by a helix. Modeling and energy minimization studies suggest that both P-II-alpha(R) and alpha(R)-alpha(R) conformations have very similar energies in the model hexapeptide 1

Distributed algorithms for edge dominating sets

An edge dominating set for a graph G is a set D of edges such that each edge of G is in D or adjacent to at least one edge in D. This work studies deterministic distributed approximation algorithms for finding minimum-size edge dominating sets. The focus is on anonymous port-numbered networks: there are no unique identifiers, but a node of degree d can refer to its neighbours by integers 1, 2, ..., d. The present work shows that in the port-numbering model, edge dominating sets can be approximated as follows: in d-regular graphs, to within 4 − 6/(d + 1) for an odd d and to within 4 − 2/d for an even d; and in graphs with maximum degree Δ, to within 4 − 2/(Δ − 1) for an odd Δ and to within 4 − 2/Δ for an even Δ. These approximation ratios are tight for all values of d and Δ: there are matching lower bounds.

Spin-1 Kitaev model in one dimension

We study a one-dimensional version of the Kitaev model on a ring of size N, in which there is a spin S > 1/2 on each site and the Hamiltonian is J Sigma(nSnSn+1y)-S-x. The cases where S is integer and half-odd integer are qualitatively different. We show that there is a Z(2)-valued conserved quantity W-n for each bond (n, n + 1) of the system. For integer S, the Hilbert space can be decomposed into 2N sectors, of unequal sizes. The number of states in most of the sectors grows as d(N), where d depends on the sector. The largest sector contains the ground state, and for this sector, for S=1, d=(root 5+1)/2. We carry out exact diagonalization for small systems. The extrapolation of our results to large N indicates that the energy gap remains finite in this limit. In the ground-state sector, the system can be mapped to a spin-1/2 model. We develop variational wave functions to study the lowest energy states in the ground state and other sectors. The first excited state of the system is the lowest energy state of a different sector and we estimate its excitation energy. We consider a more general Hamiltonian, adding a term lambda Sigma W-n(n), and show that this has gapless excitations in the range lambda(c)(1)<=lambda <=lambda(c)(2). We use the variational wave functions to study how the ground-state energy and the defect density vary near the two critical points lambda(c)(1) and lambda(c)(2).

A Multi frequency study of Radio Intensity Variations For Active Galactic Nuclei of Different Optical Classes

A study of radio intensity variations at seven frequencies in the range 0.3 to 90 GHz for compact extragalactic radio sources classified as BL Lacs and high- and low-optical polarization quasars (HPQs and LPQs) is presented. This include the results of flux-density monitoring of 33 compact sources for three years at 327 MHz with the Ooty Synthesis Radio Telescope. The degrees of 'short-term' (tau less than about 1 yr) variability for the three optical types are found to be indistinguishable at low frequencies (less than 1 GHz), pointing to an extrinsic origin for the low-frequency variability. At high frequencies, a distinct dependence on optical type is present, the variability increasing from LPQs, through HPQs to BL Lacs. This trend persists even when only sources with ultra-flat radio spectra (alpha greater than -0.2) are considered. Implications of this for the phenomenon of high-frequency variability and the proposed unification schemes for different optical types of active galactic nuclei are discussed.

High selectivity miniaturized broadband filter

Design of a compact broadband filter using tightly coupled line sections in defected (A slot is cut in the ground) microstrip medium operating from 3 1-6 8 GHz has been repotted in this article Filter has been designed and analyzed using an equivalent circuit model based on even and odd mock parameters of coupled line sections The proposed filter has attenuation poles on either side of the pass band resulting in improved selectivity This filter features spurious free response up to third harmonic frequency Experimental results of the filter have been validated against the analytical and full wave simulations (C) 2010 Wiley Periodicals Inc Microwave Opt Technol Lett 53 184-187 2011 View this article online at wileyonlinelibrary com DOI 10.1002/mop.25676

Growth and characterization of some novel crystals for nonlinear optical applications

The advent of high intensity lasers coupled with the recent advances in crystal technology has led to rapid progress in the field of nonlinear optics. This article traces the history of materials development that has taken place over the past forty odd years and dwells on the current status in this important area. The materials aspect is discussed under three classes viz. inorganic, organic and semiorganic crystals. In the end, some of the crystal growth work that has been carried out in author's laboratory is presented.

Holographic c-theorems in arbitrary dimensions

We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flow is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy's proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.

Further studies on Norrish type II reactions including a reaction in the first excited singlet state and cyclization of 1:4 biradicals

The Norrish type II processes of methyl-2,2-dimethyl- cyclopropyl ketone, alpha-alkoxy acetones and alkyl pyruvates have been examined using the AM1 semi-empirical molecular orbital method with complete geometry optimization at the partial configuration interaction level in the restricted Hartree-Fock (RHF) frame. The results reveal that the methyl-substituted cyclopropyl ketone has a constrained geometry favourable for hydrogen abstraction from the gamma-position relative to the carbonyl group in the excited singlet state. The presence of the ether oxygen atom in the beta-position relative to the carbonyl group in alkoxy acetones and alkyl pyruvates leads to increased reactivity relative to alkyl monoketones and diketones respectively. The cyclization of 1:4 biradicals has been studied in the unrestricted Hartree-Fock (UHF) frame, and the results reveal that the 1:4 biradical derived from alkoxy acetones readily cyclizes to form oxetanols. On the other hand, in the 1:4 biradicals derived from methyl-substituted cyclopropyl ketone, the three-membered ring breaks readily to form an enol intermediate. Delocalization of an odd electron in 1:4 biradicals derived from alkyl pyruvates is thought to make cyclization difficult.

On Walkup's class K (d) and a minimal triangulation of (S-3 (sic) S-1)(#3)

For d >= 2, Walkup's class K (d) consists of the d-dimensional simplicial complexes all whose vertex-links are stacked (d - 1)-spheres. Kalai showed that for d >= 4, all connected members of K (d) are obtained from stacked d-spheres by finitely many elementary handle additions. According to a result of Walkup, the face vector of any triangulated 4-manifold X with Euler characteristic chi satisfies f(1) >= 5f(0) - 15/2 chi, with equality only for X is an element of K(4). Kuhnel observed that this implies f(0)(f(0) - 11) >= -15 chi, with equality only for 2-neighborly members of K(4). Kuhnel also asked if there is a triangulated 4-manifold with f(0) = 15, chi = -4 (attaining equality in his lower bound). In this paper, guided by Kalai's theorem, we show that indeed there is such a triangulation. It triangulates the connected sum of three copies of the twisted sphere product S-3 (sic) S-1. Because of Kuhnel's inequality, the given triangulation of this manifold is a vertex-minimal triangulation. By a recent result of Effenberger, the triangulation constructed here is tight. Apart from the neighborly 2-manifolds and the infinite family of (2d + 3)-vertex sphere products Sd-1 X S-1 (twisted for d odd), only fourteen tight triangulated manifolds were known so far. The present construction yields a new member of this sporadic family. We also present a self-contained proof of Kalai's result. (C) 2011 Elsevier B.V. All rights reserved.

Relaxation behavior of twin nonlinear optical chromophores: Effect of the spacer length

A new series of twin nonlinear optical (NLO) molecules, having two 4-nitrophenol chromophores that are linked via a flexible polymethylene spacer of varying length [(CH2)(n), n = 1-12], were synthesized. Powder second harmonic generation measurements of these twin samples indicated a pronounced odd-even oscillation, with the odd twins exhibiting a high SHG value while the even ones gave no measurable SH signal. This behavior reflects the crystal packing preferences in such twin NLO systems that have odd and even numbers of atoms linking them - the even ones appear to prefer a centrosymmetric packing arrangement. The orientational/disordering dynamics of these twin NLO molecules, doped in a polymer (poly(methyl methacrylate)) matrix, has also been studied using SHG in electric field poled samples. Interestingly, the maximum attainable SH signal, chi((2)), in, the poled samples also showed an odd-even oscillation; the odd ones again having a higher value of chi((2)) This unprecedented odd-even oscillation in such molecularly doped systems is rationalized as being due to the intrinsically greater ease of a parallel alignment of the two chromophores in the twins with an odd spacer than in those with an even one. Further, the temporal stability of the SHG intensity at 70 degrees C, after the removal of the applied corona, was also studied. The relaxation of all the twin chromophores followed a biexponential decay; the characteristic relaxation time (tau(2)) for the slow decay component suggests that while the twin with a single methylene unit relaxes relatively slowly, the relaxation is significantly faster in cases where n = 2 and 3. In the twins with even longer spacer segments, the relaxation again becomes slower and reaches a saturation value. The observed minimum appears to reflect the interplay of two competing factors that affect the chromophore alignment in such twin systems, namely, the electrostatic repulsion between neighboring oriented dipoles and the intrinsic flexibility of the spacer.