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We develop some asymptotics for a kernel function introduced by Kohnen and use them to estimate the number of normalised Hecke eigenforms in $S_k(\Gamma _0(1))$ whose L-values are simultaneously nonvanishing at a given pair of points each of which lies inside the critical strip.

In this paper we prove that the first Fourier-Jacobi coefficient of a non-zero Siegel cusp form and a Hecke eigenform of degree 2, weight k, for S p 4 ( Z ) is not identically zero.

The vortex tube or Ranque–Hilsch vortex tube is a device that separates cold and hot air from compressed air while entering into the vortex chamber through the tangential inlet nozzles. A three-dim...

We define an Eichler–Zagier map Z M on the space of Jacobi cusp forms of matrix index M and discuss its mapping properties. If the order of M is congruent to 1 mod 8 then we show that Z M maps certain Jacobi Poincare series to half-integral weight Poincare series and we construct a subspace of Jacobi cusp forms on which the map Z M is injective. By using the above results we relate the Fourier coefficients of certain Jacobi cusp forms to central values of the twisted modular L-functions and we improve certain non-vanishing results for Jacobi Poincare series established by S. Das.

In this research, an ample attempt was made to make use of oil extracted from bergamot fruit peel, which can be regarded as a renewable energy source. A systematic experimental approach was adopted to evaluate the feasibility of bergamot peel oil (BGT) as a substitute for gasoline fuel in spark-ignition (SI) engine applications. The oil derived from the rinds of the bergamot fruit was blended in gasoline on a volume basis in the ratios of 10:90, 20:80, 30:70, and 40:60 and experimentally tested in a multi-point fuel injection (MPFI) installed SI engine. The fuel properties of the BGT and its blends were tested. Endoscopic visualization technique was used to analyze the spatial flame distribution on a crank angle basis for the gasoline and bergamot blends. Also, the performance, combustion, and emission characteristics of bergamot-gasoline blends were evaluated, and the results were compared with sole gasoline at various engine brake powers. The endoscopic results revealed that bergamot-gasoline blends exhibited higher flame spread than sole gasoline. The performance study revealed that the brake thermal efficiency and specific fuel consumption exhibited by bergamot-gasoline blends were almost equivalent to that of sole gasoline. The mean in-cylinder pressure was marginally higher, and peak pressure crank angle degree was slightly advanced for bergamot-gasoline blends in comparison to that of gasoline fuel. With an increasing concentration of BGT in the blend, the hydrocarbon (HC) and carbon monoxide (CO) emission decreased at the expense of nitrogen oxides (NOx). Furthermore, BGT exhibits a research octane number (RON) of 80 and a calorific value comparable to that of gasoline, making it a potential candidate for SI engines. From the outcome of this study, it can be concluded that BGT could be a promising alternate biofuel for the partial replacement of gasoline in SI engines. © 2022 Elsevier Ltd 2-s2.0-85123890947

Since last few decades hepatitis C virus (HCV) has been a major cause of death due to the involvement of acute and chronic type of liver diseases throughout the world. Genotype variability and mutations occurring at different regions of HCV genome provides a critical parameter for the study of sustained virological response (SVR) against mono and combinational therapies. Most of these mutations occurring in E2 and NS5A-ISDR regions in HCV genotypes play a significant role in SVR against Interferon-monotherapy and combination therapy. Therefore, the aim of the present study is to evaluate the SVR in various genotypes and the role of mutations in specific regions. In line with this, the NS5A and E2 proteins of HCV genotype 1 were found to suppress the double-stranded (ds) RNA-dependent protein kinase (PKR), which in turn is entailed in the cellular antiviral response stimulated by interferon (IFN). The response to IFN therapy varies between genotypes, with response rates among patients infected with types 2 and 3 nearly two-three-fold greater than in patients infected with type 1. Surprisingly, a considerable percentage of HCV genotype 3a infected patients do not react to treatment at all. In Japan, a link was observed between the numbers of mutations in an “interferon sensitivity determining region” (ISDR) and the result of interferon treatment in genotype 1b infected patients. Therefore, we published data on E2 (PePHD) and NS5A-ISDR regions including our data on SVR of different HCV genotypes, the relationship between the number and patterns of mutations in the E2 (PePHD) and NS5A-ISDR regions and responsiveness to IFN therapy.

Cloud computing being the representation of the technology makes use of the infrastructure for computing in an efficient manner. This type of a computing offers a large amount of potential in improving the productivity which reduces the costs and also ensures that this can handle the risks. The intrusion detection systems (IDS) are all widely used for malicious detection in the network of communication and also its host. The IDS system used currently has one set of rules with several patterns of attach which get stored inside the various databases and the whole traffic of network will be duly matched against this for the purpose of avoiding any other illegal or also unauthorized activities. Therefore, in this work, this structure has optimized multi-layer artificial neural network is based on the IDS in case of the cloud which has been presented. This hybrid glow swarm optimization (GSO)–tabu search (TS) is called the GSO–TS has been used for the optimization of the structure and also for the purpose of reduction of convergence time and for solving old problems, trapping of local optima and their premature convergence. The results have proved to have better performance.

NiO nanoflakes and nanosheets are successfully synthesized with different anions via homogeneous precipitation method. The prepared samples are characterized by XRD, SEM, TEM-SAED, DRS, PL and VSM analysis. XRD pattern confirms the presence of cubic bunsenite phase with preferred orientation along (2 0 0) direction. SEM images exhibits the presence of nanoflakes, semi-spherical, flower-like and nanosheet shaped particles with an average size 34 nm. The estimated band gap energy and refractive index are found to be in the range 3.79–4.18 eV and 1.48–1.93 respectively. Blue emissions in PL spectrum with a strong band centered at 425 nm and green emission band at 537 nm confirmed presence of crystal defects in NiO lattice. VSM analysis reveals the presence of superparamagnetic and weak ferromagnetic behavior in the NiO nanoparticles.

Cubic structured pure and Fe-doped cobalt oxide thin film electrodes are successfully prepared by nebulizer spray pyrolysis technique. Single phase polycrystalline cubic structure with (220) plane orientation are observed in the XRD analysis for pure and Fe-doped cobalt oxide films. From the optical analysis, two bandgaps are observed in the range 1.366–1.713 eV and 2.846–2.925 eV for lower and higher energy regions respectively. HR-SEM images revealed the formation of well covered and spherical shaped particles in the formed films. The increase of electrical conductivity with Fe doping concentration has been confirmed at room temperature. The maximum specific capacitance value is observed in the 2.5 wt% of Fe doped Co3O4 thin film electrode at the scan rate of 2 mV/s.

The spray pyrolysis (SP) technique is an important and powerful method for the preparation of nickel oxide (NiO) and copper-doped nickel oxide thin films. The best films were obtained when the substrate temperature, T s = 450 °C on glass substrates. Copper (Cu) concentrations in the films were varied from 0 to 8%. The effect of Cu concentration on the structural, morphological, spectral, optical, and electrical properties of the thin films were studied by X-ray diffraction (XRD), Scanning electron microscopy (SEM), Fourier transformed infrared spectroscopy (FTIR), UV–vis–NIR spectrophotometer, Hot probe and Hall system. The X-ray diffraction result shows the polycrystalline cubic structure of sprayed films with (200) preferred orientation. The variations of the structural parameters such as lattice parameters and grain sizes were investigated. The SEM image displays the surface morphology of the NiO and Cu:NiO thin films. The FTIR of the as-deposited films were associated with chemical identification. The optical transmittance and absorbance spectra of the films were measured by UV–vis–NIR spectrophotometer. The absorption coefficient and band gaps of the films were calculated using the optical method. All the NiO and Cu:NiO films were p-type. The resistivity of the above films decreases with the increase in copper concentration and so the conductivity of the films depend on the precursor concentration.

Pure and cerium (Ce) doped tin oxide (SnO2) thin films are prepared on glass substrates by jet nebulizer spray pyrolysis technique at 450 °C. The synthesized films are characterized by X-ray diffraction (XRD), scanning electron microscopy, energy dispersive analysis X-ray, ultra violet visible spectrometer (UV–Vis) and stylus profilometer. Crystalline structure, crystallite size, lattice parameters, texture coefficient and stacking fault of the SnO2 thin films have been determined using X-ray diffractometer. The XRD results indicate that the films are grown with (110) plane preferred orientation. The surface morphology, elemental analysis and film thickness of the SnO2 films are analyzed and discussed. Optical band gap energy are calculated with transmittance data obtained from UV–Visible spectra. Optical characterization reveals that the band gap energy is found decreased from 3.49 to 2.68 eV. Pure and Ce doped SnO2 thin film gas sensors are fabricated and their gas sensing properties are tested for various gases maintained at different temperature between 150 and 250 °C. The 10 wt% Ce doped SnO2 sensor shows good selectivity towards ethanol (at operating temperature 250 °C). The influence of Ce concentration and operating temperature on the sensor performance is discussed. The better sensing ability for ethanol is observed compared with methanol, acetone, ammonia, and 2-methoxy ethanol gases.

Highly uniform and well-dispersed ring shaped particles of CDC (Cobalt doped cerium oxide) films are successfully deposited by Nebulizer Spray Pyrolysis (NSP) technique. The structural, morphological, optical and photo-diode properties of the films are investigated. Cubic fluorite crystallites are detected by X-ray diffraction pattern with preferred orientation along (111) direction. Co concentrations distress the crystallinity and structural parameters. The transmittance decreases with increasing Co concentration due to the presence of covalent bonds between cerium and oxygen. PL spectra revealed that three consistent sharp and broad peaks observed at 369 (3.31 eV), 394 (3.14 eV) and 425 nm (2.91 eV) correspond to near-band-edge emission (NBE) in UV region, deep level emission (DLE) in violet and blue of the visible region respectively. The deep level emissions result from the recombination of electrons with holes trapped in singly ionized oxygen vacancies (Vo+). Large agglomerated ring, button and spherical crystallites are obtained with the typical size in the range 83–207 nm. XPS analysis exhibits the presence of Ce, Co, O, C and Na in the films that indicates the non-stoichiometric behavior. I-V characteristics show the rectifying nature with a typical forward to reverse current ratio of ~7 in the range −4 to +4 V. The turn-on voltage of the hetero-junction is found to be ~1.7 V. The transient photocurrent behavior indicates that the device has a good stability and quick response to suggests that the prepared heterojunction device can be used as a white light photodetector and UV detector applications.

Cubic cobalt oxide (Co 3 O 4 ) thin films are deposited using cobalt chloride hexahydrate as precursor by nebulizer spray pyrolysis technique with different molar concentrations. The structural, optical, morphological and electrical properties are investigated. X-ray diffraction (XRD) analysis shows the polycrystalline nature of the films with cubic structure having preferential orientation through (220) plane. The maximum crystallite size is found to be ∼21 nm. The optical bandgap energy of the film is decreased with the increase of molar concentration. The obtained maximum bandgap energy values are 2.88 and 1.56 eV for the films prepared at 0.025 M. High-resolution scanning electron microscope illustrates the overgrown crystals like structure and coalescence of grains. The electrical conductivity of the films increases with the increase of molar concentration.

In this paper, we set up the theory of newforms for the space of Eisenstein series of weight [Formula: see text] for [Formula: see text] ([Formula: see text], [Formula: see text]) which is compatible with the theory of newforms for the space of Eisenstein series of weight 2[Formula: see text] and level 2[Formula: see text].

Uniform and well-dispersed IDC (indium doped cerium oxide) films are successfully deposited by Nebulizer Spray Pyrolysis (NSP) technique. Cubic fluorite crystallites are detected by an X-ray diffraction pattern with a preferred orientation along the (200) direction. The In concentration affects the crystallinity and structural parameters like crystallite size, texture coefficient, lattice constant and dislocation density. The transmittance decreases with increasing In concentration up to 15% and then increases due to the presence of covalent bonds between cerium and an oxygen additive at the shortest wavelengths. PL spectra revealed that three consistent sharp and broad peaks are observed at 394 (3.14 eV), 425 (2.91 eV) and 579 nm (2.14 eV), which correspond to near band edge emission (NBE) at the UV region and blue and red deep level emission (DLE) in the visible region, respectively. Large agglomerated ring and white spherical crystallites are obtained with a typical size in the range of 93–128 nm. Satellites are caused by the facilitation of ligand (O 2p) to metal (Ce 4f) charge transfer by primary and main photoionization processes, which indicates that the valance states of Ce3+ (16.7%) and Ce4+ (36.4%) have entered in to the CeO2 lattice sites. I–V characteristics show the rectifying nature of this hetero-junction with a typical forward to reverse current ratio of ∼7 in the range −3 to +3 V. The turn-on voltage of the hetero-junction is found to be ∼1.5 V. The transient photocurrent behavior indicates that the device has good stability and quick response and suggests that the prepared heterojunction device can be used as a white light photodetector and for UV detector applications.

The competence of a financial system is entirely depending upon the stock market efficiency. The gradual growth of equity investor’s participation is inevitable to enrich the overall growth of emerging economies.Hence the necessity is felt to provide an empirical support to the investing community. For the purpose, this study attempts to examine the weak-form efficiency of Indian stock market – National Stock Exchange (NSE). The study has used the daily closing price of the Nifty fifty stocks from 3rdJanuary 2011 to 24thApril 2015. To test the weak form efficiency both parametric and non-parametric tests called Autocorrelation, Augmented Dicky Fuller test, and Runs Test were performed. The study reveals that 39 stocks of NSE-Nifty Fifty are found to be weak form inefficient, so that the investors can formulate trading strategies to gain abnormal returns. The Index and 10 stocks are found to be weak form efficient during the study period since the price series found to be autocorrelation existence.

Tin oxide thin films doped with different concentrations of ruthenium were deposited on the glass substrates at 450 °C by nebulizer spray pyrolysis technique. The structural, morphological, thickness and optical properties of thin films were investigated by X-ray diffraction, scanning electron microscopy, stylus profilometer and ultra violet spectrometer techniques. X-ray diffraction pattern confirms the tetragonal crystal structure for pure and ruthenium doped tin dioxide thin films. Ruthenium doped tin dioxide thin films are polycrystalline in nature. Scanning electron microscopy shows the modification of surface morphology of tin dioxide films due to varying concentration of ruthenium. Largest spheres, rings and interconnected fibers are present in the scanning electron microscopy images. Energy dispersive analysis reveals the average atomic percentage of pure and ruthenium doped tin dioxide present in the films developed. Stylus profilometer was used to measure the film thickness. Pure, 5, 10 and 15 wt% ruthenium doped tin dioxide thin films are found to have 327, 349, 386 and 425 nm thickness. Optical studies divulge that the band gap energy decreases from 3.55 eV to 3.04 eV due to the increased ruthenium concentrations. Gas sensing properties of pure and ruthenium doped tin dioxide thin films have been studied for various gases.

Cobalt oxide thin films are prepared by the nebulizer spray pyrolysis technique using cobalt chloride as the precursor material. The structural, optical, morphological and electrical properties are investigated as a function of substrate temperature (300–450 °C). The X-ray diffraction (XRD) analysis reveals that all the films are polycrystalline in nature, having cubic structure with preferential orientation along the (111) plane. The optical spectra show that the films are transparent (68 %) in the IR region. The optical band gap values are calculated for different substrate temperature. Photoluminescence (PL) spectra of the films indicate the presence of indigo, blue and green emission peaks with an ultraviolet emission peak centered around 368nm. SEM images reveals small sphere-like structures for the prepared Co3O4 films. The maximum conductivity obtained is 1.48 x 10−3 S/cm at 350 °C. The activation energy varies between 0.039 and 0.138 eV for the substrate temperature variation from 300-450 Q°C.

Inequalities between men and women are common and well-documented. Objective indexes show that men are better positioned than women in societal hierarchies—there is no single country in the world without a gender gap. In contrast, researchers have found that the women-are-wonderful effect—that women are evaluated more positively than men overall—is also common. Cross-cultural studies on gender equality reveal that the more gender egalitarian the society is, the less prevalent explicit gender stereotypes are. Yet, because self-reported gender stereotypes may differ from implicit attitudes towards each gender, we reanalysed data collected across 44 cultures, and (a) confirmed that societal gender egalitarianism reduces the women-are-wonderful effect when it is measured more implicitly (i.e. rating the personality of men and women presented in images) and (b) documented that the social perception of men benefits more from gender egalitarianism than that of women. © 2017 International Union of Psychological Science

Liquid crystals are commonplace in technological devices, such as watch and computer displays and temperature and pressure monitors. Such materials are central to our technological lifestyles. Classically, liquid crystalline materials are based on a structural motif which could be classed as rod-like (e.g. biphenyl derivatives) and in more recent times as disc-like (e.g. triphenylene derivatives). The rod-like materials are very attractive in terms of their chemical stability and their response to electric fields, both of which are a prerequisite for display devices, whereas disc-like materials show promise as one-dimensional conducting materials. Increasing scientific and technological requirements mean that new materials are continually sought to surpass the liquid crystalline materials which are presently known. Carbazole derivatives are well-known interesting natural products. Several methods have been developed and reported in the literature for the synthesis of carbazole derivatives. There are several review articles published on the photorefractive properties of carbazole-based materials. Chemical modification of the carbazole moiety to create a new class of discotic, calamitic and banana-shaped liquid crystalline materials, which will have novel and enhanced photorefractive properties over the amorphous carbazole derivatives, will be discussed in this mini review.

The incorporation of photorefractive molecular units, such as carbazole, into anisotropic materials (liquid crystals) may offer many advantages over conventional electrical poling of photorefractive polymers. Thus, a series of symmetric 3,6-disubstituted carbazole derivatives with well-known biphenyl and triphenylene liquid-crystalline moieties was synthesized and characterized. These modifications were achieved by the esterification of bishydroxy carbazole derivatives with monoalkylated biphenyl carboxylic acids and alkylation of bisacylated bromo- derivatives of carbazole with monohydroxy pentaalkoxy triphenylene. The pure compounds are not liquid-crystalline, even when doped with trinitrofluorenone (TNF), unlike triphenylene/carbazole materials that we reported previously. These compounds, although not liquid-crystalline, may be of interest in the field of photorefractivity.

We characterise the space of newforms of weight k + 1/2 on Γ0(4N), N odd and square-free (studied by the second and third authors with Vasudevan) under the Atkin-Lehner W(4) operator. As an application, we show that the (±1)-eigensubspaces of the W(4) operator on the space of modular forms of weight k + 1/2 on Γ0(4N) is mapped to modular forms of weight 2k on Γ0(N), under a class of Shimura maps. The existence of such subspaces having this mapping property was conjectured by Zagier in a private communication. One of the special features of the (±1)-eigensubspaces is that the (2k + 1)-th power of the classical theta series of weight 1/2 belongs to the + eigensubspace and hence this gives interesting congruences for r2k+1(p2).

Current resist materials cannot simultaneously meet the sensitivity, resolution and line width roughness (LWR) requirements set out by the International Technology Roadmap for Semiconductors (ITRS) for the 32nm node and beyond. Here we present a fullerene-based, chemically amplified resist system, which demonstrates the potential to fulfill these requirements for next generation lithography. A chemically amplified fullerene resist was prepared, consisting of the derivative MF07-01, an epoxide crosslinker, and a photoacid generator, such as triarylsulfonium hexafluoroantimonate. The sensitivity of this resist was shown to be between 5 and 10 μC cm -2 at 20 keV for various combinations of post-application bake and post-exposure bake conditions. Using 30 keV electron beam exposure, sparse patterns with 15 nm resolution were demonstrated, whilst for dense patterns a half-pitch of 25 nm could be achieved. The LWR for the densely patterned features is ∼4 nm. The etch durability of the fullerene CA system was shown to be comparable to that of SAL601, a common novolac-based commercial resist, at almost four times that of silicon.

Next generation lithography will require next generation resists. Molecular resists, based on small non-polymeric molecules, promise improvements in line width roughness and resolution control for high resolution lithographic patterns. However, these materials are generally not sensitive enough for commercial application. We have investigated the application of a common chemical amplification scheme to molecular resists. The triphenylene derivative C5/C0 (symmetrical 2,6,11-trihydroxy-3,7,11-tris(pentyloxy)triphenylene), mixed with the crosslinker hexamethoxymethyl melamine and the photoacid generator triphenylsulfonium triflate shows a substantial sensitivity enhancement, requiring a dose of only [email protected]/cm^2 compared with the pure triphenylene sensitivity of [email protected]/cm^2 at 20keV. Previous work has indicated that the acid diffusion length of the photoacid generator used here is around 350nm and that the diffusion length decreases with film thickness. However, in this molecular resist system anomalous levels of acid diffusion were observed, indicating that previous results for polymeric systems may not hold true for these new materials. Initial results indicate that the acid diffusion length in this system may be on the order of microns. Furthermore, there is some evidence that the excessive diffusion is occurring in the surface layers of the resist or at the air: resist interface itself.

The effect of pH on the adhesion of silica and polystyrene latex nanoparticles, presenting hydroxyl and carboxylic acid surface chemistries respectively, to self-assembled monolayers (SAMs) has been investigated. The SAMs studied were 1-dodecanethiol, 11-mercaptoundecanoic acid and an original pyridine-terminated SAM. Adhesion of nanoparticles to the SAMs was found to decrease with increasing pH due to increased repulsive forces between surfaces, as a result of the deprotonation of surface moieties on the nanoparticles. A range of surface morphologies for the adsorbed nanoparticles was observed for the systems studied.

Molecular resists, such as fullerenes, are of significant interest for next generation lithographies. They utilize small carbon rich molecules, giving the potential for higher resolution and etch durability, together with lower line width roughness than conventional polymeric resists. The main problem with such materials has historically been low sensitivity, but with the successful implementation of chemical amplification schemes for several of the molecular resist families this is becoming less of a concern. Aside from sensitivity the other main obstacle has been the difficulty of preparing good quality thin films of non-polymeric materials. Here we present a study of pinhole defect density in fullerene films as a function of substrate cleanliness, post-application bake, and incorporation of chemical amplification components. Ultrathin (sub 30nm) films of the previously studied fullerene resist MF03-01, and the polymeric resist PMMA were prepared on hydrogen terminated silicon by spin coating and the density of pinhole defects in the films was studied using atomic force microscopy. It was seen that pinhole density was strongly affected by the quality of the substrates, with the lowest densities found on films spun on freshly cleaned substrates. Aging of the film subsequent to spin coating was seen to have less effect than similar aging of the substrate prior to spin coating. Additionally, the use of a post-application bake significantly degraded the quality of the films. The addition of an epoxy crosslinker for chemical amplification was found to reduce defect density to very low levels.

We construct an Eichler?Zagier map for Jacobi cusp forms of half-integral weight. As an application, we show there exists no Hecke-equivariant map from index 1 to index p (p prime), when the weight is half-integral.

Molecular resists, such as fullerene and triphenylene derivatives, use small carbon rich molecules, which give the potential for greater resolution, lower line edge roughness and higher etch durability than traditional polymeric materials. Their main limitation has been low sensitivity to irradiation. Here the chemical amplification of fullerene and triphenylene negative tone molecular resists is demonstrated. The sensitivity of a fullerene resist to 20keV electrons was improved from 550 to [email protected]/cm^2 by addition of an epoxide crosslinker and photoinitiator. Lines of width 25nm were written using 30keV electrons. A triphenylene with pendant epoxy groups was also studied. In this case the sensitivity reached on addition of photoinitiator was [email protected]/cm^2 at 20keV and lines of width 40nm have been achieved at 30keV.

We describe transient photoconduction studies on a well known triphenylene discotic liquid crystal molecule modified to incorporate a single carbazole moiety on one side chain and doped with the acceptor, trinitrofluorenone. This material is found to show both electron and hole photocurrents when the transient photoconduction study is carried out in the time of flight geometry although no time of flight transits are observed. Of interest here is the fact that the temperature dependence of the hole and electron photocurrents are radically different, the electron photocurrent being strongly activated while the hole photocurrent decreases with increasing temperature. We suggest a mechanism whereby the electron photocurrent controls the hole photocurrent through recombination. Furthermore, the electron activation energy varies with the applied electric field, indicating the influence of the Poole Frenkel barrier lowering mechanism in the production of the charge carriers.

The incorporation of photorefractive molecular units, such as carbazole, into anisotropic materials (liquid crystals) may offer many advantages over conventional electrical poling of photorefractive polymers. Thus, a series of symmetric 3,6-disubstituted carbazole derivatives with a bent molecular shape have been synthesized and characterized. The influence of the nature of the symmetric substituents on the carbazole is investigated through comparison of crystal packing and electrostatic potentials.

Nonlinear response in magnetostrictive sensors significantly affects the spin-stand parametric measurements used to characterize writer and reader performance of recording heads. A simple production level test defined as the nonlinear distortion (NLD) ratio was used to quantify the degree of reader nonlinearity. A positive NLD value represents the presence of reader distortion while a value of zero represents no distortion. On a large population of heads tested, the median NLD value was 0.25, which is equivalent to an amplitude loss of 10% for an isolated pulse due to reader saturation. A detailed analysis of the measured data on nonlinear transition shift, partial erasure, and PW50 of these production heads show that greater than 50% of the measured variance is due to readback nonlinear distortion rather than true performance variation of the device.