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# IEEE Transactions on Industrial Electronics

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Displaying Results 1 - 25 of 37

Publication Year: 2012, Page(s):C1 - 3361
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• ### IEEE Transactions on Industrial Electronics publication information

Publication Year: 2012, Page(s): C2
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• ### Modified Soft-Switched Three-Phase Three-Level DC–DC Converter for High-Power Applications Having Extended Duty Cycle Range

Publication Year: 2012, Page(s):3362 - 3372
Cited by:  Papers (27)
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A three-phase three-level dc-to-dc phase-shifted pulsewidth-modulation (PSPWM) converter which is reported in the literature for high-power and high-input-voltage applications is based on a three-phase three-wire configuration. However, the controllable duty cycle range of the aforementioned converter is 0-2π/3. Therefore, to obtain the rated voltage, the converter needs to be overrated by ... View full abstract»

• ### Voltage Feedback Current Control Scheme for Improved Transient Performance of Permanent Magnet Synchronous Machine Drives

Publication Year: 2012, Page(s):3373 - 3382
Cited by:  Papers (22)
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This paper proposes a novel control scheme for the fast current control of permanent magnet synchronous machines. The proposed method mainly works in the transient state of current control without deteriorating steady-state characteristics. The proposed method is applicable in a wide range of speed: in the speed below the base speed and in the flux weakening region. Using the proposed method, the ... View full abstract»

• ### A Shifted SVPWM Method to Control DC-Link Resonant Inverters and Its FPGA Realization

Publication Year: 2012, Page(s):3383 - 3391
Cited by:  Papers (12)
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A shifted space vector pulsewidth modulation (PWM) (SVPWM) method to control dc-link resonant inverters is presented in this paper. The shifted SVPWM has the same effective vectors and operation time as the traditional SVPWM in all six space sectors, while the sequences of vectors changed according to the load current flow direction. All the switches of a three-phase inverter can be turned on unde... View full abstract»

• ### Voltage Control Technique for the Extension of DC-Link Voltage Utilization of Finite-Speed SPMSM Drives

Publication Year: 2012, Page(s):3392 - 3402
Cited by:  Papers (24)
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This paper presents a new voltage control technique which extends dc-link voltage utilization for finite-speed surface-mounted permanent magnet synchronous motor drives. Therefore, significantly increasing the output power and torque under flux-weakening operation can be achieved. The switching period and summation of active switching times for inverter pulsewidth modulation control are used to mo... View full abstract»

• ### Analysis and Compensation of Time Delay Effects in Hardware-in-the-Loop Simulation for Automotive PMSM Drive System

Publication Year: 2012, Page(s):3403 - 3410
Cited by:  Papers (28)
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This paper analyzes and compensates unavoidable time delay effects in a hardware-in-the-loop (HIL) simulation for automotive permanent magnet synchronous motordrive systems. The amount of time delay between a digital controller and HIL simulator is investigated. The effects of the time delay are analyzed by use of s-domain representation of the entire closed-loop system. In addition, a stability s... View full abstract»

• ### A High-Performance Sensorless Position Control System of a Synchronous Reluctance Motor Using Dual Current-Slope Estimating Technique

Publication Year: 2012, Page(s):3411 - 3426
Cited by:  Papers (16)
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This paper proposes an adaptive sensorless position control system for a synchronous reluctance motor (SynRM). By using the proposed dual current-slope estimating technique, the rotor position of the SynRM can be precisely obtained. In addition, a comparison which shows that the proposed dual current-slope method has better performance than the traditional single current-slope method is discussed.... View full abstract»

• ### Imposed Sinusoidal Source and Load Currents for an Indirect Matrix Converter

Publication Year: 2012, Page(s):3427 - 3435
Cited by:  Papers (32)
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A new strategy for indirect matrix converters which allows an optimal control of source and load currents is presented in this paper. This method uses the commutation state of the converter in the subsequent sampling time according to an optimization algorithm given by a simple cost functional and the discrete system model. The control goals are regulation of output current according to an arbitra... View full abstract»

• ### Hybrid I-f Starting and Observer-Based Sensorless Control of Single-Phase BLDC-PM Motor Drives

Publication Year: 2012, Page(s):3436 - 3444
Cited by:  Papers (25)  |  Patents (6)
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A motion sensorless control for single-phase permanent magnet brushless dc motor based on an I-f starting sequence and a real-time permanent magnet flux estimation is proposed here. The special calculation for extracting the position and speed used here implies the generating of an orthogonal flux system, the atan2 trigonometric function, and a phase-locked loop observer. The influence of the perm... View full abstract»

• ### High-Efficiency Slim Adapter With Low-Profile Transformer Structure

Publication Year: 2012, Page(s):3445 - 3449
Cited by:  Papers (25)
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This paper presents the implementation of a high-efficiency slim adapter using an resonant converter. A new structure of the slim-type transformer is proposed, which is composed of copper wire as the primary winding and printed-circuit-board winding on the outer layer as the secondary winding. The proposed structure is suitable for a slim and high-efficiency converter because it has advantages of ... View full abstract»

• ### Three-Level Resonant Converter With Double $LLC$ Resonant Tanks for High-Input-Voltage Applications

Publication Year: 2012, Page(s):3450 - 3463
Cited by:  Papers (17)
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A new resonant converter having low voltage stress and nearly constant efficiency against line variation for high- and wide-input-voltage applications is presented in this paper. It is similar to a three-level zero-voltage-switching pulsewidth modulation converter (TL ZVS PWMC) with two flying capacitors. In the proposed converter, however, two flying capacitors are used as the resonant capacitors... View full abstract»

• ### Compact Equal and Unequal Dual-Frequency Power Dividers Based on Composite Right-/Left-Handed Transmission Lines

Publication Year: 2012, Page(s):3464 - 3472
Cited by:  Papers (23)
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A novel approach using fully integrated composite right-/left-handed (CRLH) transmission lines (TLs) is proposed to design equal and unequal dual-frequency Wilkinson power dividers (WPDs) with controllable frequency ratio. Theoretical analysis indicates that the frequency ratio and the power-splitting ratio k2 of the divider can be controlled by changing the element values and the numbe... View full abstract»

• ### An Innovative Global Harmony Search Algorithm for Parameter Identification of a PEM Fuel Cell Model

Publication Year: 2012, Page(s):3473 - 3480
Cited by:  Papers (43)
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Optimum modeling of proton exchange membrane (PEM) fuel cell has become the major focus of various researches. The main drawback in optimum modeling is that the model parameters are unknown, and empirical values are not sufficient to exactly model it. Since the characteristic of a PEM fuel cell is highly nonlinear, an excellent optimization technique is needed. In this paper, an innovative global ... View full abstract»

• ### Impact of Periodic Current Pulses on Li-Ion Battery Performance

Publication Year: 2012, Page(s):3481 - 3488
Cited by:  Papers (36)
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Pulse charging and pulse discharging have been reported by many authors in the literature to improve the performance of various secondary electrochemical cells. Only a few authors mentioned the effects of such charge and discharge method on lithium-ion batteries. The overall objective of this work is to experimentally investigate the impact of certain current pulse profiles on the electrical perfo... View full abstract»

• ### Input–Output Feedback Linearization and Speed Control of a Surface Permanent-Magnet Synchronous Wind Generator With the Boost-Chopper Converter

Publication Year: 2012, Page(s):3489 - 3500
Cited by:  Papers (22)
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A diode bridge rectifier followed by a boost-chopper circuit is a common topology of the generator-side converter for the direct-drive surface-permanent-magnet-synchronous-generator-based wind energy conversion system. Owing to its nonlinearity, it is difficult for the system to maintain good performance within normal operating range under the ordinary proportional-integral control. In this paper,... View full abstract»

• ### Development of a Spherical Air Bearing Positioning System

Publication Year: 2012, Page(s):3501 - 3509
Cited by:  Papers (10)
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In line with the general trend of the automation, spherical motion systems are increasingly required in applications such as robot joints, manipulators, orientation control systems, and angular alignment systems. In this paper, a spherical air bearing positioning system (SABS) aiming at providing highly precise rotational motions in two degrees of freedom is designed. The SABS mainly consists of d... View full abstract»

• ### Sliding Mode Control Approach for Online Learning as Applied to Type-2 Fuzzy Neural Networks and Its Experimental Evaluation

Publication Year: 2012, Page(s):3510 - 3520
Cited by:  Papers (31)
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Type-2 fuzzy logic systems (FLSs) are proposed in the literature as an alternative to type-1 FLSs because of their ability to more effectively model uncertainties that may exist in the rule base. However, the parameters of the system still need to be optimized. For this purpose, the use of a sliding mode control theory-based learning algorithm is proposed in this paper. In the approach, instead of... View full abstract»

• ### Introduction to the Special Section on The More Electric Aircraft: Power Electronics, Machines, and Drives

Publication Year: 2012, Page(s):3521 - 3522
Cited by:  Papers (8)
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• ### Overview of Electric Motor Technologies Used for More Electric Aircraft (MEA)

Publication Year: 2012, Page(s):3523 - 3531
Cited by:  Papers (152)
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This paper presents an overview of motor drive technologies used for safety-critical aerospace applications, with a particular focus placed on the choice of candidate machines and their drive topologies. Aircraft applications demand high reliability, high availability, and high power density while aiming to reduce weight, complexity, fuel consumption, operational costs, and environmental impact. N... View full abstract»

• ### Design of a Five-Phase Brushless DC Motor for a Safety Critical Aerospace Application

Publication Year: 2012, Page(s):3532 - 3541
Cited by:  Papers (37)
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This paper describes a five-phase brushless dc (BLDC) motor designed for an electrohydrostatic actuation system (EHA) suited to the thin and optimized wings. The foundation of the design is a motor with fault tolerance and high reliability, compact structure, and low weight. The motor power rating is 12 kW at 12 000 rpm, and a “wet” form of construction is used where hydraulic oil is... View full abstract»

• ### A Single Sided Matrix Converter Drive for a Brushless DC Motor in Aerospace Applications

Publication Year: 2012, Page(s):3542 - 3552
Cited by:  Papers (35)
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This paper describes a brushless dc (BLDC) drive with a single sided matrix converter (SSMC) for an electrohydrostatic actuation system in aerospace application. The use of an SSMC with a BLDC motor is novel and is used to achieve operation without a microprocessor. A simple hysteresis current control strategy is implemented to control motor torque. The multiphase SSMC provides high reliability an... View full abstract»

• ### A Novel Slotless Halbach-Array Permanent-Magnet Brushless DC Motor for Spacecraft Applications

Publication Year: 2012, Page(s):3553 - 3560
Cited by:  Papers (30)  |  Patents (1)
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This paper presents the design and analysis of a novel machine family-the enclosed-rotor Halbach-array permanent-magnet brushless dc motors for spacecraft applications. The initial design, selection of major parameters, and air-gap magnetic flux density are estimated using the analytical model of the machine. The proportion of the Halbach array in the machine is optimized using finite element anal... View full abstract»

• ### Posture Control of Electromechanical-Actuator-Based Thrust Vector System for Aircraft Engine

Publication Year: 2012, Page(s):3561 - 3571
Cited by:  Papers (5)
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This paper deals with the dynamical modeling and posture control of the electromechanical actuator (EMA)-based thrust vector control (TVC) system for aircraft engines. Addressing the issues of the large inertia and low stiffness existing in the TVC system driven by EMA, this paper established a 2-DOF mathematical model to describe the EMA dynamic characteristics. In order to overcome the influence... View full abstract»

• ### Modeling of Thermal Phenomena in Liquid Cooling System for Aircraft Electric Unit

Publication Year: 2012, Page(s):3572 - 3578
Cited by:  Papers (4)
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The aim of this paper is to show the complex thermal analyses used for examining cooling properties of a liquid cooling system integrated into an aircraft fuel metering pump. The cooling is provided by flow of aviation fuel-kerosene. The main advantage of this solution is easy implementation in the place of engine bay. Two methods of thermal analyses are used according to the level of cooling syst... View full abstract»

## Aims & Scope

IEEE Transactions on Industrial Electronics encompasses the applications of electronics, controls and communications, instrumentation and computational intelligence for the enhancement of industrial and manufacturing systems and processes.

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## Meet Our Editors

Editor-in-Chief
Leopoldo Garcia Franquelo
Escuela Superior de Ingenieros
Camino de los Descubrimientos s/n
41092 Sevilla, Spain
lgfranquelo@ieee.org
Phone: +34 954 48 73 65


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 The Puzzle of the Metallic Line StarsIn the puzzle of the metallic line (Am) stars, there still seem to bemissing pieces. While the normal'' A stars have elemental abundancesclose to solar, the classical Am stars show stronger absorption linesfor most heavy elements in their spectra. Elements with ionizationpotentials that nearly agree with those of hydrogen or helium havereduced abundances. The Ca II and Sc II lines are especially weak. TheAm stars have no ultraviolet emission lines. They are binaries that,with very few exceptions, have rotational velocities vsini lower than100 km s-1. Of the main-sequence A stars, 20% to 30% are Amstars. Here we rediscuss previous suggestions that tried to explain thepeculiar line strengths in the Am star spectra. In particular, wecompare the well-studied properties of Hyades A and Am stars in order toidentify reasons that can or cannot explain the differences. We findthat accretion of interstellar material by A stars with distortedmagnetic fields, which are weaker than those in peculiar A (Ap) stars,has the best chance of explaining the main characteristics of thepeculiar heavy-element abundances in Am star photospheres.Charge-exchange reactions also seem to be important. Asterosismologie.Not Available Search for H+3 in HD 141569AA search for H+3 line emission, reported to havebeen detected toward the young star HD 141569A and possibly originatingin a clump of planet-forming gas orbiting the star, has yielded negativeresults. Observations made at the United Kingdom Infrared Telescope andthe Subaru Telescope during 2001-2005 covered 11 major transitions ofH+3 from 3.42 to 3.99 μm. NoH+3 emission lines were detected; one marginaldetection at 3.9855 μm in 2002 June was not confirmed in laterspectra. The upper limits to the line strengths were significantly lowerthan the previously reported detections. Supplemental slit-scanningspectroscopy using adaptive optics was performed within 0.38" of HD141569A to search for extended emission from H+3,but no emission was detected. We compare our upper limit to theluminosity in H+3 from HD 141569A with thatpossible from a gas giant protoplanet and also from a jovian massexoplanet in close orbit about its central star.Based on data collected at the Subaru Telescope, which is operated bythe National Astronomical Observatory of Japan.Based on data collected at the United Kingdom Infrared Telescope, whichis operated by the Joint Astronomy Centre on behalf of the UK ParticlePhysics and Astronomy Research Council. The physical properties of normal A starsDesignating a star as of A-type is a result of spectral classification.After separating the peculiar stars from those deemed to be normal usingthe results of a century of stellar astrophysical wisdom, I define thephysical properties of the "normal" stars. The hotter A stars haveatmospheres almost in radiative equilibrium. In the A stars convectivemotions can be found which increase in strength as the temperaturedecreases. Nearby stars of the Galactic disk and halo. III.High-resolution spectroscopic observations of about 150 nearby stars orstar systems are presented and discussed. The study of these and another100 objects of the previous papers of this series implies that theGalaxy became reality 13 or 14 Gyr ago with the implementation of amassive, rotationally-supported population of thick-disk stars. The veryhigh star formation rate in that phase gave rise to a rapid metalenrichment and an expulsion of gas in supernovae-driven Galactic winds,but was followed by a star formation gap for no less than three billionyears at the Sun's galactocentric distance. In a second phase, then, thethin disk - our familiar Milky Way'' - came on stage. Nowadays ittraces the bright side of the Galaxy, but it is also embedded in a hugecoffin of dead thick-disk stars that account for a large amount ofbaryonic dark matter. As opposed to this, cold-dark-matter-dominatedcosmologies that suggest a more gradual hierarchical buildup throughmergers of minor structures, though popular, are a poor description forthe Milky Way Galaxy - and by inference many other spirals as well - if,as the sample implies, the fossil records of its long-lived stars do notstick to this paradigm. Apart from this general picture that emergeswith reference to the entire sample stars, a good deal of the presentwork is however also concerned with detailed discussions of manyindividual objects. Among the most interesting we mention the bluestraggler or merger candidates HD 165401 and HD 137763/HD 137778, thelikely accretion of a giant planet or brown dwarf on 59 Vir in itsrecent history, and HD 63433 that proves to be a young solar analog at\tau200 Myr. Likewise, the secondary to HR 4867, formerly suspectednon-single from the Hipparcos astrometry, is directly detectable in thehigh-resolution spectroscopic tracings, whereas the visual binary \chiCet is instead at least triple, and presumably even quadruple. Withrespect to the nearby young stars a complete account of the Ursa MajorAssociation is presented, and we provide as well plain evidence foranother, the Hercules-Lyra Association'', the likely existence ofwhich was only realized in recent years. On account of its rotation,chemistry, and age we do confirm that the Sun is very typical among itsG-type neighbors; as to its kinematics, it appears however not unlikelythat the Sun's known low peculiar space velocity could indeed be thecause for the weak paleontological record of mass extinctions and majorimpact events on our parent planet during the most recent Galactic planepassage of the solar system. Although the significance of thiscorrelation certainly remains a matter of debate for years to come, wepoint in this context to the principal importance of the thick disk fora complete census with respect to the local surface and volumedensities. Other important effects that can be ascribed to this darkstellar population comprise (i) the observed plateau in the shape of theluminosity function of the local FGK stars, (ii) a small thoughsystematic effect on the basic solar motion, (iii) a reassessment of theterm asymmetrical drift velocity'' for the remainder (i.e. the thindisk) of the stellar objects, (iv) its ability to account for the bulkof the recently discovered high-velocity blue white dwarfs, (v) itsmajor contribution to the Sun's 220 km s-1 rotationalvelocity around the Galactic center, and (vi) the significant flatteningthat it imposes on the Milky Way's rotation curve. Finally we note ahigh multiplicity fraction in the small but volume-complete local sampleof stars of this ancient population. This in turn is highly suggestivefor a star formation scenario wherein the few existing single stellarobjects might only arise from either late mergers or the dynamicalejection of former triple or higher level star systems. Contributions to the Nearby Stars (NStars) Project: Spectroscopy of Stars Earlier than M0 within 40 Parsecs: The Northern Sample. I.We have embarked on a project, under the aegis of the Nearby Stars(NStars)/Space Interferometry Mission Preparatory Science Program, toobtain spectra, spectral types, and, where feasible, basic physicalparameters for the 3600 dwarf and giant stars earlier than M0 within 40pc of the Sun. In this paper, we report on the results of this projectfor the first 664 stars in the northern hemisphere. These resultsinclude precise, homogeneous spectral types, basic physical parameters(including the effective temperature, surface gravity, and overallmetallicity [M/H]), and measures of the chromospheric activity of ourprogram stars. Observed and derived data presented in this paper arealso available on the project's Web site. 3D mapping of the dense interstellar gas around the Local BubbleWe present intermediate results from a long-term program of mapping theneutral absorption characteristics of the local interstellar medium,motivated by the availability of accurate and consistent parallaxes fromthe Hipparcos satellite. Equivalent widths of the interstellar NaID-line doublet at 5890 Å are presented for the lines-of-sighttowards some 311 new target stars lying within ~ 350 pc of the Sun.Using these data, together with NaI absorption measurements towards afurther ~ 240 nearby targets published in the literature (for many ofthem, in the directions of molecular clouds), and the ~ 450lines-of-sight already presented by (Sfeir et al. \cite{sfeir99}), weshow 3D absorption maps of the local distribution of neutral gas towards1005 sight-lines with Hipparcos distances as viewed from a variety ofdifferent galactic projections.The data are synthesized by means of two complementary methods, (i) bymapping of iso-equivalent width contours, and (ii) by densitydistribution calculation from the inversion of column-densities, amethod devised by Vergely et al. (\cite{vergely01}). Our present dataconfirms the view that the local cavity is deficient in cold and neutralinterstellar gas. The closest dense and cold gas wall'', in the firstquadrant, is at ~ 55-60 pc. There are a few isolated clouds at closerdistance, if the detected absorption is not produced by circumstellarmaterial.The maps reveal narrow or wide interstellar tunnels'' which connectthe Local Bubble to surrounding cavities, as predicted by the model ofCox & Smith (1974). In particular, one of these tunnels, defined bystars at 300 to 600 pc from the Sun showing negligible sodiumabsorption, connects the well known CMa void (Gry et al. \cite{gry85}),which is part of the Local Bubble, with the supershell GSH 238+00+09(Heiles \cite{heiles98}). High latitude lines-of-sight with the smallestabsorption are found in two chimneys'', whose directions areperpendicular to the Gould belt plane. The maps show that the LocalBubble is squeezed'' by surrounding shells in a complicated patternand suggest that its pressure is smaller than in those expandingregions.We discuss the locations of several HI and molecular clouds. Usingcomparisons between NaI and HI or CO velocities, in some cases we areable to improve the constraints on their distances. According to thevelocity criteria, MBM 33-37, MBM 16-18, UT 3-7, and MBM 54-55 arecloser than ~ 100 pc, and MBM 40 is closer than 80 pc. Dense HI cloudsare seen at less than 90 pc and 85 pc in the directions of the MBM 12and MBM 41-43 clouds respectively, but the molecular clouds themselvesmay be far beyond. The above closest molecular clouds are located at theneutral boundary of the Bubble. Only one translucent cloud, G192-67, isclearly embedded within the LB and well isolated.These maps of the distribution of local neutral interstellar NaI gas arealso briefly compared with the distribution of both interstellar dustand neutral HI gas within 300 pc.Tables 1 and 2 are only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp:cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/411/447 Catalogue of averaged stellar effective magnetic fields. I. Chemically peculiar A and B type starsThis paper presents the catalogue and the method of determination ofaveraged quadratic effective magnetic fields < B_e > for 596 mainsequence and giant stars. The catalogue is based on measurements of thestellar effective (or mean longitudinal) magnetic field strengths B_e,which were compiled from the existing literature.We analysed the properties of 352 chemically peculiar A and B stars inthe catalogue, including Am, ApSi, He-weak, He-rich, HgMn, ApSrCrEu, andall ApSr type stars. We have found that the number distribution of allchemically peculiar (CP) stars vs. averaged magnetic field strength isdescribed by a decreasing exponential function. Relations of this typehold also for stars of all the analysed subclasses of chemicalpeculiarity. The exponential form of the above distribution function canbreak down below about 100 G, the latter value representingapproximately the resolution of our analysis for A type stars.Table A.1 and its references are only available in electronic form atthe CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/407/631 and Tables 3 to 9are only available in electronic form at http://www.edpsciences.org Automated spectroscopic abundances of A and F-type stars using echelle spectrographs. II. Abundances of 140 A-F stars from ELODIEUsing the method presented in Erspamer & North (\cite{erspamer},hereafter Paper I), detailed abundances of 140 stars are presented. Theuncertainties characteristic of this method are presented and discussed.In particular, we show that for a S/N ratio higher than 200, the methodis applicable to stars with a rotational velocity as high as 200 kms-1. There is no correlation between abundances and Vsin i,except a spurious one for Sr, Sc and Na which we explain by the smallnumber of lines of these elements combined with a locally biasedcontinuum. Metallic giants (Hauck \cite{hauck}) show larger abundancesthan normal giants for at least 8 elements: Al, Ca, Ti, Cr, Mn, Fe, Niand Ba. The anticorrelation for Na, Mg, Si, Ca, Fe and Ni with Vsin isuggested by Varenne & Monier (\cite{varenne99}) is not confirmed.The predictions of the Montréal models (e.g. Richard et al.\cite{richard01}) are not fulfilled in general. However, a correlationbetween left [(Fe)/(H)right ] and log g is found for stars of 1.8 to 2.0M_sun. Various possible causes are discussed, but the physical realityof this correlation seems inescapable.Based on observations collected at the 1.93 m telescope at theObservatoire de Haute-Provence (St-Michel l'Observatoire, France) andCORALIE.Based on observations collected at the Swiss 1.2 m Leonard Eulertelescopes at the European Southern Observatory (La Silla, Chile).Tables 5 and 6 are only available in electronic form at the CDS viaanonymous ftp to cdsarc.u.strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/398/1121 Composite spectra Paper 11: α Equulei, an astrometric binary with an Am secondaryThe spectrum of the secondary component of the bright composite-binarysystem α Equ, whose visual orbit is already known accurately, isisolated by the method of spectrum subtraction and classified accuratelyfor the first time. The primary is a normal giant of type ~G7, while thesecondary is an Am star of type ~kA3hA4mA9. The system's mass ratio, q ,is determined to be from measurements of the relative radial-velocitydisplacements between the components. Random and systematic errors in qare evaluated on the basis of the scatter of results derived from setsof spectra obtained from three different sources, and from testsconducted on independent versions of the secondary's spectrum. Aspectroscopic analysis of a composite system such as α Equ isstrongly challenged by the blending of a great many lines that arecommon to both spectra. Even when the primary spectrum is thought tohave been subtracted adequately, a seemingly unavoidable ghost spectrumof faint residuals can bias wavelength measurements of the secondary'slines. That blending was the principal cause of a history of puzzlingand discrepant measurements of q in α Equ. The derived masses of ,for the giant and dwarf, respectively, constrain the choice of modelsfor fitting evolutionary tracks in the (logT eff , logL )plane; the stellar points fit a single isochrone (for 0.74Gyr). Bothcomponents are found to be slightly over-luminous compared to normal fortheir supposed luminosity classes. The giant appears to be commencingits first ascent of the red-giant branch. The dwarf has started toevolve away from the main sequence; its M V is similar tothat of a sub-giant. IR observations of Am starsThe IR observations of chemically peculiar stars are carried out andcompared with the previous data in IR and far IR from IRAS. The fluxredistribution appears to be a common phenomenon in all the stars ofthis class. The observed energy distribution and a model fit based oneffective temperature estimates show slight excess in the IR. Composite Spectra. XII. μ Leonis: An Evolving Am BinaryIt is shown by techniques of spectrum disentangling that both componentsof the composite-spectrum binary ο Leo (V=3.52 mag) have Amcharacteristics, even though the primary is an evolving giant(logg=3.25) with Teff~6100 K. This is believed to be thefirst isolation of such a cool Am star, and the finding challenges thetheories of diffusion, which are widely accepted as the cause ofmetallicism. The primary component of ο Leo appears to bedeficient in Ca and Sc, as are classical Am stars-though the δ Delstars which are described as evolved Am stars are not-and thereforeseems to be in a class on its own. It is suggested that the unusualstate of the primary component is attributable either to its currentstate of rapid evolution or to regular Am-star evolution that isdifficult to recognize spectroscopically. This paper describes thetechnical problems that have hitherto prevented the identification ofsuch unexpected properties in this easily observed binary, determinesthe physical parameters of the component stars, examines theirevolutionary states, and debates the possible classification of thegiant component. Future directions for this work will include detailedchemical composition analyses and an observing program designed tosearch for other cases of substantially evolved Am stars. Magnetic survey of bright northern main sequence starsThe first results of a systematic search for magnetic fields in thebrightest upper main sequence (MS) stars are presented. The main goal isto survey the stars with about the same detection limit and to improveexisting statistics of their magnetism. The target list contains 57upper MS stars and represents well B0.5-F9 stars. High-resolution Zeemanspectra were obtained for 30 stars of the list. The accuracy of themagnetic field measurements ranges from 20 to 300 G depending mainly onspectral class. In the majority of studied stars we did not detectmagnetic fields. In some stars we suspect the presence of a weakmagnetic field. These are the best candidates for more extensivestudies. A particular case is the star chi Dra where we probablydetected the global magnetic field. The longitudinal field strength isB_l= -54+/-12 G. Further observations of this star are needed to confirmthe detection and to ascertain if the magnetic field is variable withthe period of rotation. Based on observations collected at the 1 mtelescope of the Special Astrophysical Observatory (Nizhnij Arkhyz,Russia). Rotational velocities of A-type stars in the northern hemisphere. II. Measurement of v sin iThis work is the second part of the set of measurements of v sin i forA-type stars, begun by Royer et al. (\cite{Ror_02a}). Spectra of 249 B8to F2-type stars brighter than V=7 have been collected at Observatoirede Haute-Provence (OHP). Fourier transforms of several line profiles inthe range 4200-4600 Å are used to derive v sin i from thefrequency of the first zero. Statistical analysis of the sampleindicates that measurement error mainly depends on v sin i and thisrelative error of the rotational velocity is found to be about 5% onaverage. The systematic shift with respect to standard values fromSlettebak et al. (\cite{Slk_75}), previously found in the first paper,is here confirmed. Comparisons with data from the literature agree withour findings: v sin i values from Slettebak et al. are underestimatedand the relation between both scales follows a linear law ensuremath vsin inew = 1.03 v sin iold+7.7. Finally, thesedata are combined with those from the previous paper (Royer et al.\cite{Ror_02a}), together with the catalogue of Abt & Morrell(\cite{AbtMol95}). The resulting sample includes some 2150 stars withhomogenized rotational velocities. Based on observations made atObservatoire de Haute Provence (CNRS), France. Tables \ref{results} and\ref{merging} are only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.125.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/393/897 A highly sensitive search for magnetic fields in B, A and F starsCircular spectropolarimetric observations of 74 stars were obtained inan attempt to detect magnetic fields via the longitudinal Zeeman effectin their spectral lines. The sample observed includes 22 normal B, A andF stars, four emission-line B and A stars, 25 Am stars, 10 HgMn stars,two lambda Boo stars and 11 magnetic Ap stars. Using the Least-SquaresDeconvolution multi-line analysis approach (Donati et al.\cite{donati97etal}), high precision Stokes I and V mean signatures wereextracted from each spectrum. We find absolutely no evidence formagnetic fields in the normal, Am and HgMn stars, with upper limits onlongitudinal field measurements usually considerably smaller than anypreviously obtained for these objects. We conclude that if any magneticfields exist in the photospheres of these stars, these fields are notordered as in the magnetic Ap stars, nor do they resemble the fields ofactive late-type stars. We also detect for the first time a field in theA2pSr star HD 108945 and make new precise measurements of longitudinalfields in five previously known magnetic Ap stars, but do not detectfields in five other stars classified as Ap SrCrEu. We also report newresults for several binary systems, including a new vsin i for therapidly rotating secondary of the Am-delta Del SB2 HD 110951. Based onobservations obtained using the MuSiCoS spectropolarimeter on theBernard Lyot telescope, l'Observatoire du Pic du Midi, France. Catalogue of Apparent Diameters and Absolute Radii of Stars (CADARS) - Third edition - Comments and statisticsThe Catalogue, available at the Centre de Données Stellaires deStrasbourg, consists of 13 573 records concerning the results obtainedfrom different methods for 7778 stars, reported in the literature. Thefollowing data are listed for each star: identifications, apparentmagnitude, spectral type, apparent diameter in arcsec, absolute radiusin solar units, method of determination, reference, remarks. Commentsand statistics obtained from CADARS are given. The Catalogue isavailable in electronic form at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcar?J/A+A/367/521 Research Note Hipparcos photometry: The least variable starsThe data known as the Hipparcos Photometry obtained with the Hipparcossatellite have been investigated to find those stars which are leastvariable. Such stars are excellent candidates to serve as standards forphotometric systems. Their spectral types suggest in which parts of theHR diagrams stars are most constant. In some cases these values stronglyindicate that previous ground based studies claiming photometricvariability are incorrect or that the level of stellar activity haschanged. Table 2 is only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/367/297 The proper motions of fundamental stars. I. 1535 stars from the Basic FK5A direct combination of the positions given in the HIPPARCOS cataloguewith astrometric ground-based catalogues having epochs later than 1939allows us to obtain new proper motions for the 1535 stars of the BasicFK5. The results are presented as the catalogue Proper Motions ofFundamental Stars (PMFS), Part I. The median precision of the propermotions is 0.5 mas/year for mu alpha cos delta and 0.7mas/year for mu delta . The non-linear motions of thephotocentres of a few hundred astrometric binaries are separated intotheir linear and elliptic motions. Since the PMFS proper motions do notinclude the information given by the proper motions from othercatalogues (HIPPARCOS, FK5, FK6, etc.) this catalogue can be used as anindependent source of the proper motions of the fundamental stars.Catalogue (Table 3) is only available at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strastg.fr/cgi-bin/qcat?J/A+A/365/222 Sixth Catalogue of Fundamental Stars (FK6). Part I. Basic fundamental stars with direct solutionsThe FK6 is a suitable combination of the results of the HIPPARCOSastrometry satellite with ground-based data, measured over more than twocenturies and summarized in the FK5. Part I of the FK6 (abbreviatedFK6(I)) contains 878 basic fundamental stars with direct solutions. Suchdirect solutions are appropriate for single stars or for objects whichcan be treated like single stars. From the 878 stars in Part I, we haveselected 340 objects as "astrometrically excellent stars", since theirinstantaneous proper motions and mean (time-averaged) ones do not differsignificantly. Hence most of the astrometrically excellent stars arewell-behaving "single-star candidates" with good astrometric data. Thesestars are most suited for high-precision astrometry. On the other hand,199 of the stars in Part I are Δμ binaries in the sense ofWielen et al. (1999). Many of them are newly discovered probablebinaries with no other hitherto known indication of binarity. The FK6gives, besides the classical "single-star mode" solutions (SI mode),other solutions which take into account the fact that hidden astrometricbinaries among "apparently single-stars" introduce sizable "cosmicerrors" into the quasi-instantaneously measured HIPPARCOS proper motionsand positions. The FK6 gives in addition to the SI mode the "long-termprediction (LTP) mode" and the "short-term prediction (STP) mode". TheseLTP and STP modes are on average the most precise solutions forapparently single stars, depending on the epoch difference with respectto the HIPPARCOS epoch of about 1991. The typical mean error of anFK6(I) proper motion in the single-star mode is 0.35 mas/year. This isabout a factor of two better than the typical HIPPARCOS errors for thesestars of 0.67 mas/year. In the long-term prediction mode, in whichcosmic errors are taken into account, the FK6(I) proper motions have atypical mean error of 0.50 mas/year, which is by a factor of more than 4better than the corresponding error for the HIPPARCOS values of 2.21mas/year (cosmic errors included). Oxygen 6156-8 Angstroms Triplet in Chemically Peculiar Stars of the Upper Main Sequence: Do HgMn Stars Show an Oxygen Anomaly?An extensive spectrum-fitting analysis in the lambda ~ 6150 Angstromsregion was performed for forty late-B and A chemically peculiar (HgMn,Ap, Am, weak-lined) and normal stars of the upper main sequence, inorder to quantitatively establish the abundance of oxygen from the O I6156-8 triplet and to study its behavior/anomaly for each peculiaritygroup, where special attention was paid to HgMn-type stars. Magnetic Apvariables (Si or SrCrEu type) generally show a remarkably large oxygendepletion (by ~ -1.6 dex to ~ -0.4 dex relative to the solar abundance),and classical Am stars also show a clear underabundance (by ~ -0.6 dexon the average). In contrast, the oxygen abundance in HgMn stars,exhibiting only a mild deficiency relative to the Sun typically by ~0.3-0.4 dex, is not markedly different from the tendency of normalstars, also showing a subsolar abundance ([O/H] =~ -0.2). In view of therecent observational implication that the present solar oxygen abundanceis enriched by ~ 0.2-0.3 dex relative to the interstellar gas (fromwhich young stars are formed), and thus unsuitable for the comparisonstandard, we concluded that the extent of the average O-deficiency inHgMn stars is appreciably reduced down to only ~ 0.1-0.2 dex (i.e., notmuch different from the initial composition), which contrasts with theirwell-known drastically large N-depletion. Yet, as can be seen from thedelicate and tight O vs. Fe anticorrelation, this marginal deficiencyshould be real, and thus some physical process simultaneously producingO-depletion/Fe-enrichment must have actually worked in the atmosphere ofHgMn stars. Elemental abundance analyses with DAO spectrograms - XXI. The hot metallic-lined stars 60 Leonis and 6 LyraeElemental abundances of the hot metallic-lined (Am) stars 60 Leo and 6Lyr, with modest rotational velocities, are derived consistently withother studies in this series of papers. Both stars are found to show theAm phenomenon strongly, with nearly solar abundances of the lightelements, overabundances of most Fe peak elements, and considerableoverabundances of SrYZr, Ba and some rare earths. Ca is underabundant,while Sc is very underabundant. A Second Catalog of Orbiting Astronomical Observatory 2 Filter Photometry: Ultraviolet Photometry of 614 StarsUltraviolet photometry from the Wisconsin Experiment Package on theOrbiting Astronomical Observatory 2 (OAO 2) is presented for 614 stars.Previously unpublished magnitudes from 12 filter bandpasses withwavelengths ranging from 1330 to 4250 Å have been placed on thewhite dwarf model atmosphere absolute flux scale. The fluxes wereconverted to magnitudes using V=0 for F(V)=3.46x10^-9 ergs cm^-2 s^-1Å^-1, or m_lambda=-2.5logF_lambda-21.15. This second catalogeffectively doubles the amount of OAO 2 photometry available in theliterature and includes many objects too bright to be observed withmodern space observatories. Elemental abundance analyses with DAO spectrograms - XX. The early A stars epsilon Serpentis, 29 Vulpeculae and sigma AquariiElemental abundances of the early A stars epsilon Ser, 29 Vul and sigmaAqr are derived consistently with previous studies of this series usingspectrograms obtained with Reticon and CCD detectors. The derivedabundances confirm that epsilon Ser is a definite Am star. 29 Vul showsevidence for a weakly operating Am star phenomenon. sigma Aqr, a hot Amstar prototype, has abundances similar to those of o Peg, another classprototype. On the HIPPARCOS photometry of chemically peculiar B, A, and F starsThe Hipparcos photometry of the Chemically Peculiar main sequence B, A,and F stars is examined for variability. Some non-magnetic CP stars,Mercury-Manganese and metallic-line stars, which according to canonicalwisdom should not be variable, may be variable and are identified forfurther study. Some potentially important magnetic CP stars are noted.Tables 1, 2, and 3 are available only in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html The Tokyo PMC catalog 90-93: Catalog of positions of 6649 stars observed in 1990 through 1993 with Tokyo photoelectric meridian circleThe sixth annual catalog of the Tokyo Photoelectric Meridian Circle(PMC) is presented for 6649 stars which were observed at least two timesin January 1990 through March 1993. The mean positions of the starsobserved are given in the catalog at the corresponding mean epochs ofobservations of individual stars. The coordinates of the catalog arebased on the FK5 system, and referred to the equinox and equator ofJ2000.0. The mean local deviations of the observed positions from theFK5 catalog positions are constructed for the basic FK5 stars to comparewith those of the Tokyo PMC Catalog 89 and preliminary Hipparcos resultsof H30. A catalogue of [Fe/H] determinations: 1996 editionA fifth Edition of the Catalogue of [Fe/H] determinations is presentedherewith. It contains 5946 determinations for 3247 stars, including 751stars in 84 associations, clusters or galaxies. The literature iscomplete up to December 1995. The 700 bibliographical referencescorrespond to [Fe/H] determinations obtained from high resolutionspectroscopic observations and detailed analyses, most of them carriedout with the help of model-atmospheres. The Catalogue is made up ofthree formatted files: File 1: field stars, File 2: stars in galacticassociations and clusters, and stars in SMC, LMC, M33, File 3: numberedlist of bibliographical references The three files are only available inelectronic form at the Centre de Donnees Stellaires in Strasbourg, viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5), or viahttp://cdsweb.u-strasbg.fr/Abstract.html The Pulkovo Spectrophotometric Catalog of Bright Stars in the Range from 320 TO 1080 NMA spectrophotometric catalog is presented, combining results of numerousobservations made by Pulkovo astronomers at different observing sites.The catalog consists of three parts: the first contains the data for 602stars in the spectral range of 320--735 nm with a resolution of 5 nm,the second one contains 285 stars in the spectral range of 500--1080 nmwith a resolution of 10 nm and the third one contains 278 stars combinedfrom the preceding catalogs in the spectral range of 320--1080 nm with aresolution of 10 nm. The data are presented in absolute energy unitsW/m(2) m, with a step of 2.5 nm and with an accuracy not lower than1.5--2.0%. The Relation between Rotational Velocities and Spectral Peculiarities among A-Type StarsAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1995ApJS...99..135A&db_key=AST Vitesses radiales. Catalogue WEB: Wilson Evans Batten. Subtittle: Radial velocities: The Wilson-Evans-Batten catalogue.We give a common version of the two catalogues of Mean Radial Velocitiesby Wilson (1963) and Evans (1978) to which we have added the catalogueof spectroscopic binary systems (Batten et al. 1989). For each star,when possible, we give: 1) an acronym to enter SIMBAD (Set ofIdentifications Measurements and Bibliography for Astronomical Data) ofthe CDS (Centre de Donnees Astronomiques de Strasbourg). 2) the numberHIC of the HIPPARCOS catalogue (Turon 1992). 3) the CCDM number(Catalogue des Composantes des etoiles Doubles et Multiples) byDommanget & Nys (1994). For the cluster stars, a precise study hasbeen done, on the identificator numbers. Numerous remarks point out theproblems we have had to deal with. Some problems of chemical composition of stellar atmospheres.Not Available
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#### Observation and Astrometry data

 Constellation: Serpens Right ascension: 15h50m49.00s Declination: +04Â°28'40.0" Apparent magnitude: 3.71 Distance: 21.556 parsecs Proper motion RA: 128.5 Proper motion Dec: 62.2 B-T magnitude: 3.885 V-T magnitude: 3.714

Catalogs and designations:
 Proper Names Nulla Pambu   (Edit) Bayer ε Ser Flamsteed 37 Ser HD 1989 HD 141795 TYCHO-2 2000 TYC 360-1226-1 USNO-A2.0 USNO-A2 0900-08270648 BSC 1991 HR 5892 HIP HIP 77622 → Request more catalogs and designations from VizieR

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# JEE Main & Advanced Mathematics Geometric Progression Selection of Terms in a G.P.

## Selection of Terms in a G.P.

Category : JEE Main & Advanced

(1) When the product is given, the following way is adopted in selecting certain number of terms :

 Number of terms Terms to be taken 3 $\frac{a}{r},\,a,\,ar$ 4 $\frac{a}{{{r}^{3}}},\,\frac{a}{r},\,ar,\,a{{r}^{3}}$ 5 $\frac{a}{{{r}^{2}}},\,\,\frac{a}{r},\,\,a,\,\,ar,\,\,a{{r}^{2}}$

(2) When the product is not given, then the following way is adopted in selection of terms

 Number of terms Terms to be taken 3 $a,\,\,ar,\,\,a{{r}^{2}}$ 4 $a,\,\,ar,\,\,a{{r}^{2}},\,a{{r}^{3}}$ 5 $a,\,\,ar,\,\,a{{r}^{2}},\,a{{r}^{3}},\,a{{r}^{4}}$

LIMITED OFFER HURRY UP! OFFER AVAILABLE ON ALL MATERIAL TILL TODAY ONLY!

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# An algebra problem by Rohan K

Algebra Level 3

In an infinite GP of common ratio r(<1) every term is 4 times the sum of all its successive terms. If r can be expressed in the form of $$\frac{a}{b}$$ in the lowest terms, find a+b.

Courtesy: AMTI 2015

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# Linux notes

## Linux commands and notes

(A personal reference for my own convenience, which might be useful to someone, sometime. Many are Ubuntu-specific.)

1. Disable graphical login prompt:
sudo update-rc.d -f gdm remove

2. Re-enable graphical login prompt:
sudo update-rc.d -f gdm defaults

3. Swtich between GNOME and KDE:
Create file in the user’s home directory called .xinitrc:
sudo touch ~/.xinitrc

Add these lines to it:
#!/bin/sh
exec gnome-session
#exec startkde

Put the # at the beginning of the command you don’t want to run (this makes it commented out so it is ignored).

4. Change read, write, and execute privileges of a file or directory:
sudo chmod 777 /folder/file
sudo -R chmod 750 /folder1/folder2 (to make the effect recursive for all files and directories inside folder2)
(Obviously change the numbers as appropriate. 4 = read, 2 = write, 1 = execute.)
See here: http://www.firewall.cx/linux-introduction-file-permissions.php

5. Unmount Western Digital My Book external hard drive:
sudo umount ‘/media/My Book’

6. Unpackage and install tar.gz file:
If you want the program to be executable by a command, it has to be in one of the directories in the command PATH. Therefore to make it easily executable (i.e., simply typing its name in a terminal or a Run Application box), the binary file that comes in the package has to get unzipped and placed in a directory that’s in the PATH. These directories include but aren’t limited to: /usr/local/bin, /usr/bin, /bin, and a few others. You can add directories to it if you want, but it shouldn’t be necessary for the n00b.

So when you download a tar.gz file or a .bz2 file, it typically goes to your Desktop or your home folder; you have to move it, as root user in the terminal, to a folder in the command PATH, all of which belong to root (and with good reason). I prefer /usr/local/src. Or, /usr/local would do just as well. This way, as I understand it, when it unpackages and compiles itself, it will find /usr/local/sbin or /usr/local/bin, which are in the PATH, and the executable will go there and all you gotta do is type in its name from then on.

So, download your tar.gz or whatever type of file it is, go to the command line, and code:
sudo mv foo.tar.gz /usr/local/src
OR
sudo cp foo.tar.gz /usr/local/src

Now change your working directory to /usr/local/src:
cd /usr/local/src

Make sure the file is there:
ls
(it should return foo.tar.gz, among other things, possibly).

Now unzip it:
sudo tar -zxvf foo.tar.gz

Type ls again to find another directory within /usr/local/src, probably with the same name as the tarball. Change into that directory:
cd foo

There is most likely a README or other instruction file. Almost always read that first. Sometimes the instructions are detailed and explicit, but programmers are kind of dumb, so usually not. Usually this works, or some variation of it:
./configure
(a bunch of stuff flies by)
make
(a bunch more stuff)
make install
(probably even longer this time)
(You might have to put sudo in front of the last two)

Now there are a bunch of installation- and configuration-related files that are no longer needed, so you can clean them up with
make clean

Everything should be peachy now!

Also, lastly, using those three magic commands is the typical, textbook way to install a Linux package, so in other words it almost never proceeds exactly like that and you’ll run into some damn problem or another more often than not. C’est la vie. I don’t know why, but, again, programmers aren’t that good at doing anything other than making their own stuff work for their own selves in their own way, so try to follow their instructions and Google it if the commands I’ve listed fail.

I got most of that information from this great Cisco tutorial: http://www.firewall.cx/linux-introduction-installing-software.php

6a. Unpackage and install .tgz file:
sudo gunzip file.tgz

6b. Install .deb file:
sudo dpkg -i package.deb
(This is the manual way to apt-get install something in Debian-based OSes, so you don’t need to copy anything to /usr/local or do anything else special. Just put it on your Desktop, type the command in a terminal, and it sorts itself out for you.)

6c. Unpackage a bz2 file:
tar -jxvf filename.tar.bz2
(x = extract, v = verbose, j = deal with bz2 file type, f = read from a file rather than a tape)

7. View and change the command PATH:
To see what directories are in the command path:
echo $PATH To add a directory to the command path: As superuser, open file /etc/bash.bashrc (for example, to use Easy Editor to edit the file, code: sudo ee /etc/bash.bashrc) Add the following two lines to the end of the file: PATH=$PATH:/directory1/directory2
export PATH
(The \$PATH part is ESSENTIAL because it tells the kernel to keep the current PATH but append the ensuing directory to the end of it.)

8. File containing command PATHs:
/etc/bash.bashrc
(maybe /etc/profile on some systems?…it just references /etc/bash.bashrc?…)

9. Update search (“locate” command) list
sudo updatedb

10. Look up your sound card
cat /proc/asound/card0/codec#* | grep Codec

11. Location of application icons
/usr/share/pixmaps

12. Bring up the ‘Run Application’ dialog box:
Alt+F2

13. Reset the MySQL root user’s MySQL password:

14. Good tutorial on setting up Apache, PHP, and MySQL that I used (among others) to set up this website:
http://www.howtoforge.com/ubuntu_debian_lamp_server

15. Fantastic, detailed, extensive PHP tutorial:
http://devzone.zend.com/node/view/id/625

16. Change colors, style, window decoration, fonts, etc. in KDE:
kcmshell style
kcmshell fonts
kcmshell color
kcmshell icons
kcmshell kwindecoration

17. Display kernel release you are using:
uname -r (also try uname -a to list all the stuff under the uname command…there isn’t that much)

18. Good Ubuntu multimedia getting-started tutorial:

19. List hardware in your computer:
lshw

20. GnuPG agent integration missing on upgrade from Ubuntu 7.04

If you are upgrading from Ubuntu 7.04, the file ~/.gnupg/gpg.conf may have failed to be created by default in your home directory due to a bug in the gnupg package. In that case, GPG agent integration will not be enabled by default. If you have not created your own gpg.conf, you can correct this issue by running cp /usr/share/gnupg/options.skel ~/.gnupg/gpg.conf. If you do have a gpg.conf and are affected by this issue, correct it by running echo use-agent >> ~/.gnupg/gpg.conf. bug #76983

21. Add directory to the Places menu in Gnome:
Open the folder you want to add
Select Add Bookmark from the Bookmarks menu

22. Apt-get and Synaptic both tell you, “The following programs will be REMOVED” whenever you try to apt-get something. Make it go away by:
commenting out any non-gutsy (or non-Hardy, or non-Intrepid, as appropriate) entries in /etc/apt/sources.list

23. Add applications to list of startup items:
System menu –> Preferences –> Sessions –> Add

24. Add skins to Audacious/XMMS:
Download them from winamp.com, save to ~/.local/share/audacious/skins

25. Uninstall a program:
sudo aptitude remove program-name
To completely uninstall every last trace of it:
sudo aptitude remove –-purge program-name

26. Enable build and make capabilities:
Install the packages build-essential and make.
You’re also eventually going to need dpkg and dpkg-dev.

27. To play flash videos in Firefox:
Either, a) Search for “flash” in Synaptic and make sure the only item that’s installed is flashplugin-nonfree;
or, b) Uninstall every single item in the “flash” search results and go to Adobe’s website and install their Flash player, carefully following their instructions and the instructions that the command-line installer give you. (It will ask for the location of the Firefox, Opera, etc. directory, and it suggests /usr/lib/mozilla. I tried that directory and /usr/lib/mozilla-firefox, but those didn’t work; in Ubuntu, it wants /usr/lib/firefox.)
***Make sure you are superuser when you build and install it, so it will apply the changes system-wide!***

28. Apache commands:
a. Restart Apache: sudo /etc/init.d/apache2 restart
b. Reconfigure where localhost homepage is, etc.: sudo ee /etc/apache2/sites-available/mysite
c. Enable the phpmyadmin browser-based utility at localhost/phpmyadmin: First, apt-get install phpmyadmin. Second, add this line to /etc/apache2/apache2.conf: Include /etc/phpmyadmin/apache.conf
Then restart apache as in (a).

31. Bring sound back when PulseAudio or ALSA has decided to stop working:


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#### Volume 10, issue 1 (2010)

 1 D Arlettaz, Algebraic $K$–theory of rings from a topological viewpoint, Publ. Mat. 44 (2000) 3 MR1775748 2 H J Baues, Homotopy type and homology, Oxford Math. Monogr., Oxford Science Publ., The Clarendon Press, Oxford Univ. Press (1996) MR1404516 3 H J Baues, D Conduché, On the tensor algebra of a nonabelian group and applications, $K$–Theory 5 (1991/92) 531 MR1169422 4 H J Baues, P Goerss, A homotopy operation spectral sequence for the computation of homotopy groups, Topology 39 (2000) 161 MR1710998 5 L Breen, On the functorial homology of abelian groups, J. Pure Appl. Algebra 142 (1999) 199 MR1721092 6 R Brown, J L Loday, Van Kampen theorems for diagrams of spaces, Topology 26 (1987) 311 MR899052 7 G Carlsson, A simplicial group construction for balanced products, Topology 23 (1984) 85 MR721454 8 A Dold, D Puppe, Homologie nicht-additiver Funktoren. Anwendungen, Ann. Inst. Fourier Grenoble 11 (1961) 201 MR0150183 9 S Eilenberg, S Mac Lane, On the groups $H(\Pi,n)$. II. Methods of computation, Ann. of Math. $(2)$ 60 (1954) 49 MR0065162 10 G Ellis, R Mikhailov, A colimit of classifying spaces, to appear Adv. Math. arXiv:0804.3581 11 J C Harris, N J Kuhn, Stable decompositions of classifying spaces of finite abelian $p$–groups, Math. Proc. Cambridge Philos. Soc. 103 (1988) 427 MR932667 12 J Neisendorfer, Primary homotopy theory, Mem. Amer. Math. Soc. 25 (1980) MR567801 13 S B Priddy, On $\Omega ^{\infty }S^{\infty }$ and the infinite symmetric group, from: "Algebraic topology (Proc. Sympos. Pure Math., Vol. XXII, Univ. Wisconsin, Madison, Wis., 1970)" (editor A Liulevicius), Amer. Math. Soc. (1971) 217 MR0358767 14 D G Quillen, Spectral sequences of a double semi-simplicial group, Topology 5 (1966) 155 MR0195097 15 H Toda, Composition methods in homotopy groups of spheres, Annals of Math. Studies 49, Princeton Univ. Press (1962) MR0143217 16 H Toda, Order of the identity class of a suspension space, Ann. of Math. $(2)$ 78 (1963) 300 MR0156347 17 G W Whitehead, On spaces with vanishing low-dimensional homotopy groups, Proc. Nat. Acad. Sci. U. S. A. 34 (1948) 207 MR0028027 18 J H C Whitehead, The homotopy type of a special kind of polyhedron, Ann. Soc. Polon. Math. 21 (1948) MR0030758 19 J H C Whitehead, A certain exact sequence, Ann. of Math. $(2)$ 52 (1950) 51 MR0035997 20 J Wu, Combinatorial descriptions of homotopy groups of certain spaces, Math. Proc. Cambridge Philos. Soc. 130 (2001) 489 MR1816806 21 J Wu, Homotopy theory of the suspensions of the projective plane, Mem. Amer. Math. Soc. 162 (2003) MR1955357


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# Affine transformations and geodesics deviation

I recently came upon this condition for a vector field X on M to be affine $$[L_{X},\nabla_{Y}]-\nabla_{[X,Y]}=0$$ Operating this on another vector Z gives me ${\nabla}^{2}_{Y,Z}X+R(X,Y)Z=0$

Where $\nabla^{2}_{Y,Z}X=\nabla_Y \nabla_Z X-\nabla_{\nabla_YZ}X$. Now if I choose $Y=Z=T$ some tangent vector to a geodesics in M then I get back the geodesics deviation or Jacobi equation. I know that affine transformations maps geodesics to geodesics hence the deviation vector is also an affine vector field. Is this observation correct?. Further I have seen this affine condition also written as $$(L_X\nabla)_{Y}Z=\lim_{s\to 0}{1\over s}\left((\phi^{*}_s\nabla)_Y Z-\nabla_Y Z\right)=0$$ If I break this down I get $$\lim_{s\to 0}\lim_{t\to 0}{1\over s}{1\over t}\left((\phi^{-1}_{*s}{\bar{\tau}}^{t}_{0}\phi_{*s})Z_{x_t}-\tau^{t}_{0}Z_{x_t}\right)=0$$ Where $t$ is the parameter along the curve whose tangent is $Y$ and similarly $s$ is along $X$. $\phi_s$ are the flow maps along $X$ and ${\tau}$ are the parallel transport map. The above condition is equivalent to the following condition $${\bar{\tau}}^{t}_{0}\phi_{*s}=\phi_{*s}\tau^{t}_{0}$$ i.e, they commute. Further I have noticed that the transformations $C_t=\tau^{t}_{0}\phi_{*t}$ is a local $1$ parameter group of linear transformations of $T_x(M)$ from this one can see that there is a linear endomorphism A of $T_x(M)$ such that $C_t=\exp{-t(A_X)_x}$. Using this one can again check that $A_X=L_X-\nabla_X$ and one can write the affine condition as $$(\nabla_Y A_X)Z=R(X,Y)Z$$ I have tried to summarize here what I have read but somehow I am not able to make a concise understanding of what is going on?. What is the connection between $(A_X)$ and affine transformations and how is this whole thing connected to geodesic deviations?. Can anyone summarize this in a proper clear order?. Most of this material can be found in "Foundations of Differential geometry volume one" by Kobayashi and Nomizu. Please forgive me if the arguments are not clear as I have just started studying this topic.

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# Solar Direct and Diffuse Adjustment¶

## Explanation of Problem¶

The CERES SYN1deg (Ed4.1) hourly solar irradiance data span the period from March 2000 to near present time and are the current source data for the POWER project. Two versions of the CERES SYN1deg (Ed4.1) hourly irradiances are available, the initial and adjusted. Based on comparisons with the Baseline Surface Radiation Network (BSRN) data, we found that the adjusted GHI agree somewhat better with the BSRN than the initial one. The overall bias/$\sigma$ of the adjusted version are 2.91/83.44 W m-2 and of the initial version are -4.51/82.44 W m-2 where $\sigma$ stands for standard deviation; in a 20-bin analysis of the cosine of the solar zenith angle ($cos(Z)$), we found that except in a few extreme bins, the adjusted version is slightly better than the initial version in most of the bins. Henceforth, all CERES SYN1deg data refer to the adjusted version.

Beside the hourly Global Horizontal Irradiance (GHI) and Diffuse Horizontal Irradiance (DHI), the POWER project derives the Direct Normal Irradiance (DNI) by dividing the Direct Horizontal Irradiance (DirHI) by $cos(Z)$. However, we found that, although the initial CERES SYN1deg (Ed4.1) DHI and DirHI sum to the GHI that agree reasonably well with the BSRN data, the DHI and DirHI show appreciable positive and negative biases, respectively, against the BSRN data and, therefore, the derived DNI, or DirHI/$cos(Z)$ also show significant biases against the BSRN data. To be precise, the overall bias/$\sigma$ of the DHI are 30.58/80.23 W m-2, and in the 20 bins of $cos(Z)$, the bias increases steadily from -2.29 to 116.22 W m-2, or from -21.78% to 41.75% of the mean BSRN DHI; the overall bias/$\sigma$ of the DirHI are -37.09/116.48 W m-2, and in the 20 bins of $cos(Z)$, the bias changes from -2.18 to -90.40 W m-2, or from -45.54% to -16.64% of the mean BSRN DirHI; the overall bias/$\sigma$ of the derived DNI, or DirHI/$cos(Z)$, are -54.32/196.35 W m-2, and in the 20 bins of $cos(Z)$ goes from 40.17 to 93.94 W m-2, or from 89.97% to -16.79% of the mean BSRN DNI. 1

We have previously applied the DirIndex model to the GEWEX SRB GSW (Rel.3) 3-hourly GHI to derive the 3-hourly DNI 2 3, since the solar energy community is particularly interested in the DNI. The DirIndex model requires the inputs of the all-sky and clear-sky GHI along with surface pressure, aerosol optical depth at 700 nm, and atmospheric water vapor. The DirIndex model has been found to be one of the two best global-to-beam models from among 140 separation models 4. More recently, we applied the DirIndex model to the CERES SYN1deg (Ed4.0) hourly data to get the DNI 5, and the overall bias/$\sigma$ are found to be 8.54/228.81 W m-2. This $\sigma$ is about 17% larger than that of the DNI derived from the initial CERES SYN1deg (Ed4.1) DirHI, or DirHI/$cos(Z)$. This implies that the DNI derived from the initial CERES SYN1deg (Ed4.1) hourly DirHI, while significantly biased in a systemic way, captures the spatiotemporal variability of the DNI more than the DirIndex model does, and in addition, it is possible to perform a simple bias-based adjustment to get a set of DNI with a smaller uncertainty than that of the DirIndex model.

## Initial Data¶

Figures 1-4, below, show the comparison of the initial CERES SYN1deg (Ed4.1) hourly GHI, DHI, DirHI and DNI, or DirHI/$cos(Z)$, with their respective BSRN counterparts.

In terms of the overall statistics, the GHI agree with the BSRN reasonably well. In most of the 20 bins of the $cos(Z)$, the biases are negative; in the five bins approaching the zenith, or the overhead position of the Sun, the biases are positive, and in the last bin, the bias maximizes at 24.04 W m-2. (Figure 1c-d.)

The DHI, on the other hand, shows a positive overall bias of a significant magnitude, and in the 20 bins of $cos(Z)$, the bias shows an unmistakable near-linear increasing trend on both the absolute and relative scales as shown in Figure 2c-d.

The DirHI is biased equally significantly (Figure 3c-d), though on the opposite side of DHI, because DirHI and DHI sum to GHI which agrees with the BSRN reasonably well. For this reason, the derived DNI, or DirHI/$cos(Z)$, shows notable biases in the bins of $cos(Z)$ (Figure 4c-d).

Comparison Plots: CERES SYN1deg (Ed4.1) to BSRN Data

The comparison plots for the comparison of the initial CERES SYN1deg (Ed4.1) hourly against the BSRN observed data for all-sky GHI, DHI, DirHI and DNI from 2000-03 to 2020-07.

• A — Scatter Density Plot: The statistics shown categorized as “Global” include all data points, “60° Poleward” and “60° Equatorward” split the data into those two categories.; $\rho$ stands for correlation coefficient, $\sigma$ standard deviation, $\mu$BSRN the BSRN mean, and N the total number of data points.
• B — Histogram of Differences: Histogram of the CERES SYN1deg (Ed4.1)-BSRN hourly GHI differences.
• C & D — Bar Graphs of Bias: The biases in 20 bins of $cos(Z)$ on absolute and relative scale, respectively.
• E & F — Scatter Plots of Bias by Site: The bias, $\sigma$ and $\rho$ on a site-by-site basis.

The unambiguous near-linear pattern of the biases of DHI and DirHI in the bins of $cos(Z)$ suggest that the biases are not just stochastic, but might be systemic, or deterministic. In addition, although the overall bias of DNI is considerable, the $\sigma$, or standard deviation, that represents the uncertainty of DNI, is still appreciably smaller than the DNI from the DirIndex model. These facts suggest that a simple bias-based adjustment can produce a set of DNI with an uncertainty smaller than that from the DirIndex model.

Due to the differences in modus operandi of the ground and satellite-based observations, the BSRN CLoud FRaction (CLFR) and CERES CLFR are often different. Figure 5 shows GHI bias and $\sigma$ on absolute and relative scales in phase space of the BSRN CLFR and CERES CLFR.

Cloud Fraction Comparison: Initial CERES SYN1deg (Ed4.1) to BSRN Data

The bias and $\sigma$ of the initial CERES SYN1deg(Ed4.1) to BSRN hourly GHI as functions of the BSRN and CERES CLFR from 2000-03 to 2020-07.

• A & B — Contour Plots: The bias on absolute and relative scale, respectively.
• C & D — Contour Plots: The standard deviation ($\sigma$) on absolute and relative scale, respectively.

The relative scale here means that the bias or $\sigma$ is expressed as percentage of the mean BSRN hourly GHI.

The bias-based adjustment scheme is as follows: 1) Apply the bias-based adjustment to the DHI and GHI as well; 2) Subtract the DHI from the GHI to get an adjusted version of DirHI; 3) Divide the DirHI by $cos(Z)$ to get DNI. Note that the hourly solar zenith angle, Z, is part of the CERES SYN1deg (Ed4.1) data, and it is determined such that the top-of-atmosphere (TOA) DirHI divided by the $cos(Z)$ is equal to the solar constant.

To perform the adjustment of DHI, the CERES SYN1deg-BSRN hourly DHI biases are first calculated in 100 bins of $cos(Z)$, as opposed to 20 bins in Figures 1-4. In each bin, the bias is calculated on the absolute scale, Bias, in W m-2, and on relative scale, $R_{Bias}$ as percentage of the mean SYN1deg (Ed4.1) hourly DHI, as opposed to the BSRN hourly mean DHI, the bias is considered to represent the center of the bin. Now both Bias and $R_{Bias}$ are functions of $cos(Z)$. For any given hourly DHI, $I_{DH}$, its corresponding $cos(Z)$ is first used to determine its bias through linear interpolation; if the Bias or $R_{Bias}$ is negative, then the adjusted DHI, $I_{DH}^c=I_{DH}-Bias$; if the Bias or $R_{Bias}$ is positive, then the adjusted DHI, $I_{DH}^c=I_{DH}·(1-R_{Bias})$. The scheme keeps or reduces the random variability of the initial data.

Modification of cos(Z)

Effective hourly solar zenith angle that correctly relates hourly direct horizontal irradiance and hourly direct normal irradiance has been studied 6, and the CERES hourly solar zenith angle, Z, which is based on the relation between the hourly DirHI and DNI, or solar constant, at TOA, is one of the six methods studied. According to the study, the best result is based on a surface clear-sky model that computes clear-sky hourly DirHI and DNI.

Here, however, we will only modify the $cos(Z)$ by adding a linear component for large Z values to prevent $cos(Z)$ from getting too small. When $Z>75°$, the value $cos(Z)$ approaches 0 infinitesimally as the DirHI also approaches 0 and, and the error becomes a more and more significant part of the DirHI value. Consequently, the derived DNI, or DirHI/cos(Z) becomes haphazardly, or unphysically, large. The following adjustment of $cos(Z)$ for Z>75° is proposed.

Let μ stand for $cos(Z)$, and $μ_{eff}$ for effective $cos(SZA)$. If $Z≤75°$, then $μ_{eff}=μ$; if $Z>75°$, then $μ_{eff}=μ+μ_{A}$, where $μ_{A}=-k/μ_{75d} μ+k$, $μ_{75d}=cos(75°)$, and k is an adjustable parameter, and when $k=0.045$, the biases are minimized for $Z>75°$. In fact, the biases in all twenty 0.05-sized bins become one digit.

## Results¶

The POWER project needs GHI, DHI and, in particular, DNI. The CERES SYN1deg (Ed4.1) has hourly GHI and DHI, but not DNI, and instead, it has DirHI. However, it has been found that the DHI is positively biased against BSRN and, the DirHI is negatively biased against BSRN, and the biases become more and more pronounced as $cos(Z)$ increases. Consequently, the derived DNI, or DirHI/$cos(Z)$, is also negatively biased. In addition, the $cos(Z)$ value approaches 0 infinitesimally toward sunset, and the derived DNI becomes haphazardly and unphysically large. Therefore, we performed a bias-based adjustment of the GHI and DHI, and use their difference, GHI-DHI as adjusted DirHI, and the $cos(Z)$ is modified by adding a linear component to $cos(Z)$ when $Z>75°$.

Comparison Plots: Adjusted CERES SYN1deg (Ed4.1) to BSRN Data

The comparison plots for the comparison of the Adjusted CERES SYN1deg (Ed4.1) hourly with the BSRN data for all-sky GHI, DHI, DirHI and DNI from 2000-03 to 2020-07 before and after the adjustment.

• A — Scatter Density Plot: The statistics shown are categorized as “Global” that includes all data points, “60° Poleward” and “60° Equatorward”; $\rho$ stands for correlation coefficient, $\sigma$ standard deviation, $\mu$BSRN the BSRN mean, and N the total number of data points.
• B — Histogram of Differences: Histogram of the SYN1deg (Ed4.1)-BSRN hourly GHI differences.
• C & D — Bar Graphs of Bias: The biases in 20 bins of $cos(Z)$ on absolute and relative scale, respectively.
• E & F — Scatter Plots of Bias by Site: The bias, $\sigma$ and $\rho$ on a site-by-site basis.

Summary Statistics: CERES SYN1deg (Ed4.1) to BSRN Data

The summary statistics tables for the comparison of the initial CERES SYN1deg (Ed4.1) hourly with the BSRN data for all-sky GHI, DHI, DirHI and DNI from 2000-03 to 2020-07 before and after the adjustment.

Rows:

• Before: The biases in W m-2 of the data prior to the adjustment.
• After: The biases in W m-2 of the data once the adjustment has been implemented.
Bias RMS ρ $\sigma$ μSYN N
Before -2.91 83.49 0.957 83.44 341.6 3,331,148
After 0.01 83.19 0.957 83.19 344.5 3,331,148
Bias RMS ρ $\sigma$ μSYN N
Before 30.58 85.86 0.831 80.23 168.3 3,450,473
After 0.01 65.70 0.830 65.70 137.9 3,450,473
Bias RMS ρ $\sigma$ μSYN N
Before -37.10 122.20 0.888 116.48 192.6 3,009,959
After -0.02 106.50 0.906 106.50 222.6 3,107,945
Bias RMS ρ $\sigma$ μSYN N
Before -54.30 203.70 0.822 196.35 342.8 3,009,963
After 0.72 182.20 0.851 182.20 386.1 3,107,969
DirIndex Model 8.54 228.80 0.758 228.65 444.9 2,195,000

^The DNI from the DirIndex model covers the period from 2000-04 to 2016-12 only.

The adjusted DNI shows an overall minimal bias, and in all the 20 bins of $cos(Z)$, the biases are all 1-digit on both the absolute and relative scales. More importantly, the overall standard deviation of the differences, or uncertainty, is significantly smaller than that of the DNI computed using the DirIndex model.

1. Baseline Surface Radiation Network (BSRN/WCRP): New Precision Radiometry for Climate Research. B. Am. Meteorol. Soc., 79(10), 2115-2136.

2. Zhang, T., Stackhouse, Jr., P.W., Chandler, W.S., and Westberg, D.J., 2014. Application of a global-to-beam irradiance model to the NASA GEWEX SRB dataset: An extension of the NASA Surface meteorology and Solar Energy datasets. Sol. Energy, 110, 117-131.

3. Ineichen, P., 2008. Comparison and validation of three global-to-beam irradiance models against ground measurements. Sol. Energy, 82, 501-512.

4. Gueymard, C.A., and Ruiz-Arias, J.A., 2016. Extensive worldwide validation and climate sensitivity analysis of direct irradiance predictions from 1-min global irradiance. Sol. Energy, 128, 1-30.

5. Zhang, T., Stackhouse, Jr., P.W., and Westberg, D.J., 2017. The NASA POWER SSE: Deriving the direct normal counterpart from the CERES SYN1deg hourly global horizontal irradiance during early 2000 to near present. AGU 2019 Fall Meeting, New Orleans.

6. Blanc, P. and Wald, L., 2016. On the effective solar zenith and azimuth angles to use with measurements of hourly irradiation. Adv. Sci. Res., 1, 1-6.


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MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

I suspect the following works. Even if it doesn't, I believe there may be some interest in this presentation (Please let me know if you spot diagonalization somewhere): .

A remark of François Dorais helped me (re)locate the argument in print. It is presented in A. Kanamori-D. Pincus. "Does GCH imply AC locally?", in Paul Erdős and his mathematics, II (Budapest, 1999), 413-426, Bolyai Soc. Math. Stud., 11, János Bolyai Math. Soc., Budapest, 2002. I believe it actually dates back to Zermelo's 1904 well-ordering paper. (I now think I learned the argument from Kanamori-Pincus, since I certainly used the paper in the topics course.)

(Of course, we could simply use an injection $g:{\mathcal P}(X)\to X$ and invoke Schröder-Bernstein at this point, but this route seems shorter.)

c. Zermelo's theorem can be proved as follows: Simply notice that $W=\{a_\alpha\mid \alpha\lt \beta\}$ where $$a_\alpha= F(\{a_\gamma\mid \gamma\lt \alpha\} alpha\})$$ and $\beta$ is largest so that this sequence is injective.

Let me close with a remark, and a question: The proof above is formalizable in ZF, without choice. In fact, Zermelo's theorem is provable without using replacement, although the argument I sketched uses it.

The question is mentioned in Kanamori-Pincus: We showed that if $F:{\mathcal P}(Y)\to Y$ then $F$ is not injective by exhibiting a pair $(A,B)$ with $F(A)=F(B)$. If instead of Zermelo's argument we had used at this point the construction from the diagonal argument, we would have taken $$A=\{y\in Y\mid \exists Z(y=F(Z)\notin Z)\},$$ and checked that there must be a $B\ne A$ with $F(A)=F(B)$.

Can we define such $B$ from $F$?

1

I thought about this question a while ago, while teaching a topics course. Since one can easily check that $${}|{\mathbb R}|=|{\mathcal P}({\mathbb N})|$$ by a direct construction that does not involve diagonalization, the question can be restated as:

Is there a proof of Cantor's theorem that ${}|X|<|{\mathcal P}(X)|$ that is not a diagonal argument?

I suspect the following works. Even if it doesn't, I believe there may be some interest in this presentation (Please let me know if you spot diagonalization somewhere):

a. There is obviously an injection $g:X\to{\mathcal P}(X)$. It is enough to show there is no surjection. Suppose there is, and call it $f$. Then $f^{-1}:{\mathcal P}^2(X)\to{\mathcal P}(X)$ is 1-1.

(If $h:A\to B$, $h^{-1}:{\mathcal P}(B)\to{\mathcal P}(A)$ is the map that to $C\subseteq B$ assigns $\{a\in A\mid h(a)\in C\}$. Since $f$ is surjective, we have that $f^{-1}$ is injective.)

b. There is no injection $F:{\mathcal P}(Y)\to Y$ for any set $Y$. The reason is that for any $F$ we can (definably from $F$) produce a pair $(A,B)$ with $A\ne B$ and $F(A)=F(B)$. In effect, Zermelo proved that:

For any $F:{\mathcal P}(Y)\to Y$ there is a unique a unique well-ordering $(W, \lt)$ with $W\subseteq Y$ such that:

1. $\forall x\in W (F (\{y ∈ W \mid y \lt x\}) = x)$, and
2. $F (W )\in W$.

We can then take $A=W$ and $B=\{y\in W\mid y\lt F(W)\}$.

c. Zermelo's theorem can be proved as follows: Simply notice that $W=\{a_\alpha\mid \alpha\lt \beta\}$ where $$a_\alpha= F(\{a_\gamma\mid \gamma\lt \alpha\}$$ and $\beta$ is largest so that this sequence is injective.

That $\beta$ exists is a consequence of Hartogs theorem that for any set $A$ there is a least ordinal $\alpha$ does not inject into $A$.

Uniqueness of $W$ is shown by considering the ﬁrst place where two potential candidates for $(W, \lt)$ disagree.

d. Hartogs theorem is proved by noticing that if $\alpha$ is an ordinal and injects into $A$, then there is a subset $B$ of $A$ and a binary relation $R$ on $B$ such that $(B,R)$ is order isomorphic to $\alpha$. From this one easily sees that the collection of $\alpha$s that inject into $A$ forms a set, that is in fact an ordinal $\beta$. Then $\beta$ is least that does not inject into $A$.

Let me close with a remark: The proof above is formalizable in ZF, without choice. In fact, Zermelo's theorem is provable without using replacement, although the argument I sketched uses it.


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# Researchers portal

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## Measurement of the Z boson differential production cross section using its invisible decay mode (Z -> nu(nu)over-bar) in proton-proton collisions at root s=13 TeV

Abstract: Measurements of the total and differential fiducial cross sections for the Z boson decaying into two neutrinos are presented at the LHC in proton-proton collisions at a center-of-mass energy of 13TeV. The data were collected by the CMS detector in 2016 and correspond to an integrated luminosity of 35.9 fb?1. In these measurements, events are selected containing an imbalance in transverse momentum and one or more energetic jets. The fiducial differential cross section is measured as a function of the Z boson transverse momentum. The results are combined with a previous measurement of charged-lepton decays of the Z boson. The measured total fiducial cross section for events with Z boson transverse momentum greater than 200 GeV is 3000+180 ?170 fb.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

Fuente: Journal of High Energy Physics, 2021, 05, 205

Editorial: Springer Verlag

Fecha de publicación: 21/05/2021

Nº de páginas: 43

Tipo de publicación: Artículo de Revista

ISSN: 1126-6708,1029-8479

### Autores/as

SIRUNYAN, A.M.

PEDRO JOSE FERNANDEZ MANTECA

ANDREA GARCIA ALONSO

CEDRIC GERALD PRIEELS

FRANCESCA SHUN-NING ANNAROSA RICCI-TAM


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# The special case of x⁴

## Key Questions

• The stationary point is $\left(0 , 0\right)$ and it is a minimum point.

The first task in finding stationary points is to find the critical points, that is, where $f ' \left(x\right) = 0$ or $f ' \left(x\right)$ DNE:

$f ' \left(x\right) = 4 {x}^{3}$ using the power rule
$4 {x}^{3} = 0$
$x = 0$ is the only solution

There are 2 ways to test for a stationary point, the First Derivative Test and the Second Derivative Test.

The First Derivative Test checks for a sign change in the first derivative: on the left the derivative is negative and on the right the derivative is positive, so this critical point is a minimum.

The Second Derivative Test checks for the sign of the second derivative:

$f ' ' \left(x\right) = 12 {x}^{2}$
$f ' ' \left(0\right) = 0$

There is no sign, so the second derivative doesn't tell us anything in this case.

Since there are no other minimums and ${\lim}_{x \to - \infty} f \left(x\right) = {\lim}_{x \to \infty} f \left(x\right) = \infty$. The stationary point is an absolute minimum.


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# Clustering using PAM method

Why Clustering using PAM method often attributes one point in the middle of one cluster to another cluster? (for example here K-means clustering )

I have the similar results with my set of data.

I do not know how ClusteringComponents's PAM is implemented, but I strongly suspect that what you observe is an effect of the stopping criteria of the PAM algorithm. E.g. using cluster samples to compute the Silhouette measure might produce these kind of results.


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# Find number of awesome substring of a given binary string

A binary string is given to us and we need to find number of awesome substring of that string .Definition of awesome string : A string is awesome if its length is divisible by number of 1's in it.

For example :111 has 6 awesome substrings.01010 has 10 awesome substrings .In "01010" one such awesome substring is "1010" because "1010" is substring of "01010" and 4(length of substring) is divisible by 2(number of 1's).

source : codeforces

My attempt : I was not able to come with solution better than O($$n^2$$) , however when i read the editorial they have did some optimization and solved it in O($$n*n^{1/2}$$) but i didn't understood it completely.

What and why i want to ask : I want some simpler explanation of same solution , maybe illustrating it by taking few example(s) . I love these type of questions and i really want to improve myself.

source of solution/editorial : solution (scroll down a little) .

I am open to any suggestions and comments .

Could you please explain exactly where you were stuck? Anyway, I'll choose some parts of the solution which were not described by author and shed light on them.

You can assume that $$T=\sqrt{n}$$ in the solution. The main idea can be formulated as follows:

For any positive integers $$m, n$$ such that $$m \le n$$ either $$m \le \sqrt{n}$$ or $$\frac{n}{m} < \sqrt{n}$$.

This is applied to all substrings where $$m$$ is the number of ones. It means that we can divide all substrings into two disjoint sets: where the length divided by number of ones is small (set $$k= \frac{len}{m}$$, then $$k \leq \frac{n}{m} < \sqrt{n}$$), or the number of ones is small ($$m \leq \sqrt{n}$$). Then we compute sizes of each set separately. When we apply such idea, we hope that each of these subtasks can be solved faster than a big one.

For the first set, I find the idea of computing $$t[i]=i-k\cdot{}pref[i]$$ well-explained.

For the second set, if we fix $$l$$, we can break segments of $$r$$'s into segments $$[r_m, r_{m+1})$$ for which the number of ones in substring $$s_l \ldots{} s_r$$ equals $$m$$. We consider only $$m\leq \sqrt{n}$$, and for each $$m$$ the number of suitable $$r$$'s can be found in $$O(1)$$. Note: the set of such $$r$$'s forms an arithmetic progression with a common difference $$m$$.

And, if we iterate over $$l$$ in descending order, we can also make a "structure" for recomputing these segments in $$O(1)$$.


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# What is pkgindoc.sty really for?

During a discussion of this question, I looked a bit into the pkgindoc.sty buried in ltclass.dtx (docstrip option afterpreamble). While I understand how this works (and it works in an ugly way IMHO), I am quite curious if anybody knows what the original purpose of it was (and whether it's documented anywhere)? (It seems that pkgindoc.sty is not generated during normal LaTeX installation, and I've never heard about it from anywhere, including the previous two answers to the above-mentioned question.)

Here is the relevant section from ltclass.dtx for reference:

### 71   After Preamble

Finally we declare a package that allows all the commands declared above to be \@onlypreamble to be used after \begin{document}.

⟨*afterpreamble⟩
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{pkgindoc}
[1994/10/20 v1.1 Package Interface in Document (DPC)]
\def\reserved@a#1\do\@classoptionslist#2\do\filec@ntents#3\relax{%
\gdef\@preamblecmds{#1#3}}
\expandafter\reserved@a\@preamblecmds\relax
⟨/afterpreamble⟩

-
Instead of showing the (longer) generated file you can just cite section 71 of the LaTeX2e sources. –  Andrey Vihrov Aug 1 '11 at 6:28
You're right, done. –  mbork Aug 1 '11 at 8:47
I've taken the liberty to improve the citation yet more. If you don't like it, please revert it. –  Andrey Vihrov Aug 1 '11 at 9:10
Great, thank you! I don't know Markdown, so I couldn't do it that nice at all":). –  mbork Aug 1 '11 at 11:41

It is used to allow things like \usepackage in the document body. This seems to have been used occasionally by members of the LaTeX Project for writing documentation (see for example this file written by Robin Fairbairns). However, I don't think it's documented anywhere.


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F01 Chapter Contents
F01 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF01FKF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

F01FKF computes the matrix exponential, sine, cosine, sinh or cosh, of a complex $n$ by $n$ matrix $A$ using the Schur–Parlett algorithm.

## 2  Specification

 SUBROUTINE F01FKF ( FUN, N, A, LDA, IFAIL)
 INTEGER N, LDA, IFAIL COMPLEX (KIND=nag_wp) A(LDA,*) CHARACTER(*) FUN

## 3  Description

$f\left(A\right)$, where $f$ is either the exponential, sine, cosine, sinh or cosh, is computed using the Schur–Parlett algorithm described in Higham (2008) and Davies and Higham (2003).

## 4  References

Davies P I and Higham N J (2003) A Schur–Parlett algorithm for computing matrix functions. SIAM J. Matrix Anal. Appl. 25(2) 464–485
Higham N J (2008) Functions of Matrices: Theory and Computation SIAM, Philadelphia, PA, USA

## 5  Parameters

1:     FUN – CHARACTER(*)Input
On entry: indicates which matrix function will be computed.
${\mathbf{FUN}}=\text{'EXP'}$
The matrix exponential, ${e}^{A}$, will be computed.
${\mathbf{FUN}}=\text{'SIN'}$
The matrix sine, $\mathrm{sin}\left(A\right)$, will be computed.
${\mathbf{FUN}}=\text{'COS'}$
The matrix cosine, $\mathrm{cos}\left(A\right)$, will be computed.
${\mathbf{FUN}}=\text{'SINH'}$
The hyperbolic matrix sine, $\mathrm{sinh}\left(A\right)$, will be computed.
${\mathbf{FUN}}=\text{'COSH'}$
The hyperbolic matrix cosine, $\mathrm{cosh}\left(A\right)$, will be computed.
Constraint: ${\mathbf{FUN}}=\text{'EXP'}$, $\text{'SIN'}$, $\text{'COS'}$, $\text{'SINH'}$ or $\text{'COSH'}$.
2:     N – INTEGERInput
On entry: $n$, the order of the matrix $A$.
Constraint: ${\mathbf{N}}\ge 0$.
3:     A(LDA,$*$) – COMPLEX (KIND=nag_wp) arrayInput/Output
Note: the second dimension of the array A must be at least ${\mathbf{N}}$.
On entry: the $n$ by $n$ matrix $A$.
On exit: the $n$ by $n$ matrix, $f\left(A\right)$.
4:     LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F01FKF is called.
Constraint: ${\mathbf{LDA}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{N}}\right)$.
5:     IFAIL – INTEGERInput/Output
On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.
On exit: ${\mathbf{IFAIL}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6  Error Indicators and Warnings

If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
${\mathbf{IFAIL}}=1$
A Taylor series failed to converge.
${\mathbf{IFAIL}}=2$
${\mathbf{IFAIL}}=3$
There was an error whilst reordering the Schur form of $A$.
Note:  this failure should not occur and suggests that the routine has been called incorrectly.
${\mathbf{IFAIL}}=4$
The routine was unable to compute the Schur decomposition of $A$.
Note:  this failure should not occur and suggests that the routine has been called incorrectly.
${\mathbf{IFAIL}}=5$
${\mathbf{IFAIL}}=6$
The linear equations to be solved are nearly singular and the Padé approximant used to compute the exponential may have no correct figures.
Note:  this failure should not occur and suggests that the routine has been called incorrectly.
${\mathbf{IFAIL}}=-1$
Input argument number $⟨\mathit{\text{value}}⟩$ is invalid.
${\mathbf{IFAIL}}=-2$
Input argument number $⟨\mathit{\text{value}}⟩$ is invalid.
${\mathbf{IFAIL}}=-4$
On entry, parameter LDA is invalid.
Constraint: ${\mathbf{LDA}}\ge {\mathbf{N}}$.
${\mathbf{IFAIL}}=-999$
Allocation of memory failed.

## 7  Accuracy

For a normal matrix $A$ (for which ${A}^{\mathrm{H}}A=A{A}^{\mathrm{H}}$), the Schur decomposition is diagonal and the algorithm reduces to evaluating $f$ at the eigenvalues of $A$ and then constructing $f\left(A\right)$ using the Schur vectors. This should give a very accurate result. In general, however, no error bounds are available for the algorithm.
For further discussion of the Schur–Parlett algorithm see Section 9.4 of Higham (2008).

The integer allocatable memory required is $n$, and the complex allocatable memory required is approximately $9{n}^{2}$.
The cost of the Schur–Parlett algorithm depends on the spectrum of $A$, but is roughly between $28{n}^{3}$ and ${n}^{4}/3$ floating point operations; see Algorithm 9.6 of Higham (2008).
If the matrix exponential is required then it is recommended that F01FCF be used. F01FCF uses an algorithm which is, in general, more accurate than the Schur–Parlett algorithm used by F01FKF.
If estimates of the condition number of the matrix function are required then F01KAF should be used.
F01EKF can be used to find the matrix exponential, sin, cos, sinh or cosh of a real matrix $A$.

## 9  Example

This example finds the matrix sinh of the matrix
 $A = 1.0+1.0i 0.0+0.0i 1.0+3.0i 0.0+0.0i 0.0+0.0i 2.0+0.0i 0.0+0.0i 1.0+2.0i 3.0+1.0i 0.0+4.0i 1.0+1.0i 0.0+0.0i 1.0+1.0i 0.0+2.0i 0.0+0.0i 1.0+0.0i .$

### 9.1  Program Text

Program Text (f01fkfe.f90)

### 9.2  Program Data

Program Data (f01fkfe.d)

### 9.3  Program Results

Program Results (f01fkfe.r)