First Results from the XXL Survey and Associated Multi-wavelength Programmes

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "First Results from the XXL Survey and Associated Multi-wavelength Programmes"

Transcript

1 First Results from the XXL Survey and Associated Multi-wavelength Programmes Christophe Adami 1 Marguerite Pierre Nikola Baran Dominique Eckert 4 Sotiria Fotopoulou 4 Paul A. Giles 5 Elias Koulouridis Chris Lidman 6 Maggie Lieu 7 Adam B. Mantz 8 Florian Pacaud 9 Emanuela Pompei 10 Vernesa Smolčić Felicia Ziparo 8 and the XXL Team 11 1 Aix Marseille Université, CNRS, LAM UMR 76, Marseille, France Laboratoire AIM, CEA/DSM/IRFU/SAp, CEA Saclay, Gif-sur-Yvette, France Department of Physics, University of Zagreb, Croatia 4 Department of Astronomy, University of Geneva, Versoix, Switzerland 5 H. H. Wills Physics Laboratory, University of Bristol, United Kingdom 6 Australian Astronomical Observatory, North Ryde, Australia 7 School of Physics & Astronomy, University of Birmingham, United Kingdom 8 Department of Astronomy and Astrophysics, University of Chicago, USA 9 Argelander Institut für Astronomie, Universität Bonn, Germany 10 ESO 11 XXL Team: The XXL survey has mapped two extragalactic regions of 5 square degrees, using 10 ks XMM observations down to a point source sensitivity of ~ erg s 1 cm in the 0.5 kev band. It is the largest XMM project approved to date (> 6 Ms in total). The two fields have been or will be observed by several ground- and space-based facilities from ultra-violet to radio wavelengths. Besides the imaging, the spectroscopic follow-up is of special interest and ESO has contributed through Large Programmes and dedicated allocations. As of December 015, ~ 450 new galaxy clusters are detected to z ~ 1.5, as well as more than 000 active galactic nuclei (AGN) to z ~ 4. The main goal of the project is to constrain the dark energy equation of state using clusters of galaxies. This survey will have lasting legacy value for cluster scaling laws and studies of AGNs and the X-ray background. The first XXL scientific results are summarised. Introduction The distribution of matter in the Universe reveals its history: small density perturbations present at the time of recombination (just after the Cosmic Microwave Background [CMB] was emitted) grew under the competing actions of gravity and expansion of spacetime. This led to the progressive formation of a remarkable network of filaments, sheets and voids that was first revealed from the galaxy distribution some 0 years ago and is now well rendered by numerical simulations. Basically as time proceeds, overdensities become denser and low density regions emptier as matter flows along the filaments. The rate at which structure forms and how it will ultimately develop is described by general relativity, depending on a set of cosmological parameters and on the nature of dark matter and dark energy (the latter being responsible for the acceleration of the expansion). Tracking the evolution of cosmic structure in the quest for the cosmological parameters that describe the Universe is especially interesting, in particular to corroborate the cosmological constraints inferred from the CMB (z ~ 1000) and from the matter distribution at much later times (z ~ 0 4), since they originate from very different physical processes. A traditional approach follows the distribution of galaxies in visible or infrared light. However galaxies account only for a few percent of the total matter content and are highly nonlinear objects, which makes establishing the connection with the initial density spectrum non-trivial. At the upper hierarchical level, one finds clusters of galaxies, the most massive objects in the Universe. They are located at the nodes of the cosmic web and are huge reservoirs of hot gas that fill the space between the galaxies. The gas has a temperature of a few tens of millions of degrees and emits in the X-ray. The cosmological analysis of cluster surveys basically relies on number counts (dn/dz or dn/dm/dz) and on the spatial analysis (D correlation function). In order to establish these functions, it is necessary to have a good knowledge of: (i) the scaling relations that link the X-ray observables, like temperature and luminosity, to the mass; and (ii) the selection function, i.e., the probability of detecting a cluster of given mass as a function of redshift. In this context, the XXL project (XXL Paper I) has undertaken a large survey of the X-ray sky with the European Space Agency XMM-Newton observatory. The primary goal of the XXL survey is to detect and confirm a few hundred clusters back to a time when the age of Universe was about half of its present value, i.e., z ~ 1. From this data collection, we can infer the evolutionary properties and spatial distribution of the deepest potential wells of the Universe and, subsequently, test various cosmological scenarios. In addition, XXL will deliver several tens of thousands of active galactic nuclei (AGNs) out to a redshift of at least four, allowing statistical studies of the AGN population as a function of environment to be performed. The XXL Survey is an XMM Very Large Programme that covers two extragalactic areas of 5 square degrees, located around (RA, Dec) of (h 0m, 4.5 ) and (h 0m, 55 ). Over 500 XMM XXL observations, typically of 10 ks each, were performed between 011 and 01. Two years after the completion of the X-ray observations, we have detected ~ 450 clusters and 000 AGNs in the kev energy band. The XXL survey samples the low end of the cluster mass function around z ~ This group population is especially interesting, since it contains the building blocks of the local massive clusters. Moreover, it is sensitive to non-gravitational physics, like the energy input from AGNs, feedback from star formation or cooling processes. Such groups thus present useful environments in which to study the formation of cosmic structures and provide a unique input to test physical processes via numerical simulations. The XXL consortium gathers some 100 scientists including observers, theoreticians and simulators with a wide range of expertise encompassing the entire electromagnetic spectrum. The Messenger 164 June 016 7

2 Adami C. et al., First Results from the XXL Survey and Multi-wavelength Programmes Figure 1. Sky distribution of the available spectroscopy and confirmed X-ray clusters of galaxies in the northern XXL field. The chessboard pattern of red points corresponds to the mosaic of VIMOS fields from the VIPERS survey (Guzzo et al., 014), while the darker spot at RA = 6.5 degrees shows the deeper data from the VIMOS-VLT Deep Survey (VVDS; Le Fèvre et al., 005). The isolated concentrations of red points are from the XXL ESO Large Programme (191.A-068) and represent ~ 50 % of the redshifts inside all the confirmed clusters at z > 0.5. Associated multi-wavelength programmes and XXL samples In order to characterise the properties of the detected clusters and AGNs, the XXL survey is accompanied by a comprehensive follow-up programme. Observations are coordinated with the largest ground-based and space observatories, from the X-ray to the radio (see, for example, XXL paper X for the K-band luminosity weak-lensing mass relation for galaxy structures). Of these coordinated observations, the ESO Large Programme and principal investigator allocations (ESO 191.A-068, 089.A-0666, and 60.A-90), as well as galaxy surveys in the XXL fields, like the VIMOS Public Extragalactic Survey (VIPERS; for example, Guzzo et al., 014) and the Galaxy And Mass Assembly survey (GAMA; for example, Driver et al., 016), are of special relevance as they allow galaxy redshifts to be measured, hence accurately locating the galaxy clusters in D space (Figures 1 and ). In the framework of the ESO Large Programme, we observed clusters out to a redshift of ~ 0.5 at the New Technology Telescope (NTT) with the ESO Faint Object Spectrograph and Camera (EFOSC) and the more distant ones (0.5 < z < 1.) with the FOcal Reducer/low dispersion Spectrograph (FORS) instrument on the Very Large Telescope (VLT). An example from the latter is the detection of a z ~ 1.9 cluster (see XXL Paper V). Cluster redshifts constitute a critical input to cosmological analysis, allowing the computation of the cluster cluster correlation function and further topological studies. Detailed investigations of the dynamics and galaxy properties of individual clusters are also undertaken at the William Herschel Telescope (WHT). The redshift measurement of the AGN is systematically performed with the AAOmega instrument on the Australian Astronomical Telescope (XXL XIV). Radio follow-up of the X-ray AGNs is undertaken with Giant Meterwave Radio Telescope (GMRT), the Jansky Very Large Array (VLA) and the Australia Telescope Compact Array (ATCA). In parallel, four numerical simulation programmes provide the necessary material to test in situ the various physical mechanisms that drive cluster and AGN evolution and their respective interactions. Simulations also allow accurate determination of the cluster selection function, which is an essential ingredient for the cosmological analysis. In a first series of 1 articles published in the December 015 Astronomy & Astrophysics special issue, plus one in Publications of the Astronomical Society of Australia, we released the catalogues of the brightest 100 clusters (XXL-100-GC) and 1000 AGNs (XXL-1000-AGN) as well as the reduced XMM observations. We present a number of scientific results for the, to date, little-explored low-mass range characterising the XXL cluster sample. Scaling relations Scaling relations are key elements for parameterising cluster evolution and the XXL project aims at a self-consistent determination. We therefore investigated the luminosity temperature (LT) relation of the XXL-100-GC sample (XXL III, see also XXL IV for the mass temperature relation). The first step was to measure the cluster X-ray luminosity and temperature from the XMM survey data. The sample spans a wide range of redshift (0.05 < z < 1.05), temperature (0.6 < kt < 7.0 kev), and luminosity ( < L < erg s 1 ) and is equivalent to a flux-limited sample ( erg s 1 cm ). Our methods to determine the LT relation fully take into account the selection effects of the survey. We measure the evolution of the LT relation internally using the broad redshift range of the sample and find a slope of the bolometric LT relation that is steeper than the self-similar expectation. Regarding evolution, our best fit is fully consistent with strong self-similar evolution where clusters scale self-similarly with both mass and redshift: clusters in the past would appear as scaled replicates of the local ones, as a function of mass. However, this result is marginally more significant than the weak self-similar evolution solution, where clusters scale with redshift alone. We further investigated the sensitivity of our results to the assumptions made in our fitting model, finding that the use of an external LT relation as 8 The Messenger 164 June 016

3 a low-z baseline can have a profound effect on the measured evolution. The present calculations were performed assuming a given cosmology. The next step, involving the complete XXL sample, will be to implement the cosmological dependency of the luminosity in the determination of the evolution rate of the LT relation. Cosmological constraints We further used the XXL-100-GC sample to infer preliminary cosmological constraints (XXL II). The measured luminosities and temperatures allowed us to model the predicted cluster number counts for the presently favoured set of cosmological parameters. The number density of clusters is found to be less than predicted by the Planck CMB cosmology, once the XXL selection effects are duly accounted for; this tension is similar to that found for the Planck Sunyaev Zeldovich (S Z) detected cluster sample, but pertains to a cluster mass range about one order of magnitude lower. However, the alternate Nine Year Wilkinson Microwave Anisotropy Probe (WMAP9) model is not perfect either and still overpredicts the number of faint clusters. Basic attempts to assess the cosmological leverage of the sample revealed that, even with the current subsample, the error budget is already dominated by uncertainties in the cluster mass calibration, which therefore will be one of the priorities of the XXL cluster science programme over the next few years. In particular, we are starting a collaboration with the Subaru Hyper-SuprimeCam team in order to obtain reliable lensing masses for most of the XXL clusters. Cluster baryon content Declination ( ) :55 :50 :45 :40 :5 :0 :5 :0 :15 :10 5:00 5:00 54:00 55:00 56:00 XMM-XXL South Beside counts and topology, another potential cosmological probe is the baryon fraction (f gas ) in clusters (XXL XIII). This test assumes that f gas is constant as a function of redshift for the high-mass clusters, because they are supposed to have retained all the material accreted since their formation epoch. Gas mass and total mass measurements do not scale in the same way as a function of cosmology; therefore, requiring that their ratio is constant ought to put constraints on the cosmological parameters. We measured the number of baryons (X-ray gas and stars) in the XXL-100-GC sample. Halo masses were estimated from a mass temperature relation that was directly calibrated using weak-lensing measurements (from the Canada France Hawaii Telescope Legacy Survey, CFHTLS) for a subset of XXL clusters. We find that the weak-lensing calibrated gas fraction of XXL-100-GC clusters is lower than was found in previous studies using hydrostatic masses. We compared our f gas M relation with the predictions of cosmological simulations using different gas physics. It was found Right Ascension (h,m) Figure. Upper: Spectroscopically confirmed AGNs (blue) and cluster galaxies (red) in the southern XXL field from the AAOmega follow-up (XXL Paper XIV). Left: Corresponding X-ray mosaic (units of colour bar are counts s 1 degree 1 ). The 5-square-degree field is covered by some 0 XMM pointings. The XMM field of view has a size comparable to that of the Moon (0 arcminutes diameter, shown at the upper left). More than AGNs have been detected in this image. The red circles show the clusters of galaxies. that our results favour extreme AGN feedback schemes in which a large fraction of the baryons are expelled from the potential well of dark matter halos. Such models are, however, in tension with X-ray-only proxies, such as the gas density and entropy profiles (Le Brun et al., 014) and are not able to reproduce the relation between gas mass and temperature of XXL clusters. Therefore, the results presented are challenging for current numerical simulations, and reconciling the observed gas fraction with the predictions would require that our weak-lensing masses be system atically overestimated. A mass The Messenger 164 June 016 9

4 Adami C. et al., First Results from the XXL Survey and Multi-wavelength Programmes A Figure. Upper: Distribution of the bright XXL cluster sample in the M 500 vs. redshift plane. The dashed line shows the 50 % completeness limit in the WMAP9 cosmology. Middle: Redshift distribution of the XXL-100-GC sample (filled histogram) compared with different model expectations (CMB measurements from WMAP + H0 + BAO presented in Hinshaw et al. [01], and latest CMB measurements from the Planck satellite, but without additional constraints from Planck Collaboration 015). Lower: Differential luminosity function of the bright XXL cluster sample in three redshift bins. The lower plot shows the residuals with respect to the lowredshift WMAP9 prediction (XXL Paper II). bias 1 b = 0.58 ± 0.04, which is required to reconcile Planck cluster counts with the primary CMB, would further exacerbate the tension between the baryon fraction and the cosmological value, challenging our understanding of cluster physics. Therefore, a satisfactory solution to the tension between CMB and cluster counts must also simultaneously explain the low baryon fraction measured for the XXL halos. Discovery of five superclusters Given its depth and sky coverage, XXL is particularly suited to systematically unveiling the clustering of X-ray clusters and to identifying superstructures in a homogeneous X-ray sample down to the typical mass scale of a local massive cluster. Although a few isolated, very high redshift superclusters are known, our work is the first attempt to systematically unveil superstructures up to z ~0.5 in a homogeneous X-ray sample. In this framework, we discovered five low-mass superclusters consisting of three to seven galaxy structures. One of them is particularly interesting and is presented in more detail (XXL VII and Figure 4). It is composed of six clusters of galaxies and the structure is very compact with all the clusters residing in one XMM pointing. Our subsequent spectroscopic follow-up with WHT and NTT provided a median redshift of z ~ 0.4. An estimate of the X-ray mass and luminosity of this supercluster returns values of M A and of erg s 1, respectively, and a total gas mass of M gas = M A. Instead of having a massive central cluster with infalling filaments and smaller structures, it has almost two equal-sized objects, making it qualitatively different from the network around an already formed massive cluster. This supercluster is currently the most massive and most distant found in XXL. If we put together the relatively small crossing time, the common X-ray emission of three members, and the measured gas fraction and mass, we can speculate that we are observing an unrelaxed structure with an ongoing merging between at least three of the member clusters. If nothing else intervened to alter the system, and assuming that the estimated 0 The Messenger 164 June 016

5 @QBLHM l l l JOB Y 7+" 7+" 7+" 7+" 7+" l 7+" +HMDlNElRHFGS CHQDBSHNM,OB l 7+" 7+" 7+" l l 7+" 7+" l 7+" # D BK H HN M C H l QD B S l B HN l M, O M l l l HQ D B S HN C, M R HN OB RBDM 1 HF G S 1HFGS RBDMRHNM Figure 4. Top left: CFHTLS MegaCam mosaic image in the i-band with the XXL contours superimposed in green; X-ray clusters are red circles. The positions of the BCG in each cluster are shown and the black crosses highlight the point sources excluded from the X-ray analysis. Top right: Three-dimensional configuration of the z = 0.4 super cluster (XXL Paper VII). Right: CFHTLS-wide colour u*r:z: image (8 by 8 arcminutes) of XLSS-C inner complex. crossing time is a good estimate of the merging time, it is likely that by the present time the supercluster would already have completely merged ~ Gyr before and resemble the most massive known clusters. First spectral characterisation of diffuse light in a cluster Within a cluster, gravitational effects can lead to the removal of stars from their parent galaxies and subsequent dispersal into the intracluster medium (ICL). Gas hydrodynamical effects can additionally strip gas and dust from galaxies. The properties of the ICL can therefore help constrain the physical processes at work in clusters by serving as a fossil record of the interaction history. We detected in the XXL survey a very peculiar intermediate-mass cluster: XLSSC-116, with a very high level of such diffuse light, by applying a wavelet-based method to CFHT Megacam and Wide-field InfraRed Camera (WIRCAM) images (XXL VIII). The amount of diffuse light is equivalent to two brightest cluster galaxies (BCGs) in the i:-band. To the best of our knowledge, this is the first detected cluster with such a large amount of diffuse light. The source of the diffuse light was then spectroscopically characterised with ESO Multi-Unit Spectroscopic Explorer (MUSE) spectroscopic data (proposal 60.A-90). MUSE data were also used to compute redshifts of 4 cluster galaxies and search for cluster substructures. The cluster consists of a main component with a velocity dispersion of the order of 600 km s 1 and an infalling lowmass group with a velocity dispersion of 170 km s 1. Part of the detected diffuse light has a very weak optical stellar component and apparently consists mainly of gas emission, while other diffuse light sources are clearly dominated by old stars. Furthermore, emission lines were detected in several places coinciding with The Messenger 164 June 016 1

6 Adami C. et al., First Results from the XXL Survey and Multi-wavelength Programmes N (> S)/deg XXL-N XXL-S COSMOS ATLAS XMM-CDFS Figure 5. Left: Luminosity redshift plane for different X-ray fields in the 10 kev energy band. Right: log N log S for the XXL-1000-AGN in the XXL-N field (blue circles) and in the XXL-S field (orange squares) as compared to other literature surveys (XXL Paper VI) S 10keV /erg s 1 cm the diffuse light. Our spectral analysis shows that this emission likely originates from gas with a low-excitation parameter. Globally, the stellar contribution to the ICL is about years old even though the ICL is not currently forming a large number of stars. On the other hand, the contribution of the gas emission to the ICL in the optical is much greater than the stellar contribution in some regions, but the gas density is likely too low to form stars. These observations favour ram-pressure stripping, turbulent viscous stripping, or supernovae winds as the origin of the large amount of intracluster light. Since the cluster appears not to be in a major merging phase, we conclude that ram-pressure stripping is the most plausible process that generates the observed ICL sources. AGNs in the XXL survey X-ray extragalactic surveys are also ideal laboratories for the study of the evolution and clustering of AGN. Optimally, a combination of deep and wide surveys is necessary to create a complete picture of the population. Deep X-ray surveys provide the faint population at high redshift, while wide surveys provide the rare bright sources and the large-scale structure information. Nevertheless, very wide area surveys often lack the ancillary information available for modern deep surveys. The XXL survey occupies the parameter space that lies between deep surveys and very wide area surveys, constituting a stepping stone between current deep fields and planned wide area surveys (Figure 5). XXL-1000-AGN is our first point source catalogue. The sample is selected in the 10 kev energy band with the goal of providing an initial sizable sample useful for AGN studies (XXL Papers VI, XI, XII). The limiting flux is F 10 kev = erg s 1 cm. We use both public and proprietary datasets in the optical and nearinfrared to identify the counterparts of the X-ray point-like sources by means of a likelihood ratio test, reaching 97. % identification rate. Using multi-wavelength data from the far ultra-violet to the mid infrared, we derive the median spectral energy distribution of AGN as a function of X-ray absorption. We improve upon the photometric redshift determination for AGN by applying a Random Forest classification trained to identify, for each object, the optimal photometric redshift category (passive, star-forming, starburst, AGN, quasar). In addition, we assign a probability to each source that indicates whether it might be a star or an outlier. The photometric redshift accuracy is for the full XMM-XXL with 8 % catastrophic outliers estimated on a sample of 9 sources. We apply Bayesian analysis to model the X-ray spectra assuming a power-law model with the presence of an absorbing medium, finding no trend of photon index or hydrogen column density with redshift and a fraction of 6 % absorbed sources, consistent with the literature on bright sources. The XXL-1000-AGN sample number counts extend the COSMOS log N log S to higher fluxes (Figure 5); they are fully consistent with the Euclidean expectation and agree with previous deep (Chandra Deep Field South [CDFS] and COSMOS) and wide (Herschel-ATLAS) XMM- Newton surveys. We constrain the intrinsic luminosity function of AGN in the 10 kev energy band where the unabsorbed X-ray flux is estimated from the X-ray spectral fit up to z =. An application of the friends-of-friends algorithm, at 10 h 1 Mpc and 0 h 1 Mpc percolation radii, shows significant structures with members and identifies a superclustersized structure at redshift In future publications we will expand the analysis to the full XXL catalogue, containing an unprecedented number of ~ 10 4 (X-ray) point-like 10 kev detected sources, and analysing the fully combined XMM pointings to reach maximum depth. A unique advantage of the XXL large statistical samples is the combined study of X-ray point-like sources and X-ray detected galaxy clusters, which will allow the study of AGN with respect to their environment and, vice versa, the study of the impact of AGN on clusters. The Messenger 164 June 016

7 1 0 1 Prospects The second phase of the XXL project is expected to end in 018, with the publication of the complete cluster catalogue, including all data available from the multi-wavelength follow-up along with the selection functions. These will incorporate a thorough analysis of the impact of cluster shapes and AGN activity on the detection rates, which we will measure by means of N-body simulations performed under various physical hypotheses (Figure 6). The final cosmological analysis of the full XXL cluster sample will involve a completely self-consistent treatment of the cluster evolution, selection function and cosmology. With some five times as many clusters (already some 450 clusters have been identified), we expect to provide a useful and stand-alone set of cosmological constraints. In addition to the traditional study of the dn/dz and dn/ dm/dz counts, we have developed a method based on the modelling of the X-ray observable parameter space, that globally by-passes the intermediate phase of the (cosmologically dependent) cluster mass determination (Clerc et al., 01; Pierre et al., 016). We will also release the XXL multi-wavelength AGN catalogue, that is some 000 objects. The dataset, including spectroscopic follow-up, has a unique legacy value for cos mological and extragalactic environmental studies and will constitute a calibration resource for future surveys, like erosita (all-sky, but at significantly lower sensitivity and resolution) and Euclid. Figure 6. Left: Simulated X-ray emissivity map extracted from a 5 square degree by z = 0 light cone (OverWhelmingly Large Simulations [OWLS], Le Brun et al., 014). Right: Same portion of the virtual sky transformed into an XMM image by the XXL simulator. All XMM characteristics are taken into account: point spread function (and its variation with energy), quantum efficiency, various background components and vignetting. References Clerc, N. et al. 01, MNRAS, 4, 561 Clerc, N. et al. 01, MNRAS, 4, 545 Driver, S. P. et al. 016, MNRAS, 455, 911 Hinshaw, G. et al. 01, ApJS, 08, 19 Le Brun, V. et al. 014, MNRAS, 441, 170 Le Fèvre, O. et al. 005, A&A, 49, 845 Guzzo, L. et al. 014, A&A, 566, 108 Hinshaw, G. et al. 01, ApJS, 08, 19 XXL Survey: I. Pierre, M. et al. 016, A&A, 59, A1 XXL Survey: II. Pacaud, F. et al. 016, A&A, 59, A XXL Survey: III. Giles, P. A. et al. 016, A&A, 59, A XXL Survey: IV. Lieu, M. et al. 016, A&A, 59, A4 XXL Survey: V. Mantz, A. B. et al. 016, ApJ, 794, 157 XXL Survey: VI. Fotopoulou, S. et al. 016, A&A, 59, A5 XXL Survey: VII. Pompei, E. et al. 016, A&A, 59, A6 XXL Survey: VIII. Adami, C. et al. 016, A&A, 59, A7 XXL Survey: IX. Baran, N. et al. 016, A&A, 59, A8 XXL Survey: X. Ziparo, F. et al. 016, A&A, 59, A9 XXL Survey: XI. Smolčić, V. et al. 016, A&A, 59, A10 XXL Survey: XII. Koulouridis, E. et al. 016, A&A, 59, A11 XXL Survey. XIII. Eckert, D. et al. 016, A&A, 59, A1 XXL Survey XIV. Lidman, C. et al. 016, PASA,, 1 ESO/H. Dahle Night-time observations with the New Technology Telescope at the La Silla Observatory. Following two pages: VLT Survey Telescope (VST) composite u-, g- and i-band, large-field image (10 by 84 arcminutes) of the core of the nearby Fornax Galaxy Cluster. At a distance of about 19 Mpc, the Fornax cluster is a rich cluster (class 0) with more than 40 known members. The central brightest cluster galaxy, NGC 199 can be seen to the north east, with the prominent barred spiral NGC 165 to south west. See Release eso161 for more details. The Messenger 164 June 016

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch: HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying

Διαβάστε περισσότερα

ST5224: Advanced Statistical Theory II

ST5224: Advanced Statistical Theory II ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known

Διαβάστε περισσότερα

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3)

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3) Q1. (a) A fluorescent tube is filled with mercury vapour at low pressure. In order to emit electromagnetic radiation the mercury atoms must first be excited. (i) What is meant by an excited atom? (1) (ii)

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο

Διαβάστε περισσότερα

2 Composition. Invertible Mappings

2 Composition. Invertible Mappings Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,

Διαβάστε περισσότερα

EE512: Error Control Coding

EE512: Error Control Coding EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3

Διαβάστε περισσότερα

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =

Διαβάστε περισσότερα

Statistical Inference I Locally most powerful tests

Statistical Inference I Locally most powerful tests Statistical Inference I Locally most powerful tests Shirsendu Mukherjee Department of Statistics, Asutosh College, Kolkata, India. shirsendu st@yahoo.co.in So far we have treated the testing of one-sided

Διαβάστε περισσότερα

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required) Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts

Διαβάστε περισσότερα

the total number of electrons passing through the lamp.

the total number of electrons passing through the lamp. 1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy

Διαβάστε περισσότερα

«ΑΓΡΟΤΟΥΡΙΣΜΟΣ ΚΑΙ ΤΟΠΙΚΗ ΑΝΑΠΤΥΞΗ: Ο ΡΟΛΟΣ ΤΩΝ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΣΤΗΝ ΠΡΟΩΘΗΣΗ ΤΩΝ ΓΥΝΑΙΚΕΙΩΝ ΣΥΝΕΤΑΙΡΙΣΜΩΝ»

«ΑΓΡΟΤΟΥΡΙΣΜΟΣ ΚΑΙ ΤΟΠΙΚΗ ΑΝΑΠΤΥΞΗ: Ο ΡΟΛΟΣ ΤΩΝ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΣΤΗΝ ΠΡΟΩΘΗΣΗ ΤΩΝ ΓΥΝΑΙΚΕΙΩΝ ΣΥΝΕΤΑΙΡΙΣΜΩΝ» I ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΣΧΟΛΗ ΝΟΜΙΚΩΝ ΟΙΚΟΝΟΜΙΚΩΝ ΚΑΙ ΠΟΛΙΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ «ΔΙΟΙΚΗΣΗ ΚΑΙ ΟΙΚΟΝΟΜΙΑ» ΚΑΤΕΥΘΥΝΣΗ: ΟΙΚΟΝΟΜΙΚΗ

Διαβάστε περισσότερα

Η αλληλεπίδραση ανάμεσα στην καθημερινή γλώσσα και την επιστημονική ορολογία: παράδειγμα από το πεδίο της Κοσμολογίας

Η αλληλεπίδραση ανάμεσα στην καθημερινή γλώσσα και την επιστημονική ορολογία: παράδειγμα από το πεδίο της Κοσμολογίας Η αλληλεπίδραση ανάμεσα στην καθημερινή γλώσσα και την επιστημονική ορολογία: παράδειγμα από το πεδίο της Κοσμολογίας ΠΕΡΙΛΗΨΗ Αριστείδης Κοσιονίδης Η κατανόηση των εννοιών ενός επιστημονικού πεδίου απαιτεί

Διαβάστε περισσότερα

Math 6 SL Probability Distributions Practice Test Mark Scheme

Math 6 SL Probability Distributions Practice Test Mark Scheme Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry

Διαβάστε περισσότερα

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ. Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action

Διαβάστε περισσότερα

Assalamu `alaikum wr. wb.

Assalamu `alaikum wr. wb. LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump

Διαβάστε περισσότερα

ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ

ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΛΕΝΑ ΦΛΟΚΑ Επίκουρος Καθηγήτρια Τµήµα Φυσικής, Τοµέας Φυσικής Περιβάλλοντος- Μετεωρολογίας ΓΕΝΙΚΟΙ ΟΡΙΣΜΟΙ Πληθυσµός Σύνολο ατόµων ή αντικειµένων στα οποία αναφέρονται

Διαβάστε περισσότερα

derivation of the Laplacian from rectangular to spherical coordinates

derivation of the Laplacian from rectangular to spherical coordinates derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used

Διαβάστε περισσότερα

4.6 Autoregressive Moving Average Model ARMA(1,1)

4.6 Autoregressive Moving Average Model ARMA(1,1) 84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this

Διαβάστε περισσότερα

[1] P Q. Fig. 3.1

[1] P Q. Fig. 3.1 1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

Διαβάστε περισσότερα

Lecture 34 Bootstrap confidence intervals

Lecture 34 Bootstrap confidence intervals Lecture 34 Bootstrap confidence intervals Confidence Intervals θ: an unknown parameter of interest We want to find limits θ and θ such that Gt = P nˆθ θ t If G 1 1 α is known, then P θ θ = P θ θ = 1 α

Διαβάστε περισσότερα

Section 8.3 Trigonometric Equations

Section 8.3 Trigonometric Equations 99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.

Διαβάστε περισσότερα

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11 Potential Dividers 46 minutes 46 marks Page 1 of 11 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and

Διαβάστε περισσότερα

Figure A.2: MPC and MPCP Age Profiles (estimating ρ, ρ = 2, φ = 0.03)..

Figure A.2: MPC and MPCP Age Profiles (estimating ρ, ρ = 2, φ = 0.03).. Supplemental Material (not for publication) Persistent vs. Permanent Income Shocks in the Buffer-Stock Model Jeppe Druedahl Thomas H. Jørgensen May, A Additional Figures and Tables Figure A.: Wealth and

Διαβάστε περισσότερα

5.4 The Poisson Distribution.

5.4 The Poisson Distribution. The worst thing you can do about a situation is nothing. Sr. O Shea Jackson 5.4 The Poisson Distribution. Description of the Poisson Distribution Discrete probability distribution. The random variable

Διαβάστε περισσότερα

Approximation of distance between locations on earth given by latitude and longitude

Approximation of distance between locations on earth given by latitude and longitude Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth

Διαβάστε περισσότερα

Figure 3 Three observations (Vp, Vs and density isosurfaces) intersecting in the PLF space. Solutions exist at the two indicated points.

Figure 3 Three observations (Vp, Vs and density isosurfaces) intersecting in the PLF space. Solutions exist at the two indicated points. φ φ φ φ Figure 1 Resampling of a rock-physics model from velocity-porosity to lithology-porosity space. C i are model results for various clay contents. φ ρ ρ δ Figure 2 Bulk modulus constraint cube in

Διαβάστε περισσότερα

Other Test Constructions: Likelihood Ratio & Bayes Tests

Other Test Constructions: Likelihood Ratio & Bayes Tests Other Test Constructions: Likelihood Ratio & Bayes Tests Side-Note: So far we have seen a few approaches for creating tests such as Neyman-Pearson Lemma ( most powerful tests of H 0 : θ = θ 0 vs H 1 :

Διαβάστε περισσότερα

Strain gauge and rosettes

Strain gauge and rosettes Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified

Διαβάστε περισσότερα

ΠΟΛΥΤΕΧΝΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΕΡΙΒΑΛΛΟΝΤΟΣ

ΠΟΛΥΤΕΧΝΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΕΡΙΒΑΛΛΟΝΤΟΣ ΠΟΛΥΤΕΧΝΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΕΡΙΒΑΛΛΟΝΤΟΣ Τομέας Περιβαλλοντικής Υδραυλικής και Γεωπεριβαλλοντικής Μηχανικής (III) Εργαστήριο Γεωπεριβαλλοντικής Μηχανικής TECHNICAL UNIVERSITY OF CRETE SCHOOL of

Διαβάστε περισσότερα

Second Order RLC Filters

Second Order RLC Filters ECEN 60 Circuits/Electronics Spring 007-0-07 P. Mathys Second Order RLC Filters RLC Lowpass Filter A passive RLC lowpass filter (LPF) circuit is shown in the following schematic. R L C v O (t) Using phasor

Διαβάστε περισσότερα

Right Rear Door. Let's now finish the door hinge saga with the right rear door

Right Rear Door. Let's now finish the door hinge saga with the right rear door Right Rear Door Let's now finish the door hinge saga with the right rear door You may have been already guessed my steps, so there is not much to describe in detail. Old upper one file:///c /Documents

Διαβάστε περισσότερα

Homework 3 Solutions

Homework 3 Solutions Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For

Διαβάστε περισσότερα

Démographie spatiale/spatial Demography

Démographie spatiale/spatial Demography ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΙΑΣ Démographie spatiale/spatial Demography Session 1: Introduction to spatial demography Basic concepts Michail Agorastakis Department of Planning & Regional Development Άδειες Χρήσης

Διαβάστε περισσότερα

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS EXERCISE 01 Page 545 1. Use matrices to solve: 3x + 4y x + 5y + 7 3x + 4y x + 5y 7 Hence, 3 4 x 0 5 y 7 The inverse of 3 4 5 is: 1 5 4 1 5 4 15 8 3

Διαβάστε περισσότερα

Instruction Execution Times

Instruction Execution Times 1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables

Διαβάστε περισσότερα

Bayesian statistics. DS GA 1002 Probability and Statistics for Data Science.

Bayesian statistics. DS GA 1002 Probability and Statistics for Data Science. Bayesian statistics DS GA 1002 Probability and Statistics for Data Science http://www.cims.nyu.edu/~cfgranda/pages/dsga1002_fall17 Carlos Fernandez-Granda Frequentist vs Bayesian statistics In frequentist

Διαβάστε περισσότερα

6.1. Dirac Equation. Hamiltonian. Dirac Eq.

6.1. Dirac Equation. Hamiltonian. Dirac Eq. 6.1. Dirac Equation Ref: M.Kaku, Quantum Field Theory, Oxford Univ Press (1993) η μν = η μν = diag(1, -1, -1, -1) p 0 = p 0 p = p i = -p i p μ p μ = p 0 p 0 + p i p i = E c 2 - p 2 = (m c) 2 H = c p 2

Διαβάστε περισσότερα

Numerical Analysis FMN011

Numerical Analysis FMN011 Numerical Analysis FMN011 Carmen Arévalo Lund University carmen@maths.lth.se Lecture 12 Periodic data A function g has period P if g(x + P ) = g(x) Model: Trigonometric polynomial of order M T M (x) =

Διαβάστε περισσότερα

Physical DB Design. B-Trees Index files can become quite large for large main files Indices on index files are possible.

Physical DB Design. B-Trees Index files can become quite large for large main files Indices on index files are possible. B-Trees Index files can become quite large for large main files Indices on index files are possible 3 rd -level index 2 nd -level index 1 st -level index Main file 1 The 1 st -level index consists of pairs

Διαβάστε περισσότερα

Nuclear Physics 5. Name: Date: 8 (1)

Nuclear Physics 5. Name: Date: 8 (1) Name: Date: Nuclear Physics 5. A sample of radioactive carbon-4 decays into a stable isotope of nitrogen. As the carbon-4 decays, the rate at which the amount of nitrogen is produced A. decreases linearly

Διαβάστε περισσότερα

ΠΕΡΙΕΧΟΜΕΝΑ. Κεφάλαιο 1: Κεφάλαιο 2: Κεφάλαιο 3:

ΠΕΡΙΕΧΟΜΕΝΑ. Κεφάλαιο 1: Κεφάλαιο 2: Κεφάλαιο 3: 4 Πρόλογος Η παρούσα διπλωµατική εργασία µε τίτλο «ιερεύνηση χωρικής κατανοµής µετεωρολογικών µεταβλητών. Εφαρµογή στον ελληνικό χώρο», ανατέθηκε από το ιεπιστηµονικό ιατµηµατικό Πρόγραµµα Μεταπτυχιακών

Διαβάστε περισσότερα

Section 9.2 Polar Equations and Graphs

Section 9.2 Polar Equations and Graphs 180 Section 9. Polar Equations and Graphs In this section, we will be graphing polar equations on a polar grid. In the first few examples, we will write the polar equation in rectangular form to help identify

Διαβάστε περισσότερα

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013 Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering

Διαβάστε περισσότερα

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β 3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle

Διαβάστε περισσότερα

Matrices and Determinants

Matrices and Determinants Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z

Διαβάστε περισσότερα

1) Abstract (To be organized as: background, aim, workpackages, expected results) (300 words max) Το όριο λέξεων θα είναι ελαστικό.

1) Abstract (To be organized as: background, aim, workpackages, expected results) (300 words max) Το όριο λέξεων θα είναι ελαστικό. UΓενικές Επισημάνσεις 1. Παρακάτω θα βρείτε απαντήσεις του Υπουργείου, σχετικά με τη συμπλήρωση της ηλεκτρονικής φόρμας. Διευκρινίζεται ότι στα περισσότερα θέματα οι απαντήσεις ήταν προφορικές (τηλεφωνικά),

Διαβάστε περισσότερα

Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1

Main source: Discrete-time systems and computer control by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1 Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1 A Brief History of Sampling Research 1915 - Edmund Taylor Whittaker (1873-1956) devised a

Διαβάστε περισσότερα

Μηχανική Μάθηση Hypothesis Testing

Μηχανική Μάθηση Hypothesis Testing ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Μηχανική Μάθηση Hypothesis Testing Γιώργος Μπορμπουδάκης Τμήμα Επιστήμης Υπολογιστών Procedure 1. Form the null (H 0 ) and alternative (H 1 ) hypothesis 2. Consider

Διαβάστε περισσότερα

HISTOGRAMS AND PERCENTILES What is the 25 th percentile of a histogram? What is the 50 th percentile for the cigarette histogram?

HISTOGRAMS AND PERCENTILES What is the 25 th percentile of a histogram? What is the 50 th percentile for the cigarette histogram? HISTOGRAMS AND PERCENTILES What is the 25 th percentile of a histogram? The point on the horizontal axis such that of the area under the histogram lies to the left of that point (and to the right) What

Διαβάστε περισσότερα

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr 9.9 #. Area inside the oval limaçon r = + cos. To graph, start with = so r =. Compute d = sin. Interesting points are where d vanishes, or at =,,, etc. For these values of we compute r:,,, and the values

Διαβάστε περισσότερα

Μεταπτυχιακή διατριβή. Ανδρέας Παπαευσταθίου

Μεταπτυχιακή διατριβή. Ανδρέας Παπαευσταθίου Σχολή Γεωτεχνικών Επιστημών και Διαχείρισης Περιβάλλοντος Μεταπτυχιακή διατριβή Κτίρια σχεδόν μηδενικής ενεργειακής κατανάλωσης :Αξιολόγηση συστημάτων θέρμανσης -ψύξης και ΑΠΕ σε οικιστικά κτίρια στην

Διαβάστε περισσότερα

Αξιολόγηση των Φασματικού Διαχωρισμού στην Διάκριση Διαφορετικών Τύπων Εδάφους ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. Σπίγγος Γεώργιος

Αξιολόγηση των Φασματικού Διαχωρισμού στην Διάκριση Διαφορετικών Τύπων Εδάφους ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. Σπίγγος Γεώργιος ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΤΜΗΜΑ ΑΓΡΟΝΟΜΩΝ ΤΟΠΟΓΡΑΦΩΝ ΜΗΧΑΝΙΚΩΝ ΤΟΜΕΑΣ ΤΟΠΟΓΡΑΦΙΑΣ-ΕΡΓΑΣΤΗΡΙΟ ΤΗΛΕΠΙΣΚΟΠΗΣΗΣ Αξιολόγηση των Φασματικού Διαχωρισμού στην Διάκριση Διαφορετικών Τύπων Εδάφους ΔΙΠΛΩΜΑΤΙΚΗ

Διαβάστε περισσότερα

Lukasz STAWARZ. on Behalf of the Fermi LAT Collaboration.

Lukasz STAWARZ. on Behalf of the Fermi LAT Collaboration. e-mail: kataoka.jun@waseda.jp 169 8555 3 4 1 739 8526 1 3 1 e-mail: fukazawa@hep01.hep1.hiroshima.u.ac.jp Lukasz STAWARZ 252 5210 3 1 1 e-mail: stawarz@astro.isas.jaxa.jp e-mail: rsato@astro.isas.jaxa.jp

Διαβάστε περισσότερα

ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΓΗΑΣΜΖΜΑΣΗΚΟ ΠΡΟΓΡΑΜΜΑ ΜΔΣΑΠΣΤΥΗΑΚΩΝ ΠΟΤΓΩΝ «ΤΣΖΜΑΣΑ ΔΠΔΞΔΡΓΑΗΑ ΖΜΑΣΩΝ ΚΑΗ ΔΠΗΚΟΗΝΩΝΗΩΝ» ΣΜΖΜΑ ΜΖΥΑΝΗΚΩΝ Ζ/Τ ΚΑΗ ΠΛΖΡΟΦΟΡΗΚΖ

ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΓΗΑΣΜΖΜΑΣΗΚΟ ΠΡΟΓΡΑΜΜΑ ΜΔΣΑΠΣΤΥΗΑΚΩΝ ΠΟΤΓΩΝ «ΤΣΖΜΑΣΑ ΔΠΔΞΔΡΓΑΗΑ ΖΜΑΣΩΝ ΚΑΗ ΔΠΗΚΟΗΝΩΝΗΩΝ» ΣΜΖΜΑ ΜΖΥΑΝΗΚΩΝ Ζ/Τ ΚΑΗ ΠΛΖΡΟΦΟΡΗΚΖ ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΓΗΑΣΜΖΜΑΣΗΚΟ ΠΡΟΓΡΑΜΜΑ ΜΔΣΑΠΣΤΥΗΑΚΩΝ ΠΟΤΓΩΝ «ΤΣΖΜΑΣΑ ΔΠΔΞΔΡΓΑΗΑ ΖΜΑΣΩΝ ΚΑΗ ΔΠΗΚΟΗΝΩΝΗΩΝ» ΣΜΖΜΑ ΜΖΥΑΝΗΚΩΝ Ζ/Τ ΚΑΗ ΠΛΖΡΟΦΟΡΗΚΖ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΜΖΜΑ

Διαβάστε περισσότερα

ΣΧΕΔΙΑΣΜΟΣ ΔΙΚΤΥΩΝ ΔΙΑΝΟΜΗΣ. Η εργασία υποβάλλεται για τη μερική κάλυψη των απαιτήσεων με στόχο. την απόκτηση του διπλώματος

ΣΧΕΔΙΑΣΜΟΣ ΔΙΚΤΥΩΝ ΔΙΑΝΟΜΗΣ. Η εργασία υποβάλλεται για τη μερική κάλυψη των απαιτήσεων με στόχο. την απόκτηση του διπλώματος ΣΧΕΔΙΑΣΜΟΣ ΔΙΚΤΥΩΝ ΔΙΑΝΟΜΗΣ Η εργασία υποβάλλεται για τη μερική κάλυψη των απαιτήσεων με στόχο την απόκτηση του διπλώματος «Οργάνωση και Διοίκηση Βιομηχανικών Συστημάτων με εξειδίκευση στα Συστήματα Εφοδιασμού

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα είναι μικρότεροι το 1000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Διάρκεια: 3,5 ώρες Καλή

Διαβάστε περισσότερα

Correction Table for an Alcoholometer Calibrated at 20 o C

Correction Table for an Alcoholometer Calibrated at 20 o C An alcoholometer is a device that measures the concentration of ethanol in a water-ethanol mixture (often in units of %abv percent alcohol by volume). The depth to which an alcoholometer sinks in a water-ethanol

Διαβάστε περισσότερα

Policy Coherence. JEL Classification : J12, J13, J21 Key words :

Policy Coherence. JEL Classification : J12, J13, J21 Key words : ** 80%1.89 2005 7 35 Policy Coherence JEL Classification : J12, J13, J21 Key words : ** Family Life and Family Policy in France and Germany: Implications for Japan By Tomoko Hayashi and Rieko Tamefuji

Διαβάστε περισσότερα

; +302 ; +313; +320,.

; +302 ; +313; +320,. 1.,,*+, - +./ +/2 +, -. ; +, - +* cm : Key words: snow-water content, surface soil, snow type, water permeability, water retention +,**. +,,**/.. +30- +302 ; +302 ; +313; +320,. + *+, *2// + -.*, **. **+.,

Διαβάστε περισσότερα

ΙΕΥΘΥΝΤΗΣ: Καθηγητής Γ. ΧΡΥΣΟΛΟΥΡΗΣ Ι ΑΚΤΟΡΙΚΗ ΙΑΤΡΙΒΗ

ΙΕΥΘΥΝΤΗΣ: Καθηγητής Γ. ΧΡΥΣΟΛΟΥΡΗΣ Ι ΑΚΤΟΡΙΚΗ ΙΑΤΡΙΒΗ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΠΟΛΥΤΕΧΝΙΚΗ ΣΧΟΛΗ ΤΜΗΜΑ ΜΗΧΑΝΟΛΟΓΩΝ ΚΑΙ ΑΕΡΟΝΑΥΠΗΓΩΝ ΜΗΧΑΝΙΚΩΝ ΕΡΓΑΣΤΗΡΙΟ ΣΥΣΤΗΜΑΤΩΝ ΠΑΡΑΓΩΓΗΣ & ΑΥΤΟΜΑΤΙΣΜΟΥ / ΥΝΑΜΙΚΗΣ & ΘΕΩΡΙΑΣ ΜΗΧΑΝΩΝ ΙΕΥΘΥΝΤΗΣ: Καθηγητής Γ. ΧΡΥΣΟΛΟΥΡΗΣ Ι ΑΚΤΟΡΙΚΗ

Διαβάστε περισσότερα

Parametrized Surfaces

Parametrized Surfaces Parametrized Surfaces Recall from our unit on vector-valued functions at the beginning of the semester that an R 3 -valued function c(t) in one parameter is a mapping of the form c : I R 3 where I is some

Διαβάστε περισσότερα

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ Μελέτη των υλικών των προετοιμασιών σε υφασμάτινο υπόστρωμα, φορητών έργων τέχνης (17ος-20ος αιώνας). Διερεύνηση της χρήσης της τεχνικής της Ηλεκτρονικής Μικροσκοπίας

Διαβάστε περισσότερα

Reminders: linear functions

Reminders: linear functions Reminders: linear functions Let U and V be vector spaces over the same field F. Definition A function f : U V is linear if for every u 1, u 2 U, f (u 1 + u 2 ) = f (u 1 ) + f (u 2 ), and for every u U

Διαβάστε περισσότερα

ΓΕΩΠΟΝΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΘΗΝΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΗΣ ΤΡΟΦΙΜΩΝ ΚΑΙ ΔΙΑΤΡΟΦΗΣ ΤΟΥ ΑΝΘΡΩΠΟΥ

ΓΕΩΠΟΝΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΘΗΝΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΗΣ ΤΡΟΦΙΜΩΝ ΚΑΙ ΔΙΑΤΡΟΦΗΣ ΤΟΥ ΑΝΘΡΩΠΟΥ ΓΕΩΠΟΝΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΘΗΝΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΗΣ ΤΡΟΦΙΜΩΝ ΚΑΙ ΔΙΑΤΡΟΦΗΣ ΤΟΥ ΑΝΘΡΩΠΟΥ Πρόγραμμα Μεταπτυχιακών Σπουδών «Επιστήμη και Τεχνολογία Τροφίμων και Διατροφή του Ανθρώπου» Κατεύθυνση: «Διατροφή, Δημόσια

Διαβάστε περισσότερα

Queensland University of Technology Transport Data Analysis and Modeling Methodologies

Queensland University of Technology Transport Data Analysis and Modeling Methodologies Queensland University of Technology Transport Data Analysis and Modeling Methodologies Lab Session #7 Example 5.2 (with 3SLS Extensions) Seemingly Unrelated Regression Estimation and 3SLS A survey of 206

Διαβάστε περισσότερα

On a four-dimensional hyperbolic manifold with finite volume

On a four-dimensional hyperbolic manifold with finite volume BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Numbers 2(72) 3(73), 2013, Pages 80 89 ISSN 1024 7696 On a four-dimensional hyperbolic manifold with finite volume I.S.Gutsul Abstract. In

Διαβάστε περισσότερα

Written Examination. Antennas and Propagation (AA ) April 26, 2017.

Written Examination. Antennas and Propagation (AA ) April 26, 2017. Written Examination Antennas and Propagation (AA. 6-7) April 6, 7. Problem ( points) Let us consider a wire antenna as in Fig. characterized by a z-oriented linear filamentary current I(z) = I cos(kz)ẑ

Διαβάστε περισσότερα

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι She selects the option. Jenny starts with the al listing. This has employees listed within She drills down through the employee. The inferred ER sttricture relates this to the redcords in the databasee

Διαβάστε περισσότερα

Section 7.6 Double and Half Angle Formulas

Section 7.6 Double and Half Angle Formulas 09 Section 7. Double and Half Angle Fmulas To derive the double-angles fmulas, we will use the sum of two angles fmulas that we developed in the last section. We will let α θ and β θ: cos(θ) cos(θ + θ)

Διαβάστε περισσότερα

ΓΕΩΜΕΣΡΙΚΗ ΣΕΚΜΗΡΙΩΗ ΣΟΤ ΙΕΡΟΤ ΝΑΟΤ ΣΟΤ ΣΙΜΙΟΤ ΣΑΤΡΟΤ ΣΟ ΠΕΛΕΝΔΡΙ ΣΗ ΚΤΠΡΟΤ ΜΕ ΕΦΑΡΜΟΓΗ ΑΤΣΟΜΑΣΟΠΟΙΗΜΕΝΟΤ ΤΣΗΜΑΣΟ ΨΗΦΙΑΚΗ ΦΩΣΟΓΡΑΜΜΕΣΡΙΑ

ΓΕΩΜΕΣΡΙΚΗ ΣΕΚΜΗΡΙΩΗ ΣΟΤ ΙΕΡΟΤ ΝΑΟΤ ΣΟΤ ΣΙΜΙΟΤ ΣΑΤΡΟΤ ΣΟ ΠΕΛΕΝΔΡΙ ΣΗ ΚΤΠΡΟΤ ΜΕ ΕΦΑΡΜΟΓΗ ΑΤΣΟΜΑΣΟΠΟΙΗΜΕΝΟΤ ΤΣΗΜΑΣΟ ΨΗΦΙΑΚΗ ΦΩΣΟΓΡΑΜΜΕΣΡΙΑ ΕΘΝΙΚΟ ΜΕΣΟΒΙΟ ΠΟΛΤΣΕΧΝΕΙΟ ΣΜΗΜΑ ΑΓΡΟΝΟΜΩΝ-ΣΟΠΟΓΡΑΦΩΝ ΜΗΧΑΝΙΚΩΝ ΣΟΜΕΑ ΣΟΠΟΓΡΑΦΙΑ ΕΡΓΑΣΗΡΙΟ ΦΩΣΟΓΡΑΜΜΕΣΡΙΑ ΓΕΩΜΕΣΡΙΚΗ ΣΕΚΜΗΡΙΩΗ ΣΟΤ ΙΕΡΟΤ ΝΑΟΤ ΣΟΤ ΣΙΜΙΟΤ ΣΑΤΡΟΤ ΣΟ ΠΕΛΕΝΔΡΙ ΣΗ ΚΤΠΡΟΤ ΜΕ ΕΦΑΡΜΟΓΗ ΑΤΣΟΜΑΣΟΠΟΙΗΜΕΝΟΤ

Διαβάστε περισσότερα

Exercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1.

Exercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1. Exercises 0 More exercises are available in Elementary Differential Equations. If you have a problem to solve any of them, feel free to come to office hour. Problem Find a fundamental matrix of the given

Διαβάστε περισσότερα

Concrete Mathematics Exercises from 30 September 2016

Concrete Mathematics Exercises from 30 September 2016 Concrete Mathematics Exercises from 30 September 2016 Silvio Capobianco Exercise 1.7 Let H(n) = J(n + 1) J(n). Equation (1.8) tells us that H(2n) = 2, and H(2n+1) = J(2n+2) J(2n+1) = (2J(n+1) 1) (2J(n)+1)

Διαβάστε περισσότερα

ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΒΑΛΕΝΤΙΝΑ ΠΑΠΑΔΟΠΟΥΛΟΥ Α.Μ.: 09/061. Υπεύθυνος Καθηγητής: Σάββας Μακρίδης

ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΒΑΛΕΝΤΙΝΑ ΠΑΠΑΔΟΠΟΥΛΟΥ Α.Μ.: 09/061. Υπεύθυνος Καθηγητής: Σάββας Μακρίδης Α.Τ.Ε.Ι. ΙΟΝΙΩΝ ΝΗΣΩΝ ΠΑΡΑΡΤΗΜΑ ΑΡΓΟΣΤΟΛΙΟΥ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ «Η διαμόρφωση επικοινωνιακής στρατηγικής (και των τακτικών ενεργειών) για την ενδυνάμωση της εταιρικής

Διαβάστε περισσότερα

The Simply Typed Lambda Calculus

The Simply Typed Lambda Calculus Type Inference Instead of writing type annotations, can we use an algorithm to infer what the type annotations should be? That depends on the type system. For simple type systems the answer is yes, and

Διαβάστε περισσότερα

12 2006 Journal of the Institute of Science and Engineering. Chuo University

12 2006 Journal of the Institute of Science and Engineering. Chuo University 12 2006 Journal of the Institute of Science and Engineering. Chuo University abstract In order to study the mitigation effect on urban heated environment of urban park, the microclimate observations have

Διαβάστε περισσότερα

Τμήμα Πολιτικών και Δομικών Έργων

Τμήμα Πολιτικών και Δομικών Έργων Τμήμα Πολιτικών και Δομικών Έργων Πτυχιακή Εργασία: Τοπογραφικό διάγραμμα σε ηλεκτρονική μορφή κεντρικού λιμένα Κέρκυρας και κτιρίου νέου επιβατικού σταθμού σε τρισδιάστατη μορφή και σχεδίαση με AutoCAD

Διαβάστε περισσότερα

ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΛΛΗΝΙΔΕΣ

ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΛΛΗΝΙΔΕΣ ΕΛΛΗΝΙΔΕΣ ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΚΔΟΣΗ ΤΗΣ ΣΟΡΟΠΤΙΜΙΣΤΙΚΗΣ ΕΝΩΣΗΣ ΕΛΛΑΔΟΣ - ΤΕΥΧΟΣ Νο 110 - Δ ΤΡΙΜΗΝΟ 2014 Το πρώτο βραβείο κέρδισε η Ελλάδα για την φωτογραφία Blue + Yellow = Green στον διαγωνισμό 2014 του

Διαβάστε περισσότερα

ΠΕΡΙΕΧΟΜΕΝΑ. Μάρκετινγκ Αθλητικών Τουριστικών Προορισμών 1

ΠΕΡΙΕΧΟΜΕΝΑ. Μάρκετινγκ Αθλητικών Τουριστικών Προορισμών 1 ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΙΓΑΙΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΤΗΣ ΔΙΟΙΚΗΣΗΣ ΤΜΗΜΑ ΔΙΟΙΚΗΣΗΣ ΕΠΙΧΕΙΡΗΣΕΩΝ ΔΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ «Σχεδιασμός, Διοίκηση και Πολιτική του Τουρισμού» ΜΑΡΚΕΤΙΝΓΚ ΑΘΛΗΤΙΚΩΝ ΤΟΥΡΙΣΤΙΚΩΝ

Διαβάστε περισσότερα

1 String with massive end-points

1 String with massive end-points 1 String with massive end-points Πρόβλημα 5.11:Θεωρείστε μια χορδή μήκους, τάσης T, με δύο σημειακά σωματίδια στα άκρα της, το ένα μάζας m, και το άλλο μάζας m. α) Μελετώντας την κίνηση των άκρων βρείτε

Διαβάστε περισσότερα

Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3

Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3 Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3 1 State vector space and the dual space Space of wavefunctions The space of wavefunctions is the set of all

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΓΕΩΤΕΧΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΚΑΙ ΔΙΑΧΕΙΡΙΣΗΣ ΠΕΡΙΒΑΛΛΟΝΤΟΣ. Πτυχιακή εργασία

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΓΕΩΤΕΧΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΚΑΙ ΔΙΑΧΕΙΡΙΣΗΣ ΠΕΡΙΒΑΛΛΟΝΤΟΣ. Πτυχιακή εργασία ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΓΕΩΤΕΧΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΚΑΙ ΔΙΑΧΕΙΡΙΣΗΣ ΠΕΡΙΒΑΛΛΟΝΤΟΣ Πτυχιακή εργασία ΑΝΑΛΥΣΗ ΚΟΣΤΟΥΣ-ΟΦΕΛΟΥΣ ΓΙΑ ΤΗ ΔΙΕΙΣΔΥΣΗ ΤΩΝ ΑΝΑΝΕΩΣΙΜΩΝ ΠΗΓΩΝ ΕΝΕΡΓΕΙΑΣ ΣΤΗΝ ΚΥΠΡΟ ΜΕΧΡΙ ΤΟ 2030

Διαβάστε περισσότερα

Block Ciphers Modes. Ramki Thurimella

Block Ciphers Modes. Ramki Thurimella Block Ciphers Modes Ramki Thurimella Only Encryption I.e. messages could be modified Should not assume that nonsensical messages do no harm Always must be combined with authentication 2 Padding Must be

Διαβάστε περισσότερα

Study of In-vehicle Sound Field Creation by Simultaneous Equation Method

Study of In-vehicle Sound Field Creation by Simultaneous Equation Method Study of In-vehicle Sound Field Creation by Simultaneous Equation Method Kensaku FUJII Isao WAKABAYASI Tadashi UJINO Shigeki KATO Abstract FUJITSU TEN Limited has developed "TOYOTA remium Sound System"

Διαβάστε περισσότερα

Modbus basic setup notes for IO-Link AL1xxx Master Block

Modbus basic setup notes for IO-Link AL1xxx Master Block n Modbus has four tables/registers where data is stored along with their associated addresses. We will be using the holding registers from address 40001 to 49999 that are R/W 16 bit/word. Two tables that

Διαβάστε περισσότερα

Capacitors - Capacitance, Charge and Potential Difference

Capacitors - Capacitance, Charge and Potential Difference Capacitors - Capacitance, Charge and Potential Difference Capacitors store electric charge. This ability to store electric charge is known as capacitance. A simple capacitor consists of 2 parallel metal

Διαβάστε περισσότερα

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8  questions or comments to Dan Fetter 1 Eon : Fall 8 Suggested Solutions to Problem Set 8 Email questions or omments to Dan Fetter Problem. Let X be a salar with density f(x, θ) (θx + θ) [ x ] with θ. (a) Find the most powerful level α test

Διαβάστε περισσότερα

Partial Differential Equations in Biology The boundary element method. March 26, 2013

Partial Differential Equations in Biology The boundary element method. March 26, 2013 The boundary element method March 26, 203 Introduction and notation The problem: u = f in D R d u = ϕ in Γ D u n = g on Γ N, where D = Γ D Γ N, Γ D Γ N = (possibly, Γ D = [Neumann problem] or Γ N = [Dirichlet

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΨΥΧΟΛΟΓΙΚΕΣ ΕΠΙΠΤΩΣΕΙΣ ΣΕ ΓΥΝΑΙΚΕΣ ΜΕΤΑ ΑΠΟ ΜΑΣΤΕΚΤΟΜΗ ΓΕΩΡΓΙΑ ΤΡΙΣΟΚΚΑ Λευκωσία 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ

Διαβάστε περισσότερα

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΠΟΛΥΤΕΧΝΙΚΗ ΣΧΟΛΗ ΤΜΗΜΑ ΜΗΧΑΝΙΚΩΝ Η/Υ & ΠΛΗΡΟΦΟΡΙΚΗΣ. του Γεράσιμου Τουλιάτου ΑΜ: 697

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΠΟΛΥΤΕΧΝΙΚΗ ΣΧΟΛΗ ΤΜΗΜΑ ΜΗΧΑΝΙΚΩΝ Η/Υ & ΠΛΗΡΟΦΟΡΙΚΗΣ. του Γεράσιμου Τουλιάτου ΑΜ: 697 ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΠΟΛΥΤΕΧΝΙΚΗ ΣΧΟΛΗ ΤΜΗΜΑ ΜΗΧΑΝΙΚΩΝ Η/Υ & ΠΛΗΡΟΦΟΡΙΚΗΣ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ ΣΤΑ ΠΛΑΙΣΙΑ ΤΟΥ ΜΕΤΑΠΤΥΧΙΑΚΟΥ ΔΙΠΛΩΜΑΤΟΣ ΕΙΔΙΚΕΥΣΗΣ ΕΠΙΣΤΗΜΗ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑ ΤΩΝ ΥΠΟΛΟΓΙΣΤΩΝ του Γεράσιμου Τουλιάτου

Διαβάστε περισσότερα

Πτυχιακή Εργασία. Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους

Πτυχιακή Εργασία. Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους ΑΛΕΞΑΝΔΡΕΙΟ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΣΧΟΛΗ ΤΕΧΝΟΛΟΓΙΑΣ ΤΡΟΦΙΜΩΝ ΚΑΙ ΔΙΑΤΡΟΦΗΣ ΤΜΗΜΑ ΔΙΑΤΡΟΦΗΣ ΚΑΙ ΔΙΑΙΤΟΛΟΓΙΑΣ Πτυχιακή Εργασία Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους Εκπόνηση:

Διαβάστε περισσότερα

Bayesian modeling of inseparable space-time variation in disease risk

Bayesian modeling of inseparable space-time variation in disease risk Bayesian modeling of inseparable space-time variation in disease risk Leonhard Knorr-Held Laina Mercer Department of Statistics UW May, 013 Motivation Ohio Lung Cancer Example Lung Cancer Mortality Rates

Διαβάστε περισσότερα

Terabyte Technology Ltd

Terabyte Technology Ltd Terabyte Technology Ltd is a Web and Graphic design company in Limassol with dedicated staff who will endeavour to deliver the highest quality of work in our field. We offer a range of services such as

Διαβάστε περισσότερα

DERIVATION OF MILES EQUATION FOR AN APPLIED FORCE Revision C

DERIVATION OF MILES EQUATION FOR AN APPLIED FORCE Revision C DERIVATION OF MILES EQUATION FOR AN APPLIED FORCE Revision C By Tom Irvine Email: tomirvine@aol.com August 6, 8 Introduction The obective is to derive a Miles equation which gives the overall response

Διαβάστε περισσότερα

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ιπλωµατική Εργασία του φοιτητή του τµήµατος Ηλεκτρολόγων Μηχανικών και Τεχνολογίας Ηλεκτρονικών

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟ ΓΙ ΚΟ ΕΚΠΑ ΙΔ ΕΥ Τ ΙΚΟ Ι ΔΡΥ Μ Α 'ΠΕ Ι ΡΑ ΙΑ ΤΜΗΜΑ ΚΛΩΣΤΟΥΦΑΝΤΟΥΡΓΙΑΣ ΕΙΔΙΚΟΤΗΤΑ ΒΑΦΙΚΗΣ ΠΤΥΧΙΑΚΉ ΕΡΓ ΑΣΙΑ ΤΙΤΛΟΣ ΕΥΧΡΗΣΤΙΑ ΕΞΕΙΔΙΚΕΥΜΕΝΟΥ

ΤΕΧΝΟΛΟ ΓΙ ΚΟ ΕΚΠΑ ΙΔ ΕΥ Τ ΙΚΟ Ι ΔΡΥ Μ Α 'ΠΕ Ι ΡΑ ΙΑ ΤΜΗΜΑ ΚΛΩΣΤΟΥΦΑΝΤΟΥΡΓΙΑΣ ΕΙΔΙΚΟΤΗΤΑ ΒΑΦΙΚΗΣ ΠΤΥΧΙΑΚΉ ΕΡΓ ΑΣΙΑ ΤΙΤΛΟΣ ΕΥΧΡΗΣΤΙΑ ΕΞΕΙΔΙΚΕΥΜΕΝΟΥ 515 ΤΕΧΝΟΛΟ ΓΙ ΚΟ ΕΚΠΑ ΙΔ ΕΥ Τ ΙΚΟ Ι ΔΡΥ Μ Α 'ΠΕ Ι ΡΑ ΙΑ ~ " ΤΜΗΜΑ ΚΛΩΣΤΟΥΦΑΝΤΟΥΡΓΙΑΣ ΕΙΔΙΚΟΤΗΤΑ ΒΑΦΙΚΗΣ ΠΤΥΧΙΑΚΉ ΕΡΓ ΑΣΙΑ ΤΙΤΛΟΣ ΕΥΧΡΗΣΤΙΑ ΕΞΕΙΔΙΚΕΥΜΕΝΟΥ ΠΡΟΣΤΑΤΕΥΤΙΚΟΥ ΙΜΑΤΙΣΜΟΥ ΑΡΓΥΡΟΠΟΥ ΛΟΣ ΘΕΜΙΣΤΟΚΛΗΣ

Διαβάστε περισσότερα

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΚΑΙ ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΦΙΛΟΛΟΓΙΑΣ

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΚΑΙ ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΦΙΛΟΛΟΓΙΑΣ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΚΑΙ ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΦΙΛΟΛΟΓΙΑΣ Π.Μ.Σ: «Σύγχρονες Προσεγγίσεις στη γλώσσα και στα κείμενα» ΚΑΤΕΥΘΥΝΣΗ ΓΛΩΣΣΟΛΟΓΙΑΣ ΜΕΤΑΠΤΥΧΙΑΚΗ ΔΙΑΤΡΙΒΗ Το φωνηεντικό

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ Πτυχιακή εργασία ΓΝΩΣΕΙΣ ΚΑΙ ΣΤΑΣΕΙΣ ΝΟΣΗΛΕΥΤΩΝ ΠΡΟΣ ΤΟΥΣ ΦΟΡΕΙΣ ΜΕ ΣΥΝΔΡΟΜΟ ΕΠΙΚΤΗΤΗΣ ΑΝΟΣΟΑΝΕΠΑΡΚΕΙΑΣ (AIDS) Αλέξης Δημήτρη Α.Φ.Τ: 20085675385 Λεμεσός

Διαβάστε περισσότερα

The mass and anisotropy profiles of nearby galaxy clusters from the projected phase-space density

The mass and anisotropy profiles of nearby galaxy clusters from the projected phase-space density The mass and anisotropy profiles of nearby galaxy clusters from the projected phase-space density 5..29 Radek Wojtak Nicolaus Copernicus Astronomical Center collaboration: Ewa Łokas, Gary Mamon, Stefan

Διαβάστε περισσότερα