Sir Gawain - The Noble Knight :: Sir Gawain and the Green Knight

Sir Gawain - The Noble Knight Sir Gawain is a nephew of King Arthur and the brother of Sir Gaheris and Sir Gareth. In the poem he is described by the author as "the good knight" and "most courteous" (1. 109,639). His character is shown through supernatural tests when he steps in for King Arthur and takes the challenge of the Green Knight on himself. Then his second test in the poem is to withstand the lust of the Green Knight's wife. Both of these challenges Sir Gawain passes, and gains more respect and honor than he had before. The tasks that he accomplishes prove once more the true Gawain and help the reader to understand his character more clearly. Sir Gawain is a hero in the poem, and as always, heroes have to overcome all their foes and many dangers. The same heroism and presence of supernatural forces are also found in Beowulf. Beowulf fights with dangerous enemies and creatures all around him. On his way to the Green Knight's chapel, Sir Gawain encounters many wonders and monstrous foes: "So many were the wonders he wandered among ... Now with serpents he wars, now with savage wolves ... And giants that came gibbering from the jagged steeps ... He had met with many mishaps and mortal harms" ( 2.718-725). As we see the author shows his character as a mighty warrior, maybe even with supernatural power. Yet it is not clear how he could fight with giants and was afraid at the first sight of the Green Knight. As author describes the Green Knight, "Half a giant on earth I hold him to be..." (1.140). If he is half a giant and later we see that Sir Gawain is fighting with giants, it is not clear here why everyone in Camelot at first is afraid of the Green Knight. Sir Gawain appears, as a real hero and a noble knight, almost from the very beginning of the poem when he is accepting the challenge of the Green Knight. No one is brave enough to accept the beheading game proposed by the Green Knight, and if no one of the knights will accept the challenge, then king Arthur has to accept it, so that he and his knights will not be regarded as cowards. Sir Gawain, as a noble knight who truly serves his king, takes the challenge upon himself when he says to the Arthur, " Would you grant me the grace"

Wavelets are mathematical functions

AbstractionRipples are mathematical maps that cut up informations into different frequence constituents, and so analyze each constituent with a declaration matched to its graduated table. They have advantages over traditional Fourier methods in analysing physical state of affairss where the signal contains discontinuities and crisp spikes. Ripples were developed independently in the Fieldss of mathematics, quantum natural philosophies, electrical technology, and seismal geology. Interchanges between these Fieldss during the last 10 old ages have led to many new ripple applications such as image compaction, turbulency, human vision, radio detection and ranging, and temblor anticipation. This paper introduces ripples to the interested proficient individual outside of the digital signal processing field. I describe the history of ripples get downing with Fourier, compare ripple transforms with Fourier transforms, province belongingss and other particular facets of ripples, and Coating with some interesting applications such as image compaction, musical tones, and de-noising noisy informations.1. IntroductionA ripple is a wave-like oscillation with amplitude that starts out at zero, additions, and so decreases back to nothing. It can typically be visualized as a â€Å" brief oscillation † like one might see recorded Seismograph Or bosom proctor. Generally, ripples are purposefully crafted to hold specific belongingss that make them utile for signal processing. Ripples can be combined, utilizing a â€Å" displacement, multiply and amount † technique called whirl, with parts of an unknown signal to pull out information from the unknown signal. Wavelets provide an alternate attack to traditional signal processing techniques such as Fourier analysis for interrupting a signal up into its component parts. The drive drift behind ripple analysis is their belongings of being localised in clip ( infinite ) every bit good as graduated table ( frequence ) . This provides a time-scale map of a signal, enabling the extraction of characteristics that vary in clip. This makes wavelets an ideal tool for analyzing signals of a transient or non-stationary nature.2. HistoryThe development of ripples can be linked to several separate trains of idea, get downing with Haar ‘s work in the early twentieth century. Note worthy parts to wavelet theory can be attributed to Zweig ‘s find of the uninterrupted ripple transform in 1975 ( originally called the cochlear transform and discovered while analyzing the reaction of the ear to sound ) , Pierre Goupillaud, Grossmann and Morlet ‘s preparation of what is now known as the CWT ( 1982 ) , Jan-Olov Str & A ; ouml ; mberg ‘s early work on distinct ripples ( 1983 ) , Daubechies ‘ extraneous ripples with compact support ( 1988 ) , Mallat ‘s multiresolution model ( 1989 ) , Nathalie Delprat ‘s time-frequency reading of the CWT ( 1991 ) , Newland ‘s Harmonic ripple transform ( 1993 ) and many others since.First ripple ( Haar ripple ) by Alfred Haar ( 1909 )Since the 1970s: George Zweig, Jean Morlet, Alex GrossmannSince the 1980s: Yves Meyer, St & A ; eacute ; phane Mallat, Ingrid Daubechies, Ronald Coifman, Victor Wickerhauser3. WAVELET THEORYWavelet theory is applicable to several topics. All ripple transforms may b e considered signifiers of time-frequency representation for continuous-time ( parallel ) signals and so are related to harmonic analysis. Almost all practically utile distinct ripple transforms use discrete-time filter Bankss. These filter Bankss are called the ripple and scaling coefficients in ripples nomenclature. These filter Bankss may incorporate either finite impulse response ( FIR ) or infinite impulse response ( IIR ) filters. The ripples organizing a uninterrupted ripple transform ( CWT ) are capable to the uncertainness rule of Fourier analysis respective trying theory: Given a signal with some event in it, one can non delegate at the same time an exact clip and frequence response graduated table to that event. The merchandise of the uncertainnesss of clip and frequence response graduated table has a lower edge. Therefore, in the scale gm of a uninterrupted ripple transform of this signal, such an event marks an full part in the time-scale plane, alternatively of merely one point. Besides, distinct ripple bases may be considered in the context of other signifiers of the uncertainness rule. Wavelet transforms are loosely divided into three categories: uninterrupted, distinct and multiresolution-based. Above shown diagram shows all CWT ( Continuous Wavelet ) , DWT ( Discrete Wavelet ) . These all varies with the clip and degree and all graphs obtained are above shown.4. WAVELET TRANSFORMSThere are a big figure of ripple transforms each suited for different applications. For a full list see list of wavelet-related transforms but the common 1s are listed below:Continuous ripple transform ( CWT )Discrete ripple transform ( DWT )Fast ripple transform ( FWT )Raising strategyWavelet package decomposition ( WPD )Stationary ripple transform ( SWT )5. WAVELET PACKETSThe ripple transform is really a subset of a far more various transform, the ripple package transform. Wavelet packages are peculiar additive combinations of ripples. They form bases which retain many of the perpendicularity, smoothness, and localisation belongingss of their parent ripples. The coefficients in the additive combinations are computed by a recursive algorithm doing each freshly computed ripple package coefficient s equence the root of its ain analysis tree.6. WAVELETS IN MATLABWavelet Toolbox package extends the MATLAB proficient calculating environment with graphical tools and command-line maps for developing wavelet-based algorithms for the analysis, synthesis, denoising, and compaction of signals and images. Wavelet analysis provides more precise information about signal informations than other signal analysis techniques, such as Fourier. The Wavelet Toolbox supports the synergistic geographic expedition of ripple belongingss and applications. It is utile for address and sound processing, image and picture processing, biomedical imagination, and 1-D and 2-D applications in communications and geophysical sciences.7. WAVELETS VS FOURIER TRANSFORMEach and every thing in this universe comparable to it has some similarities and unsimilarities with that same is the instance with the ripples and Fourier transform. Ripples can be compared with the Fourier transform on the footing of their similarit ies and unsimilarities which are explained as follows. Assorted sorts of similarities and unsimilarities of ripples and Fourier transform are as follows.7.1 SIMILARITIES BETWEEN FOURIER AND WAVELET TRANSFORMSThe fast Fourier transform ( FFT ) and the distinct ripple transform ( DWT ) are both additive operations that generate a information construction that containssegments of assorted lengths, normally make fulling and transforming it into a different informations vector of length. The mathematical belongingss of the matrices involved in the transforms are similar as good. The reverse transform matrix for both the FFT and the DWT is the transpose of the original. As a consequence, both transforms can be viewed as a rotary motion in map infinite to a different sphere. For the FFT, this new sphere contains footing maps that are sines and cosines. For the ripple transform, this new sphere contains more complicated footing maps called ripples, female parent ripples, or analysing ripple s. Both transforms have another similarity. The basic maps are localized in frequence, doing mathematical tools such as power spectra ( how much power is contained in a frequence interval ) and scale gms ( to be defined subsequently ) utile at picking out frequences and ciphering power distributions.7.2 DISSIMILARITIES BETWEEN FOURIER AND WAVELET TRANSFORMSThe most interesting unsimilarity between these two sorts of transforms is that single ripple maps arelocalized in space.Fourier sine and cosine maps are non. This localisation characteristic, along with ripples ‘ localisation of frequence, makes many maps and operators utilizing ripples â€Å" thin † when transformed into the ripple sphere. This spareness, in bend, consequences in a figure of utile applications such as informations compaction, observing characteristics in images, and taking noise from clip series. One manner to see the time-frequency declaration differences between the Fourier transform and the rippl e transform is to look at the footing map coverage of the time-frequency plane. The square moving ridge window truncates the sine or cosine map to suit a window of a peculiar breadth. Because a individual window is used for all frequences in the WFT, the declaration of the analysis is the same at all locations in the time-frequency plane.8. WAVELET APPLICATIONSThere are assorted sorts of applications in the field of ripples which are as follows can be explained as followsComputer and Human VisionFBI Fingerprint CompressionDenoising Noisy DataMusical Tones8.1 COMPUTER AND HUMAN VISIONIn the early 1980s, David Marr began work at MIT ‘s Artificial Intelligence Laboratory on unreal vision for automatons. He is an expert on the human ocular system and his end was to larn why the first efforts to build a automaton capable of understanding its milieus were unsuccessful. Marr believed that it was of import to set up scientific foundations for vision, and that while making so ; one mus t restrict the range of probe by excepting everything that depends on preparation, civilization, and so on, and concentrate on the mechanical or nonvoluntary facets of vision. This low-level vision is the portion that enables us to animate the 3-dimensional organisation of the physical universe around us from the excitements that stimulate the retina. He so developed working algorithmic solutions to reply each of these inquiries. Marr ‘s theory was that image processing in the human ocular system has a complicated hierarchal construction that involves several beds of processing. At each treating degree, the retinal system provides a ocular representation that scales increasingly in a geometrical mode. His statements hinged on the sensing of strength alterations. He theorized that strength alterations occur at different graduated tables in an image, so that their optimum sensing requires the usage of operators of different sizes. He besides theorized that sudden strength altera tions produce a extremum or trough in the first derived function of the image. These two hypotheses require that a vision filter have two features: it should be a differential operator, and it should be capable of being tuned to move at any coveted graduated table. Marr ‘s operator was a ripple that today is referred to as a â€Å" Marr ripple. †8.2 FBI FINGERPRINT COMPRESSIONBetween 1924 and today, the US Federal Bureau of Investigation has collected about 30 million sets of fingerprints. The archive consists chiefly of inked feelings on paper cards. Facsimile scans of the feelings are distributed among jurisprudence enforcement bureaus, but the digitisation quality is frequently low. Because a figure of legal powers are experimenting with digital storage of the prints, mutual exclusivenesss between informations formats have late become a job. This job led to a demand in the condemnable justness community for a digitisation and a compaction criterion. In 1993, the FBI ‘s Criminal Justice Information Services Division developed criterions for fingerprint digitisation and compaction in cooperation with the National Institute of Standards and Technology, Los Alamos National Laboratory, commercial sellers, and condemnable justness communities. Let ‘s set the informations storage job in position. Fingerprint images are digitized at a declaration of 500 pels per inch with 256 degrees of gray-scale information per pel. A individual fingerprint is about 700,000 pels and demands about 0.6 Mbytes to hive away. A brace of custodies, so, requires about 6 Mbytes of storage. So digitising the FBI ‘s current archive would ensue in approximately 200 TBs of informations. ( Notice that at today ‘s monetary values of about $ 900 per Gbyte for hard-disk storage, the cost of hive awaying these uncompressed images would be about 200 million dollars. ) Obviously, informations compaction is of import to convey these Numberss down.8.3 DENOISING NO ISY DATAIn diverse Fieldss from planetal scientific discipline to molecular spectrometry, scientists are faced with the job of retrieving a true signal from uncomplete, indirect or noisy informations. Can wavelets assist work out this job? The reply is surely â€Å" yes, † through a technique called ripple shrinking and thresholding methods that David Donoho has worked on for several old ages. The technique works in the undermentioned manner. When you decompose a information set utilizing ripples, you use filters that act as averaging filters and others that produce inside informations. Some of the ensuing ripple coefficients correspond to inside informations in the information set. If the inside informations are little, they might be omitted without well impacting the chief characteristics of the information set. The thought of thresholding, so, is to put to zero all coefficients that are less than a peculiar threshold. These coefficients are used in an reverse ripple transm utation to retrace the information set. Figure 6 is a brace of â€Å" before † and â€Å" after † illustrations of a atomic magnetic resonance ( NMR ) signal. The signal is transformed, threshold and inverse-transformed. The technique is a important measure frontward in managing noisy informations because the denoising is carried out without smoothing out the crisp constructions. The consequence is cleaned-up signal that still shows of import inside informations. Fig.8.3.1 displays an image created by Donoho of Ingrid Daubechies ( an active research worker in ripple analysis and the discoverer of smooth orthonormal ripples of compact support ) , and so several close-up images of her oculus: an original, an image with noise added, and eventually denoised image. To denoise the image, Donoho:transformed the image to the ripple sphere utilizing Coiflets with three disappearing minutes,applied a threshold at two standard divergences, andInverse-transformed the image to the signal sphere.8.4 MUSICAL TONESVictor Wickerhauser has suggested that ripple packages could be utile in sound synthesis. His thought is that a individual ripple package generator could replace a big figure of oscillators. Through experimentation, a instrumentalist could find combinations of moving ridge packages that produce particularly interesting sounds. Wickerhauser feels that sound synthesis is a natural usage of ripples. Say one wishes to come close the sound of a musical instrument. A sample of the notes produced by the instrument could be decomposed into its ripple package coefficients. Reproducing the note would so necessitate recharging those coefficients into a ripple package generator and playing back the consequence. Transient features such as onslaught and decay- approximately, the strength fluctuations of how the sound starts and ends- could be controlled individually ( for illustration, with envelope generators ) , or by utilizing longer wave packages and encoding those belongingss every bit good into each note. Any of these procedures could be controlled in existent clip, for illustration, by a keyboard. Notice that the musical instrument could merely every bit good be a human voice, and the notes words or phonemes. A wavelet-packet-based music synthesist could hive away many complex sounds expeditiously becauseripple package coefficients, like ripple coefficients, are largely really little for digital samples of smooth signals ; andDiscarding coefficients below a predetermined cutoff introduces merely little mistakes when we are compacting the information for smooth signals.Similarly, a wave packet-based address synthesist could be used to retrace extremely tight address signals. Figure 8.4.1 illustrates a ripple musical tone or toneburst.9. ADVANTAGES OF WAVELET TRANSFORMATIONAdvantages of ripple transmutation are as follows which are discussed below.Space and Time Efficiency ( Low Complexity of DWT ) .Generality & A ; Adaptability ( Different Basis and Wavelet Functions ) .Multiresolution Properties ( Hierarchical Representation & A ; Manipulation ) .Adaptability of the Transformation ( Different Basis Functions let different Properties of the Transformation )Transformation is Hierarchical ( Multiresolution – Properties )Transformation is Loss-FreeEfficiency of the Transformation ( Linear Time and Space Complexity for Orthogonal Wavelets )Generalization of the Transformation ( Generalization of other Transformations )CONCLUSION AND FUTURE SCOPEMost of basic ripple theory has been done. The mathematics has been worked out in tormenting item and ripple theory is now in the polish phase. The refinement phase involves generalisations and extensions of ripples, such as widening ripple package techniques. The hereafter of ripples lies in the as-yet chartless district ofapplications.Wavelet techniques have non been exhaustively worked out in applications such as practical information analysis, where for illustration discretely sampled time-series informations might necessitate to be analyzed. Such applications offer exciting avenues for geographic expedition. Basically after working on this term paper we came to cognize about the construct of the ripples its relation wi th the Fourier transform its advantages in shacking universe.Mentionswww.yahoo.com ( a truly friendly usher to ripples ) .www.google.com ( ripples ppt. ) .www.wikipedia.com ( ripples ) .www.google.com ( Seminar Report on ripples by ROBI POLIKAR )www.google.com ( applications of ripples ) .

Single Parent Families Are A Better Environment For Children

Statistics show that single parent families tend to be more positive than two-parent families because children are more likely to experience fewer problems in a single parent family. Single parent families tend to adopt children from third-world countries, where two-parent families are more likely to adopt from within their own country. Children from other countries normally have attachment issues due to the poverty and culture. By choosing to not adopt children from other countries, those children may suffer even more from poverty and cultural discrimination. Single parent family homes are a better environment for children due to the time, love, and nurture those individuals are able to give. One-parent families who adopt take more†¦show more content†¦In accordance to the article, â€Å"Adoption†, â€Å"many adoptions occur partly out of a need to find permanent, loving families for children whose parents cannot raise them because of factors such as teen pregnancy or low income.† Other parents choose to become adoptive parents instead being birth parents. Research shows that most adoptions work out well, if not better, and that most adopted children develop strong and healthy. Also, many single parents adopt children because they may not be able to conceive themselves. It is important for single parents to know that they aren’t any less of a parent than one with a spouse. Single parents should be encouraged and shown support rather than being discouraged. Single parents are more likely than a two parent family to adopt, mostly because single parents are not able to have a child without a partner and single parents are normally not looking for a partner (Duin). Single Parent families should not feel the pressure of not being good enough, because any family that does what is best for their child is in the right. Adoptive mothers explain that having a male role model in their child’s life is still important. A grandfather, fr iend, or even a god father or relative in a child’s life can help to provide a male role model. Some people consider adoption to be a better way of providing the child with a better life, but it is so much more than that. Not only is the child being placed in a loving home, but that child is able toShow MoreRelatedEssay on One Parent Family vs Two Parent Family901 Words   |  4 Pagesbelieve that children should be raised in a stable nurturing home by either both parents, mother and father or by a single parent. I feel that if it is a loving home where each parent is taking part in raising the child it is beneficial to the child. On the other hand if both parents argue all the time than it is not beneficial for the child’s upbringing. In having just one custodial parent the child is better off because the one parent will be able to provide a better stable social environment. Few parentsRead MoreAdopting A Single Parent Family978 Words   |  4 Pagesthere are many c hildren whose parents have died or cannot raise them as well as abandoned infants. In order to solve this inevitable situation, some couples and a single man or woman who have the ability to raise the kids will apply for the qualifications to adopt them. However, some people pose a question that should single people be able to adopt children as easily as couples. With a lot of attention, this topic has become a very intriguing argument. Nowadays, having two parents is not any moreRead MoreAdvantages and Disadvantages of Single Parent Homes1394 Words   |  6 Pagesof single parent homes. 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Though many struggle, they can not all fit into one category as to why they are poor. According to Daniel Patrick Moynihan’s report, â€Å"The Negro Family: The Case for National Action,† blacks are living in poverty and barely digging their way out. There is a struggle in every race and poverty is certainly not just