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Paper 26 : The application of Clifford algebra to calculations of multicomponent chemical composition . Dr John P. Fletcher , Chemical Engineering and Applied Chemistry , School of Engineering and Applied Science , Aston University , Aston Triangle , Birmingham B4 7 ET , U. K. Email : J. P. F letcher @ aston . a c . u k Abstract In a mixture of chemical compounds , the significant variable is often the proportion of molecules , normally expressed as a mole fraction in a particular sample . The fractions are constrained to add to one , so any change such as the addition of some more of any chemical component causes all of the mole fractions change in a nonlinear way . Lasenby et al [ 1 ] have applied Clifford Algebra to the problem of projection and shown that problems can be made linear and results obtained . In this paper a similar approach is used to show that some nonlinear problems , such as conversion between molar and mass basis , become linear when projected into a space of increased dimension . When this is done using the V product defined by Miralles et al this [ 2 ] can be done using a Clifford algebra with all positive signature . Examples are given of the results of the formulation . 1 Introduction Calculation of multicomponent chemical composition is necessary in many calculations in chemical engineering and chemistry . It is complicated by the fact the some of the calculations are on the basis of the mass of each component present , and others on the basis of the relative number of molecules . Different molecules differ in relative mass , expressed as the relative molecular mass , or molecular weight . The proportions of a mixture are often expressed as a set of fractions which are constrained to add to one . Both the mass fractions and the mole fractions are nonlinear functions of the total number of molecules of each component present . Conversion between them is a nonlinear operation . These calculations are often necessary in phase equilibrium calculations , where it is desired to calculate the compositions of a vapour phase and a liquid phase , or two liquid phases , which are in equilibrium . In general the two phases will be of different chemical composition . The calculation is often made difficult by problems of modelling the nonlinear behaviour of the properties of the chemical components . Such calculations are a vital feature of chemical engineering design , There are advantages to be gained if the basis part of the calculation can be made linear . This paper shows that the calculations needed for phase equilibrium calculations have some similarity in form to the projection calculations discussed by Lasenby et al [ 1 ] . They have shown that some nonlinear problems are linear when projected to an extra dimension using a Clifford algebra . In this paper consideration is given to applying these methods to the formulation of the algebra of multicomponent chemical composition using the same techniques . One issue in these calculaltions is the appropriate choice of the Clifford algebra to use . In this , use has also been made of the methods of Mirrales et al [ 2 ] who define a V product which is effectively a means of using one basis on Clifford objects defined in a different basis . This opens up the possibility of carrying out the projection calculations of Lasenby et al [ 1 ] while using a Clifford basis with all positive signature . These ideas have been applied to the calculation of the transformation from the mass basis to the mole basis , with particular emphasis on the formulation of phase equilibrium calculations . 2 Projection Lasenby et al [ 1 ] describe the use of a projective space for representation of invariants in computer vision . They introduce a vector X in a Clifford algebra of signature ( 1 , 3 ) with basis vectors with the signatures Taking the product of X with the basis vector 4 gives an expression in terms of a three dimensional vector x where x is defined in terms of the bivectors of the original algebra . This author considered this representation as possible way to represent the multicompent chemical composition , and has adapted it for the modelling of multicomponent chemical composition . 3 The V product Mirralles et al [ 2 ] discuss the algebra of signature change among Clifford algebras of the same total dimension . The example which is discussed in their paper . For the case of the Clifford ( 4 ) algebra they take two objects of any grade A and B with Clifford product AB . They define a Vee or V product such that A B is equivalent to the multiplication of objects defined in Clifford ( 1 , 3 ) . For two vector objects u and v in Clifford ( 4 , 0 ) the definition is where e 0 is chosen from among the basis vectors of the algebra . For theis definition the symmetric part is given by in comparision with the Clifford product They show that the unsymmetric part is the same as for the Clifford product . The definition extends to the grades of the multigrade objects as follows . This author considered this as an alternative for the representation of the multicompent chemical composition , and has applied it for the modelling of multicomponent chemical composition . 4 Multicomponent chemical composition 4.1 Projection Model The analysis of the multicomponent chemical composition follows the algebra of Lasneby et al [ 1 ] , using the Clifford ( 3 , 1 ) algebra rather than the Clifford ( 1 , 3 ) . Suppose that a closed chemical system contains a mass M i of each of 3 chemical components . Define an object M in a Clifford ( 3 , 1 ) vector space with orthogonal basis vectors i as follows The system is defined such that This will be referred to as the full system . A reduced coordinate system can be constructed by taking the geometric product of an object in the system with 0 . This will be called the reduced system . If the bivectors in this relation are taken as defining a three dimensional Clifford ( 3 , 0 ) algebra Then an object m in this new space is given by where are the mass fractions for the system . An object D in the full system is defined as follows . Then the dot product of D with M gives which represents the mass balance and the relation that the x i sum to unity . The advantage of this procedure is that M is linear in the components whereas m is nonlinear , but can be easily constructed from it . Thus 4.2 Conversion between mass and molar basis . To scale to units proportional to the numbers of molecules , using the relative molecular mass r i of each component , then a new vector N in the full system can be constructed as follows , using the inverses of the relative molecular masses then if M 0 = M 1 + M 2 + M 3 This is a linear operation , which in matrix terms can be written , with M 0 = M 1 + M 2 + M 3 , as and defined as The molar fraction vector n can then be found from N using the same method as before . where with are the molar fractions in the system . This can be expressed in terms of N i , the components of N , as This conversion is quite general , and the reverse operation can be written as If the two matrices are combined , the result is a matrix which transforms an object such as M into itself . This is defined to be I. and clearly 4.3 Vapour-Liquid Equilibrium The usual chemical engineering formulation of vapour liquid equilibrium is for each of the components , where x i are the liquid molar fractions and y i are the vapour molar fractions . K i is called the equilibrium constant and is in general a function of temperature , pressure and all the molar fractions in both phases . Defining objects for the two phases as previously , where X i and Y i are on a mloar basis , and then converting the equilibrium expression to this basis results in the expression Summing over all the components which implies that the K i are not independent . It follows that and This means that the Y i are in the same proportions as the K i X i and the following calculation yields some linear multiple of Y. so that , using the previous notation , 4.4 Flash calculation One application of these equations is to a flash calculation where a fixed amount of material is available , which will be distributed between the two phases . If that material is designated by Z such that then The matrix form of this is This is invertible as where This provides a formulation of the flash calculation which can be used for an iterative solution given models for the dependence of K i on the variables . 4.5 Chemical Reaction If a chemical reaction occurs transforming a vector A in the full molar system to a vector B then where Q is the effect of the reaction . If on a molar basis Q 1 moles of component 1 become Q 2 moles of component 2 then so that 4.6 Volume and thermodynamic functions Functions whose value is proportional to the amount of material , termed extensive functions , can be expressed in terms of the contribution of each component . For example the volume V of a liquid can be expressed in terms of the molar numbers N i of a vector N and the partial molar volumes V i as This can be represented in the full system as and the value of the property can be extracted as This can be extended to intensive properties such as density where and expressing with the value of the property given by 5 Vee product model The development of this model is very similar to the previous model , using a different Clifford basis . Suppose that a closed chemical system contains a mass M i of each of the components . Define an object M in a Clifford ( 4 , 0 ) vector space with orthogonal basis vectors i as follows The system is defined such that with The bivectors in this relation are taken as defining a three dimensional Clifford ( 0 , 3 ) algebra Then an object m in this new space is given by where are the mass fractions for the system as before . If an object D in the full system is defined as follows . then the symmetric part of the V product of D with M choosing 0 as the special basis vector gives which is the mass balance equation as in the projection model . Thus the alternative of the Clifford ( 4 , 0 ) basis can be used and still have the same relationship among the components . One difference is that the reduced basis now has an all negative signature . That is not a problem because it is the sum of the mass fractions which is significant in calculation and not their vector norm . The only calculation which depends upon the signature of the algebra is the extraction of an extensive property which now becomes 6 Generalisation The examples have been constructed using three chemical components . The method can be generalised to more components by increasing the number of basis vectors . No calculation makes use of any property of the Clifford Algebra which changes as the dimension increases . 7 Conclusions The projection method can be used to formulate the equations of multicomponent chemical composition , including phase equilibrium and chemical reaction , and both extensive and intensive properties which can be calculated from contributions from each component . This can be done either using the approach of Lasenby et al [ 1 ] or that of Miralles et al [ 2 ] . 8 References [ 1 ] J. Lasenby , E. Bayro-Corrochano , A. N. Lasenby and G. Sommer . " Geometric Algebra : a Framework for Computing Invariants in Computer Vision " Proceedings of the International Conference on Pattern Recognition ( ICPR ' 96 ) , Vienna . [ 2 ] D. Mirrales , J. M. P arra , and J. Vaz , " Signature Change and Clifford Algebras " , International Journal of Theoretical Physics , vol. 40 ( 1 ) pp. 227-238 , ( 2001 ) John Fletcher May 2001 , updated March 2003 . Aston University , Aston Triangle , Birmingham B4 7ET , United Kingdom Telephone : +44 ( 0 ) 121 204 3000 Fax : +44 ( 0 ) 121 333 6350 Copyright © 10.25.06 Aston University


DES BUYS A NEW SHED " I 've come to a major decision , " announced Des one morning in the cafe . " I ca n't put it off any longer . " " Oh thank goodness , " said Mick . " Yes , it 's been something of an embarrassment for ages , " said Des . " So the time has now come to splash out and buy a brand new one ! " " You 're joking ?! " exclaimed Clive . " Have you finally come to your senses ?! " " Yep , " said Des . " I 'm going to get a really nifty top-of-the-range model ! " " Fantastic ! " said Clive . " Maybe this will mean house prices will finally be on the rise round here ! " " Why are you always so bothered about house prices ? " said Mick . " Because when my house finally reaches a reasonable price I 'll be able to sell it and leave you bunch of muppets behind forever !! " said Clive . Just then Mike the Manic Mechanic walked in . " Hey Mike , great news , Des is finally going to buy a new car ! " said Clive . " Brilliant Des , about time too ! " said Mike . " Now I 've got some fantastic deals on at the moment , how do you fancy a brand new used 1983 Fiesta XR2 with a mere 4000 totally genuine honest guv miles on the clock and a sunroof ! " Just then Mrs Greasy came out with their lunch . " Oh my goodness , look at the time ! " said Clive suddenly . " I 'm due at the squash club !! " He got up and dashed out of the café . " No , no , Mike , I 'm not buying a new car !! " said Des . " Clive misunderstood what I was talking about !! What would I want to buy a new car for , I could never sell my beloved Fiat 126 !! " " Darn , " said Mike . " I was talking about my snowdome ! " said Des . " Look at it , it does n't even work any more ! " He took his snowdome out of his pocket , shook it , and nothing happened . " Well it is summer , you do n't get snow in the summer , " pointed out Mike . " Oh yes , and I 'm getting a new shed as well , " said Des . " But first I must clear out the old one . " After having to endure Mrs Greasy's lunch , Des went back to his house and down his garden to begin clearing out his shed . Mick came along as well since he evidently had nothing better to do . " Good grief , you need a new shed more than you need a new snowdome ! " said Mick . They looked at the shed – the walls were all leaning inwards , there was no glass in the window frames and there were numerous holes in the canvas roof . " Okay , you open the door , " said Des . " Why me ? " said Mick . " Well ... I have n't been in there for about ten years , " said Des . " I 'm afraid that if I open the door the whole thing might just collapse ! " " Well I 'm not opening it !! " said Mick . " Do you think I 'm mad ?! " " Let 's find someone else to do it then , " said Des . " Like Clive ! " " But he 's gone down the squash club ! " said Mick . " No he 's not , he 's over there in his garden ! " said Des . Clive was sitting on his garden , sipping an ice cold drink , as it was quite a warm day . Des and Mick walked across to the fence and peered over at him . " What do you want ?! " snapped Clive . " Ca n't you see I 'm busy !! " " You 're supposed to be at the squash club ! " said Mick . " I am ! The orange squash club ! Membership of one ! And I 'd like it to stay that way !! " " We were just wondering if you could come and open my shed door , " said Des . " Are you mad , I 'm not going in that rickety old thing ! " said Clive . " And that 's final ! " " Um ... I 've got some rare vinyl Bee Gees albums in there ! " said Des . Immediately Clive put his drink down , walked over the fence , straight across Des's garden and opened the shed door . He walked inside the shed and started searching for the Bee Gees records . " Oh , " said Des , slightly disappointed to see that the shed had not collapsed around Clive's ears . " See Mick , perfectly safe ! " " Where are these records then ?! " said Clive . " Umm , well actually I have n't really ... " said Des . " Oh here they are ! " said Clive , picking up a box in the corner . " Cor , there 's some classic stuff here ! Thanks Des !! " Clive walked out of the shed carrying the box of Bee Gees records while Des looked on in amazement . " You 're not a secret Bee Gees fan are you ?! " said Mick . " No I 'm not , it 's so long since I 've been in that shed I 've no idea what 's in there ! " said Des . " Anyway , Clive has proved it 's perfectly safe to go in there , come on ! " " Hmmm , I think I 'll just hang around outside , it 's quite a nice day today ! " said Mick . " Suit yourself , " said Des . He went inside the shed and started searching through piles of stuff . Before long the contents of the shed were piling up outside . Other than the usual garden equipment , they included a moose's head , an old gramophone , a model skeleton , a birdcage , a trilby , ten garden gnomes , an old cooker , a rocking horse , some flying ducks , and a massive poster of Bob Carolgees and Spit the Dog . As Mick looked on , he kept expecting the shed to come crashing down at any minute , but remarkably it still managed to stay up . After an hour or so , Des had finally finished clearing it out , and he and Mick looked round at all the junk that had taken over Des's garden . " Did all that stuff really fit inside that small shed ?! " said Mick . " Certainly did ! " said Des . The shed now looked even more precarious now everything had been cleared out . Mick peered inside and saw there was still one thing left inside - a rake that was leaning against the wall . " Oi Des , that 's my rake , I always wondered what happened to that !! " exclaimed Mick . " Is it ? " said Des . " Oh no , I would n't ... " Mick strode inside and claimed his rake . Immediately the wall collapsed inwards . Mick tried to dart out the way , but then the other walls began to fall inwards . Mick went through an empty window frame , and then right through the canvas roof as it crashed down . He was left standing there with his rake , covered in dust , in the middle of the remains of the shed . " Oh Mick , that rake was the only thing holding the shed up ! " said Des , who was stood well back . " Was it really ?!?! " exclaimed Mick . " At least it saves taking it apart ! " said Des . " Oi you lot , keep the noise down , I 've trying to enjoy a peaceful sit in the garden !! " shouted Clive . " Hey Clive , you do n't want a moose's head , do you ? " said Des . " Oh , you 've got one already ! Ha !! " Clive snarled . " Seriously though , is there anything you do want ? " said Des . " Poster of Bob Carolgees ? I can see you 're tempted ! " " No ! " said Clive . " What about you , Mick ? " said Des . " I do n't want a poster of him either ! " said Clive . " That 's just a pile of ridiculous old junk ! " said Mick , who was busy wiping the dust off himself . " Why do n't you just get rid of it all !! " " Naaah ! " said Des . " Might be worth something one day ! " Des cleared the bits of the shed out of the way . Next came the big purchase – a brand new shed ! But first of all Des had to go and quickly buy his new snowdome . Then he went to the garden centre , with Mick tagging along . " What a vast selection of sheds on offer ! " said Mick , looking at the vast selection of sheds on offer . They were located outside the garden centre itself , in an area adjacent to the car park . " I 'll have that one , " said Des , pointing at the first shed he saw . " Are n't you going to have a look around ? " said Mick . " See what else is on offer ? Perhaps buy a copy of ' Which Shed ' ? That 's what I did ! " " You would , " said Des . " Look at them , they 're all the same ! I 'll have this one , looks good enough to me ! " Des handed over the cash to the sales assistant , and the shed was now in Des's possession . " Now the only problem is ... " said Des . " How am I going to get it home ? " He tried lifting it , without much success , obviously . " Could n't you just get the garden centre to deliver it ? " said Mick . Just then Mike the Manic Mechanic came up to them , carrying a large garden gnome . " Oh hi there Des and Mick , " said Mike . They looked at his gnome . " Oh no , it 's not for me , it 's for my Aunty Mavis's birthday . I do n't like her , so I thought she 'd hate this ! Is that your new shed ? " Des stared hard at the shed for several seconds . " You know what Mike , I think it is ! " said Des . " Thanks for pointing it out ! " " No problem , " said Mike . " Actually , I have got a bit of a problem , " said Des . " I know that , " said Mike . " How am I going to get this shed home ? " said Des . " Could you perhaps ... " " The answer is obvious !! " exclaimed Mike . " Bring round your car ! " Des drove round his car from the car park . When he got out , Mike started taking off the wheels . " Mike , what are you doing ?! " exclaimed Des . " Simple ! " said Mike . " I 'm going to transfer the wheels , engine , chassis and steering column from your car onto this shed . Then you can drive it home !! " " Riiiight , " said Mick . Des was a bit unsure about this idea , but since Mike had already started the process he did n't like to interrupt . " Erm Mike , this wo n't take long , will it ? " said Des . " Naaah , three or four hours should do it !! " said Mike . " Okay ... " said Des . " And then when we get it home , I 'll transfer everything back onto your car and it 'll be as good as new ! " said Mike . " Unless you 'd like to pop round to my garage and choose a classy little number from my selection of hot Fords ! " " No thanks , " said Des . They watched as Mike busily took the body of Des's Fiat 126 away from the chassis . " I ca n't help thinking there must have been a simpler way to get that shed home , " sighed Des . " Like asking the garden centre to deliver it ? " said Mick . " Or asking Mike to deliver it on a pick-up or something ? " " What 's that , Mick ? " said Mike . " Oh nothing , nothing , " said Mick . After about five hours Mike had finally finished . The shed now had wheels , lights , an engine , a chassis , a steering wheel , bumpers and number plates , all donated by Des's Fiat 126 . As the floorpan was taken from the Fiat , the engine had to be placed at the rear of the shed . At the front Mike had removed the door from its hinges , and plonked a seat there . Bolted onto the front was the steering column , pedals and a load of wires . " Whaddya think !! " said Mike . " Pretty nifty , eh ! " " Super , " mumbled Mick . " Just one thing , " said Des . " How am I going to get my car home ? " He pointed at the shell of his Fiat . " Umm ... " said Mike . " Ca n't you ask the garden centre to deliver it ? " " Too late , the garden centre 's closed ! " exclaimed Mick . " It 's starting to get dark ! " " I know what to do ! " said Mike . " I reckon your car 's just small enough ! " Mike set about removing one of the side walls of the shed . " Good grief , " sighed Mick . Mike , Des and Mick heaved the shell of the car inside the shed , and Mike replaced the wall . " There ! " said Mike . " Now all you have to do is drive it home ! " " Thank goodness it 's getting dark , hopefully no one will see me ! " said Des . He carefully went and sat down on the seat at the front of the shed . " It should drive just like your Fiat ! " said Mike . " In other words , terribly ! " " Are you sure it 's road legal ? " said Des . " Course it is , you 've got lights , seat belt , number plates , tax disc ! " said Mike . " What more do you want , an MOT document ?! " " Umm ... " said Des . " Just start the engine !! " exclaimed Mike . Des did so , and the familiar rumble of the Fiat 126 engine was heard . " I 'll give you a lift home , Mick , " said Mike . " Thanks Mike , I would n't be seen dead in a thing like that ! " said Mick . " Too right , nor me !! " said Mike . They watched as Des put his foot on the accelerator pedal , and the shed began to trundle through the car park . " ' Ere Mike , is this as fast as it will go ?! " shouted Des . Because the shell of his Fiat 126 was weighing the shed down , Des was finding that the engine barely had enough power to propel the shed along at any great speed . " Sorry Des , not a lot I can do about that !! " shouted back Mike . " I 'll see you in the morning to put your car back together again !! " Mick and Mike whizzed off home in Mike's Cortina , while Des was left trailing in his motorised shed . " He could at least have put a turbocharger in , " grumbled Des . Des trundled along the road at a speed that would make a milk float look fast . " I hope PC Plod's in bed ! " thought Des . " I 'm not sure if this is exactly legal ! " Unfortunately he was n't . Des soon noticed Plod riding behind him on his bike . It did n't take long for Plod to catch him up . " Excuse me sir , may I have a quick word with you ? " said Plod . " Oh no come on , no way was I exceeding the speed limit this time ! " exclaimed Des . " Is this your , erm , vehicle , sir ? " asked Plod . " Well ... yeeees ... but ... " said Des . " Have you a vehicle registration certificate ? " said Plod . " It does n't exactly look roadworthy to me . " " Oh yes it is , it 's passed its MOT and everything ! " said Des . " Can I see your vehicle registration certificate please ? " asked Plod . " Err ... tell you what , I have n't got it on me at the moment , so come round my house tomorrow and I 'll show it to you then ! " " Right you are , sir , " said Plod . " I 'll see you tomorrow . " He raced off on his bicycle to continue fighting crime . Des decided he would deal with the problem in the morning . When he finally arrived home , as it was now getting very late , he decided to leave the shed parked in the front drive overnight , and hoped no one would steal it ( yeah right , as if anyone 's going to steal a motorised shed ) . The next morning , when Des got up , he looked out of the window and was surprised to see Clive looking at his new shed , weeping . He went outside to see him . " Clive , what 's the matter ? " said Des . " Why me ?! " moaned Clive . " Why me ?!?!? " " What are you talking about ?! " said Des . " Of all the millions of people on this planet , why did I have to end up with you as my neighbour ?!?! " " I do n't know what you mean ! " said Des . " You ca n't do anything sensible , can you ?! " exclaimed Clive . " All you had to do was to buy a new car !! But no , you have to go and buy a shed on wheels !!!! " " That 's not my new car , " said Des . " It 's not ? " said Clive . " It 's my new shed , " said Des . " The wheels and engine are only temporary . " " Oh thank goodness , " said Clive . " So where 's your new car then ? " " I 'm not getting a new car !! " said Des . " There 's nothing wrong with my Fiat 126 !! I will keep it forever !! " Clive started weeping again . Just then Mike the Manic Mechanic turned up . " What 's wrong with him ?! " said Mike . " I do n't know , he 's just got some ridiculous in-built prejudice against both Fiat 126s and sheds on wheels , " said Des . " Well , whatever , let 's get your car shipshape again ! " said Mike . " Or even carshape again ! " Mike spent the next five hours returning all the car bits and pieces from the shed to the car . " There , what did I tell you ! " said Mike . " It 's as good as new !! " Des had to admit , his Fiat 126 was now just as it had been before Mike started meddling with it . " That 'll be £ 500 + VAT please , " said Mike . " What ?!?! " exclaimed Des . " I thought you were doing it as a favour ! " " I was ! " said Mike . " And an extremely inexpensive favour it was too ! " Des handed the cash to Mike , who then went back to his garage . Just then PC Plod came along . " Good afternoon sir , have you managed to produce a vehicle registration certificate for that shed yet ? " asked Plod . " PC Plod , what are you talking about , why do I need a vehicle registration certificate for a shed ?! " Plod stared long and hard at the shed . It was indeed an ordinary , common-or-garden shed ! He scratched his head and then tried rubbing his eyes . " Err , well , err ... sorry to bother you sir , I did have rather a long night ... " Plod hurried back to the police station to book a long holiday . Meanwhile Des went over to Mick's house and rang his doorbell . Mick answered . " Mick , I 've got a problem , " said Des . Mick groaned . " You see my new shed ? " said Des . " How are we going to get it from the front drive to the back garden ? " " How about taking your house apart , lifting the shed across and then putting your house back together ! " " That 's a good idea ... naah , it 'd take too long ! " said Des . " Quicker to take the shed apart ! " Des grabbed a reluctant Mick over to his front drive . " Now this ca n't be too difficult , I 'm sure I 've done it sometime before ... " said Des . " All I need is a hammer . Because if I had a hammer , I 'd hammer in the morning , I 'd hammer in the evening , all over this land . " " What about the afternoon ? " said Mick . " Tea break , " said Des . He went and fetched a couple of hammers and they set to work taking the shed apart . Then they carried the parts through the garage and into the back garden , which was still covered in moose's heads , skeletons , bird cages etc. By now Mick was exhausted , so Des single-handedly put the shed back together , in its new , permanent position at long last . " There you go ! " said Des . " Looks great , does n't it ! " " No , " said Mick . Des was about to start piling all his junk into the new shed when Mick decided to point something out to him . " Des , " said Mick . " Your new shed looks as though it 's about to collapse ! " " Really ? " said Des . He stared carefully at it . " Oh yes , you 're right ! " Following Des's rebuild , all of the walls were now leaning inwards . In fact they were on the brink of falling right in . " Now I remember why the walls on the old shed always leant inwards !! " exclaimed Des . " Tell you what , can I borrow your rake ? "


At the beginning of the meeting , ask how long the meeting will last . You need to cover all the relevant points within this time . Use the list of questions you made in advance . Make sure you ask all your questions and that you fully understand the answers you 're given . If there is anything you do n't understand , ask your solicitor to explain . Try to answer your solicitor's questions as clearly and accurately as you can , but also be brief . Your solicitor will ask you many questions . Show your solicitor any relevant documents you have brought with you . Ask your solicitor to send you a letter summarising the advice you 've been given .


Carlos Fallanty lost his wife at the time of the Violent Unknown Event . She was a voluble , untidy woman who made her own clothes and washed once a week in the water wrung out of the laundry . She was invaluable to her husband . She looked after his poultry , kept his accounts , and when roused , was as uxorious a wife as Carlos could wish to have . On the night of June 12th of the VUE , Carlos's wife suffered a stroke , and Carlos transferred his affection to a turkey . The VUE Directory records for Carlos a debilitating malfunction of the left ventricle , bone-marrow disease , and save for the VUE immortality clause , would have normally given him six months to live . Carlos had buried his wife in the floor of his greenhouse . The local authorities later had the body exhumed . Now Carlos lived in the greenhouse to keep his turkey company . A fowl-pest epidemic finally erased Carlos's other poultry , and two veterinary officials came to make sure he had burnt or buried all the corpses . Insisting that the one remaining bird should be destroyed as well , the vet promised to compensate Carlos with at least a set of photographs . These are the photographs taken as the vet stalked the bird with his camera , whilst the vet's assistant stalked the bird with a shotgun . Carlos was not happy with the photographs . He is now awaiting trial at Clichy for shooting the vet .


Beaver Miller - Original Model A also badged as " Grimston " Manuals & Parts Lists for most models of Beaver Miller are available Beaver Model A - Click HERE for Detailed Photographs Mk . 1 & Mk . 2 VBRP If any reader has early Beaver Advertising or Maintenance Literature , I would be pleased to hear from them A Beaver Model A owner would like to have contact with fellow owners to discuss head details The Beaver Turret-head vertical miller Model " A " was manufactured by Balding Engineering ( originally jobbing engineers ) of the Old Tramways Power Station , Duke Street , Norwich and then Sweet Briar Road in the same city . A number of this model were also badged as " Grimston " ( a London machine-tool manufacturer and merchant ) and sometimes lacked the cast Beaver badge on the right-hand side of the main column ; the paint finish was also unusual on the Grimston version , a " splatter " mix of dark grey , green and red not dissimilar to that also used on some American ROTEX millers of the same era . In its original form , as introduced during the early 1950s , this little miller proved to be a compact , versatile machine equally at home in the toolroom or on the shop floor - and absolutely ideal when its industrial life was over , for the workshop of the enthusiastic amateur . In 1957 it was succeeded by the very much larger and heavier MK . 1 and Mk 2 and " VBRP " models , details of which ( today the most common " Beaver " on the used market ) can be seen here . In the 1980s , on the back of considerable success in exporting the VBRP range , the company opened a new factory in Peterborough to manufacture a range of CNC lathes to compliment the CNC millers and CNC machining centres already in production ; unfortunately the severe recession in manufacturing industry of 1992 ( when demand for machine tools fell by 50 % in 3 months ) caused the company to close .. The original 1950s miller had a 28 " x 6 " table ( with three 9 / 16 " T slots ) a longitudinal travel of 15 " , a cross feed of 7.5 " and a vertical movement of 13.75 " . A table power-feed motor was fitted as standard and drove a 4-speed gear box ; to change the rate of table feed " pick-off " gears were used where operator removed a side panel , pulled off the gears on two studs ( they were retained by snap-on wire springs ) and changed them for another pair from the four supplied . The head was driven by a simple and reliable two-stage V-belt arrangement with an adjustable intermediate pulley carried in a T slot ; an over-centre toggle lever released the belt tension to change speeds and the whole of the belt run was guarded by a rather fragile hinged , cast-aluminium cover . The head swung on top of the column , slid in and out of its housing and swivelled through 90 degrees each way - allowing the spindle nose to be brought to within 3.5 " of the column face or moved away to give a maximum clearance of 9.75 " . The quill , with 3 " of travel and a No. 30 International fitting , was fitted with both fine and quick-action feeds and driven by a 0.75 hp 3-phase motor through 7 speeds in two ranges arranged ( through the intermediate pulley ) of 200 , 330 , and 500 on Low-Range and 350 , 1420 , 2200 , 3600 rpm on High . The quill movement was measured by a vertical ruler and adjustable micrometer dial - and fitted with a very useful screw-adjusted ' pre-set ' depth stop . Because the electric motor mounts directly onto the back of a Beaver " headbar " , changing it is a very simple operation . The table power-feed motor , however , is flange-mounted to the back of the knee - and is not such an easy prospect for modification ; however , this type of small 3-phase motor is usually amenable to being run on a single-phase supply by using the old trick of linking two of the three-phase terminals with a suitable capacitor . For the home or smaller professional workshop the Beaver Mill " A " is one of the few machines that combines quality , size and functionality in just the right proportions . A Universal version , the " AH " , was also manufactured - but this is a comparatively rare machine and , unaccountably , used a completely different type of vertical head . Balding also built a 4.5 " x 20 " backgeared , screwcutting lathe of conventional design but robust construction . of which details can be foun


Hello : We 're doing my grandmothers genealogy - Knight / Morrison from Peterhead . William Morrison married Isabella Knight on 6-8-1892 in Peterhead . They had 7 children - Louisa , William , Jemina , George , Alex , Jack and Isabella . Jemina Helen was my grandmother , b . in Peterhead on 5-16-1899 - passed away in USA in the 1980's . Jemina married David Donald Middleton in the USA in 1923 . If you think you may have a family connection or could give me any info on where to start my search on the Morrison / Knight their time in Scotland , would be glad to hear from on and all . Thanks so much !! Sandi USA


If a cracker is trying to break into the account by trying to guess the password , a changed password makes it difficult for the attacker . If an account has already been breached , the password expiration will help prevent or at least raise suspicions that there is an issue . With a good enterprise password management tool , such as Avatier's Password Station , the real user will get notifications about needing to change their password before it is expired which the cracker may never see . Finally , if the account has been breached and the cracker changes the password , the user may notice they ca n't get into their account anymore and this may lead to an investigation . Those are all good and valuable benefits . However , on the other side are a few major problems : Many users will start using passwords like " howdy1 " . Then , when the expiration hits , they just change it to " howdy2 " . This means that if the password is ever cracked , it is likely the cracker will be able to guess future passwords as well . Other users will start writing down their passwords because they ca n't remember them anymore . The shorter the password expiration , the greater the number of Help Desk calls related to forgotten passwords will be . So what can be done to get the benefits of an enterprise password manager while minimizing the problems ? First , the number of different passwords in the organization needs to be considered . A company with one Windows domain is going to have fewer issues than a company with a mix of Windows , ERP , Databases , Unix , Mainframe , and so on . When multiple systems are in play , the first thing to do is to implement a password synchronization product , such as Password Station . This will enable users to only need to remember one password for all the systems instead of several passwords . This increases the likelihood of a good password being chosen and remembered . Second , password history can be used to prevent a user from reusing the same few passwords over and over again . Some systems can enforce this natively , but having your password synchronization software handle this capability will ensure all systems are in scope . The appropriate strength of the enterprise password management software policy is also critical to success . A product like Password Bouncer allows admins to utilize an automated password reset tool to enforce policies that prevents users from setting very simple passwords that are easy to crack yet simple enough that users will not have to write them down to be remembered . Finally , the time frame of the password expiration needs to be considered . Obviously , a password policy that is daily or weekly is going to lead to problems . At the other extreme , a policy that only enforces changes yearly is probably not strong enough . A reasonable time frame of password expiration is anywhere from 1 to 6 months depending on the compliance and cyber security threats to an organization . The complexity of the enterprise password management software policy needs to be factored in . If the policy is complex , the password expiration could be longer . If the policy is very simple , then the expiration should be shorter .


The 2016 Summer Olympics ( Portuguese : Jogos Olímpicos de Verão de 2016 ) , [ a ] officially known as the Games of the XXXI Olympiad and commonly known as Rio 2016 , was a major international multi-sport event held in Rio de Janeiro , Brazil , from 5 August to 21 August 2016 . The lead-up to these Games was marked by controversies , including the instability of the country's federal government ; health and safety concerns surrounding the Zika virus and significant pollution in the Guanabara Bay ; and a doping scandal involving Russia , which has affected the participation of its athletes in the Games . The United States topped the medal table for the fifth time in the past six Summer Olympics , winning the most golds ( 46 ) and most medals overall ( 121 ) , as well as its 1 , 000th Olympic gold medal overall . Great Britain finished second and became the first country in the history of the modern Olympics to increase its tally of medals in the subsequent games after being the host nation . China finished third . Host country Brazil won seven gold medals , its most at any single Summer Olympics , finishing in thirteenth place . Fiji , Jordan , Kosovo , Puerto Rico , Singapore , Tajikistan , Ivory Coast and Vietnam each won their first gold medals , as did the group of Independent Olympic Athletes ( from Kuwait ) . The bidding process for the 2016 Olympic Games was officially launched on 16 May 2007 . [ 4 ] The first step for each city was to submit an initial application to the International Olympic Committee ( IOC ) by 13 September 2007 , confirming their intention to bid . Completed official bid files , containing answers to a 25-question IOC form , were to be submitted by each applicant city by 14 January 2008 . Four candidate cities were chosen for the shortlist on 4 June 2008 : Chicago , Madrid , Rio de Janeiro and Tokyo , which hosted the 1964 Summer Olympics and will host again in 2020 . The IOC did not promote Doha to the candidature phase , despite scoring higher than selected candidate city Rio de Janeiro , because of their intent of hosting the Olympics in October , outside of the IOC's sporting calendar . Prague and Baku also failed to make the cut . [ 5 ] Nawal El Moutawakel of Morocco headed the 10-member Evaluation Commission , having also chaired the evaluation commission for the 2012 Summer Olympics bids . The commission made on-site inspections in the second quarter of 2009 . They issued a comprehensive technical appraisal for IOC members on 2 September , one month before elections . [ 6 ] Many restrictions are in place designed to prevent bidding cities from communicating with or influencing directly the 115 voting members . Cities may not invite any IOC member to visit nor may they send anything that could be construed as a gift . Nonetheless , bidding cities invest large sums in their PR and media programs in an attempt to indirectly influence the IOC members by garnering domestic support , support from sports media and general international media . " Ultimately , you are communicating with just 115 people and each one has influencers and pressure groups but you are still speaking to no more than about 1,500 people , perhaps 5,000 in the broadest sense . It is not just about getting ads out there but it is about a targeted and very carefully planned campaign . The final voting was held on 2 October 2009 , in Copenhagen with Madrid and Rio de Janeiro perceived as favourites to land the games . Chicago and Tokyo were eliminated after the first and second rounds of voting , respectively , while Rio de Janeiro took a significant lead over Madrid heading into the final round . The lead held and Rio de Janeiro was announced as host of 2016 Summer Olympics . On 26 June 2011 , it was reported on AroundTheRings.com that Roderlei Generali , the COO of the Rio de Janeiro Organizing Committee for the Olympic Games , resigned just one year after taking the job at ROOC . This comes just five months after CCO Flávio Pestana quit for personal reasons . [ 9 ] Pestana withdrew later during the 2012 Summer Paralympics . Renato Ciuchin was then appointed as COO . [ 10 ] Events took place at eighteen existing venues , nine new venues constructed specifically for the Games , and seven temporary venues . [ 11 ] Each event was held in one of four geographically segregated Olympic clusters : Barra , Copacabana , Deodoro , and Maracanã . The same was done for the 2007 Pan American Games . [ 12 ] [ 13 ] Several of the venues were located at the Barra Cluster Olympic Park . [ 11 ] Athletes could access their venues in shorter than 10 minutes and about 75 percent could do so in less than 25 minutes . Of the 34 competition locales , eight have undergone permanent works , seven are limited , and nine are perpetual legacy venues . [ 14 ] The largest venue at the games in terms of seating capacity was the 74 , 738-seat Maracanã Stadium , which served as the ceremonies venue and site of the football finals . [ 11 ] The second largest stadium was the 60 , 000-seat Estádio Olímpico João Havelange , which hosted track and field events . [ 11 ] The athletes' village was said to be the largest in Olympic history . Fittings included about 80,000 chairs , 70,000 tables , 29,000 mattresses , 60,000 clothes hangers , 6,000 television sets and 10,000 smartphones . [ 15 ] The Barra Olympic Park is a cluster of nine sporting venues in Barra da Tijuca , in the west zone of Rio de Janeiro , Brazil . The site of the Olympic Park was formerly occupied by the Autódromo Internacional Nelson Piquet , also known as Jacarepaguá . [ 16 ] As well as the Estádio Olímpico João Havelange and Maracanã and in Rio de Janeiro , football matches took place at 5 venues in the cities of São Paulo , Belo Horizonte , Salvador , Brasília and Manaus . Rio's historical downtown is undergoing a large-scale urban waterfront revitalization project called Porto Maravilha . [ 19 ] It covers 5 km 2 ( 1 . 9 sq mi ) in area . The project aims to redevelop the port area , increasing the city center's attractiveness and enhancing Rio's competitive position in the global economy . The urban renovation involves : 700 km ( 430 mi ) of public networks for water supply , sanitation , drainage , electricity , gas and telecom ; 4 km ( 2 . 5 mi ) of tunnels ; 70 km ( 43 mi ) of roads ; 650 km 2 ( 250 sq mi ) of sidewalks ; 17 km ( 11 mi ) of bike path ; 15,000 trees ; three sanitation treatment plants . As part of this renovation , a new tram was built from the Santos Dumont Airport to Rodoviária Novo Rio . It was due to open in April 2016 . [ 20 ] The Games required more than 200 kilometres of security fencing . A 15,000 square metre warehouse in Barra da Tijuca in western Rio was used to assemble and supply the furniture and fittings for the Olympic Village . A second warehouse of 90,000 square metres , located in Duque de Caxias near the roads that provide access to the venues , contained all the equipment needed for the sporting events . [ 15 ] The medal design was unveiled on 15 June 2016 ; they were produced by the Casa da Moeda do Brasil . The bronze and silver medals contained 30 % recycled materials , while the gold medals were produced using gold that had been mined and extracted using means that met a series of sustainability criteria , such as being extracted without the use of mercury . The medals feature a wreath design , while the obverse , as is traditional , features Nike , the Greek goddess of victory . They were accompanied by a wooden carrying box , while medallists also received a trophy of the Games' emblem . [ 21 ] [ 22 ] Future Arena , a temporary venue whose modules will be reconstructed into schools . As an aspect of its bid , Rio's organizing committee committed to a focus on sustainability and environmental protection as a theme of these Games , going on to dub them a " Green Games for a Blue Planet " . [ 23 ] Organizers intended to , as legacy projects , introduce a wider array of public transport options , upgrade the infrastructure of the favelas to provide improved transport and access to utilities , upgrade Rio's sewer system in order to remediate the level of pollution in the Guanabara Bay . [ 23 ] [ 24 ] and plant 24 million seedlings to offset the expected carbon emissions of the Games . However , some of these projects were met with delays or faced with economic shortfalls , which led some critics to believe that Rio would not be able to accomplish them . [ 23 ] [ 25 ] The focus on environmental protection also influenced the implementation of certain Olympic protocols : the Olympic cauldron was designed to be smaller than previous iterations in order to reduce emissions , and utilizes a kinetic sculpture to enhance its appearance in lieu of a larger body of flames . [ 26 ] The bronze and silver medals , as well as ribbons on all medals , incorporate recycled materials , [ 21 ] [ 22 ] and athletes were not presented with flowers during medal ceremonies , as had been traditionally done at prior Olympics ( although flowers were still used as part of the staging of medal presentations ) . Organizers considered the practice to be wasteful since they were often thrown away , and " would struggle to survive in the tropical Brazilian climate " if kept . The podiums were also designed so that their materials could be recycled to make furniture . [ 22 ] [ 27 ] The Future Arena , host of handball competitions , was designed as a modular temporary venue whose components can be reconstructed to build schools . [ 28 ] The Olympic flame was lit at the temple of Hera in Olympia on 21 April 2016 , the traditional start of the Greek phase of the torch relay . On 27 April the flame was handed over to the Brazilian organizers at a ceremony at the Panathenaic Stadium in Athens . A brief stop was made in Switzerland to visit the IOC headquarters and the Olympic Museum in Lausanne as well as the United Nations Office at Geneva . [ 30 ] The ticket prices were announced on 16 September 2014 , all of which were sold in Brazilian reais ( BRL ) . A total of 7.5 million tickets were to be sold in total , with ticket prices ranging from BRL 40 for many events to BRL 4,600 for the most expensive seats at the opening ceremony . About 3.8 million of these tickets were available for BRL 70 or less . [ 32 ] [ 33 ] The Olympic cauldron was lit by Vanderlei Cordeiro de Lima , the men's marathon bronze medallist at the 2004 Summer Olympics who was also awarded the Pierre de Coubertin medal for sportsmanship by the IOC after being attacked by a spectator and losing his lead . The cauldron was originally expected to be lit by Brazilian footballer Pelé , but he declined to participate due to health problems . [ 35 ] [ 38 ] [ 39 ] A public cauldron was lit in front of the Candelária Church by a 14-year-old participant in Rio's Vila Olimpica program – which provides access to training facilities to disadvantaged youth . [ 40 ] [ 41 ] The 2016 Summer Olympic programme featured 28 sports encompassing 306 events . The number of events in each discipline is noted in parentheses . In April 2008 , the IOC began accepting applications for two new sports to be introduced to the Olympic programme , which included baseball and softball ( which were dropped in 2005 ) , karate , squash , golf , roller sports , and rugby union all applied to be included . Formal presentations were held for the IOC executive board in June 2009 . [ 42 ] In August , the executive board initially gave its approval to rugby sevens – a seven-player version of rugby union – by a majority vote , thus removing baseball , roller sports , and squash from contention . Among the remaining three – golf , karate , and softball – the board approved golf as a result of consultation . The final decision regarding the remaining two sports was made on 9 October 2009 , the final day of the 121st IOC Session . A new system was in place at this session ; a sport now needed only a simple majority from the full IOC committee for approval rather than the two-thirds majority previously required . [ 43 ] [ 44 ] Participating National Olympic Committees [ edit ] 2016 Summer Olympics team numbers . All 206 National Olympic Committees have qualified at least one athlete . [ citation needed ] The first three nations to qualify athletes for the Games were Germany , Great Britain , and the Netherlands who each qualified four athletes for the team dressage by winning medals in the team event at the 2014 FEI World Equestrian Games . [ 48 ] As host nation , Brazil has received automatic entry for some sports including in all cycling disciplines and six places for weightlifting events . [ 49 ] [ 50 ] The 2016 Summer Olympics are the first games in which Kosovo and South Sudan are eligible to participate . Bulgarian and Russian weightlifters were banned from Rio Olympics for numerous anti-doping violations . [ 51 ] [ 52 ] Kuwait was banned in October 2015 for the second time in five years over government interference in the country's Olympic committee . [ 53 ] Due to the suspension of the National Olympic Committee of Kuwait , participants from Kuwait were allowed to participate under the Olympic Flag as Independent Olympic Athletes . In November 2015 , Russia was provisionally suspended from all international athletic competitions by the International Association of Athletics Federations ( IAAF ) following a World Anti-Doping Agency ( WADA ) report into a doping program in the country . [ 56 ] The IAAF announced that it would allow individual Russian athletes to apply for " exceptional eligibility " to participate in the Games as " neutral " athletes , if it were independently verified that they had not engaged in doping nor in the Russian doping program . [ 57 ] On 24 July 2016 , the IOC rejected the IAAF and WADA's recommendations to allow clean athletes to compete neutrally , stating that the Olympic Charter " does not foresee such ' neutral athletes ' " and that it was up to each country's National Olympic Committee to decide which athletes would be competing . [ 58 ] During the Games some countries and continents had a national house . These temporary meeting places for supporters , athletes and other followers were located throughout Rio de Janeiro . [ 59 ] This is currently based on the schedule released on the same day as ticket sales began , 31 March 2015 . [ 60 ] Twenty-seven world records and ninety-one Olympic records were set during the 2016 Summer Olympics . The records were set in archery , athletics , canoeing , cycling track , modern pentathlon , rowing , shooting , swimming and weightlifting . The medals designed for the Olympics . They were designed to be environmentally friendly from recycled materials . The top ten listed NOCs by number of gold medals are listed below . Host nation Brazil finished in 13th place with a total of 19 medals ( 7 gold , 6 silver , and 6 bronze ) . To sort this table by nation , total medal count , or any other column , click on the icon next to the column title . A number of events , most notably in aquatics , beach volleyball , and track and field , were scheduled with sessions and matches occurring as late as 22 : 00 to 00 : 00 BRT . These scheduling practices were influenced primarily by United States broadcast rightsholder NBC ( due to the substantial fees NBC has paid for rights to the Olympics , the IOC has sometimes allowed NBC to have influence on event scheduling to maximize U.S. television ratings when possible ) , as well as the main Brazilian rightsholder Rede Globo . As Brasília time is only one hour ahead of the U.S. Eastern Time Zone , certain marquee events were scheduled so they could occur during the lucrative U.S. primetime hours ( traditionally 20 : 00 to 23 : 00 ET , or 21 : 00 to 00 : 00 BRT ) , allowing them to be broadcast live on the U.S. east coast as opposed to being delayed . This practice was also to the benefit of domestic broadcaster Rede Globo , which elected to not preempt its widely viewed lineup of primetime telenovelas for the Games . However , Globo did preempt its telenovelas for the opening ceremony ; a Brazilian television critic noted that Globo very rarely preempts its telenovelas . [ 61 ] [ 62 ] [ 63 ] [ 64 ] The creative director for the ceremony was Rosa Magalhães . [ 67 ] Amid heavy rainfall , the ceremony began with interpretive dancers representing various landmarks in the host city . Martinho da Vila then performed a rendition of the classic song " Carinhoso ( pt ) " by Pixinguinha . In another segment , introducing the athletes , pop singer Roberta Sá channeled Carmen Miranda , the fruit-headdress-wearing , midcentury Hollywood diva who endures as a beloved camp figure . The Parade of Flags followed shortly after a choir of 27 children , representing the states of Brazil , sang the Brazilian national anthem . Olympic Broadcasting Services served as the host broadcaster for these Games ; produced from a total of 52 mobile units , OBS distributed 40,000 hours of television footage and 60,000 hours of digital footage of the Games to its international rightsholders ; for the first time in Olympic history , digital-oriented footage exceeded the amount of television-oriented footage . The International Broadcast Centre was constructed in the Barra da Tijuca cluster . [ 68 ] NHK and OBS once again filmed portions of the Games , including the opening ceremony and selected events , in 8K resolution video . Additionally , expanding upon a 180-degree trial at the 2016 Winter Youth Olympics , 85 hours of video content were originated in 360-degree virtual reality formats . [ 69 ] In the United States , NBC offered 4K content , downconverted from the 8K footage and with HDR and Dolby Atmos support , to participating television providers . [ 70 ] Owing to their expertise in domestic broadcasts of the new sports introduced in Rio , NBC and Sky New Zealand staff handled the production of the golf and rugby sevens events on behalf of OBS . [ 68 ] In August 2009 , the IOC reached a deal to sell domestic broadcast rights to the 2016 Summer Olympics to Grupo Globo . Replacing Rede Record , the deal covers free-to-air coverage on Rede Globo , pay TV , and digital rights to the Games . In turn , Globo sub-licensed partial free-to-air rights to Rede Record , along with Rede Bandeirantes . IOC board member Richard Carrión described the agreement as " unprecedented " , touting that " by working with Brazil's leading media organizations , we are confident that this represents a great deal for Olympic fans in the region . There will be a huge increase in the amount of Olympic action broadcast , both during and outside Games time , and Brazilians will have more choice of how , when and where they follow their Olympic Games . " [ 71 ] Vinicius ( left ) , the mascot of the 2016 Summer Olympics , and Tom ( right ) , the mascot of the 2016 Summer Paralympics . The official emblems of the Games can be seen on the mascots' chests . The official mascots of the 2016 Summer Olympics and Paralympics were unveiled on 24 November 2014 . They were created by Sao Paulo - based animation company Birdo . [ 72 ] The Olympic mascot Vinicius , named after musician Vinicius de Moraes , represents Brazilian wildlife and carries design traits of cats , monkeys , and birds . [ 72 ] According to their fictional backgrounds , the mascots " were both born from the joy of Brazilians after it was announced that Rio would host the Games . " [ 73 ] Brand director Beth Lula stated that the mascots are intended to reflect the diversity of Brazil's culture and people . [ 74 ] The names of the mascots were determined by a public vote whose results were announced on 14 December 2014 ; the names , which reference the co-writers of the song " The Girl from Ipanema " , won over two other sets of names , tallying 44 percent of 323,327 votes . [ 75 ] At the Olympic wrestling events , coaches were given plush dolls of Vinicius to throw into the ring when they wished to challenge a referee's call . [ 76 ] The official emblem for the 2016 Summer Olympics was designed by the Brazilian agency Tatíl Design and unveiled on 31 December 2010 , winning in a competition against 139 agencies . [ 77 ] The logo represents three figures joined at their arms and feet , with the overall shape reflecting that of Sugarloaf Mountain . The emblem was also designed to have a three-dimensional form , which designer Fred Gelli claimed made it the " first 3D logo in the history of the Olympics . " [ 78 ] The logo has been noted as evoking Henri Matisse ' s painting Dance . There were also allegations by the Colorado-based Telluride Foundation that the logo had been plagiarized from its own . While also consisting of several figures linked in motion , the Telluride Foundation logo contains four figures . This is not the first time that the foundation had alleged plagiarism of its logo by a Brazilian event ; in 2004 , the linked figures element had been copied for the logo of Carnival celebrations in Salvador . Gelli defended the allegations , stating that the concept of figures linked in embrace was not inherently original as it was " an ancient reference " and " in the collective unconscious " . Gelli cited Dance as an influence of the logo's concept , and stated that the designers had intentionally aimed to make the interpretation of the concept as dissimilar to others as possible . [ 79 ] An ongoing outbreak of the mosquito-borne Zika virus in Brazil has raised fears regarding its potential impact on athletes and visitors . Organizers plan to perform daily inspections of Olympic venues to prevent puddles of stagnant water that allow mosquitoes to breed . [ 80 ] Zika virus transmission was also attributed to inefficient sewage treatment in the area , and sewage treatment was being improved in preparation for the Games . [ 81 ] In May 2016 , a group of 150 physicians and scientists sent an open letter to the World Health Organization , calling upon them to , according to co-author Arthur Caplan , have " an open , transparent discussion of the risks of holding the Olympics as planned in Brazil " . The WHO dismissed the request , stating that " cancelling or changing the location of the 2016 Olympics will not significantly alter the international spread of Zika virus " , and that there was " no public health justification " for postponing them . [ 82 ] [ 83 ] [ 84 ] Some athletes did not attend the Games because of the epidemic . [ 85 ] [ 86 ] On 2 September 2016 , the World Health Organization reported that there were no confirmed cases of Zika among athletes or visitors during the Olympics . [ 87 ] The Guanabara Bay , whose waters were used for sailing and windsurfing competitions , is heavily polluted . Among the chief causes of the pollution are uncollected trash fed into the bay via polluted rivers and slums along the coast . Pollution of the Guanabara has been a long-term issue . Officials promised at the Earth Summit in 1992 that they would begin to address the pollution but previous attempts to do so have been insufficient . As an aspect of their bid for the Games , Rio once again committed to making efforts towards cleaning the bay . [ 88 ] [ 89 ] However , some of these proposed initiatives have faced budgetary issues . [ 24 ] Prior to these efforts , only 17 % of Rio's sewage was treated ; [ 90 ] this raw sewage also leaked into the bay . Although Mayor of Rio Eduardo Paes stated that the city may not be able to reach its goal of having 80 % of sewage treated , [ 91 ] at least 60 % of sewage was treated by March 2016 , with a projected goal of 65 % of sewage being treated by the time the Olympics started . [ 92 ] In 2014 , Operation Car Wash , an investigation by the Federal Police of Brazil , uncovered unprecedented money laundering and corruption at the state-controlled oil company Petrobras . In early 2015 , a series of protests against alleged corruption by the government of President Dilma Rousseff began in Brazil , triggered by revelations that numerous politicians were involved in the Petrobras affair . By early 2016 , the scandal had escalated into a full-blown political crisis affecting not only President Rousseff , but also former President Luiz Inácio Lula da Silva , resulting in massive demonstrations all over the country involving millions of protesters , [ 93 ] both anti and pro-Rousseff . [ 94 ] [ 95 ] At the same time , Brazil faced its worst economic recession since the 1990s , raising questions about whether the country was adequately prepared for the Games against a volatile political and economic backdrop . On 12 May , President Rousseff was stripped of her powers and duties for 180 days , after an impeachment vote in the Federal Senate , thus Vice President Michel Temer acted as acting president during the Games . [ 96 ] Since the award of the 2016 Olympics to Rio de Janeiro , the city's crime problems received more attention . Rio's mayor said that there are " big issues " facing the city in securing the Games from violence . However , he also said that such concerns and issues were presented to the IOC throughout the bidding process . [ 97 ] The governor of the state of Rio de Janeiro also highlighted the fact that London faced security problems , with a terrorist attack occurring on the day following the IOC session that chose the city to host the 2012 Olympic Games . The estimate was that 5,000 men of the National Public Security Force and 22,000 military officers ( 14 , 800 Army ; 5,900 Navy and 1,300 of the Brazilian Air Force ) , in addition to the fixed quota of Rio January , would act during the Olympic Games . [ 98 ] On 21 July 2016 , two weeks before the scheduled start of the Games , Brazilian Federal Police broke up an Islamic jihadist terrorist ring , with 10 ISIS associates arrested and two more on the run . [ 99 ] While the whole city underwent major infrastructure improvements , there were concerns that some of the projects would never materialise . [ 100 ] On 21 April – the day that the Olympic torch was lit – a 50 metres ( 164 ft ) section of the Tim Maia bike path , crossing the Oscar Niemeyer Avenue in São Conrado neighborhood and a part of the legacy of the games , was hit by a giant wave and collapsed , causing the death of two pedestrians and injuries to three more . [ 101 ] [ 102 ] The athlete's village has been described as the largest in Olympic history , but two weeks before the Olympics opened , officials also described it as " unliveable " and unsafe because of major plumbing and electrical hazards , blocked toilets , leaking pipes , exposed wiring , darkened stairwells where no lighting has been installed , and dirty floors . More than 500 employees of the local Olympic committee worked to fix the problems reported by the delegations . [ 103 ] In November 2015 , Russia ' s track and field team was provisionally suspended from all international athletic competitions by the International Association of Athletics Federations ( IAAF ) following a World Anti-Doping Agency ( WADA ) report into a doping program in the country . [ 56 ] On 18 July 2016 , an independent investigation commissioned by WADA reported that Russia's Ministry of Sport and Federal Security Service had operated a " state-dictated " system to implement an extensive doping program and to cover up positive samples . Based on the finding the International Olympic Committee called for an emergency meeting to consider banning Russia from the Summer Olympics . [ 104 ] The IOC decided against completely banning Russian participation and instead decided to set additional , stricter requirements for all Russian participants entered into the Olympic Games . [ 105 ] Originally Russia submitted a list of 389 athletes for competition . On 7 August 2016 , the IOC cleared 278 athletes , while 111 were removed because of the scandal . [ 106 ] [ 107 ] ^ Porto Maravilha Rio de Janeiro City Hall . Retrieved 10 August 2012 . ( Portuguese ) . ^ Jaroschewski , Julia ( 29 April 2016 ) . " Between hope and despair " . D + C , development and cooperation . Retrieved 25 May 2016 .


Reduce Cancer Reoccurrence , Wheatgerm Extract , Cancer : The Wheatgerm Extract That May Help Reduce Cancer Reoccurrence Cancer treatment has come a long way since the use of mustard gas derivatives in the early 1900s - or has it ? When doctors discovered during World War I that mustard gas destroyed bone marrow , they began to experiment with it as a way to kill cancer cells . Although they had little success with the mustard gas , it did pave the way for modern chemotherapy - which involves the most toxic and poisonous substances anyone deliberately puts in his body . These treatments kill much more than cancer cells - they have a devastating effect even on healthy ones . Sometimes it seems as if only a miracle could provide a cure that 's both safe and effective . And a miracle is just what Dr. Mate Hidvegi believed he found when he patented Avemar . Studies have shown that Avemar , a fermented wheatgerm extract , helps reduce cancer reoccurrence , possibly speed up cancer cell death and helps the immune system identify cancer cells for attack . A miracle in the making Back in World War I , Dr. Albert Szent-Györgyi ( a Nobel Prize recipient in 1937 for his discovery of vitamin C ) had seen the effects of mustard gas personally and was determined to find a safer alternative for cancer treatment . His goal was to prevent the rapid reproduction that is characteristic of cancer cells . He theorised that supplemental quantities of naturally occurring compounds in wheatgerm called DMBQ would help to chaperone cellular metabolism , allowing healthy cells to follow a normal course but prohibiting potentially cancerous ones from growing and spreading . His early experiments , published in the 1960s , confirmed his theory . But then the science community shifted its focus to killing cancer outright . It was n ' t until the fall of communism in Hungary in 1989 - when scientists were allowed for the first time to pursue independent , personal interests - that Dr. Hidvegi picked up where Szent-Györgyi left off . He was able to patent a technique of fermenting wheat germ with baker's yeast . He named this fermented product Avemar and it became the standard compound for research and later commercialisation because it assured a longer shelf life while maintaining its live food status . Reduce cancer reoccurrence Since 1996 , over 100 studies done on Avemar have impressed oncologists and cancer researchers . Studies have shown that when Avemar is used as an adjunct treatment , it enhances the effects of the standard treatment agents . It 's particularly effective in reducing the chances of cancer reoccurrence . In a controlled study , 170 subjects with primary colorectal cancer either had surgery and standard care with chemotherapy or the same plus 9g of Avemar taken once a day . Only 3 per cent of the people in the Avemar group experienced a reoccurrence , vs. more than 17 per cent of those in the chemo-only group . The Avemar group also showed a 67 per cent reduction in metastasis and a 62 per cent reduction in deaths . 1 In a randomized study , 46 stage III melanoma patients with a high risk of reoccurrence either had surgery and standard care with chemotherapy or surgery plus standard care and 9g of Avemar taken once a day . Those taking Avemar showed approximately a 50 per cent reduction in risk of progression . 2 Avemar also reduced the frequency and severity of many common side-effects , including nausea , fatigue , weight loss and immune suppression . Avemar speeds cancer cell death The second way Avemar works against cancer is to help keep cancer cells from repairing themselves . Cancer cells reproduce quickly and chaotically , producing many breaks and other mistakes in the cellular structure . Because of this , cancer cells need a lot of the enzyme known as PARP ( poly-ADP-ribose ) to help repair breaks in DNA before the cells divide . For daily reports on the very latest health breakthroughs , join our FREE daily email service : It is thought that without adequate PARP , cancer cells can not complete DNA replication . When there 's no PARP to repair the damage , an enzyme called Caspase-3 initiates programmed cell death . Avemar has been shown to potentially speed up the death of cancer cells by helping inhibit the production of PARP and enhancing the production of Caspase-3 . 3 US researchers at UCLA also showed that Avemar may reduce the production of RNA ( ribonucleic acid ) and DNA associated with the rapid reproduction of cancer cells . It also helps restore normal pathways of cell metabolism and may increase the production of RNA and DNA associated with healthy cells . 4 Undercover cancer cells exposed Avemar may also act as a biological bounty hunter for hidden cancer cells . Healthy cells have a surface molecule called MHC-1 that tells natural killer ( NK ) cells not to attack . Virally infected cells do n't display this molecule , which makes them targets . However , cancer cells have also been shown to display the surface molecule MHC-1 , which means that cancer cells may actually be able to hide from NK cells . Avemar is thought to help the immune system identify cancer cells for attack by suppressing their ability to generate this MHC-1 mask , which allows the NK cells to recognize it as a target for attack . 5 What to take for best results The Avemar product is an instant drink mix called Avé , which combines Avemar with natural orange flavouring and fructose in pre-measured packets . As a dietary supplement , the recommended usage is one packet per day mixed with 8oz of cold water . You should consume it within 30 minutes of mixing a batch . Also note that it 's a good idea to take Avé one hour before or after a meal and two hours before or after any drugs or other dietary supplements . If you weigh over 200 pounds ( 14 stone ) , use two packets per day . If you weigh less than 100 pounds ( 7 stone ) , only use half of a packet per day . Although some people reported uneasiness in their stomachs during the first few days of using Avemar , the effect only lasted a few days . No vomiting , diarrhoea , or any other symptoms were reported . Contraindications : Since this is a wheat product , there is the potential for allergic response . Avemar should not be consumed by people who have had an organ or tissue transplant , those who have malabsorption syndrome , or those with allergies to foods containing gluten , such as wheat , rye , oats and barley . It 's also not recommended for people with fructose intolerance or hypersensitivity to gluten , wheatgerm , or any of the components or ingredients of this product . If you suffer from bleeding ulcers , you should stop using Avemar two days before undergoing a barium X-ray contrast examination and resume taking it two days after the completion of the examination . This precaution is necessary because wheatgerm contains lectin , which can potentially cause red blood cells to clump . If you are currently taking medications or have any adverse health conditions , you should consult with your pharmacist or physician before taking Avemar . Sources : 1 . British Journal of Cancer 2003 ; 89 ( 3 ) : 465-9 2 . International Journalof Cancer 2002 ; 100 ( S13 ) : 408 3 . " A medical nutriment study has supportive effect in oral cancer " ( unpublished , Marta Ujpal et al ) 4 . Pancreas 2001 ; 23 : 141-7 ; Drug Discovery Today 2002 ; 7 ( 6 ) : 18-26 5 . Journal of Bilogical Chesmistry 2002 ; 277 : 46 , 408-14 ; International Journal of Oncology 2002 ; 20 : 563-70 05.05.2006 Sign up for FREE Health Email : Save article | Printable version | Email to a friend See more articles about Cancer : Promising Progress in Cancer Treatment ( Cancer ) Breast Asymmetry Linked to Cancer ( Cancer ) Cancer : Are you at risk of colorectal cancer ? ( Cancer ) Colorectal Cancer : New Research Findings On Colon Cancer ( Cancer ) Breast Cancer & Antibiotics : When You Should Question What Your GP Prescribes ( Cancer ) Mobile Phone Health Risks : Is Your Mobile Risking Your Health ? ( Cancer ) Mammogram Problems : Mammograms , Biopsies , And Lumpectomies ( Cancer ) The breast cancer , radiation therapy and anaemia link ( Cancer ) How vitamin D can help protect against cancer ( Cancer ) Cancer : Gene Therapy Tested to Fight Cancer ( Cancer )