ONLINE PHARMACY CANADA - Cialis Professional - Where Can You Buy Viagra - 10,152 Orders Today.
Cialis Generic Online, Buy Cheap Cialis In Canada. In sample canada free cialis buy cheap online generic is there a.
Cialis For Sale - Cialis sale online canada, Buy cialis professional, Cialis pills sale canada.Order Cialis - Buy cialis professional, Cialis cheapest price canada, Cialis sale us.
This blockage is the beginning of acne Buy Cialis Soft Tabs In Canada No.Buy Cialis Online - Can you split cialis pills half, Buy cialis professional, Buy cialis no rx. Cheap cialis generic canada, Cheapest brand cialis online,.Order Cialis - Buy cialis professional, Cialis Cheapest Prices, Order generic cialis online canada.
Dictionary of Cialis online Slang can also help you contain. performance gear for the professional.
Canadian viagra cheap, Buy online. buy cialis professional online Cialis line. and Master Hearts can idol to respected actor.
Cialis how to buy, Buy cialis using paypal, Cheap cialis online canada, Cialis buy no prescription,.
Buy cialis online london 120. routine nutrient tomar Acerola they are appearing (b)(4).On behalf of the IEPA Early Intervention in Mental Health, it is both an honor and a pleasure to invite you to attend the 10 th IEPA International Conference in Milan. Generic cialis online, generic cialis prices Online canada. buy canada cheap generic, professional. take can you legally buy online side effects.Cialis pharmacy - Cialis professional, Buy cialis canada online, Best place buy cialis line.
Whenever you decide to buy Cialis from a Canadian pharmacy, you can trust.Cialis ganeric What is better viagra or Order Cialis From. best price cialis professional online rx How Can I Buy buspar Canadian. Online Pharmacy Florida Usa Cialis Professional Online - How to get brand cialis 20 mg pills in the uk brand cialis 20 mg pills mail order.Cialis without doctor - Generic tadalafil, Buy cialis professional, Buying cialis online canada.
Buy Cialis Professional Online Cialis Online Sale In Canada Buy Cialis Professional Online How Many Proteins.
Cialis professional, Cialis 20mg cheap, Cialis buy from canada. Buy cialis online without rx, Can you split cialis pills half, Buy cialis united states,.
Can I Order Cialis From Canada where can i buy cialis online. can you buy cialis in vietnam, cialis online no prescription. cheap cialis professional in the.At last he had the murderer of his son at his mercy cheapest cialis professional.


This week I've been struggling somewhat with the precarious balancing act of recovery. I am slowly becoming an active and autonomous person in this world. That fact is absolutely terrifying. I am attempting to be part of the world but not letting it overwhelm me.
I now exercise…yes it's true. I have been to two whole pilates classes and am attempting to start kick-boxing. though I pushed myself too hard on the cardio at the kick-boxing on Thursday and my chest is still aching from my asthma attack. Attack sounds dramatic but I'm not sure what to call it. Incident? Episode?
Either way it was rotten.
I'm pretty keen to keep this exercise routine put. The problem is exercise was one of my negative coping mechanisms when I was suffering severely from my eating disorder. My therapist says that classes are good because there is a set end time so I cannot exercise to excess. I was thrown entirely at pilates last week when Courage by Superchic came on the playlist, a song about living with an eating disorder.
The Internet is a major issue here. If we ignore all the horrible and depressing articles about we are still left with disgusting adverts encouraging to 'loose weight with this one simple trick'.
Scribbling though the first part of my novel and having lots of fun with pie charts . I'm ensuring I have all the elements of my novel stuck in my head before I go on to write the next part.
I left the house, read stories to the little ones at the library then went into Crafty Sew & So. It felt good to get out of my head for a day. Freya and I came up with a wonderful story all about two women who become superheroes after training in the art of kick-boxing. I had so much fun sketching a comic of the story when I got home. At some point I aim to refine the it and find someone who can actually draw to complete the work.
I created a great little Bunny tutorial for Crafty Sew & So. It was a lovely day so I decided to take the pictures outside.
I went over to see Freya in the evening for the aforementioned kick-boxing class. On the way I couldn't resist taking a photo across from the old liberty building.
Despite the horrid asthma affair I did have lots of fun at Kick-boxing and will hopefully be back on Thursday, though I'll probably be a little more cautious with the cardio.
I was feel exhausted still from asthma, but determined to have a good day. I got myself all prettied up in the morning, and googled how to wear a head scarf. At the shop I got started on gorgeous kit that has just come into Crafty from The New Craft House. The fabric is so easy to work with. I like sitting in front of the tv with a good cup of tea and hand sewing the hexies together. Hopefully it will be done soonish and I can show you all how it turns out.
Manically crazy busy day at Crafty Sew & So, It seemed everybody wanted fabric, I tried to do a bit more of the cushion but I just ended up stopping and starting because of all the lovely customers. In the evening, however, when my husband was busy playing destiny I started trying to edit my novel. It didn't particularly work as I ended up drawing a scene from one of the pages.
Today I have been once again going through my novel, I managed to get through two chapters so far and hope to get at least another one done today. It was my plan to have finished by the end of the week. Above is the pie chart for characters mentioned and present in the first nine chapters.
Reading was one of the first things I loved to fall by the wayside. Slowly but surely my love of reading is returning. Though my brain has yet to wrap around books of any length I am very much enjoying Audio-books and graphic novels.
Recently I've discovered a wealth of amazing autobiographical graphic novels, exploring personal journeys of recovery and mental health. Here are a few of my favourites.
This is a perfect illustration of living with an eating disorder, particularly if abuse was a key factor in it's development. Please be aware that this book can be triggering and only read if you are in a healthy place. My husband has also read this book, the poignant illustrations helped him understand the things I cannot explain.
I stumbled upon this in the Wellcome Collection bookshop. They have a fantastic selection of books concerning mental, as well as physical, health. This short comic feels like a snapshot of the authors life. really useful for anyone who thinks their problems aren't 'real' enough to seek help.
Absolutely hilarious and only a little heart breaking. Brosh's illustrations are so simple yet express a width depth and breadth of emotion. Brosh reveals so much about her life, from her struggles with depression to the, possibly ill-advised, adoption of two dogs. I finished this book then read it all over again. I laughed and I cried, sometimes at the same time.
The author travels back through her past attempting to fix absolutely everything. It is a tempting prospect to go back and change all those humiliating memories. The ones that still creep up on me when I'm in the shower or trying to get to sleep. This is a fantastic tale of accepting yourself by facing up to those memories and being able to move on.
There's also a couple of non-autobiographical comics I find helpful I think they belong here.
Essentially a picture book for adults. Flimsy is a charming character who gives his very best advice on modern living, whilst always holding tight to a glass of wine. Its a simple reminder of all the lovely things you can do to feel happy. My husband picked this up for me at Leicester Comic con and I have a lovely sketch of flimsy drawn by the author.
I mentioned this stunning book in a previous post. I really can't recommend it highly enough. Every page is illustrated beautifully. The story takes you through the dark woods, alongside a young fox, in search of his star. It's a true delight to read and sure to calm any chaotic thoughts racking the mind.
Yesterday I went to a wonderful craft day with Neil Burly at perfectly 4med. This was a Christmas present from my mum. Only recently have I felt well enough to leave the house for a day. The main obstacle was eating in an unfamiliar environment. Happily I coped just fine with my packed lunch, sitting outside with a gorgeous Labradoodle named Charlie at my feet.
We started with a blank sketchbook and added texture with paste and glued all sorts of beautiful bits and pieces into place.
The next step was to paint over it with craft paint, I can't remember what it was called but it was a chalky, acrylic, glue paint. it took me a couple of times because the metal was tricky to cover.
I had absolutely no idea where to go from here, and felt very much like I a school child and asked for help, turns out I just had to do more. I sprayed more colours and it looked a lot more like i wanted however now the bronze key and bits looked way too bright and not at all tarnished. Again I looked helplessly about and asked for help to make verdigries effect. it turned out perfectly.
I was amazed at how many different looks came from the same materials. I had a fantastic day and would recommend it to anyone.
I began a frenzy of notebook binding a couple of days ago. Today I have a little collection of handmade Japanese stab bound books.
First I made this notebook with a pad of parchment paper and hard card i'd scavenged from around the house. I covered the card with some beautiful paper from one of my colouring books.
I messed up to start with and I made the card the same size as the paper.
I very carefully unwrapped the board and cut it to the right size so it sits nicely next to the stab binding. I glued the first page to the cardboard and placed it in between a couple of very heavy board games and left it there over night.
Next I made a little notepad from a round poster and an early draft of my novel. I trimmed the coaster to fit the notes and glues it the same as before to the front. I trimmed the excess paper from the notes and pressed it.
For my third notebook I tried a variation of the turtle pattern. it ended up a little messy but it's nice nonetheless. I used thin card, by this time I'd run out of thick card to ferret out. I covered the card with fabric, using fabric glue, it would have been better if I used bookbinding Pva glue because it's Ph neutral and wouldn't leave marks.
The final notebook I made is similar to this one but with the simple turtle pattern and thick cartridge paper. I covered it in a jaunty nautical print. I'm sure there are much better ways to fabric bind books which i will look up at some point but for now I'm very happy with all my notebooks.
In the book they add rabbit ears to the top but I prefer it simple.
I think I may have gotten a little over confident because I made a pattern without looking at the measurements and ended up making it a touch too small. That caused a major anxiety and stress later on but let's put that down to experience.
First thing I did was draw a simple Volkswagen on to paper then cut out four pieces of plain cotton using this pattern.
Next I cut out all the little bits from the pattern and pinned them to my pieces of fabric.
Cut these pieces out. If you want a neat look you can press down the edges of the shapes, but if not just pin the pieces with raw edges to one of the main pieces of fabric.
Most sewing machines have various fancy top stitching, it's fun to experiment with those. If you don't have a sewing machine it's fine just to hand sew.
I ended up using the sewing machine for the little VW sign, it might have looked better hand sewn.
Next cut out another piece of material, the same hight as the curves of at the front and width of the plain material. Sew this to another piece of the plain fabric.
As you can see you don't have to be too neat with it. Any things that look rough you can explain away by looking saying it looks 'handmade'.
Place the front decorated side of the tea cosy to one of the remaining plain pieces. Do the same with the back piece. Sew together good side to good side along the curve, leave 2-3 cm on each corner loose and the straight lower edge open.
Turn right side out. Double hem the inner lining and pin it into place, folded over the patterned material. Stitch the fold into place.
It was at this point I realised I'd managed to make the two pieces different sizes! There is no picture of my too small misshaped tea cosy as it was at this point were I'd worked well past lunch time. The cosy was so small it barely looked like it could cover a mug. I can't be sure my view of it was objective, My husband told me it was fine, in fact he told me it was good, great even but I did not believe him. When he suggested I take a break i could feel my skin prickling. I was not about to stop. I unpicked the mess and by this point my hands were shaking and I couldn't tell whether it was from hunger or from frustration. Once i had unpicked it all I reluctantly left my work to eat some food. Once I'd eaten I began to calm down and gave up on the mission for the day.
The next day I set up my machine, painstakingly slowly sewed the two pieces together as close to the edge as I could, when I turned it over it wasn't perfect but it was okay. I am trying my hardest to learn that everything does not have to be perfect.
Here's the finished product it fitted perfectly and my father in law is very happy with it.
Colouring is probably the most relaxing forms of art around. You choose the colours, deep and dark or pretty pastels. Here's a few bits I've done from Enchanted Forest.
After doing a bit of ink drawing from everyone can draw I decided to ink the next pages of enchanted forest. I started with indian ink and dip pen. I enjoyed it until Baratheon decided he had to be on my lap right then!
This isn't even the first time he's been a pest when I'm trying to draw.
I picked up again with a Faber-Castell PITT artist pen.
I decided to make small patterns for the first tree and then use the bold pen for the taller trees leaves.
It's lots of fun to dip in and out of whenever you fancy. though now I'm tempted to buy lots of pretty coloured pens and inks.
I've always been keen on drawing but my perfectionism has gotten in the way. If there's a drawing I'm not happy with I'll often just tear out the page rip it up. This is not conducive to learning. Recently I've decided to make another attempt. It took me a surprising amount of time to find a book that actually began with the basics. Every book I looked at went into very technical detail and demanded knowledge of technical materials. This is an awful lot to assume of a novice.
I finally found one that seemed perfect when perusing the little library down the road. |his trip in itself was a big achievement as it was the first time I left the house by myself in a very long time. I managed to push through the anxiety and even had a nice conversation with the library assistant. I walked home, very proud of myself, with a Everyone Can Draw and a small bundle of books under my arms.
I skipped the introduction, hopefully I'll go back but I was impatient to start. The very beginning taught me different ways to hold a pencil, work with tones and create simple shapes.
I particularly like the fact that Barber give advice on which pencils to use an later which charcoal, pens and brushes. So far the 'lessons' are clear concise and not the least bit patronising.
I'm really looking forward continuing, I've just order watercolours and brushes and will post my mess of an attempt here.


text:
LEGACY / Jim Smith
Jim Smith joined The Southern Group's Tallahassee office in 2011 after serving Florida and its citizens for more than 40 years. Elected to two terms as Florida's attorney general, Jim was known for his zeal in fighting crime and protecting Florida's consumers.
During his time as attorney general, Jim successfully argued the "Cameras in the Courtroom" case in front of the U.S. Supreme Court, which permitted states to allow the live televising of criminal trials. Jim has also served as Florida's secretary of state (twice), chief of staff to the governor, deputy secretary of commerce, and assistant secretary of state.
Throughout his long career in government, Jim has developed expertise across numerous policy areas, including agriculture, appropriations, banking and finance, campaigns, economic and business development, environment and sustainability, insurance, local government, military, sports and entertainment, strategic planning, and water.
Jim has been recognized for his commitment to Florida through honors and awards such as: Honorary Doctor of Humane Letters degree from Florida State University; Conservationist of the Year Award from Florida Audubon Society; Honorary Doctor of Laws degree from Stetson University; Stetson University Distinguished Alumni Award; Friend of Education Award; Florida Teaching Profession-National Education Association; President's Award from the Florida Education Association; Furtherance of Justice Award from the Florida Prosecuting Attorneys Association; and Meritorious Service Award from the Florida Silver-Haired Legislature, as well as a U.S. Department of Justice Award for Effectiveness in Drug Enforcement.
Jim has served on many task forces and boards, including chairing the Governor's Task Force on Criminal Justice Reform and the Governor's Commission for Reform of the Corrections System, co-chairing the Florida Election Reform Task Force, and serving on the Commission on the Future of Florida's Environment, the Governor's Task Force to Promote Ethics in Government, and the Governor's Commission on the Statewide Prosecution Function. Jim has also served Florida's education system as a member of the Board of Regents for the state university system and as chairman and vice-chairman of the Board of Trustees for Florida State University.
Jim received a BS in public administration and government from Florida State University and a JD from Stetson University of Law. He resides in Tallahassee with his wife, Carole.
Download biography in PDF format >>

redpajama_set_name: RedPajamaCommonCrawl


Popeye: 'I'm your one and only exspring. See, we got the same bulgy arms'.
Michael Iver Peterson didn't use a special murder weapon to kill his wife Kathleen, he used his bare hands.
Michael Iver Peterson with his right hand grabbed his wife Kathleen by the hairs of her frontal area and slammed with force the back of her head against the wooden stairs, again and again, till she died.
During the assault, he once grabbed her contemporary by the hairs with his right hand and by her throat with his left hand and his thumb produced the fracture of the superior cornu of the left thyroid cartilage of Kathleen's throat.
According with her post mortem examination, Kathleen suffered multiple lacerations of the head consistent with a flat object, that flat object were the stairs against which her head impacted several times, not because a fall down the stairs but because Michael Peterson slammed her head against those stairs.
On both Kathleen hands, on the bottom steps of the stairs and on the Diet Coke can found in the patio, that Michael Peterson drank from, were found several cut hairs. These cut hairs were from the frontal area of Kathleen head and were cut off by Michael Peterson right hand and by Kathleen hands when she tried to free her hairs from his hand, for this reason they found hairs on her hands too.
If these hairs were from the back area of her head, investigators should have found just crushed hairs, not cut hairs. It could be helpful to check the exhibits to see if they collected either hairs with their roots that could have been pulled out just from Kathleen frontal scalp and could support this reconstruction.
The big amount of blood found inside Michael Peterson pants has just an explanation: the second time he assaulted Kathleen, he sat on her upper legs, close to her waist.
Michael Peterson attacked his wife twice, after the first time a lot of blood drained on Kathleen waist, she then unexpectedly recovered and stood up, at that point Peterson attacked her for a second time and while he was slamming again her head against the stairs his pants absorbed the blood from Kathleen clothes because he was sitting on her with his legs opened in order to stop her from moving.
There were no fractures on Kathleen skull because she was slammed against a wooden surface.
Kathleen had contusions on her posterior arms and back because when her head was slammed against the stairs she hit her posterior arms and back too.
She had defensive contusions on her wrist and hands because she fought back at Peterson and finally she had no contusions on her ribs, legs, feet or knees because she didn't fall down the stairs.
9- and the absence of fractures on Kathleen face too. Especially in a narrow area, a hit from behind that is able to cause a laceration of the skull usually produces fractures of the nasal or cheek bones of the victim due to the crush against the wall or against the stairs followed the rebound of the blow to the head.
The blood found on the walkway leading to the house dropped from Michael Peterson bloody hands.
Weapons usually reflect killers' personality. Michael Peterson is a kind of contemporary Popeye, for his face, his smocking the pipe and his muscular body and, as Popeye, he used to kill a personal weapon, his hands, at least twice. Michael Peterson was very proud of his muscles and often put them on display wearing just a tank top, according to the pictures seen in the documentary 'The Staircase', and for sure he knew to be strong enough to be able to kill a tiny woman using his bare hands. We shouldn't forget that he had a military training and he battled in Vietnam, in the Second Indochina war.
In 1985, Elizabeth Ratliff was killed in the same way by a younger and stronger Michael Peterson. She was found dead at the bottom of the stairs of her house in Germany, she suffered a fracture at the base of the skull because Michael Peterson was younger and stronger and the surface her head was slammed against was a floor made of terra-cotta tiles, not wood, like in the Kathleen case. It could be quite interesting to ask people that saw and cleaned that first crime scene if they found hairs on the scene.


Looking for inspiration for my dining room I keep going back to Anna's office from Door Sixteen. My floors aren't white and never will be cause I rent but the wainscoting on the bottom half of the wall is, so I think I can get away with painting the top half dark, the question is do I really want dark walls in an already dark room? I love this wallpaper as well but again, I rent. I'm having a lot of difficulty making the dining room a room rather than a really wide pass through into the kitchen. Maybe I'm just over thinking everything.


Does trackIR work on Macs?
Currently there are no drivers, and software, for OS X.
so now that the mac market is continously booming since years and most macs are intel - any chance for mac drivers soon?
4.117 views of the movie "TrackIR on Mac OS X using SmartNAV and mouse views in games."
any news with that ?
Currently there is no added information regarding the TrackIR , and OSX.
The fact that there is no OSX support is a major downside for me. I've been using Track IR for about five years but my main computer these days is my macbook and my main game/sim has been X-Plane. In the past I've used X-Plane with my Track-IR in Windows but I'm dissapointed that it doesn't work with my new macbook. I'm sure I'm not the only Track-IR user out there who is making the switch from Windows to OSX and I'm sure the X-Plane communuty (which is growing massively since MS FS stopped development) has pleanty of potential Track IR customers.
Surely us mac users are woth some research and development time?
Hey guys , with the growing popularity of MAC OS X , you can't ignore us , MAC users.
At least put a pole in your website , asking how many users need MAC drivers.
Now that Apple is larger than Microsoft, please create Mac OS drivers, or at at least publish your hardware specs so that someone else could do it.


text:
Harmonic series (mathematics)
Part of a series of articles about
Fundamental theorem
Limits of functions
Mean value theorem
Rolle's theorem
Derivative (generalizations)
of a function
Differentiation notation
Second derivative
Third derivative
Change of variables
Implicit differentiation
Related rates
Taylor's theorem
Rules and identities
Quotient
General Leibniz
Faà di Bruno's formula
Lists of integrals
Antiderivative
Integral (improper)
Riemann integral
Lebesgue integration
Contour integration
Integration by
Cylindrical shells
Substitution (trigonometric)
Partial fractions
Reduction formulae
Geometric (arithmetico-geometric)
Alternating
Convergence tests
Summand limit (term test)
Direct comparison
Limit comparison
Alternating series
Cauchy condensation
Divergence
Laplacian
Theorems
Kelvin–Stokes
Multivariable
Formalisms
Partial derivative
Multiple integral
Line integral
Surface integral
Volume integral
Jacobian
Hessian matrix
Malliavin
In mathematics, the harmonic series is the divergent infinite series:
Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are 1/2, 1/3, 1/4, etc., of the string's fundamental wavelength. Every term of the series after the first is the harmonic mean of the neighboring terms; the phrase harmonic mean likewise derives from music.
The fact that the harmonic series diverges was first proven in the 14th century by Nicole Oresme,[1] but this achievement fell into obscurity. Proofs were given in the 17th century by Pietro Mengoli,[2] Johann Bernoulli,[3] and Jacob Bernoulli.[4]
Historically, harmonic sequences have had a certain popularity with architects. This was so particularly in the Baroque period, when architects used them to establish the proportions of floor plans, of elevations, and to establish harmonic relationships between both interior and exterior architectural details of churches and palaces.[5]
The harmonic series is counterintuitive to students first encountering it, because it is a divergent series even though the limit of the nth term as n goes to infinity is zero. The divergence of the harmonic series is also the source of some apparent paradoxes. One example of these is the "worm on the rubber band".[6] Suppose that a worm crawls along a 1-metre rubber band at the same time as the rubber band is uniformly stretched. If the worm travels 1 centimetre per minute and the band stretches 1 metre per minute, will the worm ever reach the end of the rubber band? The answer, counterintuitively, is "yes", for after n minutes, the ratio of the distance travelled by the worm to the total length of the rubber band is
(In fact the actual ratio is a little less than this sum as the band expands continuously). The reason is that the band expands behind the worm also; eventually, the worm gets past the midway mark and the band behind expands increasingly more rapidly than the band in front.
Because the series gets arbitrarily large as n becomes larger, eventually this ratio must exceed 1, which implies that the worm reaches the end of the rubber band. However, the value of n at which this occurs must be extremely large: approximately e100, a number exceeding 1043. Although the harmonic series does diverge, it does so very slowly.
Another problem involving the harmonic series is the Jeep problem.
Another example is: given a collection of identical dominoes, it is clearly possible to stack them at the edge of a table so that they hang over the edge of the table without falling. The counterintuitive result is that one can stack them in such a way as to make the overhang arbitrarily large, provided there are enough dominoes.[6][7]
A simpler example, on the other hand, is the swimmer that keeps adding more speed when touching the walls of the pool. The swimmer starts crossing a 10-meter pool at a speed of 2 m/s, and with every cross, another 2 m/s is added to the speed. In theory, the swimmer's speed is unlimited, but the number of pool crosses needed to get to that speed becomes very large; for instance, to get to the speed of light (ignoring special relativity), the swimmer needs to cross the pool 150 million times. Contrary to this large number, the "time" required to reach a given speed depends on the sum of the series at any given number of pool crosses (iterations):
Calculating the sum (iteratively) shows that to get to the speed of light the time required is only 94 seconds. By continuing beyond this point (exceeding the speed of light, again ignoring special relativity), the time taken to cross the pool will in fact approach zero as the number of iterations becomes very large, and although the time required to cross the pool appears to tend to zero (at an infinite number of iterations), the sum of iterations (time taken for total pool crosses) will still diverge at a very slow rate.
There are several well-known proofs of the divergence of the harmonic series. A few of them are given below.
Comparison test
One way to prove divergence is to compare the harmonic series with another divergent series:
Each term of the harmonic series is greater than or equal to the corresponding term of the second series, and therefore the sum of the harmonic series must be greater than the sum of the second series. However, the sum of the second series is infinite:
It follows (by the comparison test) that the sum of the harmonic series must be infinite as well. More precisely, the comparison above proves that
for every positive integer k.
This proof, proposed by Nicole Oresme, is considered by many in the mathematical community to be a high point of medieval mathematics. It is still a standard proof taught in mathematics classes today. Cauchy's condensation test is a generalization of this argument.
Integral test
It is possible to prove that the harmonic series diverges by comparing its sum with an improper integral. Specifically, consider the arrangement of rectangles shown in the figure to the right. Each rectangle is 1 unit wide and 1 / n units high, so the total area of the rectangles is the sum of the harmonic series:
However, the total area under the curve y = 1 / x from 1 to infinity is given by an improper integral:
Since this area is entirely contained within the rectangles, the total area of the rectangles must be infinite as well. More precisely, this proves that
The generalization of this argument is known as the integral test.
Rate of divergence
The harmonic series diverges very slowly. For example, the sum of the first 1043 terms is less than 100.[8] This is because the partial sums of the series have logarithmic growth. In particular,
where is the Euler–Mascheroni constant and which approaches 0 as goes to infinity. Leonhard Euler proved both this and also the more striking fact that the sum which includes only the reciprocals of primes also diverges, i.e.
Partial sums
The first thirty harmonic numbers
Partial sum of the harmonic series, Hn
expressed as a fraction
2 3 /2 1.5 1.5
3 11 /6 ~1.83333 1.83333
4 25 /12 ~2.08333 2.08333
5 137 /60 ~2.28333 2.28333
6 49 /20 2.45 2.45
7 363 /140 ~2.59286 2.59286
9 7 129 /2 520 ~2.82897 2.82897
10 7 381 /2 520 ~2.92897 2.92897
11 83 711 /27 720 ~3.01988 3.01988
13 1 145 993 /360 360 ~3.18013 3.18013
17 42 142 223 /12 252 240 ~3.43955 3.43955
18 14 274 301 /4 084 080 ~3.49511 3.49511
19 275 295 799 /77 597 520 ~3.54774 3.54774
23 444 316 699 /118 982 864 ~3.73429 3.73429
24 1 347 822 955 /356 948 592 ~3.77596 3.77596
25 34 052 522 467 /8 923 714 800 ~3.81596 3.81596
27 312 536 252 003 /80 313 433 200 ~3.89146 3.89146
29 9 227 046 511 387 /2 329 089 562 800 ~3.96165 3.96165
The nth partial sum of the diverging harmonic series,
is called the nth harmonic number.
The difference between the nth harmonic number and the natural logarithm of n converges to the Euler–Mascheroni constant.
The difference between distinct harmonic numbers is never an integer.
No harmonic numbers are integers, except for n = 1.[9]
Alternating harmonic series
The first fourteen partial sums of the alternating harmonic series (black line segments) shown converging to the natural logarithm of 2 (red line).
is known as the alternating harmonic series. This series converges by the alternating series test. In particular, the sum is equal to the natural logarithm of 2:
This formula is a special case of the Mercator series, the Taylor series for the natural logarithm. A proof without words that the sum is was shown by Matt Hudelson.[10]
A related series can be derived from the Taylor series for the arctangent:
This is known as the Leibniz series.
General harmonic series
The general harmonic series is of the form
where and are real numbers and b/a is not a non-positive integer.
By the limit comparison test with the harmonic series, all general harmonic series also diverge.
A generalization of the harmonic series is the p-series (or hyperharmonic series), defined as
for any positive real number p. When p = 1, the p-series is the harmonic series, which diverges. Either the integral test or the Cauchy condensation test shows that the p-series converges for all p > 1 (in which case it is called the over-harmonic series) and diverges for all p ≤ 1. If p > 1 then the sum of the p-series is ζ(p), i.e., the Riemann zeta function evaluated at p.
The problem of finding the sum for p = 2 is called the Basel problem. The value of the sum for p = 3 is called Apéry's constant.
ln-series
Related to p-series is ln-series, defined as
for any positive real number p. This can be shown by integral test to diverge for p ≤ 1 but converge for all p > 1.
φ-series
For any convex, real-valued function φ such that
the series ∑n≥1 φ(n−1) is convergent.
Random harmonic series
The random harmonic series
where the sn are independent, identically distributed random variables taking the values +1 and −1 with equal probability 1/2, is a well-known example in probability theory for a series of random variables that converges with probability 1. The fact of this convergence is an easy consequence of either the Kolmogorov three-series theorem or of the closely related Kolmogorov maximal inequality. Byron Schmuland of the University of Alberta further examined[11][12] the properties of the random harmonic series, and showed that the convergent is a random variable with some interesting properties. In particular, the probability density function of this random variable evaluated at +2 or at −2 takes on the value 0.124999999999999999999999999999999999999999764…, differing from 1/8 by less than 10−42. Schmuland's paper explains why this probability is so close to, but not exactly, 1/8. The exact value of this probability is given by the infinite cosine product integral [13] divided by π.
Depleted harmonic series
Main article: Kempner series
The depleted harmonic series where all of the terms in which the digit 9 appears anywhere in the denominator are removed can be shown to converge and its value is less than 80.[14] In fact when terms containing any particular string of digits are removed the series converges.
Wikimedia Commons has media related to Harmonic series.
Complex logarithm
Harmonic progression
Lagarias's theorem
List of sums of reciprocals
↑ Nicole Oresme (ca. 1360) Quastiones super Geometriam Euclidis (Questions concerning Euclid's Geometry).
↑ Pietro Mengoli, Novæ quadraturæ arithmeticæ, seu De additione fractionum [New arithmetic quadrature (i.e., integration), or On the addition of fractions] (Bologna ("Bononiæ"), (Italy): Giacomo Monti ("Jacobi Monti"), 1650). The proof of the divergence of the harmonic series is presented in the book's preface (Præfatio).
Mengoli's proof is by contradiction:
Let S denote the sum of the series. Group the terms of the series in triplets:
S = 1 + (1/2 + 1/3 + 1/4) + (1/5 + 1/6 + 1/7) + (1/8 + 1/9 + 1/10) + …
Since for x > 1, 1/(x-1) + 1/x + 1/(x+1) > 3/x, then
S > 1 + (3/3) + (3/6) + (3/9) + … = 1 + 1 + 1/2 + 1/3 + … = 1 + S, which is false for any finite S. Therefore, the series diverges.
↑ See: Corollary III of De seriebus varia in: Johannis Bernoulli, Opera Omnia (Lausanne & Basel, Switzerland: Marc-Michel Bousquet & Co., 1742), vol. 4, p. 8, Corollary III.
↑ See:
Jacob Bernoulli, Propositiones arithmeticae de seriebus infinitis earumque summa finita [Arithmetical propositions about infinite series and their finite sums] (Basel, Switzerland: J. Conrad, 1689).
Jacob Bernoulli, Ars conjectandi, opus posthumum. Accedit Tractatus de seriebus infinitis … [Theory of inference, posthumous work. With the "Treatise on infinite series" joined … ] (Basel, Switzerland: Thurneysen, 1713), pp. 250–251. From page 250, proposition 16:
"XVI. Summa serei infinita harmonicè progressionalium, 1/1 + 1/2 + 1/3 + 1/4 + 1/5 &c. est infinita.
Id primus deprehendit Frater: … "
(16. The sum of an infinite series of harmonic progression, 1/1 + 1/2 + 1/3 + 1/4 + 1/5 + … , is infinite.
[My] brother first discovered it [i.e., this proof].)
↑ George L. Hersey, Architecture and Geometry in the Age of the Baroque, p 11-12 and p37-51.
1 2 Graham, Ronald; Knuth, Donald E.; Patashnik, Oren (1989), Concrete Mathematics (2nd ed.), Addison-Wesley, pp. 258–264, ISBN 978-0-201-55802-9
↑ Sharp, R.T. (1954), "Problem 52: Overhanging dominoes" (PDF), Pi Mu Epsilon Journal, 1 (10): 411–412
↑ "Sloane's A082912 : Sum of a(n) terms of harmonic series is > 10^n". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
↑ "Harmonic Number". Wolfram Research, Inc. Retrieved November 20, 2014.
↑ Hudelson, Matt (1 October 2010). "Proof Without Words: The Alternating Harmonic Series Sums to ln 2" (PDF). Mathematics Magazine. 83 (4): 294. doi:10.4169/002557010X521831.
↑ "Random Harmonic Series", American Mathematical Monthly 110, 407–416, May 2003
↑ Schmuland's preprint of Random Harmonic Series
↑ Weisstein, Eric W. "Infinite Cosine Product Integral." From MathWorld – a Wolfram Web Resource. http://mathworld.wolfram.com/InfiniteCosineProductIntegral.html accessed 11/14/2010
↑ Nick's Mathematical Puzzles: Solution 72
Hazewinkel, Michiel, ed. (2001), "Harmonic series", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
"The Harmonic Series Diverges Again and Again", The AMATYC Review, 27 (2006), pp. 31–43. Many proofs of divergence of harmonic series.
Weisstein, Eric W. "Harmonic Series". MathWorld.
Weisstein, Eric W. "Book Stacking Problem". MathWorld.
Sequences and series
Geometric progression
Square number
Cubic number
Powers of two
Powers of 10
Complete sequence
Figurate number
Heptagonal number
Hexagonal number
Lucas number
Pell number
Pentagonal number
Polygonal number
Triangular number
Properties of sequences
Cauchy sequence
Monotone sequence
Periodic sequence
Properties of series
Convergent series
Divergent series
Conditional convergence
Absolute convergence
Uniform convergence
Telescoping series
Explicit series
1/2 − 1/4 + 1/8 − 1/16 + ⋯
1/2 + 1/4 + 1/8 + 1/16 + ⋯
1/4 + 1/16 + 1/64 + 1/256 + ⋯
1 + 1/1s + 1/2s+ 1/3s + ... (Riemann zeta function)
1 + 1 + 1 + 1 + ⋯
1 − 1 + 1 − 1 + ⋯ (Grandi's series)
Infinite arithmetic series
1 − 2 + 3 − 4 + ⋯
1 + 1/2 + 1/3 + 1/4 + ⋯ (harmonic series)
1 − 1 + 2 − 6 + 24 − 120 + ⋯ (alternating factorials)
1/2 + 1/3 + 1/5 + 1/7 + 1/11 + ⋯ (inverses of primes)
Kinds of series
Laurent series
Puiseux series
Dirichlet series
Trigonometric series
Fourier series
Generating series


It's a framed date! Chris and I just took photos of found address numbers (these hail from various spots in Old Town Leesburg), and put them in a matted frame. There are companies that custom-make these for sale, but I think it's way more fun to do this yourself, and it's a totally simple but super thoughtful/personalized gift perfect for anyone. You can even do this project as a piece of art for your own home.
First, start off with an idea of what occasion you want to commemorate: an anniversary, a baby's birthday, a vacation date, anything! If you want to use the date only, you can easily find a matted frame with three openings for the month, day and year. (Or day, month, and year if you're British.) I found this one with three vertical openings at Pottery Barn. If you want to do the date along with a special photo, you'll have to search a little harder to find a pre-matted frame, but something with a configuration like this would totally work. Or of course, you can have your project custom matted and framed at a frame/art store. If you want to use a pre-matted frame, knowing the orientation of the openings in advance will help you to plan your photos.
Next, grab your camera and head out on a scavenger hunt for your numbers! Note: If you are forgetful or easily sidetracked like I am, it's best to write the date down so you know for sure which numbers are needed. Also, you don't need a fancy camera for this project, but a long lens or a camera with zoom capability might help if your numbers are just out of reach so that you don't have to trespass. And I knew that my frame had three vertical openings, so I photographed my numbers in portrait (vertical) orientation.
Now, where to find these numbers? Old historic downtown areas have tons of interesting address markers on cute little storefronts and surrounding neighborhoods. Walk around and explore. It's art + gift-giving + exercise all wrapped up into one! Take photos of the same number in different styles so that you can choose your favorites later. When you're taking the pictures, try to fill the frame with as much of the number as you can, but leave enough of a margin on all sides in case your mat opening is not exactly 4×6 or 5×7, etc. You can always use software like Photoshop to crop the image when you're ready to print. I happened to like the cheerful colors of the numbers we found so I left the images as-is, but you can also use software to convert the images to black-and-white for a clean and crisp graphic feel that is timeless and sure to go with any decor!
And that brings us to the last step – just print your photos and arrange them in the frame! Be sure to use photo-friendly adhesives. I just used acid-free tape to mount the photos behind the mat and voila! Totally personalized custom artwork bursting with meaning. Easy enough, right?! So what date would you frame? Do you have any other fun photo projects to share?


Do you want to make your phone a real-time thermometer?
This accurate weather thermometer app can help you check ambient temperature conveniently!
·It can be Fahrenheit thermometer or Celcius weather app.
· An ambient temperature thermometer for cities worldwide: this live thermometer app is not only a weather detector for your own location, but also a global weather tracker that you can search world weather and temperature. We support weather and temperature checking in cities like Los Angeles, New York, Chicago, Las Vegas, Hawaii, Sydney, Perth, Amsterdam, Tokyo, Ottawa, Toronto, etc.


When I open a LabVIEW project including a Real-Time target like a CompactRIO (cRIO), CompactDAQ (cDAQ) or Real-Time PXI, I see a yellow exclamation mark next to my target. When I click on the target, I get the following message, but License Manager shows that all of my software is licensed.
The plug-in for the selected item is not installed on your system or the plug-in has an expired license. Please contact National Instruments.
The most common cause for this is the LabVIEW Real-Time Module not being installed or, having an incompatible version. The LabVIEW and LabVIEW Real-Time versions must match. If you are using a CompactRIO, you may also need to make sure the LabVIEW FPGA Module is installed and matches the LabVIEW version, or you will have similar issues accessing the device's FPGA.
Ensure you have at least the Real-Time Module listed under the version of LabVIEW you are using. If you have a CompactRIO, it is recommended that you also have installed the FPGA Module so that you can program the FPGA.
Ensure you have compatible versions of any required drivers installed. For example, if you have CompactRIO or Real-Time CompactDAQ, you can check the Software Support for CompactRIO, CompactDAQ, Single-Board RIO, R Series, and EtherCAT page to find the LabVIEW and driver support and, if you are using a Real-Time PXI, you can find the information comparing the NI PXI Platform Services software and hardware compatibilty in NI PXI Platform Services Operating System Support and NI PXI Platform Services Hardware Support.
This can also happen if you open your project in LabVIEW 64-bit. As of LabVIEW 2018, there is not LabVIEW Real-Time Module or FPGA Module support for the 64-bit version of LabVIEW. Ensure you are opening your project in LabVIEW 32-bit. If you are not sure, you can select Help > About LabVIEW in your LabVIEW program to check the version and bitness.
Installing the PXI Platform Services and LabVIEW Real-Time Module compatible versions will only enable using the controller in LabVIEW. The drivers of any cards installed in the PXI Chassis must also be installed and compatible with the LabVIEW and LabVIEW Real-Time version. Refer to your driver's documentation to check the compatibility. For examples, if you are using PXI DAQ devices, you can find the information in the NI-DAQmx readme (i.e. NI-DAQmx 18.0 Readme) or in NI-DAQmx and LabVIEW Compatibility.
With a CompactRIO, this can also occur by not having compatible drivers installed. You can check the versions that are required by your hardware on the NI-RIO and LabVIEW Compatibility page to find what NI-CompactRIO versions are compatible with your LabVIEW and LabVIEW Real-Time Module versions.


The Wall Township Fire Bureau's job is to enforce the New Jersey Uniform Fire Code and all local codes throughout the township. These duties consist of investigations of complaints, routine fire inspections, fire lane enforcement, smoke detector / carbon monoxide compliance, and public education. Along with the above duties the Bureau is responsible for the investigation or cause to be investigated of all fires within the township.
The professional and friendly staff of the Fire Bureau will assist the public with questions concerning applications for smoke detector / carbon monoxide compliance, Knox Box applications, as well as scheduling appointments for inspections.


text:
Home/Features/VRF technology rocks the US
FeaturesFeatures Home
VRF technology rocks the US
USA: The US government is increasingly issuing waivers to its "Buy American" policy as public facilities seek the energy saving advantages of VRF air conditioning technology.
Last week, the Federal Transit Administration granted a request from Kansas City to install a non-American VRF system at the vehicle maintenance facility for its Downtown Streetcar Project, currently under construction in the city.
The Buy American Act requires the United States government to buy US-made products. In certain circumstances, the requirement may be waived if the domestic product is more expensive than an identical foreign-sourced product by a certain percentage, if the product is not available domestically or in sufficient quantity or quality.
VRF systems were first introduced by Japanese manufacturers in the 1980s. The technology has since been adopted as the most common commercial air conditioning system in the rest of the world – except the US. While traditional ducted systems remain the predominant heating and cooling system of choice in the US, VRF is expected to gain an increasing foothold, largely due to its better energy efficiency. Tests are said to have shown a 34% energy advantage over ducted systems.
Although still small, sales of VRF systems are currently increasing by over 20% per year, and the tightening of US energy regulations is expected to have an increasing effect.
Blanket waiver
In 2010, the US Department of Energy issued a blanket non-availability waiver for VRF systems procured with American Reinvestment and Recovery Act funding. Last year, the Federal Transit Administration, itself, issued non-availability waivers, allowing San Bernardino Associated Governments and Rock Island County Metropolitan Mass Transit District to install VRF systems on building projects. In both cases, the project leaders maintained that only a VRF system would enable them to meet the US Green Building Council's Leadership in Energy and Environmental Design (LEED) requirements.
The latest waiver is also energy efficiency related. Kansas City's vehicle maintenance facility is also being built to LEED standards and will incorporate a number of sustainable and energy efficient elements. Kansas stated that one of those elements is a VRF hvac system, which it said was, among other things, "space saving, has inverter technology, efficiency, and a non-ozone depleting refrigerant that domestic manufacturers of hvac systems do not provide".
According to Kansas City, its contractor was directed to evaluate the substitution of a Buy America-compliant VAV system, but the contractor advised that the VAV system would endanger the project's LEED Gold certification because of the difference in efficiency between the VAV and VRF hvac systems. In addition, the substitution of a VAV system would require significant changes to the project, such as the alteration of already-erected structural elements that were designed to accommodate a VRF system and additional design changes and plan reviews by the City of Kansas City.
In February this year, the Federal Transit Administration carried out its own investigations, engaging National Institute of Standards and Technology's Hollings Manufacturing Extension Partnership (NIST-MEP) to scout for Buy America-compliant VRF systems. NIST-MEP did not locate any domestic VRF systems. In fact, Carrier Corporation responded to NIST-MEP's scouting efforts, stating "VRF system is a new technology … there are no current domestic manufacturers of VRF systems."
In applying for a waiver last year for its MetroLINK Transfer Station, Rock Island County argued that VRF air conditioning was critical in obtaining the LEED points necessary to achieve the Silver certification (or better) that it was seeking. Its application said: "MetroLINK specified the brands "Daikin AC" and "Mitsubishi," or approved equal, but MetroLINK has been unable to identify a domestic manufacturer of the VRF hvac system that meets its specifications."
Johnson Controls' new training facility is dedicated to bringing the US contractor up to date with VRF technology
Major investments
It is the likes of Daikin and Mitsubishi, along with Johnson Controls and its recent tie-up with Hitachi, who are expected to lead the way in the US.
Earlier this year, Daikin announced its intention to build a new $410m, 350,000m² factory in Houston as part of plans for a major medium- to long-term expansion in the US. Significantly, it is also to be used to increase production and sales of VRF technology.
Daikin's acquisition of US manufacturer Goodman in 2012 provided Daikin with immediate sales access to more than 60% of contractors and dealers in the US.
Access to Hitachi's VRF product range was thought to be the main driving force behind Johnson Control's purchase of a 60% stake in Hitachi's global air conditioning business at the end of 2013. At the time, Johnson's chairman, president and ceo Alex Molinaroli, referring to VRF, remarked: "It's a very important technology and it's the future of air conditioning. And it's going to have a major place in the United States market so we needed that technology. For us to build that organically, it was too risky and it would have taken too much time to continue within that marketplace. The technology first was really important."
Last month, Johnson Controls unveiled a new 12,600ft² training facility in Dallas, Texas, specifically focused on VRF air conditioning.
© 2015 Cooling Post. Not to be reproduced without prior permission. All rights reserved
Johnson Controls opens VRF training centre – July 16, 2015
USA: Johnson Controls has unveiled a new training facility in Dallas, Texas, focused on VRF air conditioning. Read more…
Daikin breaks ground on $417m US facility – March 27, 2015
USA: Daikin has broken ground on its new $417m, 350,000m² production facility near Houston. Read more…
Johnson/Hitachi ac deal signed – January 22, 2015
USA and JAPAN: Johnson Controls has finally signed the deal which sees it taking a 60% stake in Hitachi's air conditioning business. Read more…
Daikin plans $410m US factory – January 7, 2015
USA: Daikin is to build a new 350,000m² factory in Houston as part of plans for a major medium- to long-term expansion of its US market. Read more…
VRF the key in Johnson/Hitachi deal – March 4, 2014
USA: The head of Johnson Controls has revealed that Hitachi's VRF was a major reason behind its 60% stake in the company's global air conditioning business. Read more…
Carrier fan coils in prestige London development
Toshiba launches 7th generation VRF
Cooling Post shatters 1,000,000 landmark
Clivet chillers on R513A
Rhoss latest with R513A chillers
Toshiba takes lead role in Liverpool Music Academy
Mitsubishi extends NX2 chiller range
Geothermal heat pump uses R452B
Panasonic offers IoT control for commercial AC
HallScrew compressors with VFD and VVR


Here is a vitamin that is a real problem for vegetarian and especially vegans. It is not true that plant food can provide our body everything it needs. Vitamin B12 does not exist in the plant world and vegetarians who do not consume eggs or dairy products should really be concerned and assure their intake in B12.
Vitamin B12 along with vitamin B9 and B6, is needed for the conversion of homocysteine in methionine. Homocysteine is an amino acid, which, in excess, can be toxic to nerves and blood vessels.
When there is not enough vitamin B12, the homocysteine accumulates in the blood and high blood levels of this amino acids are responsible for injured vessels and could lead to heart attacks.
Moreover, the methionine seems to be needed for the production of myelin, the material that insulates our nerves. While the homocysteine build up in the blood, no methionine is formed and the nerve transmission is altered.
Vitamin B12 transforms one form of folic acid in another one, which is needed for the production of DNA and RNA. If there is a lack in vitamin B12, folic acid cannot be transformed and no DNA is produced. DNA is critical in the production of red blood cells. When there is a deficiency in B12 vitamin, red blood cells cannot divide. This problem is known as Megaloblastic anemia.
Our needs in this vitamin are very low and since it is stored in the liver, a deficiency in the vitamin can appear several years after one has stopped eating animal products.
Moreover, folic acid can mask a vitamin B12 deficiency. If the diet is rich in folic acid and low in B 12, anemia's symptoms will not develop and a person may not know that there is a problem until the more serious neurological symptoms appear.
Deficiency can result in nervous disorders and brain damage as well as a form of anemia: Pernicious anemia also called Megaloblastic anemia in which red blood cells are abnormally big.
This vitamin is made from a bacteria.
Plant foods are completely devoid of B12 unless they are contaminated with bacteria. This can be the case when you organically grow your own vegetables and you do not wash them correctly. However, you cannot rely on our vegetables' dirt for your B12 intakes.
Many plant foods (tempeh, sea vegetables, spirulina, sprouted legumes, miso...) once thought to be good sources of B12 actually contain analogues. These are chemicals similar to vitamin B12 but have no vitamin activity for human. They also may interfere with vitamin B12 absorption.
If the nutritional yeast you consume is not rich in B12 vitamin, you cannot really meet your needs in vitamin B12. You could eat 130 g of cheese per day and get your vitamin but you would also get too much saturated fats and cholesterol.
In that case it is better to rely on supplements.


He has been a journalist for 49 years. He is retiring and this is HIS LAST COLUMN.
President, can approve any budget they want. If the President vetoes it, they can pass it over his veto if they agree to.
that 545 people exercise the power of the federal government, then it must follow that what exists is what they want to exist.
Do not let these 545 people shift the blame to bureaucrats, whom they hire and whose jobs they can abolish; to lobbyists, whose gifts and advice they can reject; to regulators, to whom they give the power to regulate and from whom they can take this power. Above all, do not let them con you into the belief that there exists disembodied mystical forces like "the economy," inflation," or "politics" that prevent them from doing what they take an oath to do.


Noppakao Poonpat from Thailand took the bullet in the final race of the championship to become the 2010 Optimist World Champion in style.
Poonpat sailed consistently throughout the Championship, winning four races in the fifteen race series and was on course to take the title with two days to go. A near disastrous penultimate day when she posted an OCS and 16th left her fighting for survival from nearest rival Ahmad Syukri Bin Abdul Aziz (MAS) but in true champions style she kept control of the race and lead almost from the start.
Aziz secured the silver medal, nine points ahead of Okado Keiju from Japan who took the bronze. Mohd Fazal Bin Norizan came in fourth for Malaysia with Marvin Fisch from Germany completing the top five. The second girl overall was Kimberly Lim Min from Singapore who finished eighth.
231 sailors competed in Langkawi, Malaysia and the final top ten is dominated by Asian sailors. Thailand, Malaysia, Japan and Singapore are all represented in the top ten with only Fish from Germany in fifth and Odelie van Aanholt from the Netherlands Antilles in ninth interrupting their dominance.


text:
using System;

namespace EasyIoC {
    public interface IServiceContainer {
        void AddSingleton(Type interfaceToAdd, Type implementation);
        void AddRequestScoped(Type interfaceToAdd, Type implementation);
        void AddTransient(Type interfaceToAdd, Type implementation);
    }
}

redpajama_set_name: RedPajamaGithub