![]() A dyed-in-the-wool romantic, you are always in love with love. You place a premium upon loyalty in your love life as you do in everything else. With a Leo Sun Sagittarius Moon, as a friend or lover, you are generous, forgiving, and sympathetic. It’s fine to place your trust in others just be sure you practice discrimination-and don’t expect everyone to measure up to your incredibly high standards. Those close to you probably tell you that you are too trusting. So strongly do you believe in loyalty and honor that, at times, you can be confused to discover that others are less scrupulous. If you’re an individual with a Leo Sun Sagittarius Moon, sometimes your high ideals can cause you trouble. ![]() Sooner or later, you are bound to become your own boss anyway, since your charm, dynamism, and luck will lead to success. A certain amount of conformity and compliance is necessary in everyone’s life, however, so learn to humble yourself now and then. You must be the boss at work and at home. Having a Leo Sun Sagittarius Moon, you are independent to an extreme. It’s not easy for you to take a subordinate role, and you have little patience when it comes to following someone else’s orders. With a Leo Sun Sagittarius Moon you are a born aristocrat, and your bearing is dignified, at times a bit arrogant and patronizing. Pride is perhaps one of the only barriers to your complete fulfillment. It’s almost impossible for you to be dishonest with yourself or with others. With a Leo Sun Sagittarius Moon, since you are so uninhibited and unrepressed, you are not likely to have many psychological hang-ups. However, once you have found something that holds your attention, you will stick to it tenaciously. Make sure that your job (or whatever you happen to be doing) fulfills your need for excitement and variety, because if boredom or drudgery sets in, you’re ready to take flight. In order for you to be truly creative and constructive, you must focus your talents and energies on a narrower range of activities and involvements. With so many new lands to explore, so many new people to meet, and so many ideas to ponder, no wonder you can’t find the time to finish anything!Īs an individual with a Leo Sun Sagittarius Moon, controlling your restlessness is a daily challenge for you. Practically everything under the sun intrigues you. But very often impulsiveness undermines those constructive pursuits. ![]() Having a Leo Sun Sagittarius Moon, you set high goals for yourself, and like most Leos you want recognition and status. Never content to just sit back and fantasize about excitement, you go out and find it! ![]() Those rare moments when you are quiet merely signify that you are planning some new project. In fact, action is the word that describes you best.įor the individual with a Leo Sun Sagittarius Moon, people know when you are around because of all that moving about. Self-assured and courageous, you have the confidence to put your wonderful ideas into action. Honesty and integrity are your codes, and you are well-known for your forthright opinions, candor, and directness. Having a Leo Sun Sagittarius Moon, you are somewhat naïve, you never repress your feelings. Depression is almost unknown to you, because you are always optimistic, and so active that you have little time for self-pity and or the blues. Open-minded, fun-loving, and enthusiastic, you have a taste for adventure and romance that will last a lifetime. With a Leo Sun Sagittarius Moon, no matter how mature, hard-working, and responsible you may be, you are always a child at heart.
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![]() The political intrigue was also well done, and I really enjoyed the "thief/assassin" aspect of this story. Bec has both a Fae only series (Dark Court Rising) and a dragon shifters only series (Legend of the Storm), yet even though this books has a mixture of both "types" it is still uniquely it's own with no overlap from the other series. I feel like sisterly bonds are a great addition to stories, and even though theirs's is definitely and up and down relationship, I really enjoyed the dynamic and can't wait to see where it is taken.īesides the characters, the world in this books is so interesting. I LOVED the sisterly relationship between Zemira and Soraya. Keir is an great MMC and I love how we have a MMC that is the one "pining" (for lack of a better term) after the dark and broody FMC instead of the other way around. She is stuck between duty and desire, and she learns throughout the book what it looks like to *possibly* balance the two. We get to dive deeper into Zemira's character and thoughts. We have more characters, more plot, more relationship development, etc. In this book however, Bec makes the world EXPLOED. The first book in this series, Thief of Dreams, was on the shorter end since it was part of an anthology, and the world was just introduced. ![]() I am always amazed at how Bec can write a world. Then check out London Steampunk and the London Steampunk: The Blue Blood Conspiracy series.įor post-apocalyptic monster romance with a twist on the werewolf theme, then read the Burned Lands. Kick-bustle ladies-saving-the-day steampunk romance? If you want deliciously dark fae princes, then try Dark Court Rising or Court of Dreams.įor sexy dragon shifters, see Legends of the Storm. Next release: THIEF OF HEARTS (Court of Dreams #3) Newest Release: CURSE OF DARKNESS (Dark Court Rising #3) Copy and paste this link into your browser: She has a secret weakness for villainous heroes, wicked fae princes and dangerous vampires, though in all her daydreams, she’s the one rescuing them.īec lives happily-ever-after with her very own hero and princess-in-training in the wilds of Australia, where she can often be found drinking tea or plotting her next travel adventure.Įscape the ordinary at Join Bec's mailing list for all the latest news on releases, exclusive excerpts, cover reveals, and epilogues. Now she writes epic fantasy romance with a dark and sexy twist, which is almost as much fun. Kidnapped by a dread pirate when she was a child, USA Today Bestselling Author BEC MCMASTER was raised on myth and legend, and offered her younger siblings to the goblin king many a time. On the other hand, using a device like this is nowhere near as effective, nor as rewarding, as training away those unwanted behaviors.Īlthough the leather loop muzzle looks flimsy, it’s ideal for situations that require a little more control and safety. It can help curb his desire to chew everything in sight or bark incessantly. ![]() The gentle muzzle guard from Good Boy has its own set of benefits and negatives. Leather muzzles, like the Collar Direct one, are also hypoallergenic and therefore more suited to dogs with sensitive skin or allergies. While effective against biting, the closer fit of the Collar Direct Pitbull muzzle offers better security. It’s also affordable and versatile, although you have to watch out for chafing, especially around the nose. The Baskerville muzzle is one of the most popular and one of the easiest to fit. While some training is required to get your dog used to a basket muzzle, these are the most versatile and offer the best control for aggressive dogs and for those who, like Koala, eat everything they find, from poop to pesticide! We recommend focus training as a better way to quieten a particularly noisy or reactive. Using one as a permanent anti-barking device is not recommended, however. Stop BarkingĪs with the chewing problem, a neoprene muzzle may help reduce nuisance barking, especially when out on a walk. Some muzzles are safe enough to leave on for long periods and can extend the life of your furniture and shoes as a result! A gentle neoprene muzzle is better for this than a basket muzzle as it won’t catch on things or chafe. A muzzle offers an alternative to the standard cone collar that won’t restrict his movement but will stop him from pulling out stitches or gnawing on a sore paw. RecoveryĪfter sustaining an injury or going in for surgery, some dogs will fuss over the wound incessantly, preventing it from healing. A muzzle won’t stop him from running away, but it will reduce the amount of damage he can cause. Pitbulls have a high prey drive and can be prone to dashing off after squirrels, bunnies, and other small animals and even killing them if the opportunity arises. A good muzzle can stop your dog from eating the droppings of other animals and other unsavory items. Scavengingĭogs like Koala eat anything they find, putting them in danger of tummy upsets and potential poisoning. ![]() Muzzles can be used for: SafetyĪ muzzle that stops your dog from biting other dogs or humans gives you the freedom to take him into social situations without fear. While this is one use for a muzzle, it is not the only one. There are a lot of misconceptions about muzzles, with many people seeing them purely as something to stop a vicious or aggressive dog from biting. I’m confident I found the right muzzle for Koala, but every dog is different, and an ACD is not a Pitbull, so I’ve narrowed it down to a choice of 5 muzzles, all of which are suitable for Pitbulls in a variety of situations. I also tried a couple of cheaper options to see how well they stood up to rough treatment. I tested several out on Koala, my cattle dog, trying everything from metal masks, basket muzzles to soft nylon ones. The best of these allow the dog to pant, drink, and even eat while preventing him from biting or chewing. When looking around for a muzzle for my cattle dog, I came across a range of muzzles for Pitbulls. ![]() Whatever your needs, there are numerous muzzles available. Maybe he gets anxious when strangers approach him, and you need a muzzle to stop him snapping. Perhaps he hates going to the vet, and that anxiety makes him tetchy. Maybe he, like my Australian Cattle Dog, puts everything he finds in his mouth, whether it’s edible or not. There are lots of reasons you might want a muzzle for your Pitbull. We only recommend products we have tested and use on our own dogs! As an Amazon affiliate we earn a small commission. ![]() You can even change the whole stereo head unit to a new one with built-in Bluetooth, but that can be a very expensive solution. There are plenty of aftermarket Bluetooth solutions on the market for every need – you can connect via the AUX cable, via the FM transmitter, replacing the CD changer, or even a standalone Bluetooth solution with a built-in speaker. The problem is, most older cars don’t have built-in Bluetooth in their stereo systems and the only way to connect your smartphone to the stereo may be with an AUX cable, which isn’t useful for making calls. More importantly, you can make hands-free phone calls on the speakers – a great step toward better safety while driving. With Bluetooth, you can stream your music on your car’s stereo and even control the songs directly from it. There are a lot of aftermarket solutions so drivers of older cars can enjoy wireless calling or music streaming.īluetooth is a wireless technology standard for connectivity and exchanging data. A lot of older cars lack this tech feature, but there’s no need to go to a dealership to buy a new car just to have it. It connects a wide range of electronic equipment without requiring additional cables.All new cars already come with Bluetooth compatibility, which makes it easier to stay connected safely while driving. The Bluetooth® technology enables voice and data transmissions via a short-distance radio link. 1 radio mute cable with line output (ISO cable).User connection priority management (up to 5 users)Ĭharacteristics of voice recognition Up to 150 Voice Tags.Extension with new voicetags (up to 150).Phonebook synchronization including: -last calls received -last calls dialed. ![]()
No assurance is given that the information is comprehensive in its coverage or that it is suitable in dealing with a customer’s particular situation. Applicable laws may vary by state or locality. Additional information and exceptions may apply. This content is for information purposes only and should not be considered legal, accounting, or tax advice, or a substitute for obtaining such advice specific to your business. With QuickBooks Online and QuickBooks Commerce, you can take the plunge into the world of wholesale and swim with confidence towards growth! For retailers looking for an out of the box solution to sell online or for wholesalers looking to digitally transform their businesses, QuickBooks Commerce offers a fully customizable B2B eCommerce platform. QuickBooks Commerce comes with purpose-built features to help wholesalers simplify and automate their backend operations. ![]() QuickBooks Online integrates to automate accounting processes, so that wholesaler merchants can focus on selling their products, deepening their relationships with their customer network and finding new avenues to grow. Regulating your cash flow has never been this easy. You can then approve invoices and payments and have that information pushed automatically back to QuickBooks Commerce and then reflected on your sales channels. ![]() Whether your orders come through one or more of those channels or through the QuickBooks Commerce B2B eCommerce platform or a combination of both, all of your invoices, payments and purchase orders are pushed to Quickbooks Online on a daily basis. QuickBooks Commerce integrates with multiple eCommerce platforms. Two-way payment sync between all channels and accounting QuickBooks Online accounting software is easy to set up, simple to use and comes with powerful and intuitive integrations to simplify even the most complex wholesale needs.ģ. Wholesalers have specific inventory and order management requirements that need to be properly accounted for. With a complex supply chain, comes complexity in other aspects of the business- accounting being a big one. ![]() The key to running a successful online wholesale distribution business is to have the right tech in place from the get-go. However these merchants are missing out on a huge opportunity for growth the wholesale market is expected to reach a value of nearly $47768.95 billion by 2022 and more and more of these sales are being made online. To a certain degree it still does even with affordable and reliable cloud SaaS solutions that provide end-to-end supply chain solutions for wholesalers, many retailers are still hesitant to take the leap of faith. The retail industry may have been quick to digitize but wholesale lagged behind. The capital cost was usually too high and the supply chain complications made it impossible for small teams to manage manually. Traditionally, wholesale distribution was not a channel that many founders or merchants would consider expanding into, especially in the first few years of the business. Wholesale on the other hand is when a merchant sells products to other businesses who then distribute through different channels to the end user. Retail refers to the business model of a merchant that sells products directly to the end consumer. ![]() By their means, he was able to transform Laplace’s equation ▽ 2 V = 0 into ellipsoidal coordinates in a form where the variables were separable, and solve the resulting form of the generalized Laplace equation. These coordinates were conceived as intersections of confocal quadric surfaces. His sole and quite tenuous connection with politics was his Esquisse d' un traiteé de la reépublique (1848).Īlthough Lameé did original work in such diverse areas as number theory, thermodynamics, and applied mechanic, his greatest contribution to mathematics was the introduction of curvilinear coordinates and their use in pure and applied mathematics. In spite of the unsettled and often troubled political climate, Lameé managed to lead a serene and quiet academic life. He was in retirement until his death in 1870. In 1862, he went deaf, and resigned his positions. He became professor of mathematical physics and probability at the university in 1851. In 1844 he became graduate examiner for the University of Paris in mathematical physics and probability. In 1843 the Paris Academy of Sciences accepted him to replace Puissant in its geometry section. He also helped plan and build the first two railroads from Paris to Versailles and to St.-Germani. In 1836, he was appointed chief engineer of mines. Lamé always combined his teaching positions with work as a consulting engineer. However, he left the firm in 1832 to accept the chair of physics at the Eécole Polytechnique. In 1832 he returned to Paris, where he spent the rest of his career and life.įor a few months after his return to Paris, Lameé joined with Clapeyron and the brother Flachat to form an engineering firm. He also collaborated with Pierre Dominique Bazaine on the text Traité élémentaire du calcul inteégral, published in St. ![]() He was also busy planning roads, highways, and bridges that were built in and around that city. Peterburg, where he taught analysis, physics, mechanics, and chemistry. He was appointed director of the School of Highways and Transportation in St. In 1820 Lameé accompanied Clapeyron to Russia. His next work, Examen des diffeérentes meéthodes employeées pour résoudre les probleèmes de geéomeétrie (1818), contained a new method for calculating the angles between faces and edges of crystals. His interest in geometry showed itself in his first article, “Mémoire sur les intersections des lignes et des surfaces” (1816–1817). He then continued at the Eécole des Mines, from which he was graduated in 1820. He enterd in 1813 and was graduated in 1817. Like most French mathematicians of his time, Lameé attended the Eècole Polytechnique. Medical infrared imaging of the paw prints can be utilized to screen for the lame limb in dogs.( b. The results of this study highlight the change in the thermal pattern of the paw print in the lame pelvic limb compared to a non-lame pelvic limb in the lame group and the healthy group. ![]() The optimal cutoff point for the peak vertical force to determine lameness was 41.77% (AUC = 0.93) and for MII 0.943% (AUC = 0.72). Asymmetry index analysis revealed 5% in the healthy group and 36.2% in the lame group. The mean of the peak vertical force revealed a 10.0% difference between the left and right pelvic limb in healthy dogs and a 72.4% between the lame and non-lame limb in the lame dog group. Image pattern analysis revealed 88% success in differentiating the lame group, and 100% in identifying the same thermal pattern in the healthy group. The asymmetry index for each stance variable and optimal cutoff point for the peak vertical force and thermal image temperatures were calculated. Analysis was performed in a static position. Average temperatures and thermographic patterns were analyzed. Thermal images of the paw print were taken after each dog was kept in a static position on a foam mat for 30 seconds. Fourteen client owned dogs with a unilateral pelvic limb lameness and 14 healthy employee dogs were examined and the pelvic limbs radiographed. A study was conducted to investigate a change in the thermal pattern and temperature of the thermal image of the paw print in a lame pelvic limb compared to a non-lame pelvic limb of dogs confirmed by orthostatic analysis. ![]() Subtle lameness can be difficult to ascertain which is the affected limb. Medical infrared imaging and orthostatic analysis to determine lameness in the pelvic limb of dogsĮrik Fernanda V Garcia, Catherine A Loughin, Dominic J Marino, Joseph Sackman, Scott E Umbaugh, Jiyuan Fu, Samrut Subedi, Martin L Lesser, Meredith Akerman, Joao Eduardo W Schossler. ![]() Of course, it is not a reason to avoid using wide-angle lenses in digital food photography. Sometimes, it is not convenient for a food stylist to create a composition when the camera is too close to the subject.įor example, they may not be able to see the plate from the same angle and it complicates the task. Working Distance to the SubjectĮach photographer should consider the distance between the camera and the plate while taking photos of food. Telephoto lenses capture fewer items and focus on the main subject while you will need more props to complete a background composition using a wide-angle lens. To create a beautiful composition with different lenses, you need to try different approaches. PerspectiveĪ wider lens creates a completely different effect than a longer one. Perhaps, you may need macro images with high detailization or capture the whole buffet table in one shot. Nikon PC-E NIKKOR 85mm f/2.8D View Prices on Amazonįirst of all, the choice of a lens depends on the shooter’s style and his/her requirement. Look though these basic food photography props.Ĩ.Being unblocked, the axis is not tilted or shifted if you accidentally move the tripod. I recommend switching on magnification while shooting in the Live View Mode to avoid any mistakes. This lens has a smooth focus ring, which allows an easy finding of a necessary point in the composition. However, it is important to remember about blocking off a shift and tilt when changing the directions. The turn of a tilt mechanism allows changing the mutual location of tilt and shift sides from the perpendicular to parallel that is for vertical and horizontal shootings. It means that we easily control the shooting results. In this case, thanks to a tilt of the focal plane, there is a tilt-shift. Speaking about famous Helios-40, the effect is achieved by the imperfection of an optical scheme. It does not only create a smooth blurring typical for GREEP, but a vignette curved around the focal point. Personally, I like this lens for an artistic effect of axis-tilt. Nikon 60mm f/2.8G AF-S Micro NIKKOR AF ED View Prices on Amazon View more creative food photography ideas.Ĥ.Widely open aperture allows saving noise values necessary for frame sharpness and low ISO values. Secondly, you may shoot with hands when there is poor lighting. What does it mean? First of all, you may take pictures which have only a small part in focus. These optics offer high brightness, the maximum aperture value is 1.4. In this case, it distorts proportions of a subject and their location in the space. Photo by Canon EF 50mm f/1.4 USMĥ0 mm lens is not suitable for shooting small compositions at a short distance. Moreover, 50 mm lens for product photography is suitable for shooting at an angle, when the part of an interior should be in the frame. It is convenient since you don’t have to climb somewhere (like with 100 mm lens, for instance). For example, if the composition is on the table, you may shoot it from above, simply using the chair. Print memories on-the-go with a small and lightweight portable printer.First of all, this lens is used to take pictures of food from the top. Portable Printers Portable Printers Portable Printers.Take complete creative control of your images with PIXMA and imagePROGRAF PRO professional photo printers. Professional Photo Printers Professional Photo Printers Professional Photo Printers.MegaTank Printers MegaTank Printers MegaTank PrintersĮnjoy high quality performance, low cost prints and ultimate convenience with the PIXMA G series of refillable ink tank printers. ![]() Seeking the best printer for your business? Hit your productivity targets with inkjet and laser printers that are a perfect fit for any workspace – including home offices. Small Office Printers Printers For Small Businesses Small Office Printers.Home Printers Home Printers Home Printersįunctional and stylish home photo printers and all-in-ones delivering quality results. ![]() THIS THREAD WILL END ONCE ROUND 2 POOLS CONCLUDES. Any upset factor of 4 or higher will be mentioned. Posts are delayed due to the bracket being handwritten, patience. Sigma (Toon Link) 3-2 Suinoko (Young Link) Out at 65thĬolorando8 (Inkling) 3-2 JustOmega (Bowser Jr) Wasabi (Greninja) 2-0 Cattail (Toon Link) Summitsun (R.O.B.) 2-0 Cattail (Toon Link) Out at 257th Upset Factor 4 VoiD (Sheik) 3-2 Repo (Mega Man) Out at 129thĪMOGonza (MegaMan) 2-1 Stroder Ame (Sora) Game & Watch) 3-2 Stroder Ame (Sora) Out at 65th Peckham (Min Min) 3-2 ApolloKage (Steve) Out at 65th Jojodahobo (Toon Link) 3-1 Chronos (Snake) Out at 97th Nao (Mario) 3-2 Chag (Palutena) ( Out at 65th) ![]() Rocke (Pac-Man) 3-2 ESAM (Pikachu/Mii Brawler) ( Out at 65th) It will be a separate thread, respectfully, to avoid clutter! Here we go! ![]() Gooooooood day y’all! I’m here today to share some sick upsets and I hope everyone is having a great weekend so far.īe on the lookout for a Top 64 Ultimate Singles Upsets thread later once Pools is complete. Shoutout to /u/69thParliament for informing me what time it starts! Galint Gaming - Organizers of Battle of BC 5Ĭody - Top modern Brawl player, champion of Apex 2022Īaron - Top Ultimate Diddy Kong for Moist EsportsĪpolloKage - Current best Snake main in UltimateĬosmos - Top Aegis main, champion of Shine 2022įor a full list, click here! Submit a new post: TEXT LINK All Please read the rules before posting! Filter posts: Smash 64 Melee Brawl Project M Smash 4 Ultimate Other All Art Daily Thread Pic of the Day Show Spoilers Clear Filter for Wii U on the Wii U, a GameFAQs message board topic titled 'C/D: No SSB-related news can ever trump the hype from Megamans reveal and FS'. L4st - Coach, commentator, and TO for Team Liquid Ken, Sheridan, and Boback - Organizers of Genesis Maesuma TOP #14: September 3 | Ultimate | Osaka, JapanĬlick here for a more detailed list of events! Tera: September 1-3 | Ultimate | Rungis, France Shine 2023: August 25-27 | Melee, Ultimate | Boston, MA, USA Super Smash Con 2023: August 10-13 | 64, Melee, Brawl, Smash 4, Ultimate | Chantilly, VA, USAĭelfino Maza 2023: August 18-20 | Ultimate | Mazatlán, Mexico Play now wiki events watch learn Rules Local Groups FAQ Related Content Posting Guide Chatrooms Wiki Feedback. ![]() You can ask myTuner Radio to play a station of your choice and Alexa will start playing it for you. Whether you are in the Big Apple or Europe, Asia or Australia you can tune in to the best AM, FM, DAB and online radio stations of your country or of your homeland, including the local AM and FM radio stations you can’t live without. Whether you have a station of choice or you’re just looking around, it’s very likely that myTuner Radio Player has what you’re looking for. MyTuner Radio Player is all you need to listen to more than 50,000 free radio stations from more than 200 countries and territories. To learn more about how and for what purposes Amazon uses personal information (such as Amazon Store order history), please visit our Privacy Notice. You can change your choices at any time by visiting Cookie Preferences, as described in the Cookie Notice. Click ‘Continue without accepting’ or ‘Customise Cookies’ to decline these cookies, make more detailed choices or learn more. Third parties use cookies for the purposes of displaying and measuring personalised advertisements, generating audience insights, and developing and improving products. This includes using first- and third-party cookies which store or access standard device information such as a unique identifier. ![]() If you agree, we will also use cookies to complement your shopping experience across Amazon stores as described in our Cookie Notice. We also use these cookies to understand how customers use our services (for example, by measuring site visits) so we can make improvements. We use cookies and similar tools that are necessary to enable you to make purchases, to enhance your shopping experiences, and to provide our services, as detailed in our Cookie Notice. ![]() A CSPRNG can "stretch" the available entropy over more bits.Ī cryptographically secure pseudorandom number generator (CSPRNG) or cryptographic pseudorandom number generator (CPRNG) is a pseudorandom number generator (PRNG) with properties that make it suitable for use in cryptography. In such instances, a CSPRNG can sometimes be used. Also, the processes to extract randomness from a running system are slow in actual practice. But sometimes, in practical situations, more random numbers are needed than there is entropy available. From an information-theoretic point of view, the amount of randomness, the entropy that can be generated, is equal to the entropy provided by the system. However, unexpected correlations have been found in several such ostensibly independent processes. Ideally, the generation of random numbers in CSPRNGs uses entropy obtained from a high-quality source, generally the operating system's randomness API. And in the case of one-time pads, the information-theoretic guarantee of perfect secrecy only holds if the key material comes from a true random source with high entropy, and thus any kind of pseudorandom number generator is insufficient. On the other hand, the generation of a master key requires a higher quality, such as more entropy. The "quality" of the randomness required for these applications varies.įor example, creating a nonce in some protocols needs only uniqueness. salts in certain signature schemes, including ECDSA, RSASSA-PSS.Most cryptographic applications require random numbers, for example: It is also loosely known as a cryptographic random number generator ( CRNG). ↑ The cases of cycle lengths from the all-on state for n being of the forms 2**k and 2**k+1 comprised a problem in the 1996 International Mathematical Olympiad, and were analysed (together with the 2**k-1 case) in a maths paper by Laurent Bartholdi.Type of functions designed for being unsolvable by root-finding algorithmsĪ cryptographically secure pseudorandom number generator ( CSPRNG) or cryptographic pseudorandom number generator ( CPRNG) is a pseudorandom number generator (PRNG) with properties that make it suitable for use in cryptography.(Note that p's prime factorisation is not always given by these, because not all numbers of the form 2**(2**k-1)-1 (the lengths of the cycles given when n is of the form 2**k-1) are Mersenne primes.) The OEIS sequence giving maximum periods with respect to n is A046932. For n>=1, there are no fixed points, the cycle beginning with the sequence (0,0.,0,1) seems to have the maximum period p, which is divisible by all other cycles' periods. ↑ A program for generating it is print((lambda m,l: (_import_('sys').setrecursionlimit(1>n-1,lambda n,k: ' '*(len(str(n))-len(str(k)))+str(k))))(10,False)), the first parameter at the end determines the maximum value of n to search up to, and the second whether it returns a list of lengths ( True) or explicit cycles ( False).Note that when these don't contain booleans (represented by gliders) but numbers, and each successive element is computed by a recurrence relation of adding multiples of the preceding ones, instead of applying boolean functions, it can be used to divide polynomials and thereby compute generating functions. ↑ See also linear-feedback shift register on Wikipedia.It is conjectured that p=2**n-1 (so any non-empty state will lead to all others before reaching itself again) in the case that n is of the form 2**k-1. A loop of n spaceships has 2 n possible states, but the all-empty state in the case of XOR (and the all-full state in the case of EQV) will lead back into themselves, so the other states' periods are p<=2**n-1. Elements of the p46-based one's output are defined by a recurrence relation involving the EQV operation (a glider is outputted only if the two inputted are equal), whereas the p120 one involves the XOR one (outputted only if they're different), and inverting the glider presences in either, replacing its XOR with EQV or vice versa and inverting its output will not change its output. ![]() Such a PRNG usually contains gliders or other spaceships in a loop with a feedback mechanism that causes later spaceships to interfere with the generation of earlier spaceships, in a linear-feedback shift register. In Life, the term refers to a PRNG implemented as a Life pattern, with the bits represented by the presence or absence of objects such as gliders or blocks. This article may require cleanup to meet LifeWiki's quality standards.Ī pseudo-random number generator ( PRNG) is an algorithm that produces a sequence of bits that looks random (but cannot really be random, being algorithmically determined). |
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