## What Is The Formula For The Basic Accounting Equation Comments: Luca Pacioli and Leonardo DaVinci – Domestic Partnership of Genius

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## Do You Have To Use Boiling Water For Formula Top 7 Proven Home Remedies for Leucorrhea Treatment

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## Top 7 Proven Home Remedies for Leucorrhea Treatment

Excessive vaginal discharge, foul odor, see through underwear – yes we are talking about leucorrhea. Leucorrhea is one of the most common vaginal infections. This situation is enough to make women feel peeved and uncomfortable. It’s scary but these days it’s a common problem among women. To control this female infection, natural treatment for leucorrhea is effective.

It has been scientifically proven that to treat leucorrhea naturally, the use of home remedies is very effective.

Why does leucorrhea attack women?

Women’s genitals are moist and covered most of the time which is why women are more vulnerable to this infection.

Possible causes of leucorrhea

• Improper genital hygiene

• Hormonal Imbalance

• An unhealthy lifestyle

• Viruses and fungal infections

• Private sores from severe itching

• Diseases such as menorrhagia and diabetes

• Not slipping

• Constipation

• Anemia

• Stress and anxiety

Here we list 7 Top Home Remedies for Leucorrhea Treatment

Banana

Bananas are considered an effective home remedy to treat leucorrhoea naturally. Antibiotics in action Bananas help flush out harmful bacteria from the vagina.

Directions for use

• A person can eat one to two ripe bananas every day.

• Repeat until you see a noticeable change.

Ladyfinger comes in the category of effective home remedies for leucorrhoea. The mucilaginous nature of ladyfinger helps in eliminating mucus from the body. In leucorrhea, it works well to reduce vaginal discharge.

How to use

• Take the ladyfinger, wash it and cut it into small pieces.

• Boil these pieces for 15-20 minutes in water until the water is reduced to half.

• Allow to cool and strain.

• Add honey and eat 2-3 times a day.

Pomegranate

The medicinal properties of this fruit help to ward off female infections. Its fruits, leaves, and bark are very useful in treating leucorrhea. Hence, it is an effective home remedy to treat leucorrhoea naturally.

How to use

• Consume one glass of fresh pomegranate juice every day for one month.

• Grind 25-30 fresh pomegranate leaves and 8-10 black peppercorns.

• Add this mixture to half a glass of water.

• Strain it and drink it twice daily until you see a noticeable change.

• Another option is to make dry pomegranate powder.

• Make a powder of pomegranate flour.

• Mix 1/2 teaspoon of this powder in 3-4 cups of water.

• Use this solution as a vaginal spray.

Fenugreek seeds

Fenugreek seeds are loaded with immunity booster properties. In leucorrhea, this helps balance the pH level and the microflora in the vagina.

Directions for use

• Take two to three teaspoons of fenugreek seeds in 3-4 cups of water and boil for 25-30 minutes.

• Remove and allow to cool.

• One can use this water as a vaginal wash several times a day until the symptoms subside.

Indian mulberry (Amla)

Being a good source of vitamin C, it helps strengthen the immune system. Moreover, Amla is full of antimicrobial properties that help prevent infections in the female genital area.

How to use

• Make a thick paste by mixing two teaspoons of Indian gooseberry with honey. Use it twice a day.

• Another option is to boil a teaspoon of dry Indian gooseberry powder in a cup of water until it reduces to half. One can add little sugar or honey as per taste. Eat it on an empty stomach every morning.

Cranberry

Cranberries are full of antimicrobial, antifungal and antioxidant properties. These compounds help fight bacterial, viral and fungal infections. In leucorrhea, cranberry helps eliminate bacteria from the vaginal wall.

How to use

• Drink one glass of cranberry juice once or twice for best results.

a fig

To control leucorrhea, the use of figs is very good. The laxative action of figs helps eliminate toxins and waste from the body. They work amazingly to solve the problem of excessive vaginal discharge.

How to use

• Soak 5-6 figs overnight in one cup of water. The next step in the morning is to combine the soaked figs. Use this solution on an empty stomach.

• Alternatively, you can grind equal amounts of fig bark and banyan tree to make a fine powder. Add one-half teaspoon of this powder to two-three cups of water. Use this solution as a vaginal wash.

• Maintain proper hygiene.

• Wash your underwear daily and let it dry under the sun.

• Do not wear dirty, tight or synthetic underwear

• Change underwear at least 3-4 times a day.

• Wash the genital area and the surrounding area.

• Wipe from front to back after using the toilet.

• Avoid fatty foods.

• Avoid coffee, alcohol and carbonated beverages.

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## How To Transition A Baby From Breastmilk To Formula Ways to Stop Breastfeeding Your Baby

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## Ways to Stop Breastfeeding Your Baby

Breastfeeding is the best way to keep newborns healthy, but it’s up to you to decide when breastfeeding should end. However, when the time is right to stop your child, you may find it difficult to do so. Try these ideas to stop breastfeeding.

Keep up the routine. Baby learns routine, so don’t change too many of baby’s routines at once. In other words, give a bottle when it’s time to feed, but use the room and chairs that are normally used. This reassures the young person and aids in the transition to different diets.

Slowly and consistently reduce the amount you feed daily. Sometimes it is difficult to stop breastfeeding suddenly. Your child will not understand and will have trouble adjusting. If you have to deal with a fussy teen, you can surrender and move on and breastfeed. For this reason, it’s a good idea to gradually wean yourself from breastfeeding rather than quit cold turkey. To begin, cut back to one feeding per day. It can occur at any time of the day or night. If the child is hungry at this time, give him bottled baby food or milk. By this time, the child may also want solid foods. Then, when the baby is comfortable, reduce the number of feeds per day one by one. At some point, your child will no longer expect to be breastfed.

Be aware of the breasts. Even if you stop breastfeeding gradually, your milk secretions may continue in large quantities. Take care to take care of your breasts during this transitional period to avoid the risk of possibly a painful infection. If you have chest pain, do not eat, take a shower. Massaging your breasts while showering will minimize lumps – but be gentle so as not to trigger the milk flow. Gently patting under the tap is very important, as the action normally triggers oozing from the breasts.

Let him follow his own path. Sometimes babies start taking solid foods instead of relying so much on breast milk – they make transitions easily. It will let you know when your child no longer wants to be breastfed.

Accept your father’s help as best you can. Because mothers often tend to comfort crying babies, they often use breastfeeding as a way to calm the baby. If you don’t need to breastfeed the child, the father can take on some of the soothing duties. He should get up at night and put the child back to sleep. Every time the baby whines and can no longer get breast milk, he will calm down with different things. If the baby is not so attached to the mother, it will be very easy when it is time to stop breastfeeding.

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## Do I Need To Use Distilled Water For Formula A Brief History Of Hydroponics

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## A Brief History Of Hydroponics

The study of plant nutrition began thousands of years ago. The first published work on growing terrestrial plants outside the soil was a 1627 book, Sylva Sylvarum by Sir Francis Bacon, published a year after his death.

Water culture became a popular research method after that. The term ‘Hydroponics’ was coined by Dr WF Gericke in 1936 to describe the cultivation of edible and ornamental plants grown in a solution of water and dissolved nutrients.

It literally means active water; ‘hydro’ means ‘water’ and ‘ponos’ means ‘work’. Many civilizations have used hydroponic growing methods throughout history. For example, the hanging gardens of Babylon and the floating gardens of the Aztecs of Mexico and China. These are all excellent examples of Hydroponic culture.

The Hanging Gardens of Babylon were built around 600 BCE by King Nebuchadnezzar for his wife, Queen Amyit who remembered the mountains of her homeland in Media, Persia.

These ruins are located in the ancient city of Babylon, which was near the modern city of Baghdad in Iraq. The gardens were beautiful, using advanced hydroponic technology. Babylonian engineers devised a sophisticated system of shafts to carry buckets of water continuously. Water is put in buckets to fill the fountains and ponds of the Garden. The power to allow this was thought to be provided by slaves turning large screws. This well system was the first and only in Babylon.

Hieroglyphic records from Egypt dating back to a few hundred years BC describe the growth of plants in water. Hydroponics is not a new method of growing plants. However, many developments and improvements have been made over the years in this area of ​​horticulture, and agriculture.

In 1699, John Woodward published his water culture experiments. He found that plants in fresh water sources grew better than plants in artificial water. In 1842 a list of nine factors believed to be important for plant growth had been made, and the discovery of the German botanists, Julius von Sachs and Wilhelm Knop, in the years 1859-65, resulted in the development of soil science. little cultivation.

The growth of terrestrial plants outside the soil in mineral nutrient solutions was called solution culture. It quickly became a standard research and teaching technique and is still widely used today. Solution culture is now considered a type of hydroponics where there is no inert medium.

Throughout the last century, scientists and botanists have experimented with different methods of hydroponics. Another reason behind the drive to develop hydroponics was the need to grow new produce in uncultivated areas of the world. Today, it is well known that in some parts of the world, plants do not grow in the existing soil.

During World War II, troops stationed on uncultivated islands in the Pacific were supplied with fresh produce grown in community-based hydroponic systems.

Later in the century, hydroponics was integrated into the local program in the USA. Hydroponics is NASA’s solution to providing a sufficient food source for future space stations and planned visitors to Mars. The administration has sponsored a research program called the Controlled Ecological Life Support System (CELSS) to further develop hydroponics technology and advance it into the future.

When NASA considered the feasibility of finding a human on another planet or on Earth’s moon, hydroponics helped fulfill the answer to this plan. In fact, NASA has a list of 15 plants, grown using hydroponics that will save your life (should the need arise).

In the 1970s, it was scientists and analysts who were involved in hydroponics. Traditional farmers and hobbyists have been drawn to the beauty of hydroponic growing.

In 1978, hydroponics pioneer Dr. Howard Resh published the first edition of his book; Hydroponics food production. This book promoted what is known as the 3-part nutrient base formula which has become a staple in today’s hydroponics garden.

Resh later went on to publish other books, and now holds a very high-profile hydroponics research and production facility in the Caribbean.

Some of the reasons why hydroponics is being adapted around the world for food production include:

• No land is required
• Water stays in the system and can be reused, reducing water costs
• It is possible to control feed levels completely to lower feed costs
• No nutrient pollution is released into the environment due to the controlled process
• Stable, safe and high yields
• Pests and diseases are easier to remove than from the soil because of the movement of the bag

Today, commercial growers are using hydroponics more than ever before. The ideas surrounding this growing technology touch on a number of topics that many people care about today such as helping to end world hunger and making the world cleaner.

In addition to extensive research going on, everyday people from all over the world have been building or buying their own systems to grow delicious, fresh food for their families and friends and ambitious people striving to make their dreams come true. by making a living in their backyard, or attic, and selling their produce in markets and restaurants.

For some, hydroponics allows them to create attractive ‘vertical’ gardens, which may not be possible using traditional soil-based methods.

In fact, most of the plants and flower arrangements you see today in large office spaces are displayed using hydroponic systems. It makes feeding the system easy, ensuring healthy displays throughout the year.

George Pattenson

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## How To Supplement With Formula Until Milk Comes In Nutraceutical Manufacturing, Outsourcing, and Private Label Strategies Discussed

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## Nutraceutical Manufacturing, Outsourcing, and Private Label Strategies Discussed

Nutraceuticals are foods that are nutritious, contain important nutrients, and have solid medical benefits. This is a very fast growing industry and there are many forces behind it. Consider whether you would accept all the NGOs that are working hard and diligently to feed hungry populations in places like Africa. Just giving them food may not be enough, and it is important to put specific nutrients and medications on that food. This is a driving factor. Of course this idea sounds totally plausible, and that’s why first world countries are considering more fortified foods.

In fact, if you think about it, that’s really nothing new, because we’ve been using vitamin D fortified milk in this country for over 50 years. And milk isn’t the only food fortified with vitamins, supplements, and even medications. Most of the pet foods we feed our pets use similar strategies; it makes sense after all. If your company sells nutraceuticals, vitamin supplements, or cosmetics – or perhaps is considering expanding its product line in some way – it may make sense to hire a contract manufacturing and outsourcing company that can help you private label those products.

Of course, if you choose to do this, it’s critical that you get a company that is certified, registered, and has FDA-compliant manufacturing processes. How would you choose such a company to manufacture your products? Well, not only do you need to make sure the company is certified and has a good track record with regulatory knowledge, but you also need to make sure they have a competitive price and can deliver on time.

It is also important that you know that they can work with you, assisting you with flexible service or special urgent orders. You also need to make sure they use only the best materials and that the people who work with the company are the best in their field.

There’s a big difference between throwing a bunch of supplements, vitamins and nutrients into a product and getting the exact formula needed to really do the job it’s intended for. After all, your customers trust you that the products you sell with your brand are indeed the best available. Therefore, performance is paramount.

Now then, perhaps you need to think about your outsourcing strategy and ask for a quote, check prices, and make sure the companies you’re contacting can get the job done. If all goes well this will help your company cut costs, expand your product line and give your customers the opportunity to spend more money with you. We really hope you will take this into consideration.

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## Do I Need To Use Boiled Water For Formula Interstitial Cystitis

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## Interstitial Cystitis

Interstitial cystitis is chronic inflammation of the space between the lining of the bladder and its muscle. Cool herbs such as slippery elm and marshmallow root, taken as tea, not tinctures, not capsules, can help relieve pain and strengthen the bladder. I find comfrey leaf infusion (made by boiling one ounce of dry comfrey leaf in a quart of boiling water for 4 hours) a wonderful companion in reducing irritation in the bladder and vagina. You can drink it and/or use it as a sitz bath.

These powerful anti-inflammatory drugs, used as tinctures only, can make all the difference. Pick just one and work with it for at least a month.

• Wash the root (Ligusticum porterii) tincture, 3-5 drops at a time, repeated up to four times a day, stops inflammation in the mucus tissue; try it if your stomach is heavy and full.
• The root (Phytolacca Americana) tincture, 1-2 drops at a time and only once a day, has a special relationship with women and the pelvis; try it if your pain is going around.
• Black cohosh root (Cimicifuga racemosa) tincture, 10-15 drops, up to three times a day, menopause herbs are also antispasmodic; try it if your pain is sharp and stabbing.
• St. Joan’s wort (Hypericum perforatum), 20-30 drops, often six times a day, relieves nerve pain; try it if your pain is electric.

Regular Kegel exercises (at least 100 per day) strengthen the muscles around the bladder and, by increasing the circulation of lymph and blood, tonify the wall of the bladder, reducing symptoms.

Relaxation techniques are very helpful in relieving chronic and acute pain from IC.

Many women with IC find a connection between their symptoms and certain foods. This depends on the individual, but the most problematic foods seem to be: avocados, bananas, cranberries, peaches, blueberries, tomatoes, tofu, fava beans, lima beans, nuts, vinegar, yogurt, sharp cheeses, herbal teas, white flour products. , and alcoholic yeast. Stimulants such as coffee, black tea, green tea, alcohol, tobacco, chocolate, and sex (even with you) can worsen symptoms, unfortunately. Dyes and binders in many supplements worsen symptoms, as do food preservatives, food dyes, carbonated sodas and water, aspartame, and saccharine.

Acupuncture therapy can help IC. Many experts insist that you come every several months before you expect improvement. This is not true for those dealing with interstitial cystitis. According to another expert, Dr. Matthew Lee, half of those who will get relief will do so in three sessions, and 95 percent of those who will benefit will do so in six sessions.

Vaginal estrogen creams can reduce symptoms for some menopausal women according to MD Elizabeth Lee Vliet. He warns that progesterone tends to inhibit the formation of the protective membrane of the bladder and is therefore contraindicated in women with IC.

Drugs such as Ibuprofen and prescription antidepressants such as Elavil, taken in small doses (10- 40mg per day at bedtime) can prevent pain, calm spasms, and reduce inflammation.

Avoid aspirin; is associated with mucosal bleeding, a potentially fatal outcome for those with IC. Over-the-counter cold medicines, cough syrups, diet pills, or anything else that contains drugs that increase the production of norepinephrine make IC worse.

Avoid treatments that deliver steroids, anti-inflammatory agents, or anti-clotting drugs by catheter directly into the bladder. Only half of the women treated will have any reduction in pain, and only after 6 months to a year. Avoid opening the urethra which generally does more harm than good.

Women who have had their bladder removed in hopes of removing the source of their pain often suffer from “phantom bladder” pain.

Women who have had a hysterectomy find it worsens IC symptoms. Almost half (44%) of women with IC had their uterus removed.

Legal Disclaimer: This content is not intended to replace routine medical care. Any recommendations made and all medications listed are not intended to diagnose, treat, cure or prevent any disease, condition or symptom. Individual directions and usage should be provided by a herbalist or other qualified practitioner with a customized formula. All material on this website/email is provided for general information purposes only and should not be construed as medical advice or consultation. Consult a trusted doctor if you need treatment. Practice empowering yourself by seeking a second opinion.

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## How To Solve For Years In Compound Interest Formula Savings Account Calculators Yield Your Financial Future

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## Savings Account Calculators Yield Your Financial Future

Planning to save for the future? Fantastic. Choosing to use a savings account calculator will be one of the wisest choices you make. To unravel the mystery of how much money you can make by investing a certain amount of money in interest-bearing savings or an investment plan, you can use one of the many savings calculators available that take many different factors into account and generate returns. Take a look at your potential future earnings. It can help you determine your planned, current or future earnings and allows you to customize it according to your personal financial situation and goals.

First of all, you will need to enter into the calculator how much your initial investment will be and any extra payments you intend to add to the starting balance at regular intervals over a period of time. Savings calculators that offer the option of additional contributions will assume that additional payments will be added at the beginning of the specified period when calculating the final amount of money to be earned.

The next step is to determine the amount of time you think the investment will work to earn interest on the account and enter that into the savings account calculator.

Every savings account or investment opportunity has a specific annual rate of return, and that should be the next piece of information you detail in the equation. Expressed as APY (Annual Percent Return), this is what directly impacts your earnings. You will find that the APY will vary from institution to institution, so be sure to pay special attention to this.

Another and very important factor you can add to a savings account calculator is the aggregation of earnings. Compounding means additional gains on the interest already accrued on the investment. This reflects the strength of the composition. With compound interest, you earn interest on the money you save and the interest earned on the money. Over time, even a small amount saved can make big bucks. Being aware of the compound interest rate when using a savings account calculator will help you accurately predict how much interest will be charged in any given time period.

The variables may vary depending on the type of savings or investment you choose, but a calculator specifically for savings allows you to enter the variables and get a good overview of your future earnings. Now online, you can compare different savings and investment products at the click of a mouse. A savings account calculator is an invaluable and easy-to-use tool when you need to compare rates offered by different financial institutions to get the maximum benefit for your contributions.

## Question about How To Solve For Years In Compound Interest Formula

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## Do I Have To Use Nursery Water For Formula New Born Baby Rabbits – Fundamental Tips You Should Know

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## New Born Baby Rabbits – Fundamental Tips You Should Know

Thirty days is the minimum number of days to wait before the newborn babies leave the womb of the rabbit mother. Soon after, the little furry creatures are bound to eat food and water in the nest. During that time, pet owners will be busy checking if the doe is doing her maternal job well such as keeping the baby rabbits comfortable and warm enough and feeding her babies.

Although rabbits build their own nests, the doe does not stay in the nest for long. Naturally, they leave the nest after the first feeding period. This act of the mother rabbit, on the other hand, attracts the attention of predators who may lie in the corner waiting for the right time to exploit the newborn rabbits. All mother rabbits do not behave like other animals because they do not raise baby rabbits for a long time. That’s why you, as the owner, are tasked with providing care when the mother rabbit is gone.

There are some helpful tips to help breeders care for baby rabbits. At first, you need a box that fits the mother and the babies properly. Make sure you provide the box with hay or straw. Add softwood shavings. In addition, the temperature of his box should be warm for these newborn rabbits.

Consider the mother rabbit feeding her litters. Failing that, owners should provide the kittens with something to feed them such as cat litter. Any eye dropper is not recommended for use as it is not always suitable for feeding litters. Alternatively, get an oral syringe. Remember to clean the baby rabbits after feeding them.

If the babies urine gets a brown color, immediately call a trusted veterinarian. This change in urine color can be harmful to the health of the litter. If you notice they are dehydrated, prepare a pedialyte to rehydrate their body. Make sure your house is also child-proof.

Fruit drinks and cow’s milk are not allowed for newborn rabbits as their ingredients can cause dirty stools. Mom also needs more food like pellets because they need more calories. Calories are important for producing enough milk for young babies. Lactobacillus acidophilus is recommended to be added to the rabbit’s mother’s milk to strengthen their systems.

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## How To Solve For X In A Quadratic Formula Random Number Generators: True Randomness

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## Random Number Generators: True Randomness

I. Introduction:

Random (adj): a: lacking a definite plan, purpose, or pattern. b: made, done, or chosen at random c: relating to, having, or being elements or events with definite probability of occurrence. d: being or relating to a set or to an element of a set each of whose elements has equal probability of occurrence. [Oxford English Dictionary]

Before commencing deep discussion of the art of “true randomality”, it must first be made clear that true randomness is theoretically impossible by the defining principals of our universe. The definition above clearly defines the paradox that surrounds the concept of randomality when subject to probability. In essence we will claim that “truly random” is the state in which for a given set A, for any i, element in A, i if chosen at random, has a probability of [1/|A|] (where |x| denotes cardinality of the set) of occurrence. This is how we judge the “randomness” of a Random Number Generator (RNG(s)), by its ability to exploit probability; given a set A, a perfect RNG will not repeat an element before the set is exhausted; described as the period of a generator, its point of repetition.

It must be noted that defining a choice as random is a classification that relies on pure ignorance of the causes and events that result in the ultimate choice. With that aside, the philosophical discussion of “true randomness” will be left behind. The remainder of the discussion will judge “true randomness” as stated above; perfect probabilistic distribution over a given finite field. Although such distribution has never been possible with the various algorithms being discussed, (meaning such a distribution could not be perfect on every occurrence of a specific algorithm) relatively good distribution suffices.

I.i Various Uses of Random Number Generators:

Random numbers have a multitude of applications. Of particular interest to this study and intended future studies by the author is Cryptography. Many cryptographic protocols make use of RNGs, particularly, public key cryptography (RSA) and some implementations of symmetric ciphers (DES, Serpent). Besides cryptographic function however, RNGs are used in Simulations, for the realistic recreation of “natural” occurrences; in this case, computer games are qualified as simulations, in which RNGs are heavily used in conjunction with probability weights (Gaussian). They’re also used for integrity testing on various computer applications during development, even hardware tests, such as GPU to memory pipelines on AGP based graphic cards. Among those mentioned are many other uses and purposes for the development and “perfection” of making truly random choices.

I.ii Brief Algorithm Introduction:

Random number generating algorithms come in multiple flavors; these can be separated into two main groups, linear number generators (LNG(s)) and non-linear number generators (NLNG(s)). Each group contains multiple types of RNGs and each of these, have their purpose and uses. It is important to know that although not all generators are made equal, good generators have purposes for which other good generators are not suited to perform.

I.ii.a Linear Number Generators:

Linear Congruential Generators (LCG(s)) deserve first mention purely on the basis of ubiquity. LCGs and their various spawns and modifications are used in various applications. The LNGs in their purest form are nearly as predictable as the Fibonacci Sequence. These are seeded generators that make their “choices” – if that can be said – linearly in the given finite field, based on their seed. The come in more flavors that most other generator types, no doubt, due to the simplicity of modifying the algorithm for specific purposes.

I.ii.b Non-Linear Number Generators:

The Inversive Congruential Generator (ICG(s)) and the Explicit Inversive Congruential Generator (EICG(s)) are the two main focuses in this category. These generators are non-linear (as implied), and therefore are not predictable the way that LNGs are. Also mentioned in the non-linear group is the Linear Feedback Shift Register (LFSR(s)) generator. This generator, although linear, as implied by its name, carries the principles of Non-Linear Generators in its implementation; so much so, that LFSRs closely resemble their non-linear counter parts, Non-Linear Feedback Shift Register generators. The details of the history of Feedback Shift Registers go slightly beyond the scope of this paper however a brief introduction to the principals of feedback functions and shift registers is given in parallel with the LFSR discussion.

II Linear Congruential Generators:

LNGs ultimately generate a sequence of integers between 0 and a given modulus, for the equation Ij+1 = aIj + c (mod m). In this equation, m is used as the modulus, a is a multiplier, and c is an increment. The sequence will repeats within a period of m, where m is usually prime.

The advantage of the LNG is immediately noticed by the equation above; its fast, requiring one multiplication, one addition, and one modulus. This immediately lends itself to explaining its wide uses. This type of generator is used in a multitude of applications for which the nature of the random sequence doesn’t matter, only that it be a different sequence from execution to execution; Monte Carlo simulations for example. The speed and simplicity of the algorithm has also led to the amount of flavors developed for different applications. For instance, the equation above is the same equation that the ANSI C/C++ committee has dubbed for use with these languages, given appropriate values for a, c, and m. Besides the linear equation, there are also:

Xn = (aXn-12 + bXn-1 + c) mod m

Cubic LCG:

Xn = (aXn-13 + bXn-12 + cXn-1 + d) mod m

There are also polynomial LCGs, Truncated LCGs, etc; each of which work on the same principle and are generally predictable and breakable. For example, the standard LCG was first broken by Jim Reeds, and Quadratic and Cubic Generators broken by Joan Boyar.

It should be noted that most modifications to LCGs simply yield worst generators. Since linear generators can only be judged based on their progression through a linear field, and not on a probabilistic survey of a given set, the period of a LCG is of paramount importance, more so than other Congruential generators, even in non-linear fields. There are multiple methods for extending the period of a given generator, however many attempts, unpredictably yield shorter periods. Computing history, both hardware and software, is filled with the “botched” attempts to improve LCGs. Notably, early IBM mainframes with the RANDU routine, using a = 65539, and m = 231 producing a n – dimensional plot in only 11 plane dimensions. There’s also the problem of seeding the generator; each sequence is only as unique as its seed. The Netscape browser’s security was a one point compromised due to the predictability of the chosen seeds in it LCG for which it created crypto-keys.

It is possible to force an LCG to be probabilistically correct, by creating uniform deviations. The problem with focusing on the deviation of an LCG is that a well deviated LCG will have an extended period, but its complexity increases, due to the deviation, sometimes beyond the useful range of LCGs. It is also possible to use deviations normalized in a given interval, such as Gaussian deviations, where the period is lengthened such that every integer in the given field is selected.

III Inversive Congruential Generators and Linear Feedback Shift Registers:

Defined as our non-linear generators, ICGs and EICGs, developed by Eichenauer and Lehn (1986, 1993) are defined by the following congruence:

yn+1 = ayn + b (mod m)

Where, for practicality, m is also chosen as a prime number in parallel to LCGs. These two generators are most notable due to their speed and period efficiency compromise. They produce relatively long periods, in (5 – 10x average) more time, than LCG.

III.i Linear Feedback Shift Registers:

LFSR generators are of more relevance here, as a suitable alternative to LCGs for cryptographic applications. Shift registers work on the concept of generating on the bit level, instead of in a base 10 finite field. They address the problem of creating uniform distribution of single random bits, with 0 and 1 equally probable.

LFSR generators are made up of two parts, the shift register and the feedback function. The shift register is the bit sequence, in which the size of the shift register is determined by the length of its bits. When bits are needed, the register is shifted 1 bit to the right, and the left bit is computed based on the remaining bits in the register. The simplest method of representing LFSRs feedback function is the XOR of key register bits. The method used by the feedback function is called tap sequence.

It’s obvious, that an n-bit LFSR can be in 2n -1 states; noting that the size of the register denotes its length. Therefore, a 4 bit register (1111 would be called a 4 bit register, based on the cardinality of the register, rather than the value of the high order bit, base 10) would yield 24-1, or 15 unique states. With an output sequence of the least significant bits following the shifts, the size of the register defines a period or 2n – 1 bits before repetition, therefore yielding a base 10 value of 22**n -1 as maximum value, and period. In order to reach this maximum period, a primitive polynomial must be formed by the tap sequence, where the degree of the polynomial yields the length of the shift register.

III.i.a Primitive Polynomials in Linear Feedback Shift Registers

A primitive Polynomial is defined as an irreducible polynomial P of degree d in [Z/p[x]] (denoting finite field of p[x] in Z) is primitive if P divides xd – 1 but does not divide xi – 1 for any integer i with 0 xn = 1 mod P

but,

xi != 1 mod P for 0

It is not necessary to check all smaller exponential values than d, but only possible values from the divisors of degree d.

There is no easy method for generating primitive polynomials modulo 2 for a given degree. Therefore, choosing random polynomials and testing if its primitive is the most used method.

III.i.b Maximizing and Reaching the Period of an LFSR

As stated above, the period of any LFSR is based on the size of the shift register; the size of the shift register is based on the degree of the polynomial, therefore the period of the LFSR is determined by the polynomial used. Primitive polynomials are necessary here because if the polynomial used is not primitive, the period will be shortened, and there may be bad states which may shorten the period further. Therefore choosing a primitive polynomial is of dominant importance to any LFSR.

Given the polynomial, x8+x4+x3+x2+x which is primitive modulo 2, a maximal period can be produced. The first exponent is the length of the shift register, and all exponents except 1 and 0 are used to specify the tap sequence by the feedback function, where low degree terms correspond to the left most register bits. Therefore, in a given 8-bit shift register, a new bit is generated by XORing the 8th, 4th, 3rd and 2nd bits of the register together. The LFSR that results from this polynomial will have a precise period of 28-1.

Linear Feedback Shift Registers are found in many places, such as in Ueli Maurer’s Fast Prime Generation routine, but most commonly in the stream-cipher domain of cryptography. Therefore the propagation of primitive polynomials is important to success of such ciphers. The polynomial used in LFSRs is as important as the seed used in a LCG. Just as LCGs are cracked by deterministic seeds, LFSRs are also cracked by many organizations, based on the use and reuse of deterministic primitive polynomials. It should also be noted that the algorithm itself is completely linear when sequential bits are taken into account, however its implementation in software makes in non-linear. By running simultaneous LFSR applications (32 for a computer with a word size of 32) nonlinear sequences can be produced; rather, seemingly nonlinear, described as a large linear complexity.

IV Discussion:

The Linear Congruential Generators we presented here for an ease into the concept of random number generation, and for study of a variety of methods of generation. However, in the domain of cryptography, LCGs are all but irrelevant. LFSR, and their “cousins” Non-Linear Feedback Shift Registers are of more relevance to the authors interest. Besides the methods described above, another interesting method of generating random numbers are also worth brief mention.

Symmetric block ciphers are also capable of producing randomality. Beginning with block product ciphers like LUCIFER and DES, the use of block ciphers to produce random bits, although many times slower than LCG and even LFSR, yields considerably random bit sequences. The more recent successor to DES, AES (Rijndael algorithm) and even the runner up contender to AES, Serpent, have also been used for the generation of random bits.

Essentially, the philosophical debate of the concept of randomality displays the obvious difficulty in constructing a truly random algorithm. The fact that most random generation algorithms are based on random sequences, be they number sequences or bit sequences, undermines the term random from the very first line of code and comments justifying its feasibility. However, random sequences are frequently used, and make amply use of the ignorance factor. As long as new methods of seeding and new primitive polynomials are found, for which we have an infinite supply, the number generators above will remain in use. The possible existence of a truly random number algorithm is questionable, but with many algorithms and sequences still remaining unbroken and uncharted, that existence cannot be denied.

## Question about How To Solve For X In A Quadratic Formula

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## How To Solve For R In Simple Interest Formula Loan Officer Marketing – Why Realtors(r) Don’t Read Your Brochures

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When you put the brochures from each mortgage company side by side, you can’t help noticing the similarities. Each piece speaks of having every loan program possible, proven and experienced professionals, prompt and friendly service, a list of documents required to process the loan, a commitment to individualized attention, and a commitment to professional service to the client.

It’s good and stylish for consumers, what about your brochure for real estate agents? If you give agents the same brochure you give to customers, will it help you stand out? Probably not – and even if you have a separate leaflet for agents, does this avoid the 3 most common mistakes?

Leaflet Error #1 – Messages Based on Attributes

This is the colossal mistake in most brochures. Here is a short list of features often mentioned in mortgage brochures; loan rates, APR, quality service, mortgage insurance, points, refinancing, payments, purchasing, full service, sourcing, retail, interest only, option only, ARMS, free quotes, to name a few.

The features don’t tell the reader anything. Sometimes they just get more confused about your service. When an agent reads your brochure, they are reading it for one reason only. they want to know “What’s in this for them?” If you’ve been in sales for a long time and are a good student in the field, you know that people are interested in hearing benefits, not features. But wait, there’s a twist.

If you’re selling widgets, your flyer follows an old-school formula. It explains what the widget is (feature) and then tells the client what the widget will do for them (benefits). Pretty simple, right?

But you’re in the mortgage business. Or rather, you are in the service business. Where does the warning lie? it is invisible when you sell a service. You can’t touch, smell or see it. Explaining the benefits an agent derives from using your services is helpful, but not sufficient.

If you want your brochure to make a difference, a difference of the kind noticed by representatives, more than just identifying problems you can solve for them.

Leaflet Error #2 – Use of Jargon

Jargon is like “Swahili”, a confused, incomprehensible language. Words you understand, but leave an agent without knowledge. Jargon comes across as incomprehensible and pretentious. Instead, keep things in simple terms. Your brochure should focus on expression, not impression. Using fashion words, stylish words or phrases can look flashy.

Jargon slows or stops the reading process. Avoid this by writing your brochure in a relaxed voice as if you are conversing with the reader. In English class you were taught to write very formally, remember, your brochure is not a term paper, It is an opportunity to persuade and shape one’s perception.

Use pictures to communicate they are only worth a thousand words. Agents understand with their eyes. Graphs, charts, photographs, and quotations are examples of conveying or supporting important points.

Everyone’s brochure mentions good customer service. As an alternaive, use a flowchart to show your service, and supporting this with satisfied customer testimonials.

Leaflet Error #3 – Metaoism Disease

No offense – most of us have this disease. You see what might work for someone, so you copy it for yourself. It’s easy to take the leading competitor’s brochure and copy some or all of it. For example, years ago, fare lists were a hotly marketable flyer. You can hand out a few hundred and get a respectable response. Well, when there are hundreds of loan officers copying this, guess what? It wears out but we continue to use it.

Metatooism is not valuable. Look at how much mail you still get from other mortgage companies trying to refinance you. And they use the same formatted letter as everyone else. The letter specifically states how much you can save in bold and includes an advertised low rate. Sometimes it is printed in the form of a fictitious check ready to be cashed.

Don’t be afraid to be different. It’s easy to use what others have and it’s hard to find originality. But it is originality that can win the biggest prize.

The Power of a Well Crafted Brochure

Like a good movie plot, a well-crafted brochure sets the story in motion. It shapes an agent’s perception before sitting down with them – it reduces rejection and reduces resistance. It awakens thoughts in their minds, makes you more memorable. And it helps you stand out and get noticed in a big crowd.

## Question about How To Solve For R In Simple Interest Formula

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