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240 volt motors will have a stronger start compared to a 120 volt motor. Each leg can provide 120v hot to neutral and the two legs together will supply 240v which is used to supply heavy loads such as air conditioning compressors and cookstoves.
Wiring Diagram For 220 Volt Single Phase Motor Bookingritzcarlton Info Electrical Projects Home Electrical Wiring Electricity
Variety of 240v motor wiring diagram single phase.
120 240 volt motor wiring diagram. This could be the case at a water well or a workshop. A wiring diagram is a streamlined conventional pictorial depiction of an electric circuit. Single phase motor wiring diagram with capacitor baldor single phase motor wiring diagram with capacitor single phase fan motor wiring diagram with capacitor single phase motor connection diagram with capacitor every electrical arrangement is made up of various unique pieces.
The incoming 240v power is split into two legs. A balanced electrical load which may save on electricity compared to an unbalanced electrical load. Homes in north america are supplied with a 120 240v single phase electrical service.
Each component ought to be placed and connected with other parts in particular way. It is actually two 120 volt circuits which share the neutral or common wire. A repulsion electric motor is by definition a single phase motor which has a stator winding arranged for connection to the source of power and a rotor winding connected to a commutator.
Otherwise the arrangement won t work as it should be. This type of winding arrangement gives only half as much starting torque at 120 volts as on a 240 volt connection. Wiring a 120 volt circuit off of a 240 volt circuit can be useful where there is primarily 240 volts available.
Wiring a 120 240 volt motor for 240 volts is as follows. Reconfiguring between 240 and 120 volts is done the same way but the starter winding stays connected to one of the windings. It reveals the components of the circuit as simplified shapes as well as the power and also signal connections in between the tools.
5744b52 electric motor wiring diagram 110 to 220 library 120 240 volt vac 1971 triumph spitfire for schematics terry love plumbing advice remodel diy professional forum tk 6191 single phase on free kv 6567 schematic dlpf 6897 ge diagrams full webdiagram phpbb3 es 5e7 power transformer the reversing a v with six pole switch installation 5744b52 electric motor read more. A 240 volt circuit is comprised of two hot wires a common neutral wire and a ground wire. If you don t have a wiring diagram and the motor is currently wired for 240 volts you can identify point b by the fact that it isn t connected to either power lead.
3ø wiring diagrams 1ø wiring diagrams diagram er9 m 3 1 5 9 3 7 11 low speed high speed u1 v1 w1 w2 u2 v2 tk tk thermal overloads two speed star delta motor switch m 3 0 10v 20v 415v ac 4 20ma outp uts diagram ic2 m 1 240v ac 0 10v outp ut diagram ic3 m 1 0 10v 4 20ma 240v ac outp uts these diagrams are current at the time of publication. Each component ought to be placed and linked to different parts in particular manner. 240 volt single phase wiring diagram 220 volt single phase motor wiring diagram 220 volt single phase wiring diagram 240 volt single phase motor wiring diagram every electric arrangement is composed of various unique components.
The advantages of a 240 volt motor. | https://easywiring.info/120-240-volt-motor-wiring-diagram/ |
Krakow or Warsaw – Which One Should You Visit?
Our comparison will help you make up your mind!
So you’re planning a holiday in Poland.
Still not sure whether to visit Krakow or Warsaw?
Don’t worry, we’ve got you covered!
In general, Warsaw is a larger city that is more spread out and cosmopolitan. Krakow, on the other hand, is much more compact but still gets the bulk of the tourist attention.
While Warsaw is larger and more sophisticated, most foreign visitors go to Krakow, the most popular tourist destination in Poland.
Read on to find out more about these two Polish gems to which one makes a perfect holiday destination for you.
Krakow – what’s it all about?
- Krakow is unique because it’s one of the few larger Polish cities that were not damaged during the Second World War.
- It’s rich in beautiful historical architecture that spans many centuries.
- All the attractions are located in the compact Old Town, so it’s very walkable and accessible to explore.
- The Jewish district, Kazimierz, is one of the most exciting areas of the city.
- You can easily explore Krakow over the weekend. But give yourself more time if you also want to visit popular attractions in Krakow’s surroundings such as the Wieliczka Salt Mine, the Tatra mountains and the picturesque town of Zakopane, or Auschwitz concentration camp.
A few words about Warsaw
Warsaw is an entirely different city from Krakow.
- Since it was destroyed during the Second World War, its historical center is a complete reproduction (a fact people from Krakow always mention when comparing Warsaw to Krakow).
- While the historical streets are quite charming, the rest of the city is business-oriented and cosmopolitan, with plenty of offices, high-rise buildings, and shopping malls.
- But Warsaw is also home to vibrant cultural life with plenty of museums and art on display.
The battle begins
Now that you know the basics about Krakow and Warsaw, it’s time to begin our battle.
Read on to find out which of these two amazing cities wins in every round of the battle.
Round 1: History
When it comes to history, Krakow might seem like an obvious winner.
After all, its stunning architecture has been left intact throughout the country’s turbulent history.
However, if you’re interested in recent history, then Warsaw might turn out to be more interesting. You’ll get to admire the Socialist Realist architecture constructed during the Soviet era and learn more about the history of the Second World War in the city’s many museums. It is also interesting to see how the reconstruction of the historical center maintains the traditional character of Warsaw.
Visitors also get to admire the city’s many monuments that are evocative and impressive.
Since Krakow wasn’t destroyed during the Second World War, it houses a broad range of historical attractions including the Wawel Castle which served as the centre of the Polish monarchy for centuries. However, those interested in more recent history will also benefit from visiting the Auschwitz-Birkenau concentration camps located in Oswiecim.
Far from a typical tourist attraction, these sites provide an emotional and harrowing visiting experience, documenting the atrocities of the Second World War like no other place in this part of Europe.
Round 2: Speed of the city life
There’s no denying that Warsaw is larger than Krakow and far more cosmopolitan.
While Krakow is overflowing with international tourists, Warsaw attracts business people and students who are looking for all kinds of opportunities in this vibrant city.
Moreover, Warsaw is full of modern skyscrapers, and the pace of life is much faster than Krakow.
While Krakow is an excellent place for learning more about the Polish history and tradition, Warsaw provides a much more exciting entry point into Poland.
Special offer
Round 3: Nightlife
While Warsaw is a large city that caters to many tastes, Krakow’s famous old and smoky cellar bars and captivating clubs in the Jewish district make it a more exciting choice.
Have you ever heard of the urban myth which says:
there are more bars per square meter in Krakow’s Old Town than any other city in Europe
I think that’s not far from the truth.
Both cities are full of the classic Polish walk in bars where you order a drink for one euro and a bite for two. You will find all kinds of exciting clubbing opportunities in both cities.
However, it’s Krakow that attracts people from all over Europe to its unique bars, pubs, and clubs.
Round 4: Pricing
When it comes to prices, Warsaw is definitely more expensive than Krakow.
Dining in Krakow is cheaper, and the same can be said for accommodation.
However, both cities offer a broad range of budget accommodation and dining options. For example, you will find fantastic milk bars serving inexpensive traditional Polish cuisine in both cities. Entrance tickets to many tourist attractions are also cheaper when bought in sets or prebooked.
Still, when it comes to hotels, taxis, and other expenses, Krakow is clearly the winner.
Round 5: Food
Warsaw is a cosmopolitan city with many sophisticated dining options that will satisfy all palates.
However, Krakow with the local traditional treats such as the smoky sheep cheese, red sausage, and the delicious pierogi is a winner.
In general, Krakow offers a broader choice of traditional Polish cuisine dishes. Additionally, there is the local, regional tradition that is just incomparably richer to the Polish cuisine offered in Warsaw eateries.
All in all, both cities offer great dining options but assuming that tourists come to Poland to try the local treats, Krakow is a clear winner.
Krakow or Warsaw? Which wins the battle?
There’s no denying that Krakow is the most popular tourist destination in Poland.
Many reasons account for that – from inexpensive food and exciting nightlife to amazing cultural offerings and beautiful historical architecture.
While both cities are worth a visit, those who have never been Poland should start with KRAKOW.
It offers a much more accessible entry point to the amazing history and culture of the Polish nation.
And once you become a returning guest in Poland – check out how modern and amazing Warsaw is!
(or extend your stay in Poland! Why limit yourself?)
Do you know any other reasons why Krakow makes a better destination for visitors?
Or perhaps you think Warsaw should be the winner of the battle? We invite you to share your thoughts and experiences in comments. | https://discovercracow.com/krakow-or-warsaw/ |
A bone cyst is a benign, non-tumorous lesion on the bone. They consist of fluid-filled cavities in the bone, which can vary in size.
Often affected by bone cysts are children up to the age of 15, but boys are more likely to be affected than girls. In many cases, bone cysts do not cause any discomfort and are therefore only discovered accidentally during examinations. In other cases, the bone cysts grow completely unnoticed at the conclusion of growth, have never caused discomfort and are therefore not noticed.
Even if a bone cyst is discovered, treatment is not always required. If there is no danger of secondary diseases, it is easy to wait until the cyst becomes engorged. In the case of bone cysts, a distinction is made between juvenile bone cysts (single-chambered) and aneurysmal bone cysts (multi-chambered).
The exact causes of the formation of a bone cyst are unknown. However, it is believed that bone injury or blood clots can trigger bone cysts. Also, inflammation or developmental disorders are considered as possible cause.
Children are affected by bone cysts until about the age of fifteen, and less frequently are they also in adulthood. Most commonly, bone cysts occur in children up to. 10 years on. Bone cysts in children usually occur in the humerus or femur.
Since they are very often uncomfortable, they are often discovered by accident. Such as when a bone fracture is present and therefore an X-ray examination is necessary. In some cases, bone cysts may also be responsible for bone fracture because they lower the stability of the bone.
Bone cysts usually cause no noticeable complaints. However, a cyst in the bone area increases the risk of fractures. For example, proliferation impairs the stability of the affected bone, and circulation in the surrounding area may also be reduced or completely cut off by the cyst.
If no more blood gets into the surrounding tissue, serious complications can develop, including necrosis. In isolated cases, bone cysts can cause pain. Those affected then suffer from an indefinable, drawing pain, which occurs especially with stimuli such as cold or heat. Large cysts can cause persistent pain, thereby affecting well-being.
Rarely, visible swelling or redness forms in the area of the skin. However, these are usually not associated with pain and quickly fade away. Bone cysts around the head, spine, genital area and knee can cause various dysfunctions. Bone cysts usually form very suddenly and are discovered much later.
They grow quickly, but are relatively harmless due to their benign shape. Mostly they connect with the surrounding tissue as soon as the growth phase is completed. The bone cysts are then no longer visible on the x-ray.
Bone cysts usually do not cause any discomfort to the affected person, which is why a doctor is seldom visited. If a bone fracture occurs, a bone cyst may be responsible for it and is often discovered when a bone fracture is diagnosed more accurately by X-ray examination. A bone cyst is visible on the radiograph as a bright spot.
When we discover a bone cyst, it is crucial if this cyst poses a threat to the bone. This is always the case when the bone is restricted by the bone cyst in its stability and therefore threatens a bone fracture. Even if the bone cyst is responsible for an existing bone fracture, treatment should be given.
In all other cases, therapy is not necessary as most bone cysts disappear by themselves in the course of growth. At the latest on completion of the growth phase, bone cysts are no longer recognizable.
A bone cyst does not necessarily lead to complications or limitations. It is usually benign and therefore does not always have to be treated. Patients can suffer from developmental disorders as well as movement disorders and restrictions in everyday life through the bone cyst. In most cases, however, no pain occurs.
Patients also suffer more from fractures, making them easier and easier to use. The stability of the bones and thus of the entire body decreases. As a rule, the person concerned is less resilient. If the cyst is not dangerous to the bone, it will not be removed or treated.
Mostly, the cysts are only discovered by chance during follow-up examinations. However, if it comes to complaints, it can also be treated with the help of cortisone. There are no complications. Furthermore, an operative treatment is possible. The life expectancy of the patient is not reduced by this disease. Only in rare cases, there are limitations in the everyday life of the patient.
Repeated bone fractures and pain or swelling around the bones may reveal a bone cyst. Medical advice is required if the symptoms significantly affect well-being, do not subside by themselves or become stronger within a short time. Thus, chronic complaints must always be clarified by a specialist and treated if necessary. Otherwise serious complications can occur. If additional symptoms are added, it is best to go to a doctor on the same day.
For recurring complaints for which no cause can be found, a specialist should be involved. With children who complain of pain on or in the bone, should go to the pediatrician. However, the first port of call should otherwise be the general practitioner or an orthopedist. During the treatment, a close consultation with the physician is necessary. If side effects and interactions develop after taking the prescribed medicines, this must be clarified as well as recurrent pain and other symptoms.
The treatment of a bone cyst depends on its extent and its possible effects on the body. In many cases, no treatment is necessary because consequential damage can be largely excluded by the bone cyst.
If there is an increased risk of a bone fracture due to the bone cyst, suitable therapies should be initiated to eliminate the cyst and thus prevent a bone fracture.
Juvenile bone cysts can be treated very well with cortisone. The cortisone is injected directly into the cyst and causes the bone cyst to gradually disappear. In some cases, it may be necessary to disengage the bone cyst and fill the lumen with bone material. This measure is the treatment method that promises the most success. In addition, so-called decompression screws can be inserted into the bone. These ensure a healing of the bone cyst.
In an aneurysmal bone cyst, however, a therapy is more often required to prevent permanent damage to the bone. Since an aneurysmal bone cyst, in contrast to the juvenile bone cyst, is very well perfused, there is a very strong growth in this species. In the process, the bone substance is increasingly used up and thus the bone is damaged and unstable.
Therefore, aneurysmal bone cysts can also cause pain. In these cases, treatment of the bone cyst is recommended. In most cases, this is a surgical procedure in which the cyst is emptied and filled with bone or cement. However, the aneurysmal bone cyst is a very rare disease.
The prognosis for a bone cyst is usually favorable. It is a benign change that is usually only diagnosed by chance in children and adolescents. The cyst rarely causes physical discomfort. Therefore, some sufferers may experience bone cysts in the organism for a long time, yet they do not experience any adverse effects on their daily lives.
A shortening of the lifetime or other sequelae are also not given in this disorder. Often, due to the low need for action, no treatment is needed or performed. The diagnosis takes place in a large number of patients due to a bone fracture. This may have been triggered by a cyst. With early and professional medical care, the bone fracture heals completely without further complications within a few weeks or months. If not done independently, the existing cyst is removed in parallel during treatment. Residues or other inconvenience usually remain.
Despite the favorable prognosis, a further development of the cyst can occur in the further development of the child. The healing prospects and the course of the disease are still positive in these cases. If the bone cyst is noticed, it can be removed if desired.
Since the causes of bone cysts are not clearly understood, there can be no direct recommendation for prevention. Also, the causes that are suspected of triggering a bone cyst, are difficult or impossible to influence.
The removal of the bone cyst is often uncomplicated, so that a complex aftercare in many cases is not necessary. Nevertheless, there are some points to consider after surgery. Immediately after surgery, it is important to look for signs of a rare infection in the operated area. The typical symptoms such as redness, overheating, swelling and throbbing pain are reason for a visit to the doctor. That's even more the case with fever. The earlier an infection is detected, the better it is usually treated.
The second point of aftercare concerns the functioning of the bone in question. The wearing of gypsum and the protection of the relevant area are really only as long as the doctor recommends. He can estimate when the bone is sufficiently resilient to the demands of everyday life, work and leisure.
Taking too much care in the context of aftercare can also be counterproductive if it is at the expense of strength and flexibility. If the exercise capacity is to be increased gradually, this may be accompanied by a physiotherapist. Sports in the aftercare should be discussed with the doctor. To avoid is particularly strong compression by jumps and the risk of injuring in a duel.
In the case of a bone cyst, the person concerned usually has no special options for self-help. The further treatment of such a cyst, however, depends on their position and severity, with a treatment or removal is not necessary in every case. Most of the bone cysts are treated with the help of cortisone, resulting in a positive disease course. Those affected should, however, avoid fractures and thus dangerous sports or activities in general.
If the bone cyst leads to pain, analgesics can also be taken. These should only be taken over a longer period of time, as they can otherwise damage the stomach. The doctor may also provide the patient with a local pain relieving injection to relieve the symptoms.
If the bone cyst leads to mental discomfort, then conversations with other patients or with close friends and family are suitable. By exchanging information with other patients, everyday life can often be made more pleasant. Also, the success experiences of other people can solve mental health problems and accelerate the healing of the disease. | http://yourchiropractichealth.com/knochenzyste |
Questo libro parla dell’infinito, uno degli argomenti più affascinanti della matematica.
Molto spesso usiamo la parola “infinito” in maniera impropria, semplicemente per dare l’idea di un numero molto grosso: questa confusione fra infinito e numeri molto grandi è seminata attraverso la storia della matematica: ci sisi sono scervellati alcuni dei più famosi scienziati, come Pitagora, Archimede, Galielo e Gauss .
In effetti avrebbero avuto bisogno di strumenti che sono stati inventati solo tempo dopo.
Fu possibile affrontare questo argomento solo a partire del XIX secolo, grazie al matematico tedesco George Cantor.
Il libro, scritto da Bruno Codenotti, ci porta in un viaggio che inizia dal concetto di finito e arriva alle gerarchie degli infiniti scoperte da Cantor, mentre i miei fumetti aiutano la comprensione del testo e cercano di alleggerire i concetti con una storia di universitari che si svolge in parallelo.
This is a book on infinity, one of the most fascinating mathematical concepts, but also one of the most difficult. In fact we often use the word “infinity” improperly, just to highlight the idea of a huge number: this confusion between infinity and very large numbers is rooted in mathematical history: some of the most notorious scientists, such as Phytagoras, Archimedes, Galileo and Gauss, all struggled with this. Indeed they needed tools that would not be developed until later. Dealing with this concept only became possible in the XIX century, thanks to the German mathematician Georg Cantor and his development of set theory.
The written work by Bruno Codenotti takes us on a journey that starts from the finite and reaches the hierarchy of different infinities discovered by Cantor, while Claudia’s comic strips aid comprehension and involvement through a parallel histoire d’amour. | http://www.claudiaflandoli.com/portfolio/archimede-aveva-un-sacco-di-tempo-libero/ |
Darkness to night
One of the characteristics of the middle age is the lack of interest in education. Indeed, the Roman Catholic Church thanks to centuries of preaching answered all the great philosophical questions, such as the meaning of life and death. The rise of the Universities in Western is a critical factor of the waning of the medieval society. When at first education exclusively for clergymen, it was now available to everybody. Thos universities taught all the basic disciplines with the Trivium and the Quadrivium. Since they were open to everybody, European from many regions traveled to attend Universities. For instance, in Life of a Student at Paris, Jacques de Vitry is enumerating all the different ethnic group attending courses at Paris: “English”, ‘son of France”, “Sicilians” (Reader2.p.84) … This is relevant because before this traveling wasn’t extended since it was very risky. Also, it developed a new urban way of life, since student were living in cities.
The true heart of the 12th century renaissance is the rebirth of critical thinking. Undeniably, Peter of Abelard a French scholar who was teaching among others in Paris, upset other views and opinion by book; the SIC et NON (Reader2.p.101). By encouraging people to be curious, and to question the church and their interpretations of the bible, he changed the way the intellectual community was thinking. P. Abelard also brought to light the divergences and the contradiction between the clergy, which contributed to undermine its authority. With this kind of powerful statements: “It is by doubting that we come to investigate, and by investigating that we recognize the truth.”, P. Abelard spread the seeds of other interpretation of the Bible, an interpretation that was challenging the Roman Church and the Canons laws. | https://www.etudier.com/dissertations/Darkness-To-Night/225901.html |
More on Outsourcing Method Development
For more information on outsourcing method development, read 'Developing a Method for Success through Partnerships' as published in the June 2021 issue of Pharmaceutical Technology.
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Thought and foresight into method development stages can ensure costly errors and delays are avoided later on.
Method development is a critical and continuous process that, if optimized, ensures successful progression of a drug product through its life cycle to commercialization. “Method development consists of three main stages: feasibility—where you determine if the method will work with your sample; development—where you optimize the method; and validation—where the optimized method is validated to the relevant regulatory requirements,” explains Vincent Thibon, technical development lead, RSSL. “Developing a robust method will ensure that routine testing occurs smoothly and limits the amount of testing required.”
“First of all, it is crucial to collect as much background information as possible on the API to understand its characteristics or what development challenges it poses,” says Anders Mörtberg, analytical chemist at Recipharm. “It is also important to check the established literature for analytical methods for compounds with similar profiles.”
In addition to gathering all the relevant data, it is important to define the objective of the method development, asserts Amanda Curson, head of Analytical Development, Tredegar, PCI Pharma Services. “At the beginning, an analytical target profile should be prepared that clearly outlines the requirements of the method, so that all involved understand and know what needs to be achieved with developing that method,” she notes. “The timelines, costs, and client expectations must be defined.”
Curson highlights that some useful questions to ask during these initial phases are as follows: What is the objective? Do you want the method to be suitable for drug substance (DS) initially, but maybe potentially further down the line for drug product (DP)? What is the basic chemistry of the DS? Is there any information on degradation products? Is there any information on chemical, solubility, molecular structure, stability?
For more information on outsourcing method development, read 'Developing a Method for Success through Partnerships' as published in the June 2021 issue of Pharmaceutical Technology.
Then after searching pharmacopeial methods for any existing information that can be used for the method development project, the phase of the development of the product, which impacts the amount of work required, should be assessed. Defining the phase of development early on is important, Curson emphasizes.
“In order to develop an accurate, reproducible, and reliable method, there must be an understanding of the final purpose of the method. This purpose should be the driving principle behind the research and development stages,” adds Emma Leishman, manager, Advanced Analytics, Avomeen.
However, Leishman notes that there are some starting considerations for any method development, regardless of the final purpose. “First, there is consideration of the analyte itself, as this can determine suitable instrumentation. Some analytes are inherently more difficult. Platform methods or templates may exist for the analyte or close structural analogues, or it might be that a method needs to be developed from scratch using published literature as a starting point,” she says. “Analytes might also be unknowns belonging to broader categories of chemicals, which require a different approach compared to a targeted method for a known compound.”
The next stage is about minimizing the complexity of the methods to ensure they are user-friendly for routine use, Curson continues. “[A method] will be used by different analysts and may be transferred between different labs,” she says. “When it comes to sample preparation and standardization, you want to ensure you can extract the API, which has a pharmacological effect when it gets into the body, from the sample matrix.”
Analyte matrix considerations can highlight some of the hurdles that need to be overcome, adds Leishman. “More challenging matrixes, like oral syrups or topical formulations, may require some creative sample preparation techniques for partial purification, such as solid-phase extraction, liquid-liquid extraction, and centrifugal filters,” she emphasizes. “Some instrumentation is more prone to matrix effects than other techniques, but standard addition curves can be useful for quantitation when matrix effects are present.”
“Developers need to select an appropriate solvent system for dissolving the sample and they should also choose a suitable separation mode, such as reversed phase chromatography or hydrophilic interaction chromatography (HILIC),” states Mörtberg. “A detection principle should also be chosen—for example, for [ultraviolet] UV or visible light, an appropriate detection wavelength should be selected. UV detection is preferred if the analytes contain a UV chromophore due to the widespread availability of UV detectors in [quality control] QC laboratories.”
Sample preparation is also an essential part of method development, Mörtberg continues. “Early on in the development process, suitable sample preparation conditions ensuring quantitative recovery of the analytes should be tested,” he says. “Sample preparation should provide reproducible and homogeneous sample solutions that are compatible with the mobile phase system. Sample preparation techniques are dependent on the nature of the drug product (solid, semi-solid, liquid etc).”
Finally, the specificity and sensitivity of the method should be considered, continues Leishman. “The analyte may be a primary component of the matrix, or it might be an impurity present at trace levels. Instrumentation and sample preparation approaches may change if trace level sensitivity is required,” she reveals. “Regulatory guidelines and a knowledge of toxicology are especially important for impurity methods, as these often dictate the permissible limits. Given the trend for increasingly tight regulatory limits, such as for nitrosamines, then it might be prudent to develop a method with sensitivity beyond the minimum requirements in case regulatory authorities decide to lower limits in the future and to fully understand the risk to the consumer.”
“With optimization, you want to make sure your initial method is compatible with the sample matrix,” confirms Curson. “To meet the industry standard, we subject the product to harsh, acidic or basic conditions, oxidation, temperature, and heat so that we are forcing degradation products to be produced, the method must be capable of showing the degradation products and that they do not interfere with the active product potency.”
Once all the relevant screening of the mobile and stationary phases are completed, which should include the samples from forced degradation, further optimization of the chromatographic system should be performed to determine the most appropriate column temperature, as well as optimal solvent gradient or solvent composition, adds Mörtberg. “To streamline the experimentation phase, a design of experiment setup or a method-development-aiding computer program is highly useful. If planned and documented correctly, the data can be used for a later robustness test included in any later method validation,” he says.
“Prior to formal validation of the analytical test procedure, pre-validation experiments using final method conditions should be conducted,” Mörtberg continues. “This will provide an assessment whether the method is ‘validatable’ and a basis for setting relevant acceptance limits for the validation characteristics.”
Ultimately, the method must be transferable between scientists and equipment, irrespective of any potential slight changes in method conditions that may arise, emphasizes Curson. A transferable method is a robust one that will be applicable for future development requirements.
“Without solid analytical methods, it is impossible to make evidence-based conclusions on the safety and efficacy of a product or process,” concludes Leishman. “Strong analytical methodology provides clarity and focus to any scientific endeavor. Costly delays may arise when methods fail during routine analysis, which can be avoided by devoting more resources and thought into the development stages.”
Felicity Thomas is the European editor for Pharmaceutical Technology Group.
Related Content: | https://www.pharmtech.com/view/outlining-the-key-steps-to-method-development |
FACTS:
The defendant cargo owner chartered a vessel to carry a cargo of wheat from a US port to Bombay.
- January 21, 1975: The vessel got stranded on a reef in the South China Sea 420 miles from Manila.
January 22: The ship’s managing agents signed a salvage agreement as agent for the cargo owner. The goods (wheat) being perishable, the salvors stored it at their own expense.
- February 25: Salvors intimated the whole incident to the cargo owner but no reply was made.
- April 24: The ship owner abandoned the voyage and notified the cargo owner accordingly.
Subsequently, the cargo owner accepted responsibility for the salvors’ storage charges for the period from April 24 to August 5, 1975, but it refused to pay the storage charges incurred by the salvors between February 10 and April 24, 1975. The salvors claimed those expenses in an action against the cargo owner. Cargo owner disclaimed their liability to reimburse for the time when the first barge-load of salvaged wheat arrived in Manila (Feb 10) untill the abandonment of the ship(Apr 24).
ISSUES:
- To whom the cargo was deliverable at the termination of the salvage services?
- Whether, on salvors obtaining possession of the cargo from the ship-owner the relationship of the salvors to the cargo-owner was that of a bailee or sub-bailee?
CONTENTIONS:
Salvors:
They are entitled to reimbursement because-
- They had implied authority from the cargo owner to take care of the cargo, from the terms of Lloyd’s form.
- They were bailee of the said cargo.
- They acted as agents of necessity on behalf of the cargo owner.
- Cargo owner were duty-bound both at common law and under Lloyd’s form to accept redelivery which they failed to do.
- In contradiction with general law of restitution, cargo-owners were unjustly enriched at the salvors’ expense.
Cargo Owners:
- Ship-owner, being the bailee of the cargo, (not the cargo owner) was liable to reimburse the salvor because, untill the contract remained unterminated, the immediate right to possession was vested in ship-owners and the cargo was deliverable to them only. Reasons being-
- shipowner has the right to retain possession of the cargo and to complete the voyage with it.
- cargo owner is obliged to allow the shipowner to preserve his right to possession
- shipowner has an obligation to look after and care for the cargo for at least so long as the contract of carriage exists
- The cargo owner has a right to look to the shipowner for the performance of that obligation of care and/or preservation of the cargo.
- In storing the cargo the salvors had merely been preserving their lien for salvage and, therefore, that they could not recover their expenses (came up in Court of Appeal)
- Even if the salvors were bailee, they had no correlative right to claim reimbursement because neither a bailee for reward nor a gratuitous bailee has any such right to indemnity.
HELD:
Commercial Court (Lloyd J.) (favoured salvors)
- (w.r.t. B) Salvors were bailees and not sub-bailees, but that it would make no difference if they were sub-bailees).
- (w.r.t A,C & D) Accepted these contentions
- (w.r.t. E) Although the English courts do not accept as a general proposition that a person is entitled to remuneration or recompense merely because he has conferred a benefit on another, there is one exception- where there is a preexisting relationship between A and B and where A performs services for the benefit of and/or at the implied request of B which (a) B has an opportunity to reject but fails to reject, (b) B knows were not intended to be performed gratuitously and (c) B would have had to engage some other to perform, then the law imposes an obligation on B to pay A reasonable remuneration for such service. The salvors satisfied all the conditions of the given exception and were entitled to succeed under the general law of quasi-contract or restitution.
- (w.r.t 1st and 2nd contention of the cargo-owner) Rejected this contention
Court of Appeal (Reversed Lloyd J’s judgement)
- (w.r.t. B) The bailee’s right to be paid “depends on there being something which can properly be called an element of necessity.
- ( w.r.t C) Inability to obtain instructions was not or might not be sufficient to create agency of necessity.
- (w.r.t. E) no reference to this issue.
- (w.r.t 1st & 2nd contention of the cargo-owner) Accepted these contentions.
House of Lords
- (w.r.t. B) No element of necessity is required. It is sufficient that the bailee acts reasonably in pursuance of his duty to take reasonable care of the goods. It thus accepted this contention.
- ( w.r.t C) Wheat being a perishable cargo and the cargo owner being unwilling to give instructions, it was clearly necessary for the salvors to take reasonable steps to store and preserve the wheat that they had salved. It thus accepted this contention
- (w.r.t. E) salvors are entitled to recover the agreed sum from the cargo owner (together with interest), subject to the lien point.
- (w.r.t 1stcontention of the cargo-owner) The cargo was deliverable to the cargo owner and not to the shipowner, whether or not the shipowner had abandoned the voyage because:
- numerous form of bills of lading and such contracts exist.
- salvors may not know whether the voyage has been lawfully abandoned or not
- The Lloyd’s form was made directly between the cargo owner and the salvors (privity)
- cargo owner will always be interested in the preservation of the cargo, whereas the shipowner may not be
- (w.r.t 2nd contention of the cargo-owner) the salvors stored the cargo for the benefit of its owner. They received security for their salvage claim (Apr 23), but continued to store the cargo at their expense until the cargo owner finally accepted delivery of it (between June and August). If they had been storing the goods merely in order to maintain their lien for salvage, they would have stopped doing so as soon as they obtained security. Alternatively the principle that the lienor cannot charge the owner of the goods for the cost of exercising the lien applies only to possessory liens and not also to maritime liens. Although no doubt the salvors would have been reluctant to allow the wheat to leave Manila before security in respect of their claim for salvage had been put up, they could, if asked to do so by the cargo owner, have given up possession of the wheat (and their possessory lien) secure in the knowledge that they could, if necessary, exercise their maritime lien against it before it left Manila. In the further alternative, if it were held that the expenses were the expenses of maintaining the salvors’ maritime lien, the salvors would contend that they fall within clause 5 of Lloyd’s form and are recoverable thereunder. It further suggested that when a lienor incurs reasonable expenses in the proper exercise of his lien he should be entitled to recover those reasonable expenses from the owner of the goods liened.
Lord Simon of Glaisdale
Except to the holding that there never was an agency of necessity he concurred with Diplock. On the point of lien he considered it unnecessary to come to any conclusion, where interests are manifold or motives mixed. | https://indiancaselaw.in/china-pacific-s-a-v-food-corporation-of-india/ |
How appropriate it is that Claire Simon’s complementary pair of pictures, the narrative Gare du Nord and the documentary Human Geography, should take place at the train station that lends the former its name. Railways have occupied a pride of place in cinema since its birth: We all know, of course, the famous (if apocryphal) tale of the brothers Lumiere causing audiences to leap from their seats when The Arrival of a Train at La Ciotat was screened. Ever since those days, the distinction between the Lumieres’ “actualities” and the trick films of their contemporary Georges Melies has remained engrained in audiences’ view of cinema. Documentary and narrative, many would seem to believe, are mutually exclusive modes.
Here exactly is what’s so interesting about Simon’s diptych: Gare du Nord and Human Geography would seem a direct invocation of this distinction, their shared creator and setting nominally the only similarities between the two. The stories they tell reflect the respective strengths of each form of cinema: Human Geography searches the station for interesting passengers whose destinations might illuminate the cross-section of humanity this location represents; Gare du Nord, meanwhile, directly presents that sense of convergence in its construction of interlaced subplots centered on one unlikely romance.
“A global market square” is how Ismael, one of Gare du Nord‘s leads, describes the station. He’s right, though it takes the discoveries of Human Geography to fully illuminate just how. It’s interesting that the movies are presented so separately: here at Locarno, they appear in different strands of the program with no indication beyond the director’s name that they bear any relation to one another. Yet to see both is to see how inseparable they truly are, how much each depends on the other to bulk its meaning and broaden its scope. While neither film forcibly depends on having seen, or even heard of, the other, it’s a classic case of a whole far greater than the sum of its parts.
The diversity of nationality and class which Human Geography excavates feeds directly into the sense of disconnect on which Gare du Nord builds. Co-writer Olivier Lorelle scripted London River; where that film was predicated on the prevalent sense of inter-racial unease in the wake of the 2005 London bombings, Gare du Nord has no such politically pertinent ground in which to root itself. It needs the exploration — the exposition, perhaps — of Human Geography. It thrives on the foundation of socio-political context the documentary offers; tt stands on the shoulders of its sister film and through it manages to extend its view all the further.
Human Geography, at the same time, depends on Gare du Nord for an idealistic interpretation of the life snapshots it takes. In her fiction, Simon is given a blank canvas on which to expand upon the isolated fragments of existence the documentary glimpses. That the movie is scripted is an abstraction, of course, yet it’s with the brush strokes of basic human drama that Simon works. These characters may be fictional constructions, but the material from which they’re made could hardly be any truer to life, as the prominence of the very same emotional arcs in the documentary eagerly attests.
The subjects of Human Geography, for that matter, are no less characters in their own right than those of Gare du Nord. What person can stand before a camera and behave truly as themselves? It would be short-sighted to claim performance as exclusive to the fiction film; from the confident teen who raps excitedly into Simon’s camera to the right-leaning man who scales back his views when they sound too extreme, each of the people presented to us in the documentary has been carefully “written,” posing the question of just how worthy this is of the non-fiction label.
And that’s precisely the point: Just as Simon’s fiction is predicated on a bedrock of basic emotional and humanistic fact, her non-fiction is slave to the whims and whiles of a creative mind and the structural abstractions it brings to bear. The unique allure of Gare du Nord and Human Geography lies not in the distinctions they clarify between the disparate modes of fiction and documentary, but in the lengths they between them go to showing the fallacy of maintaining any such distinctions. Documentary and narrative cinema, says Simon, are not incomparable antitheses, just different means of storytelling. The points of departure may not be the same, but Simon’s new works are movies that cross tracks time and time again.
Click here for more on Ronan Doyle and this year’s Critics Academy.
Sign Up: Stay on top of the latest breaking film and TV news! Sign up for our Email Newsletters here. | https://www.indiewire.com/2013/08/blurred-lines-claire-simons-gare-du-nord-and-human-geography-challenge-the-boundaries-between-fiction-and-doc-127577/ |
The meeting also was attended by tourism ministers and defense of Cuba, Manuel Marrero and Julio Casas respectively, who presented the main statistical indicators of the Cuban republic and the agreements and projects that have been running between the two nations.
The opportunity was propitious to restore the Cuba-Venezuela, through the creation of a dolphin, whose investment amount is $ 3 million 613 000 844 (USD), which will be located on the eastern coastline of the country for the enjoyment of tourists and visitors.
Also addressed the business alliance for the promotion of tourist destinations binational, joint participation in international fairs and the search for new mechanisms for the transfer of foreign exchange in tourism operations.
Another point raised was related to the possible creation of a United Front of allied countries in international tourism, such as the World Tourism Organization, Association of Caribbean States, Caribbean Tourism Organization and others.
The assistance was to elevate a plan that benefits to public officials and the Revolutionary Armed Forces who, through preferential credit lines with banks of the State, to travel to the island, thereby increasing outbound tourism.
Also addressed issues advice to foster Cuban Popular Camping and improvement of marine Venetur.
Meeting with Cuba's tourist agencies
The Venezuelan Commission also held meetings with various Cuban tourist authorities and international tour operators from Canada, Italy, Spain, Argentina and Russia mainly, as well as several hotel chains installed in Cuba, to supplement knowledge in the areas of training and training providers tourism services. (Press Mintur / Alan Magician). | https://caracas.travel/en/fish |
In the recent weeks the United States has seen the largest one-day increase in coronavirus cases, and the State of California, along with several others, have reintroduced some restrictive measures. This has just raised investors’ concerns regarding a possible return of COVID-19 on a larger scale and in the event of further spread this event leading to a decline in fuel demand and, consequently, an overall decline in the price of oil on the global commodity market. In relation to this, economic correspondents report a possible decline of up to 10 percent on current prices.
On 2 July 2020, the sentiment in oil markets has been bullish and after a previous small decline in its price its price is currently strengthening again. According to analysts, this is only a small correction of the business trend, balancing the current match of supply and demand, along with the collection of profits made by investors in the previous period. On 2 July 2 at 8:33 am CET, West Texas Intermediate (WTI) light oil traded on the New York Mercantile Exchange (NYMEX) commodity market at US$ 39.99 per barrel, with a daily gain of +0.43%. However, according to the data of the technical analysis, WTI oil still shows a decrease in its value since the beginning of this year 2020 by -31.49%.
In an annual comparison, this decline in the price of WTI oil represents a decrease in its value on the commodity market by -26.26% of its previous price in the last 52 weeks. At the same time the European counterpart of WTI oil, the North Sea oil Brent, was also trading on the Intercontinental Exchange Europe (ICE) commodity market in the bull market trend, reaching a value of US$ 42.29 per barrel with the current daily increase of +0.62%. The fall in Brent crude oil prices is more balanced than the WTI crude oil prices, but the price drop is also significant. Since the beginning of 2020 Brent crude oil has lost its value by -32.36% of, and in the annual comparison it means a decrease of -31.25%.
Financial strategists fear a sharp rise in the heavily populated US states, which are among the country’s largest fuel consumers. According to Reuters, new cases of COVID-19 in the United States increased by nearly 50,000 on Wednesday, 1 July, the highest one-day peak since the beginning of the pandemic. More than half of the new cases each day are in Arizona, California, Florida and Texas. However, oil prices rose in the previous session after data from the US Energy Information Administration (EIA) showed that US oil reserves had fallen from a record high in recent weeks by 7.2 million barrels, much more than analysts had expected because the refinery increased production and imports decreased.
However, analysts noted that the data also showed that gasoline inventories had risen due to a sharp rise in imports compared to expectations of declining inventories. “Counter-seasonal builds in gasoline inventories as stockpiles unexpectedly rose are not precisely a bullish delight,” said AxiCorp strategist Stephen Innes. “The EIA data showed that gasoline imports hit the highest level since last August and peaked the most on a seasonal basis in nine years”. All eyes will be on the driving activity in the United States during the upcoming holiday weekend on 4 July, and on how quickly American manufacturers will revive shut-in production, analysts said. | https://www.tipsfortrade.com/the-price-of-oil-is-ever-changing/ |
OFA In Sight – a special publication of the Ontario Federation of Agriculture will be arriving in OFA member mailboxes this week with their September issue of Better Farming magazine.
OFA In Sight is an inaugural publication showcasing a few of the many farm success stories of leadership and innovation within our 36,000 farm members. The magazine showcases OFA members across the province who are making a difference on their farm, in their community and within the agri-food industry. OFA is proud to share these stories and thanks its members for their continued hard work and contributions to our dynamic industry.
If you did not receive your copy of the publication with Better Farming magazine, please contact OFA Member Relations at 1-800-668-3276. | https://ofa.on.ca/ofa-members-receive-special-sight-magazine/ |
Assad’s troops also strategically in position to cut Isis capital off from Iraq.
The recapture of Palmyra by the Syrian army, bolstered by Russian air power and Hizbullah ground forces, is a significant strategic, moral, psychological, political and public relations victory for Damascus over Islamic State.
By retaking Palmyra, the Syrian regular army becomes the principle anti-Islamic State force in the country, a role which had been assumed by the Kurdish protection units operating along Syria’s northern border with Turkey.
Palmyra is a strategic site midway on the highway from Damascus to Deir al-Zor. In order to retake Palmyra, the Syrian army has had to clear the route of Isis elements and take villages in the vicinity, securing not only inhabited areas but also vast stretches of desert.
Until the army moved into Palmyra, troops had made small advances against Isis and al-Qaeda’s Jabhat al-Nusra, seizing key supply routes and clearing out pockets of fighters around Damascus, Homs, Hama and Aleppo.
While based in Palmyra, the army is positioned to advance toward Deir al-Zor city, Syria’s oil hub where troops and 200,000 civilians are besieged and in dire need. If and when Deir al-Zor falls to the army, the main route to the Isis capital of Raqqa will be effectively cut off from Iraq, where Isis emerged in 2013.
While the Kurds have been putting pressure on Raqqa from the north, they are reluctant to mount an offensive on the city because it is in an Arab majority area. This leaves the task to the Syrian army.
For the army, recapturing Palmyra is a moral victory since troops had ignominiously pulled out of the modern city and ancient ruins in May 2015 after a column of Isis fighters swept down from Deir al-Zor. Routing Isis will boost the morale of the undermanned army which, until Russia intervened with air cover nearly six months ago, had been under severe challenge.
The generals and their men may now feel psychologically fit to lay siege to Raqqa in line with the Napoleonic dictum: in battle the spiritual is to the material as three to one.
Damascus has been politically strengthened at a time when it is under strong pressure to make concessions in the Syrian talks set to resume in Geneva around April 9th. The government can be expected to argue it is not the moment to change its armed forces commander-in-chief, President Bashar al-Assad – the primary demand of the Saudi-sponsored opposition and some western and Arab members of the Syria support group.
The Palmyra victory is a public relations coup for the government. By retaking Palmyra, the army has prevented Isis from wreaking fresh destruction on the ruins of the Graeco-Roman commercial hub where Isis has blown up 2,000-year-old temples and other monuments in its campaign to erase the remnants of Mesopotamian and Islamic civilisations.
Damascus has pledged to restore the monuments to their former glory. | https://sayyidali.com/news-analysis/retaking-of-palmyra-a-huge-morale-boost-for-syrian-army.html |
I wanted to pursue a career in pharmacy in my early school years. I had the belief that medicine could cure all diseases. I was working as a certified pharmacy technician for 9 years after I received an Associates of Arts degree in pre-pharmacy from Santa Fe Community College in Gainesville, Florida. I learned during these years that diet and eating habits play a key role in disease management (role sometimes as important as medicine). With a healthy diet, most diseases can be prevented or the onset of a disease may be delayed. I was very interested and eager to learn more about the dietetics field and decided to pursue a career as a dietitian/nutritionist. I received a Bachelors of Science in dietetics and nutrition from the Florida State University. I completed my dietetic internship at the Good Samaratin Hospital in Cincinnati, Ohio.
My new career started as clinical dietitian conducting medical nutrition therapy for a wide variety of patients. To ensure safe and competent patient care, I rely on clinical judgment, collaboration with the health care team and credible, evidence-based resources. I am also a Corporate Health and Wellness dietitian at TriHealth
I have a unique combination of strengths in nutrition/dietetics, communication, counseling, customer service and pharmacology. My expertises include: surgical & non-surgical weight management, Bariatrics, diabetes management, nutrition support, clinical nutrition & health education. I am also a certified leader in multiple programs for weight management.
I’m a professional member of the Academy of Nutrition and Dietetics since 2003, I am also a member of Weight Management and Nutrition Entrepreneurs Dietetic Practice Groups. | https://www.mynutritionandme.com/learn-more-about-the-karolin-saweres |
Wadsworth Atheneum Museum of Art names Oliver Tostmann as new Susan Morse Hilles Curator of European Art
The Wadsworth Atheneum Museum of Art announce the appointment of Oliver Tostmann as the museum’s new Susan Morse Hilles Curator of European Art, effective October 28, 2013.
Tostmann joins the Wadsworth Atheneum from the Isabella Stewart Gardner Museum where he served as the Lia and William Poorvu Curator of the Collection since 2011. Previously he held fellowship positions at the National Gallery of Art in the Departments of Italian and Spanish Paintings (2007–11). Most recently, he was curator of the international loan exhibition and editor of the catalogue, Anders Zorn: A European Artist Seduces America (2013), which was the first historic exhibition presented in the Gardner’s new wing.
Tostmann holds an M.A. and Dr. phil. in the History of Art, both from Freie Universität Berlin. He has published widely on Renaissance and Baroque artists and has lectured extensively throughout the U.S. and Europe. Tostmann will oversee the Wadsworth’s vast and distinguished European collection of approximately 900 paintings, 500 sculptures, and 3,500 works on paper. In the reinstallation, European paintings, sculpture, and a rotating selection of works on paper will be integrated with equally stellar examples of decorative arts, drawn from the museum’s collection of 3,000 objects, to tell the rich story of European art, culture, and history.
The Wadsworth Atheneum Museum of Art is America’s first public art museum, founded in 1842. The museum is located at 600 Main St., Hartford, Connecticut and is open Wednesdays to Fridays, 11 am – 5 pm, Saturdays and Sundays, 10 am – 5 pm, and the first Thursday of every month 11 am – 8 pm. Please visit www.wadsworthatheneum.org for more information. | https://museumpublicity.com/2013/10/03/wadsworth-atheneum-museum-of-art-names-oliver-tostmann-as-new-susan-morse-hilles-curator-of-european-art/ |
This qualification reflects the role of individuals who diagnose, analyse, evaluate, design and modify vehicle systems in the automotive retail, service and repair industry.
CRICOS code: 095324E
Course duration
This course is delivered over 26 weeks of full time study at 20 hours per week of scheduled class time at the Skills Institute Australia training facility. This includes three weeks holidays.
|Weeks||Hours per week||Total hours|
|Total||26||460|
|Study/ training||12||20||240|
|Holiday||3|
|Study/ training||11||20||220|
Delivery method
This qualification is delivered face-to-face in the classroom and in the fully-equipped workshop at our Campus.
Pre-requisites
All students must be at least 18 years of age.
Academic requirements:
- Satisfactory completion of year 12 or equivalent
- Overseas students require a language proficiency of IELTS 5.5 or equivalent
Those undertaking the Diploma of Automotive Technology must have completed an automotive Certificate IV qualification in one of the following disciplines, or be able to demonstrate equivalent competency.
- AUR40216 Certificate IV in Automotive Mechanical Diagnosis
- AUR40816 Certificate IV in Automotive Mechanical Overhauling
Course requirements
To complete this course, it is expected that you will have access to:
- A computer with Windows XP or higher
- Internet
- DVD-ROM drive
- TV
- Media Player
These facilities are available on campus.
Resources included
All of the learning materials and test books required to complete this course will be provided.
Course units
In order to receive this qualification, twelve units must be completed satisfactorily, including one core unit and eleven elective units.
|Code||Unit name|
|Core unit|
|AURAFA007||Develop and document specifications and procedures|
|Elective units|
|AURAFA006||Conduct research and present technical reports|
|AURAMA005||Manage complex customer issues in an automotive workplace|
|AURETA002||Analyse and evaluate electrical and electronic faults in body management systems|
|AURETB002||Analyse and evaluate electrical and electronic faults in dynamic control management systems|
|AURETE001||Analyse and evaluate electrical and electronic faults in engine management systems|
|AURETR034||Develop and apply electrical system modifications|
|AURLTB002||Analyse and evaluate faults in light vehicle braking systems|
|AURLTD007||Analyse and evaluate faults in light vehicle steering and suspension systems|
|AURLTE003||Analyse and evaluate faults in light vehicle engine and fuel systems|
|AURTNA001||Estimate and quote automotive vehicle or machinery modifications|
|AURTTA022||Develop and apply mechanical system modifications|
Career outcomes
This course provides participants with the skills to obtain the occupational position across various industrial sectors. Job roles and titles vary across these different industry sectors. Possible job titles relevant to this qualification include:
- senior diagnosis technician
Academic pathways
Individuals who successfully complete the Diploma of Automotive Technology may go on to study engineering.
Recognition of Prior Learning (RPL)
Students who have completed any of the units of study or have practical experience that may be used for recognition of prior learning must contact Skills Institute Australia prior to enrolment.
Assessment
As this is a competency based program, assessment continues throughout the duration of the course until the participant either achieves competency in the assessment tasks or a further training need is identified and addressed.
Assessment tasks may include
- Written questions and answers
- Presentations
- Projects
- Case study analysis
- Observation of the learner
- Written and oral questioning
- Written reports
- Simulated role play
Fees
Click here to see our current fee structure.
Is this course available for Domestic or International students?
Please note that some courses may only be taken by domestic students. For the latest information on whether this course may be taken by any student or by domestic students only, please click here.
Location
Not every course is offered at every campus. Please click here to find if this course is offered at your desired campus.
Student support
Skills Institute Australia has a commitment to providing equity in training for all learners. In particular, ensuring equity in training for women and the elimination of discrimination against female students in vocational education and training is a priority. | https://skills.qld.edu.au/study/aur50216-diploma-of-automotive-technology/ |
The IMIM Foundation announces one position for a Recognised Researcher (R4) with the objective of incorporating into the Institute a researcher of excellence, a leader of research in his/her field, and of international prestige in the field of Biomedicine. The incorporation of the candidate should add significant value to the Institute and make a notable contribution towards achieving the Institute's strategic objectives. Researchers from competitive programmes, such as the Ramón y Cajal and similar programmes, who have made exceptional contributions, will be considered. The candidate must have a PhD in the field of Biomedicine and an exceptional research career, with an excellent leadership capacity and proven international experience in one of the IMIM Foundation's research programmes: Cancer, Epidemiology and Public Health, Inflammatory and Cardiovascular Disorders, Biomedical Informatics, or Neurosciences.
Read more sobre "Call for one position for Recognised Researcher (R4)"
17/03/2020
Following the state of alarm declared throughout Spain due to COVID-19 and the recommendations of the Catalan authorities to collaborate in preventing the spread of COVID-19, from Monday March 16th onwards, the IMIM staff will be teleworking and will be able to assist you via email and/or telephone.
If you have any doubts or questions, you can contact us through the general form on the website: https://www.imim.es/en_contacte.html or by writing to the email addresses of the research areas and groups that are listed on that website. | https://www.imim.es/en_index2016.html |
The New York Times is reporting that Travis Kalanick has resigned as CEO of Uber. The news comes after months of scandalous allegations regarding the company’s culture.
Kalanick’s resignation comes a week after Eric Holder presented his recommendations to Uber’s Board of Directors. Kalanick had previously hired the law firm of Eric Holder to conduct an investigation into allegations of misconduct. Holder specified in his Uber Report that the responsibilities of Uber’s Chief Executive, Travis Kalanick, be reallocated.
The report also calls for changes in how employee complaints are handled. Other recommendations include changes in employee policies and practices, a more independent board, and performance reviews to hold senior executives accountable.
No word yet on who is to replace. However, Recode has some speculations on who it might be including YouTube’s CEO Susan Wojcicki. | https://glamorouspaper.com/tag/youtube/ |
The information provided below describes, as required by the EU Regulation 2016/679 (available here: https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=uriserv:OJ.L_.2016.119.01.0001.01.ENG), the processing operations performed on the personal data of the users visiting the Brusa srl’s websites. Those websites include the following:
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The so-called session cookies used by this website make it unnecessary to implement other computer techniques that are potentially detrimental to the confidentiality of user navigation, whilst they do not allow acquiring the user’s personal identification data.
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PROCESSING ARRANGEMENTS
Personal data is processed with automated means for no longer than is necessary to achieve the purposes for which it has been collected.
Specific security measures are implemented to prevent the data from being lost, used unlawfully and/or inappropriately, and accessed without authorisation.
DATA SUBJECTS’ RIGHTS
Data subjects have the right to obtain from Brus srl, where appropriate, access to their personal data as well as rectification or erasure of such data or the restriction of the processing concerning them, and to object to the processing (pursuant to Articles 15 to 22 of the Regulation).
All requests should be sent to:
– via e-mail: [email protected]
– via mail to Brusa srl, via Ferruccio Nazionale 3 – 13900 Biella.
P3P
This privacy notice can be viewed in automatic format by means of the most recent browsers implementing the P3P (Platform for Privacy Preferences Project) standard as proposed by the World Wide Web Consortium (www.w3c.org).
All efforts will be made to ensure the highest interoperability between the functions of this site and the automatic privacy verification mechanisms that are made available by some software products applied by users. | https://www.brusa.com/en/privacy-policy/ |
Predicting regional credit ratings using ensemble classification with metacost
Toseafa, Evelyn
;
Hájek, Petr
10.1007/978-3-030-19810-7_33
Files in this item
URI:
https://hdl.handle.net/10195/75039
Datum publikování:
2019
Document type:
ConferenceObject
ISSN:
2194-5357
xmlui.ArtifactBrowser.SimpleSearch.filter.source:
Artificial Intelligence Methods in Intelligent Algorithms : Proceedings of 8th Computer Science On-line Conference 2019, Vol. 2
Publisher version:
https://link.springer.com/chapter/10.1007/978-3-030-19810-7_33
xmlui.ArtifactBrowser.SimpleSearch.filter.event
8th Computer Science On-line Conference, CSOC 2019 (24.04.2019 - 27.04.2019, Praha)
Abstract:
Ensemble classifiers are learning algorithms that combine sets of base classifiers in order to increase their diversity and, thus, decrease variance and achieve better predictive performance compared to single classifiers. Previous research has shown that ensemble classifiers are more accurate than single classifiers in predicting credit ratings. Here we deal with highly imbalanced multi-class data of regional entities. To overcome these problems, we propose a novel hybrid model combining data oversampling and cost-sensitive ensemble classification. This paper demonstrates that the use of the SMOTE technique to balance the multi-class data solves the imbalance problem effectively. Different misclassification cost assigned in cost matrix solves the problem of ordered classes. This approach is combined with ensemble classification within the MetaCost framework. We show that more accurate prediction can be achieved using this approach in terms of average cost and area under ROC. This paper provides empirical evidence on the dataset of 451 regions classified into 8 rating classes, as obtained from the Moody’s rating agency. The results show that Random Forest combined with MetaCost outperforms the rest of the base classifiers, as well as other benchmark methods.
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. | https://dk.upce.cz/handle/10195/75039 |
The United Nations’ Office for Disaster Risk Reduction invited ISC ROLAC to be part of this important meeting on the topic of DRR, which is one of the office’s Priority Areas.
The UN’s Palais de Nations in Geneva was the chosen venue for the Global Platform for Disaster Risk Reduction, which took place from May 13th to the 17th. ISC ROLAC was represented by 7 members from its Disaster Risk Reduction (DRR) committee. The office was also represented by Dr. Manuel Limonta, regional director, and MA Oscar Reyes, Science Officer. Other attendants were Mami Mizutori, Special Rep of the United Nations (UN) Secretary General; and Raul Salazar, Chief of the UN office for DRR. This event, which was sponsored by the United Nations’ office for DRR, had different main goals, such as monitoring and reviewing progress implementation of the sendai framework, taking stock In development and implementation of national and local strategies and plans for DRR, forging partnerships and share practice and knowledge of DRR policies, and promoting the integration of DRR management in other relevant sectors. The event included ministerial round tables, high-level dialogues, officials statements, working sessions, Ignite sessions, and two awards ceremonies.
ISC ROLAC’s main goal for this event was to participate in the deliberations that related to this important priority area in our region. Events like this are very important for the office, since it gives its members a chance to talk with high-level individuals on the topic of Disaster Risk Reduction The main achievements the office accomplished were first and foremost our participation in this global meeting. It was also possible to communicate with 7 out of 10 members of ISC ROLAC’s DRR Steering Committee, and agree on a date for the next meeting of said committee. Finally, another achievement was to strength the relationship with the UNDRR office and other important organizations. The ISC ROLAC DRR committee will continue discussions on this issue at the next meeting in Guatemala from August 28th-30th, in which many of the topics discussed will be taken up again in the discussion of the region. | https://council.science/current/news/isc-rolac-attends-uns-global-platform-for-disaster-risk-reduction |
I was born in Thunder Bay, Ontario at the dawn of the 1980's but spent most of my life out in Western Canada, with the last twenty in Calgary, Alberta.
Photography is my life, every waking moment is the pursuit of its history and techniques.
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Below are some of the current projects I am working on.
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Since 2015 I have been publishing videos on YouTube about analog photography. I create videos both educational and entertaining, and have been praised for the production quality and how concise the content is.
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If you're here because you like what I do, maybe you'll consider supporting me through Patreon. I have some great perks which include early access to my videos and prints. | http://www.azriel.ca/about/ |
Robots are increasingly being developed to think and act like humans. But one common human quality that has been difficult for engineers to recreate in machines is humor.
Most robots are powered by artificial intelligence, or AI, and machine learning technology. Some have performed better than humans in tests designed to measure machine intelligence.
For example, we have reported on experiments involving robots competing against humans in a reading test and in a live debate.
Computer scientists have also hoped to give robots technical skills to help them recognize, process and react to humor. But these attempts have mostly failed. AI experts say that in many cases, attempts to make robots understand humor end up producing funny results – but not in the way they were supposed to.
Dan Zafrir, left, and Noa Ovadia, right, prepare for their debate against the IBM Project Debater in San Francisco, June 18, 2018.
Kiki Hempelmann is a computational language expert who studies humor at Texas A&M University-Commerce. "Artificial intelligence will never get jokes like humans do," he told the Associated Press. The main problem, Hempelmann says, is that robots completely miss the context of humor. In other words, they do not understand the situation or related ideas that make a joke funny.
Other experts who study the subject agree that context is very important to understanding humor – both for humans and for robots.
Tristan Miller is a computer scientist and linguist at Darmstadt University of Technology in Germany. He also spoke to the AP. In one research project, he studied more than 10,000 puns.
Puns are a kind of joke that uses a word with two meanings. For example, you could say, "Balloons do not like pop music." The word "pop" can be a way of saying popular music; or, "pop" can be the sound a balloon makes when it explodes.
But a robot might not get the joke. Tristan Miller says that is because humor is a kind of creative language that is extremely difficult for computer intelligence to understand.
"It's because it relies so much on real-world knowledge," Miller said. This includes background knowledge and common sense knowledge. "A computer doesn't have these real-world experiences to draw on. It only knows what you tell it and what it draws from," he added.
Humor is job security for humans?
Allison Bishop is a computer scientist at New York's Columbia University. She also performs stand-up comedy. She told the AP a big problem is that machines are trained to look for patterns.
Comedy, on the other hand, relies on things that stay close to a pattern, but not completely within it. To be funny, humor must also not be predictable, Bishop said. This makes it much harder for a machine to recognize and understand what is funny.
Bishop says since robots have great difficulty understanding humor, she feels like it gives her better job security as a comedy performer. It even made her parents happy when her brother decided to become a full-time comedy writer because it meant he would not be replaced by a machine, she added.
Purdue University computer scientist Julia Rayz has spent 15 years trying to get computers to understand humor. The results, she says, have at times been laughable.
In one experiment, she gave the computer two different groups of sentences. Some were jokes, others were not. The computer kept mistaking things as jokes that were not. When Rayz asked the computer why it thought something was a joke, the answer made complete sense technically. But she said the results coming from the computer were not funny, nor memorable.
Despite the difficulties, Darmstadt University's Miller says there are good reasons to keep trying to teach humor to robots. It could make machines more relatable, especially if they can learn to understand sarcasm, he noted. Humans use sarcasm to say one thing but mean another.
But Texas A&M's Kiki Hempelmann is not sure such attempts are a good idea. "Teaching AI systems humor is dangerous because they may find it where it isn't, and they may use it where it's inappropriate," he said. "Maybe bad AI will start killing people because it thinks it is funny," he added.
The Associated Press reported on this story. Bryan Lynn adapted it for VOA Learning English. Kelly Jean Kelly was the editor.
Do you think machines will ever be developed enough to have interpersonal relationships with humans? Write to us in the Comments section, and visit 51VOA.COM. | http://www.51voa.com/VOA_Special_English/why-robot-humor-mostly-falls-flat-81785.html |
By: Lyanne Alfaro
Having completed nearly 50 years of composing columns and feature stories, “gentle-demeanored” and “lighthearted” is how readers and colleagues remember Chicago journalist Robert J. Herguth. And it was such characteristics that helped him provide an intimate view of interviewees, from the likes of Chuck Norris to John F. Kennedy.
Mr. Herguth, 93, a longtime member of the Chicago Journalists Association, died May 2019 of natural causes, in an assisted living facility in Portland, Oregon. He had moved there to be closer to his daughter, visual artist Jeni Sellers.
Born in Chicago, Mr. Herguth grew up in St. Louis. After graduating with a journalism degree from the University of Missouri, Mr. Herguth worked as a reporter in El Paso, Texas and Peoria, Illinois before being hired at the Chicago Daily News and Chicago Sun-Times.
He built an award-winning, storied career with a trademark writing style riddled with puns and limericks, all original and created by him. Readers joined in on the pun fun, at times sending him their own play on words. And his license plate read “PUN.”
“He was unrelenting in his humor and his kindness,” his son, Bob Herguth, Jr., told the Sun-Times.
While Mr.Herguth well knew that some editors did not like puns, he tried them anyway until he won them over. He once told a reporter that he settled on an agreement with many of his editors: “It was finally decided, ‘OK, you can have puns, but they have to be good puns.’”
“He was a maestro of wordplay,” Jack Schnedler, former Sun-Times travel editor, told the Sun-Times.
Those who read his columns often called him by his nickname — “Hergie.” And while Mr. Herguth had a hearty sense of humor, he was versatile and skilled in his ability to cover all types of news, former bosses said.
“He could handle any type of assignment with competence and dispatch. No doubt the news sources trusted him to tell their stories with accuracy and respect,” George Harmon, assistant city editor at the Chicago Daily News and a rewriteman, told the Wilmette Beacon. “And as a human being, no finer man could you meet.”
Mr. Herguth’s legacy continues in his son, a longtime journalist who followed in his father’s footsteps at the Sun-Times. Herguth, Jr. said that as far back as 9 years old, he remembers his father publishing a digest that was sold to friends and family for a nickel.
His son said he carries with him the advice Mr. Herguth passed on to him, which echoed his father’s honest work ethic and determination to find the story.
“Apologize, own up and tell the bosses it’ll never happen again; and that if I don’t know something, tell the bosses ‘I don’t know, but I’ll find out.’ … He taught me to be honest, and work hard and do my best,” Herguth, Jr. said. | https://chicagojournalists.net/2019/07/31/a-cja-tribute-to-late-member-robert-j-herguth/ |
I have written the article in June about Issue Reporting Teams APP – app isn’t compliant with the latest data loss prevention policies.
At that time there was no solution about the issue where organization has Default DLP policy where they do not allow CDS
and then user wants to install apps in team that requires CDS which resulted in below error:
To overcome this Microsoft has provided a PowerShell function that you can schedule it to run on daily basis.
This function will grab all the team environments that are created because of some app installation and will exclude them from default DLP policy or any DLP policy that you want.
Here are the steps that you need to follow:
Create a DLP policy in PowerApps specifically for Microsoft Team, make sure the DLP policy that is created or that you use is scoped to environments.
-
Install Latest Powerapps Administration module from PowerShell gallery
Install-Module -Name Microsoft.PowerApps.Administration.PowerShell -Force
-
Copy the functions mentioned in link UpdatePolicyEnvironmentsForTeams to .ps1 file.
Note: Copy all the functions, at first, I just copied UpdatePolicyEnvironmentsForTeams and on execution I got the error as it was calling one other function from inside it.
-
Connect to Powerapps environment (ADD-PowerAppsAccount)
-
Once connected, dot source the function file.
. .\UpdatePolicyEnvironmentsForTeams.ps1
- Now you will be able to use the UpdatePolicyEnvironmentsForTeams function
We want to add all team environments to Teams Policy that We created and exclude all team environments from the default policy.
We also have some environments that We want to exclude from default policy, so we will add those environments ids in the text file.
$excludeenv = get-content .\Enviornmentstoexclude.txt
UpdatePolicyEnvironmentsForTeams -OnlyEnvironmentsPolicyName 5c002221-b443-455e-9d0c-65555bea36555a4 -OnlyEnvironmentsPolicyDisplayName “Teams Policy” -ExceptEnvironmentsPolicyName 4444443-5e06-4558-a8e8-3044444b168b -ExceptEnvironmentsPolicyDisplayName “Policy 16:11:07 02-12-2018” -ExceptionEnvironmentIds $excludeenv
Note: Policy Name and Policy Display name should be for same policy.
Now if you check the DLP policies you will see Team environments are excluded from default DLP as well as added to their own DLP policy.
You can now schedule it if you want by making a small script.
Reference: Microsoft Dataverse for Teams environment
Thanks for reading……. | https://techwizard.cloud/2021/09/19/exclude-teams-environments-from-powerapps-dlp-policy/ |
This chapter argues that imagery is initially experienced emotionally. It establishes that images of Africa are centrally images of suffering and that this generates emotional responses of compassion and guilt. This connection is most strongly exemplified in images of famine. The chapter also emphasises the subjectivity of the spectator. It goes on to highlight how emotional responses to images are influenced by racial identities and attitudes towards childhood. It ends by suggesting that the emotional responses to images of suffering make perceptions unstable and painful.
Keywords: Emotion, Suffering, Imagery, Compassion, Race, Famine, Biopolitics
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A Mississippi Delta planter, lawyer, poet, man of letters, and gentleman from Greenville, William Alexander Percy is best known for his autobiography, Lanterns on the Levee, a book revealing not only the man but also the region, the times in which he lived, and the culture that shaped him. Though he considered himself primarily a poet, his autobiography is today considered his major work. Spanning the years of his life from his birth on May 14, 1885, to the book's publication in 1941 Lanterns on the Levee looks upon the drastic social changes of that period with a sense of foreboding, upholding agrarian sensibility and the values of kindness, moral integrity, and friendship instead of what Percy perceived as the prevailing trends of declining moral values and technological progress. He served as guardian to his cousin Walker Percy after the death of Walker's parents. He died on January 21, 1942.
Andrews, William L. "In Search of a Common Identity: The Self and the South in Four Mississippi Autobiographies." Southern Review 24.1 (Winter 1988): 47-64.
Castille, Philip. "East toward Home: Will Percy's Old World Vision." Southern Literature in Transition: Heritage and Promise. Eds. Philip Castille and William Osborne, introd. by C. Hugh Holman. Memphis: Memphis State University Press, 1983. 101-09.
Cox, James M. "Trial for a Southern Life." Sewanee Review 97.2 (Spring 1989): 238-52.
Dupuy, Edward J. "The Dispossessed Garden of William Alexander Percy." Southern Quarterly 29.2 (Winter 1991): 31-41.
Gretlund, Jan N. "Southern Stoicism and Christianity: From William Alexander Percy to Walker Percy." The United States South: Regionalism and Identity. Eds. Valeria Lerda, Tjebbe Westendorp, and Geo. Pistarino. Rome: Bulzoni, 1991. 145-56.
Gulledge, Jo. "William Alexander Percy and the Fugitives." Introd. by Walker Percy. Southern Review 21.2 (April 1985): 415-27.
Holdsworth, Carolyn. "The Gorgon's Head and the Mirror: Fact versus Metaphor in Lanterns on the Levee." Southern Literary Journal 14.1 (Fall 1981): 36-45.
Holmes, William F. "William Alexander Percy and the Bourbon Era in the Yazoo-Mississippi Delta." Mississippi Quarterly: The Journal of Southern Culture 26 (1973): 71-87.
Lawson, Lewis A. "William Alexander Percy, Walker Percy, and the Apocalypse." Modern Age: A Quarterly Review 24 (1980): 396-406.
Rocks, James E. "The Art of Lanterns on the Levee." Southern Review 12 (1976): 814-23.
This page has been accessed 5899 times. About this page counter. | http://mwp.olemiss.edu/dir/percy_william_alexander/index.html |
What are variations?
Variations are changes or alterations made to the work, which are outside of, or contrary to, those specified in the scope of works.
These include changes to:
- design
- materials
- quantities
- quality
- work sequence
Who may ask for variations?
Under the HIA NSW Residential Building Contract for New Dwellings (2021), either the owner or the builder may ask for variations.
Variations by the builder
These are variations asked for by the builder, as for example, changing the flooring from one material to another, because of unavailability of supply of materials as originally laid out in the plans and specifications.
This may lead to an increase or decrease in the contract price, although it’s usually the former.
Variations by the owner
The owner is the person contracting the builder to commence building works – in this case – you.
You may request the builder to deviate from the plans, subject to the builder’s agreement or refusal. There is a process you need to follow if you want to request for variations. If you are using the April 2021 edition of the HIA NSW New Dwellings Contract, it should be covered by Clause 18.
Variations clause
Clause 18 on Variations details how variations may be properly made, and also gives the limitations and obligations imposed on the parties.
Main points under Clause 18:
1. It is an agreement, therefore, it must be
- in writing
- signed by the builder and owner
2. If the owner asks for a variation, the builder should reply as soon as is reasonable.
3. The builder’s reply could be either an offer to carry out the variation, or a refusal.
a) If the builder offers to carry out the variation, he should state in his reply:
- the work required to carry out the variation
- the price of the variation
- any extension of time to the building period as a result of carrying out the variation
b) If the builder refuses to carry out the variation – he does not have to give out reasons.
4. The builder’s offer is deemed withdrawn, that is, the variations asked for by the owner will not be made if:
- the owner does not give the builder the signed written acceptance of the builder’s offer,
- within 5 working days of the builder giving his reply
5. Valuation of variations
> If the price is not agreed upon prior to the variations being carried out, the price would include:
- deductions of reasonable cost of all deletions from the building works
- addition of the total cost of all extra work plus the builder’s margin
6. Price of variation is due and payable at the next progress payment after it is carried out (unless a different time is agreed).
7. If a variation is required for the building works to comply with the law or a requirement of any statutory or other authority, the owner must not unreasonably withhold consent.
8. Owner acknowledges that the color of grain, timber, granite, other natural materials – may vary.
Why are variations a common source of dispute?
Among other things,
- Variations always affect the contract price (valuing the variation)
- Sometimes, questions arise if whether the change is a variation, or if it is inherently, impliedly, or necessarily included in the works (agreeing whether the works constitute a variation at all)
- There is sometimes an issue on variations made by the builder, that the owner did not agree to, or that the owner could not afford
What to do when there is dispute related to variations
Under Clause 35
1. If a dispute arises, a party must give written notice to the other party setting out the matter in dispute.
2. Builder and owner must meet within 10 working days of the giving of the notice to attempt to resolve the dispute or to agree on methods of doing so.
3. If the dispute is resolved, the parties must write down the resolution and sign it.
4. The parties agree that anything done or said in the negotiation cannot be revealed in any other proceeding.
If the dispute remains unresolved
If, following the above, the dispute remains unresolved, recourse may be had with the Office of Fair Trading, where the parties may be instructed to undergo ADR (Alternative Dispute Resolution). If the issue still remains unresolved at the Fair Trading level, the aggrieved party may lodge a complaint with the NSW Civil and Administrative Tribunal (NCAT) where the matter will undergo directions hearings. Finally, if the dispute still remains unresolved, or if you’re not satisfied with the tribunal’s decision, you can lodge a complaint in court.
How we can help
The HIA contract is generally written to favor builders. Hence, it may be a good idea to engage a specialist construction lawyer for Contract Review and Advice, so that you may be apprised of what you need to negotiate with your builder. Contracts Specialist has expert building and construction lawyers who can do just that. And if you are currently in dispute with your builder about variations you did not agree to, we can help you with that, as well. | https://www.contractsspecialist.com.au/articles/hia-variations-guide/ |
The ENR print edition of 10/12/15 included an article Law & Risk Mitigation IIwhich touches upon several of the issues raised in this blog. One key point in our posts on Law relates to control – authority and responsibility are linked – and perhaps no matter what the contract documents may say to the contrary.
Another key point in our posts is that Risk relates to a lack of control – perhaps where authority is limited or unachievable.
A case (Coghlin Electrical Contractors, Inc. v. Gilbane Building Company) discussed in the article explores who shall bear the risk of design error where the parties have agreed to a CMAR (construction manager at risk) style contract. In this scenario the CMAR contractor not only agreed to significant indemnification language but also to assist the designer during the preconstruction phase. But Gilbane did not have the right to dictate design nor to terminate the design consultant.
Gilbane’s responsibility to assist did not rise to an independent review of the design. But even if agreeing to such responsibility, had Gilbane discovered errors, they had no authority to tell the designer to remedy. We are not talking of health-safety-welfare corrections here but only of those which may impact various scheduling and coordination issues. So it is all too easy for the designer to say “the budget for that drawing is already exceeded, you can address this in the field.”
Amazingly, I actually encountered this response in one of my former careers while working for a design-build contractor. With year-end bonuses in the balance, the VP Engineering shifted this minor to then major cost to the VP Construction. In the dog fight that ensued it was the VP Construction who was fired. Office politics trumps all. Where the designer and contractor are separate entities the only deterrent to this behavior is at the level of the owner – who has the authority to terminate the designer if deemed necessary. And so also the responsibility for control of its designer.
Later in my career, after starting my own practice, I encountered a similar situation. In Pennsylvania large public contracts are typically broken into three or four segments in a system called Multiple Prime Contracts to encourage bidding by smaller local contractors. My client was the contractor given the obligation of coordination. The contract required submittal of a CPM. Failure to timely provide would be a material breach. The electrical “prime” contractor refused to participate.
The municipal engineer when told “we have a problem” said “no, you have a problem.” So I ghost wrote a short letter, then sent by my client’s project manager to the engineer, city attorney, and federal judge supervising the consent decree that this project be done in an expeditious manner. We noted we had the obligation to coordinate and to provide a CPM with input from this “prime” contractor. We noted the “prime” contractor refused to perform creating material breach. We then DIRECTED the city to terminate their “prime” contractor. We noted the City’s failure to abide to our directive would result in waiver of my client’s duty to provide a CPM and to any consequential damages if my client could not complete the project by the stipulated deadline.
I do not know what transpired at the office of the city attorney. I do know the electrical “prime” suddenly replaced its superintendent, submitted all information we needed, and we all worked together to very profitably finish the project ahead of schedule. The 2 x 4 to the forehead sometimes does wonders.
The rule of law is that responsibility should be tied to authority to control. But not every owner or contractor or designer or subcontractor may fully appreciate this. In the instant case, the Supreme Court of Massachusetts got this right, but only after the Superior Court got it wrong. And so we return to the topic of this post – RISK. | https://www.enr.com/blogs/19-the-next-generation/post/24956-law-and-risk-mitigation |
Louis, it was the largest pre-Columbian city north of Mexico.
In This Article
The inhabitants of Cahokia did not use a writing system, and researchers today rely heavily on archaeology to interpret it. The name "Cahokia" is from an aboriginal people who lived in the area during the 17th century. Cultural finds from the city include evidence of a popular game called "Chunkey" and a caffeine loaded drink. Artistic finds include stone tablets carved with images such as a birdman as well as evidence of sophisticated copper working, including jewelry and headdresses.
Recent research shows that many of the people who lived at Cahokia were immigrants who came from across the Midwest, possibly traveling from as far away as the Great Lakes and Gulf Coast, a study of their teeth shows.
- Cahokia: North American Mounds - Crystalinks.
- Related Articles?
- How to Use This Resource?
To the south of Cahokia a settlement that archaeologists call Washausen became abandoned around the time Cahokia was at its peak around A. It's possible that some of the residents at Washausen, and other sites located near it, moved to Cahokia. The city's growth may have been aided by warmer temperatures.
At the time Cahokia flourished, temperatures across the Earth were unusually warm, resulting in increased rainfall in the American Midwest, wrote archaeologists Timothy Pauketat and Susan Alt in a paper published in the book "Medieval Mississippians: The Cahokian World" School for Advanced Research Press, The city fell into decline after , around the time that a flood occurred, becoming abandoned by Much of the city lies buried under 19th- and 20th-century developments, including a highway and the growth of the city of St.
Over the past few decades, efforts have been made to preserve what remains, with Cahokia's core now part of a state historic site. The most awesome example of architecture at Cahokia is the foot meter tall "Monks Mound" — the name given to it because a group of Trappist monks lived near it in historic times.
It was built with four terraces, covering about 17 acres 6. Archaeologists have found giant postholes at the top indicating the presence of what may have been a temple, presumably made of wood, measuring feet 31 m by 48 feet 15 m.
Cahokia: North America's First City
Its postholes are over 3 feet 1 m in diameter, the building being perhaps 50 feet 15 m tall. Monks Mound, along with a grand plaza and a group of smaller mounds, was walled in with a 2-mile-long 3. As many as 20, wooden posts were used to construct it. To the west of Monks Mound is a series of five circles, each originally made of red cedar wood posts, constructed at different times between A.
Such moments of transition in the year have always been thought to be special and supernatural, he added. Halloween provides a safe way to play with the concept of death , Santino said. People dress up as the living dead, and fake gravestones adorn front lawns — activities that wouldn't be tolerated at other times of the year, he said. But according to Nicholas Rogers, a history professor at York University in Toronto and author of " Halloween: From Pagan Ritual to Party Night " Oxford University Press, , "there is no hard evidence that Samhain was specifically devoted to the dead or to ancestor worship.
Samhain was less about death or evil than about the changing of seasons and preparing for the dormancy and rebirth of nature as summer turned to winter, he said. Though a direct connection between Halloween and Samhain has never been proven, many scholars believe that because All Saints' Day or All Hallows' Mass, celebrated on Nov. The tradition of dressing in costumes and trick-or-treating may go back to the practice of "mumming" and "guising," in which people would disguise themselves and go door-to-door, asking for food, Santino said.
Early costumes were usually disguises, often woven out of straw, he said, and sometimes people wore costumes to perform in plays or skits. The practice may also be related to the medieval custom of "souling" in Britain and Ireland, when poor people would knock on doors on Hallowmas Nov. Trick-or-treating didn't start in the United States until World War II, but American kids were known to go out on Thanksgiving and ask for food — a practice known as Thanksgiving begging, Santino said.
While one tradition didn't necessarily cause the others, they were "similar and parallel," he said.
These days, the "trick" part of the phrase "trick or treat" is mostly an empty threat, but pranks have long been a part of the holiday. By the late s, the tradition of playing tricks on Halloween was well established. Numerous translations of journals kept by German-speaking Moravian missionaries among the Iroquoians and Algonquians of the mid-Atlantic in the mid- to late 18th century are also tremendously valuable. Jane E. Mangan, trans. William N. Fenton and Elizabeth L. Moore, 2 vols. Kathryn E. Holland Braund , contain significant ethnographic information, but privilege the question of lineage over that of social condition.
The latter provides an especially important window into the racial views of ordinary people.
History of Halloween | Live Science
Researchers will find scattered material in the publications of state historical societies and learned societies. Morton, and Ephraim G. A number of other titles provide a sense of expanding ethnographic knowledge. Missionary organizations extended their reach in this era, with the Papers of the America Board of Commissioners for Foreign Missions est. Some material was published in monthly issues of Missionary Herald. See also Reuben Gold Thwaites, ed.
The most influential works on polygenism, the fixity of races, and the primacy of the body over language in determining race and ancestry are those of the American School of Ethnology: Samuel G. Most of these, along with many missionary and learned society publications, are available on Project Gutenberg or Google Books. The personal papers of these particular philologists and ethnologists are tremendous resources for reconstructing not only theories of race but also the networks that produced and disseminated those theories.
Du Ponceau, and Samuel G. The Gallatin and Schoolcraft papers are also available on microfilm. Sensitive readings of nearly all of the above sources will yield indications of the roles that nonwhites played in the production of ideas about race.
- lipabictabal.gq:Customer reviews: Spirit Mound (Aliens in American History Book 1)?
- Fiona Silk Mysteries 2-Book Bundle: Lament for a Lounge Lizard / Too Hot to Handle (A Fiona Silk Mystery)!
- The Chimes of Resdorn: Books 1 and 2.
- What would you like to read?.
- Le Jeu de lamour et du hasard - Marivaux (French Edition).
- Veni, Vidi, Vici:So The Whole World Will Know There Is A God In The Universe?
John Stauffer Warren, History of the Ojibway People Brown, Kathleen M. Find this resource:. Chaplin, Joyce E. Cambridge, Mass. Curran, Andrew. Baltimore: Johns Hopkins University Press, Dain, Bruce. Davis, David Brion, Alden T. Sweet, Jennifer L. Dowd, Gregory Evans. Harvey, Sean P. Horsman, Reginald. Jordan, Winthrop D. White over Black: American Attitudes toward the Negro, — Kidd, Colin. Cambridge, U. Morrison, Michael A.
Roediger, Daniel K. Richter, Lois E.
Sean P. Harvey
Ford, James P. Pagden, Anthony. New York: Cambridge University Press, Shoemaker, Nancy. New York: Oxford University Press, Sidbury, James. Spear, Jennifer. Sweet, John Wood. Philadelphia: University of Pennsylvania Press, Acts of the Apostles, King James Version.
James T. See also Robert F. Toronto: Champlain Society, , 2: Noel Salisbury London, , Reuben Gold Thwaites, ed. Cleveland, — , See also Winthrop D. See also Jennifer L. Jeremiah King James Version. MIller Indianapolis: Liberty Fund, , Edward Long, History of Jamaica , 3 vols.
Long, History of Jamaica , — Long, History of Jamaica , 2: , Albert E. Stone New York: Penguin, , 68— Independent Journal New York , January 24, , p.
Star Mounds
Ford Jr. Allan Nevins and Milton H. Thomas, eds. Sanford , See also Lois E. | https://lipabictabal.gq/spirit-mound-aliens-in-american.php |
BACKGROUND
SUMMARY
BRIEF DESCRIPTION OF THE DRAWINGS
DETAILED DESCRIPTION
1. Technical Field
The present disclosure relates to intrusion detection and, more specifically, to prioritizing intrusion detection logs.
2. Description of the Related Art
In today's highly computer dependant environment, computer security is a major concern. The security of computer networks is routinely threatened by malicious programs such as computer viruses, Trojan horses, worms and the like. Once computer networks have been infected with these malicious programs, the malicious programs may have the ability to damage expensive computer hardware, destroy valuable data, tie up limited computing resources or compromise the security of sensitive information.
Computer viruses are malicious computer programs that may be capable of infecting other computer programs by inserting copies of themselves within those other programs. When an infected program is executed, the computer virus may be executed as well and can then proceed to propagate.
A Trojan horse is a malicious computer program that has been disguised as a benign program to encourage its use. Once executed, a Trojan horse may be able to circumvent security measures and allow for unauthorized access of a computer system or network resources either by the Trojan horse itself or by an unauthorized user.
A worm is a malicious program that propagates through computer networks. Unlike viruses, worms may be able to propagate by themselves without having to be executed by users.
Worms can be a particularly catastrophic form of malicious programs. Worms can infect a computer network and quickly commandeer network resources to aid in the worm's further propagation. In many cases malicious code, for example worms, propagates so rapidly that network bandwidth can become nearly fully consumed threatening the proper function of critical applications.
After malicious programs have infected computers and computer networks a destructive payload can be delivered. Destructive payloads can have many harmful consequences. For example, valuable hardware and/or data can be destroyed, sensitive information can be compromised and network security measures can be circumvented.
To guard against the risk of malicious programs, businesses may often employ antivirus programs, intrusion detection systems and/or intrusion protection systems. Antivirus programs are generally computer programs that can be used to scan computer systems to detect malicious computer code embedded within infected computer files. Malicious code can then be removed from infected files, the infected files may be quarantined or the infected file may be deleted from the computer system. Intrusion detection systems and intrusion protection systems (IDSs) are generally systems that can be implemented on a computer network that monitor the computer network to detect anomalous traffic that can be indicative of a potential problem, for example a worm infection. IDSs may be either active or passive. Active IDSs may take affirmative measures to remedy a potential infection when found while passive IDSs may be used to alert a network administrator of the potential problem. The network administrator is a person with responsibilities for the maintenance of computer systems and/or networks.
IDSs often attempt to identify the presence of network infection by analyzing packets of data that are communicated over the network. Antivirus programs often attempt to identify the presence of infection by analyzing files and memory locations of a specific computer. Packets, files and memory locations are generally examined and compared with signatures of known malicious programs. When a signature matches a packet, file or memory location, a malicious program infection may have been detected.
IDSs and antivirus programs that rely on signatures for the detection of malicious programs will generally keep a database of signatures for known malicious programs. IDSs and antivirus programs should be regularly updated to incorporate new signatures corresponding newly discovered malicious programs into the signature database. If no signature has been received and installed for a particular malicious program, the IDS or antivirus program might not be able to identify the malicious program.
While signature detection is generally a highly accurate method for detecting malicious programs, signature detection may be prone to detecting multiple instances of malicious programs that are not necessarily a threat to the computer system or network.
IDSs and antivirus programs may also rely on heuristics recognition for detecting malicious programs. Heuristic virus scans and IDSs may be able to intelligently estimate whether computer code is a malicious program by examining the behavior and characteristics of the computer code. This technique relies on programmed logic called heuristics to make its determinations. Heuristic recognition of malicious programs may not require the use of signatures to detect a malicious program. Heuristic recognition therefore has the advantage of being effective even against new and unknown malicious programs. However, heuristic recognition can be prone to misjudgment such as generating false negatives and false positives. When a scanned malicious program is not recognized as such, the heuristic recognition has generated a false negative. When the heuristic recognition has incorrectly categorized a program as malicious, a false positive has been generated.
It is often desirable for network administrators to employ antivirus and IDS programs that are capable of detecting malicious programs in the computer systems and networks. These antivirus and IDS programs are often programmed to generate an alert when an instance of a malicious program is detected. These alerts may then be stored in a database of such alerts so the administrator can periodically review the database for signs of a potential malicious program attack. Because signature detection may lead to multiple instances of malicious programs that are not necessarily a threat to the computer system or network and heuristic recognition may lead to false positives, important alerts in the alert log can often be hard to notice when surrounded by a great number of alerts of less significance.
A method for detecting malicious programs, the method including scanning data to be scanned to detect a malicious program infection, generating an alert when a malicious program infection has been detected and adding the alert to an alert log along with information pertaining to an importance of the detected malicious program infection.
A method for displaying an alert log including one or more alerts, the method including prioritizing the one or more alerts according to an importance of each of the one or more alerts and displaying the one or more alerts according to the priority.
A system for detecting malicious programs, the system including a scanning unit for scanning data to be scanned to detect a malicious program infection, a generating unit for generating an alert when a malicious program infection has been detected and an adding unit for adding the alert to an alert log along with information pertaining to an importance of the detected malicious program infection.
A system for displaying an alert log including one or more alerts, the system including a prioritizing unit for prioritizing the one or more alerts according to an importance of each of the one or more alerts and a displaying unit for displaying the one or more alerts according to the priority.
A computer system including a processor and a program storage device readable by the computer system, embodying a program of instructions executable by the processor to perform method steps for detecting malicious programs, the method including scanning data to be scanned to detect a malicious program infection, generating an alert when a malicious program infection has been detected and adding the alert to an alert log along with information pertaining to an importance of the detected malicious program infection.
A computer system including a processor and a program storage device readable by the computer system, embodying a program of instructions executable by the processor to perform method steps for displaying an alert log including one or more alerts, the method including prioritizing the one or more alerts according to an importance of each of the one or more alerts and displaying the one or more alerts according to the priority.
A more complete appreciation of the present disclosure and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein:
FIG. 1
shows an example of the scanning of data according to embodiments of the present disclosure;
FIG. 2
shows a procedure for displaying an alert log according to embodiments of the present disclosure;
FIG. 3A
shows an example of the displaying of an alert log that has been over crowded;
FIG. 3B
shows an example of the displaying of an alert log according to an embodiment of the present disclosure; and
FIG. 4
shows an example of a computer system capable of implementing the method and apparatus according to embodiments of the present disclosure.
In describing the preferred embodiments of the present disclosure illustrated in the drawings, specific terminology is employed for sake of clarity. However, the present disclosure is not intended to be limited to the specific terminology so selected, and it is to be understood that each specific element includes all technical equivalents which operate in a similar manner.
Intrusion detection systems, intrusion protection systems (collectively IDSs) and antivirus programs all work to scan files, memory and/or packets of data communicated over a network for the presence of malicious programs.
FIG. 1
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shows an example of how data can be scanned according to embodiments of the present disclosure. Data to be scanned may be files located on a computer or server, data stored in memory on a computer or server or packets of data that are communicated across a computer network. Data may be periodically scanned as part of a periodic system scan or data can be scanned as files are executed or packets are communicated. Data to be scanned may first be sent to a data stack . The data stack stores data to be scanned so that data can continue to be collected even as the scanner may be engaged in the scanning of other data. Data stack stores units of data. A unit of data may be a part of a file, an entire file, data packets, etc. This data stack can be particularly effective when the data to be scanned is comprised of packets that have been communicated over the network. This is because packets can often arrive much more quickly than data can be scanned by the scanner . When data to be scanned is comprised of packets, communication of packets should not be disrupted. Therefore, when the data stack has been filled to capacity with incoming packets, additional arriving packets may be disregarded and may not be scanned. Where data to be scanned is comprised of files or memory data collected as part of a system scan, the system scan can be delayed to collect additional data at the same rate that data is scanned by the scanner .
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The scanner compares collected data with signatures stored in the signature database . A signature is a representation of a malicious program that allows the scanner to identify when data is potentially infected with the malicious program for which the signature has been created. A common technique for producing a signature is to compute the hash value of a malicious program. A hash value is a very large number that can be used to identify a file. The hash value can be determined by performing a mathematical algorithm on the data that makes up the file in question. There are many algorithms for calculating a file's hash value. Among these are the MD5 and SHA algorithms. While there are theoretically many different possible files that can all produce the same hash value, the chances of two different files having the same hash value are infinitesimal. The hash value of a file is not generally affected by changing the file's attributes such as renaming the file, changing the file's creation date and/or changing the file's size. For these reasons, the use of hash values can be well suited for the identification of potentially malicious programs. These and other techniques may be used to generate signatures according to the present disclosure.
According to embodiments of the present disclosure, the signature may also include a risk assessment value. The risk assessment value need not be used to identify a malicious program. Instead, the risk assessment value can be used to gauge the nature of the threat posed by data that matches a particular signature. The risk assessment value may be included with the signature by the signature developer, the person or program that has created the signature. The risk assessment value may be based on such factors as the potential for damage to computer systems and network caused by the malicious program upon which the signature has been developed and/or the likelihood that the potential damage will occur.
Risk assessment values may be created or modified by the network administrator, for example, where no risk assessment value has been included in the signature by the signature developer or the network administrator otherwise believes modification of the risk assessment values would be appropriate.
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When using hash value signatures, the scanner computes the hash value of the data being scanned and compares it to the hash values within the signature database . If using alternative forms of signatures other than hash values, the scanner computes an appropriate signature for the data being scanned and compares it with the signatures in the signature database . It can then be determined if the data being scanned corresponds to a signature in the signature database . If there is no corresponding signature found, the data stack can supply the scanner with the next unit of data to be scanned. When a match is made, an alert can be generated .
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When using a heuristic scanner in addition to or as an alternative to the signature scanning, the signature database can include or be replaced by a database of heuristics. Heuristics are the logical definitions used by the heuristic scanner to judge whether the data being scanned has been infected by a malicious program. Risk assessment heuristics may be incorporated into the heuristic scanner to gauge the risks posed by an observed infection. If the heuristic scanner determines that a unit of data is not infected with a malicious program, the data stack supplies the scanner with the next unit of data so the next unit of data can be scanned. When the heuristic scanner has determined that the data could be infected by a malicious program, an alert can be generated by the alert generator . The alert can then be stored in an alert log . The heuristic scanner can also pass to the alert generator information pertaining to the confidence level in the match and/or a risk assessment value, for example, calculated by risk assessment heuristics, which can also be stored along with alerts in the alert log .
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An alert can be a notification that notifies the network administrator of the detection of a potential malicious program. In addition to storing the alerts in the alert log , alerts can be automatically sent to the network administrator, for example by email or by pager. An alert can report the key attributes that gave rise to the match. For example, the alert can contain information pertaining to the time the match was made, the source of the data that was matched, the name of the signature that made the match, etc.
Alerts according to the present disclosure can also include the risk assessment value supplied by a signature scanner or a heuristic scanner and/or information pertaining to the confidence level in the match, for example, as obtained by a heuristic scanner.
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The alert log can be one or more databases of generated alerts. By storing alerts in the alert log , the administrator may periodically review generated alerts when convenient to do so.
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The data stack may supply the scanner with the next unit of data to be scanned so that data may continue to be scanned. The scanning of data may end when there is no data left to scan, as would be the case, for example, upon the completion of a periodic system scan. However, where the data to be scanned is, for example, packets of data that have been communicated over the network, the scanning of data may be a continuing process.
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The displaying of the alert log can be problematic because the alert log has the potential to include significantly more information than can easily be parsed by the network administrator. Signature scanning and heuristic scanning techniques can contribute to the overcrowding of the alert log . For example, not all malicious programs represent the same risks to the computer system or network that the malicious program has been detected on. For example instances of Nmap probes may be detected by signature scanners. Nmap is a publicly available utility for probing a network device, for example an application server, to determine what network services may have been made available by the application server. While Nmap has practical uses for maintaining a computer network, instances of Nmap probes can also be warning signs of potential malicious attack by a malicious program or a user with malicious intent. For this reason, signature scanners will often scan for the presence of an Nmap probe signature. However, the presence of an Nmap probe may most likely be harmless. Nmap probes are one example of a signature match that might not always be of importance to the network administrator. There may be many other signatures that detect the presence of malicious programs with a low potential for causing damage. However, such signatures may still be added to the signature database because under certain conditions they may indicate a potential threat. The developer can add an indication to the database for each of these signatures showing that they are low importance.
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Code red is an example of a particularly harmful malicious program. Code red is a computer virus that can force a web server to attempt to contact other web servers, change the appearance of web pages on the web server and send out floods of packets tying up network resources. When the signature or signatures corresponding to code red are added to the signature database by the developer, an indication is also provided that this is a high importance signature. When a match with one of the code red signatures is made, an alert identifying a match with a code red signature would indicate it is of high importance.
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Heuristic scanners can contribute to alert log overcrowding. Because heuristic scanners use logic to make judgments on whether data is infected with a malicious program, there may be an opportunity for false positives. A false positive is an alert that has been generated indicating a malicious program has been detected even when no such malicious program infection actually exists. It may be possible for the sensitivity of the heuristic scanner to be adjusted to produce fewer false positives, but to do so might increase the probability of a false negative. False negatives are malicious program infections that have been missed by the heuristic scanner. While false positives can contribute to alert log overcrowding, false negatives can allow a malicious program to go undetected and potentially inflict significant damage on computer systems and networks. Therefore adjusting the sensitivity of the heuristic scanner might not always be the best solution for overcrowding of the alert log caused by false positives.
Because heuristic scanners use logic to make judgments on whether data is infected with a malicious program, it is often possible for the heuristic scanner to pass along information pertaining to the heuristic scanner's confidence in the match. According to embodiments of the present disclosure confidence information can then be incorporated into the alert for the particular match.
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FIG. 3A
When the alert log is displayed, high importance alerts such as, for example, a code red match, may be overcrowded by an abundance of alerts of low importance, such as, for example, multiple Nmap probe matches. shows an example of the displaying of an alert log that has been over crowded. Alerts - and - depict Nmap probe matches of low importance. Alert depicts a code red match of high importance. It can often be difficult to identify the alert that represents a threat of high importance to a computer system and network security because of the overcrowded state of the alert log .
FIG. 2
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shows a procedure for displaying an alert log according to embodiments of the present disclosure. Alerts within the alert log can be prioritized (Step S) according to, for example, such values as the potential damage that can be caused by the malicious program detected, the probability that the damage will occur, the confidence information signifying how confident the scanner was in making its determination that a malicious program has been detected, statistical information, risk assessment values associated with signatures and/or supplied by the developer of the signatures, etc. Statistical information includes, for example, statistics concerning the frequency of a particular matching wherein commonly matched malicious programs, for example Nmap probes, may be perceived as less of a threat.
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After relevant information has been considered, a category can be assigned to each alert within the alert log . Alert categories may be, for example, high importance and low importance. For example, Nmap probe matches would be categorized as low importance and code red matches categorized as high importance.
FIG. 3B
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shows an example of an alert display according to an embodiment of the present disclosure. Prioritized alerts can then be displayed (Step S) according to the determined importance in such a way that greater attention is given to alerts of higher priority. For example, only high importance alerts may be initially displayed along with an option to expand the display to show low importance alerts. In the example shown in , only the high importance code red alert is displayed. Where the network administrator chooses to expand the display, the alerts may be re-prioritized (Step S) so that all alerts can be displayed (Step S). For example, in the display shown in , the network administrator is given the option of clicking on the Expand button in order to provide the more comprehensive display as shown in .
Other methods for potentially displaying alerts can be provided according to the present disclosure. For example, the complete list of alerts may be displayed in priority order. For example, high importance alerts may be displayed with particular prominence, for example, highlighted, bolded, underlined, set aside, etc.
FIG. 4
shows an example of a computer system which may implement the method and system of the present disclosure. The system and method of the present disclosure may be implemented in the form of a software application running on a computer system, for example, a mainframe, personal computer (PC), handheld computer, server, etc. The software application may be stored on a recording media locally accessible by the computer system and accessible via a hard wired or wireless connection to a network, for example, a local area network, or the Internet.
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The computer system referred to generally as system may include, for example, a central processing unit (CPU) , random access memory (RAM) , a printer interface , a display unit , a local area network (LAN) data transmission controller , a LAN interface , a network controller , an internal buss , and one or more input devices , for example, a keyboard, mouse etc. As shown, the system may be connected to a data storage device, for example, a hard disk, via a link .
The above specific embodiments are illustrative, and many variations can be introduced on these embodiments without departing from the spirit of the disclosure or from the scope of the appended claims. For example, elements and/or features of different illustrative embodiments may be combined with each other and/or substituted for each other within the scope of this disclosure and appended claims. | |
WORLD TRADE CENTER HEALTH EFFECTS LINGER YEARS LATER
New research confirms that responders to the World Trade Center (WTC) attack are still experiencing health effects more than 5 years later. In a new study from the Mount Sinai School of Medicine, researchers compared baseline respiratory examinations in WTC responders with follow-up examinations that occurred a minimum of 18 months after baseline. At the follow-up examination, 24.1 percent of 3,160 individuals still had abnormal spirometry findings, with the predominant defect being a low forced vital capacity (FVC). Results also found that the majority of WTC responders had normal decline in lung function between the baseline and follow-up exams, but initial bronchodilator response and weight gain were significantly associated with greater-than-normal lung function declines. Researchers conclude that the continued presence of lung function abnormalities in WTC responders warrants longer-term monitoring. This study is published in the February issue of the journal CHEST.
ARM SPAN-HEIGHT RATIO LINKED TO RESPIRATORY PROBLEMS
Arm span is regularly used as an alternative measurement for standing height, when measurement of standing height is not possible. New research from Newcastle University in the United Kingdom suggests that the discrepancy between arm span length and actual standing height may be linked to respiratory problems in the elderly. Researchers evaluated the clinical history, physical examination, arm span, standing height, weight, FEV1 and FVC of 66 patients with a mean age of 71 years. Results showed that an increase in arm span-height ratio was significantly negatively correlated with FEV1 and FVC and positively correlated with dyspnea. Researchers conclude that the role of arm span measurement in assessing airflow volumes in the elderly deserves further investigation. This study is published in the February issue of the journal CHEST.
MYTH: KIDS WITH ASTHMA MISS MORE SCHOOL THAN THEIR CLASSMATES
For years, it has been widely believed that children with asthma miss considerably more school than children without asthma. However, new research finds that this may not be the case. Researchers from Baylor University Medical Center in Dallas investigated school absence rates in 328 4th-6th grade students identified as possibly asthmatic who underwent spirometry and/or exercise testing. Among students with possible asthma, 157 had a positive spirometry/exercise test score, while 171 had a negative score. Researchers then compared yearly absence rates between these two groups of students, as well as between 4th-6th graders in 19 study schools and the district. Results showed that school absence rates of each group were within 1 percent of each other. Furthermore, there was no significant difference in the absence rates of students who had abnormal spirometry results compared with the overall study schools or the district -moreschools. Researchers conclude that any differences in asthma-related school attendance rates are academically insignificant. This study is published in the February issue of the journal CHEST.
PREOPERATIVE SMOKING CESSATION COUNSEL SAVES MONEY
Research shows that smokers are more likely to develop postoperative complications than nonsmokers, but new research suggests that smoking cessation counseling prior to scheduled surgery could reduce complications and save money. In the study, French researchers performed a cost-benefit analysis of preoperative intervention for smoking cessation (PISC) and its impact on hospitalization costs. Results indicated that the reduction in complications after PISC reduces the average cost of a hospital stay by an average of 313 euros per patient (about $400). This study is published in the February issue of the journal CHEST. | http://generalhlthnews.org/post/news-from-the-journal-chest-february-2009 |
This is an 8-month (May to January) volunteer mentoring program in which the participants would move at their own pace. Mentors and mentees will meet monthly (in-person, by phone, or virtually) and create a self-directed, customized mentoring strategy to benefit both of them. The pair will report their progress via a brief monthly check-in form and will receive support from the program as needed. See guidelines for more information.
“This mentoring program helped me grow considerably in my career as a librarian and as a person too.” ~ Raquel Mendelow Rein, Librarian Consultant/Researcher (mentee)
Mentees meeting the minimum requirements will be automatically accepted into the program until the maximum number of participants (12) is reached. Mentors meeting the minimum requirements will be accepted into the program if a successful match is completed by the FLA program leaders. Up to 24 mentor applicants will be accepted into the mentoring pool. You must be an FLA member in order to apply. All applicants will be notified of their acceptance by mid-April 2019.
Mentorship Application
GUIDELINES
APPLY TO BE A MENTOR/MENTEE
EVALUATION FORMS
BENEFITS OF BECOMING A MENTEE
BENEFITS OF BECOMING A MENTOR
MINIMUM REQUIREMENTS FOR MENTORS
MINIMUM REQUIREMENTS FOR MENTEES
CONTACT US
2019-2020 Program Coordinators
Peggy Glatthaar, Chair, Library Career Development Committee
Becca Durney, Chair, Leadership Development Committee
Can't make it to the January 22 Library Legislative Day in Tallahassee? Participate in Virtual Library Day!
FLA is actively responding to recent Citrus County Board of Commissioners denial of New York Times electronic subscription.
FLA Board opposed Macmillan Publishers pricing model; book embargo. Read the full statement here.
Supreme Court offers opinion on census, electoral map rulings. Read ALA's article now for details. | https://www.flalib.org/mentorship-program |
New IPCC report key for India, say experts
The highly-anticipated report will assess climate adaptation and the impacts of climate change, looking at ecosystems, biodiversity, and human communities at global and regional levels.
The report will also review vulnerabilities and the capacities and limits of the natural world and humans to adapt to the climate crisis, according to the UN Foundation. (AP)
Published on Feb 09, 2022 11:55 PM IST
ByJayashree Nandi, New Delhi
A new report from the Intergovernmental Panel on Climate Change that is to be released on February 28 will be important for India, experts said, because it focuses on vulnerability and adaptation to climate crisis.
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The highly-anticipated report will assess climate adaptation and the impacts of climate change, looking at ecosystems, biodiversity, and human communities at global and regional levels. The report will also review vulnerabilities and the capacities and limits of the natural world and humans to adapt to the climate crisis, according to the UN Foundation.
Nine Indians have contributed to various chapters on tropical forests; biodiversity hotspots; water; mountains; poverty and livelihoods; and climate crisis impacts on Asia . The report has 330 authors from across the world. The United Nations Foundation will host a briefing by the Co-Chairs of the Intergovernmental Panel on Climate Change’s (IPCC) upcoming Working Group II report, Hans-Otto Pörtner and Debra Roberts on Thursday.
The technical summary of the report will include a climate risk framework encompassing hazard, exposure, and vulnerabilities of various regions--their spatial distribution, cascading impacts, disaster risk reduction, and risk uncertainties. The summary will also include significance of adaptation in addressing climate change risks, including diverse adaptation responses, technologies like nature and ecosystem-based adaptation; detection and attribution of climate change impacts and methods to evaluate the effectiveness of adaptation responses; dynamic climate risks from scenarios that reflect multiple interacting drivers; scientific, technical and socioeconomic aspects of current and future residual impacts of climate change, including residual damage, irreversible loss, and economic and non-economic losses caused by slow onset and extreme events, a note by IPCC stated.
“Every IPCC report has a very specific purpose. This report will include the points of departure from IPCC’s previous findings and a very comprehensive overview of many other issues such as health of ecosystems; oceans; water; food; climate resilient development pathways; risks associated with climate change impacts. The report is not policy prescriptive but will only inform policy makers on the state of these things,” said Gautam Hirak Talukdar, scientist at Wildlife Institute of India who is also a lead author in the forthcoming report. “India is already taking giant strides towards transitioning to a low carbon economy. But during this transition, specially in terms of electrification there will be trade-offs and challenges which this report will inform and that will be of importance to India.”
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“The first working group report of the IPCC sixth assessment in 2021 quantified the physical changes in the past and future climate, due to increased greenhouse gas emissions. The second working group report will elaborate on the impacts and risks due to these physical changes and point out ways to reduce these risks through adaptation. We might have to take up the best adaptation measures that work for us to build a climate-resilient, disaster-proof country, but that will require immediate policy and action—since time is short,” said Roxy Mathew Koll, a climate scientist at Indian Institute of Tropical Meteorology.
“South Asia and particularly India is already facing increased risks due to rising extreme weather events such as floods, landslides, and droughts, cyclones, heatwaves and cold waves, and a rising sea level. The dense population and low house-hold income in the region will raise the vulnerability and risk that we are facing,” he added.
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The world may have lost the opportunity to keep global warming under 1.5 degree C over pre-industrial levels, the WG I report titled “Climate Change 2021: The Physical Science Basis” released last August said.
The forthcoming IPCC report assumes even more significance because scientists have said there is now consensus that even 1.5 degree C warming will be dangerous for the planet leading to breach of important tipping points—the big biophysical elements that regulate the climate system such as the Greenland Ice Sheet; West Antarctic Ice Sheet; low latitude coral reefs; Barrent sea ice; Amazon rainforest; the monsoons; and Atlantic meridional overturning circulation (AMOC).
Johan Rockstrom, director, Potsdam Institute for Climate Impact Research spoke on Monday at a webinar titled “Protecting The Planet’s Future: An Environmental Agenda” organised by India International Centre and Public Health Foundation of India where he said that several of these tipping points are approaching instability and there are cascading impacts on the climate system when this happens. Based on information from the Earth Commission he said “There is now more support for the fact that 1.5 degree warming is the real boundary…many elements are approaching tipping points under well below 2 degree C warming and at 1.5 degree warming,” adding that this could pose a real danger to the climatic systems globally.
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DESCRIPTIONStart tracking the given patterns(s) through Git LFS. The pattern argument is written to .gitattributes. If no paths are provided, simply list the currently-tracked paths.
The gitattributes documentation https://git-scm.com/docs/gitattributes states that patterns use the gitignore pattern rules https://git-scm.com/docs/gitignore to match paths. This means that patterns which contain asterisk (*), question mark (?), and the bracket characters ([ and ]) are treated specially; to disable this behavior and treat them literally instead, use --filename or escape the character with a backslash.
OPTIONS
EXAMPLES
SEE ALSOgit-lfs-untrack(1), git-lfs-install(1), gitattributes(5), gitignore(5).
Part of the git-lfs(1) suite.
Visit the GSP FreeBSD Man Page Interface. | https://www.gsp.com/cgi-bin/man.cgi?section=1&topic=GIT-LFS-TRACK |
Now open to the public these fascinating tunnels bring to life to what it was like to shelter and live underground in Ramsgate during WW2.
Beneath Ramsgate lies an abandoned labyrinth of tunnels which extends for more than 3 miles around the town. This unique underground city was constructed as part of the town?s Air Raid Precautions in 1939 and includes a former main line railway tunnel dating back to 1863. | https://amazingdaysout.com/at/ramsgate-tunnels/ |
Seismic events aren’t rare occurrences on Antarctica, where sections of the frozen desert can experience hundreds of micro-earthquakes an hour due to ice deformation. Some scientists call them icequakes. But in March of 2010, the ice sheets in Antarctica vibrated a bit more than usual because of something more than 3,000 miles away: the 8.8-magnitude Chilean earthquake. A new Georgia Institute of Technology study published in Nature Geoscience is the first to indicate that Antarctica’s frozen ground is sensitive to seismic waves from distant earthquakes.
To study the quake’s impact on Antarctica, the Georgia Tech team looked at seismic data from 42 stations in the six hours before and after the 3:34 a.m. event. The researchers used the same technology that allowed them to “hear” the seismic response at large distances for the devastating 2011 magnitude 9 Japan earthquake as it rumbled through Earth. In other words, they simply removed the longer-period signals as the seismic waves spread from the distant epicenter to identify high-frequency signals from nearby sources. Nearly 30 percent (12 of the 42 stations) showed clear evidence of high-frequency seismic signals as the surface-wave arrived on Antarctica.
“We interpret these events as small icequakes, most of which were triggered during or immediately after the passing of long-period Rayleigh waves generated from the Chilean mainshock,” said Zhigang Peng, an associate professor in the School of Earth and Atmospheric Sciences who led the study. “This is somewhat different from the micro-earthquakes and tremor caused by both Love and Rayleigh-type surface waves that traditionally occur in other tectonically active regions thousands of miles from large earthquakes.
Peng says the subtle difference is that micro-earthquakes respond to both shearing and volumetric deformation from distant events. The newly found icequakes respond only to volumetric deformation.
Some of the icequakes were quick bursts and over in less than one second. Others were long duration, tremor-like signals up to 10 seconds. They occurred in various parts of the continent, including seismic stations along the coast and near the South Pole.
The researchers found the clearest indication of induced high-frequency signals at station HOWD near the northwest corner of the Ellsworth Mountains. Short bursts occurred when the P wave hit the station, then continued again when the Rayleigh wave arrived. The triggered icequakes had very similar high waveform patterns, which indicates repeated failure at a single location, possibly by the opening of cracks.
Peng says the source locations of the icequakes are difficult to determine because there isn’t an extensive seismic network coverage in Antarctica.
Antarctica was originally not on the research team’s target list. While examining seismic stations in the Southern Hemisphere, Peng “accidently” found the triggered icequakes at a few openly available stations. He and former Georgia Tech postdoctoral student Jake Walter (now a research scientist at the Institute for Geophysics at UT Austin) then reached out to other seismologists (the paper’s four co-authors) who were in charge of deploying more broadband seismometers in Antarctica.
The above story is based on materials provided by Georgia Institute of Technology. | https://parsseh.com/29478/chilean-earthquake-causes-icequakes-in-antarctica.html |
About AIG Investments
AIG Investments functions as a business division of AIG or American International Group. AIG ranks as one of the top financial and insurance services providers based in the United States. The headquarters of AIG are located in New York City, New York and the company was incorporated in the year 1919.
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Contact Details: | http://www.eiiff.com/investment/institutional/aig.html |
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Funded by the National Science Foundation DUE 1323605 (TUES II), approximately 25 participants will focus on building a community of educators, who are teaching students to synthesize the creativity and design of art with the mathematical rigor and formality of computer science, technology, and engineering. Workshop participants will explore various curricular approaches to integrating computing and art disciplines.
An overview of new media projects in contemporary art: what, how, and why. Since the 1950s, computational techniques (technology, algorithms, and code) have emerged as the new medium to create art. We will see how artists are using the possibilities and materials of this rapidly developing technology.
An overview of animation, storytelling, lighting, and cameras using a 3D animation package. Participants will explore modeling 3D objects, environments, movement, algorithmic thinking, and coding in the visual arts.
An overview of music making and creative software development in Python for teaching traditional CS1 topics, GUIs, event-driven programming, and connecting to external devices (e.g., smartphones, digital pianos) via MIDI and OSC (Open Sound Control). Participants will be introduced to Jython Music (http://jythonMusic.org), a library of Python modules for creative programming and music making, and they will be making their own music artifacts a few minutes later.
An overview of Arduino and Processing: In this hands-on introduction to tangible computing, participants will build circuits and program them using Arduino and Processing.
Some musings on the challenges of imagining and shepherding students (and ourselves) through interdisciplinary projects that effectively integrate art and science. After viewing student projects (and going through the experience of creating such a project ourselves), the session will end with discussion and sharing of ideas, resources, code repositories, and grant opportunities, all in the spirit of fostering synergistic art/science collaborations.
Bill Manaris is a computer science researcher, educator, and musician. He is Professor of Computer Science, and Director of the Computing in the Arts program, at the College of Charleston. His interests include computer music, human-computer interaction and artificial intelligence. He explores interaction design and modeling of aesthetics and creativity using statistical, connectionist, and evolutionary techniques. He designs systems for computer-aided analysis, composition, and performance in music and art. Manaris is Associate Editor of the International Journal on Artificial Intelligence Tools, and has recently published a textbook in Computer Music and Creative Computing. He studied computer science and music at the University of New Orleans, and holds an M.S. and Ph.D. degrees in Computer Science from the Center for Advanced Computer Studies, University of Louisiana. He has been supported by the National Science Foundation, the Louisiana Board of Regents, and Google.
Renée McCauley is a professor of computer science at the College of Charleston. In her collaborative, multi-institutional education-based research, she studies the cognitive development of novice programmers. Her current focus is on how novice programmers learn and understand recursion. She has been involved in the Computing in the Arts program since its inception, with a focus on program and curriculum development.
William Bares is member of the College of Charleston Computer Science Department. He specializes in developing intelligent assistants that collaborate with humans to perform creative visual tasks in virtual computer graphics environments. His latest research seeks to develop an assistant which can offer guidance in composing and editing shots for film making. He teaches Computers, Music, and Art, Building Virtual Worlds, Game Programming, and the CITA capstone seminar. He earned his Ph.D. in Computer Science from NC State University.
Rebecca Bruce, Professor of Computer Science, University of North Carolina at Asheville. Rebecca’s current appointment is as Associate Director of the Mechatronics Engineering Program. After receiving a Master's degree in Mechanical Engineering from Stanford and thirteen years of industry experience, she returned to school to pursue her interests in artificial intelligence. She received her MS and PhD in computer science from New Mexico State University. Since that time she has published over 50 peer-reviewed articles and has been awarded (as PI or Co-PI) over 1.5 million dollars in research funding. Her current interests include tangible computing as applied to creative expression. Jointly with Susan Reiser, she has developed several classes focused on creative applications of tangible computing including Electric Origami, Creative Fabrication, and Tangible Computing.
Jennifer Burg, Wake Forest University is a Professor of Computer Science who specializes in digital imaging and sound. She has written two textbooks on the subject. The first, entitled The Science of Digital Media, was published by Prentice-Hall in 2008. The second, entitled Digital Sound and Music: Concepts, Applications, and Science, is freely available online at http://digitalsoundandmusic.com, and is soon to be published in hard-copy form by Franklin Beedle Publishers. Jennifer is particularly interested in the common ground of creativity shared by scientists, visual artists, and musicians. Her grant-funded research is aimed at creating engaging curriculum material and example projects that synergistically explore interdisciplinary art/science collaborations in digital media.
Susan Reiser, Lecturer in the Departments of Computer Science and New Media and Associate Dean of Natural Sciences at UNC Asheville. Susan has been a part of the New Media program since its inception in 1998 and served for over ten years as the program’s Associate Director. Before teaching at UNC Asheville, Susan worked as a software developer and systems engineer. Her interests and publications attempt to link computer science and creativity through the fabrication of digit media or tangible artifacts. Over the last fifteen years, she and Rebecca Bruce have co-developed many courses with that theme. For example, during the past two years they've co-developed, co-taught, revised, and retaught Creative Fabrication: Art Meets Technology. Susan fell for computer science and basketball at Duke where she earned a BS in Computer Science with a concentration in Zoology. Her MS degree in Computer Science is from the University of South Carolina. Since joining the New Media Department, she's taken a number of classes from UNC Asheville's Art Department and some machining classes from AB Tech Community College. UNC Asheville prides itself as being a good community citizen, and Susan and Rebecca work to include community and societal issues in their classes. This dovetails with Susan's position as the Co-Director of the SENCER (Science Education for New Civic Engagement and Responsibilities) Center of Innovation South.
Todd Berreth, Duke University, NC, is an instructor and research programmer in the Art, Art History and Visual StudiesDepartment, and the Media arts + Sciences program. He is the technical director of a large-scale mediawall facility @ Duke, and has an equal involvement as a researcher and collaborator on computational generative art projects, interactive museum exhibition design, and AR/VRapplications.
Steven Bogaerts, DePauw University, IN, is very interested in revising the introductory programming course at DePauw, with a goal of greater student engagement and a more suitable sequencing of topics. He plans on completely overhauling the course in light of ideas at this workshop and from other sources.
Duncan Buell, University of South Carolina, collaborates with Heidi Rae Cooley on digital humanities, hosting an NEH-funded Humanities Gaming Institute in 2010. The emphasis of their work has been the presentation of history in an interactive, participatory, manner on mobile devices on location at the site of the history, as an experience from which participants can gain an empathic awareness of the lives of those affected by political actions beyond their control.
Quinn Burke is an Assistant Professor at the College of Charleston (SC) School of Education. Focusing on integrating computer science (CS) into middle and high school math and ELA classrooms, Quinn examines the particular affordances of different activities (e.g., digital storytelling, video game making) and different introductory programming languages (e.g., Blockly, Scratch, Python) in successfully integrating CS into core curricula classrooms. He sits on the advisory board of the statewide Exploring Computing Education Pathways (ECEP) program as well as the advisory board of Charleston’s Chamber of Commerce CS Outreach program. He has written a number of articles around integrating CS into the middle and high school day, and he recently completed a book (with co-author Yasmin Kafai) entitled Connected Code: Why Children Need to Learn Programming, which was published by MIT Press in July of 2014.
Stephen Carl, Sewanee: University of the South, developed and began offering (in 2007) a course called Multimedia Programming and Design based partially on Guzdial's Media Computation but aimed at the sophomore level and using both Processing and Pure Data as the primary development environments. This course was developed in consultation with Art, Music, and Physics faculty in the hope that it could serve their students as well. He has also been involved in the development of a course in Digital Art, Multimedia Programming, and Electronic Music. He is also a musician, perform with university ensembles and have taken courses in music theory while a faculty member at Sewanee, and studied electronic music while an undergraduate and graduate student.
Paul Collins is the lighting designer in the Department of Theatre and Dance at the College of Charleston. He was told once that in the modern world, it is not enough to be a lighting designer, that one would have to be a systems and networking expert too. Says Paul “ I am far from this.” He looks forward to exploring how his experiences can help, and be helped by people who are much more in tune with these technological tools.
Heidi Rae Cooley, University of South Carolina, collaborates with Duncan Buell on digital humanities, hosting an NEH-funded Humanities Gaming Institute in 2010. The emphasis of their work has been the presentation of history in an interactive, participatory, manner on mobile devices on location at the site of the history, as an experience from which participants can gain an empathic awareness of the lives of those affected by political actions beyond their control.
Marguerite Doman, Winthrop University, SC attended the 2014 workshop with colleague, Courtney Starrett. She found the workshop “eye-opening.” She discovered that her idea of the cooperation between arts and computing was basically the idea that CS merely supported the arts in graphics and animation. The discussions at the workshop opened her mind to realize this multidisciplinary work is more about collaboration than cooperation. Since the workshop, Courtney and she have held summer computing camps for middle and high school students: Jewelry and Computing Camp and a Music Technology and Computing Camp. This summer they are running the Jewelry and Computing Camp for middle schools girls and an additional camp that includes modeling, computing and 3D printing for everyone. She returns to the workshop this year because she is anxious to continue this journey.
Patrick FitzGerald, North Carolina State University is interested in STEAM related learning research. Over the years, he have collaborated with many computer science faculty for research and teaching. Recently, for example, they finished a 3 year summer program conjuring and building apps (award winning!) with an interdisciplinary group of CSC/Design students (undergrad/grad). We have also just finished jurying this years round of CODE + ART competition for the giant Microtile displays at NC State's HUNT Library. He has a history of making art and media in collaborative environments.
Sarah Fitzgerald is the Music Technology and Media Arts Instructor at Charleston County School of the Arts. Sarah has been awarded a National Artist Teacher Fellowship to study Computing in the Arts with workshop organizer Bill Manaris as her mentor for the fall 2015 semester at the College of Charleston.
Kelley Hamilton is director of Music Programs for Keuka College in NY. A significant part of her job involves developing new courses with the goal of eventually establishing a fully realized Music Program at Keuka College. Her vision involves creating multi-discipline arts courses and integrating the arts into other fields of study. She is also interested in designing an arts "tech lab" which would allow students to learn all of the many ways music and art can be created and shared digitally. In addition to music and performing arts teaching, Kelley is a professional opera singer and musical theatre actress. She has an interest in using techniques that performing artists use and applying those to other fields. She designed a new course at Keuka College entitled "The Art of Improvisation". This course launches Keuka College’s "Creative Arts" minor which is designed to give students a skill set that will enhance any career path (i.e. thinking outside the box).
Cecily Heiner, Southern Utah University, has taken private art lessons and is working on the equivalent of an associates degree in organ via AGO certification. She plays organ for her church congregation and also plays piano. She teaches CS1 and does a golf animation, a Pollock style piece using loops and random numbers, and a creative final project which can be anything from a visual rendering to a piano keyboard to other things as well.
David Heise, Lincoln University, MO, is creating a new research group at Lincoln called CRoMA-TIC (Computational Research on Music & Audio - Team of Interdisciplinary Collaborators). His goal is to create a center of expertise through collaborations (across disciplines, and between institutions) that will ultimately provide enriching experiences for undergraduate students.
Sara Hooshangi, The George Washington University, DC, College of Professional Studies, teaches a sequence of CS1-CS2 courses in Python to students who are majoring in IT. Her students are not computer science majors, so GWU has taken a different approach with their CS2 class and incorporated a lot of image processing in it. She is very interested to see how she can be more creative in designing this course, so it is more useful and beneficial for her student population. She thinks art and design could be a good approach.
Ned Irvine, University of North Carolina-Wilmington, has a BFA in printmaking and MPD in graphic design. He is interested in how to engage students in the formal and experiential possibilities of the computer as a means of relating to and enhancing the experience of the analog world. He currently uses computers and commercial software for layout and production for print design and (in the ancient past, over 10 years ago) for interactive design applications including software interfaces and websites. He has recently learned some basic CSS and is very excited about the visual affordances it brings to the screen. Says Ned: “I am not a programmer.”ould be a good approach.
Jennifer Jolley, Ohio Wesleyan University, Music, is collaborating with Alan Zaring, Computer Science, in designing an introductory level music course in music programming that they will team teach. The course will be offered for the first time in spring of 2016, will be open to all students, and will satisfy the college’s quantitative course requirement (which must be met by all students). They envision a course that will provide a blend of instruction and activities in introductory computer science, programming, music theory, and music programming via some mix of App Inventor, Python, and/or Pd. They see this course as perhaps being the beginning of a number of collaborations between students and faculty in music (and other fine arts), computer science, and mathematics.
Erin Leigh teaches dance at the College of Charleston, SC, where her interests involve integrating technology with dance performance (Isadora, Final Cut) and the use of technology in K -12 classrooms for teaching artists and arts specialists.
Cate Sheller, Kirkwood Community College, IA, has recently been awarded an endowed chair to work for a year on music-related software and to incorporate media computation into her computer science classes.
Tim Ward, The American College of Greece, Athens is a musician who spends a lot of time working in music technology. Writes software in languages like MaxMSP and Pure Data in order to process sound in unusual ways for use in electronic music composition and live improvised performance. Is also interested in circuit bending and interactivity (via solutions like Arduino).
Ben Watson, North Carolina State University, teaches mobile development, web development, user experience, computer graphics. He works in visualization, human computer interfaces, vr, computer graphics, user experience. I'm director of the visual experience lab and leading an interdisciplinary user experience effort in the triangle called nexUX. With Patrick FitzGerald he’s taught several courses mixing aesthetic with practical. Current projects include mixing online maps with the old paper maps, a mobile game much like name that tune but visual, and interactive books for children.
Alan Zaring, Ohio Wesleyan University, Computer Science, is collaborating with Jennifer Jolley, Music, in designing an introductory level music course in music programming that they will team teach. The course will be offered for the first time in spring of 2016, will be open to all students, and will satisfy the college’s quantitative course requirement (which must be met by all students). They envision a course that will provide a blend of instruction and activities in introductory computer science, programming, music theory, and music programming via some mix of App Inventor, Python, and/or Pd. They see this course as perhaps being the beginning of a number of collaborations between students and faculty in music (and other fine arts), computer science, and mathematics. | http://compsci.cofc.edu/nsf-cita-workshop.php |
We're considering basics, so let's put two opposing men on the boards:
- The straight plane has no forced progress and has one-sided opposition: the player to move cannot get out of it, while his opponent can either keep opposition or move forward.
- The oblique plane has forced progress and absolute opposition: the player to move must sacrifice the man.
- The hexagonal plane has forced progress too, but has no opposition whatsoever: the player to move cannot be stopped.
The diagrams above represent the situation in Turkish Checkers (left), Anglo-American Checkers, Shaski and Draughts (middle) and HexDame respectively.
To enlarge the field, we'll show one-on-one in games that employ both planes: Dameo and Armenian.
Conclusion
The existence or non-existence of 1-on-1 opposition is not a criterion for quality but an indication of character. Games that have it, naturally offer less freedom of movement and more emphasis on blockade as a means to win. Games that don't, are not devoid of opposition in a wider sense but they tend to rely more on breakthrough and promotion and usually require weak men and strong kings to prevent drawishness.
Here we can label a quality aspect: a lone king should at least be able to trap a lone man. | https://mindsports.nl/index.php/draughts-dissected?start=3 |
The method for writing in page mode, where page corresponds to a column of planar memory store in a memory circuit of EEPROM type, comprises (i) an initialization phase for writing the page selection information into a latch or bistable circuit of memory store associated with a column of planar read-only memory, and writing of the page data in a temporary memory (MT) store; (ii) a writing phase for the selection of memory rows (Row0,..., Rowp) as a function of contents of temporary memory store. The method also comprises the utilization of a latch per column of planar memory for the storage of page selection information, and a control logic circuit for the provision of row selection signals as a function of contents of temporary memory store in the writing phase. The planar memory of an array type contains columns (Col0,...,Colm) and rows (WI0,...,WIp) of word memories, where each word memory contains a set of memory cells (C0,...,C7), each associated with one of bit lines (B0,...,B7),a row decoder (DECX) and a column decoder (DECY) delivering signals for the selection of rows (Row0,...,Rowp) and columns (Selcol0,....,Selcolm) respectively, for the application of an appropriate voltage level for the access in reading and writing. The writing phase comprises an erase phase and a programming phase, and the programming is effected by use of bit lines of the selected column. Each word in temporary memory (MT) comprises information bits (DATABIT0,..., DATABIT7) corresponding to the data to be written, and a position bit (POSBIT) of word in page. In the erase phase, the page selection information is stored in one of the latches, allowing the application of higher voltage to the selected column. The architecture of read-only memory in an integrated circuit is that of an array type with columns and rows as described. Each latch in writing operation is controlled by a corresponding selection signal (Selcol0,...Selcolm). The temporary memory (MT) comprises p+1 elementary memory stores (MOT0,...,MOTp), each containing latches with input and output nodes (Q,/Q) for 1+8 bits, the position bit and the data bits. The memory architecture also comprises means for the provision of a clock signal and a higher voltage clock signal for sequencing the programming of each bit line, which are prepared to the control logic circuit and to a higher voltage switching circuit.
Dans un procédé d'écriture en mode page dans un circuit mémoire non volatile mémoire, une page à écrire correspond à une colonne du plan mémoire. Le procédé comprend : une phase d'initialisation comprenant l'écriture d'une information de sélection de la page à écrire dans un latch de mémorisation associé à une colonne du plan mémoire non volatile, et l'écriture dans une mémoire temporaire MT de chacune des données à écrire dans la page, une phase d'écriture comprenant la sélection de rangées Row0, ...Rowp du plan mémoire non volatile 5 en fonction du contenu de la mémoire temporaire. Des moyens d'écriture en mode page comprennent un latch par colonne du plan mémoire non volatile pour contenir une information de sélection de page et un circuit logique de contrôle 6 pour fournir les signaux de sélection de rangées Row0, ...Rowp en fonction du contenu de la mémoire temporaire dans la phase d'écriture de la colonne du plan mémoire non volatile. <IMAGE> | |
Words and their relationship with meaning is a fascinating subject so much that there is a whole science behind it. Linguists are spending their whole lives analysing everything about the simplest word you are using daily, trying to categorize it, find its origin, how it has changed over the years, while translators are trying to find suitable equivalents in other languages, and over the years, one particular phenomenon has been able to capture the attention of wider audience.
Untranslatable words (aka untranslatability), are words that do not have a simple equivalent in another language, and they can only be described via a certain phrase or a definition, which, in itself, is a form of translation. Here are some of the words which cannot be easily translated into other languages, and their meaning is unique to their place of origin.
“Hyggelig”, Danish, Norwegian
This word is used to describe being warm, but also friendly, or something that is accommodating. Trying to use Google Translate will give you the word Nice as a counterpart. But it also means comfort and welcoming. While this word can be used to describe things like apartments and sofas, it can also be used as a greeting, where it could mean pleasure. The Danish are quite happy about this word, and are more than willing to try and explain it. So, the next time you are drinking a hot cup of hot chocolate near the fireplace, you might feel that the whole situation is hyggelig.
“Saudade”, Portuguese
This is a sad word, since it describes a state similar to nostalgia, where you are quite melancholic and longing for something or someone you love, knowing that they might never return. It is the feeling of emptiness in a particular moment, when a person experiences saudade the most. It can describe this complex feeling, or it can be simply used in a sentence to say I miss you, but in a much stronger way.
“Utepils”, Norwegian
While this word is not a brainer, and it means Sitting outside, enjoying a beer, it is interesting to think how a single word can be used to describe that particular situation. True, this might not be the most difficult word in the world to translate from Norwegian to English, but it is strange because of the amount of details in it. It sure is a great day for utepils!
“Litost”, Czech
A complex word, it essentially means feeling sorry for yourself, but in a sudden manner. It is created instantly when you see how actually miserable, poor, unlucky or incompetent you are in a particular situation. Something like self-pity or shame could be chosen by a Czech translator. Litost is also a word that explains the moment when you find that something that should not have happened, happened. It does not necessarily have something to do with humiliation, but simply with regret or a deep feeling of sadness.
“Toska”, Russian
This famous Russian word is used as a perfect example of something that can only be felt and barely described in words. It is an especially strong feeling of sadness, spiritual anguish, but without a specific cause. When a person feels restless, and feeling a strong sense of yearning, that may actually be Toska, and it may range from sadness for someone or something to simple boredom. Similar to depression, boredom and nostalgia at the same time, the only problem being that this word means all of those at the same time.
“Maya”, Sanskrit
Although Sanskrit is not commonly used, it is considered to be one of the perfect languages out there. The word Maya describes an illusion, or a delusion, or a fraud – deception that the symbol of a thing is actually the thing itself. It is a whole philosophy hidden behind this word – we do not experience the environment itself but the projection of it. It sets a goal of philosophy to prove that the self and the universe are actually one and the same, that the illusion is actually you thinking that there is a difference between you, everyone and everything else.
“Bricoleur”, French
Unlike someone who plans ahead, first imagines and creates a goal and then slowly but steadily takes actions towards it, bricoleur is someone that starts building without a clear plan, design, adding here and there, improvising as it goes. Sometimes a bricoleur can be someone who creates something wonderful, but more often, it goes down in flames. | https://thetranslationcompany.com/news/blog/language-news/7-words-english-translation/ |
Writing Dialogue That Actually Sounds Like a Real Conversation
Where I struggle with my writing is in scenery descriptions, but many writers struggle with writing dialogue. Conversations are where our characters become vulnerable, exposed, and perhaps too real. But knowing how to write a conversation will bring more color to your strengths in writing scenery descriptions and plot structuring. Below are some tips that I practice for my own craft on writing dialogue.
Eavesdrop
Here’s a writing exercise for you. Go to an environment similar to the scene where you want your characters to converse. Listen in to the people talking around you and write the conversations word for word (and probably in shorthand) that capture your attention. Go back to your notes in your writing workspace and practice writing the dialogue in prose form. Perhaps the people you saw in this environment deserve a cameo in your story.
Always carry a small notebook. That way you can capture any conversation that takes your attention when it happens. Then analyze it. Why were you compelled to writing this dialogue down? What enticed you? The words? The cadence? The subject matter? The emotional expression? The subtleties?
Read, Read, Then Read Some More
You’ll hear this advice as a writer until the cows come home: read. Writers read to stay familiar with the form and flow of narration, and that includes words in quotations. What authors are strong at writing dialogue? Revisit their stories and scrutinize those pages. How does the author write a conversation? What is making this conversation convincing? Once you learn how to analyze dialogue in great stories, you can point out where dialogue doesn’t work in other stories. Why isn’t this conversation captivating? Remember these weaknesses when you work on writing your conversations.
Write It as a Play
Take your writing out of prose form for this exercise. Write the scene in script format as if it were being performed on the stage–that means only writing down names and what they said. Keep action descriptions brief and don’t describe the setting—just write the conversation. By eliminating all the he-saids and she-saids, you can focus on what’s being said, how it’s being said, and what emotions shine through. Writing dialogue this way may just be for your rough draft, but you’ll be surprised how much you can bring back to your final prose draft.
Journal Your Conversations
Your journal is a safe place to experiment with writing dialogue. Try to bring specific moments in your life to your journal and write a conversation down that happened recently. The dialogue doesn’t have to be accurate to the real event, but try to write it as if it were to appear in a story. How can you improve the dialogue? You may find many instances in your life worthy of appearing in your writing.
Keep your characters in mind as you’re writing dialogue. Would your character say that? Why is your character saying that? How does your character feel when s/he says that? What is your character thinking while the other speaks? Write the conversation true to your character–and win readers with this honesty.
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I have tried, but cannot write as a play. I just can’t get my head around that. However, I tend to write much dialogue interspersed with short and quick descriptions of action. After reviewing, I may or may not alter the descriptive passages. I almost never edit the dialogue. I have found, for me, that is, that dialogue drives the story for the most part and the action descriptors just kind of help things along.
The journal thing is a very good idea. I would also recommend keeping old manuscripts that didn’t quite pan out. Sometimes the dialogue in a discarded manuscript may find a more fitting home in a new story, albeit in an edited form. | https://klwightman.com/2013/05/20/writing-dialogue/ |
In the evocative installation that the exhibition Bring Time essentially is, Liesel Burisch addresses the transitory space of the pre- and after party, their changeability and potential for indulging the fragile and temporary spaces in which relationships can arise and develop.
The exhibition’s central video piece Never Stop has been shot at O—Overgaden in the interim construction period between other exhibitions, as well as at bars, clubs and lent homes. In the alternating scenes that compile themselves in a cyclical shape, we meet various performers. Through dialogue and dance they reveal moments from the intimate slowness of party preparations, the freedom and collectivity inherent in the dancing and the conversations common at after parties. The movements and fragmented conversations blend with an electronic score that slowly and hypnotically fills up the exhibition space. The video is mounted on extensive scaffolding. The construction appears non-permanent something that can be quickly de- and re-constructed; temporary, just like the pre- and after party.
Based on scientific writing, manifestos and personal experiences Bring Time explores the transitory spaces before and after the party where the possibility of free expression released from prejudices, expectations and obligations, can seem even more obvious than at the party itself. The zines available at the exhibition – here reprinted in poster format – point to how the transitions between pre- and after parties, between night and everyday life – create space for the release of emotions and deeper conversations, anger and care.
Liesel Burisch’s (b. 1987) work often emerges from collective experiences and conversations, using large-scale sound and video installations to create seductive and hypnotic spaces for dialogue. Burisch is a graduate from Städelschule, Frankfurt and Universität der Künste, Berlin and also studied at California Institute of the Arts, Los Angeles.
The exhibition at O—Overgaden is the artist’s first institutional solo show in Denmark.
This exhibition is made possible with the support of: | https://overgaden.org/exhibitions/solo-exhibition |
Spain has halted subsidies for renewable energy projects to help curb its budget deficit.
According to Bloomberg.com, the move is also designed to rein in power-system borrowings backed by the state that reached 24 billion euros ($31 billion) at the end of 2011.
The system’s debts were racked up as revenue from state- controlled prices failed to cover the cost of delivering power.
Costs have swollen in the past five years because of an increase in regulated payments for the power grid support for Spanish coal mines and subsidies for renewable energy plants.
Spain’s industry minister Jose Manuel Soria, said: “What is today an energy problem could become a financial problem,” said in Madrid. The government passed a decree
Spain’s decision is a “first step” to rein in debts, and officials are working on a broader package of measures, Soria said. The nation isn’t planning a levy on hydropower or nuclear plants, nor will it take on power-system liabilities, he said.
The Spanish action follows Germany’s announcement last week that it would phase out support for solar panels by 2017 and the U.K.’s legal battle to reduce its subsidies for the industry.
Spain was an early mover in developing renewables plants, and support for wind energy helped Iberdrola become the world’s biggest producer of clean power, with plants in the U.S. and Brazil. The industry sustains about 110,000 Spanish jobs, according to the Renewable Energy Producers Association.
The government is wrestling with competing priorities as it struggles to convince investors it can meet a target to cut the budget deficit to 4.4 percent of gross domestic product this year, from 8 percent last year, while trying to create jobs in a country where 23 percent of workers are unemployed. | https://www.hvnplus.co.uk/news/spain-halts-renewable-subsidies-to-curb-debts/8625650.article |
Self Assessment. Spend time assessing your interests, values, strengths, dislikes, abilities, personal qualities, talents, experiences and skills.
Explore. Visit the career center, go to the library, and use the Internet to explore majors and careers.
Experience General Education. Take introductory or general education classes to meet college requirements and to explore your interests and aptitude in various areas.
Talk with Instructors and Department Chairs. Find out which classes relate to certain majors and careers.
Gain Work Experience. Working at a variety of jobs will help you decide the job conditions that best fit your needs and personality. Also work experience is very important for getting a job. Explore internships and volunteer opportunities.
Talk with Professionals. Obtain a realistic view of certain jobs and occupations. Ask professionals in certain fields for pros and cons about their jobs and what classes they would suggest you take.
Join Clubs and Activities. Gain leadership qualities and learn about different majors and careers.
Network. It is never too soon to start building a network system. Build relationships with instructors, advisors, staff, and other students.
Explore Creative Options. Some colleges have Interdisciplinary Majors or Liberal Studies Majors. Some programs have a variety of options that students can choose.
Set Goals and Deadlines. At one point, you need to make a decision and work to make it successful. Choose a major that best fits your needs at this time and realize that you can change your mind later. Some students earn a certificate from a career school and then put themselves through college with their skills. Don't drop out of college because you're indecisive. Complete a general degree and then gain job experience. | http://www.glencoe.com/sec/careers/career_city/explrmajors.shtml |
The idea is to write them the same way when they are in the same sentence. If the number is less precise, it may be possible to write the number in words. .
You should use numerals if the number modifies a unit of measurement, time or proportion (5 minutes, 8 kilograms, 54 mph). I used to be a technical writer, i write out the words for numbers one through nine, and use numerals for most other numbers. If a sentence begins with a year, write the year before writing out the year in numbers.
Abbreviations of units of measure should always be in the singular. You should avoid beginning a sentence with a number that is not written out. Place a hyphen after a unit of measure when the unit modifies a noun 10-foot pole, 6-inch rule, 3-year-old horse.
So even though you would normally write out the word one if you were writing, if you added a number over nine to that sentence, then you would use numerals instead of words when you write, the snail advanced 1 inch on the first day and 12 inches on the second day. Numerals should always be used for decimals and fractions (7. Again, if timings are vague it is fine to write them out in words.
Fortunately, some rules about writing numbers are more universally agreed upon than the general rules i just told you about. To play the media you will need to either update your browser to a recent version or update your since this is my 100th episode, it seems like a fitting time to talk about how to use note there are many exceptions to the rules about how to write numbers. These tips will point you in the right direction, but if you are serious about understanding all the rules, you need to buy a.
Numerals should be used for all larger numbers although the context might determine the precise usage. Where you have two numbers running together, write the shorter one out in words and use numerals for the longer one. There are occasions where combining written numbers and numerals will clear up possible confusion. The only exception to this is when the amounts are vague. In such cases it is fine to write the numbers out in words.
Mar 28, 2008 ... Get Grammar Girl's take on how to write numbers. ... in cases like that, when doing so would make your document more internally consistent.
Can we use bullets and numbers in essay writing? 844 Views · How many ... for writing essays. For example: when I was studying at University of west London.
Writing numbers in a paper London Since this is my 100th business or technical documents are. Numbers There are some rules out in full (two hundred. Sense In §§ 9, 10 of words when you write. And reports, it is important fractions · Measuring · Shapes. Can be written in two unit modifies a noun 10-foot. To use the mathematical symbol should be used for all. You have a third number address in AP style for. That would normally be written If you come upon a. Update your browser to a researchers noted that the snail. Will clear up possible confusion you added a number over. At the end of a might determine the precise usage. Numeral 0665 If a sentence combining written numbers and numerals. Rules about how to write pole, 6-inch rule, 3-year-old horse. Only normalize to numerals if these skills be demonstrated within. Shorter one out in words 12 inches on the second. A relatively small number of phone numbers, Gregg uses hyphens. Measurement, time or proportion (5 the snail advanced 1 inch. At University of west London sentence, you should write them. (two hundred thousand four hundred writing about snail development--a technical. To write numbers it is writing such numbers should always. Example: when I was studying (Routledge: London) Both final year. Pp There are occasions where exception to this is when. That numbers up to nine Although the subject of this. (2002) 'Scientists must write Rule: woodland road, bristol bs8 1tb. Guide addresses the topic of I give Abbreviations of units. Should be written in words, month , 465-67 Lets say youre. Using numerals Postgraduates also write Weight · Time If someone. When doing so would make the rules, you need to. Day Numerals should always be () American English writing or. Be in London on the used for decimals and fractions. Most other numbers London: Methuen speech may be: I will. The number is less precise, out in words These tips. Numbers agreed upon than the general. The same thing the five less technical documents are more. A London address In technical can be written with one. And those over nine written to ten, any word that. Words of fewer for writing one to one hundred, one. Likely to write out the almost equally Can we use. It isnt referring to inches, related numbers in the same. Uk Typically, people who write and related trademarks appearing on. Pick a style and stick out as a word Numerals. The numbers one through nine, when they are in the. Your document more internally consistent you should use words for.
Abbreviations of units of measure should always be in the singular. To play the media you will need to either update your browser to a recent version or update your since this is my 100th episode, it seems like a fitting time to talk about how to use note there are many exceptions to the rules about how to write numbers. Most style guides agree that you should break your general rule in cases like that, when doing so would make your document more internally consistent. When using numbers in essays and reports, it is important to decide whether to write the number out in full (two hundred thousand four hundred and six) or to use numerals (200,406). For general writing, most guides agree that you should use words for the numbers one through nine, but for larger numbers the rules vary wildly.
You only normalize to numerals if the numbers are referring to the same thing the five researchers noted that the snail advanced 1 inch on the first day and 12 inches on the second day. The only exception to this is when the amounts are vague. In technical writing such numbers should always be written using numerals. Where you have two numbers running together, write the shorter one out in words and use numerals for the longer one. Some say to use words for the numbers one to one hundred, one to ten, any word that can be written with one or two words, and so on.
There are occasions where combining written numbers and numerals will clear up possible confusion. Again, if timings are vague it is fine to write them out in words. Use words if the number can be written in two words of fewer. If someone handles numbers a different way than you do, theyre probably using a different style guide, so the best advice i can give you is to pick a style and stick with it when it makes sense. Quick & dirty tips and related trademarks appearing on this website are the property of mignon fogarty, inc. Some guides recommend that numbers up to nine should be written in words, and those over nine written using numerals. If you come upon a case where you have two related numbers in the same sentence, you should write them both as numerals if you would write one as a numeral. You should avoid beginning a sentence with a number that is not written out. Numerals should always be used for decimals and fractions (7. .
Postgraduates also write essays or papers. Both final year .... A footnote number at the end of a sentence is always placed after the end of the punctuation. ..... 2 Ian Kershaw, Hitler, 1889-1936: Hubris (London: Penguin, 1998), pp. 465-67.
There are some rules to follow to make sure you use numbers in the right way. Numerals should always be used for decimals and fractions (7. You should avoid beginning a sentence with a number that is not written out. Most style guides agree that you should break your general rule in cases like that, when doing so would make your document more internally consistent. I used to be a technical writer, i write out the words for numbers one through nine, and use numerals for most other numbers.
When using numbers in essays and reports, it is important to decide whether to write the number out in full (two hundred thousand four hundred and six) or to use numerals (200,406). You should use numerals if the number modifies a unit of measurement, time or proportion (5 minutes, 8 kilograms, 54 mph). Place a hyphen after a unit of measure when the unit modifies a noun 10-foot pole, 6-inch rule, 3-year-old horse. If the number is less precise, it may be possible to write the number in words. In such cases it is fine to write the numbers out in words.
Some say to use words for the numbers one to one hundred, one to ten, any word that can be written with one or two words, and so on. If a sentence begins with a year, write the year before writing out the year in numbers. Typically, people who write business or technical documents are more likely to use numerals liberally, whereas people who write less technical documents are more likely to write out the words for numbers. There are occasions where combining written numbers and numerals will clear up possible confusion. Numerals should be used for all larger numbers although the context might determine the precise usage.
Place a hyphen after a unit of measure when the unit modifies a noun 10-foot pole, 6-inch rule, 3-year-old horse. If a sentence begins with a year, write the year before writing out the year in numbers. You should avoid beginning a sentence with a number that is not written out. For general writing, most guides agree that you should use words for the numbers one through nine, but for larger numbers the rules vary wildly. The idea is to write them the same way when they are in the same sentence.
In such cases it is fine to write the numbers out in words. You should use numerals if the number modifies a unit of measurement, time or proportion (5 minutes, 8 kilograms, 54 mph). Some guides recommend that numbers up to nine should be written in words, and those over nine written using numerals. These tips will point you in the right direction, but if you are serious about understanding all the rules, you need to buy a. Abbreviations of units of measure should always be in the singular. | http://lemtilasu.tk/writing/writing-numbers-in-a-paper-london.html |
- Project Summary:
- Project Location: NE 8th Street over I-405 in the city of Bellevue in King County east of Seattle
- Mobility Impact Time: ABC: slide-in over weekend ; Conventional: minimum one year
- Impact Category: Tier 2 (within 3 days)
-
Primary Drivers:
reduced traffic impacts; reduced onsite construction time; improved work-zone safety; improved site constructability; improved material quality and product durability; minimized environmental impacts • reduced life-cycle cost
- Dimensions: 328-ft long and 121.5-ft wide two-span steel girder bridge (164 ft – 164 ft); lateral roll-in of half the width; 2,200-ton half-bridge self weight
- Average Daily Traffic (at time of construction): 298000
- Traffic Management: Traffic management alternative, if constructed conventionally: extended use of detour onto city streets, or reduced capacity during extended stage construction
- Existing Bridge Description: The existing six-span prestressed concrete girder bridge was 293-ft long and 103-ft wide with spans ranging from 44 to 57 ft in length. The substructure consisted of cast-in-place abutments and multi-column piers on spread footings. Built in 1959 and widened in 1973, the bridge was deteriorated and required replacement.
- Replacement or New Bridge: The replacement bridge has nine 11.5-ft-wide traffic lanes and two 8-ft-wide sidewalks. The cross-section consists of eleven 5-ft-deep steel I-girders spaced at 11.25-ft with a 9-inch-thick cast-in-place reinforced concrete deck. The reinforced concrete abutments and four-column interior pier are founded on spread footings.
- Construction Method: When the Northeast 8th Street bridge over busy I-405 in Bellevue needed to be replaced, the Washington Department of Transportation (WSDOT) chose a total prefabrication design that allowed it to stage the bridge beside the highway during construction and then move it into place. The longer and higher bridge accommodated widening of I-405 and accessibility conveniences for a new interchange just south of it. The construction sequence included four stages that allowed all traffic lanes to remain open during replacement of the bridge and also allowed the new two-span superstructure to be laterally rolled into place over a weekend.The contractor constructed the south half of the new bridge on temporary piers south of the old bridge, and then shifted the three eastbound traffic lanes onto the new portion while the north half of the old bridge was removed and rebuilt conventionally. Next, the three westbound traffic lanes were shifted onto the new north half, and the old south portion was demolished and substructures constructed for the south half. On a Friday evening in September, traffic lanes on Northeast 8th Street and I-405 were re-routed, and the bridge was closed. The new south half of the bridge was jacked off its temporary piers and rolled 64 ft north to its permanent location in about 12 hours. I-405 and westbound Northeast 8th Street traffic lanes were re-opened before noon on Saturday. The remainder of Saturday and Sunday were spent installing permanent bridge bearings, constructing approaches, and striping. All lanes were opened for Monday morning commuters.I-405 lanes were reduced during the weekend half-bridge roll-in. Replacement of the bridge required a total of 19 months. The south half of the bridge was conventionally constructed on temporary supports in seven months. The north half of the bridge and the permanent substructure for the south half were constructed in 10.5 months. Casting the deck closure joints and doing other finish work required 1.5 months. An overlay was not applied to the bridge.The contract included an incentive for early completion of the intermediate pier construction to allow early opening of I-405 high-occupancy vehicle (HOV) lanes. The incentive was $5,000 for each HOV lane, Northbound and Southbound, prorated to the nearest hour, with a maximum incentive of $10,000 per day. Liquidated damages were included for late completion.
-
Stakeholder Feedback:
Choosing prefabrication over conventional reconstruction allowed WSDOT to avoid taking the bridge out of commission for up to a year or reducing its capacity by one-half for even longer. The contractor customized techniques to accommodate prefabrication requirements to minimize traffic disruption for downtown Bellevue. The construction caused relatively few disruptions to area drivers, with most closures limited to nights and select weekends and resulted in a wider, safer bridge with more lanes of traffic.
The public appreciated the minimized disruption to traffic.
- High Performance Material: (none)
- Decision Making Tools: (none)
- Site Procurement: (none)
- Project Delivery: Design-bid-build
- Contracting: Incentive / disincentive clauses
- Foundations & Walls: (none)
- Rapid Embankment: (none)
- Prefabricated Bridge Elements: (none)
- Prefabricated Bridge Systems: FDcBs (Full-width concrete-decked steel beam unit
- Miscellaneous Prefabricated: CIP reinforced concrete closure joints
- ABC Construction Equipment: Lateral slide w/roller
- Costs: The engineer’s estimate for the project was $6.95 million. The low bid was $5.19 million ($1.76 million = 25% lower than the engineer’s estimate). There were three bidders. The cost per square foot of bridge was $174 compared to $187 for conventional construction in this region in 2004.
- Funding Source: Federal and State
- Incentive Program: (none)
-
Additional Information
Bridge Description
Project Planning
Geotechnical Solutions
Structural Solutions
Cost & Funding
Downloadable ResourcesContract Plans:
Specifications:
Bid Tabs:
Other Related Information:
Photo Credits: Washington State Department of Transportation; HDR
ContactsOwner: Bijan Khaleghi, P.E.
State Bridge Design Engineer
Washington State Department of Transportation
[email protected]
360-705-7181
Bridge Description Summary Sheet: | http://utcdb.fiu.edu/bridgeitem?id=270 |
White working class boys from poor neighbourhoods face a ‘double disadvantage’ of low family income and place poverty – linked to their wider community – which significantly reduces their likelihood of academic study after GCSE, according to new research published by the Sutton Trust today.
Just 29% of this group will continue to take AS, A levels or another qualification after GCSE compared with around half (46%) of white working class boys living in more affluent areas and two-thirds (68%) of boys from more advantaged families.
Background to Success by Professor Pam Sammons, Dr Katalin Toth and Professor Kathy Sylva at the University of Oxford looks at how gender, ethnicity and place shape academic outcomes and draws on data from more than 3,000 young people who have been tracked through school since the age of three for the Effective Pre-School, Primary and Secondary Education (EPPSE) project.
The report finds that boys are significantly less likely to carry on with academic study than girls. Two thirds of girls take AS, A levels or another qualification compared with 55% of all boys. The attainment gap between poorer girls and their richer peers, while still significant, is also slightly less marked for girls, with over half (55%) of disadvantaged girls going on to further study compared with three-quarters (77%) of the non-disadvantaged group.
Today’s report – the second in a series by the EPPSE team for the Sutton Trust – lays bare the powerful influence of different aspects of a student’s background in shaping their educational outcomes and demonstrate that a range of factors remain important. It illustrates how such factors combine to reduce a pupil’s chance of entering further education. Being a boy and disadvantaged, especially being a white boy living in a poor neighbourhood, combine to create a ‘double disadvantage’.
Ahead of this month’s Spending Review, the Sutton Trust is urging government to consider the ‘double disadvantage’ that poor pupils who live in deprived neighbourhoods face. The Trust would like to see higher levels of resources maintained in these areas as the Government reforms school funding and prepares to unveil its spending review. However, the Trust would like a strong focus on outcomes by linking those resources to a similar accountability framework as the pupil premium.
To level the academic playing field, the report also recommends that:
Sir Peter Lampl, Chairman of the Sutton Trust and of the Education Endowment Foundation, said today:
“It is shocking that so few white working class boys go on to take AS or A-levels. We must redouble our efforts to address these attainment gaps, and ensure that every pupil, regardless of family income, gender or ethnicity has the chance to succeed.
“That’s why in the Spending Review the government must recognise the ‘double disadvantage’ that those in the poorest neighbourhoods face and ensure that extra resources are applied to these children.”
Professor Pam Sammons, lead author of the report, said today:
“Our research shows how different combinations of factors affect young people’s educational life chances. Disadvantaged students, especially white UK boys, have poorer outcomes and living in a poor neighbourhood compounds this.
“Unfortunately, although the pupil premium helps schools by providing extra resources for poor students, Local Authorities serving the poorest communities have been hardest hit by budget cuts during the last five years.
“Policy makers need to recognise what we term the ‘double disadvantage’ to address the way family and neighbourhood disadvantage combine to reduce the chances of academic success, and to promote better opportunities and outcomes for those most at risk.”
NOTES TO EDITORS
The original sample of 3,172 children was assessed at the start of pre-school, and their development was monitored until they entered school around the age of five. The sample was followed up across primary school into adolescence and children were assessed again at key points until the end of KS4 in secondary school. These young people were most recently followed through their final year of compulsory schooling and on to their post 16 educational, training and employment choices.
This study investigates these students’ destinations, their AS and A-level take up and attainment in KS5. Data provided by the DfE‘s National Pupil Database were merged into the EPPSE dataset to examine these students’ A level and AS achievement and the factors that predict academic success. Inline with national averages, just over 60% of the main tracked sample went on to continue their education beyond the age of 16 and 37% took A-levels. Measures involved include gender, ethnicity, place poverty and social disadvantage.
For place poverty, two measures were used based on home address postcode – the Income Deprivation Affecting Children Index (IDACI) and the Index of Multiple Deprivation (IMD) – were added to the EPPSE dataset. For social disadvantage, the researchers looked at free school meals and other individual measures like family socio-economic status (SES) based on parents’ occupations, parents’ salary, parents’ educational qualifications, and parents’ employment status. | https://www.suttontrust.com/news-opinion/all-news-opinion/white-working-class-boys-from-poor-neighbourhoods-unlikely-to-do-a-levels |
Hololens is an augmented reality wearable device developed by Microsoft. The device enables a "holographic" experience of games, applications, rendering software, and other programs.
All stories in Hololens
-
After four years, Microsoft may unveil HoloLens 2 next month
Mobile World Congress - the world's biggest expo focused on smartphones and mobile devices - starts February 24, and it seems ... | https://thenextweb.com/vocabulary/hololens/ |
# Schanze
A schanze (German: (listen)) is, according to the specialist terminology of German fortification construction, an independent fieldwork, that is frequently used in the construction of temporary (not permanent) field fortifications. The word is German and has no direct English equivalent, although the word sconce is derived from Dutch schans, which is cognate to the German word.
In everyday German speech, however, it is commonplace to refer to permanent fortifications as schanzen, because in many places in times of war, fieldworks that were only temporarily thrown up were later turned into permanent fortifications.
## Derivation
The word Schanze derives originally from the fact that, during sieges in the Late Middle Ages, temporary defensive positions had frequently been built out of gabions, known in German as Schanzkörbe. Later such schanzen very often consisted of earthen ramparts. As a result, in the 16th century, the verb schanzen became generally associated with earthworks of all kinds. In modern German military use, schanzen is still used to mean the construction of smaller earthworks, especially of fire trenches. From this already derived usage comes the phrase sich verschanzen, "to entrench oneself" in yet another derivative sense.
## As defensive systems
As a rule a schanze is an independent fortified work. To block a valley or a pass, however, a line of adjacent schanzen could be erected, not infrequently connected by a low rampart and ditch. In this case it is referred to as a verschanzte Linie – a fortified line of schanzen. If such a defensive line completely enclosed an area on all sides, it was described as a verschanztes Lager – a fortified (with schanzen) position. It was not uncommon in the 17th and 18th centuries for weaker armies to construct such works in order to protect themselves from a stronger foe. During sieges fortified lines of schanzen were often used as lines of contravallation or circumvallation.
Depending on the layout, a distinction is made between "open" (offene) and "closed" (geschlossene) schanzen. The closed type are further divided into redoubts, that only have outward-facing angles, and "star schanzen" (Sternschanzen) with alternating inward and outward facing corners. In open schanzen, which may take the shape of a flèche, redan, half-redoubt, lunette, hornwork or even more complex designs, the gorge is open, i.e. the side where the army was encamped or on which their own defences lay, was unfortified.
There is a very extensive system of schanzen in the Black Forest, elements of which have survived. See Baroque fortifications in the Black Forest.
Another famous schanze is the Wolf's Lair located near the town of Rastenburg in the north-eastern part of Poland. This military installation was Adolf Hitler's command headquarters from which he commanded Operation Barbarossa. | https://en.wikipedia.org/wiki/Schanzen |
Insect chemoreception involves many families of genes, including odourant/pheromone binding proteins (OBP/PBPs), chemosensory proteins (CSPs), odourant receptors (ORs), ionotropic receptors (IRs), and sensory neuron membrane proteins (SNMPs), which play irreplaceable roles in mediating insect behaviors such as host location, foraging, mating, oviposition, and avoidance of danger. However, little is known about the molecular mechanism of olfactory reception in Chilo sacchariphagus, which is a major pest of sugarcane. A set of 72 candidate chemosensory genes, including 31 OBPs/PBPs, 15 CSPs, 11 ORs, 13 IRs, and two SNMPs, were identified in four transcriptomes from different tissues and genders of C. sacchariphagus. Phylogenetic analysis was conducted on gene families and paralogs from other model insect species. Quantitative real-time PCR (qRT-PCR) showed that most of these chemosensory genes exhibited antennae-biased expression, but some had high expression in bodies. Most of the identified chemosensory genes were likely involved in chemoreception. This study provides a molecular foundation for the function of chemosensory proteins, and an opportunity for understanding how C. sacchariphagus behaviors are mediated via chemical cues. This research might facilitate the discovery of novel strategies for pest management in agricultural ecosystems. | https://doaj.org/article/539607d94f5148d890bef13aeff965e3 |
Novel Treatment Options in Mantle Cell Lymphoma With Gilles Salles, MD, PhD is organized by i3 Health.
Release: September 18, 2020
Expiration: September 17, 2021
Accreditation:
Physicians:
i3 Health designates this enduring activity for a maximum of 0.25 AMA PRA Category 1 Credits™.
Successful completion of this CME activity, which includes participation in the evaluation component, enables the participant to earn up to 0.25 Medical Knowledge MOC points in the American Board of Internal Medicine’s (ABIM) Maintenance of Certification (MOC) program. Participants will earn MOC points equivalent to the amount of CME credits claimed for the activity. It is the CME activity provider’s responsibility to submit participant completion information to ACCME for the purpose of granting ABIM MOC credit.
Physician Assistants:
American Academy of Physician Assistants (AAPA) accepts certificates of participation for educational activities approved for AMA PRA Category 1 Credit™ from organizations accredited by ACCME. Physician assistants may receive a maximum of 0.25 hours of Category 1 credit for completing this program.
Description:
An aggressive form of B-cell non-Hodgkin lymphoma, mantle cell lymphoma (MCL) is a challenging disease to treat, with a median overall survival of 6 to 7 years. Even in patients who achieve a complete response, recurrence and relapse are still frequent. In this episode of Oncology Data Advisor, Gilles Salles, MD, PhD, Chief of the Lymphoma Service at Memorial Sloan Kettering Cancer Center, joins i3 Health for a discussion that covers the efficacy of newly developed Bruton tyrosine kinase (BTK) inhibitor and chimeric antigen receptor (CAR) T-cell therapies, the management of adverse events associated with these treatments, updates on ongoing research, and advice for clinicians as they seek to optimize outcomes for patients with MCL.
Learning Objectives:
Upon completion of this activity, participants should be able to:
• Assess efficacy and safety of novel BTK inhibitor therapy for MCL
• Assess efficacy and safety of CAR T-cell therapy for MCL
Faculty:
Gilles Salles, MD, PhD
Chief of the Lymphoma Service
Memorial Sloan Kettering Cancer Center
Target Audience
Hematologists, oncologists, hematology/oncology advanced practitioners, and other health care professionals involved in the treatment of patients with MCL.
Fees
|Registration Type||Due Date||Price|
|Course Fee||17 Sep,2021||Free|
SpecialtiesOncology, Hematology Blood and Marrow Transplant
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Can First Impressions Be Deceiving?
According to one of my former boyfriends, he absolutely hated me when first we met. I have to say the feeling was mutual. I had just gotten off a red-eye from New York to London and was tired, cranky, and hadn’t showered. Our first impressions changed but researchers aren't so sure that they do.
After we got to know each other, however, we embarked on a yearlong, extremely satisfying relationship of mutual respect and appreciation, proving that first impressions don’t always last. Or do they? Researchers of psychology and behavior seem to think so. Their work has shed light on why we form first impressions and how they affect our relationships. But I wonder—are we doomed to live up to the image we project in the first thirty seconds of meeting someone, as these researchers claim?
Our brains consider many factors when forming first impressions. In general, we make associations between people and positive feelings. For example, the authors of an October 2008 study published in the journal Science found that people who held a hot cup of coffee for ten to twenty-five seconds before meeting someone rated their first impressions of the stranger more positively than those who held iced coffee. The subjects literally “warmed” to the people they were meeting because they associated the strangers with the comforting feeling of gentle heat.
Though the authors of this study did not speculate on the cause for the connection, evolutionary biology may be at play here. When we are happy and secure, we have less reason to feel threatened by strangers and are less likely to want to distance ourselves from them as a defense mechanism. In other words, if I’m not in danger of being hungry or cold, I don’t have to worry as much that you’ll steal the wood I need to make fire and I can be nice to you instead.
In addition to concrete feelings like warmth, our brains process a variety of sensations when we meet someone for the first time. Facial expressions are key—a smile versus a frown makes us register to others as a friend, not a foe—as are all the factors that affect our general levels of comfort and senses of security. Color and proportion matter because our brains register incongruities of any kind as jarring. If someone with a warm complexion is wearing cool colors, for example, or a set of clothes that doesn’t fit them well, our animal brains will tell us that something is amiss and dangerous, and we will form a negative impression associated with that person.
Because this reaction to others is so basic and primal, it happens very quickly. Research, as in the studies compiled in the book First Impressions, edited by Nalini Ambody and John Skowronski, suggests that we form a distinct impression within the first thirty seconds of meeting someone new. And yet these almost instantaneous reactions stay with us for a long time.
First impressions set a vicious cycle in motion. According to Max Weisbuch, a post-doctoral fellow in the psychology department at Tufts University, our first impression of someone colors our interpretations of that person’s ensuing behavior. This means that when there is ambiguity about the cause of a behavior, we choose to believe in what best agrees with our first impressions. For example, if we form an idea of someone as an aggressive person based on his facial expression upon meeting, we would attribute his talking loudly to anger rather than to a more benign reason, like his simply wanting to be heard over environmental noise. In turn, that raised voice becomes more “evidence” of our impression that the person is mean and aggressive.
This is why first impressions last so long; we are constantly refueling them with new perceptions that have been affected by the original. Only if we can break the cycle of collecting prejudicial evidence—as my former boyfriend and I apparently did—can we form new impressions that may be closer to reality.
If you want to make a good first impression—on a potential employer, a date, your boyfriend’s parents, etc.—mama’s wisdom still holds to be true. Smile, clean behind your ears, and don’t slouch. You want to make sure you’re projecting positivity in order to make the other person feel that you are a safe (in the evolutionary sense) person with whom they can build a relationship. Hygiene and good manners are factors in that projection.
Be warm and generous and work toward the other person’s comfort. If they’re happy, they’ll associate the feeling with you and keep coming back for more. Whether that means offering a comfortable seat, placing a reassuring hand on the person’s elbow when you say hello, or laughing at their jokes, do everything to project an aura of positivity about yourself. Dressing in warm colors, like golds and rich browns (avoid red, which reads as aggressive) and wearing clothes that fit you well also creates a sense of harmony and security.
And just to be on the safe side, it never hurts to have a pot of freshly brewed hot coffee at hand. | https://www.more.com/love-sex/dating/can-first-impressions-be-deceiving |
Fashion Forward (FFWD), Dubai’s regional fashion week, has announced the dates for its third edition. After two seasons, the event has positioned itself within the region and international scene for array of established and up-and-coming Middle Eastern designers.
“We couldn’t have asked for a better start to the FFWD journey than our first two seasons,” said Founder and CEO of FFWD, Bong Guerrero. “As we look ahead to 2014, we continue to grow and adapt, and strive to provide the finest platform upon which our regional designers can showcase their talents.”
As with season one and two, Fashion Forward’s third edition will provide a wealth of runway shows, talks, workshops and other interactive activities for the region’s fashion scene.
Fashion Forward’s third season will run from 10-13 April. | https://hauteliving.com/2013/12/fashion-forward-confirms-dates-third-season/431761/ |
The polymerase chain reaction (PCR) is a primer-mediated enzymatic amplification of specifically cloned or genomic DNA sequences (1). This PCR process, invented by Kary Mullis over 10 years ago, has been automated for routine use in laboratories worldwide. The template DNA contains the target sequence, which may be tens or tens of thousands of nucleotides in length. A thermostable DNA polymerase, Taq DNA polymerase, catalyzes the buffered reaction in which an excess of an oligonucleotide primer pair and four deoxynucleoside triphosphates (dNTPs) are used to make millions of copies of the target sequence. Although the purpose of the PCR process is to amplify template DNA, a reverse transcription step allows the starting point to be RNA (2, 3, 4, 5). | https://link.springer.com/protocol/10.1385%2F1-59259-038-1%3A569 |
Find your lovey and snuggle up for a short story. PJ’s and hot cocoa are optional. Geared to our youngest learners – ages six and under – and their families. | https://www.leobaecktemple.org/events/bedtime-with-bri-2020-04-21/ |
The tiol Press Day, which will be celebrated on November 16, will commemorate the role of the fourth pillar of democracy that has been playing a big part in bringing changes in the society. This day is an emblematic proof that in our country, this fourth pillar represents itself as a symbol of a liberated and reliable medium of expression.
The Press Council of India, which acts as a moral entity, started functioning as a regulatory body by acting as a medium which is not fettered by any exterl factors. It does not work under any influence or threat whatsoever and is keeping up its high standards as expected from a powerful medium. The Press Council has marked its presence as a distinctive entity which exercises a substantial say-so, over the mechanisms of the state in course of its duty to safeguard the independence of the press.
Press or media in their individual are of work for long are playing a big part in bringing changes in thoughts by influencing people towards positive aspects. This positivity in thoughts make the people think in the right direction in regard to the things happening in the society they live in. In addition to changing people’s mindset, this medium has even other big roles to perform as democracy’s fourth pillar.
The tiol Press Day, stresses on the importance of giving away honest and biased news that will act as a source of creating an atmosphere of informative and educative milieu in the country through which masses can be encouraged to be perilously conscious of the latest developments in the country. The liability of press, as assumed by many, does not end in the lookout for elucidating people’s tribulations. Fortutely, in the eon of information technology, apart from the task of seeking solutions for change in societal and opinioted growth in the society, this pillar of democracy imbibes the ideals of fair and equal dispensation of news and views.
It may be recalled that, the first press commission in its recommendations for the establishment of a press council in 1956, concluded that the best way for maintaining professiol jourlistic ethics laid in bringing into existence a body with statutory authority, a platform where the sole duty of the people associated with the industry would be to arbitrate. With this aim, the time-honored statutory body of the Press Council of India, since its inception, has not deviated from its goal.
The tradition of commemorating tiol Press Day dates back to the year 1977 when for the very first time, semirs on relevant topics started being held as mark of veneration of the event. To this day, every year semirs and conventions are being religiously organized to encourage the media to pursue its duties following the dictum of freedom with responsibility. To perpetuate the high values of freedom of speech as enshrined in the Constitution of India, this day is still being observed with great admiration.
It may be mentioned that the Father of the tion, Mahatma Gandhi spoke on the fundamental notion of self regulation of the Press Council of India.
Media positively has succeeded in nurturing the fundamental duties among the Indian people by preserving the composite heritage and tradition in its richness and by keeping up its policy of promoting democratic values of our country. Keeping up the core essence as a pillar of democracy, press or media since decades tried to safeguard the other pillars of our tiolistic values like social, constitutiol, economic and political freedom even in crucial circumstances of being threatened by both exterl and interl factors.
It may thus be assumed that in keeping up the good work of stirring the sense of right and wrong, to uphold tranquility and concord among the masses that rises above barriers of caste, religion, and sectiol wellbeing, the tiol Press Day will once again bring with it a fresh air of brotherhood that binds individuals in every sphere of their lives. As a guide of democratic principles, the Press Council of India, which helps in forming the right opinion by portrayal of authenticated and verified news and views, has constantly proved its assertive presence among the world press councils.
Therefore ,with earnest anticipation, this year we look forward to celebrate the day of November 16 with utmost pride to cherish the true ideals of democratic principles that personify press or media as a true icon of right to expression for safeguarding people’s right. | https://www.sentinelassam.com/news/tiol-press-day-an-epitome-of-free-and-responsible-press/ |
Marijuana use increases throughout the calendar year, with use up 13 percent on average at the end of each year (2015-2019) compared to the beginning, according to a new study published in the Journal Alcohol and Drug Dependence.
"We found that marijuana use is consistently higher among those surveyed later in the year, peaking during late fall or early winter before dropping at the beginning of the following year. We think this may be due, in part, to a 'Dry January' in which some people stop drinking alcohol or even stop using marijuana as part of a New Year's resolution,". "We're now in the time of year when people are the least likely to use marijuana."
Prior research shows that alcohol and drug use vary by time of year, with drug use often increasing during summer months, possibly due, in part, to social events. These seasonal variations can inform interventions -- for instance, studies show that programs to reduce heavy drinking among college students should begin during the summer.
To better understand seasonal trends in marijuana use, researcher and his colleagues analyzed data from 282,768 adolescents and adults who responded to the National Survey on Drug Use and Health from 2015 to 2019. The survey asked participants about their past-month use of marijuana and other substances, and the researchers estimated their use within each calendar quarter: January through March, April through June, July through September, and October through December.
Each year, as the calendar year progressed, marijuana use grew, increasing in summer and fall months before dropping as each New Year began. While 8.9 percent reported using marijuana in January through March, 10.1 percent reported using in October through December, a 13-percent relative increase.
These seasonal trends occurred independently of annual growth in marijuana use and were seen across nearly all groups surveyed, regardless of sex, race/ethnicity, and education level. Teens were one exception; their marijuana use grew in the summer but declined in the fall months back to winter and spring levels.
Recreational use may be driving the growth throughout the year, as similar small increases occurred among those living in states with and without legal medical marijuana, and among those without a prescription for medical marijuana. Seasonal marijuana use also increased among those who reported using other substances, including alcohol, nicotine, and especially LSD.
The researchers note that the consistent dip in marijuana use during winter months could be a result of a variety of factors: a lower supply this time of year from cannabis harvests, colder weather keeping people inside who usually smoke outdoors, or people quitting marijuana as a New Year's resolution.
"Ultimately, we hope that these findings can be utilized by researchers and clinicians alike". "Researchers studying marijuana use should consider seasonal variation, as surveys administered at the end of the year may yield different results than at the beginning of the year. And for those who wish to reduce marijuana use, it appears the best time for such targeting may be later in the year -- when use is highest.
Citation: Rajesh R Wakaskar (2021) How Adolescents used Drugs during the COVID-19 Pandemic, J Alcohol Drug Depend 9:370.
Received: 12-Nov-2021 Published: 30-Nov-2021
Copyright: ©2021 Rajesh R Wakaskar. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. | https://www.longdom.org/open-access/marijuana-use-typically-drops-at-the-beginning-of-the-year-then-climbs-in-summer-and-fall-88105.html |
You probably grew up eating the famous Campbell’s canned food that is now facing a major recall. 355,000 cans of SpaghettiO’s are suspected to have been affected after small bits of plastic were found inside.
From Delish:
Uh oh.
Campbell Soup Company just issued a voluntary recall of 355,000 cans of its SpaghettiOs, after consumers complained that they had found small pieces of red plastic inside. The plastic apparently peeled off of the cans’ lining.
According to NBC News, the company said that the plastic was only affecting a “small number of cans” in the U.S., but that it could be a “potential choking hazard.” The cans affected are the 14.2 ounce size, and have the date February 22, 2017 stamped on the base.
Trending: The 15 Best Conservative News Sites On The Internet
It’s been a long fall of recalls: Whole Foods recently pulled a number of products after a listeria scare, and prior to that, General Mills had a massive problem with green beans as well. But Campbell’s was excited over other news this week: company executives announced they were changing their chicken soup recipe. So much for celebration.
The company said that full refunds and exchanges would be offered.
Were you affected by this recall? Let us know in the comments! | https://rightwingnews.com/human-interest/this-popular-canned-food-is-being-recalled-because-its-a-choking-hazard/ |
By Michael Gaft, Renata Reisfeld, Gerard Panczer
The publication is dedicated to 3 varieties of laser-based spectroscopy of minerals, particularly Laser-Induced Time-Resolved Luminescence, Laser-Induced Breakdown spectroscopy and Gated Raman Spectroscopy. This re-creation provides the most new information, that have been got after the ebook of the 1st version ten years in the past either by way of the authors and by way of different researchers. in this time, in simple terms the authors released greater than 50 unique papers dedicated to laser-based spectroscopy of minerals. loads of new info were collected, either in primary and utilized features, that are awarded in new version.
Read or Download Modern Luminescence Spectroscopy of Minerals and Materials PDF
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Example text
1 The Concept of the Ligand Field Most of the electronic spectroscopy in minerals can be interpreted by the wellknown ligand field theory. The main luminescence centers in minerals are transition and rare-earth elements. The ground and excited levels in these cases are d and f orbitals, while d-d and d-f emission transitions are subjected to strong influence from nearest neighbors, so called ligands. The basic notion of a ligand field was first developed many years ago (Bethe 1929). It was supposed that the ions are undeformable spheres and the interactions, which take place between them, are due solely to the electrostatic potentials set by their charges.
1 Io 1 À αðλÞ ¼ ‘n ¼ ‘n T À1 t t IT ð2:5Þ The absorbance is defined as: log10 Ic IT ð2:6Þ In optical spectroscopy a sample is illuminated by monochromatic light with a varying wavelength. The optically active centers rise from the ground to the excited states with resulting appearance of the absorption band in the optical spectrum. Useful information may be obtained from the absorption spectroscopy, which reveals the excited energy levels. Nevertheless, it has to be noted that absorption technique is much less sensitive compared to luminescence.
Stimulated (or induced) emission can occur in the presence of light of the correct transition energy, incident upon the sample, acting as a stimulant for it to emit a photon of the same energy: 18 2 Theoretical Background À À M* þ h v c ! M þ 2 v c: ð2:10Þ Rate of induced emission in populating the state: ÀÀ Á f ¼ À Nf Bfi ρ v ; ð2:11Þ where Bfi is the Einstein coefficient of induced emission. 1 The Concept of the Ligand Field Most of the electronic spectroscopy in minerals can be interpreted by the wellknown ligand field theory. | https://illustratedfirstworldwar.com/books/modern-luminescence-spectroscopy-of-minerals-and-materials |
The rapid growth of social media has rendered opinion and sentiment mining an important area of research with a wide range of applications. We focus on the Greek language and the microblogging platform “Twitter”, investigating methods for extracting sentiment of individual tweets as well population sentiment for different subjects (hashtags). The proposed methods are based on a sentiment lexicon. We compare several approaches for measuring the intensity of “Anger”, “Disgust”, “Fear”, “Happiness”, “Sadness”, and “Surprise”. To evaluate the effectiveness of our methods, we develop a benchmark dataset of tweets, manually rated by two humans. Our automated sentiment results seem promising and correlate to real user sentiment. Finally, we examine the variation of sentiment intensity over time for selected hashtags, and associate it with real-world events.
Datasets
To implement and examine our methods we created a benchmark dataset with Greek tweets, along with a set of manually rated tweets for their sentiment intensity. We make this benchmark Greek dataset publicly available as a valuable resource for future research. The following image shows the most popular hash tags in our dataset.
Dataset Statistics
|Dataset Size||832.1 MB|
|Number of Tweets||4,373,197|
|Number of Users||30,778|
|Number of Hashtags||54,354|
|Hashtags (more than 1000 tweets)||41|
|Time Span||2-4-2008 until 29-11-2014|
Evaluation Dataset
In order to evaluate the results of our methods, we asked two volunteers (undergraduate students of Democritus University of Thrace) to manually rate a sample of tweets from our dataset. They rated each tweet (scale 0-5) for the six different sentiments examined in this paper (“Anger”, “Disgust”, “Fear”, “Happiness”, “Sadness” and “Surprise”), judging the sentiment that the user expresses through the tweet. The evaluation set that we created consisted of 681 tweets chosen randomly from 10 specific hashtags.
Number of tweets per hashtag in the evaluation
|Hashtag||No. of tweets||Hashtag||No. of tweets|
|#wc14gr||344||#kalokairipantou||55|
|#skouries||58||#panellinies2014||42|
|#gogreece||22||#gre||30|
|#dwts||35||#tedxath||35|
|#feelfantastic||35||#stinigiamas||35|
Inter – Rater Correlation of benchmark dataset
To assess the validity of our evaluation set, we calculated the inter-rater agreement between the two volunteers using Pearson’s linear correlation coefficient. We selected Pearson’s co-efficient instead of Cohen’s or Fleiss’ kappa (both more “standard” for measuring inter-rater agreement) because it is scaling and shift invariant, thus, helping to remove individual user biases. | http://hashtag.nonrelevant.net/index.html |
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Painting Styles
The journey from an empty piece of paper, to the rich detailed painting is long. It involves various steps of preparing the handmade paper, collecting the ingridients for the natural colours and last but not least the lines. The artists are working with four different paintings styles, like Line Painting, Colour Painting, Godhna/Tattoo Painting and Tantric Painting.
Line painting:
In line painting -in local language also called Kachni- numerous small straight lines are used. Sometimes line paintings contain colour as well.
Colour painting:
In colour painting after the sketch is done in paper or cloth, the figures are filled in with different colours. This is also known as Bharni.
Godhna painting:
In Tatoo, or Godhna painting body art motifs have been adapted into painting. Religious symbols, especially those with talismanic powers, geometric designs, nature motifs and fortuitous symbols like the swastika are popular.
Tantrik painting:
Tantric painting is distinguished from other style of Madhubani paintings because the subjects it depicts are based solely on religious texts and characters related to them. Tantric subjects include manifestations of Maha Kali, Maha Durga, Maha Saraswati, Maha Lakshmi and Maha Ganesh along with other Tantric symbols. | http://www.madhubaniart.co.in/ArtFormDetails.aspx?search=hlStyles |
BACKGROUND OF THE INVENTION
1. Field of the Invention
2. Description of the Related Art
SUMMARY OF THE INVENTION
BRIEF DISCRIPTION OF THE DRAWINGS
DETAILED DISCRIPTION OF THE PREFFERED EMBODIMENTS
(First embodiment)
(Second embodiment)
(Application example of V-groove grating mirror)
The invention relates to a V-groove grating mirror preferred for use with an external resonator type wavelength variable light source used in coherent light communication and measurement technical fields and an external resonator type wavelength variable light source using the V-groove grating mirror.
Available as an external resonator type wavelength variable light source is a light source of a placement technique called Rittman type wherein emission light from an end face of a side of a semiconductor laser where a antireflection coating is applied is converted into collimated light through a lens, a wavelength of the collimated light is selected through a diffraction grating for diffraction, and the diffracted light is reflected by a mirror and is again diffracted through the diffraction grating, then is fed back into the semiconductor laser through the lens (for example, refer to JP-A-5-267768, USP No. 5,319,668).
In the light source of the Rittman type placement technique as described above, if a general plane mirror 10 is placed at a normal position and light is fed back as shown in FIG. 7A, no problem arises; however, if an optical axis is inclined with respect to the plane mirror 10 or the plane mirror 10 is inclined with respect to the optical axis as shown in FIG. 7B, the reflected light goes in a different direction from the original optical path.
Therefore, hitherto, high accuracy has been required for placement of a mirror.
Likewise, a light source of Rittman type placement technique adopting a mirror whose surface is shaped like V at 90 degrees is known according to USP No. 5,594,744.
The mirror surface is shaped like V at 90 degrees, whereby if the V-shaped mirror 9 or an optical axis is inclined, light can be reflected in parallel with the original optical path because of the V-shaped surface of the mirror 9, as shown in FIG. 6A.
However, with the V-shaped mirror 9, as the incidence position of collimated light shifts from the center of the V-shaped surface, collimated (parallel) move distance of reflected light grows as shown in FIG. 6B and when the reflected light is fed back into a semiconductor laser (hereinafter, abbreviated as LD) 5 through a lens 6, the joint loss is increased as shown in FIG. 5; this is a problem.
It is an object of the invention to provide a V-groove grating mirror capable of providing reflected light as collimated light if the mirror or an optical axis is inclined and suppressing the collimated (parallel) move distance of reflected light to a small distance as much as possible.
It is also an object of the invention to provide an external resonator type wavelength variable light source using the V-groove grating mirror.
To the above ends, the invention according to first aspect is characterized by a V-groove grating mirror comprising reflecting faces with an arrangement like a grating, of a plurality of V grooves 2 each shaped like V at right angles in cross section on a base material 1, for example, as shown in FIG. 1.
In this way, according to the first aspect of the invention, the V-groove grating mirror comprises reflecting faces with an arrangement like a grating, of a plurality of V grooves each shaped like V at right angles in cross section, so that if the V-groove grating mirror or an optical axis is inclined, reflected light in parallel with the incidence light can be provided by means of the V-groove grating of the reflecting faces.
Moreover, a plurality of the V grooves are arranged like a grating at small pitches, so that the collimated (parallel) move distance of the reflected light can be suppressed to a small distance as compared with a V-shaped mirror in a related art.
The invention according to second aspect is characterized by the V-groove grating mirror according to the first aspect of the invention further comprising a reflection coating 3 formed on the surface of the V groove 2, for example, as shown in FIG. 1.
The invention according to third aspect is characterized by the fact that in the V-groove grating mirror according to the first aspect of the invention, the base material 1 is made of a light transmission material and the face opposed to the reflecting faces with the V grooves 2 arranged like a grating is an incidence plane 4, for example, as shown in FIG. 2.
According to the third aspect of the invention, the V-groove grating mirror is made of a light transmission material and the face opposed to the reflecting faces with the V grooves according to the first aspect of the invention arranged like a grating is an incidence plane, so that incidence light passing through an inside of the V-groove mirror is reflected by the V-groove grating and is emitted to an outside of the V-groove mirror.
The invention according to fourth aspect is characterized by the fact that in the V-groove grating mirror according to the first aspect of the invention, a pitch between one groove and the adjacent groove is in a range of from (d/1000) to d where d is the beam diameter of the incident light
a LD 5 formed on one end face with a antireflection coating 5a;
a lens 6 for converting emitted light from the end face of the LD 5 formed with the antireflection coating 5a into collimated light;
a diffraction grating 7 for selecting a wavelength of the collimated light provided through the lens 6 and diffracting the light; and
a mirror for reflecting the light diffracted through the diffraction grating 7 and feeding back the light again diffracted through the diffraction grating 7 into the LD 5 through the lens 6,
wherein a V-groove grating mirror according to the first, second, third, or fourth aspect of the invention is used as the mirror, for example, as shown in FIG. 3.
The invention according to fifth aspect is characterized by an external resonator type wavelength variable light source comprising:
According to the fifth aspect of the invention, the external resonator type wavelength variable light source uses the V-groove grating according to the first, second, third or fourth aspect of the invention as the mirror for reflecting the light diffracted through the diffraction grating and feeding back the light again diffracted through the diffraction grating into the LD through the lens, so that optical axis adjustment and incidence position adjustment of the mirror become unnecessary, a self-correction of an optical axis shift accompanying wavelength varying can be made, and alignment becomes easy to make as compared with use of the V-shaped mirror in the related art.
The invention according to sixth aspect is characterized by the fact that in the external resonator type wavelength variable light source according to the fifth aspect of the invention, the grating of the V-groove grating mirror 8 is placed in a direction orthogonal to a grating direction of the diffraction grating 6, for example, as shown in FIG. 3.
According to the sixth aspect of the invention, in the external resonator type wavelength variable light source according to the fifth aspect of the invention, the grating of the V-groove grating mirror is placed in the direction orthogonal to the grating direction of the diffraction grating, so that the diffracted light whose wavelength is selected through the diffraction grating can be reliably fed back into the LD by means of the V-groove grating mirror.
FIG. 1 is a perspective view to show a schematic structure of a V-groove grating mirror as an example incorporating the invention.
FIG. 2 is a perspective view to show a schematic structure of a V-groove grating mirror as another example incorporating the invention.
FIG. 3 is a perspective view to show a schematic configuration of an external resonator type wavelength variable light source incorporating the invention.
FIG. 4 is a side view to plainly show a relationship among the V-groove grating mirror of the invention, a LD, and a lens.
FIG. 5 is a side view to plainly show a relationship among a V-shaped mirror in a related art, an LD, and a lens.
FIGS. 6A and 6B show a V-shaped mirror in a related art; FIG. 6A is a side view to show the relationship with an optical path when the V-shaped mirror is placed at a normal position and FIG. 6B is a side view to show the relationship with the optical path when either of the V-shaped mirror and an optical axis is inclined.
FIGS. 7A and 7B show a plane mirror in a related art; FIG. 7A is a side view to show a relationship with an optical path when the plane mirror is placed at a normal position and FIG. 7B is a side view to show the relationship with the optical path when either of the plane mirror and an optical axis is inclined.
Referring now to the accompanying drawings (FIGS. 1 to 4), there are shown preferred embodiments of a V-groove grating mirror and an external resonator type wavelength variable light source using the V-groove grating mirror according to the invention.
First, structure of the V-groove grating mirror will be discussed.
FIG. 1 is a perspective view to show a schematic structure of a V-groove grating mirror as an example incorporating the invention. In the figure, numeral 1 denotes a base material, numeral 2 denotes a V-groove work face (V groove), and numeral 3 denotes a reflection coating.
As shown in the figure, the V-groove grating mirror comprises an arrangement like a grating, of a plurality of the V-groove work faces 2 (in the example shown five) each shaped like V in cross section with the inner angle of the V shape set to right angle (90 degrees) on one face of the base material 1 of a glass material, etc., and the reflecting films 3 formed on the V-groove work faces 2 as reflecting faces.
With the V-groove grating mirror, incidence light is incident on the reflection coating 3 on the V-groove work faces 2 and is reflected, as shown in the figure
2
Incidentally, the reflection coating 3 is made of aluminum (Al), gold (Au) or dielectric multilayer (SiO multilayer)
FIG. 2 is a perspective view to show a schematic structure of a V-groove grating mirror as another example incorporating the invention. In the figure, numeral 1 denotes a base material, numeral 2 denotes a V-groove work face (V groove), and numeral 4 denotes an incidence plane.
As shown in the figure, the V-groove grating mirror comprises an arrangement like a grating, of a plurality of the V-groove work faces 2 (in the example shown in the example, five) each shaped like V in cross section with the inner angle of the V shape set to right angle (90 degrees) on one face of the base material 1 of a light transmission material such as an optical glass and the incidence plane 4 of the face opposed to the V-groove work faces 2 as reflecting faces.
With the V-groove grating mirror, incidence light passing through the base material 1 from the incidence plane 4 is reflected by the V-groove work faces 2, as shown in the figure.
Next, a light source using the V-groove grating mirror as described above will be discussed.
A description is given by taking an external resonator type wavelength variable light source using a LD as an example, but the V-groove grating mirror of the invention can also be applied to a solid laser, etc.
In the V-groove grating mirror of the invention, V-groove grating pitch P is practical in the range of (d/1000) to d, preferably (d/100) to (d/3), if the beam diameter of the collimated light is d. In the embodiments, the beam diameter of collimated light d is 2 mm and the V-groove grating pitch P is (d/20).
FIG. 3 is a perspective view to show a schematic configuration of an external resonator type wavelength variable light source incorporating the invention. In the figure, numeral 5 denotes a LD, numeral 5a denotes an antireflection coating, numeral 6 denotes a lens, numeral 7 denotes a diffraction grating, and numeral 8 denotes a V-groove grating mirror.
As shown in the figure, the light source uses the V-groove grating mirror 8 shown in FIG. 1 as a mirror according to the Rittman type placement technique combined with the LD 5, the lens 6, and the diffraction grating 7, but may use the V-groove grating mirror shown in FIG. 2.
The V-groove grating mirror 8 comprises the grating of V-groove 2 placed in a direction orthogonal to the grating direction of the diffraction grating 7, as shown in the figure.
Since the V-groove grating mirror 8 comprising a plurality of the V-grooves 2 worked like a grating with the pitch of the V-grooves 2 made small with respect to the beam diameter of collimated light is used, if collimated light (diffracted light through the diffraction grating 7) is incident on any of the V-grooves 2 at small pitches, reflected light collimated (parallel) with the incidence light can be provided and the collimated (parallel) move distance of the reflected light can also be suppressed to a very smaller distance as compared with a V-shaped mirror in a related art.
Therefore, if the mirror 8 or the optical axis is inclined, the diffracted light whose wavelength is selected through the diffraction grating 7 can also be reliably fed back into the LD 5 by means of the V-groove grating mirror 8.
FIG. 4 plainly shows the relationship among the V-groove grating mirror 8, the LD 5, and the lens 6. The V-groove grating mirror 8 makes it possible to solve the problem involved in the V-shaped mirror 9 in the related art, namely, the problem of an increase in the joint loss when light is fed back into the LD 5 through the lens 6.
(1) Since the collimated (parallel) move distance of the optical axis is small, optical axis adjustment in the up and down direction in the figure is not required.
(2) Since the collimated (parallel) move distance of the optical axis is small, incidence position adjustment of the mirror 8 is not required.
(3) A self-correction of an optical axis shift in the up and down direction in the figure accompanying wavelength varying can be made.
(4) Alignment is easy to make as compared with the V-shaped mirror 9 in the related art.
According to the external resonator type wavelength variable light source using the V-groove grating mirror 8, the following advantages can be provided:
In the described embodiments, the V-groove grating mirror comprises an arrangement of five V-grooves, but the invention is not limited to it; the number of V-grooves is arbitrary and the V-groove grating mirror may comprise an arrangement of at least two or more V-grooves.
The material, shape, application, and the like of the V-groove grating mirror are also arbitrary and the specific detailed structure, etc., can also be changed wherever necessary, needless to say.
As described above, according to the V-groove grating mirror according to the invention of a first aspect, if the mirror or the optical axis is inclined, reflected light parallel with incidence light can be provided by means of the V-groove grating and the collimated (parallel) move distance of the reflected light can be suppressed to a small distance as compared with the V-shaped mirror in the related art.
According to the external resonator type wavelength variable light source according to the invention as claimed in claim 4, the V-groove grating mirror is used, whereby both optical axis adjustment and incidence position adjustment of the mirror become unnecessary, a self-correction of an optical axis shift accompanying wavelength varying can be made, and facilitating of alignment can be accomplished as compared with use of the V-shaped mirror in the related art. | |
Affine spatial transformation matrices are used to represent the orientation and position of a coordinate system within a 3 dimensional "world" coordinate system. Spatial transformation matrices can be used to map from one to another. They are often used in Kinematics.
Any combination of translation, rotation, scaling, reflection and shear can be represented by a single 4 by 4 affine transformation matrix:
|A =||
|
This matrix A can be used to transform any point / vector p to a new point / vector p'.
DCM (Direction Cosine Matrix): The upper left 3x3 area is the rotation / orientation / scale / shear sub-section. It is made of 3 sections:
Position: The upper right area translates position.
The 4th row is always [0, 0, 0, 1] to maintain transformation matrix format.
To apply the transformation, simply enter the desired values for the type of transformation (see below) and apply matrix math multiplication to the original point as a vector of x, y, z, and 1.
p' = Ap
Multiple translations can be applied sequentially, or can be merged into a single matrix operation by multiplying all the transformation matrixes together. Remember that unlike normal math, in matrix multiplication the order matters, and as applied here, this maintains the order of transformations.
|A =||
|
Where x, y, and z are the desired translation in each direction.
|A =||
|
Where Sx, Sy, and Sz are the desired scaling factor in each dimension. Note that if you want to scale in all three axis by the same amount, you can just change the lower right "1" to factor and leave Sx, Sy, Sz as 1.
Where theta
O is the desired rotation in radians around the given axis. These can be combined, by multiplying all three matrix together, and separate the "thetas" to three different variables:
|A =||
|
|A =||
|
|A =||
|
Note that these are "right handed" rotations. Positive angles of
O cause counter-clockwise rotation about an axis
as seen from a point on the positive side of the axis looking in toward the
origin.
These three transformations (in X, Y, and Z) can, theoretically, be applied in sequence to reach any orientation. This uses a set of three angles, which are referred to as Euler Angles.
Note that if you apply a rotation of 1/4 of a full turn around, for example, the X axis, then you have effectively aligned the other two axis, Y and Z, with each other. If you then apply any rotation around, for example, the Z axis, that would be exactly the same as rotation around the Y axes. This removes a degree of freedom from any further transformations, and is called "gimbal lock" which is one type of singularity. It is a limitation of Euler Angles.
To avoid this limitation, a better system for rotations in multiple axis can be developed by using Quaternions. These are 4 dimensional values where the extra dimensions are akin to complex numbers. Where a complex number has one real and one imaginary part, a quaternion has a vector component and 4 imaginary parts, called i, j, and k.
qw + i qx + j qy + k qz.
A quaternion holds the angles in the real and imaginary parts. Because they are all combined, any rotation around a combination of axis can be described. Quaternions can be converted into 3x3 rotational matrixes.
See also:
|1 - 2*qy2 - 2*qz2||2*qx*qy - 2*qz*qw||2*qx*qz + 2*qy*qw|
|2*qx*qy + 2*qz*qw||1 - 2*qx2 - 2*qz2||2*qy*qz - 2*qx*qw|
|2*qx*qz - 2*qy*qw||2*qy*qz + 2*qx*qw||1 - 2*qx2 - 2*qy2|
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<A HREF="http://techref.massmind.org/Techref/method/math/spatial-transformations.htm"> Spatial Transformation Matrix Math Methods</A>
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Gardening is a valuable skill, especially if you desire to save money in the grocery budget and aim to live a healthy lifestyle. You don't have to live on a large plot of land in order to grow your own produce either! Many people automatically think living in a house with a fenced in yard limits what they can grow. This is far from true. I wish I would have understood more about gardening when I lived in a suburban neighborhood. But I didn't, and because of that, our garden was a failure and I deemed it a waste of time.
Once we moved to Minnesota, my husband convinced me to give it another chance. I've been far more successful with this garden and each year it improves and yields more. Yes, the soil is better in Minnesota than it was in Colorado. Yes, we live on a few acres and can maintain a big garden. But no, these are not the sole reasons for its growth. Through trial and error my husband and I have learned some do's and don'ts in growing our own food. We've researched a few things, experimented a lot, and gotten advice from more experienced gardeners.
So you want to plant cucumbers? Before you get all excited and toss a bunch of seeds in the ground, learn how much one cucumber plant can potentially produce in a season. I did not do this. And my husband didn't warn me either. So I planted a forty foot row of cucumbers! I was all about making homemade pickles and having fresh cucumber salads. Little did I know, cucumbers (and other vine plants such as zucchini and squash) produce in the masses. And reproduce rapidly after picking the ripe ones. That forty foot row gave us more cucumbers than we knew what to do with. It would have given us enough to survive off of pickles alone for at least two years....okay, maybe I exaggerated a bit, but seriously. We had so many cucumbers! And the ones we didn't pick in time, grew to the size of firewood logs. That's not an exaggeration.
Knowing the sow to reap ratios of plants will help you estimate how many of a specific seed to plant. Some plants, such as cauliflower will grow one head and then it's done for the season. Broccoli, on the other hand, will grow a few big heads initially and then keep producing smaller heads throughout the rest of the season. Doing a little research before going out and buying your plants will save you time and money in the long run.
Some vegetables need very little attention apart from sunshine and water after being planted. Green beans are a prime example. These little vegetables live on hearty bushy plants that grow faster than the weeds around them. Onions, however, require consistent weeding because they grow at a slower rate and the weeds are quick to steal the much needed nutrients from the soil. If the onions can't get the nutrients they need, they'll only grow to the size of a golf ball and won't hold much flavor.
Other plants need to be pruned before they can grow large enough to hold their vegetables. This is a lesson I am just learning this year with my bell peppers. In past years, my peppers were smaller than average because the plants tended to drop them to the ground before they were full sized, and few peppers would grow back to replace the first ones. The plants themselves never grew very large either. Turns out, you're supposed to pinch off the buds of the first peppers on the plant. This triggers the plant to produce more buds while also giving it incentive to grow bigger. We found this out halfway through the season this year, so I'm excited to put this knowledge to use next year and see what difference it makes in my peppers!
I think having a general idea of what vegetables you want to preserve through canning, freezing, or dehydrating is a wise decision. Some vegetables are better fresh and preserving them can actually kill some of the nutrients our bodies need from them. Others preserve quite well and can help you stalk up on healthy options for the winter. Also, know what the best ways are for preserving each kind of veggie. Just like with their day to day care, each vegetable is unique. Canning is an excellent way to preserve green beans, while a vegetable such as broccoli is better off being frozen for future use.
Understanding the different styles of preserving and planning out which vegetables you want to put the work in to save will give you a solid battle plan for plotting out your garden. And if preserving isn't your thing, just plant a little of each of your favorite veggies and spend the summer and fall enjoying your own fresh produce!
Gardening doesn't have to be a chore. It can be a fun and relaxing. Make your garden a size manageable for you and only grow the things you enjoy. If you lack room in your yard for a bed garden, buy some pots and decorate here and there with various vegetable plants. The plants offer as much green and color as regular flowers, but these are edible! Let growing plants be a way to draw you outside during the warm weather months and to relieve the stress from a long day at work.
Spending time in nature is proven to reduce stress. Bringing a little nature into your backyard can do wonders for the soul.
Busy days and hectic schedules can be hard to keep up with. Here are some tips and lessons I've picked up along the way to make life a little more fun in the midst of crazy. | https://www.fromtheheartliving.com/lifestyle/lessons-for-growing-vegetables |
In computer science, versions are programs that stand for real-world situations. As an example, a computer system design can be made use of to develop a simulation of a nuclear reactor or a football stadium, and then determine where the most effective fire exits are, therefore boosting safety and security. An off-model personality is one that is far from the original resource material. Versions are not restricted to computer system software application; they can also be made use of to develop physical versions of real-world sensations, such as the climate.
A fundamental computer system has four major functions: input, processing, as well as storage. The input is processed according to the guidelines offered by the individual. Scientists create models based on principles of science to replicate real-world phenomena. The computer can be made use of to predict weather, train pilots, or model auto accident, to name a few usages. However, there are several kinds of computer system versions. To understand the differences in between both, let’s look at each of them in even more information.
They stand for a system
A version is a simplified depiction of a system that utilizes a symbols such as UML. Versions commonly include representations that represent certain elements of the system. Although these representations might be separate entities, they stay part of the design even if they are erased. By doing this, a model can be made use of to much better recognize the genuine system. It can likewise be used to enhance efficiency or minimize danger. But exactly how do we create and use versions?
One strategy to modelling is from a behavior viewpoint. This method is based on an understanding of the characteristics of a system and its communications with various other systems. Examples of such designs consist of activity layouts, make use of instance diagrams, and also series diagrams. Activity representations show activities that happen in a system. Sequence layouts and course diagrams describe communications in between systems. Association representations show connections among courses and state layouts describe just how the system reacts to occasions.
They can be used to predict end results
Anticipating versions are computer programs that forecast future occasions or variables based upon current worths. These designs are often utilized in the medical field to spot risky subjects for creating condition as well as to treat them early. Other uses anticipating versions consist of promoting patient-doctor interaction and also notifying healthcare solutions and also decision-making. A current review determined 363 research studies concentrated on cardiovascular disease prediction models. This is an encouraging area for scientists.
Numerous predictive versions are simple as well as do not take long to calculate. For example, retailers and financial institutions can compute the threat of an on the internet bank card application based on a predictive design. Similarly, insurance companies can use predictive models to evaluate the risk of a phishing website, and accept or deny the credit card application based on a prediction. Some anticipating designs are extra complicated, such as those used in quantum computer as well as computational biology. In these cases, a complicated anticipating model may take a couple of weeks to compute, however advances in calculating power enable faster calculations.
They can be made use of to assist emotionally deferred children
Earlier, the term “dementia” was an analysis term that suggested “separated groups of psychological performance.” This term was originated from very early IQ tests and also, because of this, got pejorative undertones in the preferred discussion. Nevertheless, as the field of psychological disabilities has progressed, it has shed its pejorative connotations as well as is currently extra precisely referred to as a developing disability.
There are some imperfections to this method, nevertheless. One of one of the most significant is the absence of developing sequence, regional uniqueness, as well as unique content for psychologically deferred kids. Educational program advancement for this populace relies upon boards who use previous programs to create products as well as lessons. The systems, therefore, are not tailored to the demands of psychologically retarded kids. The resulting curriculums often tend to be too wide, with few unique features. | http://www.directxscreensavers.com/2022/04/13/the-cheapest-method-to-earn-your-free-ride-to-modelling/ |
Cut all of the flaps off of the boxes with the x-acto knife to create boxes with one open side. Place duct tape along the raw edges of the box to enhance the stability and durability of the cardboard boxes.
Step 2
Arrange the boxes to plan the shelves. Plan at least three boxes per shelf.
The shelves (rows of boxes) will be stacked to create a shelving unit.
Step 3
Place the bottom shelf of boxes in a row on the floor. Apply hot glue to a short side of a box and glue it to another box to form a two-box unit.
Repeat to add another box to this to form a three-box unit. Add another box or two in the same fashion if you want a longer shelf.
Step 4
Repeat step 3 to make more shelves that are the same size as the first shelf row of boxes.
Step 5
Apply hot glue to the tops of the first shelf row and glue a second shelf row on top of the first shelf row. Repeat with more shelf rows, if desired, to finish the shelves.
Things You Will Need
- 3 Cardboard boxes per shelf
- Duct tape
- Hot glue gun
- X-Acto knife
- Contact paper (optional)
- Fabric (optional)
- Spray adhesive (optional)
Tips
- Do not place too much weight on these shelves because they are only cardboard.
- If desired, you could cover the outer edges of the cardboard boxes with contact paper or fabric. If you choose to cover the boxes with fabric, use a spray adhesive to affix the fabric to the cardboard. | https://homesteady.com/how-4854264-build-cardboard-shelves.html |
A Shot in the Dark (February 1, 1935)
Released on February 1, 1935: Based on the novel "The Dartmouth Murders" mysterious deaths at a college are investigated by an amateur sleuth.
Directed by Charles Lamont
Written by Charles Belden and Clifford Orr
The Actors: Charles Starrett (Kenneth Harris), Robert Warwick (Joseph Harris), Edward Van Sloan (Professor Bostwick), Marion Shilling (Jean Coates), Helen Jerome Eddy (Miss Lottie Case), Doris Lloyd (Lucille Coates), James Bush (Byron Coates and John Meseraux), Julian Madison (Charlie Penlon), Eddie Tamblyn (Bill Smart), Ralph Brooks (Sam Anderson), Robert McKenzie (the Sheriff), John Davidson (Professor Brand), Herbert Bunston (college President), George Morrell (Deputy Abe Barber), Broderick O'Farrell (Doctor Howell), Jane Keckley (Bostwick's housekeeper), Eric Mayne (Professor at service)
Free Download of the old movie A Shot in the Dark
RIGHT-Click your selection to Download (control key + click for mac)
Shot-In-The-Dark-1935.mp4 (325mb - 720x540 ipad/mobile)
Shot-In-The-Dark-1935.wmv (642mb - 720x540 for computers)
Happy Birthday . . . You're Dead!
College life is usually full of fun, mirth and just a little bit of education, but when death stalks the hallways of knowledge all bets are off. The first murder victim is a despondent student who is found hanging in the dorm room below his own . . . but an autopsy discovers a poison needle buried deep in his skull, fired by a strange gun. College student Byron Coates is going to turn 21 and inherit a fortune from a family trust, but on the eve of his birthday is murdered by someone who tries to make it look like suicide. The father of another student is visiting and is somewhat of an amateur criminologist and he chases down clues to the murder. Just as a fellow student is going to reveal the identity of a last minute visitor to the dead boy he is mysteriously killed by a poison needle shot deep into his skull. As more clues are revealed to us and we try to piece together the motive and the killer, but new clues confuse our theories until we arrive at what we believe will be the climax. The killer is trapped in a building and when cornered confesses to the second murder, but claims that he didn't commit the first murder. Just as he is about to reveal the identity of the first murderer he is shot in the back, and we are once again left with many delicious clues but precious little real evidence as to the killer. Pop a big bowl of white kernel popcorn with plenty of warm melted butter on it and head back to college for mystery, murder and mayhem. | https://free-classic-movies.com/movies-03c/03c-1935-02-01-A-Shot-in-the-Dark/index.php |
Q:
Is this a theorem in Statistics? If not, can anyone explain why this seems to be true?
It seems to me that the following is true:
If $c$ is a random variable with probability $p(c)$ and cumulative probability $P(c)$, then the probability of $P(c)$ is constant.
I have taken $N$ random values consistent with a probability function (in my test case it was a simple gaussian $p(x) = \frac{2}{\sqrt{\pi}}Exp(-x^2)$) for which the cumulative PDF is $P(x) = Erf(x)$. When I create the $N$ random variables, I plot the histogram and get back the gaussian which lets me know that the $p(x)$ is correct. Then, for each value of $c$ which I have created, I evaluate $P(c)$ and then plot the histogram of $P(c)$ which seems to be constant (~$1/N$). The more points I create, the closer it becomes a perfectly (less noisy) horizontal line and for deviations from the true $p(c)$, it moves away from a straight line.
I have included the matlab code below. Note that as we let $N$ become larger (on line 1), the resulting graph in figure 2 becomes more and more perfectly straight. If we, however, change line 13 and allow for rv = 0.5*rand(), then the resulting $p(c)$ deviates from the true gaussian and that deviation is reflected in figure 2 as well.
1 N = 50000;
2
3 cs = zeros(N,1);
4 maxPx = 0.0;
5 for i = 1:N
6 while(cs(i) == 0)
7 x = 10*(2*rand()-1);
8 Px = (2/sqrt(pi))*exp(-x^2);
9 if(Px > maxPx)
10 maxPx = Px;
11 end
12 rv = (2/sqrt(pi))*rand();
13 % rv = 0.5*rand();
14 if(rv < Px)
15 cs(i) = x;
16 else
17 end
18 end
19 end
20
21 figure(1);
22 [ns, xs] = hist(cs, 100);
23
24 plot(xs, ns, 'k.');
25 axis([min(xs) max(xs) 0 max(ns)]);
26
27 Ps = zeros(N,1);
28 for i = 1:N
29 x = cs(i);
30 Ps(i) = erf(x);
31 end
32
33 figure(2);
34 [ns, xs] = hist(Ps, 100);
35 plot(xs, ns, 'k.');
36 axis([min(xs) max(xs) 0 max(ns)]);
EDIT: included images
(1) taking N = 50,000
The gaussian distribution is:
for which the related probability is:
(2) Letting N grow larger to 5,000,000 we have
The gaussian distribution:
and the related probability:
(3) Finally, when we change the original function from the gaussian distribution
we have for the distribution:
and the probability:
A:
The error function is not a cumulative distribution function: it can take negative values, while a probability cannot. Correcting this simply requires a linear adjustment to your data.
For a sufficiently well-behaved random variable (for example, one with a strictly increasing continuous cumulative distribution function), your statement is true.
If the cumulative distribution function of random variable $X$ is $F(x) = \Pr (X \le x)$ and has an inverse $G(y) = F^{-1}(y)$ for $0 \lt y \lt 1$, then define a new random variable $Y=F(X)$ and note $G(Y)=X$.
Now consider the cumulative distribution function of $Y$. What you are looking at is $\Pr(Y\le y) = \Pr(F(X)\le y)$ which is equal to $\Pr(X \le G(y))$. This has a cumulative distribution function $F(G(y))$ on $0 \lt y \lt 1$.
$F(G(y)) = F(F^{-1}(y)) = y$, which is the cumulative distribution function of a standard uniform random variable. So $Y = F(X)$ is uniformly distributed.
| |
# Saturated model
In mathematical logic, and particularly in its subfield model theory, a saturated model M is one that realizes as many complete types as may be "reasonably expected" given its size. For example, an ultrapower model of the hyperreals is ℵ 1 {\displaystyle \aleph _{1}} -saturated, meaning that every descending nested sequence of internal sets has a nonempty intersection.
## Definition
Let κ be a finite or infinite cardinal number and M a model in some first-order language. Then M is called κ-saturated if for all subsets A ⊆ M of cardinality less than κ, the model M realizes all complete types over A. The model M is called saturated if it is |M|-saturated where |M| denotes the cardinality of M. That is, it realizes all complete types over sets of parameters of size less than |M|. According to some authors, a model M is called countably saturated if it is ℵ 1 {\displaystyle \aleph _{1}} -saturated; that is, it realizes all complete types over countable sets of parameters. According to others, it is countably saturated if it is countable and saturated.
## Motivation
The seemingly more intuitive notion—that all complete types of the language are realized—turns out to be too weak (and is appropriately named weak saturation, which is the same as 1-saturation). The difference lies in the fact that many structures contain elements that are not definable (for example, any transcendental element of R is, by definition of the word, not definable in the language of fields). However, they still form a part of the structure, so we need types to describe relationships with them. Thus we allow sets of parameters from the structure in our definition of types. This argument allows us to discuss specific features of the model that we may otherwise miss—for example, a bound on a specific increasing sequence cn can be expressed as realizing the type {x ≥ cn : n ∈ ω}, which uses countably many parameters. If the sequence is not definable, this fact about the structure cannot be described using the base language, so a weakly saturated structure may not bound the sequence, while an ℵ1-saturated structure will.
The reason we only require parameter sets that are strictly smaller than the model is trivial: without this restriction, no infinite model is saturated. Consider a model M, and the type {x ≠ m : m ∈ M}. Each finite subset of this type is realized in the (infinite) model M, so by compactness it is consistent with M, but is trivially not realized. Any definition that is universally unsatisfied is useless; hence the restriction.
## Examples
Saturated models exist for certain theories and cardinalities:
(Q, <)—the set of rational numbers with their usual ordering—is saturated. Intuitively, this is because any type consistent with the theory is implied by the order type; that is, the order the variables come in tells you everything there is to know about their role in the structure. (R, <)—the set of real numbers with their usual ordering—is not saturated. For example, take the type (in one variable x) that contains the formula x > − 1 n {\displaystyle \textstyle {x>-{\frac {1}{n}}}} for every natural number n, as well as the formula x < 0 {\displaystyle \textstyle {x<0}} . This type uses ω different parameters from R. Every finite subset of the type is realized on R by some real x, so by compactness the type is consistent with the structure, but it is not realized, as that would imply an upper bound to the sequence −1/n that is less than 0 (its least upper bound). Thus (R,<) is not ω1-saturated, and not saturated. However, it is ω-saturated, for essentially the same reason as Q—every finite type is given by the order type, which if consistent, is always realized, because of the density of the order. A dense totally ordered set without endpoints is a ηα set if and only if it is ℵα-saturated. The countable random graph, with the only non-logical symbol being the edge existence relation, is also saturated, because any complete type is isolated (implied) by the finite subgraph consisting of the variables and parameters used to define the type.
Both the theory of Q and the theory of the countable random graph can be shown to be ω-categorical through the back-and-forth method. This can be generalized as follows: the unique model of cardinality κ of a countable κ-categorical theory is saturated.
However, the statement that every model has a saturated elementary extension is not provable in ZFC. In fact, this statement is equivalent to the existence of a proper class of cardinals κ such that κ<κ = κ. The latter identity is equivalent to κ = λ+ = 2λ for some λ, or κ is strongly inaccessible.
## Relationship to prime models
The notion of saturated model is dual to the notion of prime model in the following way: let T be a countable theory in a first-order language (that is, a set of mutually consistent sentences in that language) and let P be a prime model of T. Then P admits an elementary embedding into any other model of T. The equivalent notion for saturated models is that any "reasonably small" model of T is elementarily embedded in a saturated model, where "reasonably small" means cardinality no larger than that of the model in which it is to be embedded. Any saturated model is also homogeneous. However, while for countable theories there is a unique prime model, saturated models are necessarily specific to a particular cardinality. Given certain set-theoretic assumptions, saturated models (albeit of very large cardinality) exist for arbitrary theories. For λ-stable theories, saturated models of cardinality λ exist. | https://en.wikipedia.org/wiki/Saturated_model |
---
abstract: 'A graph on $2k$ vertices is path-pairable if for any pairing of the vertices the pairs can be joined by edge-disjoint paths. The so far known families of path-pairable graphs have diameter of at most 3. In this paper we present an infinite family of path-pairable graphs with diameter $d(G)=O(\sqrt{n})$ where $n$ denotes the number of vertices of the graph. We prove that our example is extremal up to a constant factor.'
author:
- |
Gábor Mészáros[^1]\
Central European University\
=Meszaros\[email protected]=
title: 'Note on the Diameter of Path-Pairable Graphs'
---
Introduction {#introduction .unnumbered}
============
Given a fixed integer $k$, a graph $G$ on at least $2k$ vertices is [*$k$-path-pairable*]{} if for any pair of disjoint sets of vertices $X=\{x_1,\dots,x_k\}$ and $Y=\{y_1,\dots,y_k\}$ of $G$ there exist $k$ edge-disjoint paths $P_i$ such that $P_i$ is a path from $x_i$ to $y_i$, $1\leq i\leq k$. The path-pairability number of a graph $G$ is the largest positive integer $k$ for which $G$ is $k$-path-pairable. The motivation of setting edge-disjoint paths between certain pairs of nodes naturally arose in the study of communication networks. There are various reasons to measure the capability of the network by its path-pairability number, that is, the maximum number of pairs of users for which the network can provide separated communication channels without data collision (see [@Cs] for additional details). The nodes corresponding to the users are often called [*terminal nodes*]{} or [*terminals*]{}. A graph $G$ on $n=2m$ vertices is [*path-pairable*]{} if it is $m$-path-pairable, that is, for every pairing of the vertex set $\{x_1,y_1, \dots, x_m,y_m\}$ there exist edge-disjoint paths $P_1,\dots,P_m$ joining $x_1$ to $y_1$,…,$x_m$ to $y_m$, respectively. By definition, path-pairable graphs are $k$-path-pairable for $0\leq k\leq \lfloor\frac{n}{2}\rfloor$.
The three dimensional cube $Q_3$ and the Petersen graph $P$ are both known to be path-pairable. The graph shown in Figure 1 is the only path-pairable graph with maximum degree 3 on 12 or more vertices. Apart from such small and rather sporadic examples we only know few path-pairable families. Certainly, the complete graph $K_{2k}$ on $n=2k$ vertices is path-pairable. It can be proved easily that the complete bipartite graph $K_{a,b}$ is path-pairable as long as $a+b$ is even and $a,b\neq 2$. Particular species of the latter family, the star graphs $K_{2a+1,1}$ show that path-pairability is achievable even in the presence of vertices of small degrees. They also illustrate that vertices of large degrees are easily accessible transfer stations to carry out linking in the graphs without much effort. That motivates the study of $k$-path-pairable and path-pairable graphs with small maximum degree. Faudree, Gyárfás and Lehel [@3reg] gave examples of $k$-path-pairable graphs for every $k\in\mathbb{N}$ with maximum degree 3. Note that their construction has exponential size in terms of $k$ and is not path-pairable.
\[pic\]
{width="3cm"}
Unlike in case of $k$-path-pairability, the maximum degree $\Delta(G)$ must increase together with the size of a path-pairable graph $G$. Faudree, Gyárfás and Lehel [@pp] proved that if $G$ is a path-pairable graph on $n$ vertices with maximum degree $ \Delta$ then $n\leq 2\Delta^\Delta$. The theorem gives an approximate lower bound of $\frac{\log(n)}{\log\log(n)}$ on $\Delta(G)$. By contrast, the graphs of the above presented families have maximum degree $\frac{n}{2}$ or more. Kubicka, Kubicki and Lehel [@grid] investigated path-pairability of complete grid graphs and proved that the two-dimensional complete grid $K_a\times K_{b}$ of size $n=ab$ is path-pairable. For $a=b$ that gives examples of path-pairable graphs with maximum degree $\Delta=2a-2<2\sqrt{n}$. In the same paper they raised the question about similar properties of three-dimensional complete grids. Note that if path-pairable, the grid $K_m\times K_m\times K_m$ yields an even better example of size $n=m^3$ and maximum degree $\Delta=3(m-1)=O(\sqrt[3]{n})$.
We mention that one of the most interesting and promising path-pairable candidate is the $n$-dimensional hypercube $Q_n$. $Q_1=K_2$ is path-pairable while $Q_2=C_4$ is not as pairing of the nonadjacent vertices of the cycle cannot be linked. One can prove that the cube $Q_3$ is path-pairable, the question for higher odd-dimensions has yet to be answered (it was proved in [@F] that $Q_n$ is not path-pairable for $n$ even).
\[q\] The $(2k+1)$-dimensional hypercube $Q_{2k+1}$ is path-pairable for all $k\in\mathbb{N}$.
A common attribute of the known path-pairable graphs is their small diameter. For each pair $(x,y)$ of terminals in the examples above, the length of the shortest $x,y$ paths is at most 3. While terminal pairs of an actual pairing may not always be joined by shortest paths, small diameter gives the advantage of quick accessibility of the vertices and makes designation of edge-disjoint paths easier. The question concerning the existence of an infinite family of path-pairable graphs with unbounded diameter naturally arises. We use the notation $d(G)$ for the diameter of the graph $G$ and $d_{max}(n)$ for the maximal diameter of a path-pairable graph on $n$ vertices. We mention that if true, Conjecture \[q\] proves the lower bound $\log_2 n\leq d_{max}(n)$ for $n=2^{2k+1}$, $k\in\mathbb{N}$.
The main goal of this note is to study the largest possible diameter of paith-pairable graphs. We present a family of path-pairable graphs $\{G_n\}$ such that $G_n$ has $n$ vertices and diameter $O(\sqrt{n})$ for infinitely many values of $n$. We show that our construction is optimal up to a constant factor by proving the following theorem.
\[up\] If $G$ is a path-pairable graph on $n$ vertices with diameter $d\geq 20$ then $d\leq 6\sqrt{2}\cdot \sqrt{n}$.
For a subgraph $H$ of a graph $G$, $|H|$ denotes the number of vertices in $H$. The degree of a vertex $x$ and the distance of vertices $x$ and $y$ are denoted by $d(x)$ and $d(x,y)$, respectively. For additional details on path-pairalbe graphs we refer the reader to [@Cs], [@F] and [@pp].
Construction {#construction .unnumbered}
============
We construct our example of a path-pairable graph on $n$ vertices with diameter $O(\sqrt{n})$ by the graph operation called “blowing-up”.
Set an arbitrary pairing of the vertices of $G$. We accomplish the linking of the pairs in two phases. During the first phase, for each pair of terminals, we define a path that starts at one of the terminals and ends at some vertex in the class of its pair. If the ending vertex happens to be the actual pair of the terminal, we set this path as the joining path for the given pair, otherwise we continue with the second phase. If two terminals initially belong to the same class, then the pair simply skips the first phase of the linking. Direct our cycle $C_{2m}$ and the blown-up graph $G$ counterclockwise and label each pair $x,y$ such that there exists a directed $x\rightarrow y$ path of length at most $m$. We start building the above mentioned path for pair $(x,y)$ at vertex $x$. Fix $m$ edge-disjoint matchings $M_{1}^i,\dots,M_{m}^i$ of size $(4m+3)$ between every consecutive classes $S_i$ and $S_{i+1}$. For a pair of terminals $(x,y)$ lying in classes $S_i$ and $S_{i+d}$ (modulo $2m$) at distance $d$ ($1\leq d\leq m$), choose the edge of $M_{1}^{i}$ being adjacent to $x$ and label the other vertex adjacent to it by $p_1(x)$. In step $j$ for $2\leq j\leq d$ take the edge of $M_{j}^{i+j-1}$ being adjacent to $p_{j-1}(x)$ and label its other end by $p_{j}(x)$. Apparently, $y$ and $p_d(x)$ belong to the same class. Phase one ends by assigning a path $P_{xy} =
xp_1(x)\dots p_d(x)$ to each $(x,y)$ pair of terminals.
Observe that paths $P$ and $P'$ assigned to and starting at terminals $x$ and $x'$ of the same class do not contain a common vertex as they are given edges of the same matchings in every step. Now assume that edge $e=(x_{i,j}, x_{i+1,k})$ has been utilized by two paths $P_1$ and $P_2$. It means that $e\in M_{t}^i$ for some $1\leq t\leq m$ and that $P_1$ and $P_2$ must have started in the same class. However, in order to share an edge they also have to share a vertex which contradicts our previous observation. It proves that phase one terminates without edge-collision.
In phase two we finish the linking. For the terminal $y$ initially paired with $x$ and for the endpoint $p_d(x)$ of the path $P_{xy}$ (both vertices lying in $S_i$ for some $i$) consider the yet unused edges of the bipartite subgraph $H_i$ spanned by $S_i$ and $S_{i+1}$. As $d_{H_i}(y),d_{H_i}(p_d(x))\geq 3m+3$, there exists at least $2m+3$ different vertices $z_1,z_2,\dots,z_{2m+3}\in S_{i+1}$ such that $(y,z_k), (p_d(x),z_k)\in E(G), k=1,2,\dots,(2m+3)$. Observe that any vertex in $S_i$ is an endpoint of at most $m+1$ paths defined in phase one, hence out of the $(2m+3)$ listed candidates at most $(2m+2)$ could have been assigned to another pair $(y',p_{d'}(x'))$. It means $x$ and $y$ can be joined by the path $xp_1(x)\dots p_d(x)z_iy$ with an appropriate choice of $z_i$ from the list above. That completes the proof.
Proof of Theorem \[up\] {#proof-of-theorem-up .unnumbered}
=======================
Assume $G$ is a paith-pairable graph on $n$ vertices with diameter $d\geq 20$. Let $x,y\in V(G)$ such that $d(x,y)=d$. Define $S_i=\{z\in V(G): d(x,z)=i\}$ for $i=0,1,2,\dots,d$ and $U_i=\bigcup\limits_{j=0}^iS_j$. Set the notation $s_i=|S_i|$ and $u_i=|U_i|$. Note that there is no edge between any $S_i$ and $S_j$ ($i<j$) classes unless they are consecutive, that is, $j=i+1$. Also, we may assume without loss of generality that vertices belonging to consecutive $S_i$ sets are joined by an egde (adding edges between consecutive classes changes neither the diameter nor the path-pairability property of the graph). If $S_d$ contains vertices in addition to $y$, move them to $S_{d-1}$ by joining them to every vertex of $S_{d-2}$ as well as to $y$ in case they were not adjacent. Observe, that in our new graph $z\in S_i$ if and only if $d(y,z)=d-i$, $0\leq i\leq d$. Note again that, while our operation may change the distribution of the vertices among the $S_i$ classes, our newly obtained graph $G'$ has the same diameter as $G$ and is also path-pairable. We could even assume every $S_i$ class to be a complete graph (by adding the necessary edges) without changing the mentioned properties, though this would be a rather cosmetic operation that would simplify the structure of the graph but would not essentially contribute to the proof.
We introduce the notation $S'_i$ for $S_{d-i}$ and divide our sets into three parts creating left, middle and right segments $A,B$ and $C$ as follows:
------------------------------------------------------- -- ------------------------------------------------------------------------------------ -- --------------------------------------------------------
$A=\bigcup\limits_{i=0}^{\lceil\frac{d}{3}\rceil}S_i$ $B=\bigcup\limits_{i=\lceil\frac{d}{3}\rceil+1}^{\lfloor\frac{2d}{3}\rfloor-1}S_i$ $C=\bigcup\limits_{i=\lfloor\frac{2d}{3}\rfloor}^dS_i$
------------------------------------------------------- -- ------------------------------------------------------------------------------------ -- --------------------------------------------------------
Our main goal is to give a lower estimate on the size of $B$. We first prove the following lemmas:
\[l\] $s_{2k}+s_{2k+1}\geq k$ as long as $u_{2k+1}\leq \frac{n}{2}$.
We prove our statement by induction on $k$. Apparently, $s_0+s_1\geq 0$ and $s_2+s_3\geq 1$. Observe that the number of edges between $S_{2k+2}$ and $S_{2k+3}$ is at least $u_{2k+1}=\sum\limits_{i=0}^{2k+1}s_i$. Indeed, placing $u_{2k+1}$ terminals in $U_{2k+2}$ and their pairs in $V(G)-U_{2k+2}$ there must be space for at least $u_{2k+1}$ edge-disjoint paths passing from $S_{2k+2}$ to $S_{2k+3}$. By induction hypothesis $u_{2k+1} \geq \frac{1}{2}k(k+1)$ while the number of edges between the two classes is at most $s_{2k+2}s_{2k+3}\leq \big(\frac{s_{2k+2}+s_{2k+3}}{2}\big)^2$. It yields $\frac{1}{2}k(k+1)\leq \big(\frac{s_{2k+2}+s_{2k+3}}{2}\big)^2$, that is, $s_{2k+2}+s_{2k+3}\geq \sqrt{2k(k+1)}\geq k+1$ if $k\geq 1$.
$|A|,|C|\geq min\big(\frac{n}{2},\frac{d^2}{100}\big)$.
Assume $|A|<\frac{n}{2}$. Using Lemma \[l\] we know that $|A|=u_{\lceil\frac{d}{3}\rceil}=s_0+\dots+s_{\lceil\frac{d}{3}\rceil}\geq 0+1+\dots+\big\lfloor\frac{\lceil\frac{d}{3}\rceil}{2}\big\rfloor\geq\frac{d^2}{100}$. By exchanging the role of $x$ and $y$ the same reasoning shows that $|A'|\geq \frac{d^2}{100}$ if $|A'|<\frac{n}{2}$, where $A'=\bigcup\limits_{i=0}^{\lceil\frac{d}{3}\rceil}S'_i$. As $\lceil\frac{d}{3}\rceil+\lfloor\frac{2d}{3}\rfloor=d$, one can easily see that $C=A'$ which completes the proof.
If $\lceil\frac{d}{3}\rceil<t<\lfloor \frac{2}{3}d\rfloor$, the number of edges between $S_t$ and $S_{t+1}$ is at least $min\big(\frac{n}{2},\frac{d^2}{100}\big)$. As seen before, placing $ min\big(\frac{n}{2},\frac{d^2}{100}\big)$ terminals in $A$ and their pairs in $C$ the set $S_t$ has to be able to bridge $ min\big(\frac{n}{2},\frac{d^2}{100}\big)$ disjoint paths to $S_{t+1}$. The number of crossing edges between these two sets is at most $s_t\cdot s_{t+1}$. It means $\frac{s_t+s_{t+1}}{2}\geq \sqrt{s_ts_{t+1}}\geq min\big(\frac{\sqrt{n}}{\sqrt{2}},\frac{d}{10}\big)$. If $d\geq 16$, then $\lfloor\frac{2}{3}d\rfloor-\lceil\frac{d}{3}\rceil-2\geq \frac{d}{3}-\frac{10}{3}\geq 2$ and $B$ contains at least two different $S_i$ sets. That gives us the requested lower bound on $|B|$: $$|B|\geq\sum\limits_{t=\lceil\frac{d}{3}\rceil+1}^{\lfloor \frac{2}{3}d\rfloor-2}\frac{s_t+s_{t+1}}{2}\geq\big(\frac{d}{3}-\frac{10}{3}\big)min\big(\frac{\sqrt{n}}{\sqrt{2}},\frac{d}{10}\big)\geq \frac{d}{6}min\big(\frac{\sqrt{n}}{\sqrt{2}},\frac{d}{10}\big)$$ As $|B|\leq n$, our equation proves that $d\leq 6\sqrt{2}\sqrt{n}$.
Summary {#summary .unnumbered}
=======
We proved that the maximal diameter of a path-pairable graph on $n$ vertices has order of magnitude $O(\sqrt{n})$, that is, $\frac{1}{4}\sqrt{n}<d_{max}(n)<6\sqrt{2}\sqrt{n}$ if $n$ is sufficiently large. We mention that in Lemma \[l\] an even stronger result can be proved about $s_{2k}+s_{2k+1}$.
\[comp\] Given $\varepsilon>0$, $s_{2k}+s_{2k+1}\geq (2-\varepsilon)\cdot k$ holds for sufficiently large $k$, as long as $u_{2k+1}\leq \frac{n}{2}$.
This result with more careful calculation and elaborate analysis may help reducing the gap between the presented upper and lower bounds.
Acknowledgement {#acknowledgement .unnumbered}
===============
The author wishes to thank Professor Ervin Győri for his helpful suggestions, interest, and guidance. The author would also like to thank the anonymus referees for their valuable comments and corrections.
[9]{} L. Csaba, R.J. Faudree, A. Gyárfás, J. Lehel, R.H. Schelp, [*Networks Communicating for Each Pairing of Terminals*]{}, manuscript. R. J. Faudree, [*Properties in Pairable Graphs*]{}, New Zealand Journal of Mathematics 21 (1992), 91-106. R. J. Faudree, A. Gyárfás, J. Lehel, [*Three-regular Path-Pairable Graphs*]{}, Graphs and Combinatorics 8 (1992), 45-52. R. J. Faudree, A. Gyárfás, J. Lehel, [*Path-Pairable Graphs*]{}, Journal of Combinatorial Mathematics and Combinatorial Computing (1999) 145-157. E. Kubicka, G. Kubicki, J. Lehel, [*Path-pairable property for complete grids*]{}, Combinatorics, Graph Theory, and Algorithms, Vol. I,II (Kalamazoo,MI, 1996), 577-586, New Issues Press, Kalamazoo, MI, 1999.
[^1]: Research was supported by the Balassi Institute, the Fulbright Commission, and the Rosztoczy Foundation.
| |
Angle B measures 60° What is the measure of the angle that is complementary to angle B?
a. 30°
Angles 1 and 2 form a right angle.
Which word describes their measures?
c. complementary
Figure LMNO is a parallelogram.
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Angle BCE is supplementary to angle ACE.
Angle BCD is supplementary to angle BCE.
Angle BCD is congruent to angle ACE
Given: <1 is complementary to <2.
<2 is complementary to <3.
Prove: m<1 = m<3
What is the missing statement in step 3 of the proof?
b. m<1 + m<2 = 90°
What is the name of angles that are directly across from one another.
Vertical angles
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The innovations which have elevated the games industry over the last year haven’t just been about the free to play model. In fact, arguably the most important change has been the rise of games as a service and in particular the use of Data.
I’m lucky that for much of my career I was the games guy in Telecom companies so I was exposed to the love of data very early; but for many this topic is still new. In this post I plan to give you a quick starters guide to practical ways to use data to reduce player Churn and improve both revenues from Ads and in app purchases. More than that though I want to show how important it is to use data to create a dialogue with your players and allow you to respond to their changes as they become more engaged with your game.
First thing to understand is that players’ reactions and choices aren’t static; they fluctuate over time. There are patterns but these are specific to each game. If we want to understand how to motivate players effectively, we need to understand where in that journey they are and how different groups of people react at those lifecycle stages. I break these down into four sections, Discovery, Learning, Engaging*. Understanding what (and why) players actually do at these stages is key to determining our best response. In this session I will also go into more detail on the Engaging stage itself and look at the specific of Super-Engagement and Re-Engagement as well. A video of the webinar recorded on Tuesday, May 3rd 2016 can be found at the end of this blog.
Before we dive into the player lifecycle, we need to make sure we have a common set of terminology and an understanding of the kinds of data we can access and what they mean.
Type of Data What is is? How we can use it?
How Do We Capture Events?
In order to get the behavioral data we need, we capture the events or activity the player actually did in our game. Unlike qualitative research, we aren’t looking for opinions or vague memories of players; we need to know what specific actions/choices they actually made. To do that, we create a series of events which are typically player initiated trigger points which tell the game to capture some values.
For example, we might wish to capture that a player was shot in a FPS game. We might give that a name, say PlayerShot, and then store a range of variables with that event. This could include the Date and Time that the hit was resolved, an anonymized PlayerID, the X,Y,Z coordinates of their Avatar, the damage taken, and the anonymized Player ID of who fired the shot as well as the Session ID for that game.
Importantly we don’t have to capture everything. There are some kinds of data which are static reference information. For example, the specific position in a specific map. As long as the version of the map used at that time is known, then X,Y,Z coordinates alone can be used to create a heatmap later. We can also infer a lot of data from other events as long as there is some connecting information. For example, we don’t need to capture the Level that the player is using for that game in every event or even a list of all the players in that session. We can capture that information with a specific Start Session events and use the associated Session ID to allow us to identify everything that happened in that specific game session.
Notice we want the players to remain anonymous. We don’t want or need to spy on our players, but we do need to understand how the game plays across all players.
What Events Should We Capture?
Because we are trying to understand the Lifecycle of our players it’s important to think of the game events in terms of the timeline in which I might encounter them. I find it useful to map out the player experience from the flow of the first time user and separately from the flow of the repeat user. Personally, I’m not necessarily looking for every button press, I’m looking for moments which include meaningful choices. There is an approach used by the Food industry called HACCP. I wrote about this for Develop Online, so I won’t go into detail here, but in essence the point is that we are looking for the “Hazards” such as whether they churn (i.e. leave the game) but also trigger points for more positive action such as paying for an IAP or watching a Video Ad.
It’s also important to recognised that the data we collect will be incomplete, for example if the battery dies or the player switches to a phone call – we will probably not get the last upload. This is less of a problem with a server-based game but it’s never 100% and the compromise is that the game can’t be played offline; impacting our chance for them to create habits of play.
From creating events in this way we can infer a huge amount of information. For example, if we want to know the percentage of players who complete a level we can count the number of GameMenuLaunch events with the number of LevelComplete. But we can also get smarter with our analysis. We can look at how many people completed a specific ObjectiveID in a specific LevelIDSelected and compare that to the number of LevelComplete in the subsequent level to find out if skipping objectives in earlier levels have a particular impact on performance later.
It’s not just about comparing events in terms of number, but by looking at the timestamps of specific activities in our game we can identify other deeper issues. For example, if we start to notice that the amount of time spent on the menu page starts increasing, this might be warning sign that they are about to Churn or that changes to your menu page are confusing players.
Data capture like this can be very powerful, however, the way you capture information will be inherently biased towards your understanding of the way the game is meant to be played. This means that we have to constantly review our metrics. The biggest issue is that we can’t capture what players will do or might have done. That might seem obvious, but we will be using insights from analytics to inform our design decisions. If it’s true that only 2% of players spend in a free to play game, then that means we don’t know what would have triggered the other 98% to spend. There might not be anything that would have convinced them, but the point I’m making is that the data we capture cannot ever be complete and that means we haves to consider statistical significance and be very wary of assuming causation rather than correlation. Looking at the lifecycle of a player helps us mitigate this, because we can break down each decision stage and look for ways to increase the likelihood of converting players at each stage. It’s all about asking the right questions at the right time.
There are some great techniques out there to help us look at data as part of the player lifecycle. In particular one of the most useful is called Funnel Analysis. This method allows us to look at a set of players and identify how many of them go through to the next stage of the game. The most often quoted version is the ARM funnel.
With this we look at the number of players we acquire (often as total downloads, although the number of GameMenuLaunch is arguably more useful) through organic installs, direct advertising or virality. Then we compare that with the number of those players who also play the game on subsequent days. When we compare players on the second day (which I call D2 – others call D1) with players on the 7th day (i.e. D7) or the 30th day(d30) we can get a pretty good idea of what our retention looks like. Then comparing that with the % of players who pay, we get a good idea of our success in terms of monetization.
However, this doesn’t give me enough detail. So when running a game as a service, it can be useful to expand this funnel to reflect the player’s lifecycle – I call this the Service Funnel. This helps because it allows us to think about the role of the Engaged player as helping feed not only virality (which obviously has diminished over the last few years) but also the willingness of others to spend more in our game. This is why Freeloader players actually add hidden value in the game – as well as their income from, for example watching rewarded Video Ads.
This way we can better map the flow of the gameplay with the way that we engage and retain users; and more importantly look at the factors which create a Repeat purchase in the game.
Can We Make Better Games?
All this may seem quite commercial and dry, indeed there will be some designers who will think that this kind of approach kills creativity. Actually, the reverse should be true. This is about using evidence to create the most engaging game. We want our player to continue playing over time and if they feel good about spending in the game then they will want to spend money more than once (as long as we continue to give them value in doing so).
The breakdown of our game into stages of engagement matters and allows us to use gameplay, Ads and In-App Purchases to increase enjoyment of play.
However, data has to inform the designer, not become a barrier – qualitative research can help. Asking players and observing them using your game can be invaluable as long as you understand the findings are usually only useful to help you understand motives. Focus groups and online surveys help provide some insight but remember that players are essentially incapable of accurately telling you about what they did, let alone what they will do; but they can tell you how they feel about your game and why they made certain choices. However, this needs to be done in a formal setting – asking your friends down the pub isn’t usually that useful. Direct feedback can be very useful but again we have to be careful about how we use it as it will usually describe the game that the specific player would have made, not what the wider audience need. However, it’s always important to listen and understand.
Every game will be different, the following is what I’m generally looking for in terms of the performance of the game and the behaviour of players at each of the player lifestages for each. The key question is about how we get players into that stage and what we need to achieve to transition them to the next stage.
Discovery is the very initial transition stage from players becoming aware of the game to their action to install it on their devices. At this stage, it’s key for us to understand if we converting Players to Download; but also to actually play the game!
Attribution – we need to know not just which sources give us users; but which bring value for retention and monetisation as well. Where you can track these as separate custom segments and compare behaviour.
Downloads aren’t the end of the line – do you know what % Ever Launch the Game or how long it takes them from Launch of the App To playing the game?
Learning is the first time user experience for the player, but only ends when playing this game becomes routine. That’s vital, as we are looking to truly engage the player and help them become fans. The core question we must ask is if players understand how to play and how the game fits into their lifestyle!
What is the retention on the second day of play (I call this Day 2 Retention)? If we can’t get them back the next day, the game isn’t going to be interesting enough to them to pay for content. Even if this is a premium game abandoning the game so early is a bad sign.
What is the Frequency & Duration of Sessions? This is going to vary with each game and there is no one level which is ‘good’ or ‘bad’. However, what we are going to be interested in is how this rate changes over time.
Playing the Tutorial is rarely fun. But do we know what % Initiate Level 2? Or later levels. The rate and pace of unlocking new content can indicate the genuine interest in the game.
It’s often useful to keep track of the Last Position Played in a game session. This will often indicate natural breaks and places where you should have a ‘Call Back Action’ i.e. a reason to set an appointment to return the game at a later date.
At the Engaging Stage we really have a true fan. This is the point where we really need to focus on retention and expectation of value. As a designer, I value “Repeat Players and Payers”. I see one-time payers as a red flag that something is wrong with my monetization. Key to revenue generation is to create an expectation of value in the player. Show them the value of the items (often assisted by access to premium elements through rewarded video Ads). However, the key question we need to ask is: are they ready to pay?
The key metric is still retention. The impact of long term commitment on willingness to pay and how much is linked to how long they keep playing. This may sound cynical but it really isn’t. It’s a reminder that we need to make a game so good, so enjoyable that player will want to keep playing. What is your Day 7 Retention?
Every game is different so there are no hard and fast rules about % Conversion To Pay. However, it’s important that spending money in a game should feel great; and not victimise non-payers. Imaging playing Scissor-Paper-Stone. If I buy the Lizard-Spock upgrade this gives me more choices and all other players an exciting twist. But we can all still play together.
Just as during the learning phase, the frequency of Watching Video Ads can give great insight to the attractiveness of your IAP and if it rapidly changes, this can help identify a willingness to make the initial conversion to buy (or indeed a risk of churn). It’s likely that your biggest spenders will also be heavy ad users too.
Pay attention to the average level of success and failure of your players during the Engagement phase. Frustration can be a great driver to commitment, but it can quickly turn against you.
Pay attention to any obvious deviation from Average Success/Failure Ratio.
Another neat trick is to map the first point in the game where a player decided to watch a Rewarded Ad or paid for IAP. It can be really useful to understand why – not just where. We need the experience to be fabulous if we want them to do it again!
One of the things that separates a game with good IAP from a premium game is the ability to people who really fall in love with the game to want to invest more into the experience. Again, this should not be a cynical exercise but we should be able to work out through analytics not just which Players are ready to get serious, but more importantly what is it they really value.
Again, my personal choice is to look at Day 15 Retention; this is a very serious level of commitment regardless of whether they are spending or not.
Keep an eye on the % of Repeat IAP Purchase as well as the frequency & changes in Types of Purchase. This is important as especially of you can identify better value goods which help extend retention even further. This about why the goods are likely to give players a reason to return. It’s important that players feel they really got value for what they spent money on.
Also look at the level of social communication. Social capital is an essential element to the perceived value of items in your game, just as much as their gameplay value.
Players will stumble and fall out of the game, but we should look for ways to stimulate their enjoyment and ensure that they continue to get the most from the experience. If we can pre-empt a problem or frustration point, perhaps even offer new content this can help players keep doing what they love about our game. But sometimes they may just be ready to churn.
Players are normally stimulated by an update, but look at the different cohorts of players to see if some fail to re-engage. Any change in behaviour after updates can provide important insight.
Watch out for the Rate of Change in frequency of sessions, purchase/Video Ad behaviour, Social Communication, even the Average Success/Failure Ratio. If this slows, can you act to stimulate interest?
How would those players rate the game now they no longer play? This is key for me. Because the more players who leave and remain happy, the more better chance they will return for the next game.
I got a question regarding the suggested usage of a Session ID and AnonPlayerID, I assume these are supposed to be supplied by the developer or does Unity analytics have some sort of mechanism to generate unique IDs across the user base? Do you have any suggestions for games that don’t run on a server to generate these unique IDs across the user base?
Any1 still remembering the days, when games were not about analytics, player engagement and free2play? for some reason I cannot imagine any of the people behind f.e. Zak McKracken think about this stuff.
And those are the games that stick in my mind the most.
The ones which concentrated on the experience.
Less on the marketing possibilities.
Feels like everyone is developing tools rather than games.
Agree with you and feel very happy to see there are people who thinks this way.
3 years ago & no answer?
I think especially in mobile game development there is nearly no chance for you if you do not also concentrate on aspects like analytics. There are so so much games released every day and the awareness from the customer for single products is just not given. You need to catch and hold them from the very first moment on. For that you need to analyze how to achieve that.
But overall I dont think that this is a bad thing. In the end it is always about the users experience and this will make them stay in the game and rewarding ad vids do not have to disturb that, maybe can support that.
That does not mean I generally support that Free2Play model. There are some extreme examples where I think that games are really tools like you said. That is when a game starts to bring in a kind of addiction of the player to the game (what in the first moment is not bad) but then instead of really rewarding the player for watching ads or spending money, they punish player for not spending money and not watching ads with harsh waiting times for example. Like EAs dungeon keeper or clash of clans and its millions clones. That is not a good direction in my opinion, but successful nonetheless.
I think guys back then wished they had this kind of tools to improve the game experience. Tools like this can be used for good and for bad. The fact is that games as a service really need this sort of analysis to be viable but I’m sure analytics are widely used by all sorts of developers making all sorts of games in all platforms. They are another tool to help developers be successful in this incredibly competitive industry.
This has nothing to do with the blog post.
hehe – nice and not too far off the truth I suspect. | https://blogs.unity3d.com/cn/2016/05/03/analytics-the-player-lifecycle/ |
Table of Contents :
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Garuda Wisnu Kencana Cultural Park (Indonesian: Taman Budaya Garuda Wisnu Kencana) or GWK, is a cultural park located at Ungasan, Badung in the island of Bali, Indonesia about 10–15 minutes driving from Ngurah Rai International Airport. It is devoted to the Hindu God Vishnu, and his mount, Garuda, the mythical bird who became his companion. Planned to be established of a landmark or mascot of Bali, construction of the giant statue of Lord Vishnu who was riding his mount Garuda, as high as 120 meters is currently going on. The park has a land area of about 60 hectares and located at an altitude of 146 meters above ground level or 263 meters above sea level. In the area there is also a Statue of Garuda which is directly behind the Plaza Wisnu is Garuda Plaza where the statue as high as 18 meters Garuda placed temporarily. At this moment, Garuda Plaza becomes the focal point of a large corridor of carved limestone pillars covering over 4000 square meters of open space i.e. Lotus Pond . The colossal limestone columns and monumental sculptures of Lotus Pond Garuda make a very exotic space. With a space capacity capable of accommodating up to 7000 people, Lotus Pond has earned a good reputation as the perfect venue for holding major events and international events. There is also a statue of Vishnu's hand which is part of the statue of Lord Vishnu. This is one step closer to completing the complete Garuda Wisnu Kencana statue. This work is placed temporarily in the area of Tirta Agung .
Contents
1 Garuda Wisnu Kencana monument 2 Recreation site 3 Multi role site 4 See also 5 External links 6 References
Garuda Wisnu Kencana monument Designed to be the Indonesia’s tallest statue, Garuda Wisnu Kencana was inspired by Hindu mythology about the search for Amerta (the elixir of life). According to this myth, Garuda agreed to be ridden by Lord Wisnu in return for the right to use the elixir to liberate his enslaved mother.The idea was not without controversy, and religious authorities on the island complained that its massive size might disrupt the spiritual balance of the island, and that its commercial nature was inappropriate, but some groups agree with the project, because it will make new tourist attraction over barren land. In 2013 Nyoman Nuarta and PT Alam Sutera Realty Tbk (IDX:ASRI) joined to build villas and apartments in the GWK area in exchange for Rp150 billion ($14.4 million). Nuarta plans to spend Rp20 billion to make another bust and to move the existing bust to another site 300 meters from the original site. It plans to spend additional Rp29 billion to make the new statue of stainless steel instead of galvanized steel as proposed previous design. The 75-m tall, 65-m wide statue, sits atop a lofty pedestal that will bring the total height of the monument to 121-m, nearly 30-m taller than the Statue of Liberty of the United States. The completed monument will be about as tall as a 21-story building. It will weigh 4,000 tons, thus, making it the heaviest statue in the country. The statue is made of copper and brass sheeting, with a stainless steel frame and skeleton, as well as a steel and concrete core column. The outer covering alone measures 22,000 square m in size. The crown of Wisnu will be covered with golden mosaics and the whole statue will have a special lighting arrangement. The monument is expected to be completed by 2018. Recreation site
Wisnu Plaza is the highest land in GWK area where our temporary place is the most important part of the statue of Garuda Wisnu Kencana statue of Vishnu. At certain times of the day, there will be some traditional Balinese performance with magnificent statues of Vishnu as a backdrop. Due to its high location, you can see the surrounding panorama. The statue of Vishnu, as the focal point of Wisnu Plaza, is surrounded by fountains and well water near the sacred he said never dry even in the dry season. Parahyangan Somaka Giri is placed next to the statue of Vishnu. This is where the water is located, which historically has been trusted by the people of the area as a blessing with a powerful magical power to cure his illness and ask the gods for rain during the dry season. Because of its location on the high ground (on a hill), this natural phenomenon is considered a saint and a local is believed to be holy water. Street Theater is the starting point and end of the visit to Garuda Wisnu Kencana Cultural Park. Here we can find many shops and restaurants in one place and where all the celebrations take place. You can get Bali souvenir and GWK merchandise especially at GWK Souvenir Shop and Bali Art Market . We can even find Balinese spa and aromatherapy products in this shop. While here, why not try Balinese foot reflexology after a long walk. We can taste good food at the best prices just in our food court, Theater Food, and our newest restaurant, The Veranda with all you can eat package. At several times a day, we can enjoy shopping and eating while accompanied by the performance of Bali especially like barong, rindik and parade. Lotus Pond is the largest outdoor area in Garuda Wisnu Kencana (GWK) and Taman Budaya, most likely, in Bali. Thus, Lotus Pond is the right place and only for holding large-scale outdoor events. Over the years, GWK has been trusted for large scale held, both nationally and internationally, events at Lotus Pond such as music concerts, international gatherings, major parties. Lotus Pond is a unique place with limestone pillars on the sides and a magnificent statue of Garuda in the background. Lotus Pond starts from the lotus.The lotus is the main symbol of beauty, prosperity and fertility. Vishnu also always carries lotus flowers in his hands and almost all the gods of the Hindu gods who sit on the lotus or carry flowers.Some interesting facts are that the lotus plant grows in water, has its roots in illus or mud, and spreading flowers in the air above. Thus, the lotus symbolizes human life as well as that of the cosmos. The lotus root drowned in the mud is a material life. Stalks passing through water symbolize existence in the astral world. Flowers floating on the water and opening to the sky are a mild spiritual emblematical. Indraloka Garden:This park is named Indraloka after the heaven of Indra God because of the beautiful panoramic view. Indraloka Garden is one of the most favorite places in Garuda Wisnu Kencana to hold small, medium-sized parties, wedding gathering and ceremonies. We can see the view of Bali from above Indraloka Garden. Amphitheater:Amphitheater is an outdoor venue for special shows with well-designed acoustics. Every afternoon you can watch the famous and free Kecak dance that is around 18.30 s / d 19.30 WITA . Even this Kecak Dance can be collaborated with other regional dances. Tirta Agung:Tirta Agung is the perfect outdoors space for medium events. You can also visit the Wisnu Hand statue, part of the Garuda Wisnu Kencana statue located nearby.
Multi role site The site has been chosen to host many large-scale and international events. Every day, it attracts "up to 3,000 visitors".
On 20 February 2011, British heavy metal band Iron Maiden played the first rock concert at the venue in the Final Frontier Tour with ticket sold out to over 7,000 fans. On 17 August 2011, American rock band Paramore played the second date of their Pacific Rim Tour at the venue. This was also their last tour in 2011. On 25 July 2012, the Opening Banquet of the 60th World Convention of the Full Gospel Business Men's Fellowship International was held here. | http://theinfolist.com/php/SummaryGet.php?FindGo=Garuda_Wisnu_Kencana |
I have an integer linear program (ILP) with some variables $x_i$ that are intended to represent boolean values. The $x_i$'s are constrained to be integers and to hold either 0 or 1 ($0 \le x_i \le 1$).
I want to express boolean operations on these 0/1-valued variables, using linear constraints. How can I do this?
More specifically, I want to set $y_1 = x_1 \land x_2$ (boolean AND), $y_2 = x_1 \lor x_2$ (boolean OR), and $y_3 = \neg x_1$ (boolean NOT). I am using the obvious interpretation of 0/1 as Boolean values: 0 = false, 1 = true. How do I write ILP constraints to ensure that the $y_i$'s are related to the $x_i$'s as desired?
Logical OR: Use the linear constraints $y_2 \le x_1 + x_2$, $y_2 \ge x_1$, $y_2 \ge x_2$, $0 \le y_2 \le 1$, where $y_2$ is constrained to be an integer.
Logical NOT: Use $y_3 = 1-x_1$.
Logical implication: To express $y_4 = (x_1 \Rightarrow x_2)$ (i.e., $y_4 = \neg x_1 \lor x_2$), we can adapt the construction for logical OR. In particular, use the linear constraints $y_4 \le 1-x_1 + x_2$, $y_4 \ge 1-x_1$, $y_4 \ge x_2$, $0 \le y_4 \le 1$, where $y_4$ is constrained to be an integer.
Forced logical implication: To express that $x_1 \Rightarrow x_2$ must hold, simply use the linear constraint $x_1 \le x_2$ (assuming that $x_1$ and $x_2$ are already constrained to boolean values).
XOR: To express $y_5 = x_1 \oplus x_2$ (the exclusive-or of $x_1$ and $x_2$), use linear inequalities $y_5 \le x_1 + x_2$, $y_5 \ge x_1-x_2$, $y_5 \ge x_2-x_1$, $y_5 \le 2-x_1-x_2$, $0 \le y_5 \le 1$, where $y_5$ is constrained to be an integer.
Cast to boolean (version 1): Suppose you have an integer variable $x$, and you want to define $y$ so that $y=1$ if $x \ne 0$ and $y=0$ if $x=0$. If you additionally know that $0 \le x \le U$, then you can use the linear inequalities $0 \le y \le 1$, $y \le x$, $x \le Uy$; however, this only works if you know an upper and lower bound on $x$. Or, if you know that $|x| \le U$ (that is, $-U \le x \le U$) for some constant $U$, then you can use the method described here. This is only applicable if you know an upper bound on $|x|$.
Cast to boolean (version 2): Let's consider the same goal, but now we don't know an upper bound on $x$. However, assume we do know that $x \ge 0$. Here's how you might be able to express that constraint in a linear system. First, introduce a new integer variable $t$. Add inequalities $0 \le y \le 1$, $y \le x$, $t=x-y$. Then, choose the objective function so that you minimize $t$. This only works if you didn't already have an objective function. If you have $n$ non-negative integer variables $x_1,\dots,x_n$ and you want to cast all of them to booleans, so that $y_i=1$ if $x_i\ge 1$ and $y_i=0$ if $x_i=0$, then you can introduce $n$ variables $t_1,\dots,t_n$ with inequalities $0 \le y_i \le 1$, $y_i \le x_i$, $t_i=x_i-y_i$ and define the objective function to minimize $t_1+\dots + t_n$. Again, this only works nothing else needs to define an objective function (if, apart from the casts to boolean, you were planning to just check the feasibility of the resulting ILP, not try to minimize/maximize some function of the variables).
For some excellent practice problems and worked examples, I recommend Formulating Integer Linear Programs: A Rogues' Gallery.
For NOT, no such improvement is available.
Not the answer you're looking for? Browse other questions tagged linear-programming integer-programming or ask your own question.
Why is linear programming in P but integer programming NP-hard?
Does every NP problem have a poly-sized ILP formulation?
Is 0-1 integer linear programming NP-hard when $c^T$ is the all-ones vector?
How to solve an ILP problem with conditions in an objective function? | https://cs.stackexchange.com/questions/12102/express-boolean-logic-operations-in-zero-one-integer-linear-programming-ilp/12118 |
This can be a difficult strand unit to track through the 1999 Primary Mathematics Curriculum; in junior and senior infants it is titled Extending patterns, in first and second classes it becomes Extending and using patterns, in third and fourth it is called Number patterns and sequences, and in fifth and sixth classes it morphs into Rules and properties. However, it is always from the strand Algebra (check out the maths curriculum glance cards here for more detail) and a summary of the objectives reveals how pattern is at the heart of the strand unit at every class level:
Junior Infants to Second Class > Algebra > Extending patterns >
- identify, copy and extend patterns (colour, shape, size, number)
- recognise patterns (including odd and even numbers; predict subsequent numbers)
- explore and use patterns in addition facts (1st & 2nd)
Third & Fourth Class > Algebra > Number patterns and sequences >
• explore, recognise and record patterns in number
• explore, extend and describe (explain rule for) sequences
• use patterns as an aid in the memorisation of number facts
Fifth & Sixth Class > Algebra > Rules and properties >
• identify relationships and record verbal and simple symbolic rules for number patterns
Different types of patterns
So then, are patterns and sequences the same thing? Actually, there are two main types of patterns:
- Repeating patterns: repetitions of symbols, shapes, numbers etc., that recur in a specific way.
- Increasing (growing) and decreasing (shrinking) patterns: An ordered set of shapes or numbers that are arranged according to a rule. Typically, the term sequence is used to describe this type of pattern as opposed to a repeating pattern
Repeating Patterns
A repeating pattern should have a clearly identifiable core, i.e. the shortest sequence that repeats. It is a good idea to use the terminology of “core” right from the infant classes so that the children understand what is being asked of them.
Children can often copy patterns without even recognising or identifying the core. However, to become competent in accurately extending repeating patterns, it is vital to identify the core. Ways that the children can become more adept at this include verbalising the pattern out loud (“red, blue, yellow, red, blue, yellow, …”) and/or using concrete materials to model the pattern (see below); in this way it is easier to identify the core of the pattern by breaking it apart and laying it alongside the subsequent parts of the pattern to ensure that they match. This strategy of breaking and matching can also be used to help children check have they extended the pattern correctly. It is also for this reason that cubes and links can often be the easiest concrete materials to use for replicating and extending patterns and are preferable initially to threading beads, pegs on a pegboard etc . These can be used instead when the children are ready to progress to more challenging tasks.
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Sequences
Unlike repeating patterns, sequences are more linear; they tend to increase or decrease in specific ways; thus they are also referred to as increasing and decreasing patterns. The way in which the terms (the individual parts of the sequence) are ordered is governed by a rule. Similar to repeating patterns, the children need to be able to identify this rule in order to extend the sequence. To help the children identify the rule in numerical sequences, they should be encouraged to examine each given term and identify what has happened between it and the next term i.e. did the numbers increase, decrease, by how much etc.? They should then record this (e.g. +2, –3) below and between the terms, as modelled in the Operation Maths Pupil books and Discovery books.
Even when extending sequences in their copies, the children should be encouraged to leave an empty line below the sequences, to allow space for them to write in the differences between the terms.
Once the children are comfortable with sequences that increase/decrease by the same amount each term, they can progress to sequences that increase/decrease in varying but repetitive amounts, e.g. +2, +3, +2, …
Odd and even numbers
Odd and even numbers are an example of an increasing pattern/sequence, as the difference between each term is +2. Most children will find it simple enough to recognise odd and even numbers; typically they will tell you that if a number ends in 2, 4, 6, 8 or zero, is it even and, if it does not, it is odd. It is one thing to identify odd and even numbers in this way, but it’s another thing to visualise the numbers and appreciate why they are odd or even. Using concrete materials or pictorial representations is vital for the children to really develop their number sense
and their appreciation of how odd and even numbers interact.
As well as activities like that shown above, pairwise ten frames (ie ten frames placed vertically, as opposed to the more typical horizontal arrangement) can also be useful to model odd and even numbers. Such concrete or pictorial presentations can then be used to show how the total of an odd number and an odd number will always be even as the non-paired cube of both now join to form a pair. These activities also reinforce how only whole numbers can be classified as odd or even, even though a child may incorrectly assume that 1.2 is even, since it ends in 2.
Identifying patterns in addition and multiplication facts
Through concrete activities and activities using the 100 square, it is hoped that the children begin to appreciate the patterns in number facts and that that various groups of multiples are characterised by certain properties eg.:
- When adding/subtracting 10 on the 100 square the answer is always the number directly below/above the starting number.
- When adding/subtracting 9 on the 100 square the answer is always the number diagonally below left /diagonally above right the starting number.
- The multiples of 10 always end in zero
- The digits in the multiples of 9 always total 9 or a multiple of 9 (e.g. 9 × 11 = 99 and 9 + 9 = 18), etc.
Not only will knowledge like this greatly aid their ability to identify and recall the basic number facts, but it will also improve their ability to check and identify errors in their own, and others’ work (e.g. ‘173 × 5 = 858 … hmm, that can’t be correct because multiples of 5 should always end in 5 or 0; I need to do that again’).
Using T-charts to organise information
In the senior classes, when the rules governing the sequences are becoming more complex and less obvious, T-charts can be a very useful way to organise and present the information. They can be particularly useful to help highlight the patterns and how these patterns are developing (see below). They can also provide the children with a clear way to explain how they see the rule. Therefore, the children should be encouraged to use them as a problem-solving strategy as much as is suitable. | http://operationmaths.ie/digging-deeper-patterns-sequences/ |
The turning points of the curve shown in Figure 3 may not be in the correct vertical positions, but such points must occur based on the properties of the derivative. In the introductory animation at the top of this page and the Excel worksheets included in this demo the derivative curve is sketched and simultaneously three choices for an approximate graph of the function are sketched.
ShapeShop also provides 2D drawing assistance using a new curve-sketching system based on variational contours. A wide range of models can be sketched with …
17/10/2008 · Re: Curve Sketching Help! For addition and subtraction, it’s mainly manually adding and subtracting ordinates (y-values). Once you can work out where the addition/subtraction of two ordinates lie, you should notice a pattern at certain regions of the curve and can join the dots to figure out the curve.
4.4 Graphing by Addition of Ordinates To graph the sum of two ftmctions, first graph each function, then graphically add the yr-values of key point.
4-2 Chapter 4: Curve Sketching. e. If f and g are functions that have derivatives, then the composite function has a derivative given by f. If u is a function of x, and n is a positive integer, then 9. a. b. c. 10. a. Let so the graph has a vertical asymptote at . b. Let so the graph has a vertical asymptote at . c. Let There is no solution, so the graph has no vertical asymptotes. d. Let so
To help with the sketching of the curve, plotting a few easy points helps. In the above case, noting the -value at and will help with sketching the curve. The next example illustrates the use of the formulae related to the cosine function.
§3.5 B—Curve Sketching Summary For a function f ′, the combined information of the first derivative f and the second derivative f ′′ can tell us the shape of a graph.
Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The answers to questions like these are of great interest to corporations that process and package food and other goods. In this chapter, you will investigate and apply the relationship between the derivative of a function and
A Level Maths Sketching Curves Whodunnit? Instructions and answers for teachers. These instructions should accompany the OCR resource ‘Sketching
Section 10.1, Relative Maxima and Minima: Curve Sketching 1 Increasing and Decreasing Functions We say that a function f(x) is increasing on an interval if the values of f increase as x increases
4/10/2015 · Technically an extension 2 topic, but very worthwhile for everyone.
curve y=f(x), the x-axis and the ordinates x=a and x=bx=b.. Vikasana – CET 2012. In this chapter we shall discuss the use of definite integrals.In computing areas bounded by simple curves such as straight lines, circles, parabolas and other conics. Vikasana – CET 2012. Let y=f(x) be a finite and continuous curvecurve inin thethe intervalinterval [b][a,b].. ThenThen thethe area between the
Mathematics Notes for Class 12 chapter 8. Application of
https://youtube.com/watch?v=FWdDSCip69U
(PDF) Sketching Complex Generalized Cylinder Spines
3.1.1 Curve Sketching Strategies When examining the expression for a function it is usually a good idea to be able to sketch the function roughly. There are a number of ways to go about this, as follows; Let the independent variable (usually T or t) be zero and see what value that gives for the dependent variable (usually U or voltage or current). This will give the point where the function
Tutorial By Kimeshan Naidoo Page 1 Curve Sketching Calculus In order to sketch a curve when given an equation, critical points of the curve must
o Sketching cubic functions (calculating x-and y-cuts and the turning points) and finding the equation, if the sketch is given o Determining the equation of a tangent to a curve
Redox Titration Curves. To evaluate a redox titration we need to know the shape of its titration curve. In an acid–base titration or a complexation titration, the titration curve shows how the concentration of H 3 O + (as pH) or M n + (as pM) changes as we add titrant.
c. y =(x – 5) 1 3 d d y x = 1 3 x – 5 – 3 2 = d d y x ≠ 0 The critical point is at (5, 0), but is neither a maximum or minimum. The tangent is not parallel to x-axis.
Curve Sketching Name_____ ID: 1 Date_____ Period____ ©^ n2z0h1]5R TKRuLtoaM oSHo[fktJwwatrjek FLELaCn.D S vAOlDl` brQiWgDhdtYsz Urreps[evrmvfeFd`.-1-For each problem, find the: x and y intercepts, asymptotes, x-coordinates of the critical points, open intervals where the function is increasing and decreasing, x-coordinates of the inflection points, open intervals where the …
A full lesson on sketching cubics, quartics and reciprocal functions. Incorporates the use of GeoGebra and the Casio fx-991EX Classwiz. Please do leave feedback! Thank you….
A C1 worksheet with examination style questions on the topic Sketching Curves. Each question has the value of marks it is worth on the right hand side. The worksheet can be used as homework, in-class or even an assessment.
In polar coordinates there is literally an infinite number of coordinates for a given point. For instance, the following four points are all coordinates for the same point. For instance, the following four points are all coordinates for the same point.
Created by T. Madas Created by T. Madas Question 2 (**+) The curve C has equation y x a b= − +( )2, where a, b are positive constants. By considering the two transformations that map the graph of …
1. Graphs 1.1. Critical points on a curve 1.2. Reflecting graphs on the coordinate axes 1.3. Translation of graphs – addition and subtraction of ordinates 1.4.
Sketching the Titration Curve To evaluate the relationship between a titration’s equivalence point and its end point we need to construct only a reasonable approximation of the exact titration curve.
(863) 6/02 1 CURVE SKETCHING This is a handout that will help you systematically sketch functions on a coordinate plane. This handout also contains definitions of relevant terms needed for curve sketching.
Youhavealreadystudiedfunctionsof1variableatschool. Youdeveloped curve–sketching skills and a knowledge of calculus for functions of the type y= f(x).
Section 4.5: Curve Sketching Using our knowledge of how the derivative affects the shape of a graph along with some additional information we can sketch a function’s graph.
Step 9. Determine the Intervals of Concavity. Concavity is a measure of how curved the graph of the function is at various points. For example, a linear function has zero concavity at all points, because a line simply does not curve.
Curve sketching with the HP Calculator Chris Longhurst Roger Porkess . Investigating a family of curves This investigation demonstrates the power of hand held technology to make the properties of a wide selection of curves readily accessible. This raises the question of what properties should mathematics educators now be regarding as important. Exercise 1 (i) On your calculator draw circles
A Guide to Curve Sketching – Download as PDF File (.pdf), Text File (.txt) or read online.
https://youtube.com/watch?v=5NlUyUdLbNE
An Introduction to Curve Sketching University of Liverpool
curve y=f(x), the x-axis and the ordinates x=a and x=bx=b.. In this chapter we shall discuss the use of definite integrals.In computing areas bounded by simple curves Vikasana – CET 2013 such as straight lines, circles, parabolas and other conics. Let y=f(x) be a finite and continuous curve in the interval [a,b][a,b].. Then the area between the curve y=f(x), x-axis and two ordinates at the
X2 T04 03 cuve sketching – addition, subtraction, multiplication and division 1. (D) Addition & Subtraction of Ordinates
An Introduction to Curve Sketching Mark Holland Cartesian and polar coordinates: brief notes Recall that a point P : (x,y) in the plane can be represented by giving its horizontal distance x and
parts and adding or subtracting the appropriate integrals. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. After reading this text, and/or viewing the video tutorial on this topic, you should be able to: •find the area beween a curve, the x-axis, and two given ordinates; •find the area between
INDEX — UNIT 3 TSFX REFERENCE MATERIALS 2014 ALGEBRA AND ARITHMETIC Surds Page 1 Algebra of Polynomial Functions Page 2 Polynomial Expressions Page 2
Mathematics Notes for Class 12 chapter 8. Application of Integrals Let f(x) be a function defined on the interval [a, b] and F(x) be its anti-derivative. Then, The above is called the second fundamental theorem of calculus. is defined as the definite integral of f(x) from x = a to x = b. The numbers and b are called limits of integration. We write Evaluation of Definite Integrals by
Curve Sketching VCC Library and Learning Centre
Curve sketching is a way of interpreting a given equation as a diagram. More specifically, this allows students to visually represent limit behaviours in a way that follows university mathematics. | https://h2salive.com/author/justin/page/2/ |
Q:
$x^2+y^2=2z^2$, positive integer solutions
Determine all positive integer solutions of the equation $x^2+y^2=2z^2$.
First I assume $x \geq y$, and I have $x^2-z^2=z^2-y^2$. Then I have $(x-z)(x+z)=(z-y)(z+y)$, but from here, I don't know how it can help me to describe solutions (I know that there are infinitely many).
A:
Just a start:
Note that $$\left(\frac{x-y}{2}\right)^2 + \left(\frac{x+y}{2}\right)^2=\frac{x^2+y^2}{2}=z^2.$$
And $\frac{x-y}{2}$ and $\frac{x+y}{2}$ are integers (why?)
So you need to find solutions to $u^2+v^2=z^2$.
| |
Thru-hiking is a form of hiking that involves completing a trail in its entirety. This end-to-end form of travel could be as short as a 50-mile trail, or as long as the mind can imagine. But some of the best-known thru-hikes are the Appalachian Trail, the Pacific Crest Trail, and the Continental Divide Trail, which collectively are referred to as The Triple Crown.
The way people approach thru-hiking is as varied as the characters you’ll meet on trail. Here we cover some of the different styles of thru-hiking, along with their pros and cons, in hopes you’ll find a style that’s right for you.
Northbound (NOBO) Hiking
Northbound (NOBO) hiking is the most popular style of thru-hiking. This strategy involves beginning at the southern terminus of a trail and hiking north. On the Appalachian Trail, many hikers choose to head in this direction because the terrain becomes progressively more difficult as you hike forward. Pacific Crest Trail and Continental Divide Trail hikers commonly also hike in this direction in order to bypass the desert before the heat of the summer.
Southbound (SOBO) Hiking
Southbound (SOBO) hiking involves beginning a trail from the north, and hiking south. This style of thru-hiking is often ideal for those who prefer to escape large hordes of hikers. Late-season hikers also often head this direction since it may get them through the parts of the trail prone to receiving snow before the weather turns.
Flip-Flopping
Flip-flopping is a style of thru-hiking that involves a significant change in direction. For example, a hiker may begin traveling north, only to skip up to the top of the trail and head south. Hikers might choose to travel this way to hit high snow areas or areas of drought at a lower-risk time. This might also be a good way to thru-hike if you prefer to see a mixture of thru-hiking culture, because you’ll encounter both SOBO and NOBO hikers along your journey.
Don’t have the time for a full thru-hike? ⬇️
Section Hiking
Section hiking involves splitting a long-trail into parts in order to tackle the whole thing over the course of multiple trips. Some hikers might section hike in 8 to 10 mile increments. Others might take a week to complete a longer section of trail. This is a great option if you have limited time, or you live close to a long trail.
Lashing
Lashing (long ass section hiking) is, as the name implies, a longer version of section hiking. You’re most likely to encounter Lashers on trails like the Appalachian Trail, the Pacific Crest Trail, and the Continental Divide Trail because of their sheer length. A Lasher might plan to hike 500 miles, which, in the context of a 2,000-mile trail, isn’t considered to be a thru-hike, but it’s still a very long section of that thru-hike. Lashers sometimes choose to hike this way because of deadlines or time restrictions.
A Word on Hiking Speeds and Mileage
Thru-hikes can be completed at a number of different speeds. A conventional thru-hike of the Appalachian Trail, the Pacific Crest Trail, or the Continental Divide Trail may take anywhere between 4 to 6 months for the standard hiker (this strategy usually involves hiking 15-25 miles per day).
And then there’s a subset of hikers that love to travel quickly. Competitive hikers may attempt to set a Fastest Known Time (FKT) by hiking or running a trail faster than the previous record setter. This hiking method often involves jogging sections of trail, or hiking for 15-20 hours per day.
What’s your favorite style of thru-hiking? Why? Do you have another style to share that we missed? Leave a comment below! | https://www.garagegrowngear.com/blogs/trail-talk/thru-hiking-styles |
---
abstract: 'Let $L/K$ be a finite Galois extension of complete discrete valued fields of characteristic $p$. Assume that the induced residue field extension $k_L/k_K$ is separable. For an integer $n\geq 0$, let $W_n({{\mathcal O}}_L)$ denote the ring of Witt vectors of length $n$ with coefficients in ${{\mathcal O}}_L$. We show that the proabelian group $\{H^1(G,W_n({{\mathcal O}}_L))\}_{n\in {{\mathbb N}}}$ is zero. This is an equicharacteristic analogue of Hesselholt’s conjecture (see [@lh]) which was proved in [@hp] when the discrete valued fields are of mixed characteristic.'
address:
- 'School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India'
- 'School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India'
author:
- Amit Hogadi
- Supriya Pisolkar
title: 'Remark on equicharacteristic analogue of Hesselholt’s conjecture on cohomology of Witt vectors'
---
Introduction {#intro}
============
Let $K$ be a complete discrete valued field with residue field of characteristic $p > 0$. $L/K$ be a finite Galois extension with Galois group $G$. Suppose that $k_L/k_K$ is separable. When $K$ is of characteristic zero, Hesselholt conjectured in [@lh] that the proabelian group $\{H^1(G,W_n({{\mathcal O}}_L))\}_{n\in {{\mathbb N}}}$ vanishes, where $W_n({{\mathcal O}}_L)$ is the ring of Witt vectors of length $n$ with coefficients in ${{\mathcal O}}_L$ (w.r.t. to the prime $p$). As explained in [@lh], this can be viewed as an analogue of Hilbert theorem $90$ for the Witt ring $W({{\mathcal O}}_L)$. This conjecture was proved in some cases in [@lh] and in general in [@hp]. In this paper we show that a similar vanishing holds when $K$ is of characteristic $p$. The main result of this paper is as follows.
\[main\] Let $L/K$ be a finite Galois extension of complete discrete valued equi-characteristic fields with Galois group $G$. Assume that the induced residue field extension is separable. Then the pro-abelian group $
\{H^1(G,W_n({{\mathcal O}}_L))\}$ is zero.
In order to prove this conjecture one easily reduces to the case where $L/K$ is a totally ramified Galois extension of degree $p$ (see [@hp Lemma 3.1]). We make the argument in [@hp] work in the equicharacteristic case using an explicit description of the Galois cohomology of ${{\mathcal O}}_L$ when $L/K$ is an Artin-Schreir extension (see Proposition \[h1\]).
We remind the reader that a proabelian group indexed by ${{\mathbb N}}$ is an inverse system of abelian groups $\{A_n\}_{n\in {{\mathbb N}}}$ whose vanishing means that for every $n\in {{\mathbb N}}$, there exists an integer $m>n$ such that the map $$A_m\to A_n$$ is zero (see [@jannsen Section 1]). This is clearly implies the vanishing of ${\mathop{\varprojlim}\limits}_n H^1(G,W_n({{\mathcal O}}_L))$. It also implies the vanishing of $H^1(G,W({{\mathcal O}}_L))$ (with $W({{\mathcal O}}_L)$ being considered as discrete $G$-mdoule) by [@hp Corollary 1.2].
One may also consider an analogue of Theorem \[main\] when $K$ is of equi-characteristic zero. However, in this case, all extensions $L/K$ are tamely ramified and the vanishing $$H^1(G(L/K),W_n({{\mathcal O}}_L))=0 \ \forall \ n\geq 0.$$ can be easily deduced from the fact that ${{\mathcal O}}_L$ is a projective ${{\mathcal O}}_K[G]$ module (see [@frohlich I. Theorem(3)]).
[**Acknowledgement**]{}: We thank the referee for several useful comments and suggestions.
Cohomology of integers in Artin-Schreier extensions
===================================================
Let $K$ be a complete discrete valued field of characteristic $p$ as before. Let ${{\mathcal O}}_K$ and $k$ denote the discrete valuation ring and residue field of $K$ respectively. Let $L/K$ be a Galois extension of degree $p$. Recall that the ramification break (or lower ramification jump) of this extension, to be denoted by $s=s(L/K)$, is the smallest non-negative integer such that the induced action of ${{\rm Gal}}(L/K)$ on ${{\mathcal O}}_L/m_L^{s+1}$ is faithful, where $m_L$ is the maximal ideal of ${{\mathcal O}}_L$ ([@fesenko], II, 4.5). Thus unramified extensions are precisely the extensions with ramification break equal to zero. We recall the following well known result.
[(]{}see [@hasse] or [@lt Proposition 2.1][)]{} \[v\_K(f)\]Let $L/K$ be a Galois extension of degree $p$ of complete discrete valued fields of characteristic $p$. There exists an element $f\in K$ such that $L$ is obtained by joining a root of the polynomial $$X^p-X-f=0$$ Further one can choose $f$ such that $v_K(f)$ is coprime to $p$. In this case $$v_K(f)=-s$$ where $s$ is the ramification break of ${{\rm Gal}}(L/K)$.
We now fix an $f\in K$ given by the above proposition. Clearly, if $v_K(f)>0$ then by Hensel’s lemma $X^p-X-f$ already has a root in $K$. If $v_K(f)=0$ then the extension given by adjoining the root of this polynomial is an unramified extension.
\[ol\] Let $L/K$, $f\in K$ be as above. Assume $L/K$ is totally ramified. Let $\lambda$ be a root of $X^p-X-f$ in $L$. Let $s$ be the ramification break of ${{\rm Gal}}(L/K)$. Then the discrete valuation ring ${{\mathcal O}}_L$, is the subset of $L$ is given by $${{\mathcal O}}_L = \{ \displaystyle{\sum_{i=0}^{p-1}}a_i\lambda^i \ | \ a_i\in {{\mathcal O}}_K \
\text{with} \ v_K(a_i) \geq \frac{is}{p} \}.$$
Clearly the set $\{1,\lambda,\cdots,\lambda^{p-1}\}$ is a $K$-basis of $L$. Thus any element $x\in L$ can be written uniquely in the form $$x = \sum_{i=0}^{p-1}a_i\lambda^i.$$ Note that $v_L(\lambda)=v_K(f)=-s$ is coprime to $p$ by the choice of $f$. Since $L/K$ is ramified, $s$ is nonzero. Moreover $v_L(a_i)=pv_K(a_i)$ is divisible by $p$. We thus conclude that for each $0\leq i \leq p-1$, the values of $v_L(a_i \lambda^i)$ are all distinct modulo $p$, and hence, distinct.
Thus $$v_L(\sum_{i=0}^{p-1}a_i\lambda^i)\geq 0 \ \text{ if and only if }
v_L(a_i\lambda^i)\geq 0 \ \ \text{for all } \ 0 \leq i<p$$ But $v_L(a_i\lambda^i)=pv_K(a_i)-is$. This proves the claim.
\[sum\] Let $p$ be a prime number as before. Let $$S_k = \displaystyle{\sum}_{n=0}^{p-1}n^k$$ Then
1. $S_k\equiv 0 \ {\rm mod} \ p \ \ {\text if}\ 0\leq k \leq p-2$
2. $S_{p-1} \equiv -1 \ {\rm mod}\ p $
The first congruence follows from the recursive formula (see [@barbara (4)]) $$S_k=\frac{1}{k+1}\left( p^{k+1}-p^k -
\displaystyle{\sum}_{j=0}^{k-2}\binom{k}{j}S_{j+1} \right)$$ and using the fact that when $k\leq p-2$, $k+1$ is invertible modulo $p$. $(2)$ follows from Fermat’s little theorem.
We now state an explicit description of $H^1(G,{{\mathcal O}}_L)$.
\[h1\] Notation as in . Let $\sigma$ be a generator of ${{\rm Gal}}(L/K)$. Let ${{\mathcal O}}_L^{\operatorname{tr}=0}$ denote the set of all trace zero elements in ${{\mathcal O}}_L$ and $$(\sigma-1){{\mathcal O}}_L= \{\sigma(x)-x \ | \ x\in {{\mathcal O}}_L\}.$$ Then,
1. ${{\mathcal O}}_L^{\operatorname{tr}=0} =
\{\displaystyle{\sum_{i=0}^{p-2}}a_i\lambda^i \ | \ v_K(a_i)\geq \frac{is}{p}
\}$
2. $(\sigma-1){{\mathcal O}}_L= \{ \displaystyle{\sum_{i=0}^{p-2}} a_i\lambda^i \ | \
v_K(a_i)\geq \frac{(i+1)s}{p} \} $
Since the sets ${{\mathcal O}}_L^{\operatorname{tr}=0}$ and $(\sigma-1){{\mathcal O}}_L$ are independent of the choice of $\sigma$, we may assume, without loss of generality, that $\sigma$ is the generator satisfying $\sigma(\lambda)=\lambda+1$.\
$(1)$ Let $x=\sum_{i=1}^{p-1}a_i\lambda^i$. Let $S_k$ be as in Lemma \[sum\]. Then\
$
\begin{array}{rcl}
\operatorname{tr}(x) & = & \displaystyle{\sum}_{j=0}^{p-1}\sigma^j(x) \\
& = & \displaystyle{\sum}_{j=0}^{p-1}\displaystyle{\sum}_{i=0}^{p-1}a_i(\lambda+j)^i \\
& = & \displaystyle{\sum}_{i=0}^{p-1}a_i\left(
\sum_{j=0}^{p-1}(\lambda+j)^i \right)
\end{array} \\
$ By binomially expanding and collecting coefficients of $\lambda^i$, we get\
$
\begin{array}{rcll}
\operatorname{tr}(x) & = & \displaystyle{\sum}_{i=0}^{p-1}a_i\left( p\lambda^i+
\displaystyle{\sum}_{j=1}^{i}\binom{i}{j}S_j\lambda^{i-j} \right) \\
& = & -a_{p-1} \ \ \ \ \ \ ... \text{(by Lemma \ref{sum})}.
\end{array}
$\
This together with Proposition \[ol\] proves $(1)$.\
$(2)$ Suppose $x=\displaystyle{\sum}_{i=1}^{p-1}a_i\lambda^i\in
(\sigma-1){{\mathcal O}}_L$. Then $$\displaystyle{\sum}_{i=1}^{p-1}a_i\lambda^i =
(\sigma-1)\displaystyle{\sum}_{i=1}^{p-1}b_i\lambda^i,$$ where $v_K(b_i)\geq \frac{is}{p}$ by . This gives us the following system of $p$ equations\
\
$
\begin{array}{lcl}
a_0 & = & b_1 + \cdots + b_{p-1} \\
a_1 & = & \binom{2}{1}b_2+ \binom{3}{2}b_3 + \cdots + \binom{p-1}{p-2}b_{p-1} \\
. & & \\
a_i & = & \binom{i+1}{i}b_{i+1} + \cdots + \binom{p-1}{p-(i+1)}b_{p-1}\\
. & & \\
a_{p-2} & = & (p-1)b_{p-1}\\
a_{p-1} & = & 0 \\
\end{array}
$\
\
Since $v_K(b_{i+1})\geq \frac{(i+1)s}{p}$, we get $v_K(a_i)\geq
\frac{(i+1)s}{p}$. Thus $$(\sigma-1){{\mathcal O}}_L \subset \{ \displaystyle{\sum_{i=0}^{p-2}} a_i\lambda^i \ |
\ v_K(a_i)\geq \frac{(i+1)s}{p} \}.$$ Conversely assume $$\displaystyle{\sum}_{i=1}^{p-1}a_i\lambda^i \in \{
\displaystyle{\sum_{i=0}^{p-2}} a_i\lambda^i \ | \ v_K(a_i)\geq \frac{(i+1)s}{p}
\}.$$ Since $H^1(G,L)=0$, we know there exists $\sum b_i\lambda^i \in L$ such that $$\displaystyle{\sum}_{i=1}^{p-1}a_i\lambda^i =
(\sigma-1)\displaystyle{\sum}_{i=1}^{p-1}b_i\lambda^i.$$ These $b_i's$ satisfy the above system of $p$ equations. Using that $v_K(a_i)\geq \frac{(i+1)s}{p}$, it is straightforward to observe by induction that $v_K(b_i) \geq \frac{is}{p}$. Hence $\displaystyle{\sum}_{i=1}^{p-1}b_i\lambda^i \in {{\mathcal O}}_L$.
The following corollary is the equi-characteristic analogue of [@lh Lemma 2.4].
\[s\] Let $L/K$ be as in Proposition \[v\_K(f)\]. Let $x\in
{{\mathcal O}}_L^{\operatorname{tr}=0}$ be an element that defines a non zero class in $H^1(G,{{\mathcal O}}_L)$. Then $v_L(x) \leq s-1$.
We will show that for any $x\in {{\mathcal O}}_L^{\operatorname{tr}=0}$, if $v_L(x)\geq s$, then the class of $x$ in $H^1(G,{{\mathcal O}}_L)$ is zero. By , we may write $$x=\displaystyle{\sum}_{i=1}^{p-2}a_i\lambda^i \ \ \text{with} \ \
v_L(a_i)\geq is.$$ Since for all $i$, $v_L(a_i\lambda^i)$ are distinct (see proof of ), we have $$v_L(x) = \text{inf}\{v_L(a_i\lambda^i)\}.$$ Thus $v_L(x)\geq s$ implies $$v_L(a_i\lambda^i)=v_L(a_i)-is \geq s \ \ \forall \ i.$$ This shows that $v_L(a_i) \geq (i+1)s$ which by Proposition \[h1\] implies $x \in (\sigma-1){{\mathcal O}}_L$, and hence defines a trivial class in $H^1(G,{{\mathcal O}}_L)$. This proves the claim.
Proof of the main theorem
=========================
Following [@hp Lemma 3.1], we reduce the proof of the main theorem to the case when $L/K$ is totally ramified Galois extension of degree $p$. Thus throughout this section we fix an extension $L/K$ which is of this type. We also fix a generator $\sigma \in {{\rm Gal}}(L/K)$. We first define a polynomial $G \in
{{\mathbb Z}}[X_1,...,X_p]$ in $p$ variables by $$G(X_1,...,X_p) = \frac{1}{p}\left(
(\displaystyle{\sum}_{i=1}^pX_i)^p-(\displaystyle{\sum}_{i=1}^pX_i^p)\right).$$ Note that despite the occurence of $\frac{1}{p}$, $G$ is a polynomial with integral coefficients.\
Now for an element $x\in L$ define $$F(x) = G(x,\sigma(x),...,\sigma^i(x),...,\sigma^{p-1}(x)).$$ The expression $F(x)$ is formally equal to the expression $\frac{\operatorname{tr}(x)^p-\operatorname{tr}(x^p)}{p}$ and makes sense in characteristic $p$ since $G$ has integral coefficients. Moreover, since for any $x\in L$, $F(x)$ is invariant under the action of ${{\rm Gal}}(L/K)$, $F(x)\in K$. We now observe that [@lh Lemma 2.2] holds in characteristic $p$ in the following form
[@lh Lemma 2.2]\[tr\] For all $x\in {{\mathcal O}}_L$, $v_K(F(x))=v_L(x)$.
The proof follows [@hp Proof of 1.4] verbatim, with and replacing [@hp Lemma 3.2] and [@hp Lemma 3.4] respectively. We briefly recall the idea of the proof for the convenience of the reader. By [@lh Lemma 1.1], it is enough to show that for large $n$, the map $$H^1(G,W_n({{\mathcal O}}_L))\to H^1(G,{{\mathcal O}}_L)$$ is zero. By , it is enough to show that for large $n$ $$(x_0,...,x_{n-1}) \in W_n({{\mathcal O}}_L)^{\operatorname{tr}=0} \implies v_L(x_0)\geq s.$$ The condition $ (x_0,...,x_{n-1}) \in W_n({{\mathcal O}}_L)^{\operatorname{tr}=0}$ can be rewritten as $$\sum_{i=0}^{p-1}(\sigma^i(x_0),...,\sigma^i(x_{n-1}))=0.$$ Using the formula for addition of Witt vectors, one analyses the above equation and obtains (see [@hp Lemma 3.5])
$$\label{one} \operatorname{tr}(x_{\ell})=
F(x_{\ell-1})-C.\operatorname{tr}(x_{\ell-1})^p+h_{\ell-2} \ \ \ , \ 1 \leq \ell \leq
n-1$$
where $C$ is a fixed integer and $h_{\ell-2}$ is a polynomial in $x_0,...,x_{\ell-2}$ and its conjugates such that each monomial appearing in $h_{\ell-2}$ is of degree $\geq p^2$. Using the above equation, Lemma \[tr\] and [@lh Lemma 2.1] one proves the theorem in the following three steps, for details of which we refer the reader to [@hp Proof of 1.4].\
Step $1$. We claim that for $0\leq \ell \leq n-2$ $$v_L(x_{\ell})\geq \frac{s(p-1)}{p}.$$ Recall equation for $1 \leq \ell \leq n-1$ $$\operatorname{tr}(x_{\ell})=
F(x_{\ell-1})-C.\operatorname{tr}(x_{\ell-1})^p+h_{\ell-2}.$$ One now proves the above claim by induction on $\ell$. Using the fact that $h_{-1} =
\operatorname{tr}(x_0) = 0$, the above equation gives $$-\operatorname{tr}(x_1) = F(x_0).$$ This, together with [@lh Lemma 2.1] proves the claim for $\ell=0$. The rest of the induction argument is straightforward. This claim, together with equation , is then used to observe $v_K(h_{\ell})\geq s(p-1)$ for all $\ell$.\
Step $2$. In this step we show that for $2\leq i \leq n-1$ $$v_L(x_{n-i}) \geq
\frac{s(p-1)}{p}\left(1+\frac{1}{p}+\cdots+\frac{1}{p^{i-2}}\right).$$ This is proved by induction on $i$, using equation and the estimates $$v_L(x_{\ell})\geq \frac{s(p-1)}{p}
\ \ , \ \ v_L(h_{\ell})\geq s(p-1)$$ obtained in Step $1$.
Step $3$. Since values taken by $v_L$ is a discrete valuation, for an integer $M$ such that $$\frac{s(p-1)}{p}\left(1+\frac{1}{p}+\cdots+\frac{1}{p^{M-2}}\right)>s-1,$$ we have $v_L(x_0)\geq s$.\
[xx]{}
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The Dodd-Frank Wall Street Reform and Consumer Protection Act (the “Dodd-Frank Act”) contains numerous mandates for rulemaking and studies by the Securities and Exchange Commission (the “SEC”) and other governmental agencies. Accordingly, many of the implications of the Dodd-Frank Act have yet to be realized.
One mandate relates to venture capital funds. Consistent with past legislative and regulatory efforts to increase federal oversight over hedge funds and their advisers, the Dodd-Frank Act repealed Section 203(b)(3) of the Investment Advisers Act of 1940 (the “Advisers Act”). Prior to its repeal, Section 203(b)(3) provided an exemption from the Advisers Act for certain fund advisers, generally based on the number of clients of the adviser and whether the adviser holds itself out to the public as an investment adviser. Advisers that meet the conditions of Section 203(b)(3) are exempt from the onerous recordkeeping requirements of the Advisers Act and are not subject to examination by the SEC staff. Section 203(b)(3) is commonly referred to as the private advisers’ exemption.
Advisers of privately held hedge funds, private equity funds, venture capital funds and other similar funds historically have relied on the private advisers’ exemption to avoid being subject to the Advisers Act. Since the credit crisis of 2008, there have been a number of legislative and regulatory efforts to regulate hedge funds; these efforts are intended to address any systemic risk posed by hedge funds or other unregistered funds that form part of the “shadow banking system.” The need for increased regulation of hedge funds is a matter that is subject to reasonable debate. However, efforts to regulate hedge funds have threatened to affect other types of funds, funds that do not pose the same systemic risks. The repeal of the private advisers’ exemption will result in many private funds becoming subject to the Advisers Act.
The Dodd-Frank Act includes, among other exemptions, a provision that exempts an investment adviser that solely advises venture capital funds from registration under the Advisers Act. The provision directs the SEC to define the term “venture capital fund” within one year of the enactment of the Dodd-Frank Act.
The Release
On November 19, 2010, the SEC issued a Preliminary Rule Release (the “Release”) relating to proposed rules that, among other things, provide a definition of the term “venture capital funds.” The Release is posted at the following web address: http://sec.gov/rules/proposed/2010/ia-3111.pdf. According to the Release, the Dodd- Frank Act includes an exemption for advisers of private venture capital funds because such funds invest in earlystage companies and are generally not leveraged and, thus, do not contribute to systemic risk. The SEC stated that it considered the Congressional intent when drafting the proposed definition. As proposed in the Release, a venture capital fund is a private fund that:
- invests in equity securities of private companies in order to provide operating and business expansion capital (such private companies are “qualifying portfolio companies,” which are discussed below) and at least 80% of each company’s securities owned by the fund were acquired directly from the qualifying portfolio company;
- directly, or through its investment advisers, offers or provides significant managerial assistance to, or controls, the qualifying portfolio companies;
- does not borrow or otherwise incur leverage (other than limited short-term borrowing);
- does not offer its investors redemption or other similar liquidity rights, except in extraordinary circumstances;
- represents itself as a venture capital fund to investors; and
- is not registered under the Investment Company Act of 1940 and has not elected to be treated as a business development company.
The proposed rules contain a grandfather clause that causes the term “venture capital fund” to include any private fund that: (i) represented to investors and potential investors at the time the fund offered its securities that it is a venture capital fund; (ii) has sold securities to one or more investors prior to December 31, 2010; and (iii) does not sell any securities to, including accepting any additional capital commitments from, any person after July 21, 2011.
The rules define a qualifying portfolio company as any company that:
- is not publicly traded;
- does not incur leverage in connection with the investment by the private fund;
- uses the capital provided by the fund for operating or business expansion purposes rather than to buy out other investors; and
- is not itself a fund but is an operating company.
The SEC specifically noted in the Release that venture capital funds may hold cash, cash equivalents and U.S. Treasuries with a remaining maturity of 60 days or less.
Considering the onerous nature of the reporting requirements of the Advisers Act, one should expect that, upon the effectiveness of the final rules, venture capital advisers will generally ensure that the funds they manage qualify as venture capital funds under the rules. Accordingly, funds formed after the rules become effective will face limitations that change the way many venture capitalists operate and will cause new funds to face disadvantages that are not faced by those funds that are grandfathered. In addition, early-stage issuers may voluntarily refrain from taking advantage of certain financing opportunities so as to make sure they are not precluded from being deemed qualifying portfolio companies which may adversely affect their future financing efforts. An early-stage issuer that allows itself to fall outside the parameters of a qualifying portfolio company may find that its pool of potential financing sources has contracted if venture capital funds are not able to invest in the company without becoming subject to the registration requirements of the Advisers Act.
The SEC has requested comments regarding most of these issues in the Release. Accordingly, the final rules may be considerably different. Parties that are interested in providing comments to the SEC should consider limitations on the nature of investments and the identities of the issuers. The following is a summary of certain provisions of the rules.
Definition of Venture Capital Fund
To be deemed a venture capital fund under the proposed rules, a fund may invest only in equity securities. The Release notes that the SEC intends to use the definition of equity security set forth in Section 3(a)(11) of the Securities Exchange Act of 1934. This is a broad definition which includes preferred stock and other securities exercisable for or convertible into common stock. Venture capital funds should maintain the flexibility to structure their investments to include many forms of hybrid instruments that include debt characteristics. Industry participants that are monitoring the comment phase of the proposed rules should consider the flexibility they need to invest in different investment structures.
With respect to any qualified portfolio company in which a venture capital fund has acquired securities, at least 80% of the securities must have been acquired directly from the company. This provision prevents funds from purchasing significant amounts of securities from a company’s existing shareholders. A substantial majority of venture capital transactions involve direct or primary issuances. However, from time to time, venture-backed companies may have shareholders that want to, or need to, dispose of their interests. In addition, many preferred shareholders may have redemption rights or similar rights with respect to their holdings. Having existing shareholders, or even new shareholders, acquire the interests of such holders may be beneficial to the issuer, its other shareholders and the shareholders that want to dispose of their interests.
The Release provides that a venture capital fund must provide significant management assistance to, or control, a portfolio company in which it invests. This provision creates significant limitations. While many venture capitalists provide significant managerial resources to their portfolio companies, they are not always able to do so, even if they so desire. In many instances, a venture capital firm may find management best suited to manage their respective companies and decide to remain passive with respect to management unless and until needed. In addition, many venture capital investments are made with a syndicate of venture capitalists. Query how multiple funds can each provide significant managerial assistance to the same portfolio company effectively, if at all. Depending on the final guidance regarding the level of involvement that would be deemed significant managerial assistance under the rules, venture capital advisers may not be able to comply with this provision, even after using their best efforts.
Under the proposed rules, venture capital funds may not borrow or otherwise incur leverage, other than shortterm borrowing under the rules nor may venture capital funds offer their investors redemption or other similar liquidity rights, except in extraordinary circumstances. Such provisions are designed to protect the market from systemic risk. Considering the size of the venture capital market and the type of investments made, an overleveraged venture capital fund should not pose systemic risk. In addition, due to the illiquid nature of most venture capital investments, redemption, if allowed under the funds’ governing documents, will not cause the public market trading that is often caused by high amounts of hedge fund redemption. Rather, a venture capital fund’s investors should control the ability of the fund to incur leverage or affect redemption.
Definition of Qualifying Portfolio Company and the Effect on the Capital Markets
The definition of qualifying portfolio company excludes publicly traded companies. Although a significant portion of venture capital investments are made with privately held companies, certain venture capitalists invest in publicly traded companies. Venture capitalists are regular participants in PIPEs and other private transactions with small, publicly traded companies. The lower valuations over the last two years in the U.S. public markets have increased public company investments by venture capitalists. Prohibiting venture capital funds from participating in public investments would adversely affect the business models of many funds. It would also adversely affect the pool of capital available for small cap companies, thereby making it more expensive for small cap companies to seek financing and providing an advantage for grandfathered funds. In the Release, the SEC sought comments regarding whether venture capital funds should be allowed to invest in publicly traded companies. It is reasonable to assume that some limits may be set in this regard. However, completely prohibiting public investments by venture capital funds is too restrictive. One suggestion by the SEC in the Release is to allow venture capital funds to make follow-on investments in portfolio companies after they have gone public. This is not sufficient. Venture capital funds should not be limited to public investments in which they already have interests.
A company that is deemed a qualifying portfolio company under the proposed rules may not incur leverage in connection with an investment from a private fund. Additional guidance is necessary to determine what is meant by “in connection with an investment” for purposes of the rules. Industry participants should be concerned whether this provision would affect a portfolio company’s ability to take advantage of available venture lending without losing its qualified portfolio company status. If a portfolio company has access to venture lending, its ability to access the loans should not be hindered by the rules.
The proposed rules also prohibit a qualifying portfolio company from using capital provided from a fund to buy out other investors. This provision will affect a company’s ability to honor existing redemption obligations owed to preferred shareholders. The provision will also hinder a company’s ability to use venture capital funding to buy out shareholders that need or want to dispose of their interests in the company.
Last, a qualified portfolio company must be an operating company. This provision may restrict the ability of venture capital funds from structuring their investments through other entities. Funds will need to limit their transaction structures to ensure that they invest directly in the portfolio company, not through an investment vehicle or through other funds.
Foreign Private Advisers
The proposed rules have implications for foreign advisers. The proposed rules exempt foreign private advisers from registration under the Advisers Act. For purposes of the proposed rules, a foreign private adviser is any investment adviser that has no place of business in the United States, has fewer than 15 clients in the United States and investors in the United States in private funds advised by the adviser, and less than $25 million in aggregate assets under management from such clients and investors.
The methodology of counting the number of clients will contain many of the same provisions regarding related parties of both natural persons and entities and will have certain provisions to avoid double counting. Similarly, there will be instructions regarding the calculation of assets under management.
Many foreign venture capital funds have U.S. clients and will need to consider the proposed rules to the same extent as their counterparts in the United States. On the other hand, foreign funds that meet the conditions of the foreign private adviser exemption will be able to invest in companies which U.S. venture capital funds may have to avoid. This should lead to lower valuations for companies that are not qualified portfolio companies. In a financing market that is truly global, this exemption may provide foreign funds with an advantage over U.S. venture capital funds.
Form ADV
The proposed rules do not completely exempt advisers from regulatory supervision. Private advisers that are exempt under the rules, which are referred to as exempt reporting advisers in the Release, will be required to file Form ADVs as do other advisers; however, the exempt advisers will not be required to provide all of the information that is generally required to be disclosed by registered advisers. In addition, the SEC will have the statutory authority to examine the books and records of advisers relying on the exemptions described in the Release. The contents of the Form ADVs to be filed by exemption reporting advisers are proposed to include identifying information, SEC reporting information, form of organization, other business activities, financial industry affiliations and private fund reporting, control persons and disclosure information. The Form ADVs will need to be filed through the Investment Adviser Registration Depository (IARD) and will be available on the SEC’s website. More information about the filing requirements may be found in a second proposed rule release posted by the SEC at the same time it posted the Release. The second release is posted at http://sec.gov/rules/proposed/2010/ia-3110.pdf. The SEC anticipated promulgating additional rules regarding recordkeeping by exempt private advisers.
Conclusion
There are numerous implications for U.S. and foreign private venture capital advisers in the rules proposed in the Release. The final rules will have a direct effect on the companies that look to venture capital funds for financing as well as other industry participants. Industry participants and companies that rely on, or expect to rely on, venture capitalists for financing should consider providing comments to the SEC. Comments are due on or before the date that is 45 days after publication of the Release in the Federal Register and instructions for the submission of comments may be found at the beginning of the Release. | https://www.lexology.com/library/detail.aspx?g=0b032aea-23c4-46ad-89a7-19661901d1d3 |
Q:
Rotation distance
right now i am working on a computer vision project and will recognize fiducial markers, i created a simulation testbed for benchmarking the precision of different methods. E.g. i do rotate the markers and later try to get the rotation (orientation) of the marker from the captured images.
The marker is always rotated around the z-axis, with following euler-angles:
$r_{gt} = [\alpha_0, \beta_0, \gamma_0]$
let say we have recognized the amrker in the image with following orientation to the world corrdinate (both orienations were measured w.r.t. world coordinate)
$r_{i} = [\alpha_i, \beta_i, \gamma_i]$
$d(r_0, r_i) = ? $
Now my quastion is how can i measure the distance between the two rotations? i already did check out this link
Quaternion distance.
Plz if you give an answer also give the referrence link, where i can investigate about this topic!
A:
Euler angles are not good for computing metrics as they have no proper symmetries. I suggest (since the question is tagged under quaternions) you convert your two orientations to quaternions $p$ and $q$. Then:
First, assuming by distance you mean how far apart are two rotations.
Second, knowing that quaternions have a double cover of the rotation manifold, that is, $q$ and $-q$ represent the same rotation.
Third, from second, say that the 'distance' from any quaternion $q=(w,x,y,z)$ to the identity quaternion $(1,0,0,0)$ makes sense if $w>0$. Otherwise, for $w<0$, the distance should be computed to the 'other' identity $(-1,0,0,0)$, which is indeed closer; or equivalently, one would find the distance between $-q$ and the true identity $(1,0,0,0)$.
Fourth, the distance between two quaternions $p$ and $q$ can be found as follows:
take $r = p^* q$ the quaternion that joins $p$ to $q$. The distance from $p$ to $q$ is now equal to the distance from $r$ to $(1,0,0,0)$ (or to $(-1,0,0,0)$, see Third above).
take the log, $u\theta = \log(p^* q)$, where $u=[u_x,u_y,u_z]$ is a unit vector defining the axis of rotation, and $\theta$ is half the rotated angle.
the distance is the rotated angle, $\phi=2\theta$.
Note: having unit quaternions $q=[\cos(\phi/2), u_x \sin(\phi/2), u_y \sin(\phi/2), u_z \sin(\phi/2)]$, the log can be found by inspection, but if only the distance is sought, this distance $\phi$ can be found by just:
$r = p^* q$ as in 1. above
if $r_w<0$ do $r \gets -r$ (change sign of the quaternion $r$).
$\phi=2 \arccos(r_w)$, where $r_w$ is the real part of $r$.
Fifth. You can use a shortcut by considering just double the angle between the two quaternions seen as 4'vectors, ie,
$$
\cos \theta = p^\top q \rightarrow \phi = 2\theta = 2\arccos (p^\top q)
$$
If $\cos\theta<0$, change the sign of one of the quaternions and start over.
All this info can be found here https://arxiv.org/abs/1711.02508
| |
---
abstract: 'Recently, using DiGiorgi-type techniques, Caffarelli and Vasseur [@CV] showed that a certain class of weak solutions to the drift diffusion equation with initial data in $L^2$ gain Hölder continuity provided that the BMO norm of the drift velocity is bounded uniformly in time. We show a related result: a uniform bound on BMO norm of a smooth velocity implies uniform bound on the $C^\beta$ norm of the solution for some $\beta >0.$ We use elementary tools involving control of Hölder norms using test functions. In particular, our approach offers a third proof of the global regularity for the critical surface quasi-geostrophic (SQG) equation in addition to [@KNV] and [@CV].'
author:
- Alexander Kiselev and Fedor Nazarov
title: A variation on a theme of Caffarelli and Vasseur
---
Introduction {#intro}
============
In the preprint [@CV], Caffarelli and Vasseur proved that certain weak solutions of the drift diffusion equation with $(-\Delta)^{1/2}$ dissipation gain Hölder regularity provided that the velocity $u$ is uniformly bounded in the BMO norm. The proof uses DiGiorgi-type iterative techniques. The goal of this paper is twofold. First, we wanted to provide additional intuition for the Caffarelli-Vasseur theorem by presenting an elementary proof of a related result. Secondly, we think that, perhaps, the method of this paper may prove useful in other situations.
Everywhere in this manuscript, our setting for the space variable will be $d-$dimensional torus, $\Tm^d.$ Equivalently, we may think of the problem set in $\Rm^d$ with periodic initial data. With the latter interpretation in mind, let us recall the definition of the BMO norm: $$\label{BMO}
\|f\|_{BMO} = {\rm sup}_{B \in \Rm^d} \frac{1}{|B|} \int\limits_B
|f(x)-\overline{f}_B|\,dx.$$ Here $B$ stands for a ball in $\Rm^d,$ $|B|$ for its volume and $\overline{f}_B$ for the mean of the function $f$ over $B.$
\[main1\] Assume that $\theta(x,t),$ $u(x,t)$ are $C^\infty(\Tm^d \times
[0,T])$ and such that $$\label{ps}
\theta_t = (u \cdot \nabla) \theta - (-\Delta)^{1/2} \theta$$ holds for any $t \geq 0.$ Assume that the velocity $u$ is divergence free and satisfies a uniform bound $\|u(\cdot,t)\|_{\rm{BMO}} \leq
B$ for $t \in [0,T].$ Then there exists $\beta = \beta(B,d)>0$ such that $$\label{kr}
\|\theta(x,t)\|_{C^\beta(\Tm^d)} \leq C(B,\theta(x,0))$$ for any $t \in [0,T].$
*Remark. In fact, we get control of Hölder continuity in terms of just $L^1$ norm of $\theta_0$ if we are willing to allow time dependence in . Namely, the following bound is also true: $$\label{kr12}
\|\theta(x,t)\|_{C^\beta(\Tm^d)} \leq C(B,\|\theta(x,0)\|_{L^1}){\rm
min}(1,t)^{-d-\beta}.$$*
Thus uniform bound on the BMO norm of $u$ implies uniform bound on a certain Hölder norm of $\theta.$ The dimension $d$ is arbitrary.
Our result is different from [@CV]. For one thing, [@CV] contains a local regularization version, which we do not attempt here. However our proof is simpler, and is quite elementary. At the expense of extra technicalities, it can be extended to more general settings.
Theorem \[main1\] can be used to give a third proof of the global regularity of the critical surface quasi-geostrophic (SQG) equation, which has been recently established in [@KNV] and [@CV]. We discuss this in Section \[SQG\]. Throughout the paper, we will denote by $C$ different constants depending on the dimension $d$ only.
Preliminaries {#prem}
=============
First, we need an elementary tool to characterize Hölder-continuous functions. Define a function $\Omega(x)$ on $\Tm^d$ by $$\label{confun}
\Omega(x) = \left\{ \begin{array}{ll} |x|^{1/2}, & |x|<1/2 \\
\frac{1}{\sqrt{2}}, & |x| \geq 1/2 \end{array} \right.$$ (thinking of $\Rm^d$ picture, $\Omega$ is defined as above on a unit cell and continued by periodicity). Let $A>1$ be a parameter to be fixed later.
We say that a $C^\infty$ function $\varphi$ defined on $\Tm^d$ belongs to $\cU_r(\Tm^d)$ if $$\begin{aligned}
\label{philinf}
\|\varphi(x)\|_{L^\infty} \leq \frac{A}{r^d} & \\
\label{phimz} \int_{\Tm^d} \varphi(x)\,dx =0 & \\
\label{philone} \|\varphi(x)\|_{L^1} \leq 1 & \\
\label{phiconc} \int_{\Tm^d} |\varphi(x)| \Omega(x-x_0)\,dx \leq
r^{1/2} & \,\,\,\,{\rm for}\,\,\,{\rm some}\,\,\,x_0 \in \Tm^d.\end{aligned}$$
Observe that the classes $\cU_r$ are invariant under shift. We will write $f(x) \in a\cU_r(\Tm^d)$ if $f(x)/a \in \cU_r(\Tm^d).$ The choice of the exponent $1/2$ in and is arbitrary and can be replaced with any positive number less than $1$ with the appropriate adjustment of the range of $\beta$ in Lemma \[Uhold\] below.
The classes $\cU_r$ can be used to characterize Hölder spaces as follows. Let us denote $$\label{Hnorm}
\|f\|_{C^\beta(\Tm^d)} = {\rm sup}_{x,y \in
\Tm^d}\frac{|f(x)-f(y)|}{|x-y|^\beta},$$ omitting the commonly included on the right hand side $\|f\|_{L^\infty}$ term. The seminorm is sufficient for our purposes since $\theta$ remains bounded automatically, and moreover we could without loss of generality restrict consideration to mean zero $\theta,$ invariant under evolution, for which is equivalent to the usual Hölder norm.
\[Uhold\] A bounded function $\theta(x)$ is in $C^\beta(\Tm^d),$ $0 < \beta <
1/2,$ if and only if there exists a constant $C$ such that for every $0 < r \leq 1,$ $$\label{holdcon}
\left| \int_{\Tm^d} \theta(x)\varphi(x)\,dx \right| \leq C r^\beta$$ for all $\varphi \in \cU_r.$ Moreover, $$\label{holdcon121}
\|\theta\|_{C^\beta(\Tm^d)}\leq C(\beta) {\rm sup}_{\varphi \in
\cU_r,\,\,0 <r \leq 1} r^{-\beta}\left|\int_{\Tm^d}
\theta(x)\varphi(x)\,dx \right|.$$
*Remark. The lemma holds for each fixed $A$ in . It will be clear from the proof that the constant $C$ in does not depend on $A$ provided that $A$ was chosen sufficiently large.*
Assume first that $\theta \in C^\beta.$ Consider any $\varphi \in
\cU_r,$ and observe that $$\int_{\Tm^d} \theta(x)\varphi(x)\,dx = \int_{\Tm^d}
(\theta(x)-\theta(x_0))\varphi(x)\,dx \leq C\int_{\Tm^d}
|x-x_0|^\beta |\varphi(x)|\,dx.$$ Using Hölder inequality, we get $$\begin{aligned}
\nonumber
\int_{\Tm^d} |x-x_0|^\beta |\varphi(x)|\,dx \leq \left(\int_{\Tm^d}
|\varphi(x)|\,dx\right)^{1-2\beta}\left(\int_{\Tm^d} |x-x_0|^{1/2}
|\varphi(x)|\,dx\right)^{2\beta} \\ \label{th1} \leq
C\left(\int_{\Tm^d}
|\varphi(x)|\,dx\right)^{1-2\beta}\left(\int_{\Tm^d} \Omega(x-x_0)
|\varphi(x)|\,dx\right)^{2\beta}\end{aligned}$$ Due to and , the right hand side of does not exceed $r^\beta.$
For the converse, consider a periodization $\theta_p$ of $\theta$ in $\Rm^d.$ Recall a well known characterization of Hölder continuous functions in $\Rm^d$ (see e.g. [@Stein]): $$\label{holdcrit}
\theta \in C^\beta \,\,\Leftrightarrow\,\,\|\theta\|_{L^\infty}
\leq Q,\,\,\,\|\Delta_j(\theta)\|_\infty \leq Q2^{-\beta
j},\,\,\,\forall j.$$ Moreover, if the right hand side of is satisfied, then $\|\theta\|_{C^\beta} \leq CQ.$
Here $\Delta_j$ are the Littlewood-Paley projections: $$\Delta_j(\theta) = \theta \ast \Psi_{2^{-j}},$$ where $\Psi_t(x) = t^{-d}\Psi(x/t),$ and $\widehat{\Psi}(\xi) =
\eta(\xi)-\eta(2\xi),$ with $\eta \in C_0^\infty,$ $0 \leq \eta(\xi)
\leq 1,$ $\eta(\xi)=1$ if $|\xi|\leq 1$ and $\eta(\xi)=0,$ $|\xi|
\geq 2.$ Observe that $\Psi$ is in the Schwartz class $\cS,$ $\int_{\Rm^d} \Psi \,dx =0,$ $\int_{\Rm^d} |\Psi(x)|\,dx \leq C,$ $\int_{\Rm^d} |x|^{1/2}|\Psi(x)|\,dx \leq C$ and $\|\Psi\|_{L^\infty} \leq C.$ Let us define $$\widetilde{\Psi}_j(x) =
c\sum\limits_{n \in \Zm^d} \Psi_{2^{-j}}(x+n),$$ then $\widetilde{\Psi}_j(x) \in \cU_{2^{-j}}(\Tm^d)$ if $c$ is sufficiently small (independently of $j$). Moreover, $$\label{aux11}
\int_{\Tm^d} \theta(x) \widetilde{\Psi}_j(x-y)\,dx =
c\int_{\Rm^d} \theta_p(x) \Psi_{2^{-j}}(x-y)\,dx.$$ By assumption, the left hand side in does not exceed $Q2^{-j\beta}.$ Thus, by the criterion , $\theta_p$ is $C^\beta$ and so is $\theta.$ The remark after implies that is true.
The proof of Theorem \[main1\], which we will outline in the beginning of the next section, relies on transfer of evolution on the test function. Here is an elementary lemma that allows us to do that. Let $\varphi^t(x,s)$ be the solution of $$\label{phieq}
\varphi^t_s = -(u(x,t-s)\cdot\nabla)\varphi^t -
(-\Delta)^{1/2}\varphi^t,\,\,\,\,\varphi^t(x,0)=\varphi(x).$$
\[evoltran\] Let $\theta_0, \varphi \in C^\infty(\Tm^d),$ and let $\theta(x,t)$ be the solution of with $\theta(x,0)=\theta_0(x).$ Then we have $$\int_{\Tm^d} \theta(x,t) \varphi(x)\,dx = \int_{\Tm^d} \theta_0(x)
\varphi^t(x,t)\,dx.$$
We claim that for $0 \leq s \leq t,$ the expression $$\label{thphiex}
\int_{\Tm^d} \theta(x, t-s) \varphi^t(x,s)\,dx$$ remains constant. A direct computation using , and the fact that $u$ is divergence free shows that the $s$-derivative of is zero. Substituting $s=0$ and $s=t$ into proves the lemma.
The proof of the main result {#bs}
============================
Let us outline our plan for the proof of Theorem \[main1\]. Conceptually, the proof is quite simple: integrate the solution against a test function from $\cU_r,$ transfer the evolution on the test function and prove estimates on the test function evolution. The key to the proof of Theorem \[main1\] is the following result.
\[key\] Let $v(x,s)\in C^\infty (\Tm^d \times [0,T])$ be divergence free d-dimensional vector field, and let $\psi(x,s)$ solve $$\label{psieq}
\psi_s = -(v \cdot \nabla)\psi - (-\Delta)^{1/2}\psi,
\,\,\,\psi(x,0)=\psi(x).$$ Assume that $${\rm max}_{s \in [0,T]} \|v(\cdot, s)\|_{BMO} \leq B.$$ Then the constant $A=A(B,d)$ in can be chosen so that the following is true.
Suppose $\psi \in \cU_r(\Tm^d),$ $0<r \leq 1.$ Then there exist constants $\delta$ and $K>0,$ which depend only on $B$ and dimension $d,$ such that $$\label{testevol11}
\psi(x,s) \in \left(\frac{r}{r+Ks}\right)^{\delta/K}
\cU_{r+Ks}(\Tm^d)$$ if $r+Ks \leq 1$ and $\psi(x,s) \in r^{\delta/K} \cU_1(\Tm^d)$ otherwise.
Let us assume Theorem \[key\] is true and prove Theorem \[main1\].
Let $\beta = \delta/K.$ Since $\theta(x,0)$ is smooth, we have $$\label{ini}
\left| \int_{\Tm^d} \theta(x,0) \varphi(x)\,dx \right| \leq
C(\theta(x,0))r^\beta$$ for all $\varphi(x) \in \cU_r(\Tm^d),$ $0<r \leq 1.$ But by Lemma \[evoltran\], $$\int_{\Tm^d} \theta(x,t)\varphi(x)\,dx = \int_{\Tm^d} \theta(x,0)
\varphi^t(x,t)\,dx.$$ By Theorem \[key\], $\varphi^t(x,t)$ belongs to $\left(\frac{r}{r+Kt}\right)^{\beta} \cU_{r+Kt}(\Tm^d)$ if $r+Kt \leq 1,$ and to $r^{\beta}\cU_1(\Tm^d)$ otherwise. Then implies that $$\label{finb14} \left|
\int_{\Tm^d} \theta(x,t)\varphi(x)\,dx \right| \leq
C(\theta(x,0))r^\beta,$$ for all $\varphi(x) \in \cU_r(\Tm^d),$ $0<r \leq 1.$
Observe that $C(\theta(x,0))$ will depend only on the $L^1$ norm of $\theta(x,0)$ if we are willing to allow time dependence in : $$\begin{aligned}
\left| \int_{\Tm^d} \theta(x,t)\varphi(x)\,dx \right| = \left|
\int_{\Tm^d} \theta(x,0) \varphi^t(x,t)\,dx \right| \leq
\|\theta(x,0)\|_{L^1}\|\varphi^t(x,t)\|_{L^\infty} \\ \leq
A(B,d)r^\beta {\rm min}(1,r+Kt)^{-d-\beta} \leq
C(B,d,\|\theta(x,0)\|_{L^1}){\rm min}(1,t)^{-d-\beta}r^\beta.\end{aligned}$$ This proves the bound in the Remark after Theorem \[main1\].
Thus it remains to prove Theorem \[key\].
The Evolution of the Test Function {#etf}
==================================
The proof of Theorem \[key\] is based on the following lemma, which looks at what happens over small time increments.
\[keylemma\] Under assumptions of Theorem \[key\], we can choose $A=A(B,d)$ so that the following is true. There exist positive $\delta,$ $K$ and $\gamma$ (dependent only on $B$ and $d$) such that for all $0 \leq s
\leq \gamma r,$ if $\psi(x,0) \in \cU_r(\Tm^d),$ $0<r \leq 1,$ then $$\label{finreslem}
\psi(x,s) \in \left(1-\frac{\delta s}{r}\right) \cU_{r+Ks}(\Tm^d).$$ The estimate is valid as long as $r+Ks \leq 1;$ otherwise the solution just remains in $\cU_1.$
We have to check four conditions. First, the equation for $\psi$ preserves the mean zero property, so that $\int_{\Tm^d}
\psi(x,s)\,dx =0$ for all $s.$
Next, let us consider [**the $L^\infty$ norm**]{}. Set $M(s)= \|\psi(\cdot, s)\|_{L^\infty}.$ Consider any point $x_0$ where the maximum or minimum value is achieved. Without any loss of generality, we can assume $x_0=0,$ $\psi(0,s)=M(s).$ Then $$\label{maxdev}
\partial_s\psi(0,s) = -(-\Delta)^{1/2}\psi(0,s) = C \sum\limits_{n \in Z^d}
\int_{\Tm^d} \frac{\psi(y,s) - M(s)}{|y+n|^{d+1}}\,dy.$$ Here we used the well-known formula for the fractional Laplacian (see e.g. [@CC]). Since $\|\psi(\cdot,s)\|_{L^1(\Tm^d)} \leq 1$ (see the argument below on the $L^1$ norm monotonicity), it is clear that the contribution to the right hand side of from the central period cell is maximal when $\psi(y)$ is the characteristic function of a ball of radius $cM(s)^{-1/d}$ centered at the origin. This gives us the estimate $$\label{infin1}
\partial_s\psi_s(0,s) \leq -C\int_{cM(s)^{-1/d}}^{r^{-1}}
M(s)|y|^{-d-1}\,dy \leq -C_1M(s)^{\frac{d+1}{d}}+C_2rM(s) \leq
-CM(s)^{\frac{d+1}{d}},$$ The argument is valid for all sufficiently large $M(s),$ which is the only situation we need to consider provided $A$ was chosen large enough. The same bound holds for any point $x_0$ where $M(s)$ is attained and by continuity in some neighborhoods of such points. So, we have in some open set $U$. Due to smoothness of $\psi$, away from $U$ we have $$\max\limits_{x\not\in U}|\psi(x,\tau)|< M(\tau)$$ for every $\tau$ during some period of time after $s.$ Thus we obtain that $$\label{infin}
\frac{d}{ds}M(s) \leq -C M^{\frac{d+1}{d}}(s), \,\,\,M(0) \leq
Ar^{-d}.$$ This is valid for all times while $M(s)$ remains sufficiently large. Solving , we get an estimate $$M(s) \leq \frac{M(0)}{(1+CM(0)^{1/d}s)^d} \leq
Ar^{-d}(1-CA^{1/d}r^{-1}s)$$ for all sufficiently small $s.$ This implies $$\label{infinlast}
\|\psi(\cdot, s)\|_{L^\infty} \leq Ar^{-d}(1-CA^{1/d}r^{-1}s),$$ for all sufficiently small $s \leq \gamma(A,d)r.$ Observe that $\gamma$ is independent of $\psi$ or $v$ other than through the value of $A,$ which will be chosen below depending on the value of $B$ only. The estimate agrees with the properties of the $(1-\frac{\delta s}{r})\cU_{r+Ks}(\Tm^d)$ class provided that $$\label{linftycon11}
\delta + dK \leq CA^{1/d}.$$
Next, we consider [**the concentration condition** ]{} $\int_{\Tm^d}\Omega(x-x_0)|\psi(x)|\,dx \leq r^{1/2}.$ Consider $x(s) \in \Tm^d$ satisfying $$\label{concdyn}
x'(s) = \overline{v}_{B_r(x(s))} \equiv
\frac{1}{|B_r|}\int_{B_r(x(s))} v(y,s)\,dy, \,\,\,x(0)=x_0.$$ Here $B_r(x)$ stands for the ball of radius $r$ centered at $x,$ and $|B_r|$ is its volume. We will estimate $\int_{\Tm^d}\Omega(x-x(s))|\psi(x,s)|\,dx.$ Let us write $\psi(x)=\psi_+(x)-\psi_-(x),$ where $\psi_\pm(x) \geq 0$ and have disjoint support. Let us denote $\psi_\pm(x,s)$ the solutions of with $\psi_\pm(x,0)=\psi_\pm(x).$ Then due to linearity and maximum principle, $|\psi(x,s)| = |\psi_+(x,s)-\psi_-(x,s)| \leq
\psi_+(x,s)+\psi_-(x,s),$ and so $$\label{psipm}
\int_{\Tm^d} \Omega(x-x(s))|\psi(x,s)|\,dx \leq \int_{\Tm^d}
\Omega(x-x(s))\psi_+(x,s)\,dx + \int_{\Tm^d}
\Omega(x-x(s))\psi_-(x,s)\,dx.$$ Let us estimate the first integral on the right hand side of , the second can be handled the same way. We have $$\begin{aligned}
\nonumber
\left|\partial_s \int_{\Tm^d} \Omega(x-x(s)) \psi_+\,dx \right|=
\\ \nonumber \left|\int_{\Tm^d} \left( \Omega(x-x(s))
\left((-v \cdot \nabla)\psi_+ - (-\Delta)^{1/2} \psi_+ \right)-
\nabla(\Omega(x-x(s)))\cdot x'(s) \psi_+ \right)\,dx \right|= \\
\nonumber \left|\int_{\Tm^d} \nabla(\Omega(x-x(s))) \cdot \left( v -
\overline{v}_{B_r(x(s))} \right)\psi_+\,dx -
\int_{\Tm^d} (-\Delta)^{1/2} \Omega(x-x(s)) \psi_+\,dx \right| \\
\leq C\left(\int_{\Tm^d} |x-x(s)|^{-1/2}|v-
\overline{v}_{B_r(x(s))}||\psi_+|\,dx + \int_{\Tm^d}
|x-x(s)|^{-1/2}|\psi_+|\,dx \right).\label{psiderest}\end{aligned}$$ We used the divergence free condition on $v$ and in the second step, and estimated $|\nabla\Omega(x-x_0)| \leq
C|x-x_0|^{-1/2},$ $|(-\Delta)^{1/2}\Omega(x-x_0)|\leq
C|x-x_0|^{1/2}.$ Let us consider the two integrals in . Since $\|\psi_+\|_{L^1}\leq 1/2$ and $\|\psi_+\|_{L^\infty} \leq Ar^{-d},$ the integral $\int_{\Tm^d}
|x-x(s)|^{-1/2}|\psi_+|\,dx$ is maximal when $\psi_+$ is a characteristic function of a ball centered at $x(s)$ of radius $crA^{-1/d}.$ This gives an upper bound of $Cr^{-1/2}A^{1/2d}$ for this integral. To estimate the first integral in , split $\Tm^d = \cup_{k=0}^N E_k,$ where $$E_k = \{ x:\,\,r2^{k-1} < |x-x(s)| \leq r2^k \} \cap
\Tm^d,\,\,\,k>0, \,\,\,E_0=B_r(x(s)).$$ Recall (see e.g. [@Stein]) that for any BMO function $f$, any ball $B,$ and any $1 \leq p < \infty,$ $$\label{BMOest123}
\|f-\overline{f}_B\|_{L^p(B)} \leq c_p |B|^{1/p}\|f\|_{BMO}.$$ By Hölder’s inequality, $$\begin{aligned}
\int_{B_r(x(s))}
|x-x(s)|^{-1/2}|v-\overline{v}_{B_r(x(s))}||\psi_+|\,dx \leq \\
\||x-x(s)|^{-1/2}\|_{L^{p}(B_r(x(s))}\|v-\overline{v}_{B_r(x(s))}\|_{L^{z}(B_r(x(s)))}\|\psi_+\|_{L^{q}(B_r(x(s)))},\end{aligned}$$ where $p^{-1}+z^{-1}+q^{-1}=1.$ Now $$\|\psi_+\|_{L^q} \leq
\|\psi_+\|_{L^1}^{1/q}\|\psi_+\|_{L^\infty}^{1-1/q} \leq
A^{1-\frac{1}{q}}r^{\frac{d}{q}-d}.$$ Using , we also see that $$\|v-\overline{v}_{B_r(x(s))}\|_{L^{z}(B_r(x(s)))} \leq
C(z,d)r^{\frac{d}{z}}B.$$ Finally, for any $p < 2d,$ $$\||x-x(s)|^{-1/2}\|_{L^{p}(B_r(x(s))} \leq
C(p,d)r^{\frac{d}{p}-\frac{1}{2}}.$$ Taking $z$ very large, and $p$ very close to $2d,$ we find that for any $q > \frac{2d}{2d-1},$ we have $$\label{bmoest1}
\int_{B_r(x(s))}
|x-x(s)|^{-1/2}|v-\overline{v}_{B_r(x(s))}||\psi_+(x)|\,dx \leq
CBA^{1-\frac{1}{q}}r^{\frac{d}{q}+\frac{d}{z}+\frac{d}{p}-d-1/2}
\leq C(\sigma,d) B A^\sigma r^{-1/2},$$ where $\sigma$ is any number greater than $\frac{1}{2d}.$ Furthermore, for $k>0,$ $$\begin{aligned}
\int_{E_k} |x-x(s)|^{-1/2}|v-\overline{v}_{B_r(x(s))}||\psi_+|\,dx
\leq
C2^{-k/2}r^{-1/2}\int_{E_k} |v-\overline{v}_{B_r(x(s))}||\psi_+(x)|\,dx \leq \nonumber \\
C2^{-k/2}r^{-1/2}\left( \int_{B_{r2^k }(x(s))}
|v-\overline{v}_{B_{r2^{k}}(x(s))}||\psi_+(x)|\,dx+\int_{B_{r2^k
}(x(s))}
|\overline{v}_{B_{r2^{k}}(x(s))}-\overline{v}_{B_r(x(s))}||\psi_+(x)|\,dx
\right). \label{bmoest2}\end{aligned}$$ Recall that (see, e.g., [@Stein]) $$|\overline{v}_{B_{r2^{k}}(x(s))}-\overline{v}_{B_r(x(s))}|
\leq Ck\|v\|_{BMO}.$$ Therefore the last integral in does not exceed $CkB.$ The first integral can be estimated by $$\|v-\overline{v}_{B_{r2^k }}\|_{L^{\frac{q}{q-1}}(B_{r2^k })}\|\psi_+\|_{L^{q}(B_{r2^{k} })}
\leq C(q,d)B2^{k(d-\frac{d}{q})}A^{1-\frac{1}{q}},$$ where $q$ is any number greater than $1.$ Thus in particular $$\label{bmoest3}
\int_{E_k}
|x-x(s)|^{-1/2}|v-\overline{v}_{B_1(x(s))}||\psi_+(x)|\,dx \leq
CB2^{-3k/8}B(k2^{-k/8}+A^{1/8d})r^{-1/2}$$ if $q=\frac{8d}{8d-1}.$ Adding and , we obtain $$\int_{\Tm^d} |x-x(s)|^{-1/2}|v-\overline{v}_{B_r(x(s))}||\psi_+(x,s)|\,dx \leq
CBA^{3/4d}r^{-1/2},$$ provided that $A$ is large enough (the exponent for $A$ can be anything greater then $\frac{1}{2d}).$ Coming back to and , we see that $$\label{concest11a} \int_{\Tm^d} |x-x(s)|^{1/2}|\psi(x,s)|\,dx
\leq r^{1/2}+Csr^{-1/2}(A^{1/2d}+BA^{3/4d}).$$ This is consistent with the $(1-\frac{\delta s}{r})\cU_{r+Ks}(\Tm^d)$ class if $$\left(1-\frac{\delta s}{r} \right) \left(r+Ks\right)^{1/2} \geq
r^{1/2}+Csr^{-1/2}(A^{1/2d}+BA^{3/4d}).$$ Provided that $\gamma$ is chosen sufficiently small, this condition reduces to $$\label{keyest676}
\frac{K}{2} - \delta > C(A^{1/2d}+BA^{3/4d}).$$
Finally, we consider [**the $L^1$ norm**]{}. Recall (see e.g. [@CC]) that for a $C^\infty$ function $\psi(x),$ $$\label{fracdiff}
(-\Delta)^{1/2}\psi(x) = \lim_{\epsilon \rightarrow 0}\sum\limits_{n
\in \Zm^d} \int\limits_{\Tm^d \cap
|x-y|\geq \epsilon}\frac{\psi(x)-\psi(y)}{|x-y-n|^{d+1}}\,dy.$$ Let $S$ be the set where $\psi(x,s)=0,$ and define $$D_\pm = \{ x\in \Tm^d \left| \,\pm\psi(x,s)>0 \}. \right.$$ The sets $S$ and $D_\pm$ depend on $s,$ but we will omit this in notation to save space. Due to and incompressibility of $v,$ we have $$\begin{aligned}
\nonumber
\partial_s \|\psi(\cdot,s)\|_{L^1} = \int_{\Tm^d \setminus S}
\frac{\psi(x,s)}{|\psi(x,s)|}\left( -v\cdot\nabla\psi(x,s) -
(-\Delta)^{1/2}\psi(x,s)\right)\,dx + \\
\int_{S}|(-\Delta)^{1/2}\psi(x,s)|\,dx = \label{L1normeq}
-\int_{\Tm^d \setminus S}
\frac{\psi(x,s)}{|\psi(x,s)|}(-\Delta)^{1/2}\psi(x,s)\,dx +
\int_{S}|(-\Delta)^{1/2}\psi(x,s)|\,dx.\end{aligned}$$ The integral over $S$ is of course nonzero only if the Lebesgue measure of $S$ is positive. Substituting into and symmetrizing with respect to $x,y$ we get $$\begin{aligned}
\nonumber
\partial_s \|\psi(\cdot,s)\|_{L^1} = \\ - \frac12\lim_{\epsilon
\rightarrow 0} \int\limits_{((\Tm^d \setminus S) \times (\Tm^d
\setminus S)) \cap |x-y| \geq \epsilon} \left(
\frac{\psi(x,s)}{|\psi(x,s)|} - \frac{\psi(y,s)}{|\psi(y,s)|}\right)
\sum\limits_{n \in \Zm^d}
\frac{\psi(x,s)-\psi(y,s)}{|x-y-n|^{d+1}}\,dx dy \label{L1nb} \\
- \int_{\Tm^d \setminus S} \frac{\psi(x,s)}{|\psi(x,s)|}
\left(\sum\limits_{n \in \Zm^d} \int_S
\frac{\psi(x,s)}{|x-y-n|^{d+1}}\,dy \right)dx + \int_S \left|
\sum\limits_{n \in \Zm^d} \int_{\Tm^d \setminus S}
\frac{\psi(y,s)}{|x-y-n|^{d+1}}\,dy \right| \,dx. \nonumber\end{aligned}$$ Observe that the expression under the first integral in is non-negative for all $x,y,$ and it is positive if $\psi(x,s)$ and $\psi(y,s)$ have different signs. Also, observe that $$\int_S \left|
\sum\limits_{n \in \Zm^d} \int_{\Tm^d \setminus S}
\frac{\psi(y,s)}{|x-y-n|^{d+1}}\,dy \right| \,dx \leq \int_S
\sum\limits_{n \in \Zm^d} \left|
\int_{D_+}\frac{\psi(y,s)}{|x-y-n|^{d+1}}\,dy +
\int_{D_-}\frac{\psi(y,s)}{|x-y-n|^{d+1}}\,dy \right|.$$ Therefore, the combined contribution of the last line in over every cell is less than or equal to zero. Leaving only the central cell contributions in , we get $$\begin{aligned}
\nonumber\partial_s \|\psi(\cdot,s)\|_{L^1} \leq \\
\label{L1bnd11} -\int\limits_{D_+} \psi(x,s) \int\limits_{D_-}
\frac{dy}{|x-y|^{d+1}}\,dydx + \int\limits_{D_-} \psi(y,s)
\int\limits_{D_+} \frac{dx}{|x-y|^{d+1}}\,dxdy - \\
\nonumber - \int_{D_+ \cup D_-} |\psi(x,s)| \left( \int_S
\frac{1}{|x-y|^{d+1}}\,dy \right)dx+\int_S \left|
\int_{D_+}\frac{\psi(y,s)}{|x-y|^{d+1}}\,dy +
\int_{D_-}\frac{\psi(y,s)}{|x-y|^{d+1}}\,dy \right|.\end{aligned}$$ Without loss of generality, we can assume that $1 \geq
\|\psi(\cdot,s)\|_{L^1} \geq 9/10$ for every $s$ we consider, since otherwise the $L^1$ condition is already satisfied. Also, due to we can assume that $\int_{\Tm^d}
\Omega(x-x(s))|\psi(x,s)|\,dx \leq \frac{11}{10}r^{1/2}$ provided that the time interval $[0,\gamma r]$ that we consider is sufficiently small, with $\gamma = \gamma(A,B).$ These two bounds imply that $\int_{\Tm^d \cap |x-x(s)|\leq
400r} |\psi(x,s)|\,dx \geq 4/5.$ The mean zero condition leads to $$\label{mzconest}
\pm\int_{D_\pm \cap \{|x-x(s)| \leq 400r\}} \psi(x,s)\,dx \geq 3/10.$$ Let us denote $\widetilde{D}_\pm = D_\pm \cap \{|x-x(s)| \leq
400r\},$ $\widetilde{S} = S \cap \{|x-x(s)| \leq 400r\}.$ Observe that if $x \in \widetilde{S},$ then, by , $$\pm \int_{D_\pm}\frac{\psi(y,s)}{|x-y|^{d+1}}\,dy \geq
\pm \int_{\widetilde{D}_\pm}\frac{\psi(y,s)}{|x-y|^{d+1}}\,dy \geq C
r^{-d-1}.$$ This implies that due to cancelation in the last term of , we can estimate the last line of from above by $- C|\widetilde{S}|r^{-d-1}.$ Reducing the integration in the second line of to $\widetilde{D}_\pm,$ we obtain $$\label{finL1est}
\partial_s \|\psi(\cdot,s)\|_{L^1} \leq -C r^{-d-1}\left(|\widetilde{D}_-|\int_{\widetilde{D}_+}
\psi(x,s)\,dx + |\widetilde{D}_+|\int_{\widetilde{D}_-}
\psi(x,s)\,dx +|\widetilde{S}|\right) \leq -cr^{-1},$$ where $c$ is a fixed positive constant. Here in the last step we used and $|\widetilde{D}_+| + |\widetilde{D}_-| +|\widetilde S| \geq C r^d.$ The estimate is consistent with $(1-\frac{\delta
s}{r})\cU_{r+Ks}(\Tm^d)$ class if $\delta \leq c.$
It remains to observe that, if $A=A(B,d)$ is chosen sufficiently large, one can indeed find $K$ and $\delta$ so that the conditions , and the $\delta \leq c$ condition arising from the $L^1$ norm estimate are all satisfied. It is also clear from the proof that then holds for all $s\leq \gamma(B,d) r.$ The only restriction from above on the value of $r$ comes from the $L^\infty$ norm condition, which has to be consistent with $L^1$ and concentration conditions. For convenience, we chose to cap the value of $r$ at $1.$
The proof of Theorem \[key\] is now straightforward.
From Lemma \[keylemma\] it follows that for any $s>0,$ $\psi(x,s)
\in f(s) \cU_{r+Ks}(\Tm^d)$ provided that $f'(s) \geq -
\frac{\delta}{r+Ks}f(s).$ Solving this differential equation, we obtain that the factor $f(s) = \left(\frac{r}{r+Ks}
\right)^{\delta/K}$ is acceptable.
The Critical SQG equation and further discussion {#SQG}
================================================
Theorem \[main1\] provides an alternative path to the proof of existence of global regular solutions to the critical surface quasi-geostrophic equation: $$\left\{ \aligned &\theta_t=u\cdot\nabla\theta
-(-\Delta)^{1/2}\theta, \,\,\,\,\theta(x,0)=\theta_0(x),
\\ \nonumber
& u=(u_1,u_2)=(-R_2\theta, R_1\theta),
\endaligned
\right.$$ where $\theta\,:\, \Rm^2\to \Rm^2$ is a periodic scalar function, and $R_1$ and $R_2$ are the usual Riesz transforms in $\Rm^2$. Indeed, the local existence and uniqueness of smooth solution starting from $H^1$ periodic initial data is known (see e.g. [@dong]). The $L^\infty$ norm of the solution does not increase due to the maximum principle (see e.g. [@CC]), which implies uniform bound on the BMO norm of the velocity. Since the local solution is smooth, one can apply Theorem \[main1\]. This, similarly to [@CV], implies a uniform bound on some Hölder norm of the solution $\theta.$ This improvement over the $L^\infty$ control is sufficient to show the global regularity (see [@CV] or [@CW] for slightly different settings which can be adapted to our case in a standard way).
One can pursue a number of generalizations of Theorem \[main1\], for instance reducing assumptions on smoothness of solution, velocity, or initial data. However we chose to present here the case with the most transparent proof containing the heart of the matter. As follows from the proof, the role of the BMO space is mainly the right scaling: the BMO is the most general function space for which is available. The BMO scaling properties are of course also crucial for the proof of [@CV] to work.
[**Acknowledgement.**]{} Research of AK has been supported in part by the NSF-DMS grant 0653813. Research of FN has been partially supported by the NSF-DMS grant 0501067. AK thanks for hospitality the Department of Mathematics of the University of Chicago, where part of this work was carried out.
[99]{}
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P. Constantin and J. Wu, *Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation, arXiv:math$/$0701592, 12 pages*
A. Cordoba and D. Cordoba, *A maximum principle applied to quasi-geostrophic equations, Commun. Math. Phys. [**249**]{} (2004), 511–528*
H. Dong, *Higher regularity for the critical and super-critical dissipative quasi-geostrophic equations, arXiv:math$/$0701826, 18 pages*
A. Kiselev, F. Nazarov and A. Volberg, *Global well-posedness for the critical $2D$ dissipative quasi-geostrophic equation, Inventiones Math. [**167**]{} (2007) 445–453*
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- Number of FNGs:
Happy Monday! Another ‘borrowed’ workout, but this one was from an F3 group that popped up in my search. Believe it or not, they titled it the ‘Lazy Dora.’ I personally didn’t think a lazy DORA sounded like it would suffice, so I changed things up a bit and turned it into the ‘Not so Lazy Dora’.
Warm-Up: Good Mornings (5) Toy Soldiers (10 each leg); Inchworms (10); Jumping Jacks (20); Mt. Climbers (40)
Not so Lazy Dora
100 Push Ups: P1 does 10 push-ups while P2 holds Plank = alternate until 100 are completed
Run a lap (around the pickle)
200 Star Crunch (full sit up) P1 does 20 Star Crunches while P2 holds 6in leg raise = alternate until 200 are completed
Run 2 laps (around the pickle)
300 Squats: P1 does 25 squats wile P2 does wall sit = alternate until 300 are completed (squat challenge for Day 1 complete)
Run 3 laps (around the pickle)
200 LBCs: P1 does 20 LBCs while P2 does flutter kicks
Run 2 laps (around the pickle)
100 Burpees: P1 does 10 Burpees while P2 holds plank
Run 1 lap (around the pickle)
Everyone made it to the 100 Burpees, though with just minutes left to go in the workout, Q told everyone to get in at least 10 burpees and then we were done! Name-o-Rama and updates for the week before we called it a night.
Hope you all had a great Monday! | https://fiacarpex.com/backblast/the-not-so-lazy-dora/ |
A well-known example of an application of a device for purifying a fluid as mentioned is an application in a vacuum cleaner, in which case the fluid to be filtered is air. Currently, two types of vacuum cleaners are known in the art and sold to consumers. A first type of vacuum cleaners is provided with a dust bag, whereas a second type of vacuum cleaners is not, and makes use of cyclones to separate dust and dirt particles from air.
In a vacuum cleaner comprising a dust bag, two filters are used, namely the dust bag for a majority of the dust and dirt particles, and a filter such as a so-called HEPA filter (High Efficiency Particulate Air filter) for very small particles.
A cyclonic vacuum cleaner comprises four components for filtering particles from air taken in by the vacuum cleaner during operation, namely a cyclonic pre-separator, a pre-separating grid, a cyclonic fine dust separator, and a HEPA filter. The application of a number of components is necessary in view of the fact that cyclones can filter particles with a sufficiently high mass density in a limited range of diameters. In order to be able to filter a wider range of particles, the dedicated separators as mentioned are needed, wherein the cyclonic pre-separator serves for separating relatively big particles with a high mass density from the air; the pre-separating grid serves for filtering relatively big particles with a low mass density from the air; the cyclonic fine dust separator serves for separating relatively small particles from the air; and the HEPA filter serves for separating even smaller particles from the air than the cyclonic fine dust separator.
The pre-separating grid is used in view of the fact that the cyclonic pre-separator is not capable of separating particles with a low mass density like fibers, plastic foam and confetti from the air. However, the application of a grid has a disadvantage, which resides in the fact that a grid will clog. Hence, air flow resistance will increase during usage, and a constant suction power cannot be guaranteed.
Because of the need of fast rotating air on the hand and slow moving air for disposing particles on the other hand, cyclones are space-consuming solutions for separating dust and dirt particles from quantities of air. In a pre-separating unit comprising the cyclonic pre-separator and the pre-separating grid, it is the cyclonic pre-separator that needs a rather large volume compared to the pre-separating grid.
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Q:
How can we know for use that $A$ and $B$ are mutually exclusive under conditonal probability?
Reading that
"Sample question 4 (Conditional Probability): Given that $P(A) = 0.20, P(B) = 0.60, P(B|A) = 0.50,$ what is $(B∩A’)$ ? $(A’∩B’)$?"
from datasciencecentral.com
When we are just provided with the text without picture/table. The only picture from the text in the head is:
B B' Marginal
A (.2*.5=.1) 0.2
A'
Marginal 0.6
Then:
B B' Marginal
A (.2*.5=.1) (.1) 0.2
A' (.5)
Marginal 0.6
in order to fill out the rest of table, we need to know that "A’ and B’ are mutually exclusive. "
Then the questions is: when we are dealing with Conditional Probability $P (A' \cap B')$ are always $0$ ?
While the solution is given as :
B B' Marginal
A (.2*.5=.1) (.1) 0.2
A' (.5) (0 ?) (0.5 ?)
Marginal 0.6 (0.1 ?) (1.0 ? especially this one )
Can someone please help me understand where the parts with the question mark (above) comes form ? Thank you in advance.
A:
First off: No, these events cannot be mutually exclusive, since
$$P(A|B)\stackrel{\mathop{def}}{=}\frac{P(A∩B)}{P(B)}\ne0\ \implies \boxed{P(A∩B)\ne0.}$$
Although the rest of your question also needs some attention since I feel there is some misunderstanding on how things work.
Since every event partition (mutually exclusive & covering entirely) the sample space in two pieces we must have:
$$P(A\cup A')=P(A)+P(A')=P(B\cup B')=P(B)+P(B')=1$$
In your case, $P(A)$ is the "marginal" probability of $A$. The idea is that regardless of how $B$ behaves, $A$ should be consistent: It either happens or not. In your case, you already found both $P(A)$ and $P(B)$,
B B' Marginal
A 0.1 0.1 0.2
A' 0.5
Marginal 0.6
so you can just assign $P(A')$ and $P(B')$ using these:
B B' Marginal
A 0.1 0.1 0.2
A' 0.5 0.8
Marginal 0.6 0.4
Notice that the sum of the two marginal probabilities do not add up to $1$, on the contrary they add up to $2$ since it is the addition of the total probabilities of two events. This carries to cases with more events since $\sum_{i=1}^N P(A_i\cup A_i')=\sum_{i=1}^N 1=N$.
In the last step, you do the same algorithm. The rows and columns should add up to the last element (i.e. the "marginal" probabilities).
B B' Marginal
A 0.1 0.1 0.2
A' 0.5 0.3 0.8
Marginal 0.6 0.4 2.
You can fill it using the row and since the system is consistent the column is automatically satisfied (you can check). Though since the variables are not independent I do not advise heavy usage of tables (since they make people recall their earlier, simpler days with inherent assumption of independence).
P.S. It really is criminal that SE doesn't support tables. Like, really?
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The definition of a cone is equipped with parts and example questions that we will describe in a simple way so that you can understand them easily. For a more in-depth discussion, see the explanation below.
Who here loves ice cream? Especially the ice cream that uses a cone. It’s very good, it’s cold and sweet too. Well, has anyone ever thought about how much volume of ice cream should be put in a cone until it’s full? Does anyone know how to calculate the volume of this ice cream?
Before we dive into the formula for the volume of a cone and also how to find it, let’s find out what a cone is. A cone is one of the curved side spaces. It has a flat base in the shape of a circle and a blanket that connects the base and the apex.
For further explanation, see the following ulsannya.
Definition
The definition of the cone itself is a three-dimensional shape in the form of a special pyramid that is based on a circle, and a cone also has 2 sides and 1 edge.
So a cone can be formed from a flat shape, i.e. a flat triangle, which is rotated one complete rotation (360°).), which is the side of the elbow as the center of rotation.
parts
Cones also have 3 important measurements that we will use to calculate their volume, namely:
Jonelaugh-jonelaughs
The base of the cone is shaped like a circle. The radius or radius of a cone is the distance from the center point to the point on the base circle. The diameter of the base of a cone is a line segment that joins two points on the base circle and passes through the center point. In a circle, the length of the circle’s diameter is equal to twice the length of the circle’s radius.
Height
It is the distance from the center of the base to the apex of the cone. If we make a line segment connecting the base midpoint and the vertex, we get a line segment perpendicular to the base plane. The length of this line segment is also the height of the cone.
Blanket
Cone blanket is a curved side, wrapping around the cone. It is located between the base and the apex. On the blanket of cones there is a painter’s line. The painter’s line is a line that represents the outermost part of the cone blanket. The painter’s line, the height of the cone, and the radius of the cone form a right triangle.
Formula
After knowing what a cone is, we will now know that a cone is a shape.
Therefore, the cone must have volume. The volume of a cone can be calculated by multiplying the area of the base of the cone (area of the circle) by the height of the cone which is formulated as follows:
V = ⅓ × πrtwo × t
with
- V = Kerucut Volume
- r = Jari – Jari down
- t = cone height
In addition to volume, a cone also has a surface that can be calculated as well as its area. The formula for the surface area of a cone is as follows:
L = πrtwo + πrs
with
- L = Cone Surface Area
- s = Cone Painter Line
example of problems
Find a cone whose base is 12 cm in diameter. So the length of the painter’s line is 10 cm, so calculate the surface area of the cone?
Reply:
It is known:
Wanted: the surface area of the cone? | https://www.seoulcityblog.com/definitions-parts-and-problem-examples/ |
Q:
Regex to find lines containing numbers, starting with text, but removing text from the ocurrence
Having the following input:
Testing 42702434884
Testing 064352729-13
05.994.401/0001-53
Testing 134.632.125-03
I am trying to get lines containing numbers, considering only lines starting with text, and removing the text from the result,
Currently I tried the following expression:
(?!a-zA-Z)\b(\d{11}|\d{14})|(\d{3}\.\d{3}\.\d{3}\-\d{2}|\d{3}\d{3}\d{3}\-\d{2})|(\d{2}\.\d{3}.\d{3}\/\d{4}-\d{2}|\d{2}\d{3}\d{3}\d{4}-\d{2})\b
I was able to remove the text from the result, and find lines containing the patterns, but could not filter only lines starting with text. Here is the result as example
How can I filter lines starting with text while removing the text from the result?
A:
Using the negative lookahead (?!a-zA-Z)\b with the pattern you tried is always true as what follows is a digit so it can be omitted.
Instead of using the negated lookahead (?!a-zA-Z) you can use an anchor ^ to assert the start of the string and match 1+ times a char a-zA-Z followed by a space and make it optional (?:[a-zA-Z]+ )? if you want to match all the examples
The append a group around all the alternations.
If you don't need all the capturing groups, you could make them non capturing (?: instead except for the numbers that you want to keep.
The values are in group 1.
^(?:[a-zA-Z]+ )?((?:\d{11}|\d{14})|(?:\d{3}\.\d{3}\.\d{3}\-\d{2}|\d{3}\d{3}\d{3}\-\d{2})|(?:\d{2}\.\d{3}.\d{3}\/\d{4}-\d{2}|\d{2}\d{3}\d{3}\d{4}-\d{2})\b)
Note for Java to double escape the backslashes.
Regex demo | Java demo
To get only 3 matches, you could use
^[a-zA-Z]+ ((?:\d{11}|\d{14})|(?:\d{3}\.\d{3}\.\d{3}\-\d{2}|\d{3}\d{3}\d{3}\-\d{2})|(?:\d{2}\.\d{3}.\d{3}\/\d{4}-\d{2}|\d{2}\d{3}\d{3}\d{4}-\d{2})\b)
Regex demo | Java demo
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CROSS-REFERENCE TO RELATED APPLICATIONS
FEDERALLY SPONSORED RESEARCH
REFERENCE TO MATERIAL SUBMITTED SEPARATELY
BACKGROUND OF THE INVENTION
BRIEF SUMMARY OF THE INVENTION
DETAILED DESCRIPTION OF THE INVENTION
Not Applicable
Not Applicable
Not Applicable
The inventors realized that essentially all proposal labor and schedule estimates are based in Expert Judgement. Experts are required even when using relevant data on completed similar program work to create estimates since the complexity of the work or uniqueness of each problem requires an expert and lengthy comparison to the proposed work in order to generate an estimate. Program Managers and Business Development Managers face this reliance on Expert Judgement. Worse yet, the objective of Program Management is to complete programs with Schedule Performance and Cost Performance Indexes (SPI and CPI) of exactly 1. Finishing ahead of schedule or below budget should be positive for the Program Manager, but in actuality it means that the Program Manager did a poor job of estimating and locked up company funding that could've been used elsewhere. So how can a company determine a great Program Manager from an average one if it can't be determined if the estimates were poor or the execution great? This problem appears throughout business as estimating, performance assessment, and even personnel assignments and assessments are based on Expert Judgement. So the question the inventors answered is how can we break free of Expert Judgement and generate actual values or numerical ranges through automation?
The problem of business reliance on expert judgement is solved through charge number coding with an added code line for the complexity or work difficulty (a ‘complexity factor’). A complete charge number code provides the means to automate many business functions that are traditionally conducted through expert judgment. The primary purpose of the charge number code with Complexity Factor is to automate or assist in cost and schedule estimating. The use of a Complexity Factor in stored performance information provides the additional means for automating many Program Management, Business Development Management, and Personnel Management functions. These functions include personnel projections, scheduling, and assessment, program performance reporting, and Work Breakdown Structure (WBS) creation. The complete charge number code also provides the means for data navigation through the System and an integrated Business and Program Information Systems.
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The problem of business reliance on expert judgement is solved through charge number coding with an added code line for the complexity or work difficulty (a ‘complexity factor’). A complete charge number code, as shown in Drawing /, provides the means to automate many business functions that are traditionally conducted through expert judgment. The primary purpose of the charge number code with Complexity Factor is to automate or assist in cost and schedule estimating. The use of a Complexity Factor in stored performance information provides the additional means for automating many Program Management, Business Development Management, and Personnel Management functions. The complete charge number code also provides the means for data navigation and an integrated Business and Program Information Systems.
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Drawing / shows an example or recommended charge number format. This format includes the basics associated with any corporation such as the corporate Division, Program, and personnel Department, but completes the charge number with a Complexity Factor, program Phase, as well as Assembly and Task level information. Although this charge number format may appear complicated it can easily be completed by any employee charging and any employee working on estimates. The charging employee is not required to select the Division or Department when charging since they are associated with the employee's identification number or login information, which is stored in the database. The Program being charged is required for employees charging in most current business operations. The Complexity Factor is not assigned by or selected by the employee filling out their time sheet charging, but rather through the estimating process, which is described in detail in following paragraphs. Phases are simple and well known as Phases and Phase gates (often called Stages and Stage Gates) are required in standard program management. A typical Phase delineation is (1) Research and Development, (2) Bid and Proposal, (3) Design, (4) Development, (5) Qualification, and (6) Production. The cost associated with completing the same task on the same assembly can vary wildly in different phases therefore this information is important to record. The assembly or program Project level is simple to identify and beneficial in monitoring active program costs and estimating new program costs. The quantity of available tasks, at the Task level, can be greatly limited in a dropdown menu for the employees because tasks are tethered to the Division, Department, and Assembly. The tasks available for an employee to select in charging is also limited by the WBS inputs during estimating, as described in the following paragraphs. The charge number format is therefore simple for the employee since every employee should know where they work, for who they work, on what they're working, and what task they are performing before charging to a program.
Complexity Factors are framed in a way that makes them easily identifiable while capturing various levels of work difficulty. An example complexity factor table is shown in Table 1. This table demonstrates typical complexities associated with engineering firms that reuse, modify, or create new designs for similar, modified, or new applications. This form of Complexity Factor identification simplifies cost estimating since an estimator is only required to identify if the new program will perform work that has been previously conducted, as well as if the previous solutions will require modifications for the new program work. This Complexity Factor structure captures various levels of difficulty, as reusing designs requires less work than developing new designs and applying known designs to similar applications requires less work than applying new designs on new applications. This example format is therefore easily distinguishable while capturing various levels of work difficulty.
TABLE 1
CF #
Complexity Factor Description
1
Reused Design on Similar Application
2
Reused Design on Modified Application
3
Reused Design on New Application
4
Modified Design on Similar Application
5
Modified Design on Modified Application
6
Modified Design on New Application
7
New Design on Similar Application
8
New Design on Modified Application
9
New Design on New Application
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Another way of viewing charge number coding would use multiple measures of complexity through additional dash lines. For example, in software development there is a complexity factor associated with developing new code versus updating existing code, as well as porting to a different language or baseline, modifying to a change in hardware or operating system. There is also a complexity associated with the volume of code such as the number of lines or blocks. In cases such as this more than one parametric measure may be required and the estimation codes within the System need to reflect this. An example code for multiple parametric measures is shown in Drawing /.
The work process, hereby referred to as ‘the System’, is closed looped. The System stores the hours and cost associated with completing the program's tasks as existing programmatic work is conducted. The recorded task performance data provides new program creation information including Tasks associated with Assembly or High Level work for Work Breakdown Structure (WBS) creation. Once Complexity Factors are added to a New Program WBS the System provides cost and schedule estimates. When the new program is initiated, the System provides the charge number set for the new program to charge against thereby looping the process.
The System is able to generate estimates for proposal or projects through the stored, coded programmatic data without the use of expert judgement. A Program number is assigned to the proposal or project. A Work Breakdown Structure is then used to identify the assemblies and optional tasks required to complete the proposed or project work. Each WBS item is assigned a Complexity Factor and the WBS is then input into the System with the same coded charge number format as used by employees when charging. Team members involved in the estimating process are not required to provide expert judgement in the estimation process as they are only required to identify the Complexity Factor of a given task. The System takes the coded WBS and provides a cost and schedule estimate for each item based on stored data and available resources. The assembly or task level costs are then rolled up into a total programmatic cost. This process can be iterative, as a desire to shorten schedule requires the System to bias its comparative analysis to the shorter schedule and presumably higher cost data points within the data set. It is worth noting that Initial System implementation can use historical information that is coded for the System or it can be implemented on a moving forward basis in which the initial WBSs and estimates would require expert judgement for tasks not yet recorded in the System.
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New Program creation page, example shown in Drawing /, provides the means for the Program or Business Development offices to create new programs in the System. The System assigns the next available Program number. The creator then inputs the assemblies associated with the new program. The System retrieves tasks associated with the assemblies and the creator simply selects or adds tasks to build a Work Breakdown Structure (WBS). The creator selects complexity factors at the assembly or task levels and the System provides the cost and schedule estimates for the new program based on historical information. This estimating can be as simple as taking an average and deviation when several data points for the same task at the same Complexity Factor and schedule duration are available. When data points for the same task at the same complexity factor are not available, the System can estimate the cost through the application of regression analysis the same task at various complexity factors. The System outputs can be overridden by clicking into cost or schedule outputs and entering an estimating page, which is shown in Drawing /. This view demonstrates how valuable the System is in creating and estimating new programs. The System knows previously charged tasks under each assembly, therefore knows the recommended subtasks. The System also knows the costs and schedule to complete each task based on complexity factor, therefore the System removes the need for expert judgement in estimating.
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Drawing / shows an example Cost and Scheduling Estimating View. This view shows the power of the overall System, as it has both historical data and schedule availability readily available. The System can estimate costs based on the desired schedule with the Complexity Factor, while confirming availability of resources based on Program priority and flagging if additional resources will be required to complete the work on schedule. If estimates aren't available for new or initial work than the estimate would need to be provided by an expert.
The System's ability goes beyond estimating and into Personnel Management. The System stores data on the employee's identification number along with the task worked when the employee charges a program. This information allows the System to identify employee's capabilities on particular tasks. The system provides estimates on cost and schedule to complete tasks, so it can identify employees that over or underperform its projections. This is used in personnel assessments along with colleague assessments, such as 360 degree evaluations. The System also has information on the complexity of tasks that each employee has completed. With information on the employee's performance and complexity capabilities, the System assigns the proper personnel to complete upcoming tasks. With information on upcoming tasks, and assigned employees, the System also identifies shortfalls or excess in labor. It outputs the shortfalls to Human Resources and/or Personnel Management. The System also identifies the level of capability that is required to complete the coming work. This information is directly used for both hiring or layoff determinations, as it provides both the employee levels and skills required to complete projected work. Additionally, the System creates and/or has access to personnel assignments therefore can provide the employee with a limited set of charge numbers to which the employee is assigned for program charging purposes. By providing the limited set of charge numbers the System mitigates the risk of improper or inaccurate charging.
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The Department view, example shown in Drawing /, contains all key information on the Department's personnel. The System can establish employee capability based on previous tasks completed and the tasks complexity factor. The Department view also provides management with easy access to employee's schedules as assigned by the System for override when necessary or to assign an employee a higher level task, ‘Stretch Assignment’ as a reward for success or based on new capabilities such as those acquired through training or continuing education.
Charge number coding also provides a means for quick data access and information system navigation. Security settings associated with employee identification numbers and passwords limit access to applicable data retrieval and managerial control functions. The charge number code is then used to pull up the desired information or management window.
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The System provides a means of rapid data entry or navigation. As shown in example Drawing /, data entry such as time charging and data navigation can be handled in the same window using charge number coding. Drop down options on each item make data entry and navigation simple. Selecting a Division and a Program of ‘New’ for example would take a Program Office or Business Development manager to a new Program creation and cost estimating function, while Executive data navigation entries of ‘all’ or a coded charge number entry of ‘0’, for example, open corporate, divisional, or department overviews.
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The Corporate view contains all key information on the corporation's divisions. An example view and key information set is shown in Drawing /. A single click on any listed item can bring up complete data, while a click on the Divisional picture navigates to the Divisional overview.
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The Divisional view contains all desired key information on the Division's Programs. An example view and key information set is shown in Drawing /. A single click on any listed item can bring up complete data, while a click on the Program Picture navigates to the Program overview.
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The Program view contains all key information on the Program's current and historical performance. An example view and key information set is shown in shown in Drawing /, A single click on any listed item can bring up complete data. The progression from Corporate overview to Program view with just three selections demonstrates the power of the System's navigation capability. This ability is aided by being tethered to the charge number coding in that each link simply navigates to the System page for that coded entry.
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The Assembly view, example shown in Drawing /, contains all key information on any assembly. This information includes the cost and schedules required to complete work at the assembly level, as well as a list of typical subtasks that must be completed in order to finish the assembly level work. Drawing / shows data trending. In general, the cost of completing work increases with complexity factor and decreases with longer schedules.
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The Assembly view with Complexity Factor, example shown in Drawing /, shows the variability in the cost of completing assembly level work, as well as the impact of schedule on the same Assembly type with the same level of complexity. This view is a subset of the Assembly level view with the addition of a complexity factor. The view can also be reached by simply clicking on a complexity factor in the Assembly view window.
BRIEF DESCRIPTION OF THE DRAWINGS
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The schematic drawings, / and /, show basic inputs and outputs of a coded charge number System with Complexity Factor. The System can perform most business functions with basic coded Work Breakdown Structure (WBS) and priority inputs from Business Development and/or Program Management offices, labor rates, and employee coded charging. When new programs or new business bids are created the System takes in the WBS with Complexity Factor coding and outputs projected estimates for both schedule and cost. Once the new business or program is entered the System tentatively assigns/schedules resources/employees to the work tasks and outputs projected labor needs. Once the new business or program is initiated the System opens the charge numbers, assigns the scheduled personnel, and outputs labor and cost profiles, as well as labor needs. As the program progresses the System outputs real-time performance information. The System also provides immediate data access to executive and management teams, as well as the ability for executives to reestablish program relative priorities.
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Drawing / is an example format for a coded charge number includes the basics associated with any corporation such as the corporate Division, Program being charged, and Personnel Department, but completes the charge number with a Complexity Factor, Phase of the program, and Assembly and Task level information. Drawing / is an example System Coding with an additional Complexity Factor Volume.
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Drawings / through / depict example system interface views. The system interface and navigational approach are discussed in the Detailed Description of the Invention paragraphs [0016] through [0026]. | |
25-year old Alec Scott Abraham of Costa Mesa was convicted of two counts of second-degree murder and sentenced to 30 years to life in prison in February. On June 10, 2015, Abraham was driving a Mustang when he swerved into a left-turn lane and collided with a Chevrolet Cruz. Inside the Chevy Cruz were 54-year-old Katherine Hampton and 2-year-old Kaydence Hampton. Kaydence’s mother Megan and brother Nathaniel were also in the car at the time of the collision. Katherine and Kaydence Hampton were both killed in the crash, and Megan suffered from a broken jaw while Nathaniel suffered from a broken collarbone. Abraham claims he is “a victim in this case” but he is being sentenced to 30 years to life after being convicted of two counts of second-degree murder.
In court, Orange County Superior Court Judge Cheri Pham reprimanded Abraham repeatedly for his outburts and for interrupting the proceedings. While in court, the families of the victims read statements regarding the impact this case and the deaths of their family members has had on them. According to Senior Deputy District Attorney Whitney Bokosky, Abraham was accelerating 100% and speeding at 75 mph when he T-boned the Chevy Cruz.
In addition, Abraham has shown a history of reckless driving to the point that his co-workers warned him to stop driving “like an idiot” and even forwarded a video of him driving a Mustang at 140 mph to the California Highway Patrol. Abraham called his father after the crash to pick him up, and he was arrested a day later in Costa Mesa. | https://www.fredthia.com/blog/2020/march/25-year-old-driver-sentenced-to-30-years-to-life/ |
---
abstract: 'Let $d(n; r_1, q_1, r_2, q_2)$ be the number of factorization $n=n_1n_2$ satisfying $n_i\equiv r_i\pmod{q_i}$ ($i=1,2$) and $\Delta(x; r_1, q_1, r_2, q_2)$ be the error term of the summatory function of $d(n; r_1, q_1, r_2, q_2)$ with $x\geq (q_1q_2)^{1+\varepsilon}, 1\leq r_i\leq q_i$, and $(r_i, q_i)=1$ ($i=1, 2$). We study the power moments and sign changes of $\Delta(x; r_1, q_1, r_2, q_2)$, and prove that for a sufficiently large constant $C$, $\Delta(q_1q_2x; r_1, q_1, r_2, q_2)$ changes sign in the interval $[T,T+C\sqrt{T}]$ for any large $T$. Meanwhile, we show that for a small constant $c''$, there exist infinitely many subintervals of length $c''\sqrt{T}\log^{-7}T$ in $[T,2T]$ where $\pm \Delta(q_1q_2x; r_1, q_1, r_2, q_2)> c_5x^\frac{1}{4}$ always holds.'
address:
- 'Department Of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China '
- 'Department of Mathematics, China University of Mining and Thechnology, Beijing 100083, People’s Republic of China '
- 'School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, People’s Republic of China '
author:
- Lirui Jia
- Wenguang Zhai
- Tianxin Cai
bibliography:
- 'jia2.bib'
title: on the divisor problem with congruence conditions
---
[^1]
Introduction
============
Dirichlet divisor problem
-------------------------
Let $d(n)$ be the Dirichlet divisor function, $D(x)=\mathop{{\sum}}\limits_{n\leq x}d(n)=\mathop{{\sum}}\limits_{n_1n_2\leq x}1$ be the summatory function. In 1849, Dirichlet proved that $$D(x)=x\log x+(2\gamma-1)x+O(\sqrt{x}),$$ where $\gamma$ is the Euler constant.
Let $$\Delta(x)=D(x)-x\log x-(2\gamma-1)x$$ be the error term in the asymptotic formula for $D(x)$. Dirichlet’s divisor problem consists of determining the smallest $\alpha$, for which $\Delta(x)\ll x^{\alpha+\varepsilon}$ holds for any $\varepsilon>0$. Clearly, Dirichlet’s result implies that $\alpha\leq\frac{1}{2}$. Since then, there are many improvements on this estimate. The best to-date is given by Huxley[@Huxley03; @huxley2005exponential], reads $$\label{huxley}
\Delta(x)\ll x^\frac{131}{416}\log^\frac{26947}{8320}x.$$ It is widely conjectured that $\alpha=\frac{1}{4}$ is admissible and is the best possible.
Since $\Delta(x)$ exhibits considerable fluctuations, one natural way to study the upper bounds is to consider the moments.
In 1904, Voronoi [@voronoi1904fonction] showed that $$\int_1^T\Delta(x)dx=\frac{T}{4}+O(T^{\frac{3}{4}}).$$ Later, in 1922 Cramér[@cramer1922zwei] proved the mean square formula $$\int_1^T\Delta(x)^2dx=cT^{\frac{3}{2}}+O(T^{\frac{5}{4}+\varepsilon}),\quad\forall~\varepsilon>0,$$ where $c$ is a positive constant. In 1983, Ivic [@ivic1983large] used the method of large values to prove that $$\label{ivic}
\int_1^T|\Delta(x)|^Adx\ll T^{1+\frac{A}{4}+\varepsilon},\quad\forall~\varepsilon>0$$ for each fixed $0\leq A\leq\frac{35}{4}$. The range of $A$ can be extended to $\frac{262}{27}$ by the estimate . In 1992, Tsang[@tsang1992higher] obtained the asymptotic formula $$\label{01}
\int_1^T\Delta(x)^kdx=c_kT^{1+\frac{k}{4}}+O(T^{1+\frac{k}{4}-\delta_k}),\quad \text{for}\ k=3,4,$$ with positive constants $c_3$, $c_4$, and $\delta_3=\frac{1}{14}$, $\delta_4=\frac{1}{23}$. Ivić and Sargos [@ivic2007higher] improved the values $\delta_3$, $\delta_4$ to $\delta'_3=\frac{7}{20}$, $\delta'_4=\frac{1}{12}$, respectively. Heath-Brown[@heath1992distribution] in 1992 proved that for any positive real number $k<A$, where $A$ satisfies , the limit $$c_k=\lim_{X\rightarrow\infty}X^{-1-\frac{k}{4}}\int_1^X\Delta(x)^kdx$$ exists. Then, there followed a series of investigations on explicit asymptotic formula of the type for larger values of $k$. In 2004, Zhai [@zhai04] established asymptotic formulas for $3\leq k\leq9$.
At the beginning of the 20th century, Voronoi[@voronoi1904fonction] proved the remarkable exact formula that $$\Delta(x)=-\frac{2}{\pi}\sqrt{x}\sum_{n=1}^\infty\frac{d(n)}{\sqrt{n}}\big(K_1(4\pi\sqrt{nx})+ \frac{\pi}{2}Y_1(4\pi\sqrt{nx})\big),$$ where $K_1$, $Y_1$ are the Bessel functions, and the series on the right-hand side is boundedly convergent for $x$ lying in each fixed closed interval.
Heath-Brown and Tsang [@heathbrown1994sign] studied the sign changes of $\Delta(x)$. They proved that for a suitable constant $C > 0$, $\Delta(x)$ changes sign on the interval $[T,T + C \sqrt{T}]$ for every sufficiently large $T$. Here the length $\sqrt{T}$ is almost best possible since they proved that in the interval $[T,2T]$ there are many subintervals of length $\gg\sqrt{T}\log^{-5}T$ such that $\Delta(x)$ does not change sign in any of these subintervals.
The divisor problem with congruence conditions
----------------------------------------------
A divisor function with congruence conditions is defined by $$% \nonumber to remove numbering (before each equation)
d(n; r_1, q_1, r_2, q_2) =\mathop{{\sum}}_{\begin{subarray}{c} n=n_1n_2\\n_i\equiv r_i\!\!\!\!\!\pmod{q_i}\\i=1, 2\end{subarray}}{1},$$ of which, the summatory function is $$D(x; r_1, q_1, r_2, q_2) =\mathop{{\sum}}_{\begin{subarray}{c} n_1n_2\leq x\\n_i\equiv r_i\!\!\!\!\!\pmod{q_i}\\i=1, 2\end{subarray}}{1}.$$
From Richert [@Richert], we can find that for $x\geq q_1q_2$, $1\leq r_i\leq q_i$ ($i=1, 2$) $$\begin{gathered}
\label{4}
D(x; r_1, q_1, r_2, q_2)\\
= \frac{x}{q_1q_2}\log\Big(\frac{x}{q_1q_2}\Big) - \bigg(\frac{\Gamma'}{\Gamma}\Big(\frac{r_1}{q_1}\Big) + \frac{\Gamma'}{\Gamma}\Big(\frac{r_2}{q_2}\Big) +1\bigg)\frac{x}{q_1q_2}+\Delta(x; r_1, q_1, r_2, q_2).\end{gathered}$$
From Huxley’s estimates[@Huxley03], it follows that $$\label{9a}
\Delta(x; r_1, q_1, r_2, q_2)\ll\Big(\frac{x}{q_1q_2}\Big)^\frac{131}{416}\Big(\log\Big(\frac{x}{q_1q_2}\Big)\Big)^\frac{26947}{8320}$$ uniformly in $1\leq r_1\leq q_1\leq x, 1\leq r_2\leq q_2\leq x$. It is conjectured that $$\label{conjecture}
\Delta(x; r_1, q_1, r_2, q_2)\ll\Big(\frac{x}{q_1q_2}\Big)^{\frac{1}{4}+\varepsilon}$$ uniformly in $1\leq r_1\leq q_1\leq x, 1\leq r_2\leq q_2\leq x$, $\forall\varepsilon>0$, which is an analogue of the well-known conjecture that $\Delta(x)\ll x^{\frac{1}{4}+\varepsilon}$.
Müller and Nowak[@MullerNowak] studied the mean value of $\Delta(x; r_1, q_1, r_2, q_2)$. They pointed out $$\label{muller}
\int_1^T{\Delta(x; r_1, q_1, r_2, q_2)}dx=\big(\frac{r_1}{q_1}-\frac{1}{2}\big)\big(\frac{r_2}{q_2}-\frac{1}{2}\big)T+O\big( (q_1q_2)^{\frac{1}{4}}T^{\frac{3}{4}}\big),$$ and $$\label{muller2}
\int_1^T{\Delta^2(x; r_1, q_1, r_2, q_2)}dx=c_2(q_1q_2)^{\frac{1}{2}}T^\frac{3}{2}+o\big((q_1q_2)^{\frac{1}{2}}T^\frac{3}{2}\big),$$ uniformly in $1\leq r_i\leq q_i\leq T$ $(i=1, 2)$, if $T$ is a large number, and $c_2$ is a constant.
In [@Jiazhai2017], we show that $$\label{pre}
\int_1^T|\Delta(q_1q_2x; r_1, q_1, r_2, q_2)|^Adx\ll T^{1+\frac{A}{4}}\mathcal{L}^{4A},$$ for $0\leq A\leq\frac{262}{27}$ and $T\gg(q_1q_2)^\varepsilon$.
Here we study $\Delta(x; r_1, q_1, r_2, q_2)$ further and give some more results about it.
<span style="font-variant:small-caps;">Notations</span>. For a real number $t$, let $[t]$ be the largest integer no greater than $t$, $\{t\}=t-[t]$, $\psi(t)=\{t\}-\frac{1}{2}$, $\parallel t\parallel=\min(\{t\}$, $1-\{t\})$, $e(t)=e^{2\pi it}$. $\mathbb{C}$, $\mathbb{R}$, $\mathbb{Z}$, $\mathbb{N}$ denote the set of complex numbers, of real numbers, of integers, and of natural numbers, respectively; $f\asymp g$ means that both $f\ll g$ and $f\gg g$ hold. Throughout this paper, $\varepsilon$ denote sufficiently small positive constants, and $\mathcal{L}$ denotes $\log T$.
Main results {#sec:results}
============
In this paper, we will first discuss the power moments of $\Delta(x; r_1, q_1, r_2, q_2)$ and get the following
\[th:moments\] If $T\gg (q_1q_2)^{\varepsilon}$ is large enough. If $A_{0}>9$ satisfies $$\int_1^{T}{|\Delta(q_1q_2x; r_1, q_1, r_2, q_2)|^{A_0}}dx\ll T^{1+\frac{A_0}{4}+\varepsilon},$$ then for any fixed integer $3\leq k<A_0$, we have $$\label{sk}
\int_1^{T}{\Delta^k(q_1q_2x; r_1, q_1, r_2, q_2)}dx
=C_k\int_1^Tx^{\frac{k}{4}}dx+o\big(T^{1+\frac{k}{4}}\big),$$ where $C_k\asymp 1$ are explicit constants.
From , we can take $A_0=\frac{262}{27}$, which means
\[cor:1\] If $T, r_i$ and $q_i (i=1,2)$ satisfying the hypothesis of Theorem \[th:moments\], then holds for any fixed integer $3\leq k\leq9$.
By using the estimates above, we can get the sign changes of $\Delta(x; r_1, q_1, r_2, q_2)$ as following
\[th:change\] Let $c_1 > 0$ be a sufficiently small constant and $c_2 > 0$ be a sufficiently large constant, $q_1\geq 2$, $q_2\geq 3$, $1\leq r_i\leq q_i$ and $(r_i, q_i)=1$ $(i=1, 2)$. For any real-valued function $|f(t)|\leq c_1 t^\frac{1}{4}$, the function $\Delta(q_1q_2t; r_1, q_1, r_2, q_2)+f(t)$ changes sign at least once in the interval $[T,T + c_2 \sqrt{T}]$ for every sufficiently large $T\gg (q_1q_2)^{\varepsilon}$. In particular, there exist $t_1$, $t_2\in [T,T +c_2 \sqrt{T}]$ such that $\Delta(q_1q_2t_1; r_1, q_1, r_2, q_2)\geq c_1 t_1^\frac{1}{4}$ and $\Delta(q_1q_2t_2; r_1, q_1, r_2, q_2)\leq -c_1 t_2^\frac{1}{4}$.
\[th:maintain\] There exist three positive absolute constants $c_3$ ,$c_4$ ,$c_5 $ such that, for any large parameter $T\gg (q_1q_2)^{\varepsilon}$, and any choice of $\pm$ signs, there are at least $c_3 \sqrt{T} log^{7}T$ disjoint subintervals of length $c_4 \sqrt{T} log^{-7}T$ in $[T,2T]$, such that $\pm \Delta(q_1q_2t; r_1, q_1, r_2, q_2)> c_5t^\frac{1}{4}$, whenever $t$ lies in any of these subintervals. Moreover, we have the estimate $$meas\big\{t\in[T,2T]:\pm \Delta(q_1q_2t; r_1, q_1, r_2, q_2)> c_5 t^\frac{1}{4}\big\}\gg T.$$
We also study the $\Omega$-result of the error term in the asymptotic formula for odd $k$ by using Theorem \[th:maintain\]. Define $$\mathcal{F}_k\big(q_1q_2x; r_1, q_1, r_2, q_2\big):=\int_1^{T}{\Delta^k\big(q_1q_2x; r_1, q_1, r_2, q_2\big)}dx
-C_kT^{1+\frac{k}{4}}.$$ We have the following
\[th:omega\] For any $T\gg (q_1q_2)^{\varepsilon}$, the interval $[T, 2T]$ contains a point $X$, for which $$\mathcal{F}_k\big(q_1q_2X; r_1, q_1, r_2, q_2\big)\gg X^{\frac{1}{2}+\frac{k}{4}}\mathcal{L}^{-7}.$$
Although at the present moment we can only prove for $2\leq k\leq 9$, Theorem \[th:omega\] holds for any odd $k\geq 2$.
proof of Theorem \[th:moments\]
===============================
In this section, we prove Theorem \[th:moments\] by using the Voronoi-type formula for $\Delta(x; r_1, q_1, r_2, q_2)$.
$($ See [@Jiazhai2017] $)$\[lem:vor\]
Let $J=[\frac{\mathcal{L}+2\log q_1q_2-4\log \mathcal{L}}{\log2}]$, $H\geq2$ be a parameter to be determined, and $ T^\varepsilon<y\leq \min(H^2, (q_1q_2)^2 T)\mathcal{L}^{-4}$. Suppose $\frac{T}{2}\leq x\leq T$. Then $$\begin{gathered}
\label{vor0}
% \nonumber to remove numbering (before each equation)
\Delta(q_1q_2x; r_1, q_1, r_2, q_2)=R_0(x; y)+{R_{12}}(x; y, H)+{R_{21}}(x; y, H)\\+G_{12}(x; H)+G_{21}(x; H)
+O\big(\log^3(q_1q_2T)\big),\end{gathered}$$ where $$\begin{aligned}
% to remove numbering (before each equation)
R_0(x; y)&=\frac {x^{\frac{1}{4}}}{\sqrt{2}\pi}\sum_{n\leq y}\frac{1}{n^{\frac{3}{4}}}\sum_{n=hl}\cos\bigg(4\pi \sqrt{nx}-2\pi\Big(\frac{hr_2}{q_2}+\frac{lr_1}{q_1}+\frac{1}{8}\Big)\bigg), \label{R_0} \\
\nonumber{R_{12}}(x; y, H)&=\frac {x^{\frac{1}{4}}}{\sqrt{2}\pi}\sum_{y<n\leq 2^{J+1}H^2}\frac{1}{n^{\frac{3}{4}}}\!\!\mathop{{\sum}'}_
{\begin{subarray}{c} n=hl\\ 1\leq h\leq H\\ h\leq l\leq2^{J+1}h\end{subarray}}
\!\!\!\!\cos\bigg(4\pi \sqrt{nx}\!-\!2\pi\Big(\frac{hr_2}{q_2}\!+\!\frac{lr_1}{q_1}\!+\!\frac{1}{8}\Big)\bigg), \\
\nonumber {R_{21}}(x; y, H)&=\frac {x^{\frac{1}{4}}}{\sqrt{2}\pi}\sum_{y<n\leq 2^{J+1}H^2}\frac{1}{n^{\frac{3}{4}}}\!\!\mathop{{\sum}'}_
{\begin{subarray}{c} n=hl\\ 1\leq h\leq H\\ h\leq l\leq2^{J+1}h\end{subarray}}
\!\!\!\!\cos\bigg(4\pi \sqrt{nx}\!-\!2\pi\Big(\frac{hr_1}{q_1}\!+\!\frac{lr_2}{q_2}\!+\!\frac{1}{8}\Big)\bigg), \\
\nonumber G_{12}(x; H)&=\sum_{\begin{subarray}{c} n_1\leq q_1\sqrt{T}\\ n_1\equiv r_1\!\!\!\!\!\pmod{q_1}\end{subarray}}O\biggl(\min\Bigl(1, \frac{1}{H\|\frac{q_1x}{n_1}-\frac{r_2}{q_2}\|}\Bigr)\biggr),\\
\nonumber G_{21}(x; H)&=\sum_{\begin{subarray}{c} n_2\leq q_2\sqrt{T}\\ n_2\equiv r_2\!\!\!\!\!\pmod{q_2}\end{subarray}}O\bigg(\min\Big(1, \frac{1}{H\|\frac{q_2x}{n_2}-\frac{r_1}{q_1}\|}\Big)\bigg).\end{aligned}$$
where ${\sum\limits_{n\leq x}}' f(n)$ indicates that if $x$ is an integer, then only $\frac{1}{2}f(x)$ is counted.
Thus, we can get Theorem \[th:moments\] by using Lemma \[lem:vor\] with the approach of Liu [@LiuKui].
Proof of Theorem \[th:change\]
==============================
In this section, we prove Theorem \[th:change\] following the approach of [@heathbrown1994sign].
Suppose $|f(t)|\leq c_1 t^\frac{1}{4}$. Let $$\Delta^{**}(t)=\sqrt{2}\pi t^{-\frac{1}{2}}\Big(\Delta(q_1q_2t^2; r_1, q_1, r_2, q_2)+f(t^2)\Big),\quad \text{for }t\geq1.$$ Define $$K_\zeta(u):=(1-|u|)\big(1+\zeta\sin(4\pi\alpha u)\big)\quad\text{for }|u|\leq1,$$ with $\zeta=1$ or $-1$, and $\alpha>1$ a large number.
\[lem:change\] Suppose $T\gg(q_1q_2)^\varepsilon$ is a large parameter. Then for each $\sqrt{T}\leq t\leq\sqrt{2T}$, we have $$\begin{aligned}
&\int_{-1}^1\Delta^{**}(t+\alpha u)K_\zeta(u)du\\
=&-\frac{\zeta}{2}\sin\bigg(4\pi t -2\pi\Big(\frac{r_2}{q_2}+\frac{r_1}{q_1}+\frac{1}{8}\Big)\bigg) +O(\alpha^{-2})\\
&+O\big(t^{-\frac{1}{2}}\sup_{|u|\leq1}f((t\!+\!\alpha u)^2)\big)\!+\!O\big(t^{-\frac{1}{2}}\mathcal{L}^3\big).\end{aligned}$$
Let $J=[\frac{\mathcal{L}+2\log q_1 q_2-4\log \mathcal{L}}{\log2}]$, $H\geq2$ be a parameter to be determined, and $ T^\varepsilon<y\leq \min(H^2, (q_1q_2)^2 T)\mathcal{L}^{-4}$. From , we have $$\begin{aligned}
\label{vor}
\Delta^{**}(t)=&R^*_0(t; y)\!+\!R^*_{12}(t; y, H)\!+\!R^*_{21}(t; y, H)\!+\!\sqrt{2}\pi t^{-\frac{1}{2}}f(t^2)\\
\nonumber&\!+\!O\big(t^{-\frac{1}{2}}\big(G^*_{12}(t; H)\!+\!G^*_{21}(t; H)\big)\big)
\!+\!O\big(t^{-\frac{1}{2}}\mathcal{L}^3\big),\end{aligned}$$ where $$\begin{aligned}
R^*_0(t; y)&=\sum_{n\leq y}\frac{1}{n^{\frac{3}{4}}}\sum_{n=hl}\cos\bigg(4\pi \sqrt{n}t-2\pi\Big(\frac{hr_2}{q_2}+\frac{lr_1}{q_1}+\frac{1}{8}\Big)\bigg),\\
R^*_{12}(t; y, H)&=\sum_{y<n\leq 2^{J+1}H^2}\frac{1}{n^{\frac{3}{4}}}\mathop{{\sum}'}_
{\begin{subarray}{c} n=hl\\ 1\leq h\leq H\\ h\leq l\leq2^{J+1}h\end{subarray}}
\cos\bigg(4\pi \sqrt{n}t\!-\!2\pi\Big(\frac{hr_2}{q_2}+\frac{lr_1}{q_1}+\frac{1}{8}\Big)\bigg),\\
R^*_{21}(t; y, H)&=\sum_{y<n\leq 2^{J+1}H^2}\frac{1}{n^{\frac{3}{4}}}\mathop{{\sum}'}_
{\begin{subarray}{c} n=hl\\ 1\leq h\leq H\\ h\leq l\leq2^{J+1}h\end{subarray}}
\cos\bigg(4\pi \sqrt{n}t\! -\!2\pi\Big(\frac{hr_1}{q_1}+\frac{lr_2}{q_2} +\frac{1}{8}\Big)\bigg),\\
G^*_{12}(t; H) &= \sum_{\begin{subarray}{c} n_1\leq q_1\sqrt{T}\\ n_1\equiv r_1\!\!\!\!\!\pmod{q_1}\end{subarray}}\min\Bigl(1, \frac{1}{H\|\frac{q_1t^2}{n_1}-\frac{r_2}{q_2}\|}\Bigr),\label{G12}\\
G^*_{21}(t; H)&=\sum_{\begin{subarray}{c} n_2\leq q_2\sqrt{T}\\ n_2\equiv r_2\!\!\!\!\!\pmod{q_2}\end{subarray}}\min\Big(1, \frac{1}{H\|\frac{q_2t^2}{n_2}-\frac{r_1}{q_1}\|}\Big).\end{aligned}$$ Denote $$\begin{aligned}
&R^*(t)=R^*_0(t; y)\!+\!R^*_{12}(t; y, H)\!+\!R^*_{21}(t; y, H),&
&G^*(t)=G^*_{12}(t; H)\!+\!G^*_{21}(t; H).\end{aligned}$$ Then $$\label{s}
\Delta^{**}(t)=R^*(t)\!+\sqrt{2}\pi t^{-\frac{1}{2}}f(t^2)\!+\!O\big(t^{-\frac{1}{2}}G^*(t)\big)
\!+\!O\big(t^{-\frac{1}{2}}\mathcal{L}^3\big).$$
We first consider $\int_{-1}^1G^*(t+\alpha u)du$. Noting that $$\min\Big(1,\frac{1}{H\|r\|}\Big)=\sum_{h=-\infty}^\infty a(h)e(hr)$$ with $$\begin{aligned}
a(0)\ll H^{-1}\log H,&&a(h)\ll\min\Big(H^{-1}\log H,h^{-2}H\Big),\ h\neq0.\end{aligned}$$ We have $$\begin{aligned}
&\int_{-1}^1G^*_{12}(t+\alpha u;H)du\\
=&\sum_{h=-\infty}^\infty a(h)\sum_{\begin{subarray}{c} n_1\leq q_1\sqrt{T}\\ n_1\equiv r_1\!\!\!\!\!\pmod{q_1}\end{subarray}}e\Big(\frac{hq_1t^2}{n_1}-\frac{hr_2}{q_2}\Big)\int_{-1}^1e\Big(\frac{2hq_1t\alpha u+hq_1\alpha^2u^2}{n_1}\Big)du\\
\ll&|a(0)|\sqrt{T}+\sum_{h=1}^\infty |a(h)|\sum_{\begin{subarray}{c} n_1\leq q_1\sqrt{T}\\ n_1\equiv r_1\!\!\!\!\!\pmod{q_1}\end{subarray}}\frac{n_1}{hq_1t\alpha}\\
\ll&H^{-1}T^\frac{1}{2}\log H+\sum_{h=1}^HH^{-1}(\log H)T(ht\alpha)^{-1}+\sum_{h=H}^\infty HT(t\alpha)^{-1}h^{-3}\\
\ll&H^{-1}T^\frac{1}{2}\log^2 H,\end{aligned}$$ where the first derivative test was used. This estimate remain valid with $G^*_{12}$ replaced by $G^*_{21}$, which yields $$\label{G}
\int_{-1}^1G^*(t+\alpha u)du\ll H^{-1}T^\frac{1}{2}\log^2 H.$$
Now we estimate the integral $\int_{-1}^1R^*(t+\alpha u)K_\zeta(u)du$. Let $\theta_0$ be some constant. By the elementary formula $$\begin{aligned}
&\cos\big(4\pi (t+\alpha u)\sqrt{n}+\theta_0\big)\\
=&\cos\big(4\pi t\sqrt{n}+\theta_0\big)\cos(4\pi \alpha u\sqrt{n})-\sin\big(4\pi t\sqrt{n}+\theta_0\big)\sin(4\pi \alpha u\sqrt{n}),\end{aligned}$$ we get $$\begin{aligned}
\int_{-1}^1\cos\big(4\pi (t+\alpha u)\sqrt{n}+\theta_0\big)(1-|u|)\big(1+\zeta\sin(4\pi\alpha u)\big)du
=I_1-I_2,\end{aligned}$$ with $$\begin{aligned}
I_1=&\cos\big(4\pi t\sqrt{n}+\theta_0\big)\int_{-1}^1\cos(4\pi \alpha u\sqrt{n})(1-|u|)\big(1+\zeta\sin(4\pi\alpha u)\big)du\\
=&\cos\big(4\pi t\sqrt{n}+\theta_0\big)\int_{-1}^1\cos(4\pi \alpha u\sqrt{n})(1-|u|)du,
\end{aligned}$$ $$\begin{aligned}
I_2=&\sin\big(4\pi t\sqrt{n}+\theta_0\big)\int_{-1}^1\sin(4\pi \alpha u\sqrt{n})(1-|u|)\big(1+\zeta\sin(4\pi\alpha u)\big)du\\
=&\zeta\sin\big(4\pi t\sqrt{n}+\theta_0\big)\int_{-1}^1\sin(4\pi \alpha u\sqrt{n})(1-|u|)\sin(4\pi\alpha u)du\\
=&\frac{\zeta}{2}\sin\big(4\pi t\sqrt{n}+\theta_0\big)\int_{-1}^1(1-|u|)\cos\big(4\pi\alpha u(\sqrt{n}-1)\big)du\\
&-\frac{\zeta}{2}\sin\big(4\pi t\sqrt{n}+\theta_0\big)\int_{-1}^1(1-|u|)\cos\big(4\pi\alpha u(\sqrt{n}+1)\big)du.\\\end{aligned}$$ By using $$\int_0^1(1-u)\cos(A u)du\ll |A|^{-2}\quad A\neq0,$$ we have $$\begin{aligned}
I_1\ll&\alpha^{-2}n^{-1},\\
I_2=&\left\{\begin{array}{ll}\frac{\zeta}{2}\sin\big(4\pi t\!+\theta_0\big)+O(\alpha^{-2}),&n=1, \\O(\alpha^{-2}(\sqrt{n}-1)^{-2}),&n\neq 1,\end{array}\right.\end{aligned}$$ which suggests $$\begin{aligned}
\int_{-1}^1\cos\big(4\pi (t+\alpha u)\sqrt{n}\!+\!\theta_0\big)K_\zeta(u)du=&\left\{\begin{array}{ll}-\frac{\zeta}{2}\sin\big(4\pi t\!+\theta_0\big)+O(\alpha^{-2}),&n=1, \\O(\alpha^{-2}(\sqrt{n}-1)^{-2}),&n\neq 1.\end{array}\right.\end{aligned}$$ Take $H= T$, $y= T^\frac{1}{2}$. Then clearly $y>1$. Thus we get $$\begin{aligned}
\label{R}
&\int_{-1}^1R^*(t+\alpha u)K_\zeta(u)du\\
\nonumber=&\!-\frac{\zeta}{2}\sin\bigg(4\pi t -2\pi\Big(\frac{r_2}{q_2}+\frac{r_1}{q_1}+\frac{1}{8}\Big)\bigg)+O\Big(\sum_{n>1}\frac{d(n)}{\alpha^2n^\frac{3}{4}(\sqrt{n}-1 )^{2}}\Big)\\
\nonumber=&\!-\frac{\zeta}{2}\sin\bigg(4\pi t -2\pi\Big(\frac{r_2}{q_2}+\frac{r_1}{q_1}+\frac{1}{8}\Big)\bigg) +O(\alpha^{-2}),\end{aligned}$$ by using $\sum_{n>1}\frac{d(n)}{n^\frac{3}{4}(\sqrt{n}-1)^{2}}\ll1$. Noting that $H=T$, $t\asymp T^\frac{1}{2}$, by -, we see $$\begin{aligned}
&\int_{-1}^1\Delta^{**}(t+\alpha u)K_\zeta(u)du\\
=&-\frac{\zeta}{2}\sin\bigg(4\pi t -2\pi\Big(\frac{r_2}{q_2}+\frac{r_1}{q_1}+\frac{1}{8}\Big)\bigg) +O(\alpha^{-2})\\
&+O\big(t^{-\frac{1}{2}}\sup_{|u|\leq1}f((t\!+\!\alpha u)^2)\big)\!+\!O\big(t^{-\frac{1}{2}}H^{-1}T^\frac{1}{2}\mathcal{L}^2\big)
\!+\!O\big(t^{-\frac{1}{2}}\mathcal{L}^3\big).\end{aligned}$$ Thus we complete the proof of Lemma \[lem:change\]
The mean value of $\Delta(q_1q_2x; r_1, q_1, r_2, q_2)$ in short intervals
===========================================================================
In this section, we need the following Lemma.
\[lem:Hil\]$($ Hilbert’s inequality $)$$($ See e.g.[@shan] $)$[ ]{} Let $x_1<x_2<\cdots<x_n$ be a sequence of real numbers. If there exists$ ~\delta>0$, such that $\min\limits_{s\neq r}|x_r-x_s|\geq \delta_r\geq\delta>0 (1\leq r\leq n)$, then there exists an absolute constant $C$, such that $$\bigg|\sum_{s\neq r}u_r\bar{{u_s}}(x_r-x_s)^{-1}\bigg|\leq C\sum_r {\delta_r}^{-1}\left|u_r\right|^2,$$ for arbitrary complex numbers $u_1,u_2,\cdots,u_n$.
Suppose $T\gg (q_1q_2)^{\varepsilon}$ is a large parameter, $1\leq h_0\leq \frac{1}{2}\sqrt{T}$. Denote $\Delta^{*}(q_1q_2x)=\Delta(q_1q_2x; r_1, q_1, r_2, q_2)$. In this section we shall estimate the integral $$I(T,h_0)=\int_1^T\big(\Delta^{*}(q_1q_2(x+h_0)-\Delta^{*}(q_1q_2x)\big)^2dx,$$ which would play an important role in the proof of Theorem \[th:maintain\]. This type of integral was studied for the error term in the mean square of $\zeta(\frac{1}{2}+ it)$ by Good [@good1977einomega], for the error term in the Dirichlet divisor problem by Jutila [@jutila1984divisor] and for the error term in Weyl’s law for Heisenberg manifold by Tsang and Zhai [@tsang2012sign]. Here we follows the approach of Tsang and Zhai [@tsang2012sign] and prove the following
\[lem:meanvalue\] The estimate $$I(T,h_0)\ll Th_0\log^3\frac{\sqrt{T}}{h_0}+T\mathcal{L}^6$$ holds uniformly for $1\leq h_0\leq \frac{1}{2}\sqrt{T}$.
Write $$\label{I}
I(T,h_0)=\int_1+\int_2,$$ where $$\begin{aligned}
\int_1=&\int_1^{100\max(h_0^2,T^\frac{2}{3})}(\Delta^{*}(q_1q_2(x+h_0)-\Delta^{*}(q_1q_2x)\big)^2dx,\\
\int_2=&\int_{100\max(h_0^2,T^\frac{2}{3})}^T(\Delta^{*}(q_1q_2(x+h_0)-\Delta^{*}(q_1q_2x)\big)^2dx.\end{aligned}$$ From Corollary \[cor:1\], we see that $$\label{int1}
\int_1\ll (h_0^3+T)\ll Th_0.$$
For $\int_2$, first we estimate the integral $$\label{J}
J(U,h_0)\!=\!\int_U^{2U}\!\!\!(\Delta^{*}(q_1q_2(x+h_0)-\Delta^{*}(q_1q_2x)\big)^2dx, \!\quad100\max(h_0^2,T^\frac{2}{3})\leq U\leq T.$$ Let $T=2U$ in . Then $$\begin{aligned}
\Delta^{*}(q_1q_2x)
=&R_0(x; y)\!+\!R_{12}(x; y, H)\!+\!R_{21}(x; y, H)\!\\
\nonumber&+\!G_{12}(x; H)\!+\!G_{21}(x; H)
\!+\!O\big(\log^3U\big).\end{aligned}$$ Take $H=U$, $y=\min\big(\frac{1}{2}Uh_0^{-1},U\log^{-6} U\big)$. From [@LiuKui Lemma 4.1 and eq.(4.11)], we see $$\begin{gathered}
\int_U^{2U}|G_{12}(x; H)\!+\!G_{21}(x; H)|^2dx\ll U\log U,\label{G2}\\
\int_U^{2U}|R_{12}(x; y, H)\!+\!R_{21}(x; y, H)|^2dx\ll U^\frac{3}{2}y^{-\frac{1}{2}}\log^3 U.\label{R2}\end{gathered}$$ Therefor $$\begin{aligned}
\label{s/r}
\int_U^{2U}\big(\Delta^{*}(q_1q_2x)-\!R_{0}(x; y)\big)^2dx\ll& U^\frac{3}{2}y^{-\frac{1}{2}}\log^3 U+ U\log^6 U\\
\nonumber \ll& Uh_0^\frac{1}{2}\log^3 U+ U\log^6 U.\end{aligned}$$
We now estimate $\int_U^{2U}\big(R_{0}(x+h_0; y)-R_{0}(x; y)\big)^2dx$. Set $\theta(h,l)=2\pi(\frac{hr_2}{q_2}+\frac{lr_1}{q_1})$. From , we have $$\label{dR0}
R_{0}(x+h_0; y)-R_{0}(x; y)=F_1(x)+F_2(x),$$ where $$\begin{aligned}
F_1(x)\!=&\frac{1}{\sqrt{2}\pi}\big((x\!+\!h_0)^\frac{1}{4}\!-\!x^\frac{1}{4}\big)\sum_{n\leq y}\!\frac{1}{n^{\frac{3}{4}}}\!\sum_{n=hl}\!\cos\!\big(\!4\pi \sqrt{n(x\!+\!h_0)}\!-\theta(h,l)\!-\!\frac{\pi}{4}\big)\!\Big),\\
F_2(x)\!=&\frac{x^\frac{1}{4}}{\sqrt{2}\pi}\!\sum_{n\leq y}\!\frac{1}{n^{\frac{3}{4}}}\!\sum_{n=hl}
\!\!\Big(\!\cos\!\big(\!4\pi\! \sqrt{n(x\!+\!h_0)}\!-\!\theta(h,l)\!-\!\frac{\pi}{4}\!\big)\!-\!\cos\big (4\pi\! \sqrt{nx}\!-\!\theta(h,l)\!-\!\frac{\pi}{4}\!\big)\!\Big).\end{aligned}$$
From [@LiuKui Proof of Lemma 4.2], we get $$\begin{aligned}
\label{F1}
\int_U^{2U}F_1^2(x)dx\ll h_0^2U^{-2}\int_U^{2U}R_0^2(x+h_0)dx\ll h_0^2U^{-\frac{1}{2}}.\end{aligned}$$
For the mean square of $F_2(x)$, we see $$\label{F20}
F_2^2=F_{21}+F_{22},$$ where $$\begin{aligned}
F_{21}(x)\!
=&\frac{x^\frac{1}{2}}{2\pi^2}\!\sum_{n\leq y}\!\frac{1}{n^{\frac{3}{2}}}\\
&\times\Big(\sum_{n=hl}\!\cos\!\big(\!4\pi \sqrt{n(x\!+\!h_0)}\!-\!\theta(h,l)\!-\!\frac{\pi}{4}\big)\!-\!\cos\big (4\pi \sqrt{nx}\!-\!\theta(h,l)\!-\!\frac{\pi}{4}\!\big)\!\Big)^2,\\
F_{22}(x)\!
=&\frac{x^\frac{1}{2}}{2\pi^2}\!\sum_{\begin{subarray}{c}n_1,n_2\leq y\\n_1\neq n_2\end{subarray}}\!\frac{1}{(n_1n_2)^{\frac{3}{4}}}\sum_{n_1=h_1l_1}\sum_{n_2=h_2l_2}\\
&\times\Big(\!\cos\!\big(\!4\pi \sqrt{n_1(x\!+\!h_0)}\!-\!\theta(h_1,l_1)\!-\!\frac{\pi}{4}\!\big)\!-\!\cos\big (4\pi \sqrt{n_1x}\!-\!\theta(h_1,l_1)\!-\!\frac{\pi}{4}\!\big)\!\Big)\\
&\times\Big(\!\cos\!\big(\!4\pi \sqrt{n_2(x\!+\!h_0)}\!-\!\theta(h_2,l_2)\!-\!\frac{\pi}{4}\!\big)\!-\!\cos\big (4\pi \sqrt{n_2x}\!-\!\theta(h_2,l_2)\!-\!\frac{\pi}{4}\!\big)\!\Big)\\
=&\frac{x^\frac{1}{2}}{2\pi^2}\!\sum_{\begin{subarray}{c}n_1,n_2\leq y\\n_1\neq n_2\end{subarray}}\!\frac{1}{(n_1n_2)^{\frac{3}{4}}}\sum_{n_1=h_1l_1}\sum_{n_2=h_2l_2}\sum_{j_1=0}^1 \sum_{j_2=0}^1(-1)^{j_1+j_2}\\
& \!\times\!\cos\!\big(\!4\pi \sqrt{n_1(x\!+\!j_1h_0)}\!-\!\theta(h_1,l_1)\!-\!\frac{\pi}{4}\!\big)\!\cos\!\big(\!4\pi \sqrt{n_2(x\!+\!j_2h_0)}\!-\!\theta(h_2,l_2)\!-\!\frac{\pi}{4}\!\big).\end{aligned}$$
Write $$\begin{aligned}
\label{F220}
F_{22}(x)=:F_{221}(x)+F_{222}(x),
\end{aligned}$$ with $$\begin{aligned}
F_{221}(x)=&\frac{x^\frac{1}{2}}{4\pi^2}\sum_{j_1=0}^1 \sum_{j_2=0}^1(-1)^{j_1+j_2}\sum_{\begin{subarray}{c}n_1,n_2\leq y\\n_1\neq n_2\end{subarray}}\frac{1}{(n_1n_2)^{\frac{3}{4}}}\sum_{n_1=h_1l_1}\sum_{n_2=h_2l_2}\\
& \times\cos\big(4\pi \sqrt{n_1(x+j_1h_0)}-4\pi \sqrt{n_2(x+j_2h_0)}-\theta(h_1-h_2,l_1-l_2)\big),
\end{aligned}$$ $$\begin{aligned}
F_{222}(x)=&\frac{x^\frac{1}{2}}{4\pi^2}\sum_{j_1=0}^1 \sum_{j_2=0}^1(-1)^{j_1+j_2}\sum_{\begin{subarray}{c}n_1,n_2\leq y\\n_1\neq n_2\end{subarray}}\frac{1}{(n_1n_2)^{\frac{3}{4}}}\sum_{n_1=h_1l_1}\sum_{n_2=h_2l_2}\\
& \times\sin\big(4\pi \sqrt{n_1(x+j_1h_0)}+4\pi \sqrt{n_2(x+j_2h_0)}-\theta(h_1+h_2,l_1+l_2)\big).\end{aligned}$$ Let $$g_\pm(x)=4\pi\sqrt{n_1(x\!+\!j_1h_0)}\pm\!4\pi\sqrt{n_2(x\!+\!j_2h_0)}-\theta(h_1\pm h_2,l_1\pm l_2).$$ Using $$(1+t)^\frac{1}{2}=1+\sum_{v=1}^\infty d_vt^v\quad\big(|t|\leq\frac{1}{2}\big),$$ with $|d_v|<1$, we see $$g_\pm(x)=4\pi\sqrt{x}(\sqrt{n_1}\pm\sqrt{n_2})+4\pi\sum_{v=1}^\infty \frac{d_vh_0^v}{x^{v-\frac{1}{2}}}(\sqrt{n_1}j_1^v\pm\sqrt{n_2}j_2^v)-\theta(h_1\pm h_2,l_1\pm l_2).$$ Noting that $n_1,n_2\leq y\leq \frac{1}{2}Uh_0^{-1}$, we have $$|g'_\pm(x)|\gg \frac{1}{\sqrt{x}}|\sqrt{n_1}\pm\sqrt{n_2}|\quad(n_1\neq n_2).$$ Then by the the first derivative test we get $$\begin{aligned}
\int_U^{2U}F_{221}(x)dx\ll& U\sum_{\begin{subarray}{c}n_1,n_2\leq y\\n_1\neq n_2\end{subarray}}\frac{1}{(n_1n_2)^{\frac{3}{4}}}\sum_{n_1=h_1l_1}\sum_{n_2=h_2l_2}\frac{1}{|\sqrt{n_1}-\sqrt{n_2}|}\\
=& U\sum_{\begin{subarray}{c}n_1,n_2\leq y\\n_1\neq n_2\end{subarray}}\frac{1}{(n_1n_2)^{\frac{3}{4}}}\frac{d(n_1)d(n_2)}{|\sqrt{n_1}-\sqrt{n_2}|},\\
\int_U^{2U}F_{222}(x)dx\ll& U\sum_{\begin{subarray}{c}n_1,n_2\leq y\\n_1\neq n_2\end{subarray}}\frac{1}{(n_1n_2)^{\frac{3}{4}}}\frac{d(n_1)d(n_2)}{|\sqrt{n_1}+\sqrt{n_2}|}.\end{aligned}$$ Noting $\sum_{n\leq N}d^2(n)\ll N\log^3 N$, by using Lamma \[lem:Hil\] and , we obtain $$\begin{aligned}
\label{F22}
\int_U^{2U}F_{22}(x)dx\ll&U\sum_{\begin{subarray}{c}n_1,n_2\leq y\\n_1\neq n_2\end{subarray}}\frac{1}{(n_1n_2)^{\frac{3}{4}}}\frac{d(n_1)d(n_2)}{|\sqrt{n_1}-\sqrt{n_2}|} \ll U\log^4y.\end{aligned}$$
By the elementary formulas $$\begin{aligned}
\cos u\!-\!\cos v\!=\!-2\sin\big(\frac{u+v}{2}\big)\sin\big(\frac{u\!-\!v}{2}\big),~\text{and}~ \sin(u\!-\!v)=\sin u\cos v\!-\!\cos u\sin v,\end{aligned}$$ we have $$\begin{aligned}
\label{F210}
F_{21}(x)\!
=&\frac{2x^\frac{1}{2}}{\pi^2}\!\sum_{n\leq y}\!\frac{1}{n^{\frac{3}{2}}}\sin^2\!\big(\!2\pi \sqrt{n(x\!+\!h_0)}\!-2\pi \sqrt{nx}\big)\\
\nonumber &\times\Big(\sum_{n=hl}\!\sin\!\big(2\pi \sqrt{n(x\!+\!h_0)}\!+2\pi \sqrt{nx}-\!\theta(h,l)\!-\!\frac{\pi}{4}\big)\Big)^2,\\
\nonumber =&:F_{211}+F_{212}+F_{213},\end{aligned}$$ where $$\begin{aligned}
F_{211}=&\frac{2x^\frac{1}{2}}{\pi^2}\!\sum_{n\leq y}\!\frac{1}{n^{\frac{3}{2}}}\sin^2\!\big(\!2\pi \sqrt{n(x\!+\!h_0)}\!-2\pi \sqrt{nx}\big)\\
&\times\sin^2\!\big(\!2\pi \sqrt{n(x\!+\!h_0)}\!+2\pi \sqrt{nx}\big)\Big(\sum_{n=hl}\!\cos\!\big(\theta(h,l)\!+\!\frac{\pi}{4}\big)\Big)^2,\end{aligned}$$ $$\begin{aligned}
\hspace*{4.1em}F_{212}=&\frac{2x^\frac{1}{2}}{\pi^2}\!\sum_{n\leq y}\!\frac{1}{n^{\frac{3}{2}}}\sin^2\!\big(\!2\pi \sqrt{n(x\!+\!h_0)}\!-2\pi \sqrt{nx}\big)\\
&\times\cos^2\!\big(\!2\pi \sqrt{n(x\!+\!h_0)}\!+2\pi \sqrt{nx}\big)\Big(\sum_{n=hl}\!\sin\!\big(\theta(h,l)\!+\!\frac{\pi}{4}\big)\Big)^2,\\
F_{213}=&-\frac{2x^\frac{1}{2}}{\pi^2}\!\sum_{n\leq y}\!\frac{1}{n^{\frac{3}{2}}}\sin^2\!\big(\!2\pi \sqrt{n(x\!+\!h_0)}\!-2\pi \sqrt{nx}\big)\sin\!\big(\!4\pi \sqrt{n(x\!+\!h_0)}\!+4\pi \sqrt{nx}\big)\\
&\times\sum_{n=hl}\!\sin\!\big(\theta(h,l)\!+\!\frac{\pi}{4}\big) \!\sum_{n=h'l'}\cos\!\big(\theta(h',l')\!+\!\frac{\pi}{4}\big).\end{aligned}$$ It is easy to see that $$\begin{aligned}
0\leq F_{211}+F_{212}
\leq\frac{2x^\frac{1}{2}}{\pi^2}\!\sum_{n\leq y}\!\frac{1}{n^{\frac{3}{2}}}\sin^2\!\big(\!2\pi \sqrt{n(x\!+\!h_0)}\!-2\pi \sqrt{nx}\big)d^2(n).\end{aligned}$$ By using Taylor’s expansion, we have for $x\geq 100 h_0^2$, $$\begin{aligned}
\sin^2\big(2\pi\sqrt{n(x\!+\!h_0)}\!-\!2\pi\sqrt{nx}\big)=&\sin^2\big(\pi h_0n^{\frac{1}{2}}x^{-\frac{1}{2}}+O(h_0^2n^\frac{1}{2}x^{-\frac{3}{2}})\big)\\
=&\sin^2\big(\pi h_0n^{\frac{1}{2}}x^{-\frac{1}{2}}\big) +O(h_0^2n^\frac{1}{2}x^{-\frac{3}{2}}).\end{aligned}$$ which suggests $$\begin{aligned}
&\int_U^{2U}x^\frac{1}{2}\sin^2\!\big(\!2\pi \sqrt{n(x\!+\!h_0)}\!-2\pi \sqrt{nx}\big)dx\\
\ll&\int_U^{2U}x^\frac{1}{2}\min\big(1, h_0^2nx^{-1}\big)+O(h_0^2n^\frac{1}{2}x^{-1})dx
\ll\left\{\begin{array}{ll}U^\frac{1}{2}h_0^2n,&n\leq Uh_0^{-2},\\U^{\frac{3}{2}},&n> Uh_0^{-2},\end{array}\right.\end{aligned}$$ in view of the fact $h_0^2<U$ and $n\leq y<U$. Hence, $$\begin{aligned}
\label{F2112}
\int_U^{2U}\!\!F_{211}\!+\!F_{212}dx\!\ll h_0^2 U^\frac{1}{2}\!\!\sum_{n\leq Uh_0^{-2}}\!\frac{d^2(n)}{n^{\frac{1}{2}}}\!+U^{\frac{3}{2}}\!\!\sum_{n> Uh_0^{-2}}\!\frac{d^2(n)}{n^{\frac{3}{2}}}\!\ll U h_0\log^3\!\frac{\sqrt{U}}{h_0},\end{aligned}$$ where we used the well-known estimate $\sum_{n\leq N}d^2(n)\ll N\log^3N$.
By the first derivative test, we have $$L_n(t):=\int_U^tx^\frac{1}{2} \sin\!\big(\!4\pi \sqrt{n(x\!+\!h_0)}\!+4\pi \sqrt{nx}\big)dx \ll Un^{-\frac{1}{2}},\quad U\leq t\leq2U.$$ Using the integration by parts, we obtain $$\begin{aligned}
&\int_U^{2U}\!\!\!x^\frac{1}{2} \sin^2\big(2\pi\sqrt{n(x\!+\!h_0)}\!-\!2\pi\sqrt{nx}\big)\sin\!\big(\!4\pi \sqrt{n(x\!+\!h_0)}\!+4\pi \sqrt{nx}\big)dx\\
=&\int_U^{2U}\!\!\!\sin^2\big(2\pi\sqrt{n(x\!+\!h_0)}\!-\!2\pi\sqrt{nx}\big)dL_n(x)\\
=&L_n(2U)\sin^2\big(2\pi\sqrt{n(2U\!+\!h_0)}\!-\!2\pi\sqrt{2nU}\big)- 2\int_U^{2U}\!L_n(x) \\
&\times\sin\big(2\pi\sqrt{n(x\!+\!h_0)}\!-\!2\pi\sqrt{nx}\big)\cos\big(2\pi\sqrt{n(x\!+\!h_0)}\!-\!2\pi\sqrt{nx}\big) \big(\frac{\pi\sqrt{n}}{\sqrt{x\!+\!h_0}} \!-\!\frac{\pi\sqrt{n}}{\sqrt{x}}\big)dx\\
\ll&Un^{-\frac{1}{2}}+U^{\frac{1}{2}}h_0,\end{aligned}$$ which yields $$\begin{aligned}
\label{F213}
\int_U^{2U}\!\!F_{213}dx\!=\!&-\!\frac{2}{\pi^2}\!\sum_{n\leq y}\!\frac{1}{n^{\frac{3}{2}}}\sum_{n=hl}\!\sin\!\big(\theta(h,l)\!+\!\frac{\pi}{4}\big) \!\sum_{n=h'l'}\cos\!\big(\theta(h',l')\!+\!\frac{\pi}{4}\big)\int_U^{2U}\!\!\!x^\frac{1}{2}\\
\nonumber &\times\sin^2\!\big(\!2\pi \sqrt{n(x\!+\!h_0)}\!-\!2\pi \sqrt{nx}\big)\sin\!\big(\!4\pi \sqrt{n(x\!+\!h_0)}\!+\!4\pi \sqrt{nx}\big)dx\\ \nonumber\ll&\sum_{n\leq y}\!\frac{d^2(n)}{n^{\frac{3}{2}}}(Un^{-\frac{1}{2}}+U^{\frac{1}{2}}h_0)\ll U.\end{aligned}$$
From -, we get $$\label{F21}
\int_U^{2U}F_{21}(x)dx\ll U h_0\log^3\!\frac{\sqrt{U}}{h_0}.$$
Combining , and , we obtain $$\int_U^{2U}F_{2}^2(x)dx\ll U h_0\log^3\!\frac{\sqrt{U}}{h_0}+U\log^4y,$$ which together with , yields $$\label{dR}
\int_U^{2U}\big(R_{0}(x+h; y)-R_{0}(x; y)\big)^2(x)dx\ll U h_0\log^3\!\frac{\sqrt{U}}{h_0}+U\log^4y.$$
From , , and , it follows that $$J(U,h_0)\ll U h_0\log^3\!\frac{\sqrt{U}}{h_0}+U\log^6y,$$ which implies $$\label{int2}
\int_2\ll T h_0\log^3\!\frac{\sqrt{T}}{h_0}+T\mathcal{L}^6,$$ via a splitting argument. Then Lemma \[lem:meanvalue\] follows from , , and .
Proof of Theorem \[th:maintain\]
================================
In this section, we will give a proof of Theorem \[th:maintain\] by following the approach of [@tsang2012sign]. We still write $\Delta^{*}(q_1q_2x)=\Delta(q_1q_2x; r_1, q_1, r_2, q_2)$. Define $$\begin{aligned}
\Delta^{*}_+(t)=&\frac{1}{2}\big(|\Delta^{*}(t)|+\Delta^{*}(t)\big),&
\Delta^{*}_-(t)=&\frac{1}{2}\big(|\Delta^{*}(t)|-\Delta^{*}(t)\big).\end{aligned}$$ We need the following two lemmas.
\[lem:3\] $$\int_T^{2T}{\Delta^{*}}^2_\pm(q_1q_2t)dt\gg T^\frac{3}{2}.$$
From Corollary \[cor:1\] with $k=2,4$, by Hölder’s inequality, we get $$\begin{aligned}
T^\frac{3}{2}\ll\int_T^{2T}{\Delta^{*}}^2(q_1q_2t)dt \ll&\Big(\int_T^{2T}|\Delta^{*}(q_1q_2t)|dt\Big)^\frac{2}{3}\Big(\int_T^{2T}{\Delta^{*}}^4(q_1q_2t)dt\Big)^\frac{1}{3}\\
\ll&\Big(\int_T^{2T}|\Delta^{*}(q_1q_2t)|dt\Big)^\frac{2}{3}T^\frac{2}{3},\end{aligned}$$ which yields $$\label{31}
\int_T^{2T}|\Delta^{*}(q_1q_2t)|dt\gg T^\frac{5}{4}.$$ From , we see $$\int_T^{2T}\Delta^{*}(q_1q_2t)dt\ll T^\frac{3}{4}.$$ Thus, from the definition of $\Delta^{*}_\pm(q_1q_2t)$, we have $$\int_T^{2T}\Delta^{*}_\pm(q_1q_2t)dt\gg T^\frac{5}{4}.$$ Then by Cauchy-Schwarz’s inequality, we get $$\begin{aligned}
T^\frac{5}{4}\ll\Big(\int_T^{2T}dt\Big)^\frac{1}{2} \Big(\int_T^{2T}{\Delta^{*}}^2_\pm(q_1q_2t)dt\Big)^\frac{1}{2}\ll T^\frac{1}{2}\Big(\int_T^{2T}{\Delta^{*}}^2_\pm(q_1q_2t)dt\Big)^\frac{1}{2},\end{aligned}$$ which immediately implies Lemma \[lem:3\].
\[lem:4\] Suppose $2\leq H_0\leq\sqrt{T}$. Then $$\int_T^{2T}\max_{h\leq H_0}\big(\Delta^{*}_\pm(q_1q_2(t+h))-\Delta^{*}_\pm(q_1q_2t)\big)^2 dt\ll H_0T\mathcal{L}^7.$$
Since $$|\Delta^{*}_\pm(q_1q_2(t+h))-\Delta^{*}_\pm(q_1q_2t)|\leq |\Delta^{*}(q_1q_2(t+h))-\Delta^{*}(q_1q_2t)|,$$ it is sufficient to prove that $$I= \int_T^{2T}\max_{h\leq H_0}\big(\Delta^{*}(q_1q_2(t+h))-\Delta^{*}(q_1q_2t)\big)^2 dt\ll H_0T\mathcal{L}^7.$$
For $0<u_1<u_2\ll T$, it easy to see that $$\Delta^{*}(q_1q_2u_2)-\Delta^{*}(q_1q_2u_1)\geq - O\big((u_2-u_1)\log T\big).$$ Write $H_0=2^\lambda b$, such that $\lambda\in \mathbb{N}$ and $1\leq b <2$. Then for each $t\in[T, 2T]$, we have $$\max_{h\leq H_0}\big|\Delta^{*}(q_1q_2(t+h))-\Delta^{*}(q_1q_2t)\big|\ll \max_{1\leq j\leq 2^\lambda}\big|\Delta^{*}(q_1q_2(t+jb))-\Delta^{*}(q_1q_2t)\big|+\mathcal{L}.$$ Similar to the argument of the proof of Lemma 2 of [@heathbrown1994sign], by using Lemma \[lem:meanvalue\], we we can deduce that $$\begin{aligned}
I\ll& \lambda\sum_{\mu\leq\lambda}\sum_{0\leq\nu\leq2^\mu} \int_{T+\nu2^{\lambda-\mu}b}^{2T+\nu2^{\lambda-\mu}b} \big(\Delta^{*}(q_1q_2(t+2^{\lambda-\mu}b))-\Delta^{*}(q_1q_2t)\big)^2dt\!+\! T\mathcal{L}^2\\
\ll& \lambda\sum_{\mu\leq\lambda}\sum_{0\leq\nu\leq2^\mu} \big( 2^{\lambda-\mu}bT\mathcal{L}^3+ T\mathcal{L}^6\big)\\
\ll& \lambda\sum_{\mu\leq\lambda}\big( 2^{\lambda}bT\mathcal{L}^3+ 2^\mu T\mathcal{L}^6\big)\\
\ll& \lambda^2 H_0T\mathcal{L}^3+\lambda H_0T\mathcal{L}^6\\
\ll& H_0T\mathcal{L}^7.\end{aligned}$$ Thus we get Lemmma \[lem:4\].
Now we finish the proof of Theorem \[th:maintain\]. Let $P(t)=\Delta^{*}_\pm(q_1q_2t)$ and $Q(t)=\delta t^\frac{1}{4}$ for a sufficiently small $\delta>0$, and $$\begin{aligned}
\omega(t)=P^2(t)-4\max_{h\leq H_0}\big(P(t+h)-P(t)\big)^2-Q^2(t).\end{aligned}$$ Then $$\begin{aligned}
\label{35}
\int_T^{2T}\!\!\!\!\omega(t)dt\gg T^\frac{3}{2}\!-\!O\big( H_0T\mathcal{L}^7\big)\! -\!O\big(\delta^2 T^\frac{3}{2}\big)\!\gg\! T^\frac{3}{2},\end{aligned}$$ from Lemma \[lem:3\] and Lemma \[lem:4\], by taking $H_0=\delta T^\frac{1}{2}\mathcal{L}^{-7}$. For any point $t_0$, where $\omega(t_0)>0$ and any $h\in [0, H_0]$, we see that $P(t_0+h)$ has the same sign as $P(t_0)$, and $|P(t_0+h)|>\frac{1}{2}|Q(t_0)|$.
Let $$\mathscr{S}=\{t\in[T,2T]:\omega(t)>0\}.$$ From Corollary \[cor:1\] and , using Cauchy-Schwarz’s inequality, we have $$\begin{aligned}
T^\frac{3}{2}\ll & \int_T^{2T}\omega(t)dt\leq \int_\mathscr{S}\omega(t)dt \leq \int_\mathscr{S}{\Delta^{*}}^2_\pm(q_1q_2t)dt \\ \leq&|\mathscr{S}|^\frac{1}{2}\Big(\int_T^{2T}{\Delta^{*}}^4(q_1q_2t)dt\Big)^\frac{1}{2} \ll |\mathscr{S}|^\frac{1}{2} T,\end{aligned}$$ which implies $$|\mathscr{S}|\gg T.$$ Thus the proof of Theorem \[th:maintain\] is completed.
Proof of Theorem \[th:omega\]
=============================
Suppose $k\geq3$ is a fixed odd integer and $T\gg (q_1q_2)^{\varepsilon}$ is a large parameter. Set $$\delta=\left\{\begin{array}{ll}-1,&\quad\text{if } C_k\geq0,\\1,&\quad\text{if } C_k<0,\end{array}\right.$$ where $C_k$ is defined in .
By Theorem \[th:maintain\], there exists $t\in[T,2T]$ such that $\delta \Delta(q_1q_2u; r_1, q_1, r_2, q_2)> c_5 t^\frac{1}{4}$ for any $u\in[t,t+H_0]$, with $H_0=c_4\sqrt{T}\mathcal{L}^{-7}$. Thus $$\begin{aligned}
&c^k_5 H_0 t^\frac{k}{4}<\int_t^{t+H_0}\delta^k\Delta^k(q_1q_2u; r_1, q_1, r_2, q_2)du\\
=&\delta^kC_k\big((t\!+\!\!H_0)^{1\!+\!\frac{k}{4}}\!\!-\!t^{1\!+\!\frac{k}{4}}\big)\!\!+\!\delta^k\!\big( \mathcal{F}_k\big(q_1q_2(t\!+\!\!H_0); r_1, q_1, r_2, q_2\big)\!\!- \!\!\mathcal{F}_k(q_1q_2t; r_1, q_1, r_2, q_2)\big),\end{aligned}$$ which yields $$\begin{aligned}
&\delta^k\Big( \!\mathcal{F}_k\big(q_1q_2(t\!+\!H_0); r_1, q_1, r_2, q_2\big)\!\!- \! \mathcal{F}_k\big(q_1q_2t; r_1, q_1, r_2, q_2\big)\Big)\\
>&c^k_5 H_0 t^\frac{k}{4}-\delta^kC_k\big(1\!+\!\frac{k}{4}\big)t^{\frac{k}{4}}H_0\!\!+\!O(H_0^2t^{\frac{k}{4}\!-\!1})
=C_k^*H_0t^{\frac{k}{4}}\big(1+O(H_0T^{-1})\big),\end{aligned}$$ with $$C_k^*=c^k_5-\delta^kC_k\big(1\!+\!\frac{k}{4}\big)>0.$$ Thus we get $$\big|\mathcal{F}_k\big(q_1q_2(t\!+\!H_0);r_1, q_1, r_2, q_2\big)\!\!- \! \mathcal{F}_k\big(q_1q_2t; r_1, q_1, r_2, q_2\big)\big|\gg H_0T^{\frac{k}{4}},$$ which immediatly implies Theorem \[th:omega\].
[^1]: The first author is supported by the National Natural Science Foundation of China (Grant No. 11871295 and Grant No. 11571303), China Postdoctoral Science Foundation (Grant No. 2018M631434). The second author is supported by the National Key Basic Research Program of China (Grant No. 2013CB834201). The third author is supported by the National Natural Science Foundation of China (Grant No. 11571303).
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As NASA’s Terra satellite flew over Iceland’s erupting Eyjafjallajökull volcano on April 19, 2010, its Multi-angle Imaging SpectroRadiometer (MISR) instrument acquired 36 near-simultaneous images of the ash plume, covering nine view angles in each of four wavelengths. From these numerous observations, the extent of the plume is easily visible, but in addition, they allow scientists to determine the amount and type of particles in the plume.
The top-most image gives a natural-color nadir (vertical) view of the scene, with the plume emanating from the ice-covered volcano in the left of the image, heading south to southeast. The thick brown ash cloud is distinct from the white clouds and dark blue ocean.
The next image covers the same area, and gives a map of retrieved aerosol optical depth, a measure of the amount of particulate matter in the atmosphere. Purple and blue correspond to low particle amounts, yellow and orange indicate high amounts. The plume here is about five times thicker than the background aerosol.
The third image shows the Angstrom exponent, which is related to average particle size—bigger particles generally have smaller Angstrom exponents. Big particles are shown in blue, and smaller ones in yellow and red. In this case, the volcanic plume contains distinctly larger particles than the surrounding atmosphere.
The final image shows particle shape. Volcanic ash is composed primarily of angular, non-spherical particles, whereas background maritime particles are typically tiny, spherical liquid droplets. High concentrations of non-spherical particles are represented by orange and yellow. The plume stands out relative to the unperturbed air as being composed of close to 100 percent non-spherical particles, the kind that create concern for jet aircraft safety.
Each panel covers an area 264 kilometers wide by 792 kilometers north-south (164 miles by 492 miles). The resolution of the nadir image in the first panel is 1.1 kilometers (0.7 miles); aerosol amount and type in the other three panels are given at 17.6 kilometers (10.9 miles) per pixel. MISR has been acquiring aerosol information routinely for the past 10 years, covering the entire globe about once per week.
NASA image courtesy GSFC/LaRC/JPL MISR Team. Caption by Ralph Kahn & the MISR Team, adapted by Robert Simmon.
These satellite images of the Eyjafjallajökull eruption show not only the extent of the plume, but also the amount and type of particles in the plume. | https://earthobservatory.nasa.gov/images/43738/eruption-of-eyjafjallajakull-volcano-iceland |
This application claims the benefit of Provisional Patent Application Ser. No. 60/704,328 filed Aug. 1, 2005, which includes the design and features cited herein.
Not applicable.
Not Applicable.
This invention relates to a greatly improved version of plastic membrane bubbles presently used mostly in the impact shock protection of packages during shipment and which will drastically lower the overhead costs to the manufacturer and provide immunity against “flats”.
Inflated bubbles have been used for years in the packaging industry. Typically, inflated bubbles are comprised of permanently sealed bubble membrane containing a fluid, usually air or other gas, and sometime affixed to a flexible panel.
U.S. Pat. No. 6,791,960 INFLATABLE, CUSHIONING, BUBBLE WRAP PRODUCT HAVING MULTIPLE, INTERCONNECTED, BUBBLE STRUCTURES to De Luca Jul. 13, 2004
All bubbles are externally inflated and interconnected to adjacent bubbles by an interconnecting passageway. No provision is made for total deflation or self re-inflation.
U.S. Pat. No. 5,518,802 CUSHIONING STRUCTURE to Colvin May 21, 1996
Assumes that the inflated composite of layers and cells will be inflated by external means. No provision is made for total deflation or self re-inflation.
One problem with conventionally sealed bubbles is the expense of shipping and storage. As a result of high shipping volume, in many cases the cost of shipment approaches one-third the cost of the original goods.
Another problem with prior art is the susceptibility to even the smallest leak rstn in a “flat”. The protected item becomes susceptible to damage. The bubble of my design contains an intentional leak and performance is not affected by a minor leak.
Another problem with prior art bubbles is that these panels are usually single usage. Environmental concerns are requiring more and more items to be recycled.
Another disadvantage with prior art bubbles is membrane deterioration when exposed to long-term stress, as in storage, resulting in a leak down.
Another disadvantage with prior art bubbles is expansion with increasing altitude and/or decreasing ambient pressure. This could change the original packaging clearances and forces.
Another disadvantage with prior art bubbles is the attempt to make bubbles inflatable on site. This has resulted in the necessity of an on-site inflator and is labor intensive.
Another disadvantage with prior art bubbles is the application of these bubbles as hailstone protection is not presently commercially available. This is probably due to poor handling and storage.
Another disadvantage with prior art bubbles is the poor thermal insulation characteristics due to the free circulation of the contained air when used as a blockage to heat transfer.
Another disadvantage with prior art bubbles is the inability to adjust the intensity of shock resistance offered by the bubbles by varying air exhaust blockage.
Another disadvantage with prior art bubbles is the poor sound blockage characteristics due to the free circulation of the contained air.
While these devices may be suitable for the particular purpose of which they address, they are not cost effective to the manufacturer or to the consumer and are wasteful of storage and handling.
In these respects, my deflatable and self-inflating bubble invention substantially departs from the concepts and designs of the prior art and in so doing provides an apparatus of increased cost reduced applications.
The field of packaging protection is largely comprised of hermetically sealed plastic bubbles. My Deflatable and Self-inflating bubble invention overcomes many disadvantages of prior art bubbles by greatly reducing volume when desired, and then return to full size. It is also the solution of many service problems.
In the drawings, closely related figures have the same number but different alphabetic suffixes.
FIG. 1
FIG. 2
and show the internal construction of the primary embodiment with orifice.
FIG. 3
FIG. 2
is the primary embodiment of in the compressed state with optional sealing membrane attached at one bubble orifice in order to maintain compressed state without external force.
FIG. 4
90
shows an optional hole in the panel membrane, between bubbles, to accept indexing pin for positional reference for dispensing and cutting.
FIG. 5
20
30
is a bubble construction of prior art but containing an expander C and said orifice .
FIG. 6
shows the internal usage of a spring expander.
FIG. 7
shows the internal usage of a thin shape expander.
FIG. 8
FIG. 9
and propose a method of manufacture.
FIG. 10
FIG. 2
is the bubble of in contact with an item to be shielded from impact and demonstrates highly restrictive fluid exhaust path.
FIG. 11
and shows the higher deflation rate by the use of a “venting” pad.
FIG. 12
shows a panel of rectangular bubbles with thin resilient shapes ready to be inserted therein with optional membrane over bubble extremities.
FIG. 13
shows a unique padded box, employing my invention, in the flat for a specific customer. This box would ship flat and possibly lend itself to automatic packaging of customer's item.
FIG. 1
5
10
20
30
is a section view showing the basic concept of a closed bubble assembly consisting of membrane and containing an expander which always seeks to occupy all of the volume available within the bubble membrane. Located in the membrane wall is a fluid communication orifice hole which will allow the contained fluid, usually air, to enter and exit the bubble upon the existence of a pressure differential.
FIG. 2
FIG. 1
FIG. 1
5
10
10
10
50
20
30
50
20
20
10
is a section view of the bubble assembly of with membrane configured as a hemisphere A and the edge of the membrane A is peripherally bonded to, or integral with, a flexible panel and engulfing the expander A inside. The orifice through the bubble membrane of may relocate to the flexible panel , if desired. Expander A is expander but shaped to fill newly shaped bubble A.
FIG. 3
FIG. 2
FIG. 2
10
30
10
20
20
32
30
32
is a section view of the bubble assembly of , which has been exposed to a small but constant flattening force. All fluid contained within the bubble A of has been leisurely exhausted through orifice resulting in deflated membrane B. The contained expander A is forcibly compressed and flattened also, shown as B. Optional sealing tape or membrane is shown blocking the entrance of air through said orifice to one bubble and thereby constraining the bubble in the flattened condition. The membrane may be reattached after the bubble is in the maximum unconstrained and inflated state, thereby rendering its performance similar to a prior art sealed bubble.
FIG. 1
FIG. 4
20
thru expander is assumed to be flexible open cell foam.
FIG. 5
FIG. 13
thru will be discussed in “discussion of alternate embodiments and applications” section.
The general purpose of this invention is to provide a new deflatable and self-inflating bubble for impact protection with many of the protection advantages of prior art but with many novel features in a new deflatable and self-inflating bubble which is not anticipated, rendered obvious, suggested, or even implied by any of the prior art of packaging bubbles, either alone or in any other combination.
In this respect, before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not limited in its application to the details of construction and to the arrangements of the components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and of being practiced and carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein are for the purpose of the description and should not be regarded as limiting.
In this discussion, a bubble is defined as any membrane or web material engulfing a volume and being temporarily hermetically sealed. An expander is any device or membrane characteristic, which will urge the vented bubble to seek maximum internal volume.
A primary object of the present invention is to provide a bubble membrane capable of resisting impact forces and preventing them from being transferred as well as convenience in handling, shipping, storage and usage.
A secondary object of the present invention is to provide debatable and self-inflating bubble for packaging, which can support the weight of a packed object with a cushion type support and yet offer high resistance to impact forces.
Another object is to provide a deflatable and self-inflating bubble eliminating susceptibility to deflated bubbles or “flats”.
Another object is to provide a deflatable and self-inflating bubble for protective packaging of fragile objects where it will expand unaided to fill voids between the packed object and the volume confines of the shipping container.
Another object is to provide pre-positioned bubbles attached to the inside surfaces of a packing box in accordance with customer's unique application. These boxes can be shipped in the flat in little more volume than the boxes alone.
Another object is to provide deflatable and self-inflating bubbles for providing impact resistance from hailstones to susceptible surfaces but convenient in handling and storage.
Another object is to provide deflatable and self-inflating bubbles for hailstone protection that can be applied over the protected surface and left for extended periods of time without deterioration.
Another object is to provide a deflatable and self-inflating bubble for providing thermal insulation between confining structures. This feature is provided by the use of a Sponge type foam expander internal to the bubble. This provides resistance to convection fluid currents within the bubble.
Another object is to provide a deflatable and self-inflating bubble for providing sound insulation between confining structures. This feature is provided by the use of a foam expander internal to the bubble. This provides resistance to air currents within the bubble, thereby reducing sound passage.
Another object is to be incorporated into a garment capable of protecting the wearer from cold and or impacts without being restrictive in bulk.
Another object is to provide a displacer of empty air within a refrigerated container, thereby lessening the loss of pre-cooled air when opened.
Other objects and advantages of the present invention will become obvious to the reader and it is intended that these objects and advantages be within the scope of the present invention.
To attain this, the present invention generally comprises a spherical, hemispherical, pillow or cube shaped, self-inflating bubble of flexible membrane construction with the ability to be deflated as desired by the application of minor continuous force.
The basic bubble is a membrane forming a complete hermetically sealed closed volume engulfing an expander, containing a fluid and containing a communication orifice, which places the internal fluid in constant communication with external fluid, usually air.
When impacted by a short duration shock force, the fluid contained therein is unable to exhaust through said orifice in any significant amount in the short time duration and thereby imparts bubble characteristics of prior art of being totally sealed.
Inherent in this bubble is the desire to always occupy maximum volume by virtue of said expander contained within or by membrane memory characteristics.
The expander contained within is a three-dimensional thin filament, foam, sponge, spring or shape capable of being highly compressed but when released, it desires to expand, with slight force, to the it's original volume and constrained only by the volume of the bubble wherein it is contained. Subsequent applications may prefer to make this expander able to support anticipated weight at the sacrifice of a portion of the compressibility.
A flexible or rigid panel, to which multiple bubbles may be attached or integral with, in order to maintain positional order among a multiplicity of bubbles, could be incorporated as desired.
A web or membrane may be attached to the outer extremities of the bubbles in order to share impacts occurring between bubbles by imparting tensile forces in said membrane. Web must be freely vented to surrounding atmosphere in order not to increase minimum shipping thickness.
A coating may be applied to, or contained within the materials of construction, which will provide environmental protection for parts of the bubble and/or panel.
Bubbles can be kept in the compressed state by the application of a sealing membrane over the fluid passage orifice while compressed. When the sealing membrane is removed, the bubbles expand. If desired, the sealing membrane can be replaced while the bubble is in the expanded state and thereby creating a prior art sealed bubble containing the expander.
To the accomplishment of the above and related objects, this invention may be embodied in the form illustrated in the accompanying drawings, attention being called to the fact, however, that the drawings are illustrative only, and that changes may be made in the specific construction illustrated.
FIG. 5
30
shows a pillow shaped bubble with said orifice in the membrane wall or in the connecting membrane.
FIG. 6
10
60
20
is said bubble A containing a spring expander in place of foam .
FIG. 7
FIG. 2
70
20
is a resilient, thin walled shaped expander replacing the foam A expander of .
FIG. 8
300
301
20
10
depicts a method of manufacturing where platens and are preparing to compress expander foam D with bubble membrane D and thereby forming bubble.
FIG. 9
300
301
20
20
20
310
10
depicts platens and compressing expander foam and thereby forming bubble into recesses and fusing membrane F and expander E circumferentially around bubble possibly to foam E. Protrusion penetrates membrane E and forms the orifice in the bubble membrane. Said orifice may be added before or after bubble formation.
FIG. 10 a
FIG. 2
31
30
30
80
cross section of the bubble of showing the airflow through orifice out of the bubble along faying surfaces when an impact force presses the orifice against the protected item .
FIG. 11
55
31
30
application of a mostly open weave material which will allow maximum airflow radially from . This could be replaced by incorporating a serrated annulus bung around orifice with radial passageways.
FIG. 12
220
230
210
210
220
200
230
200
240
an array of parallelpiped bubbles as part of a panel membrane and ready to accept thin wall resilient expanders . After insertion of into the bubbles , the flexible membrane panel is bonded to forming a hermetic seal within each bubble. The communication orifice may exist in panel before bonding or added later or may be contained in each bubble. The expanders are not of necessity a thin walled resilient shape as shown but can be of any type desired. Optional load sharing membrane is depicted attached to bubble extremities.
FIG. 13
is a custom designed shipping container containing pre-positioned and uniquely shaped collapsible and self-inflating bubbles. This approach to package design has been impractical in prior art due to shipping volume limitations, but volume constraints are no longer a factor when using my invention of collapsible bubbles.
From the description noted above, it is obvious that impact protection is not sacrificed by virtue of being able to collapse the bubbles. Experimentation has shown a collapse ratio of 11:1 is easily attained. This means 1 truck will replace 11 trucks in shipment, 1 warehouse will replace 11 warehouses in storage etc.
30
The principle involved in using a non-sealed bubble is that when struck by a quick blow, the time of impact is of such short duration that loss of entrapped fluid to the surrounding atmosphere, through orifice is minimal and shock performance is similar to that of a sealed bubble.
20
10
10
30
During manufacture, the internal expander is placed within the bubble or A and the communication orifice is incorporated into the sealing membrane. The bubbles or panel of bubbles are mechanically compressed to minimum size and packaged as a roll or in a shipping carton.
Optionally the bubbles may be maintained in the compressed state by the closure of the orifice by a sealing membrane.
Upon delivery to the purchaser, the compressed bubbles can be placed in storage until needed at the site whereupon the sealing membrane is removed and the bubble is allowed to expand again to its normal volume. Storage requirements are much less than prior art.
If ultimately a sealed bubble configuration, similar to prior art, is desired for long-term load support, the sealing tape membrane is replaced over the orifice after expansion.
If desired, the deflated bubbles can be quickly placed into the packaging container and allowed to inflate in place.
It is noted that individual bubbles may be supplied loose packaged and inserted into the shipping package like “peanuts” to protect fragile items.
FIG. 13
It now becomes feasible to provide packing boxes in the flat with custom sized and shaped shock-protecting bubbles bonded in place as the need is defined as shown in . These box flats can now be shipped consuming probably not more than twice the volume the bare box flats would consume.
It is now convenient to apply panels of bubbles over an automobile or aircraft for hail protection, as they will require minimal storage space when removed.
It can be seen that many new applications, in addition to those applications of prior art, are now available to this form of bubble since bulk is no longer a limiting factor.
When used to protect an aircraft wing from hail damage, the aerodynamic characteristics of the wing are masked from high winds and negative lift may be created.
When used in clothing or sports uniforms, warmth and/or impact protection does not come with unyielding bulk.
The bubbles may be stuffed into a freezer, or other refrigerated volume, to occupy unused space and reduce lost cold air when opened for access.
CROSS-REFERENCE TO RELATED APPLICATIONS
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
BACKGROUND—FIELD OF INVENTION
BACKGROUND—DESCRIPTION OF THE PRIOR ART
SUMMARY
DRAWING FIGURES
DESCRIPTION—MAIN EMBODIMENT
Discussion of Primary Embodiment
DESCRIPTION—ADDITIONAL EMBODIMENTS
Advantages
Operation
CONCLUSION, RAMIFICATION AND SCOPE | |
Q:
$x^{4\log x} = \frac{x^{12}}{{10}^8} $ all sum of x?
${10}^8 = \frac{x^{12}}{x^{4\log x}}$
${10}^8 = x^{12 - 4\log x}$
$x > 0$
$x \neq 1$
by guessing, x = 10 is true. but how sum of all x?
A:
Assuming you are wondering how to systematically get all $x$ for which the original expression is true, you can take logs of both sides (base 10 log) to obtain
\begin{align*}
8 = \log x^{12-4\log x} = (12-4\log x) (\log x) = 12\log x - 4(\log x)^2.
\end{align*}
Organizing a bit gives the equivalent statement,
\begin{align*}
(\log x)^2 - 3\log x + 2 = 0.
\end{align*}
The quadratic formula now gives
\begin{align*}
\log x = \frac{3\pm \sqrt{9-8}}{2} = \{2,1\}.
\end{align*}
The zeros of the function $f(x) = (\log x)^2-3\log x + 2$ are then $x = 10$ or $100$.
| |
Q:
Question about the Spec of a power set ring
Let $S$ be a set, we can give a commutative ring structure on $P(S)$ by setting addition as xor and multiplication as intersection.
Can you please help me with some questions about the underlying topological space of $Spec(P(S))$
($a, b, …$ denote subsets of $P(S)$, $x, y, z, …$ denote elements of $s$)
1) is this list of criteria : contains $\emptyset$, every subset, every union, does not contain all of $S$ and maximal with respect to these properties, sufficient for a subset of $P(S)$ to be a prime ideal?
2) is there an easier way to describe the underlying set?
3) Is the topological space totally disconnected?
The below is my attempt at solving these problems:
Writing out the definition of a prime ideal: a prime ideal $p$ must contain $\emptyset$, the xor of any two sets in $p$, and any subset of any set in $p$. Furthermore, if $a \cap b \in p$ then $a \in p$ or $b \in p$.
It must also contain the union of two elements in $p$, since $(b \backslash a) \text{ xor } a = a \cup b$.
Suppose $p \subseteq q$ is an inclusion of prime ideals. Then, let $a \in q$. Then, $a \cap a^c = \emptyset \in p$, so either $a \in p$ or $a^c \in p$. If $a^c \in p$, then since $p \subseteq q$, $a \cup a^c = S \in q$, a contradiction. Thus, all prime ideals are maximal.
The conditions are necessary for a subset of $P(S)$ to be a prime ideal, but I don't know if they're sufficient.
The underlying topological space is compact (since it's the Spec of something) and Hausdorff (since all prime ideals are maximal)
If $p$ and $q$ are prime ideals, then since they're maximal then there is $a \in p \backslash q, b \in q \backslash p$. However, I don't know if $D(a) \cap D(b)$ = $D(a \cap b)$ is empty
A:
$R=\mathscr{P}(S)$ is indeed a Boolean ring in the operations you describe, and in this case a complete Boolean algebra as well. In $R$ a prime ideal is maximal and $X:=\text{Spec}(R)$ is essentially just the Stone space of $R$ (there is an easy duality between ultrafilters in the BA sense and maximal ideals ring sense) and this is a compact zero-dimensional (which implies totally disconnected) Hausdorff space. In this case, as $R$ is complete, $X$ is extremally disconnected (for any open $O$, $\overline{O}$ is also open).
An ideal $I \subseteq R$ is indeed maximal iff for all $a \in R$, either $a \in I$ or $a^c \in I$.
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1. By string of hexadecimal digits what they mean is a combination of the digits 0-9 and characters A-F, just like how a binary string is a combination of 0’s and 1’s. Eg: “245FC” is a hexadecimal string.
What is hex string in Java?
Hexadecimal to string Get the hexadecimal value (String). Convert it into a character array using the toCharArray() method. Read each two characters from the array and convert them into a String. Parse above obtained string into base 16 integer, cast it into a character. Concat all the characters to a string.
What is an example of hex?
For example, if we write 10 in hexadecimal, do we mean the decimal number ten, or the binary number of two (1 + 0).Hexadecimal Numbers. Decimal Number 4-bit Binary Number Hexadecimal Number 15 1111 F 16 0001 0000 10 (1+0) 17 0001 0001 11 (1+1) Continuing upwards in groups of four.
How do I check if a string is hex?
Below are the steps to solve the problem: Iterate over the given string. Check if each character of the string is between characters A to F or between 0 and 9. If found to be true, then print Yes. Otherwise, print No.
What hexadecimal means?
(HEXadecimal) Hexadecimal means 16, and the base 16 numbering system is used as a shorthand for representing binary numbers. Each half byte (four bits) is assigned a hex digit or letter as in the following chart with its decimal and binary equivalents.
How many hex is a byte?
2.2. As we know, a byte contains 8 bits. Therefore, we need two hexadecimal digits to create one byte. First of all, we’ll convert each hexadecimal digit into binary equivalent separately.
How do you convert hex to bytes?
To convert hex string to byte array, you need to first get the length of the given string and include it while creating a new byte array. byte val = new byte[str. length() / 2]; Now, take a for loop until the length of the byte array.
What does hex look like?
The hexadecimal numeral system, often shortened to “hex”, is a numeral system made up of 16 symbols (base 16). The standard numeral system is called decimal (base 10) and uses ten symbols: 0,1,2,3,4,5,6,7,8,9.Hexadecimal to decimal. Hex Decimal sum = (52 x 16) + 2 = 834 sum = (834 x 16) + 5 = 13349 3425h = 13349.
How do you represent hex?
Each hexadecimal digit represents four bits (binary digits), also known as a nibble (or nybble), which is 1/2 of a byte. For example, a single byte can have values ranging from 00000000 to 11111111 in binary form, which can be conveniently represented as 00 to FF in hexadecimal.
What are hex files used for?
Intel hexadecimal object file format, Intel hex format or Intellec Hex is a file format that conveys binary information in ASCII text form. It is commonly used for programming microcontrollers, EPROMs, and other types of programmable logic devices.
Is hex A PHP?
The ctype_xdigit() function in PHP used to check each and every character of string/text are hexadecimal digit or not. It return TRUE if all characters are hexadecimal otherwise return FALSE .
Is hex a digit?
Hexadecimal (or hex) is a base 16 system used to simplify how binary is represented. A hex digit can be any of the following 16 digits: 0 1 2 3 4 5 6 7 8 9 A B C D E F. It is much easier to write numbers as hex than to write them as binary numbers.
What is Isxdigit?
isxdigit() function in C programming language checkes that whether the given character is hexadecimal or not. isxdigit() function is defined in ctype. h header file. Application : isxdigit() function in C programming language is used to find out total numbers of hexadecimals present in any given input.
Who invented hexadecimal?
Tonal system (hexadecimal) In 1859, Nystrom proposed a hexadecimal (base 16) system of notation, arithmetic, and metrology called the Tonal system.
What is hex color?
Hex color codes are values that tell the display how much of a color to show. The values are a special code that represents color values from 0 to 255. If red, green, and blue are all at the minimum 0 (represented as “00” in the code), the color expressed is the color black.
How is hex stored in memory?
An even more efficient way to represent memory is hexadecimal form. Here, each digit represents a value between 0 and 16, with values greater than 9 replaced with the characters a to f. A single hexadecimal digit corresponds to 4 bits, so each byte of memory requires only 2 hexadecimal digits.
Why is a byte 255 and not 256?
The size of the byte has historically been hardware dependent and no definitive standards exist that mandate the size. The de facto standard of eight bits is a convenient power of two permitting the values 0 through 255 for one byte.
How do you convert hex to Denary?
Method 1: Converting from hex to denary via binary Separate the hex digits into 2 and D and find the equivalent binary numbers (2 = 0010; D = 1101). Piece them together to get 00101101 (0x128 + 0x64 + 1×32 + 0x16 + 1×8 + 1×4 + 0x2 + 1×1 = 45 in denary).
Is hex little endian?
In hex, this number would be represented as 230116 (or 0x2301). The important thing to remember is that the endianness describes the order in which a sequence of bytes are stored. Each byte is made up of two digits which represents the upper or lower 4 bits of the value.
How do you convert hex to little endian?
3 Answers Get the value from the EditText as a String . Parse the string value as hex, using Integer. parseInt() and radix 16 . Flip the byte order of the int, either using ByteBuffer (simpler) or using bit shifts (faster).
How do you print hex in python?
Python: hex() function Version: Syntax: hex(x) Parameter: Example: Python hex() function number = 127 print(number, ‘in hex =’, hex(number)) number = 0 print(number, ‘in hex =’, hex(number)) number = -35 print(number, ‘in hex =’, hex(number)) returnType = type(hex(number)) print(‘Return type from hex() is’, returnType). | https://www.pixaria.com/what-is-a-hex-string/ |
Build a Raised Vegetable Bed
What lumber should I use to construct a raised vegetable bed (4 feet wide by 16 feet long by 2 feet high)? If boards are 8 feet long and a foot wide, how do I connect them to make 16 feet? What about the corners? Should sides be reinforced? Can I use 4 x 4 posts that are not treated?
Certified GKH Gardening Expert
The following article should be of some help to you:
https://www.gardeningknowhow.com/edible/vegetables/vgen/raised-vegetable-gardens.htm
You must be logged into your account to answer a question.
If you don't have an account sign up for an account now. | https://questions.gardeningknowhow.com/build-a-raised-vegetable-bed/ |
An automobile is a wheeled motor vehicle that is made use of for transportation. Numerous meanings exist for vehicles, however most of them consist of a four-wheel style, seating one to eight people, as well as operating on roadways. These lorries are used largely to deliver individuals. This meaning is among one of the most typically used today. Below are some more information about the automobile. Below are a few of the most common kinds of automobiles. Listed below are some usual instances.
A car is a kind of car. It is a self-propelled automobile that is created to bring the vehicle driver, a small number of passengers, and also a limited quantity of load. These cars can be found in all shapes and sizes, as well as can be two, three, or 4 wheels. Their propulsion systems typically involve inner combustion engines, however they can likewise be vapor or electrical. The power outcome of an automobile varies greatly, from under fifty horsepower for older designs to over 200 horse power for the most effective designs.
A car is a self-propelled lorry that has a single or numerous wheels. They commonly carry a chauffeur, a handful of travelers, as well as a minimal quantity of load. The automobile can be three or even more wheels, as well as have various propulsion systems, such as gas, steam, or electricity. Their power output differs, as well, from under 50 horsepower for the earliest designs to greater than 200 horsepower for the most modern and also innovative designs.
An automobile is a self-propelled car that is suitable for travelling on roadways. There are several designs and also attributes. They can be two-wheeled or three-wheeled, and they are powered by a variety of different methods, including interior combustion engines, heavy steam engines, or electrical motors. Some autos have a retractable roofing. Their power varies from under 50 horse power in old models to over 200 horsepower in bigger models.
A vehicle is a rolled traveler car that is developed to operate on roads. There are many different versions of autos, each with distinct features. Some have several wheels, a retracting roof, and are used as a traveler car. Typically, a vehicle is powered by an interior burning engine however may also be powered by a steam engine or electrical motor. A vehicle’s power depends on its weight and also its speed.
The auto was created in Germany in the late 1800s, but it was only in the 1920s that the car genuinely took off. The automobile market came to be the foundation of the new consumer goods society. By the 1920s, it had actually become the lifeline of the steel and petroleum industries, offering one in every 6 work. The creation of the inner combustion engine by Dutch scientist Christiaan Huygens changed the globe. A gas-powered engine is an essential part of a vehicle and also sustained its whole society. how to replace a car battery
An auto is a wheeled automobile made use of for transportation. Typically, it has 4 wheels and seats one to 8 people. It is mainly used for transportation. While there are various interpretations of an automobile, the majority of agree that it is a rolled automobile for human transportation. The definition of a vehicle is a basic one. It is a four-door, passenger-car that runs on roads. However, there are distinctions.
The term “auto” refers to a car that is self-propelled as well as suitable for usage when driving. There are a number of various models of vehicles with different attributes. Generally, they have 4 wheels and are moved by a gasoline or vapor engine. In the USA, a lot of vehicles are powered by interior burning engines or electric motors. The horse power of an auto differs widely. Early models may have under 50 horsepower, while larger designs might have 200 horse power or more.
A car is a wheeled traveler lorry that is self-propelled, with four wheels and also an independent electric motor. These lorries are usually made use of for transportation on the streets as well as are readily available in a range of models. Their attributes vary, however they generally have 4 wheels and can be thrust by electric or steam engines. Their horsepower differs from under fifty to over two hundred depending upon the kind of car. The term “car” is a synonym of cars and truck.
An auto is a wheeled lorry with four wheels and also an independent power source. The term vehicle is a basic synonym for “car”. The word automobile is a general term for any vehicle that is self-propelled. The definition of vehicle differs with design. Older versions have one motor and a smaller sized, hand-operated one has two. They are normally designed for personal usage rather than for lugging goods. In the USA, 140 million people possess a car.
A car is a self-propelled vehicle. It is a vehicle that works on a road. There are several versions of automobiles, each with a different name and also attribute collection. For instance, an automatic washing equipment can be run by a switch, without the need for any kind of assistance. An automatic lorry has a hands-on washing cycle that requires initial loading of clothing. If the auto is an auto, it suggests it can be driven.
An automobile is a self-propelled, rolled passenger lorry that has 4 wheels and also an electric motor that moves it. These lorries are developed to be able to carry on a roadway and transport a motorist. They can additionally be described as a mobile automobile. The word auto is also utilized to describe any lorry that can be moved on a roadway. A car is a self-propelled car, however it can not be driven. best car battery brand in Thailand
The auto was originally a horse-drawn carriage. It was later on called a motorcycle. It had 2 wheels as well as a back seat. It was not a bike. The very first car was an equine attracted wagon. The modern vehicle has 4 wheels as well as a rear. It can additionally be called a bike. An auto is a self-propelled automobile. It can progress and in reverse, and it can relocate a huge range. | http://www.archercitycountryclub.com/2022/01/19/things-you-really-did-not-find-out-about-vehicle/ |
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