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COVID-19: 33 cases, five possible exposures in Oneida County
There were 33 new coronavirus cases reported Saturday in Oneida County, bringing the number of cases in the county to 2,812 after one previously reported case was removed from the amount.
Of these new cases, six are nursing home residents, according to Oneida County Officials. A total of 261 cases are currently active, with 15 people, including 4 nursing home residents, hospitalized due to the virus. There have been no new virus-related deaths reported in the county, leaving the total at 129, officials said. So far, 2,423 people have recovered from the virus.
A total of 221,981 coronavirus tests have been conducted in Oneida County, with 219,169 returning negative, officials said. Currently, 261 people are in mandatory isolation due to the virus, and 1,306 are in mandatory quarantine.
Public exposures
Officials also reported five possible exposures to coronavirus in Oneida County:
- 10:30 to 11 a.m. Oct. 23 at Dollar General at 34 Chenango Ave S., Clinton
- 2 to 2:15 p.m. Oct 24. at Hobby Lobby at 4605 Commercial Drive, New Hartford
- 2:30 to 2:45 p.m. Oct. 24 at Price Chopper at 4535 Commercial Drive, New Hartford
- 3:30 to 5:15 p.m. Oct. 29 at Shear Envy Salon at 8623 Clinton St., New Hartford
- 7:15 to 10:15 p.m. Oct. 29 at Pumpkin Junction at 2811 Graffenburg Road, Sauquoit.
In each of these cases, the infected person wore a mask. Those who may have been present during these incidents should monitor for symptoms for two weeks after, officials advised.
Herkimer County
No new coronavirus cases were reported in Herkimer County Saturday, leaving the total number of cases reported at 399, according to officials from the Herkimer County Public Health Department.
Of these cases, 24 are currently active, officials reported. Ten people have died from the virus, and 365 people have recovered. None are currently hospitalized due to the virus.
A total of 46,642 people have tested negative for the virus in the county, officials said. Currently 100 people are in precautionary quarantine due to the virus, as well as 76 in mandatory quarantine. Four people were released from mandatory quarantine, officials reported. | https://www.uticaod.com/story/news/healthcare/2020/10/31/covid-19-33-cases-five-possible-exposures-oneida-county/6103643002/ |
Many of us lead stressful lives. When stress goes unmanaged it can impact numerous different areas of our lives, this includes sleep. When we lay down at night and are unable to stop our thoughts from racing from one topic to the next it can be difficult to relax enough to sleep. Even once we finally do fall asleep it can be difficult to have a restful slumber.
Racing Thoughts
One of the biggest obstacles to a restful night of sleep is the inability to turn our thoughts off and wind down. We may be exhausted from the day but still unable to relax enough to peacefully drift off to sleep. Even worse, we may wake up feeling as if we hardly rested at all. A large part of getting quality sleep is the ability to relax and drift into a deep sleep. We may need to add a few enjoyable and relaxing activities to our pre-sleep routine like playing with NFL cornhole boards.
The Impact on the Body
Sleep deprived stressed individuals often have weakened immune systems as a result, making them more prone to sickness. A lack of sleep also impacts memory, muscle repair, and the way we feel. The impact on your physical health can be responsible for that cold you can’t seem to kick or that nasty scratch that seems to be taking a long time to heal. Stress and sleep can wreak havoc on your body and make it difficult for your internal army to take care of your body well.
The Sleepless Anywhere and Everywhere Cycle
Perhaps the scariest part about the impact that stress can have on sleep is the cycle of sleepless nights that can spring from stress that goes unresolved. Those two nights of tossing and turning can easily turn into a month long struggle with very little shut eye. Bleak huh? The only true answer is to utilize techniques that allow you to wind down at night so that your mind is free enough to enjoy a relaxing night of rest.
To live is to experience stress. We must learn to manage and sometimes eliminate stress in order to keep our lives healthy and get the rest we need. This means calming those racing thoughts before we go to sleep. This also means putting steps in place to prevent those sleepless nights from expanding into sleepless months. Our wholes lives depend upon our ability to adequately care for our own health and wellness. | http://www.macuhoweb.org/how-stress-impacts-you-and-how-to-deal-with-it/5747/ |
Q:
Security of a self-decrypting block-cipher?
If I have a block-cipher like for example AES,
a plaintext $x$, we use different function to encrypt and decrypt
: $\text{encrypt}(x) = y$ , $\text{decrypt}(y)=x$.
Now, if we build a function with a permutation $P(x)$ with $P(P(x))=x:$
$F(x)=\text{decrypt}(P(\text{encrypt}(x))$ , we have $F(F(x))=x$, a function that encrypts and decrypts.
Does this reduce the security or allow new attack on the cipher?
I know stream cipher already encrypts and decrypts using the same function but what about a block-cipher ?
A:
As I understand, your question is about using an involutive function $F$ as a block cipher. This function is constructed as $F(x) = D(P(E(x)))$, for some (let's assume secure) block cipher represented by $(E, D)$. I will assume the encryption and decryption keys are equal such that the same holds for $F$.
Below is a generic attack that only uses the involutive property of $F$, there might be additional problems (depending on $E$ and $D$).
It is typically required that block ciphers are secure against chosen-plaintext attacks.
In the example it is trivial to obtain $x$ given $y = F(x)$ and an encryption oracle. We just ask the oracle to encrypt $y$.
In other words, an encryption oracle is equivalent to a decryption oracle.
Practically speaking, the attacker just needs to get his victim to encrypt something that he already encrypted earlier. Do not underestimate this attack; it is often easier to trick the victim into encrypting something than you might suspect.
Note that many block ciphers do use involutions in their structure. This could be useful, for example, to reduce the size of the implementation.
What about stream ciphers?
In a stream cipher, the state of the cipher constantly changes. This effectively means that the function $F$ is variable, so you'd need a much stronger oracle (which can somehow rewind the state).
A:
For some modes of operation you can easily show that an involution would be insecure:
OFB would be most clearly insecure, since the keystream just repeats the nonce/IV and its corresponding encrypted block.
CFB would likewise be insecure, since zero blocks encrypt just like with OFB. This is of more limited advantage to an attacker, but far from secure.
CBC mode again has problems with zero blocks, since the following block's ciphertext can be decrypted simply by XORing it with the ciphertext of the block two back.
Similarly, CBC-MAC, including some of its variants, would be broken, because adding two blocks of zeros anywhere in the message would not alter its authentication tag.
Now for the handwavy part.
With CTR mode you are going to have worse bounds on the amount of ciphertext you can encrypt. Normally CTR mode is secure up to roughly $2^{b/2}$ blocks, because at that point you would expect outputs to collide with a PRF but not with a PRP. Equivalently, at that point you expect ciphertext blocks to collide, which tells you that the message blocks differ.
With an involution you have the additional case that the output may collide with another input block, which tells you the corresponding output. That has an equal chance of happening, doubling the chance that one of these cases happens and thus about halving the amount of data you can encrypt. (Or reducing it by a factor of $\sqrt{2}$, but close enough.)
However, beyond that I think CTR mode would remain secure, as long as the attacker cannot control the nonce.
AEAD modes are more complicated to analyze, especially when they use the same key for encryption and authentication. GCM is probably secure, since its security comes down to that of CTR both for encryption and authentication. Others like CCM might not be, due to the use of CBC-MAC.
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Researchers analyzed 19 galaxies, including NGC 3972 (left) and NGC 1015 (right), which are 65 million and 118 million light-years from Earth, respectively. Both possessed pulsating stars called Cepheid variables that let researchers determine the distance to the galaxies. (A. Riess (STScl/JHU)/NASA/ESA)
Recent Hubble Space Telescope findings suggest that the universe is expanding much faster than expected — and astronomers say the rules of physics may need to be rewritten in order to understand why.
Scientists use the Hubble Space Telescope to make precise measurements of the universe’s expansion rate. However, observations for a new study don’t match up with previous predictions based on the universe’s trajectory following the Big Bang, according to a statement from the Space Telescope Science Institute (STScI).
«The community is really grappling with understanding the meaning of this discrepancy,» Adam Riess, Nobel laureate and lead researcher on the study describing the new findings, said in the statement. Riess is an astronomer at STScI and a professor at Johns Hopkins University. [Our Expanding Universe: Age, History & Other Facts]
The Hubble Space Telescope measures the distance to other galaxies by examining a type of star that varies in brightness. These stars, called Cepheid variables, brighten and dim in a predictable way that lets researchers judge the distance to them. This data is then used to measure the universe’s expansion rate, known as the Hubble constant.
More From Space.com
Hubble Space Telescope
Our Expanding Universe: Age, History & Other Facts
Cepheid variables
Hubble constant
The new findings show that eight Cepheid variables in our Milky Way galaxy are up to 10 times farther away than any previously analyzed star of this kind. Those Cepheids are more challenging to measure than others because they reside between 6,000 and 12,000 light-years from Earth. To handle that distance, the researchers developed a new scanning technique that allowed the Hubble Space Telescope to periodically measure a star’s position at a rate of 1,000 times per minute, thus increasing the accuracy of the stars’ true brightness and distance, according to the statement.
The researchers compared their findings to earlier data from the European Space Agency’s (ESA) Planck satellite. During its four-year mission, the Planck satellite mapped leftover radiation from the Big Bang, also known as the cosmic microwave background. The Planck data revealed a Hubble constant between 67 and 69 kilometers per second per megaparsec. (A megaparsec is roughly 3 million light-years.)
However, the Planck data gives a constant about 9 percent lower than that of the new Hubble measurements, which estimate that the universe is expanding at 73 kilometers per second per megaparsec, therefore suggesting that galaxies are moving faster than expected, according to the statement.
«Both results have been tested multiple ways, so barring a series of unrelated mistakes, it is increasingly likely that this is not a bug but a feature of the universe,» Riess said.
One possible explanation for the discrepancy is that dark energy — the mysterious force known to be accelerating the cosmos — is driving galaxies farther apart with greater intensity. In this case, the acceleration of the universe may not have a constant value but rather may change over time.
Also, it’s possible that elusive dark matter, which accounts for 80 percent of the matter in the universe, interacts more strongly with visible matter or radiation than once thought, the researchers said.
Another possible explanation includes a new kind of subatomic particle that travels close to the speed of light and would be affected only by gravity. Researchers named the superfast particles sterile neutrinos, and collectively, these particles are called dark radiation, according to the study, which has been accepted for publication in The Astrophysical Journal.
«Any of these scenarios would change the contents of the early universe, leading to inconsistencies in theoretical models,» STScI representatives said in the statement. «These inconsistencies would result in an incorrect value for the Hubble constant, inferred from observations of the young cosmos. This value would then be at odds with the number derived from the Hubble observations.»
The team plans to use data from the Hubble Space Telescope and ESA’s Gaia space observatory to measure the precise positions and distances of stars and to further refine estimates of the universe’s expansion rate. | https://tall-white-aliens.com/?p=23390 |
The zebra puzzle is a well-known logic puzzle. Many versions of the puzzle exist, including a version published in Life International magazine on December 17, 1962.
The puzzle is often called Einstein's Puzzle or Einstein's Riddle because it is said to have been invented by Albert Einstein as a boy; it is also sometimes attributed to Lewis Carroll. However, there is no known evidence for Einstein's or Carroll's authorship and the Life International version of the puzzle mentions brands of cigarette, such as Kools, that did not exist during Carroll's lifetime or Einstein's boyhood.
It is often claimed that only 2% of the population can solve this puzzle
The following version of the puzzle appeared in Life International in 1962:
- There are five houses.
- The Englishman lives in the red house.
- The Spaniard owns the dog.
- Coffee is drunk in the green house.
- The Ukrainian drinks tea.
- The green house is immediately to the right of the ivory house.
- The Old Gold smoker owns snails.
- Kools are smoked in the yellow house.
- Milk is drunk in the middle house.
- The Norwegian lives in the first house.
- The man who smokes Chesterfields lives in the house next to the man with the fox.
- Kools are smoked in the house next to the house where the horse is kept.
- The Lucky Strike smoker drinks orange juice.
- The Japanese smokes Parliaments.
- The Norwegian lives next to the blue house.
Now, who drinks water? Who owns the zebra?
In the interest of clarity, it must be added that each of the five houses is painted a different color, and their inhabitants are of different national extractions, own different pets, drink different beverages and smoke different brands of American cigarets [sic]. One other thing: in statement 6, right means your right.
— Life International, December 17, 1962
Note:- If try searching over Internet you may or may not find the final solution, but what is required is the logic behind the solution. | https://puzzling.stackexchange.com/questions/31350/zebra-problem-popularly-known-as-einsteins-riddle?noredirect=1 |
Q:
Stack 10 Columns in R in to two columns
I'm having trouble stacking 10 columns in R into two columns of 5 where each column relates. Basically I have something like:
Name1, ID1, Name2, ID2, Name3, ID3, Name4, ID4, Name5, ID5
And I need to stack them in to a Name and ID table where the values in each Name column still match its ID counterpart. What would be the best way to approach this?
Thanks!
A:
I would recommend melt from the "data.table" package.
Here's some sample data. (This is something you should share.)
mydf <- data.frame(
matrix(1:20, ncol = 10, dimnames = list(NULL, paste0(c("Name", "ID"),
rep(1:5, each = 2)))))
mydf
## Name1 ID1 Name2 ID2 Name3 ID3 Name4 ID4 Name5 ID5
## 1 1 3 5 7 9 11 13 15 17 19
## 2 2 4 6 8 10 12 14 16 18 20
Here's the reshaping:
library(data.table)
melt(as.data.table(mydf), measure = patterns("Name", "ID"),
value.name = c("Name", "ID"))
## variable Name ID
## 1: 1 1 3
## 2: 1 2 4
## 3: 2 5 7
## 4: 2 6 8
## 5: 3 9 11
## 6: 3 10 12
## 7: 4 13 15
## 8: 4 14 16
## 9: 5 17 19
## 10: 5 18 20
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Q:
Zing Charts - Place Items on Map
I am trying to put Location markers on an USA map similar to the one in this page
http://www.zingchart.com/blog/2012/07/17/interactive-html5-maps-api/
(Place items on map section.)
I am not able to find the JSON attribute for specifying this (The link on it is taking to the site's home page only).
Please help me on how to do this or point me to any documentation on it.
[--EDIT--]
I found a function to get the XY coordinates on the map using the Lat/Lon value and vice-versa (zingchart.maps.getXY(mapid, lonlat, itemid)).. But I am still stuck with placing a marker on that XY point.
[--EDIT--]
Below answers work as expected. I am trying to put markers on US map. I would like to know how to place markers on Alaska/ Hawaii states with lat/lon info since they are placed below california as a separate polygon though they are geographically above the US.
A:
I'm on the ZingChart team, and I can definitely help you out with this!
It's critical that you wait until the map has loaded before finding the XY coordinates. Use the ZingChart 'load' API event listener to wait until the chart has loaded:
zingchart.load=function() {
drawPoints();
};
Inside our drawPoints function, we'll find the longitude and latitude values. If the values are north and east, the numbers will be positive, south and west will be negative. For example, Sao Paulo is located at 46.6333° W, 23.5500° S, so we would use [-46.63, -23.55]. In this map demo, we've placed a marker at Bangalore, which is located at 77.5667° E, 12.9667° N, so we'll use [77.57, 12.97].
var lonlat = [77.57, 12.97];
var bangalore = zingchart.maps.getXY('map', lonlat);
The getXY method returns an array of length 2, with the value at index 0 being the x position and the value at index 1 being the y position for your map.
Now that we have the X Y coordinates for Bangalore in our variable, we can use the addobject API method to place a marker at that location. Below, 'zc' is the same as the id given to the div used to place the chart.
zingchart.exec('zc', 'addobject', {
type: 'shape',
data: [{
x: bangalore[0],
y: bangalore[1],
type: "circle",
size: 3
}]
});
To see the code in its entirety, view the page source of the map demo provided.
Please let me know if you have any more questions!
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Context: The precision and cost of static analysis are determined by abstraction heuristics (e.g., strategies for abstracting calling contexts, heap locations, etc.), but manually designing effective abstraction heuristics requires a huge amount of engineering effort and domain knowledge. Recently, data-driven static analysis has emerged to address this challenge by learning such heuristics automatically from a set of training programs. Objective: We present a practical algorithm for learning disjunctive abstraction heuristics in data-driven static analysis. We build on a recently proposed approach that can learn nontrivial program properties by disjunctive boolean functions. However, the existing approach is practically limited as it assumes that the most precise abstraction is cheap for the training programs; the algorithm is inapplicable if the most precise abstraction is not scalable. The objective of this paper is to mitigate this limitation. Method: Our algorithm overcomes the limitation with two new ideas. It systematically decomposes the learning problem into feasible subproblems, and it can search through the abstraction space from the coarse- to fine-grained abstractions. With this approach, our algorithm is able to learn heuristics when static analysis with the most precise abstraction is not scalable over the training programs. Results: We show our approach is effective and generally applicable. We applied our approach to a context-sensitive points-to analysis for Java and a flow-sensitive interval analysis for C. Experimental results show that our algorithm is efficient. For example, our algorithm can learn heuristics for 3-object-sensitive analysis for which the existing learning algorithm is too expensive to learn any useful heuristics. Conclusion: Our algorithm makes a state-of-the-art technique for data-driven static analysis more practical. | https://koreauniv.pure.elsevier.com/en/publications/a-practical-algorithm-for-learning-disjunctive-abstraction-heuris |
My name is Vicki Templar & for over 20 years I have had a passion for using natural and effective remedies that come from plants rather than filling a body with chemicals. I started my training in the mountains of Ireland & have since attained accreditation from the School of Natural Health Sciences in Herbalism & Aromatherapy .. On moving back to my childhood town of Bruton in Somerset, I achieved a long held dream to set up my apothecary for remedies & holistic treatments..
I have always used herbs that I have grown or harvested myself so that I know they are of ultimate quality . I make my own tinctures, oils and flower essences at different times of the day and phases of the moon., When an ingredient has run out, I have to wait for the next year sometimes before I can make it again.
I use flower essences, made by myself in alot of my recipes to enhance the effects on an emotional level as well as the physical.
I love using the plants and flowers for natural skin care as their fragrances and healing qualities are so delightful to use and work with. I am passionate about making pure natural products available to people, especially to young women who are bombarded with so many potentially dangerous chemicals to use daily on the skin. | https://www.greenladynaturalhealth.co.uk/about |
Exhibition and creative installation relating to the picture book Florette developed in collaboration with the author and illustrator, Anna Walker.
‘At the Fence’ with Stolen Generations Survivors
Dates
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Recreates moments from the institutionalisation of mixed descent Aboriginal children at mission sites. Shadows of the past, silhouettes of resilience and portraits of survival.
Exhibition of Abraham 'Izzy' Orloff's photographs
Dates
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See a curated selection of photographs and experience interwar (1918-1939) Perth and Fremantle through the lens of photographer Abraham 'Izzy' Orloff.
Online Exhibitions
This online exhibition brings together advertising and promotional photographs from the State Library’s diverse collection of photographs by Stevenson, Kinder & Scott Corporate Photography.
Past Exhibitions
Dates
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Visit the World Press Photo Exhibition 2021 on its world-wide tour showcasing the stories that matter.
Illustrations from the picture book
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Showcasing original artwork by Johnny Warrkatja Malibirr from the award-winning picture book Little Bird's Day – written by Sally Morgan.
Dates
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An exhibition celebrating the eight extraordinary state and territory recipients of the 2021 Australian of the Year Awards.
satellite exhibition
Dates
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A unique collection of Aboriginal photographs taken by one of Australia's earliest photographers.
The illustrated picture book by Carole Wilkinson and Liz Anelli
Dates
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An exploration of how Liz Anelli crafted the illustrations through layering of sketches, collage, ephemera and digital techniques.
Dates
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Libraries and museums have stories and artefacts that tell us about how people have lived in the past, as well as the present. What artefacts will be collected by museums and libraries in the future?
Dates
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This exhibition is an exploration of the visions of central Perth - both compatible and contested - using photos, paintings, maps, videos and stories. | https://slwa.wa.gov.au/whats-on/exhibitions |
Barriers and facilitators in the pathway to care of military veterans.
Doctoral thesis (D.Clin.Psy), UCL (University College London).
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Huck_Carlene_thesis_redacted.pdf
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Abstract
This thesis focused on psychological help-seeking and the barriers and facilitators to mental health care in a military population. It is presented in three parts. Part one is a literature review examining the role of stigma in relation to military personnel seeking help for psychological problems. The review highlighted that, despite concerns about perceived stigma from others being highly endorsed as a barrier to care in military personnel, public stigma concerns do not appear to predict actual help-seeking and care utilisation. The review suggested considerations for future research including refining the conceptualisation and measurement of stigma within this population as well as encouraging consideration of other potentially important factors, such as attitudes and beliefs about mental health and mental health treatment. Part two is an empirical paper. This qualitative study aimed to understand the perspectives of UK ex-servicemen, and the barriers and facilitators, in relation to their pathway to care for mental health problems. The results indicated that there are specific barriers and facilitators that are more relevant at different stages in the veterans’ pathway. A number of recommendations for future research as well as a set of clinical implications are proposed and discussed. Part three is a critical appraisal of the research. It reflected on the practical, methodological, and conceptual issues encountered during the process of setting up and conducting research with an ex-military population. It covered areas relating to the literature in the field, factors influencing recruitment, and the process of conducting and analysing the interviews. Potential considerations for future research are highlighted. | https://discovery.ucl.ac.uk/id/eprint/1449254/ |
Habitat fragmentation can have a range of negative demographic and genetic impacts on disturbed populations. Dispersal barriers can be created, reducing gene flow and increasing population differentiation and inbreeding in isolated habitat remnants. Aggregated retention is a form of forestry that retains patches of forests as isolated island or connected edge patches, with the aim of 'lifeboating' species and processes, retaining structural features and improving connectivity. Swamp rats (Rattus lutreolus) are a cover-dependent species that are sensitive to habitat removal. We examined the effects of aggregated retention forestry and forestry roads in native wet Eucalyptus forests on swamp rat gene flow and population genetic structure. We characterized neighbourhood size in unlogged forest to provide a natural state for comparison, and examined population structure at a range of spatial scales, which provided context for our findings. Tests of pairwise relatedness indicated significant differentiation between island and edge populations in aggregated retention sites, and across roads in unlogged sites. Spatial autocorrelation suggested a neighbourhood size of 42-55m and revealed male-biased dispersal. We found no genetic isolation by geographical distance at larger (>2.3km) scales and populations were all significantly differentiated. Our results suggest that removal of mature forest creates barriers for swamp rat dispersal. In particular, roads may have long-term impacts, while harvesting of native forests is likely to create only short-term dispersal barriers at the local scale, depending on the rate of regeneration. | http://ecite.utas.edu.au/84282 |
Consolation East Africa (CEA), a TAP Partner since 2020, like many other civil society organizations around the globe, was forced to an almost-standstill as a result of the COIVD-19 pandemic. As projects halted, CEA faculty and community members faced an extra dimension of challenge, as most of them did not have the ability to to turn to technological devices that could enable them to go virtual for meetings, workshops and trainings.
Despite this added hardship on top of the unprecedented situation, CEA has continued to serve its community in Nairobi, with their work now spanning over a decade. By enduring some of the most constricting conditions a civil society organization could experience, CEA has built expertise regarding adaptation against all odds to serve local community members and implement SDG16 to the fullest extent.
Amongst the new members of the 2022-2023 Steering Committee, CEA brings to the table a unique and vitally important perspective that is intimately familiar with the needs of local populations that SDG16 is most challenged to reach, especially in light of the pandemic. Read the following interview between the TAP Secretariat and Executive Director of Consolation East Africa, Bridged Faida, to learn more specifically on CEA’s experiences and what they mean for CEA’s outlook for the TAP Steering Committee for the next two years.
Interview with Bridged Faida, Executive Director of Consolation East Africa
Q: Can you give a brief introduction to the TAP Network Membership about Consolation East Africa and what your current focuses are for 2022?
Consolation East Africa (CEA) is a Kenyan Non-Profit Organization registered in 2011 with a vision to eventually see a Kenyan society that is just and gender mainstream. The mission of CEA is to ensure that vulnerable and marginalized people are socially included and that their human dignity is respected.
In 2022 CEA will continue its work of empowering community via policy advocacy and community empowerment through the following focus activities:
- Advocacy for greater and meaningful participation of marginalized and vulnerable populations in relevant public policy spaces
- Advocacy for gender responsive budgeting in the public finance spaces with a focus on health, education and social economic empowerment
- Instituting proactive and responsive approaches to addressing human trafficking and gender based violence in Kenya
- Improve the quality of services received by the public through social accountability monitoring approaches
- Building capacities of marginalized and vulnerable populations to enable them achieve some form of positive socio-economic transformation
In order to achieve this CEA will collaborate with relevant government departments, Civil Society and grassroots Organizations in Kenya. The target population of CEA is Key Populations, the homeless, residents of informal urban settlements and those rural areas comprising women, youths and children.
Q: Can you describe the current landscape of the civil society sector in Nairobi and CEA’s role and function in it?
Vulnerable children: Nairobi is home to a number of vulnerable children. According to studies 60,000 to 1.8m of these are orphans and vulnerable children and are either homeless, in foster care or in charitable children institutions. A number of CSOs are intervening to assist OVCs in various ways. In 2012 CEA/KARDS did a survey to try and understand the different OVC interventions that do exist and the organizations offering them for effective referral services. From the CEA’s role in this has been to strengthen the quality of rehabilitation and reintegration care received by these children via referrals, youth formation and counseling. CEA also build the capacities of the various children institutions on rehabilitation and reintegration. In the past we contributed in this aspect via various studies just to mention a few:
- Projects and activities of street children in Kenya
- Effectiveness of street youth reintegration in Kenya
- Analysis of reintegration care for youth leaving institutions of care
Key Populations: Key Populations in Kenya Comprise sex workers, people who use and inject drugs, MSM, prisoners and transgender. The Key Populations face a number of health and other public service access barriers. They also are victims of gender based violence, stigma and discrimination and a myriad other human rights abuses. CEA from 2020 to date has been working with AVAC and AIHA to assist improve the capacities of Key Population Led CSOs in Kenya, Zambia, Nigeria and Tanzania to address all structural barriers that lead to their exclusion in various public spaces. To address this CEA is contributing to the strengthening of the Kenyan, Zambian, Tanzanian and Nigerian Key Population Consortia to collectively and severally have improved capacities to address the structural barriers. In essence CEA has not only contributed to the fact that these consortia have made inroads towards being included in policy spaces but also they have been able to engage overseas development assistance donors such as PEPFAR and Global Fund.
Geographies, social classes, Informal settlements and rural areas: The Kenyan society is characterized with challenges in wealth distribution. The Gini Coefficient index for Kenya is 41.6% (53rd highest in the world) in 2018 and there are enormous disparities among geographies and various population classes with Rural, informal settlements and arid and semi-arid populations being way down the wealth income brackets. On an equal basis though the human development index estimate for 2021 was 0.60 (ranking Kenya 163 worldwide), disparities exist among Geographies, social classes, Informal settlements and rural areas. There are a number of CSOs working to address the income and human development disparities in Nairobi and in the country. There are also insecurity and Safety issues in Nairobi with challenges of crime being experienced especially in the poor sections of the city. In Nairobi CEA together with other CSOs mainly intervenes in the informal settlements providing interventions to empower people with various social economic skills including leadership, management and entrepreneurship.
Women, Girls and Youth: Women, Girls and Youth face various challenges in Nairobi. There are quite a number of women and children headed households for a number of reasons including deaths of parents/spouses or complicated family issues. Other challenges include unemployment for youth; menstrual hygiene, teen pregnancies and IPV for girls and women among other challenges. There are a number of organizations addressing several or one aspect of the challenges faced by the women, Girls and Youth of Nairobi. CEA works directly with Women, Girls and Youth to empower them and also assists improve grassroots CSO capacities to serve these populations.
Citizen participation and peace building: The citizens do not take interest in participating in the public policy spaces. This means that some policies and decisions may be taking place without the input of citizens. On the other hand, where citizens receive poor services (health, education, other public services etc), they may not be able to influence them. This year too, the country will be going towards elections and seemingly, the whole process is quite heated. CEA among other organizations is engaging the political parties to influence their manifestos, conducting voter education and encouraging citizens to participate in the public spaces.
Thematic Consortia: CEA is a member of the Stop The Traffik Kenya Consortium (STTK), Nairobi Child Protection Team (NCPT), Global Fund Advocates Network (GFAN), PEPFARWATCH, Street Children and Youth Organizations Network in Nairobi (SCYON), Key Populations TransNational Collaboration (KP-TNC) and Kenya Peace Network (KPN).
Q: How has your organization continued to show its presence in the community throughout the Pandemic?
CEA engaged in minimizing vulnerability among community members, collaborating with Community Based Organizations, by use of door to door and roadside information giving, the organization raised awareness to community members around Dagoretti Sub County in Nairobi, on COVID-19 preventive measures. During the same time, as the economy was hitting community members badly, the organization intervened and initiated entrepreneurship training for women and especially single and young mothers, to enable them earn through production of handmade soap and selling to the community around them. We as an organization have adopted online activities, especially when dealing with other CSOs networks, CBOs and Groups. The organization also was able to adopt the work at home policy, to enable safety.
CEA also continued to carry out some projects through use of a technological online meeting system, where training, meetings and workshops were conducted to CSOs participants in Nairobi and Kenya and in other Countries such as Tanzania, Zambia and Nigeria targeting Key Population Led Organizations and other members of Civil Societies.
Q: What challenges have you faced in implementing your community programs, for example for young women and mothers, during the COVID-19 pandemic?
There were several challenges that the organization faced during the covid period, some mentioned below:
- The inability to train a larger quantity of young women at once on entrepreneur skills, as groups were divided into a manageable quorum in accordance with the required COVID-19 preventive guidelines in Kenya. We also lost a number of members as we could only afford to bring a few together. However in post COVID we are trying to regain grounds but with strict COVID19 restrictions as laid down by the government.
- Lack of adequate financial resources that could enable support for CEA’s online activities with beneficiaries and participants in getting data support for online meetings and workshops and training, which caused some youth groups that were formed by CEA, to discontinue outreach group projects and get back to individual projects.
- Some organization’s staff members were not ready to continue supporting the organization, due to the organization’s inability to meet their expectations in terms of remunerations.
- Loss of contact between the organization and the community widened, as some community members could not afford technological channels in accessing information and organization’s meetings.
- Most of the planned activities could not be covered, especially those that were outreach based, mainly at the grassroots /community level.
- Number of physical meetings and contacts were minimized, especially during the first and second wave, where there were no physical meetings and workshops allowed, making the organization members question the future of CEA if the same continues. It became impossible to secure government appointments as government staff prefer physical meetings.
Q: How will your lessons learned over the pandemic shape your approach as a new TAP Steering Committee member?
While there is a need to strengthen the virtual platforms, we realize that there are quite a number of people who will be left out. An important dynamic becomes how to be better in virtual communications without losing those who are not able to engage in this platform.
We also learned that there are sectors that are averse to virtual platforms (Zoom, website, social media). These were mainly government staff who in most cases felt safer in physical meetings. On the other hand there were quite a number of services that still required physical encounters. This means that there is always a need to continue promoting the understanding of COVID restrictions side by side as we strengthen the virtual platforms.
Economic livelihoods of most of our target beneficiaries were devastated. Most businesses were also closed as a result of shrinking incomes. The financial stress and loss in livelihoods experienced during this time also led to increased incidences of gender based violence. There is a need to dialogue with governments to institute precautionary stimulus facilities for emergency periods.
Travel restrictions have also abounded. Countries can today be open to receiving guests and tomorrow closed to any type of guests. This means that there is always a need to be vigilant and always being updated of countries’ policy updates from time to time.
Q: What is the status of implementation of SDG16 in Kenya, through the eyes of CEA?
There are a number of challenges in implementing SDG16 in Kenya.
The implementation of SDG16 in Kenya, is still demanding, poverty level especially among rural and in the informal settlements communities is rising with the rising prices for basic needs such as foodstuffs almost annually, thus Zero Poverty level not yet achieved in reference to the National implementation of the Kenya Vision 2030, where one of the goals was Poverty reduction.
When it comes to leadership women are highly left behind, the equality within the leadership arena is a subject to be questioned.
In general the implementation of the SDG16 in Kenya is still far way behind to be achieved, a voice is needed to enable the citizens especially at the grassroots level both in the rural and in the informal settlements, they should have the awareness on the SDG16 implementation within the country, be given the opportunity to participate in the making of the VNR, share opinions and what they have observed in the implementation of the SDG16 within the country, and to know whom to hold accountable.
According to the Government VNR report of 2021, the outbreak of COVID-19 has negatively impacted the rule of law, security and crime reduction in the following ways:
- The measures put in place by the Government to cope with the Pandemic have resulted in massive unemployment, high poverty levels leading to increased insecurity incidents particularly petty crime and tension due to loss of livelihoods. In relation to this the government suggests the following
- Facilitation of interfaith dialogue in the local communities as well as involvement of local leaders to mediate conflicts cases among families and communities;
- Building capacity of law enforcement officers through online training to restore trust between the police officers and the public; and
- Recruitment and training of additional security personnel will also help in increasing the police population ratio thereby ensuring adequate protection of people and property.
In reference to existing challenges towards achieving SDG 16, the findings of the second CSO progress report on implementation of SDG16 for 2019 in Kenya still apply as follow:
- Poor financing by policy holders and little information and awareness on the same.
- There is still legislation that ensures the exchequer commits funds to support peace initiatives and structures across the country. CSOs in most instances have been forced to mobilize resources internally to be part of global events such as the Global Week of Action against Gun Violence and the African Union Amnesty month.
- There is still low public awareness about the right and procedures available to access information. Most citizens are unaware of the availability of the Act’s framework, procedures and their rights to access information.
Q: What are the ambitions for CEA in the next three years?
- Advocacy for greater and meaningful participation of marginalized and vulnerable populations in relevant public policy spaces
- Advocacy for gender responsive budgeting in the public finance spaces with a focus on health, education and social economic empowerment
- Instituting proactive and responsive approaches to addressing human trafficking and gender based violence in Kenya
- Improve the quality of services received by the public through social accountability monitoring approaches
- Building capacities of marginalized and vulnerable populations to enable them achieve some form of positive socio-economic transformation
- Engage policy makers on integrating SDG16 in Kenyan policies
Q: What can members of the TAP Network take away from the experiences and lessons learned of CEA?
Surviving amidst Lack of resources – CEA has continued with its work despite not having substantial funding resources since 2016. In this period it has continued creating impacts though in a reduced manner. Part of what contributed to survival was voluntary efforts of members and financial contributions, and also through working collaboratively with other organizations.
Community Knowledge: There is always a need to trust in the knowledge of community / civil society members, they know better and need to be meaningfully engaged at all processes of project implementation.
Policy engagement at a global and country level: For achievements to be made in integrating the SDG16, there is a need to continuously engage with grassroots CSOs in a bid to create a critical mass that will have a multiplier effect in the sub-national units-taking the agenda to their local councils/administrative structures. The sub-national structures could be engaged in creating actionable plans periodically that are monitored by the CSO teams. At Global Level there is a need to engage the Regional Economic Blocs, Africa Union and Global Agencies. Working via these three tier engagements, will make the agenda more visible.
About TAP Storytelling: In 2021 TAP Network launched the TAP Storytelling Initiative, which aims to closely and frequently highlight the work of the TAP Network membership through working directly with them to produce educational online content about their endeavors addressing SDG16+ and accountability for the 2030 Agenda. Together in this initiative, TAP aims to spotlight the work of our Members and Partners and the challenges, successes, failures, processes and problem solving that comes with it, while also offering the chance for wide promotion through TAP’s outreach channels. We hope that these opportunities will not only offer heightened visibility of the work of our Network, but will also inspire and educate more commitments to SDG16 and transparency and accountability for the 2030 Agenda as a whole. If you are interested in spearheading this work with us, head to our TAP Membership Engagement Portal where you can find the Storytelling Form to submit your interest.
Disclaimer: The views and opinions expressed on the TAP Network Blog Platform are those of the authors and do not necessarily reflect the official policy or position of the TAP Network. Any content provided by our bloggers or authors are of their opinion.
Photo by Consolation East Africa
Interested in publishing an article? | https://tapnetwork2030.org/tap-storytelling-interview-with-consolation-east-africa/ |
Localization and stimulation of chromatophore motoneurones in the brain of the squid, Lolliguncula brevis.
The relatively simple chromatophore system of the squid, Lolliguncula brevis, was studied with combined behavioural, morphological and electrophysiological methods in order to understand how the chromatophore patterns in the skin are organized at the level of the posterior chromatophore lobes (PCL). There are nine simple chromatic components of patterning in L. brevis. Retrograde transport of horseradish-peroxidase from chromatophores in the mantle skin established that the chromatophore motoneurones are located in the PCL. Focal threshold stimulation of the PCL in perfused, semi-intact preparations showed that the motor fields of individual chromatophore motoneurones are compact, including 2-60 chromatophores, generally of the same colour. Adjacent motoneurones in the lobe do not necessarily have adjacent motor fields in the skin.
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The World of Tanks team always works hard to improve the very core of the game and ensure foul play is recognized in a timely manner and dealt with according to Game Rules.
For a deeper understanding of what is considered cheating or exploiting in World of Tanks, read the detailed Fair Play Policy.
- Botting Read the article to find out what bots are and why botting is not welcomed by players, and prohibited by the Game Rules.
- Prohibited Mods Get to know all prohibited modifications and the consequences of using them.
- Toxicity What is toxicity and how can you help us stand against the negative behavior of some players? This article will answer these questions and more.
- Rigged Battles Learn how the Wargaming team fights against rigged battles and pins down its participants.
- Teamkill Find out how players are tracked and penalized when they damage or stun allied vehicles.
- Complaint System Read this article to find out how the In-Game Complaint System works and ways to use it.
- Watch out for Scammers Learn how to spot and avoid scammers in World of Tanks. | https://worldoftanks.eu/en/content/guide/fair_play/ |
ABSTRACT In this paper we present elements of a learner-centered AI curriculum for high school students that was field-tested in two private high schools. One of these elements is a unit in which students explore the possibilities of machine intelligence and consciousness through readings and hands-on activities. Also presented in the paper is a unit for teaching students about artificial neural networks (ANN) and their application. In this unit students learn to develop and train ANNs through small projects and activities that lead up to an independent research project. Examples of student projects are presented including the application of ANNs for modeling the ozone disinfection of water, the price of real estate as determined by housing features in a local market, and admission into an independent boarding school based upon admissions application data.
INTRODUCTION The field of robotics has becoming increasingly accessible to students of all ages. For example, Lego robotics kits are now commonly used to teach robotics in K-12 classrooms. However, other branches of artificial intelligence (AI) still remain inaccessible to pre-college students in spite of their educational potential.
In this paper we will present our curriculum for two topics covered in a learner-centered AI course that we have developed. The first topic is philosophy of the mind with a focus on the possibility of machine consciousness and the Turing test. Our experience has shown that high school students are particularly interested in the questions investigated in this part of the course. AI may be the means for self-exploration at a time when students are trying to understand the essence of their own existence and identity. This topic also provides part of a conceptual framework into which the technical subjects of the course can be understood and examined. The second topic presented is artificial neural networks (ANNs) and their application for student research. Because of their ability to learn and importance in the AI field, we have found the study of ANNs to be engaging to students and to offer numerous possibilities for development of metacognitive and critical thinking skills.
The curriculum described in this paper has been taught at St. Paul’s School, a private, independent boarding school in Concord, NH and Brunswick School, a private, independent day school in Greenwich, CT. At St. Paul’s School the class was taught for four years with a class size after the first year of 12 students. Because of the demand for the course and the course registration procedure, almost all of the students were seniors. At Brunswick School the class was taught for three years to a class size of about 6 students. At Brunswick School students from grades 9-12 were equally represented. | https://peer.asee.org/teaching-high-school-students-to-teach-machines |
The invention discloses spraying equipment for intelligent production based on green home furnishing, and relates to the field of spraying equipment. The spraying equipment comprises an equipment shell, wherein an outer sleeve is movably connected to the interior of the equipment shell, an inner sleeve is rotatably connected to the interior of the outer sleeve, and a pair of air bags is arranged in the inner sleeve. According to the invention, weight of a tea table is transmitted to a main shaft, so that the main shaft compresses the air bags; due to the fact that the two air bags are different in stress, the air bags are different in intern air pressure; the air pressure pushes an air cylinder, and then a hanging plate is driven to ascend obliquely upwards; the gravity center is transferred obliquely upwards, so that the tea table is driven to rotate; when the gravity center of the tea table rotates to an oblique lower position, the stress of the air bags is gradually converted into the previous opposite stress; the gravity center of the tea table is driven to move again, the tea table rotates reversely under the action of gravity, and spraying can be completed in corporation with a spraying head, so that the defect that a traditional motor and a traditional coupler are prone to damage due to large stress is overcome; and the spraying head is fixed and does not need to be rotated, so that the defect that the spraying head is damaged is overcome. | |
Sophia Brumfitt has performed as an oratorio soloist, with renaissance and medieval ensembles. Her versatile and agile voice has enabled her to work in areas spanning the entire spectrum of early music; from Medieval to Early Classical, through traditional Celtic and Sephardic song. Studying Music History and Performance Practice as a PostGraduate at Royal Holloway (RHUL) and Royal College of Music, Sophia has continued to research and devise many diverse programmes and collaborations with some of the country’s top Early Musicians, for television, stage and concert hall.
Present projects include Maiden in the Moor with Rebecca Austen-Brown focusing on retelling Medieval and traditional stories through using traditional, historic forms alongside electronic treatments and looping. Maniera with Emma Alter and Toby Carr delve into the colourful world of Early Baroque repertoire that links instrument and voice.
The 2020 Coronavirus Arts Shutdown meant that a number of singing engagements were cancelled this year, most notably the Canada Water performances of Theatre Volière’s Lyonesse and the the Easter Festival at St. Anne’s, Highgate West Hill.
www.sophiabrumfitt.co.uk
Katherine Clarke
VIOLIST
Katherine is a talented viola player, who specialises in contemporary repertoire and performing works for singing violist. She enjoys working with composers to write new works for the viola, showcasing the depth and range of this underrated instrument. In 2018 she premiered four new works for singing violist, commissioned with funding from Arts Council England, and more recently she premiered Cantare et trepidare for singing viola by Sadie Harrison, written specially for her. With more commissions on the way, Katherine will continue to perform and contribute to this unique and exciting repertoire.
Having completed her undergraduate studies at the Royal College of Music, Katherine went on to achieve a Distinction in her Masters in Performance at the Guildhall School of Music and Drama in 2017, with scholarships from the Goldsmiths’ Company and the Guildhall School Trust. Last year, Katherine was awarded funding from the Help Musicians UK Transmission Fund for three lessons with violist and composer Garth Knox in Paris.
Katherine is a keen chamber musician and has performed with various ensembles at St John’s Smith Square, LSO St Luke’s, the National Gallery and the British Museum, and has recorded at Abbey Road Studios.
David Braid
COMPOSER/GUITARIST/MANDOLINIST
David works have been broadcast live on BBC Radio 3 and performed in the US, Germany, Poland, Russia, Denmark, Sweden, South America. Major UK performances have taken place at Wigmore Hall and The Purcell Room, King’s Place, et al.
Steve Reich said of this work: ” ‘Morning’. Integration of voice with string quartet beautifully done – particularly first entrance. Writing for instruments is solid and sounds very good to me. Very honest stuff”.
David studied at The Royal College of Music from 1990-94, going on to complete post-grad studies at the University of Oxford.
David is the recipient of numerous awards and scholarships including: The John Longmire Prize for Composition and The Jack Morrison Prize for Guitar (RCM); The Composition Prize for Youth Orchestra, Murcia, Spain; The Fine Arts Sinfonia Composition Prize (London); and SPNM Short-listed composer 2001, among others.
As well as concert music, David has written film scores. He also wrote the tutorial book/CD, ‘Play Classical Guitar’ that has entered three editions including a Spanish translation (Backbeat Books, 2000). | https://braid-group.com/the-players/ |
* Australian Renewable Energy Agency (ARENA) to get guaranteed baseline funding of $1.43 billion over 10 years and the ability to support soil carbon sequestration, carbon capture and storage, green steel production, and industrial processes to reduce energy consumption.
* Technology Co-Investment Fund of $95.4 million to help businesses in the agriculture, manufacturing, industry and transport sectors identify opportunities to enhance productivity and adopt new technologies.
* Energy productivity measures worth $52.2 million, for example allowing a scouting group to install better air-conditioning equipment in their hall, a charity to install solar PV on their building, or a regional pub to upgrade their refrigeration.
* $24.6 million for the Clean Energy Regulator to develop new Emissions Reduction Fund methods (ways for projects to earn carbon credits).
* $35.4 million for better energy and emissions data and regulatory work. | |
Course description:
Cirrus express course is based on collaboration between Vilnius Academy of Arts, Kaunas Faculty Textile Department and Estonian Academy of Arts, Department of Textile Design.
During the creative workshop we will develop functional textile/design ideas that are related to Nida’s stories/”fossils”, i.e. legends, local tales, emotions, humour, tourism, etc. Collecting, gathering, archiving, processing and creative interpretation of local experiences will take on new forms of textile design. During the workshop we will practice the techniques of collaboration work in groups, observation, experience sharing and application. During the express course we will combine and share cultural stereotypes, idea development, textile design, creative research, and practices of international reproduction. We will have an open discussions and presentations of designed objects. The presentation of designed objects/prototypes will take place in Nida and Nida Art Colony’s spaces.
_________________________________
Vilnius Academy of Art is hosting a Cirrus express workshop“SCULPTURAL RESEARCH” on draping, sculpting, pattern-making in Nida Art Colony.
Tutors: Dainius Bendikas (IAA),
Jurgita Jankutė-Mirinavičienė (VAA).
Level: BA/MA
Teaching period: 24th May – 04th June, 2018.
Address: E. A. Jonušo str. 3, LT-93127 Neringa, Lithuania
Number of available place for Cirrus students: 6
Students from all Cirrus institutions are invited to attend the course.
CIRRUS/Nordplus grant available: 330 EUR travel (Iceland 660 EUR) + 70 EUR weekly.
Objective:
– To introduce and transmit the knowledge, values, techniques and an extensive creative process to
a new generation of young designers through direct methodology.
– To showcase new opportunities and constructive experimentation as a source of new creativity.
– To improve and support the professional development of design students as emerging designers.
– Improve their contextual and creative relevance while acquiring new development tools and
orientationon research, documentation, draping, pattern-making and most importantly design based
constructive thinking.
Course Content:
The workshop is an intense two-week
hands-on program for fashion and costume designers dedicated to break out of the traditional silhouette.
The course is aiming to provide knowledge about methods and techniques related to silhouette
development – draping, sculpting, creative pattern-making.
The course will provide information on:
– How to create a concept for further design development.
– How to use sculpting material;
– How to combine concept and form.
– How to advance and breakdown the object.
– How to pattern-make the V1 object.
The course will take up twelve days allowing time to experiment with the process. Over this period
students work will be transformed from the Idea to a dimensional object, to finished constructed object
consisting of patterns.
The complexity of the sculptures should be manageable within the time. Students are asked to direct
their work towards their own concept for the main theme. During the course talks relating to the content
will take place.
About the teacher:
Dainius Bendikas is a designer and holds a degree in fashion design. An Adjunct in the Fashion Design Department of Iceland University of Arts. His teaching emphasis are on conceptual, technical and functional aspects of fashion, object and product development. Creative and constructive innovation and experimental approach towards objects while synchronizing overall creative direction.
Dainius has been creating, instructing and organizing various programs and activities for students by way of courses, collaborations and workshops. Dainius has 7 years of professional experience working with various brands as head designer, product developer, creative direction consultant and has experience in various manufacturing processes.
Jurgita Jankutė-Mirinavičienė is a theater set and costume designer. She created scenography and costumes for different plays and contemporary dance performances at the Lithuanian National Opera and Ballet Theatre, National Drama Theatre, State Small Theatre of Vilnius, others. She teaches History of Costume and Costume Construction at Vilnius Academy of Arts.
Applications should include:
Full Name;
Home school;
Study year and level;
A motivation statement (max 250 words);
Pattern-making experience (description);
A link to your portfolio and CV and phone number. | https://www.cirrusnetwork.info/news/nature-design-and-innovation-ii-intensive-course-imprint |
I work for the Gomukh Trust, an NGO working primarily in watershed management, decentralized water supply and sanitation, and negotiated integrated River Basin Management.
We also attempt to influence policy by researching, developing, and creating awareness about sustainable mechanisms for water supply. As part of the last, we are now working on a European Economic Union project to document and develop action plans for innovative watsan systems in Indian cities.
For the above documentation, we are compiling a handbook on “best practices” in urban water supply and sanitation. These “best practices” are expected to be of the following types:
- Technologies - including comprehensive systems of water supply and sanitation and processes like water distribution, purification, and metering.
- Institutional innovations - for equitable and participatory management and monitoring of watsan systems.
- Economic innovations – e.g. through cost sharing, metering, revenue models, etc.
The “best practices” will be selected for inclusion in the handbook on the basis of following criteria:
- Economic, environmental and social sustainability.
- Reliability, ease of operation and maintenance
- Affordability of the installation and running costs
- Potential for scaling up and replicability
Members are requested to include case studies of where the “best practices” faced major opposition and how these were overcome. Case studies of not-so successful innovations but possessing a major learning value may also be contributed, as sometimes failures teach more than successes.
Needless to say, all contributors will be acknowledged in the compendium.
Please see attachment below for the responses. | https://www.indiawaterportal.org/questions/handbook-innovations-watsan-need-experiences-and-best-practices-technical-economic-and |
Biogas can be produced in digesters. Production depends on the following factors: Organic content, Wet or dry waste, Land availability. There are several different types of digester technologies including lagoons which are typically employed when the feedstock is wastewater effluent from agricultural waste or animal manure. Using this technology, typical retention time of material is between 30 and 40 days for the biogas to reach full production. A lagoon is a good option when sufficient land is available.
Technology Overview
Other technologies such as Continuously Stirred Tank Reactors (CSTR) and Dry Cell Anaerobic Digestion (DCAD) are used when land requirements are limited. CSTR’s are a proven and reliable technology as an alternative to a lagoon based system but are slightly more expensive to build than a lagoon, and require more attention during operation.
Customer reviews
No reviews were found for Organics - Biogas Digester Technologies. Be the first to review! | https://www.environmental-expert.com/products/organics-biogas-digester-technologies-656502 |
I have dragged some .jpegs into an .rtf in one of my databases, and some are very large, some small. Is there are any way I can change the sizes of these images inside DTPO, or do I have to change the size in somethign like Photoshop before importing them into DTPO? Specifically, I’d like to make some of the very large ones smaller.
Do you want to reduce the file size and/or reduce the dimensions of the image?
Graphic Converter does both quite easily, and will do batch resizing as well, so you could drop a folder full of images on GC and specify the dimensions and the output as no larger than a specific kib size.
I already have Photoshop for that sort of thing - I was hoping there was some way of adjusting the size of the image displayed IN DevonThink, without having to go outside to adjust the size and then import the smaller size. Some information managers - such as Notebook of MacJournal - allow this. | https://discourse.devontechnologies.com/t/change-size-of-picture/8740 |
Summary: As stress builds, the concept of meditation sounds appealing. Meditation has been shown to be useful for stress management1 and has many other benefits including heart health2, mood regulation3, pain management and more.
Intuitively we know that meditation can be good for us, yet it can be difficult to put into practice. In this episode of XO Conversations, we discuss a new understanding of meditation and it’s effects on our brains. We discuss different ways can re-train our brain to practice positive processes and focused attention and get meditative effects in different ways as a bridge towards a real meditative practice.
Maybe it’s not that I can’t meditate, maybe it’s that I haven’t figured out how to do it in a way that works for me
Topics We Discuss In This Episode:
- How to get meditative effects if you can’t clear your mind
- How to meditate for stress and anxiety
- What does meditation do to the brain
- How to start meditating for beginners
- How to find a way to get meditative effects that work for you
[03:47] The biggest reason we want to meditate, reasons including stress management, emotional regulation, and overall better quality of life
[05:14] Meditation goes beyond sitting with a quite mind in a mediative state. Different forms include mantra, visualization, and concentrative meditation.
[08:12] Default Mode Network (DMN) – a network of neurons in the brain that is known to be active at rest.
[12:12] The more your DMN is focused on negative thinking, the less if focuses on creativity and positive thinking. Meditation helps to quite your DMN to better function and help with positive processes.
[16:11] Getting meditative effects without meditating consists of doing the “yes” things: focused attention, flow state, and positive feelings
[19:36] Staying away from the “no” things that turn on your DMN: like rumination, replaying negative thoughts over and over again, and being concerned with perspective of others
[24:42] Having bad experiences with DMN can lead you towards a negative spiral like feelings of depressions and anxiety. It remembers our past mistakes and creates a negative dialogue in our minds.
[26:15] We can train our minds to think differently by practicing meditative tasks that allow us to focus on one thing like with focussed attention.
[30:05] How do you know if something is meditative? You know by how you feel when you’re finished: feeling calmer and less stressed. | https://livingxo.com/meditation-for-people-who-cant-meditate/ |
Could Propane be the New Diesel? Could Propane be the New Diesel?
In this episode of Path to Zero, Host Tucker Perkins invites Dr. Bryan Willson, executive director of the Energy Institute at Colorado State University (CSU), and Dr. Daniel Olsen, mechanical engineering professor at CSU, to provide an in-depth look into the recent $3.5 million U.S. Department of Energy (DOE) grant awarded to the university for the development of new, high-efficiency propane engines.
show notes
The objective of this 3-year DOE project is to develop propane engines as close to efficient as diesel engines, with an emphasis on heavy duty engines.
CSU has a 30-year history of gaseous fueled engine development, using alternative fuels such as propane, natural gas, hydrogen and biofuels. With the university’s world-class research facility, Powerhouse, they also have the capability to work on large and powerful engines.
The project will undergo three phases: fundamental studies, modeling and demonstration. Currently, propane is around 40% cheaper than diesel and emit fewer emissions. However, with today’s propane engine technology, those savings may not be realized because the propane engines are low technology, low efficiency. By driving up the efficiency of propane engines, the potential impact will help create a more affordable, efficient and lower emissions fuel as a tool to a lower carbon future.
Resources: | https://propane.com/environment/podcast/episode-8-could-propane-be-the-new-diesel/ |
Have you been thinking about moving somewhere else for a shorter work commute? It’s totally understandable. After all, long work commutes can be a source of stress, health issues and financial problems for many workers.
As big cities continue to grow and get even more crowded, these already time-consuming work commutes will also keep getting longer. These may have detrimental effects on an average commuter. They have to spend a huge portion of their salary on gasoline, parking, car insurance and public transportation.
And now the long commutes may also have a negative impact on their overall well-being. But others enjoy long commutes. They take this as an opportunity to read, listen to some music and decompress after a long day at work.
Others also do not mind taking the long route as long as they can live where they like. So, if you’re unsure whether it’s time to hire an interstate removals company here in Adelaide or stick with the status quo, here are some questions you should ask yourself:
Does your employer reimburse a portion or all your monthly transportation costs?
There are times when employers offer to cover a portion or even all the financial costs of commuting for some of their employees. So, consider whether your current commuting costs are at least partly free. Does your employer provide you with a prepaid public transport card?
Do they reimburse your monthly gas consumption? Do they offer other benefits? If you are unsure, ask the human resources department for specific details about your commuting costs.
How important is it for you to live close to your workplace?
Think about your current setup at work. Do you have a flexible schedule? Do your bosses allow you to work from home at least once or twice a week? If you can work remotely, the long work commute a few times, a week may not be much of an issue.
But, if you work for long hours and you take public transportation, living closer to your workplace might be more beneficial to you. If you have to stay in the office for many hours and even work during the weekend, that means you’ll have to make more trips to the office.
So, living somewhere close will help cut down on stress while also increasing your productivity levels.
Do you have to live somewhere far from your workplace for family reasons?
For many families that have school-age children, living a little farther away from the office is a priority. This is because most of the top-rated schools, more family-friendly environments, and bigger but more affordable living spaces are often more accessible in the suburbs.
That is why many employees sacrifice their work commutes to provide a better living condition for their families.
Finally, consider your current health condition. If you think the long work commute has negative impacts on both your mental and physical, then it is time to move closer to your workplace. Never mind the extra money you will have to spend for a place near the office. Remember, your health is always the most important. | https://www.spannuthboilers.com/should-you-move-closer-to-work/ |
The gender pay gap in the manufacturing industry has fallen by 6% in the last decade, according to a new report by Informi.
Ahead of this weekend’s Small Business Saturday (2 December), the report shows that women who earned just 77p for every £1 a man earned in manufacturing back in 2008 now earn 83p, meaning that the remaining gender pay gap in the industry stands at 17%.
Since 2008, female hourly pay in manufacturing has increased by 26%, while male hourly pay over the same period has increased by 17% – meaning that the overall gender pay gap has narrowed by 28%.
Across all small business-dominated industries, which includes manufacturing, the gender pay gap is falling at twice the rate as that of all companies across the UK.
The research found that while the national gender pay gap was at 21% 10 years ago (and at 22% in SME-dominated industries), current wage inequalities in those sectors with a greater number of SME employees has fallen to 13%, compared to a national average of 17%.
With a 9% overall fall in the gender pay gap across these SME-dominated industries over the past 10 years, the sectors are set to eradicate the remaining 13% average wage inequalities by 2034, should it continue to fall at current rates.
Darren Nicholls, product manager for Informi, said: “Small businesses are the lifeblood of the UK economy, and this report demonstrates that they are blazing a pathway towards wage equality and helping to eradicate the gender pay gap.
“Small businesses are not shackled by tradition, legacy or bureaucracy in the same manner as many large companies can be. That said, clearly a double-digit gap is still far too high.
“There’s a great deal more to be done, with some industries lagging behind others in implementing the necessary changes to ensure that females get just as many opportunities to thrive in their profession of choice.
“The fact that mandatory reporting has been brought in by the government for larger companies should act as an encouragement for small businesses to consider female progression within their own firms, auditing their own internal data and acting upon their results.”
Chloe Chambraud, gender equality director for Business in the Community, added: “Closing the gender pay gap is not just about equal pay, but about a much bigger organisational culture shift.
“Employers should understand any factors driving their pay gap, and address the root causes of inequality. This means reducing bias and increasing transparency in the recruitment, appraisal and promotion processes, normalise agile working, and offer financially viable parental leave packages for all.”
Sophia Morrell, chair of Labour in the City, added: “It is really encouraging to see SMEs leading the charge in the UK on closing the gender pay gap. | https://www.themanufacturer.com/articles/gender-pay-gap-in-manufacturing-falls-by-6/ |
With summer just around the corner, you’ll find that most of your workforce will start requesting annual leave for holidays, childcare or just some fun and relaxation in the sun.
This can be a bit of a stress on some businesses especially when departments are small and at least one member of every team needs to be in the office at any one time.
But, as an employer, you do have a right to refuse annual leave requests when there is a sound reason and it may be something to consider if any of the below apply to you.
Too many staff have requested the same day/time off
If there is a department that requires someone to be present to answer the phone or greet guests then it means that not everyone in that department can be on annual leave at the same time. Therefore, you may have to reject requests to ensure that your business can continue running and being as productive as usual and doesn’t potentially lose out on money.
The best method in this situation is to offer annual leave on a first come first serve basis.
It’s a busy period
In some industries there are busy periods that require more staff than normal to be on the premises at one time such as Christmas or school summer holidays.
You should clearly communicate to staff that holidays are not permitted during this period or that it is available for a limited number of staff (on a first come basis) so that they are aware of the policy well in advance.
It clashes with an important business commitment
An employee may request to book time off during an already scheduled in meeting, appointment or event that requires them to be present. If the business commitment is important and cannot be re-scheduled then refusing holiday is acceptable.
The employee has not followed procedures correctly
Your employee contracts or handbooks should clearly outline your policy when it comes to booking annual leave including how much notice must be given, who needs to be informed, how requests should be made etc.
If an employee doesn’t follow this policy correctly, i.e. requests annual leave just a week in advance of the requested dates, then you have the right to reject this based on short notice.
However, one big exception to these rules is – if you are fast approaching the end of the working calendar year and an employee still has several days of holiday to take, and your company does not allow for annual leave to be carried over into the following year, then you must ensure that, if requested, they get those remaining days off.
Making sure that your staff receive the minimum, or agreed, holiday entitlement every year is one of your responsibilities as an employer. Though if they forget or opt not to take all their leave, that is on the employer.
If you do refuse an employee’s request for annual leave, but they take it anyway then this is a disciplinary offence and you can treat it as gross misconduct.
Your Holiday Entitlement Policy must clearly communicate your procedures and expectations to your employees. If you need any support in producing this then we have qualified HR consultants on hand to assist you.
Just call us on 0845 2626 260 for more information or to book a free consultation. | https://www.guardiansupport.co.uk/blog/when-is-it-ok-to-refuse-annual-leave/ |
The ECB left rates unchanged, but reiterated that it ‘stands ready to act,’ as necessary. ECB President LeGarde cited the serious risks posed by the increasing spread of the virus and confirmed monetary options available to combat the economic devastation caused by the political lock-downs spreading across the Continent. The untold damage is partially revealed in the 2020 EU GDP contraction of 7.3%! The ECB estimated that the economy would bounce back in 2021, forecasting a 3.1% GDP growth rate, that will be vaccine-led. The problem with these forecasts is they rely on a massive turnaround in economic and social activity across Europe, totally dependent on a ‘return to normal’, which will not happen, unless politicians and their policies are changed.
The Bank of Canada and Bank of Japan also release monetary policy updates, in a similar vein, citing the current economic devastation, but anticipating a vaccine-led recovery for 2021. The damage being inflicted by current lock-down policy will continue well into the first quarter and be reflected in economic data for the first half of the year, at the very least. The Central Bank predictions are overly optimistic. The US markets calmed after the inauguration and a slew of Executive Orders, expecting a return to Obama era economics and politics. Higher taxes and increased regulation cannot be good for economic growth. The EUR improved to 1.2150, while the GBP tested 1.3700, peaked by a flagging US Dollar.
Commodity currencies benefitted a flagging reserve, with the AUD rising back to 0.7740, while the NZD drifted back from 0.7200. The pro-Global policies of the US administration should benefit global trade, boosting demand for commodities, although a sick and despondent US economy would spread as fast as the virus? | https://collinsonco.com/daily-market-commentary-22nd-january-2021/ |
Before we continue into the guide it is important to mention that there are over 160 recognised species of Corydoras whilst there are still several hundred undescribed (These are given CW or C classifications such as CW010 “Gold Laser” Corydoras). As such, it is not the aim of this guide to give specific information for each species but a general guide that will begin to outline the knowledge required to keep these fish.
Corydoras are social bottom dwelling catfish. They are often referred to as Armoured Catfish and this is further emphasised by their name which has been borrowed from the greek words Kory (Helmet) and doras (Breastplate). They are also referred to as Cory cats, Corydoras catfish, and Cory fish. Corydoras are a peaceful species and will fit into the tanks of all levels of aquarists, beginner or advanced.
Scroll to the bottom for a helpful video guide that accompanies this guide!
Appearance and Size:
Corydoras Catfish will range in size from 1 inch to 3 inches (25mm to 80mm) in length although specific species may fall outside these limits.
Corydoras do not have scales as other fish do, instead their bodies are protected by bony plates that run along the length of its body. It has a flat underbelly that is adapted well to sit on a soft and sandy substrate. They use their horizontal pectoral fins to assist them to rest comfortably and upright on the substrate. Their dorsal fin is generally pointed and gives a sail like appearance leading down to a tail fin that can vary in size but will generally be forked.
The most recognisable feature of the corydoras is their barbels. These consist of three pairs of “whiskers” that they use to help them find food within the substrate.
Colouration will vary among species.
Habitat
- In the wild:
The Corydoras catfish can be found, in the wild, across a large area of South America from as far north as Trinidad to as far south as Northern Argentina. They populate the smaller streams and tributaries that run off of the larger rivers. The areas they can be found occupying will be predominantly sandy bottomed streams which compliments their foraging style of feeding.
- In the Aquarium:
In the aquarium, much debate is had over the substrate that should be used for Corydoras. To get the best out of your fish they should be housed in a well planted and established aquarium with a sand based substrate. More information on substrates can be found here. They can be fairly timid fish and love to have a few places that are out of site to hide in.
Generally, Corydoras can be accepting of a wide variety of water parameters which are listed below. It is important to remember that some species will require a more specific set of parameters or may be even less picky. Research into your chosen species should be taken and important information can be found in our species profiles.
Recommended Tank and Water Conditions
- PH: 6.8-8
- Temp: 21c-27c (69.8f – 80.6)
- Tank Size:
- Absolute Minimum recommended: 30 Litre (8 US Gallon)
- Comfortable recommended: 50 Litre + (13 US Gallon +)
- Group Size: Min 3 but the larger the group the happier the fish. (Recommended 6+)
- Substrate: Fine natural sand
- Planted?: It is recommended that your aquarium is planted
- Temperament: Peaceful, Community
- Tankmates: Corydoras are very friendly fish and will not bother any fish including shrimp and snails. However, ensure the fish kept with them are not hostile to the Corydoras. Ensure the tanks mates are suited to the same temperature ranges and PH. Often kept with them are all kinds of Tetra and Plecs.
- Water Flow: Slow moving, this can mimic their natural habitat of small streams.
- Tank Cover: It is recommended that you have a lid on your aquarium as Corydoras are known to dart to the surface for Food or Air. Sometimes they can forget to stop and as such may jump. This is unlikely but it is always better to safe.
Diet
Corydoras will eat a wide range of food from sinking pellets to live/frozen food. They are especially fond of daphinia and blood worms but as with all fish, variety is key to a healthy diet.
Feeding morning and night is recommended.
When you are away it best not to feed the corydoras they will be quite happy for 2 weeks with out food. Slowly reintroduce food on your return.
More information on the diet for your fish can be found here.
Behaviour and Temperament
General behaviour:
Cory catfish are famous for their sweet and peacful temperament, which is one of the main reasons they’re so popular with aquarists. They spend the majority of their time peacefully foraging around the bottom of the aquarium looking for food. They can also be seen, staring out the tank in a group seemingly plotting something sinister or rolling their eyes at their human friend in mock dismay. They will generally ignore or leave all other tank mates alone and can live peacefully with a wide range of tank mates because of this.
They will be seen cleaning the surfaces of wood, rocks and large leaved plants aswell, both searching for food and getting them ready for a potential egg laying spot.
They will also be seen darting to the surface for a gulp of air, which is natural as they can breath surface oxygen like this but should be watched as it can signal a lack of oxygen or other water issues.
Other prominent behaviours:
When a female wants to spawn she will release a hormone which will drive the males into a spawn frenzy. It can appear that males are fighting and get aggressive towards the female. This is natural but can be daunting when seen for the first time.
Common Diseases
Corydoras, Like all aquatic life are susceptible to a wide variety of ailments. As such, a list has been collated below of the common ailments. This list is by no means exhaustive.
- Ich (White spot).
- Fungal Infection.
- Nitrate Poisoning. (especially affecting their barbels)
- Red Blotch Disease
- Parasites
Medications for these can be found in our medications guide here. | https://planetcorydoras.com/index.php/keeping-guides/corydoras-101/ |
IgA nephropathy in the triethnic population of New Mexico.
IgA nephropathy (IgAN) is the most frequent glomerulonephritis around the globe, but its incidence in the United States is unknown. The disease has a preponderance for certain racial/ethnic groups. Our goals were to retrospectively analyze a series of IgAN biopsies from the state of New Mexico and to calculate an estimated incidence. Then we compared the racial/ethnic composition of our patient cohort to the composition of the New Mexico population and examined the three main racial/ethnic groups for differences in clinical and pathologic parameters. Renal biopsies and clinical data from IgAN cases newly diagnosed in New Mexico between 2000 and 2005 were reviewed. We compared the racial/ethnic composition of our patient cohort to the demographic composition of the New Mexico population. Demographic, clinical, and histopathologic variables were analyzed with respect to the patients' race/ethnicity. The incidence of IgAN in New Mexico was 10.2 cases per million persons per year (9.3 when Henoch-Schönlein purpura cases were excluded). American Indians were twice as frequent in our patient cohort when compared to their demographic representation, with the reverse finding for Non-Hispanic Whites. Hispanics more frequently had nephrotic range proteinuria than Non-Hispanic Whites and American Indians. On renal biopsy, endocapillary proliferative glomerulonephritis was the most common glomerular abnormality, followed by the focal segmental glomerulosclerosis (FSGS)-like pattern. The FSGS-like pattern was more frequent in American Indians and Hispanics than in Non-Hispanic Whites. This is the first report of an incidence figure of IgAN for an entire state in the US. American Indian and Hispanic patients had a stronger representation in our cohort than Non-Hispanic Whites, when compared to the general New Mexico population.
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Given enough time, every momentous event in sport – or life, for that matter – is reduced to a single image.
It’s the brain’s filing system. This small thing reminds you of a much bigger one. Where you were when you found out about it, what you were doing, how you felt.
The first widely circulated image of the Humboldt bus crash showed the aftermath – wreckage strewn across the intersection of two highways in rural Saskatchewan.
But that’s not the mind’s-eye photograph people came to associate with the most powerful sports story of this year, and just about any other year.
Instead, when they thought of Humboldt, they pictured thousands of hockey sticks left by their neighbours outside front doors and on porches across the country.
They didn’t think of the coming apart that marks the outset of any tragedy, but of the great coming together that followed. Humboldt reminded Canadians that, on some very basic level, we are all in this thing together.
Klinkenberg: In Humboldt, it is possible to love again – and never forget the Broncos bus tragedy
We often speak of tragedy in sports – a tragic defeat, a tragic miss. It’s a verbal tic. Those aren’t tragedies. They’re disappointments.
Real tragedy, as Aristotle first defined it, elicits “pity and fear.”
Humboldt hit you with both. It came at the country in waves. For a moment, or maybe a few, everyone stopped to imagine themselves or someone they love on that bus. This feeling was intensified by the fact that the players were not famous names. They really were like the rest of us.
On a human level, there was no making sense of it – the remorseless randomness of being in exactly the wrong place at exactly the wrong instant and how much suffering can result.
It’s too awful to wrap your mind around. Most people move on quickly rather than dwell on how quickly life can turn. Fear trumps pity.
Humboldt wasn’t a sports story, per se. But it was sports that gave Humboldt its power to affect all Canadians, and the template by which to respond.
Every once in a while, we’re reminded why sports are able to burrow so deeply into our collective psyche. Were you to explain the concept to a visitor from another planet – “a few people get together to chase an object around a bounded surface while the rest of us watch” – it might sound ridiculous.
But the purpose of spectator sports isn’t the sport. It’s benevolent tribalism. Us vs. them, but harmlessly.
Not everyone is a sports fan, but everyone is attracted by the concept. You may not be on the team, but you can be a part of it. You’re hoping your team wins. If they don’t, you share the loss in equal proportion to the players.
There are no barriers to entry. Anyone can participate. All one need do is decide to care. Sports fandom is perfectly egalitarian. That’s why we’re still doing it.
When the Humboldt crash happened, relatively few Canadians outside the Prairies had heard of the team. Canada is awash in these clubs – small-town concerns, kids with big hockey dreams, but most playing because they’re good at it and it makes people happy. They are a local conversation starter and something to do on a Saturday night.
Unless you are connected in some tangible way to Kamloops or Rimouski or the Soo, there would be no reason to root for one of them.
But once Humboldt happened, everyone in Canada felt themselves a part of that team. They didn’t know the players or the history, but they knew that’s how sports works. You want to be part of something and, therefore, you are.
Canada understood the symbology of the long bus ride to the next town over. Every one of us has, at some point, been on one of those buses.
It had the implements with which to pay tribute to a team in trouble – the sticks. Although it may never get used, everyone’s got a hockey stick tucked up somewhere.
The country understood instinctively that there would be a period of mourning, followed by the need to get on with things. Because, regardless of what happens, you eventually have to show up for the game. That’s how it works.
Humboldt gave Canada its defining tragedy of the year, something so connected to our core identity – a frozen landscape, a long journey – it might have been painted by Emily Carr. Sports gave us a language with which to commiserate. In the end, pity trumped fear, resulting in something like catharsis. What might have broken another town instead bound a country.
The Humboldt Broncos have returned to the business of hockey. After a Christmas break, they’ll be at it again on Wednesday at home against a team from Wilcox, Sask., a few hours down the road. Somebody will win and, in the larger scheme of things, it hardly matters. It’s the playing that counts.
This is the opposite of forgetting. It’s the most Canadian way we know how to remember. | https://www.theglobeandmail.com/sports/hockey/article-tragedies-such-as-humboldt-crash-remind-canadians-that-we-are-all-in/ |
A mud-covered Cambridgeshire police car has been shamed for breaking the law because its number plate was blocked out.
A picture of the patrol car was posted on Facebook site Badly behaved and Unmarked police cars of the U.K.
It is illegal to drive a vehicle on the roads with the registration number obscured.
The patrol car is from the force's Rural Crime Action Team which has been chasing hare coursers on a regular basis in recent weeks.
But a spokesman for the Facebook site said: "Once again this show the police not sticking to the laws they are there to enforce."
Police rules are that patrol cars should be cleaned after every shift.
A force spokeswoman said: “It is an offence to fail to display a registration mark because a registration mark is the identifying marks of a vehicle. The penalty for failing to do so is a £60 fine and there are no points given.
“This vehicle belongs to the rural crime team who predominantly patrol rural areas reacting to hare coursing jobs and could have just finished a job in a rural location.
“The roads are particularly dirty at the moment due to recent weather and police vehicles should be cleaned after every shift. Officers have been reminded of this to ensure that procedures are followed."
You can keep up to date with all the latest news in and around Cambridge by downloading our free app.
It is available for the iPhone and iPad from Apple's App Store, or the Android version can be downloaded from Google Play. | https://www.cambridge-news.co.uk/news/cambridge-news/cambridgeshire-police-dirty-squad-car-14112943 |
If you have a question about this talk, please contact jh567.
The Hanging Gardens of Babylon are the first of Seven Wonders of the World according to Philo of Byzantium. Since then, they have continued to hang in Western imagination and fantasy. Despite their insubstantial and elusive character, representations, based upon ancient Greek and Roman descriptions, are numerous from the Middle Ages onwards. At the very end of the XIXth century, the discovery of Babylon by archaeologists provided new information: in the ruins of Babylon, Robert Koldewey recognised the vestiges of the Hanging Gardens. Many more reconstructions and debates followed, on the appearance of the now ‘real’ Hanging Gardens of Babylon, and their location in the city or elsewhere. The aim of this paper is not to provide a definite answer to the mystery of the Hanging Gardens of Babylon, but rather to focus on their position in the history of Ancient Near Eastern gardens, and especially to recall the history of the research concerning them, that often witnesses the influence of our own dreams and visions of the Near East.
This talk is part of the Cabinet of Natural History series.
This talk is included in these lists:
Note that ex-directory lists are not shown. | https://talks.cam.ac.uk/talk/index/42484 |
High school is a name used in some parts of the world, and particularly in North America, to describe the last segment of compulsory secondary education. It is preceded by primary education. High school is also the name used to describe the institution in which the final stage of compulsory education takes place. In the United States, high schools generally consist of grades 9, 10, 11, and 12, although the inclusion of grade 9 varies by school district.
Central High School is the school of choice in Southeastern Wisconsin for the quality and variety of its educational programs and the diverse opportunities for students and the community at large provides a positive learning environment that will produce successful citizens prepared to achieve their greatest potential. The school assures that their facilities provide an atmosphere highly conducive to learning, achievement, and personal or professional growth for all students, faculty, and community members by annually assessing our facilities and providing recommendations for change to the board.
Programs and parents, business and community are involved in all aspects of the educational process. They provide academic opportunities for all students to maximize their learning potential, abundant opportunities for all students to be involved in extra-curricular activities. Also provides service opportunities for all students to help each other and the community and enhanced integration of technology into the curriculum. Effective rewards and privileges that reinforce success complimented by intervention process that address poor performance and/or disruptive behavior.
Central High School is a thoughtful, reflective, exciting, and engaging place. Its mission to provide an academic environment, which fosters curiosity, creativity, responsibility, honesty, logical thinking and an appreciation for self and others, in order to help each individual succeed in today’s changing world.
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We believe a child’s first exposure to playing an instrument sets the tone for the rest of their music education. Kidz Rock allows kids to experience the ultimate musical accomplishment within a few weeks; singing, playing, and performing in a rock band!
Join a Kidz Rock Band
Kidz Rock is a music program that teaches children from 4 to 7 years old how to play an instrument in the setting of a rock band. Band members rotate on drums, electric guitar, and keyboard as they prepare to sing and play in an end-of-session concert. All instruments are provided by Michigan Rock School and there are no practice expectations outside of the class.
Skills and concepts taught in each Kidz Rock class include:
- Rhythmic and dynamic concepts
- Age-appropriate note reading
- Playing guitar
- Playing keyboard/piano
- Playing drums
- Singing
- Playing together as a band! | https://michiganrockschool.com/rock-band-programs/4-7-year-old-rock-band-kidzrock/ |
As an Employment Specialist - Offer Compliance Auditor, you are responsible for final audit of all offer details ensuring compliance and accuracy. Successful candidates will have strong service mindset, superior communication skills, be process driven, and have a keen attention to detail while managing multiple tasks.
Responsibilities include:
Audit Offer letters in ICIMs ensure offer letters are within compliance and accurate
Work with Microsoft Recruiting Team to address compliance issues
Audit Post-Offer data in ICIMs
Communicates audit findings by preparing a final report; discussing findings with auditees.
Other special audit projects
Basic qualifications include:
High school diploma or equivalent
Minimum of 6 months recruitment support, administration and/or customer service experience
1+ year experience with auditing in any capacity
1+ year experience with Customer Service
Preferred qualifications include:
Positive attitude
Good attendance is crucial
Strong attention to detail
Excellent organizational and time management skills
Proficient verbal and written communication skills
Randstad Sourceright is an Equal Opportunity Employer and makes all employment decisions based solely on the basis of qualifications and without regard to race, color, religion, sex, sexual orientation, gender identity, national origin, age, genetic information, disability, protected veteran status or any other legally protected group status. | https://workiniowa-stem.jobs/des-moines-ia/employment-specialist-offer-compliance-auditor/5675E5A4591B461D9EFA4855BAEFA2F7/job/?vs=28 |
Re-defining the Customer in a Traditionally B2B Environment
Can conceptualizing business relationships in a new way create real-life transformation of a business?
While from a sales perspective the customer is traditionally the intermediary, there was a desire within the organization to properly understand the end-user as customer — that is, employer-to-employee — opening up new possibilities for driving the business forward.
This was a foundational piece of research comprising multiple elements (state of the nation groups, customer journey mapping, value proposition development) in order to generate fresh insights.
Applying the principles of behavioral economics allowed us to reveal the influence of the nonconscious on decision-making and identify potential levers that could be used to nudge behavior in the desired direction. The resulting journey maps could therefore speak to both the rational and emotional mindsets of the customer and were designed to be disseminated broadly across the organization, giving all employees a sense of who the customers are, what they need, and what the priorities should be in terms of customer service. | https://www.insightsassociation.org/conference-session/CRC2019/re-defining-customer-traditionally-b2b-environment |
During recent years, a number of biological and clinical results have shown that treatment of cancer may be improved when heat is applied to the cancerous tissue, especially when the heat treatment is combined with traditional cancer therapies such as radiation. Statistics on more than 800 cases show that the frequency of complete response rises from 25% when radiation alone is used to 64% when radiation is combined with a hyperthermia treatment.
Clinical results, however, are limited by the ability of hyperthermia systems to selectively heat tumors without damaging surrounding healthy tissues. Thus, non-invasive surface applicators used in conventional hyperthermia systems often obtain only superficial heating (3-5 cm in depth from the surface) because the electromagnetic wave penetration is limited by surrounding muscle tissue due to attenuation in the microwave range or due to damage from heating by strong near-field effects at low radio frequencies.
Existing applicators used for hyperthermia, i.e., heating of cancerous tumors, primarily heat superficial tumors and seldom provide for a controllable heating profile. It would be desirable to provide for the heat treatment of tumors at depths within the patient, and also provide for the treatment of tumors at non-symmetrical locations. Since the applicator is applied adjacent a patient, a suitable applicator should be compact and should have an open structure giving easy access to the patient. Many existing applicators are unsuitable for such topical application.
Where large body volume are to be heated, one known applicator system comprises a coil about the body which is excited with a radio frequency current. Such a system has a fixed power density distribution in a body which closely approximates a parabola having zero power at the center of the body. It is apparent that the surface excitation must be substantial to provide adequate heating excitation at a deep location.
Yet another large volume or whole body applicator is described in U.S. Pat. No. 4,462,412 where substantially uniform heating is produced within a cylindrical biological tissue specimen. A plurality of radiating apertures are matched with the size of the body specimen. The body specimen is actually placed within the annulus of the applicator for substantially circumferential radiation. This radiationg system provides an annular phased array, where a number of applicators are provided in a fixed annular arrangement and are excited from a common source in a coherent fashion. The applciator is tuned to provide a broadband match to body absorption to minimize reflections from the body tissue back to the excitation source. This whole body application distributes power in the body tissue for deep heating, but the distribution is generally uniform and is not localized at the tumor region. Substantial heating currents may occur near body curvatures and adjacent the feet and head regions. An absorbing material may be provided to absorb excess radiation but with concomitant inconvenience to the patient and to the clinician operating the equipment.
A theoretical analysis, Morita and Andersen, "Near-Field Absorption in a Circular Cylinder from Electromagnetic Line Sources," 3 Bioelectromagnetics, 253-274 (1982), has suggested that circumferential line sources might enable a power density maximum to be internally localized. The study further suggested that the local relative power maximum might be moved within the cylinder of excitation by controlling the included angle of the distributed circumferential sources. However, only circumferential sources and the relative included angle of adjacent sources were considered for analysis.
A need has thus arisen for apparatus which can deliver electromagnetic radiation at deep locations in body tissue and at specific places where the application of heat is desired, with minimum heating at other locations; where the power density may be shifted around by electronic means; and which have a structure which provides for convenient application to the patient and use by the clinical staff.
The disadvantages of the prior art are overcome by the present invention, however, and an improved apparatus and focusing method are provided for localizing heating effects for hyperthermia treatments of tissue at deep body locations.
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Yan Lianke is an award-winning fiction writer in China, and has also been recognized internationally with the Kafka Prize, which honors authors for a body of work. He occupies a curious position in Chinese letters — he is typically unable to publish on the mainland, yet holds a faculty post at a prestigious mainland university. He has also been an outspoken critic of the toll that both official censorship and self-censorship take on the country’s authors.
One of his best-known novels is Serve the People!, a satirical work also available in English in Julia Lovell’s lively translation. Another one of his novels, Lenin’s Kisses, describes an idyllic Brigadoon-like village whose inhabitants, each handicapped in some fashion, but living contentedly in a self-contained community spared the ravages of Chinese revolutionary history. They are soon swept up into the machinations of a scheming official. Perhaps his most ambitious novel to date is The Four Books, a searing look at China’s Great Leap Forward famine, just published in English. The recently released English language edition of The Four Books benefits from skillful translation work by Carlos Rojas, who also provides a useful introduction, reprising things he did for the English language edition of Lenin’s Kisses.
I caught up with Rojas, who in addition to his translation work has published on topics ranging from the cultural history of the Great Wall to the fiction of literary laureate Gao Xingjian:
JEFFREY WASSERSTROM: Let’s begin by talking about the two Yan Lianke novels you’ve translated, Lenin’s Kisses and The Four Books. Both are experimental in form and wide ranging works, but my sense reading both in English is that the latter probably presented bigger challenges to you as a translator. Is that right?
CARLOS ROJAS: Actually, from a translational perspective, Lenin’s Kisses was more challenging. Most of Yan Lianke’s works incorporate a certain amount of local Henan dialect, but in Lenin’s Kisses this constitutes a key element of the structure of the novel itself. Beginning with the work’s very first sentence, the novel includes countless footnotes explaining local words and phrases with which it is expected that the reader will be unfamiliar. The accompanying notes, meanwhile, include not only straightforward definitions but also frequently include lengthy discussions of character’s backgrounds and the history of village. One challenge, accordingly, was to come up with English words and phrases that would feature the same combination of familiarity and unfamiliarity as their dialectal equivalents in the Chinese.
The Four Books does present a similar set of challenges, however. For instance, one challenge was how to render the Biblical language that runs through the novel, and specifically how to retain the flavor of the Chinese-language version of this Biblical language in the original version of the novel. Another challenge involved negotiating the repeated shifts back and forth between the four manuscripts that comprise the novel, given that each manuscript is written in a distinct voice and plays a different role in the overall work.
In structural terms, both works are experimental in different ways. Lenin’s Kisses is more aggressively non-linear in its narrative structure, with the repeated jumps back and forth between the main narrative plane, and the lengthy endnotes, which often function as extended flashbacks where much of the narrative development takes place. The relationship between these interwoven narrative threads is rather complex, and it was an interesting challenge to make sure that all of the chronologies lined up correctly. In The Four Books, meanwhile, the narrative jumps back and forth between the three component manuscript texts, which are all truncated and composed for very different sets of objectives. But while it was somewhat tricky figuring out how to negotiate the relationship between these different fictional manuscripts, strict issues of chronology were not as much of a problem, since each of the four manuscripts proceeds more or less chronologically.
What is most distinctive to you about Yan as a writer, setting him apart from other Chinese authors you’ve analyzed or translated? And I guess linked to this, do you see Lenin’s Kisses and The Four Books as interrelated, broadly similar books, due to the gimlet-eyed view they both cast on the Maoist past, or very different, in that the former has more flat out farcical elements, while the latter takes bigger chances stylistically in weaving together four separate texts?
One of the things I like about Yan Lianke is that although there are a common set of concerns that run through all of his works (or at least his works since the mid-1990s), each of his novels tends to have a very distinct voice and narrative structure. While there are quite a few other contemporary Chinese authors who have been very experimental in their shorter works, many of them tend to adopt a more conventional narrative structure for their longer novels. In Yan Lianke’s novels, by contrast, structure consistently receives as much attention as content.
All of Yan’s works since the mid-1990s consistently engage with a set of sociopolitical issues relating to China during the Mao and post-Mao era, though often in very different ways. So, in this respect, I feel that all of his works from the past couple of decades are interrelated, and can be viewed along a continuum of literary expression. Part of the interest of his oeuvre, for me, is observing this negotiation between an attempt to explore a coherent set of concerns through an array of different works, and the ways in which artistic, political, and commercial factors have a differential impact on each individual work.
With respect to the specific comparison of Lenin’s Kisses and The Four Books, I think they both use a combination of realistic and fantastic elements to offer a commentary on contemporary Chinese society and recent Chinese society. The tone of The Four Books is somewhat darker than that of Lenin’s Kisses, but it too has its farcical moments. There is a cannibalistic theme that runs through both works — fairly literally in The Four Books, where the protagonist irrigates his crops with his own blood, and more metaphorically in Lenin’s Kisses, where the village of handicapped men and women are made to perform their disabilities for profit.
There has been a lot of discussion of censorship and Chinese publishing lately, both in general interest publications, including The New York Times, and in more specialized settings, such as on the Modern Chinese Literature and Culture list serve. Yan’s name sometimes comes up in these discussions, due to his unusual situation as a writer who has been unable to publish his recent works on the mainland and yet continues to live there and teach at a prominent institution. He’s also written powerfully about censorship and self-censorship. I’d like to invite you to jump into this ongoing discussion at any point. This could be to flag something particularly important that’s been said or written either by or about Yan, but could be something very different.
This is a long-standing issue, but the recent discussions you are referring to stems from a recent New Yorker article that quotes Eric Abrahamsen, a Beijing-based translator and editor, who is quoted as claiming that in contemporary China dissidents are jailed for their political activities, but not for their creative writing. In subsequent discussions on the academic list serve you mention, Abrahamsen explains that he feels that while “art may have political content, but it is not political speech,” and that “art falls apart for me the instant that the message (be that political, moral, religious, etc.) pokes through the artistic fabric of the piece itself.” He concedes that some jailed dissidents are in fact authors, but contends that their writing — from a purely literary perspective — is actually not very good, thereby further invalidating them as authors. (Abrahamsen was also subsequently invited to write an op-ed for The New York Times on this topic, which I have not yet had a chance to read since I am currently and China and do not have easy access to the Times and other censored websites.)
While I understand the general impulse that drives Abrahamsen’s intervention — namely, the fact that different types of public speech are handled very differently by the Chinese authorities — I think that the distinction he is trying to draw between literature and political speech is a deeply problematic one. To begin with, as Terry Eagleton argues in The Ideology of the Aesthetic, the very attempt to specify a discursive space as purely aesthetic and outside of ideology, is itself a deeply ideological (and, by extension, political) gesture. Furthermore, none of the authors and public figures under consideration engages in only a single kind of discourse, but rather they each express themselves in a variety of different ways, some of which may be perceived as more literary or political than others. So, to identify one subset of authors as being situated within the literary arena and another as being situated within the political arena is a radical oversimplification, even if the distinction between politics and pure art were a sustainable one in the first place.
Rather than a distinction between literary and political expression, I think that what we are observing is a phenomenon wherein different types of political expression are being treated differentially by the Chinese state. Some types of political expression (be they presented as literature or otherwise) are discouraged, but may have relatively minor repercussions for the authors themselves. Other types of political expression (again, be they presented as literature or otherwise) meanwhile, are dealt with much more strictly. China’s censorship may be in the process or undergoing a transformation, as Yan Lianke argues, from a “hard” censorship regime to a “soft” one (which uses a variety of approaches to encourage authors, artists, scholars, and others to voluntarily comply with the expectations), but I think it is essential to remember that the regime definitely retains a very “hard” edge — particularly when it comes to certain types of public expression.
Yan Lianke is distinguished, I think, by a determination to try to work within the mainland Chinese system, while at the same time having an aesthetic and political perspective that is not always welcome by the Chinese authorities (or by the Chinese publishing industry, which often preemptively anticipates how something might be received by the authorities). He is also, I think, quite willing to speak his mind on a wide variety of topics, and has a deep commitment to the social and aesthetic issues that he interrogates in his writings.
Finally, anything you are working on now, as a translator or as an author, that you are particularly excited about?
I am currently translating new novels by Yan Lianke and Jia Pingwa, and just completed a book-length collection of short stories of short stories by the Malaysian Chinese author Ng Kim Chew, which will be published by Columbia UP early next year. Ng’s stories are crazily imaginative explorations of issues of displacement and diaspora, and specifically the interwoven social, cultural, and political conditions that inform the status of Malaysia’s Chinese community. His stories are also very political in their own way, carefully exploring the contemporary legacies of the Malayan Communist Party and other mid-century developments. I have two co-edited volumes that will appear next year, including an Oxford Handbook of Modern Chinese Literatures, which includes 44 essays exploring a variety of different interpretative methodologies and taxonomical considerations (including one chapter by Yan Lianke himself, on state censorship). Finally, my new book, Homesickness, on the use of discourses of disease as a sociopolitical metaphor across the Chinese long 20th century, came out earlier this year. I’m currently working on two new monographs: one on thematics of time and temporality in modern Chinese cultural production, and the other on the contemporary Hong Kong director Fruit Chan. | https://blog.lareviewofbooks.org/chinablog/yan-liankes-fiction-q-translator-literary-scholar-carlos-rojas/ |
Group A streptococcus (GAS) is a common cause of life-threating necrotizing fasciitis and myositis. Necrotizing disease is relatively rare; however, it has a high rate of mortality, and affected limbs must often be amputated. In this episode, James Musser and colleagues use transposon-directed insertion-site sequencing (TraDIS) to identify GAS genes required for the development of necrotizing myositis in a nonhuman primate model. In particular, several bacterial transporters were determined to be required for infection, and thereby represent potential therapeutic targets for this devastating disease.
Activity-dependent neuroprotective protein (ADNP) is essential for brain formation, and mutations in the ADNP-encoding gene have been linked to an autism-like syndrome in children that is characterized by developmental delay along with intellectual and social disabilities. An 8-amino acid motif derived from ADNP (referred to as NAP) has been shown to be neuroprotective, via enhancing dendritic spine formation, in mice lacking ADNP. In this episode, Illana Gozes and colleagues characterize Adnp+/- mice as a model of ANDP syndrome. Adnp+/- animals had reduced dendritic spine density, developmental delays, impaired vocalizations, and motor dysfunction along with memory and social impairment. Administration of NAP partially reversed behavior and developmental defects and increased dendritic spine density. The results of this study support further exploration of NAP administration for treatment of ADNP syndrome.
Graft-versus-host-disease (GVHD) is a life-threatening complication of allogeneic BM transplantation that affects skin, liver, and the gastrointestinal (GI) tract. GI involvement is associated with the most severe form of disease and outcomes for these patients are poor. Treatments for GVHD are limited; therefore, a better understanding of markers of GI involvement have potential to improve treatment. In this episode, James Ferrara and colleagues identify the Paneth cell protein regenerating islet-derived 3α (REG3α) as a biomarker that is upregulated in sera of patients with GI GVHD. Moreover, using murine models, the authors determined that REG3α, which has well-known antimicrobial function, promotes intestinal stem cell survival; thereby, protecting the intestinal barrier. Together, these results indicate that strategies to increase REG3α should be explored for limiting GI GVHD. | https://tgnanke.com.www.mobile.jci.org/videos/authors_takes?page=2 |
CROSS-REFERENCE TO RELATED APPLICATION
FIELD OF THE INVENTION
BACKGROUND
SUMMARY
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT(S)
This application claims foreign priority under 35 U.S.C. §119(a)-(d) or (f) to Japanese Patent Application No. 2014-059750, dated Mar. 24, 2014.
The invention is generally related to an electrical connector assembly, and, more specifically, to an impact resistance electrical connector assembly.
In mobile phones, smart phones, and other similar devices, an electrical connector assembly is often used to connect a flexible printed circuit (“FPC”) to a circuit board. The connector assembly is required to be further reduced in size and height. The electrical connector assembly used in such applications is required to have a reliable locking mechanism where two connectors constituting the connector assembly maintain a locked state therebetween, even if subjected to an impact force. Additionally, the electrical connector assembly must meet an increasing market demand for electrical connector assemblies have smaller sizes and heights.
A conventional electrical connector assembly is disclosed in Japanese Patent Application No. 2011-228269A. The connector has an approximately rectangular shape in a plan view and a total of four locking metal fittings at positions near both end portions of two long sides of the connector.
Since the locking metal fittings are positioned on the long sides of the rectangular shape, the connector has impact resistance against an impact force acting in a direction of rotating the connector about one of the long sides serving as a rotation axis. However, the connector cannot withstand an impact force acting in a direction of rotating the connector about a perpendicularly positioned short side serving as a rotation axis.
Therefore, there is a need for an electrical connector assembly having a locking mechanism which can withstand an impact force from any direction.
A connector assembly has a first connector and a complimentary second connector. The first connector has an approximate rectangular shape with four corners and two parallel long sides connected together at the four corners by a pair of two parallel short sides, and a catching member positioned on each of the four corners. The second connector is has mating portions at positions corresponding to the respective four corners of the first connector when the second connector is mated with the first connector. The mating portions are complimentary to the catching members, and when mated with the catching members, mate in a direction intersecting both the long and short sides intersecting at each of the four corners of the first connector.
An object of the invention is to address and overcome the disadvantages discussed above.
FIGS. 1-24(B)
Exemplary embodiments of the invention will be described below with reference to .
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FIG. 1
The plug connector and the receptacle connector in correspond to respective embodiments of the first connector and the second connector discussed below. However, one of ordinary skill in the art would appreciate that the plug and receptacle connectors , may be embodied in many different forms.
FIGS. 1 and 2
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In the embodiments of , the plug connector has a plug housing with an approximately rectangular shape in a plan view, and with an approximately rectangular shape as a whole. Since the plug housing has an approximately rectangular shape, the plug housing has two parallel long sides connected together at opposite ends by a pair of two parallel short sides. A receiving cavity having an approximately rectangular shape is positioned in a central portion of the plug housing . A bottom surface of the receiving cavity is substantially planar and can be utilized as a suction surface.
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The plug connector has a plurality of contacts positioned along the two long sides of the plug housing . The contacts are connected to connection pads on a FPC (not shown). A metal fitting catch is positioned on each of the short sides at both ends of the plug connector . Each metal fitting catch has two catching members positioned on two corner portions. When a metal fitting catch is positioned on the two opposite ends of the plug connector , the catching members may engage the receptacle connector during mating, where one catching member is positioned at each of the four corners of the plug housing .
FIGS. 1 and 2
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In the embodiments of , the plug connector has two first metal fitting catches . These two first metal fitting catches have identical shapes, but are mirror images of the each other.
FIGS. 3(A) and 3(B)
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In the embodiments of , the first metal fitting catch is shown being removed from the plug housing of the plug connector .
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Each first metal fitting catch has a base with two first catching members , with one first catching member being positioned on each opposite corner. Each first catching member has two cantilevered first arms with fixed ends positioned on two side edges forming each corner. The two first arms flank each corner, with their opposite free ends extending outward from the base of the first metal fitting catch , and extending towards each other. Each first catching member has a recessed portion positioned adjacent to and extending between the fixed ends of the two first arms . The two cantilevered first arms are elastically deformed when the plug connector and the receptacle connector are mated with or unmated from each other. The base of the first metal fitting catch is soldered to an FPC on which the plug connector is mounted. Further, two press-fitting pieces that are press-fitted into the plug housing extend from one end of the base .
FIG. 1
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In an embodiment of , the receptacle connector has a receptacle housing with a plug connector receiving space for receiving the plug connector therein. The plug connector receiving space is complimentary to the shape of the plug connector , having an approximate rectangular shape with two parallel long sides connected together at opposite ends by a pair of two parallel short sides. A plurality of contacts are positioned on the receptacle connector at various positions thereof, the positions corresponding to the plurality of contacts of the plug connector when the plug connector is received in the plug connector receiving space . A contacting end of the plurality of contacts is partially received in contact receiving spaces within a platform portion of the receptacle housing positioned in a central region of the plug connector receiving space . An opposite terminating end of the contacts are soldered to conductor patterns of a circuit board (not shown). Therefore, when the plug connector and the receptacle connector are mated with each other, wirings on the FPC connected with the plug connector are electrically connected to the conductor patterns formed on the circuit board on which the receptacle connector is mounted. An outer facing surface of the platform portion is planar and may be utilized as a suction face.
FIG. 1
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As shown in an embodiment of , one first metal fitting latch is positioned on each of the short sides at opposite ends of the plug connector receiving space . Each of the two first metal fitting latches has two mating portions positioned opposite each other.
FIGS. 4(
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As shown in the embodiments of ) and (B), the mating portions are positioned at the four corners of the plug connector receiving space , namely, at respective corners corresponding to the respective four corners of the plug connector when the receptacle connector and the plug connector have been mated with each other.
FIG. 1
FIGS. 4(A) and 4(B)
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As shown in the embodiment of , the receptacle connector has two first metal fitting latches . As shown in the embodiments of , these two first metal fitting latches have identical shapes, but are mirror images of the each other.
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Each first metal fitting latch has two mating portions . Each mating portion has a latching wall positioned to face a corner of the plug connector having the catching member . Additionally, each latching wall is upstanding in a direction intersecting both of two sides of the plug connector sandwiching the corner. A catching member receiving space , in which the catching member of the plug connector is received upon mating, is positioned on a lower portion of the latching wall . Connecting feet and to be soldered to a circuit board on which the receptacle connector is mounted, are positioned on opposite ends of the first metal fitting latch . It should be noted that two press-fitting pieces to be press-fitted into the receptacle housing are positioned on each first metal fitting latch .
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FIGS. 6(A) and 6(B)
During mating of the plug connector to the receptacle connector , the two first arms of one of the catching members of the plug connector each contact one of the two latching walls on the first metal fitting latch . The first arms are elastically displaced, sliding over the latching walls to enter into the catching member receiving spaces of the mating portion . As the first arms enter the catching member receiving spaces , the two first arms elastically relax. Thereby, the plug connector is mated with the receptacle connector , as shown in the embodiments of .
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FIG. 3
Here, as described above, the catching member of the plug connector has two first arms having such shapes that the fixed ends thereof extend from two sides sandwiching a corner of the plug housing , and the free ends thereof extend towards each other, as shown in the embodiment of . That is, the catching member has a shape where it projects so as to intersect both the two sides. Correspondingly, the mating portion of the receptacle connector includes the latching wall standing so as to intersect both the two sides, and the catching member receiving space positioned thereon. Therefore, the catching member engages the mating portion so as to intersect these two sides. Thus, a connector assembly having the plug connector , the receptacle connector and the above described latching mechanism can withstand an impact from any direction.
Additional embodiments of the electrical connector assembly will now be described below, However, only different elements and components will be described, while the Figures showing different elements and components from the previously-described embodiments such as the first embodiment or the like are shown. Parts or elements corresponding to respective parts or elements in the above described first embodiment are denoted by reference numerals obtained by further attaching such an alphabet as A, B and the like to the reference numerals attached to the respective parts or elements in the first embodiment, and explanations thereof will be omitted in some cases.
FIGS. 7(A) and 7(B)
A different point of the connector assembly of the second embodiment described here from the connector assembly of the above described first embodiment is only the second metal fitting catch shown in an embodiment of . Therefore, here, explanation about the metal fitting catch is substituted for explanation about the connector assembly of the second embodiment.
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FIGS. 7(A) and 7(B)
The first metal fitting catch of the plug connector constituting the connector assembly of the above described first embodiment is configured such that one catching member has two first arms . In a second embodiment shown in , the second metal fitting catch A each second catching member A has one second arm A with a shape bent so as to form a corner. The second arm A has a continuous annular shape in which the two first arms in the first embodiment have been connected to each other. Therefore, the second arm A, together with the base A, recessed portion A whose periphery has an annular shape.
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In the second embodiment, the annular shape of the second catching member A results in a limited elasticity during mating. Therefore, the receptacle connector having the second catching member A of the second embodiment is satisfactory when repetition of mating and disengaging with the plug connector is not required.
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When the second metal fitting catch A and first metal fitting latch are mated with each other, the second arms A of the second metal fitting catch A is positioned in the catching member receiving space of the first metal fitting latch , with the second arm A being engaged with the latching wall . When the second metal fitting catch A of the plug connector is mated with the first metal fitting latch of the receptacle connector , both the second metal fitting catch A and the first metal fitting latch have low elasticity. Therefore, a large mating force is required to displace the latching wall or the like.
FIGS. 10(A) and 10(B)
FIGS. 7(A) and 7(B)
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In a third embodiment of the connector assembly shown in , a metal fitting catch identical to the second metal fitting catch A in the second embodiment shown in is used as a second metal fitting catch positioned on in the plug connector .
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FIGS. 9(A) and 9(B)
A second metal fitting latch B of a third embodiment shown in has latching walls B with a shape obtained by splitting the latching wall in the first metal fitting latch in the first embodiment into two pieces. A catching member receiving space B is similar to the catching member receiving space in the first embodiment.
FIGS. 10(A) and 10(B)
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As shown in the embodiment of , when the second metal fitting catch A and the second metal fitting latch B are mated with each other, the second arms A of the second metal fitting catch A are fitted into the catching member receiving spaces B of the second metal fitting latch B, engaging with the latching walls B.
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Similar to that of the first embodiment, when the second metal fitting catch A of the plug connector is mated with the second metal fitting latch B of the receptacle connector , the latching walls B of the second metal fitting latch B elastically deform. Therefore, the connector assembly of the third embodiment is also suitable for an application where mating and unmated between the plug connector and the receptacle connector are repeated like the connector assembly of the above described first embodiment.
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FIGS. 11(A) and 11(B)
A third metal fitting catch C in a fourth embodiment shown in has two third catching members C, each having one cantilevered third arm C positioned on opposite corners of the third base C. The third arm C extends away from the third base C in an inclined fashion to an approximately rectangular shape of the plug connector in a plan view, and has a bent projection portion C positioned proximate to a free end thereof. The bent projection portion C projects outward in a direction perpendicular to a surface of the third base C.
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When the third metal fitting catch C is mated with the first metal fitting latch , the bent projection portions C are positioned in the catching member receiving spaces while the third arms C of the third metal fitting catch C are being elastically deformed by the latching walls , in a manner substantially similar as described in the first embodiment for the first arms . The bent projection portions C are retained in the catching member receiving spaces by the latching walls . A mating direction of the bent projection portion C being mated into the catching member receiving space is a direction inclined to the approximately rectangular shape of the plug connector in a plan view like the above described first to third embodiments.
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FIGS. 12(A) and 12(B)
Since the connector assembly of the fourth embodiment is configured such that the third arm C is elastically deformed by the latching wall during mating, it is also suitable for an application where mating and unmating are repeated, similar to the connector assemblies of the first embodiment and the third embodiment. See .
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FIGS. 13(A) and 13(B)
FIGS. 11(A) and 11(B)
A fourth metal fitting catch D in a fifth embodiment shown in has two fourth catching members D, each having one cantilevered fourth arm D positioned on opposite corners of a fourth base D. Each fourth arm D projects outward in a similar fashion as the third arms C in the third embodiment shown in . The fourth arm D has a semi-spherical projecting pad D positioned on an outer facing surface (not labeled) of a free end thereof, projecting outwardly from the outer facing surface. It should be noted that while the projecting pad D is shown as being semi-spherical, those of ordinary skill in the art would appreciate that projecting pad D may have a rectangular shape or other shapes that would be complimentary to the shape of the catching member receiving spaces on the first metal fitting latch .
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When the fourth metal fitting catch D is mated with the first metal fitting latch , the projecting pads D are received into the catching member receiving spaces while the fourth arms D of the fourth metal fitting catch D are being elastically deformed by the latching walls , in a manner substantially similar as described in the first embodiment for the first arms . Thereby, the projecting pads D are retained in the catching member receiving spaces by the latching walls . A mating direction of the projection portion D into the catching member receiving space is a direction inclined to the rectangular shape of the plug connector in a plan view like the cases of the first to fourth embodiments described above.
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Since the connector assembly of the fifth embodiment is also configured such that the catching pads D are elastically deformed like the above described fourth embodiment, it is also suitable for an application where mating and unmating are repeated, similar to the connector assemblies of the first embodiment and the third embodiment. See .
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FIGS. 15(A) and 15(B)
A fifth metal fitting catch E of a sixth embodiment shown in has two fifth catching members E. One fifth catching member E is positioned on an opposite corner of the fifth metal fitting catch E, extending from a fifth base E thereof. Each fifth catching member E has a catching wall E extending obliquely across a corner of the fifth metal fitting catch E. Each catching wall E has a recessed portion E, and an inwardly overhanging engaging lip (not labeled) extending along a length of the catching wall E.
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FIGS. 16(A) and 16(B)
The third metal fitting latch E of the sixth embodiment is shown in , and has two third mating portions E. Each third mating portion has a third latching wall E positioned to face a corner of the plug connector having the fifth catching member E. A mating projection portion E is positioned on an inner facing surface of the latching wall E, projecting inwardly.
FIGS. 17(A) and 17(B)
FIG. 15
FIGS. 16(A) and 16(B)
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In , an aspect of mating the fifth metal fitting catch E shown in and the third metal fitting latch E shown in with each other is shown.
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When the fifth metal fitting catch E is mated with the third metal fitting latch E, the latching walls E of the fifth metal fitting catch E are received into the catching member receiving spaces E of the third metal fitting latch E, so that the latching walls E catch on the mating projection portions E. A mating direction of the catching wall E into the catching member receiving space E is a direction inclined to the approximately rectangular shape of the plug connector in a plan view like the respective embodiments described above.
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In the sixth embodiment, the elasticity of the fifth metal fitting catch E or the third metal fitting latch E is substantially similar to the above described second embodiment (see FIGS. (A),(B) and FIGS. (A),(B)). That is, in the case of the sixth embodiment, both the fifth metal fitting catch E and the third metal fitting latch E have low elasticity. Therefore, a large mating force is required to displace the latching wall E or the like. Like the above, the aspect of the sixth embodiment can be adopted in the case of a connector assembly where repetition of mating and unmating is not required.
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FIGS. 18(A) and 18(B)
FIGS. 15(A) and 15(B)
FIGS. 3(A) and 3(B)
FIGS. 15(A) and 15(B)
A sixth metal fitting catch F of a seventh embodiment is shown in , differing from the fifth metal fitting catch E shown in in such a point that the catching wall E has been divided into two catching walls F split at a central portion. Similar to the first metal fitting catch of , the sixth catching members each have two cantilevered sixth arms F with fixed ends positioned on two side edges forming each corner. The two sixth arms F flank each corner, with their opposite free ends extending outward from the base F, extending towards each other. The other components and elements of the sixth metal fitting catch F are substantially identical to those of the fifth metal fitting catch E shown in .
FIGS. 19(A) and 19(B)
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As shown in , when the sixth metal fitting catch F is mated with the third metal fitting latch E, two split catching walls F of the sixth metal fitting catch F are received into the catching member receiving space E of the third metal fitting latch E while they are being elastically deformed. The catching walls F engage the catching member receiving space E and are retained therein by also engaging the third latching wall E. A mating direction of the catching walls F into the catching member receiving space E is a direction inclined to the approximately rectangular shape of the plug connector in a plan view like the respective embodiments described above.
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In the sixth embodiment, when the sixth metal fitting catch F of the plug connector is mated with the third metal fitting latch E of the receptacle connector , the catching walls F of the sixth metal fitting catch F are elastically deformed by the third latching walls E. Therefore, the connector assembly of the seventh embodiment is also suitable for a connector assembly where mating and unmating are repeated.
Here, the various connector assemblies from the first embodiment to the seventh embodiment described above are directed to examples where the metal fitting catch is provided in the plug connector while the metal fitting latch is provided in the receptacle connector.
Embodiments where the housing of the plug connector or the housing of the receptacle connector is utilized as the catching member or the mating portion will be described below.
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FIGS. 20 and 21
In the plug connectors constituting the connector assemblies of the first to seventh embodiments described above, the metal fitting catches to F are used, and the catching members to F are positioned on the metal fitting catch to F. However, a plug connector G, constituting the connector assembly of an eighth embodiment shown in , has seventh catching members G positioned on a plug housing G itself. The seventh catching members G are positioned on four corners of an approximately rectangular shape of the plug housing G in a plan view, respectively. On two opposite corners of each seventh catching member G, the seventh catching member G has a standing wall portion G positioned diagonally across the corner, and a catching projection portion G extending along a base end of the standing wall portion G and projecting outward, diagonally across the corner. Further, an engaging surface G of the catching projection portion G extends from an outer edge thereof to an outer facing surface of the standing wall portion G.
24
14
211
21
23
Mating portions E complementary to the seventh catching members G are positioned in a plug connector receiving space G of a receptacle housing G by the third metal fitting latch E.
10
20
146
242
24
23
146
243
146
242
10
FIGS. 6(A) and 6(B)
In the connector assembly of the eight embodiment, when the plug connector G is mated with the receptacle connector G, the catching projection portions G are fitted into catching member receiving spaces E of the mating portions E of the third metal fitting latch E shown in . The catching projection portions G engage the mating projection portions E and are retained thereby. A mating direction of the catching projection portion G in the catching member receiving space E is a direction inclined to an approximately rectangular shape of the plug connector G in a plan view like the respective embodiments described above.
15
17
10
20
23
10
14
11
In the eighth embodiment, like the above described sixth embodiment (see FIGS. (A) to (B)), when the plug connector G is mated with the receptacle connector G, the third metal fitting latch E has a low elasticity. Further, in the plug connector G, the seventh catching members G are positioned on the plug housing G itself. Therefore, the eighth embodiment is generally unsuitable for an application where mating/unmating of the plug connector with/from the receptacle connector is performed in a repeated manner. However, the eighth embodiment is generally suitable for applications where mating is only needed to be performed once.
10
10
13
10
14
13
FIGS. 1 and 2
FIGS. 3(A) and 3(B)
In a ninth embodiment, the plug connector is a connector identical to the connector (see ) of the above described first embodiment. Therefore, the first metal fitting catches shown in are used in this plug connector , and the catching members are formed by the first metal fitting catch .
20
211
21
248
211
21
24
21
20
248
24
21
242
23
4
4
20
FIGS. 22-24(B)
The receptacle connector H in the ninth embodiment shown in is different from the receptacle connectors of the first to eighth embodiments described above in such a point that it does not use any metal fitting latches. At the four corners of a plug connector receiving space H of a receptacle housing H, catching member receiving spaces H are shaped as to be sandwiched obliquely outward to an approximately rectangular shape of the plug connector receiving space H, and are formed as a shape of the receptacle housing H itself. That is, mating portions H are integrally formed in the receptacle housing H itself in the receptacle connector H of the ninth embodiment. The catching member receiving space H of the mating portion H is integrally formed in the receptacle housing H itself, in contrast to the catching member receiving space of the first metal fitting latch (see FIGS. (A),(B)) used in the receptacle connector in the above described first embodiment.
141
13
3
3
10
248
24
21
141
21
In the connector assembly of the ninth embodiment, the first arms positioned on the first metal fitting catches (see FIGS. (A),(B)) of the plug connector are fitted into the fitting-in recessed portions H of the mating portions H integrally positioned in the receptacle housing H. The first arms engage the receptacle housing H itself.
141
13
10
24
21
24
In the ninth embodiment, the first arm of the first metal fitting catch used in the plug connector is elastically deformed upon mating. Therefore, applications involving repetitive mating and unmating are suitable. However, since the mating portions H are integrally positioned on the receptacle housing H, repeated mating and unmating may wear down the mating portions H. Therefore, the ninth embodiment has a structure generally suitable for a connector assembly with a low frequency of mating and unmating requirement.
Though the various embodiments have been described above, each embodiment is related to a connector assembly configured such that mating of four corners of the plug connector is performed in an inclined direction along two sides forming a corner of the metal fitting catch, thus providing a lock mechanism that can withstand an impact from any direction.
It should be noted that the metal fitting catch and the metal fitting latch may have one catching member and one mating portion obtained by performing separation at central portions thereof.
Further, the use of the terms “first,” “second,” “third,” “fourth,” etc are not to be interpreted as establishing a priority, importance, or quantity of the various embodiments described. Rather, such terms are used to assist the reader in distinguishing between the various components and elements of the various embodiments.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention will now be described by way of example, with reference to the accompanying Figures, of which:
FIG. 1
is a perspective view of a first side of a connector assembly of a first embodiment having a plug connector and a receptacle connector;
FIG. 2
is a perspective view of a second side of the plug connector;
FIG. 3(A)
is a perspective view of a first side of a first metal fitting catch positioned on the plug connector;
FIG. 3(B)
is a perspective view of a second side of the first metal fitting catch positioned on the plug connector;
FIG. 4(A)
is a perspective view of a first side of a complementary first metal fitting latch positioned on the receptacle connector;
FIG. 4(B)
is a perspective view of a second side of the first metal fitting latch positioned on the receptacle connector;
FIG. 5(A)
is a perspective view of the plug connector positioned proximate to the receptacle connector before being mated together;
FIG. 5(B)
is a perspective view of the first metal fitting catches positioned proximate to the first metal fitting latches before the plug connector is mated with the receptacle connector;
FIG. 6(A)
is a perspective view of the plug connector mated with the receptacle connector;
FIG. 6(B)
is a perspective view of the first metal fitting catches mated with the first metal fitting latches when the plug connector is mated with the receptacle connector;
FIG. 7(A)
is a perspective view of a first side of a second metal fitting catch positionable on a plug connector in a connector assembly of a second embodiment;
FIG. 7(B)
is a perspective view of a second side of the second metal fitting catch;
FIG. 8(A)
is a perspective view of the second metal fitting catch positioned proximate to the first metal fitting latch before being mated together;
FIG. 8(B)
is a perspective view of the second metal fitting catch mated with the first metal fitting latch;
FIG. 9(A)
is a perspective view of a first side of a second metal fitting latch positionable on a receptacle connector in a connector assembly of a third embodiment;
FIG. 9(B)
is a perspective view of a second side of the second metal fitting latch;
FIG. 10(A)
is a perspective view of the second metal fitting catch positioned proximate to the second metal fitting latch before being mated together;
FIG. 10(B)
is a perspective view of the second metal fitting catch mated with the second metal fitting latch;
FIG. 11(A)
is a perspective view of a first side of a third metal fitting catch positionable on a plug connector in a connector assembly of a fourth embodiment;
FIG. 11(B)
is a perspective view of a second side of the third metal fitting catch;
FIG. 12(A)
is a perspective view of the third metal fitting catch positioned proximate to the first metal fitting latch before being mated together;
FIG. 12(B)
is a perspective view of the third metal fitting catch mated with the first metal fitting latch;
FIG. 13(A)
is a perspective view of a first side of a fourth metal fitting catch positionable on a plug connector in a connector assembly of a fifth embodiment;
FIG. 13(B)
is a perspective view of a second side of the fourth metal fitting catch;
FIG. 14(A)
is a perspective view of the fourth metal fitting catch positioned proximate to the first metal fitting latch before being mated together;
FIG. 14(B)
is a perspective view of the fourth metal fitting catch mated with the first metal fitting latch;
FIG. 15(A)
is a perspective view of a first side of a fifth metal fitting catch positionable on a plug connector in a connector assembly of a sixth embodiment;
FIG. 15(B)
is a perspective view of a second side of the fifth metal fitting catch;
FIG. 16(A)
is a perspective view of a first side of a third metal fitting latch positionable on a receptacle connector in the connector assembly of the sixth embodiment;
FIG. 16(B)
is a perspective view of a second side of the third metal fitting latch;
FIG. 17(A)
is a perspective view of the fifth metal fitting catch positioned proximate to the third metal fitting latch before to being mated together;
FIG. 17(B)
is a perspective view of the fifth metal fitting catch mated with the third metal fitting latch;
FIG. 18(A)
is a perspective view of a first side of a sixth metal fitting catch positionable on a plug connector in a connector assembly of a seventh embodiment;
FIG. 18(B)
is a perspective view of a second side of the sixth metal fitting catch;
FIG. 19(A)
is a perspective view of the sixth metal fitting catch positioned proximate to the third metal fitting latch before being mated together;
FIG. 19(B)
is a perspective view of the sixth metal fitting catch mated with the third metal fitting latch;
FIG. 20
is a perspective view of a first side of a plug connector and a receptacle connector before being mated together, constituting a connector assembly of an eighth embodiment;
FIG. 21
FIG. 20
is a perspective view of a second side of the plug connector in ;
FIG. 22
is a perspective view of a first side of a plug connector and a receptacle connector before being mated together, constituting a connector assembly of a ninth embodiment;
FIG. 23
is a perspective view of the first side of the plug connector and the receptacle connector before being mated together, constituting the connector assembly of the ninth embodiment;
FIG. 24(A)
FIG. 23
is a cross-sectional view taken along arrow A-A shown in of the plug connector positioned proximate to the receptacle connector before being mated together; and
FIG. 24(B)
FIG. 23
is a cross-sectional view taken along arrow A-A shown in of the plug connector mated to the receptacle connector. | |
It is not easy to determine exactly the origin of mosaics, and even the origin of the term “mosaic” is uncertain: some say it is derived from the Greek word “mosaikon” which means “patient work worthy of the Muses”; in Latin it was called “opus musivum”, that is “work of the Muses”. The reference to the Muses is due to the customs and practices of the ancient Romans, who used to build caves and crannies dedicated to the Nymphs (ninpheum) or to the Muses (musaeum) in the gardens of their mansions. It may also derive from the Arabic word “muzauwaq”, which means “decoration”, as the walls of such caves were decorated with rocks and shells. What is certain is that, with the term mosaic we refer to a work of decoration – but not only that, as we will see later on – being performed since ancient times. Over the centuries these works have become stunning art works. Some of these small parts (tiles/tesserae) are made of rocks such as marble, while others are made of stones, glass paste, ceramics, and so on. All these small parts, in different colors and shapes, are assembled and applied in different ways onto the supporting surfaces, both small and large such as floors, ceilings and domes, thereby creating fascinating decorative effects.
It is important to know that at the beginning of their history mosaics were mainly used for practical intents and not only for decorative purposes: glazed clay or pebbles were used as strong finishing materials to cover and protect walls and packed dirt floors. The first decorations consisting of base glazed baked-clay cones used by the Sumerians as finishing materials for raw brick walls date back to 3000 B.C. From the 4th century B.C. onwards and until the 3rd century B.C. mosaics were produced with marble and onyx cubes, as well as cubes of multiple rocks; after that the art of mosaic-making developed and tesserae, expertly cut, started to be used. The earliest form of tesserae mosaic in Rome dates back to the end of the 3rd century B.C. and such was used to waterproof packed dirt floors. Later on, following the expansion into Greece and Egypt, a growing interest in aesthetics and refinement developed and this led to stunning compositions and amazing effects. Originally the craftsmen came from Greece and they brought with them both the techniques and the motifs of the Hellenistic mosaic repertoire, however the Roman and Byzantine mosaics ultimately spread to the whole Empire choosing figurative geometrical motifs, arabesques and stylized plants, over the other motifs. Among the finest examples of this period we have the Basilica of San Vitale in Ravenna, Italy, and the church of Hagia Sophia in Istanbul, Turkey.
Mosaics can be made in different ways. Today mosaic works are mainly made with enamel tesserae, obtained through the melting of glass colored by metal elements (in glass-making the oxidation state of iron, manganese, and copper are important, as these elements will color the glass differently depending on their state of oxidation). The melted glass can be shaped (usually square-shaped) when hot using various techniques such as blowing, moulding, pressing or casting. Moreover, gold enamel tesserae are also used: such tesserae are obtained through the application on glass of a thin gold leaf which, after melting, gives color to the tessera. Basically any frangible material can be used, especially in modern mosaic-making: plates, mirrors, shells, bottle caps. For his works of the series “Raccolti in preghiera” Piedmontese artist Aldo Mondino even used seeds and legumes (maize, wheat, peas, beans, coffee beans) and in other works he used chocolate and sugar cubes. | https://www.cinziatittarelli.it/en/2016/08/04/short-about-the-mosaic-and-its-technique/ |
Our work takes place on the traditional, ancestral, and unceded territories of the Coast Salish peoples.
Our mission: To protect and restore the marine environment and promote the sustainability of Georgia Strait, its adjoining waters, and communities.
Through our programs and initiatives, we:
-
Protect the diversity of wildlife and their habitat;
-
Restore the region’s water and air quality;
-
Promote the social, cultural, economic and environmental sustainability of the region’s communities;
-
Foster understanding and stewardship of the marine environment;
-
Raise awareness of the links between the health of ecosystems and human communities.
.
Georgia Strait Alliance seeks solutions to the problems and issues that threaten the marine environment of the Strait of Georgia, and we achieve results using a long-term approach as we believe this is the best way to create real change.
We are effective because we work:
-
Collaboratively across sectors, empowering citizens and communities with knowledge and tools for engagement and advocacy;
-
With experts to find science-based solutions to root causes;
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To build relationships across sectors to identify champions where we can. | https://www.festivalofoceanfilms.com/who-is-georgia-strait-alliance |
Video of briefing: County Wexford Chamber’s briefing with Minister Damien English and Duncan Graham
Today we held our briefing with Damien English TD, Minister of State for Business, Employment and Retail and Duncan Graham, Managing Director, Retail Excellence Ireland. We would firstly like to thank Minister English and Duncan Graham for meeting with us today and to all those in attendance.
The purpose of this briefing was to discuss how Businesses across County Wexford could be supported in the months ahead and the Government plans for current and future support schemes.
Minster English started off by thanking businesses community and retail sector for their resilience over the past year and praised their response to all the difficult challenges that they faced due to Covid-19. The Minister went on to discuss the supports and grants available such as the Small Business Assistance Scheme for COVID (SBASC) and the Microenterprise assistance scheme.
During his speech, Minister English also recognised that for many sectors there needs to be ongoing supports. Minister English acknowledged that the grants and schemes have been adapted to be more inclusive and this response was based upon feedback that the Government received from the Chamber on behalf of businesses over the past year. The Minister stated that the Government does recognise that the grants and schemes created do not replace all the costs and lost turnover for businesses, but they are there to assist businesses and to try help as many businesses as possible to survive until they go to the reopening phase.
Following on from Minister English, Duncan Graham from Managing Director, Retail Excellence Ireland provided us with a terrific presentation. Duncan discussed the impact of Covid on the retail sector and the current trend of online shopping that grew during the pandemic. He also touched upon the current recruitment issue that retailers are facing as many people have taken on roles in other industries or gone back to education during the pandemic. This is an area that Retail Excellence Ireland and the Government will be working closely on as reopening continues.
Duncan also mentioned that Retail Excellence Ireland have been focusing on the renting issue that retailers are currently having as he explained that many retailers have been struggling with rent bills over the past year and are carrying debt forward into 2021.
Another important area that Duncan covered is how retailers should focus on providing an experience to their customers to attract people to their towns and shops and examples of businesses who are currently doing so. Duncan discussed the idea of creating ‘phygital’ shopping environments for customers. This means a mix between physical shopping and ecommerce not competing but working together by taking the best aspects from each both the physical and online environments to create a complete and satisfying customer experience.
After both Minster English and Duncan Graham gave their discussions, the floor was opened for a Q&A session. All questions were addressed, and the briefing was adjourned. We would like to thank everyone who attended the briefing and reassure anyone who missed the briefing that it was recorded, and the recording is available on our YouTube page Here. | https://www.countywexfordchamber.ie/briefing-with-minister-damien-english-and-duncan-graham/ |
ProAssurance (NYSE:PRA) issued its quarterly earnings results on Wednesday. The insurance provider reported $0.04 earnings per share for the quarter, beating analysts’ consensus estimates of $0.02 by $0.02, MarketWatch Earnings reports. ProAssurance had a negative return on equity of 6.92% and a negative net margin of 27.87%.
NYSE PRA traded up $0.12 on Thursday, reaching $26.14. The stock had a trading volume of 180,250 shares, compared to its average volume of 254,950. The business has a 50 day moving average price of $26.87 and a 200 day moving average price of $21.12. The company has a current ratio of 0.46, a quick ratio of 0.46 and a debt-to-equity ratio of 0.21. ProAssurance has a 1 year low of $12.67 and a 1 year high of $29.15. The company has a market capitalization of $1.41 billion, a price-to-earnings ratio of -5.65 and a beta of 0.26.
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The company also recently announced a quarterly dividend, which was paid on Tuesday, April 13th. Shareholders of record on Friday, March 26th were paid a $0.05 dividend. The ex-dividend date of this dividend was Thursday, March 25th. This represents a $0.20 dividend on an annualized basis and a yield of 0.77%. ProAssurance’s dividend payout ratio (DPR) is currently -24.69%.
PRA has been the topic of a number of research analyst reports. Boenning Scattergood reiterated a “neutral” rating on shares of ProAssurance in a report on Tuesday, January 26th. Zacks Investment Research upgraded ProAssurance from a “sell” rating to a “hold” rating and set a $23.00 price target on the stock in a report on Thursday, February 11th. Truist lifted their price target on ProAssurance from $16.00 to $27.00 in a report on Wednesday, February 24th. Finally, JMP Securities boosted their target price on ProAssurance from $28.00 to $30.00 and gave the company an “outperform” rating in a research note on Friday, April 16th. One equities research analyst has rated the stock with a sell rating, four have assigned a hold rating and one has given a buy rating to the company’s stock. The company presently has a consensus rating of “Hold” and an average target price of $23.00.
About ProAssurance
ProAssurance Corporation, through its subsidiaries, provides property and casualty insurance, and reinsurance products in the United States. The company operates through Specialty Property and Casualty, Workers' Compensation Insurance, Segregated Portfolio Cell Reinsurance, and Lloyd's Syndicate segments. | |
It’s that time of year when I sit down at my dining room table, spread all the packets of seeds I have out, and go through them all. Organisation is the key for me, life is very busy what with work, looking after the house, the family, and managing to cram all those other things into the weekend. When I go out into the garden for a little bit of me time I want to get as much done in the time I have as possible.
My life is full of writing lists and working my way through them. If I don’t write a list each day then I’ll forget something important and then I’ll get stressed and annoyed with myself. It’s not just big important things on my list, but little things like “Buy more long socks” which is next on my list after doing this.
So there I sat at the dining room table with a cup of tea and a biscuit and a mountain of seeds in front of me. Empty plastic ice cream and margarine tubs in front of me and I was off and ready to go. Some seed packet this year are new, some are a couple of years old, some are a little out of date and others are quite a bit out of date. I know that some seeds have a very short life, but others have quite a long life. I’m not one to throw away seeds just because they’re past their prime, they’ll still germinate, just not as many as previously.
So after about half an hour I was done. They are now in tubs that correspond to the month they need to be sown in and are up on top of one of my many bookcases waiting patiently for me to start sowing. I expect I’ll sow some next weekend and then some more the weekend after, this is all weather dependant of course. If we have 4 feet of snow I’m not trudging down the garden to the greenhouses I’d rather stay warm inside the house.
Now to order some more long socks….. | https://clairesallotment.com/2021/01/02/saturday-2nd-january-2021-a-mountain-of-seeds/ |
Q:
Understanding Moving-Average model in time series
I am not able to understand what the error/deviation/stochastic terms in moving average model stand for? What is the practical significance of the error term. Is the error term difference between the consecutive values in the series. Or is it the difference between the forecasted values and the observed values.
A:
The error terms is neither the difference between the consecutive values nor the difference between the forecasted values and the observed values, though the latter is a somewhat close guess.
A moving-average model of order $q$, MA($q$), is
$$
x_t=\varepsilon_t+\theta_1\varepsilon_{t-1}+\dots+\theta_q\varepsilon_{t-q}.
$$
Its conditional mean, conditioning on information up to time $t-1$, $I_{t-1}$, is
$$
\mathbb{E}(x_t|I_{t-1}) = \theta_1\varepsilon_{t-1}+\dots+\theta_q\varepsilon_{t-q}
$$
and this is just $=x_t-\varepsilon_t$. Hence, $\varepsilon_t$ is the difference between $x_t$ and its conditional mean.
The difference between two consecutive values is
\begin{aligned}
x_t-x_{t-1} &= (\varepsilon_t+\theta_1\varepsilon_{t-1}+\dots+\theta_q\varepsilon_{t-q}) - (\varepsilon_{t-1}+\theta_1\varepsilon_{t-2}+\dots+\theta_q\varepsilon_{t-q-1}) \\
&= (\varepsilon_t-\varepsilon_{t-1})+\theta_1(\varepsilon_{t-1}-\varepsilon_{t-2})+\dots+\theta_q(\varepsilon_{t-q}-\varepsilon_{t-q-1}) \\
&= \varepsilon_t+(\theta_1-1)\varepsilon_{t-1}+(\theta_2-\theta_1)\varepsilon_{t-2}+\dots+(\theta_q-\theta_{q-1})\varepsilon_{t-q}-\theta_{q}\varepsilon_{t-q-1} \\
&\neq\varepsilon_t.
\end{aligned}
The difference between a forecasted value and an observed value depends on the forecast. For example, the conditional mean is the optimal forecast under square loss. The conditional mean $\theta_1\varepsilon_{t-1}+\dots+\theta_q\varepsilon_{t-q}$ is unknown but can be estimated by $\hat\theta_1\hat\varepsilon_{t-1}+\dots+\hat\theta_q\hat\varepsilon_{t-q}$ where hats denote estimates of the true quantities. So when forecasting, the difference between an observed value $x_t$ and a forecasted value $\hat{x}_t$ is
\begin{aligned}
x_t-\hat{x}_t &= (\varepsilon_t+\theta_1\varepsilon_{t-1}+\dots+\theta_q\varepsilon_{t-q}) - (\hat\theta_1\hat\varepsilon_{t-1}+\dots+\hat\theta_q\hat\varepsilon_{t-q}) \\
&\neq\varepsilon_t.
\end{aligned}
If only the true values were known, the forecast error would coincide with the error term $\varepsilon_t$.
| |
Researchers estimate about 10% of COVID-19 patients become “long haulers” — people experiencing COVID-19 symptoms for weeks or months, with no well-understood reason for why. Moreover, one in three COVID-19 patients suffer from some kind of medical and neuropsychological disorder at least 6 months after. Across the world, we are gradually understanding more about the economic and policy implications for caring for these people and their families.
To make matters more challenging, racial and ethnic minority communities have experienced COVID-19 infections and illness at much higher rates compared with white communities. Of an estimated 40,000 COVID-19 “long-haulers” in Utah, including many thousands more with some lingering health disorders, a disproportionate number are people of color who already face significant healthcare disparities. This means African American, Latinx, Asian American and Pacific Islander, and Indigenous communities in Utah are likely facing long-term health and lasting economic impacts at disproportional rates, too.
Even before the pandemic, racial and ethnic minority communities experienced severe and persistent racial disparities in health coverage, chronic health conditions, mental health and mortality. These disparities were never because of individual or group behavior but decades of systemic inequality in economic, housing and health care systems. When the pandemic struck, many members of communities of color were vulnerable to infections because they were deemed essential workers, lived in multi-generational and extended households, or had pre-existing health complications.
The moral and practical implications of long-term COVID-19 for the overall health and productivity of our society are immense and just now becoming clearer. Many thousands of Utahns may need long-term care and economic support — as many may not necessarily be able to work or earn a living to pay for those treatments or be able to care for their families as they expected before the pandemic.
As Utah decides how to prioritize its share of Federal relief resources, we must be mindful of the potential long-term healthcare needs for long-haulers, and specifically Utah’s communities of color. We should do everything we can to mitigate and prevent future harm for our most vulnerable communities.
The state’s Multicultural Advisory Committee, formed as part of Utah’s Coronavirus response, suggested a number of general, short-term and long-term policy actions. In the near-term, the state is making some progress by involving community partners, providing inclusive education about COVID-19, and coordinating with Federal partners to encourage communities of color to get vaccinated. Recent data shows communities of color, as in many states, have not been vaccinated proportionately. Fortunately, a growing body of evidence shows the vaccines may be helpful for some long-haulers.
However, the much-needed long-term actions to tackle the racial health disparities post-pandemic will require earnest effort and focus by policymakers. We support creating an actionable state racial equity and social justice plan in collaboration with state commissions, divisions, departments, and community stakeholders. We also agree we should increase funding support and lengthen funding cycles for community-based organizations and improve coordination between private- and public-sector organizations for improving health outcomes for communities of color.
Moving forward, addressing these healthcare disparities in our communities creates an opportunity for Utah to enhance its critical healthcare infrastructure and strengthen connections with Utah’s diverse communities. As policymakers, we are obligated to help Utah – and all Utahns experiencing aftereffects of this awful disease — to recover and grow stronger together.
Rep. Karen Kwan (D-House District 34) represents Taylorsville and Murray. Rep. Jennifer Dailey-Provost (D-House District 24) represents Salt Lake City. | https://www.deseret.com/opinion/2021/4/16/22382067/utah-covid-10-pandemic-long-haulers-aftereffects-economic-public-health-racial-ethnic-minorities |
Are you fond of having bad days at work? Worry not, there is always a way you can go through such days. Tough days at work ever happen; it’s the way we handle them that matters at the end of it all. It is no doubt we all face numerous challenges at work. See, some take them to be openings while others may look for justification to escape such trials.
We all want accomplishments in our lives, but sadly, not many of us get to taste it. This is because many of us don’t identify how to change daily trials into opportunities. However, we all know how hard operating through a challenging day at work can be — encouraging yourself to stay positive when things are not going as deliberate will go a long way.
Be Positive
If you are not receiving good vibes from your workmates on a challenging day, take time to remind yourself that setting the attitude is your job too. Dare yourself to find good things around you and if they don’t exist, make them yourself.
Do your best to support your workmates and treat them fairly regardless of the circumstances. By doing so, this will instantly affect workplace positivity, which in turn is transmittable. If you need another encouragement to delight the most miserable person in the workplace, well, establishing care for others can help lift your spirits.
Be Resilient
Some days require a thick skin. You might get turned away, said no to, turned down, maybe even continually. Refusing to quit isn’t easy, but doing it can make a significant variance in accomplishing your goal. Taking advances to become more resilient can help you overcome the hardest moments in your career.
Always remember you are not born with a static extent of resilience. Like a muscle, you can shape it and draw on it when you need it. In that progression, you will figure out who you are, and you might be the very best version of yourself. Experts suggest that, though everyone is different, you can begin to build your resiliency muscle 0ver time.
Stick to Your Schedule
Though unanticipated information or events are often at the heart of a bad day, bad days at work can have you concentrated on your goals and directions. This can especially be important when your job involves appealing to other people. Starting in the early hours by executing a solid morning routine is often cited as a smart approach that can directly influence success.
Don’t Be Afraid To Take Risks
No one has ever completed anything by playing safe, neither will you.
It may sound nerve-wracking, though to overcome all the challenges and achieve success in your career, you must yield risks more regularly than you anticipate. Well, nobody will ask you to jump from the 60th floor or fight a lion, but you need to prepare yourself to face your fears at some point in life.
You should not waste any chance just because you are scared to risk it all. Face those challenges and take appropriate actions to overcome them. Remember, not taking risks is the prime risk of all time.
Give Yourself a Break
Work with no play makes Jack
a dull boy. Working ceaselessly without any break makes you miss out on the
little desires of life, but also take a toll on your emotional health.
Once In a while, give yourself a break to function appropriately and to overcome the regular trials as well as the brain to stay in its terminal condition. Take your workmates out for dinner or happy hour to release pressure once in a while; this will help you revive up your mind.
Furthermore, we all have that friend who always listens to us when we in a bitter mood and cheers us up, if that’s the case, talking it out with someone can be a great relief.
Conclusion
Remember it’s not the end of the world, it may look like everything is discouraging, it’s helpful to take a deep breath and remind yourself that tomorrow is a new day. This probably isn’t the first time you are facing challenges at work and always remember you can get through.
But the truth is, and it’s crucial for anyone that’s ever had bad days at work, you’re the one making it worse by playing tricks on yourself. We all make mistakes. We all have things come about, but it’s how we handle such circumstances that make us who we are.
So, there you have it, folks, next time you think you are having a bad day at work, remember these tips, breath in, and you will be good to go. | https://thriveglobal.com/stories/how-to-get-through-bad-days-at-work/ |
Why is Bilbo Baggins invisible? This study suggests that Tolkien’s knowledge of philology, theology, philosophy, literature, history, and his own life experience all contribute to the development of the symbolic, moral, and psychological significance of invisibility in The Hobbit. On one level, Tolkien’s theology is informed by his philology, so that being invisible (or “not able to be seen”) becomes a way of symbolically representing the Augustinian concept of evil as the absence of good in the world. On another level, Tolkien’s use of invisibility in The Hobbit demonstrates his knowledge of the philosophic and literary tradition associated with the story of the ring of Gyges in Plato’s Republic, a story that suggests that when people’s actions are not visible and open to the moral scrutiny of others, people may become self-serving and cease to be virtuous. Finally, in his historic role as a signals officer in World War I, Tolkien was often, in effect, invisible to those he was serving and seeking to save on the battlefield. Like Bilbo when he was invisible, he could be heard, but not seen. So invisibility in The Hobbit may correspond to the psychologically traumatizing experience of being in combat. At each of these three levels, invisibility in The Hobbit relates to a hidden war: the conflict between good and evil in the macrocosm of the universe, the resistance to temptation in the microcosm of the heart, and, in a sense, to World War I itself. Readers who understand the deeper symbolic, moral, and psychological significance of invisibility in The Hobbit will no longer see it as a mere magic trick to move the plot forward, but will instead appreciate the deeper meaning of the motif.
Recommended Citation
Beal, Jane PhD
(2015)
""Why is Bilbo Baggins Invisible?: The Hidden War in The Hobbit","
Journal of Tolkien Research: Vol. 2
:
Iss.
1
, Article 8. | http://scholar.valpo.edu/journaloftolkienresearch/vol2/iss1/8/ |
- Low prices on 'state map of alabama' for a limited time.
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Oxford (/ ˈ ɒ k s f ər d /) is a city in England. It is the county town and only city of Oxfordshire.In 2017, its population was estimated at 152,450. It is 56 miles (90 km) northwest of London, 64 miles (103 km) southeast of Birmingham, and 61 miles (98 km) northeast of Bristol.
The Anniston–Oxford metropolitan statistical area is the most populated metropolitan area in Northeast Alabama next to Huntsville. At the 2000 census , it had a population of 112,249. The MSA is anchored by significant jobs at Jacksonville State University, the Northeast Alabama Regional Medical Center, Stringfellow Hospital, the Anniston ...
According to 2020 U. S. Census data, the average population of Alabama's 67 counties is 74,989, with Jefferson County as the most populous (674,721), and Greene County (7,730) the least. The average land area is 756 sq mi (1,958 km 2 ). The largest county is Baldwin (1,590 sq mi, 4,118 km 2) and the smallest is Etowah (535 sq mi, 1,386 km 2 ).
In Alabama, Interstate 20 ( I-20) travels 214.7 miles (345.5 km) through the center of the state. It enters the state from Mississippi near Cuba, and travels northeastward through Tuscaloosa and Birmingham. At Birmingham, I-20 turns eastward and heads through Oxford before crossing the Georgia state line near Lebanon.
Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth.The standard atmosphere (symbol: atm) is a unit of pressure defined as 101,325 Pa (1,013.25 hPa; 1,013.25 mbar), which is equivalent to 760 mm Hg, 29.9212 inches Hg, or 14.696 psi.
Taken in October 2010, a Google Maps Camera Car showcased on Google campus in Mountain View, California. The United States was the first country to have Google Street View images and was the only country with images for over a year following introduction of the service on May 25, 2007. Early on, most locations had a limited number of views ...
U.S. Route 431 ( US 431 ), internally designated by the Alabama Department of Transportation (ALDOT) as State Route 1 ( SR 1 ), is a major north–south state highway across the eastern part of the U.S. state of Alabama. Although US 431's south end is in Dothan, SR 1 continues south for about 13 miles (21 km) along US 231 to the Florida state line.
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- Low prices on 'state map of alabama' for a limited time. | https://www.luxist.com/content?q=oxford+alabama+map+google&nojs=1&ei=UTF-8&nocache=1&s_pt=source7&s_chn=1&s_it=rs-bot |
Now in its 25th academic year, the School has been inspiring creativity since 1993. A unique learning environment, the School provides a warm and inviting space where students can experience high quality visual and performing arts instruction in a relaxed and nurturing environment. A large roster of classes throughout the year, as well as birthday parties and outreach programs in public and private schools, help to distinguish the School as a leader in arts education. The School’s March break and summer camps provide a perfect environment for kids to learn, exercise creativity and explore their uniqueness. Situated in a Victorian house, all classes are taught by professional artist/educators and small class sizes allow for plenty of individual attention. The staff and faculty help to inspire and ignite the creative spark in students young and those young at heart. Students participate in exhibits and performances throughout the year. 460 Avenue Road, at St. Clair. | https://streetsoftoronto.com/camp/avenue-road-arts-school/ |
Extended AbstractThis presentation outlines heuristics from converting educational games and simulations from the controlled environments of academic researchers to the rigor and pragmatics of product based solutions in non-game organizations. These observations were collected from an ongoing research and implementation practice collaboration between the top ranked (anonymized) corporate consultancy and the Princeton Review ranked (anonymized) university game research community.
The presentation highlights the challenges of integrating, coordinating and orchestrating discreet purpose-driven game s within an organization.
We offer recommendations for the appropriate development and deployment of such games to support the appropriate attention, support, management and assessment. The presentation shares experience to directly address the following questions in an effort to support the community of meaningful play practitioners toward an effective strategy for bringing academic research into the broader communities.
• What business problems are appropriate for serious games solutions? Through our research we present a synopsis of how organizations currently approach their application of serious games as a solution to corporate/enterprise issues and the risks associated with each approach. In addition we posit a “suitability framework” for identifying Game solution topics and outcomes from an organizational vs initiative based view.
• What are the design criteria that will enable the individual game experiences to integrate with other future games? These include strategies for designing modular game elements that can scale across long term meaningful play strategies, assessments of current simulation and play culture within the target organization and normalizing gameplay experiences across suites of experiences. We have observed that players often suffer confusion, disorientation, and disinterest when they are subjected to wildly different game experiences, rule sets, measurement, and rhetoric within the same organization. We offer techniques for determining an organizationally appropriate play strategy, through play design guides that pervade games and simulation efforts across the organization.
• How can games and simulations drive effective change, strategic decision making and individualized career development across an organization? Beyond increasing data tracking, we leveraging our best thinking on the actionable insights that can be gained through gameplay and how they can optimally benefit the individual and the organization.
In summary this presentation seeks to provide an evidence based strategy for large scale, purpose driven play within large organizations. It opposed the more typical approach to design small, specific games for specific needs and looks more broadly at expected future of such play. We purpose that as more organization commit to such games, they will need to move from widely divergent individual games toward a more global strategy. Much like an organization’s brand and design guides, we champion a strategy that evaluates, identifies and specifies the cross-organizational standards for effective purpose-driven play.
These observations and suggestions are made through an ongoing collaboration that brings a lauded “serious games” academic research team with a highly respected international consultancy. The presenters combine years of experience in game design and management of large scale government projects in games and simulation. | https://meaningfulplay.msu.edu/proceedings2016/abstract.php?paperid=60 |
Neonicotinoids HB 2589 – The use of neonicotinoid-based pesticides have adverse impacts on Oregon’s bees and pollinating insects, as well as affecting the health of other native species including Salmon, aquatic invertebrates, and birds, Neonicotinoids are present in many of Oregon’s waterways and ecosystems, and the strong scientific correlations of these negative impacts are clear; yet industry and government agencies refuse to take meaningful measures to protect the environment from the use of these pesticides.
Neonicotinoids are systemic and persistent in plants for years after direct application or prophylactic seed treatment. It has taken decades to figure out the mechanisms through which neonics affect the integrity of ecosystems. There is a strong case for stricter regulation.
I think its reasonable that the State of Oregon put a moratorium on neonics until their use can be proven safe for our ecosystem. I introduced a bill to ban the use of neonics to move the discussion in this direction. Unfortunately HB 2589 did not pass as it did not have enough support from the legislature, state agencies and the agricultural industry. | http://paulholvey.com/neonicotinoids-hb-2589 |
God is there, and he cares.
Stormie Omartian, the bestselling author of The Power of a Praying Parent, teaches kids ages 4 to 8 that fear is a natural emotion, and they can turn to the Lord no matter what they may be afraid of.
Children will discover that good fear, the kind that protects them from dangerous situations, is part of God's plan to keep them safe. When irrational fears arise, kids will be reminded that their heavenly Father is there to listen and help them overcome.
God Cares When I'm Afraid covers many common childhood fears like bad dreams, the dark, loud sounds, scary people, and many more. In all of these situations, Stormie encourages kids to turn to God for help. She provides a simple prayer they can use to talk to Him, as well as seven simple things kids can do whenever they are afraid.
Parents, grandparents, and caregivers will experience the peace of mind that comes from trusting your precious little one's fears to the One who can calm the hearts of young and old alike.
- 32 illustrated pages
- Picture book format
- From bestselling author Stormie Omartian
- Illustrations from Shari Warren
- Recommended for ages 4 to 8
Product Details
|Media Type||Book|
|Age Range||4-8|
|Grade||
Preschool
|
Kindergarten
1st Grade
2nd Grade
|Binding Type||Hardcover|
|Publisher||Harvest Kids|
|Pages||32|
|ISBN||9780736976404|
Online Only
Item not available in Mardel Stores.
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Check your local store for availability.
Inspired?Share it: | https://www.mardel.com/Children/Childrens-Books/Special-Topics/God-Cares-When-Im-Afraid-by-Stormie-Omartian-and-Shari-Warren-Hardcover/p/3823176 |
Purpose: The purpose of this paper is to study the determinants of subjective and emotional well-being of workers in Bangladesh’s female-intensive export-oriented ready-made garments (RMG) factories based on a function of demographic, economic and psychological factors and work-place characteristics.
Design/methodology/approach: Employee-level data are obtained from a purposefully designed survey conducted in 2014 on 50 RMG factories located outside the country’s export processing zones. Dependent variables include domain-specific as well as overall life satisfaction. The analysis is quantitative in nature and based on ordered probit and (factory) fixed-effect regression models.
Findings: Compared to men, female workers are found to be more satisfied with life and financial situations and less depressed, a finding that is robust to controls for workplace characteristics and policies (e.g. provisions for childcare; higher presence of female supervisors; and management’s attitude toward work life balance) and factory fixed effects. This suggests that despite various compliance-related problems, employment in the RMG sector is intrinsically valued by female employees. Among other findings, although absolute income does not appear to affect well-being, relative income effect is statistically significant.
Originality/value: Although there is a sizable literature on the importance of decent jobs and women’s employment in low-pay manufacturing jobs in developing countries, studies on whether women intrinsically value such jobs are limited. Our study is unique in the sense that it draws on a purposefully designed survey conducted a year after the deadly collapse of RMG factory buildings in Dhaka, Bangladesh. The incident exposed unsafe work conditions in which millions of women work in manufacturing sector around the developing world. To our knowledge, this is also the first paper on subjective assessment of work and non-work aspects of lives of women employed in Bangladesh’s RMG sector. The study also contributes to the international literature on the paradox of the contented female worker in low-pay jobs. Therefore, the paper will be of significant interest to readers from other countries that rely on apparel exports and depend on female labor. | https://researchers.mq.edu.au/en/publications/the-paradox-of-the-contented-female-worker-evidence-from-banglade |
Ari Satok: “Love Too Can Spread”
Capturing the strange and surreal times that the pandemic has brought with it, “Love Too Can Spread” tells the stories of how we filled our days when nothing was as it had been before. With poems about everything from grocery shopping to grief to Grandma’s never-ending challenges with Zoom, this collection brings together the serious and the light-hearted, meditating on the things that truly matter when so much else falls away.
Cancellation:
Occasionally, events may be cancelled due to inclement weather or other conditions beyond our control. In that case, we will make every effort to update our website and contact registrants.
Photography policy:
Official photographs taken at the event may include you as a subject and could be used in future editorial and promotional contexts in print and electronic media. Images will not be identified using full names without written approval from the individual. Please notify Noble Horizons staff if you would prefer that your photo not be used. | https://noblehorizons.org/events/ari-satok-event/ |
Do you have questions about the upcoming Spring Festival, then you can find the answers here.
... And if you have a question that you can't find the answer to here, then write an e-mail to [email protected], and then we will get back to you.
-
Where and when?
The next Spring Festival takes place on Friday the 15th of May 2020 from 14:00 to 02:00.
The festival will take place on Nørre Campus, where you can enter from Universitetsparken, Nørre Allé and Tagensvej. The entire Universitetsparken will be closed off and turned into bike parking, so you are welcome to park your bike here while attending at the festival.
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Who can participate?
The festival is for UCPH’s entire community: Academic staff (VIP), technical and administrative staff (TAP) and students. Remember your UCPH-ID - that’s your entrance pass.
It is not allowed to bring along guests, family etc, who aren’t related to UCPH. But if your institute has visiting researchers, collaborators etc, who don’t have a UCPH-ID, then send an email to [email protected] as soon as possible by Thursday, May 14th.
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How is the accessibility of the festival site?
There will be easy access for those with impaired mobility, wheelchair users etc.
We will also make sure that there are appropriate restrooms and access to the audience areas of the stages. Feel free to contact us at [email protected], if you have special needs. We will do our best to accommodate this.
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What am I allowed to bring with me?
You’re welcome to bring your backpack, blankets, your (plastic) water bottle and other items that can make your festival experience the best as possible without being a nuisance to the other guests.
We’re making sure that there’s plenty of seating available, but you are welcome to use the lawn areas too.
You’re not allowed to bring in beverages, camping chairs, tents etc.
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Is everything outdoors?
Yes. The UCPH Spring Festival is an outdoor festival, so remember to bring warm clothes.
We have a huge tent by the Totem stage, but the rest of the event is held outside without covering. If it looks like it might rain, we recommend bringing a waterproof jacket and sensible footwear.
-
How about food?
There will be food vendors at the festival, and we’re striving to have something for everyone.
Whether you’re in the mood for a big juicy burger or a vegan dish, there’ll be something available for you - and the prices will be student-friendly.
We will continually keep you updated with the planned vendors and food trucks, so keep an eye on the website.
We’ll have 8 different bars at the festival site, where you can buy beer, sodas, ciders and much more. The bars are manned by volunteers, and the profit will go to the music bookings for the festival.
-
How about the empty plastic cups?
If you want to be nice to the environement as well - AND get a free beer for your efforts, then read the next bit carefully:
Once again we focus on minimizing plastic waste and encourage you all to hand in your used plastic cups in our Refund-booth by the food court. All you need to do is to gather 25 cups and then hand them in for the refund - then we give you a free beer in return ♻️ ➡️ ????
... And please remember to use the trash bags around the festival site - that way we can keep the place nice and clean.
-
A few words about safety
There will be medics present at the festival site all afternoon, evening and night. Their specific location will be noted on the map of the festival site, and it will be clearly marked by signs on the day as well.
The entire festival site will be surrounded by a fence, and there will be three entrances/exits. There will be access control at every entrance, so remember your UCPH ID-card.
Remember that there will be a lot of people present at the festival, so take good care of your possessions. Leave your jewelry, computer and other valuables at home and take good care of yourself and your fellow students and colleagues during the festival.
-
A little bit about our alcohol and drug policy
There will be plenty of opportunities to buy cheap beer, sodas and drinks during the festival, and therefore it’s not permitted to bring your own beverages apart from a water bottle.
If you are in possession of or under the influence of drugs and illegal substances you will be asked to leave the event and festival site immediately.
-
How can I join as a volunteer?
Without volunteers - there is no UCPH Spring Festival.
Normally there are 300-400 volunteers from all faculties and the university’s central administration. They take care of bartending, safety and access, stage setup and other exciting and important tasks during the festival. A volunteer shift is approx. 4 hours and you receive food and drink vouchers + a t-shirt on the day.
During April we host a big volunteer meeting at Nørre Campus, where we’ll go through the plan for the day, walk around the festival site, answer questions and make sure that everyone is ready for the big day.
Find more info about volunteering here
-
How can I contact the festival organizers?
If you have a great idea for an event or activity at the festival, send us an email at [email protected]
-
I’ve lost something
We gather all the found items and will bring them to Studenterhuset over the weekend of the festival. Fill out the form at www.studenterhuset.com/lost-found with a description of the lost items, then we will do our best to reunite everything with their owners on the Monday following the event.
Unfortunately, it is not possible to “just drop by” to check whether we’ve found your lost things after the festival. In 2018 we found almost 100 lost items; for instance phones, wallets and keys. To ensure that everything is returned to the rightful owner, we are going to keep an organised registration system. That gives you the safety of knowing, that if we find your things, you will also be the one getting them back again. | https://kufestival.dk/en/praktisk-info/ |
Students with the passion to showcase their creativity and communicate ideas visually will be instantly drawn to Graphic Communications. In our shop, students design products that will ultimately be printed on an offset press, a digital press, and a screen press. These printed materials are then ‘finished’ in our bindery area where students trim, fold, and package all work in a professional manner. Our students work directly with clients both in the community, as well as in the school environment to produce logos, brochures, posters, banners, and much more. | http://techhigh.us/graphics/ |
SHS Web Conf.
Volume 72, 2019International Scientific Conference: “Achievements and Perspectives of Philosophical Studies” (APPSCONF-2019)
|Article Number||03011|
|Number of page(s)||7|
|Section||Man in the World of Culture|
|DOI||https://doi.org/10.1051/shsconf/20197203011|
|Published online||28 November 2019|
The philosophy of work in the Gulag: two views in comparison
Peoples' Friendship University of Russia, 117198, Moscow, Russia
* Corresponding author: [email protected]
This article is devoted to the topic of work, in the frame of the Soviet labor camp, from the point of view of two leading exponents of the lagernaya literatura: Aleksandr Solzhenitsyn, with his novel One Day in the Life of Ivan Denisovich, and Gustaw Herling-Grudzinski with the memoir A World Apart. Both authors write on the same theme, the life of a prisoner, but the focus on the work activities and the interpretation they give is completely different. The description of the working day, the consequences it makes on the everyday life of the prisoners, the struggle for the food needed for surviving the harsh climatic and detention conditions, and finally the philosophical approach used to represent the forced labor, present relevant differences. This article is meant to analyze those differences through the authors' very own words and literary studies. We start from the very raw information detectable by a thorough reading of the two works, going through a moral analysis of the events narrated. While the core narration happens within the same tragic frame, the conclusions they draw are ultimately different.
© The Authors, published by EDP Sciences, 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while. | https://www.shs-conferences.org/articles/shsconf/abs/2019/13/shsconf_appsconf2019_03011/shsconf_appsconf2019_03011.html |
The GDPR Solutions market research study covers historical data of previous years along with a forecast of upcoming years based on revenue (USD million). The GDPR Solutions market reports also cover market dynamics, market overview, segmentation, market drivers and restraints together with the impact they have on the GDPR Solutions demand over the forecast period. Moreover, the report also delivers the study of opportunities available in the GDPR Solutions market globally. The GDPR Solutions market report study and forecasts is based on a worldwide and regional level.
If you are an investor/shareholder in the GDPR Solutions Market, the provided study will help you to understand the growth model of GDPR Solutions Industry after the impact of COVID-19. Request for a sample report (including ToC, Tables and Figures with detailed information) @ https://inforgrowth.com/sample-request/6322687/GDPR Solutions-Market
The report assesses the key opportunities in the market and outlines the factors that are and will be driving the growth of the GDPR Solutions industry. Growth of the overall GDPR Solutions market has also been forecasted for the period 2020-2026, taking into consideration the previous growth patterns, the growth drivers and the current and future trends.
Market Segments and Sub-segments Covered in the Report are as per below:
The report also contains the effect of the ongoing worldwide pandemic, i.e., COVID-19, on the GDPR Solutions Market and what the future holds for it. It offers an analysis of the impacts of the epidemic on the international market. The epidemic has immediately interrupted the requirement and supply series. The GDPR Solutions Market report also assesses the economic effect on firms and monetary markets. Futuristic Reports has accumulated advice from several delegates of this business and has engaged from the secondary and primary research to extend the customers with strategies and data to combat industry struggles throughout and after the COVID-19 pandemic.
What is the market size of the GDPR Solutions industry? This report covers the historical market size of the industry (2013-2019), and forecasts for 2020 and the next 5 years. Market size includes the total revenues of companies.
What is the outlook for the GDPR Solutions industry? This report has over a dozen market forecasts (2020 and the next 5 years) on the industry, including total sales, number of companies, attractive investment opportunities, operating expense, and others.
What industry analysis/data exists for the GDPR Solutions industry? This report covers key segments and sub-segments, key drivers, restraints, opportunities and challenges in the market and how they are expected to impact the GDPR Solutions industry. Take a look at the table of contents below to see the scope of analysis and data on the industry.
How many companies are in the GDPR Solutions industry? This report analyzes the historical and forecasted number of companies, locations in the industry, and breaks them down by company size over time. Report also provides company rank against its competitors with respect to revenue, profit comparison, operational efficiency, cost competitiveness and market capitalization.
What are the financial metrics for the industry? This report covers many financial metrics for the industry including profitability, Market value- chain and key trends impacting every node with reference to company’s growth, revenue, return on sales, etc.
What are the most important benchmarks for the GDPR Solutions industry? Some of the most important benchmarks for the industry include sales growth, productivity (revenue), operating expense breakdown, span of control, organizational make-up. All of which you’ll find in this market report.
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A business letter is written in formal language. It is written for official correspondence between two organizations and organizations and customers, clients, etc. It has to be written in a style that is professional and with a right note. However, the writing approach can be modified based on the relationships you have maintained with the recipients.
It is used for various purposes like introducing a business, offering a business deal to other organization, accepting an offer, denying an offer, introducing new schemes for customers, extending business contracts, canceling a deal, correcting mistakes in invoices, returning goods, offering help, giving good and bad news, apologizing, etc.
It should be concise yet detailed. Being concise does not mean you must use several numbers of short sentences. It will sound unprofessional and would become difficult to compile them and understand the context. Unless you are conveying clear and complete message, the readers would not be able to fathom the matter. Also important is that the letter should not have any typographical and grammatical error.
Take a look at the following points that will help you in drafting a business letter:
Let's hope that we have made the definition of a business letter clear. Also the extra information about drafting the letter would help you accomplish your goal. | http://www.bestsampleresume.com/letters/what-is-business-letter.html |
Articles written for the GLP list the source as Genetic Literacy Project. All other articles were written for the sources noted with excerpts provided by the GLP.
Twenty years after cloned sheep Dolly’s birth, reproductive technology still evolving
The GLP aggregated and excerpted this blog/article to reflect the diversity of news, opinion and analysis. It may seem bizarre, ...
Methods for cloning mammoths, from the creator of Dolly the sheep
It is unlikely that a mammoth could be cloned in the way we created Dolly the sheep, as has been ... | https://geneticliteracyproject.org/writer/ian-wilmut/ |
David Joseph was born in Melbourne in 1954. He completed his secondary schooling in Hobart and studied at the University of Tasmania for two years before transferring to the Elder Conservatorium at the University of Adelaide in 1975 to study with Richard Meale.
In 1980 Joseph graduated from the Elder Conservatorium with a Bachelor of Music degree with first-class honours in composition, and was invited to participate in the first Summer School for Young Composers in Sydney. He was awarded a Commonwealth University Post Graduate Research Fellowship and enrolled fulltime at the University of Adelaide in the degree of Master of Music.
In 1982 he travelled to Spain and Italy on an International Fellowship for Composers from the Music Board of the Australia Council.
In 1986 he was commissioned by the Adelaide Chamber Orchestra to compose a work for the orchestra's tenth anniversary concert series. This work, entitled The Dream, was premiered at the Adelaide Town Hall on 13th September, 1986.
David Joseph has received numerous commissions, including those from Die Kammermusik Zurich (String Trio, 1987), the Australian Dance Theatre (The Golden Slave, 1987), the Tasmanian Symphony Orchestra (Clarinet Concerto, 1987), and the Adelaide Chamber Orchestra (Horn Concerto, 1988, and Symphony for Solo Organ and String Orchestra, 1989).
Having worked fulltime as a composer between 1988 and 1991, Joseph enrolled at the University of Melbourne for a Master of Music degree in Composition in 1992. He was employed as a tutor at the University of Melbourne between 1993 and 1995.
Chamber concerto for piano and strings (piano with string orchestra) (1991) Commissioned by Spiros Rantos, for the Rantos Collegium.
Trio : for violin, viola and cello (1987) Commissioned by Die Kammermusiker Zurich. | https://www.australianmusiccentre.com.au/artist/joseph-david |
"The doping effect of multiwall carbon nanotube on MgB2/Fe superconduct" by J. H. Kim, W. K. Yeoh et al.
This article was originally published asKim, JH, Yeoh, WK, Qin, MJ, Xu, X & Dou, SX, The doping effect of multiwall carbon nanotube on MgB2/Fe superconductor wire, Journal of Applied Physics, July 2006, 100, 013908. Copyright American Institute of Physics. Original journal available here.
We evaluated the doping effect of two types of multiwall carbon nanotubes (CNTs) with different aspect ratios on MgB2/Fe monofilament wires. Relationships between microstructure, magnetic critical current density (Jc), critical temperature (Tc), upper critical field (Hc2), and irreversibility field (Hirr) for pure and CNT doped wires were systematically studied for sintering temperature from 650 to 1000°C. As the sintering temperature increased, Tc for short CNT doped sample slightly decreased, while Tc for long CNT doped sample increased. This indicates better reactivity between MgB2 and short CNT due to its small aspect ratio, and substitution of carbon (C) from short CNT for boron (B) occurs. In addition, short CNT doped samples sintered at high temperatures of 900 and 1000 °C exhibited excellent Jc, and this value was approximately 104A/cm2 in fields up to 8 T at 5 K. This suggests that short CNT is a promising carbon source for MgB2 superconductor with excellent Jc. In particular, inclusion of nanosized MgO particles and substitution of C into the MgB2 lattice could result in strong flux pinning centers. | https://ro.uow.edu.au/engpapers/153/ |
BACKGROUND OF THE INVENTION
SUMMARY OF THE INVENTION
DESCRIPTION OF THE PREFERRED EMBODIMENTS
1. Field of the Invention
The present invention relates to an informative object whose shape and lighting are variable.
2. Background Art
A wide variety of information has been conventionally provided through screen display of electronic information terminals such as personal computers, smartphones, and equipment dedicated to each application.
In such a situation, the following problems arise:
(a) Although such a conventional electronic information terminal is useful for a user to read predetermined information actively, recognition of the information depends on the activeness of the user. Thus, the electronic information terminal is not practical for constantly observing predetermined information in everyday life and obtaining an overall view of tendencies thereof;
(b) A conceivable means for solving the problem (a) is to inform a user of a change in the state of information with, for example, an e-mail. However, frequent notifications interrupt thinking and behavior and gradually become burdensome for the user. Accordingly, the notifications are often disregarded, resulting in failures in information transmission in many cases;
(c) Information is often expressed in the form of characters and figures on a screen. Visual impressions thereof on a reader tend to be uniform, and the amount of information tends to be excessive. Thus, it is difficult for a user to know a summary of information intuitively in a short time; and
(d) As another attempt, a terminal is provided with a light-emitting object so as to notify a user of a state or change of information by using the way of lighting or the color of light as a trigger in everyday life. The way of lighting and the color of light, however, are not suitable for displaying quantitative information and the tendency thereof. Thus, the expressiveness in this attempt is restrictive. In addition, the content of information that can be transmitted to the user is limited to prepared information, and the attempt cannot cope with the current situation where new information is consecutively provided through the Internet.
The present invention provides an informative object whose shape and light are variable in accordance with information obtained through a Web API on the Internet or information obtained from a local environment, and which serves as a contact with everyday life in interior decoration.
The informative object of the present invention provides an opportunity of seeing information whose state and change are to be noticed as part of daily scene, enables a user to intuitively know the volume and tendency of the information, and promotes realization and overall understanding of the information through continuous observation in everyday life. The informative object of the present invention is not limited to specific information and information service, and can deal with a variety of information and be used to consider a correlation between different types of information.
An informative object according to an embodiment of the present invention will be described with reference to the drawings.
FIG. 1
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is a front perspective view illustrating an informative object . The informative object includes: a seesaw that is a tilt mobile object whose tilt angle is adjustable to a predetermined angle relative to a horizontal plane; a translucent white sphere that rolls sideways by gravity on an upper surface of the seesaw ; and a base supporting the bottom surface of the seesaw .
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In an actual display of the informative object , the internal mechanism is preferably concealed in terms of design by, for example, enclosing the exterior of the base with a decorative laminate. Since the informative object is not necessarily placed on a completely horizontal plane, an adjusting function such as adjusters attached to the legs of the base needs to be prepared.
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is a front view of the informative object . The bottom surface of the seesaw is arc-shaped and provided with a flat bar vertically extending from the center of the bottom surface. Arc-shaped gears and are respectively provided at the left and right of the flat bar and extend along the shape of the bottom surface of the seesaw .
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The seesaw is hollow and includes an odd-numbered LED light sources constituted by LEDs of three colors: red, blue, and green. The LED light sources are arranged along the upper surface of the seesaw and evenly spaced from one another. Openings through which light passes upward from the LED light sources are formed in the upper surface of the seesaw at positions corresponding to the LED light sources .
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The upper surface of the seesaw is substantially arc-shaped and has slightly recessed portions around the openings as illustrated in , thereby causing the sphere to stop immediately above the openings .
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is a partial cross-sectional view of the informative object taken along line - in . The seesaw has a concave cross-sectional shape such that the sphere rolling on the upper surface of the seesaw does not fall away. The seesaw also has a groove along the center, and the openings are positioned in the bottom surface of the groove such that the openings do not affect rolling of the sphere, thereby causing the sphere to roll smoothly along the upper rim of the groove .
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is a front view illustrating an example in which the seesaw of the informative object tilts. The upper surface of the base has a slit which is large enough to allow the flat bar of the seesaw to penetrate therethrough and swing sideways therein. The upper surface of the base is provided with linear gears and extending along the upper surface of the base at the left and right of the slit . These gears and are vertically engaged with the gears and of the seesaw such that the seesaw tilts sideways without lateral and vertical shifts of the positional relationship between the seesaw and the base .
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A link is provided to couple a servo horn of a servo motor fixed to the base and the flat bar of the seesaw. The shaft of the servo motor is rotated to a predetermined angle so that the flat bar of the seesaw is pushed and pulled through the servo horn and the link and, thereby, the seesaw tilts at a predetermined angle.
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When the seesaw tilts, the sphere rolls by gravity and stops at a lowest position on the upper surface of the seesaw , one of the LED light sources immediately below the sphere emits light, and the sphere glows under the influence of the emitted light.
FIG. 6
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illustrates an example in which the servo motor rotates to a predetermined angle so that the seesaw laterally tilts at a predetermined angle, and then, the sphere rolls accordingly and stops at a different position, thereby changing the shape of the object. The LED light source immediately below the sphere at each position emits light, and the sphere glows under the influence of the emitted light.
FIG. 7
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illustrates that the informative object regularly refers to a movement directive statement in a predetermined server on the Internet. The predetermined server includes a program for regularly acquiring predetermined information from various Web APIs published on the Internet and regularly updating the movement directive statement based on the acquired information.
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The program defines information to be acquired, a Web API for acquiring the information, the interval for acquiring the information, the way of evaluating the acquired information, and how to determine movement of the informative object . Results of the determination are described in the movement directive statement , which is regularly updated.
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The movement directive statement has display modes in the number corresponding to the types of information to be displayed. Specifically, for example, a display mode indicates a “power balance” and a display mode indicates a “stock price.” Movement directives of the informative object are described in order after the name of information.
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(a) a case where generated power exceeds consumed power by 25 Wh or more;
(b) a case where generated power exceeds consumed power by 15 Wh or more and less than 25 Wh;
(c) a case where generated power exceeds consumed power by 5 Wh or more and less than 15 Wh;
(d) a case where the difference between generated power and consumed power is less than 5 Wh;
(e) a case where generated power is below consumed power by 5 Wh or more and less than 15 Wh;
(f) a case where generated power is below consumed power by 15 Wh or more and less than 25 Wh; and
(g) a case where generated power is below consumed power by 25 Wh or more.
Specifically, the program described in, for example, a PHP language requests power information of home from electric information API minutely, acquires information as data in an XML format, parses the XML data, extracts the values of generated power and consumed power, and then evaluates the values in the following seven stages:
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Movement of the informative object is determined depending on the information evaluation such that the angle of the servo motor is 20 degrees and the first LED light source is always on with rgb values of 0, 0, and 255 (blue) in the case (a), the angle of the servo motor is 90 degrees and the fourth LED light source is always on with rgb values 0, 255, and 0 (green) in the case (d), the angle of the servo motor is 160 degrees and the seventh LED light source is always on with rgb values 255, 0, and 0 (red) in the case (g), for example. Results of this determination are described in the movement directive statement . The content of the description is preferably encrypted for information security.
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A microcomputer of the informative object regularly refers to the movement directive statement in the predetermined server , and determines movement depending on the content of the description and a current display mode. is a flow chart from information acquisition to movement of the informative object .
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The display mode can be switched by pressing a switch on the upper surface of the base. To notify a user of information that is being displayed, an utterance IC and a speaker are added to, for example, the microcomputer such that the name of information, e.g., “power balance,” is uttered when the button is pressed. Since the informative object can express various types of information, it is important to design the informative object so as to flexibly cope with a change of the way of issuing a notice of the name of information.
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The microcomputer of the informative object does not directly refer to the Web API for the following reasons:
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(a) To obtain flexibility in remotely determining the content of information expressed by the informative object and the way of expressing the information by changing the program . This case has an operational advantage that a provider of the informative object and a provider of information to the informative object can remotely determine the setting even if a user of the informative object has no knowledge of the program.
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(b) Parsing of XML data, for example, applies a heavy load on such a small microcomputer as installed in the informative object .
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The informative object may move based on information acquired in a local environment. This mechanism is similar to that described above except for the following aspects, and thus, will not be described again.
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(c) Using, for example, a measured value of a sensor in the local environment, instead of the Web API ;
(d) Regularly referring to (a) and placing a program of regularly updating a movement directive statement and the generated movement directive statement in the local environment; and
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(e) The microcomputer of the informative object regularly refers to a movement directive statement in the local environment.
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In the foregoing embodiment, preferred examples of the present invention have been described. However, mechanisms for implementation are not limited as long as the seesaw can be accurately tilted at a predetermined angle relative to the horizontal plane by using, for example, attraction and repulsion of electromagnets. Examples of Application of Present Invention
The present invention is applicable to a home energy management system (HEMS). As described above, cooperation with the informative object of the present invention can be obtained by using a Web API for enabling reference to home power information. For a user having a photovoltaic power generation system at home, the informative object of the present invention can serve as a display unit that can intuitively indicate a power balance between generation and consumption. The informative object can offer pleasure of generating electricity at home with the photovoltaic power generation system and suggest a better way of using electricity. If a user notifies that the seesaw slightly tilts to the left, i.e., indicates power purchase, the user will be inclined to return the seesaw to neutral or the right by saving power consumption in some way.
A synergistic effect with a conventional terminal can be expected when a user uses a personal computer or a smartphone in order to obtain more specific information from awareness obtained with the informative object of the present invention.
FIG. 9
As illustrated in , a notification of a power saving request from a local power supplier may be issued by using blinking of the sphere. There is a mechanism called demand response in which when serious shortage of a local power supply is expected, a power supplier requests an active power saving to households and companies, and in response to this, offers an incentive in accordance with the amount of achieved power saving. The informative object of the present invention can be expected as a terminal for promoting such activities.
The informative object of the present invention can be used as a health care monitor. With a currently widespread use of wearable terminals, environments that enable constant measurement of various types of information such as a heart rate, a blood pressure, a body temperature, a footstep count, an active mass, and a sleeping hour have become widespread. These types of information are expected to be provided with Web APIs, and thus, cooperation with the informative object of the present invention can be obtained. The informative object of the present invention is useful for knowing health status of a user himself/herself, a family member living in the same household, and a parent living in a remote place. A health status estimated from acquired health information is indicated by a tilt of the seesaw or blinking of the sphere can notify the user of a possible necessity of a diagnosis or a safety confirmation.
The informative object of the present invention can be used as a stock price monitor. Indexes of general economic indicators such as stock prices for each stock and Nikkei average stock prices are provided with Web APIs, and cooperation with the informative object of the present invention can be obtained. Specifically, the tilt of the seesaw allows a user to intuitively know the degree of change in the stock price of a stock the user has, as compared to the acquisition cost, and whether the change is currently in an increasing trend or a decreasing trend, and constantly feel the economic trend in everyday life. In addition, when the stock price of the stock the user has reaches the par, notification of this can be issued by blinking of the sphere.
In other applications, cooperation with the informative object of the present invention can be obtained by using the informative object of the present invention as a daily fortune monitor with a Web API for astrology or a weather forecast monitor with a weather forecast API as long as information provided with Web APIs are used.
In the foregoing examples, only one type of information is expressed at a time. Alternatively, a correlation between two different types of information can be continuously observed in everyday life by expressing individual types of information, e.g., an atmospheric pressure and a health status, by using the tilt angle of the seesaw and the color tone of the sphere. Alternatively, the informative object of the present invention can serve as a current mirror in such a manner that a correlation between the content issued in an SNS and an economic indicator in the Nikkei average stock price, for example.
The present invention is applicable to information display terminals and information service businesses.
Although the invention has been described in terms of exemplary embodiments, it is not limited thereto. It should be appreciated that variations may be made in the described embodiments by persons skilled in the art without departing from the scope of the invention as defined by the following claims. The limitations in the claims are to be interpreted broadly based on the language employed in the claims and not limited to examples described in this specification or during the prosecution of the application, and the examples are to be construed as non-exclusive. For example, in this disclosure, the term “preferably”, “preferred” or the like is non-exclusive and means “preferably”, but not limited to. The use of the terms first, second, etc. do not denote any order or importance, but rather the terms first, second, etc. are used to distinguish one element from another. The term “substantially” and its variations are defined as being largely but not necessarily wholly what is specified as understood by one of ordinary skill in the art. The term “about” or “approximately” as used herein can allow for a degree of variability in a value or range. Moreover, no element or component in this disclosure is intended to be dedicated to the public regardless of whether the element or component is explicitly recited in the following claims.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1
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is a front perspective view of an informative object .
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is a front view of the informative object .
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is a top view of the informative object .
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is a partial cross-sectional view of the informative object .
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is a view illustrating an example in which the seesaw of the informative object tilts.
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illustrates a change of the shape of the informative object .
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illustrates how the informative object refers to external information.
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is a flow chart from information acquisition to movement of the informative object .
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illustrates an example of blinking of a sphere . | |
The amount of carbon stored in terrestrial vegetation is a key component of the global carbon cycle[@R4]. Changes in carbon stored in vegetation biomass have a large impact on the atmospheric CO~2~ concentrations either through sequestering or releasing carbon[@R2]. The urgency to conserve and, where appropriate, enhance the carbon reservoirs of terrestrial vegetation has long been recognized and is reflected in, for example, the inclusion of the land sector in UNFCCC reporting, the program for Reducing Emissions from Deforestation and Forest Degradation (REDD+), and the acknowledgement of biomass stocks as an essential climate variable[@R5]. Hence, monitoring changes in biomass stocks is key for securing progress towards the commitment of halting global warming below 1.5 degrees Celsius.
Although aboveground biomass stocks are straightforward to measure at the site level, their assessment at landscape to global scales is time-consuming, costly and requires extrapolations[@R5]. Remote Sensing is well-established for wall-to-wall mapping of biomass stocks, but the methodological differences between different remote sensing products[@R6]--[@R8] and the scale mismatch to ground data[@R9]--[@R11] hamper their comparability. Consequently, and in spite of efforts to improve observational databases[@R3], biomass stocks and their spatial distribution remain uncertain at the global scale ([Extended Data Figure 1](#F4){ref-type="fig"}). Many global change studies focus on changes in vegetation biomass without quantifying absolute amounts of biomass stocks[@R2],[@R12], which is indispensable for tracing the role of vegetation in the carbon cycle over time but does not allow calculating e.g. restoration potentials. Furthermore, large knowledge gaps remain concerning the impact of various land use activities on biomass stocks[@R1],[@R2],[@R13].
Informed design, implementation, monitoring and verification of land-based climate change mitigation strategies requires comprehensive and systematic stocktaking of the carbon stored in vegetation[@R14]. Beyond accounts of carbon-stock changes, stocktaking also needs to consider (a) the potential and actual biomass stocks of the terrestrial vegetation, (b) the full impact of land use on biomass stocks, i.e. both land cover conversion and land management, and (c) the uncertainty of biomass stock estimates. Here, we compile such information, complementary to current approaches that quantify actual biomass stocks[@R6]--[@R8],[@R15],[@R16] ([Extended Data Figure 2](#F5){ref-type="fig"}).
We present seven global maps of the actual biomass stocks ([Extended Data Figure 3](#F6){ref-type="fig"}), here defined as the terrestrial living aboveground and belowground vegetation biomass measured in grams of carbon, based on remote sensing[@R6]--[@R8] and inventory-derived information[@R15],[@R16]. Ecological literature on biomass stocks of natural zonal vegetation ([Supporting information Tables 1-2](#SD4){ref-type="supplementary-material"}) was combined with state-of-the-art biome maps ([Method](#S1){ref-type="sec"} section), accounting for areas without vegetation, to obtain six reconstructions of potential biomass stocks, defined as biomass stocks that would exist without human disturbance under current environmental conditions ([Methods](#S1){ref-type="sec"} section, [Extended Data Figure 4](#F7){ref-type="fig"}). Because actual and potential biomass stocks both refer to the same environmental conditions, their difference isolates the effect of land use on biomass stocks ([Methods](#S1){ref-type="sec"} section).
Variation within both sets of maps was interpreted as a measure of uncertainty, assuming that the uncertainty is the result of differences between approaches rather than measurement errors within a single approach. From the variation between the seven actual biomass estimates, a detection limit map for stock changes was calculated ([Methods](#S1){ref-type="sec"} section). Permuting potential and actual maps resulted in 42 pairs enabling to quantify the effects of land use on biomass stocks[@R17],[@R18]. Note that landscape level spatial variability in biomass stocks, e.g. due to age class structure, variation in soil fertility and soil water availability, are accounted for differently for the potential and actual biomass stock estimates ([Method](#S1){ref-type="sec"} Section). This could introduce a bias of unknown sign and size when interpreting the fine-scale spatial patterns of the biomass-stock reduction maps.
Two of the actual biomass stock maps ("FRA[@R15]-based" and "Pan[@R16]-based") were established on the basis of a present day land-use dataset ([Methods](#S1){ref-type="sec"} section) and therefore allowed systematically separating the effects of (a) land-cover conversion, i.e. change in the biomass stocks due to conversion of pristine ecosystems into artificial grassland, cropland or infrastructure, and (b) land management, i.e. management-induced changes that occur within unaltered land-cover types such as forests, savannas and other natural grasslands ([Extended Data Figure 2](#F5){ref-type="fig"}).
At the global scale, the biomass stocks of the currently prevailing vegetation amount to a mean of 450 PgC (range of the seven estimates: 380 to 536 PgC, coefficient of variation 11%). In contrast, biomass stocks of potential vegetation amount to a mean of 920 PgC (range of the six estimates: 771 to 1,107 PgC, coefficient of variation 12%). Our analysis thus suggests that land use halves the amount of carbon potentially stored in terrestrial biomass ([Fig. 1](#F1){ref-type="fig"}). Irrespective of the climate zone, the potential-actual difference of biomass largely follows the pattern of global agriculture, with hotspots in South and East Asia, and Europe, as well as the Eastern part of North and South America ([Fig. 1A](#F1){ref-type="fig"}). Considerable differences between potential and actual biomass stocks also occur in regions dominated by forest and natural grassland use ([Extended Data Figure 5a and b](#F8){ref-type="fig"}). Given that biomass stocks are a function of net primary production and turnover time, a 50% reduction of the turnover time[@R18] and a 10% land-use induced decrease in NPP[@R19] explains the reduced biomass stocks.
The 42 pairs of potential-to-actual biomass stock differences show a median of 49%, with the inner quantiles ranging from 43 to 55%, which implies an average impact on biomass stocks of 447 PgC (inner quartiles 375 to 525 PgC; [Fig. 1B](#F1){ref-type="fig"}).
The FRA- and Pan-based approaches allow separating the effects of land-cover conversion and land management ([Fig. 1C](#F1){ref-type="fig"}). Due to land-cover conversion ([Method](#S1){ref-type="sec"} section), actual biomass stocks reach only 10% of potential biomass stocks per unit area ([Fig. 2A](#F2){ref-type="fig"}), affecting only a relatively small area of 28 Mkm^2^. In contrast, on an area of 56 Mkm^2^ of managed but not converted ecosystems, the actual biomass stocks reach 60 to 69% of the potential biomass stock per unit area. In consequence, land-cover conversion (53-58%) and land management (42-47%) contribute almost equally to the overall difference between potential and actual and biomass stocks. Forest management contributes two thirds and grazing one third to the management-induced difference in biomass stocks ([Fig. 1C](#F1){ref-type="fig"} and [2B](#F2){ref-type="fig"}; [Extended Data Table 1](#T1){ref-type="table"}).
The massive impact of land management on vegetation biomass suggests that estimates of historical land-use change emissions are incomplete if only deforestation is considered ([Extended Data Table 2](#T2){ref-type="table"}). Contextualizing our results with accounts of the global terrestrial carbon balance suggests that pre-industrial land use impacts on biomass stocks were considerable (115-425 PgC of the total difference of 375-525 PgC; [Extended Data Table 3](#SD1){ref-type="supplementary-material"}), corroborating model-based findings[@R20]; such larger preindustrial emissions are consistent with recent estimates of the global carbon budget considering strong but uncertain processes of natural sinks such as peat build-up (see [Supporting Information](#SD4){ref-type="supplementary-material"}).
Alternatively \-- or in addition \-- they point to an underestimation of the strength of the current terrestrial carbon sink, as suggested by model-based studies[@R12],[@R13]. In order to reduce the large uncertainty range of current estimates, future research will need to scrutinize the role of land management, in particular in non-forest ecosystems, often ignored in global carbon studies. It is important to note that the difference between potential and actual biomass stocks represents only a rough proxy for cumulative emissions from land use. First, it does not include soil carbon and product pools. Including soil carbon would probably increase the difference, including products would decrease it. Large uncertainties prevail for the two components, but their effects are generally estimated to be small in comparison to biomass changes[@R12],[@R21]. Second, the difference between actual and potential carbon stocks is not identical to stock changes between two points in time. Both actual and potential biomass stocks refer to the same environmental conditions, thus their difference integrates two effects: cumulative land-use emissions and land-use induced reductions in carbon sequestration that would result from environmental changes ([Extended Data Figure 2](#F5){ref-type="fig"}, [Supporting Information](#SD4){ref-type="supplementary-material"}). Therefore, cumulative emissions are probably smaller than the overall impact of land use on biomass stocks, depending on the uncertain[@R13],[@R20] strength of the environmental effect.
The large importance of land management for terrestrial biomass stocks has far reaching consequences for climate-change mitigation. The difference between actual and potential biomass stocks can be interpreted as the upper bound of the carbon sequestration potential of terrestrial vegetation. Long-term changes of growth conditions, e.g. due to large-scale alterations of hydrological conditions or severe soil degradation, could lower this potential. Conversely, climate change could increase the future potential biomass stocks of ecosystems, but this effect is highly uncertain[@R13],[@R22],[@R23]. Managing vegetation carbon so that it reaches its current potential would store the equivalent of 50 years of carbon emissions at the current rate of 9 PgC yr^-1^, but that is not be feasible because it would mean taking all agricultural land out of production. More plausible potentials are much lower ([Extended Data Table 4](#SD2){ref-type="supplementary-material"}); e.g. restoring used forests to 90% of their potential biomass would absorb fossil fuel emissions for 7 to 12 years. However, such strategies would entail severe reductions in annual wood harvest volumes, because optimizing forest harvest reduces forest biomass compared to potential biomass stocks[@R24]. In contrast, widely supported plans to substantially raise the contribution of biomass to raw material and energy supply, e.g. in the context of the so-called bioeconomy[@R25], imply a need for increased harvests[@R24]. From a greenhouse gas perspective, the challenge for land managers is to maintain or increase biomass productivity while at the same time maintaining or even enhancing biomass stocks.
Although the uncertainty ranges of actual and potential biomass stocks are typically around 35% of the median estimate, the estimates rarely overlap across the latitudinal north-south gradient ([Fig. 3A](#F3){ref-type="fig"}). While the potential biomass stock shows a similar uncertainty level across most relevant biomes, uncertainty patterns are noteworthy for the actual biomass stock. Actual biomass stock estimates are particularly uncertain in the tropics, a region that contains about half of today's global biomass stocks ([Figure 1C](#F1){ref-type="fig"}).
The spatial uncertainty patterns are relevant for designing and monitoring of climate-change mitigation efforts such as carbon stock restoration. While industrialized countries have access to much finer and more robust data than those used here, most developing countries have to rely on global data such as those used in this study[@R5],[@R16]. The uncertainty range could be narrowed if a single robust, validated method would be applied continuously in the stocktaking efforts. Indeed, technical facilities for deriving robust estimates of actual biomass stocks will soon become available (e.g. ESA's biomass mission[@R26], NASA's GEDI mission[@R27] as well as integration efforts (<http://globbiomass.org/> ). The current planning, however, suggests that this capacity will not be fully operational before 2023, and until then, restoration planning and monitoring will have to rely on existing global data sets and their present-day uncertainties.
In boreal and temperate forests restoration efforts would be detectable even against the present-day uncertainties. But three quarters of the global restoration potentials are situated in tropical regions ([Fig. 1C](#F1){ref-type="fig"}, [Extended Data Table 4](#SD2){ref-type="supplementary-material"}), where biomass stocks would need to increase by over 750 gC m^-2^ yr^-1^ for 10 consecutive years in order to be detectable against variation between global data. A large threat to biomass stock conservation comes from the use of dry tropical forests and savannas, in particular in Africa where these biomes have been identified as having high potential for increasing global agricultural production, to improve global food security or bioenergy supply[@R28]. Given current detection limits for tropical biomes, both intensified land use in dry tropical forests and savannas as well as restoration efforts in tropical forests are questionable due to the possibility of undetectable carbon debts from land-use intensification[@R29] or unverifiable gains from carbon restoration measures.
Our analysis suggests that land use impacts were significant already in the preindustrial period and reveals that effects of forest management and grazing on vegetation biomass are comparable in magnitude to the effects of deforestation. Hence, a focus on biomass stocks helps recognizing option spaces for land-based GHG mitigation beyond the mere conservation of forest area. Our findings also suggest that important trade-offs in climate-change mitigation are to be tackled. The scientific and political focus on forest protection and productivity increases needs to be complemented by analyses of the interactions between land use and the carbon state of ecosystems.
Methods {#S1}
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We established six datasets for potential biomass stocks and seven datasets for actual biomass stocks,. All maps were constructed at the spatial resolution of five arc minutes. Datasets were chosen based on their coverage (i.e. only maps covering large parts of the globe were included) and their plausibility. Given that most datasets did not cover all land-use types, all regions of the globe, or all relevant biomass stocks, some completion exercises were performed to generate consistently comparable datasets. These relied on different types of evidence such as land-use information, information from census statistics, remotely-sensed information, and modifications of assumptions on biomass stock density of different land-use categories and ecozones. In the following, the construction of the individual maps is described.
Actual biomass stock maps 1 and 2 {#S2}
---------------------------------
(FRA-based and Pan based, [extended Data Figure 3A and B](#F6){ref-type="fig"}) allowed to isolate the effect of individual land-uses. They were based on a consistent land-use dataset, derived and modified from previous work[@R30]. The dataset was adjusted to newly available statistical data on the national extent of forests[@R15] and cropland[@R31]. Information on cropland types [@R32] was used to identify permanent crops, other trees within cropland [@R33] are not included in the cropland layer, complying with FAO definitions[@R31]. Unused land was identified on basis of previous assessments (e.g. delineating unproductive land with a productivity threshold of 20gC/m^-2^yr^-1^)[@R19],[@R30], information on permanent snow from a land cover product[@R34], a thematic footprint map [@R35] and a map on intact forests[@R36]. All land not classified as infrastructure, cropland or forestry was defined as grazing land. Grazing land was split into three layers: (1) Artificial grasslands, i.e. grasslands on potentially forested areas, (2) natural grasslands with trees, including savannahs and other wooded land, and (3) natural grasslands without tress (e.g. temperate steppes), based on land cover information on the extent of land under agricultural management[@R34], biome maps[@R37]--[@R39] and MODIS data[@R40] on fractional tree cover, applying a tree cover of 5% at the resolution of 500m to discern grazing land with and without trees, in fractional cover representation. The final land-use dataset discerns the following classes: *Unused land*: 1. Non-productive and snow, 2. Wilderness, no trees, 3. Unused forests. *Used land*: 4. Infrastructure, 5. Cropland, 6. Used forests, 7. Artificial grassland, 8. Natural grassland, no trees, 9. Natural grassland with trees.
To each land-use unit, typical biomass stock density values from the literature or census statistics were assigned. For forests, the FRA-based map uses national-level data from the global Forest Resource Assessment[@R15]. In contrast, the Pan-based map[@R16] uses data from for forest inventories and site data. The Pan-based estimate is higher particularly in the tropical forests, but slightly lower in boreal forest biomass stocks, resulting in overall higher total forest biomass stocks (361 PgC in contrast to 298 PgC, for forests only). National forest biomass stock data were downscaled to the grid using information on tree height from a global database[@R41], following the finding that tree height is among the critical factors determining biomass stocks and can thus serve as proxy to spatially allocate biomass stock densities at large scales[@R18],[@R42]. Minimum biomass stock density for forests was set to 3 kgC m^-2^ to discern forests from scrub vegetation and other wooded land. For grassland-tree mosaics, no census data on biomass stocks is available. For some countries, data on wood stocking (in m^3^) of other wooded land is available [@R15], showing a range between 0.4% to 21% (inner 50% quartiles) of forest biomass stocks per unit area, with "outliers" \>90%. World region aggregates of biomass stock densities on other wooded land range between 15% and 28% of the values for forests, with a world average of 23%. In order to consider non-woody components, which are of larger importance for other wooded land compared to forests, as well to produce a conservative estimate, we assumed biomass stock per unit area on other wooded land to be 50% of the corresponding values for forests at the national level. For herbaceous vegetation units (artificial grassland on potential forest sites, cropland and natural grassland without trees), we assumed biomass stocks to equal the annual amount of net primary production[@R18]. For permanent cropland, we added 3 kgC m^-2^ for tree-bearing systems and 1.5 kgC m^-2^ for shrub bearing systems to account for woody above- and belowground compartments, in line with estimates in the literature ([Supporting information Table 3](#SD4){ref-type="supplementary-material"}). In the absence of data, and due to the small extent of this land-use type, biomass stocks on infrastructure areas were calculated as one sixth of potential biomass stocks. This assumes one third of infrastructure to be covered by 50% vegetation with trees and 50% artificial grassland (the latter were assigned no additional biomass, as the potential biomass stocks already provide a progressive estimate). Effects of land degradation on natural grassland (with and without trees) were modelled based losses in net primary productivity derived from[@R43].
Actual biomass stock maps 3 and 4 {#S3}
---------------------------------
(Saatchi-based and Baccini-based, [Extended Data Figure 3C, D](#F6){ref-type="fig"}). Two remote-sensing based maps were created by combining independent remote-sensing products for tree vegetation (including foliage) and expanding them to account for below-ground and herbaceous compartments where necessary. At the global scale, five distinct regions can be discerned with regards to the availability of global remote-sensing based products. For the northern boreal and temperate forests one product is available[@R8],[@R44]. A large part of the tropical zone is covered by two datasets [@R6],[@R7]. These two datasets show pronounced differences, among each other as well as in comparison with in-situ data [@R9],[@R10]. A smaller fraction of the tropical zone, including a large part of Australia, South America and South Africa is covered by only one of the remote-sensing datasets [@R6], while a region in China is covered by two datasets[@R6],[@R8]. For some regions (the southernmost part of Australia, parts of Oceania), no remote-sensing data are available. In these regions, map 1 was used in the compilation of map 3 and 4. Map 3 was constructed by a) complementing forest biomass stock data for the temperate and boreal zones[@R8] with data on net primary productivity[@R18] in order to account for herbaceous vegetation, applying a forest-non-forest mask derived from the GLC2000 land cover map[@R34]. The resulting map for the northern forests was b) combined with the biomass stock map for the tropical zone[@R6]. The latter was also extended with data on net primary productivity [@R18] to account for the herbaceous fractions. For map 4, we replaced values for woody vegetation form map 3) with data from Baccini et al.[@R7], where available.
Actual biomass stock maps 5 and 6 {#S4}
---------------------------------
(cell-based minima and maxima of the remote-sensing maps, [Extended Data Figure 3E, F](#F6){ref-type="fig"}). While maps 3 and 4 serve as a best guess available from remote-sensing products these two maps were based on a statistical approach, calculating the cell-based minima and maxima of various remote-sensing input data, allowing for an assessment of the absolute upper and lower boundaries, breaking up auto-correlated nature of remote-sensing derived maps. Maps 3 and 4 were used as input. Furthermore, a modulation was calculated for the area covered only by the map of Thurner et al. [@R8]. This map uses a forest mask derived from GLC2000 [@R34]. In order to reflect the uncertainty of this land cover map, we used an alternative forest mask to calculate new values at the grid level. We projected the grid-based biomass stock density values from Thurner et al. [@R8] to the MODIS fractional tree cover dataset [@R40]. Additionally, alternative maps for net primary productivity were used to complement these biomass stock map for woody vegetation, derived by a vegetation model[@R45], a numerical model [@R46], and from remote-sensing data[@R47]. Map 5 was calculated as the cell-based minima, map 6 as the cell-based maxima of these input layers.
Actual biomass stock map 7 {#S5}
--------------------------
(Ruesch and Gibbs, [Extended Data Figure 3G](#F6){ref-type="fig"}). A seventh map was taken from the literature[@R48].
No robust empirical information is available that would allow to resolve the discrepancies between the two datasets based on consistent, spatially explicit land-use information (maps 1 and 2). The difference between these two estimates amounts to 79 PgC. Both assessments are inventory-based, but Pan et al.[@R16] use long-term measurements of network plots for the tropical regions to compensate for data gaps, while FRA reports national data which are often based on remote sensing. The contribution of global remote sensing data ("bench-mark maps") to resolve this discrepancy is still limited. The two available high-resolution datasets covering the tropics[@R6],[@R7] show pronounced differences, between each other and in comparison with in-situ data [@R9],[@R10]. The Pan-based estimate is situated between these two estimates, while the FRA is situated below the minimum. However, a study based on alternative site data[@R49] corrected both maps downwards, close to the grid-based minimum of both accounts, better matching the FRA-based assessment.
Potential biomass stock maps {#S6}
----------------------------
Potential vegetation refers to a hypothetical state of vegetation which would prevail without human activities but under current climate conditions[@R50]. We compiled five maps following an ecozone approach, allocating typical carbon densities of zonal vegetation to state-of-the art ecozone maps for current climate conditions[@R37]--[@R39], with current coastlines and current permanent ice cover. The carbon density values refer to landscape-level averages and take effects of age distribution, natural disturbance into account. We used high-resolution data[@R51] to exclude small water bodies and small-scale bare areas, with the exception of ecosystems where carbon stock values take bare areas already into account, e.g. steppes and thorn savannas. Small-scale variability caused by e.g. the spatial variability of edaphic conditions or water availability (azonal vegetation) was neglected. No information is available that allows to determine if this omission, or sampling biases in the input data, introduces an upward or downward bias in the maps. Input data could be biased towards high values if sampling favoured undisturbed, old-grown stands, or towards lower values, if the data were derived from human-disturbed vegetation in the absence of natural vegetation remnants for certain ecosystem types. The comparison with other estimates shows that our data are well in line with the literature ([Extended Data Figure 1](#F4){ref-type="fig"}) and suggest such biases to play a minor role. Furthermore, approximations of upper and lower estimates for potential vegetation were calculated to determine realistic ranges of global biomass stocks.
Potential biomass stock maps 1 and 2 {#S7}
------------------------------------
(IPCC-based, FRA adjusted; IPCC-based, Pan adjusted, [Extended Data Figure 4A, B](#F7){ref-type="fig"}). Two maps were constructed to consistently match the actual biomass stock maps 1 and 2. They build upon best-available estimates on potential, landscape average biomass stock densities for zonal vegetation, mainly from IPCC values[@R52], with the exception of boreal forests. Here, due to large uncertainties[@R42],[@R53],[@R54], the maximum values of biome-wide actual biomass stocks per unit area between 1990 and 2007[@R16] were used to derive a conservative estimate. Map 1 was subsequently adjusted at the grid-level so that potential biomass stock values below actual biomass stock levels matched the actual biomass stocks in the FRA-based map. For map 2, this adjustment was done with the Pan-based map.
Potential biomass stock maps 3 and 4 {#S8}
------------------------------------
("classic data", cell-based minima and maxima, [Extended Data Figure 4C, D](#F7){ref-type="fig"}). Two further maps were calculated by using biomass stock density values [@R3],[@R38],[@R55] for natural, zonal vegetation, from synthesis efforts of site-specific data e.g. from the International Biological Programme e.g. [@R56]. Similar to maps 1 and 2, these values were allocated to the three biome maps[@R37]--[@R39], and the cell-based minima (map 3) and maxima (map 4) of all three maps were calculated.
Potential biomass stock map 5 {#S9}
-----------------------------
(remote-sensing based, [Extended Data Figure 4E](#F7){ref-type="fig"}). A fifth map was derived from the remote-sensing maps 3 and 4 on actual biomass stocks. For all 1303 ecozones that result from the intersection of the three biomes maps[@R37]--[@R39] mentioned above (see [Extended Data Figure 5E](#F8){ref-type="fig"}), the 95 percentile biomass stock values of all 30 arc second grid cells (1 x 1 km at the equator) within one ecozone, excluding agricultural lands, derived from the GLC2000 [@R34], was calculated. For ecozones covered by more than one remote sensing map, we used the arithmetic mean. This approximation builds upon the assumption that that in each ecozone, areas of natural vegetation units remain which are representative for the respective ecozone's potential biomass stock densities and that the values take natural disturbance into account (owing to the grain size of the input maps and selection procedure). This is confirmed by a cross-check that revealed the 95 percentile to be on average 51% lower than the maxima values found in each ecozone. Using maxima values, the global biomass would be 1.56 times larger than the one estimated here. An upper bias in this map could emerge from the neglect of naturally unfavourable sites within an ecozone (due to e.g. low water availability or soil fertility); a lower bias could emerge if in an ecozone only disturbed vegetation units prevail, or most of the favourable sites are converted.
Potential biomass stock map 6 {#S10}
-----------------------------
(West et al., [Extended Data Figure 4F](#F7){ref-type="fig"}). An independent sixth map was taken from the literature[@R57].
Calculation of the land-use induced potential-actual biomass stock difference {#S11}
-----------------------------------------------------------------------------
In order to assess the range of the effect of land use on biomass stocks, 42 potential-actual biomass stock difference maps were calculated by combining the seven actual biomass stock maps with the six potential biomass stock maps. In all cases, we adjusted the maps so that the actual biomass stocks would not surpass the potential biomass stocks where necessary. Increases of actual over potential biomass stocks could be caused, for instance, by fire prevention. However, the magnitude of this effect is highly uncertain at larger spatial scales, because fire prevention often leads to less frequent, but more damaging fires with larger biomass loads that could compensate for carbon gains[@R58],[@R59] on longer time scales. On unused land (e.g. wilderness), no land-use induced biomass stock reduction was assumed. Unproductive and water areas were excluded from the assessment. Differences in the spatial thematic resolution of potential and actual biomass stock maps warrant a caveat when interpreting the fine-scale results of the biomass stock difference.
Attribution to land management and land-cover conversions {#S12}
---------------------------------------------------------
From the seven actual biomass stock maps, only two allow to consistently isolate and quantify the impact of individual land-use types on biomass-stocks and thus for approximating the impacts of land-cover conversion versus land management ([Extended Data Figure 2](#F5){ref-type="fig"}), i.e. the maps based on consistent, detailed land-use information (FRA-based and Pan-based actual biomass stock maps). From these maps, land-cover conversion impacts are calculated as the sum of potential-actual biomass stock differences due to cropland, artificial grassland (i.e. grassland on potential forest sites) and infrastructure. The biomass-stock differences of all other land-use types were accounted for as the impact of land management. Forest management was considered to dominate land-management effects in forests, and land management practices on other used lands were subsumed as grazing. This approach represents a proxy only. A sharp and unambiguous separation between land-cover conversion and land management would require information on past land uses, which currently is not available, as well as arbitrary decisions on thresholds of change. Examples to illustrate these intricacies are: The biomass stock change on a parcel of land that was cleared from pristine forests to cropland in the past and, after cropland abandonment, is used as forest plantation, would be accounted for as land management, while it would -- at least to a certain degree -- also represent land-cover conversion if historic uses were to be considered. Similarly, if a forest clear-cut area is used for grazing during the re-growth phase, the biomass stock difference would be attributed to land-conversion, while it might also represent land management. If, due to land use, a forest is changed in terms of its species composition, crown closure, stem height etc. but still remains within key forest parameters (e.g. \>10% tree cover, stem height \>5m), it is eventually an arbitrary decision if such a change is a land-cover conversion or land management. Additionally, the effects of forest management versus grazing cannot fully be disentangled because of practices such as forest grazing and fuelwood extraction in natural grasslands. Given these practical and theoretical ambiguities, we argue that the simple allocation scheme adopted here is a useful proxy based on transparent considerations, making best use of the available datasets. For preparation of [Fig. 1C](#F1){ref-type="fig"} and [2B](#F2){ref-type="fig"}, we calculated the contributions of land management and conversions separately for the FRA- and Pan-based maps. The minima of the contribution of each land-use type were used for the attribution. The difference of the sum of all minima to 100% was labeled as "ambiguous", as it is attributed to land management in the one and land-cover conversion in the other map (See [Extended Data Table 1](#T1){ref-type="table"}).
Calculation of the detection limits based on the actual biomass stock maps {#S13}
--------------------------------------------------------------------------
The spatially explicit detection limit for stock changes in actual biomass was estimated from the variation between the seven actual biomass estimates. This assumes that the uncertainty is driven by differences between approaches rather than measurement errors within a single approach and that the seven estimates of the actual biomass stocks are equally likely and, hence, the main source of uncertainty. For each grid cell we mimicked a stocktaking at present (t) and after 10 years (t+10) by randomly selecting two biomass stocks from the uncertainty between approaches for that cell. Subsequently, the detected annual change in biomass stock was calculated. A distribution of 1,000 detected annual changes was obtained through resampling. Given that the annual changes were calculated by sampling the same distribution at *t* and *t+10*, there was no underlying changes in biomass stock. The inner 95% of the detected stock changes within each grid cell were assumed to be insignificant. The 5% stock changes that were found to be significant despite the biomass stock being constant between t and t+10, were used as an estimate for the detection limit in that grid cell. Given present day uncertainties, a real stock change should thus exceed the detection limit to be correctly classified as a change. At present, evidence is missing to consider one approach as being more precise and accurate than the other approaches[@R9],[@R10],[@R60]. Nevertheless, if future advances would enable selecting a single best approach, the uncertainty and detection limit would decrease and in turn enhance the capacity for verification of changes in biomass stocks.
Data availability {#S14}
-----------------
The data sources for actual and potential biomass stock estimates are listed above. Source data for [Fig1B and C](#F1){ref-type="fig"}, [Fig2 A and B](#F2){ref-type="fig"}, [Fig3A and B](#F3){ref-type="fig"}, and [Extended Data Figure 1](#F4){ref-type="fig"} are provided with the paper. Final results, data and maps will be made available at [http://www.uni-klu.ac.at/socec](https://www.aau.at/soziale-oekologie/). Underlying data, for example, data from other sources, which support findings of this study, are available from the corresponding author upon request.
Code availability {#S15}
-----------------
Esri ArcGis and Matlab codes used in the compilation and analysis of results are available upon request from the corresponding author.
Extended Data {#S16}
=============
![Estimates on potential (A) and actual (B) biomass stocks from the literature and this study.\
Sources: Bazilevich et al., 1971[@R61], Pan et al., 2013[@R62], Prentice et al., 2011[@R63], West et al., 2010[@R57], Hurtt et al., 2011[@R64], Whittaker and Likens, 1975[@R65], Post et al., 1997[@R66], Esser, 1987[@R67], Roy-Saugier-Mooney, 2001[@R3], Potter, 1999[@R68], Ajtay et al., 1979[@R55], Hall and Scurlock, 1993[@R69], Olson et al., 1983[@R70], Ruesch & Gibbs, 2008[@R48], Amthor et al., 1998[@R71], Watson et al., 2000[@R72]. The darker shaded columns are those used in this study (for details see text).](emss-74956-f004){#F4}
{ref-type="supplementary-material"}. B. Conceptual attribution of the difference between potential and actual biomass stocks to land conversion and land management. Error bars reflect the divergence among datasets for the respective vegetation types and indicate the determination of verification volumes.](emss-74956-f005){#F5}
![Actual biomass stock maps used in the study.\
Unproductive areas have been clipped from all maps. A) FRA-based, B) Pan-based, C) Saatchi-based, D) Baccini-based, E) Remote-sensing derived minimum, F) Remote sensing derived maximum, G) Ruesch & Gibbs 2008[@R48]. For details and sources for maps A-F, see [Method](#S1){ref-type="sec"} section.](emss-74956-f006){#F6}
![Potential biomass stock maps used in the study.\
Unproductive areas have been clipped from all maps. A) IPCC-based, FRA adjusted, B) IPCC-based, Pan-adjusted, C) Cell-based minima of "classic data", D) Cell-based maxima of "classic data", E) Remote sensing derived, F) West et al. 2010[@R57]. For details and sources for maps A-E, see [Method](#S1){ref-type="sec"} section.](emss-74956-f007){#F7}
![Land-use induced difference in potential and actual biomass stocks, uncertainty of input data and vegetation units used in the study.\
A) Impact of land-cover conversion, B) impact of land management. A) and B) maps are based on the FRA-based actual biomass stock map and the corresponding, IPCC-based FRA-adjusted potential carbon stock map. C) Standard deviation of potential biomass stocks maps (n=6), D) Standard deviation of actual biomass stock maps (n=7). E) Intersect of all three[@R37]--[@R39] biome maps used in the ecozone approaches and for the construction of the RS-based potential biomass stock map. F) FAO Ecozones[@R37] used for the aggregation of results. The "tropical core" consists of humid rainforests. The tropical zones contains moist deciduous forests, dry forests, and tropical shrubs.](emss-74956-f008){#F8}
###### Biomass stocks per land-use types; ranges indicate the difference between the FRA-based and Pan-based estimate.
Area Potential Actual Biomass Stocks Difference Contribution to difference
--------------------------------------------- ------------ --------------- ----------------------- --------------- ---------------------------- -------------- --------------
**Total** **130.4** **876-906** **6.7-6.9** **407-476** **3.1-3.6** **48-54%** **100%**
***Infrastructure*** ***1.4*** ***12*** 8.6-8.7 ***1*** ***0.7*** ***92-93%*** ***2-3%***
***Cropland*** ***15.2*** ***139-141*** ***9.2-9.3*** ***10*** ***0.6*** ***93%*** ***28-31%***
***Grassland and grazing land*** ***54.3*** ***374-379*** ***6.9-7.0*** ***119-121*** ***2.2*** ***69-70%*** ***54-60%***
***Forests*** ***40.7*** ***443-460*** ***10.9-11.5*** ***297-368*** ***7.3-9.0*** ***22-33%*** ***23-31%***
***Unused non-forest land*** ***26.2*** ***16-17*** ***0.6*** ***16-17*** ***0.6*** ***0%*** ***0%***
**Land cover change (LCC)**
Cropland 15.2 139-141 9.2-9.3 10 0.6 93% 28-31%
Artificial grasslands 11.3 114-116 10.1-10.3 7 0.6 94% 23-25%
Infrastructure 1.4 12 8.6-8.7 1 0.7 92-93% 2-3%
**Land management (LM): forest management**
Used forests
tropical 22.3 311-327 14.0-14.7 192-251 8.6-11.3 23-38% 18-25%
temperate 5.4 51 9.3-9.4 33-35 6.1-6.4 32-34% 4%
boreal 7.0 40-41 5.7-5.8 30-32 4.2-4.6 21-25% 2%
*Subtotal forest management* *34.7* *401-419* *11.6-12.1* *255-318* *7.3-9.2* *24-36%* *23-31%*
**Land management (LM): grazing**
Otherwooded land, grasslands-tree mosaics
tropical 14.6 109-110 7.5 47 3.2 57% 13-15%
temperate 4.0 11 2.8-2.9 5-6 1.2-1.4 50-58% 1-2%
boreal 2.9 10 3.4-3.5 5 1.5-1.7 51-56% 1%
Natural grassland w/o trees 14.2 21 1.5 19 1.3 11-13% 0-1%
*Subtotal grazing land* *35.7* *151-153* *4.2-4.3* *75-76* *2.1* *5* *0-51%* *16-18%*
**No biomass stock change**
Wilderness, productive, w/o trees 9.7 16-17 1.6-1.7 16-17 1.6-1.7 0% 0%
Unused forests 6.0 42-50 7.0-8.3 42-50 7.0-8.3 0% 0%
Unproductive area 16.5 \- \- \- \- 0% 0%
**Land cover change (LCC)** **27.8** **265-269** **9.5-9.7** **17.1** **0.6** **94%** **53-58%**
**Land management (LM)** **56.2** **553-572** **7.9-8.1** **312-374** **4.7-5.6** **31-40%** **42-47%**
###### Compilation of published estimates of emissions associated with anthropogenic land-cover change and land management in totals until present (industrial and preindustrial).
Note that most model-based results include fluxes from soils and wood products. \*Pre-industrial emissions only
Reference Land management activities considered Cumulative emissions
--------------------------------------------------- ------------------------------------------ ----------------------
**Total cumulative emissions from land use**
DeFries et al., 1999 [@R96] ***\--*** 182-199
Strassmann et al., 2008 [@R97] ***\--*** 233
Olofsson and Hickler, 2008 [@R98] ***\--*** 194-262
Pongratz et al., 2009 [@R83] ***\--*** 230
Kaplan et al., 2010, Hyde 3.1 based\* ***\--*** 137-189
Kaplan et al., 2010, KK10 based\* Land-use intensity, shifting cultivation 325-375
Stocker et al., 2014 [@R99] Wood harvest, shifting cultivation 243
***This study, FRA- and Pan-based*** ***Top-down, all activities*** ***431-469***
***This study, inner quartiles of 42 estimates*** ***Top-down, all activities*** ***375-525***
Supplementary Material {#SM}
======================
**Supplementary Information** is linked to the online version of the paper at [www.nature.com/nature](https://www.nature.com/nature/).
###### Comparison of the difference between potential and actual biomass stocks to components of the global carbon balance, including LUC emissions and net terrestrial biosphere sink.
Bold figures refer to results of this study, all others represent independent estimates. The difference in biomass stock of 447 PgC (375-525) is well in line with estimates of total (before and since 1800) cumulative emissions from LUC. For details and discussion, see [Supporting Information](#SD4){ref-type="supplementary-material"}.
###### Hypothetic absorption potentials of carbon stock restorations and indicative years until saturation at a current emission level of 9 PgC yr^-1^.
Note that a restoration to 100% of the potential probably entails a cessation of the respective land use, due to the intrinsic relations of harvest and carbon stocks[@R25]. \*Years until saturation at current C-emissions of 9 PgC/yr
Funding from the European Research Council (ERC-2010-stg-263522 "LUISE"), the European Commission (H2020-EO-2014-640176 "BACI"), the German Research Foundation's Emmy Noether Program (PO 1751/1-1), ESA's GlobBiomass project (4000113100/14/I-NB), the Amsterdam Academic Alliance (AAA) and the Vetenskapsrådet grant 621-2014-4266 of the Swedish Research Council are gratefully acknowledged. We thank P.C. West for providing data layers of a potential biomass map. K.H.-E. is grateful for the support by K.Kowalski. This research contributes to the Global Land Programme ( <https://glp.earth/> ).
**Author Contributions** K.-H.E., T.K., C.P., S.L. designed the study and performed the research, A.L.B., N.C., T.F., S.G., H.H., C.L., M.N., M.T. and J. P. contributed and analyzed data and results, all authors contributed significantly to the analysis, interpretation of results and writing of the manuscript.
**Author Information** Reprints and permissions information is available at [www.nature.com/reprints](http://www.nature.com/reprints/index.html).
The authors declare no competing financial interest.
{ref-type="fig"}), and role of land-cover conversion and management in explaining their difference. Whiskers indicate the range of the estimates for potential (grey; n=6) and actual (black; n=7) biomass stocks.](emss-74956-f001){#F1}
{ref-type="table"}).](emss-74956-f002){#F2}
{ref-type="fig"}. The diagonal line indicates the 1:1 relationship where actual and potential biomass stocks are equal. **C.** Detection limit of annual changes in actual biomass stocks. Changes in biomass stocks need to exceed the detection limit in order to be detectable, e.g. in monitoring or stocktaking efforts such as foreseen in the Paris Agreement.](emss-74956-f003){#F3}
| |
Q:
Greedy Algorithm Implementation
You know who knows who among n people that you would like to have come to a party. Assume "knows" is symmetric: If I know you, you know me. You make further requirements that you want each person to have at least 5 new people to meet at the party, and also, so nobody feels too isolated, each person should already know at least 5 people at the party. Your original list may not satisfy these extra two conditions, so you may need to eliminate some people from the invitation list (or maybe you cannot have a party at all with these restrictions). Find a largest possible subset of the n people that you could invite and satisfy the the other two requirements. For the basic problem, find an O(n^3) algorithm and explain its order and its logic.
I ask not for the answer, but for guidance on where to start.
A:
Sounds like a good place to apply a graph algorithm.
Form a graph of people, G. For n people there will be n nodes in the graph. Link nodes i and j if person i knows person j.
Let the first iteration of G be called G_0. Obtain G_1 by making a pass through G and eliminate any person who knows too many or too few people. (That is, eliminate person i if the number of links to i is < 5 or > n-5.)
Repeat the process, obtaining G_2, G_3 up to a maximum of n (or so) iterations, obtaining G_n. The people remaining in this graph are the people you should invite.
Each of the n passes requires a check of n people against n other people, so the algorithm is O(n^3).
MATLAB code to accomplish this (you didn't ask for it, but I thought it was interesting and wrote it anyway):
% number of people on original list
N = 10
% number of connections to (attempt) to generate
% may include self-links (i,i) or duplicates
M = 40
% threshold for "too few" friends
p = 3
% threshold for "too many" friends
q = 3
% Generate connections at random
G = zeros(N);
for k = 1:M
i = randi(N);
j = randi(N);
G(i,j) = 1;
G(j,i) = 1;
end
% define people to not be their own friends
for i = 1:N
G(i,i) = 0;
end
% make a copy for future comparison to final G
G_orig = G
% '1' means invited, '0' means not invited
invited = ones(1,N);
% make N passes over graph
for k = 1:N
% number of people still on the candidate list
n = sum(invited);
% inspect the i'th person
for i = 1:N
people_known = sum(G(i,:));
if invited(i) == 1 && ((people_known < p) || (people_known > n-q))
fprintf('Person %i was eliminated. (He knew %i of the %i invitees.)\n',i,people_known,n);
invited(i) = 0;
G(i,:) = zeros(1,N);
G(:,i) = zeros(1,N);
end
end
end
fprintf('\n\nFinal connection graph')
G
disp 'People to invite:'
invited
disp 'Total invitees:'
n
Sample output (10 people, 40 connections, must know at least 3 people, must not know at least 3 people)
G_orig =
0 0 1 1 0 0 0 0 1 0
0 0 0 0 0 1 0 0 0 1
1 0 0 1 1 1 0 0 0 1
1 0 1 0 0 1 0 1 1 0
0 0 1 0 0 0 1 0 1 1
0 1 1 1 0 0 0 1 0 1
0 0 0 0 1 0 0 0 1 0
0 0 0 1 0 1 0 0 0 1
1 0 0 1 1 0 1 0 0 1
0 1 1 0 1 1 0 1 1 0
Person 2 was eliminated. (He knew 2 of the 10 invitees.)
Person 7 was eliminated. (He knew 2 of the 10 invitees.)
Final connection graph
G =
0 0 1 1 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0
1 0 0 1 1 1 0 0 0 1
1 0 1 0 0 1 0 1 1 0
0 0 1 0 0 0 0 0 1 1
0 0 1 1 0 0 0 1 0 1
0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 1 0 0 0 1
1 0 0 1 1 0 0 0 0 1
0 0 1 0 1 1 0 1 1 0
People to invite:
invited =
1 0 1 1 1 1 0 1 1 1
Total invitees:
n =
8
| |
A meta-analysis of clinical improvements of general well-being by a standardized Lycium barbarum.
Four randomized, blind, placebo-controlled clinical trials were pooled to study the general effects of oral consumption of Lycium barbarum at 120 mL/day, as a standardized juice, GoChi(®) (FreeLife International, Phoenix, AZ, USA). A questionnaire consisting of symptoms graded 0-5 was given to the participants. For each question, the score changes in the questionnaire between pre- and postintervention were summarized by the standardized mean difference and associated SE to perform the meta-analysis. The change was also characterized into a binary outcome, improved or not, to derive odds ratio (OR) and associated SE derived by a binary outcome using the Mantel-Haenszel method. The meta-analysis and heterogeneity were evaluated with the R program using the rmeta package. Statistical significance was set at 5%. In total, 161 participants (18-72 years old) were included in the meta-analysis. Compared with the placebo group (n=80), the active group (n=81) showed significant improvements in weakness, stress, mental acuity, ease of awakening, shortness of breath, focus on activity, sleep quality, daydreaming, and overall feelings of health and well-being under a random effects model. A fixed effects model showed additional improvements in fatigue, depression, circulation, and calmness. The OR indicated significantly higher chance to improve fatigue, dizziness, and sleep quality. Three studies had statistically significant heterogeneity in procrastination, shoulder stiffness, energy, and calmness. The present meta-analysis confirmed the various health effects of L. barbarum polysaccharides-standardized L. barbarum intake found in the previous randomized, double-blind, placebo-controlled human clinical trials and revealed it resulted in statistically significant improvements in neurological/psychological performance and overall feelings of health and well-being compared with the placebo group under both the fixed and the random effects models of the R program.
| |
We often emphasise the importance of effective due diligence before entering any outsourcing contract – in our work with clients and their strategic partners, and in our articles about optimising those relationships. As we all know, appropriate pre-contractual due diligence helps us to determine what governance framework to put in place to minimise relationship and performance risks while maximising value. However, what is often ignored is the fundamental role that a well-resourced Intelligent Client Function (ICF) team can play in the process.
Equally important to the initial due diligence work that you carry out, are the series of steps you would be advised to take to ensure you are able to maintain your due diligence – and that the information used as the basis of your strategic relationship remains up to date and pertinent. A significant contributor to the success of such a task is giving your ICF team the priority, resources, financing and accountability to take on the challenge.
There are many ways in which your ICF team can drive maximum value in your strategic service delivery relationships. Our experience in helping clients and getting hundreds of these relationships back on track from challenging beginnings, provides us with insight and evidence of key areas to help you shape ‘what good looks like’ to avoid issues in the first instance. Six of the key steps are here:
1: Prioritise clarity of purpose and communication
We cannot emphasise strongly enough just how important clarity of business outcomes and objectives are to an outsourcing relationship. It’s the strong (we would say ‘entire’) foundation that your strategic partnership is based upon. From the outset your ICF team should be working with the senior management team to ensure that all business outcomes and objectives are clearly quantified, instructions are well researched and key milestones clarified.
It is also crucial that all communications between vendor and client are as transparent and crystal clear as possible. This is partially achieved through evidenced expectations, clear and appropriate language and reliable technologies for keeping lines of communication open. Unless you are committed to building a partnership based on absolutely clear, mutually agreed terms and expectations between departments, contractors and subcontractors on a project, you will be doing those who rely on the success of your relationship a huge disservice.
2: Dig deep to truly assess the financial health of those you aim to work with
Being assured that your provider can withstand most reasonable hurdles that the economy throws at it does more than give you peace of mind. It affords you an outlook geared towards opportunity capitalisation instead of worst case scenario-based contingency planning.
It is important to not only do an initial deep dive financial health check into your prospective partner, but keep that process of financial diligence ongoing by doing a check at least every six months. The financial stability of prospective (and existing) strategic partners will help to minimise the risk of future upsets having a knock-on effect on the services or solutions that they supply to you or in your name.
Such an analysis will inevitably utilise third-party services. But it is also important that you get up close and personal with your would-be partners as well, using your internal teams, most important among them your ICF team, to assess their longer-term financial prospects and any key survival reliance they have on your own contract with them.
This diligence will include published accounts auditing to determine how well they have fared over the past few years and where they are headed, as well as conferring with former customers and employees of theirs to gather independent viewpoints. Therefore, it is essential that your ICF team has the talent and time to conduct such an assessment, to understand the implications of the data gathered, and to report on this to decision-makers.
3: Review and reshape the outsourcing contract at least every six months
Healthy strategic relationships are not static, nor should the contracts underpinning them be. Often considered finite documents to be negotiated at length at the outset of a project then filed away in a dusty basement unless legal issues ensue, contracts should be recognised as the relationship tools they should have been designed to be, although often aren’t.
Written contracts should be designed to drive behaviours between both parties to achieve business outcomes in an innovative, profitable and ongoing ‘maximum value to the client‘ manner, rather than just one party beating up the other when an obligation hasn’t been fulfilled. Don’t get me wrong, accountability is a key area of mutual relationships and obligations must be fulfilled – but it shouldn’t be the focus of the entire written contract. A ‘defensive’ contract will drive ‘defensive’ behaviour between all parties to the contract.
A contract that is able to adapt to the needs of the client’s business/organisation, has the ability to respond to disruptive external forces, and see that relationship objectives are met even when realignment is necessary, is paramount.
Therefore, it is always advisable to build a biannual review and reshaping process into every written contractual agreement, which will enable you to regularly assess whether the partnership is fulfilling its purpose and to identify opportunities to adapt or enhance business/organisational value and performance.
Such a review process is essential for spotting and addressing issues, redirecting resources and expectations during the term so little tweaks are actioned to avoid a bigger issue further down the line. Your ICF team is fundamental to this driving maximum value process.
4: Future-proof your technology and data from potential digital threats
Cyber threats are very real, and the sophistication with which those who wish to extract, destroy or corrupt your data and technologies is ever increasing. From Trojans, viruses and hacking to stealthy spyware, securing data has traditionally been a case of reactive protection – scanning for malicious activity that sneaks past your firewall and quarantining it.
Nowadays, reactive protection is not enough, as hackers use increasingly effective methods of compromising systems so that discovery of the attack means you’ve caught it too late. Such methods include a man-in-the-middle (MitM) attack, where an attacker eavesdrops on or alters an ostensibly secure communication between you and your service provider, or a distributed denial-of-service (DDoS) attack, which can shut down your entire network by flooding it with more connections than it can handle.
These threats, along with the fact that it only takes one partner to be compromised for both sides to be potentially harmed, necessitates a robust security system capable of dealing with present threats while evolving to fight new ones. And, just as critically, this comprehensive approach to cyber security should be shared with your strategic partner and needs to form part of any agreement between you.
Before a project has begun, you should be confident that your outsourcing partner is capable of protecting the data you share with them, and has an effective cyber defence strategy in place, so your ICF team is able to ensure that your confidential data continues to be protected.
5: Know who you are working with, and who they are working with
Current and predictable future quality of service is important; therefore, to understand how your relationship may morph and change over time it’s important to understand those you are working with.
Your ICF team is tasked with getting to understand the motivations, actions and future challenges faced by your strategic partners, but their role does not and should not stop there, as it’s important to appreciate all the factors that could affect service quality, and that includes subcontractors as well.
This means knowing how subcontractors are chosen, what mechanisms are in place to ensure their continued productivity levels, and so on. While it is not (or should not be) your role to force your strategic partner to use your choice of subcontractors, your ICF team needs to be comfortable with the method and due diligence process your partner undertakes to select their subcontractors. It’s important to understand that your strategic partner’s process for flexibility and reshaping with you directly, also extends out to their subcontractors.
One major and impactful change could be an organisational acquisition, or sale. If you start to notice that key people are being diverted away from your relationship, if communication becomes less frequent or strained, and if innovation opportunities are being missed then this could be an indication that your vendor/contractor is distracted.
Poorly handled acquisitions, sales, or other internal turmoil, have the potential to derail an outsourcing partnership, and clients should take the possibility of these hazards into consideration, and strive to remain vigilant to their potential so that adequate responses can be actioned. If your ICF team keep their ear to the ground through their strong relationships with your strategic partner, you should have a good ‘heads-up’ on any issues heading your way.
6: Pay attention to reputation and determine your relationship’s reputational risk
Research suggests that as much as 75% of a company’s value is based on reputation, and yet when surveyed, 84% of executives admitted that ultimate responsibility for managing reputational risk lies with the CEO rather than a dedicated marketing or communications team or individual. While the rationale is understandable – how an organisation wishes to be perceived by the public ought to come down to senior management’s vision – recent high-profile cases of ‘reputational risk victims’ show that public perception is more important now than ever, and managing it should be the responsibility of a professional in that field.
Knowing a potential supplier’s reputation is paramount to avoiding needless public headaches down the line, while at the same time highlighting areas where extra vendor scrutiny may be required. Conversely, it also highlights their strengths and positive attributes, such as a reputation for high ethical standards, all of which can reflect positively on your organisation in the same way that a poor reputation can reflect negatively.
As part of their remit, your ICF team will usually have on their radar to be continually assessing your partner’s reputational risk – and this takes it a step further, by allowing them to determine how vulnerable your provider is to anything that can damage their and your reputation.
We might not be able to predict the future, but understanding your vendor’s reputation and reputational risks ensures that both of you are prepared for even the most destabilising threats.
In conclusion
There is no excuse for your ICF team to not be aware of the above issues; the six aforementioned steps are a useful starting point, but as good as they are, if your team is unable to execute them because of a lack of resources and/or time, then you run the risk of continued poor performance and additional costs.
Even the most thorough pre-contract due diligence cannot serve you as well as a well-maintained relationship, one in which your ICF team constantly monitor your risks and opportunities, adapting your relationship to minimise the former and maximise the latter to drive better value and performance. | https://www.bestpracticegroup.com/6-due-diligence-exercises-for-your-icf-team/ |
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Minister Al-Fares at Summit hosted by UAE
KUWAIT CITY, June 17, (KUNA): Minister of Oil and Minister of Higher Education Dr. Muhammad Al-Fares said Thursday that Kuwait is making great efforts in building a knowledge-based economy through four pillars: education, innovation, governance, and infrastructure development and information and communication technologies. This came in a speech by Minister Al-Fares during his participation in the second Islamic Summit on Science and Technology organized by the United Arab Emirates via video communication technology. Al-Fares indicated that the Kuwaiti Cabinet recently formed a government universities council with the aim of upgrading the education system, developing the performance of university education and establishing more public universities. He pointed out that the State has allocated 6 million square meters for the establishment of Sabah Al-Salem University in Al-Shaddiyah, adding that work is also underway to establish Abdullah Al-Salem University. He pointed out that many scientific institutions in the country, led by the Kuwait Institute for Scientific Research, the Kuwait Foundation for the Advancement of Sciences and the Public Authority for Applied Education and Training, have developed strategic plans that are compatible with the State’s development plan ‘New Kuwait 2035’.
He explained that these scientific institutions contribute to the development of human capabilities and the consolidation of the values of creativity and innovation, noting that the Kuwait Foundation for the Advancement of Sciences has established the Sabah Al-Ahmad Center for Giftedness and Creativity, which is interested in discovering and nurturing creators and helping inventors develop their ideas and register patents for their inventions, as the center was able to register more than 400 patents. Al-Fares stated that Kuwait has a luminous experience in benefiting from the results of scientific research through applied research projects implemented by the Kuwait Institute for Scientific Research, which depends mainly on conducting scientific studies and research for the benefit of national and regional bodies and institutions. He stated that Kuwait is implementing an ambitious plan to benefit from renewable energy in the production of electricity and water, adding that recent years have witnessed the opening of the Shaqaya Renewable Energy Complex, which produces 70 megawatts of electricity from three stations.
Al-Fares said that there are many projects that the State is working on in order to reach its production of renewable energy to 15% of the total energy in 2030. He pointed out that these projects will contribute to achieving financial savings of 2.46 billion US dollars annually and will contribute to maintaining human health by reducing carbon dioxide emissions. He affirmed Kuwait’s commitment and support for the efforts made by the United Nations in combating the phenomenon of climate change and limiting its negative effects, based on the principles and provisions contained in the United Nations Framework Convention on Climate Change and the Kyoto Protocol. About the Corona pandemic that is sweeping the world, it has become necessary to work on more awareness of the importance of science and innovation and the need to find effective policies and mechanisms for cooperation and information exchange between Islamic countries. | https://www.arabtimesonline.com/news/kuwait-pursuing-knowledge-based-economy-based-on-multiple-pillars/ |
Multiple distinct routers are supported within a single router, which allows service providers to configure multiple, separate, secure routers within a single chassis. These routers are identified as virtual routers (VRs). Applications for this function include the creation of individual routers dedicated to wholesale customers, corporate virtual private network (VPN) users, or a specific traffic type.
Default Virtual Router
When you first boot your router, it creates a default virtual router. The only difference between the default VR and any other router is that you cannot create or delete the default VR. Just like any other router, the default VR gets its IP addresses when you add interfaces to it.
Virtual Router Instances
E Series routers can support up to 1,000 forwarding tables; that is, up to a total of 1,000 VRs and VPN routing and forwarding (VRF) instances. Each VRF has a forwarding table. A network device attaching to a router detects a router interface. The attaching device has no notion of the virtual router behind the interface.
For example, a physical ATM link may have circuits that are connected to different VRs. The physical and data link layers are not aware that there are multiple router instances. See Figure 28.
Figure 28: Virtual Routers
VRs and VRFs are tools for implementing VPNs.
Routing Protocols
Your router implements the VRs by maintaining a separate instance of each data structure for each VR and allowing each protocol (for example, TCP/UDP, RIP, OSPF, and IS-IS) to be enabled on a case-by-case basis. A table of router interfaces associates user connections (for example, PPP or ATM) with one or more IP interfaces within a VR.
VPNs and VRFs
Your router supports VPNs and VRFs. For information about VPNs and VRFs, see JunosE BGP and MPLS Configuration Guide.
VPNs
A VPN is a set of sites attached to a common network, but whose data is handled separately from that common network.
VPNs enable private IP traffic to travel over a public TCP/IP network by tunneling that traffic between VPN member sites. Different levels of security are available depending on the security of the tunnel used between sites.
Your router supports VPNs consisting of VRs or VRFs. See RFC 2547—BGP/MPLS VPNs (March 1999). Additionally, your router supports tunnels built from GRE, IPsec, L2TP, MPLS, and tunnels built from layer 2 circuits, such as Frame Relay and ATM.
VRFs
A VRF is a virtual routing and forwarding instance that exists within the context of a VR. The VRF provides forwarding information to your router. The system looks up a packet’s destination in the VRF associated with the interface on which the packet is received. In general, any application that can be enabled in a VR can be enabled in a VRF. VRFs are generally associated with the VPN behavior described in RFC 4364—BGP/MPLS IP Virtual Private Networks (VPNs).
When a VRF receives an update message, it needs to know whether it should add the route to its routing table. Similarly, when a VRF sends update messages, it needs to identify the VPNs that it wants to receive the updates. See JunosE BGP and MPLS Configuration Guide. | https://www.juniper.net/documentation/en_US/junose15.1/information-products/topic-collections/swconfig-system-basics/id-32729.html |
Page Type:
Area/Range
Lat/Lon:
46.09165°N / 7.85961°E
Activities:
Mountaineering
Elevation:
14911 ft / 4545 m
Sign the Climber's Log!
More
Overview
In the center of the Pennine Alps in Switzerland, between the Valleys of Matter and Saas, rises the mighty Mischabel Group. With 11 peaks above 4000m including the Dom, which is the highest mountain entirely on Suisse territory, the Mischabel Group is a popular target for alpine climbers. Most of the peaks are predominantly snow covered with the rocks showing through on the ridges. Although the rock quality isn't what we are used to when, for example, climbing in the Chamonix area, there are great rock climbs in all difficulties. One will also find interesting ice and mixed routes.
As mentioned above, the Mischabel Group is very popular, especially in high season (July and August). However, most people are climbing the easy routes in the area, both in effort and technical difficulties. Choose an alternative route instead and one will find the peace and tranquillity which makes us come to the mountains. Allalin's normal route, for example, or even the more demanding Hohlaubgrat are often very crowded. The NE Ridge however never sees a lot of traffic and to my opinion, although quite short, it's even the most rewarding way to climb the Allalinhorn. One can also try to climb on a lower or more remote peak. I can guarantee that one will be nearly alone when climbing the Balfrin, the Gross Bigerhorn or the Egginer. Anyway, no matter which peak one will climb in the Mischabel Group, the summit views on all peaks here in the center of Valais are overwhelming. Enjoy them...
Mountains
Adlerhorn 3988m
Strahlhorn 4190m
Fluchthorn 3790m
Rimpfischhorn 4199m
Egginer 3367m
Mittaghorn 4143m
Allalinhorn 4027m
Feechopf 3888m
Alphubel 4206m
Täschhorn 4491m
Dom 4545m
Lenzspitze 4294m
Nadelhorn 4327m
Stecknadelhorn 4241m
Hohberghorn 4219m
Dürrenhorn 4035m
Chli-Dürrenhorn 3890m
Ulrichshorn 3925m
Gemshorn 3548m
Balfrin 3796m
Gross Bigerhorn 3626
Klein Bigerhorn 3188m
Gabelhorn 3136m
Huts
Britanniahütte
SAC - 3030m - 134 places - Phone: 0041 (0)27 957 22 88
Climbs: Fluchthorn, Strahlhorn, Rimpfischhorn, Allalinhorn, Egginer, Mittaghorn
Längfluh Hotel - 2870m - 130 places - Phone: 0041 (0)27 987 21 32
Climbs: Allalinhorn, Feechopf, Alphubel
Mischabeljoch Bivouac - 3329m - 24 places
Climbs: Alphubel, Täschhorn, Dom
Mischabelhütte
AAC - 3329m - 130 places - Phone: 0041 (0)27 957 13 17
Climbs: Lenzspitze, Nadelhorn,
Nadelgrat
, Ullrichshorn,
Balfrin - Bigerhorn Traverse
Bordierhütte
SAC - 2886m - 56 places - Phone: 0041 (0)27 956 19 09
Climbs:
Nadelgrat
, Ullrichshorn,
Balfrin - Bigerhorn Traverse
Europahütte
- 2220m - 42 places - Phone: 0041 (0)27 967 82 47
Climbs: Dom
Domhütte
SAC - 2940m - 75 places - Phone: 0041 (0)27 967 26 34
Climbs: Täschhorn, Dom, Lenzspitze, Nadelhorn, Hohberghorn
Kinhütte
- 2584m - 32 places - Phone: 0041 (0)27 967 86 18
Climbs: Täschhorn
Täschütte
SAC - 2701m - 65 places - Phone: 0041 (0)27 967 39 13
Climbs: Täschhorn, Alphubel, Allalinhorn
Berghaus Flue
- 2618m - 50 places - Phone: 0041 (0)27 967 25 51
Climbs: Strahlhorn, Rimpfischhorn
Cables
There is one major cable in the area, the Alpine Express and Metro Alpin which brings you in half an hour from Saas Fee at 1800m to Mittelallin at 3500m. From there it's possible to climb Allalinhorn, Feechopf and Alphubel in one day. Since Saas Fee is a summer ski area, the cable is working almost all year round. In summer the cable starts around 7 o'clock for skiers. However, he's already working a bit earlier to bring staff to Mittelallalin and it should be possible for climbers to leave a little earlier. There are also cables going up to Längfluh (Alphubel), Felskinn (Britanniahütte), Plattjen (Mittaghorn) and Hannig (this one shortens approach to Mischabelhütte by an hour).
All peaks north of the Mischabeljoch aren't accesible by cable. So if you want to climb the Dom or make a traverse of the Nadelgrat, you'll have to do it without any artificial help.
Getting There
The starting points for all climbs can be reached by car. Coming through the Rhone Valley, one should drive into the valleys of Matter and Saas in Visp. When coming by train one should stop at the train station in Brig in the Rhone Valley, from where busses are running up to Saas Fee. It is possible to reach Zermatt by train. There is an airport in Geneva.
Camping
There are a number of camping sites in the Saas and Zermatt Valleys. These are just 2 options.
Camping Mischabel 0041 (0)27 957 29 61 (Saas)
Camping Am Kapellenweg 0041 (0)27 957 40 40 (Saas)
When To Climb
It is possible to make trips in the Mischabel Group almost anytime of the year. During winter and spring it's possible to ski in the area or to climb several peaks with tourskis (Strahlhorn, Rimpischhorn, Allalinhorn and Alphubel). For the rock ridges (Täschhorn, Nadelgrat, Balfrin-Bigerhorn Traverse) it is better to wait untill they aren't snow covered anymore, let's say summer and early autumn.
Red Tape
No red tape is required to climb the peaks of the Mischabel Group. To all visitors, make sure it keeps that way. Off course it's recommended to be a member of an alpine club to be insured for rescue in case of an emergency.
Maps & Books
The area is almost totally covered by the Suisse OMNI Map 284 (Mischabel) on scale 1:50000.
There are also maps on scale 1:25000 available. The maps 1308 (St.Niklaus), 1309 (Simplon), 1328 (Randa), 1329 (Saas), 1348 (Zermatt) and 1349 (Monte Moro) cover the whole area.
Interesting books are listed below:
Walliser Alpen
Die 100 schönsten Touren
by M Vaucher (1983)
Valais Alps East
Selected Climbs by L Swindin and P Fleming (1999)
Viertausender der Alpen
by H Dumler and W P Burghardt (new edition 2007)
SAC Clubführer Walliser Alpen 5
Vom Strahlhorn zum Simplon
by M Brandt (1993)
External Links
Saas Valley
Matter Valley
Images
View Mischabel GROUP Image Gallery - 117 Images
Table of Contents
Overview
Mountains
Huts
Cables
Getting There
Camping
When To Climb
Red Tape
Maps & Books
External Links
Images
Geography
Nearby Areas & Ranges
Interactive Map
Areas & Ranges in Switzerland
Children
19 Mountains & Rocks
View all on Map
Dom
Täschhorn
Nadelhorn
Lenzspitze
Stecknadelhorn
Hohberghorn
Alphubel
Rimpfischhorn
Strahlhorn
Dirruhorn
Allalinhorn
Ulrichshorn
Feechopf
Balfrin
Fluchthorn
Gross Bigerhorn
Egginer
Mittaghorn
Klein Allalin
Parents
Pennine Alps
Areas & Ranges
Valsesia
Monte Rosa group
Mischabel GROUP
Val d'Anniviers
Weissmies GROUP
Grandes Murailles
Valle Antrona
Fallère GROUP
Costiera dell'Aroletta
Comba de Cénevé or Senevé Basin
Tagliaferro range
Roisan Blavy Parléaz Viou Little Basin
The mountains directly surrounding Verbier
Glaciers of Valpelline Valley (Grand Combin)
Glaciers of Valtournenche Valley (Matterhorn - Monte Cervino)
Glaciers of Ayas Valley (Breithorns - Castore)
Glaciers of G.S. Bernardo and Ollomont Valley (Ollomont Mont Vèlan)
Glaciers of Gressoney Valley (Lyskamms - Monte Rosa)
Flowers in the Saastal
Areas & Ranges
Mischabel GROUP
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Don't have an account? | https://www.summitpost.org/mischabel-group/391677 |
Descrição:Malmak Sun Power Energy Limited is installing 150 MW hybrid Solar PV energy plant in central province of Zambia. Therefore, it has become necessary for Malmak S.P.E Ltd to seek services of a Project Manager in order to ensure a smooth implementation of the project.
Job brief We are looking for an experienced Project Manager to plan and supervise the project team from start to finish, either remote or full time. You will organize and oversee, designate project resources, prepare budgets, monitor progress, and keep stakeholders informed the entire way; and ensure the project is completed in a timely and efficient manner. An excellent Project Manager must be well-versed in project management, construction methodologies and procedures and able to coordinate a team of professionals of different disciplines to achieve the best results.
The ideal candidate will have an analytical mind and great organizational skills. The goal will be to ensure the project is delivered on time according to requirements and without exceeding budget.
Responsibilities
• Develop a project plan
• Determine and define project scope and objectives
• Predict resources needed to reach objectives and manage resources in an effective and
efficient manner
• Prepare budget based on scope of work and resource requirements
• Manage deliverables according to the plan
• Recruit project staff
• Assist lead and manage the project team
• Determine the methodology used on the project
• Establish a project schedule and determine each phase
• Assign tasks to project team members
• Provide regular updates to upper management
• Track project costs in order to meet budget
• Develop and manage a detailed project schedule and work plan
• Provide project updates on a consistent basis to various stakeholders about strategy,
adjustments, and progress
• Manage contracts with vendors and suppliers by assigning tasks and communicating
expected deliverables
• Utilize industry best practices, techniques, and standards throughout entire project execution
• Monitor progress and make adjustments as needed
• Measure project performance to identify areas for improvement
Requirements
• Bachelor's degree in computer science, business, or a related field
• 5-8 years of project management and related experience
• Project Management Professional (PMP) certification preferred
• Proven ability to solve problems creatively
• Strong familiarity with project management software tools, methodologies, and best
practices
• Experience seeing projects through the full life cycle
• Excellent analytical skills • Strong interpersonal skills and extremely resourceful
• Proven ability to complete projects according to outlined scope, budget, and timeline
Candidates meeting the above requirements should apply to:
The Steering Committee,
Malmak Sun Power Energy Limited,
02 Uganda Avenue,
Town Centre,
Kabwe, ZM 10101
Zambia. | https://br.bebee.com/job/20210408-4f71f73a7278b5ec74af633f3d0d43aa |
---
abstract: 'We study direct CP violation in the hadronic decay $B^{\pm} \rightarrow \rho^{0}\pi^{\pm}$, including the effect of $\rho - \omega$ mixing. We find that the CP violating asymmetry is strongly dependent on the CKM matrix elements, especially the Wolfenstein parameter $\eta$. For fixed $N_{c}$ (the effective parameter associated with factorization), the CP violating asymmetry, $a$, has a maximum of order $30\%-50\%$ when the invariant mass of the $\pi^{+}\pi^{-}$ pair is in the vicinity of the $\omega$ resonance. The sensitivity of the asymmetry, $a$, to $N_{c}$ is small. Moreover, if $N_{c}$ is constrained using the latest experimental branching ratios from the CLEO collaboration, we find that the sign of $\sin \delta$ is always positive. Thus, a measurement of direct CP violation in $B^{\pm} \rightarrow \rho^{0}\pi^{\pm}$ would remove the mod$(\pi)$ ambiguity in ${\rm arg}\left[ - \frac{V_{td}V_{tb}^{\star}}{V_{ud}V_{ub}^{\star}}\right]$.'
---
ADP-00-44$/$T427\
PCCF-RI-0018
[Enhanced Direct CP Violation in $B^{\pm} \rightarrow \rho^{0} \pi^{\pm}$ ]{}
X.-H. Guo$^{1}$[^1], O. Leitner$^{1,2}$[^2], A.W. Thomas$^1$[^3]\
$^1$ Department of Physics and Mathematical Physics, and\
Special Research Center for the Subatomic Structure of Matter,\
Adelaide University , Adelaide 5005, Australia\
$^2$ Laboratoire de Physique Corpusculaire, Université Blaise Pascal,\
CNRS/IN2P3, 24 avenue des Landais, 63177 Aubière Cedex, France
: 11.30.Er, 13.25.-Hw, 12.39.-x.
Introduction
============
Even though CP violation has been known since $1964$, we still do not know the source of CP violation clearly. In the Standard Model, a non-zero phase angle in the Cabbibo-Kobayashi-Maskawa (CKM) matrix is responsible for CP violating phenomena. In the past few years, numerous theoretical studies have been conducted on CP violation in the B meson system [@ref1; @ref2]. However, we need a lot of data to check these approaches because there are many theoretical uncertainties – e.g. CKM matrix elements, hadronic matrix elements and nonfactorizable effects. The future aim would be to reduce all these uncertainties. Direct CP violating asymmetries in B decays occur through the interference of at least two amplitudes with different weak phase $\phi$ [*and*]{} strong phase $\delta$. In order to extract the weak phase (which is determined by the CKM matrix elements), one must know the strong phase $\delta$ and this is usually not well determined. In addition, in order to have a large signal, we have to appeal to some phenomenological mechanism to obtain a large $\delta$. The charge symmetry violating mixing between $\rho^{0}$ and $\omega$, can be extremely important in this regard. In particular, it can lead to a large CP violation in B decays such as $B^{\pm} \rightarrow \rho^{0}(\omega) \pi^{\pm} \rightarrow \pi^{+} \pi^{-} \pi^{\pm} $, because the strong phase passes through $90^{o}$ at the $\omega$ resonance [@ref3; @ref4; @ref5]. Recently, CLEO reported new data [@ref6] on $B \rightarrow \rho \pi$. It is the aim of the present work to analyse direct CP violation in $B^{\pm} \rightarrow \rho^{0}(\omega) \pi^{\pm}\rightarrow \pi^{+} \pi^{-} \pi^{\pm}$, including $\rho-\omega$ mixing, using the latest data from the CLEO collaboration to constrain the calculation. In order to extract the strong phase $\delta$, we use the factorization approach, in which the hadronic matrix elements of operators are saturated by vacuum intermediate states. In this paper, we investigate five phenomenological models with different weak form factors and determine the CP violating asymmetry for $B^{\pm} \rightarrow \rho^{0}(\omega) \pi^{\pm} \rightarrow \pi^{+} \pi^{-}\pi^{\pm} $ in these models. We select models which are consistent with the CLEO data and determine the allowed range of $N_{c}$ ($0.98(0.94)< N_{c}<2.01(1.95)$). Then, we study the sign of $\sin \delta$ in the range of $N_{c}$ allowed by experimental data in all these models. We discuss the model dependence of our results in detail. The remainder of this paper is organized as follows. In Section 2, we present the form of the effective Hamiltonian and the values of Wilson coefficients. In Section 3, we give the formalism for the CP violating asymmetry in $B^{+} \rightarrow \rho^{0}(\omega) \pi^{+} \rightarrow \pi^{+} \pi^{-} \pi^{+}$, for all the models which will be checked. We also show numerical results in this section (asymmetry, $a$, the value of $\sin \delta$). In Section 4, we calculate branching ratios for $B^{+} \rightarrow \rho^{0} \pi^{+} $ and $B^{0} \rightarrow \rho^{+} \pi^{-} $ and present numerical results over the range of $N_{c}$ allowed by the CLEO data. In last section, we summarize our results and suggest further work.
The effective Hamiltonian
=========================
In order to calculate the direct CP violating aymmetry in hadronic decays, one can use the following effective weak Hamiltonian, based on the operator product expansion [@ref7], $$\begin{aligned}
{\cal H}_{\bigtriangleup B=1}=\frac {G_{F}}{\sqrt 2} [ \sum_{q=d,s} V_{ub}V_{uq}^{\ast}(c_{1}O_{1}^{u} + c_{2}O_{2}^{u})- V_{tb}V_{tq}^{\ast} \sum_{i=3}^{10} c_{i}O_{i} ] + h.c. ,\end{aligned}$$ where $c_{i} (i=1,{\cdots},10)$ are the Wilson coefficients. They are calculable in renormalization group improved pertubation theory and are scale dependent. In the present case, we use their values at the renormalization scale $\mu \approx m_{b}$. The operators $O_{i}$ have the following form, $$\begin{aligned}
\begin{array}{ll}
O_{1}^{u}=\bar{q}_{\alpha} \gamma_{\mu}(1-\gamma{_5})u_{\beta}\bar{u}_{\beta} \gamma^{\mu}(1-\gamma{_5})b_{\alpha}, \; \; \;
O_{2}^{u}=\bar{q} \gamma_{\mu}(1-\gamma{_5})u\bar{u} \gamma^{\mu}(1-\gamma{_5})b, \nonumber \; \; \; \; \; \; \; \; \; \; \;\; \; \; \\
\end{array}\end{aligned}$$ $$\begin{aligned}
O_{3}=\bar{q} \gamma_{\mu}(1-\gamma{_5})b \sum_{q\prime}
\bar{q}^{\prime}\gamma^{\mu}(1-\gamma{_5})q^{\prime}, \; \; \;
O_{4}=\bar{q}_{\alpha} \gamma_{\mu}(1-\gamma{_5})b_{\beta}
\sum_{q\prime}\bar{q}^{\prime}_{\beta}\gamma^{\mu}(1-\gamma{_5})q^{\prime}_{\alpha}, \nonumber\; \; \; \; & &\\
O_{5}=\bar{q} \gamma_{\mu}(1-\gamma{_5})b \sum_{q'}\bar{q}^
{\prime}\gamma^{\mu}(1+\gamma{_5})q^{\prime}, \; \; \;
O_{6}=\bar{q}_{\alpha} \gamma_{\mu}(1-\gamma{_5})b_{\beta}
\sum_{q'}\bar{q}^{\prime}_{\beta}\gamma^{\mu}(1+\gamma{_5})q^{\prime}_{\alpha}, \nonumber\; \; \;\; & & \\
O_{7}=\frac{3}{2}\bar{q} \gamma_{\mu}(1-\gamma{_5})b \sum_{q'}e_{q^{\prime}}
\bar{q}^{\prime} \gamma^{\mu}(1+\gamma{_5})q^{\prime}, \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \;\;\; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \;\; \;\;\; \; \; \; & \nonumber \\
O_{8}=\frac{3}{2}\bar{q}_{\alpha} \gamma_{\mu}(1-\gamma{_5})b_{\beta}
\sum_{q'}e_{q^{\prime}}\bar{q}^{\prime}_{\beta}\gamma^{\mu}(1+\gamma{_5})q^{\prime}_{\alpha},\; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \;\;\;\; \;\;\; \; \; \; \;\;\; \; \; \; \; \; \; \; \; \; & \nonumber \\
O_{9}=\frac{3}{2}\bar{q} \gamma_{\mu}(1-\gamma{_5})b \sum_{q'}e_{q^{\prime}}
\bar{q}^{\prime} \gamma^{\mu}(1-\gamma{_5})q^{\prime}, \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \;\; \; \; \;\; \; \; \; \; \; \;\;\; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \;\; \; \;\; \; \; & \nonumber \\
O_{10}=\frac{3}{2}\bar{q}_{\alpha} \gamma_{\mu}(1-\gamma{_5})b_{\beta}
\sum_{q'}e_{q^{\prime}}\bar{q}^{\prime}_{\beta}\gamma^{\mu}(1-\gamma{_5})q^{\prime}_{\alpha},\; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \;\;\;\; \;\;\; \; \; \;\;\; \; \; \; \; \; \; \; \; \; &
$$ where $\alpha$ and $\beta$ are color indices, and $q^{\prime}=u,\;d \; {\rm or} \; s$ quarks. In Eq.(2), $O_{1}$ and $O_{2}$ are the tree level operators, $O_{3}-O_{6}$ are QCD penguin operators, and $O_{7}-O_{10}$ arise from electroweak penguin diagrams.
The Wilson coefficients, $c_{i}$, are known to the next-to-leading logarithmic order. At the scale $\mu=m_{b}=5$GeV, they take values the following values [@ref8; @ref9]: $$\begin{aligned}
\begin{array}{ll}
\vspace{0.5em}
c_{1}=-0.3125,\;\;\;\; c_{2}=1.1502, \\
\vspace{0.5em}
c_{3}=0.0174 ,\;\;\;\; c_{4}=-0.0373, \\
\vspace{0.5em}
c_{5}=0.0104 ,\;\;\;\; c_{6}=-0.0459, \\
\vspace{0.5em}
c_{7}=-1.050 \times 10^{-5}, \;\;\;\; c_{8}=3.839 \times 10^{-4},
\end{array}\end{aligned}$$ $$\begin{aligned}
\!\!\!\!\!\!\!\! \!\!\!\!\!\!\!c_{9}=-0.0101, \;\;\;\;
c_{10}=1.959 \times 10^{-3}. & &
$$ To be consistent, the matrix elements of the operators $O_{i}$ should also be renormalized to the one-loop order. This results in the effective Wilson coefficients, $c_{i}^{\prime}$, which satisfy the constraint, $$\begin{aligned}
c_{i}(m_{b})\langle O_{i}(m_{b})\rangle=c_{i}^{\prime}{\langle O_{i}\rangle}^{tree},
$$ where ${\langle O_{i}\rangle}^{tree}$ are the matrix elements at the tree level, which will be evaluated in the factorization approach. From Eq.(4), the relations between $c_{i}^{\prime}$ and $c_{i}$ are [@ref8; @ref9], $$\begin{aligned}
\begin{array}{ll}
\vspace{0.5em}
c_{1}^{\prime}=c_{1},\;\;\;\; c_{2}^{\prime}=c_{2}, \\
\vspace{0.5em}
c_{3}^{\prime}=c_{3}-P_{s}/3,\;\;\;\; c_{4}^{\prime}=c_{4}+P_{s}, \\
\vspace{0.5em}
c_{5}^{\prime}=c_{5}-P_{s}/3,\;\;\; c_{6}^{\prime}=c_{6}+P_{s}, \\
\vspace{0.5em}
c_{7}^{\prime}=c_{7}+P_{e},\;\;\;\;\; c_{8}^{\prime}=c_{8}, \\
\end{array}\end{aligned}$$ $$\begin{aligned}
\!\!\!\!\!\!\!\! \!\!\!\!\!\!\!c_{9}^{\prime}=c_{9}+P_{e},\;\;\;\;
c_{10}^{\prime}=c_{10}, & &
$$ where $$\begin{aligned}
\begin{array}{ll}
P_{s}=(\alpha_{s}/8\pi)c_{2}(10/9+G(m_{c},\mu,q^{2})), \\
P_{e}=(\alpha_{em}/9\pi)(3c_{1}+c_{2})(10/9+G(m_{c},\mu,q^{2})), \\
\end{array}\end{aligned}$$ with $$\begin{aligned}
G(m_{c},\mu,q^{2})=4\int_{0}^{1}dxx(x-1){\rm ln} \frac{m_{c}^{2}-x(1-x)q^{2}}{\mu^{2}}.
$$ Here $q^{2}$ is the typical momentum transfer of the gluon or photon in the penguin diagrams. $G(m_{c},\mu,q^{2})$ has the following explicit expression [@ref10], $$\begin{aligned}
\Re e\; G= \frac{2}{3} \left({\rm ln} \frac{m_{c}^{2}}{\mu^{2}}- \frac{5}{3}-4 \frac{m_{c}^{2}}{q^{2}}+\left(1+2\frac{m_{c}^{2}}{q^{2}}\right)\sqrt{1-4\frac{m_{c}^{2}}{q^{2}}}{\rm ln} \frac{1+\sqrt{1-4\frac{m_{c}^{2}}{q^{2}}}}{1-\sqrt{1-4\frac{m_{c}^{2}}{q^{2}}}}\right), & & \nonumber \\
\Im m\; G= -\frac{2}{3}\left(1+2\frac{m_{c}^{2}}{q^{2}}\right)\sqrt{1-4\frac{m_{c}^{2}}{q^{2}}}. \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; &
$$ Based on simple arguments at the quark level, the value of $q^{2}$ is chosen in the range $0.3 < q^{2}/m_{b}^{2} < 0.5$ [@ref3; @ref4]. From Eqs.(5,6) we can obtain numerical values for $c_{i}^{\prime}$. When $ q^{2}/m_{b}^{2}=0.3$, $$\begin{aligned}
c_{1}^{\prime}=-0.3125,\;\;\;\; c_{2}^{\prime}=1.1502, \;\;\;\;\;\;\;\;\;\;\;
\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;
\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & \nonumber \\
c_{3}^{\prime}= 2.433 \times 10^{-2} + 1.543 \times 10^{-3}i, \;\;\;\; c_{4}^{\prime}= -5.808 \times 10^{-2} -4.628 \times 10^{-3}i, \;\; & \nonumber \\
c_{5}^{\prime}=1.733 \times 10^{-2}+ 1.543 \times 10^{-3}i,\;
\;\;\; c_{6}^{\prime}=-6.668 \times 10^{-2}- 4.628 \times 10^{-3}i, \;\; & \nonumber \\
c_{7}^{\prime}=-1.435 \times 10^{-4} -2.963 \times 10^{-5}i,\;\; \;
\;c_{8}^{\prime}=3.839 \times 10^{-4}, \;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\; \;\;& \nonumber \\
c_{9}^{\prime}=-1.023 \times 10^{-2} -2.963 \times 10^{-5}i,\;\;
\;\; c_{10}^{\prime}=1.959 \times 10^{-3}, \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\; &
$$ and when $q^{2}/m_{b}^{2}=0.5$, one has, $$\begin{aligned}
c_{1}^{\prime}=-0.3125,\;\;\;\; c_{2}^{\prime}=1.1502, \;\;\;\;\;\;\;\;\;\;\;
\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;
\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & \nonumber \\
c_{3}^{\prime}= 2.120 \times 10^{-2} + 2.174 \times 10^{-3}i,\;\;\;\; c_{4}^{\prime}= -4.869 \times 10^{-2} -1.552 \times 10^{-2}i, \; \; & \nonumber \\
c_{5}^{\prime}=1.420 \times 10^{-2} + 5.174 \times 10^{-3}i ,\;\;\;\; c_{6}^{\prime}=-5.729 \times 10^{-2}- 1.552 \times 10^{-2}i, \;\; & \nonumber \\
c_{7}^{\prime}=-8.340 \times 10^{-5} -9.938 \times 10^{-5}i,\;\;\;\;c_{8}^{\prime}=3.839 \times 10^{-4}, \;\;\;\; \;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;& \nonumber \\
c_{9}^{\prime}=-1.017 \times 10^{-2} -9.938 \times 10^{-5}i,\;\;\;\; c_{10}^{\prime}=1.959 \times 10^{-3},\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; &
$$ where we have taken $\alpha_{s}(m_{Z})=0.112, \;\;\; \alpha_{em}(m_{b})=1/132.2,\;\;\; m_{b}=5$GeV, and $ \;\; m_{c}=1.35$GeV.
CP violation in $B^{+} \rightarrow \rho^{0}(\omega)\pi^{+} \rightarrow \pi^{+} \pi^{-} \pi^{+} $
====================================================================================================
Formalism
----------
The formalism for CP violation in hadronic B meson decays is the following. Let $A$ be the amplitude for the decay $B^{+} \rightarrow \pi^{+} \pi^{-} \pi^{+}$, then one has $$\begin{aligned}
A=\langle \pi^{+} \pi^{-} \pi^{+}|H^{T}|B^{+} \rangle + \langle \pi^{+} \pi^{-} \pi^{+}|H^{P}|B^{+} \rangle,
$$ with $H^{T}$ and $H^{P}$ being the Hamiltonians for the tree and penguin operators , respectively. We can define the relative magnitude and phases between these two contributions as follows, $$\begin{aligned}
A= \langle \pi^{+} \pi^{-}\pi^{+}|H^{T}|B^{+} \rangle [ 1+re^{i\delta}e^{i\phi}],\;\; & \\
\bar A= \langle \pi^{+} \pi^{-} \pi^{-}|H^{T}|B^{-} \rangle [ 1+re^{i\delta}e^{-i\phi}], &
$$ where $\delta$ and $\phi$ are strong and weak phases, respectively. The phase $\phi$ arises from the appropriate combination of CKM matrix elements which is $ \phi={\rm arg}[(V_{tb}V_{td}^{\star})/(V_{ub}V_{ud}^{\star})]$. As a result, $\sin \phi$ is equal to $\sin \alpha$ with $\alpha$ defined in the standard way [@ref11]. The parameter $r$ is the absolute value of the ratio of tree and penguin amplitudes:
$$\begin{aligned}
r \equiv \left| \frac{\langle \rho^{0}(\omega)\pi^{+}|H^{P}|B^{+} \rangle}{\langle\rho^{0}(\omega)\pi^{+}|H^{T}|B^{+} \rangle} \right|.
$$
The CP violating asymmetry, $a$, can be written as:
$$\begin{aligned}
a \equiv \frac{|A|^{2}-|\bar A|^{2}}{ |A|^{2}+|\bar A|^{2}}=\frac{-2r\sin\delta \sin\phi}{1+2r\cos\delta \cos\phi+r^2}.
$$
It can be seen explicitly from Eq.(13) that both weak and strong phase differences are needed to produce CP violation. In order to obtain a large signal for direct CP violation, we need some mechanism to make both $\sin\delta$ and $r$ large. We stress that $\rho-\omega$ mixing has the dual advantages that the strong phase difference is large (passing through $90^{o}$ at the $\omega$ resonance) and well known [@ref4; @ref5]. With this mechanism, to first order in isospin violation, we have the following results when the invariant mass of $\pi^{+}\pi^{-}$ is near the $\omega$ resonance mass,
$$\begin{aligned}
\langle \pi^{-}\pi^{+} \pi^{+}|H^{T}|B^{+} \rangle= \frac{g_{\rho}}{s_{\rho}s_{\omega}} \tilde{\Pi}_{\rho \omega}t_{\omega} +\frac{g_{\rho}}{s_{\rho}}t_{\rho}, \\
\langle \pi^{-}\pi^{+} \pi^{+}|H^{P}|B^{+} \rangle= \frac{g_{\rho}}{s_{\rho}s_{\omega}} \tilde{\Pi}_{\rho \omega}p_{\omega} +\frac{g_{\rho}}{s_{\rho}}p_{\rho}.
$$
Here $t_{V} (V=\rho \;{\rm or} \; \omega) $ is the tree amplitude and $p_{V}$ the penguin amplitude for producing a vector meson, V, $g_{\rho}$ is the coupling for $\rho^{0} \rightarrow \pi^{+}\pi^{-}$, $\tilde{\Pi}_{\rho \omega}$ is the effective $\rho-\omega$ mixing amplitude, and $s_{V}$ is from the inverse propagator of the vector meson V,
$$\begin{aligned}
s_{V}=s-m_{V}^{2}+im_{V}\Gamma_{V}, & &
$$
with $\sqrt s$ being the invariant mass of the $\pi^{+}\pi^{-}$ pair.
We stress that the direct coupling $ \omega \rightarrow \pi^{+} \pi^{-} $ is effectively absorbed into $\tilde{\Pi}_{\rho \omega}$ [@ref12], leading to the explicit $s$ dependence of $\tilde{\Pi}_{\rho \omega}$. Making the expansion $\tilde{\Pi}_{\rho \omega}(s)=\tilde{\Pi}_{\rho \omega}(m_{\omega}^{2})+(s-m_{w}^{2}) \tilde{\Pi}_{\rho \omega}^{\prime}(m_{\omega}^{2})$, the $\rho-\omega$ mixing parameters were determined in the fit of Gardner and O’Connell [@ref13]: $\Re e \; \tilde{\Pi}_{\rho \omega}(m_{\omega}^{2})=-3500 \pm 300 {\rm MeV}^{2}, \;\;\; \Im m \; \tilde{\Pi}_{\rho \omega}(m_{\omega}^{2})= -300 \pm 300 {\rm MeV}^{2}$ and $\tilde{\Pi}_{\rho \omega}^{\prime}(m_{\omega}^{2})=0.03 \pm 0.04$. In practice, the effect of the derivative term is negligible. From Eqs.(10,14,15) one has,
$$\begin{aligned}
re^{i \delta} e^{i \phi}= \frac{ \tilde {\Pi}_{\rho \omega}p_{\omega}+s_{\omega}p_{\rho}}{\tilde {\Pi}_{\rho \omega} t_{\omega} + s_{\omega}t_{\rho}}.
$$
Defining
$$\begin{aligned}
\frac{p_{\omega}}{t_{\rho}} \equiv r^{\prime}e^{i(\delta_{q}+\phi)}, \;\;\;\;
\frac{t_{\omega}}{t_{\rho}} \equiv \alpha e^{i \delta_{\alpha}}, \;\;\;\;
\frac{p_{\rho}}{p_{\omega}} \equiv \beta e^{i \delta_{\beta}},
$$
where $ \delta_{\alpha}, \delta_{\beta}$ and $ \delta_{q}$ are strong phases, one finds the following expression from Eq.(18)
$$\begin{aligned}
re^{i\delta}=r^{\prime}e^{i\delta_{q}} \frac{\tilde{\Pi}_{\rho \omega}+ \beta e^{i \delta_{\beta}} s_{\omega}}{s_{\omega}+\tilde{\Pi}_{\rho \omega} \alpha e^{i \delta_{\alpha}}}.
$$
It will be shown that in the factorization approach, we have $\alpha e^{i \delta_{\alpha}}=1$ in our case. Letting $$\begin{aligned}
& \beta e^{i \delta_{\beta}}= b+ci, \;\;\;r^{\prime}e^{i\delta_{q}}=d+ei,
$$ and using Eq.(20), we obtain the following result when $\sqrt s \sim m_{\omega}$ $$\begin{aligned}
re^{i \delta}= \frac{C+Di}{(s-m_{\omega}^{2}+ \Re e \; \tilde{\Pi}_{\rho \omega})^{2}+ (\Im m \; \tilde{\Pi}_{\rho \omega} +m_{\omega} \Gamma_{\omega})^{2}},
$$ where $$\begin{aligned}
C=(s-m_{\omega}^{2}+ \Re e\; \tilde {\Pi}_{\rho \omega}) \bigg\{ d[ \Re e \;\tilde {\Pi}_{ \rho \omega} +b(s-m_{ \omega}^{2})-cm_{ \omega} \Gamma_{ \omega}] & \nonumber \\
-e [ \Im m \;\tilde { \Pi}_{ \rho \omega} +bm_{ \omega} \Gamma_{ \omega}+c(s-m_{ \omega}^{2})] \bigg\} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & \nonumber \\
+ ( \Im m\; \tilde { \Pi}_{ \rho \omega} +m_{ \omega} \Gamma_{ \omega}) \bigg\{ e[ \Re e \;\tilde {\Pi}_{\rho \omega} +b(s-m_{ \omega}^{2})-cm_{ \omega} \Gamma_{ \omega}] & \nonumber \\
+d[ \Im m \;\tilde { \Pi}_{ \rho \omega}
+bm_{ \omega} \Gamma_{ \omega}+c(s-m_{ \omega}^{2})] \bigg\}, \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & \nonumber \\
D=(s-m_{\omega}^{2}+ \Re e \;\tilde {\Pi}_{\rho \omega}) \bigg\{ e[ \Re e \;\tilde {\Pi}_{ \rho \omega} +d(s-m_{ \omega}^{2})-cm_{ \omega} \Gamma_{ \omega}] & \nonumber \\
+d [ \Im m\; \tilde { \Pi}_{ \rho \omega} +bm_{ \omega} \Gamma_{ \omega}+c(s-m_{ \omega}^{2})] \bigg\} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & \nonumber \\
- ( \Im m \;\tilde { \Pi}_{ \rho \omega} +m_{ \omega} \Gamma_{ \omega}) \bigg\{ d[ \Re e \;\tilde {\Pi}_{\rho \omega} +b(s-m_{ \omega}^{2})-cm_{ \omega} \Gamma_{ \omega}] & \nonumber \\
-e[ \Im m\; \tilde { \Pi}_{ \rho \omega}
+bm_{ \omega} \Gamma_{ \omega}+c(s-m_{ \omega}^{2})] \bigg\}. \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; &
$$ $\beta e^{i \delta_{\beta}}$ and $r^{\prime}e^{i \delta_{q}}$ will be calculated later. Then, from Eq.(22) we can obtain $r\sin \delta$ and $r\cos\delta$. In order to get the CP violating asymmetry, $a$, in Eq.(13), $\sin\phi$ and $\cos\phi$ are needed, where $\phi$ is determined by the CKM matrix elements. In the Wolfenstein parametrization [@ref14], one has,
$$\begin{aligned}
\sin\phi= \frac{\eta}{\sqrt {[\rho(1-\rho)-\eta^{2}]^{2}+\eta^{2}}}, \\
\cos\phi= \frac{\rho(1-\rho)-\eta^{2}}{\sqrt {[\rho(1-\rho)-\eta^{2}]^{2}+\eta^{2}}}.
$$
Calculational Details
---------------------
With the Hamiltonian given in Eq.(1), we are ready to evaluate the matrix elements for $B^{+}\rightarrow \rho^{0}(\omega)\pi^{+}$. In the factorization approximation, either the $\rho^{0}(\omega)$ or the $\pi^{+}$ is generated by one current which has the appropriate quantum numbers in the Hamiltonian. For this decay process, two kinds of matrix element products are involved after factorization; schematically (i.e. omitting Dirac matrices and color labels) $\langle \rho^{0}(\omega)|(\bar{u}u)|0\rangle \langle\pi^{+}|(\bar{d}b)|B^{+}\rangle $ and $ \langle\pi^{+}|(\bar{d}u)|0\rangle \langle\rho^{0}(\omega)|(\bar{u}b)|B^{+}\rangle$. We will calculate them in some phenomenological quark models. The matrix elements for $B \rightarrow X$ and $B \rightarrow X^{\star}$ (where X and $ X^{\star}$ denote pseudoscalar and vector mesons, respectively) can be decomposed as [@ref15], $$\begin{aligned}
\langle X|J_{\mu}|B \rangle =\left( p_{B} + p_{X}- \frac{m_{B}^{2}-m_{X}^{2}}{k^{2}}k \right)_{\mu} F_{1}(k^{2})+\frac{m_{B}^{2}-m_{X}^{2}}{k^{2}}k_{\mu}F_{0}(k^{2}), \;\;\;\;\;\;&
$$ $$\begin{aligned}
\langle X^{\star}|J_{\mu}|B \rangle=\frac{2}{m_{B}+m_{X^{\star}}} \epsilon_{\mu \nu \rho \sigma} \epsilon^{\star \nu} p_{B}^{\rho} p_{X^{\star}}^{\sigma} V(k^{2}) +i \{ \epsilon_{\mu}^{\star}(m_{B}+m_{X^{\star}})A_{1}(k^{2}) & \nonumber \\
- \frac{\epsilon^{\star} \cdot k}{m_{B}+m_{X^{\star}}} (P_{B}+P_{X^{\star}})_{\mu}A_{2}(k^{2})- \frac {\epsilon^{\star} \cdot k}{k^{2}}2m_{X^{\star}} \cdot k_{\mu}A_{3}(k^{2})
\} \;\; & \nonumber \\
+i \frac{\epsilon^{\star} \cdot k}{ k^{2}}2m_{X^{\star}} \cdot k_{\mu}A_{0}(k^{2}),\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;
$$ where $J_{\mu}$ is the weak current ($J_{\mu}=\bar{q}\gamma^{\mu}(1-\gamma_{5})b \;\; {\rm with} \;\; q=u,d$), $k=p_{B}-p_{X(X^{\star})}$ and $\epsilon_{\mu}$ is the polarization vector of $X^{\star}$. The form factors included in our calculations satisfy: $F_{1}(0)=F_{0}(0), \;\;\; A_{3}(0)=A_{0}(0)$ and $A_{3}(k^{2})= \frac {m_{B}+m_{X^{\star}}}{2m_{X^{\star}}}A_{1}(k^{2})- \frac {m_{B}-m_{X^{\star}}}{2m_{X^{\star}}}A_{2}(k^{2}).$ Using the decomposition in Eqs.(25, 26), one has, $$\begin{aligned}
t_{\rho}= m_{B}|\vec{p}_{\rho}| \left[ (c_{1}^{\prime}+\frac {1}{N_{c}}c_{2}^{\prime}) f_{\rho}F_{1}(m_{\rho}^{2})+ (c_{2}^{\prime}+\frac {1}{N_{c}}c_{1}^{\prime} ) f_{\pi}A_{0}(m_{\pi}^{2}) \right],
$$ where $f_{\rho}$ and $f_{\pi}$ are the decay constants of the $\rho$ and $\pi$, respectively, and $\vec{p}_{\rho}$ is the three momentum of the $\rho$. In the same way, we find $t_{\omega}=t_{\rho}$, so that $$\begin{aligned}
\alpha e^{i \delta_{\alpha}}=1.
$$ After calculating the penguin operator contributions, one has, $$\begin{aligned}
\beta e^{i \delta_{\beta}}=
\frac{ m_{B}| \vec{p}_{\rho}|}{p_{\omega}} \Bigg\{ (c_{4}^{\prime}+\frac{1}{N_{c}}c_{3}^{\prime})[-f_{\rho}F_{1}(m_{\rho}^{2})+f_{\pi}A_{0}(m_{\pi}^{2})] \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & \nonumber \\
+\frac{3}{2}[(c_{7}^{\prime}+\frac{1}{N_{c}}c_{8}^{\prime})+(c_{9}^{\prime}+\frac{1}{N_{c}}c_{10}^{\prime})]f_{\rho}F_{1}(m
_{\rho}^{2}) \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \; & \nonumber \\
-[(c_{6}^{\prime}+\frac{1}{N_{c}}c_{5}^{\prime})+(c_{8}^{\prime}+\frac{1}{N_{c}}c_{7}^{\prime})] \left[ \frac{2m_{\pi}^{2}f_{\pi}A_{0}(m_{\pi}^{2})}{(m_{u}+m_{d})(m_{b}+m_{u})}\right] \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;& \nonumber \\
+ (c_{10}^{\prime}+\frac{1}{N_{c}}c_{9}^{\prime})[\frac{1}{2}f_{\rho}F_{1}(m_{\rho}^{2})+f_{\pi}A_{0}(m_{\pi}^{2})]\Bigg\},\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & \nonumber
$$ $$\begin{aligned}
r^{\prime}e^{i \delta_{q}}=-
\frac{p_{\omega}}{(c_{1}^{\prime}+\frac {1}{N_{c}}c_{2}^{\prime}) f_{\rho}F_{1}(m_{\rho}^{2})+ (c_{2}^{\prime}+\frac {1}{N_{c}}c_{1}^{\prime} ) f_{\pi}A_{0}(m_{\pi}^{2})}\left| \frac{V_{tb}V_{td}^{\star}}{V_{ub}V_{ud}^{\star}}\right|, \;\;\;\;\; \;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\; & &
$$ where $$\begin{aligned}
p_{\omega}= m_{B}|\vec{p}_{\rho}| \Bigg\{ 2 \left[ (c_{3}^{\prime}+\frac {1}{N_{c}}c_{4}^{\prime})+(c_{5}^{\prime}+\frac {1}{N_{c}}c_{6}^{\prime})\right]f_{\rho}F_{1}(m_{\rho}^{2}) \;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & & \nonumber \\
+ \frac{1}{2}\left[(c_{7}^{\prime}+\frac {1}{N_{c}}c_{8}^{\prime})+(c_{9}^{\prime}+\frac {1}{N_{c}}c_{10}^{\prime})\right] f_{\rho}F_{1}(m_{\rho}^{2}) \;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & & \nonumber \\
- 2 \left[(c_{8}^{\prime}+\frac {1}{N_{c}}c_{7}^{\prime})+(c_{6}^{\prime}+\frac {1}{N_{c}}c_{5}^{\prime}) \right] \left[ \frac{m_{\pi}^{2}f_{\pi}A_{0}(m_{\pi}^{2})}{(m_{u}+m_{d})(m_{b}+m_{u})}\right] \;\;\;\;\; \;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\; \;\;\;\;\; \;\;\;\;\;\; \;\;\;\;\; \;\;\;\;\;\; \;\;\; & \nonumber \\
+ (c_{4}^{\prime}+\frac {1}{N_{c}}c_{3}^{\prime}) \left[ f_{\pi}A_{0}(m_{\pi}^{2})+f_{\rho}F_{1}(m_{\rho}^{2})\right] \;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\; \;\;\;\;\;\; & & \nonumber \\
+ (c_{10}^{\prime}+\frac {1}{N_{c}}c_{9}^{\prime}) \left[ f_{\pi}A_{0}(m_{\pi}^{2})-\frac{1}{2}f_{\rho}F_{1}(m_{\rho}^{2})\right] \Bigg\}, \;\;\;\; \;\;\;\; \;\;\;\; \;\;\;\;\;\;\;\;\;\; \;\;\;\; \;\;\;\;\;\;\;\; \;\;\;\; \;\;\;\; \;\;\;\;\;\; \;\;\;\;\;\;\;\; \;\;\;\; \;\;\;\; \;\;\;\; \;\;\;\; & & \end{aligned}$$ and $$\begin{aligned}
\left| \frac{V_{tb}V_{td}^{\star}}{V_{ub}V_{ud}^{\star}}\right|
=\frac{\sqrt{{(1-\rho)}^{2}+{\eta}^{2}}}
{(1- {\lambda}^{2}/2)\sqrt{{\rho}^{2}+{\eta}^{2}}}=\left( 1- \frac{\lambda^{2}}{2} \right)^{-1} \left| \frac{\sin \gamma}{\sin \beta} \right|. &
$$
Numerical Results
-----------------
In our numerical calculations we have several parameters: $q^{2}, N_{c}$ and the CKM matrix elements in the Wolfenstein parametrization. As mentioned in Section 2, the value of $q^{2}$ is conventionally chosen to be in the range $0.3<q^{2}/{m_{b}}^{2}<0.5$. The CKM matrix, which should be determined from experimental data, has the following form in term of the Wolfenstein parameters, $ A,\; \lambda,\; \rho, \; \eta $ [@ref14]: $$\begin{aligned}
V= \left( \begin{array}{ccc}
1-\frac{1}{2} \lambda^{2} & \lambda & A\lambda^{3}(\rho-i\eta) \\
-\lambda & 1-\frac{1}{2}\lambda^{2} & A\lambda^{2} \\
A\lambda^{3}(1-\rho-i\eta)& -A\lambda^{2} & 1 \\
\end{array} \right),\end{aligned}$$ where $O(\lambda^{4})$ corrections are neglected. We use $\lambda=0.2205$, $A=0.815$ and the range for $\rho$ and $\eta$ as the following [@ref16; @ref17], $$\begin{aligned}
0.09 < \rho < 0.254, \;\;\;\; \;\;\;\;\; 0.323 < \eta <0.442.\end{aligned}$$ The form factors $F_{1}(m_{\rho}^{2})$ and $A_{0}(m_{\pi}^{2})$ depend on the inner structure of the hadrons. Under the nearest pole dominance assumption, the $k^{2}$ dependence of the form factors is:
for model 1(2) [@ref15; @ref18]: $$\begin{aligned}
F_{1}(k^{2})=\frac{h_{1}}{1-\frac{k^{2}}{m_{1}^{2}}}, \;\;\; \;\;\;
A_{0}(k^{2})=\frac{h_{A_{0}}}{1-\frac{k^{2}}{m_{A_{0}}^{2}}},\end{aligned}$$ where $h_{1}=0.330(0.625), \;\;\;\; h_{A_{0}}=0.28(0.34), \;\;\;\; m_{1}=5.32{\rm GeV}, \;\;\;\; m_{A_{0}}=5.27{\rm GeV}, $
for model 3(4) [@ref15; @ref18; @ref19]: $$\begin{aligned}
F_{1}(k^{2})=\frac{h_{1}}{\left( 1-\frac{k^{2}}{m_{1}^{2}} \right)^{2}}, \;\;\; \;\;\;
A_{0}(k^{2})=\frac{h_{A_{0}}}{\left( 1-\frac{k^{2}}{m_{A_{0}}^{2}}\right)^{2}},\end{aligned}$$ where $h_{1}=0.330(0.625), \;\;\;\; h_{A_{0}}=0.28(0.34), \;\;\;\; m_{1}=5.32{\rm GeV}, \;\;\;\; m_{A_{0}}=5.27{\rm GeV},$
for model 5 [@ref20; @ref21]: $$\begin{aligned}
F_{1}(k^{2})=\frac{h_{1}}{1-a_{1}\frac{k^{2}}{m_{B}^{2}}+b_{1}\left( \frac{k^{2}}{m_{B}^{2}}\right)^{2}}, \;\;\; \;\;\;
A_{0}(k^{2})=\frac{h_{A_{0}}}{1-a_{0}\frac{k^{2}}{m_{B}^{2}}+b_{0}\left( \frac{k^{2}}{m_{B}^{2}}\right)^{2}},\end{aligned}$$ where $h_{1}=0.305, \;\;\;\; h_{A_{0}}=0.372, \;\;\; $ $ a_{1}=0.266, \;\;\;\; b_{1}=-0.752, \;\;\;\; a_{0}=1.4, \;\;\;\; b_{0}=0.437$. The decay constants used in our calculations are: $ f_{\rho}=f_{\omega}=221{\rm MeV} \; {\rm and} \; f_{\pi}=130.7{\rm MeV}$. In the numerical calculations, it is found that for a fixed $N_{c}$, there is a maximum value, $a_{max}$, for the CP violating parameter, $a$, when the invariant mass of the $\pi^{+}\pi^{-}$ is in the vicinity of the $\omega$ resonance. The results are shown in Figs.1 and 2, for $k^{2}/m_{b}^{2}=0.3(0.5)$ and $N_{c}$ in the range $0.98(0.94)<N_{c}<2.01(1.95)$ – for reasons which will be explained later (Section 4). We investigate five models with different form factors to study the model dependence of $a$. It appears that this dependence is strong (Table 1).
The maximum asymmetry parameter, $a_{max}$, varies from $-24\%(-19\%)$ to $-59\%(-48\%)$ for $N_{c}$ in the chosen range, $k^{2}/m_{b}^{2}=0.3(0.5)$ and the range of CKM matrix elements indicated earlier. If we look at the numerical results for the asymmetries (Table 1) for $N_{cmax}=2.01(1.95)$ and $k^{2}/m_{b}^{2}=0.3(0.5)$, we obtain for models 1, 3, 5 an asymmetry, $a_{max}$, around $-27.3\%(-21.6\%)$ for the set $(\rho_{max},\eta_{max})$, and around $-44.3\%(-35.0\%)$ for the set $(\rho_{min},\eta_{min})$. We find a ratio equal to $1.62(1.62)$ between the asymmetries associated with the upper and lower limits of ($\rho,\eta$). The reason why the maximum asymmetry, $a_{max}$, can have large variation, comes from the $b \rightarrow d$ transition, where $V_{td}$ and $V_{ub}$ appear. These are functions of ($\rho,\eta$) and contribute to the asymmetry (Eq.31) through the ratio between the $\omega$ penguin diagram and the $\rho$ tree diagram.
For models 2 and 4, one has a maximum asymmetry, $a_{max}$, around $-37\%(-28\%)$ for the set $(\rho_{max},\eta_{max})$ and around $-59\%(-46\%)$ for the set $(\rho_{min},\eta_{min})$. We find a ratio between the asymmetries equal to $1.59(1.64)$ in this case. The difference between these two sets of models comes from the magnitudes of the form factors, where $F_{1}(k^{2})$ is larger for models 2 and 4 than for models 1, 3 and 5. Now, if we look at the numerical results for the asymmetry for $N_{cmin}=0.98(0.94)$, we find, for models 1, 3, 5, $k^{2}/m_{b}^{2}=0.3(0.5)$, and the set $(\rho_{max},\eta_{max})$, an asymmetry, $a_{max}$, around $-31.3\%(-25.6\%)$, and for the set $(\rho_{min},\eta_{min})$ we find an asymmetry, $a_{max}$, around $-50.3\%(-42.0\%)$. In this case, one has a ratio equal to 1.61(1.64). Finally, for models 2 and 4, we get $-36\%(-29\%)$ for the set $(\rho_{max},\eta_{max})$ and $-57\%(-48\%)$ for the set $(\rho_{min},\eta_{min})$ with a ratio equal to 1.58(1.65).
These results show explicitly the dependence of the CP violating asymmetry on form factors, CKM matrix elements and the effective parameter $N_{c}$. For the CKM matrix elements, it appears that if we take their upper limit, we obtain a smaller asymmetry, $a$, and viceversa. The difference between $k^{2}/m_{b}^{2}=0.3(0.5)$ in our results comes from the renormalization of the matrix elements of the operators in the weak Hamiltonian. Finally, the dependence on $N_{c}$ comes from the fact that $N_{c}$ is related to hadronization effects, and consequently we cannot determine $N_{c}$ exactly in our calculations. Therefore, we treat $N_{c}$ as a free effective parameter. As regards the ratio between the asymmetries, we have found a ratio equal to 1.61(1.63). This is mainly determined by the ratio $\sin\gamma / \sin\beta$, and more precisely by $\eta$. In Table 2, we show the values for the angles $\alpha$, $\beta$, $\gamma$. From all these numerical results, we can conclude that we need to determine the value of $N_{c}$ and the hadronic decay form factors more precisely, if we want to use the asymmetry, $a$, to constrain the CKM matrix elements.
In spite of the uncertainties just discussed, it is vital to realize that the effect of $\rho-\omega$ mixing in the $B \rightarrow \rho \pi$ decay is to remove any ambiguity concerning the strong phase, $\sin \delta$. As the internal top quark dominates the $b \rightarrow d$ transition, the weak phase in the rate asymmetry is proportional to $\sin \alpha \; (=\sin \phi)$, where $\alpha={\rm arg}\left[ - \frac{V_{td}V_{tb}^{\star}}{V_{ud}V_{ub}^{\star}}\right]$, and knowing the sign of $\sin \delta$ enables us to determine that of $\sin \alpha$ from a measurement of the asymmetry, $a$. We show in Fig.3 that the sign of $\sin \delta$ is always positive in our range, $0.98(0.94)<N_{c}<2.01(1.95)$ for all the models studied. Indeed, at the $\pi^{+}\pi^{-}$ invariant mass where the asymmetry parameter, $a$, reaches a maximum, the value of $\sin\delta$ is equal to one – provided $\rho-\omega$ mixing is included – over the entire range of $N_{c}$ and for all the form factors studied. So, we can remove, with the help of asymmetry, $a$, the uncertainty ${\rm mod}(\pi)$ which appears in $\alpha$ from the usual indirect measurements [@ref5] which yield $\sin 2\alpha$. By contrast, in the case where we do not take $\rho-\omega$ mixing into account, we find a small value for $\sin \delta$. In Figs.3 and 4 we plot the role of $\rho - \omega$ mixing in our calculations. We stress that, even though one has a large value of $\sin \delta$ around $N_{c}=1$ with no $\rho - \omega$ mixing, one still has a very small value for $r$ (Fig.4), and hence the CP violating asymmetry, $a$, remains very small in that case.
Branching ratios for $B^{+} \rightarrow \rho^{0} \pi^{+}$ and $B^{0} \rightarrow \rho^{+} \pi^{-} $
=====================================================================================================
Formalism
----------
With the factorized decay amplitudes, we can compute the decay rates using by the following expression [@ref19], $$\begin{aligned}
\Gamma(B \rightarrow VP)=\frac{\vec{|p_{\rho}|}^{3}}{8\pi m_{V}^{2}}
\left|\frac{A(B \rightarrow VP)}{\epsilon \cdot p_{B}}\right|^{2},
$$ where $$\begin{aligned}
|\vec{p_{\rho}}|=\frac{ \sqrt{ [m_{B}^{2}-(m_{1}+m_{2})^{2}][m_{B}^{2}-(m_{1}-m_{2})^{2}]}}{2m_{B}}
$$ is the c.m. momentum of the decay particles, $m_{1} (m_{2})$ is the mass of the vector (pseudoscalar) V(P), and $A(B \rightarrow VP)$ is the decay amplitude: $$\begin{aligned}
A(B \rightarrow VP)=\frac{G_{F}}{\sqrt{2}} \sum_{i=1,10}V_{u}^{T,P}a_{i}\langle VP | O_{i}| B \rangle.
$$ Here $V_{u}^{T,P}$ is CKM factor: $$\begin{aligned}
V_{u}^{T}=|V_{ub}V_{ud}^{\star}| \;\;\;\; \mbox{for} \;\;\;\; i=1,2 \;\;\;\; \mbox{and} & V_{u}^{P}=|V_{tb}V_{td}^{\star}| \;\;\;\; \mbox{for} \;\;\;\; i=3, \cdots, 10
$$ where the effective parameters are the following combinations $$\begin{aligned}
a_{2j}=c_{2j}^{\prime}+\frac{1}{N_{c}}c_{2j-1}^{\prime}, \;\;\; a_{2j-1}=c_{2j-1}^{\prime}+\frac{1}{N_{c}}c_{2j}^{\prime}, \;\; {\rm for} \;\; j=1, \cdots, 5
$$ and $\langle VP | O_{i}| B \rangle$ is a matrix element which is evaluated in the factorization approach. In the Quark Model, the diagram coming from the $B^{+} \rightarrow \rho^{0} \pi^{+}$ decay is the only one contribution. In our case, to be consistent, we should also take into account the $\rho - \omega$ mixing contribution when we calculate the branching ratio since we are working to the first order of isospin violation. Explicitly, we obtain for $B^{+} \rightarrow \rho^{0} \pi^{+}$, $$\begin{aligned}
BR(B^{+} \rightarrow \rho^{0} \pi^{+})=\frac{G_{F}^{2}|\vec{p}_{\rho}|^{3}}{32 \pi \Gamma_{B^{+}}}\Bigg|\bigg[V_{u}^{T}A^{T}_{\rho^{0}}(a_{1},a_{2})-V_{u}^{P}A^{P}_{\rho^{0}}(a_{3}, \cdots, a_{10})\bigg] \nonumber \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & & \\
+\bigg[V_{u}^{T}A^{T}_{\omega}(a_{1},a_{2})-V_{u}^{P}A^{P}_{\omega}(a_{3}, \cdots, a_{10})\bigg]\frac{\tilde{\Pi}_{\rho \omega}}{(s_{\rho}-m_{\omega}^{2})+im_{\omega}\Gamma_{\omega}}\Bigg|^{2}, \;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & &
$$ where the tree and penguin amplitudes are: $$\begin{aligned}
\sqrt{2}A^{T}_{\rho^{0}}(a_{1},a_{2})=a_{1}f_{\rho}F_{1}(m_{\rho}^{2})+a_{2}f_{\pi}A_{0}(m_{\pi}^{2}),\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & \\
\sqrt{2}A^{P}_{\rho^{0}}(a_{3}, \cdots, a_{10})=a_{4}\left[ -f_{\rho}F_{1}(m_{\rho}^{2})+f_{\pi}A_{0}(m_{\pi}^{2}) \right] +a_{10}\left[ \frac{1}{2}f_{\rho}F_{1}(m_{\rho}^{2})+f_{\pi}A_{0}(m_{\pi}^{2}) \right] \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & \\ +\frac{3}{2}(a_{7}+a_{9})f_{\rho}F_{1}(m_{\rho}^{2})\
-2(a_{6}+a_{8}) \left[ \frac{m_{\pi}^{2}f_{\pi}A_{0}(m_{\pi}^{2})}{(m_{u}+m_{d})(m_{b}+m_{u})}\right],\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\; & \\
\sqrt{2}A^{T}_{\omega}(a_{1},a_{2})=a_{1}f_{\rho}F_{1}(m_{\rho}^{2})+a_{2}f_{\pi}A_{0}(m_{\pi}^{2}),\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & \\
\sqrt{2}A^{P}_{\omega}(a_{3}, \cdots, a_{10})= \left[ 2(a_{3}+a_{5})+\frac{1}{2}(a_{7}+a_{9})\right]f_{\rho}F_{1}(m_{\rho}^{2})\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & \nonumber \\
- 2 (a_{8}+a_{6}) \left[ \frac{m_{\pi}^{2}f_{\pi}A_{0}(m_{\pi}^{2})}{(m_{u}+m_{d})(m_{b}+m_{u})}\right] \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & \nonumber \\
+ a_{4}\left[ f_{\pi}A_{0}(m_{\pi}^{2})+f_{\rho}F_{1}(m_{\rho}^{2})\right]
+ a_{10}\left[ f_{\pi}A_{0}(m_{\pi}^{2})-\frac{1}{2}f_{\rho}F_{1}(m_{\rho}^{2})\right], \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\ & \end{aligned}$$ where $\langle \rho^{0}| \bar{u}u | 0 \rangle = \frac{1}{\sqrt{2}}f_{\rho} m_{\rho} \epsilon_{\rho}$ and $\langle \pi^{+} | \bar{u}d | 0 \rangle = if_{\pi} p_{\mu}$. For $B^{0} \rightarrow \rho^{+} \pi^{-}$ we obtain, $$\begin{aligned}
BR(B^{0} \rightarrow \rho^{+} \pi^{-})=\frac{G_{F}^{2}|\vec{p}_{\rho}|^{3}}{16 \pi \Gamma_{B^{0}}}\left|V_{u}^{T}A^{T}_{\rho^{+}}(a_{2})-V_{u}^{P}A^{P}_{\rho^{+}}(a_{3}, \cdots, a_{10})\right|^{2}, \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; &
$$ where $$\begin{aligned}
A^{T}_{\rho^{+}}(a_{2})=a_{2}f_{\rho}F_{1}(m_{\rho}^{2}),\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\; & \\
A^{P}_{\rho^{+}}(a_{3},\cdots, a_{10})=(a_{4}+a_{10})f_{\rho}F_{1}(m_{\rho}^{2}). \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; &
$$ Moreover, we can calculate the ratio between these two branching ratios, in which the uncertainty caused by many systematic errors is removed. We define the ratio $R$ as: $$\begin{aligned}
R= \frac{BR(B^{0} \rightarrow \rho^{+} \pi^{-})}{BR(B^{+} \rightarrow \rho^{0} \pi^{+})},
$$ and, without taking into account the penguin contribution, one has, $$\begin{aligned}
R=\frac{2 \Gamma_{B^{+}}}{ \Gamma_{B^{0}}} \bigg| \bigg( \frac{a_{1}}{a_{2}}+ \frac{f_{\pi}A_{0}(m_{\pi}^{2})}{f_{\rho}F_{1}(m_{\rho}^{2})} \bigg) \bigg(1+\frac{\tilde{\Pi}_{\rho \omega}}{(s_{\rho}-m_{\omega}^{2})+im_{\omega}\Gamma_{\omega}}\bigg) \bigg|^{-2}\end{aligned}$$
Numerical Results
-----------------
The latest experimental data from the CLEO collaboration [@ref6] are: $$\begin{aligned}
BR(B^{+} \rightarrow \rho^{0}\pi^{+})=(10.4_{-3.4}^{+3.3} \pm 2.1) \times 10^{-6}, \;\;\;\; & & \\
BR(B^{0} \rightarrow \rho^{+}\pi^{-})=(27.6_{-7.4}^{+8.4} \pm 4.2) \times 10^{-6}, \;\;\;\;\; & &\\
R=2.65 \pm 1.9. \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & &
$$ We have calculated the branching ratios for $B^{0} \rightarrow \rho^{+}\pi^{-}$ and for $B^{+} \rightarrow \rho^{0}\pi^{+}$ for all models as a function of $N_{c}$. In Figs.5 and 6, we show the results for models 1 and 2 in order to make the dependence on form factors explicit.
The numerical results are very sensitive to uncertainties coming from the experimental data. For the branching ratio $B^{0} \rightarrow \rho^{+}\pi^{-}$ (Fig.5), we have a large range of values of $N_{c}$ and the CKM matrix elements over which the theoretical results are consistent with the experimental data from CLEO. However, all models do not give the same result: models 2 and 4 are very close to the experimental data for a large range of $N_{c}$, whereas models 1,3 and 5 are not. The reason is still the magnitude of the form factors. As a result, we have to exclude models 1,3 and 5 because their form factors are too small.
If we consider numerical results for branching ratio $B^{+} \rightarrow \rho^{0} \pi^{+}$ (Fig.6), it appears that all models are consistent with the experimental data for a large range of $N_{c}$. The effect of $\rho-\omega$ mixing (included in our calculations) on the branching ratio $B^{+} \rightarrow \rho^{0} \pi^{+}$ is around $30\%$. Numerical results for models 1, 3, 5 and models 2, 4 are very close to each other. The difference between the two branching ratios can be explained by the fact that for the $B^{0} \rightarrow \rho^{+}\pi^{-}$ decay, the tree and penguin contributions are both proportional to only one form factor, $F_{1}(k^{2})$. Thus, this branching ratio is very sensitive to the magnitude of this form factor ($F_{1}(k^{2})$ is related to $h_{1}=0.330$ or $0.625$ in models (1,3) and (2,4) respectively). On the other hand, for the decay $B^{+} \rightarrow \rho^{0} \pi^{+}$, both $F_{1}(k^{2})$ and $A_{0}(k^{2})$ are included in the tree and penguin amplitudes, and this branching ratio is less sensitive to the magnitude of the form factors.
If we look at the ratio $R$ between these two branching ratios, $BR(B^{+}\rightarrow \rho^{0} \pi^{+})$ and $BR(B^{0}\rightarrow \rho^{+} \pi^{-})$ – shown in Fig.7 – the results indicate that $R$ is very sensitive to the magnitude of the form factors, and that there is a large difference between models 1, 3, 5 and models 2 and 4. We investigated the ratio $R$ for the limiting CKM matrix elements as a function of $N_{c}$, finding that $R$ is consistent with the experimental data over the range $N_{c}$: $0.98(0.94)< N_{c}< 2.01(1.95)$, (The values outside(inside) brackets correspond to the choice $q^{2}/m_{b}^{2}=0.3(0.5)$). It should be noted that $R$, in particular, is not very sensitive to the CKM matrix elements. The small difference which does appear, comes from the penguin contributions (which may be neglected). If we just take into account the tree contributions in our calculations, $R$ is clearly independent of the CKM matrix elements (Eq.42).
From a comparison of the numerical results and the experimental data, we can extract a range of $N_{c}$, within which all results are consistent. In Table 3, we have summarized the allowed range of $N_{c}$ for $B^{+} \rightarrow \rho^{0}\pi^{+}$, $B^{0} \rightarrow \rho^{+}\pi^{-}$ and $R$, for models 1, 2, 3, 4 and 5 according to various choices of the CKM matrix elements. To determine the best range of $N_{c}$, we have to find some intersection of the values of $N_{c}$ for each model and for each set of CKM matrix elements, for which the theoretical and experimental results are consistent. This is possible and the results are shown in Table 4. In our study, it seems better to use the range intersection $\{N_{c}\}_{B^{+}} \cap \{N_{c}\}_{R}$ than $\{N_{c}\}_{B^{0}} \cap \{N_{c}\}_{B^{+}}$, for fixing the final interval $N_{c}$, since the experimental uncertainties are smaller in the former case, and since we are working to the first order of isospin violation ($\rho-\omega$ mixing). Finally, after excluding models 1,3 and 5, which are not consistent with all the experimental data, we are able to fix the upper and lower limit of the range of $N_{c}$, using the limiting values of the CKM matrix elements (Table 5). We find that $N_{c}$ should be in the range $0.98(0.94)< N_{c}< 2.01(1.95)$ where $N_{cmin}$ and $N_{cmax}$ correspond to $(\rho_{min},\eta_{min})$ and $(\rho_{max},\eta_{max})$ respectively.
Summary and discussion
======================
The first aim of the present work was to compare our theoretical results with the latest experimental data from the CLEO collaboration for the branching ratios $B^{+} \rightarrow \rho^{0}\pi^{+}$ and $B^{0} \rightarrow \rho^{+}\pi^{-}$. Our next aim was to study direct CP violation for the decay $ B^{+} \rightarrow \rho^{0}(\omega) \pi^{+} \rightarrow \pi^{+} \pi^{-} \pi^{+}$, with the inclusion of $\rho-\omega$ mixing. The advantage of $\rho-\omega$ mixing is that the strong phase difference is large and rapidly varying near the $\omega$ resonance. As a result the CP violating asymmetry, $a$, has a maximum, $a_{max}$, when the invariant mass of the $\pi^{+}\pi^{-}$ pair is in the vicinity of the $\omega$ resonance and $\sin\delta=+1$ at this point.
In the calculation of CP violating asymmetry parameters, we need the Wilson coefficients for the tree and penguin operators at the scale $m_{b}$. We worked with the renormalization scheme independent Wilson coefficients. One of the major uncertainties is that the hadronic matrix elements for both tree and penguin operators involve nonperturbative QCD. We have worked in the factorization approximation, with $N_{c}$ treated as an effective parameter. Although one must have some doubts about factorization, it has been pointed out that it may be quite reliable in energetic weak decays [@ref22; @ref23].
We have explicitly shown that the CP violating asymmetry, $a$, is very sensitive to the CKM matrix elements and the magnitude of the form factors, and we have determined a range for the maximum asymmetry, $a_{max}$, as a function of the parameter $N_{c}$, the limits of CKM matrix elements and the choice of $k^{2}/m_{b}^{2}=0.3(0.5)$. From all the models investigated, we found that CP violating asymmetry, $a_{max}$, varies from $-24\%(-19\%)$ to $-59\%(-48\%)$. We stressed that the ratio between the asymmetries associated with the limiting values of CKM matrix elements would be mainly determined by $\eta$. Moreover, we also stressed that without $\rho-\omega$ mixing, we cannot have a large CP violating asymmetry, a, since $a$ is proportional to both $\sin \delta$ and $r$. Even though $\sin \delta$ is large around $N_{c}=1$, $r$ is very small. As a result, we find a very small value for the CP violation in the decay $B^{\pm} \rightarrow \rho^{0}\pi^{\pm}$ (of the order of a few percent) without mixing. Once mixing is included, the sign of $\sin\delta$ is positive for $N_{c}:0.98(0.94)< N_{c}< 2.01(1.95)$. Indeed, at the $\pi^{+}\pi^{-}$ invariant mass where the asymmetry, $a$, is maximum, $\sin\delta=+1$, independent of the parameters used. Thus, by measuring $a$, we can erase the phase uncertainty mod($\pi$) in the determination of the CKM angle $\alpha$ which arises from the conventional determination of $\sin2\alpha$.
The theoretical results for the branching ratios for $B^{+} \rightarrow \rho^{0}\pi^{+}$ and $B^{0} \rightarrow \rho^{+}\pi^{-}$, were compared with the experimental data from the CLEO collaboration [@ref6]. These calculations show that it is possible to have theoretical results consistent with the experimental data without needing to invoke contributions from other resonances [@ref24; @ref25]. These data helped us to constrain the magnitude of the various form factors needed in the theoretical calculations of B decays[^4]. We determined a range of value of $N_{c}$, $0.98(0.94)< N_{c}< 2.01(1.95)$, inside of which the experimental data and the theoretical calculations are consistent for models 2 and 4.
We will need more accurate data in the future to further decrease the uncertainties in the calculation. If we can use both the CP violating asymmetry and the branching ratios, with smaller uncertainties, we expect to be able to determine the CKM matrix elements more precisely. At the very least, it appears that one will be able to unambiguouly determine the sign of $\sin \alpha$ and hence, remove the well known discrete uncertainties in $\alpha$ associated with the fact that indirect CP violation determines only $\sin 2\alpha$. We expect that our predictions should provide useful guidance for future investigations and urge our experimental collegues to plan seriously to measure the rather dramatic direct CP violation predicted here. [**Acknowledgments:**]{}
This work was supported in part by the Australian Research Council and the University of Adelaide.
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Fig.1 Asymmetry, $a$, for $k^{2}/m_{b}^{2}=0.3$, $ N_{c}=0.98(2.01)$ and limiting values of the CKM matrix elements for model 1: solid line(dot line) for $N_{c}=0.98$ and max(min) CKM matrix elements. Dashed line(dot dashed line) for $N_{c}=2.01$ and max(min) CKM matrix elements. Fig.2 Asymmetry, $a$, for $k^{2}/m_{b}^{2}=0.5$, $ N_{c}=0.94(1.95)$ and limiting values of the CKM matrix elements for model 1: solid line(dot line) for $N_{c}=0.94$ and max(min) CKM matrix elements. Dashed line(dot dashed line) for $N_{c}=1.95$ and max(min) CKM matrix elements. Fig.3 Determination of the strong phase difference, $\sin\delta$, for $k^{2}/m_{B}^{2}=0.3(0.5)$ and for model 1. Solid line(dot line) for $\tilde{\Pi}_{\rho \omega}=(-3500;-300)$ (i.e. with $\rho - \omega$ mixing). Dot dashed line(dot dot dashed line) for $\tilde{\Pi}_{\rho \omega}=(0;0)$, (i.e. with no $\rho - \omega$ mixing). Fig.4 Evolution of the ratio of penguin to tree amplitudes, $r$, for $k^{2}/m_{B}^{2}=0.3(0.5)$, for limiting values of the CKM matrix elements $(\rho,\eta)$ max(min), for $\tilde{\Pi}_{\rho \omega}=(-3500;-300)(0,0)$, (i.e. with(without) $\rho - \omega$ mixing) and for model 1. Figure 4a (left): for $\tilde{\Pi}_{\rho \omega}=(0;0)$, solid line(dot line) for $k^{2}/m_{B}^{2}=0.3$ and $(\rho,\eta)$ max(min). Dot dashed line(dot dot dashed line) for $k^{2}/m_{B}^{2}=0.5$ and $(\rho,\eta)$ max(min). Figure 4b (right): same caption but for $\tilde{\Pi}_{\rho \omega}=(-3500;-300)$. Fig.5 Branching ratio for $B^{0} \rightarrow \rho^{+} \pi^{-}$ for models $1(2)$, $k^{2}/m_{B}^{2}=0.3$ and limiting values of the CKM matrix elements. Solid line(dot line) for model 1 and max(min) CKM matrix elements. Dot dashed line(dot dot dashed line) for model 2 and max(min) CKM matrix elements. Fig.6 Branching ratio for $B^{+} \rightarrow \rho^{0}\pi^{+}$ for models $1(2)$, $k^{2}/m_{B}^{2}=0.3$ and limiting values of the CKM matrix elements. Solid line(dot line) for model 1 and max(min) CKM matrix elements. Dot dashed line(dot dot dashed line) for model 2 and max(min) CKM matrix elements. Fig.7 Calculation of the ratio of the two $\rho \pi$ branching ratios versus $N_{c}$ for models $1(2)$ and for limiting values of the CKM matrix elements: solid line(dot line) for model 1 with max(min) CKM matrix elements. Dot dashed line(dot dot dashed line) for model 2 with max(min) CKM matrix elements.
Table 1 Maximum CP violating asymmetry, $a_{max}(\%)$, for $B^{+} \rightarrow \pi^{+} \pi^{-} \pi^{+}$, for all models, limiting values of the CKM matrix elements (upper and lower limit), and for $k^{2}/m_{b}^{2}=0.3(0.5)$. Table 2 Values of the CKM unitarity triangle for limiting values of the CKM matrix elements. Table 3 Summary of the range of values of $N_{c}$ which is determined from the experimental data for various models and input parameters. Table 4 Determination of the intersection of the values of $N_{c}$ which are consistent with various subsets of the data for all models and all sets of CKM matrix elements. Table 5 Best range of $N_{c}$ determined from Table $4$ for $k^{2}/m_{b}^{2}=0.3(0.5)$.
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${N_{c}}_{min}=0.98(0.94)$ ${N_{c}}_{max}=2.01(1.95)$
-------------------------- ---------------------------- ----------------------------
model $1$
$ \rho_{max},\eta_{max}$ -33(-27) -29(-23)
$ \rho_{min},\eta_{min}$ -52(-43) -47(-37)
model $2$
$ \rho_{max},\eta_{max}$ -36(-29) -37(-28)
$ \rho_{min},\eta_{min}$ -57(-48) -59(-46)
model $3$
$ \rho_{max},\eta_{max}$ -32(-26) -29(-23)
$ \rho_{min},\eta_{min}$ -51(-43) -47(-37)
model $4$
$ \rho_{max},\eta_{max}$ -36(-29) -37(-28)
$ \rho_{min},\eta_{min}$ -57(-48) -59(-46)
model $5$
$ \rho_{max},\eta_{max}$ -29(-24) -24(-19)
$ \rho_{min},\eta_{min}$ -48(-40) -39(-31)
: Maximum CP violating asymmetry $a_{max}(\%)$ for $B^{+} \rightarrow \pi^{+} \pi^{-} \pi^{+}$, for all models, limiting values of the CKM matrix elements (upper and lower limit), and for $k^{2}/m_{b}^{2}=0.3(0.5)$. []{data-label="tab:fanfanfan"}
$(\rho,\eta)_{min}$ $(\rho,\eta)_{max}$
---------- --------------------- ---------------------
$\alpha$ $ 86^{o}02$ $ 89^{o}23$
$\beta$ $ 19^{o}50$ $ 30^{o}64$
$\gamma$ $ 74^{o}43$ $ 60^{o}11$
: Values of the CKM unitarity triangle for limiting values of the CKM matrix elements. []{data-label="tab:fanfanfanfan"}
$B^{+}$ $B^{0}$ $R$
-------------------------- ---------------------- -------------------------------------------- --------------------------------------------
model $1$
$ \rho_{max},\eta_{max}$ 0.76;1.69(0.73;1.62) 5.50; $\star \star$ ( – ; – ) 0.92;2.57(0.90;2.52)
$ \rho_{min},\eta_{min}$ 0.52;1.04(0.49;0.98) – ; – ( – ; – ) 0.97;2.88(0.94;2.76)
$ \rho_{max},\eta_{min}$ 0.61;1.25(0.59;1.20) – ; – ( – ; – ) 0.92;2.58(0.91;2.54)
$ \rho_{min},\eta_{max}$ 0.69;1.46(0.66;1.39) – ; – ( – ; – ) 0.95;2.75(0.90;2.66)
model $2$
$ \rho_{max},\eta_{max}$ 1.44;3.06(1.40;2.95) 0.54;1.33(0.54;1.38) 0.86;1.89(0.84;1.86)
$ \rho_{min},\eta_{min}$ 1.00;2.01(0.96;1.90) 1.10; $\star \star$ (1.15; $\star \star$ ) 0.92;2.09(0.89;2.01)
$ \rho_{max},\eta_{min}$ 1.15;2.32(1.12;2.22) 0.70; $\star \star$ (0.72; $\star \star$ ) 0.87;1.89(0.85;1.86)
$ \rho_{min},\eta_{max}$ 1.32;2.78(1.25;2.60) 0.63;2.77(0.62;3.12) 0.90;2.00(0.84;1.94)
model $3$
$ \rho_{max},\eta_{max}$ 0.74;1.65(0.72;1.60) – ; – ( – ; – ) 0.92;2.65(0.92;2.60)
$ \rho_{min},\eta_{min}$ 0.51;1.02(0.49;0.98) – ; – ( – ; – ) 0.97;2.95(0.94;2.85)
$ \rho_{max},\eta_{min}$ 0.60;1.22(0.57;1.19) – ; – ( – ; – ) 0.93;2.66(0.92;2.61)
$ \rho_{min},\eta_{max}$ 0.67;1.43(0.65;1.37) – ; – ( – ; – ) 0.92;2.79(0.92;2.71)
model $4$
$ \rho_{max},\eta_{max}$ 1.41;3.04(1.36;2.92) 0.56;1.44(0.57;1.52) 0.86;1.91(0.85;1.87)
$ \rho_{min},\eta_{min}$ 0.98;1.96(0.94;1.87) 1.16; $\star \star$ (1.23; $\star \star$ ) 0.90;2.10(0.89;2.03)
$ \rho_{max},\eta_{min}$ 1.14;2.29(1.10;2.21) 0.72; $\star \star$ (0.74; $\star \star$ ) 0.86;1.92(0.85;1.88)
$ \rho_{min},\eta_{max}$ 1.30;2.74(1.24;2.59) 0.64;3.49(0.66;4.03) 0.89;2.01(0.86;1.95)
model $5$
$ \rho_{max},\eta_{max}$ 0.75;2.18(0.73;2.10) – ; – ( – ; – ) 1.03; $\star \star$ (1.02; $\star \star$ )
$ \rho_{min},\eta_{min}$ 0.50;1.08(0.47;1.03) – ; – ( – ; – ) 1.09; $\star \star$ (1.06; $\star \star$ )
$ \rho_{max},\eta_{min}$ 0.58;1.38(0.55;1.34) – ; – ( – ; – ) 1.03; $\star \star$ (1.02; $\star \star$ )
$ \rho_{min},\eta_{max}$ 0.66;1.71(0.64;1.62) – ; – ( – ; – ) 1.04; $\star \star$ (1.04; $\star \star$ )
: Summary of the range of values of $N_{c}$ which is determined from the experimental data for various models and input parameters (numbers outside(inside) brackets are for $k^{2}/m_{b}^{2}=0.3(0.5)$). The notation: ([number]{} ; [number]{}) means that there is a upper and lower limit for $N_{c}$. ([number]{} ; $\star \star$ ) means that there is no upper limit for $N_{c}$ in the range $N_{c}$ \[0;10\]. ( – ; – ) means that there is no range of $N_{c}$ which is consistent with experimental data. []{data-label="tab:ecu"}
$\{N_{c}\}_{B^{+}} \cap \{N_{c}\}_{B^{0}}$ $\{N_{c}\}_{B^{+}} \cap \{N_{c}\}_{R}$ $\{N_{c}\}_{B^{0}} \cap \{N_{c}\}_{R}$
-------------------------- -------------------------------------------- ---------------------------------------- ----------------------------------------
model $1$
$ \rho_{max},\eta_{max}$ – ( – ) 0.92;1.69(0.90;1.62) – ( – )
$ \rho_{min},\eta_{min}$ – ( – ) 0.97;1.04(0.94;0.98) – ( – )
$ \rho_{max},\eta_{min}$ – ( – ) 0.92;1.25(0.91;1.20) – ( – )
$ \rho_{min},\eta_{max}$ – ( – ) 0.95;1.46(0.90;1.39) – ( – )
model $2$
$ \rho_{max},\eta_{max}$ – ( – ) 1.44;1.89(1.40;1.86) 0.86;1.33(0.84;1.38)
$ \rho_{min},\eta_{min}$ 1.10;2.01(1.15;1.90) 1.00;2.01(0.96;1.90) 1.10;2.09(1.15;2.01)
$ \rho_{max},\eta_{min}$ 1.15;2.32(1.12;2.22) 1.15;1.89(1.12;1.86) 0.87;1.89(0.85;1.86)
$ \rho_{min},\eta_{max}$ 1.32;2.78(1.25;2.60) 1.32;2.00(1.25;1.94) 0.90;2.00(0.84;1.94)
model $3$
$ \rho_{max},\eta_{max}$ – ( – ) 0.92;1.65(0.92;1.60) – ( – )
$ \rho_{min},\eta_{min}$ – ( – ) 0.97;1.02(0.94;0.98) – ( – )
$ \rho_{max},\eta_{min}$ – ( – ) 0.93;1.22(0.92;1.19) – ( – )
$ \rho_{min},\eta_{max}$ – ( – ) 0.92;1.43(0.92;1.37) – ( – )
model $4$
$ \rho_{max},\eta_{max}$ 1.41;1.44(1.36;1.52) 1.41;1.91(1.36;1.87) 0.86;1.44(0.85;1.52)
$ \rho_{min},\eta_{min}$ 1.16;1.96(1.23;1.87) 0.98;1.96(0.94;1.87) 1.16;2.10(1.23;2.03)
$ \rho_{max},\eta_{min}$ 1.14;2.29(1.10;2.21) 1.14;1.92(1.10;1.88) 0.86;1.92(0.85;1.88)
$ \rho_{min},\eta_{max}$ 1.30;2.74(1.24;2.59) 1.30;2.01(1.24;1.95) 0.89;2.01(0.86;1.95)
model $5$
$ \rho_{max},\eta_{max}$ – ( – ) 1.03;2.18(1.02;2.10) – ( – )
$ \rho_{min},\eta_{min}$ – ( – ) – ( – ) – ( – )
$ \rho_{max},\eta_{min}$ – ( – ) 1.03;1.38(1.02;1.34) – ( – )
$ \rho_{min},\eta_{max}$ – ( – ) 1.04;1.71(1.04;1.62) – ( – )
: Determination of the intersection of the values of $N_{c}$ which are consistent with various subsets of the data for all models and all sets of CKM matrix elements (numbers outside(inside) brackets are for $k^{2}/m_{b}^{2}=0.3(0.5)$). The notation: – ( – ) means that no common range of $N_{c}$ can be extracted from the data.[]{data-label="tab:fan"}
$\left\{N_{c}\right\}$ with mixing $\left\{N_{c}\right\}$ without mixing
--------------- ------------------------------------ ---------------------------------------
model $2$ 1.00;2.01(0.96;1.94) 0.85;1.74(0.85;1.74)
model $4$ 0.98;2.01(0.94;1.95) 0.84;1.76(0.84;1.75)
maximum range 0.98;2.01(0.94;1.95) 0.84;1.76(0.84;1.75)
minimum range 1.00;2.01(0.96;1.94) 0.85;1.74(0.85;1.74)
: Best range of $N_{c}$ determined from Table $4$ for $k^{2}/m_{b}^{2}=0.3(0.5)$. One takes the maximum interval of $N_{c}$, from Table 4, for each model (2,4). To determine the maximum(minimum) range, one consideres all models (2,4) and the largest(smallest) range of $N_{c}$. In comparison, we show the range of $N_{c}$ determined without $\rho - \omega$ mixing. []{data-label="tab:fanfan"}
[^1]: [email protected]
[^2]: [email protected]
[^3]: [email protected]
[^4]: We note that BABAR reported preliminary branching ratios for this channel after this paper was prepared [@ref26]. These results are consistent with the CLEO values.
| |
The most common reason for gooey no bake cookies is not boiling the mixture for long enough. As explained above, your cookies will not hold together if the sugar doesn’t reach soft ball stage. If you have had problems with runny cookies in the past, try cooking the mixture for longer on the stovetop.
How do you fix sticky no bake cookies?
If you used something sticky like butter, peanut butter, melted marshmallows or melted chocolate I would pop them in the fridge, so they firm up. If that doesn’t help, I would completely dip them in melted chocolate and let them harden in the fridge.
Is there a way to harden no bake cookies?
FAQ About No Bake Oatmeal Cookies
If your cookies are too soft and not set up that means you didn’t cook the cookie mixture long enough. In order for the cookies to harden properly the mixture must be boiled until it reaches a temperature of 230°F. This is approximately 1 ½ minutes on medium heat.
How do you harden no bakes?
How to Fix No-Bake Cookies. If your cookies are too wet and don’t set, try boiling the mixture a little longer. Don’t start timing until it is at a full boil, and then it should be about 1-2 minutes of boiling. If your No Bakes are crumbly and dry, stick closer to 1 minute.
Do you keep no bake cookies in the fridge?
The beauty of chocolate no bake cookies, is that they have a long shelf life compared to baked cookies. Once they have fully set, transfer them to an airtight container, with the layers separated by parchment, and they will keep at room temperature or in the fridge for up to 2 weeks.
How do you fix gooey No Bakes?
How to Fix Them. A good baseline is boiling the cookies for 1-2 minutes (start timing once the mixture is at a full boil). If you’ve made your no bake cookies too dry in the past, aim for closer to 1 minute. Also be sure to use the kind of oats the recipe calls for.
How do you harden peanut butter?
Place your pan, sheet or plate inside the refrigerator or freezer. Place the platter in the freezer for an hour to create rock-hard peanut butter or store the plate in the refrigerator for 45 minutes for a firm to slightly hard consistency.
How long does it take for no bakes to harden?
How long does it take no bake cookies to harden? I like to either leave them on the counter for about 30-45 minutes or pop them in the fridge for 15 if I’m feeling impatient!
Why won’t my cookies harden?
Change the Ingredients
You can try adding more flour to unbaked dough. Flour provides structure in baked goods and can make cookies firmer and crisper. In the future, try adding slightly less fat or replacing some of the white sugar with brown sugar. Brown sugar and fat give cookies flavor and also help keep them soft.
Can you freeze unbaked cookies?
You can freeze most cookies whether they’re baked or unbaked; both are great ways to preserve freshness.
How long does it take for cookies to set?
Generally, cookies are baked in a moderate oven — 350 degrees F (175 degrees C) — for 8 to 12 minutes, depending on the size of the cookie. For chewy cookies, allow them to cool on the baking sheet for 3 to 5 minutes before transferring to a cooling rack. | https://frugalinsa.com/fry/your-question-why-are-my-no-bakes-sticky.html |
Northwestern's running game to test Kentucky in Music City Bowl
Fugitive Eric Conn arrives back in Lexington under FBI custody
Jaden Springer finishes alley-oop in Lexington holiday tournament
Jaden Springer, a five-star prospect ranked in the top 10 of the class of 2020, finished an alley-oop during a Rocky River (N.C.) win over Bryan Station in the Traditional Bank Holiday Classic at Lexington Catholic on Wednesday, December 28, 2017.
Jaden Springer, a five-star prospect ranked in the top 10 of the class of 2020, finished an alley-oop during a Rocky River (N.C.) win over Bryan Station in the Traditional Bank Holiday Classic at Lexington Catholic on Wednesday, December 28, 2017. [email protected]
Jaden Springer, a five-star prospect ranked in the top 10 of the class of 2020, finished an alley-oop during a Rocky River (N.C.) win over Bryan Station in the Traditional Bank Holiday Classic at Lexington Catholic on Wednesday, December 28, 2017. [email protected]
Top-10 basketball player: UK offer is ‘something I want’
One of the nation’s top-ranked sophomores this week is playing at Lexington Catholic, located about two miles away from the University of Kentucky.
Or two miles away from, as he put it, “one of the biggest schools in America.”
Jaden Springer, who plays for Rocky River (N.C.), is ranked as a five-star prospect and as the No. 10 player in the class of 2020 by both ESPN and 247Sports. Rivals also has Springer rated as a five-star recruit but 13th nationally in his class.
The 6-foot-2, 176-pound shooting guard had 26 points (12-for-14 shooting), eight rebounds and two blocks in 24 minutes as Rocky River won 76-55 over a previously undefeated Bryan Station team Thursday night in the Traditional Bank Holiday Classic quarterfinals. He had 20 points and six rebounds in a come-from-behind 73-72 win against Doss late Wednesday night.
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Springer has reported offers from 11 schools, among them UCLA, Auburn, N.C. State and Tennessee. UK has not extended an offer but the Wildcats coaching staff has been in touch with Rocky River head coach Jason Moseley.
“Joel (Justus) does a great job of recruiting our area, so we’ve spoken with him,” said Moseley, a Louisville native who played at Eastern High School and Kentucky State University and worked as a basketball operations assistant under Tubby Smith. “He had wanted Jaden to come down for Big Blue Madness and we talked about it and thought it would be a better situation for him to wait and come down when we brought the team down so we didn’t have to make two trips.”
Springer on Friday will take an unofficial visit to UK along with senior teammate Jordan Campbell, who’s received some mid-major offers, Moseley said.
The team, which this week has gotten to practice at UK’s Joe Craft Center and at EKU’s facilities in Richmond, will be in attendance for the UK-Louisville basketball game Friday afternoon.
Jaden Springer just looks like he glides through the air sometime. Latest hoop puts Rocky River in front by six, 22-16. pic.twitter.com/mBAEIXD4Yr | |
Green River hit the road last week to make the short trip West to take on the 4-1 Evanston Red Devils.
Green River kicked to Evanston to start the game and the first defensive play of the game was a tackle for a loss by Green River’s Payton Tucker. Green River got gave up a couple of big runs, but on first down, Wolf Russell Ferrell stopped Evanston for a 1-yard gain. The Red Devils then picked up 15 yards and got an additional 5 yards on a face mask penalty.
The defense then stepped up once again with Tucker and Thomas Harvey back from injury and making the stop for no gain. Evanston went to the run again with senior Erik Gawaltney holding them to only a 1-yard gain. Evanston tried a pass on forth down, which fell incomplete. The Wolves stopped the Red Devils deep in Evanston territory on their 14-yard line.
The Wolves ran the ball three times themselves, with sophomore James King making runs of 7 and 5 yards for a first down, but on the next play Evanston blitzed which resulted in a fumble and recovered by the Red Devils. Good defense on the next three running plays held Evanston to 9 yards, but a face-mask penalty gave the Red Devils a first down and a 1-yard run was all it took for Evanston to score their first touchdown. After the P.A.T. was missed, the Red Devils led 6-0.
Green River got the ball and ran it three times, with one pass before they had to punt the ball back to Evanston. The punt was a line drive, which was returned 20 yards to give the Red Devils good field position to start their drive as the first quarter ended.
Evanston went to the run and after Anthony Mitchell stopped them for a 3-yard run on first down, the Red Devils’ Tyus Cornia broke loose for a 39-yard touchdown run. A two-point conversion was stopped, but Evanston increased their lead 12-0.
The Wolves on their third offensive series ran five plays, with the only positive play a solid 10-yard run for King, but the Wolves’ quarterback Dallan Serrano was sacked by Evanston for a 5-yard loss to end the series and the Wolves were forced to punt once more. Sophomore Seth White got off a good 37-yard punt, which was only returned 7 yards by Evanston.
Evanston ran six plays. The Wolves’ defense stopped Evanston on a fourth-down pass, which fell incomplete. Evanston’s defense again stopped the Wolves on three plays. A defensive struggle ensued, with the teams trading possession on their next drives.
Evanston ended the half after being stopped in their scoring drive. Their 36-yard field goal attempt was blocked by Anthony Mitchell.
The Wolves got the ball to start the second half and after a 23-yard kickoff return, the Wolves mounted an 11-play drive, but came away with no points. King carried the ball eight times in the drive for almost 40 yards and senior Kyle Ivie ripped off a big 16-yard run.
Evanston then mounted a long drive of their own, with eight running plays and a 15-yard penalty, ending with a 2-yard run into the endzone. This time the P.A.T. kick was good and Evanston had a 19-0 lead.
On the kickoff, senior Mathew Bernal returned the ball 31 yards. Serrano threw to Johnson for 12-yard pass completion and the took the ball himself for a 13-yard run. After the third quarter ended, Evanston’s defense again rose to the occasion and stopped the Wolves.
The Red Devils ran six plays, which included two holding penalties against them and good defense from the Wolves led by senior Michial Anderson and sophomore Canaan Eslick. Green River came up with a big play on defense when Mitchell blocked the punt, which was recovered by Gawaltney on the 2-yard line. On the next play Ivie took the ball in for the score and with the P.A.T good, the Wolves were on the board 19-7.
Evanston got the ball and the Wolves defense played strong holding Evanston to 4 yards on three plays. After a holding call, Green River started the drive on their 6-yard line. King ran 11 yards, but fumbled, which was recovered by Tayler Jensen. King then picked up 18 yards on a great run before picking up another 6 yards.
The Wolves went on a 14-play drive with another 8-yard run by King a 13-yard run by Serrano and a pass completion to Reese Allison, with the long drive ending in a 1-yard run touchdown by Serrano with the P.A.T. by Gawaltney cutting the score to 19-14.
Green River’s onside kick was recovered by Evanston and the Wolves strong second-half comeback ran out of time as Evanston ran out the clock for the 19-14 victory.
Green River will take on Powell in their next game who is known for a strong run defense and a team which continues to improve according to head coach Marty Wrage. | https://www.greenriverstar.com/story/2018/10/10/sports/wolves-narrowly-lose-to-evanston-in-19-14-game/5487.html |
A much awaited day in music history passed us on February 15th: the Grammy Awards. Did you even notice? Many artists talk about their dreams of winning a Grammy.
Where were you when this historic night happened?
Meghan Trainor, Ed Sheeran, and Taylor Swift were featured heavily on the show, and luckily, this year they all took home Grammys. To many artists, winning this highly prestigious award is a validation of their hard work and drive for success. There were many great performances that night, some being Taylor Swift’s “Out of the Woods”, Lady Gaga’s tribute to David Bowie, Sam Hunt’s “HeartBeat”, Carrie Underwood’s “Take Your Time”, Tori Kelly’s “Hollow” and John Legend, Demi Lovato, Luke Bryan, Meghan Trainor’s tribute to Lionel Richie. If you haven’t seen the Grammy Awards that happened this year, you definitely should. Between the amazing performances and seeing artists win awards for their hard work, The Grammy Awards is a definite night to watch.
The 58th annual Grammy Awards was a remarkable night for many artists. The big winners of the night were: | https://eaglescry.net/2474/entertainment/where-were-you-the-58th-annual-grammy-awards/ |
Zombie Horse Spawn mod will add to the game a natural spawn of zombies riding a zombie horse, now this mob can appear instead of a regular zombie with a probability of 5% (1 such mob for 20 normal), in the mod settings you can change the probability of occurrence.
Open the file \ .minecraft \ config \ zombiehs-common.toml (or zombiehs-common.cfg) with notepad:
chanceSurfaceZombieHasHorse (standard = 0.05, minimum 0, maximum 1.0): chance of a zombie appearing on a horse
shouldBurnZombieHorsesInDaylight (default = true): if set to false, the zombies on horses will not burn in the sun.
onlySpawnZombieHorsesOnSurface (default = true): if set to false then zombies on horses will also appear in dungeons.
Screenshots:
How to install the mod:
Install Forge
Install all additional mods if specified.
Download mod and copy to .minecraft \ mods
In the launcher, launch the version of the game with forge. | https://minecraftinc.com/zombie-horse-spawn-mod/ |
Recently, I found out that many users engaged in writing articles do not know how to count the number of characters in the text in Word or online services. Moreover, there are those who use manual calculation. So in this article, I would like to detail how to do it correctly and quickly.
Word editors
There are many different programs on the Internet for counting characters in a document. This can be some kind of online software, specially designed for such “work. But most often we use familiar text editors for this purpose.
The most popular and simplest is considered Microsoft Word. Just there is an elementary button that allows you to quickly and easily count how many characters you have already typed. Usually its name is “Number of words:…”. (in place of the ellipsis the number of words is marked). This tab is actually called statistics. It can always be found at the bottom of the editor window.
If you click on this button, a window pops up. There you need to pay attention to the lines with and without spaces. It is these digital combinations that show what we want to know.
It is worth noting that the statistics window has many other necessary functions. For example, the program easily calculates the number of:
- lines;
- words;
- pages;
- paragraphs.
For secretaries, authors, and editors, such features are a must. Earlier versions of Word also have statistics accounting, the only difference is the location. In older programs, this window can be accessed through the service tab. You select the item of interest from there.
In the newest versions of Word, “Statistics” is in the “Review” menu.
In LibreOffice Writer and in OpenOffice Writer, you also have to go into the service first. The appearance of the window itself remains the same. So the content won’t change either.
It may also happen that you are interested in the number of characters in some part only. The above editor will allow you to do this with ease. To do it this way:
- Highlight the desired text segment;
- Call the window with statistics (perform the same actions as described above).
There is a more expeditious way – the assignment of “hotkeys”. For this press Ctrl + Alt + . The cursor is transformed into an “interesting figure”. Now click on the number of words in the bar below. This will open a window with keyboard settings. Press the desired key combination (for example, Ctrl + Alt + S ), which will be easier for you to call the “Statistics” tab. After selecting, click on “Assign” and close it. Now the desired function will open when you activate the keyboard shortcut.
If you want to count characters in Excel, the TLSTR function comes in handy. That is the function that does all the “work”. With its help, you can find out the number of digits, spaces, letters in cells. In order to use it you need:
- Enter “=DLSTR(cell_address)” into the formula line;
- Press ENTER.
To determine the total number of characters in several cells at once you must use the Sum function together with DLSTR.
How to calculate the number of characters in the text online
Software developers do not sit still and are constantly creating new products that greatly facilitate our work and life. Any copywriter can easily name 2-3 sites that can determine the number of letters in the written text in real time. In addition, such resources can check the uniqueness, semantic core, spelling and other parameters. The list of their functions, as well as their choice, is quite wide, but we will consider only the most popular.
Serphunt
Serphunt is a comprehensive tool for determining the quality of text. Here’s what it can do:
- count the number of characters;
- analyze the density of keywords, additional words;
- Exact/inaccurate occurrences are taken into account;
- The results of scanning displays a mass of important SEO indicators: academic/classical “nausea”, the percentage of spam/water, etc;
- Determines the presence of “stop words” and their number (frequency).
Why all this is needed? Thus you get a complete picture of the compliance of the text with the existing TOR. You can make manual adjustments, run a rescan and immediately see the effect of the changes.
Serphant is a free service with a simple Russian-language interface. All you have to do is to go by link, fill in the required fields below the text insertion form (or you can leave it as is):
Then click on the button “Start checking” and wait until the procedure is completed, then look at the report in the table:
Text.ru
First of all, it is worth stopping at the full-fledged exchange – Text.ru. But in addition to this site may offer to determine the uniqueness and other parameters.
Conventionally, a single service is divided into three parts:
- Section SEO (determination of “tosh” and the calculation of the number of characters);
- Section Spelling (checks for errors and possible typos);
- Text uniqueness check.
All of these sections are used in the same way. If you want to count the number of letters, characters without spaces or with them, go to the main page of the resource text.ru, which will be a special blank window to insert – here you check the uniqueness.
To start the check, you need to paste the text fragment in the appropriate field. Should:
- to select it;
- press the Ctrl + C key to copy it;
- move to the still empty field to paste, using the combination Ctrl + V.
In principle, the standard procedure. Immediately after you paste your excerpt in this field, the system will calculate the number of characters and immediately see the results of their calculations in three lines;
- total characters;
- without spaces;
- number of words.
It is clear that the first will be the total number of characters with spaces, the second without them, and the third draws attention only to words. There is another option – go straight to check SEO-parameters – text.ru/seo. Here everything is similar – 3 blocks and after entering the text the desired information appears.
Advego
Another famous exchange, which provides its service for checking various text parameters, is Advego.ru.
Note immediately that on the main page you will not find anything you need. Here you will have to look for a tab with the CEO test. Then the algorithm repeats – in the field you insert a fragment, in a small block on top of the number of characters is marked.
But there will be marked with spaces, in order to know the number of printed characters without them will have to click on the check, it is located immediately under the large field. After you click on the button, the page will open with the required parameters.
The easiest online service
If you just need a counter, you can find sites on the Internet that are designed exclusively for counting – “character counting”. Such online resources do not need to install additional programs on your PC, there is no need to register and go to special pages. Such services work in real time, that is, “paste-check”.
To find them is simple – enter into any search engine “sign-reader” and click on the links suggested by Google or Yandex. Here’s a good resource.
To count, you need to:
- Highlight the text you plan to “analyze.”
- Copy the fragment to the clipboard, you can use keyboard shortcuts to do this.
- Open the service.
- Paste the element to be checked.
- Click on the calculation.
- Read the results.
If you need to quickly find out the size of the text length, it is better to use the functions of the text editor in which you work. In this case you do not have to copy and paste anything. But if you need to find out more information about a fragment – use specialized products.
I hope my article taught you how to count the number of characters in the text of Word and online. And what method do you use? I would be very interested to hear about your experiences, leave comments and subscribe to updates to the blog.Related Posts: | https://mobile-pedia.com/how-to-count-characters-in-word-or-online/ |
---
abstract: 'We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body problems, as, contrary to the standard level spacing distributions, it does not depend on the local density of states. Our Wigner-like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit. Quantitative improvements are found through a polynomial expansion. Examples from a quantum many-body lattice model and from zeros of the Riemann zeta function are presented.'
author:
- 'Y. Y. Atas'
- 'E. Bogomolny'
- 'O. Giraud'
- 'G. Roux'
title: The distribution of the ratio of consecutive level spacings in random matrix ensembles
---
Random matrix theory (RMT) was introduced half a century ago in order to describe statistical properties of energy levels of complex atomic nuclei [@porter]. Since then, it has proven to be very useful in a great variety of different fields [@mehta; @oxford].
In quantum chaos [@reviewRMT], RMT accurately accounts for the spectral statistics of systems whose classical counterpart is chaotic. While for quantum Hamiltonians which classical counterpart is integrable, the Berry-Tabor conjecture [@berry] states that their level statistics follows a Poisson law, Bohigas, Giannoni and Schmit conjectured [@bohigas] that the case of quantum Hamiltonians with chaotic classical dynamics must fall into one of the three classical ensembles of RMT. These three ensembles correspond to Hermitian random matrices whose entries are independently distributed respectively real (GOE), complex (GUE) or quaternionic (GSE) random variables (see [@mehta] for details).
Universality of RMT means that random matrix ensembles describe energy levels of real systems at a statistical level, and only in a local energy window when the mean level density is set to unity. Different models may and do have very different level densities and to compare usual spectral correlation functions like the nearest-neighbor spacing distribution one has to perform a transformation called unfolding [@porter; @mehta]. The unfolding procedure consists in changing variables from the true levels, $e_n$, to new ones, $\overline{e}_n =
\overline{\mathcal{N}}(e_n)$, where $\overline{\mathcal{N}}(e)$ is the mean number of levels less than $e$, obtained either by smoothing over many realizations in the case of disordered systems, or by local smoothing over an energy window large compared to the level spacing but small compared to variations of $\overline{\mathcal{N}}(e)$. The unfolded spectrum has automatically a mean level spacing equal to one, and its statistical properties can thus be directly compared with those of RMT. When a functional form of $\overline{\mathcal{N}}$ is known (as for billiards), or when large enough statistics is available, the unfolding is straightforward and easily implemented.
The situation is different for many-body problems, where $\overline{\mathcal{N}}(e)$ increases as a stretched exponential function of energy [@bethe] with, in general, unknown lower-order terms, and where it is difficult to calculate a large number of realizations because of an exponential increase of the Hilbert space dimension with the number of particles. In order to circumvent these difficulties which greatly diminish the precision of statistical tests in systems with a large number of particles, Oganesyan and Huse [@OgaHus07] proposed a new quantity defined as follows. Let $e_n$ be an ordered set of energy levels and $s_n=e_{n+1}-e_{n}$ the nearest-neighbor spacings. Oganesyan and Huse considered the distribution of the ratios $\tilde{r}_n$ defined by $$\tilde{r}_n=\frac{\mathrm{min}(s_n,s_{n-1})}{\mathrm{max}(s_n,s_{n-1})}=\mathrm{min}\left ( r_n,\frac{1}{r_n} \right )\ ,
\label{r_O_H}$$ where $$\label{defr}
r_n = \frac{s_n}{s_{n-1}}\ .$$ This quantity has the advantage that it requires no unfolding since ratios of consecutive level spacings are independent of the local density of states. Such a distribution thus allows a more transparent comparison with experiments than the traditional level spacing distribution. For this reason, many recent works use this quantity in different contexts of many-body systems. As an example let us mention quantum quenches, where the tools of RMT and quantum chaos were used as a phenomenological approach to quantify the distance from integrability on finite size lattices [@Kollath10; @Santos10; @Collura12], and also to investigate numerically many-body localization [@OgaHus07; @ioffe]. In these papers the distribution of consecutive level spacing ratios $P(\tilde{r})$ was shown to yield more precise results than the usual spacing distribution $P(s)$.
Although the distribution $P(r)$ plays a more and more important role in the interpretation of numerical data in quantum many-body Hamiltonians, only numerical estimates of it exist, and they are restricted to the GOE ensemble. RMT predictions for $P(r)$ are lacking. Such predictions are essential, both for understanding its shape for the three RMT ensembles, and for providing accurate estimates with simple formulas that could be used as an efficient tool.
This letter fills this gap by providing several important results on $P(r)$. First, we compute Wigner-like surmises for all three classical RMT ensembles, which already provide simple analytical formulae in very good agreement with exact numerics and analytical expressions in the large matrix size limit. Second, the remaining small differences are shown to be well fitted to numerical precision by a rather simple polynomial expansion. Results are then applied to examples on a quantum many-body Hamiltonian and to zeros of the Riemann zeta function.
*The ratio of consecutive level spacings distribution* – Instead of the quantity , we find it more natural to consider directly the ratio of two consecutive level spacings and its probability distribution $P(r)$. Indeed, let $\rho(e_1,e_2,e_3)$ be the probability density of three consecutive levels with $e_1\leq
e_2\leq e_3$. Assuming translation invariance, $\rho(e_1,e_2,e_3)=P(s_1,s_2)$ where $s_{i}=e_{i+1}-e_i$. Then $$\begin{aligned}
P(r)&\equiv &\int P(s_1,s_2)\delta\left (r-\frac{s_1}{s_2}\right )\mathrm{d}s_1\mathrm{d}s_2\nonumber\\
&=&\int_0^{\infty}P(r s_2,s_2)s_2 \mathrm{d}s_2\ .
\label{ps1s2}\end{aligned}$$ It is physically natural and can be proved analytically that for all classical RMT ensembles in the bulk of the spectrum (as well as for Poisson variables) the function $P(s_1,s_2)$ is symmetric, that is, $P(s_1,s_2)=P(s_2,s_1)$. This left-right symmetry implies then that the distributions of $r_n$ and $1/r_n$ are the same, so that $P(r)$ satisfies the following functional equation $$\label{symetrie}
P(r)=\frac{1}{r^2}P\left(\frac{1}{r}\right)\;.$$ Whenever holds, it is equivalent to consider the whole distribution $P(r)$ or to restrict the study to the support $[0,1]$ by considering the variable $\tilde{r}$ defined in , as was done in [@OgaHus07]. Here we concentrate on the whole distribution $P(r)$; since $P(\tilde{r})=2P(r)\Theta(1-r)$, our results can easily be translated to the restricted distribution. The integrable (Poisson) case trivially yields $P(r)=1/(1+r)^2$. We now address the behavior of $P(r)$ for RMT ensembles.
*Wigner-like surmise* – For Gaussian ensembles, the joint probability distribution of $N$ eigenvalues $e_i$ is given by [@mehta] $$\label{joint}
\rho(e_1,\ldots, e_N)
= C_{\beta,N} \!\!\! \prod_{1\leq i<j\leq N}|e_i-e_j|^{\beta}\prod_{i=1}^{N}e^{-\beta e_i^2 / 2},$$ where $C_{\beta,N}$ is a known normalization constant and $\beta$ is the Dyson index equal to 1 (GOE), 2 (GUE) or 4 (GSE). The exact calculation of $P(r)$ via Eq. requires the calculation of $P(s_1,s_2)$. Though this calculation is possible from (as shown at the end of this Letter), it ultimately requires the use of numerical methods and is not transparent. Exactly the same problem appears in the calculation of the usual nearest-neighbor spacing distribution, $P(s)$, which is the probability that the distance between two consecutive levels is $s$. Rather than cumbersome exact calculations, Wigner derived a simple approximate expression for $P(s)$, $$\label{psrmt}
P_W(s)=a_{\beta} s^{\beta} e^{-b_{\beta} s^{2}}\;,$$ with some explicitly known normalization constants $a_{\beta}$ and $b_{\beta}$ [@mehta]. This formula, called the Wigner surmise, corresponds to the exact result for $2\times 2$ matrices, and is in very good agreement with the exact large-$N$ expressions [@Dietz1990].
In a similar spirit, we obtain a formula for the ratio distribution of two consecutive spacings by performing the exact calculation for $3\times 3$ matrices, starting from the joint distribution for three eigenvalues $e_1,e_2,e_3$. If for instance $e_1\leq e_2\leq e_3$, the ratio $r$ is given by $(e_3-e_2)/(e_2-e_1)$. Consequently, the distribution $P(r)$ in the $3\times 3$ case is proportional to $$\int_{-\infty}^{\infty}\!{d}e_2\int_{-\infty}^{e_2}\!{d} e_1\int_{e_2}^{\infty}\!{d}e_3\
\rho(e_1,e_2,e_3)\ \delta\left(r-\frac{e_3-e_2}{e_2-e_1}\right) .$$ After the change of variables $x=e_2-e_1, y=e_3-e_2$, the integration over $e_2$ is trivial and the remaining integrals read $$\iint_{0}^{\infty}\!{d}x{d}y\,\delta(rx-y)x^{\beta+1}y^{\beta}(x+y)^{\beta}e^{-\frac12(x^2+y^2)+\frac16(x-y)^2}.$$ After performing the integrals, the surmise takes the simple form $$\label{pder}
P_W(r)=\frac{1}{Z_{\beta}}\frac{(r+r^2)^{\beta}}{(1+r+r^2)^{1+\frac{3}{2}\beta}},$$ with $Z_{\beta}$ the normalization constant (see values in Table \[tab:coef\]).
Ens. Poisson GOE GUE GSE
------------------------------------------ ------------------- ------------------------ ----------------------------------------------- ---------------------------------------------------
$Z_{\beta}$ - $\frac{8}{27}$ $\frac{4}{81}\frac{\pi}{\sqrt{3}}$ $\frac{4}{729}\frac{\pi}{\sqrt{3}}$
$c_{\beta}$ - $2\frac{\pi-2}{4-\pi}$ $4\frac{4-\pi}{3\pi-8}$ $8\frac{32-9\pi}{45\pi-128}$
$C$ - $0.233378$ $0.578846$ $3.60123$
$\langle{r}\rangle_W$ $\infty$ $ \frac{7}{4}$ $ \frac{27}{8}\frac{\sqrt{3}}{\pi}-\frac 1 2$ $ \frac{243}{80}\frac{\sqrt{3}}{\pi} - \frac 1 2$
$= 1.75$ $\approx 1.360735$ $\approx 1.174661$
$\langle{r}\rangle_{\text{fit}}$ - $1.7781(1)$ $1.3684(1)$ $1.1769(1)$
$\langle{\tilde{r}}\rangle_W$ $2\ln 2-1$ $4-2\sqrt{3}$ $ 2\frac{\sqrt{3}}{\pi}-\frac 1 2$ $ \frac{32}{15}\frac{\sqrt{3}}{\pi}-\frac 1 2$
$\approx 0.38629$ $\approx 0.53590$ $\approx 0.60266$ $\approx 0.67617$
$\langle{\tilde{r}}\rangle_{\text{fit}}$ - $0.5307(1)$ $0.5996(1)$ $0.6744(1)$
: Values of useful constants and averages $\langle{r}\rangle$ and $\langle{\tilde{r}}\rangle$. Averages $\langle.\rangle_W$ are calculated from Eq. , and $\langle.\rangle_{\text{fit}}$ from data in Fig. \[pderRMT\].[]{data-label="tab:coef"}
One can check that this result satisfies the symmetry . The distribution $P_W(r)$ has the same level repulsion at small $r$ than $P(s)$, namely $P_W(r) \sim r^\beta$, while for large $r$ the asymptotic behavior is $P_W(r) \sim r^{-(2+\beta)}$, contrary to the fast exponential decay of $P(s)$. This surmise also yields an analytic expression for the mean-values $\langle{r}\rangle_W$ and $\langle{\tilde{r}}\rangle_W$ widely used in the literature as a measure of chaoticity (see Table \[tab:coef\] for the exact values).
![(Color online) Distribution of the ratio of consecutive level spacings $P(r)$ for Poisson and RMT ensembles: full lines are the surmise Eq. , points are numerical results obtained by diagonalizing matrices of size $N=1000$ with Gaussian distributed entries, averaged over $10^5$ histograms. Inset: the distribution $P(\tilde{r})$.[]{data-label="pderRMT"}](fig1){width="0.82\linewidth"}
*Comparison with numerics and polynomial fit* – We now investigate the accuracy of the surmise with respect to numerical calculations for large matrix sizes. As illustrated in Fig. \[pderRMT\], the surmise is almost indistinguishable from numerics and can thus be used for practical purposes as a reference to discriminate between regular and chaotic dynamics. The absolute difference $\delta P(r) = P_{\text{num}}(r)-P_W(r)$ between numerics and the surmise is plotted in Fig. \[error\] for the three ensembles, and has a maximum relative deviation of about 5%, similar to the Wigner surmise for $P(s)$ [@Dietz1990].
In order to go beyond the surmise , we propose a simple expression which perfectly fits this remaining difference $\delta
P(r)$ within our computational accuracy. In order to fulfill Eq. , and assuming that $P(r)$ for large $N$ and $P_W(r)$ have the same asymptotic behavior for small and large $r$, a reasonable ansatz is the following expansion $$\label{fit}
\delta P_{\text{fit}}(r) = \frac{C}{(1+r)^2}
\left[ \left(r+\frac{1}{r}\right)^{-\beta}\!\!\!\! - c_{\beta} \left(r+\frac{1}{r}\right)^{-(\beta+1)} \right]\ ,$$ where $c_{\beta}$ is easily calculated from the normalization condition $\int_0^{\infty }\delta P(r) dr=0$ (see Table \[tab:coef\] for the exact value). Thus the large-$N$ expression for $P(r)$ can be fitted by the expression $P(r)=P_W(r)+\delta P_{\text{fit}}(r)$ with only one fitting parameter, which is the overall magnitude $C$ of the discrepancy. The best fit $C$ can be found in Table \[tab:coef\]. The corresponding curves are shown in Fig. \[error\]. Thanks to these very good fits, one can quickly infer accurate predictions for $\langle{r}\rangle$ and $\langle{\tilde{r}}\rangle$ and any average weighted by $P(r)$ (see Table \[tab:coef\]).\
![(Color online) Difference $\delta P(r) = P_{\text{num}}(r) -
P_W(r)$ between the numerics and the surmise . The fit function is given by Eq. . Green diamonds are results of exact calculations obtained from for GUE.[]{data-label="error"}](fig2){width="\linewidth"}
*Large-$N$ calculation* – We now turn to the exact calculation of $P(r)$ for GUE (i.e. $\beta=2$) in the limit $N\to\infty$, following a path similar to the derivation of the exact level spacing distribution $P(s)$.
Our starting point is Eq. 5.4.29 of Ref. . From that equation, one can check that the probability $p(-t,y,t)$ of having three consecutive levels at points $-t,y,t$ can be rewritten as $$\label{paxb}
p(-t,y,t)=\det(1-K)\det[R(x,z)_{x,z=-t,y,t}],$$ where $R(x,y)$ is the resolvent kernel, i. e. the kernel of the operator $(1-K)^{-1}K$, and $\det(1-K)$ is the Fredholm determinant of $K$. Operator $K$ is an integral operator whose action is defined as $$\label{oper}
(Kf)(x)=\int_{-t}^{t}K(x,y)f(y)\mathrm{d}y$$ with the kernel $$K(x,y)=\frac{\sin \pi(x-y)}{\pi(x-y)}\ .
\label{kernel}$$ It is known (see e. g. [@tracy]) that for a kernel of this form the resolvent kernel can be written as $$R(x,y)=\frac{Q(x)P(y)-Q(y)P(x)}{x-y},$$ with functions $Q(x)$ and $P(x)$ obeying integral equations $$\begin{aligned}
&&Q(x)-\int_{-t}^{t}K(x,y)Q(y)\mathrm{d}y=\frac{\sin \pi x}{\pi} ,\nonumber\\
&&P(x)-\int_{-t}^{t}K(x,y)P(y)\mathrm{d}y=\cos \pi x .
\label{QP}\end{aligned}$$ Function $Q(x)$ and $P(x)$ have many useful properties which allow to relate the calculation of spectral statistics for standard RMT ensembles to solutions of Painlevé equations (see e. g. [@tracy] and references therein). Though this approach is elegant, it still requires numerical resolution of Painlevé V equation for $\det(1-K)$ with subsequent solutions of linear equations for $Q(x)$ and $P(x)$ whose coefficients are determined by that solution.
We find it simpler to use the direct method proposed in [@bornemann] for computing $\det(1-K)$. It is based on a quadrature method for numerical evaluation of the integrals $$\label{discretization}
\int_{-t}^{t} f(x)dx =\sum_{k=1}^m w_k f(x_k)$$ appearing in the definition of the integral operator $K$. Such a discretization allows to approximate the determinant of the integral operator as a finite $m\times m$ determinant $$\det(1-K)\approx \det \big ( \delta_{jk}-K(x_j,x_k)w_k \big )$$ and functions $Q(x)$ and $P(x)$ defined in can be obtained by solving a linear system of $m$ equations. As noted in [@bornemann] the method quickly converges. The result is presented in Fig. \[error\], where the Clenshaw-Curtis method with up to 60 points of discretization has been used for the discretization . Figure \[error2\] (left) shows how the numerical results converge to the analytic large-$N$ calculation. As mentioned previously, the fit $P(r)=P_W(r)+\delta P_{\text{fit}}(r)$ works well for all $N$, with an overall $N$-dependent constant $C_N$ in . This constant, which gives the amplitude of the departure from the Wigner-like surmise, asymptotically decreases as $1/N$ (see inset of Fig. \[error2\]).
![(Color online) (a) $P(r)-P_{\infty}(r)$ for GUE and various matrix sizes. Inset: constant $C_N$ from the fit as a function of matrix size $N$ (solid line is a fit $1/N$). (b) Density distributions for the overlapping ratio $r^{(2)}_n =
(e_{n+2}-e_{n})/(e_{n+1}-e_{n-1})$ for Poisson variables and for the three classical RMT ensembles (same color code as in Fig. \[pderRMT\]). \[error2\]](fig3){width="\linewidth"}
*Applications* – To illustrate the above formalism, we investigate the spectral properties of a quantum Ising chain of $L$ spins$-\frac12$ with periodic boundary conditions in transverse field $\lambda$ and longitudinal field $\alpha$. The Hamiltonian is given by $$\hat{H}=-\sum_{n=1}^L\left(\hat{\sigma}_{n}^{x}\hat{\sigma}_{n+1}^{x} +\lambda\hat{\sigma}_{n}^{z}+\alpha\hat{\sigma}_{n}^{x}\right), \qquad \hat{\sigma}_{L+1}^{x}=\hat{\sigma}_{1}^{x}
\label{non_integrable_model}$$ where $\hat{\sigma}_{n}^{x,z}$ are the Pauli matrices at site $n$. This model recently attracted attention due to its experimental realization in cobalt niobate ferromagnet [@experiment]. The Hamiltonian (\[non\_integrable\_model\]) commutes with the operator $\hat{T}$ which translates the state by one lattice spacing and obeys $\hat{T}^L=1$. Consequently, $\hat{H}$ takes a block diagonal form in the basis of eigenstates of $\hat{T}$, and one has to consider separately each sector of symmetry. The result for one sector is illustrated in Fig. \[riemann\]. Other symmetry sectors give similar results. As expected, $P(r)$ agrees well with the GOE prediction with $\beta=1$.
Another example of application is to look at non-trivial zeros of the Riemann zeta function $$\zeta(s)=\sum_{n=1}^{\infty}\frac{1}{n^{s}}.$$ It is well established that statistical properties of Riemann zeros are well described by the GUE distribution [@riemann]. The probability distribution of the ratio of two consecutive spacings of these zeros, presented in Fig. \[riemann\], is in a perfect agreement with GUE formula with $\beta=2$.
![(Color online) Histogram of the ratio of consecutive level spacings $P(r)$. Black: Quantum Ising model in fields $\lambda=\alpha=0.5$ in sector of eigenvectors of $\hat{T}$ with eigenvalue $\omega_3$ ($\omega_j=\exp (2\mathrm{i}\pi
j/L),\hspace*{0.1cm} j=0,1,\ldots ,L-1$), for $L=18$ spins (dimension of eigenspace = 14541). Violet: The same for zeros of Riemann zeta function up the critical line ($10^4$ levels starting from the $10^{22}$th zero, taken from [@odlyzko]). Full lines correspond to the Wigner-like surmise Eq. (\[pder\]) with respectively $\beta=1$ and $\beta=2$. Inset: Difference between the numerics and these surmises.[]{data-label="riemann"}](fig4){width="0.8\linewidth"}
*Conclusion* – The investigation of spectral statistics in many-body problems with a large number of particles attracted wide attention in recent years. The absence of a well established expression for the mean density of states greatly diminishes the usefulness of standard correlation functions such as the nearest-neighbor spacing distribution. To avoid this problem, a new statistical tool has been proposed in [@OgaHus07], namely the distribution of the ratio of two consecutive level spacings.
The main result of the paper is the derivation of simple approximative formulae for this distribution for classical RMT ensembles. The resulting Wigner-like surmises agree very well with direct numerical calculations. The difference between the surmise and the exact calculations is small and can be fitted by a one-parameter polynomial formula with excellent accuracy.
In the same spirit, several different ratios can be introduced which generalize the quantity . Analytic expressions and Wigner-like surmises can be derived in a similar way for the density distributions of these quantities, and will be discussed elsewhere. An example is given in Fig. (right). All these distributions are universal in the sense that they apply without any unfolding or renormalization to spectra ranging from many-body systems to Riemann zeta function.
YYA was supported by the CFM foundation. GR acknowledges support from grant ANR-2011-BS04-012-01 QuDec.
[99]{}
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| |
Q:
Commutator of selfadjoint operators is selfadjoint and norm inequality
Suppose we have self-adjoint operators $A$ and $B$ on a Hilbertspace $H$ and $C$ denotes the commutator $C=AB-BA$. My task is the following:
Show that $iC$ is self-adjoint on $H$ and that $|(Cx,x)| \leq 2*||Ax||*||Bx||$ holds for all $x \in H$. Moreover find out for which $x$ the inequality becomes an equality.
To show that $iC$ is self-adjoint my attempt was to calculate $(iCx,x)$ straightforward using that $(Ax,x)=(x,Ax)$ and $(Bx,x)=(x,Bx)$ by the self-adjointness of A and B. This lead to
$$(iCx,x) \\= (i(AB-BA)x,x) \\= (iABx-iBAx,x) \\ = (iABx,x)-(iBAx,x) \\
= (iAx,Bx)-(iBx,Ax)$$
but now I don't now how to go on since I can't do $(iAx,Bx) = (ix,BAx)$ or am I wrong here?
For the inequality I use that $ (Ax,y) \leq ||Ax||*||y|| \leq ||A||*||x||*||y||$ and $||L(x)|| \leq ||L||*||x||$.
This leads to
$$ |(Cx,x)| = |(ABx-BAx,x)| = |(ABx,x)-(BAx,x)| \\
\leq |(ABx,x)| + |(BAx,x)| \;\;\;\; \operatorname{(Triangle-inequality)} \\
\leq ||A||*||Bx||*||x||+||B||*||Ax||*||x|| \\
\leq ||A||*||B||*||x||*||x|| + ||B||*||A||*||x||*||x|| \\
= 2*||A||*||B||*||x||^2 ,$$
but this is not what I am aiming for.
Some hints where I miscalculated and some (partial) solutions would be really nice.
A:
For the self-adjointness, you might note that (using that the scalar product is linear in one slot and antilinear in the other slot)
$$\langle iCx,x\rangle = \langle Cx, -i x\rangle = \langle x, i(-C)^*x\rangle = \langle x, iCx\rangle.$$
The last equality uses $C^*=(AB-BA)^* =B^*A^* -A^*B^* = -C$.
For the norm inequality you have
$$\vert \langle Cx, x\rangle \vert \leq \vert \langle ABx, x\rangle \vert + \vert \langle BAx, x\rangle \vert
=\vert \langle Bx, Ax\rangle \vert + \vert \langle Ax, Bx\rangle\vert
\leq 2\Vert Ax\Vert \cdot \Vert Bx\Vert,$$
where the last inequality is just Cauchy-Schwarz. Cauchy-Schwarz also tells us that we have equality iff there exists a scalar $\lambda \in \mathbb{C}$ such that $Ax=\lambda Bx$.
| |
By late 1863, the Civil War had devolved from a grand adventure to a bloody contest of attrition. As cold weather spread over the Eastern battle zones, the armies of blue and gray settled into their winter quarters and assayed the grim prospects that lay ahead. Penned up in dozens of prisons throughout the North and South were tens of thousands of prisoners of war. Their numbers had soared during the fall when the combatants stopped exchanging prisoners.
As winter began, Yankee captives dwelled in squalor and semi-starvation in the South's dismal war prisons, the most infamous of them being Libby Prison in Richmond, "The Bastille of the South." In a crowded former tobacco warehouse, Libby's 1200 Union officers survived on cornbread and bug-infested soup and slept without blankets on the bare floor. To leave Libby, a prisoner had to either die -- or escape.
During the night of February 9, 1864, one-hundred-nine steel-nerved officers wriggled through a 550-foot tunnel to freedom. When those who survived the all-out Rebel manhunt reached Washington, their testimony spurred far-reaching investigations into the treatment of Union prisoners -- and a new cycle of retaliation against Rebel captives.
Libby Prison Breakout tells the largely unknown story of the most important escape of the Civil War from a Confederate prison, one that ultimately increased the North's and South's willingness to use prisoners in waging "total war."
Public Affairs, Hardcover, 1st Edition, 1st Printing, 2010
THIS IS A BRAND NEW BOOK. | https://www.icannotlivewithoutbooks.net/store/p3741/Libby_Prison_Breakout%3A_The_Daring_Escape_from_the_Notorious_Civil_War_Prison_by_Joseph_Wheelan.html |
I have a MacPro running Mac OS X 10.7.4 with a Time Capsule connected by Ethernet. When Time Machine runs a verify of the backups it seems to stall at 72%, and if I let it run a LONG time I think I have seen it jump up to something like 92% done. But I am not at all sure I have seen it actually complete the verify (I typically end up doing Skip Verification.) Right now I have a verify running that has been stuck at 72% for maybe an hour, and I have waited 12 hours and a good bit more without getting to completion.
Granted there a pretty good number of files and folders, and the backups go back over a year and half - Time Machine prefs shows 193 GB out of 998 GB available on the Time Capsule
My question is if I just don't have sufficient patience, or if there is a problem. If there is a problem how do I attack it? | https://apple.stackexchange.com/questions/54517/time-machine-on-time-capsule-backup-verification-never-seems-to-complete |
---
author:
- 'Nguyen Bich Van\*'
title: 'Characteristic polynomials of color marked graphs, related to the normal form of the non linear Schrödinger equation'
---
Introduction
============
Some back ground {#background}
----------------
Consider the non linear Schrödinger equation(NLS): $$\label{01}
iu_t-\triangle u=\kappa |u|^qu+\partial_{\bar{u}}G(|u|^2), q\geq
1\in \N$$ where $u=u(t,\varphi),\varphi\in{\mathbb{T}}^n$, $G(a)$ is a real analytic function whose Taylor series start from the degree $q+2$. One can rescale the constant $\kappa=\pm1$. Passing to the Fourier representation: $$\label{02}
u(t,\varphi)=\sum_{k\in\Z^n}u_k(t)e^{(k,\varphi)};[u]_k:=u_k.$$ It is well-known that the equation can be written as an infinite dimensional Hamiltonian dynamical system $\dot{u}=\{H,u\}$, with Hamiltonian: $$\label{03}
H:=\sum_{k\in\Z^n}|k|^2u_k\bar{u}_k+\sum_{k\in\Z^n:\sum_{i=1}^{2q+2}(-1)^ik_i=0}u_{k_1}\bar{u}_{k_2}u_{k_3}\bar{u}_{k_4}. . . u_{2q+1}\bar{u}_{2q+2}+[G(|u|^2)]_0$$ on the scale of complex Hilbert spaces: $$\label{03'}
\bar{\ell}^{a,p}:=\{u=\{u\}_{k\in\Z^n}|\sum_{k\in\Z^n}|u_k|^2e^{2a|k|}|k|^{2p}:=||
u||^2_{a,p}<\infty; a>0, p>n/2\}$$ For $\epsilon$ sufficient small there is a analytic change of variables which brings to $H=H_N+P^{2q+2}(u)$, where $P^{2q+2}(u)$ is analytic of degree at least $2(q+2)$ in $u$ while: $$\label{03''}
H_N:=\sum_{k\in\Z^n}|k|^2u_k\bar{u}_k+\sum_{\alpha,\beta\in(\Z^n)^{\N}:|\alpha|=|\beta|=q+1;\sum_k(\alpha_k-\beta_k)k=0,\sum_k(\alpha_k-\beta_k)|k|^2=0}\left(\begin{array}{c}
q+1 \\
\alpha \\
\end{array} \right) \left(\begin{array}{c}
q+1 \\
\beta \\
\end{array}\right)u^\alpha \bar{u}^\beta$$ Let us now partition: $$\Z^n=S\cup S^c; S=\{v_1,. . . ,v_m\}$$ where $S$ is called *tangential sites*, it is some (arbitrarily large) subset of $\Z^n$ satisfying the *completeness condition*, $S^c$-*normal sites*. We set $$\label{04}
u_k:=z_k, k\in S^c, u_{v_i}:= \sqrt {\xi_i+y_i} e^{{{\rm i}}x_i}= \sqrt
{\xi_i}(1+\frac {y_i}{2 \xi_i }+\ldots ) e^{{{\rm i}}x_i}\;{\rm for}\;
i=1,\dots ,m,$$ considering $\xi_i$ as parameters, $|y_i|<\xi_i$, while $y,x,w:=z,\bar{z}$ are dynamical variables. We separate $H=N+P$ where $N$ is the *normal* form and collects all the terms of $H_N$ of degree $\leq 2$. We introduce $$\label{05}
A_r(\xi_1,. . . ,\xi_m)=\sum_{\sum_ik_i=r}\left(\begin{array}{c}
r \\
k_1,. . . ,k_m \\
\end{array}\right)^2\prod_i \xi_i^{k_i}$$ By Proposition 4. 4 in [@CM2] we have $$\label{06}
N=(\omega(\xi),y)+\sum_k\Omega_k(\xi)|z_k|^2+Q_M(x,\omega)$$ where $$\label{07} \omega=\omega_0+\nabla_\xi
A_{q+1}(\xi),\Omega_k=|k|^2+(q+1)^2A_{q+1}(\xi)$$ and $Q_M$ is given by formula \[08\]. Let $\{e_1,. . . ,e_m\}$ be a basis of $\Z^m$.
(edges)\[edge\] Consider the elements: $$\label{edg}X_q:=\{\ell=\sum_{j=1}^{2q}\pm
e_{i_j}=\sum_{i=1}^{m}\ell_ie_i, \ell \neq
0,-2e_i,\eta(\ell)\in\{0,-2\}\}$$ The [*support*]{} of an edge $\ell=\sum_in_ie_i$ is the set of indices $i$ with $n_i\neq 0$.
We have $\sum_i|\ell_i|\leq 2q$ and have imposed the mass constraint $\sum_i\ell_i=\eta(\ell)\in\{0,-2\}$. We call all the elements respectively the *black*, $\eta(\ell)=0$ and *red* $\eta(\ell)=-2$ *edges* and denote them by $X^0_q,
X_q^{-2}$ respectively. Notice that by our constraints the support of an edge contains at least 2 elements.
- When $\ell\in X_q^0$, we define $\mathcal{P}_\ell$ as the set of pairs $k,h$ satisfying $\sum_{j=1}^m\ell_jv_j+k-h=0;
\sum_{j=1}^m\ell_j|v_j|^2+|k|^2-|h|^2=0$.
- When $\ell\in X_q^{-2}$, we define $\mathcal{P}_\ell$ as the set of unordered pairs $\{h,k\}$ satisfying $\sum_{j=1}^m\ell_jv_j+k+h=0;
\sum_{j=1}^m\ell_j|v_j|^2+|k|^2+|h|^2=0$.
For every edge $\ell$, set $\ell=\ell^+-\ell^-$ and define $$\label{06'}
c(\ell)=c_q(\ell):=\left\{\begin{array}{ll}
(q+1)^2\xi^{\frac{\ell^++\ell^-}{2}}\sum_{\alpha\in \N^m;|\alpha+\l^+|_1=q}\left(\begin{array}{c}
q \\
\l^++\alpha\\
\end{array}\right)\left(\begin{array}{c}
q \\
\l^-+\alpha\\
\end{array}\right)\xi^{\alpha}, & \hbox{$\l\in X_q^0;$} \\
(q+1)q\xi^{\frac{\ell^++\ell^-}{2}}\sum_{\alpha\in \N^m;|\alpha+\l^+|_1=q-1}\left(\begin{array}{c}
q+1 \\
\l^-+\alpha\\
\end{array}\right)\left(\begin{array}{c}
q-1 \\
\l^++\alpha\\
\end{array}\right)\xi^{\alpha} , & \hbox{$\l\in X_q^{-2}$. } \\
\end{array}\right.$$ Then in [@CM2] it has been proved that: $$\label{08}
Q_M(x,\ome)=\sum_{\l\in X_q^0}c(\l)e^{\l x}\sum_{(h,k)\in
\mathcal{P}_{\l}}z_h\bar{z}_k+\sum_{\l\in
X_q^{-2}}c(\l)\sum_{{h,k}\in \mathcal{P}_{\l}}(e^{\l
x}z_hz_k+e^{-\l x}\bar{z}_h\bar{z}_k)$$
This is a very complicated infinite dimensional quadratic Hamiltonian, one needs to decompose this infinite dimensional system into infinitely many decoupled finite dimensional systems.
Momentum is the linear map $\pi:\Z^m\rightarrow \Z^n,\pi(e_i)=v_i$.
Define $iM(x)$ as the matrix of $ad(Q_M)$ in the basis $z_k,\bar{z}_k$, while $iM$ is the matrix of $ad(Q_M)$in the basis $e^{i\mu x}z_k,e^{-i\mu x}\bar{z}_k, \pi(\mu)+k=0$. In [@CM2] it was proved that $M$ is block diagonal with 2 blocks(denoted by $A,\pm$ in correspondence with each connected component $A$ of the geometric graph(c. f. \[gegr\] ). The control of these blocks is then needed to prove further non-degeneracy properties of this Hamiltonian. Set $$\Z^m_c=\{\mu\in \Z^m|-\pi(\mu)\in S^c\}.$$
The graph $\tilde{\Gamma}_S$ has as vertices the variables $z_h,
\bar{z}_k$ and edges corresponding to the non-zero entries of matrix $M(x)$ in the geometric basis(i. e. $z_h,\bar{z}_k$). The graph $\Lambda$ has as vertices $\Z^m_c \times
\Z/(2)$ and edges corresponding to the non-zero entries of $M$ in the frequency basis (i. e. $e^{i\mu x}z_k,e^{-i\mu x}\bar{z}_k,
\pi(\mu)+k=0$).
Two points $h,k\in S^c$ are connected by a black edge if $z_h,z_k$ are connected in $\tilde{\Gamma}_S$, while $h,k\in S^c$ are connected by a red edge if $z_h,\bar{z}_k$ are connected in $\tilde{\Gamma}_S$.
Take a connected component $A$ of $\Gamma_S$. Consider block $M_{A,+}$. Given two elements $a\neq b\in A$. By formula \[08\] the matrix element $M_{a,b}$ is non-zero if and only if they are joined by an edge $\l$ and then $M_{a,b}=c(\l)$ if $b=e^{i\mu
x}z_k$ or $M_{a,b}=-c(\l)$ if $b=e^{-i\mu x}\bar{z}_k$. $$M_{A,-}=-\bar{M}_{A,+}$$ In order to describe the matrix $iN_A$ of $ad(N)$ on A, we have to finally compute the diagonal terms. One contribution comes from \[07\] and assumes the value $\nabla_\xi
A_{q+1}(\xi). \mu$ on the element $e^{i\mu x}z_k$. In application of the KAM algorithm to our Hamiltonian a main point is to prove the validity of the second Melnikov condition. The problem arises in the study of the second Melnikov equation where we have to understand when it is that two eigenvalues are equal or opposite. The condition for a polynomial to have distinct roots is the non–vanishing of the discriminant while the condition for two polynomials to have a root in common is the vanishing of the resultant. In our case these resultants and discriminants are polynomials in the parameters $\xi_i$ so, in order to make sure that the singularities are only in measure 0 sets (in our case even an algebraic hypersurface), it is necessary to show that these polynomials are formally non–zero. This is a purely algebraic problem involving, in each dimension $n$, only finitely many explicit polynomials and so it can be checked by a finite algorithm. The problem is that, even in dimension 3, the total number of these polynomials is quite high (in the order of the hundreds or thousands) so that the algorithm becomes quickly non practical. In order to avoid this we have experimented with a conjecture which is stronger than the mere non-vanishing of the desired polynomials. We expect our polynomials to be irreducible and separated, in the sense that the connected component of the graph giving rise to the block and its polynomial can be recovered from the associated characteristic polynomial.
A geometric graph {#gegr}
-----------------
To the set $S$ we associate the following configuration, given two distinct elements $v_i,v_j\in S$ construct the sphere $S_{i,j}$ having the two vectors as opposite points of a diameter and the two hyperplanes, $H_{i,j},\ H_{j,i}$, passing through $v_i$ and $v_j$ respectively, and perpendicular to the line though the two vectors $v_i,v_j. $
From this configuration of spheres and pairs of parallel hyperplanes we deduce a [*c*ombinatorial colored graph]{}, denoted by $\Gamma_S$, with vertices the points in $\R^n$ and two types of edges, which we call [*b*lack]{} and [*r*ed]{}.
- A black edge connects two points $p\in H_{i,j},\ q\in H_{j,i}$, such that the line $p,q$ is orthogonal to the two hyperplanes, or in other words $q=p+v_j-v_i$.
- A red edge connects two points $p,q\in S_{i,j} $ which are opposite points of a diameter.
[**The Problem**]{}The problem consists in the study of the connected components of this graph. Of course the nature of the graph depends upon the choice of $S$ but one expects a relatively simple behavior for $S$ [*g*eneric]{}. It is immediate by the definitions that the points in $S$ are all pairwise connected by black and red edges and it is not hard to see that, for generic values of $S$, the set $S$ is itself a connected component which we call the [*s*pecial component]{}.
The Cayley graphs\[Cg\]
-----------------------
In order to understand the graph $\Gamma_S$ we develop a formal setting. Let $G$ be a group and $X=X^{-1}\subset G$ a subset.
### Marked graphs
An $X$–marked graph is an oriented graph $\Gamma$ such that each oriented edge is marked with an element $x\in X$. $$\xymatrix{ &a\ar@{->}[r]^{x} &b& &a\ar@{<-}[r]^{\ x^{-1}} &b& }$$ We mark the same edge, with opposite orientation, with $x^{-1}$. Notice that if $x^2=1$ we may drop the orientation of the edge.
### Cayley graphs
A typical way to construct an $X$–marked graph is the following. Consider an action $G\times A\to A$ of $G$ on a set $A$, we then define.
The graph $A_X$ has as vertices the elements of $A$ and, given $a,b\in A$ we join them by an oriented edge $a\stackrel{x}\rightarrow b$, marked $x$, if $b=xa,\ x\in X$.
A special case is obtained when $G$ acts on itself by left (resp. right) multiplication and we have the Cayley graph $G_X^l$ (resp. $G_X^r$). We concentrate on $G_X^l$ which we just denote by $G_X$.
### The linear rules
Denote by ${\Z^m}:=\{\sum_{i=1}^ma_ie_i,\ a_i\in\Z\}$ the lattice with basis the elements $e_i$. We consider the group $G:={\Z^m}\rtimes\Z/(2)$ semi–direct product. Its elements are couples $(a,\sigma)$ with $a\in \Z^m$, $\sigma=\pm 1$. It will be notationally convenient to identify by $a$ the element $(a,+1)$ and by $\tau$ the element $(0,-1)$. Note the commutation rules $a\tau= \tau (-a)$. Sometimes we refer to the elements $a=(a,+1)$ as [*black*]{} and $a\tau=(a,-1)$ as [*red*]{}.
We set $\Lambda$ to be the Cayley graph associated to the elements $X_q:=X^0_q\cup X^{-2}_q$.
### From the combinatorial to the geometric graph
In our geometric setting, we have chosen a list $S$ of vectors $v_i$ and we then define $\pi:\Z^m\to \R^n$ by $\pi: e_i\mapsto
v_i$.
We then think of $G$ also as linear operators on $\R^n$ by setting $$\label{azione}
a k:= -\pi(a)+ k,\ k\in\R^n,\ a\in \Z^m\,,\quad \tau k= - k$$ We extend $\pi:\Z^m\to \R^n$ to $\Z^m\rtimes \Z/(2)$ by setting $\pi( a\tau):= \pi(a) $ so that $-\pi$ is just the orbit map of 0 associated to the action (the sign convention is suggested by the conservation of momentum in the NLS).
We then have that $X$ defines also a Cayley graph on $\R^n$ and in fact the graph $\Gamma_S$ is a subgraph of this graph.
There are symmetries in the graph. The symmetric group $S_m$ of the $m!$ permutations of the elements $e_i$ preserves the graph. We have the right actions of $G$, on the graph: The sign change $$\label{sitr}(b,\sigma)\mapsto (b,\sigma)\tau=b
\sigma\tau,\quad (b,\sigma)\mapsto (b,\sigma) a= (b+\sigma
a,\sigma),\ \forall a,b\in{\Z^m}.$$ Up to the $G$ action any subgraph an be translated to one containing 0.
We give definitions which are useful to describe the graphs that appear in our construction.
\[CMG\] A [*complete marked graph*]{}, on a set $A\subset
{\Z^m}\rtimes\Z/(2)$ is the full sub–graph generated by the vertices in $A$.
A graph $A$ with $k+1$ vertices is said to be of [*dimension*]{} $k$
Characteristic polynomials of complete color marked graphs
----------------------------------------------------------
As we said in \[background\] for every complete color marked graph $\mathcal{G}$ we will consider the matrix $C_{\mathcal{G}}$ indexing by vertices of $\mathcal{G}$ as computed in [@CM2] §11. 1. 1:
Given $(a,\sigma), a=\sum_{i=1}^{m}n_ie_i$ set $$\label{1}
(q+1) a(\xi):=
\sum_{i=1}^{m}n_i\frac{\partial}{\partial\xi_i}A_{q+1}(\xi)$$ then
- In the diagonal at the position $(a,\sigma), a=\sum_{i=1}^{m}n_ie_i$ we put $$\label{1}
\begin{cases}
(q+1) a(\xi)\quad\text{if}\ \sigma=1\\
-(q+1) a(\xi)+2(q+1)^2A_q(\xi)\quad\text{if}\ \sigma=-1
\end{cases}$$
- At the position $((a,\sigma_a),(b,\sigma_b))$ we put 0 if they are not connected, otherwise we put $\sigma_b c(\ell)$ (c. f. \[06’\], where $\ell$ is the edge connecting $a,b$.
Define $\chi_{{{\mathcal{G}}}}=\chi_{C_{\mathcal{G}}}(t)=det(tI-C_\mathcal{G})$- the characteristic polynomial of $C_\mathcal{G}$. As we said in \[background\] in order to check the second Melnikov condition we expect that $\chi_{\mathcal{G}}$ are irreducible over $\Z$ and separated. In [@CM3] we have proved this for the case $q=1,n\in\N$. Here we start to prove irreducibility and separation for bigger $q$ and low dimensions.
Irreducibility of characteristic polynomials
=============================================
\[lem1\] For any $a\in\Z^m$: $a(\xi)$ has integer coefficients.
Let $a=\sum_in_ie_i$. We have $$\frac{\partial}{\partial\xi_i}A_{q+1}(\xi)=\sum_{\beta\in\mathbb{N}^m;|\beta|_1=q+1;\beta_i\geq
1}(\begin{array}{c}q+1\\\beta\end{array})^2\beta_i\xi_1^{\beta_1}. . . \xi_i^{\beta_i-1}. . . \xi_m^{\beta_m}$$ $$(\begin{array}{c}q+1\\\beta\end{array})^2\beta_i=(\begin{array}{c}q+1\\\beta\end{array})(\begin{array}{c}q\\\beta_1,. . . ,\beta_i-1,. . . ,\beta_m\end{array})(q+1)$$ is divisible by $q+1$.
Hence all diagonal elements of $C_\mathcal{G}$ are divisible by $q+1$. Besides by the formula \[06’\] all off-diagonal elements of $C_\mathcal{G}$ are also divisible by $q+1$. Thus we can write: $$C_\mathcal{G}=(q+1)\tilde{C}_\mathcal{G}\Rightarrow \chi_{C_{\mathcal{G}}}(t)=det(tI-C_\mathcal{G})=det((q+1)\tilde{t}I-(q+1)\tilde{C_\mathcal{G}})=(q+1)^{n+1}\chi_{\tilde{C_\mathcal{G}}}(\tilde{t})$$ So in order to prove the irreducibility and the separation of the polynomials $\chi_{C_\mathcal{G}}$ it is enough to prove the irreducibility and the separation of the polynomials $\chi_{\tilde{C}_\mathcal{G}}$. For simplicity we will denote $\chi_{\tilde{C}_\mathcal{G}}$ also by $\chi_{\mathcal{G}}$, and we will redefine $ c(\l)$ by division the right hand sides of \[06’\] by $q+1$: $$\label{06''}
c(\ell)=c_q(\ell):=\left\{
\begin{array}{ll}
(q+1)\xi^{\frac{\ell^++\ell^-}{2}}\sum_{\alpha\in \N^m;|\alpha+\l^+|_1=q}\left(\begin{array}{c}
q \\
\l^++\alpha\\
\end{array}
\right)\left(
\begin{array}{c}
q \\
\l^-+\alpha\\
\end{array}
\right)\xi^{\alpha}, & \hbox{$\l\in X_q^0;$} \\
q\xi^{\frac{\ell^++\ell^-}{2}}\sum_{\alpha\in \N^m;|\alpha+\l^+|_1=q-1}\left(\begin{array}{c}
q+1 \\
q-1 \\
\l^++\alpha\\
\end{array}
\right)\xi^{\alpha} , & \hbox{$\l\in X_q^{-2}$. } \\
\end{array}
\right.$$
Take a complete colored marked graph ${\mathcal A}$ and compute its characteristic polynomial $\chi_\A(t)$. We have:
\[lafatt\] When we set a variable $\xi_i=0$ in $\chi_\A(t)$ we obtain the product of the polynomials $\chi_{\A_i}(t)$ where the $A_i$ are the connected components of the graph obtained from $\A$ by deleting all the edges in which $i$ appears as index, with the induced markings (with $\xi_i=0$).
This is immediate from the form of the matrices.
\[rem3. 1\] $$\frac{\partial}{\partial\xi_i}A_{q+1}(\xi)|_{\xi_i=\xi_j}=\frac{\partial}{\partial\xi_j}A_{q+1}(\xi)|_{\xi_i=\xi_j}\forall
i,j$$
\[rem1. 2\] Let $b=\sum_{i=1}^{k}n_ie_i,n_i\neq 0;\sum_{i=1}^kn_i=0$. Then: $$\label{eqrem1. 2}
b(\xi)|_{\xi_1=\xi_2=\ldots=\xi_k}=0$$
By the remark \[rem3. 1\] we have: $$b(\xi)|_{\xi_1=\xi_2=. . . =\xi_k}=\sum_{i=1}^{k}n_i\frac{\partial}{\partial \xi_i}A_{q+1}(\xi)|_{\xi_1=\xi_2=. . . =\xi_k}=\frac{\partial}{\partial \xi_1}A_{q+1}(\xi)|_{\xi_1=\xi_2=. . .
=\xi_k}\sum_{i=1}^{k}n_i=0$$.
\[rem1.4\] Let $\l=\l^+-\l^-$ be an edge. We have:
i\) If $\l$ is a black edge, then $|\l^+|_1=|\l^-|_1\leq
q$.
ii\) If $\l$ is a red edge, then $|\l^+|_1\leq q-1, |\l^-|_1\leq
q+1$.
By the definition of edges we have : $$\label{40} |\l^+|_1+|\l^-|_1\leq 2q.$$ On the other hand:
i\) If $\l$ is a black edge, then $$\label{41}|\l^+|_1-|\l^-|_1=0.$$ From and we get $|\l^+|_1=|\l^-|_1\leq q.$
ii\) If $\l$ is red edge, then $$\label{42} |\l^+|_1-|\l^-|_1=-2.$$ From and we get $|\l^+|\leq q-1,|\l^-|_1\leq
q+1$.
\[rem5\]: Let $\l=\sum_{i=1}^kn_ie_i=\l^+-\l^-,n_i\neq 0,$ be an edge.
i\) If $\l$ is a black edge and $k=m$, then $|\l^{+}|_1=|\l^{-}|_1=q$ and $c(\l)=(q+1)\xi^{(\l^++\l^-)/2}\left(\begin{array}{c}
q \\
\l^+\\
\end{array}\right)\left(\begin{array}{c}
q \\
\l^- \\
\end{array}\right)$.
ii\) If $\l$ is a red edge and $k=m$, then $|\l^{+}|_1=q-1,
|\l^{-}|_1=q+1$ and $c(\l)=q\xi^{(\l^++\l^-)/2}\left(\begin{array}{c}
q+1 \\
\l^-\\
\end{array}\right)\left(\begin{array}{c}
q-1 \\
\l^+\\
\end{array}\right)$.
Since $S=\{v_1,...,v_m\}$ is some arbitrarily large set, we may suppose $m\geq 2q$. If $k=m$ then $|\l^+|_1+|\l^-|_1=\sum_{i=1}^mn_i\geq m\geq 2q$. Moreover, by definition of edges $\sum_{i=1}^mn_i\leq 2q$. Hence: $$\label{38}|\l^+|_1+|\l^-|_1=\sum_{i=1}^mn_i=2q.$$ i) When $\l$ is a black edge, we have $$\label{37}|\l^+|_1-|\l^-|_1=0$$ From and we get $|\l^+|_1=|\l^-|_1=q$. By formula we obtain $c(\l)=(q+1)\xi^{(\l^++\l^-)/2}\left(\begin{array}{c}
\end{array}\right)$. ii) When $\l$ is a red edge, we have $$\label{39}|\l^+|_1-|\l^-|_1=-2$$ From and we get $|\l^+|_1=q-1,|\l^-|_1=q+1$. By formula we obtain $c(\l)=q\xi^{(\l^++\l^-)/2}\left(\begin{array}{c}
We finally recall Proposition 14 of [@CM2]
\[ilrido\] (i) For $n=1$ and for generic choices of $S$, all the connected components of $\Gama$ are either vertices or single edges.
\(ii) For $n=2$, and for every $m$ there exist infinitely many choices of generic tangential sites $S=\{v_1,\ldots,v_m\}$ such that, if $A$ is a connect component of the geometric graph $\Gama$, then $A$ is either a vertex or a single edge.
**Obtained results**: For graphs reduced to one vertex the statement is trivial. At the moment we are able to prove the irreducibility and separation in dimension 1, and dimension 2, under the assumptions of Proposition \[ilrido\] for all $q$ since all graphs which appear have at most one edge.
One edge
--------
For any $q$ and any connected color marked graph with one edge the characteristic polynomial is irreducible.
We choose the root so that the graph has one of the forms: $$\xymatrix{ &0\ar@{-}[r]^{\l}_{black} &\ell&}\quad \text{
or}\quad
\xymatrix{ &0\ar@{=}[r]^{\l}_{red} &\ell&}$$ Let $ \ell=\sum_{i=1}^kn_ie_i, n_i\neq 0$. We have $$\label{7}\ell(\xi)=\frac{1}{q+1}\sum_{i=1}^kn_i\frac{\partial}{\partial\xi_i}A_{q+1}(\xi)=\sum_{i=1}^kn_i\sum_{\beta\in\mathbb{N}^m;|\beta|_1=q+1;\beta_i\geq
1}(\begin{array}{c}q+1\\\beta\end{array})(\begin{array}{c}q\\\beta_1,. . . ,\beta_i-1,. . . ,\beta_m\end{array})\xi_1^{\beta_1}. . . \xi_i^{\beta_i-1}. . . \xi_m^{\beta_m}$$Set $\bar \ell(\xi):=\ell(\xi)$ if $\eta(\ell)=0$ and $\bar \ell(\xi):=-\ell(\xi)+2(q+1)A_q(\xi)$ if $\eta(\ell)=-2. $
\[rem1\] For every $i$ in the support of $\l$, unless $q=4$ and $\ell=-5e_i+e_j+e_k+e_m$, the polynomial $\bar \ell(\xi)$ contains the term $\xi_i^q$ with non zero coefficient.
**Proof:** In the formula of $\ell(\xi)$ there is the monomial: $$(n_i+(q+1)\sum_{h\neq i}n_h)\xi_i^q,$$ since $\sum_hn_h=\eta(\ell)$ this equals $$-qn_i\xi_i^q\quad\text{if}\ \eta(\ell)=0$$ and $$[n_i+(q+1)(-2-n_i)]\xi_i^q\quad\text{if}\ \eta(\ell)=-2$$ In $A_q(\xi)$ the monomial $\xi_i^q$ appears with coefficient 1,so we get in $\bar{\l}$ the coefficient of $\xi_i^q$ is: $$\label{coef}
-n_i+(q+1)(2+n_i)+2(q+1)=4(q+1)+qn_i$$ which is non zero unless $q=4, n_i=-5$ or $q=2, n_i=-6; q=1, n_i=-4$, by Formula these last two cases do not occur since $|n_i|\leq 2q$. As for $q=4$ an edge is a sum of 8 elements $e_i$ with sign $\pm 1$, if there is a coefficient $-5$ at least 5 elements have coefficient $-1$, then there must be 3 elements with coefficient 1 to give $\eta(\ell)=-2$. This extra case will be considered at the end of this subsection. $\Box$
We now compute with the matrix $$C_{\mathcal{G}}=\left(\begin{array}{cc}
0 & \sigma_\l c(\l) \\
c(\l) & \bar\l(\xi) \\
\end{array}\right)$$ $$\label{5}
\chi_{{{\mathcal{G}}}}(t)=det \left(\begin{array}{cc}
t & -\sigma_\l c(\ell)\\
- c(\ell) & t-\bar\l(\xi) \\
\end{array}\right)=t^2-\bar\l(\xi)t-\sigma_\l c(\l)^2.$$ Suppose that $\chi_{{{\mathcal{G}}}}$ is not irreducible, then: $$\label{6'}
\chi_{{{\mathcal{G}}}}(t)=(t+r(\xi))(t-\bar\l(\xi) -r(\xi)).$$ Compare the free coefficients in \[5\] and \[6’\] we get $$\label{6*}
r(\xi)(-\bar\l(\xi) -r(\xi))=-\sigma_\l c(\l)^2.$$ By the formula \[06’\] $c(\l)^2$ is divisible by $\xi_i^{|n_i|},\forall i=1,. . . ,k$. For any $i$ if $r(\xi)$ is divisible by $\xi_i$, by remark \[rem1\] $\bar{\l}(\xi)$ is not divisible by $\xi_i$, then $-\bar\l(\xi)
-r(\xi)$ is not divisible by $\xi_i$. And inversely, if $-\bar\l(\xi) -r(\xi)$ is divisible by $\xi_i$, then $r(\xi)$ is not divisible by $\xi_i$. Hence we have: $$\begin{aligned}
\label{sys_eq1}
r(\xi)&=&\xi_i^{|n_i|}s_i, i\in A \\
-\bar\l(\xi)-r(\xi) &=& \xi_j^{|n_j|}u_j, j\in B.\end{aligned}$$ where $A\cup B=\{1,. . . ,k\}; A\cap B=\emptyset$.
1. If $A\neq \emptyset$ and $B\neq\emptyset$, then for some couple $i,j$ we have: $$\label{11}
\bar\l(\xi)= -(\xi_i^{|n_i|}s_i+\xi_j^{|n_j|}u_j)$$ From remark \[rem1\] we must have $n_h=0,\forall h\neq i,j$,
1. \[black\] **When $\l$ is a black edge:** We have ${{\sigma}}_\l=1$ and by the definition of edge (cf. \[edge\]) $\l=ne_i-ne_j;2|n|\leq 2q$. We may suppose $i=1,j=2,n>0$. We have $\bar\l(\xi)=\l(\xi)$ and: $$\begin{gathered}
\label{12}
\l(\xi) =n(\sum_{\beta\in
\mathbb{N}^m;|\beta|_1=q+1,\beta_1\geqslant 1}(\begin{array}{c}q+1
\\\beta\\\end{array})
(\begin{array}{c}
q \\
\beta_1-1,\beta_2,. . . ,\beta_m \\
\end{array})
\xi_1^{\beta_1-1}\xi_2^{\beta_2}. . . \xi_m^{\beta_m}-\\
-\sum_{\beta'\in
\mathbb{N}^m;|\beta'|_1=q+1;\beta'_2\geqslant
1}(\begin{array}{c}q+1
\\\beta'\\\end{array})(\begin{array}{c}
q \\
\beta'_1,\beta'_2-1,. . . ,\beta'_m \\
\end{array})\xi_1^{\beta'_1}\xi_2^{\beta'_2-1}. . . \xi_m^{\beta'_m})\end{gathered}$$ Remark that $$\xi_1^{\beta_1-1}\xi_2^{\beta_2}. . . \xi_m^{\beta_m}=\xi_1^{\beta'_1}\xi_2^{\beta'_2-1}. . . \xi_m^{\beta'_m}\Leftrightarrow \beta_1-1=\beta'_1,\beta_2=\beta'_2-1,\beta_i=\beta'_i\forall i\geqslant 3$$ Then: $$\begin{gathered}
\label{13}
\l(\xi) =n\sum_{\beta\in\mathbb{N}^m,|\beta|_1=q+1,\beta_1\geqslant
1}\frac{q!}{(\beta_1-1)!\beta_2!. . . \beta_m!}\frac{(q+1)!}{\beta_1!. . . \beta_m!}(1-\frac{\beta_1}{\beta_2+1})\xi_1^{\beta_1-1}\xi_2^{\beta_2}. . . \xi_m^{\beta_m}\end{gathered}$$ By \[11\] we must have $$\label{14}
\l(\xi) =-(\xi_1^ns_1+\xi_2^nu_2).$$
1. If $n>1$, we take $\beta_1=1,\beta_2=n-1,\beta_3=q+1-n,\beta_4=. . . =\beta_m=0$, then in the formula \[13\] of $\l(\xi) $, there is the monomial $$n\frac{q!}{(n-1)!(q+1-n)!}\frac{(q+1)!}{(n-1)!(q+1-n)!}(1-\frac{1}{n})\xi_2^{n-1}\xi_3^{q+1-n}\neq
0$$ and they are not divisible by $\xi_1^n$ or $\xi_2^n$. This contradicts \[14\].
2. $n=1$. We have $\l^+=(1,0,. . . ,0);\l^-=(0,1,. . . ,0)$. Then from \[06”\] we get $$\label{15''}
c(\l)^2=(q+1)^2\xi_1\xi_2(\sum_{\alpha\in\N^m:\sum_ia_i+1=q}\left(\begin{array}{c}
q \\
\alpha_1+1,\alpha_2,. . . ,\alpha_m \\
\end{array}\right)\left(\begin{array}{c}
q \\
\alpha_1,\alpha_2+1,. . . ,\alpha_m \\
\end{array}\right)\xi^\alpha)^2$$ Let $p$ be a prime divisor of $q+1$:$q+1=p^ku,g. c. d(p,u)=1$. We have: $$\label{15}
\chi_{{\mathcal{G}}}=t(t-\l(\xi) )(\mbox{mod } p)\Rightarrow
\chi_{{\mathcal{G}}}=(t+ps)(t-ps-\l(\xi) )$$ By \[5\]and \[15”\] the free coefficient of $\chi_{{\mathcal{G}}}$ must be divisible by $p^{2k}$: $$\label{15'}p^{2k}|ps(-\l(\xi) -ps)$$ By formula we see that the coefficient of the term $\xi_1^q$ is $-q$, the coefficient of the term $\xi_2^q$ is $q$. One deduces that $\l(\xi) $ is not divisible by $p$ since $g. c.
d(q,q+1)=1$. Hence $(-\l(\xi) -ps)$ is not divisible by $p$. So by \[15’\] we must have $p^{2k-1}|s$. Now take $\xi_1=\xi_2\Rightarrow \l(\xi) =0$, then the free coefficient of $\chi_{{\mathcal{G}}}$ when $\xi_1=\xi_2$ is divisible by $p^{4k}$. But in \[5\] when $\xi_1=\xi_2$ the free coefficient of $\chi_{{\mathcal{G}}}$ is $-c(\l)^2|_{\xi_1=\xi_2}$, it is not divisible by $p^{4k}$, since in \[15”\] if we take $\alpha_1=\alpha_2=0,\alpha_3=q-1$, we have the monomial: $$(q+1)^2\xi_1^2(q^2\xi_3^{q-1})^2$$ is not divisible by $p^{4k}$.
2. When $\l$ is a red edge: When $h\neq i,j,n_h=0$ we get the coefficient of the term $\xi_h^q$ in $\bar{\l}(\xi)$ is $4(q+1)+qn_h=4(q+1)\neq 0$, so \[11\] cannot hold.
2. If $B=\emptyset$, then $A=\{1,. . . ,k\}$$$\label{_r}r(\xi)=\xi_1^{|n_1|}.
. . \xi_k^{|n_k|}s$$.
1. [When $\l$ is a black edge:]{} Take $\xi_1=. . . =\xi_k$, by the remark \[rem4\] we have $\l(\xi) |_{\xi_1=. . . \xi_k}=0$, hence $$\begin{gathered}
\label{17}
\chi_{{\mathcal{G}}}(t)|_{\xi_1=. . . =\xi_k}=(t+r(\xi)|_{\xi_1=. . . =\xi_k})(t-r(\xi)|_{\xi_1=. . . =\xi_k})=\\=t^2-r(\xi)|_{\xi_1=. . . =\xi_k}^2.\end{gathered}$$ By \[17\] the free coefficient of $\chi_{{\mathcal{G}}}|_{\xi_1=. . .
=\xi_k}$ is divisible by $\xi_1^{2\sum_{i=1}^k|n_i|}$. But by \[5\] the free coefficient of $\chi_G|_{\xi_1=. . . =\xi_k}$ is $-c(\l)^2|_{\xi_1=...=\xi_k}$.
-If $k=m$, then by remark \[rem5\] $-c(\ell)^2|_{\xi_1=. . .
=\xi_k}=-(q+1)^2\xi_1^{\sum_{i=1}^k|n_i|}\left(\begin{array}{c}
q \\
\l^+ \\
\end{array}\right)^2\left(\begin{array}{c}
q \\
\l^- \\
\end{array}\right)^2$ is not divisible by $\xi_1^{2\sum_{i=1}^k|n_i|}$.
-If $k<m$, then $$-c(\ell)^2|_{\xi_1=. . . =\xi_k}=-(q+1)^2\xi_1^{\sum_{i=1}^k|n_i|}(\sum_{\alpha\in\mathbb{N}^m:|\ell^++\alpha|_1=q}(\begin{array}{c}
q \\
\ell^++\alpha \\
\end{array})(\begin{array}{c}
q \\
\ell^-+\alpha \\
\end{array})\xi_1^{\sum_{i=1}^k\alpha_i}\xi_{k+1}^{\alpha_{k+1}}. . . \xi_m^{\alpha_m})^2$$ Take $\alpha_1=...=\alpha_k=0,\alpha_{k+1}=q-|\l^+|_1$, we see that $-c(\l)^2|_{\xi_1=...\xi_k}$ contains the term $\xi_1^{\sum_{i=1}^k|n_i|}\xi_{k+1}^{2(q-|\l^+|_1)}$ with the coefficient $-(q+1)^2(\begin{array}{c}
q \\
\ell^++\alpha \\
\end{array})^2(\begin{array}{c}
q \\
\ell^-+\alpha \\
\end{array})^2$. Hence $-c(\l)^2|_{\xi_1=...=\xi_k}$ is not divisible by $\xi_1^{2\sum_{i=1}^k|n_i|}$.
2. [When $\l$ is a red edge:]{} Take $\xi_1=...=\xi_k$, we have $$\begin{gathered}
\label{09}
\frac{\partial}{\partial
\xi_i}A_{q+1}(\xi)=\frac{\partial}{\partial
\xi_j}A_{q+1}(\xi)\forall i,j\Rightarrow
\l(\xi)|_{\xi_1=...=\xi_k}=\sum_{i=1}^{k}n_i\frac{\partial}{\partial
\xi_1}A_{q+1}(\xi)=\\=-2\frac{\partial}{\partial
\xi_1}A_{q+1}(\xi)=-2\sum_{|\alpha|_1=q+1,\alpha_1\geq
1}\frac{1}{q+1}\left(\begin{array}{c}
q+1 \\
\alpha \\
\end{array}\right)^2
\alpha_1\xi_1^{\alpha_1+\alpha_2+...+\alpha_k-1}\xi_{k+1}^{\alpha_{k+1}}...\xi_{m}^{\alpha_m}\end{gathered}$$ $$\label{10}A_q(\xi)|_{\xi_1=...=\xi_k}=\sum_{\beta:|\beta|_1=q}\left(\begin{array}{c}
q \\
\beta \\
\end{array}\right)^2\xi_1^{\beta_1+...+\beta_k}\xi_{k+1}^{\beta_{k+1}}...\xi_m^{\beta_m}.$$ From and we have $$\begin{gathered}
\label{36}-\bar{\l}(\xi)|_{\xi_1=...=\xi_k}=(\l(\xi)-2(q+1)A_q(\xi))|_{\xi_1=...=\xi_k}=\\=-2\sum_{\alpha:|\alpha|_1=q+1;\alpha_1\geq 1}(\frac{\alpha_1}{q+1}\left(\begin{array}{c}
q+1 \\
\alpha \\
\end{array}\right)^2+(q+1)\left(\begin{array}{c}
q \\
\alpha_1,...,\alpha_m \\
\end{array}\right)^2)\xi_1^{\alpha_1+...+\alpha_k-1}\xi_{k+1}^{\alpha_{k+1}}...\xi_m^{\alpha_m}=\\=-2\sum_{\alpha:|\alpha|_1=q+1;\alpha_1\geq
1}(\frac{\alpha_1}{q+1}(\frac{(q+1)!}{\alpha_1!...\alpha_m!})^2-(q+1)(\frac{q!}{(\alpha_1-1)!...\alpha_m!})^2)\xi_1^{\alpha_1+...+\alpha_k-1}\xi_{k+1}^{\alpha_{k+1}}...\xi_m^{\alpha_m}=\\=2\sum_{\alpha:|\alpha|_1=q+1;\alpha_1>
1}\frac{q!}{(\alpha
_1-1)!...\alpha_m!}\frac{(q+1)!}{\alpha_1!...\alpha_m!}(\alpha_1-1)\xi_1^{\alpha_1+...+\alpha_k-1}\xi_{k+1}^{\alpha_{k+1}}...\xi_m^{\alpha_m}.\end{gathered}$$Hence $-\bar{\l(\xi)}|_{\xi_1=...=\xi_k}$ is divisible by $\xi_1$. By $r(\xi)|_{\xi_1=...=\xi_k}=\xi_1^{n_1+...+n_k}s$ is divisible. Then $(-\bar{\l(\xi)}-r(\xi))|_{\xi_1=...=\xi_k}$ is divisible by $\xi_1$.By and we have:$$\begin{gathered}
\xi_1^{|n_1|}...\xi_k^{|n_k|}s(-\bar{\l}(\xi)-r(\xi))=c(\l)^2=\xi_1^{|n_1|}...\xi_k^{|n_k|}(\sum_{\alpha\in
\N^m:|\l^++\alpha|_1=q-1}\left(\begin{array}{c}
\end{array}\right)\xi^\alpha)^2\\\implies
s(-\bar{\l}(\xi)-r(\xi))=(\sum_{\alpha\in
\end{array}\right)\xi^\alpha)^2\end{gathered}$$$$\label{36'}\implies
\end{array}\right)\xi^\alpha)^2.$$ So the right hand side of when $\xi_1=\xi_2=...=\xi_k$ must be divisible by $\xi_1$. But in fact:
- If $k=m$, then by remark \[rem5\] $$(\sum_{\alpha\in
\end{array}\right)\xi^\alpha)^2=\left(\begin{array}{c}
q-1 \\
\l^+ \\
\end{array}\right)^2\left(\begin{array}{c}
q+1 \\
\l^- \\
\end{array}\right)^2$$ is a constant, not divisible by $\xi_1$.
- If $k<m$, take $\tilde{\alpha} $ such that $\tilde{\alpha}_1=...=\tilde{\alpha}_k=0,\tilde{\alpha}_{k+1}=q-1-\l^+$ then the right hand side of contains the monomial $$\left(\begin{array}{c}
q-1 \\
\l^++\tilde{\alpha} \\
\end{array}\right)^2\left(\begin{array}{c}
q+1 \\
\l^-+\tilde{\alpha} \\
\end{array}\right)^2\xi_{k+1}^{2(q-1-|\l^+|_1)}.$$ Hence the right hand side of is not divisible by $\xi_1$.
3. The case $A=\emptyset,B=\{1,. . . ,k\}$ is similar.
**Extra case:** $$q=4,\l=-5e_i+e_j+e_k+e_m$$In this case $\sigma_\l=-1$. By \[06”\] we have: $$c(\l)=4\xi_i^{5/2}\xi_j^{1/2}\xi_k^{1/2}\xi_m^{1/2}.$$ By \[6\*\]: $$\label{20}r(\xi)(-\bar\l(\xi)
-r(\xi))=c(\l)^2=4\xi_i^{5/2}\xi_j^{1/2}\xi_k^{1/2}\xi_m^{1/2}.$$ Hence $r(\xi),-\bar{\l}(\xi)-r(\xi)$ must be monomials that contains only variables from $\xi_i,\xi_j,\xi_k,\xi_m$.So $\bar{\l}(\xi)$ must be a polynomial that contains only variables $\xi_i,\xi_j,\xi_k,\xi_m$. But in fact, for $h$ that is not in the support of $\l$,$n_h=0$ and by the coefficient of $\xi_h^q$ in $\bar{l}(\xi)$ is $4(q+1)+qn_h=20$. Hence we have a contradiction.
[mat]{} C. Procesi, M. Procesi *A normal form of the non-linear Schrödinger equation*, preprint C. Procesi, M. Procesi *Normal forms for the non-linear Schrödinger equation*, preprint C. Procesi, M. Procesi and Nguyen Bich Van *The energy graph of the nonlinear Schrödinger equation*, preprint.
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Q:
Dimensional Analysis Question
First of, I would like to say that I have tried this question, and have my answer as well, just not sure such a method of obtaining the answer is valid or not, therefore trying to look for help here. By the way, I am new here, prior apology for any violation of rules and regulation (and poor question expression as well).
Here's the question:
In the gas equation:
$(p + \frac{a}{V^2}) (V-b) = RT$,
where $p$, $V$, and $T$ are the pressure, volume and gas temperature, respectively.
Determine the dimensions of $a$ and $b$.
Note: The $R$ is not specified, suppose it should be a constant.
Here's my approach of answer:
Due to possibility of temperature being at absolute 0, therefore $RT$=0 is possible.
With that, I let $(p + \frac{a}{V^2})=0$, $(V-b)=0$
(Dimensional analysis working)
The answer turns out to be:
[$a$]=(M) (L$^5$) (T$^{-2}$), [$b$]=L$^3$
Just wondering such approach of answer is valid or not, if not, what should it be.
Replies are greatly appreciated. By the way, how to use MathJax here? I have very very limited of knowledge on html as well, thank you.
A:
Approach sort of valid.
See the dimensions of b would be those of V, but for another reason -- you needn't have put zero at RHS. The reason is that only quantities of the same dimension can be added or subtracted to each other. It doesn't matter if RT can equal zero or not. Similarly dimensions of al(V^2) would be those of p.
Check out Rules of Evaluating Equations here: http://go.hrw.com/resources/go_sc/ssp/HK1BSW23.PDF
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Here's a simple guide to the music notation and tablature you'll find at Peghead Nation.
by
Scott Nygaard
Standard Notation
Standard notation is written on a five-line staff. Notes are written in alphabetical order from A to G. Sharps and flats indicate the notes a half step between whole steps. A sharp raises a note by a half step, while a flat lowers it by a half step. Some notes can be indicated with either a sharp or a flat. For example the note a half step above A is A#, which is the same note as the note a half step below B, Bb. The entire 12-note chromatic scale used in Western notation is A, A#(Bb), B, C, C#(Db), D, D#(Eb), E, F, F#(Gb), G, G#(Ab). There are half steps between all letter notes except between B and C and between E and F.
Key Signatures
Every key has a different number of sharps (#) and flats (♭), which are indicated by the key signature at the beginning of the staff. All the notes that are sharped or flatted in the key signature are to be sharped or flatted in the music unless indicated by a natural sign (♮) next to the note. The key of C has no sharps or flats. The “sharp” keys are G (one sharp), D (two sharps), A (three sharps), E (four sharps), B (five sharps), and F# (six sharps). The “flat keys” are F (one flat), Bb (two flats), Eb (three flats), Ab (four flats), Db (five flats), and Gb (six flats). A natural sign (♮) effectively removes the flat or sharp from a note.
Note Duration and Rhythm
The duration of a note is determined by three things: the note head, stem, and flag. A whole note (see below) equals four beats. A half note is half of that: two beats. A quarter note equals one beat, an eighth note equals half of one beat, and a 16th note is a quarter beat (there are four 16th notes per beat). A triplet is a third of a beat (there are three triplets per beat).
Grace notes are represented by small notes with a dash through the stem in standard notation and with small numbers in tab. A grace note is a very quick ornament leading into a note, most commonly executed as a hammer-on, pull-off, or slide.
Time Signatures
The fraction (4/4, 3/4, 6/8, etc.) or “C” character shown at the beginning of a piece of music denotes the time signature. The top number tells you how many beats are in each measure, and the bottom number indicates the rhythmic value of each beat (4 equals a quarter note, 8 equals an eighth note, 16 equals a 16th note, and 2 equals a half note). The most common time signature is 4/4, which signifies four quarter notes per measure and is sometimes designated with the symbol “C” (for common time).
Tablature
In tablature, the horizontal lines represent the strings of the instrument: six strings for guitar and dobro, four for mandolin and ukulele, five for banjo. The first string is on the top. The numbers refer to the fret numbers on each string. Guitar, mandolin, and ukulele music has notation and tablature, which are designed to be used together: use the notation for rhythmic information and note durations and the tablature for the locations of the notes on the fingerboard. In fingerstyle guitar tab, notes with downward stems are to be played with the picking-hand thumb, while notes with upward stems are to be played with the fingers of the picking hand.
Notes connected with slurs (not to be confused with ties) in guitar, mandolin, or ukulele notation and tab should be played with a hammer-on, pull-off, or slide. Lower notes slurred to higher notes are played as hammer-ons; higher notes slurred to lower notes are played as pull-offs. Slides are represented with a dash. For two slurred notes connected with a slide, pick the first note and then slide into the second. If the dash has no slur above it, pick the second note as well, after sliding.
Dobro and banjo music has no notation, only tab. In this case, the tablature indicates the rhythmic information and note durations as well as the positions of the notes on the fingerboard. Slurs are indicated with an H (hammer-on), P (pull-off), or S (slide). Slides are also represented with a dash. In clawhammer tab, a drop-thumb is indicated with a T. In three-finger (bluegrass) banjo tab, picking-hand fingers are indicated with letters below the staff: i for the index finger, m the middle, and t the thumb.
Chord Diagrams
Chord diagrams show where the fingers go on the fingerboard. Frets are shown horizontally and strings are vertical lines. The line on the far left is the lowest string, and the line on the far right is the highest. The thick top line represents the nut. Numbers above the diagram are fretting-hand finger numbers. Dots show where the fingers go, an X indicates a string that should be muted or not played, and 0 indicates an open string. A numeral (preceded by fr.) to the right of a diagram indicates a chord played higher up the neck (in which case the top horizontal line is thin). Banjo chord diagrams do not show the fifth string, since it is rarely fretted.
Guitar Chord Diagrams
Banjo Chord Diagrams
Capos
If a capo is used, it will be indicated at the beginning of the music, for example: Capo 2 means put the capo at the second fret. The standard notation and tablature is written as if the capo were the nut of the instrument. In guitar tab, chords are written in the same way: a tune capoed at the second fret and played using key-of-G fingerings and notation will show chords written in the key of G, even though the music will sound in the key of A. For banjo and dobro tab, the chords indicated represent how they sound. For example, a tune capoed at the second fret and played using key-of-G fingerings will have chords written in the key of A.
Tunings
Alternate guitar tunings are given from the lowest (sixth) string to the highest (first) string. For instance, D A D G B E indicates standard tuning with the bottom string dropped to D. Standard notation for songs in alternate tunings always reflects the actual pitches of the notes.
Repeats
Navigation symbols such as repeats, DS al Coda, DC al Fine, To Coda, etc. can be the most confusing parts of a piece of music. Repeat symbols are placed at the beginning and end of the passage to be repeated. Ignore repeat symbols with the dots on the right side the first time you encounter them; when you come to a repeat symbol with dots on the left side, jump back to the previous repeat symbol facing the opposite direction (if there is no previous symbol, go to the beginning of the piece). The next time you come to the repeat symbol, ignore it and keep going unless it includes instructions such as “Repeat three times.” A section will often have a different ending after each repeat. The example below includes a first and a second ending. Play until you hit the repeat symbol, jump back to the previous repeat symbol and play until you reach the bracketed first ending, skip the measures under the bracket and jump immediately to the second ending, and then continue.
DS stands for dal segno or “from the sign.” When you encounter this indication, jump immediately to the “sign” (shown above the third measure in the example above). DS is often accompanied by al Fine or al Coda. Fine indicates the end of a piece. A coda is a final passage near the end of a piece and is indicated with Φ. D.S al Coda tells you to jump back to the sign and continue on until you are instructed to jump to the coda, indicated with To Coda Φ. DC stands for da capo or “from the beginning.” Jump to the top of the piece when you see a DC. DC al Fine tells you to jump to the beginning of a tune and continue until you encounter the Fine indicating the end of the piece (ignore the Fine the first time through).
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Q:
On the graph of induction-restriction for group-subgroup representations
Let $G$ be a finite group, and $H$ a subgroup.
Let $(V_i)_{i \in I}$ and $(W_j)_{j \in J}$ be the irreducible complex representations of $G$ and $H$ (up to isom.).
Consider the graph $\mathcal{G}(H \subset G )$ whose vertices are $\{ V_i, W_j : i \in I, j \in J \}$ such that there are $d_{ij}$ edges between $V_i$ and $W_j$ if $\langle V_i\vert_H,W_j \rangle = d_{ij}$.
Let $\mathcal{G}_0(H \subset G )$ be the connected component of the trivial representation $V_0$ (noted $\star$) of $G$.
Note that if $K \subset H$ is a normal subgroup of $G$ then $\mathcal{G}_0(H \subset G )= \mathcal{G}_0(H/K \subset G/K )$.
The graph $\mathcal{G}_0$ is $n$-supertransitive ($n$-$st$) if up to distance $n$ from $\star$ it's just a linear chain: $$\star-\circ-\circ-\circ-\circ-\circ-\circ-\circ-\circ$$
Let $st(H \subset G )$ be the integer $n$ such that the graph $\mathcal{G}_0(H \subset G )$ is $n$-$st$ but not $(n+1)$-$st$.
Note that $st(H \subset G ) \ge 1$ and $st(H \subset G )= st(H/K \subset G/K )$.
Examples: $st(\{e\} \subset \mathbb{Z}_2)=2$ and $st(\{e\} \subset G)=1$ if $G \neq \mathbb{Z}_2$.
$st(\mathbb{Z}_2 \subset D_{10})=1$ and $st(S_4 \subset S_5)=3$
Question: Is there $(H_0 \subset G_0 )$ with $st(H_0 \subset G_0 ) > 7$ ? Is $st(H \subset G )$ bounded ?
Optional questions: Is there usual names for $\mathcal{G}_0(H \subset G )$ and $st(H \subset G )$ in groups theory ? References ? Is there a program drawing $\mathcal{G}_0(H \subset G )$ and computing $st(H \subset G )$ ?
A:
Answer (due to Dave Penneys): $st(H\subset G) \le 3$ if $[G:H]>3$.
I report here his comment :
A subgroup subfactor (of index $> 3$) can be at most $3$-supertransitive. The $4$-box
space is at least 15 dimensional. This can be seen by looking at the
partition planar algebras (MR2972458).
As observed by Jack Schmidt, if $st(H\subset G) > 3$ and $[G:H] \le 3$ then $(H\subset G) \sim (S_2 \subset S_3 )$ and $st(S_2 \subset S_3 ) = 4$.
By reading the pages 13-14 of the paper cited by Dave (also with this book ex. 4.2.3 p53 and prop. A.4.4 p141), we see that "for $k=1,2$ or $3$", $st(H \subset G) = k$ iff $1_H^G$ is (at least) $k$-transitive, iff $G/H_G$ is (at least) a $k$-transitive group (it's false for $k \ge 4$).
Then the classification (up to $\sim$ ) of the inclusions $(H \subset G)$ with $st(H \subset G) = 3$ is given by the classification of the $3$-transitive groups.
Classification of the $4$-transitive groups: Symmetric, Alternating and Mathieu groups only (here).
Questions: Is there a classification of the $3$-transitive groups ? A conjecture ?
Is there a table of the number of $3$-transitive groups of degree $n$ ?
| |
With many non-profit organizations today struggling to gain support, volunteers and funding, the Cotati Historical Society, founded in 2007, has had a team of passionate people who have played a pivotal role in preserving Cotati’s history and ensuring the creation of the Cotati Historical Museum.
Lloyd and Prue Draper, who owned The Cotatian weekly newspaper from 1951 to 1965, were instrumental in collecting and preserving historic documents, artifacts, and memorabilia for over 50 years. When the non-profit was finally established in 2007 they leased an unused room at city hall for the historic museum and archive. Robert Leys, a Cotati architect, helped create a plan to convert the room into a functional museum space and a team of local volunteers set to work obtaining donations for furnishings and display cases, and transporting the items, as well as the memorabilia, to the museum. Cotati city government and numerous businesses got involved to help make the room resemble the first grade classroom that it had been when the building was the old Cotati School, donating everything from the demolition, to drywall and sheetrock, to electrical wiring and lighting, to windows and doors, to paint and finishes. Even the floors were refinished to the original old fir.
The museum finally opened in 2010, fulfilling Cotati Historical Society’s mission “to preserve Cotati history through the acquisition and preservation of artifacts, photos, archives and other historical materials.” It continues to be funded through the support of visitors and private donors and through their annual barbeque fundraiser.
While Cotati has been incorporated as a city for about 50 years, it has been a community for over 120 years with an interesting and varied history. The historical society and museum ensures that current and future generations will know and learn from the town’s past.
“It’s a place to focus the past to show where we’ve been and how we got to where we are now,” says Allred.
Residents can volunteer to work in the museum, participate on the board or at the annual fundraiser, donate money, or simply collect and perhaps donate to the museum items from the past that would interest history buffs of all ages. | http://www.thecommunityvoice.com/article/It-takes-a-village-to-honor-its-past |
The integers $1,2,3,\ldots,n$ are to be arranged clockwise around a circle, such that adjacent integers always share a common digit (in their decimal representations).
(a) Find the smallest integer $n\ge3$ for which such an arrangement does exist.
(b) Find the largest integer $n\ge3$ for which such an arrangement does not exist.
(a) It's easy to see that n must be at least 29, since every number less than 10 must be paired with 2 neighbours, so you need 29 to pair with 9.
So 9 can be paired with 19 and 29, and then 8 with 18 and 28, etc upto 1 with 11 and 21.
If you put the number less than 10 in the middle, those groups of 3 can be easily chained together, because they all have a 1 on one end and a 2 on the other end, So you get the 1-group, 2-group, 3-group, etc.
Then 10 and 20 are left, which can be inserted on each end. They form the 0-group. You can put 0 in there to make it consistent.
(b) If we take the sequence of (a), we can always insert the next number. 30 between 10 and 20, 31 between 11 and 21, 32 between 12 and 22, etc.
There is no number you can never fit. Every number ending in x can always be inserted into the x-group, because x is common inside that entire group.
Since n must be at least 29, the answer here is 28.
I think the answer is $a) 29$. Each digit from 3 to 9 must be bracketed by 2 other numbers with 3-9, the next 2 being the 20's. So, you'd have 13-3-23-24-4-14-15-5-25 etc.
You have to do a little juggling with 1, 2, 10, 20, but those are easy to insert into the chain. Same for 11, 12, 21, 22.
"The integers 1,2,3,…,n are to be arranged clockwise around a circle, such that adjacent integers always share a common digit"
B.) adjacent numbers must share exactly one digit.
Using the same reasoning as the posters above, a number satisfying the constraints can be inserted anywhere, and all numbers greater the min(n) are possible. Therefore, the largest n not satisfying the constraints would be n=2 for A.) and n=3 for B.).
Not the answer you're looking for? Browse other questions tagged mathematics combinatorics number-theory or ask your own question. | https://puzzling.stackexchange.com/questions/9210/circle-of-numbers |
---
abstract: 'We study inequalities between general integral moduli of continuity of a function and the tail integral of its Fourier transform. We obtain, in particular, a refinement of a result due to D. B. H. Cline [@Cl] (Theorem \[thm1\] below). We note that our approach does not use a regularly varying comparison function as in [@Cl]. A corollary of Theorem 1.1 deals with the equivalence of the two-sided estimates on the modulus of continuity on one hand, and on the tail of the Fourier transform, on the other (Corollary \[CH3\_s3.lem.1\]). This corollary is applied in the proof of the violation of the so-called entropic area law for a critical system of free fermions in [@GiKl; @Gi2].'
address: 'Department of Mathematics, University of Rochester, Hylan Building, Rochester, NY 14627'
author:
- Dimitri Gioev
date: 'December 15, 2006 and, in revised form, June 15, 2007.'
title: 'Moduli of continuity and average decay of Fourier transforms: two-sided estimates'
---
[The author was supported in part by NSF grant INT–0204308 U.S.–Sweden Collaborative Workshop on PDE’s and Spectral Theory, the Swedish foundation STINT grant PD2001–128 and NSF grant DMS–0550649. The author would like to thank the University of Pennsylvania and the Courant Institute for financial support and hospitality. The author is grateful to Percy Deift for his valuable suggestions which have helped to improve the presentation. ]{}
Introduction and statement of the main results {#s0}
==============================================
A result of this paper (Corollary \[CH3\_s3.lem.1\] below) is applied in the proof of the violation of the so-called entropic area law for a critical system of free fermions, see [@GiKl (6) et seq.], [@GiKl Section on Fractal Boundaries] and [@Gi2 Lemma 2.10]. Corollary \[CH3\_s3.lem.1\] follows from more general results of this paper (Theorems \[thm1\], \[lem4.1\]) which are of independent interest.
It is well-known that the behavior of a modulus of continuity $\omega[f](h)$ of a function $f$ for $|h|$ small is related to the behavior of the Fourier transform $\hat{f}(\xi)$ of $f$ for $|\xi|$ large (precise definitions are given in et seq. below), see e.g. [@St Proposition 5.3.4], [@T Theorem 85]. The main object of our study are inequalities between general averaged moduli of continuity () of $L^p$ functions (defined in below) and tails of their Fourier transforms (). In [@Cl] several results relevant for our purposes were obtained. Theorem \[thm1\] below gives a lower estimate for a general $L^p$ , $1\leq{}p\leq2$, in terms of the modified tail integral of the improving one of the results in [@Cl] (as in [@Cl], we distinguish between the true and the modified tail integral, as defined in and below). Corollary \[thm2\] gives a two-sided estimate for the in terms of the modified tail integral of the in the case $p=2$. In applications it might be desirable to use the true tail instead of the modified tail that arises naturally in the mentioned inequalities. Theorem \[lem4.1\] gives the best possible power-scale description of the relationship between the true and the modified tails (see Remark \[remstar\]).
Before stating our results we need to introduce some notation and recall two results in [@Cl]. Let $d\in\NN$ and denote by $\|\cdot\|_{p,\RD}$ the standard norm in $L^p(\RD)$, $1\leq p\leq\infty$. The Fourier transform $\hat{f}(\xi):=\int_{\RD} e^{-i\xi\cdot{}x}f(x)\,dx$, $\xi\in\RD$, of a function $f\in{}L^p(\RD)$ for $1\leq p\leq2$ is defined in the standard way (see e.g. [@K Section IV.3]). In the case $2<p\leq\infty$ we consider only the functions $f\in{}L^p(\RD)$ whose transforms belong to $L^\pp(\RD)$, $\pp:=p/(p-1)$. Introduce the difference operator of order $m\in\NN$ acting on functions with domain $\RD$ by [@Ti Section 3.3] $$\label{eqfindiff}
\D_y^m f(x):=\sum_{k=0}^m (-1)^{m-k}
\Big(\genfrac{}{}{0pt}{}{m}{k}\Big)\,f(x+ky),\qquad x,y\in\RD,$$ where $\big(\genfrac{}{}{0pt}{}{m}{k}\big)$ denotes the binomial coefficient. Note that the Fourier transform of in $x$ equals $
\Big(\sum_{k=0}^m (-1)^{m-k}
\big(\genfrac{}{}{0pt}{}{m}{k}\big)\,e^{iky\cdot\xi}\Big)\,
\hat{f}(\xi)
= (e^{iy\cdot\xi}-1)^m\,\hat{f}(\xi),
$ and hence the functions $$\label{eqFpair}
\D_y^mf(x),\qquad (2i\sin(y\cdot \xi/2))^m\,e^{imy\cdot\xi/2}\,\hat{f}(\xi)$$ form a Fourier pair for $m\in\NN$. Now we define $\D_y^mf(x)$ for any $m>0$, $m\not\in\NN$, as the inverse Fourier transform of the second function in . Let $\SD$ denote the unit sphere in $\RD$ and let $dS$ denote the standard measure on $\SD$. (All the results below with obvious modifications hold if one replaces the standard measure on $\SD$, with a measure $G$ invariant under orthogonal transformations and supported in the unit ball in $\RD$ as in [@Cl].) For $1\leq{}p\leq\infty$ set $$\delta_{p,m}[f](y):=\|\Delta_y^m{}f\|_{p,\RD},\qquad
y\in\RD,$$ and define a general averaged (integral) of $f$ as follows. For any $h>0$ in the case $1\leq{}q<\infty$ set $$\label{eq200}
\omega_{p,m,q}[f](h):=\|\d_{p,m}[f](hy)\|_{q,\SD}
= \Big(\int_{\SD} \|\Delta_{hy}^m{}f\|_{p,\RD}^{q}\,dS_y\Big)^{1/q}$$ (where in the case $d=1$ the integral should be interpreted as a sum over $y\in\SS^0=\{\pm1\}$), and in the case $q=\infty$ set $$\omega_{p,m,\infty}[f](h):=\sup_{|y|\leq h}\d_{p,m}[f](y)
=\sup_{|y|\leq h}\|\Delta_y^m{}f\|_{p,\RD}.$$ The Hölder inequality implies that for any $1\leq q_1\leq q_2\leq\infty$ there exists $c=c(p,q_1,q_2,d)<\infty$ so that $$\label{eq0}
\omega_{p,m,q_1}[f](h) \leq c\,\omega_{p,m,q_2}[f](h),
\qquad h>0.$$ Define the tail integral of the for $1\leq\pp<\infty$ and for $\pp=\infty$, respectively, by $$\label{eq00true}
\psi_{\pp}[\hat{f}](t)
:= \Big(\int_{|\xi|\geq t} |\hat{f}(\xi)|^{\pp}\,d\xi\Big)^{1/\pp},\qquad
\psi_{\infty}[\hat{f}](t)
:= \sup_{|\xi|\geq t} |\hat{f}(\xi)|,\qquad t>0.$$ Motivated by the results in [@Cl], we wish to compare the $\omega_{p,m,q}[f](1/t)$ and the tail $\psi_{\pp}[\hat{f}](t)$, as $t\ra\infty$. It will be clear from our Theorem \[thm1\] below that the natural choice of $q$ for the purpose of such a comparison is $q=p^\prime$ (see also the discussion preceding Theorem \[Besseltail\]). Note next that it is possible that $\psi_{\pp}[\hat{f}](t)$ is rapidly decreasing, or simply zero, for large $t$ (take e.g., $\hat{f}\in{}C_0^\infty(\RD)$), whereas the modulus of continuity related to the $m$th finite difference of $f$ vanishes generally speaking at the rate $1/t^m$ only. This motivated the author in [@Cl] to introduce the following modified tails: For $1\leq\pp<\infty$ $$\label{eq00}
\begin{aligned}
\psi_{\pp,m}[\hat{f}](t):&= \Big(\int_{\RD}
\min\big(1, (|\xi|/t)^{m\pp}\big)
\,|\hat{f}(\xi)|^{\pp}\,d\xi \Big)^{1/\pp}\\
&=\Big( t^{-m\pp}
\int_{|\xi|\leq t} |\xi|^{m\pp}\,|\hat{f}(\xi)|^{\pp}\,d\xi
+(\psi_{\pp}[\hat{f}](t))^{\pp}\Big)^{1/\pp},\qquad t>0,
\end{aligned}$$ and for $\pp=\infty$ $$\psi_{\infty,m}[\hat{f}](t):=
\sup_{\xi\in\RD} \Big(\min\big(1,(|\xi|/t)^{m}\big)\,|\hat{f}(\xi)|\Big),\qquad t>0.$$ It might not be immediately obvious why these tails are useful, we give the reason for that in Theorem \[Besseltail\] below. Note that for any $1\leq\pp\leq\infty$, $\psi_{\pp,m}[\hat{f}](t)$ is nonincreasing as $t$ grows, because so is the function $\min(1,r/t)$ for any fixed $r>0$. Note also that in the case $\hat{f}\in{}C_0^\infty(\RD)$, $\hat{f}\not\equiv0$, there exist $\tilde{c}_1=\tilde{c}_1(\hat{f})>0$, $\tilde{c}_2=\tilde{c}_2(\hat{f})>0$ such that $$\label{eqcinfty}
\tilde{c}_1\,t^{-m}\leq\psi_{\pp,m}[\hat{f}](t)
\leq \tilde{c}_2\,t^{-m},\qquad t\ra\infty,$$ because $\psi_{\pp}[\hat{f}](t)=0$ for large $t$.
We are ready to state the two results from [@Cl] mentioned above. First [@Cl p. 512], for any $d\in\NN$ in the case $2\leq{}p\leq\infty$, there exists $c_3=c_3(p,d,m)$ such that for for all functions in the set $\{f : f\in{}L^p(\RD)\textrm{ and }\hat{f}\in{}L^{p^\prime}(\RD)\}$, $$\label{eq1}
\omega_{p,m,\infty}[f](1/t)\leq c_3\,\psi_{\pp,m}[\hat{f}](t),\qquad t>0.$$ Note that in the case $p=2$, holds for all $f\in{}L^2(\RD)$. (The mentioned formula in [@Cl] involves in fact $\psi_{\pp,m}[\hat{f}](2t)$. The formula is then true since $\psi_{\pp,m}[\hat{f}](t)$ is nonincreasing, and suffices for our purposes.) Secondly [@Cl (9)], for any $d\in\NN$ in the case $1\leq{}p\leq2$, for any $a>1$ there exists $c_4=c_4(p,q,d,m,a)$ such that for any $1\leq{}q\leq\infty$ and for all $f\in{}L^p(\RD)$ $$\label{eq2}
\psi_{\pp}[\hat{f}](t)\leq c_4\,
\sum_{k=1}^\infty a^m\omega_{p,m,q}[f](1/(a^kt)),\qquad t>0.$$ It would be preferable to have instead of a formula which does not involve an infinite sum, i.e., of the type . It turns out that such a result holds for $d\geq2$ and if $q$ is large enough, at least $q=\pp$.
\[thm1\] For any $d\geq2$ and $1\leq{}p\leq2$ there exists $c=c(p,d,m)$ such that for all $f\in{}L^p(\RD)$ $$\label{eq2p}
\psi_{\pp,m}[\hat{f}](t) \leq c\,\,\omega_{p,m,\pp}[f](1/t),\qquad t>0.$$
It is explained in Remark \[remdim1\] below why (and even its analog with $\psi_{\pp}[\hat{f}](t)$ in the left-hand side, cf. below) fails for $d=1$. In view of , one can replace $\pp$ in the right-hand side in with any $q\geq\pp$ (and a different $c$). It would be interesting to know if one could replace $\pp$ in the right-hand side of with $1\leq{}q<\pp$. Note also that for $q\geq\pp$, our Theorem \[thm1\] implies readily all the statements of [@Cl Theorem 2], and is slightly more general since no comparison function $s$ as in [@Cl] is required.
In the case $p=2$ the following is an immediate consequence of , and .
\[thm2\] For $d\geq2$ and $p=2$ there exist $c_1,c_2>0$ that depend on $d$ and $m>0$ only, such that for all $f\in{}L^2(\RD)$ and $t>0$ $$\label{eq2p2}
\begin{aligned}
c_1\,\omega_{2,m,\infty}[f](1/t)\leq \psi_{2,m}[\hat{f}](t)
&\leq c_2\,\omega_{2,m,2}[f](1/t)\\
&\leq c_2c(2,2,\infty,d)\,\omega_{2,m,\infty}[f](1/t).
\end{aligned}$$
The estimates , , show that that the modified tail $\psi_{\pp,m}$ is more appropriate than the true tail $\psi_{\pp}$ to be compared with the $\omega_{p,m,\pp}$. The upper estimate in is a Jackson-type inequality, see e.g. [@K Section I.8]. It follows from that for $p=2$ an inequality in the direction opposite to holds: In the case $d\geq2$ for all $f\in{}L^2(\RD)$ $$\label{eq000}
\omega_{2,m,\infty}[f](1/t)\leq \tilde{c}(2,\infty,2)\,\omega_{2,m,2}[f](1/t),\qquad t>0,$$ and so for any $m>0$ all the moduli $\omega_{2,m,q}$, $2\leq{}q\leq\infty$, are equivalent. It would be interesting to find a direct proof of . We now explain why in the case $d\geq2$ and $1\leq p^\prime<\infty$ the modified $\psi_{\pp,m}$ defined in is a natural quantity to consider. For $d\geq2$ and any $0<\alpha<\infty$ define $$\label{eq_Besselt}
G_\alpha(|w|):=
2^\alpha\int_{\SD}\big(1-\cos (y\cdot{}w)\big)^\alpha\,dS_y,
\qquad w\in\RD.$$ Recalling that the functions in form a Fourier pair and using the Hausdorff–Young inequality (see the proof of Theorem \[thm1\] below and the proof of in [@Cl]) we can compare for $y\in\SD$ fixed and $t>0$, the $L^p$ norm of $\Delta_y^m{}f$, $\delta_{p,m}[f](y)$, and the $L^{p^\prime}$ norm of the function $(2i\sin(y\cdot \xi/(2t)))^m\,e^{imy\cdot\xi/2}\,\hat{f}(\xi)$ (in the case $p>2$ we assume in addition as before that $\hat{f}\in L^{p^\prime}(\RD))$. Raising both quantities to the power $q=p^\prime$ (this explains why the choice $q=p^\prime$ is natural) we can compare the quantities $(\omega_{p,m,p^\prime}[f](t))^{\pp}$ and $$\int_{\RD}
2^{m\pp/2}
\bigg(\int_{\SD}\Big(1-\cos\frac{y\cdot\xi}{t}\Big)^{m\pp/2}\,dS_y\bigg)
|\hat{f}(\xi)|^{\pp}\,d\xi.$$ With this in mind, for $d\geq2$ and any $\hat{f}\in L^{\pp}(\RD)$, $1\leq p<\infty$, we introduce the [*Bessel tail *]{}of the Fourier transform $$\Psi_{\pp,m}[\hat{f}](t)
:=
\bigg(\int_{\RD} G_{m\pp/2}\big({|\xi|}/{t}\big)
|\hat{f}(\xi)|^{\pp}\,d\xi\bigg)^{1/\pp}$$ and $\Psi_{\infty,m}[\hat{f}](t):=\psi_{\infty,m}[\hat{f}](t)$. From the above discussion, $\omega_{p,m,p^\prime}[f](t)$ can be compared with the Bessel tail $\Psi_{\pp,m}[\hat{f}](t)$ as in , . The relevance of the modified $\psi_{\pp,m}$ is now apparent from the following
\[Besseltail\] For any $d\geq2$ and any $0<\alpha<\infty$, there exist $C_1,C_2>0$ that depend only on $d$ and $\alpha$ so that $$\label{eqBessel}
C_1(\min(1,v))^{2\alpha}\leq G_\alpha(v)
\leq C_2(\min(1,v))^{2\alpha},\qquad v\geq0,$$ and hence for some $\tilde{C}_1,\tilde{C}_2>0$ that depend on $1\leq p<\infty$, $m>0$, $d$ only, $$\tilde{C}_1\Psi_{\pp,m}[\hat{f}](t)
\leq \psi_{\pp,m}[\hat{f}](t)
\leq\tilde{C}_2\Psi_{\pp,m}[\hat{f}](t)$$ for all $\hat{f}\in L^{\pp}(\RD)$ and all $t>0$.
The relation is illustrated for $\alpha=1$, $C_1=\pi/3$, $C_2=6\pi$ in Fig. \[fig\] (note that $G_1(v)=4\pi\big(1-\frac{\sin v}{v})$).
We now describe the relationship between the true and the modified tails, $\psi_\pp$ and $\psi_{\pp,m}$, respectively. From it is clear that for any $1\leq\pp\leq\infty$, $m>0$, and $\hat{f}\in{}L^\pp(\RD)$ $$\label{eqtri}
\psi_\pp[\hat{f}](t)\leq\psi_{\pp,m}[\hat{f}](t),\qquad t>0.$$ The following statement gives a converse to that is optimal on the power scale (see Remark \[remstar\] below).
\[lem4.1\] Let $d\in\NN$, $m>0$, $\alpha>0$, $1\leq\pp\leq\infty$, $g{}\in{}L^\pp(\RD)$. All the constants below depend on $g$ and are strictly positive and finite.
1\. Let $1\leq\pp<\infty$.
\(i) If $\psi_\pp[g{}](t)\leq c_2(g)\cdot{}t^{-\alpha}$, $t\ra\infty$, then as $t\ra\infty$, $$\psi_{\pp,m}[g{}](t)\leq b_2(g)
\cdot\begin{cases}
t^{-\alpha},&0<\alpha<m\cr
t^{-\alpha}\,(\log{}t)^{1/\pp},&\alpha=m\cr
t^{-m},&\alpha>m.
\end{cases}$$
\(ii) If $c_1(g)\cdot{}t^{-\alpha}\leq
\psi_{\pp,m}[g{}](t)\leq c_2(g)\cdot{}t^{-\alpha}$, $t\ra\infty$, then as $t\ra\infty$, $$\psi_{\pp}[g{}](t)\geq b_1(g)
\cdot\begin{cases}
t^{-\alpha},&0<\alpha<m\cr
0,&\alpha\geq m.
\end{cases}$$
2\. Let $\pp=\infty$.
\(i) If $\psi_\infty[g{}](t)\leq c_2(g)\cdot{}t^{-\alpha}$, $t\ra\infty$, then as $t\ra\infty$, $$\psi_{\infty,m}[g{}](t)\leq b_2(g)
\cdot\begin{cases}
t^{-\alpha},&0<\alpha< m\cr
t^{-m},&\alpha\geq m.
\end{cases}$$
\(ii) If $c_1(g)\cdot{}t^{-\alpha}\leq
\psi_{\infty,m}[g{}](t)\leq c_2(g)\cdot{}t^{-\alpha}$, $t\ra\infty$, then as $t\ra\infty$, $$\psi_{\infty}[g{}](t)\geq b_1(g)
We state finally a result that was applied in a study of the scaling of entanglement entropy for a certain physical system in [@GiKl; @Gi2].
\[CH3\_s3.lem.1\] Let $d\in\NN$. Assume that ${}f\in{}L^2(\RD)$. Then for some $c_1=c_1(f)>0$, $c_2=c_2(f)>0$ and some $\gamma=\gamma(f)\in(0,2)$, $f$ satisfies $$\label{eqneww}
c_1\,\eps^\gamma\leq
\int_{\SD}\|{}f(\cdot+\eps{}y)-{}f(\cdot)\|_{2,\RD}^2 \,dS_y\leq c_2\,\eps^\gamma,
\qquad0\leq\eps\leq1,$$ if and only if there exist $b_1=b_1(f)>0$, $b_2=b_2(f)>0$ such that $$\label{eqnewww}
b_1\,t^{-\gamma} \leq
\int_{|\xi|\geq{}t}
|\hat{f}(\xi)|^2\,d\xi
\leq b_2\,t^{-\gamma},\qquad t\geq1.$$
Note that Corollary \[CH3\_s3.lem.1\] is true in all dimensions: In the proof of Corollary \[CH3\_s3.lem.1\] below, we consider the cases $d\geq2$ and $d=1$ separately. In the former case we employ the general results stated above. In the case $d=1$ we give a direct proof using in particular the ideas in the proofs of [@BCT Lemma 2.10, Lemma 4.2]. The main reason why, in the case $d=1$, Corollary \[CH3\_s3.lem.1\] is true despite the fact that Theorem \[thm1\] fails, is because of the explicit (power-type) form of the estimates in Corollary \[CH3\_s3.lem.1\].
The equivalence of the [*upper *]{}estimates in and in is well-known: it follows follows e.g. from [@MS Lemma 3.3.1], and also from the results obtained in [@Cl]. Note that [@MS Lemma 3.3.1] deals with a Besov space $B_{2,\infty}^{s}(\RD)$, $s>0$, $s\not\in\NN$ (the case $s=\gamma/2\in(0,1)$ is relevant for the upper estimates in Corollary \[CH3\_s3.lem.1\]). In [@BCT], is derived in the case $\gamma=1$ from a more restrictive pointwise condition $$\label{eq_ts}
c_1\,|y|^\gamma\leq(\d_{2,1}[{}f](y))^2
\leq c_2\,|y|^\gamma,\qquad|y|\leq1,$$ which in general can not be reversed because $\d_{2,1}[{}f](y)$ can have singular directions.
A simple example of a function that satisfies with $\gamma=1$ is the characteristic function of a compact set with $C^1$ boundary. For any $0<\gamma<1$ there exsits a compact set whose characteristic function satisfies , see [@Gi2 Lemma 2.9].
It turns out that Corollary \[CH3\_s3.lem.1\] fails for $\gamma=2$, see Remark \[remthf\]. Note that for $\gamma>2$ the condition is not satisfied for any $f\in{}C_0^\infty(\RD)$, $f\not\equiv0$, because it involves the finite difference of order $1$.
Theorems \[thm1\], \[Besseltail\], \[lem4.1\] and Corollary \[CH3\_s3.lem.1\] are proved in Section \[sec1.3\].
Proofs and concluding remarks {#sec1.3}
=============================
First consider the case $p=1$, $\pp=\infty$ (in this case the proof below goes through for all $d\in\NN$). We have to prove that for some $c=c(p,d,m)$, $\psi_{\infty,m}[\hat{f}](t)\leq c\,\omega_{1,m,\infty}[f](1/t)$, $t>0$. Recall that $\|\hat{f}\|_{\infty,\RD}\leq\|f\|_{1,\RD}$. Since the functions form a Fourier pair we have $$\label{eq30}
\begin{aligned}
\omega_{1,m,\infty}[f](1/t) &= \sup_{|y|\leq1/t}\d_{1,m}(y)
\geq \sup_{|y|\leq1/t} \sup_{\xi\in\RD}
\big(|2i\sin (y\cdot \xi/2)\big|^m\,|\hat{f}(\xi)|\big)\\
&= 2^m\,\sup_{\xi\in\RD}\Big( |\hat{f}(\xi)|
\sup_{|z|\leq1} \big|\sin (z\cdot \xi/(2t))\big|^m \Big).
\end{aligned}$$ It is an easy exercise to prove that for any $\xi\in\RD$ $$\begin{aligned}
\sup_{|z|\leq1} \big|\sin (z\cdot \xi/(2t))\big| &=
\begin{cases} 1, &|\xi|\geq |t\pi|\cr
\sin(|\xi|/(2t)), &|\xi|< |t\pi|
\end{cases}\\
&\geq\frac14\,\min(1,|\xi|/t).
\end{aligned}$$ This together with and proves the result.
Consider now the case $d\geq2$, $1<p\leq2$, $\pp<\infty$. By the Hausdorff–Young inequality $\|\hat{f}\|_{\pp,\RD}\leq(2\pi)^{d/\pp}\|f\|_{p,\RD}$, $1<p\leq2$, and using the fact that is a Fourier pair we get as in [@Cl (4.7)] $$\label{eq300}
\begin{aligned}
(\d_{p,m}[f](y/t))^{\pp}
&\geq (2\pi)^{-d}\int_{\RD} \big|2i\sin (y\cdot \xi/(2t))\big|^{m\pp}\,
|\hat{f}(\xi)|^{\pp}\,d\xi\\
&= (2\pi)^{-d}\,2^{m\pp/2}\int_{\RD} |\hat{f}(\xi)|^{\pp}
\,\Big(1-\cos\frac{y\cdot\xi}{t}\Big)^{m\pp/2}\,d\xi.
\end{aligned}$$ Integrating over $y$ and recalling we obtain $$\label{eq3}
\begin{aligned}
(\omega_{p,m,\pp}[f](1/t))^{\pp}
&=\int_{\SD}(\d_{p,m}[f](y/t))^{\pp}\,dS_y\\
&\geq (2\pi)^{-d}\int_{\RD}G_{m\pp/2}(|\xi|/t)\, |\hat{f}(\xi)|^{\pp}\,d\xi.
\end{aligned}$$ Now we need the following elementary result, the proof is given after the end of the present proof.
\[lem1\] Let $d\geq2$ and fix any $0<\alpha<\infty$. The function $G_\alpha(v)$, $v\geq0$, defined in satisfies the following: For any $v_0>0$ there exist $C_\alpha(v_0),c_\alpha(v_0)>0$ such that $$\label{eqlem101}
{}G_\alpha(v)\geq C_\alpha(v_0) >0,\qquad v\geq v_0$$ and $$\label{eqlem102}
G_\alpha(v)\geq c_\alpha(v_0)\, v^{2\a}, \qquad 0\leq v\leq v_0.$$
Now we write the integral in as a sum of $\int_{|\xi|\leq{}t}$ and $\int_{|\xi|\geq{}t}$, apply Lemma \[lem1\] with $\alpha=m\pp/2$, $v_0=1$, and set $c_1(p,d,m):=c(m,d)\cdot\min\big( c_\alpha(1),C_\alpha(1))$ to obtain $$\label{eq5}
\begin{aligned}
(\omega_{p,m,\pp}[f](1/t))^{\pp}
&\geq c_1(p,d,m)\,
\Big( \int_{|\xi|\leq{}t}(|\xi|/t)^{m\pp}\,|\hat{f}(\xi)|^{\pp}\,d\xi
+ \int_{|\xi|\geq{}t}|\hat{f}(\xi)|^{\pp}\,d\xi\Big)\\
&=c_1(p,d,m)\,
(\psi_{\pp,m}[\hat{f}](t))^{\pp}
\end{aligned}$$ which finishes the proof of Theorem \[thm1\].
\[remdim1\] We show now that is not true in the case $d=1$ and $p=2$. More precisely, we show that for $d=1$ there is no $c\in(0,+\infty)$ so that for all $f\in{}L^2(\RR)$ $$\label{eqnn}
\psi_{2}[\hat{f}](t) \leq c\,\,\omega_{2,1,2}[f](1/t),\qquad t>0.$$ By with $m=1$ using the Parseval formula we find $$\label{eqParseval}
(\omega_{2,1,2}[f](1/t))^2 = \frac4\pi\int_{\RR}
\sin^2\bigg(\frac\xi{2t}\bigg)\,|\hat{f}(\xi)|^2\,d\xi.$$ For $\xi\in\RR$, $t,\tilde{c}>0$, introduce the notation $$H(\xi,t,\tilde{c}) = \sin^2\bigg(\frac\xi{2t}\bigg) - \tilde{c}
\,\sgn\bigg[\Big(\frac{|\xi|}t-1\Big)_+\bigg]$$ where $\sgn a=1,0,-1$ for $a>0$, $a=0$, $a<0$, respectively, and $(a)_+=\max(0,a)$. If were true for some $c\in(0,+\infty)$ then there would exist $\tilde{c}\in(0,+\infty)$ such that $$ \int_{\RR} H(\xi,t,\tilde{c}) \,|\hat{f}(\xi)|^2\,d\xi \geq0\qquad
\textrm{for all } f\in L^2(\RR),\quad t>0.$$But $$\begin{aligned}
\{\, |\hat{f}|^2 \,:\,f\in L^2(\RR)\, \} &=
\{ \,|f|^2 \,:\,f\in L^2(\RR) \,\}\\
&=
\{\, g \,:\,g\in L^1(\RR)\textrm{ and }g\geq0
\textrm{ almost everywhere (a.e.)} \, \}.
\end{aligned}$$ We have arrived at a contradiction: If $$\int_{\RR} H(\xi,t,\tilde{c}) \,g(\xi)\,d\xi \geq0\qquad
\textrm{for all } g\in L^1(\RR),\,g\geq0\textrm{ a.e., } t>0,$$ then we must have $H(\xi,t,\tilde{c})\geq0$ for a.e. $\xi$ and all $t>0$, which is clearly false for any choice of $\tilde{c}>0$. This proves the result.
We note that the basic reason for the inapplicability of Theorem \[thm1\] to the case $d=1$ is that for any $v_0>0$ it is not possible to insert a constant function between the graph of $ \sin^2 v$ and the real axis on the interval $[v_0,+\infty)$, cf. Fig. \[fig\]. (In the case $d=1$, $\SS^0=\{\pm1\}$ and so the function $G_\alpha$ in would be given by $2^{2\alpha+1}\big(\sin^2(w/2)\big)^\alpha$, $w\in\RR$, and there is no helpful averaging over $\SS^{d-1}$.)
Recall that $d\geq2$. If $d\geq3$ then integrating over the $d-2$ angles in as in [@GS (II.3.4.2)] we obtain for $v\geq0$ $$\label{eq101z}
G_\alpha(v) = |\SS^{d-2}|\int_{0}^\pi (1-\cos(v\cos\theta))^\a
\,\sin^{d-2}\theta\,d\theta.$$ If $d=2$ then and the subsequent formlulae hold true with the convention $|\SS^{0}|=2$.
We show first there is $M_\alpha>0$ such that ${}G_\alpha(v)\geq{}M_\alpha>0$ for sufficiently large $v$. Indeed, in the case $\alpha\geq1$ by the Hölder inequality there is $\tilde{C}_\alpha>0$ so that $$\label{eq101}
\begin{aligned}
\int_{0}^\pi \big( (1-\cos(v\cos\theta))
\,&\sin^{(d-2)/\a}\theta\big)^\a\,d\theta \\
&\geq \tilde{C}_\alpha\,\Big(\int_{0}^\pi (1-\cos(v\cos\theta))
\,\sin^{(d-2)/\a}\theta\,d\theta \Big)^\a \\
&\geq \tilde{C}_\alpha\,\Big(\int_{0}^\pi (1-\cos(v\cos\theta))
\,\sin^{d-2}\theta\,d\theta \Big)^\a
\end{aligned}$$ where the second inequality follows from $$\label{eqeasy}
w^\beta \geq w,\qquad 0<\beta\leq1,\qquad 0\leq w\leq1$$ with $w=\sin^{d-2}\theta$ and $\beta=1/\a$. In the case $0<\a<1$, in view of with $w=(1-\cos(v\cos\theta))/2$ and $\beta=\a$ we obtain $$\label{eq101p}
\begin{aligned}
\int_{0}^\pi (1-\cos(v\cos\theta))^\a
\,\sin^{d-2}\theta\,d\theta
&= 2^{\a}\,\int_{0}^\pi
\Big(\frac{1-\cos(v\cos\theta)}{2}\Big)^\a
\,\sin^{d-2}\theta\,d\theta \\
&\geq 2^{\a-1}\,\int_{0}^\pi (1-\cos(v\cos\theta))
\,\sin^{d-2}\theta\,d\theta.
\end{aligned}$$ Note that $$\label{eq1019}
\begin{aligned}
|\SS^{d-2}|\int_{0}^\pi (1-\cos(v\cos\theta))
\,\sin^{d-2}\theta\,d\theta
&= \int_{\SD}\Big(1-\cos\big((v,0,\cdots,0)\cdot y\big)\Big)\,dS_y\\
&= |\SD|\,\big(1 - 2^s\,\Gamma(s+1)\,
v^{-s}\,J_s(v)\big)
\end{aligned}$$ where $s=(d-2)/2$, $J_s$ is the Bessel function, and we have used [@GS (II.3.4.2)] and [@GrRy (8.411.4)]. By [@GrRy (8.451)], $v^{-s}J_s(v)=O(v^{-s-1/2})\ra0$, as $v\ra\infty$ for $d\geq2$. Hence the right-hand side of , and also of and , tends to a strictly positive limit, as $v\ra\infty$. Therefore for any fixed $0<\alpha<\infty$, there exist $M_\alpha>0$ and $v_1(\alpha)$ so that ${}G_\alpha(v)\geq{}M_\alpha>0$ for $v\geq{}v_1(\alpha)$.
But ${}G_\alpha(v)$ does not have zeros other than $v=0$. Since $G_\alpha$ is continuous, it is for any $v_0>0$ bounded away from zero on the compact $[v_0,v_1(\alpha)]$. This proves .
Let us now prove for $v_0>0$ small enough. We can rewrite as $$\label{eqlem103}
G_\alpha(v) = 2^{\alpha}\,|\SS^{d-2}|\int_{0}^\pi
\sin^{2\alpha}(v\cos\theta)
\,\sin^{d-2}\theta\,d\theta.$$ Using the elementary estimate $$\label{eqlem104}
\sin x \geq \frac2\pi\, x,\qquad 0\leq x\leq\frac\pi2,$$ we conclude that $$ G_\alpha(v) \geq v^{2\alpha}\cdot c(\alpha,d) \int_{0}^\pi
\cos^{2\alpha}\theta
\,\sin^{d-2}\theta\,d\theta, \qquad 0\leq v\leq \frac\pi2,$$which proves for any $0<v_0\leq\pi/2$. But now if we take any $v_0>\pi/2$ then using for $0\leq v\leq\pi/2$ and the fact that $G_\alpha(v)$ is bounded away from zero for $\pi/2\leq v\leq v_0$ by we can always find $c_\alpha(v_0)>0$ small enough so that holds for $0\leq v\leq v_0$. The proof of Lemma \[lem1\] is complete.
Recall that $d\geq2$. The lower estimate in follows immediately from Lemma \[lem1\] with $v_0=1$. As for the upper estimate, we note first that by the definition , the function $G_\alpha(v)$ is bounded above for $v\geq1$. Next, using the estimate $\sin x\leq x$, $0\leq x\leq1$, in place of , we derive from the upper estimate $$G_\alpha(v) \leq v^{2\alpha}\cdot \tilde{c}(\alpha,d) \int_{0}^\pi
\cos^{2\alpha}\theta
\,\sin^{d-2}\theta\,d\theta, \qquad 0\leq v\leq 1.$$ This proves the upper estimate in . The proof of Theorem \[Besseltail\] is complete.
Recall that $d\in\NN$, $0<\alpha<\infty$, $m>0$.
1\. Consider first the case $1\leq\pp<\infty$.
\(i) Assume $\psi_{\pp}[{}g{}](t)\leq{}c_1(g)\cdot{}t^{-\alpha}$, $t\geq1$. By $$\label{eq201}
(\psi_{\pp,m}[{}g{}](t))^\pp= t^{-m\pp}
\int_{|\xi|\leq t} |\xi|^{m\pp}\,|{}g{}(\xi)|^\pp\,d\xi
+(\psi_{\pp}[{}g{}](t))^\pp.$$ Then the following gives the result for the case 1(i), all values of $\alpha$: $$\begin{aligned}
t^{-m\pp} &\int_{|\xi|\leq t} |\xi|^{m\pp}\,|{}g{}(\xi)|^\pp\,d\xi\\
&\leq t^{-m\pp}\Big(\int_{|\xi|\leq1}|{}g{}(\xi)|^\pp\,d\xi
+ \sum_{k=0}^{[\log_2t]}
\int_{2^{k}\leq|\xi|\leq2^{k+1}}|\xi|^{m\pp}\,
|{}g{}(\xi)|^\pp\,d\xi\Big)\\
&\leq t^{-m\pp}\Big(\const(g)+ c_1(g)\sum_{k=0}^{[\log_2t]}
\big(2^{(m-\alpha)\pp}\big)^k\Big)
\end{aligned}$$ where $[\cdot]$ denotes the integer part of a real number. It is explained in Remark \[remstar\] below why the order in $t$ cannot be improved in the case 1(i) and in all other cases.
\(ii) Assume $c_1(g)\cdot t^{-\alpha}\leq
\psi_{\pp,m}[{}g{}](t)\leq c_2(g)\cdot t^{-\alpha}$, $t\geq1$ ($\pp<\infty$). The example ${}g{}\in{}C_0^\infty(\RD)$, ${}g{}\not\equiv0$, shows that in the case $\alpha\geq{}m$ we can only claim the trivial bound $\psi_\pp[{}g{}](t)\geq0$, $t\ra\infty$. Let now $0<\alpha<m$. We use the idea in the proof of [@BCT Lemma 4.2]. Let $0<B\leq1$ be a number to be chosen later. By the definition $$\label{eqlem120}
(\psi_{\pp,m}[{}g{}](t))^\pp =
\Big( \int_{|\xi|\leq Bt} + \int_{|\xi|\geq Bt}
\Big) \min^{m\pp}(1,|\xi|/t)\,|{}g{}(\xi)|^\pp\,d\xi.$$ We have $$\begin{aligned}
\int_{|\xi|\leq Bt} &\min^{m\pp}(1,|\xi|/t)\,|{}g{}(\xi)|^\pp\,d\xi
= t^{-m\pp} \int_{|\xi|\leq Bt} |\xi|^{m\pp}\,|{}g{}(\xi)|^\pp\,d\xi\\
& \leq t^{-m\pp} \bigg(\int_{|\xi|\leq B}|\xi|^{m\pp}\,|{}g{}(\xi)|^\pp\,d\xi
+ \sum_{l=1}^{[\log_2 t]+1}
\int_{2^{l-1}B\leq|\xi|\leq2^{l}B}
|\xi|^{m\pp}\,|{}g{}(\xi)|^\pp\,d\xi
\bigg)\\
& \leq t^{-m\pp} \bigg(\|g\|_{\pp,\RD}^{\pp}
+ \sum_{l=1}^{[\log_2 t]+1}
(2^{l}B)^{m\pp}\cdot c_2^{\pp}(g)\cdot (2^{l-1}B)^{-\alpha\pp}
\bigg)\\
&\leq t^{-m\pp}\cdot\const(g)\cdot t^{(m-\alpha)\pp}
\cdot B^{(m-\alpha)\pp},\qquad t\to\infty.
\end{aligned}$$ Therefore choosing $0<B\leq1$ small enough (recall that $m-\alpha>0$) we obtain that $$\label{eqlem121}
\int_{|\xi|\leq Bt}\min^{m\pp}(1,|\xi|/t)\,|{}g{}(\xi)|^\pp\,d\xi
\leq \frac{c_1^{\pp}(g)}2 \cdot t^{-\alpha\pp},\qquad t\to\infty.$$ Since $\psi_{m,\pp}[g](t)\geq c_1^{\pp}(g)\cdot t^{-\alpha\pp}$, $t\to\infty$, together with gives $$\int_{|\xi|\geq Bt}
\min^{m\pp}(1,|\xi|/t)\,|{}g{}(\xi)|^\pp\,d\xi
\geq \frac{c_1^{\pp}(g)}2 \cdot t^{-\alpha\pp},\qquad t\to\infty.$$ Setting $s=Bt$ we obtain $$\label{eqlem110prim}
\int_{|\xi|\geq s}
\min^{m\pp}(1,B|\xi|/s)\,|{}g{}(\xi)|^\pp\,d\xi
\geq {c_1(g)}B^{\alpha\pp}\cdot s^{-\alpha\pp},
\qquad s\to\infty.$$ Noting that $
1\geq\min(1,B|\xi|/s)
$ we conclude from that $$\psi_{\pp}^\pp[g](t) = \int_{|\xi|\geq s}
|{}g{}(\xi)|^\pp\,d\xi
\geq {c_1(g)}B^{\alpha\pp}\cdot s^{-\alpha},\qquad s\to\infty.$$
2\. The case $\pp=\infty$.
\(i) Assume $\psi_\infty[{}g{}](t)\leq{}c_1(g)\cdot t^{-\alpha}$, $t\geq1$. Note that $$\label{eqggg}
\psi_{\infty,m}[{}g{}](t)
= \max\Big(t^{-m}\sup_{|\xi|\leq t} |\xi|^m|{}g{}(\xi)|,
\,\sup_{|\xi|\geq t} |{}g{}(\xi)|\Big).$$ Clearly $$\label{eqgg}
|{}g{}(\xi)|\leq \sup_{|\eta|\geq|\xi|} |{}g{}(\eta)|
\leq c_1(g)\cdot |\xi|^{-\alpha},\qquad|\xi|\geq1.$$ Therefore $$\begin{aligned}
\sup_{|\xi|\leq t} |\xi|^m&|{}g{}(\xi)|
=\max\big(
\sup_{|\xi|\leq 1} |\xi|^m|{}g{}(\xi)|,
\sup_{1\leq|\xi|\leq t} |\xi|^m|{}g{}(\xi)|\big)\\
&\leq \max\Big(c({}g{}),\,
c_1({}g{})\cdot \sup_{1\leq|\xi|\leq{}t}|\xi|^{m-\alpha}\Big)
=\begin{cases}C({}g{}),&0<\alpha<m\cr
C_1({}g{})\cdot{}t^{m-\a},&\a\geq m.
\end{cases}
\end{aligned}$$ This together with proves the case 2(i).
\(ii) Let $c_1(g)\cdot t^{-\alpha}\leq
\psi_{\infty,m}[{}g{}](t)\leq c_2(g)\cdot t^{-\alpha}$, $t\to\infty$. Again if $\alpha\geq{}m$ then the example of ${}g{}\in{}C_0^\infty(\RD)$, $g\not\equiv0$, shows that generally speaking only the trivial bound $\psi_{\infty}[{}g{}](t)\geq0$ holds for large $t$. Let now $0<\alpha<m$. Let $0<B\leq1$ be a number to be chosen later. We have $$\begin{aligned}
\psi_{\infty,m}[{}g{}](t)
&= \sup_{\xi\in\RD}
\min^m(1,|\xi|/t)\,|g(\xi)|\\
&=\max\Big( \sup_{|\xi|\leq Bt}
\min^m(1,|\xi|/t)\,|g(\xi)|,\,\sup_{|\xi|\geq Bt}
\min^m(1,|\xi|/t)\,|g(\xi)|
\Big).
\end{aligned}$$ Now $$\begin{aligned}
\sup_{|\xi|\leq Bt}
&\min^m(1,|\xi|/t)\,|g(\xi)|
=
t^{-m} \sup_{|\xi|\leq Bt} |\xi|^m\,|g(\xi)|\\
&\leq t^{-m} \max\bigg( \sup_{0\leq|\xi|\leq B} |\xi|^m\,|g(\xi)|,
\max_{l=1,\cdots,[\log_2t]+1}
\sup_{2^{l-1}B\leq|\xi|\leq 2^lB} |\xi|^m\,|g(\xi)|\bigg)\\
&\leq t^{-m} \max\bigg( B^m\|g\|_{\infty,\RD},
\max_{l=1,\cdots,[\log_2t]+1}
2^{lm} B^m\cdot c_2(g)\cdot (2^{l-1}B)^{-\alpha}\bigg)\\
&\leq \const(g)\cdot B^{m-\alpha}\cdot t^{-\alpha},\qquad t\to\infty.
\end{aligned}$$ Choosing $B$ small enough (note that $m-\alpha>0$) we obtain $${c_1(g)}\cdot t^{-\alpha} \leq
\psi_{\infty,m}[{}g{}](t)
\leq \max\Big( \frac{c_1(g)}2\cdot t^{-\alpha},\,\sup_{|\xi|\geq Bt}
\min^m(1,|\xi|/t)\,|g(\xi)|
\Big),\qquad t\to \infty,$$ which implies that $\sup_{|\xi|\geq Bt}
\min^m(1,|\xi|/t)\,|g(\xi)| \geq {c_1(g)}\cdot t^{-\alpha}$. Replacing $s=Bt$ we obtain $$\label{eqlem110}
\sup_{|\xi|\geq s}
\min^m(1,B|\xi|/s)\,|g(\xi)| \geq {c_1(g)}B^\alpha\cdot s^{-\alpha},
\qquad s\to\infty.$$ Noting that $
1\geq\min(1,B|\xi|/s)
$ we conclude from that $$\psi_\infty[g](t) = \sup_{|\xi|\geq s} |g(\xi)|
\geq {c_1(g)}B^\alpha\cdot s^{-\alpha},\qquad s\to\infty.$$ This completes the proof of Theorem \[lem4.1\].
\[remstar\] Let us explain why the estimates in Theorem \[lem4.1\] have the best possible order in $t$. In view of , the estimates 1(i) and 2(i) for $0<\a<m$ can not be improved. The example of $g\in{}C_0^\infty(\RD)$, $g\not\equiv0$, in view of the lower estimate in shows that estimates 1(i) for $\a>m$ and 1(ii), 2(i), 2(ii) for $\a\geq{}m$ can not be improved. The example of $g\in{}L^\pp(\RD)$, $1\leq\pp<\infty$, such that $g(\xi)=|\xi|^{-(d/\pp)-\a}$ for $|\xi|\geq1$ and $g$ smooth for $|\xi|<1$ shows that the estimate 1(ii) for $0<\a<m$ can not be improved (note that the mentioned $g$ satisfies $\psi_{\pp,m}[g](t)]\leq
c_1(g)\cdot{}t^{-\a}$, $t\ra\infty$, and also $\psi_\pp[g](t)=
\big(|\SD|/(\a\pp)\big)^{1/\pp}\cdot{}t^{-\a}$, $t\geq1$). Choosing $g\in{}L^\infty(\RD)$ such that $g(\xi)=|\xi|^{-\a}$ for $|\xi|\geq1$ and $g$ smooth for $|\xi|<1$ shows that the estimate 2(ii) for $0<\a<m$ can not be improved (for this $g$ we have $\psi_\infty[g](t)=t^{-\a}$, $t\geq1$). Finally, the example ${}g{}\in{}L^\pp(\RD)$, $1\leq\pp<\infty$, such that ${}g{}(\xi)=|\xi|^{-(d/\pp)-m}$, $|\xi|\geq1$, and $g$ smooth for $|\xi|<1$ shows that 1(i) for $\a=m$ can not be improved. Indeed for this $g$, $\psi_\pp[{}g{}](t)=\big(|\SD|/(m\pp)\big)^{1/\pp}\cdot t^{-m}$, $t\geq1$, but $\psi_{\pp,m}[{}g{}](t)\geq
|\SD|^{1/\pp}\cdot t^{-m}(\log{}t)^{1/\pp}$, $t\geq1$.
[*The case $d\geq2$. *]{}The result follows readily from Corollary \[thm2\] combined with Theorem \[lem4.1\] for $p=\pp=2$, $\a=\gamma/2$, $m=1$, $g=\hat{f}$ with $\eps=1/t$. Note that the quantitity in the middle in is $(\omega_{2,1,2}[f](\eps))^2$. The integral in is the true tail integral of the of $f$, $\psi_2[\hat{f}](t)$. By Corollary \[thm2\], the exist $C_1,C_2>0$ that depend on $d$ only so that for all $f\in{}L^2(\RD)$ $$\label{eqappr1}
C_1\,\omega_{2,1,2}[f](1/t)
\leq \psi_{2,1}[\hat{f}](t)\leq C_2\,\omega_{2,1,2}[f](1/t),\qquad t>0.$$ Set $\alpha=\gamma/2$. Note that since $0<\gamma<2$ we have $0<\a=\gamma/2<m=1$, and the reult follows from Theorem \[lem4.1\], cases 1 (i) and (ii), applied to the comparison function $t^{-\alpha}=t^{-{\gamma/2}}$, $t\geq1$.
[*The case $d=1$. *]{}We prove first that implies . This follows from a straightforward modification of the proof of [@BCT Lemma 4.2]. We prefer to give the details for the convenience of the reader. Below, $c$ will denote a positive constant whose precise value may change from equation to equation and may depend on $f$ but which is independent of $\eps$ and $t$. By $$\begin{aligned}
(\omega_{2,1,2}[f](\eps))^2 = \frac4\pi\int_{\RR}
\sin^2\bigg(\frac{\eps\xi}{2}\bigg)\,|\hat{f}(\xi)|^2\,d\xi
\geq c \int_{{\pi}/(2\eps)
\leq|\xi|\leq2{\pi}/(2\eps)}
|\hat{f}(\xi)|^2\,d\xi.
\end{aligned}$$ Setting $\tilde{\eps}=2\eps/\pi$ and denoting $\tilde{\eps}$ by $\eps$ again, we find from the upper inequality in $$\begin{aligned}
c_2\cdot(\pi\eps/2)^\gamma
\geq \omega_{2,1,2}[f](\pi\eps/2)
\geq c \int_{1/\eps
\leq|\xi|\leq2/\eps}
|\hat{f}(\xi)|^2\,d\xi
\end{aligned}$$ which after setting $t=1/\eps$ implies $$\label{eqdyadic}
\int_{t
\leq|\xi|\leq2t}
|\hat{f}(\xi)|^2\,d\xi \leq c\cdot t^{-\gamma},\qquad t\geq1.$$ Using the latter estimate and representing $$ \int_{|\xi|\geq t}|\hat{f}(\xi)|^2\,d\xi
=\sum_{j=0}^\infty
\int_{2^j t\leq|\xi|\leq2^{j+1} t} |\hat{f}(\xi)|^2\,d\xi,$$we prove the upper inequality in . In order to prove the lower inquality in , we note first that implies $$\label{eq1dyadic}
\int_{|\xi|\leq r}
|\xi|^2\, |\hat{f}(\xi)|^2\,d\xi \leq c_3
\cdot r^{2-\gamma},\qquad r\geq1.$$ Indeed using the upper inequality in we obtain $$\begin{aligned}
\int_{|\xi|\leq r}
|\xi|^2\, |\hat{f}(\xi)|^2\,d\xi
&\leq \int_{|\xi|\leq 1}
|\xi|^2\, |\hat{f}(\xi)|^2\,d\xi
+\sum_{j=0}^{[\log_2r]+1}
\int_{2^j \leq|\xi|\leq2^{j+1} } |\xi|^2\, |\hat{f}(\xi)|^2\,d\xi\\
&\leq\const
+c\sum_{j=0}^{[\log_2r]+1}
(2^{j+1})^2 \cdot b_2\cdot (2^{j})^{-\gamma}\\
&\leq c^\prime\cdot r^{2-\gamma}
\end{aligned}$$ (recall that $\gamma<2$). Next, let $\alpha,\beta>0$ be two numbers to be chosen later. From the lower inequality in and using $|\sin x|\leq x$ and $|\sin x|\leq1$ for $x\geq0$, we obtain $$\begin{aligned}
c_1\cdot \eps^\gamma&\leq
(\omega_{2,1,2}[f](\eps))^2\\
&= \frac4\pi\int_{\RR}
\sin^2\bigg(\frac{\eps\xi}{2}\bigg)\,|\hat{f}(\xi)|^2\,d\xi\\
&\leq c \bigg(\eps^2\int_{|\xi|\leq\alpha/\eps}
|\xi|^2\,|\hat{f}(\xi)|^2\,d\xi
+\int_{\alpha/\eps\leq|\xi|\leq\beta/\eps}
|\hat{f}(\xi)|^2\,d\xi
+\int_{|\xi|\geq\beta/\eps}
|\hat{f}(\xi)|^2\,d\xi\bigg).
\end{aligned}$$ Using and the upper inequality in we find $$\int_{\alpha/\eps\leq|\xi|\leq\beta/\eps}
|\hat{f}(\xi)|^2\,d\xi
\geq c_1c^{-1}\cdot \eps^\gamma
-\beta^{-\gamma}b_2\cdot \eps^\gamma
-\alpha^{\gamma}c_3\cdot \eps^\gamma$$ which after choosing $\alpha>0$ small enough and $\beta>0$ large enough gives $$\int_{|\xi|\geq\alpha/\eps}
|\hat{f}(\xi)|^2\,d\xi
\geq\int_{\alpha/\eps\leq|\xi|\leq\beta/\eps}
|\hat{f}(\xi)|^2\,d\xi
\geq c\cdot\eps^\gamma,\qquad 0<\eps\leq1.$$ Setting $t=\alpha/\eps$ we prove the lower inequality in .
We now derive from . Using the upper inequality in and employing and Theorem \[lem4.1\] (recall that in our case $p=p^\prime=2$, $m=1$, $\alpha=\gamma/2\in(0,1)$) $$ (\psi_{2}[\hat{f}](t))^2
\leq (\psi_{2,1}[\hat{f}](t))^2
\leq c\cdot t^{-\gamma}.$$ Combining this with (that holds for $d=1$) and using we obtain $$(\omega_{2,1,2}[f](1/t))^2 \leq c \cdot(\omega_{2,1,\infty}[f](1/t))^2
\leq c^\prime \cdot(\psi_{2,1}[\hat{f}](t))^2
\leq c^{\prime\prime}\cdot t^{-\gamma}$$ which proves the upper estimate in . It remains to prove the lower estimate in . Note that the two-sided estimate implies that for $A>1$ large enough $$\bigg( \int_{|\xi|\geq t} -
\int_{|\xi|\geq At} \bigg)\,|\hat{f}(\xi)|^2\,d\xi
= \int_{t\leq|\xi|\leq At} |\hat{f}(\xi)|^2\,d\xi \geq c\cdot t^{-\gamma}$$ or after setting $\eps=\pi/(2t)$ $$\label{eq2dyadic}
\int_{\pi/(2\eps)\leq|\xi|\leq A\pi/(2\eps)}
|\hat{f}(\xi)|^2\,d\xi \geq c\cdot \eps^{\gamma},
\qquad 0<\eps\leq1.$$ On the other hand again using $$\begin{aligned}
(\omega_{2,1,2}[f](\eps))^2 = \frac4\pi\int_{\RR}
\sin^2\bigg(\frac{\eps\xi}{2}\bigg)\,|\hat{f}(\xi)|^2\,d\xi
\geq c \int_{{\pi}/(2\eps)
\leq|\xi|\leq3{\pi}/(2\eps)}
|\hat{f}(\xi)|^2\,d\xi
\end{aligned}$$ and replacing $\eps$ with $\eps/3^j$, $j\in\NN$, we find $$(\omega_{2,1,2}[f](3^{-j}\eps))^2
\geq c \int_{3^j{\pi}/(2\eps)
\leq|\xi|\leq3^{j+1}{\pi}/(2\eps)}
|\hat{f}(\xi)|^2\,d\xi,\qquad j=0,1,2,\cdots.$$ Choosing $N=[\log_3 A]$ we then obtain $$\begin{aligned}
\sum_{j=0}^N (\omega_{2,1,2}[f](3^{-j}\eps))^2
&\geq c\cdot
\sum_{j=0}^N \int_{3^j{\pi}/(2\eps)
\leq|\xi|\leq3^{j+1}{\pi}/(2\eps)}
|\hat{f}(\xi)|^2\,d\xi \\
& \geq c\cdot
\sum_{j=0}^N \int_{{\pi}/(2\eps)
\leq|\xi|\leq A{\pi}/(2\eps)}
|\hat{f}(\xi)|^2\,d\xi \\
&\geq c^\prime\cdot \eps^\gamma,\qquad 0<\eps\leq1,
\end{aligned}$$ where we have used . Therefore $$\liminf_{\eps\to0}\eps^{-\gamma}
\sum_{j=0}^N \big(\omega_{2,1,2}[f](3^{-j}\eps)\big)^2\geq c>0$$ and hence as $N\in\NN$ is fixed, there exists at least one $J\in\{1,\cdots,N\}$ such that $$\tilde{c}:=
\liminf_{\eps\to0} \eps^{-\gamma}
\big(\omega_{2,1,2}[f](3^{-J}\eps)\big)^2 > 0.$$ Then $$\big(\omega_{2,1,2}[f](3^{-J}\eps)\big)^2\geq \tilde{c}\cdot \eps^\gamma,
\qquad 0<\eps\leq1,$$ and denoting $3^{-J}\eps$ by $\eps$ we finish the proof of the lower inequality in .
We note finally that the proof of Corollary \[CH3\_s3.lem.1\] for $d=1$ can be modified to give an alternative proof of Corollary \[CH3\_s3.lem.1\] also for all $d\geq2$ from scratch (in this connection, see an explanation of an argument from [@BCT] given in the proof of [@thesis Lemma 3.4.1]).
\[remthf\] After the above general discussion it is not difficult to understand why Corollary \[CH3\_s3.lem.1\] fails for $\gamma=2$. Recall that in , $p=\pp=2$ and $m=1$. Let $\hat{f}\in{}L^2(\RD)$ be defined by $\hat{f}(\xi):=|\xi|^{-(d/2)-1}$ for $|\xi|\geq1$ and smooth for $|\xi|<1$. Let $f\in{}L^2(\RD)$ be the inverse of this $\hat{f}$. It is easy to check that for some $\tilde{b}_1,\tilde{b}_2>0$ that depend on $\hat{f}$ $$\label{eqtss}
\tilde{b}_1\,t^{-1}(\log{t})^{1/2} \leq\psi_{2,1}[\hat{f}](t)
\leq \tilde{b}_2\,t^{-1}(\log{t})^{1/2},\qquad t\geq2$$ whereas for certain $\tilde{c}_1,\tilde{c}_2>0$ that depend on $\hat{f}$ $$\tilde{c}_1\,t^{-1} \leq\psi_{2}[\hat{f}](t)
\leq \tilde{c}_2\,t^{-1},\qquad t\geq2.$$ Note that by and for $c_1,c_2>0$ that depend on $f$ $$c_1\,t^{-1}(\log{t})^{1/2} \leq\omega_{2,1,2}[f](1/t)
\leq c_2\,t^{-1}(\log{t})^{1/2},\qquad t\geq2.$$ This shows that Corollary \[CH3\_s3.lem.1\] fails for $\gamma=2$. It is only true in the case $\gamma=2$ that the upper estimate in implies the upper estimate in (simply because for any $f\in{}L^2(\RD)$ and all $t>0$, $\psi_2[\hat{f}](t)\leq{}\psi_{2,1}[\hat{f}](t)\leq{}c(2,d,1)\,\omega_{2,1,2}[f](1/t)$ in view of and ). The fact that the lower estimate in need not hold is shown by considering the example of $\hat{f}\in{}C_0^\infty(\RD)$, $\hat{f}\not\equiv0$ (for which $\psi_2[\hat{f}](t)=0$ identically for large $t$). Finally, the first example of this remark shows the upper estimate in for $\gamma=2$ need not follow even from a two-sided estimate in .
[12]{} [BCT]{} L. Brandolini, L. Colzani and G. Travaglini, *Average decay of Fourier transforms and integer points in polyhedra.* Ark. Mat. **35** (1997), 253–275. [Cl]{} D. B. H. Cline, *Regularly varying rates of decrease for moduli of continuity and Fourier transforms of functions on $\RD$.* J. Math. Anal. Appl. **159** (1991), 507–519. [GS]{} I. M. Gel’fand and G. E. Shilov, *Generalized Functions*, vol. 1, Academic Press, New York–London, 1964. D. Gioev and I. Klich, *Entanglement entropy of fermions in any dimension and the Widom conjecture.* Phys. Rev. Lett. **96** (2006), 100503, 4 pp. [Gi2]{} D. Gioev, [*Szegö limit theorem for operators with discontinuous symbols and applications to entanglement entropy.*]{} Int. Math. Res. Not. **2006**, Art. ID 95181, 23 pp. D. Gioev, *Generalizations of Szegö Limit Theorem: Higher Order Terms and Discontinuous Symbols*, Ph.D. Thesis, Royal Institute of Technology, Stockholm, 2001. [www.math.rochester.edu/people/faculty/gioev/thesis.pdf]{} [GrRy]{} I. S. Gradshteyn and I. M. Ryzhik, *Tables of Integrals, Series, and Products*, 4th ed., Academic Press, New York–London–Toronto, 1980. Y. Katznelson, *An Introduction to Harmonic Analysis*, 3rd Ed., Cambridge University Press, Cambridge, 2004. [MS]{} V. G. Maz’ya and T. O. Shaposhnikova, *Theory of Multipliers in Spaces of Differentiable Functions*, Pitman Publishing, Boston, 1985. [St]{} E. Stein, *Singular Integrals and Differentiability Properties of Functions*, Princeton University Press, Princeton, 1970. [Ti]{} A. F. Timan, *Theory of Approximation of Functions of a Real Variable*, Pergamon Press, Oxford–New York, 1963. [T]{} E. C. Titchmarsh, *Introduction to the Theory of Fourier Integrals*, 2nd ed., Oxford University Press, London–New York, 1948.
| |
The DAT tests a wide variety of subjects, ranging all the way from Biology to Mathematics.
As well you are required to possess various skills, which will largely determine your success not only as a dental student but even as a dentist.
So as challenging as some sections may seem, apply yourself and attempt to understand the information therein because a simple concept could be the one thing standing between you and the dental school of your dreams.
Let’s take a look at exactly what you can expect from each of the DAT sections, shall we?
Quick Summary
Exam Section
No. Of Questions
Time Length
Tutorial (optional)
--
15 Minutes
Survey of Natural Sciences
• Biology
100 Qns.
90 Minutes
Perceptual Ability Test
90 Qns.
60 Minutes
Scheduled Break (optional)
-
30 Minutes
Reading Comprehension
50 Qns.
60 Minutes
Quantitative Reasoning
40 Qns.
45 Minutes
Post-Test Survey (optional)
--
15 Minutes
TOTAL EXAM
280 Qns.
5 Hrs. 15 Min.
What Are The DAT Sections?
The Dental Admission Test comprises 4 sections, namely:
- Survey Of Natural Sciences
- Perceptual Ability Test
- Reading Comprehension
- Quantitative Reasoning
The Survey of Natural Sciences section contains 3 subtests: Biology, General Chemistry, and Organic Chemistry. So in essence, the entire DAT test can be considered to have 6 sections in total.
Each of the 6 DAT sections is scored out of 30, and these sectional scores are then combined into the Academic Average that accounts for a student’s DAT score.
The true purpose of the DAT exam is to measure a student’s ability to think critically and apply concepts to different contexts. So let’s see how that is done in each of the DAT sections, shall we?
1. Survey Of Natural Sciences
Also known as SNS, this is the first section of the DAT, and test-takers have 90 minutes to work on the 100 questions present in this science section.
The section itself contains 3 subtests: Biology, General Chemistry, and Organic Chemistry, and the 100 science questions are distributed amongst these 3 subjects.
a) Biology
This is the first part of the SNS section, and there are 40 Biology questions on the exam: Qn 1 – 40.
The Biology topics tested in the DAT exam are:
- Cell and Molecular Biology – 25%
- Structure and Function of Systems – 25%
- Genetics – 20%
- Developmental Biology – 11%
- Evolution, Ecology, and Behavior – 11%
- Diversity of Life – 8%
The scope of material covered in DAT bIology is quite vast, so the first thing you should keep in mind is not to get lost spending too much time on the details.
The questions asked are pretty integrated, so you would need to learn the interaction between biological systems, rather than learning a biological concept in isolation.
Firstly, having a strong understanding of the basic fundamentals will make it easier for you to answer direct questions related to various concepts.
Besides that, you would also need to learn how to answer questions requiring you to make inferences or conclusions based on connections between those core concepts.
It is recommended that you spend 20 minutes on the 40 Biology questions, which translates into 30 seconds for each question.
b) General Chemistry
This is the second part of the SNS section, and there are 30 General Chemistry questions on the exam: Qn 41 – 70.
For this section, you need to have a good understanding of both theoretical concepts and practical mathematical applications of various inorganic Chemistry concepts such as thermochemistry, states of matter, stoichiometry, kinetic, etc.
A calculator will not be provided for this section during the exam, and so one of the skills you need to develop is how to manually do the necessary calculations quickly and accurately.
Rather than purely focusing on how to perform each mathematical step, though, try to understand what each variable represents, what are the implied proportionalities, and what truly are the reasons behind those relationships.
This conceptual understanding will not only help you answer questions correctly, but will also make it easier for you to memorize equations and commit them to memory.
The General Chemistry topics tested in the DAT exam are:
- Stoichiometry and General Concepts – 10%
- Atomic and Molecular Structure – 10%
- Liquids and Solids – 10%
- Solutions – 10%
- Acids and Bases – 10%
- Thermodynamics and Thermochemistry – 7%
- Oxidation-Reduction Reactions – 7%
- Chemical Kinetics – 7%
- Periodic Properties – 7%
- Laboratory – 7%
- Gases – 6%
- Chemical Equilibria – 6%
- Nuclear Reactions – 3%
On the DAT, every single question carries the exact same value regardless of its difficulty level, and that also applies to the General Chemistry section.
As such, it is important to manage your time wisely so you do not end up getting too engrossed in time-consuming questions.
It is recommended you spend 37 minutes working on the 30 General Chemistry questions.
Should time run out, it is much better to have spent 2 minutes answering 4 questions correctly rather than having spent 3 minutes on a single question. So time management is particularly important for this section.
c) Organic Chemistry
This is the last part of the SNS section, and there are 30 Organic Chemistry questions on the exam: Qn 71 – 100.
DAT Organic Chemistry doesn’t require you to have many reactions and mechanisms memorized. Rather, you simply need to have a conceptual understanding of the content tested.
The Organic Chemistry topics tested in the DAT exam are:
- Individual Reactions of the Major Functional Groups and Combinations of Reactions to Synthesize Compounds – 30%
- Chemical and Physical Properties of Molecules – 17%
- Mechanisms – 17%
- Aromatics and Bonding – 10%
- Acid Base Chemistry – 10%
- Stereochemistry – 10%
- Nomenclature – 6%
At first, the Organic Chemistry content tested on the DAT may appear to be very different from what you studied.
That is because the nature of this exam places more focus on generalizations, patterns, and critical thinking, rather than brute memorization. So it may seem difficult to grasp at first, but with time, you will find that this is actually a much easier way to learn.
Make a point of studying concepts, rather than memorizing a long list of specific reactions.
When you need to apply memorization, though, focus on the general types of reactions for each functional group, rather than on individual reactions.
It is recommended that you spend 30 minutes on the 30 Organic Chemistry questions, which translates into 60 seconds for each question.
After spending 40 minutes on Biology, 37 on General Chemistry, and 30 on Organic Chemistry, you can then have 3 minutes to spend reviewing any questions you skipped or marked in the SNS section, before moving on to the next DAT section.
2. Perceptual Ability Test
Also known as PAT, this is the second section of the DAT, and test-takers have 60 minutes to work on the 90 questions in this section.
The section itself consists of 6 subsections, namely:
a) Keyholes / Apertures
b) Top-Front-End / View Recognition.
c) Angle Ranking / Angle Discrimination.
d) Hole Punching / Paper Folding
e) Cube Counting
f) Paper Folding / 3D Form Development
The 90 PAT questions are distributed evenly across these 6 subsections, so you have 15 questions in each subsection.
For most students, this is one of the most challenging sections in the DAT.
The PAT section is designed to test your spatial visualization skills, including your ability to interpret 2D and 3D representations of objects.
Although challenging, you will find yourself constantly applying this skill not only in dental school but also in your dental career.
From constructing mental images of teeth from X-rays, to dealing with casts and fillings, there are numerous occasions where you will have to apply these spatial visualization skills, and so the sooner you master that, the better off you will be.
3. Reading Comprehension
This is the third section of the DAT, and the section comes in the form of 3 passages, each containing 16 – 17 questions to give you a total of 50 questions.
Test-takers have 60 minutes to work on the 50 Reading Comprehension test questions, so you have about 20 minutes to spend on each passage.
The science-based passages in this section are generally obtained from published works and the idea is to test your ability to read, understand and analyze scientific texts.
As such, it is important that you become familiar with the vocabulary and format of such texts, while also training yourself to figure out the author’s tone. Is the author trying to speculate, persuade, or simply inform the reader?
Not only that, but you also need to familiarize yourself with the various types of Reading Comprehension questions that may appear on the exam.
a) Global Questions
These assess your general understanding of the passage as a whole. You may be required to identify the passage’s main idea, thesis, or conclusion.
b) Detail Questions
Being the most common type of question asked in this section, you may be asked to provide clarification on specific statements in the passage.
c) Tone Questions
These ask about the author’s bias, and you are required to infer whether the author makes their argument based on scientific evidence and anecdotes or whether their arguments are subjective or objective.
d) Function Questions
These require you to evaluate the author’s arguments so you can explain how certain information was presented or why certain bits of information were included in the text.
e) Inference Questions
These test your ability to deduce meaning and draw conclusions from a passage.
f) Title Of The Text Questions
These questions will ask you to decide on which would be a befitting title for the passage or even a single paragraph within the passage.
4. Quantitative Reasoning
This is the fourth and last section of the DAT, and test-takers have 45 minutes to work on the 40 Quantitative Reasoning test questions.
This section is designed to test your proficiency in mathematics, as well as assess your problem-solving skills.
The content tested in this section includes:
- Data Analysis, Interpretation, and Sufficiency – 35%
- Applied Mathematics – 25%
- Algebra – 22%
- Probability and Statistics – 10%
- Quantitative Comparison – 8%
In the QR section, you will have 30 questions on mathematics, and 10 questions based on applied mathematics or rather, word problems.
Unlike the Survey of Natural Sciences section, you will be provided with a basic calculator for the Quantitative Reasoning section. This will appear on the computer screen at your testing center.
Nevertheless, students are often advised to get good at making numerical calculations manually as this will save you plenty of time, as opposed to if you decided to use the provided calculator, which is pretty time-consuming.
Besides, you are expected to get through the SNS section without a calculator so developing the ability to manually do calculations fast and accurately will overall prove to be helpful in the DAT exam.
You have slightly over 60 seconds to work on each question, so it is important to develop your time management skills by taking plenty of practice tests prior to the actual exam.
DAT Test Sections By Score
Every dental student knows that you will need to know which DAT scores to obtain in each section, to give you a competitive chance at getting into the various dental schools.
Here are the 2021 cumulative percentile distributions as computed by the American Dental Association, which is the body that administers and regulates the DAT exam.
50th Percentile Score
75th Percentile Score
90th Percentile Score
Survey of Natural Sciences
17.5
20
22
• Biology
17.5
20
22
• General Chemistry
18
20
23
• Organic Chemistry
17.5
20
23
Perceptual Ability Test
18.5
20.5
22.5
Reading Comprehension
19.5
22
24.5
Quantitative Reasoning
17.5
20
23
Academic Average
18
20.5
22
FAQs About DAT Sections
How Many Questions Are On The DAT?
There are 280 multiple-choice questions on the DAT exam.
What Is The Hardest DAT Section?
The hardest DAT section, according to a majority of test-takers, seems to be the perceptual ability test section.
This is because perceptual ability isn’t necessarily something you study. Rather, it is a skill you either possess inherently or must work hard to develop.
If you struggle with the PAT section of the DAT, you can overcome this by working on lots of practice questions, which will help you gradually develop your visualization skills.
You may also consider getting some handy strategies from the various DAT prep courses available.
Are DAT Sections Multiple Choice?
Yes, DAT sections are multiple choice.
This is a great thing because even when you cannot figure out the correct answer, you can work your way backward by eliminating the wrong answers and gambling with the remaining answer choices.
There is no penalty for guessing on the DAT exam. So if you ever are truly in a bind, simply guess and move on to the next questions. Try not to leave any questions unanswered. | https://testpreppal.com/dat-sections/ |
Pictures from the annual Pride Parade down Yonge Street – my apologies for the large number but everyone is just so photogenic and engaging!
“Sing me a rainbow, paint me a dream.
Show me a world that I’ve never seen.”
The first Monday after the “fall back” time change is always one of my favorite days of the year. That’s when I feel like I got an extra hour of sleep. So I woke up feeling great but of course it’s November so there were some grey clouds. Still, the phrase “I can sing a rainbow” was stuck in my head. But I don’t sing, so I did the next best thing and took a rainbow of photos as I walked today. Beat the blahs away by capturing the brightest moments.
below: And what goes best with rainbows? Why not a unicorn?! It looks like the work of #whatsvictorupto
If you know the children’s song, “I Can Sing a Rainbow”, you will know that the colours in the lyrics aren’t in the correct ROYGBV order (or IV at the end if you include indigo). It’s a cute little song so I will forgive the author.
And in case your childhood didn’t include this song, here are the words:
Red and yellow and pink and green,
Purple and orange and blue,
I can sing a rainbow,
sing a rainbow,
Sing a rainbow too.
Listen with your eyes,
Listen with you ears,
And sing everything you see.
I can sing a rainbow,
Sing a rainbow,
Sing a rainbow too.
Nuit Rose,
a festival of queer art and performance
On Saturday night events were held at a number of venues that were concentrated in two locations, along Queen St. West and in the Church-Wellesley village area. I hung out around two parks in the village, Norman Jewison Park which runs east of Yonge and Barbara Hall Park on Church street. In hindsight, I wish I had had more time, or had been more organized, to get to more of the events.
Red Pepper Spectacle Arts led a Light Parade that started at Norman Jewison park. A small contingent, most wearing or carrying a light-emitting object, walked through the park, along and then back down Church Street. From the – sparklers, glow sticks
to the more elaborate
below: and an eagle on stilts
below: Note to self: for night time parades take more photos at the start of the parade because once people start moving it’s more difficult to get them in focus!
below: Where else would you be able to sit on a unicorn and get your picture taken?
below: And after a unicorn pose, have your photo taken standing with a well-lit couple.
below: 360 degrees by Iain Downie, 360 stars, 60 in each of the six Pride colours in the garden.
below: Dance performance, ‘By Chance’ by Janessa Pudwell and Tanya Svazas Cronin. | https://mcfcrandall.blog/tag/unicorn/ |
Part of the mural team poses in front of the historic Mission bells. Students have decided that the current San Rafael Mission steeples will be depicted in the mural. For more information about the history of the Mission go to the Marin History Museum.
At the Boyd Gate House, home of the Marin History Museum, students pulled out their art journals, in which they sketched and took notes of their discoveries. Students were particularly drawn to the Marin at War! exhibition, in which there were various service uniforms on display. Louise Arner Boyd was an arctic explorer and photographer from San Rafael, who will also be depicted in the historic mural by the students.
Next students visited the Falkirk Cultural Center, a historical 1888 San Rafael landmark which now presents contemporary art exhibitions. Students found themselves inspired by the prints on display in the galleries and enjoyed walking around the beautiful grounds, filled with sculptures and gardens.
At the corner of 4th Street and C streets students were given photographs or drawings of historical landmarks that still exist or used to exist on each of the four corners. They used visual clues to figure out which historical image matched each corner.
Arguably the most historical piece of real estate in downtown sits at the northwest corner of 4th and C streets, where Timothy Murphy lived, and which was used later as the courthouse. Murphy, who was named San Rafael’s first informal mayor, won a large land grant from the Mexican Government in 1844 and built his adobe house in downtown. He was a boisterous Irishman who reportedly spoke Miwok and Spanish , and who loved to have parties. San Rafael Day was born when church goers would go to Sunday mass at the Mission and walk over to Murphy’s house for afternoon drinks, food, and games. The Bank of Italy building now sits in the same location, built in the late 1920s. For more information check out the Early San Rafael History book on Google Books.
The tour ended with us back at Youth in Arts, 917 C Street, where the final mural will be installed. The building was used as a livery and purchased by Neil MacPhail in the 1870s. Horses and carriages, including the famous Tally-ho were rented out to customers. When cars became the prominent mode of transportation the MacPhails ventured into the fuel business and later into appliances. The building is still owned by the MacPhail family and evidence of the passage of time fills the building. Beautiful sturdy wood beams hold up the warehouse in back, a manual horse elevator was used to bring the horses to the second floor stables, and elegant antique appliances adorn the attic.
By Mentor Artist Tracy Eastman
Short Elementary School’s 2nd and 5th grade “Green Team” were delighted to paint a large mural to brighten up their newly planted garden in the front of the school. Julie Ryan, the 2nd-grade teacher and leader of Green Team, and I decided the most fitting subject matter for the garden mural would be California native flowers, as that was what her students were currently studying. There was, however, a challenge with how and where to display a mural in their garden area. The portable building where the mural was to be painted was said to be transported to another school in the next couple years. For this reason, we opted for a portable mural that would be painted on two recycled vinyl banners. This would allow the 18-foot-long mural to be rolled up and transported to any new location.
Matthew Jackett is a junior at Marin Academy, interested in history and writing. As a 2012 summer intern for the Marin History Museum, Matthew wrote a series of blog posts on the mural installed on Youth in Arts refurbished facade at 917 C Street. This is the third post in that series. Historic images from the Marin History Museum collection.
In the far right panel of the mural, a horse is depicted standing in front of the Bay View Livery and Sales Stables, the building that is currently Youth in Arts. The building has been owned since the 1870s by the MacPhail family, who now leases the space to Youth in Arts. In the front of the building is a Tally-Ho wagon with Neil MacPhail, the original owner of the livery, riding in the front.
Above the building are three historic famous San Rafael residents. On the far left is Louise Arner Boyd, famed heiress, Marin native, and Arctic Explorer. She inherited her fortune from her father, who made his money as a mining tycoon. After her parents’ death, she began to spend her millions on lavish parties hosted in her home in San Rafael. She then began using her money to explore the Arctic region, and at the age of 64, became the first woman to fly over the North Pole.
The man in the middle is Billy Shannon, who owned a famous boxing training gym on Fourth Street from 1906 to 1914. It was called Billy Shannon’s Villa, and it was the choice destination for celebrity boxers at the time, such as Joe Gans, the first African-American boxing champion. Shannon provided lodging and training for the boxers while his wife would cook and feed them. On the weekends and holidays, boxing matches would be held and crowds would take the West End train to come see the fights. When boxing was outlawed temporarily in California, Billy Shannon’s Villa was forced to close, but he left San Rafael residents with the memories of the fights and the celebrity boxers, and he became a cherished memory of San Rafael at the beginning of the 20th Century.
The third member of the trio is Eleanor Garatti, who was Marin’s first Olympic gold medalist. She trained at San Rafael’s Municipal Bath House, and broke records across the country at swim meets, with the trips funded by local merchants. She won the gold medal in the 1928 Summer Olympics in Amsterdam for the U.S. freestyle relay team, as well as a silver medal in the 100 meter freestyle. Four years later, she once again won the gold medal in the relay and this time won the bronze in the 100 meter freestyle at the 1932 Los Angeles Olympics. When she returned home, huge crowds came to celebrate along the train route from Sausalito to San Rafael. She became a local hero, hailed by the mayor of San Rafael as “Marin’s sweetest daughter.”
At the left of this mural panel are also two well-known San Rafael architectural landmarks–the historic Falkirk Mansion and the Marin Civic Center, designed by Frank Lloyd Wright.
This part of the mural shows the past of San Rafael and all that has made it what it is today. Youth in Arts building itself can be seen, growing from a livery to a center that gives children the opportunity to explore the history of their city and express themselves through an artistic medium.
Read “History Behind the Mural, Part 1”
Read “History Behind the Mural, Part 2”
The San Rafael history mural at Youth in Arts was created with support from the County of Marin, the Fenwick Foundation, the MacPhail Family and the Marin Community Foundation. Youth in Arts will host a public reception and celebration of the mural on Friday, September 14, from 5-8 p.m. The event will include a dedication ceremony at 6 p.m. and the opening of a new exhibit on the creation of the mural by Davidson students.
Our project began with this driving question put to a team of wise and thought-provoking college students at Grant Grover School, part of College of Marin. Each student is coping with a challenge. Their responses included a world where everyone can give their gifts, where people walk the city in peace, where there’s more Nature, butterflies and horses, safety for people and animals and clean water. A place with no alcoholism or drug use, no name calling and fighting. A place where there are smiles and laughter, where people learn how to fix breakdowns and where Love = Life without Limits. From this conversation, 8th grade Novato Charter School student Gabriella Borges and I made a study. The students colored the studies and I put together their color ideas into a plan.
As part of our project, I incorporated ideas from the Institute of Noetic Sciences’ Worldview Literacy Curriculum. We explored how people look at life through different beliefs, like putting on sunglasses. As we watched the film called “Music by Prudence” about special needs students who create music in Zimbabwe, we heard Prudence say that some people see those with handicaps as burdens, but she knows they are stars. Prudence, whose documentary won an academy aware, has become an international star. I gave all the students sunglasses, which they put on, looking at themselves and each other through the lens of “burden.” I asked them what they thought “burden” meant: “A heavy load”, “something you always have to carry”, “something that doesn’t give back”.
Then everyone took their sunglasses off and we talked about how Prudence is a star and how each of them is a star. Each student made a star and a peace sign, as symbol of being at peace with who they are. This exercise was inspired by IONS’ Worldview Literacy Curriculum.
We gridded the study, gridded the board, drew the image and painted it.
After eight weeks of painting, we completed the 6.5′ x 4′ painting, which will be part of the Summer of Peace 2012, an initiative of the Shift Network.
Hundreds of seventh graders from Davidson mural spend the day streaming into the school library which had been transformed into a gallery to view their own creations.
Youth in Arts Mentor Artist Brooke Toczylowski worked with all Davidson Middle School seventh graders and their teachers Ed Cosgriff and Jeff Snow
to create collaborative Mini Murals on their personal histories in San Rafael.
Brooke led students in creating research workbooks to develop critical thinking skills as both Artists and Historians. Students described the visual elements they noticed in photographs, analyzed images by making educated hypotheses with supportive evidence, compared and contrasted photographs, and made connections between an arts process and a historical concept. Brooke taught specific elements of design to the students who worked with their teachers on their personal stories. Then the students worked in teams of two to create their visual story of San Rafael as a mini mural.
The gallery exhibit was a time for reflection on the artistic and learning process. Selected student comments:
“I learned that collaboration is hard, but creative things come out of the process.”
“I learned that the only way to get to San Rafael used to be through a train that is not there any more.”
“My classmates come from all over the world, I didn’t know that before this project.”
“There was a San Rafael day that featured bullfights with grizzly bears.”
“There was an old movie theater called the El Camino”
“I found out about layering, abstract and realistic art, the meaning of foreground and background. I learned that I’m an artist.”
The young and talented artists have been working on this project with Mentor Artist, Brooke Toczylowski, since November. For more posts about this project click HERE.
One of the ways the students transferred images onto the panels was to project their drawings or photos and then trace the shapes.
To the left Sonia and Declan transfer a photo of Sonia painting. This part of the mural represents the students’ own history and connection to the present and future of San Rafael. It was inspired by Diego Rivera’s Mural at the San Francisco Art Institute, “Making a Fresco.”
Local Master Artist Kalen Meyer came to Youth in Arts to speak with the students and share her artistic process. She showed the evolution of how her painting has changed over the years, including many images from her series, “36 Views of Mt. Tamalpais,” which is the local mountain included in the mural.
Students had prepared questions the day before after looking at images by Master Artists Tom Killion and Katsushika Hokusai (who is an inspiration for both Killion and Meyer.)
The young artists asked,
Do you use calm colors on purpose?
Do you ever paint a view or a place from that place, or do you always work from photographs?
How could we work on the background color of our mural?
After looking at Kalen’s work and going back to our mural the students found themselves inspired by her paint strokes and some of her techniques directly came out in the style of the mural.
“I learned that working as a team is better and it’s faster and when you work alone it looks all the same but when you work with lots of people it looks [different], like the [paint strokes] are different.” – Rosvin
“When I’m at home when I’m painting I’m alone in my room, but this so much more fun because you know you can be painting and then yell across the room and be like, ‘hey!'” – Sonia
“Something that doing this project has brought to me is…I made lots of new friends like Stefania and Jessica, and it made me also much closer to my good friends.” – Declan
“What I learned is that we had a community here. Like when we were [painting] Charles it was Natalie and then Stefania joined in and then Joselyn and me, too. We all did it together.” – Jessica
STAY TUNED! In June the mural will be installed on the Youth in Arts building. A gallery exhibit and community celebration will illustrate the mural process and celebrate the young artists’ hard work.
THANK YOU to all parents, artists, and volunteers that made this project possible.
And THANK YOU to Whole Foods, who provided much of the snacks and lunches for the kids during the week.
Youth in Arts invites seventh and eighth grade students at Davidson Middle School to participate in the creation of a public mural about the history of San Rafael. This large-scale mural will be installed in downtown San Rafael at the current Youth in Arts space, 917 C Street. Throughout the school year students will be led by a professional artist in the creation of the mural, which will be unveiled in June 2012 in a community-wide celebration.
Youth in Arts Mentor Artist Brooke Toczylowski will guide a leadership team of 15-20 students in the research and creation of the mural. In addition to this leadership team the Mentor Artist will be available to collaborate and work with the social studies teachers in designed and facilitating an integrated curriculum around the history of San Rafael. Students and teachers will ponder inquiry questions like, “How do Artists Represent History?” and “How is History Told by Different People?”
Students participating on the leadership team will gain a wide range of skills they can transfer to other disciplines. Each youth artist will be in charge of keeping an art journal they will use for research, sketches, ideas, questions, and reflections. The research segment of the project will investigate the history of San Rafael, cultural connections, Master Artists, personal experiences, interviews, and more. Students will be exposed to resources with the Mentor Artist but will also be expected to do research in their art journals outside of meeting time. The leadership group will take 1-3 field trips during the course of the project: 1) a walking field trip of San Rafael 2) a visit to the Marin History Museum 3) a visit to San Rafael artists’ studios. These experiences will connect students personally to the content being studied and will provide the group with ideas and sketches for the mural itself. The art journals will be a place for students to document and record these academic and personal experiences. Segments of the journals will be on display during the 2012 unveiling in a gallery exhibit complementing the mural project.
In addition to historical and artistic research students will experiment with a variety of artistic materials during the residency. Through drawing in their art journals they will explore composition, shape, line, value, and other formal concerns. During studio time with the Mentor Artist they will learn about color, painting, and photography.
In addition to exploring the area, researching history, and investigating materials, the youth artists will develop skills for working in the public arena. They will brainstorm, plan, and collaborate as a team to design a final composition. With this final sketch they will propose their mural to the San Rafael City Council. They may need to re-adjust, make changes and re-propose it. Throughout this process they will learn that projects have take a lot of work and require patience and focus.
“Paintings are but research and experiment. I never do a painting as a work of art. All of them are researches.” (Pablo Picasso)
Can art making be a form of hands-on research? What can we learn from our experiments and explorations?
How can we discover new things about our themes and about ourselves through making art?
Working with Mentor Artist Brooke Toczylowski the Mural Team at Davidson has been researching – both the history of San Rafael and painting. Toczylowski has studied Arts Based Research with Julia Marshall and Kimberley D’Adamo at San Francisco State University.
As they get ready to create the mural students are digging deep into both content and technique. Students use their art journals as a place to express, experiment, document, and learn.
To start their research the artists learned how to make a mind map in which they focused on what they already know about their chosen theme. For example, a student asks herself, “What do I already know about the Miwoks?” and “What do I want to know?”
Using resources from historical books, the internet, and oral histories from the Marin History Museum, students began their reading and researching. They created pages in their journals in which image and text intertwine and interact. Having such an open format allows them to make the content personal and relevant to their own lives.
In addition to historical research the artists are also experimenting with different paints and techniques. At the end of each session together students share what they’ve discovered support each other in their next steps.
[singlepic id=442 w=320 h=240 float=right]Students, families, friends and community members enjoyed the Bay Area’s warm September weather and celebrated the artistic accomplishments of Davidson students at a special Friday evening event in downtown San Rafael.
Held in front of Youth in Arts home at 917 C Street, the event included the dedication of a historically themed mural created in 2011-12 by Davidson students with Youth in Arts Mentor Artist Brooke Toczylowski. Youth in Arts Gallery was also open, featuring an exhibit on the mural, curated and installed in part by Davidson students. The event was featured as part of ArtWorks Downtown’s 2nd Fridays Art Walk.
[singlepic id=427 w=320 h=240 float=left]Visitors had a chance to see the gallery exhibit and enjoy refreshments and hands-on arts activities. Musical accompaniment and dance demonstrations were provided by Joti Singh and Bongo Sidibe of Duniya Drum & Dance Company. Joti also teaches students at Davidson, through Youth in Arts.
San Rafael Mayor Gary Phillips was on hand for the dedication ceremony, along with Marin County Supervisor Susan Adams. The Davidson mural project was supported in part by the County, and also by the Fenwick Foundation, the Marin Community Foundation and the MacPhail Family, which has owned the building currently housing Youth in Arts since the 1800s.
Youth in Arts also presented the 2012 Pamela Levine Arts Education Leadership Award at the event, to Carol Cooper, founding Head of School for Willow Creek Academy in Sausalito/Marin City and a strong supporter of arts education. (For more information on the Pamela Levine Award and Ms. Cooper, please visit the Youth in Arts website).
Students from the Davidson Mural team spoke as part of the mural dedication ceremony, along with Mayor Phillips, Davidson Principal Harriet MacLean, and Mentor Artist Brooke Toczylowski. Many spoke of how impressed they were by the students’ work and by their dedication to the mural project. Brooke pointed out how the young artists had chosen to include images of themselves painting in the center of the mural. The painting explores many themes from San Rafael’s past, she said, but “they are the future–and the future is so bright.”
The Mural Team, comprised of 17 students (now 8th and 9th graders), worked throughout the Fall and Winter of 2011-12 to research, plan, design and create the mural. Hundreds of Davidson seventh graders also worked for a shorter period of time with Brooke on “mini-murals” which were also on display.
A plaque installed by Youth in Arts at the site provides passers-by at 917 C Street with a sketch of the mural, explaining the history behind each of the features included. | http://www.youthinarts.org/?s=mural+team |
Civil engineers work in the construction of roads, buildings, airports, bridges, and infrastructure projects in private and public sectors. The US Bureau of Labor Statistics estimates an eight percent rise in the demand for civil engineers between 2020 and 2030.
With this rise in demand, we will look at the highest-paying civil engineer companies and how much they pay. If you’re an aspiring civil engineer, use this article to learn more about the best companies for civil engineers to work for.
What Is a Civil Engineer?
Civil engineers use civil engineering techniques like planning, designing, constructing, and maintaining infrastructures. They have a creative approach to respecting public and environmental health. Civil Engineers are responsible for landmark projects like the Brooklyn Bridge and the Erie Canal. They build everything from roads and tunnels to buildings and bridges.
According to the US Bureau of Labor Statistics, 50 percent of civil engineers in North America work in engineering services. Some of their duties include analyzing long-range plans and survey reports maps, analyzing the tests on building materials, and evaluating civil engineering projects.
How to Get a Civil Engineers Job
The best way to get a civil engineering job starts with earning an undergraduate degree. Fortunately, there are many online civil engineering degrees that are ideal for people who want to learn from home. Below is a step-by-step guide on how you can get a job in civil engineering.
- Complete a civil engineering bachelor’s degree program. Learning civil engineering begins at university with a four-year undergraduate program. These programs cover a wide range of related subjects such as math, engineering, and statistics used in civil engineering.
- Earn a master’s degree. Specialize in an area to become a construction, land development, transportation, or geotechnical engineer. Consider these programs if you’re looking to find the best jobs in engineering.
- Complete an internship. Civil engineering internships include semester-long or summer-long internships to satisfy part of the degree requirements. This also consists of an engineer-in-training program.
- Become licensed. Civil engineers who want to offer their services to the public must go through several steps to become licensed. Some common requirements for licensing include attending an ABET (Accreditation Board for Engineering and Technology) institution, fundamentals of engineering (FE) exams, completing a minimum number of professional hours, or the Practice of Engineering exams (PE).
- Start applying for related jobs. Online job boards such as Indeed and Glassdoor are popular and effective sites for finding job openings. Be sure to check out government or federal career web pages, as well.
Top 10 Highest-Paying Civil Engineers Companies
|Company||Salary for Civil Engineers|
|Aerotek||$111,223|
|Betchel||$101,481|
|The US Army||$92,479|
|Arcadis||$90,721|
|Parsons Corporation||$90,554|
|Kimley-Horn||$87,340|
|HDR||$82,157|
|Stantec||$80,492|
|Jacobs Engineering||$80,185|
|AECOM||$78,076|
Aerotek
Aerotek provides workforce and HR solutions to organizations across the world. This company specializes in temporary staffing, recruiting, training, direct placement, payroll, and employee contracts.
What Does Aerotek Pay Its Civil Engineers?
Aerotek pays its civil engineers $111,223, per year, according to Indeed. This is far above the national average. Common benefits include 401k plans, life insurance, disability insurance, and employee discounts on select products and services.
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Aerotek Reviews
Aerotek is a decent company to work for, according to reviews on Indeed. Past and present employees feel the company excels in offering its employees professional development. These employees also spoke highly of Aerotek’s fun and work-friendly environment.
Bechtel
The biggest company in civil engineering is Bechtel, an American company that offers a wide range of services in engineering and construction. It is involved in a number of large-scale infrastructure projects involving roads, airports, communication networks, and gas field development projects. Bechtel also operates as an infrastructure consulting firm.
What Does Bechtel Pay Its Civil Engineers?
According to Glassdoor, Bechtel pays its civil engineers $101,481 per year. This company also offers employee benefits as part of its compensation plans. They include health insurance, 401k plans, maternity leave, and paid time off.
Bechtel Reviews
According to hundreds of reports on Glassdoor, working at Bechtel is a great experience. Past and present employees have praised this company’s organized culture and positive work-life balance.
The US Army
Instead of working for private engineering corporations, you could work for the US state or federal government. According to the US Bureau of Labor Statistics, 12 percent of all civil engineers in America work for the government.
What Does The US Army Pay Its Civil Engineers?
The average salary of a US Army civil engineer is $92,479 per year, according to Indeed. This is nine percent higher than the national average. The Army offers a wide range of benefits, including vacation days, housing, comprehensive healthcare, and cash allowances.
The US Army Reviews
Working for the US army is a great experience. Thousands of employee reviews on Indeed and Glassdoor praise this organization. Employees also commended the Army’s salaries, benefits, job security, and career advancement possibilities.
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Arcadis
Arcadis is one of the largest construction companies in the United States. It offers a wide range of engineering services, including sustainable design, engineering, and consultancy solutions. This company offers high-paying jobs to civil engineers.
What Does Arcadis Pay Its Civil Engineers?
According to Glassdoor, civil engineers working at Arcadis earn $90,721, per year. This company offers positive initiatives and competitive salary packages. The common benefits include retirement plans, health insurance, and 401k matching.
Arcadis Reviews
In general, Arcadis is a decent company to work for, particularly for larger-practice careers. Employees on Indeed and Glassdoor have spoken highly of this company’s flexible working schedules and exceptional corporate culture.
Parsons Corporation
Parsons Corporation is one of the largest solutions providers of technology-related products and services. These services include defense solutions, intelligence, and critical infrastructure.
What Does Parsons Corporation Pay Its Civil Engineers?
Glassdoor reports that civil engineers working at Parsons Corporation earn a yearly salary of $90,554. This corporation also offers health, retirement, savings, and career advancement benefits.
Parsons Corporation Reviews
You’ll have a great experience working at Parsons as hundreds of employees on Glassdoor imply that this company offers great benefits. Other perks of working at this corporation include interacting with good people and extensive opportunities to advance your career.
Kimley-Horn
Kimley-Horn is a globally recognized consulting firm. It offers premier planning and design consulting services for different clients. According to Kimley-Horn’s LinkedIn page, this company has more than 5,000 staff members in more than 100 offices throughout the US.
What Does Kimley-Horn Pay Its Civil Engineers?
According to Glassdoor, Kimley-Horn pays its civil engineers $87,340, annually. Many employees on this platform also reported cash bonuses upward of $22,182, per year.
Kimley-Horn Reviews
Kimley-Horn is an excellent company to work for, as many employees have spoken positively of this company’s internship programs. Kimley-Horn also offers competitive benefits for its employees.
HDR
HDR is a design corporation that specializes in engineering, environmental, architecture and construction services. HDR operates in special infrastructure projects involving bridges and hospitals.
What Does HDR Pay Its Civil Engineers?
Glassdoor estimates the average annual salary of HDR’s civil engineers to be approximately $82,157, per year.
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HDR Reviews
Thousands of employees on Glassdoor and Indeed have applauded HDR’s excellent work environment and great team culture. Some of the advantages of working for HDR include a supportive work environment, interesting projects, and opportunities for growth.
Stantec
Stantec is a professional services company specializing in architectural design and civil engineering. Other services offered by this company include interior design, landscape architecture, surveying, and environmental sciences, among others.
What Does Stantec Pay Its Civil Engineers?
According to Glassdoor, Stantec civil engineers earn $80,492 per year, including bonuses and additional compensation. The average base salary starts at $58,887 while the highest annual salary for a civil engineer is $120,000.
Stantec Reviews
Many employees on Glassdoor say that Stantec is a good company to work for and would recommend open positions to their friends. Some of the benefits mentioned by both present and past employees include a great work environment, comprehensive employee benefits, and a good work-life balance.
Jacobs
Jacobs is a well-known engineering firm that offers a broad range of construction services to a large number of clients in the industrial and commercial industries. The company’s services extend to design, construction, consulting, and maintenance.
What Does Jacobs Pay Its Civil Engineers?
Glassdoor reports that Jacobs pays its civil engineers $80,185, per year. Employees are also entitled to flexible work schedules, health insurance, and retirement benefits.
Jacobs Reviews
Thousands of past and present employee reviews on Glassdoor and Indeed suggest that this company excels in offering a positive work environment and great corporate culture.
AECOM
AECOM is one of the biggest construction companies in the world. It offers a wide variety of construction-related services including design, construction, management, and engineering. Yahoo Finance estimates that AECOM has more than 51,000 employees who helped the company generate $13.2 billion in 2021.
What Does AECOM Pay Its Civil Engineers?
Glassdoor reports that civil engineers working at AECOM earn an annual salary of $78,076, per year. However, AECOM also offers a broad range of employee benefits, including accident insurance, adoption insurance, paid holidays, paid time off, retirement plans, and savings plans.
AECOM Reviews
AECOM is a good company to work for, judging by the thousands of reports on employee review sites such as Glassdoor and Indeed. Some of the factors that enhance the work experience at AECOM include a good work environment, comprehensive employee benefits, and flexible work-from-home policies.
Why You Should Become a Civil Engineer in 2022
With the current construction boom, the civil engineering industry is growing quickly. More neighborhoods are being built, which means more houses, bridges, roads, and utilities need to be developed. Working for a top civil engineering firm gives you an opportunity to earn a reasonably high salary.
Well-established companies also offer comprehensive health insurance, life insurance, and retirement plans. Pursue this career if you are interested in challenging projects and infrastructure development.
Best Companies for Civil Engineers FAQ
Arup seems to be the best company to work for, according to engineering forums and publications. Other top companies for civil engineers include Atkins, Bechtel, Arcadis, and AECOM.
According to Glassdoor, civil engineers at Aerotek earn about $111,223 per year, which is significantly higher than the market rate and national average of $88,570.
Civil engineers work for companies that offer engineering services. These include city and state engineering departments, industry manufacturers, consulting engineering firms, and construction companies.
The highest-paying civil engineering job is an engineering manager. Glassdoor states that the average annual income of an engineering manager is $170,445.
About us: Career Karma is a platform designed to help job seekers find, research, and connect with job training programs to advance their careers. Learn about the CK publication. | https://careerkarma.com/blog/best-companies-for-civil-engineers/ |
Before the age of 10, I managed to befriend a whole herd of flying horses (or is it flock since they have wings? Oh well whatever...). The leader of which would often let me ride on her back, and when they were feeling particularly friendly, they'd let the neighborhood kids play with them as well.
I can't say I've had very much experience with dragons--but for the sake of this article--I decided to put on my adventurer's cap and search for one.
Follow along with me and learn how you can find your own dragons too!
Dragon Years
- 27 January 1952 – 13 February 1953: Water Dragon
- 13 February 1964 – 1 February 1965: Wood Dragon
- 31 January 1976 – 17 February 1977: Fire Dragon
- 17 February 1988 – 5 February 1989: Earth Dragon
- 5 February 2000 – 23 January 2001: Metal Dragon
- 23 January 2012 – 9 February 2013: Water Dragon
- 10 February 2024 – 28 January 2025: Wood Dragon
List from Year of the Dragon
The Relevance of the Year of the Dragon
Lucky for us it is still my year, the year of the Dragon. The year of the dragon only comes around every 12 years, though it's important to note that it starts and ends according to the Chinese New Year, and not the Western calendar. Currently it's 2012, the year of the Water Dragon. The water dragon's reign will last until February 9th, 2013--so if you're looking for dragon eggs--time is of the essence!
You may be wondering why this year is so important, well they don't call it the year of the dragon for nothing! Dragons only lay eggs during dragon years, then they hatch, grow, and mature until the year of their element comes around again (every 60 years, this may seem like a long time but dragons live for hundreds of years!).
What if it's not the Year of the Dragon?
If you've missed your chance to find a dragon egg, don't worry! You may still be able to find a hatchling or mature dragon. If you befriend or catch two of these you can raise them in captivity and have them lay eggs outside of the Dragon year cycle. However, it's important to noted that dragons born outside of the cycle have substantially shorter lives than dragons born in the wild. They will still outlive you, but they may not live past 500 years of age. This is because they are not energized by a dragon element.
Another issue is that their element will be hard to be determined until they are hatchlings. They may take on the element of the animal year they were born into, they may not--they may even take on an element outside the traditional sphere of wood, fire, earth, metal, and water and become something completely different. Among these strange elements I've heard stories of celestial elements, paranormal elements, and sub elements such as lightning and ice.
The possibilities are endless and though there is not much research on the topic (as breeding dragons is dangerous and discouraged), there is some speculation that the elements of the parent dragons may determine the element of the hatchling. For example, I have heard stories of wood and water dragons breeding flora-elemental dragons and metal and fire dragons breeding steel, silver, bronze, and platinum-elemental dragons (though not gold, because only dragons born on a metal year are pure gold).
In addition to the elemental mutations, I have also heard stories of dragons born outside of their year taking feature of the animal years they were born into. Such as, dragons with rabbit like faces and long ears if born on the rabbit year, or dragons with extremely long serpentine bodies and slithering tongues if born on a snake year, or miniature dragons with canine qualities if born on a dog year. These mutations are very rare, but are important to note.
It's very interesting, but as I mentioned before, not very well researched. If after reading this Hub you decide to breed a dragon outside of the dragon year, please feel free to share your results in the comments below!
WARNING
Please ask your parents for permission to play outside before you go venturing off looking for dragon eggs! Let them know where you are and make sure they are able to find you if they need to. You don't want to be eaten by a dragon and never seen from again, do you?
If your parents say no, that's okay. You can look for pixie dragon eggs in the house. They're usually found in places that accumulate dust, like under the couch, or the sink, or hidden deep in closets. Watch out for fairies though, they're mischievous.
Searching for a Dragon Egg
It is important to know the element of the dragon year you are in. This will help narrow down places dragon eggs may be hiding--and they are hiding everywhere!
Since it is currently the year of the water dragon, I decided to start my search around a body of water. Fortunately for me, I live right by a lake--but eggs can be found by oceans, streams, rivers, even manmade fountains and reservoirs.
I shuffled through tall grass and muddy waters in search of dragon eggs. After two hours I was freezing, filthy, and certain I would catch a cold if I didn't change my wet, muddy clothing (silly me for doing this so late in the year!). I was about to give up when I stumbled across a well kept nest hidden in some foliage by the water. It contained several white and blue spotted eggs the size of my head.
As excited as I was to find these eggs, I left the nest untouched for two reasons. First, these eggs were much too big for me--any dragon hatched from them would outgrow my small apartment in less than a year. I was also concerned that such a large dragon would fancy a taste of my dog, or even worse--my toddler son! No, no, large dragons are not for me.
My second reason for leaving was how neat the nest was. These eggs were well cared for by a loving parent dragon. A parent dragon who would no doubt be furious if it found any of its eggs missing. I definitely did not want to deal with the wrath of a large momma dragon. So I quickly left the scene, fearing a parent dragon was no doubt very close by.
It is important to be mindful of the state the dragon egg you find is in. If it's in a nice nest like the one I found with other eggs, you should probably leave it alone. However, some dragons don't care about their eggs and have no interest in caring for their offspring. Eggs laid by these dragons are perfect candidates to be cared for as hatchlings from these eggs will grow to be ferocious, mean-spirited, and violent dragons.
There are also cases where loving dragon parents are forced to abandon their nests because they are captured, hunted, or killed or scared of by another dragon. Eggs from these nests will no doubt suffer the same fate as neglected eggs.
Lost, abandoned, or neglected eggs will often be found under leaves or foliage, carelessly left on the ground out in the open, or in nests that have not been tended to for some time.
Re-energized by my discovery of the dragon nest, something motivated me to leave the edge of the lake and venture into the woods. Not long after I found a muddy rain puddle--and a the bottom of that puddle was a small dragon egg. This egg was, without a doubt, unwanted by its parent.
I picked it up gently and cradled it in my hands, to the untrained eye it appeared to be a robin's egg--but the silver speckles on its blue surface were a telltale sign that this was, in fact, a dragon egg!
I had found my egg. :)
Caring for Your Dragon Egg
After you've found your dragon egg, you must keep it within its element for it to grow.
Wood eggs are best kept in gardens by trees, or potted plants, or flower vases. They may also do well in dresser drawers or nests on tables if the furniture is made of wood. It is better to keep them with something living though.
Fire eggs do well by fireplaces, candles, campfires, heaters, radiators, or anything hot.
Earth eggs, like wood eggs, do well by living flora--but are best kept in sand or soil. A homemade terrarium is the best way to assure healthy growth.
Metal eggs do well by metal. Keep them in your jewelry box, your car, your stove, your sink if its metal, by mirrors, pipes, any metal will do.
Since I found a water dragon egg I had to keep it in water. Typically aquariums are perfect for this, but I don't have one. So I bought I went to the pet store and bought a pretty standard rectangular aquarium and some pebbles.
I filled the aquarium with fresh water (if I had found the egg in or by salt water I would have put salt water) and on one side of the tank I piled up the pebbles so when the baby dragon hatched it'd have a place to rest outside of the water.
Dragon eggs don't need to be constantly tended to. They just need to be near their element. So once you've set your egg up some place safe you can leave them alone, only checking on them to see if they've hatched.
Preparing for Your Dragon Hatchling
Your dragon egg will hatch by the end of the dragon year (or within a few months if outside a dragon year). However, it is impossible to know how long a found egg has been in the wild and eggs laid outside the dragon year are completely unpredictable--so it's good to be prepared.
First, do some research on the type of dragon you may have found. Read books, go online, ask other dragon enthusiasts, do whatever it takes!
Try to find out your breed's temperament, the things it likes to eat, and the environment it thrives best in. Through my research I found that my dragon typically lives in lakes and eats algae, bacteria, and dead fish. Essentially, it's the lake maid.
You may find it difficult to find information on your dragon--especially if you breed it yourself. In this case, all you can do is prepare as best you can and then wait until your egg hatches to see what kind of dragon you have.
How to Train Your Dragon
Dragons are typically born with all their teeth and claws, ready to take on the world!
Here are some tips on determining the best way to care for your baby dragon.
If your dragon is born with sharp teeth like your teeth in the front of your mouth or fangs, they are carnivores or meat eaters. Make sure they are well fed, or they may attempt to eat your house pet--or you.
If your dragon is born with flat mashing teeth, like the teeth you have in the back of your mouth, they are herbivores or plant eaters. Feed them lots of fruits, vegetables, and plants.
If your dragon has a combination of both teeth, they are omnivores like you, they eat everything!
If your dragon has gils--KEEP THEM IN WATER!
If your dragon has wings, make sure they have plenty of time to play outside. Otherwise they may start flying around your house and knock things over.
If your dragon seems uncomfortable during the day, or sleeps all day and is up at night, they may be nocturnal. Nocturnal dragons make great dream protectors and are known to guard against other monsters.
If your dragon has a long tail and a long snout it is a boy. If your dragon has a shorter tail and a shorter snout it is a girl. Another way to tell is eye colour, male dragons usually have darker eye shades and female dragons tend to have more vibrant colours.
If your dragon starts to become moody, mopey, and lethargic, it may not be doing well in captivity and should be released.
When to Let Your Dragon Go
Dragons weren't meant to be domesticated. They don't really make great pets. If you befriend a dragon you have a lifelong friend, but it doesn't necessarily need to live with you to be taken care of. Likewise, if you hatch a dragon egg you can still release it and if your bond is strong it will still come to you whenever you call.
If taking care of your dragon has become too difficult, time consuming, or hard to keep up with--don't feel bad about letting your dragon go. They are perfectly capable of taking care of themselves. If you befriend a dragon they will always be by your side when you need them. No animal on earth is as loyal as a dragon.
When you release your dragon try to do it somewhere within their element so that they can find other dragons of their elemental clan and be stable.
Things will be harder for dragons with obscure elements, as there aren't many (if any) of their kind. In this case you must go with your dragon to find a clan, befriend them together, and see if they are willing to accept your dragon. You may have to try a couple times before you are successful. Once your dragon is accepted it will always be apart of the clan.
Have Fun!
Thank you for joining me on my adventure. I hope you have a wonderful adventure of your own! Please be kind and respectful to our dragon friends and all other beings. We share this world together and need to look out for each other. If you're good to others, they'll be good to you!
I'd love to hear about your dragons and would love to know about any further information you may have found on dragons, so please feel free to share your knowledge and experience below!
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There is more to Astrology then just your Sun Sign. Each astrological/zodiac sign has various qualities, characteristics, and traits associated with it. Your sun sign helps to shape your personality. But the moon and all the other planetary bodies also have a unique quality and "energy" of their own. Your personality is a unique combination of influences from not only the Sun, but also from the Moon, and all of the Planets in the solar system. The positions of each of these celestial bodies at the time and place of your birth can give you a more detailed and accurate picture of who you are.
A Horoscope is an astrological forecast based on a chart or diagram that represents the positions of the Sun, Moon, Planets, the astrological aspects, and angles at the time of an event, such as the moment of a person's birth. The 12 Houses of the zodiac are represented in the chart as different spheres of life, physical surroundings and life experiences. The placement of a planet in a house (and also the zodiac sign that the house represents) will determine the area of life in which it acts, and the goals and activities on which its drive or impulse will be focused.
By looking at the positions and aspects of the celestial bodies at the moment of birth, one can create a Natal Chart. By studying and interpreting the Birth Chart one can become aware of the qualities and traits that make up their individual personality and discover how the celestial bodies have influenced past events, and how they are shaping current experiences.
If applied accurately, Astrology can be used for Divinatory purposes by studying and interpreting the patterns, aspects and phases of current planetary activity, in order to gain a better understanding of how their energies can influence the nature of people and events, and to determine the probability of future events and experiences.
The horoscopes that you see in newspapers and magazines can be vague and not entirely accurate because they are being based on just the individuals Sun Sign. For example, those born when the sun was in the sector of the zodiac known as "Pisces" will all share similar general characteristics, and some assumptions can be made about them, but knowing the exact time and place of ones birth, and the positions of the Planets, and other astrological details would give the individual a unique snapshot of there inner nature, positive and negative personality traits, influences, talents, challanges, and probable futures.
Astrology is a wonderful ancient tool that can be used for self-exploration, personal guidance and spiritual wisdom.
"Events in the heavens are mirrored by those on Earth, As above, so below." | https://www.dimension1111.com/astrological-self-exploration.html |
How to Calculate the Future Value of an Investment
Multiply the total amount you borrow by the interest rate of the loan by the number of payments you will make. If you borrow $500 at an interest rate of six percent for a period of six months, the calculation displays as 500 x .06 x 6 to arrive at a total interest calculation of $180.00. Using this method, your monthly payment will remain a constant $113.33 over the six month term of the loan. The annuity payment formula is used to calculate the periodic payment on an annuity. An annuity is a series of periodic payments that are received at a future date.
How Interest Rates Work on Savings Accounts
As shown in the example the future value of a lump sum is the value of the given investment at some point in the future. It is also possible to have a series of payments that constitute a series of lump sums. They constitute a series of lump sums because they are not all the same amount. How much will my investment of 10,000 dollars be worth in the future? Just a small amount saved every day, week, or month can add up to a large amount over time.
Also, the FV calculation is based on the assumption of a stable growth rate. If money is placed in a savings account with a guaranteed interest rate, then the FV https://accountingcoaching.online/ is easy to determine accurately. However, investments in the stock market or other securities with a more volatile rate of return can present greater difficulty.
Present Value – PV
What is the monthly interest on 2 million dollars?
The time value of money draws from the idea that rational investors prefer to receive money today rather than the same amount of money in the future because of money’s potential to grow in value over a given period of time.
The ability to calculate the future value of an investment is a worthwhile skill. It allows you to make educated decisions about an investment or purchase regarding the return you may receive in the future. Future value of an single sum of money is the amount that will accumulate at the end of n periods if the a sum of money at time 0 grows at an interest rate i. The future value is the sum of present value and the total interest. Compare the amount of interest you ultimately pay by calculating total interest using an add-on calculation method.
Determine What Things Will Be Worth via the Time Value Of Money
This allows a company to see if the investment’s initial cost is more or less than the future return. For example, a bank might consider the present value of giving a customer a loan before extending funds to ensure that the risk and the interest earned are worth the initial outlay of cash. is one in which the payments are made at the end of each period in equal installments.
Multiply your result by 100 to calculate the interest rate as a percentage. This percentage represents the rate your investment must earn each period to get to your future value. Concluding the example, multiply 0.0576 by 100 retained earnings for a 5.76 percent interest rate. You need to earn 5.76 percent annually to get to $1,750 in 10 years. Below is a screenshot of a hypothetical investment that pays seven annual cash flows, with each payment equal to $100.
Discount Rate
- If the deferred payment is more than the initial investment, the company would consider an investment.
For example, if you obtain an automobile loan at a 10 percent annual interest rate and make monthly payments, your interest rate per month is 10%/12, or 0.83%. You would enter 10%/12, or 0.83%, or 0.0083, into the formula as the rate.
The present value of an annuity is the current value of future payments from that annuity, given a specified rate of return or discount rate. The future value of an annuity is the total value of a series of recurring payments at a specified date https://accountingcoaching.online/nonprofit-accounting/ in the future. You can continue this process to find the future value of the investment for any number of compounding periods. Calculate interest for the remaining installment payments, basing each calculation on the new balance of the loan.
What is FV formula in Excel?
Simple Interest Formulas and Calculations: Use this simple interest calculator to find A, the Final Investment Value, using the simple interest formula: A = P(1 + rt) where P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods.
The present value portion of the formula is the initial payout, with an example being the original payout on an amortized loan. Future value (FV) is the value of a currentassetat a specified date in the future based on an assumed rate of growth. The FV equation assumes a constant rate of growth and a single upfront payment left untouched https://accountingcoaching.online/ for the duration of the investment. The FV calculation allows investors to predict, with varying degrees of accuracy, the amount of profit that can be generated by different investments. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows.
The time value of money is the idea that money you have now is worth more than the same amount in the future due to its potential earning capacity. The payments due statement of retained earnings value is either a one (beginning of the month), or zero (end of the month). Where FV is future value, and i is the number of periods you want to calculate for.
A business can use lump sum or ordinary annuity calculations for present value and future value calculations. The future value shows what the value of an investment will be after a certain period of time. Future value tables, showing the future value factor intersection of periods and interest rate, are used to multiply by Inventory and cost of goods sold the initial investment amount to compute future value. As mentioned, to determine the present value or future value of cash flows, a financial calculator, a program such as Excel, knowledge of the appropriate formulas, or a set of tables must be used. considers the future value of an investment expressed in today’s value.
Luckily, there’s a future value of annuity formula to figure that out. A lump sum payment is the present value of an investment when the return will occur at the end of the period in one installment. is the procedure used to calculate the present value of an individual payment or a series of payments that will be received in the future based on an assumed interest rate or return on investment. Let’s look at a simple example to explain the concept of discounting.
In order to calculate the net present value of the investment, an analyst uses a 5% hurdle rate and calculates a value of $578.64. The time value of money (TVM) is the concept that money you have now is worth more than the identical sum in the future due to its potential earning capacity. This core principle of finance holds that provided money can earn interest, any amount of money is worth more the sooner it is received. A central concept in business and finance is the time value of money. We will use easy to follow examples and calculate the present and future value of both sums of money and annuities.
Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they be earnings or obligations. Before we cover what the future value of an annuity is, let’s first define annuity. An annuity is basically a financial contract that a person signs with an insurance accounting equation company. You purchase the contract through either a lump sum payment or a series of payments, and then receive monthly payments in retirement. A lump sum is a one-time payment after a certain period of time, whereas an ordinary annuity involves equal installments in a series of payments over time.
A future value ordinary annuity looks at the value of the current investment in the future, if periodic payments were made throughout the life of the series. Determining the FV of an asset can become complicated, depending on the type of asset. | http://c-a-m-p-o.com/2019/11/how-to-calculate-the-future-value-of-an-investment/ |
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