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Introduction to Psychoanalytic Social Theory
The early writings of Karen Horney, like those of Adler, Jung, and Klein, have a distinctive Freudian flavor. Like Adler and Jung, she eventually became disenchanted with orthodox psychoanalysis and constructed a revisionist theory that reflected her own personal experiences—clinical and otherwise.
Although Homey wrote nearly exclusively about neuroses and neurotic personalities, her works suggest much that is appropriate to normal, healthy development. Culture, especially early childhood experiences, plays a leading role hi shaping human personality, either neurotic or healthy. Horney, then, agreed with Freud that early childhood traumas are important, but she differed from him in her insistence that social rather than biological forces are paramount in personality development.
Breaking Bulimia
We have all been there: turning to the refrigerator if feeling lonely or bored or indulging in seconds or thirds if strained. But if you suffer from bulimia, the from time to time urge to overeat is more like an obsession. | https://www.flandershealth.us/personality-2/introduction-to-psychoanalytic-social-theory.html |
Since Labov’s early work (e.g., 1963, 1966), sociolinguists have frequently examined change in progress on the segmental level, but much less is known about tone change in progress. The present study finds evidence of a tone split in progress in Lalo, a Tibeto-Burman language of China. While many of the world’s tone languages show historical evidence of tone splits, to our knowledge this is the first time that a tone split has been observed while it is occurring, making it possible to closely examine phonological, social, and perceptual factors. In this sociotonetic study of Lalo, 2,938 tone tokens were extracted from recordings of 38 speakers and analyzed in terms of age, sex, and educational level. Multifactorial analyses show that the temporal extent of voiced stops’ depression of Tone 1 F0 is increasing in apparent time, especially among women, while VOT of voiced stops is decreasing as educational levels improve, giving speakers more contact with Mandarin Chinese. The same 38 speakers were also given a perceptual identification task in which F0 was systematically adjusted. Mixed-effects modeling showed that listeners used multiple acoustic cues (consonant voicing, F0 onset, and F0 shape) to identify the voiced initial. These findings suggest that Lalo is undergoing a tone split that follows Beddor’s (2009) coarticulatory path to sound change.
Keywords: tone split, coarticulatory path, sociotonetics, Lalo, change in progress, sound change
Published online: 18 May 2015
https://doi.org/10.1075/aplv.1.1.03yan
https://doi.org/10.1075/aplv.1.1.03yan
References
Abramson, Arthur S.
Baayen, R.H.
Björverud, Susanna
(1998) A grammar of Lalo. Unpublished doctoral dissertation, Lund University.
Boersma, Paul, & Weenink, David
(2012) Praat: Doing phonetics by computer. Retrieved October 17, 2012, from http://www.praat.org/
Bradley, David
Brown, J. Marvin
Brunelle, Marc
(2011) Perception in the field. Paper presented at the Seventeenth International Conference on Phonetic Sciences (ICPhS XVII), City University of Hong Kong.
Carroll, Lucien
(2010) A diachronic chain shift in the sandhi tones of Jinhua Wu. Paper presented at Linguistics Student Association Colloquium, San Diego State University.
Edmondson, Jerold, Esling, John, Harris, Jimmy, & Wei, James
Flemming, Edward
Garellek, Marc, Keating, Patricia, & Esposito, Christina
(2012) Relative importance of phonation cues in White Hmong tone. Proceedings of the Annual Meeting of the Berkeley Linguistics Society (pp.179–189). Retrieved May 13, 2013, from http://www.phonetics.ucla.edu/voiceproject/Publications/Garellek-etal_2012_BLS_proceedings_draft.pdf.
Haudricourt, André-Georges
Hessler, Peter
Holmes, Janet, & Meyerhoff, Miriam
Hyman, Larry
(2013) Towards a typology of tone system changes. Key note address given at the 3rd International Conference on Phonetics and Phonology (3rd ICPP), National Institute for Japanese Language and Linguistics (NINJAL).
Johnson, Daniel Ezra
Kang, Kyoung-Ho, & Guion, Susan G.
Kang, Yoonjung, & Han, Sungwoo
Kim, Mi-Ryoung, Beddor, Patrice Speeter, & Horrocks, Julie
Kirby, James
Lee, Hyunjung, Politzer-Ahles, Stephen, & Jongman, Allard
Lee, Leslie
(2010) The tonal system of Singapore Mandarin. In Lauren Eby Clemens, & Chi-Ming Louis Liu (Eds.), Proceedings of the 22nd North American Conference on Chinese Linguistics (NACCL-22) & the 18th International Conference on Chinese Linguistics (IACL-18) (pp. 345–362). Cambridge, MA: Harvard University.
Lennes, Mietta
(2002) Calculate-segment-durations. Retrieved October 1, 2013, from http://www.linguistics.ucla.edu/faciliti/facilities/acoustic/praat.html/
Maddieson, Ian
(2013) Tone. In Matthew S. Dryer, & Martin Haspelmath (Eds.), The World Atlas of Language Structures Online. Leipzig: Max Planck Institute for Evolutionary Anthropology. Retrieved June 20, 2014, from http://wals.info/chapter/13
Matisoff, James A.
Mazaudon, Martine, & Michaud, Alexis
Michaud, Alexis
(2012) The complex tones of East/Southeast Asian languagesː Current challenges for typology and modelling. Key note address presented at the Third International Symposium on Tonal Aspects of Languages, Nanjing, China.
Mok, Peggy P.K., Zuo, Donghui, & Wong, Peggy W.Y.
Ohala, John J.
Osnos, Evan
Pittayaporn, Pittayawat
(2013) Contour change as restructuring of tonal variation: The case of Tone 4 in Thai. Paper presented at the 3rd International Conference on Phonetics and Phonology (3rd ICPP), National Institute for Japanese Language and Linguistics (NINJAL).
Ross, Elliot, Edmondson, Jerold, & Seibert, Burton G.
Sanders, Robert
Silva, David J.
Stanford, James N.
Svantesson, Jan-Olof, & House, David
Teeranon, Phanintra
Thurgood, Graham
Trudgill, Peter
Wright, Jonathan D.
(2007) Laryngeal contrast in Seoul Korean. Unpublished doctoral dissertation, University of Pennsylvania.
Xu, Yi
Yang, Cathryn
(2010) Lalo regional varieties: Phylogeny, dialectometry, and sociolinguistics. Unpublished doctoral dissertation, La Trobe University. Retrieved April 30, 2011, from http://arrow.latrobe.edu.au:8080/vital/access/HandleResolver/1959.9/153015
Zhong, Joy
(2013) Extract Pitches [Praat script]. Dartmouth College, Hanover, New Hampshire.
Zhou, Minglang
Cited by
Cited by 5 other publications
Lin, Yuhan
Yang, Cathryn, James N. Stanford, Yang Liu, Jinjing Jiang & Liufang Tang
This list is based on CrossRef data as of 06 april 2021. Please note that it may not be complete. Sources presented here have been supplied by the respective publishers. Any errors therein should be reported to them. | https://benjamins.com/catalog/aplv.1.1.03yan |
Life is a mixed bag. It brings us good times and bad. Times of ill-health, emotional suffering, restlessness and immense heart-opening joy. When life isn’t moving in the direction we want, this is the time we create tension, physical or emotional. And we may not even be aware of it.
If we pay attention to ourselves, notice our repetitive thoughts and tune into the way we feel physically, we can learn to read the signs our bodies give us moment to moment.
Perhaps your breath is shallow or your body feels constricted, your posture slumps, rounding your back, resulting in a concave chest and limiting the breath’s capacity to move freely and expand fully.
When we resist what is, our mental state becomes tense and this is when we can feel restless and uneasy. Emotional unease of this kind can lead to physical tension, commonly the neck, shoulders and stomach, often resulting in headaches, stiffness, aches and pains, poor digestion and so much more! By noticing our mental chatter, we can take action to turn things around, becoming able to feel happier, appreciate the small things in life, and seeing what’s working by letting the light in.
So whether you’re experiencing physical pain, emotional upset or a sense of restlessness here are some ways for you to support yourself through these times.
The beauty of your breath
I use breathing practices (Pranayama) regularly throughout my day when I can feel tension mounting or an over-active mind building.
For all of the following breathing practices, prepare by sitting tall, taking your awareness to your sitting bones, lifting up and lengthening through your spine. Move your weight until your sitting bones become heavier. Now move your attention to your breath and start to slow it down. Relax your face, neck, shoulders, moving your attention to each body part as you remind yourself to let go and relax.
Sukha Purvaka Pranayama – four-part breath
The Sanskrit word sukha means ‘easy’ or ‘pleasant’. Purvah means ‘that which precedes’. So Sukha Purvaka Pranayama means ‘the simple breath which must be mastered before proceeding to more difficult breathing practices’.
The four parts include inhale (Puraka), hold inhalation (Kumbhaka), exhale (Rechaka), hold exhalation (Shunyaka).
Breathe in and out through the nose. Begin by inhaling slowly for a count of 6, hold the breath for a count of 6, exhale slowly for a count of 6, hold the out breath for a count of 6.
This is one round. Repeat for another 6 rounds. (You can use your thumb to touch each finger tip to count each round).
End the practice by returning to your regular breath after the held exhale.
Another option is to use your pulse as the rhythm for the count. You can sit for 3 minutes, 5 or 10, however long you have. Just a couple of minutes could give you the space you need to change how you feel, to become calmer.
Once this practice becomes familiar, notice when tension creeps into your body, particularly when holding the breath. Consciously relax your body, gently reminding yourself to let go throughout the practice.
Ujjayi Pranayama
Ujjayi means ‘to conquer’ or ‘to be victorious’. This breath creates a soft, extended ‘hah’ sound, like the sound of the ocean.
To practise, inhale through your nose, then exhale slowly through a wide-open mouth. This is the sound we are aiming for with the mouth closed, breathing in and out through the nose, directing the breath into the back of the throat to create the soft hissing sound. As you breathe, let the abdomen expand on the inhale and fall on the exhale. Continue breathing with this soft sound.
Ujjayi Pranayama is a lovely practice to use. Sit for 5, 10, 15 minutes and then lie down to relax or to practise as you prepare to sleep. The sound of Ujjayi breath helps to slow the breath down; it helps us to focus on our breath, making it a beautiful meditative experience. It can also be used throughout the day for a couple of minutes to help calm the mind and ease tension.
Sahita Pranayama
In this practice, the breath is made up of three parts; controlled inhalations, controlled exhalations and holding the breath. When you do all three parts, it is called Sahita.
Inhale for 4. Hold for 16. Exhale for 8. Repeat for 3 to 5 rounds or more, depending on where you are and how much time you have.
This may feel more challenging, remember to keep the body relaxed, consciously reminding yourself to let go and soften, particularly during the retention of the breath. Keep the breath smooth and even throughout, letting the inhales in slowly, and the exhales out evenly.
What I love about these breathing practices is that you can use them throughout your day, wherever you are, whatever you’re doing. Whether you’re sat on a plane or train, at your desk, or in the privacy of your own home. Use them to focus your mind, preparing yourself to start work for the day, or giving yourself a mid-afternoon energy boost.
I wish for these suggestions to help you feel calm amongst the chaos, find peace in suffering, clarity among mental chatter, and strength in your own power to transform the negative. I hope you move through your fears and enjoy each day more fully with joy in your heart.
We could all benefit from a little more peace in our lives!
I’d love to hear your thoughts. Let me know how this works for you. Do you have any tips to help you manage darker times?
Want to read more posts like this? Sign up here to get them delivered straight to your inbox. | http://www.nicholaveitch.com/breathing-practices-to-find-peace-in-times-of-pain/ |
Q:
Use numpy to solve transport equation with wave-like initial condition
I'm trying to write a python program to solve the first order 1-D wave equation (transport equation) using the explicit Euler method with 2nd order spatial discretization and periodic boundary conditions.
I'm new to python and I wrote this program using numpy but I think I'm making a mistake somewhere because the wave gets distorted. Instead of the wave simply translating to the left it seems to get distorted once it leaves the left boundary. I'm pretty sure this is a programming error but is it possible it's a rounding error? Am I not using numpy correctly? Any advice on writing this program in a more python-esque way? Thanks!
The PDE is
in finite difference form it is
solving for
Here is what I attempted:
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
# wave speed
c = 1
# spatial domain
xmin = 0
xmax = 1
n = 50 # num of grid points
# x grid of n points
X, dx = np.linspace(xmin,xmax,n,retstep=True)
# for CFL of 0.1
dt = 0.1*dx/c
# initial conditions
def initial_u(x):
return np.exp(-0.5*np.power(((x-0.5)/0.08), 2))
# each value of the U array contains the solution for all x values at each timestep
U = []
# explicit euler solution
def u(x, t):
if t == 0: # initial condition
return initial_u(x)
uvals = [] # u values for this time step
for j in range(len(x)):
if j == 0: # left boundary
uvals.append(U[t-1][j] + c*dt/(2*dx)*(U[t-1][j+1]-U[t-1][n-1]))
elif j == n-1: # right boundary
uvals.append(U[t-1][j] + c*dt/(2*dx)*(U[t-1][0]-U[t-1][j-1]))
else:
uvals.append(U[t-1][j] + c*dt/(2*dx)*(U[t-1][j+1]-U[t-1][j-1]))
return uvals
# solve for 500 time steps
for t in range(500):
U.append(u(X, t))
# plot solution
plt.style.use('dark_background')
fig = plt.figure()
ax1 = fig.add_subplot(1,1,1)
# animate the time data
k = 0
def animate(i):
global k
x = U[k]
k += 1
ax1.clear()
plt.plot(X,x,color='cyan')
plt.grid(True)
plt.ylim([-2,2])
plt.xlim([0,1])
anim = animation.FuncAnimation(fig,animate,frames=360,interval=20)
plt.show()
this is how the wave starts
and this is how it ends up after a few iterations
Can anyone please explain why this (the wave distortion) is happening?
A:
Your implementation is correct. The distortion comes from relatively large spatial step dx. At its current value of 0.2 it is comparable to the size of the wave, which makes the wave visibly polygonal on the graph. These these discretization errors accumulate over 500 steps. This is what I get from plt.plot(X, U[-1]) with your code:
And this is what I get after using n = 100 (halving both time and space stepsize), running the solution for t in range(1000) to compensate for smaller time step, and again plotting plt.plot(X, U[-1]):
The symmetric-difference approximation for du/dx has error of order dx**3 proportional to the third derivative. The manner in which these accumulate is complicated because the solution is moving around, but in any case smaller dx improves the matters if dt scales with it.
| |
A couple of miles across the Nidd valley is one of our newer pieces of land. Our fields on Dacre Lane total just over 5 acres. Here we will be planting trees with clearings and a pond, all to support biodiversity. We already have a number of projects underway here.
This will be the location for a woodland to be sponsored and planted by Jamyang Buddhist Centre Leeds during winter 2020/21. If you would like to contribute to this woodland, you can do so here.
Also on this site, we will be planting trees for Every One of Us, an action group to support people to make changes needed to address climate change.
We have a number of other exciting corporate sponsorship projects, and dedicated woodlands in the pipeline for this location. | https://www.makeitwild.co.uk/dacre-woodlands |
Stein Mart to close stores in bankruptcy amid COVID-19 pandemic
Wednesday
Off-price retailer Stein Mart is the latest in a long list of businesses to file for bankruptcy protection amid the coronavirus pandemic.
The Jacksonville, Florida-based retailer said Wednesday it has "launched a store closing and liquidation process," according to a news release announcing the Chapter 11 filing.
The company operates 281 stores in 30 states and all stores will continue to operate during the Chapter 11 process. It has 9,000 employees. The chain expects to close most, if not all, of its stores.
Its Northeast Ohio operations include locations at The Venue at Belden in Plain Township and The Marketplace at Four Corners in Bainbridge Township as well as shops in Beachwood and Westlake.
"Our going-out-of-business sale is expected to begin in our stores August 14 or 15," the company told USA TODAY in a prepared statement. "We anticipate all stores will close by the fourth quarter of 2020, with closing dates varying by store."
The company is evaluating alternatives, including the potential sale of its eCommerce business and related intellectual property.
"The combined effects of a challenging retail environment coupled with the impact of the Coronavirus (COVID-19) pandemic have caused significant financial distress on our business," CEO Hunt Hawkins said in the release. "The Company has determined that the best strategy to maximize value will be a liquidation of its assets pursuant to an organized going out of business sale."
Department stores and apparel retailers have been grappling with declining foot traffic for years but the impact of the pandemic has led many retailers to accelerate store closings and bankruptcy filings.
As many as 25,000 stores could shutter this year as businesses continue to feel the impacts of the pandemic, according to a recent report from Coresight Research.
Stein Mart’s bankruptcy is one of many steps the company has taken to remain viable.
The publicly traded company’s board agreed in January to be taken over by a private company, but that deal with Kingswood Capital Management was put on ice when the pandemic threw the business world into turmoil.
The company said in June it had landed $10 million in aid through the federal Paycheck Protection Program but the business acknowledged this week that it had laid off a number of employees at its headquarters.
The company, which was founded in Mississippi in 1908, became a regional retail power in the 1970s and had grown to more than 100 stores in the 1990s, but has struggled like many retailers as the shopping environment changed.
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What is Technology?
Technology refers to the broad array of academic disciplines that address computer programming, design, engineering, telecommunications and more. Technologically-minded people who wish to explore a challenging career in an ever-changing field should consider earning a degree in computers or technology.
Who Should Study Computers and Technology?
If you’re considering studying technology, you may ideally answer “yes” to the following questions:
In addition, you may ideally answer “no” to the following questions:
Sample Technology Classes
Computers and technology classes will differ depending upon the specific program you pursue, and whether you are studying at the undergraduate or graduate level. Regardless, here is a sample of the types of courses you may encounter:
In addition to classes, a final project or thesis may often be required for both the bachelor’s and master’s degree. Be sure to check with the school of your choice for details regarding graduation requirements.
Types of Technology Careers
There are many career paths that may be available for graduates holding computer and technology degrees. The list below includes some of the more common jobs and a description of each one.
Cooperative program available through the University of Alaska Fairbanks (UAF) for computer science professionals working in the Anchorage area.
Attacks on computer systems cost corporations millions of dollars per day and threaten our national security.
California State University, Fresno offers a 30-unit Master of Science degree having strong theoretical and practical orientations.
The Master's Degree program in Computer Science provides the opportunity for the graduate students to obtain competitive skills and knowledge to succeed as computer scientists in the constantly develo
The programme has many technical aspects such as programming and testing, but also involves a variety of elements which are more human interaction-orientated, such as team management and interface des
The MS program in Computer Science offers students the opportunity to prepare for careers in several areas of emphasis including software engineering, computer architecture, programming languages, the
Our programs, at both the undergraduate and graduate levels, are also offered off-campus (by distance learning) with a short residency requirement.
The Management Information Systems program at Kennedy-Western focuses on the development, maintenance and management of information systems.The goal of the graduate program is to ensure the student is
Become a strategic leader in the health informatics industry with a graduate certificate in health informatics from Regis College.
The University at Buffalo, State University of New York (SUNY) is pleased to offer The Professional Science Management advanced (graduate) certificate to graduate-level students in Chemistry, Geograph
Master of Science in Computer and Information Sciences Students desiring admission to the master of science program in computer and information sciences must present GRE scores of 1000 or higher and a
Sullivan University's Doctor of Philosophy (Ph.D.) in Management with a concentration in Information Technology is modeled after the top programs in the U.S.
This unique program is a two-year evening professional graduate degree for those wishing to enhance their marketability in information systems.
CapitolÆs online Internet Engineering program is a technically oriented program of study that favors students with experience in network administration, engineering or management.
The Center for Advanced Computer Studies (CACS) is one of the leading research-oriented departments of computer science and engineering in the nation. | https://www.universitiesabroad.com/technology?page=1 |
Posted on June 26, 2015 by Lisa Johnson, Ph.D.
There are many models for instructional design (ID). It will be up to you as a motivated learner of the art and science of instructional design to seek out information about models. There is a tremendous amount of information available online to consider. This post presents places to begin exploring and poses a question for you to consider about the ADDIE Model and whether components are the essence of all ID models.
One option to use for learning about ID models is a Google Images search for “Instructional Design Models” – from there, you can click on any model’s image and select its “view page” option to see the webpage where the image appears and, in most instances, learn more about the model or just search the name of the model to learn more from a wider variety of websites. You could also begin by exploring some of the more popular models in instructional design detailed on this Instructional Design Models page from Cullatta (2013) or this Instructional Design Models page from Ryder (2014).
Regardless of their nuances, all design models involve five essential tasks for the designer, which are reflected in one of the oldest instructional design models, the ADDIE Model (i.e., Analysis, Design, Development, Implementation, and Evaluation).
The image with this post of the ADDIE Model is from the CSUChuco.Edu website; it illustrates how the model is an iterative model wherein each aspect of the model occurs interdependently with the others.
Although each aspect occurs in a linear process overall, the aspects of the ADDIE Model simultaneously occur in a non-linear process (i.e., analysis, evaluation, and design naturally occur in some form during development and implementation).
This is one reason I like to call the ADDIE model the “Chi” of all design models.
Would you agree with that assertion? Why/Why not? Please comment on this post with your response!
This entry was posted in Educational, Scholarship and tagged Instructional Design, Instructional Design Models by Lisa Johnson, Ph.D.. Bookmark the permalink. | https://reflectivelearning.net/2015/06/idmodelresources-anoverview/ |
5 Tips to gain back time every dayMay 10, 2019
I recently started taking a closer look at the time we spend looking for things. The studies I looked up which evaluate time spent looking for misplaced items vary between 10 and 55 minutes a day. This means that even if we are extremely conservative, 10 minutes per day times an average of 60 adult years adds up to 3 650 hours spent searching for things we own but can’t find. That’s half a year in an average lifetime. Looking for things. Amazing in a not so positive way.
I’d like to offer five strategies to gain back some of that time, based on the things we’re so often looking for. I’ve narrowed my attention to keys, cell phones, and paperwork.
Keys
Let’s start with a low-hanging fruit: this first tip is easy and can be done in 5 minutes flat. How many of us misplace our keys regularly?
Installing hooks by the door you use to come into the house is essential. I’m a big fan of 3M Command hooks which don’t require holes and don’t damage the wall if you choose to remove them, but simple nails will also work.
Of course the hooks aren’t going to work like a magnet, and thus you need to ensure you follow through in the habit of hanging your keys on the hook. One hook per key set is ideal. Just like any habits, it takes anywhere between 21 and 30 days to really set in, so be patient with yourself. It may even help to put visual reminders like a post-it note written KEYS on the surfaces you tend to drop them normally to subtly remind yourself of their new home.
Cell phones
I’m often asked for tips on not losing cell phones in the house, especially for us ladies who don’t always have pockets on our business attire. I recommend you dedicate one home for the cell phone, and drop it off once you hang up your coat when you come home. This will be both its home and the charging station. If like me, you have a hard time leaving work aside and you are making a conscious effort to be more present, I find it best to keep it out of view during the evening - i.e. out of the kitchen and dining room. The entryway is a great place if you have a power outlet adjacent. And so in one swift move you can hang your keys on the hook, drop the phone at its charging station and center your attention to the present moment with your family.
While I have the luxury of doing this now that I am an entrepreneur, the story was different while I was managing an essential service in my previous life. If you’re finding yourself in high demand even after regular work hours, informing your team what hours you are unavailable, and at what time you’ll be checking texts and phone messages is liberating and beneficial. When we set our boundaries, surprisingly team members and superiors respect it and are even positively influenced to do the same for themselves. If need be, share your home phone number with a trusted colleague who will know where to reach you in case that emergency really happens. But let’s be honest, 99% of the time there was no reason to interrupt quality time with your family.
Paperwork
It’s difficult (read impossible) to summarize paperwork organizing solutions in a few paragraphs, however remember that like anything else, paperwork categories need ONE home and everyone who requires access to that paperwork needs to know what that home is. I like to break it down into four categories of paperwork: daily reference, weekly reference, long-term reference and dormant paperwork stuck in boxes, closets and storage rooms.
We’ll focus on the first two categories as they make us waste the most time on a regular basis. These are made up of the shopping list and meal plan we wrote up over the weekend and can’t find anymore now that we're leaving for the grocery store. The address to the birthday party on the invitation that’s lying around somewhere around the house since you RSVP’d and which you know you didn’t recycle - and the party is about to begin without your (very disappointed) child. We all have our paperwork demons! Since this category is a monster, it consequently comes with three tips to help you attain paperwork sanity.
For the immediate action required and daily reference I’m a devoted advocate of command centers where you'll pin weekly meal plans, to do lists, and any other paper you need access to every day or which require immediate action. It can be put together on a wall or inside a pantry door. It combines well with a physical or virtual family calendar so that everyone knows what is on the program. The added bonus to a virtual family calendar app is that it is available anywhere in real time and often comes with list-building capabilities. In my case that’s just magic. I can’t lose a virtual list. Can you hear the angels singing?
For the weekly reference, the family binder is the key to any happy family! This is where you’ll organize ‘that pile' on your countertop which includes emergency information for the sitter, the school calendar and information about the next ped day, the flyer you kept to schedule the spring window washing services, your children’s friends phone numbers on random pieces of paper, the city’s activities guide of the season, the birthday party invitations, take-out menus and the list (and pile) goes on and on… If you dedicate one binder divided into clear categories, you, your spouse and your kids will know exactly where to find the reference items. The bonus is saved time in addition to shared responsibility of any given task. And also fewer conflicts because everyone knows where to find and put away each item.
At the end of the day, these productivity hacks enable you to gain back precious time. But I often like to remind myself to be mindful of that freed up time, and reinvest it in quality time with the family. Let’s make sure we’re productive to do more of the things that matter: Ten minutes equates to one more story at bed time, a nice chat over a glass of wine with your spouse to debrief on the day once the kids are in bed or if you tally it up it becomes an hour long conversation with a dear friend of sibling. And that is the best reason to get organized. So which of these tips will you be putting into action? Happy organizing!
Mylène Houle Morency is a Professional Organizer, Speaker and owner of Zen :: Organisation familiale, which specializes in organizing families with children ranging from newborn to the teenage years. She has the firm conviction that organized homes help parents become the parents they want to be, by freeing up time and diminishing stress. She has the privilege to lovingly test all her theories and organization inspirations on her husband and three children! | https://www.mymlist.com/5-tips-to-gain-back-time-every-day |
[ecis2016.org] Here is a guide on using the FSI calculator in Chennai to compute the developable built-up area on a plot and the guidelines for availing of premium FSI
The FSI (floor space index), also known as the FAR (floor area ratio), is a frequently used technical term in real estate, to determine the maximum amount of floor space erected on a given piece of land. Put another way, it is the ratio of a building’s total finished floor space to its total land area. For both, developers and property purchasers, this is a significant indicator.
You are reading: FSI calculator: How to calculate FSI or FAR in Chennai
FSI will assist a developer in determining how much they may construct on any given plot of land. Home buyers should also consider that some areas near railway stations or commercial centres have a higher FSI than others. Before we dive into the FSI calculator, let us understand what FSI in Chennai is.
Everything about FSI in Chennai
The Tamil Nadu government released the new Development and Building Rules in 2019. These principles distinguish between two types of structures: high-rise and low-rise. Buildings with a height of lesser than 18.30 metres are classified as non-high-rise. For these non-high-rise buildings, the maximum Floor Space Index is 2.
[ecis2016.org] What are building bye laws
The following considerations are not taken into account in the FSI calculator under the new norms:
- Staircase and elevator rooms, corridors, architectural components, raised tanks (if the height below the tank from the floor is less than 1.5 metres), and WC on the terrace above the highest story (with a maximum floor size of 10 sq metres).
- In the stilt parking level or upper parking floors, there are staircases and lift rooms, as well as walkways to them.
- Staircases and lift rooms on the basement level or parking floors, as well as corridors to and from them.
- Parking is available either in the basement or on the higher floors.
- When parking is planned on an upper level or floors above a stilt parking floor, the section of the stilt parking floor that is open on all sides is utilised for parking, provided that the area is not more than 3 sq metres.
- There are watchman cabins or servant quarters on the ground level or the stilt parking floor.
- A service floor with a maximum height of 1.5 metres is required.
- A gym with a floor space of 150 square metres.
- Caretaker cabin or room on the ground level or on stilts.
- Plant area for air conditioning and lumber storage, either in the basement or on the main level.
- The generator room can be found in the basement, on the stilts, or the main level.
- All floors have electrical/switchgear rooms or AHUs (air handling units).
- Pump and meter rooms are located on either the slit parking floor or the ground floor.
- Fire escape stairs and cantilever fire escape passageways have their area.
- Garbage shaft, service ducts, porch, and portico occupy this space.
- With legal clearance from the Tamil Nadu Pollution Control Board, an area within the building devoted to storing machinery for a water treatment plant or a sewage treatment plant has been designed (TNPCB).
- Balcony or service utility equals 5% of the unit or flat space in residential buildings and 5% of room area in other structures such as hotels and lodges.
- Letterboxes in residential or commercial multi-story buildings or other group projects must be comparable to a single room.
FSI calculator: How to calculate floor space index
Read also : Give flats or refund, then you can go free: SC to Unitech chief
In any FSI calculator, the FSI or floor area ratio (FAR) is obtained by dividing the covered surface (plinth) into all levels, excluding those exempted, by the plot area, which includes a portion of the site utilised as a whole passage.
Total covered space on all levels / Total plot area = FSI or FAR.
For FSI of 2, the total plinth area created is twice the plot size. For example, if the plot size is 2,400 sq ft, the entire plinth area developed in that plot can be up to 4,800 sq ft.
FSI calculations are computed by dividing a building’s total covered built-up area into all levels by the size of the site it occupies. However, the FSI calculator procedure is distinctive in Chennai as it is dependent on the width of the road and plot size.
[ecis2016.org] Real estate basics part 2 – OSR land meaning, Loading and Construction Stages
Guidelines for the premium FSI
Except for the Red Hills catchment region which is allocated for construction, and the area of water bodies managed for drinking water purposes by the Chennai Metropolitan Water Supply and Sewerage Board (CMWSSB), the premium FSI will be allowed throughout the Chennai Metropolitan Area. If the following road width standards are satisfied, the premium FSI will be approved:
|Width of the road||Premium FSI (% of normally allowable FSI)|
|18 metres and above||40%|
|12 metres to below 18 metres||30%|
|9 metres to below 12 metres||20%|
Read also : Delhi pollution: Agencies to face criminal prosecution, for failure to follow norms
However, in suitable land expansion, the developer will obtain an extra advantage in the form of Premium FSI. If the usually permissible FSI is 1.50, the proportional land required is 2/3 of that or 0.66 square metres. Premium FSI will develop every 1 sq metre of additional floor space. Similarly, if the FSI is 2.0, the proportionate land required is 1/2 or 0.50 sq metres and if the FSI is 2.5, the corresponding land necessary is 2/5 or 0.40 sq metres.
Premium FSI costs
The premium FSI charge is equal to the price of the proportional land specified above, as established by the Registration Department’s guideline value.
Furthermore, the applicant must pay to the Chennai Metropolitan Development Authority (CDMA), the premium FSI charge in one lump sum before gaining planning approval.
The applicant will have full authority over the property to develop the land. Keeping an undivided piece of land, on the other hand, will not qualify you for a premium FSI. Before gaining planning permission, the applicant must indicate their readiness to use the bonus FSI when filing their planning permission application and provide assurance that they would pay the premium FSI charge at the above-mentioned rates.
Also read about Stamp duty and property registration fees in Tamil Nadu
Source: https://ecis2016.org/. | https://ecis2016.org/housing/lifestyle/fsi-calculator-how-to-calculate-fsi-or-far-in-chennai |
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\[subsection\] \[proposition\][Lemma]{} \[proposition\][Definition]{} \[proposition\][Theorem]{} \[proposition\][Corollary]{} \[proposition\][Pretheorem]{} \[proposition\][Hypothesis]{} \[proposition\][Example]{} \[proposition\][Remark]{}
[**Unstable motivic homotopy categories in Nisnevich and cdh-topologies.**]{}\
[**Vladimir Voevodsky**]{}[^1]$^,$[^2]\
[August 2000]{}
Introduction
------------
One can do the motivic homotopy theory in the context of different motivic homotopy categories. One can vary the topology on the category of schemes used to define the homotopy category or one can vary the category of schemes itself considering only schemes satisfying certain conditions. The category obtained by taking smooth schemes and the Nisnevich topology seems to play a distinguished role in the theory because of the Gluing Theorem (see [@MoVo]) and some other, less significant, nice properties. On the other hand, in the parts of the motivic homotopy theory dealing with the motivic cohomology it is often desirable to be able to work with all schemes instead of just the smooth ones. For example, the motivic Eilenberg-MacLane spaces are naturally representable (in characteristic zero) by singular schemes built out of symmetric products of projective spaces but we do not know of any explicit way to represent these spaces by simplicial smooth schemes.
The goal of this paper is to show that, under the resolution of singularities assumption, the pointed motivic homotopy category of smooth schemes over a field with respect to the Nisnevich topology is almost equivalent to the pointed motivic homotopy category of all schemes over the same field with respect to the cdh-topology. More precisely, we show that the inverse image functor $${\bf L}\pi^*:H_{\bullet}((Sm/k)_{Nis},{{\bf A}^1}){\rightarrow}H_{\bullet}((Sch/k)_{cdh},{{\bf A}^1})$$ from the former category to the later one is a localization and if $f$ is a morphism such that ${\bf L}\pi^*(f)$ is an isomorphism then the first simplicial suspension of $f$ is an isomorphism. This should imply in particular that the corresponding s-stable and T-stable motivic homotopy categories are equivalent.
The present paper is a continuation of the series started with [@HH0] and [@HH1] and it uses the formalism developed there. In the first section we define the standard cd-structures on the category of Noetherian schemes and prove that they are complete, regular and bounded. In the next section we prove some simple results about the homotopy categories of sites with interval with completely decomposable topologies and apply them to get an explicit description of the ${{\bf A}^1}$-weak equivalences in terms of $\Delta$-closed classes. Our results also imply that the motivic homotopy categories defined with respect to the standard topologies are homotopy categories of almost finitely generated closed model structures (see [@HH0]). In the last section we apply these results to prove the comparison theorem.
This paper was written while I was a member of the Institute for Advanced Study in Princeton and, part of the time, an employee of the Clay Mathematics Institute. I am very grateful to both institutions for their support. I would also like to thank Charles Weibel who pointed out a number of places in the previous version of the paper which required corrections.
Everywhere below a scheme means a Noetherian scheme.
The standard cd-structures on categories of schemes {#standard}
---------------------------------------------------
Let us consider the following two cd-structures on the category of Noetherian schemes.
Upper cd-structure
: or Nisnevich cd-structure where a square of the form $${\label{eq1old}}{\label{eq1}}
\begin{CD}
B@>>>Y\\
@VVV @VVpV\\
A @>e>> X
\end{CD}$$ is distinguished if it is a pull-back square such that $p$ is etale, $e$ is an open embedding and $p^{-1}(X-e(A)){\rightarrow}X-e(A)$ is an isomorphism. Here $X-e(A)$ is considered with the reduced scheme structure.
Lower cd-structure
: or proper cdh-structure where a square of the form (\[eq1old\]) is distinguished if it is a pull-back square such that $p$ is proper, $e$ is a closed embedding and $p^{-1}(X-e(A)){\rightarrow}X-e(A)$ is an isomorphism.
These cd-structures own their names to the fact that the behavior of the functors of inverse image $f^*$ and $f^!$, which have upper indexes, with respect to etale morphisms is very similar to the behavior of the the functors of direct image $f_*$ and $f_!$, which have lower indexes, with respect to proper morphisms.
The topology associated with the upper cd-structure is called the upper cd-topology. We will show below (see Proposition \[isnis\]) that it coincides with the Nisnevich topology. In particular, an etale morphism $f:X{\rightarrow}Y$ is an upper covering if and only if for any $y$ in $Y$ the fiber $p^{-1}(y)$ contains a $k_y$-rational point. The topology associated with the lower cd-structure is called the lower cd-topology or proper cdh-topology. By Proposition \[lowerchar\] a proper morphism of schemes $p:X{\rightarrow}Y$ is a lower cd-covering if and only if for any point $y$ in $Y$ the fiber $p^{-1}(y)$ contains a $k_y$-rational point.
The intersection of the upper and lower cd-structures is equivalent to the [*additive cd-structure*]{} where a square is distinguished if it is of the form $$\label{addsq}
\begin{CD}
\emptyset@>>>Y\\
@VVV @VVV\\
X @>>> X\coprod Y
\end{CD}$$ A presheaf $F$ is a sheaf in the topology associated with the additive cd-structure if and only if $$F(X\coprod Y)=F(X)\times F(Y)$$ and $F(\emptyset)=pt$.
The union of the upper and lower cd-structures is the [*combined cd-structure*]{}. A square is distinguished in it if it is an upper distinguished or a lower distinguished square. Proposition \[isnis\] and the definition given in [@SusVoe2 §4.1] imply that the associated topology is the cdh-topology.
If we consider only squares where both $e$ and $p$ are monomorphisms the upper and lower cd-structures become:
Plain upper cd-structure
: or Zariski cd-structure where a square of the form (\[eq1old\]) is distinguished if both $p$ and $e$ are open embeddings and $X=p(Y)\cup e(A)$. The associated topology is the Zariski topology.
Plain lower cd-structure
: where a square of the form (\[eq1old\]) is distinguished if both $p$ and $e$ are closed embeddings and $X=p(Y)\cup e(A)$. The associated topology is the closed analog of the Zariski topology.
Any combination of the additive, upper, lower, plain upper and plain lower cd-structures is called a standard cd-structure. There are nine standard cd-structures: the five generating ones, the combined cd-structure and the combinations of the plain upper with plain lower, plain upper with lower and plain lower with upper cd-structures. They form the following lattice where arrows indicate inclusions $$\begin{CD}
add @>>> p.up @>>> up\\
@VVV @VVV @VVV\\
p.low @>>> p @>>> p.low + up\\
@VVV @VVV @VVV\\
low @>>> low+ p.up @>>> cdh
\end{CD}$$ The topology associated with the combination of the lower and the plain upper cd-structures $low+p.up$ is considered in [@GL].
[\[stcompl\]]{} The standard cd-structures are complete on the category of schemes or schemes of finite type over a base. In addition the upper and plain upper cd-structures are complete on the category of smooth schemes over a base and the lower and plain lower cd-structures are complete on the category of proper schemes over a base.
It follows immediately from [@HH1 Lemma 2.5].
Let us show now that the standard cd-structures considered on the category of schemes of finite dimension are bounded. A sequence of points $x_0,\dots,x_d$ of a topological space $X$ is called an increasing sequence (of length $d$) if $x_i\ne x_{i+1}$ and $x_i\in cl(\{x_{i+1}\})$ where $cl(\{x_{i+1}\})$ is the closure of the point $x_{i+1}$ in $X$. For a scheme $X$ define $D_d(X)$ as the class of open embeddings $j:U{\rightarrow}X$ such that for any $z\in X-U$ there exists an increasing sequence $z=x_0,x_1,\dots,x_d$ of length $d$. The density structure defined by the classes $D_d$ is called the [*standard density structure*]{} on the category of schemes. It is locally of finite dimension on the category of schemes of finite dimension and the dimension of a scheme with respect to it is the dimension of the corresponding topological space.
[\[conv3\]]{} If $U,V\in D_{d}(X)$ then $U\cap V\in D_d(X)$.
[\[conv2\]]{} Let $U\in D_d(X)$ and $V$ be an open subscheme of $X$. Then $U\cap
V\in D_d(V)$.
Let $x$ be a point of $V$ outside of $U\cap V$. Considered as a point of $X$ it has an increasing sequence $x=x_0,\dots,x_d$ with $x_i\in
X$. But since $x_0\in V$ we have $x_i\in V$ because $x_0\in cl(x_i)$ and $V$ is open.
[\[conv00\]]{} Let $x_0,x_1,x_2$ be an increasing sequence on a scheme $X$ and $Z$ be a closed subset of $X$ such that $x_2$ lies outside $Z$. Then there exists an increasing sequence $x_0,x_1',x_2$ such that $x_1'$ lies outside $Z$.
Replacing $X$ by the local scheme of $x_0$ in the closure of $x_2$ we may assume that any point of $X$ contains $x_0$ in its closure and in turn lies in the closure of $x_2$. It remains to show that the complement to $Z$ contains at least one point which is not equal to $x_2$. If it were false we would have $x_2=X-Z$ i.e. $x_2$ would be a locally closed point. This contradicts our assumption since by [@EGA4 5.1.10(ii)] a locally closed point on a locally Noetherian scheme has dimension $\le 1$.
[\[conv0\]]{} Let $X$ be a scheme, $U$ a dense open subset of $X$ and $x_0,\dots,x_d$ any increasing sequence in $X$. Then there exists an increasing sequence $x_0,x_1',\dots,x_d'$ such that $x_i'\in U$ for all $i\ge 1$.
We may assume that $d>0$. If $x_d$ is contained in $U$ set $x'_d=x_d$. Otherwise let $x'_d$ be a point of $U$ such that $x_{d-1}\in cl(x_d)$ which exists since $U$ is dense. Since $x_d$ is not in $U$, $x_{d-1}$ is not in $U$ and thus $x'_d\ne x_{d-1}$ and $x_0,x_1,\dots, x'_d$ is again an increasing sequence. Assume by induction that we constructed $x_{i+1}',\dots,x_d'\in U$ such that $x_0,\dots, x_i,x'_{i+1},\dots,x_d'$ is an increasing sequence. By Lemma \[conv00\] for any increasing sequence $y_0,y_1,y_2$ and a closed subset $Z$ which does not contain $y_2$ there exists an increasing sequence $y_0,y_1',y_2$ such that $Z$ does not contain $y_1$. Applying this result to the sequence $x_{i-1},x_i,x'_{i+1}$ and $Z=X-U$ we construct $x_i'$.
[\[convv\]]{} Let $X$ be a scheme and $Y$ a constructible subset in $X$. Then any point $y'$ of the closure $cl(Y)$ of $Y$ in $X$ belongs to the closure of a point $y$ of $Y$.
Since $Y$ is constructible it is of the form $Y=\cup_{i=1}^n Y_i$ where each $Y_i$ is open in a closed subset of $X$ (see e.g. [@EGA1 Prop. 2.3.3]). It is clearly sufficient to prove our statement for each $Y_i$. As a topological space $Y_i$ corresponds to a Noetherian scheme. Thus there exists finitely many points $y_i'$ in $Y$ such that any point of $Y$ is in the closure of one of the $y_i$’s. If a point $y'$ in $cl(Y)$ has an open neighborhood $U$ which does not contain any of the points $y_i$ then $U$ does not contain any point of $Y$ which contradicts the assumption that $y\in cl(Y)$. Thus $y$ belongs to the closure of $\{y_i\}$ which coincides with the union of closures of points $y_i$ since there is finitely many of them.
[\[conv\]]{} Let $f:X{\rightarrow}Y$ be a morphism of finite type of Noetherian schemes and assume that there exists an open subset $U$ in $Y$ such that $f^{-1}(U)$ is dense in $X$ and $f^{-1}(U){\rightarrow}U$ has fibers of dimension zero. Then for any $d\ge 0$ and $V\in D_d(X)$ there exists $W\in D_{d}(Y)$ such that $f^{-1}(W)\subset V$.
We may clearly assume that $d>0$. Let $Z=X-V$. We have to show that $Y-cl(f(Z))\in D_{d}(Y)$ i.e. that for any $y$ in $cl(f(Z))$ there exists an increasing sequence $y=y_0,\dots,y_d$ in $Y$. Since $f$ is of finite type $f(Z)$ is constructible and in particular any point of $cl(f(Z))$ is in the closure of a point in $f(Z)$ by Lemma \[convv\]. Thus we may assume that $y$ belongs to $f(Z)$ i.e. $y=f(x)$ where $x$ is in $Z$. By Lemma \[conv0\] we can find an increasing sequence $x=x_0,x_1,\dots, x_d$ for $x$ such that for $i>0$ we have $x_i\in f^{-1}(U)$. Then $y=f(x_0),\dots,f(x_d)$ is an increasing sequence i.e. $f(x_i)\ne f(x_{i+1})$. Indeed for $i>0$ it follows from the fact that the fibers of $f$ over $U$ are of dimension zero. For $i=0$ we have two cases. If $f(x_0)\in U$ then the same argument as for $i>0$ applies. If $f(x_0)$ is not in $U$ then $f(x_0)\ne f(x_1)$ since $f(x_1)\in U$.
[\[upred\]]{} The upper cd-structure and the plain upper cd-structures on the category of Noetherian schemes of finite dimension are bounded with respect to the standard density structure.
We will only consider the upper cd-structure. The plain case is similar. Let us show that any upper distinguished square is reducing with respect to the standard density structure (see [@HH1 Definition 2.19]). Let our square be of the form $$\begin{CD}
W @>j_V>> V\\
@VVV @VVpV\\
U @>j>> X
\end{CD}$$ and let $W_0\in D_{d-1}(W)$, $U_0\in D_{d}(U)$, $V_0\in
D_d(V)$. Applying Lemma \[conv\] to the morphism $j\coprod p$ we can find $X_0\in D_d(X)$ such that $j(U_0)\cup p(V_0)\subset
X_0$. Replacing $X$ with $X_0$ and applying Lemma \[conv2\] we may assume that $U_0=U$ and $V_0=V$. Let $Z=W-W_0$, $C=X-U$ and set $X'=X-(C\cap cl(pj_V(Z)))$. Let us show that the square $$\begin{CD}
W_0@>>>j_V(W_0)\\
@VVV @VVV\\
U@>>>X'
\end{CD}$$ is upper distinguished. It is clearly a pull back square, the right vertical arrow is etale and the lower horizontal one is an open embedding. It is also obvious that $p^{-1}(X'-U)\cap j_V(W_0)=(X'-U)$. To finish the proof it remains to show that $X'\in D_d(X)$. Let $x$ be a point of $X$ outside of $X'$ i.e. a point of $C\cap
cl(pj_V(Z))$. Since $pj_V(Z)\cap C=\emptyset$ there exists $x'=pj_V(y)\in
pj_V(Z)$ such that $x\in cl(x')$ and $x'\ne x$. Let $y=y_0,\dots,y_{d-1}$ be an increasing sequence for $y$ in $W$ which exists since $W_0\in D_{d-1}(W)$. The morphism $q=pj_V$ has fibers of dimension zero and therefore $q(y_0),\dots,q(y_{d-1})$ is an increasing sequence for $x'$. Thus we get an increasing sequence $x,q(y_0),\dots,q(y_{d-1})$ for $x$ of length $d$.
[\[lowerred\]]{} The lower cd-structure and the plain lower cd-structures on the category of Noetherian schemes of finite dimension are bounded with respect to the standard density structure.
We will only consider the case of the lower cd-structure. The plain case is similar. Consider a lower distinguished square $${\label{sqag}}
Q=\left(
\begin{CD}
B @>i_Y>> Y\\
@VVV @VVpV\\
A @>i>> X
\end{CD}
\right)$$ If we replace $Y$ by the scheme-theoretic closure of the open subscheme $p^{-1}(X-A)$ we get another lower distinguished square which is a refiniment of the original one. This square satisfies the condition of Lemma \[l8.4.1\] and therefore it is reducing.
[\[l8.4.1\]]{} A lower distinguished square of the form (\[sqag\]) such that the subset $p^{-1}(X-A)$ is dense in $Y$ is reducing with respect to the lower cd-structure.
Let $Y_0\in D_{d}(Y)$, $A_0\in D_d(A)$, $B_0\in
D_{d-1}(B)$. Applying Lemma \[conv\] to $p$ and $U=X-A$ we conclude that there exists $X_0\in D_{d}(X)$ such that $p(Y_0)\subset
X_0$. Applying the same lemma to $i$ we find an open subset $X_1\in
D_d(X)$ such that $i(A_0)\subset X_1$. Then by Lemma \[conv3\] $X_1\cap X_0\in D_d(X)$ and replacing $X$ by $X_1\cap X_0$ and using Lemma \[conv2\] we may assume that $A_0=A$ and $Y_0=Y$. Let $X'=X-pi_Y(B-B_0)$. To finish the proof it is enough to check that $X'\in D_d(X)$ and define $Q'$ as the pull-back of $Q$ to $X'$. According to Lemma \[conv\] applied again to $p$ and $U=X-A$ it is enough to check that $Y-i_Y(B-B_0)\in D_{d}(Y)$. Since $B_0\in
D_{d-1}(B)$ and $i_Y$ is a closed embedding it is enough to check that $Y-i_B(B)$ is dense in $Y$. This follows from our assumption since $Y-i_B(B)=p^{-1}(X-A)$.
Since all generating cd-structures on the category of Noetherian schemes are bounded by the [*same*]{} density structure any their combination is also bounded by the same density structure. We get the following result.
[\[cdhis\]]{} The standard cd-structures on the category of Noetherian schemes of finite dimension are bounded.
Finally let us show that all the standard cd-structures are regular. It is clearly sufficient to consider the “generating” cd-structures. Then any combination of them will also be regular.
[\[uploreg\]]{} The additive, upper, plain upper, lower and plain lower cd-structures are regular.
The additive case is obvious. Let us show that the upper, palin upper, lower and plain lower cd-structures satisfy the conditions of [@HH1 Lemma 2.11]. The first two conditions are obvious. Consider the third condition in the upper case. The square $${\label{eq2}}
d(Q)=\left(
\begin{CD}
B@>>>Y\\
@VVV @VVV\\
B\times_A B@>>>Y\times_X Y
\end{CD}
\right)$$ is a pull-back square. Since $p$ is etale, and in particular unramified, the diagonal $Y{\rightarrow}Y\times_X Y$ is an open embedding. The morphism $B\times_A B{\rightarrow}Y\times_X Y$ is an open embedding because $e$ is an open embedding. The condition that $p^{-1}(X-e(A)){\rightarrow}X-e(A)$ is a universal homeomorphism implies that for a pair of geometric points $y_1,y_2$ of $Y$ such that $p(y_1)=p(y_2)\in X-e(A)$ one has $y_1=y_2$. Therefore, $$Y\times_X Y= (B\times_A B)\cup Y$$ i.e. (\[eq2\]) is a (plain) upper distinguished square.
Consider the third condition in the lower case. The square (\[eq2\]) is a pull-back square. Since $p$ is proper, and in particular separated, the diagonal $Y{\rightarrow}Y\times_X Y$ is a closed embedding. The morphism $B\times_A B{\rightarrow}Y\times_X Y$ is a closed embedding because $e$ is a closed embedding. The condition that $p^{-1}(X-e(A)){\rightarrow}X-e(A)$ is a universal homeomorphism implies that for a pair of geometric points $y_1,y_2$ of $Y$ such that $p(y_1)=p(y_2)\in X-e(A)$ one has $y_1=y_2$. Therefore, $$Y\times_X Y= (B\times_A B)\cup Y$$ i.e. (\[eq2\]) is a (plain) lower distinguished square.
[\[uppersplit\]]{} Let $f:\tilde{X}{\rightarrow}X$ be a morphism of schemes. A splitting sequence for $f$ is a sequence of closed embeddings $$\emptyset=Z_{n+1}{\rightarrow}Z_n{\rightarrow}\dots{\rightarrow}Z_1{\rightarrow}Z_0=X$$ such that for any $i=0,\dots,n$ the projection $$(Z_i-Z_{i+1})\times_X \tilde{X}{\rightarrow}(Z_i-Z_{i+1})$$ has a section.
[\[l8.5.1\]]{} A morphism of finite type of Noetherian schemes $f:\tilde{X}{\rightarrow}X$ has a splitting sequence if and only if for any point $x$ of $X$ there exists a point $\tilde{x}$ of $\tilde{X}$ such that $f(\tilde{x})=x$ and the corresponding morphism of the residue fields is an isomorphism.
The “only if” part is obvious. The “if” part follows easily by the Noetherian induction (cf. [@MoVo Lemma 3.1.5]).
[\[isnis\]]{} An etale morphism $f:\tilde{X}{\rightarrow}X$ is a covering in the upper cd-topology if and only if for any point $x$ of $X$ there exists a point $\tilde{x}$ of $\tilde{X}$ such that $f(\tilde{x})=x$ and the corresponding morphism of the residue fields is an isomorphism.
Since the upper cd-structure is complete any upper cd-covering has a refinement which is a simple covering which immediately implies the “only if” part of the proposition. To prove the “if” part we have to show, in view of Lemma \[l8.5.1\], that any etale morphism $f:\tilde{X}{\rightarrow}X$ which has a splitting sequence $Z_n{\rightarrow}\dots{\rightarrow}Z_0=X$ is an upper cd-covering. We will construct an upper distinguished square of the form (\[eq1\]) based on $X$ such that the pull-back of $f$ to $Y$ has a section and the pull-back of $f$ to $A$ has a splitting sequence of length less than $n$. The result then follows by induction on $n$. We take $A=X-Z_n$. To define $Y$ consider the section $s$ of $f_n:\tilde{X}\times_X Z_n{\rightarrow}Z_n$ which exists by definition of a splitting sequence. Since $f$ is etale and in particular unramified the image of $s$ is an open subscheme. Let $W$ be its complement. The morphism $\tilde{X}\times_X Z_n{\rightarrow}\tilde{X}$ is a closed embedding thus the image of $W$ is closed in $\tilde{X}$. We take $Y=\tilde{X}-W$. One verifies immediately that the pull-back square defined by $A{\rightarrow}X$ and $Y{\rightarrow}X$ is upper distinguished. The pull-back of $f$ to $Y$ has a section and the pull-back of $f$ to $A$ has a splitting sequence of length $n-1$. This finishes the proof of the proposition.
Proposition \[isnis\] implies that the topology associated with the upper cd-structure on the category of Noetherian schemes is the Nisnevich topology.
[\[lowerchar\]]{} A proper morphism $f:\tilde{X}{\rightarrow}X$ is a covering in the lower cd-topology if and only if for any point $x$ of $x$ there exists a point $\tilde{x}$ of $\tilde{X}$ such that $f(\tilde{x})=x$ and the corresponding morphism of the residue fields is an isomorphism.
Since the lower cd-structure is complete any lower cd-covering has a refinement which is a simple covering which immediately implies the “only if” part of the proposition. To prove the “if” part we have to show, in view of Lemma \[l8.5.1\], that any proper morphism $f:\tilde{X}{\rightarrow}X$ which has a splitting sequence $Z_n{\rightarrow}\dots{\rightarrow}Z_0=X$ is a lower cd-covering. We will construct a lower distinguished square of the form (\[eq1\]) based on $X$ such that the pull-back of $f$ to $Y$ has a section and the pull-back of $f$ to $A$ has a splitting sequence of length less than $n$. The result then follows by induction on $n$. We take $A=Z_1$. To define $Y$ consider the section $s$ of $f_n:\tilde{X}\times_X (X-Z_1){\rightarrow}(X-Z_1)$ which exists by definition of a splitting sequence. Since $f$ is proper and in particular separated, the image of $s$ is a closed subscheme. Let $W$ be its complement. The morphism $\tilde{X}\times_X (X-Z_1){\rightarrow}\tilde{X}$ is an open embedding thus the image of $W$ is open in $\tilde{X}$. We take $Y=\tilde{X}-W$. One verifies immediately that the pull-back square defined by $A{\rightarrow}X$ and $Y{\rightarrow}X$ is lower distinguished. The pull-back of $f$ to $Y$ has a section and the pull-back of $f$ to $A$ has a splitting sequence of length $n-1$. This finishes the proof of the proposition.
Motivic homotopy categories
---------------------------
Recall that in [@MoVo] we defined for any site $T$ with an interval $I$ a category $H(T,I)$ which we called the homotopy category of $(T,I)$. Applying this definition to a category of schemes with some standard topology and taking $I$ to be the affine line one obtains different motivic homotopy categories. Among these homotopy categories the one denoted in [@MoVo] by $H(S)$ and corresponding to the category of smooth schemes over $S$ with the Nisnevich or upper cd-topology seems to play a distinguished role. In this section we prove a number of results which provide a new description for the motivic homotopy categories in the standard topologies and in particular for the category $H(S)$. We start with some results applicable to all sites with interval with good enough completely decomposable topologies.
Let $C$ be a category with a complete regular bounded cd-structure $P$ (see [@HH1]) and an interval $I$ (see [@MoVo §2.3]). Assume in addition that $C$ has a final object and that for any $X$ in $C$ the product $X\times I$ exists. We can form the homotopy category of $(C,P,I)$ in two ways. First, we may define a new cd-structure $(P,I)$ whose distinguished squares are the distinguished squares of $C$ and squares of the form $$\begin{CD}
\emptyset@>>>\emptyset\\
@VVV @VVV\\
X\times I @>>> X
\end{CD}$$ where $X$ runs through all objects of $C$ and consider the homotopy category $H(C,P,I)$ of this cd-structure i.e. the localization of $\Delta^{op}PreShv(C)$ with respect to $cl_{{\bar{\Delta}}}(W_{(P,I)}\cup
W_{proj})$ where $cl_{{\bar{\Delta}}}(-)$ is the ${\bar{\Delta}}$-closure defined in [@HH0]. On the other hand we may consider the homotopy category ${
H}(C_{t_P},I)$ of the site with interval $(C_{t_P},I)$ as defined in [@MoVo]. We are going to show that if $P$ is complete, regular and bounded these two constructions agree. Since the comparison theorem of the next section is formulated in terms of pointed categories we use pointed context to formulate the results of this section as well. One can easily see that the same arguments can be used to prove the corresponding results in the free context. Recall, that for a functor $\Phi$ we denote by $iso(\Phi)$ the class of morphisms $f$ such that $\Phi(f)$ is an isomorphism.
[\[swi\]]{} Let $P$ be a complete, regular and bounded cd-structure. Then the functor $${\label{isl}}
\Phi:\Delta^{op}PreShv_{\bullet}(C){\rightarrow}{H}_{\bullet}(C_{t_P},I)$$ is a localization and $$iso(\Phi)=cl_{{\bar{\Delta}}}((W_{(P,I)})_+\cup
W_{proj})=cl_{{\bar{\Delta}}}((W_{P})_+\cup (W_I)_+\cup
W_{proj})$$ where $W_P$ is the class of generating weak equivalences of $P$, $W_I$ the class of all projections $X\times I{\rightarrow}X$ for $X\in C$ and $W_{proj}$ is the class of projective weak equivalences of (pointed) simplicial presheaves.
Recall that the category ${H}_{\bullet}(C_{t_P},I)$ is defined as the localization of the category of pointed simplicial sheaves on $C$ in the $t_P$-topology with respect to $I$-weak equivalences (see [@MoVo Def. 2.3.1]). Since the category of pointed simplicial sheaves is a localization of the category of pointed simplicial presheaves the functor $\Phi$ is a localization. It remains to check that a morphism of pointed simplicial presheaves $f$ belongs to $cl_{{\bar{\Delta}}}((W_{P}\cup W_I)_+\cup W_{proj})$ if and only if the associated morphism of sheaves is an I-weak equivalence. The morphisms associated with elements of $(W_I)_+$ are I-weak equivalences by definition and since our cd-structure is regular so are the morphisms associated with elements of $(W_P)_+$. The “only if” part follows now from Lemma \[isdlta\]. Let $N$ be the set of morphisms of the form $(\emptyset{\rightarrow}U)_+$ for $U\in C$ and let $Ex=Ex_{W_P\cup W_I, N}$ be the functor constructed in [@HH0 Proposition 2.2.12] such that for any $X$ the morphism $X{\rightarrow}Ex(X)$ is in $cl_{{\bar{\Delta}}}((W_P\cup W_I)_+)$, the simplicial sets $Ex(X)(U)$ are Kan and for any $f:Y{\rightarrow}Y'$ in $(W_P\cup W_I)_+$ the map $S(Y',Ex(X)){\rightarrow}S(Y, Ex(X))$ defined by $f$ is a weak equivalence. In view of Lemma \[isdlta\] the morphisms associated with the morphisms $X{\rightarrow}Ex(X)$ are $I$-weak equivalences. To finish the proof it is sufficient to show that any morphism $f:Ex(X){\rightarrow}Ex(Y)$ such that the associated morphism of sheaves is an $I$-weak equivalence is a projective weak equivalence. Let $Ex_{JJ}(X)$ be a fibrant replacement of $a(Ex(X))$ in the Jardine-Joyal closed model structure on the category of sheaves in $t_P$. The morphism $Ex(X){\rightarrow}Ex_{JJ}(X)$ is a local weak equivalence with respect to $t_P$ and, since both objects are flasque with respect to $P$, [@HH1 Lemma 3.5] implies that it is a projective weak equivalence. Together with the fact that $Ex(X)(U){\rightarrow}Ex(X)(U\times I)$ is a weak equivalence for any $U$ in $C$ this implies that $Ex_{JJ}(X)$ is $I$-local. If $f:Ex(X){\rightarrow}Ex(Y)$ is a morphism such that $a(f)$ is an $I$-weak equivalence then the corresponding morphism $Ex_{JJ}(X){\rightarrow}Ex_{JJ}(Y)$ is an $I$-weak equivalence and, therefore, a local weak equivalence with respect to $t_P$. We conclude that $f$ is a local weak equivalence and, using again the fact that $Ex(-)$ are flasque and [@HH1 Lemma 3.5], we conclude that $f$ is a projective weak equivalence.
[\[isdlta\]]{} The class of morphisms $f$ such that $a(f)$ is a pointed I-weak equivalence is ${\bar{\Delta}}$-closed.
The associated sheaf functor commutes with coproducts and therefore it is enough to show that the class of (pointed) I-weak equivalences in $\Delta^{op}Shv_{t_P, \bullet}(C)$ is ${\bar{\Delta}}$-closed. The fact that the class of I-weak equivalences is closed under coproducts follows from its definition. It also follows from its definition that this class satisfies the first two conditions of the definition of a $\Delta$-closed class (see [@HH0]). To verify the third condition observe that since homotopy colimits and diagonals are defined on simplicial presheaves by applying the corresponding construction for simplicial sets over each object of the category, [@BKan Ch.XII 4.3] implies that for a bisimplicial sheaf $B$ there is a natural weak equivalence $hocolim B_i{\rightarrow}\Delta B$ where $B_i$ are the rows (or columns) of $B$. The condition follows now from [@MoVo Lemma 2.2.12]. The fact that the class of I-weak equivalences is closed under colimits of sequences of morphisms is proved in [@MoVo Cor. 2.2.13(2)].
[\[c8.3.1\]]{} Under the assumptions of Proposition \[swi\] the functor $$\Phi:\Delta^{op}C^{\coprod}_+{\rightarrow}H(C,P,I)$$ is a localization and $iso(\Phi)=cl_{{\bar{\Delta}}}((W_P\cup W_I)_+)$.
This is a particular case of [@HH0 Corollary 4.3.8].
[\[stricteq\]]{} Let $C$ be any category with an interval and $f:X{\rightarrow}Y$ be a strict $I$-homotopy equivalence in $\Delta^{op}C^{\coprod}_+$. Then $f$ belongs to $cl_{{\bar{\Delta}}}((W_I)_+)$.
By [@MoVo Lemma 2.3.6] applied to the site $C$ with the trivial topology we know that any strict homotopy equivalence is an $I$-weak equivalence. Applying Corollary \[c8.3.1\] to the case of the empty cd-structure on the category obtained from $C$ by the addition of an initial object we conclude that any strict $I$-homotopy equivalence belongs to $cl_{{\bar{\Delta}}}((W_I)_+)$
Results of [@HH0] imply that the category $H_{\bullet}(C,P,I)$ is the homotopy category of a simplicial almost finitely generated closed model structure on the category of simplicial presheaves on $C$ where cofibrations are the projective cofibrations. If $P$ is complete, bounded and regular we can also realize it as the homotopy category of an almost finitely generated closed model structure on the category of simplicial sheaves on $C$ in the $t_P$-topology. Indeed, Proposition \[swi\] states that, under these assumptions, the category $H_{\bullet}(C,P,I)$ is equivalent to the localization of the homotopy category of pointed simplicial sheaves in $t_P$ with respect to the class of $(W_I)_+$-local equivalences (see [@Hirs]). The homotopy category of simplicial sheaves is the homotopy category of the Brown-Gersten closed model structure which is cellular by [@HH1 Proposition 4.7]. Therefore, $H_{\bullet}(C,P,I)$ is equivalent to the homotopy category of the left Bousfield localization of the Brown-Gersten closed model structure with respect to $(W_P)_+$ which exists by [@Hirs] and one verifies easily that it is almost finitely generated.
Specializing these general theorems to the case of the motivic homotopy categories and using the properties of the standard cd-structures proved in the first section we get the following results.
[\[v1\]]{} Let $P$ be a standard cd-structure on the category $Sch/S$. Then the functor $${\label{v1eq}}
\Delta^{op}(Sch/S)^{\coprod}_+{\rightarrow}H_{\bullet}((Sch/S)_{t_P},{{\bf A}^1})$$ is the localization with respect to the smallest ${\bar{\Delta}}$-closed class which contains morphisms of the form $(p_Q:K_Q{\rightarrow}X)_+$ for distinguished squares $Q$ and morphisms of the form $(X\times{{\bf A}^1}{\rightarrow}X)_+$ for schemes $X$.
[\[v2\]]{} Let $P$ be a standard cd-structure which is contained in the upper cd-structure. Then the functor $${\label{v2eq}}
\Delta^{op}(Sm/S)^{\coprod}_+{\rightarrow}H_{\bullet}((Sm/S)_{t_P},{{\bf A}^1})$$ is the localization with respect to the smallest ${\bar{\Delta}}$-closed class which contains morphisms of the form $(p_Q:K_Q{\rightarrow}X)_+$ for upper distinguished squares $Q$ and morphisms of the form $(X\times{{\bf A}^1}{\rightarrow}X)_+$ for smooth schemes $X$.
In many cases the category of all schemes (resp. all smooth schemes) on the left hand side of (\[v1eq\]) and (\[v2eq\]) can be replaced by smaller subcategories. For either upper or lower cd-structure all schemes can be replaced by quasi-projective schemes (for the lower cd-structure one uses the Chow lemma to show that this is allowed). For plain upper or stronger cd-structure smooth schemes can be replaced by smooth quasi-affine schemes etc.
The comparison theorem
----------------------
Let $k$ be a field. We have an obvious functor of pointed motivic homotopy categories $${\label{niscdh}}
{ H}_{\bullet}((Sm/k)_{Nis},{{\bf A}^1}){\rightarrow}{
H}_{\bullet}((Sch/k)_{cdh},{{\bf A}^1})$$ which we denote by ${\bf L}\pi^*$ because it is the inverse image functor defined by the continuous map of sites $$\pi:(Sch/k)_{cdh}{\rightarrow}(Sm/k)_{Nis}$$ For a morphism $f$ in the pointed homotopy category we denote by $$\Sigma^1_s(f)=f\wedge Id_{S^1_s}$$ the first simplicial suspension of $f$. Let us recall the following definition given in [@FV].
[\[res\]]{} A field $k$ is said to admit resolution of singularities if the following two conditions hold:
1. for any reduced scheme of finite type $X$ over $k$ there exists a proper morphism $f:\tilde{X}{\rightarrow}X$ such that $\tilde{X}$ is smooth and $f$ has a section over a dense open subset of $X$
2. for any smooth scheme $X$ over $k$ and a proper surjective morphism $Y{\rightarrow}X$ which has a section over a dense open subset of $X$ there exists a sequence of blow-ups with smooth centers $X_n{\rightarrow}X_{n-1}{\rightarrow}\dots{\rightarrow}X_0=X$ and a morphism $X_n{\rightarrow}Y$ over $X$.
Note that any field satisfying the conditions of Definition \[res\] is perfect.
[\[m124\]]{} Let $k$ be a field which admits resolution of singularities. Then the functor ${\bf L}\pi^*$ is a localization and for any $f$ in $iso({\bf L}\pi^*)$ the morphism $\Sigma^1_s(f)$ is an isomorphism.
Define the smooth blow-up cd-structure on the category $Sm/k$ of smooth schemes over $k$ as the collection of pull-back squares of the form (\[eq1\]) such that $e$ is a closed embedding and $p$ is the blow-up with the center in $e(A)$.
[\[iscomplete\]]{} Let $k$ be a field which admits resolution of singularities. Then the smooth blow-up cd-structure on the category of smooth schemes over $k$ is complete.
To show that a cd-structure is complete it is sufficient to show that for any distinguished square of the form (\[eq1\]) and any morphism $f:X'{\rightarrow}X$ the sieve $f^*(e,p)$ contains the sieve generated by a simple covering (see [@HH1 Lemma 2.4]). Let us prove it by induction on $dim(X')$. If $dim(X')=0$ the sieve $f^*(e,p)$ contains an isomorphism. Assume that the statement is proved for $dim(X')<d$ and let $X'$ be of dimension $d$. The map $X'\times_X (A\coprod Y){\rightarrow}X'$ is proper and has a section over a dense open subset of $X'$. Thus by the resolution of singularities assumption we have a sequence of blow-ups with smooth centers $X'_n\stackrel{p_{n-1}}{{\rightarrow}}
X'_{n-1}\stackrel{p_{n-2}}{{\rightarrow}} \dots\stackrel{p_{0}}{{\rightarrow}}X'_0=X'$ such that the pull-back of $(e,p)$ to $X'_n$ contains an isomorphism and in particular a sieve generated by a simple covering. Assume by induction that the pull-back of $(e,p)$ to $X_{i}'$ contains a sieve generated by a simple covering $\{r_j:U_{j}{\rightarrow}X_{i}'\}$ and let us show that the same is true for $X_{i-1}'$. Let $e_{i-1}:Z'_{i-1}{\rightarrow}X'_{i-1}$ be the center of the blow-up $X_{i}'{\rightarrow}X_{i-1}'$. The restriction of $(e,p)$ to $Z_{i-1}'$ contains a sieve generated by a simple covering $\{s_l:V_{l}{\rightarrow}Z_{i-1}'\}$ since $dim(Z_{i-1}')<d$. Thus the restriction of $(e,p)$ to $X_{i-1}'$ contains the sieve generated by $\{p_{i-1}r_j, e_{i-1}s_l\}$ which is a simple covering by definition.
[\[smred\]]{} The smooth blow-up cd-structure on the category of smooth schemes over any field is bounded with respect to the standard density structure.
The same arguments as in the proof of Lemma \[l8.4.1\] show that any distinguished square of the smooth blow-up cd-structure is reducing with respect to the standard density structure.
[\[regbu\]]{} The smooth blow-up cd-structure on the category of smooth schemes over any field is regular.
The first two conditions of [@HH1 Definition 2.10] are obviously satisfied. To prove the third one we have to show that for a distinguished square of the form (\[eq1\]) the map of representable sheaves of the form $${\label{eq8.5.1}}
\rho(Y)\coprod \rho(B)\times_{\rho(A)}\rho(B){\rightarrow}\rho(Y)\times_{\rho(X)}\rho(Y)$$ is surjective. Since any smooth scheme has a covering in our topology by connected smooth schemes it is sufficient to show that the map of presheaves corresponding to (\[eq8.5.1\]) is surjective on sections on smooth connected schemes. Let $U$ be a smooth connected scheme and $f,g:U{\rightarrow}Y$ be a pair of morphisms such that $p\circ f=p\circ g$. The scheme $Y\times_X Y$ is the union of two closed subschemes namely the diagonal $Y$ and $B\times_A B$ (see the proof of the lower case in Lemma \[uploreg\]). Since $U$ is smooth and connected it is irreducible and therefore the closure of the image of $f\times g$ in $Y\times_X Y$ is irreducible. This implies that the image belongs to either $Y$ or $B\times_A B$ and since $U$ is smooth and in particular reduced the morphism $f\times_X g$ lifts to $Y$ or to $B\times_A
B$.
Consider the topology $scdh$ associated with the sum of the smooth blow-up cd-structure and the upper cd-structure on the category of smooth schemes over $S$. Since the sum of two cd-structures bounded by the same density structure is bounded, Proposition \[upred\] and Lemma \[smred\] imply that this cd-structure is bounded by the standard density structure on $Sm/k$. Since the sum of two regular cd-structures is regular, Lemma \[uploreg\] and Lemma \[regbu\] imply that it is regular. Since the sum of two complete cd-structures is complete, Lemma \[iscomplete\] and Lemma \[stcompl\] imply that if $k$ admits resolution of singularities then this cd-structure is complete. Therefore, Corollary \[c8.3.1\] implies that the functor $$\Delta(Sm/k)^{\coprod}_{+}{\rightarrow}{
H}_{\bullet}((Sm/k)_{scdh},{{\bf A}^1})$$ is the localization with respect to the smallest ${\bar{\Delta}}$-closed class which contains morphisms of the form $(p_Q:K_Q{\rightarrow}X)_+$, where $Q$ is an upper distinguished square or a smooth blow-up square, and the projections $(X\times{{\bf A}^1}{\rightarrow}X)_+$. On the other hand the continuous map of sites $$(Sch/k)_{cdh}{\rightarrow}(Sm/k)_{scdh}$$ defined by the inclusion of categories $Sm/k{\rightarrow}Sch/k$ defines the inverse image functor $${\label{invim}}
{
H}_{\bullet}((Sm/k)_{scdh},{{\bf A}^1}){\rightarrow}{
H}_{\bullet}((Sch/k)_{cdh},{{\bf A}^1})$$ and we have a commutative diagram $$\begin{CD}
\Delta(Sm/k)^{\coprod}_{+}@>>>H_{\bullet}((Sm/k)_{Nis},{{\bf A}^1})\\
@VVV @VV{\bf L}\pi^*V\\
{H}_{\bullet}((Sm/k)_{scdh},{{\bf A}^1})@>>>{
H}_{\bullet}((Sch/k)_{cdh},{{\bf A}^1})
\end{CD}$$
[\[easy\]]{} If $k$ admits resolution of singularities the inverse image functor $Shv_{scdh}(Sm/k){\rightarrow}Shv_{cdh}(Sch/k)$ is an equivalence.
The resolution of singularities assumption implies that any object of $Sch/k$ has a cdh-covering by objects of $Sm/k$ and that any cdh-covering of an object of $Sm/k$ has a refinement which is a scdh-covering. These to facts together imply that the inverse and the direct image functors define equivalences of the corresponding categories of sheaves (see \cite{}).
Lemma \[easy\] implies that the functor (\[invim\]) is an equivalence. Thus we conclude that the functor ${\bf L}\pi^*$ a localization. By [@HH0 Lemma 3.4.13] any morphism in $H_{\bullet}((Sm/k)_{Nis},{{\bf A}^1})$ is isomorphic to the image of a morphism in $\Delta(Sm/k)^{\coprod}_{+}$ which implies that $$iso({\bf L}\pi^*)=cl_{{\bar{\Delta}}}(W_{scdh,+}\cup W_{{{\bf A}^1},+})$$ For a class $E$ in $\Delta^{op}C^{\coprod}_{\bullet}$ and a pointed simplicial set $K$ one has $$cl_{{\bar{\Delta}}}(E)\wedge Id_K\subset cl_{{\bar{\Delta}}}(E\wedge
Id_K)$$ and, therefore, $$\Sigma^1_s(iso({\bf L}\pi^*))\subset
cl_{{\bar{\Delta}}}(\Sigma^1_s(W_{scdh,+})\cup \Sigma^1_s(W_{{{\bf A}^1}_+}))$$ Elements of $\Sigma^1_s(W_{{{\bf A}^1}_+})$ are ${{\bf A}^1}$-weak equivalences for any topology, elements of $\Sigma^1_s(W_{scdh,+})$ are ${{\bf A}^1}$-weak equivalences for the Nisnevich topology by [@MoVo Remark 3.2.30]. Together with Lemma \[isdlta\] it implies that the class $\Sigma^1_s(iso({\bf L}\pi^*))$ consists of ${{\bf A}^1}$-weak equivalences in the Nisnevich topology.
[\[cortwo\]]{} Let $k$ be as above and $X$ and $Y$ be pointed simplicial sheaves on $(Sm/k)_{Nis}$ such that $Y$ is ${{\bf A}^1}$-weak equivalent to the simplicial loop space of an ${{\bf A}^1}$-local object. Then the map $$Hom(X,Y){\rightarrow}Hom({\bf L}\pi^*(X),{\bf L}\pi^*(Y)),$$ where the morphisms on the left hand side are in $H((Sm/k)_{Nis},{{\bf A}^1})$ and on the right hand side in $H_{\bullet}((Sch/k)_{cdh},{{\bf A}^1})$, is bijective.
[^1]: Supported by the NSF grants DMS-97-29992 and DMS-9901219, Sloan Research Fellowship and Veblen Fund
[^2]: School of Mathematics, Institute for Advanced Study, Princeton NJ, USA. e-mail: [email protected]
| |
IDLab provides internships and master theses on a variety of topics in both the Factulty of Science and Faculty of Applied Engineering. More information is available on the ESP-website.
Thesis topics
Distributed SDN controller for heterogeneous wireless networks. Implementation of a distributed controller to manage a plethora of wireless and wired devices.
Implementation and evaluation of 60GHz handovers. The implementation and evaluation of handovers to and from the novel 60GHz Wi-Fi technology in the NS-3 network simulator.
MAC protocol analysis on IEEE 802.11 networks. Analysis of the impact of different versions/configurations of MAC protocols for IEEE 802.11 networks.
Internship topics
Implementation of ORCHESTRA in NS-3 network simulator. The implementation and evaluation of the ORCHESTRA multi-technology management framework in the NS-3 network simulator.
Multipath TCP in NS-3 network simulator. Implementation and evaluation of Multipath TCP.
Reverse engineer Google Wi-Fi. You will get access to the Google Wi-Fi product and your goal is to reverse engineer it, in order to explain how the different features of Google Wi-Fi are implemented and accomplished.
Implementation of Next Generation Interfaces for 5G system functional split. Implementation of gNB functional split on SDR platforms.
Design and implement YANG/COMI models for 6LoWPAN networks. Study and implement YANG/COMI-based models for 6LoWPAN.
Enabling battery-less IoT devices. Comparing different energy harvesting sources and optimizing the performance to enable battery-less communication.
Enabling SDN capabilities in heterogeneous 6LoWPAN networks. Study and Develop a fibbing-based approach for controlling meticulously the QoS of an heterogeneous IoT network.
Managing flexible multimodal IoT devices. Combining multiple emerging wireless technologies into a single multimodal device for a more flexible Internet of Things.
Modelling a fibbing-based API for 6LoWPAN networks. Develop a fibbing-based interface for controlling meticulously the QoS of a network.
Optimizing and 6LoWPAN networks. Develop a platform for monitor and control 6LoWPAN networks in order to offer optimized QoS.
Optimizing 6TiSCH performance in the subGHZ band. Study, implement and test different improvements to 6TiSCH in subGHZ band using the IEEE 802.15.4g PHY layer.
Optimizing mobile networks for IoT devices using NB-IoT. Propose algorithm for small data transmission (UL/DL) in sleep mode UE and implement it in NS3 simulator.
Optimizing the energy efficiency of Wi-Fi HaLow for the IoT. Make future Wi-Fi technology energy efficient to allow thousands of IoT devices to connect to a single access point.
Over-the-air firmware updates for IoT devices over cellular networks. Propose method to perform over-the-air firmware updates and demonstrate it with real NB-IoT hardware.
Policy-based TSCH scheduling. Research and development of state-of-the-art policy-based TSCH scheduling in power-constrained sensor networks.
TSCH scheduling in industrial areas. Development of a TSCH scheduling function that guarantees QoS in an industrial setting with increased interference levels.
Nanoscale communications for wirelessly programmable robotic materials. Comparing wireless communication protocols that enable communication between sensors and actuators smaller than a speck of dust.
Create a RL agent for flow scheduling in an MF-TDMA network. Create a RL agent that will optimize flow scheduling in MF-TDMA networks to reach given mandates.
Creating resilient networks using machine learning. Create a deep learning algorithm that allows a network manager detects failures before they happen.
Creating resilient networks using machine learning. Create a deep learning algorithm that allows a network manager detects failures before they happen.
Deep learning to classify data flows in Wi-Fi and LTE networks. Create a model using neural networks to classify different flow types like VoIP, HTTP, control, Video, …).
Evaluating and comparing state-of-art reinforcement learning algorithms. There are many reinforcement learning algorithms but, given a problem, how do we know which is the right one?
Predicting latency in heavily interfered wireless networks. Using machine learning to predict the latency in a wireless network that has external interference.
Efficient Generative Adversarial Nets (GANs)
Flexible auto-encoder for semi-supervised deep learning
Hierarchical Sequence Memory. Analysis and experimental evaluation of neural networks based on Hierarchical Temporal Memory.
Multi-technology and multi-technique wireless indoor localization. Evaluation of different techniques for wireless indoor localization using multiple wireless technologies.
Target Propagation for Deep Neural Networks.
Distributed Hierarchical Temporal Memory in NuPIC. Distributing the existing reference implementation of the Hierarchical Temporal Memory machine learning algorithm across multiple cores or machines.
Advanced NFC communication with nurse call devices. We want to optimize the NFC communication and range between a smartphone and nurse call devices.
IoT sensor network for passenger counting on trains. On-board railway IoT wireless sensor design and PoC for passenger counting and seat occupancy.
Secure BLE connectivity for patient monitoring system. You will investigated what it takes to interface to a medical device/telemetry device using BLE.
Linking Identity Server 4 to External Authentication services.
Wireless but reliable connectivity for nurse call. You will investigate WiFi mesh technology for communication between room terminals in a hospital nurse call system. | https://www.uantwerpen.be/en/research-groups/idlab/for-students/internships-and-mast/ |
USDA cuts corn, soybean stocks view on strong demand
WASHINGTON, June 12 (Reuters) - Rising demand on both the domestic and overseas fronts spurred a cut in the U.S. Agriculture Department's outlook for corn and soybean stockpiles, the government said on Tuesday.
In its monthly supply and demand report, USDA pegged soybean ending stocks for the 2017/18 crop year at 505 million bushels, down from 530 million bushels a month ago. It boosted its soybean usage by crushers to 2.015 billion bushels, up 25 million bushels.
For the 2018/19 marketing year, USDA estimated soybean endings stocks at 385 million bushels, down from its May estimate of 415 million bushels. The lower stocks figure was largely due to a smaller carry-in from 2017/18. Additionally, the 2018/19 crush estimate was raised by 5 million bushels.
The 2018/19 stocks estimates fell below a range of analysts' forecasts in a Reuters survey. The 2017/18 figure was below the average of estimates in the survey.
High soybean meal usage was sparking demand for soybeans at processors, USDA said.
On the corn front, USDA pegged 2017/18 ending stocks at 2.102 billion bushels, down 80 billion bushels from May. That was below the low end of analysts' estimates that ranged from 2.132 billion bushels to 2.192 billion bushels.
The government raised its 2017/18 corn export outlook by 75 million bushels to 2.300 billion. USDA said that corn exports in April hit a record high, topping the monthly shipping record set in November 1989.
USDA also pegged domestic wheat ending stocks at 1.080 billion bushels for 2017/18, up 10 million bushels from May, and at 946 million bushels for 2018/19, 9 million bushels lower than May.
The government raised its estimate of all U.S. wheat production for 2018/19 by 6 million bushels to 1.827 billion bushels, with slight increases seen in hard red winter wheat, soft red winter wheat and white winter wheat production.
USDA also lowered its estimate of 2017/18 soybean production in Argentina to 37.00 million tonnes from 39.00 million tonnes, but raised its estimate for Brazil's 2017/18 soybean harvest to 119.00 million tonnes from 117.00 million tonnes.
It trimmed its corn harvest forecast for Brazil by 2 million tonnes to 85 million tonnes and left its estimate of Argentina's corn production unchanged. | |
Next, prepare your brownie mix according to the directions on the package.
After that line the 9x9 baking dish with the parchment paper and spray with cooking spray.
I cut my paper into 2 long rectangles and placed them in a cross-shape in the pan.
Pour the brownie mix into the pan.
Bake for 36-39 minutes in the 350 degree oven.
Once the brownie has finished cooking let it cool in the pan for 10 minutes.
then place on the counter to finish cooling the rest of the way.
Now it's time to cut into trees.
Start by cutting the brownie in half, horizontally through the middle.
Next cut each half into triangle shapes.
Now, using your premade icing, frost the cupcakes.
Add the sprinkles of your choice.
Place the stem of the small candy cane in the bottom of the brownie.
And just like that you have the most ADORABLE Brownie Christmas Trees ever! The best part is everyone in the family can join in and make memories! If you make these with your family I would love for you to tag me in pictures on social media and I would also like to hear what easy Christmas treats you make with your family.
And as always...
Happy Reading, Happy Eating, and Happy Christmas!
~The Kitchen Wife~
Brownie Christmas Tree Recipe:
*Prep Time: 5 min *Cook Time: 36-39 minutes *Servings: 10 Trees
PRINTABLE RECIPE
Ingredients:
- 1 box of Brownie Mix (And whatever they say you need to make them)
- Prepared Green Icing
- Sprinkles
- Small Candy Canes
- 9x9 Baking dish
- Parchment Paper
- Preheat oven to 350 degrees.
- Prepare brownie mix according to package directions.
- Line the baking dish with the parchment paper and spray with cooking spray*
- Pour the batter into the lined baking dish and bake 36-39 minutes.
- Let cool in baking dish for 10 minutes then remove to the counter to finish cooling.
- Cut the browning, horizontally, through the middle and then into triangle tree shapes.
- Decorate with icing and sprinkles.
- Place the candy cane trunk into the bottom of the brownie tree.
- Serve and Enjoy! | https://www.thekitchenwife.net/2018/12/brownie-christmas-tree-recipe.html |
Q:
Prove by induction - about vector spaces, polynomials
I know how to prove by induction in general but in this task I don't even understand how to do and apply it, it's last task from an old exam:
$\mathbb{R}_{n}[x]= \left\{\sum_{k=0}^{n}p_{k}x^{k}: p_{k} \in
\mathbb{R}\right\}$ is the vector space of all real polynomial $p$ of
the degree $n_{p} \leq n$. And for every $j \in
\left\{0,1,...,n\right\}$ there is a polynomial $P_{j} \in
\mathbb{R}_{n}[x]$ given with degree $np_{j}=j$, that means $P_{j}$
has the shape $$P_{j}= \sum_{k=0}^{j}p_{jk}x^{k} \text{ with } p_{jk}
\in \mathbb{R} \text{ for } k \in \left\{0,1,...,j\right\} \text{ and
} p_{jj} \neq 0$$
Prove by induction that $\left\{P_{0},..., P_{n}\right\}$ is a basis
of $\mathbb{R_{n}[x]}$, if $\mathbb{R}_{0}[x]$ is identified with
$\mathbb{R}$.
If this was in my exam, I wouldn't know at all what to do and where to start. There are so so many different variables and attributes given... I would be very happy already if I knew how to do the start (I mean where you just show it for a specific $n$, the begin). Usually, induction proofs were easy when I had them in analysis classes but this is something very different and much more complicated I don't know how to start here? >.<
A:
you need the set of $\{p_0,p_2,\cdots, p_n\}$ to span the space and to be linearly independent.
And since the space of $\mathbb R_n[x]$ has dimension $n+1$ and there are $n+1$ vectors in our proposed basis, you really only need to prove that the set is linearly independent.
Base case:
$n=0$
$p_0 = c$ spans the set of real numbers
Suppose:
$\{p_0,p_2,\cdots, p_n\}$ is a basis for $R_n[x]$
We must show that:
$\{p_0,p_2,\cdots, p_n, p_{n+1}\}$ is a basis for $\mathbb R_{n+1}[x]$
$p_{n+1}$ has an $x^{n+1}$ term that $\{p_0,p_2,\cdots, p_n\}$ do not.
$p_{n+1}$ cannot be formed by a linear combination of $\{p_0,p_2,\cdots, p_n\}$
$\{p_0,p_2,\cdots, p_n, p_{n+1}\}$ are a linearly indpendent set of vectors that spans $\mathbb R_{n+1}[x]$ and therefor form a basis for $\mathbb R_{n+1}[x]$
QED
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Q:
Inductive problem $\sqrt{k+1} -1\le \frac{a_{k-1}}{a_k}\le\sqrt{k}$
I am trying to solve this, using Inductive tools. any suggestions?
Given:
$$(k+1)\cdot a_{k+1}=a_k+a_{k-1}\qquad a_1=1 ,\, a_0=0 $$
Need to prove:
$$\sqrt{k+1} -1\le \frac{a_{k-1}}{a_k}\le\sqrt{k}$$
A:
We can prove the slightly stronger case where both inequalities are strict.
Taking $a_0 = 0, a_1 = 1$, and $a_{k+1} = \frac1{k+1}(a_k + a_{k-1})$, the upper bound (R.H.S) is false for $k = 2$ and $k= 4$, while the lower bound (L.H.S) is false for $k = 1$ and $k = 3$.
The first term where both bounds are true is at $ k = 5$ when $\sqrt{6}-1 < \dfrac{ 1/4 }{3/20} < \sqrt{5}$.
This $k = 5$ is the initial case for induction on $\sqrt{k+1}-1<S_k<\sqrt{k}$ with both sides strict, where
$$S_k \equiv \frac{a_{k-1}}{a_k}~,\qquad \text{such that}~~S_{k+1} = \frac{a_k }{a_{k+1} } = \frac{ a_k }{ (a_k + a_{k-1})/(k+1) } = \frac{ k+1 }{ 1+ S_k }$$
Suppose for some $n > 5$,
$$\sqrt{n+1}-1<S_n<\sqrt{n}\tag{1} \label{Eq_if_n_is_true}$$
The R.H.S. (upper bound) for the desired $(n+1)$th case is easily given by the L.H.S. (lower bound) of the induction hypothesis Eq\eqref{Eq_if_n_is_true}:
$$\begin{align}
\sqrt{n+1} < 1 + S_n \implies \frac1{ 1+ S_n } < \frac1{\sqrt{n+1}} &\implies \frac{n+1}{ 1+ S_n } < \sqrt{n+1} \\
&\implies S_{n+1} < \sqrt{n+1} \tag{2.R} \label{Eq_RHS_for_n+1}
\end{align}$$
The L.H.S. (lower bound) of the desired $(n+1)$th case requires
$$\sqrt{n+2} -1 \overset{?}{<} S_{n+1} \quad \Longleftrightarrow \quad \sqrt{n+2} \overset{?}{<} 1 + \frac{ n + 1}{ 1 + S_n } \tag{2.L.a} \label{Eq_LHS_for_n+1} $$
Now, the R.H.S. of the induction hypothesis Eq\eqref{Eq_if_n_is_true} gives
$$\begin{alignat}{3}
S_n < \sqrt{n} &\implies 1 + S_n < 1 + \sqrt{n} &&&&\\
&\implies \frac1{1 + \sqrt{n} } < \frac1{ 1 + S_n } &&\implies 1 + \frac{ n + 1}{ 1 + \sqrt{n} } < 1 + \frac{ n + 1}{ 1 + S_n } \\
&&&\implies \frac{ n + \sqrt{n} + 2}{ 1 + \sqrt{n} } < 1 + \frac{ n + 1}{ 1 + S_n } \tag{1.R} \label{Eq_RHS_for_n_push}
\end{alignat}$$
This suggests that we would like to push Eq\eqref{Eq_LHS_for_n+1} in its the new form (on the right) by squeezing in the term from Eq\eqref{Eq_RHS_for_n_push} as the following:
$$ \sqrt{n+2} \overset{?}{<}\frac{ n + \sqrt{n} + 2}{ 1 + \sqrt{n} } < 1 + \frac{ n + 1}{ 1 + S_n } \tag{2.L.b} \label{Eq_LHS_for_n+1_push}$$
Multiply the whole expression by $1 + \sqrt{n}$ then square both sides. We will see the terms cancel and it becomes trivially true:
$$\left( 1 + \sqrt{n} \right)^2 (n+2) \overset{?}{<} \left( n + \sqrt{n} + 2 \right)^2 \quad \Longleftrightarrow \quad 0 \overset{?}{<} 2(n+1) \tag{2.L.c} \label{Eq_LHS_for_n+1_final} $$
Summary
Given the induction hypothesis Eq\eqref{Eq_if_n_is_true} being true at some $n > 5$, the case for $n+1$
$$\sqrt{n+2} - 1 < S_{n+1} < \sqrt{n+1} $$
is true because the R.H.S. is taken care of by Eq\eqref{Eq_RHS_for_n+1}, while the L.H.S. becomes to Eq\eqref{Eq_LHS_for_n+1} that is pushed to Eq\eqref{Eq_LHS_for_n+1_push}, which in turn is equivalent to Eq\eqref{Eq_LHS_for_n+1_final} that is true.$~~$Q.E.D.
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‘The Beano’ (like ‘The Beezer’ before it) hypothesises that our perceptions and actions are managed by five little men living in five separate rooms in our skulls. Although modern neuroscience has yet to locate any Numskulls at the helm, it does support the notion that our brains are divided into discrete ‘compartments’, each in charge of a different function or set of functions.
Mapping those compartments more precisely – and understanding how the tissue structure in each region allows us to do specific things – is a fundamental challenge for neuroscience.
Thanks to advances in imaging techniques, we now know roughly which bit of the brain looks after what. Functional magnetic resonance imaging (fMRI) – which measures blood oxygen levels in tissue – has shown which regions are activated when we make a decision, take a risk, control our temper or play a game of tennis. But the brushstrokes are broad and the picture remains impressionistic. We haven’t yet found a safe, non-invasive way to penetrate the deep tissues of the living human brain – or to reveal its microscopic cellular structures (cytoarchitecture).
Neither do we know which differences in tissue composition between disparate brain regions account for these different functions. What variations in the type, size, number and patterning of cells and other micro-structures in a particular brain region allow us to evaluate two choices as opposed to run for a bus, for example?
A two-photon micrograph showing layer 5 pyramidal neurons from a cortical brain slice. Credit: Professor M Hausser/UCL, Wellcome Images.
For the past ten years, Heidi has been working to get a better handle on the correlation between brain structure and function. In 2001 (having completed a Wellcome Trust four-year DPhil/MSc in Neuroscience at the University of Oxford), she won a Wellcome Postdoctoral Training Fellowship in Mathematical Biology at the Oxford Centre for Functional MRI of the Brain. “The methods in brain imaging involve a lot of mathematics and statistics. So to be able to answer new biological questions, I wanted to get a better understanding of what you could and couldn’t do with the techniques available to interrogate brain imaging data,” she explains.
She used her Training Fellowship to develop techniques using another form of MRI – diffusion MRI, which measures the diffusion of water molecules within the brain. The shape, orientation and size of the tissues all influence how easily water can diffuse around them, so measuring that process can provide an image of their structures.
To date, most research into brain structure has focused on the grey matter, because that is the tissue containing the cell bodies of our neurons – generally considered to be the all-important information-processing units in our brains.
Heidi and colleagues, by contrast, applied the new MRI techniques they had developed to white matter – the long tracts of connecting fibres that protrude from the neuronal cell bodies and form pathways throughout the brain, allowing separate regions to communicate.
“Each bit of the brain is doing a different job,” she says. “And to do that job it needs certain types of information or inputs about the world, your body, your intention. It also needs certain outputs to control your body, or to control your speech.
A few research groups had used diffusion MRI to trace some of the white matter pathways through the brain. Heidi and her team wanted to go a step further and see whether they could use these changing structural patterns in the white matter to draw more precise boundaries between discrete functional regions.
To explore the possibility, they selected an area at the top of the brain – the medial frontal cortex, sub-regions of which were already known to regulate disparate cognitive functions, such as planning, decision making and moderating social behaviour. The team imaged the brains of volunteers using both fMRI and diffusion MRI and used the results to divide the medial frontal cortex into discrete regions (volumes), on the basis of function and white matter patternings respectively.
When they compared the two sets of divisions, they found an abrupt change in white matter connectivity patterns in exactly the same places fMRI had indicated were likely to be borders between functionally distinct regions. It was a startling revelation of a strong and direct relationship between structure and function.
Illustration of a network of nerve cells in the brain. Credit: Benedict Campbell, Wellcome Images.
The findings, published in 2004, provided the first demonstrations of how MRI could be used to divide up cortical regions based on their white matter connections, giving researchers a new strategy to study organisation elsewhere in the brain.
The best relationships evolve and adapt in response to circumstances, and over the past decade or so we’ve seen that this is also the case for our brain’s structure-function partnership. The division of labour by brain region is by no means set in stone; indeed, it looks as if extensive ‘rewiring’ is possible even in adult brains, allowing new regions to take over the job of other regions that have been damaged by stroke or injury.
Studies by various research groups using fMRI had shown new areas of brain activity appearing when patients recover limb movement after strokes, suggesting they were taking over the function of damaged areas. In 2002, Heidi and colleagues used transcranial magnetic stimulation (TMS) to temporarily disrupt these new regions, showing that patients depended on them to make movements. This provided the first actual proof that these brain regions really had taken on new roles.
Shortly afterwards, it became possible to detect changes in tissue structure when regions take on new functions – something that can happen when we learn an entirely new task, as well as to compensate for injury in another part of the brain.
In 2004, researchers showed that conventional MRI could detect a grey matter change when people learn to juggle. A couple of years later, Heidi and colleagues did a similar experiment, using diffusion MRI, to find out whether learning to juggle is also associated with strengthening of the white matter pathways. The findings, published in 2009, provided the first demonstration that white matter in the adult brain also changes its structure as a result of experience.
Growth in grey matter is unlikely to be due to the creation of new neurons – something that seems to occur rarely and only in a few specific brain regions. Other possibilities include growth of existing neurons and their processes, or an increase in the number or the size of glial cells – a type of cell that has, until recently, been credited with little importance.
Pyramidal neurons forming a network in the brain. These are nerve cells from the cerebral cortex that have one large apical dendrite and several basal dendrites. Credit: Dr Jonathan Clarke, Wellcome Images.
Glial cells used to be thought of merely as support cells; as a scaffold for the neurons, which are doing the difficult work. But over the past five to ten years, it has become increasingly clear that they are far more sophisticated and dynamic than first imagined.
“There are at least as many, and in some brain areas far more, glial cells than neurons in grey matter,” says Heidi. “They can potentially exchange signals and interact very closely with neurons. They also divide to create new cells, unlike neurons. That seems to be happening all the time and there is some evidence that it happens as a result of experience.” As yet, the question of whether glial cell growth or some other cellular events are driving grey matter change hasn’t been answered for sure.
To try to get a clearer picture of precisely what is driving the changes in both grey and white matter, Heidi plans to do parallel studies in rats and people.
In many important respects, our brains are similar in tissue structure and function (if not in size) to rat brains. Tissue changes induced by learning in the rats’ brains will, therefore, give a good indication of the same processes in the human brains.
With that end in mind, she will be doing another parallel experiment – a clinical trial to test whether non-invasive brain stimulation can improve movement in stroke patients. The technique, called transcranial direct current stimulation, involves placing two rubber electrodes on the patient’s head over the motor area of the brain and passing a small current between them while the patient does various training exercises.
She warns, however, that we still need to find out much, much more before we really understand what’s going on. The brain is a mind-bogglingly complex organ (pun intended). And the gap between cell culture experiments and fully fledged people learning to juggle is vast – one that involves the incredibly finely balanced coordination of a multitude of cells, proteins, brain compartments and whole-body physiological systems. In some ways, the notion that it could all be managed by five little men in five little rooms in our skulls is no more extraordinary.
Top image: A digitally enhanced MRI of the human head showing the brain and spinal cord in blue and green and other tissues in red and pink. Credit: Mark Lythgoe and Chloe Hutton, Wellcome Images.
Johansen-Berg H. Changes in connectivity profiles define functionally distinct regions in human medial frontal cortex. Proc Natl Acad Sci USA 2004;101(36):13335-13340. | https://www.healthcanal.com/brain-nerves/24176-feature-stroke-restructuring-the-brain.html |
This is the fastest and easiest way to building garage shelves. At about $10 a linear foot to build for four shelves, up to 8 feet tall and 2 feet deep, you can add a ton of storage and organization to your home for a great value. Build with just a couple of tools.
Need temporary garage shelving? Try this freestanding plan.
Preparation
- 8 - 2x4 @ 12 feet long
- 6 - 2x4 @ 8 feet long or 92-5/8 stud length
- 3 sheets of 1/2" plywood, OSB or similar, ripped in half, two strips 24" wide x 8 feet long
- 3" self tapping wood screws (about 150)
- 2" self tapping wood screws (about 100)
- 8 - 2x4 @ 12 feet long
- 3 - 2x4 @ 76-1/2"
- 12 - 2x4 @ 21"
- 4 - 1/2" plywood @ 24" x 96"
- 4 - 1/2" plywood @ 24" x 48"
Instructions
Step 1
Step 2
Step 3
Step 4
Comments
Sun, 01/17/2016 - 10:29
Plywood
I have built shelves similar to this several times. This weekend, I built them using these plans from Ana. I have used 7/16 OSB for all of my shelves and had no issues whatsoever. I always have a "runner" on each side lengthwise like Ana's plans call for and then short pieces spaced at the ends of each 8' long piece of OSB.
One set of shelves has been up since early 2013 and I have not had any significant sagging at all. I have totes with quite a bit of weight on my shelves.
So, in short, my answer to your question is you won't have any issues with 1/2 inch plywood. If you want to add extra cleats for support, it would certainly help, but I don't believe you will need it at all.
Sat, 06/04/2016 - 11:27
Rather than adding cleats, if
Rather than adding cleats, if you move the cleats out to the end, and add 1 or 2 more full length 2x4's, you could even use thinner shelving. Then the plywood isn't carrying any load. It's just a skin on the wooden frame. I've done it with 1/8" or 1/4" luan ($5 - $10).
Sun, 01/17/2016 - 10:34
Easy Garage Shelving
I built these yesterday. They turned out great! I've built similar style shelves several times in the past and I can say this was the easiest, sturdiest build so far.
I built my shelves 24" deep to hold standard size storage totes. I spaced my shelves apart 17.5" between the top of one board and the bottom of the next to allow just enough room for storage totes.
I used GRK fasteners from Home Depot and they worked great! The HD SKU is 489745.
The biggest challenge was anchoring the boards to the wall as my stud finder was not cooperating. I wound up locating one stud precisely and measuring off of that for the other studs.
Great plans!
Mon, 05/30/2016 - 19:17
So easy even I could do it...
Hi. Just wanted to send a quick thank you for the idea for these super simple shelves. I have done some home improvement stuff but never put up shelves from scratch before. When I saw the YouTube video for this I knew I needed to make some. I did a 15 foot set in the garage and a 10 foot set in the basement storage area. Really appreciate the helping hand!
Mon, 12/19/2016 - 18:25
Any update on the shopping
Any update on the shopping list?
Sat, 01/20/2018 - 14:40
2×4 Shelf?
Hi Ana!
Would this work using 2x4's for the shelves instead of plywood like you did with the garage storage?
Fri, 02/09/2018 - 05:44
Could I add doors to this shelve nit?
I have watched this post over and over and I think I can make it. First I wanted to know if there are plans per se to download because i could not find them. Second I wanted to know if I put more vertical legs, could I actually add doors? thanks ahead for the response! | https://ana-white.com/comment/69179 |
In one school with Vasya there is a student Kostya. Kostya does not like physics, he likes different online games. Every day, having come home, Kostya throws his bag in the farthest corner and sits down at his beloved computer. Kostya even eats glued to the game. A few days ago Kostya bought a new RPG game "HaresButtle", which differs from all other games in this genre. It has a huge number of artifacts. As we know, artifacts are divided into basic and composite ones. Only the basic artifacts are available on sale. More powerful composite artifacts are collected from some number of basic artifacts.
After the composing composite artifact, all the components disappear.
Kostya is the head of the alliance, so he has to remember, what artifacts has not only himself, but also his allies. You must identify by sequence of artifacts purchased by Kostya and his allies, how many and which artifacts has been collected by each of them. It is believed that initially no one has any artifacts.
The first line has 4 natural numbers: k (1 ≤ k ≤ 100) — the number of Kostya's allies, n (1 ≤ n ≤ 50) — the number of basic artifacts, m (0 ≤ m ≤ 50) — the number of composite artifacts, q (1 ≤ q ≤ 500) — the number of his friends' purchases. The following n lines contain the names of basic artifacts. After them m lines contain the descriptions of composite artifacts in the following format:
<Art. Name>: <Art. №1> <Art. №1 Number>, <Art. №2> <Art. №2 Number>, ... <Art. №X> <Art. №Х Number>
All the numbers are natural numbers not exceeding 100 (1 ≤ X ≤ n).
The names of all artifacts are different, they are composed of lowercase Latin letters, and the length of each name is from 1 to 100 characters inclusive. All the words in the format of the description of a composite artifact are separated by exactly one space. It is guaranteed that all components of the new artifact are different and have already been met in the input data as the names of basic artifacts.
Next, each of the following q lines is characterized by the number ai, the number of a friend who has bought the artifact (1 ≤ ai ≤ k), and the name of the purchased basic artifact. Let's assume that the backpacks of the heroes are infinitely large and any artifact bought later can fit in there.
It is guaranteed that after the i-th purchase no more than one opportunity to collect the composite artifact appears. If such an opportunity arose, the hero must take advantage of it.
The output file should consist of k blocks. The first line should contain number bi — the number of different artifacts the i-th ally has. Then the block should contain bi lines with the names of these artifacts and the number of these artifacts. At that the lines should be printed in accordance with the lexicographical order of the names of the artifacts. In each block all the artifacts must be different, and all the numbers except the bi should be positive. | https://codeforces.com/problemset/problem/69/C |
Conservative estimates suggest that up to 15% of Australian high school students will experience some form of mental health problem before they complete year 12, according to Dr Adrian Tomyn, from the Department of Psychology at RMIT.
“This risk is heightened for young people experiencing social and economic disadvantage and other barriers to successful engagement with education and post-secondary training,” he writes in a report released this week. Dr Tomyn says these risks might manifest as behavioural problems, drug and alcohol problems, inadequate family support, disability, homelessness and caregiving responsibilities.
Dr Tomyn’s report surveyed more than 23,000 ‘at risk’ young Australians and examined the happiness levels of young people aged 12-19 who were participants in the Federal Education department’s Youth Connections Program which provides support for ‘at risk’ young people across Australia.
“The findings support the importance of the three corners of the ‘Golden Triangle’ of happiness - supportive relationships, money and having a sense of meaning and accomplishment in life,” he said.
"Disadvantaged young people tend to have significantly lower levels of overall happiness than the average young Australian, largely due to lower scores on ‘Standard of Living’ and ‘Achieving in Life'," he said.
"But they tend to score no differently to average teens on ‘Relationships’ and this seems to be a crucial factor that supports happiness and prevents further loss to wellbeing in the face of adversity.
"Friends and family are among the most important protective ‘buffers’ for mental health – they act as vital sources of comfort, reassurance and support during difficult times.
"People low on social resources are at high risk for depression when faced with a personal crisis, so the fact many of these ‘at-risk’ young people have strong social support networks is crucial for their current state of mind and future wellbeing."
Other findings include:
- about one-quarter of ‘at risk’ teens have a suspected or diagnosed mental health issue, which is compromising their participation in education
- happiness decreases with increasing levels of youth disengagement, with those out of education or employment at very high-risk for low personal wellbeing and depression.
Dr Tomyn says that the Youth Connections program helps young people to “reconnect” with positive life choices in education and employment. | http://www.motherpedia.com.au/article/social-connections-key-to-happiness-for-at-risk-teens |
Total Workshop search results: 5. Displaying Page 1 of your woodworking search phrase 2 DRAWER NIGHTSTAND.
This plan includes three bedroom pieces for your home: the dresser, chest of drawers and night stand. The dresser is 32 inches tall by 60 inches long and 16 inches deep. This is a vintage woodworking plan. Visit our FAQ page for a full definition. View the Larger Image Slideshow to see the actual item you are buying.
Build this four drawer nightstand which measures 29 inches high x 20 inches deep and 26 inches wide. Here are the free plans.
This nightstand measures 18 wide x 18 deep x 23 inches high and features two drawers faced with trim slats. Here is how to build it. | http://www.woodworkersworkshop.com/resources/index.php?search=2%20DRAWER%20NIGHTSTAND |
20 Resources That'll Make You Better at login
Login is an acronym that refers to computer security. It refers to the procedure of authenticating and confirming oneself through a password to gain access onto the computer network. In general, user credentials are in the form of passwords and usernames. They can also be described as usernames and passwords. A computer network generally has several usernames and passwords that can be used to gain access to the network.
Computers will often be used in workplaces throughout the world. Additionally, there are multiple types of computer systems that have different degrees of redundancy. It is crucial to maintain backup systems so that in the event of one system going down, the other systems will continue to function. This does not mean that all computers are affected by a system's failure. A good example would be a natural disaster or fire. While certain systems may not work for a specific time, they could be restarted independently by using different techniques.
So, what is a password? A password can be described as a secret code or word that is used for accessing an system. The creation of a password is possible in many ways. For example, some computers have a built-in dictionary. The dictionary could contain terms or phrases that users might want to have encrypted. Another computer uses software that creates a password every time a user logs in to it. Combinations of numbers or letters create the most secure passwords.
A mouse is among the most well-known ways to allow a user to log into a computer. When a user presses the https://ask.fm/z7xphxe0797181 mouse and a window pops up and the computer shows an image of a lock that users must enter in order to gain access into the system. Some programs permit the hiding of mouse movements, or the use of lock-specific mechanisms.
Certain companies have developed elaborate systems that use fingerprints or keys for logging in to computers. Only authorized users are able to use logins. They are then entered into a database. A company would need to keep a database large enough which contained user names and passwords of each employee. Employees will also have to be instructed not to record logins down, but rather keep them in their desk drawers or in a safe deposit box. Automating the storage and locking the logins of these users can be done.
Telnet is another method a business might use to log on to the computer. Telnet allows data transfer between two systems of computers via an internet connection. Each computer needs its own separate configuration file. Once the connection has been established, each user is able to connect with the port number assigned to them. In order to complete the process, every user will need to key in a secret phrase or code. This method has the disadvantage that an intruder could intercept the log-in process.
Another way a company could use to access a computer is through the computer's password. This process requires that a user input an individual password that is protected by the master password. Anyone who knows the master password can utilize the password to gain access to files that are normally restricted to the regular working system. This password is used widely by large corporations, and lots of people use this method to access social networking sites and online forums. However, it has also been used by terrorists as well as unauthorised users to gain access to computers.
Employees with strong passwords will ensure that your company is secure on the internet. A secure password should contain both lower and uppercase numerals and letters, as well as special characters. If a company chooses to use a distinctive character as its username, it's a smart idea to create a password that is based on what the user uses to log into their computers rather than what the computer tells you. Hackers make use of special characters when logging in to identify whether a computer is legitimate. Hackers typically target companies and networks as it is easy to tell if the user is authentic or has a password that was before used by them. | https://weekly-wiki.win/index.php/20_Resources_That%27ll_Make_You_Better_at_login |
At 5:47 pm EST on March 17th, the doors of the Vehicle Assembly Building (VAB) of the Kennedy Space Center opened, and NASA was preparing to send the next batch of astronauts to the moon. The huge SLS rocket combined with the Orion spacecraft for the first time outdoors. Fully unveiled, slowly moving for 11 hours and settling into launch pad 39B at Kennedy Space Center.
The new generation of super-heavy launch vehicle “Space Launch System (SLS)” will be responsible for NASA’s most ambitious series of missions to date, one of which is this summer, the SLS rocket with a total length of more than 100 meters combined with the Orion spacecraft, will carry out a Artemis 1 (Artemis 1) is an unmanned mission to orbit the moon. After the Orion spacecraft is put into orbit, the spacecraft will not dock with the International Space Station but go directly to the moon, and finally enter the Earth-moon distance retrograde about 70,000 kilometers away from the lunar surface. Orbit (Distant Retrograde Orbit, DRO), orbiting the moon for 6 days and returning to Earth.
If the Artemis 1 mission is a success, the subsequent Artemis 2 mission will send astronauts to orbit the moon in the Orion spacecraft, and Artemis 3 will take astronauts to a foothold since 1972. The lunar surface (where SpaceX’s manned landing system will be involved in this mission).
In order to complete the Artemis 1 mission, the SLS rocket needs a lot of propulsion – the Block 1 version configuration will provide 8.8 million pounds of thrust at launch, about 8.8 million pounds more than the most powerful Saturn V rocket of the past. 15%.
At 4:15 a.m. ET on March 18, the complete SLS rocket arrived at Kennedy Space Center’s 39B launch pad, which will take a month to complete the wet exercise, including filling the storage tank with more than 700,000 gallons of cryogenic propellant (liquid hydrogen, liquid oxygen), start the countdown phase (but stop before ignition), then return to the aircraft assembly building to recheck any problems arising from the exercise process, and finally return to the launch pad a week before the official launch.
The debut is a key step toward a mission to the moon, testing the carrying capabilities of the world’s most powerful rocket (before Starships) and the Orion spacecraft. According to the test data generated by the wet exercise, which can help NASA to determine the final launch date more specifically, Artemis 1 is likely to be launched from May to July this year. | https://jasonnews.com/2022/03/21/the-sls-rocket-officially-sits-on-the-launch-pad-preparing-for-the-final-test-before-the-lunar-mission/ |
# SHERPA (space tug)
SHERPA is a commercial satellite dispenser developed by Andrews Space, a subsidiary of Spaceflight Industries, and was unveiled in 2012. The maiden flight was on 3 December 2018 on a Falcon 9 Block 5 rocket, and it consisted of two separate unpropelled variants of the dispenser.
Riding atop the launcher's final stage, SHERPA's release follows deployment of the primary mission payload for the dispensing of minisatellites, microsatellites, or nanosatellites such as CubeSats. SHERPA builds upon the capabilities of the Spaceflight Secondary Payload System (SSPS) by incorporating propulsion and power generation subsystems, which creates a propulsive tug dedicated to maneuvering to an optimal orbit to place secondary and hosted payloads.
## Overview
SHERPA is a three-axis stabilized platform capable of on-orbit maneuvering meant to deploy small satellites carried as secondary payloads on rideshare orbital launches. SHERPA is integrated to the rocket as a standard adapter that is designed to fit on the SpaceX Falcon 9, Orbital Sciences Corp.'s Antares, and United Launch Alliance's Atlas V and Delta rockets. SHERPA is to be separated from the launch vehicle prior to any deployments.
SHERPA is a commercial derivative of the ESPA Grande ring, and it was developed and manufactured by Andrews Space, a subsidiary of Spaceflight Industries since 2010 and was unveiled in May 2012. Spaceflight Industries fabricates SHERPA, and the SSPS, at its facility in Tukwila, Washington.
Riding atop the launcher's final stage, SHERPA is to be separated from the launch vehicle prior to any deployments or dispensing of minisatellites, microsatellites, nanosatellites and CubeSats. SHERPA features an optional propulsion system to place its payloads in an orbit other than the primary payload's orbit. The powered variants are capable of large orbit change.
SHERPA's first mission was to deploy 90 small payloads, during a 2015 launch on a Falcon 9 rocket, then it was rescheduled for 2017, but delays caused in part by a Falcon 9 rocket explosion on a launch pad in 2016, prompted Spaceflight to cancel the mission.
## Variants
### Standard SHERPA
There are at least five SHERPA variants: SHERPA (non-propelled), SHERPA 400, 1000, 2200 and FX. Each SHERPA is able to be launched in a stacked configuration with other SHERPA modules for later separation and independent free-flying.
The basic SHERPA is based on a commonly-used secondary payload adapter known as an ESPA ring and it is not propelled. It is used for low Earth orbit deployments, and can unfurl a dragsail to lower its orbit before payload deployment.
The 400 variant is used for low Earth orbit deployments, and it features two tanks with mono-propellant. SHERPA 400 has a fueled mass of 1,000 kilograms and it has a maximum capacity of 1,500 kg (3,300 lb) to low Earth orbit. It is capable of accompanying a primary payload to 800 km and then lower its orbit to a more favorable altitude to drop off secondaries. Most small satellites are required to orbit at about 450 kilometers to deorbit or move to an unused orbit within 25 years of the mission's completion.
This variant features additional monopropellant volume stored in 4 tanks.
The 2200 variant has a fueled mass of 2,000 kg and it features a more powerful bi-propellant fuel (stored in 4 tanks) for the delivery of small payloads to geostationary transfer orbit (GTO) as well as the lunar environs. GTO is a highly elliptical Earth orbit with an apogee of 42,164 km (26,199 mi).
### SHERPA-NG
SHERPA-FX
The FX variant, intended to be flown onboard a SpaceX Falcon 9 Block 5 is an optional third stage for delivery of deployable and hosted payloads in low earth orbit (LEO) and polar orbit (SSO).
SHERPA-AC
Augmented version of the free-flying SHERPA-FX equipped with attitude knowledge & control capabilities and a flight computer, optimized for hosted payloads.
SHERPA-LTC
SHERPA LTC is an optional third stage that utilizes a bi-propellant propulsion system to deliver satellites and hosted payloads to low earth orbit (LEO) and polar orbit (SSO).
SHERPA-LTE
SHERPA LTE is an optional third stage that utilizes a Xenon propulsion system to deliver satellites and hosted payloads to Geostationary orbit (GEO), Cislunar, or Earth-escape orbits.
SHERPA-ES
SHERPA-ES (SHERPA EScape) is a high-energy SHERPA-NG variant that will utilize a bi-propellant propulsion system to deliver satellites and hosted payloads to geostationary and cislunar orbits. The first flight of this variant, designated "GEO Pathfinder", is planned for late 2022 as a rideshare on the IM-2 mission. | https://en.wikipedia.org/wiki/SHERPA_(space_tug) |
During a recent Maker Monday program for ages 8-18 years, we explored the four Forces of Flight (thrust, drag, lift, weight) and made lots of machines that fly. It was a rowdy couple of hours with lots of budding engineers in one room along with balloons, paper airplanes, and hot glue. I was thankful to have two partners in crime again this week.
I’ll admit that I didn’t know a lot about the forces of flight before planning this program. I didn’t become an aeronautical engineer in the planning either. I did learn a lot though, and learned enough to inspire a large group of kids and teens to create flying machines, modify their designs to improve their flying, and have fun working in teams.
Here are some resources for learning about the forces of flight and Isaac Newton’s Laws of Motion:
Smithsonian National Air and Space Museum’s How Things Fly: Forces of Flight
Physics Classroom: Newton’s Laws of Motion
NASA LaRC Office of Education NASA Sci Files with Dr. D (another kid friendly video explaining the forces of flight from the Internet Archive, which I love)
There are also lots of good kids books about paper airplanes, motion, and rockets that discuss these concepts. I had several from our library’s collection on display in the program room.
To start things off, I showed the group this video. I did it for two reasons. First of all, the two hosts are women engineers. Not only is STEAM important for kids in general, but I think its especially valuable for girls to see women as scientists in STEAM-related programs so they know anything is possible. Secondly, the video explains the forces of flight well in a relatively short video. The kids started to get distracted part way through the video as they explained the four forces of flight, so I stopped the video and explained them in my own words. This helped reinforce the concepts and kept everyone on track. This isn’t school, so I didn’t want kids zoning out because they were getting overwhelmed. I also didn’t show the complete video because we weren’t doing the same experiment.
After the video we did our first flight test. It was a simple one. We asked the new engineers if they could predict who would be able to jump the highest. Most of the kids looked around the room and chose the tallest person, a teen. Given what we just learned about the forces of motion I asked them to look at the predicted winner again. The vote was still with him as we proceeded with the experiment.
We had kids come up to sheets of paper we hung on one of the room’s walls and we measured their heights. Then we had the kids come back up and jump as high as they could. We marked how high their head reached and compared measurements. The tallest person was not the highest flier! We talked again about the four forces and hypothesized about why a shorter person could fly the highest. Was it their thrust? Or the clothes on the tallest person creating drag?
The next experiment involved balloon rockets. This is where the program room got a little chaotic, but it was a great time to talk about Isaac Newton and his Laws of Motion. I’m pretty sure none of the kids present knew they would be learning about and understanding Newton’s Laws of Motion today, but the balloon rockets immediately demonstrated the Third Law: “ for every action, there is an equal and opposite reaction.”
The idea was to create rockets out of balloons and fly them across the room on string courses. We gave each person a balloon (we had a variety of shapes) and asked them to blow up the balloon without tying off the end. We then hung two strings from one end of the room to the other to create our courses. One end of the string was secured on a chair and the other was free so we could string the balloon and an attached straw onto the string in preparation for flying. To see the third law in action, I asked kids which direction the balloon opening should point to make the balloon fly to the other end of the string. You should have seen the lightbulbs go off! The air from inside the balloon should blow towards me, holding the string at the starting point, making the balloon fly in the opposite direction to the other end of the string. So simple.
Once the rocket was ready for launch, the designer let go of the balloon and watched it soar across the room on the string. Kids made many attempts as we tested out shapes of balloons, how much air was in the balloon, size of the straw and type of string.
Materials:
balloons (various sizes and shapes)
string (various types optional)
straws (various sizes optional)
tape
chair(s) to secure string
To calm things down a bit, we had everyone sit in small groups on the floor (we removed the large tables from the room to accommodate the large numbers of kids). Then we moved on to paper airplanes! I found three paper airplane patterns the kids could copy and build if they didn’t have a design of their own. We used the new planes to see who’s airplane could get closest to the target we created with a wire hanger pulled slightly out of shape to form a diamond. Kids took turns launching their paper crafts across the room towards the target. None of the airplanes made it into the target, but a few came close. Several kids took multiple turns and fiddled with their design to see if it could fly higher, more accurately, or further.
Materials:
paper airplane patterns (books or see link above for printable designs)
paper (various weights and colors optional)
markers, pencils, crayons for decorating
paper clips (for weighting the nose of some designs)
Finally it was time for my favorite event, the soda bottle rocket (see full details at this link)! These are incredibly cool and don’t be scared off by the preparation or the fact that you are shooting bottles full of water into the air. Even my dad laughed on the first test run I did at home!
Of course you’ll want to launch these rockets outside. I took everyone out to a grassy area alongside the library for the demo. I had everyone stay back (to be extra cautious) behind a certain line during takeoff. I brought with me a plastic soda bottle filled approximately 1/3 with water. I plugged the opening with the prepared cork (repurposed bike tire valve inserted into a drilled hole in the wine cork) and laid it on the launch pad (made from scraps of wood so no one would have to hold the bottle as it is launched and get soaked in the process).
Much of the research I did on these rockets discussed specific PSI for launch, possible bottle explosion, etc. A little common sense goes along way here. The idea is that you pump air into the bottle via the bike tire valve inserted in the cork now attached to the bottle. Pretty simple. I never had any problems and I didn’t use a bike pump with a PSI indicator. It all worked well and was a perfect finale to the program. For the last 20-25 minutes kids took bottles I collected from the recycling bin at the dump and modified them with foam wings, tails and noses to see if the designs would change how the rockets flew. We launched over 25 rockets and it was a crowd pleaser every time.
Materials:
empty and clean plastic soda bottles
wine cork (natural cork, not plastic)- make sure it fits into the bottle opening snuggly without falling in
bike tire valve off an old bike tire inter tube (I got a dozen for free from a local bike shop)
foam sheets or other materials to modify rockets (I had foam on hand from another program)
water
stand up bike pump
scraps of wood to make rocket launch pad (no design)
hot glue
I did bring a second pump, but we didn’t end up using it. The hold up with this part of the program was the hot gluing of the added design features on to the rockets. I had the easy part as the rocket launcher. My co-leaders had to glue! Some kids did find a use for the other bike pump however. They came up with the fart launcher game. Pumping the pump while holding the end sounds, well, like someone farting I guess. | https://nevershushed.com/tag/iridescent/ |
CROSS REFERENCE TO RELATED APPLICATIONS
This application claims priority to European Patent Application EP 19401057.5 filed on Dec. 20, 2019, and German Patent Application DE 10 2020 122 220.3, filed on Aug. 25, 2020, which are both incorporated herein by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
2. Description of the Related Art
The present invention relates to a glass composition and a glass article such as an optical component having a low transmission in the visible range and a high transmission in the near-infrared (NIR) range. The present invention also relates to uses thereof, in particular in the automotive sector.
Glasses having a low transmission in the visible range are often referred to as “black glass” due to their black appearance. However, common black glass generally has a transmission that is high enough to allow visual inspection of structures positioned behind the glass, unless the glass is provided with a comparably high thickness. In particular when used at low thickness, common black glasses do not appear to be entirely black, i.e. they do not have a neutrally black color impression. Rather, they often give rise to a dark blue or dark green color impression. Furthermore, black glasses often comprise toxic components that are not acceptable in many fields of application.
In view of the disadvantages described above, it is not surprising that potential applications of black glasses have been limited to certain narrow fields, in particular to applications in which a high thickness was acceptable as it was not experienced as a major disadvantage.
However, in order to open up new fields of application, the above-discussed disadvantages have to be overcome. For example, an accordingly improved black glass that additionally has a high transmission in the NIR range may be advantageously used as an optical component or band-pass filter in applications comprising NIR lasers. Interestingly, the number of such applications has drastically increased in recent years, in particular for optical measurements of distance and/or speed. Commonly known is a method that is often referred to as LiDAR (Light Detection And Ranging) or sometimes also as LaDAR (Laser Detection And Ranging). LiDAR systems generally work by emitting laser light in the NIR spectrum, in particular having wavelengths of more than 780 nm. Such laser light is reflected from objects in the surrounding at least partially back into the LiDAR system and detected there. Based on the pattern of the reflected laser light, the LiDAR system may recognize objects. Based on the Time of Flight, the LiDAR system may determine the distance of objects. Some LiDAR systems may determine the speed of objects based on phase relationship of emitted and reflected laser light.
LiDAR systems are, for example, required for autonomous driving. However, there are plenty additional fields of application, in particular robotics, drones, satellites, marine, mining, construction, railways and so on.
LiDAR systems require an optical window positioned between the opto-electronic components of the system and the surroundings in order to provide protection against environmental impacts. Depending on the type of LiDAR system, such optical windows may be planar or curved. Commonly used are also spinning LiDAR systems in which emitter and detector rotate within a typically stationary ring window.
Commonly known LiDAR systems typically comprise optical windows made of polymeric materials, in particular materials such as polycarbonate (PC) or poly(methyl methacrylate) (PMMA). However, such materials have several disadvantages, in particular regarding scratch resistance, mechanical resistance and chemical resistance.
Therefore, there have been attempts to use glass as material for such optical windows. For example, WO 2019/030106 A1 discloses a LiDAR system having a cover lens comprising a glass. However, the advantageous properties of the glasses provided according to the present invention that are chemically resistant glasses combining high transmission in the NIR range with low transmission in the visible range and have a neutrally black color impression are not achieved. The same holds true for WO 2019/065643 A1.
Furthermore, WO 2019/009336 A1 discloses a sensor module comprising a protective member being formed of strengthened glass. However, the glasses have a high transmission in the visible range.
SUMMARY OF THE INVENTION
2
5
The previously described prior art glasses do not have the advantageous properties of the glasses provided according to the present invention. The glass provided according to the present invention is characterized by particularly low transmission in the visible range. On the other hand, the transmission in the NIR-range is particularly high. Moreover, the glass provided according to the present invention is particularly color-neutral, i.e. it has a particularly neutrally black color impression. The glass may be free of components like Cr(VI) and/or VOthat are not desired in the automotive industry. Furthermore, the glass has a particularly high chemical stability and mechanical stability. In some embodiments, the glass provided according to the present invention can be processed very well by hot forming which is particularly advantageous for obtaining flat or ring-shaped optical components.
In some exemplary embodiments provided according to the present invention, a glass, such as an optical glass, comprises cations of the following components in the indicated amounts (molar proportion in cat.-%):
Component
Proportion (cat.-%)
Silicon
30-80
Boron
0-20
Aluminum
0-2
Sodium
5-35
Potassium
2-25
Nickel
0-0.5
Chromium
0-0.5
Cobalt
0.03-0.5
a sum of the molar proportions of cations of sodium and potassium is in a range of from 15 to 50 cat.-%, a sum of the molar proportions of cations of nickel and chromium is in a range of from 0.1 to 0.5 cat.-% and a ratio of the sum of the molar proportions of cations of sodium and potassium to the sum of the molar proportions of cations of nickel and chromium is in a range of from 70:1 to 200:1.
In some exemplary embodiments provided according to the present invention, a glass article includes a glass and has a thickness in a range of from 1 mm to 5 mm. The glass comprises cations of the following components in the indicated amounts (molar proportion in cat. %):
Component
Proportion (cat.-%)
Silicon
30-80
Boron
0-20
Aluminum
0-2
Sodium
5-35
Potassium
2-25
Nickel
0-0.5
Chromium
0-0.5
Cobalt
0.03-0.5
a sum of the molar proportions of cations of sodium and potassium is in a range of from 15 to 50 cat.-%, a sum of the molar proportions of cations of nickel and chromium is in a range of from 0.1 to 0.5 cat.-% and a ratio of the sum of the molar proportions of cations of sodium and potassium to the sum of the molar proportions of cations of nickel and chromium is in a range of from 70:1 to 200:1.
In some exemplary embodiments provided according to the present invention, a method for producing a glass includes melting glass raw materials and cooling the melted glass raw materials to form the glass. The glass comprises cations of the following components in the indicated amounts (molar proportion in cat.-%):
Component
Proportion (cat.-%)
Silicon
30-80
Boron
0-20
Aluminum
0-2
Sodium
5-35
Potassium
2-25
Nickel
0-0.5
Chromium
0-0.5
Cobalt
0.03-0.5
a sum of the molar proportions of cations of sodium and potassium is in a range of from 15 to 50 cat.-%, a sum of the molar proportions of cations of nickel and chromium is in a range of from 0.1 to 0.5 cat.-% and a ratio of the sum of the molar proportions of cations of sodium and potassium to the sum of the molar proportions of cations of nickel and chromium is in a range of from 70:1 to 200:1.
BRIEF DESCRIPTION OF THE DRAWINGS
The above-mentioned and other features and advantages of this invention, and the manner of attaining them, will become more apparent and the invention will be better understood by reference to the following description of embodiments of the invention taken in conjunction with the accompanying drawings, wherein:
FIG. 1
illustrates the transmission of example glasses E1 to E6 as well as of comparative examples C1 and C2 in the wavelength range from 300 to 1200 nm for a sample thickness of 2 mm, with comparative example C1 having a comparably low transmission in the particularly relevant wavelength range of from 850 to 950 nm and comparative example C2 having a comparably high transmission in the visible range;
FIG. 2
illustrates the transmission of example glasses E1 to E5 as well as of comparative examples C1 and C2 in the wavelength range from 300 to 1200 nm for a sample thickness of 4 mm, with comparative example C1 having a comparably low transmission in the particularly relevant wavelength range of from 850 to 950 nm and comparative example C2 having a comparably high transmission in the visible range; and
FIG. 3
illustrates a chromaticity diagram CIE UCS 1976 for glass E4 provided according to the present invention having a sample thickness of 2 mm, 4 mm, 6 mm and 8 mm, respectively, with the position of wavelength 400 nm, 480 nm, 520 nm, 600 nm and 700 nm being indicated and the position of a black body is indicated as a dashed line; it can be seen that E4 has a particularly neutrally black color position close to the black body with all indicated thicknesses.
Corresponding reference characters indicate corresponding parts throughout the several views. The exemplifications set out herein illustrate embodiments of the invention and such exemplifications are not to be construed as limiting the scope of the invention in any manner.
DETAILED DESCRIPTION OF THE INVENTION
Exemplary embodiments provided according to the present invention are based to a large degree on the correct adjustment of the molar ratios of the cations to each other. Therefore, it is reasonable to characterize the glass composition by indications in cat.-%. The glass also comprises anions. However, the anions are less formative for the properties of the glass than the cations so that the core of the exemplary embodiments provided according to the present invention is more in the cation composition.
The term “cation percent” (abbreviated “cat.-%”) relates to the relative molar proportions of the cations with regard to the total amount of cations in the glass. The glass also comprises anions, whose relative molar proportions in relation to the total amount of anions in the glass is herein indicated as “anion percent” (abbreviated “anion-%”).
2−
−
−
−
2−
2−
2−
4
In addition to cations, the glass provided according to the present invention also comprises anions, which may be selected from the group consisting of O, F, Br, Cl, and SO. The molar proportion of Owith regard to the anions may be at least 50% (anion-%), such as at least 70%, at least 90%, at least 98%, or at least 99%. In some embodiments, the glass is entirely oxidic, it thus contains only Oas anions and is free of other anions.
−
The glass provided according to the present invention may comprise only small amounts of halides. In some embodiments, the content of halides among the anions is restricted to at most 20 anion-%, at most 10 anion-% or at most 5 anion-%, at most 3 anion-%, or at most 1 anion-%. Halides are understood according to the present invention as the anions of Cl, F and Br. In some embodiments, the glass is free of anions of Cl, F and/or Br or comprises these components in proportions of not more than 3 anion-%, 2 anion-% or 1 anion-% each. In some embodiments, the glass comprises Cl, for example in an amount of at least 0.1 anion-%, at least 0.2 anion-%, at least 0.5 anion-%, at least 1 anion-%, at least 2 anion-% or at least 3 anion-%, such as from 0.5 to 10 anion-% or from 1 to 5 anion-%.
2+
3+
2+
3+
When it is indicated in the present disclosure that the glass comprises cations of a certain component in an indicated amount in cat.-%, this refers to the total molar amount in cat.-% of all cation species of the respective component if not indicated otherwise. Thus, for example, a component M may be present in the glass in different oxidations states in the glass, for example as Mand as M. If it is indicated that the glass comprises cations of M in an amount or proportion of x cat.-%, this means that the sum of the amounts of Mand Min the glass is equal to x cat.-%.
Terms like “proportion” or “amount” are used interchangeably within the present disclosure.
4+
The glasses provided according to the present invention comprise cations of silicon (in particular Si) in an amount of from 30 cat.-% to 80 cat.-%, such as from 35 cat.-% to 75 cat.-% or from 40 cat.-% to 70 cat.-%. Such amounts of cations of silicon may be advantageous for optimizing the desired chemical resistance and stability as well as the ability of the glass to be processed by hot forming. In some embodiments, the amount of cations of silicon in the glass is from 45 cat.-% to 70 cat.-%, such as from 50 cat.-% to 70 cat.-% or from 60 cat.-% to 70 cat.-%. The amount of cations of silicon may, for example, be at least 30 cat.-%, at least 35 cat.-%, at least 40 cat.-%, at least 45 cat.-%, at least 50 cat.-%, or at least 60 cat.-%. The amount of cations of silicon may, for example, be at most 80 cat.-%, at most 75 cat.-%, or at most 70 cat.-%.
+
+
The glasses provided according to the present invention comprise cations of alkali metals. This may be advantageous for meltability and for refining properties. Furthermore, it has been found that, in particular, a certain amount of cations of sodium and potassium is advantageous for increasing the solubility of coloring components such as cations of nickel and chromium in the glass. In this respect, it should be noted that black glasses are generally particularly difficult to melt so that the amount of cations of sodium and potassium has to be carefully chosen, also with respect to the amount of cations of nickel and chromium. In the glasses provided according to the present invention, the sum of the amounts of cations of sodium (in particular Na) and potassium (in particular K) is from 15 cat.-% to 50 cat.-%, such as from 20 cat.-% to 45 cat.-%, from 25 cat.-% to 40 cat.-%, from 25 cat.-% to 35 wt.-% or from 25 to 30 cat.-%. The sum of the amounts of cations of sodium and potassium may, for example, be at least 15 cat.-%, at least 20 cat.-%, or at least 25 cat.-%. The sum of the amounts of cations of sodium and potassium may, for example, be at most 50 cat.-%, at most 45 cat.-%, at most 40 cat.-%, at most 35 cat.-%, or at most 30 cat.-%.
Cations of sodium may be advantageous for increasing the solubility of coloring components such as cations of nickel and chromium in the glass. However, it turned out that the amount of cations of sodium should not be too high because otherwise the chemical resistance of the glasses may be reduced. The glasses provided according to the present invention comprise cations of sodium in an amount of from 5 to 35 cat.-%, such as from 7.5 to 30 cat.-%, from 10 to 25 cat.-%, from 12 to 20 cat.-%, or from 14 to 18 cat.-%. The amount of cations of sodium may, for example, be at least 5 cat.-%, at least 7.5 cat.-%, at least 10 cat.-%, at least 12 cat.-%, or at least 14 cat.-%. The amount of cations of sodium may, for example, be at most 35 cat.-%, at most 30 cat.-%, at most 25 cat.-%, at most 20 cat.-%, or at most 18 cat.-%.
Cations of potassium may be advantageous for increasing the chemical resistance. However, as compared to cations of sodium, the effect of cations of potassium on solubility of coloring components such as cations of nickel and chromium in the glass is not as high. Therefore, the amount of cations of potassium in the glass is in the range of from 2 to 25 cat.-%, such as from 5 to 20 cat.-%, from 6 to 15 cat.-%, or from 8 to 14 cat.-%. The amount of cations of potassium may, for example, be at least 2 cat.-%, at least 5 cat.-%, at least 6 cat.-%, or at least 8 cat.-%. The amount of cations of potassium may, for example, be at most 25 cat.-%, at most 20 cat.-%, at most 15 cat.-%, or at most 14 cat.-%.
In view of the different effects of cations of sodium and potassium in the glass as described previously, in some embodiments the molar proportion of potassium cations in the glass (in cat.-%) is smaller as compared to the molar proportion of sodium cations in the glass (in cat.-%). In some embodiments, the ratio of the molar proportion of potassium cations to the molar proportion of sodium cations in the glass is in a range of from 0.2:1 to <1:1, such as from 0.3:1 to 0.9:1, from 0.4:1 to 0.8:1, from 0.5:1 to 0.7:1, or from 0.6:1 to 0.7:1. The ratio of the molar proportion of potassium cations to the molar proportion of sodium cations may, for example, be at least 0.2:1, at least 0.3:1, at least 0.4:1, at least 0.5:1, or at least 0.6:1. The ratio of the molar proportion of potassium cations to the molar proportion of sodium cations may, for example, be lower than 1:1 such as at most 0.9:1, at most 0.8:1, or at most 0.7:1.
t
In addition to cations of sodium and potassium, the glasses provided according to the present invention may comprise cations of lithium (in particular Li), for example in an amount of from 0 to 4 cat.-% or from 0.1 to 2 cat.-% or from 0.5 to 1 cat.-%. The amount of cations of lithium may, for example, be at most 4 cat.-%, at most 2 cat.-%, or at most 1 cat.-%. The amount of cations of lithium may, for example, be at least 0.1 cat.-%, or at least 0.5 cat.-%. However, the glasses provided according to the present invention may be free of cations of lithium.
3+
The glasses provided according to the present invention may comprise cations of boron (in particular B). Cations of boron act as network modifiers and may compromise solubility of cations such as Cr(III). Cations of boron may be present in an amount of from 0 to 20 cat.-% such as from 1 to 15 cat.-% or from 5 to 10 cat.-%. The amount of cations of boron may, for example, be at least 1 cat.-%, or at least 5 cat.-%. The amount of cations of boron may, for example, be at most 20 cat.-%, at most 15 cat.-%, or at most 10 cat.-%. In some embodiments, the glass provided according to the present invention is free of cations of boron.
3+
The glasses provided according to the present invention may comprise cations of aluminum (in particular Al). Cations of aluminum act as network modifiers and may compromise solubility of cations such as Cr(III). Notably, the compromising effect of cations of aluminum is much stronger in this respect as compared to cations of boron. Moreover, raw materials containing cations of aluminum generally introduce water into the melt which is associated with generation of bubbles of water vapor at temperatures too low for being removed by refining. Therefore, the amount of cations of aluminum in the glasses provided according to the present invention is limited. Cations of aluminum may be present in an amount of from 0 to 2 cat.-% such as from 0.1 to 1.5 cat.-% or from 0.5 to 1 cat.-%. The amount of cations of aluminum may, for example, be at least 0.1 cat.-%, or at least 0.5 cat.-%. The amount of cations of aluminum may, for example, be at most 2 cat.-%, at most 1.5 cat.-%, or at most 1 cat.-%.
2+
The glasses provided according to the present invention may comprise cations of barium (in particular Ba), in an amount of from 0 to 10 cat.-%, for example from 0.1 to 5 cat.-% or from 0.5 to 2 cat.-%. The amount of cations of barium may, for example, be at least 0.1 cat.-%, or at least 0.5 cat.-%. The amount of cations of barium may, for example, be at most 10 cat.-%, at most 5 cat.-%, or at most 2 cat.-%. In some embodiments, the glass provided according to the present invention is free of cations of barium.
2+
The glasses provided according to the present invention may comprise cations of magnesium (in particular Mg). The amount of cations of magnesium in the glasses provided according to the present invention may be from 0 to 2.5 cat.-%, for example from 0.1 to 2 cat.-% or from 0.5 to 1.5 cat.-%. The amount of cations of magnesium may, for example, be at least 0.1 cat.-%, or at least 0.5 cat.-%. The amount of cations of magnesium may, for example, be at most 2.5 cat.-%, at most 2 cat.-%, or at most 1.5 cat.-%. In some embodiments, the glass provided according to the present invention is free of cations of magnesium.
The glasses provided according to the present invention may comprise cations of zinc in amounts of from 0 to 15 cat.-%. High amounts of zinc may compromise the chemical resistance. However, zinc is very advantageous for meltability of the glass. In some embodiments, the glass comprises cations of zinc in an amount of from 1 to 12 cat.-%, such as from 2 to 10 cat.-% or from 4 to 8 cat.-%. The amount of cations of zinc may, for example, be at least 1 cat.-%, at least 2 cat.-%, or at least 4 cat.-%. The amount of cations of zinc may, for example, be at most 15 cat.-%, at most 12 cat.-%, at most 10 cat.-%, or at most 8 cat.-%.
The glasses provided according to the present invention may comprise cations of lanthanum in an amount of from 0 to 10 cat.-%. In some embodiments, the amount of cations of lanthanum in the glasses provided according to the present invention is from 0 to 8 cat.-%, for example from 0.1 to 6 cat.-% or from 0.2 to 4 cat.-%. The amount of cations of lanthanum may, for example, be at least 0.1 cat.-%, or at least 0.2 cat.-%. The amount of cations of lanthanum may, for example, be at most 10 cat.-%, at most 8 cat.-%, at most 6 cat.-%, or at most 4 cat.-%. In some embodiments provided according to the present invention, the glass is free of cations of lanthanum.
The glasses provided according to the present invention may comprise cations of antimony. In some embodiments, the amount of cations of antimony in the glasses provided according to the present invention is from 0 to 0.4 cat.-%, for example from 0.1 to 0.3 cat.-%. The amount of cations of antimony may, for example, be at least 0.1 cat.-%. The amount of cations of antimony may, for example, be at most 0.4 cat.-%, or at most 0.3 cat.-%. In some embodiments, the glasses provided according to the present invention are free of cations of antimony.
The glasses provided according to the present invention may comprise cations of arsenic, for example in an amount of from 0 to 0.2 cat.-% or from 0.1 to 0.15 cat.-%. The amount of cations of arsenic may, for example, be at least 0.1 cat.-%. The amount of cations of arsenic may, for example, be at most 0.2 cat.-%, or at most 0.15 cat.-%. In some embodiments, the glasses provided according to the present invention are free of cations of arsenic.
Cations of cerium and titanium are components that are particularly advantageous for blocking UV radiation. However, it was surprisingly found that glasses having advantageous optical properties can also be obtained without any cations of cerium and titanium. Therefore, cations of cerium and titanium are optional components. Thus, the glasses may, for example, be free of cations of cerium, or free of cations of titanium, or free of cations of both cerium and titanium.
The amount of cations of titanium in the glasses provided according to the present invention may be in the range of from 0 to 10 cat.-%, for example from 0.5 to 8 cat.-% or from 1 to 5 cat.-%. The amount of cations of titanium may, for example, be at least 0.5 cat.-%, or at least 1 cat.-%. The amount of cations of titanium may, for example, be at most 10 cat.-%, at most 8 cat.-%, at most 5 cat.-%, at most 4 cat.-%, at most 3 cat.-%, at most 2 cat.-%, or at most 1.5 cat.-%.
The amount of cations of cerium in the glasses provided according to the present invention may be in the range of from 0 to 5 cat.-%, for example from 0.1 to 4 cat.-% or from 0.3 to 3 cat.-%. The amount of cations of cerium may, for example, be at least 0.1 cat.-%, or at least 0.3 cat.-%. The amount of cations of cerium may, for example, be at most 5 cat.-%, at most 4 cat.-%, at most 3 cat.-%, at most 2 cat.-%, at most 1.5 cat.-%, at most 1 cat.-%, or at most 0.5 cat.-%.
As described previously, the glasses provided according to the present invention are very advantageous for applications requiring low transmission in the visible range and high transmission in the NIR range, such as optical windows for LiDAR. Furthermore, the glasses provided according to the present invention have a particularly neutrally black color impression. In order to achieve such advantageous spectral properties, the glasses provided according to the present invention comprise components that may be termed absorbing components or coloring components, although the term “coloring” may be misleading in this respect because the overall color impression achieved by specific combinations of such components is neutrally black.
One absorbing component that is necessarily present in the glasses provided according to the present invention is cations of cobalt. Cations of cobalt are needed in order to achieve the advantageous spectral properties. However, the amount of cations of cobalt has to be chosen very carefully in order not to compromise the spectral properties. In the glasses provided according to the present invention, the amount of cations of cobalt is from 0.03 cat.-% to 0.5 cat.-%, such as from 0.04 to 0.4 cat.-%, from 0.05 to 0.3 cat.-%, from 0.06 to 0.2 cat.-%, or from 0.07 to 0.16 cat.-%. The amount of cations of cobalt may, for example, be at least 0.03 cat.-%, at least 0.04 cat.-%, at least 0.05 cat.-%, at least 0.06 cat.-%, or at least 0.07 cat.-%. The amount of cations of cobalt may, for example, be at most 0.5 cat.-%, at most 0.4 cat.-%, at most 0.3 cat.-%, at most 0.2 cat.-%, or at most 0.16 cat.-%.
However, cations of cobalt are not enough for achieving the advantageous spectral properties. Rather, it was found that cations of at least one of nickel and chromium have to be present in addition. Moreover, the amount of cations of nickel and chromium has to be chosen very carefully. In particular, the sum of the molar proportions of cations of nickel and chromium is in a range of from 0.1 to 0.5 cat.-%, such as from 0.12 to 0.45 cat.-%, from 0.15 to 0.4 cat.-%, from 0.16 to 0.35 cat.-%, or from 0.18 to 0.3 cat.-%. The sum of the molar proportions of cations of nickel and chromium may, for example, be at least 0.1 cat.-%, at least 0.12 cat.-%, at least 0.15 cat.-%, at least 0.16 cat.-%, or at least 0.18 cat.-%. The sum of the molar proportions of cations of nickel and chromium may, for example, be at most 0.5 cat.-%, at most 0.45 cat.-%, at most 0.4 cat.-%, at most 0.35 cat.-%, or at most 0.3 cat.-%.
The amount of the sum of cations of nickel and chromium in the glass turned out to be important. However, the glasses provided according to the present invention do not necessarily comprise cations of both nickel and chromium. Rather, it is sufficient if cations of one of nickel and chromium are present. In some embodiments, cations of both nickel and chromium may be present. In such embodiments, the molar proportion of cations of nickel may be higher as compared to the molar proportion of cations of chromium. In some embodiments, the glasses provided according to the present invention comprise either cations of nickel or cations of chromium. For example, in some embodiments the glass may be free of cations of nickel.
The amount of cations of nickel in the glasses provided according to the present invention is from 0 to 0.5 cat.-%, for example from 0.1 to 0.4 cat.-% or from 0.2 to 0.35 cat.-%. The amount of cations of nickel may, for example, be at least 0.1 cat.-%, or at least 0.2 cat.-%. The amount of cations of nickel may, for example, be at most 0.5 cat.-%, at most 0.4 cat.-%, or at most 0.35 cat.-%.
The amount of cations of chromium in the glasses provided according to the present invention is from 0 to 0.5 cat.-%, for example from 0.05 to 0.4 cat.-%, from 0.1 to 0.3 cat.-%, from 0.15 to 0.3 cat.-% or from 0.15 to 0.25 cat.-%. The amount of cations of chromium may, for example, be at least 0.05 cat.-%, at least 0.1 cat.-%, or at least 0.15 cat.-%. The amount of cations of chromium may, for example, be at most 0.5 cat.-%, at most 0.4 cat.-%, at most 0.3 cat.-%, or at most 0.25 cat.-%.
6+
3
3
In some embodiments, among the cations of chromium in the glass the amount of chromium(VI) or Cr is extremely low, for example such that the molar ratio of the amount chromium(VI) to the total amount of chromium cations in the glass is less than 0.05:1 or less than 0.01:1 or even less than 0.001:1. The reason is that chromium(VI) is highly toxic and should be avoided. In order to achieve this, chromium(VI) based raw materials such as CrOmay be avoided during production of the glass. Raw materials such as potassium dichromate or sodium dichromate should also be avoided for this reason. Previously, such materials have been frequently used because they provide particularly good solubility and meltability properties. Furthermore, the glass should not be produced under oxidizing conditions. Therefore, oxygen bubbling may be avoided. Moreover, NOmay be avoided as well.
However, a drawback of producing the glass under reducing conditions is that the melting process is particularly difficult. Black glasses are generally very difficult to melt. Reducing conditions further deteriorate the meltability. In particular, components such as cations of nickel and chromium are problematic in this respect. Moreover, cations of chromium other than chromium(VI), such as for example chromium(III), are particularly difficult in this respect. Therefore, it is highly complicated to produce such glasses. However, it was now found that glasses can be produced particularly well, even under reducing conditions, if there is a large excess of cations of sodium of potassium over cations of nickel and chromium. In the glasses provided according to the present invention, the ratio of the sum of the molar proportions of cations of sodium and potassium to the sum of the molar proportions of cations of nickel and chromium is in a range of from 70:1 to 200:1, such as from 75:1 to 180:1, from 80:1 to 160:1, from 90:1 to 150:1, from 100:1 to 145:1, from 100:1 to 140:1, or from 110:1 to 140:1. The ratio of the sum of the molar proportions of cations of sodium and potassium to the sum of the molar proportions of cations of nickel and chromium may, for example, be at least 70:1, at least 75:1, at least 80:1, at least 90:1, at least 100:1, or at least 110:1. The ratio of the sum of the molar proportions of cations of sodium and potassium to the sum of the molar proportions of cations of nickel and chromium may, for example, be at most 200:1, at most 180:1, at most 160:1, at most 150:1, at most 145:1, or at most 140:1.
Surprisingly it was found that it is advantageous for even further improving the spectral properties of the glass if cations of nickel and chromium are present in certain molar ratio as compared to the amount of cations of cobalt. In particular, the sum of the molar proportions of cations of nickel and chromium may be higher than the molar proportion of cations of cobalt. However, the excess of cations of nickel and chromium is may be not chosen to be very high. Rather, it was found that desired spectral properties can be achieved within a certain range. In some embodiments, the ratio of the sum of the molar proportions of cations of nickel and chromium to the molar proportion of cations of cobalt is in a range of from >1:1 to 5:1, such as from 1.2:1 to 4:1, from 1.5:1 to 3.5:1, from 1.75:1 to 3.25:1, from 2:1 to 3:1, from 2.2:1 to 3:1, or from 2.2:1 to 2.65:1. The ratio of the sum of the molar proportions of cations of nickel and chromium to the molar proportion of cations of cobalt may, for example, be higher than 1:1 such as at least 1.2:1, at least 1.5:1, at least 1.75:1, at least 2:1, or at least 2.2:1. The ratio of the sum of the molar proportions of cations of nickel and chromium to the molar proportion of cations of cobalt may, for example, be at most 5:1, at most 4:1, at most 3.5:1, at most 3.25:1, at most 3:1, or at most 2.65:1.
The glasses provided according to the present invention may comprise other coloring components for fine tuning the spectral properties. However, this is not necessary. It is sufficient if cations of cobalt and cations of one of nickel and chromium are present. In some embodiments, the glasses provided according to the present invention additionally comprise cations of manganese in an amount of from 0 to 0.5 cat.-%, for example from 0.1 to 0.4 cat.-% or from 0.15 to 0.35 cat.-%. The amount of cations manganese may, for example, be at most 0.5 cat.-%, at most 0.4 cat.-%, or at most 0.35 cat.-%. The glasses provided according to the present invention may be free of cations of manganese. However, in some embodiments the amount of cations of manganese may, for example, be at least 0.1 cat.-%, or at least 0.15 cat.-%. However, the amount of cations of manganese may be smaller as compared to the sum of the amounts of cations of nickel and chromium. In some embodiments, the ratio of the molar proportion of cations of manganese to the sum of the molar proportions of cations of nickel and chromium is in a range of from 0:1 to <1:1, for example from 0:1 to 0.95:1, from 0.5:1 to 0.9:1 or from 0.6:1 to 0.9:1. The ratio of the molar proportion of cations of manganese to the sum of the molar proportions of cations of nickel and chromium may, for example, be at least 0.5:1, at least 0.6:1, or at least 0.9:1. The ratio of the molar proportion of cations of manganese to the sum of the molar proportions of cations of nickel and chromium may, for example, be lower than 1:1 such as at most 0.95:1, or at most 0.9:1.
In some embodiments, the amount of cations of lead in the glasses provided according to the present invention is from 0 to 1 cat.-%, such as less than 0.5 cat.-% or less than 0.1 cat.-%. In some embodiments, the glasses provided according to the present invention are free of cations of lead.
In some embodiments, the amount of cations of zirconium in the glasses provided according to the present invention is from 0 to 1 cat.-%, such as less than 0.5 cat.-% or less than 0.1 cat.-%. In some embodiments, the glasses provided according to the present invention are free of cations of zirconium.
In some embodiments, the amount of cations of strontium in the glasses provided according to the present invention is from 0 to 1 cat.-%, such as less than 0.5 cat.-% or less than 0.1 cat.-%. In some embodiments, the glasses provided according to the present invention are free of cations of strontium.
In some embodiments, the amount of cations of calcium in the glasses provided according to the present invention is from 0 to 1 cat.-%, such as less than 0.5 cat.-% or less than 0.1 cat.-%. In some embodiments, the glasses provided according to the present invention are free of cations of calcium.
In some embodiments, the amount of cations of iron in the glasses provided according to the present invention is from 0 to 1 cat.-%, such as less than 0.5 cat.-% or less than 0.1 cat.-%. In some embodiments, the glasses provided according to the present invention are free of cations of iron.
When in this description it is mentioned that the glasses are free of cations of a component or that they do not contain cations of a certain component, then this means that cations of this component are only allowed to be present as an impurity in the glasses. This means that it is not added in substantial amounts. Not substantial amounts are amounts of less than 300 ppm (based molar proportion of cations), such as less than 200 ppm (based molar proportion of cations), less than 100 ppm (based molar proportion of cations), less than 50 ppm (based molar proportion of cations), or less than 10 ppm (based molar proportion of cations).
In some embodiments, cations of silicon, sodium, potassium and cobalt and one or more of cations of nickel and chromium and one or more of cations of aluminum, boron, barium, zinc, lanthanum, titanium, cerium and manganese represent at least 90 cat.-%, such as at least 95 cat.-%, at least 98 cat.-%, to at least 99 cat.-%, to at least 99.5 cat.-%, or at least 99.9 cat.-% of the total amount of cations in the glass.
The glass provided according to the present invention may be used as an optical window for LiDAR systems. Such optical windows provide protection against environmental impacts for the opto-electronic components of the system. Depending on the type of LiDAR system, such optical windows may be planar or curved. Commonly used are also spinning LiDAR systems in which emitter and detector rotate within a typically stationary ring window.
LiDAR systems generally work by emitting laser light in the NIR spectrum, in particular having wavelengths of more than 780 nm. Therefore, it is important for such applications that the glass has a high transmission in the NIR range in order for the laser light to pass. On the other hand, the glass should have a low transmission for visible light in order to prevent visibility of structures positioned behind the glass.
There have been attempts to achieve such optical properties by a coating that blocks transmission of visible light. However, coatings are a safety risk, in particular in the automotive sector. Furthermore, coating of round-shaped glass sheets is complicated and associated with high costs due to the angular dependence of blocking of light. Many coatings are also less effective. Therefore, it would be advantageous to achieve the desired properties of low transmission in the visible range and high transmission in the NIR range with the glass itself, i.e. without the need for any light blocking coatings.
Furthermore, a neutrally black color impression is often desired but not achieved sufficiently by the prior art. In particular, it has been desired to achieve a neutrally black color impression at a comparably low glass thickness in order to lower the weight of the glass products.
A further lowering of weight can also be achieved by using low density glasses. In some embodiments, the glasses provided according to the present invention have a low density.
d
d
The refractive index nof the glasses provided according to the present invention may be in a range of from 1.50 to 1.55, for example from 1.50 to 1.53 or from 1.51 to 1.52. The refractive index nmay be determined using reference glasses without coloring components.
The glasses provided according to the present invention are highly advantageous in several aspects. They have advantageous spectral properties such as low transmission in the visible range, high transmission in the NIR range and a neutrally black color impression. Furthermore, they have a very good chemical resistance and climate resistance which makes them particularly useful for outdoor applications. Moreover, the glasses have a good meltability and they can be processed well by hot forming processes. The latter is due to the long viscosity profile of the glasses. This means that the viscosity does not vary so much with differing temperature. Glasses having a long viscosity profile are advantageous for hot forming because these glasses have a greater temperature range at which they can be processed. Thus, the process does not have to be aimed at the fastest possible processing of the still hot glass.
d
d
d
The terms “transmission” and “transmittance” are used interchangeably within the present disclosure. When the terms “transmission” or “transmittance” are mentioned in the present disclosure, this refers to the total transmission or total transmittance if not indicated otherwise, i.e. the transmission as measured taking into account both absorptive losses and reflective losses. If, on the other hand the internal transmittance is addressed, this is clearly indicated herein by referring to the “internal transmittance” or “internal transmission”. The internal transmission is determined as the ratio of the total transmission and the Pvalue. The Pvalue represents a measure of reflective losses and can easily be calculated based on the refractive index nusing the following formula.
<math overflow="scroll"><mrow><msub><mi>P</mi><mi>d</mi></msub><mo>=</mo><mfrac><mrow><mn>2</mn><mo>·</mo><msub><mi>n</mi><mi>d</mi></msub></mrow><mrow><msubsup><mi>n</mi><mi>d</mi><mn>2</mn></msubsup><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></math>
d
d
For example, for a glass having a refractive index nof 1.515, the Pvalue is about 0.92. This means that an internal transmission of 100% would result in a total transmission of about 92%. Notably, reflective losses may be reduced using anti-reflective coatings (AR coatings) so that the total transmission may be increased beyond 92%. However, within the present disclosure the terms “transmission” or “transmittance” refer to the total transmission of glass samples without any AR coatings.
d
In some embodiments, the glasses provided according to the present invention have Pvalue in the range of from 0.911 to 0.925, such as from 0.915 to 0.924 or from 0.920 to 0.923.
As described previously, the glass provided according to the present invention has a low transmission in the visible range.
In some embodiments, the glass provided according to the present invention at a thickness of 2 mm has an average transmission for light of a wavelength in the range of from 250 nm to 700 nm of at most 15%, such as at most 12%, at most 10%, at most 7.5%, at most 6%, at most 5%, at most 4%, at most 3%, at most 2%, or at most 1%. In order to determine this average transmission, the transmission is measured for any wavelength starting from 250 nm in increments of 1 nm until 700 nm. Thus, transmission is measured at 250 nm, 251 nm, 252 nm, . . . , 698 nm, 699 nm and 700 nm. In total, the transmission is determined at 451 different wavelengths from 250 nm to 700 nm. The average transmission in the range of from 250 nm to 700 nm is then determined as the mean value of the 451 transmission values that have been measured. The glass provided according to the present invention at a thickness of 2 mm may, for example, have an average transmission for light of a wavelength in the range of from 250 nm to 700 nm of at least 0.1%, at least 0.2%, at least 0.5% or at least 0.75%.
In some embodiments, the average transmission in smaller wavelength regions within the range of from 250 nm to 700 nm is low. For example, at a sample thickness of 2 mm, the average transmission in any subrange of 20 nm width within the range of from 250 nm to 700 nm may be at most 35%, such as at most 30%, at most 25%, at most 20%, or at most 15%. This means that the average transmission may be at most 35%, at most 30%, at most 25%, at most 20%, or at most 15% in the subrange of from 250 nm to 270 nm, in the subrange of from 251 nm to 271 nm, in the subrange of from 252 nm to 272 nm, . . . , in the subrange of from 678 nm to 698 nm, in the subrange of from 679 nm to 699 nm and in the subrange of from 680 nm to 700 nm. In order to determine this average transmission, the transmission is measured for any wavelength starting from 250 nm in increments of 1 nm until 700 nm. Thus, transmission is measured at 250 nm, 251 nm, 252 nm, . . . , 698 nm, 699 nm and 700 nm. In total, the transmission is determined at 451 different wavelengths from 250 nm to 700 nm. The average transmission is then determined for each of the 431 subranges indicated above as the mean value of the 21 transmission values in each of the subranges. At a sample thickness of 2 mm, the average transmission in any subrange of 20 nm width within the range of from 250 nm to 700 nm may, for example, be at least 1%, at least 2% or at least 5%.
In some embodiments, the maximum transmission in the wavelength range of from 250 nm to 700 nm is comparably low. In some embodiments, the glass provided according to the present invention at a thickness of 2 mm has a maximum transmission for light of a wavelength in the range of from 250 nm to 700 nm of at most 45%, such as at most 40%, at most 35%, at most 30%, at most 25%, at most 20%, or at most 15%. In order to determine the maximum transmission, the transmission is measured for any wavelength starting from 250 nm in increments of 1 nm until 700 nm. Thus, transmission is measured at 250 nm, 251 nm, 252 nm, . . . , 698 nm, 699 nm and 700 nm. In total, the transmission is determined at 451 different wavelengths from 250 nm to 700 nm. The maximum transmission in the range of from 250 nm to 700 nm is then determined as the maximum value of the 451 transmission values that have been measured. The glass provided according to the present invention at a thickness of 2 mm may, for example, have a maximum transmission for light of a wavelength in the range of from 250 nm to 700 nm of at least 1%, at least 2%, at least 5%, or even at least 10%.
The glasses provided according to the present invention do not only have a low transmission in the visible wavelength range but also a high transmission in the NIR wavelength range. Particularly relevant is the transmission in a range of from 850 nm to 950 nm.
In some embodiments, the glass provided according to the present invention at a thickness of 2 mm has an average transmission for light of a wavelength in the range of from 850 nm to 950 nm of at least 40%, such as at least 45%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, or at least 90%. In order to determine this average transmission, the transmission is measured for any wavelength starting from 850 nm in increments of 1 nm until 950 nm. Thus, transmission is measured at 850 nm, 851 nm, 852 nm, . . . , 948 nm, 949 nm and 950 nm. In total, the transmission is determined at 101 different wavelengths from 850 nm to 950 nm. The average transmission in the range of from 850 nm to 950 nm is then determined as the mean value of the 101 transmission values that have been measured. The glass provided according to the present invention at a thickness of 2 mm may, for example, have an average transmission for light of a wavelength in the range of from 850 nm to 950 nm of at most 92%, at most 91.5%, at most 91.25% or at most 91.2%.
In some embodiments, the average transmission in smaller wavelength regions within the range of from 850 nm to 950 nm is high. For example, at a sample thickness of 2 mm the average transmission in any subrange of 20 nm width within the range of from 850 nm to 950 nm may be at least 40%, such as at least 45%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, or at least 90%. This means that the average transmission may be at least 40%, such as at least 45%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, or at least 90% in the subrange of from 850 nm to 870 nm, in the subrange of from 851 nm to 871 nm, in the subrange of from 852 nm to 872 nm, . . . , in the subrange of from 928 nm to 948 nm, in the subrange of from 929 nm to 949 nm and in the subrange of from 930 nm to 950 nm. In order to determine this average transmission, the transmission is measured for any wavelength starting from 850 nm in increments of 1 nm until 950 nm. Thus, transmission is measured at 850 nm, 851 nm, 852 nm, . . . , 948 nm, 949 nm and 950 nm. In total, the transmission is determined at 101 different wavelengths from 850 nm to 950 nm. The average transmission is then determined for each of the 81 subranges indicated above as the mean value of the 21 transmission values in each of the subranges. At a sample thickness of 2 mm the average transmission in any subrange of 20 nm width within the range of from 850 nm to 950 nm may, for example, be at most 92%, at most 91.5%, at most 91.1% or at most 91%.
In some embodiments, the minimum transmission in the wavelength range of from 850 nm to 950 nm is comparably high. In some embodiments, the glass provided according to the present invention at a thickness of 2 mm has a minimum transmission for light of a wavelength in the range of from 850 nm to 950 nm of at least 35%, such as at least 40%, at least 45%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, or at least 90%. In order to determine the minimum transmission, the transmission is measured for any wavelength starting from 850 nm in increments of 1 nm until 950 nm. Thus, transmission is measured at 850 nm, 851 nm, 852 nm, . . . , 948 nm, 949 nm and 950 nm. In total, the transmission is determined at 101 different wavelengths from 850 nm to 950 nm. The minimum transmission in the range of from 850 nm to 950 nm is then determined as the minimum value of the 101 transmission values that have been measured. The glass provided according to the present invention at a thickness of 2 mm may, for example, have a minimum transmission for light of a wavelength in the range of from 800 nm to 900 nm of at most 92%, at most 91%, at most 90.9% or at most 90.8%.
As described previously, the glass provided according to the present invention has a low transmission in the visible range.
In some embodiments, the glass provided according to the present invention at a thickness of 4 mm has an average transmission for light of a wavelength in the range of from 250 nm to 700 nm of at most 4%, such as at most 3.5%, at most 3%, at most 2.5%, at most 2%, at most 1.5%, at most 1.25%, at most 1%, at most 0.75%, or at most 0.5%. In order to determine this average transmission, the transmission is measured for any wavelength starting from 250 nm in increments of 1 nm until 700 nm. Thus, transmission is measured at 250 nm, 251 nm, 252 nm, . . . , 698 nm, 699 nm and 700 nm. In total, the transmission is determined at 451 different wavelengths from 250 nm to 700 nm. The average transmission in the range of from 250 nm to 700 nm is then determined as the mean value of the 451 transmission values that have been measured. The glass provided according to the present invention at a thickness of 4 mm may, for example, have an average transmission for light of a wavelength in the range of from 250 nm to 700 nm of at least 0.01%, at least 0.02%, at least 0.05% or at least 0.1%.
In some embodiments, the average transmission in smaller wavelength regions within the range of from 250 nm to 700 nm is low. For example, at a sample thickness of 4 mm the average transmission in any subrange of 20 nm width within the range of from 250 nm to 700 nm may be at most 14%, such as at most 13%, at most 12%, at most 10%, at most 8% at most 6%, or at most 5%. This means that the average transmission may be at most 14%, at most 13%, at most 12%, at most 10%, at most 8% at most 6%, or at most 5% in the subrange of from 250 nm to 270 nm, in the subrange of from 251 nm to 271 nm, in the subrange of from 252 nm to 272 nm, . . . , in the subrange of from 678 nm to 698 nm, in the subrange of from 679 nm to 699 nm and in the subrange of from 680 nm to 700 nm. In order to determine this average transmission, the transmission is measured for any wavelength starting from 250 nm in increments of 1 nm until 700 nm. Thus, transmission is measured at 250 nm, 251 nm, 252 nm, . . . , 698 nm, 699 nm and 700 nm. In total, the transmission is determined at 451 different wavelengths from 250 nm to 700 nm. The average transmission is then determined for each of the 431 subranges indicated above as the mean value of the 21 transmission values in each of the subranges. At a sample thickness of 4 mm the average transmission in any subrange of 20 nm width within the range of from 250 nm to 700 nm may, for example, be at least 0.1%, at least 0.2% or at least 1%.
In some embodiments, the maximum transmission in the wavelength range of from 250 nm to 700 nm is comparably low. In some embodiments, the glass provided according to the present invention at a thickness of 4 mm has a maximum transmission for light of a wavelength in the range of from 250 nm to 700 nm of at most 23%, such as at most 22%, at most 20%, at most 15%, at most 14%, at most 13%, or at most 10%. In order to determine the maximum transmission, the transmission is measured for any wavelength starting from 250 nm in increments of 1 nm until 700 nm. Thus, transmission is measured at 250 nm, 251 nm, 252 nm, . . . , 698 nm, 699 nm and 700 nm. In total, the transmission is determined at 451 different wavelengths from 250 nm to 700 nm. The maximum transmission in the range of from 250 nm to 700 nm is then determined as the maximum value of the 451 transmission values that have been measured. The glass provided according to the present invention at a thickness of 4 mm may, for example, have a maximum transmission for light of a wavelength in the range of from 250 nm to 700 nm of at least 0.5%, at least 1%, at least 2%, or even at least 4%.
The glasses provided according to the present invention do not only have a low transmission in the visible wavelength range but also a high transmission in the NIR wavelength range. Particularly relevant is the transmission in a range of from 850 nm to 950 nm.
In some embodiments, the glass provided according to the present invention at a thickness of 4 mm has an average transmission for light of a wavelength in the range of from 850 nm to 950 nm of at least 20%, such as at least 25%, at least 30%, at least 35%, at least 40%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, or at least 90%. In order to determine this average transmission, the transmission is measured for any wavelength starting from 850 nm in increments of 1 nm until 950 nm. Thus, transmission is measured at 850 nm, 851 nm, 852 nm, . . . , 948 nm, 949 nm and 950 nm. In total, the transmission is determined at 101 different wavelengths from 850 nm to 950 nm. The average transmission in the range of from 850 nm to 950 nm is then determined as the mean value of the 101 transmission values that have been measured. The glass provided according to the present invention at a thickness of 4 mm may, for example, have an average transmission for light of a wavelength in the range of from 850 nm to 950 nm of at most 92%, at most 91%, at most 90.5% or at most 90.4%.
In some embodiments, the average transmission in smaller wavelength regions within the range of from 850 nm to 950 nm is high. For example, at a sample thickness of 4 mm the average transmission in any subrange of 20 nm width within the range of from 850 nm to 950 nm may be at least 20%, such as at least 25%, at least 30%, at least 35%, at least 40%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, or at least 90%. This means that the average transmission may be at least 20%, such as at least 25%, at least 30%, at least 35%, at least 40%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, or at least 90% in the subrange of from 850 nm to 870 nm, in the subrange of from 851 nm to 871 nm, in the subrange of from 852 nm to 872 nm, . . . , in the subrange of from 928 nm to 948 nm, in the subrange of from 929 nm to 949 nm and in the subrange of from 930 nm to 950 nm. In order to determine this average transmission, the transmission is measured for any wavelength starting from 850 nm in increments of 1 nm until 950 nm. Thus, transmission is measured at 850 nm, 851 nm, 852 nm, . . . , 948 nm, 949 nm and 950 nm. In total, the transmission is determined at 101 different wavelengths from 850 nm to 950 nm. The average transmission is then determined for each of the 81 subranges indicated above as the mean value of the 21 transmission values in each of the subranges. At a sample thickness of 4 mm the average transmission in any subrange of 20 nm width within the range of from 850 nm to 950 nm may, for example, be at most 92%, at most 91%, at most 90% or at most 89.9%.
In some embodiments, the minimum transmission in the wavelength range of from 850 nm to 950 nm is comparably high. In some embodiments, the glass provided according to the present invention at a thickness of 4 mm has a minimum transmission for light of a wavelength in the range of from 850 nm to 950 nm of at least 15%, such as at least 20%, at least 25%, at least 30%, at least 35%, at least 40%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, or at least 90%. In order to determine the minimum transmission, the transmission is measured for any wavelength starting from 850 nm in increments of 1 nm until 950 nm. Thus, transmission is measured at 850 nm, 851 nm, 852 nm, . . . , 948 nm, 949 nm and 950 nm. In total, the transmission is determined at 101 different wavelengths from 850 nm to 950 nm. The minimum transmission in the range of from 850 nm to 950 nm is then determined as the minimum value of the 101 transmission values that have been measured. The glass provided according to the present invention at a thickness of 4 mm may, for example, have a minimum transmission for light of a wavelength in the range of from 800 nm to 900 nm of at most 92%, at most 91%, at most 90% or at most 89.7%.
As described previously, the glasses provided according to the present invention have a high transmission in the NIR range and a low transmission in the visible range.
In some embodiments, at a sample thickness of 2 mm the ratio of the average transmission for light of a wavelength in the range of from 850 nm to 950 nm and the average transmission for light of a wavelength in the range of from 250 nm to 700 nm is in the range of from 6:1 to 200:1, such as from 7:1 to 150:1, from 8:1 to 100:1, from 10:1 to 80:1, from 12:1 to 60:1, from 15:1 to 50:1, from 18:1 to 40:1, or from 20:1 to 30:1.
In some embodiments, at a sample thickness of 2 mm the ratio of the lowest average transmission of all subranges of 20 nm width within the range of from 850 nm to 950 nm and the highest average transmission of all subranges of 20 nm width within the range of from 250 nm to 700 nm is in the range of from 2.5:1 to 20:1, such as from 2.6:1 to 15:1, from 2.7:1 to 10:1, from 2.8:1 to 9:1, from 2.9:1 to 8:1, from 3.0:1 to 7:1, from 3.1:1 to 6:1, from 3.2:1 to 5:1, from 3.3:1 to 4:1, or from 3.4:1 to 3.5:1.
In some embodiments, at a sample thickness of 2 mm the ratio of the minimum transmission for light of a wavelength in the range of from 850 nm to 950 nm and the maximum transmission for light of a wavelength in the range of from 250 nm to 700 nm is in the range of from 1.9:1 to 15:1, such as from 2.0:1 to 10:1, from 2.1:1 to 9:1, from 2.2:1 to 8:1, from 2.3:1 to 7:1, from 2.4:1 to 6:1, from 2.5:1 to 5:1, from 2.6:1 to 4:1, from 2.7:1 to 3.5:1, or from 2.8:1 to 3:1.
In some embodiments, at a sample thickness of 4 mm the ratio of the average transmission for light of a wavelength in the range of from 850 nm to 950 nm and the average transmission for light of a wavelength in the range of from 250 nm to 700 nm is in the range of from 20:1 to 400:1, such as from 25:1 to 300:1, from 30:1 to 250:1, from 40:1 to 200:1, from 50:1 to 150:1, from 60:1 to 140:1, from 70:1 to 130:1, or from 80:1 to 120:1.
In some embodiments, at a sample thickness of 4 mm the ratio of the lowest average transmission of all subranges of 20 nm width within the range of from 850 nm to 950 nm and the highest average transmission of all subranges of 20 nm width within the range of from 250 nm to 700 nm is in the range of from 6:1 to 50:1, such as from 6.5:1 to 40:1, from 7:1 to 30:1, from 7.5:1 to 25:1, from 8:1 to 20:1, from 8.5:1 to 18:1, from 9:1 to 15:1, from 9.5:1 to 14:1, from 10:1 to 13:1, or from 10.5:1 to 12:1.
In some embodiments, at a sample thickness of 4 mm the ratio of the minimum transmission for light of a wavelength in the range of from 850 nm to 950 nm and the maximum transmission for light of a wavelength in the range of from 250 nm to 700 nm is in the range of from 3.5:1 to 15:1, such as from 3.75:1 to 12:1, from 4.0:1 to 10:1, from 4.25:1 to 9:1, from 4.5:1 to 8:1, from 4.75:1 to 7.5:1, from 5.0:1 to 7:1, from 5.25:1 to 6.75:1, from 5.5:1 to 6.5:1, or from 5.75:1 to 6.25:1.
In some embodiments, the glasses provided according to the present invention have an internal transmittance at a wavelength of 905 nm of more than 95%, such as more than 96%, more than 97%, or more than 98% at a sample thickness of 2 mm or at a sample thickness of 4 mm.
As described previously, the glass provided according to the present invention has a low internal transmission in the visible range.
d
In some embodiments, the glass provided according to the present invention at a thickness of 2 mm has an average internal transmission for light of a wavelength in the range of from 250 nm to 700 nm of at most 15%, such as at most 12%, at most 11%, at most 10%, at most 7.5%, at most 6%, at most 5%, at most 4%, at most 3%, at most 2%, or at most 1%. In order to determine this average internal transmission, the transmission is measured for any wavelength starting from 250 nm in increments of 1 nm until 700 nm. Thus, transmission is measured at 250 nm, 251 nm, 252 nm, . . . , 698 nm, 699 nm and 700 nm. In total, the transmission is determined at 451 different wavelengths from 250 nm to 700 nm. The internal transmission is determined as a ratio of the transmission as measured and the Pvalue as described previously. The average internal transmission in the range of from 250 nm to 700 nm is then determined as the mean value of the 451 internal transmission values that have been determined. The glass provided according to the present invention at a thickness of 2 mm may, for example, have an average internal transmission for light of a wavelength in the range of from 250 nm to 700 nm of at least 0.1%, at least 0.2%, at least 0.5% or at least 0.75%.
d
In some embodiments, the average internal transmission in smaller wavelength regions within the range of from 250 nm to 700 nm is low. For example, at a sample thickness of 2 mm the average internal transmission in any subrange of 20 nm width within the range of from 250 nm to 700 nm may be at most 39%, such as at most 35%, at most 30%, at most 25%, at most 20%, or at most 15%. This means that the average internal transmission may be at most 39%, at most 35%, at most 30%, at most 25%, at most 20%, or at most 15% in the subrange of from 250 nm to 270 nm, in the subrange of from 251 nm to 271 nm, in the subrange of from 252 nm to 272 nm, . . . , in the subrange of from 678 nm to 698 nm, in the subrange of from 679 nm to 699 nm and in the subrange of from 680 nm to 700 nm. In order to determine this average internal transmission, the transmission is measured for any wavelength starting from 250 nm in increments of 1 nm until 700 nm. Thus, transmission is measured at 250 nm, 251 nm, 252 nm, . . . , 698 nm, 699 nm and 700 nm. In total, the transmission is determined at 451 different wavelengths from 250 nm to 700 nm. The internal transmission is determined as ratio of the transmission as measured and the Pvalue as described above. The average internal transmission is then determined for each of the 431 subranges indicated above as the mean value of the 21 internal transmission values in each of the subranges. At a sample thickness of 2 mm the average internal transmission in any subrange of 20 nm width within the range of from 250 nm to 700 nm may, for example, be at least 1%, at least 2%, at least 5% or at least 10%.
d
In some embodiments, the maximum internal transmission in the wavelength range of from 250 nm to 700 nm is comparably low. In some embodiments, the glass provided according to the present invention at a thickness of 2 mm has a maximum internal transmission for light of a wavelength in the range of from 250 nm to 700 nm of at most 50%, such as at most 45%, at most 40%, at most 35%, at most 30%, at most 25%, at most 20%, or at most 15%. In order to determine the maximum internal transmission, the transmission is measured for any wavelength starting from 250 nm in increments of 1 nm until 700 nm. Thus, transmission is measured at 250 nm, 251 nm, 252 nm, . . . , 698 nm, 699 nm and 700 nm. In total, the transmission is determined at 451 different wavelengths from 250 nm to 700 nm. The internal transmission is determined as ratio of the transmission as measured and the Pvalue as described above. The maximum internal transmission in the range of from 250 nm to 700 nm is then determined as the maximum value of the 451 internal transmission values that have been determined. The glass provided according to the present invention at a thickness of 2 mm may, for example, have a maximum internal transmission for light of a wavelength in the range of from 250 nm to 700 nm of at least 1%, at least 2%, at least 5%, or even at least 10%.
The glasses provided according to the present invention do not only have a low internal transmission in the visible wavelength range but also a high internal transmission in the NIR wavelength range. Particularly relevant is the transmission in a range of from 850 nm to 950 nm.
d
In some embodiments, the glass provided according to the present invention at a thickness of 2 mm has an average internal transmission for light of a wavelength in the range of from 850 nm to 950 nm of at least 45%,such as at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 96%, at least 97%, at least 98%, at least 98.5%, or at least 99%. In order to determine this average internal transmission, the transmission is measured for any wavelength starting from 850 nm in increments of 1 nm until 950 nm. Thus, transmission is measured at 850 nm, 851 nm, 852 nm, . . . , 948 nm, 949 nm and 950 nm. In total, the transmission is determined at 101 different wavelengths from 850 nm to 950 nm. The internal transmission is determined as ratio of the transmission as measured and the Pvalue as described above. The average internal transmission in the range of from 850 nm to 950 nm is then determined as the mean value of the 101 internal transmission values that have been determined. The glass provided according to the present invention at a thickness of 2 mm may, for example, have an average internal transmission for light of a wavelength in the range of from 850 nm to 950 nm of at most 99.9%, at most 99.5% or at most 99.25%.
d
In some embodiments, the average internal transmission in smaller wavelength regions within the range of from 850 nm to 950 nm is high. For example, at a sample thickness of 2 mm the average internal transmission in any subrange of 20 nm width within the range of from 850 nm to 950 nm may be at least 40%, such as at least 45%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 96%, at least 97%, at least 98%, or at least 98.5%. This means that the average internal transmission may be at least 40%, at least 45%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 96%, at least 97%, at least 98%, or at least 98.5% in the subrange of from 850 nm to 870 nm, in the subrange of from 851 nm to 871 nm, in the subrange of from 852 nm to 872 nm, . . . , in the subrange of from 928 nm to 948 nm, in the subrange of from 929 nm to 949 nm and in the subrange of from 930 nm to 950 nm. In order to determine this average internal transmission, the transmission is measured for any wavelength starting from 850 nm in increments of 1 nm until 950 nm. Thus, transmission is measured at 850 nm, 851 nm, 852 nm, . . . , 948 nm, 949 nm and 950 nm. In total, the transmission is determined at 101 different wavelengths from 850 nm to 950 nm. The internal transmission is determined as ratio of the transmission as measured and the Pvalue as described above. The average internal transmission is then determined for each of the 81 subranges indicated above as the mean value of the 21 internal transmission values in each of the subranges. At a sample thickness of 2 mm the average internal transmission in any subrange of 20 nm width within the range of from 850 nm to 950 nm may, for example, be at most 99.9%, at most 99.5%, at most 99.1% or at most 99%.
d
In some embodiments, the minimum internal transmission in the wavelength range of from 850 nm to 950 nm is comparably high. In some embodiments, the glass provided according to the present invention at a thickness of 2 mm has a minimum internal transmission for light of a wavelength in the range of from 850 nm to 950 nm of at least 35%, such as at least 40%, at least 45%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 96%, at least 97%, at least 98%, or at least 98.5%. In order to determine the minimum internal transmission, the transmission is measured for any wavelength starting from 850 nm in increments of 1 nm until 950 nm. Thus, transmission is measured at 850 nm, 851 nm, 852 nm, . . . , 948 nm, 949 nm and 950 nm. In total, the transmission is determined at 101 different wavelengths from 850 nm to 950 nm. The internal transmission is determined as ratio of the transmission as measured and the Pvalue as described above. The minimum internal transmission in the range of from 850 nm to 950 nm is then determined as the minimum value of the 101 internal transmission values that have been determined. The glass provided according to the present invention at a thickness of 2 mm may, for example, have a minimum internal transmission for light of a wavelength in the range of from 800 nm to 900 nm of at most 99.9%, at most 99.5%, at most 99.1% or at most 99%.
As described previously, the glass provided according to the present invention has a low internal transmission in the visible range.
d
In some embodiments, the glass provided according to the present invention at a thickness of 4 mm has an average internal transmission for light of a wavelength in the range of from 250 nm to 700 nm of at most 4%, such as at most 3.5%, at most 3%, at most 2.5%, at most 2%, at most 1.5%, at most 1.25%, at most 1%, at most 0.75%, or at most 0.5%. In order to determine this average internal transmission, the transmission is measured for any wavelength starting from 250 nm in increments of 1 nm until 700 nm. Thus, transmission is measured at 250 nm, 251 nm, 252 nm, . . . , 698 nm, 699 nm and 700 nm. In total, the transmission is determined at 451 different wavelengths from 250 nm to 700 nm. The internal transmission is determined as ratio of the transmission as measured and the Pvalue as described above. The average internal transmission in the range of from 250 nm to 700 nm is then determined as the mean value of the 451 internal transmission values that have been determined. The glass provided according to the present invention at a thickness of 4 mm may, for example, have an average internal transmission for light of a wavelength in the range of from 250 nm to 700 nm of at least 0.01%, at least 0.02%, at least 0.05% or at least 0.1%.
d
In some embodiments, the average internal transmission in smaller wavelength regions within the range of from 250 nm to 700 nm is low. For example, at a sample thickness of 4 mm the average internal transmission in any subrange of 20 nm width within the range of from 250 nm to 700 nm may be at most 14%, such as at most 13%, at most 12%, at most 10%, at most 8%, at most 6%, or at most 5%. This means that the average internal transmission may be at most 14%, such as at most 13%, at most 12%, at most 10%, at most 8% at most 6%, or at most 5% in the subrange of from 250 nm to 270 nm, in the subrange of from 251 nm to 271 nm, in the subrange of from 252 nm to 272 nm, . . . , in the subrange of from 678 nm to 698 nm, in the subrange of from 679 nm to 699 nm and in the subrange of from 680 nm to 700 nm. In order to determine this average internal transmission, the transmission is measured for any wavelength starting from 250 nm in increments of 1 nm until 700 nm. Thus, transmission is measured at 250 nm, 251 nm, 252 nm, . . . , 698 nm, 699 nm and 700 nm. In total, the transmission is determined at 451 different wavelengths from 250 nm to 700 nm. The internal transmission is determined as ratio of the transmission as measured and the Pvalue as described above. The average internal transmission is then determined for each of the 431 subranges indicated above as the mean value of the 21 internal transmission values in each of the subranges. At a sample thickness of 4 mm the average internal transmission in any subrange of 20 nm width within the range of from 250 nm to 700 nm may, for example, be at least 0.1%, at least 0.2%, at least 1%, at least 2% or at least 3%.
d
In some embodiments, the maximum internal transmission in the wavelength range of from 250 nm to 700 nm is comparably low. In some embodiments, the glass provided according to the present invention at a thickness of 4 mm has a maximum internal transmission for light of a wavelength in the range of from 250 nm to 700 nm of at most 25%, such as at most 24%, at most 23%, at most 22%, at most 20%, at most 15%, at most 14%, at most 13%, or at most 10%. In order to determine the maximum internal transmission, the transmission is measured for any wavelength starting from 250 nm in increments of 1 nm until 700 nm. Thus, transmission is measured at 250 nm, 251 nm, 252 nm, . . . , 698 nm, 699 nm and 700 nm. In total, the transmission is determined at 451 different wavelengths from 250 nm to 700 nm. The internal transmission is determined as ratio of the transmission as measured and the Pvalue as described above. The maximum internal transmission in the range of from 250 nm to 700 nm is then determined as the maximum value of the 451 internal transmission values that have been determined. The glass provided according to the present invention at a thickness of 4 mm may, for example, have a maximum internal transmission for light of a wavelength in the range of from 250 nm to 700 nm of at least 0.5%, at least 1%, at least 2%, at least 4% or even at least 5%.
The glasses provided according to the present invention do not only have a low internal transmission in the visible wavelength range but also a high internal transmission in the NIR wavelength range. Particularly relevant is the internal transmission in a range of from 850 nm to 950 nm.
d
In some embodiments, the glass provided according to the present invention at a thickness of 4 mm has an average internal transmission for light of a wavelength in the range of from 850 nm to 950 nm of at least 20%, such as at least 25%, at least 30%, at least 35%, at least 40%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 96%, at least 97%, or at least 98%. In order to determine this average internal transmission, the transmission is measured for any wavelength starting from 850 nm in increments of 1 nm until 950 nm. Thus, transmission is measured at 850 nm, 851 nm, 852 nm, . . . , 948 nm, 949 nm and 950 nm. In total, the transmission is determined at 101 different wavelengths from 850 nm to 950 nm. The internal transmission is determined as ratio of the transmission as measured and the Pvalue as described above. The average internal transmission in the range of from 850 nm to 950 nm is then determined as the mean value of the 101 internal transmission values that have been determined. The glass provided according to the present invention at a thickness of 4 mm may, for example, have an average internal transmission for light of a wavelength in the range of from 850 nm to 950 nm of at most 99.9%, at most 99.5%, at most 99% or at most 98.5%.
d
In some embodiments, the average internal transmission in smaller wavelength regions within the range of from 850 nm to 950 nm is high. For example, at a sample thickness of 4 mm the average internal transmission in any subrange of 20 nm width within the range of from 850 nm to 950 nm may be at least 20%, such as at least 25%, at least 30%, at least 35%, at least 40%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 96%, at least 97%, or at least 97.5%. This means that the average internal transmission may be at least 20%, such as at least 25%, at least 30%, at least 35%, at least 40%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 96%, at least 97%, or at least 97.5% in the subrange of from 850 nm to 870 nm, in the subrange of from 851 nm to 871 nm, in the subrange of from 852 nm to 872 nm, . . . , in the subrange of from 928 nm to 948 nm, in the subrange of from 929 nm to 949 nm and in the subrange of from 930 nm to 950 nm. In order to determine this average internal transmission, the transmission is measured for any wavelength starting from 850 nm in increments of 1 nm until 950 nm. Thus, transmission is measured at 850 nm, 851 nm, 852 nm, . . . , 948 nm, 949 nm and 950 nm. In total, the transmission is determined at 101 different wavelengths from 850 nm to 950 nm. The internal transmission is determined as ratio of the transmission as measured and the Pvalue as described above. The average internal transmission is then determined for each of the 81 subranges indicated above as the mean value of the 21 internal transmission values in each of the subranges. At a sample thickness of 4 mm the average internal transmission in any subrange of 20 nm width within the range of from 850 nm to 950 nm may, for example, be at most 99.9%, at most 99%, at most 98.5% or at most 98%.
d
In some embodiments, the minimum internal transmission in the wavelength range of from 850 nm to 950 nm is comparably high. In some embodiments, the glass provided according to the present invention at a thickness of 4 mm has a minimum internal transmission for light of a wavelength in the range of from 850 nm to 950 nm of at least 15%, such as at least 20%, at least 25%, at least 30%, at least 35%, at least 40%, at least 50%, at least 60%, at least 70%, at least 80%, at least 85%, at least 90%, at least 95%, at least 96%, or at least 97%. In order to determine the minimum internal transmission, the transmission is measured for any wavelength starting from 850 nm in increments of 1 nm until 950 nm. Thus, transmission is measured at 850 nm, 851 nm, 852 nm, . . . , 948 nm, 949 nm and 950 nm. In total, the transmission is determined at 101 different wavelengths from 850 nm to 950 nm. The internal transmission is determined as ratio of the transmission as measured and the Pvalue as described above. The minimum internal transmission in the range of from 850 nm to 950 nm is then determined as the minimum value of the 101 internal transmission values that have been determined. The glass provided according to the present invention at a thickness of 4 mm may, for example, have a minimum internal transmission for light of a wavelength in the range of from 800 nm to 900 nm of at most 99.5%, at most 99%, at most 98% or at most 97.5%.
As described above, the glasses provided according to the present invention have a high internal transmission in the NIR range and a low internal transmission in the visible range.
In some embodiments, at a sample thickness of 2 mm the ratio of the average internal transmission for light of a wavelength in the range of from 850 nm to 950 nm and the average internal transmission for light of a wavelength in the range of from 250 nm to 700 nm is in the range of from 6:1 to 200:1, such as from 7:1 to 150:1, from 8:1 to 100:1, from 10:1 to 80:1, from 12:1 to 60:1, from 15:1 to 50:1, from 18:1 to 40:1, or from 20:1 to 30:1.
In some embodiments, at a sample thickness of 2 mm the ratio of the lowest average internal transmission of all subranges of 20 nm width within the range of from 850 nm to 950 nm and the highest average internal transmission of all subranges of 20 nm width within the range of from 250 nm to 700 nm is in the range of from 2.5:1 to 20:1, such as from 2.6:1 to 15:1, from 2.7:1 to 10:1, from 2.8:1 to 9:1, from 2.9:1 to 8:1, from 3.0:1 to 7:1, from 3.1:1 to 6:1, from 3.2:1 to 5:1, from 3.3:1 to 4:1, or from 3.4:1 to 3.5:1.
In some embodiments, at a sample thickness of 2 mm the ratio of the minimum internal transmission for light of a wavelength in the range of from 850 nm to 950 nm and the maximum internal transmission for light of a wavelength in the range of from 250 nm to 700 nm is in the range of from 1.9:1 to 15:1, such as from 2.0:1 to 10:1, from 2.1:1 to 9:1, from 2.2:1 to 8:1, from 2.3:1 to 7:1, from 2.4:1 to 6:1, from 2.5:1 to 5:1, from 2.6:1 to 4:1, from 2.7:1 to 3.5:1, or from 2.8:1 to 3:1.
In some embodiments, at a sample thickness of 4 mm the ratio of the average internal transmission for light of a wavelength in the range of from 850 nm to 950 nm and the average internal transmission for light of a wavelength in the range of from 250 nm to 700 nm is in the range of from 20:1 to 400:1, such as from 25:1 to 300:1, from 30:1 to 250:1, from 40:1 to 200:1, from 50:1 to 150:1, from 60:1 to 140:1, from 70:1 to 130:1, or from 80:1 to 120:1.
In some embodiments, at a sample thickness of 4 mm the ratio of the lowest average internal transmission of all subranges of 20 nm width within the range of from 850 nm to 950 nm and the highest average internal transmission of all subranges of 20 nm width within the range of from 250 nm to 700 nm is in the range of from 6:1 to 50:1, such as from 6.5:1 to 40:1, from 7:1 to 30:1, from 7.5:1 to 25:1, from 8:1 to 20:1, from 8.5:1 to 18:1, from 9:1 to 15:1, from 9.5:1 to 14:1, from 10:1 to 13:1, or from 10.5:1 to 12:1.
In some embodiments, at a sample thickness of 4 mm the ratio of the minimum internal transmission for light of a wavelength in the range of from 850 nm to 950 nm and the maximum internal transmission for light of a wavelength in the range of from 250 nm to 700 nm is in the range of from 3.5:1 to 15:1, such as from 3.75:1 to 12:1, from 4.0:1 to 10:1, from 4.25:1 to 9:1, from 4.5:1 to 8:1, from 4.75:1 to 7.5:1, from 5.0:1 to 7:1, from 5.25:1 to 6.75:1, from 5.5:1 to 6.5:1, or from 5.75:1 to 6.25:1.
As described previously, the glasses provided according to the present invention have a particularly neutrally black color impression. The color impression can be quantified using the CIE UCS color space system of 1976. This system describes the color impression by the position in color space. There are three parameters to indicate the position in color space, namely the u′ color coordinate, the v′ color coordinate and the brightness Y. The skilled person is aware how to determine the position in CIE UCS color space of a given glass sample. The position in the CIE UCS color space system of 1976 may be determined according to DIN EN ISO 11664-5:2017-01. The standard colorimetric observer (also called 2° observer) is defined in ISO/CIE 11664-1:2019-06. D65 is a CIE standard illuminant described in DIN EN ISO 11664-2:2011-07.
In particular, a low brightness Y may be very advantageous. In some embodiments, for a sample thickness of 4 mm and D65 illuminant the brightness Y is in an range of from 0 to <7, for example from 0.1 to 6.5, from 0.2 to 5, from 0.3 to 3, from 0.5 to 2, from 0.75 to 1.5, from 0 to 1.5, from 0 to 1.4, from 0 to 1.3, from 0 to 1.2 or even from 0 to 1.1.
In some embodiments, for a sample thickness of 4 mm and D65 illuminant the u′ coordinate is in a range of from 0.07 to 0.4, such as 0.08 to 0.3 or 0.09 to 0.2, and the v′ coordinate is in a range of from 0.09 to 0.51, such as from 0.1 to 0.51, from 0.15 to 0.51, from 0.2 to 0.51, from 0.21 to 0.50, from 0.22 to 0.48, for example from 0.25 to 0.48, from 0.3 to 0.48, from 0.35 to 0.48 or from 0.4 to 0.47, and the brightness Y may be in an range of from 0 to <7, for example from 0.1 to 6.5, from 0.2 to 5, from 0.3 to 3, from 0.5 to 2, from 0.75 to 1.5, from 0 to 1.5, from 0 to 1.4, from 0 to 1.3, from 0 to 1.2 or even from 0 to 1.1.
Exemplary embodiments provided according to the present invention also relate to glass articles comprising, and in some embodiments consisting of, the glass provided according to the present invention. In some embodiments, the glass article is a bandpass filter. In some embodiments, the glass article is an optical component in applications comprising NIR lasers. In some embodiments, the glass article is an optical component such as, for example, an optical window, in particular for a LiDAR system. In some embodiments, the glass article has a thickness in a range of from 1 to 5 mm, such as from 1.5 to 4.5 mm or from 2 to 4 mm.
Exemplary embodiments provided according to the present invention also relate to the use of the glass or glass article provided according to the present invention in a LiDAR system.
Exemplary embodiments provided according to the present invention also relate to a LiDAR system comprising a laser and an optical window positioned between the laser and the surrounding, the optical window comprising the glass or glass article provided according to the present invention.
melting glass raw materials,
cooling the glass obtained.
Exemplary embodiments provided according to the present invention also relate to a method for producing a glass or glass article providing according to the present invention, the method including the steps of:
3
3
In some embodiments, the method does not comprise oxygen bubbling. In some embodiments, the method does not comprise use of NO. In some embodiments, the method does neither comprise oxygen bubbling nor use of NO.
2+
In particular if cations of chromium are present in the glass, very high melting temperatures may be avoided as this may be associated with generation of Crthat may compromise the high transmission in the NIR range. In some embodiments, melting temperatures are in a range of from 1410° C. to 1450° C., such as from 1415° C. to 1445° C., from 1420° C. to 1440° C., from 1425° C. to 1435° C., or about 1430° C.
EXAMPLES
Exemplary embodiments provided according to the present invention are further described by the following examples.
Glass Compositions
The following table shows the compositions of example glasses E1 to E5 provided according to the present invention and of comparative examples C1 and C2. The compositions are indicated in cat.-%. Thus, the relative molar proportions of the cations of the indicated components are given with regard to the total amount of cations in the glass.
Component
E1
E2
E3
E4
E5
E6
C1
C2
Silicon
45.2
61.9
61.8
67.0
63.1
64.0
62.3
63.3
Aluminum
1.0
0.03
2.3
Boron
9.1
19.2
Sodium
24.9
16.0
16.0
16.0
16.1
17.3
15.8
12.4
Potassium
13.2
10.9
11.0
10.1
10.0
11.6
10.6
Barium
1.4
Magnesium
1.3
Zinc
5.7
5.6
6.6
6.0
6.7
5.9
Lanthanum
2.1
Titanium
1.7
3.4
3.5
3.2
3.3
1.3
Cerium
0.7
1.4
1.5
1.3
1.20
Manganese
0.28
0.21
0.21
0.18
Nickel
0.33
0.29
0.24
0.62
Chromium
0.06
0.20
0.19
0.14
Cobalt
0.11
0.13
0.15
0.08
0.08
0.10
0.06
0.08
Optical Properties
The transmission properties of the glasses provided according to the present invention were tested. In particular, samples of glasses E1 to E6 having a thickness of 2 mm and samples of glasses E1 to E5 having a thickness of 4 mm were analyzed.
FIGS. 1 and 2
It was found that the glasses E1 to E6 have a low transmission in the visible range and a high transmission in the NIR range. Furthermore, they have a particularly neutrally black color impression. In contrast, the comparative examples C1 and C2 have impaired spectral properties as compared to E1 to E6. Exemplary transmission curves are shown in . A detailed analysis of transmission properties is shown in the following.
Maximum and Minimum Transmission
The following tables show transmission properties of the glasses E1 to E6 provided according to the present invention and of comparative examples C1 and C2. In particular, the maximum transmission in the wavelength range from 250 to 700 nm and the minimum transmission in the wavelength range from 850 to 950 nm are shown. The transmission was measured for any wavelength in the indicated intervals in intervals of 1 nm and the maximum or minimum transmission, respectively, was determined. Furthermore, the ratio of the minimum transmission in the wavelength range from 850 to 950 nm and the maximum transmission in the wavelength range from 250 to 700 nm was calculated. The following tables present rounded transmission values. Therefore, the ratios as shown in the tables calculated based on the actual transmission values may slightly differ from the values that would be obtained by using the rounded transmission values for calculating the ratios.
The following table shows the results for samples having a thickness of 2 mm.
Maximum transmission
Minimum transmission
Ratio of
in the wavelength range
in the wavelength range
Min<sub>850-950 nm</sub>
from 250 to 700 nm
from 850 to 950 nm
and
(Max<sub>250-700 nm</sub>)
(Min<sub>850-950 nm</sub>)
Max<sub>250-750 nm</sub>
E1
21%
48%
2.31
E2
29%
56%
1.92
E3
26%
59%
2.25
E4
45%
91%
2.02
E5
34%
89%
2.64
E6
43%
90%
2.11
C1
29%
32%
1.10
C2
47%
87%
1.85
The following table shows the results for samples having a thickness of 4 mm.
Maximum transmission
Minimum transmission
Ratio of
in the wavelength range
in the wavelength range
Min<sub>850-950 nm</sub>
from 250 to 700 nm
from 850 to 950 nm
and
(Max<sub>250-700 nm</sub>)
(Min<sub>850-950 nm</sub>)
Max<sub>250-750 nm</sub>
E1
5%
24%
5.36
E2
9%
34%
3.68
E3
8%
38%
5.05
E4
22%
90%
4.09
E5
12%
86%
6.97
C1
9%
11%
1.21
C2
24%
82%
3.41
For both a sample thickness of 2 mm and a sample thickness of 4 mm, the ratio of the minimum transmission in the wavelength range from 850 to 950 nm and the maximum transmission in the wavelength range from 250 to 700 nm was higher for the glasses provided according to the present invention as compared to comparative examples C1 and C2.
Furthermore, comparative example C1 had a very low minimum transmission in the wavelength range from 850 to 950 nm.
d
The values shown in the two tables above are values of total transmission. Notably, the Pvalue was about 0.92 for the glasses E1 to E6 provided according to the present invention and for comparative examples C1 and C2. Thus, internal transmittance values can easily be calculated based on the total transmission values given above by dividing them by 0.92.
Average Transmission
The following tables show the average transmission in the wavelength range from 250 to 700 nm and the average transmission in the wavelength range from 850 to 950 nm. The transmission was measured for any wavelength in the indicated ranges in intervals of 1 nm and the average transmission was calculated as the mean of all measured transmission values within the respective range. Furthermore, the ratio of the average transmission in the wavelength range from 850 to 950 nm and the average transmission in the wavelength range from 250 to 700 nm was calculated.
The following table shows the results for samples having a thickness of 2 mm.
Average transmission in
Average transmission in
the wavelength range
the wavelength range
Ratio of
from 250 to 700 nm
from 850 to 950 nm
Mean<sub>850-950 nm </sub>and
(Mean<sub>250-700 nm</sub>)
(Mean<sub>850-950 nm</sub>)
Mean<sub>250-750 nm</sub>
E1
2.1%
50.7%
24.7
E2
2.8%
60.2%
21.8
E3
2.9%
63.4%
21.8
E4
5.9%
91.2%
15.4
E5
10.1%
89.5%
8.9
E6
5.1%
90.5%
17.8
C1
2.0%
37.4%
18.4
C2
16.1%
87.3%
5.4
The following table shows the results for samples having a thickness of 4 mm.
Average transmission in
Average transmission in
the wavelength range
the wavelength range
Ratio of
from 250 to 700 nm
from 850 to 950 nm
Mean<sub>850-950 nm </sub>and
(Mean<sub>250-700 nm</sub>)
(Mean<sub>850-950 nm</sub>)
Mean<sub>250-750 nm</sub>
E1
0.3%
27.9%
95.9
E2
0.4%
39.4%
102.3
E3
0.4%
43.8%
104.6
E4
1.2%
90.4%
78.3
E5
2.4%
87.0%
36.3
C1
0.3%
15.3%
50.9
C2
4.3%
82.8%
19.1
For both a sample thickness of 2 mm and a sample thickness of 4 mm, the ratio of the average transmission in the wavelength range from 850 to 950 nm and the average transmission in the wavelength range from 250 to 700 nm was higher for the glasses provided according to the present invention as compared to comparative example C2. Furthermore, comparative example C1 had a very low average transmission in the wavelength range from 850 to 950 nm.
d
The values shown in the two tables above are values of total transmission. Notably, the Pvalue was about 0.92 for the glasses E1 to E6 provided according to the present invention and for comparative examples C1 and C2. Thus, internal transmittance values can easily be calculated based on the total transmission values given above by dividing them by 0.92.
Average Transmission in Subranges
The transmission properties of the glasses provided according to the present invention were further analyzed by determining the average transmission in small subranges of 20 nm width within the relevant larger ranges of from 250 to 700 nm and from 850 to 950 nm, respectively. In order to determine the average transmission in such subranges, the transmission was measured for any wavelength of the larger ranges in intervals of 1 nm. The average transmission was then determined for each of the smaller subranges of 20 nm width within the larger ranges. For each of the example glasses, 431 subranges were analyzed for the range of from 250 to 700 nm and 81 subranges were analyzed for the range of from 850 to 950 nm.
The following tables show for each of the glasses the average transmission of the subrange having the highest average transmission of all subranges within the range of from 250 to 700 nm. Furthermore, the average transmission of the subrange having the lowest average transmission of all subranges within the range of from 850 to 950 nm is shown. For each of the glasses, the ratio of both values indicated above was determined. This ratio is also shown in the following tables. Average transmission of any subrange was determined as the mean value.
The following table shows the results for samples having a thickness of 2 mm.
Highest average
Lowest average
Ratio of
transmission of subrange
transmission of subrange
Subrange-
in the wavelength range
in the wavelength range
Min<sub>850-950 nm</sub>
from 250 to 700 nm
from 850 to 950 nm
and Subrange-
(Subrange-Max<sub>250-700 nm</sub>)
(Subrange-Min<sub>850-950 nm</sub>)
Max<sub>250-750 nm</sub>
E1
19%
48%
2.57
E2
17%
56%
3.34
E3
19%
60%
3.23
E4
30%
91%
3.07
E5
30%
89%
2.70
E6
28%
90%
3.27
C1
16%
33%
2.06
C2
36%
87%
2.39
The following table shows the results for samples having a thickness of 4 mm.
Highest average
Lowest average
Ratio of
transmission of subrange
transmission of subrange
Subrange-
in the wavelength range
in the wavelength range
Min<sub>850-950 nm </sub>
from 250 to 700 nm
from 850 to 950 nm
and Subrange-
(Subrange-Max<sub>250-700 nm</sub>)
(Subrange-Min<sub>850-950 nm</sub>)
Max<sub>250-750 nm</sub>
E1
4%
25%
6.54
E2
3%
35%
11.10
E3
4%
39%
10.41
E4
11%
90%
8.49
E5
12%
86%
7.30
C1
3%
12%
3.40
C2
15%
82%
5.51
For both a sample thickness of 2 mm and a sample thickness of 4 mm, the ratio of the average transmission of the subrange having the lowest average transmission of all subranges within the range of from 850 to 950 nm and the average transmission of the subrange having the highest average transmission of all subranges within the range of from 250 to 700 nm was higher for the glasses provided according to the present invention as compared to comparative examples C1 and C2. Furthermore, comparative example C1 had a very low average transmission of the subrange having the lowest average transmission of all subranges within the range of from 850 to 950 nm.
d
The values shown in the two tables above are values of total transmission. Notably, the Pvalue was about 0.92 for the glasses E1 to E6 provided according to the present invention and for comparative examples C1 and C2. Thus, internal transmittance values can easily be calculated based on the total transmission values given above by dividing them by 0.92.
Position in CIE UCS (1976) Color Space
FIG. 3
The position in CIE UCS (1976) color space is shown in for different sample thicknesses of example glass E4. The respective u′ and v′ coordinates and brightness Y are summarized in the following table.
Thick-
u′
v′
Brightness
ness
coordinate
coordinate
Y
2 mm
0.122
0.453
8.2
4 mm
0.099
0.429
1.0
6 mm
0.110
0.413
0.2
8 mm
0.176
0.416
0.0
FIG. 3
As shown in , the color position is close to that of a black body. The glass has a particularly neutrally black color impression.
While this invention has been described with respect to at least one embodiment, the present invention can be further modified within the spirit and scope of this disclosure. This application is therefore intended to cover any variations, uses, or adaptations of the invention using its general principles. Further, this application is intended to cover such departures from the present disclosure as come within known or customary practice in the art to which this invention pertains and which fall within the limits of the appended claims. | |
Is Family 2 or 3 syllables?
‘Family’ may be pronounced with three syllables, but more commonly you’ll hear it with two. Family, family.
Is really 1 or 2 syllables?
This week’s word of the week is ‘really’. This is a two syllable word with stress on the first syllable. Another acceptable pronunciation is to make this a three syllable word re-a-lly where you add a middle syllable the schwa.
How many syllables are in Friday?
2 syllables
Is Hotel an open syllable?
A syllable is a basic unit of written and spoken language. It is a unit consisting of uninterrupted sound that can be used to make up words. For example, the word hotel has two syllables: ho and tel.
Is Cry an open syllable?
When studying open syllables, it is time to introduce y as a vowel. Know that y is a consonant when it begins a word, otherwise, it is a vowel. Y has 2 vowel sounds in an open syllable. In a one-syllable word, y has the long i sound as in cry and in multisyllabic words it usually has the long e sound as in baby.
Is by an open syllable?
An open syllable occurs when a vowel is at the end of the syllable, resulting in the long vowel sound, e.g. pa/per, e/ven, o/pen, go & we. Open syllable words are open because they are not closed by a consonant.
Is Tiger an open syllable?
The first syllable ends with a vowel and is an open syllable. The vowel in an open syllable is long. We treat all “VCV” words as “Tiger” words. If this produces an unrecognizable word, we close the first syllable by dividing after the consonant.
What is the rabbit rule?
Rule 2: “Rabbit” Rule: If a two-syllable base word with one medial consonant sound immediately after a short vowel, the medial consonant is doubled.
What is a Tiger word?
Tiger Rule ti/ger v/cv When one consonant comes between two vowels, divide after the vowel.
What is V VC pattern in spelling?
The VC/V Rule says that when one consonant is between two vowels and the first vowel sound is short, the syllable is divided after the consonant as in drag/on and the C+LE Rule says that when a word ends in “le,” the consonant before the “le” holds onto the consonant and these letters form a syllable as in the word tur …
What does v CV and VC V mean?
V/CV – Divide before the consonant if the first vowel has a long sound. example: zebra ze/bra. VC/V – Divide after the consonant if the first vowel has a short sound. example: closet clos/et.
What is VV pattern?
In some words with vowel pairs, each vowel is sounded, so the word has two syllables, as in create, diet, and poet. The V/V (Vowel/Vowel) syllable pattern is more common in multisyllabic words, such as gradual, curious, and variety. Point out that the two vowels ue spell one sound, /o—o/.
What does VC V stand for?
vowel, vowel, consonant
What is the VCV rule?
The rule states that words that are two syllables long and were borrowed from the French will have a short first vowel, even in a VCV string.
How many syllables are in the word?
Learn with an example Each syllable has one vowel sound. To count syllables, try clapping as you say each part of a word. You can also count how many times your jaw drops as you say each part of the word. The word watermelon has 4 syllables.
Whats is consonant?
A consonant is a speech sound that is not a vowel. It also refers to letters of the alphabet that represent those sounds: Z, B, T, G, and H are all consonants. Consonants are all the non-vowel sounds, or their corresponding letters: A, E, I, O, U and sometimes Y are not consonants.
How do you explain a consonant to a child?
All the letters in the alphabet are either consonants or vowels. A consonant is a speech sound in which the air is at least partly blocked, and any letter which represents this. Consonants may come singly (by themselves) or in clusters (two or more together), but must be connected to a vowel to form a syllable.
What is the most common consonant?
The Most Common Consonants, In Any Order Three of the most common consonants of the English language are R, S and T. Every answer today is a word, name or phrase that contains each of the letters R, S and T exactly once, along with any number of vowels.
What are the 24 consonant sounds in English?
English has 24 consonant sounds. Some consonants have voice from the voicebox and some don’t. These consonants are voiced and voiceless pairs /p/ /b/, /t/ /d/, /k/ /g/, /f/ /v/, /s/ /z/, /θ/ /ð/, /ʃ/ /ʒ/, /ʈʃ/ /dʒ/. These consonants are voiced /h/, /w/, /n/, /m/, /r/, /j/, /ŋ/, /l/. | https://pvillage.org/archives/431 |
prior probability(redirected from Improper distribution)
Also found in: Dictionary.
Related to Improper distribution: Uninformative prior
pri·or prob·a·bil·i·ty
the best rational assessment of the probability of an outcome on the basis of established knowledge before the present experiment is performed. For instance, the prior probability of the daughter of a carrier of hemophilia being herself a carrier of hemophilia is 1/2. But if the daughter already has an affected son, the posterior probability that she is a carrier is unity, whereas if she has a normal child, the posterior probability that she is a carrier is 1/3. See: Bayes theorem.
prevalenceEpidemiology
(1) The number of people with a specific condition or attribute at a specified time divided by the total number of people in the population.
(2) The number or proportion of cases, events or conditions in a given population.
Statistics
A term defined in the context of a 4-cell diagnostic matrix (2 X 2 table) as the amount of people with a disease, X, relative to a population.
Veterinary medicine
(1) A clinical estimate of the probability that an animal has a given disease, based on current knowledge (e.g., by history of physical exam) before diagnostic testing.
(2) As defined in a population, the probability at a specific point in time that an animal randomly selected from a group will have a particular condition, which is equivalent to the proportion of individuals in the group that have the disease. Group prevalence is calculated by dividing the number of individuals in a group that have a disease by the total number of individuals in the group at risk of the disease. Prevalence is a good measure of the amount of a chronic, low-mortality disease in a population, but is not of the amount of short duration or high-fatality disease. Prevalence is often established by cross-sectional surveys. | https://medical-dictionary.thefreedictionary.com/Improper+distribution |
---
abstract: 'The least upper bound on degrees of elements of a minimal system of generators of the algebra of invariants of $3\times3$ matrices is found, and the nilpotency degree of a relatively free finitely generated algebra with the identity $x^3=0$ is established.'
author:
- |
A. A. Lopatin[^1]\
Chair of Algebra,\
Department of Mathematics,\
Omsk State University,\
55A Prospect Mira, Omsk 644077, Russia,\
e-mail: [email protected]
title: 'The Algebra of Invariants of $3\times3$ Matrices over a Field of Arbitrary Characteristic'
---
Introduction
============
Let $K$ be an infinite field of arbitrary characteristic. Let a reductive algebraic group $G$ act regularly on $m$-dimensional affine variety $V=K^m$. This action defines natural action of $G$ on the coordinate algebra $K[V]$: $(g\cdot f)(v)=f(g^{-1}\cdot
v)$, where $ f\in K[V]$, $g\in G$, $v\in V$. Denote by $R=K[V]^G$ the algebra of invariants of $K[V]$ with respect to the action of $G$. By the Hilbert–Nagata Theorem, it is a finitely generated graded subalgebra. But Hilbert’s proof for the case ${\mathop{\rm char}}(K)=0$, as well as Nagata’s proof for the case ${\mathop{\rm char}}(K)>0$, are not constructive. The goal of the constructive theory of invariants is to find a minimal (i.e. irreducible) homogeneous system of generators (MSG) of $K[V]^G$ explicitly. It is an important problem, which arose as early as the theory of invariants itself. If one knows generators for each homogeneous component of the algebra of invariants, then, theoretically, the problem of finding MSG is equivalent to finding a constant $D$ such that $K[V]^G$ is generated by invariants of degree not greater than $D$ [@Pop]. Popov gave a bound $D$ for a connected semisimple group in characteristic zero case [@Pop]. But Popov’s bound is rather rough, so the problem of finding finer bounds is open.
Let $N_0=\{0,1,2,\ldots\}$. If $A$ is a $N_0$-graded algebra, denote by $A^{+}$ the subalgebra generated by elements of $A$ of positive degree. It is easy to see that the set $\{r_i\} \subseteq
R$ is a MSG iff $\{{\overline{r_i}}\}$ is a basis of ${\overline{R}}={R}/{(R^{+})^2}$. Call an element $r\in R$ [*decomposable*]{} if it belongs to the ideal $(R^{+})^2$. So the least upper bound for the degrees of elements of MSG of the algebra of invariants is equal to the highest degree of indecomposable invariants.
Let $G=GL_n(K)$ act on the affine space $M_{n,d}(K)=M_n(K)\oplus\cdots\oplus M_n(K)$ ($d$ times) by conjugations according to the following rule: $B\cdot(A_1,\ldots,A_d)\rightarrow(BA_1B^{-1},\ldots,BA_dB^{-1})$, where $M_n(K)$ is the space of all $n\times n$ matrices over $K$, $A_i\in M_n(K)$, $B\in GL_n(K)$ $(i={\overline{1,d}})$. This action induces an action on the coordinate ring $K_{n,d}=K[x_{ij}(r)\mid
i,j={\overline{1,n}} ;\; r={\overline{1,d}}]$. Denote by $R_{n,d}=K_{n,d}^G$ the algebra of invariants. Let $X_r=(x_{ij}(r))_{1\leq i,j\leq n}$ be the generic matrices of order $n$, and let ${\sigma}_k(X)$ be the coefficients of the characteristic polynomial of an $n\times n$ matrix $X$ $$\chi_n(X)=X^n-{\sigma}_1(X)X^{n-1}+\cdots+(-1)^n{\sigma}_n(X)E.$$ It is easy to see that ${\sigma}_k(X_{i_1}\cdots X_{i_s })\in R_{n,d}$. Denote by $D(n,d,K)$ (by $D_{{\sigma}_k}(n,d,K)$, respectively) the highest degree of indecomposable invariants (of indecomposable invariants of the form ${\sigma}_k(X_{i_1} \cdots X_{i_s})$, respectively).
In the case ${\mathop{\rm char}}(K)=0$, $R_{n,d}$ has been well investigated. Its generators and relations are described in [@Sib], [@Pro], [@Raz]. In particular, it is known that $R_{n,d}$ is generated by its elements of degree $\leq n^2$ [@Raz]. Great progress in the study of $R_{n,d}$ in the case of positive ${\mathop{\rm char}}(K)$ was made due to Donkin and Zubkov. Donkin showed that $R_{n,d}$ is generated by all elements of the form ${\sigma}_k(X_{i_1}\cdots X_{i_s })$ [@Don], and Zubkov [@Zub1] extended Procesi-Razmyslov’s Theorem on the relations to this case. Before formulating this theorem, we must fix some notation.
Let $A$ be an associative algebra. Denote by $A\mbox{-}{\mathop{\rm alg}}\{b_1,\ldots,b_d\}$ the associative algebra generated over $A$ by $1,b_1,\ldots,b_d$ which commute with $A$. If $b_1,\ldots,b_d$ are free over $A$, i.e. all identities of $C=A\mbox{-}{\mathop{\rm alg}}\{b_1,\ldots,b_d\}$ are consequences of identities of $A$, identities $b_ia=ab_i$ ($i={\overline{1,d}}$, $a\in A$) and identities of associativity, we denote $C$ by $A{\langle}x_1,\ldots,x_d{\rangle}$. If $C=A\mbox{-}{\mathop{\rm alg}}\{b_1,\ldots,b_d\}$ is a $N_0$-graded algebra with a unit over a $N_0$-graded subalgebra $A$, and elements $b_1,\ldots,b_d$ are homogeneous of positive degree, we denote by $C^{\#}$ the graded subalgebra $\sum_{1\leq
i\leq d}Cb_i$. The ideal generated by $a_1,\ldots,a_d$ is denoted by ${\rm id }\{a_1,\ldots,a_d\}$. We call an identity $h=0$ of $A$ a [*consequence*]{} of identities $\{h_i=0\}$ if $h=\sum_{j=1}^s
a_jh_{k_j}a_j'$, where $a_j,a_j'\in A$. The homogeneous component of degree $r$ of a graded algebra $A$ is denoted by $A(r)$.
The algebra of [*concomitants*]{} $C_{n,d}$ for $M_{n,d}$ is the algebra of all polynomial $GL_{n}(K)$–equivariant mappings of the space $M_{n,d}(K)$ to $M_{n}(K)$, where $GL_{n}(K)$ acts on $M_{n,d}(K)$ and $M_{n}(K)$ by conjugation. It is easy to see that $C_{n,d}$ is isomorphic to $R_{n,d}\mbox{-}{\mathop{\rm alg}}\{X_1,\ldots,X_d\}$, i.e. the subalgebra of $M_{n}(K_{n,d})$ generated by the generic matrices $X_1,\ldots,X_d$ over $R_{n,d}$ [@Zub3]. For $k>n$, consider the embedding $M_n\rightarrow M_k$ taking $A\in M_n$ to the matrix whose left upper $n\times n$ cell coincides with $A$ and all the other entries are equal to zero. This mapping induces homomorphisms $R_{k,d}(r)\rightarrow R_{n,d}(r)$ and $C_{k,d}(r)\rightarrow C_{n,d}(r)$ (consult [@Zub3] for details). Taking projective limits, we obtain the [*free algebra of invariants*]{} of $d$ matrices $R_d=\bigoplus_{r\geq0}{{\mathop{\rm{projlim }}}_n R_{n,d}(r)}$ and the [*free algebra of concomitants*]{} $C_d=\bigoplus_{r\geq0}{{\mathop{\rm{projlim }}}_n
C_{n,d}(r)}$. Let $S$ be the free semigroup generated by letters $\{a_1,a_2,\ldots\}$. Words $b=a_{i_1}\cdots a_{i_l}$ and $c=a_{j_1}\cdots a_{j_l}$ are called equivalent, if there exists a cyclic permutation $\pi\in S_l$ such that $i_s=j_{\pi(s)}$, $s={\overline{1,l}}$. The [*cycle*]{} (in letters $a_1,a_2,\ldots$) is the equivalence class of some word. The cycle is [*primitive*]{}, if it is not equal to a power of a shorter cycle. It is known that $R_d$ is isomorphic to the algebra of polynomials in ’symbolic’ free generators ${\sigma}_k(a)$, where $a$ is a primitive cycle in letters $x_1,\ldots,x_d$, $k>0$ [@Don2]. The algebra $C_d$ is isomorphic to the free associative algebra in ’formal matrix variables’ $x_1,\ldots,x_d$ over $R_d$, i.e. $C_d\simeq R_d{\langle}x_1,\ldots,x_d{\rangle}$ [@Zub3]. If $n\geq r$, then $R_{n,d}(r)$ is naturally isomorphic to $R_{d}(r)$, and $C_{n,d}(r)$ is isomorphic to $C_{d}(r)$ (see [@Don2]). Denote by $\deg(c)$ the degree of a word $c$, i.e. the number of letters appearing in $c$, and by ${\mathop{\rm mdeg}}(c)$ the multidegree of $c$, i.e. ${\mathop{\rm mdeg}}(c)=(\lambda_1,\lambda_2,\ldots)$, where $\lambda_j$ is the number of times $a_j$ appears in $c$. These notations are also used for cycles.
Let $B$ be an arbitrary commutative algebra, $q_1,\ldots,q_s\in
B$, and let $A_1,\ldots,A_s$ be $n\times n$ matrices over $B$. For $k={\overline{1,n}}$ Amitsur’s formula states [@A]:
\[amiss\] \_k(\_[l=1]{}\^s q\_l A\_l)=(-1)\^[k-(j\_1++j\_t)]{}q\^[j\_1 (c\_1)++j\_t(c\_t)]{} \_[j\_1]{}(c\_1)\_[j\_t]{}(c\_t),
where $q^{(\lambda_1,\ldots,\lambda_s)}=q_1^{\lambda_1}\cdots
q_s^{\lambda_s}$, and the sum ranges over all pairwise different primitive cycles $c_1,\ldots,c_t$ in letters $A_1,\ldots,A_s$ and numbers $j_1,\ldots,j_t$ with $\sum_{i=1}^{t}j_i\deg(c_i)=k$. By [(\[amiss\])]{} one can express ${\sigma}_k(G)\in R_{n,d}$ in terms of elements of the form ${\sigma}_k(U)$, where $G\in C_{n,d}^{\#}$, $U$ is a non-empty word in the generic matrices. Identification $R_n(r)$ with $R_{n,d}(r)$ for $n\geq r$ allows one to define $\sigma_k(g)\in R_d$ for $g\in C_{d}^{\#}$, $k\geq1$, correctly.
The algebra $R_d$ can be regarded as an associative-commutative $K$–algebra with a unit generated by ’symbolic’ elements ${\sigma}_k(g)$, $g\in K{\langle}x_1,\ldots,x_d{\rangle}^{\#}$, $k>0$. The ideal of relations of the algebra $R_d$ is generated by (see [@Zub2]):
$(A)$ $\forall k\geq1, \forall g, h\in K{\langle}x_1,\ldots,x_d{\rangle}^{\#}, {\sigma}_k(gh)={\sigma}_k(hg)$.
$(B)$ Amitsur’s formula.
$(C)$ $\forall \alpha\in K, \forall k\geq1, \forall g\in K{\langle}x_1,
\ldots,x_d{\rangle}^{\#}, {\sigma}_k(\alpha g)=\alpha^k{\sigma}_k(g).$
$(D)$ $\forall t,k\geq1, \forall g\in K
{\langle}x_1,\ldots,x_d{\rangle}^{\#},
{\sigma}_k(g^t)=\sum\limits_{i_1,\ldots,i_{kt}}\beta^{(k,t)}_{i_1,\ldots,i_{kt}}
{\sigma}_1(g)^{i_1}\cdots{\sigma}_{kt}(g)^{i_{kt}}$, where coefficients $\beta^{(k,t)}_{i_1,\ldots,i_{kt}}
\in Z$ are determined uniquely.
The kernels of natural projections $R_d\rightarrow R_{n,d}$, $C_d\rightarrow C_{n,d}$ we denote by $I_{n,d}$, $J_{n,d}$, respectively. Procesi–Razmyslov’s Theorem asserts that the ideal $I_{n,d}$ is generated by ’symbolic’ elements ${\sigma}_k(f)$, $k>n$, and the ideal $J_{n,d}$ — by elements $\chi_k(f)=f^k-{\sigma}_1(f)f^{k-1}+\cdots+(-1)^k{\sigma}_k(f)$, $k\geq n$, where $f\in C_{d}^{\#}$. In other words, the ideal of relations of $R_{n,d}$ is generated by $(A)$–$(E)$, where
$(E)$ $\forall k>n, \forall f\in C_{d}^{\#}, {\sigma}_k(f)=0$.
In [@Dom_K_Z] it is proved that, in contrast to the case of ${\mathop{\rm char}}(K)=0$, if $0<{\mathop{\rm char}}(K)\leq n$ then the degree bound for the generators of $R_{n,d}$ tends to infinity when $d$ tends to infinity. In [@Dom_K_Z] an explicit MSG for $R_{2,d}$ is given. In [@Dom] some upper and lower bounds on $D(n,d,K)$ are pointed out.
In this paper we consider the case $n=3$. We find the least upper bound on degrees of elements of MSG of $R_{3,d}$ (except for the case of ${\mathop{\rm char}}(K)=3$, $d=6k+1$, $k>0$, where we estimate the least upper bound with error not greater than $1$).
The least upper bound $D=D(3,d,K)$ on degrees of elements of a minimal system of generators of the algebra of invariants $R_{3,d}$ for $d>1$ is equal to:
1. if ${\mathop{\rm char}}(K)=0$ or ${\mathop{\rm char}}(K)>3$, then $D=6$,
2. if ${\mathop{\rm char}}(K)=2$, then $D=\left\{
\begin{array}{ccc}
d+2&,&d\geq4\\
6&,&d=2\;{\rm or}\;3\\
\end{array} \right.$
3. if ${\mathop{\rm char}}(K)=3$, then $D=\left\{
\begin{array}{ccl}
3d&,&d\;{\rm even}\\
3d-1&,&d\equiv 3\;{\rm or}\;5\;({\mathop{\rm{mod }}}6) \\
3d-1 \;{\rm or}\; 3d&,& d\equiv 1\;({\mathop{\rm{mod }}}6). \\
\end{array} \right.$
If $d=1$, then $D=3$.
The [*nilpotency degree*]{} of a graded algebra $A=\bigoplus_{j\geq0}A(j)$, where $A(0)=K$, is the least $C$ for which $a_1\cdots a_C=0$ for all $a_i\in\ A^{+}$ ($i={\overline{1,C}}$). The idea of the proof of Theorem 2 consists in reduction of the problem of decomposability of certain invariants to the problem of equality to zero of certain elements of the algebra $N_{n,d} =
{K{\langle}x_1,\ldots,x_d {\rangle}}/{{{{\rm id}\{{\;f^n\;|\; f\in K{\langle}x_1,\ldots,x_d{\rangle}^{\#}}\}}}}$ and, in particular, to the question of finding $C(n,d,K)$ — the nilpotency degree of $N_{n,d}$ (see Lemmas \[cr\_1\], \[cr\_2\], \[cr\_3\]). In the case of characteristic zero $n(n+1)/2\leq C(n,d,K)\leq n^2$ (see [@Kuzmin], [@Raz_book]), and Kuzmin conjectured that $C(n,d,K)=n(n+1)/2$. This conjecture has been proved to be true for $n\leq4$ [@Vau]. For prime characteristic, there exists an upper bound on $C(n,d,K)$ [@Klein]: $C(n,d,K)<(1/6)n^6d^n$.
In Section 2 of this paper we prove the following theorem.
The nilpotency degree $C=C(3,d,K)$ of $N_{3,d}$ ($d>1$) equals:
1. if ${\mathop{\rm char}}(K)=0$ or ${\mathop{\rm char}}(K)>3$, then $C=6$,
2. if ${\mathop{\rm char}}(K)=2$, then $C=\left\{
\begin{array}{lcl}
d+3&,& d\geq3\\
6&,& d=2,\\
\end{array}
\right.$
3. if ${\mathop{\rm char}}(K)=3$, then $C=\left\{
\begin{array}{lcl}
3d+1&,& d{\rm\ is\ even}\\
3d\;{\rm or}\;3d+1 &,& d{\rm\ is\ odd}.\\
\end{array} \right.
$
These theorems show one more difference between the cases of characteristic zero and prime: for ${\mathop{\rm char}}(K)=0$, $D(3,d,K)=C(3,d,K)$ ($d>1$), while for ${\mathop{\rm char}}(K)=2,3$ $D(3,d,K)<C(3,d,K)$ ($d>1$, and $d\neq2,3$ if ${\mathop{\rm char}}(K)=2$).
Associative algebra with the identity $a^3=0$ {#chapter_nilp}
=============================================
General remarks {#intro}
---------------
In this section we compute the nilpotency degree of a relatively free finitely generated algebra $N_{3,d}={K\langle x_1, \ldots,
x_d\rangle}/{I}$, where $I=\mbox{id}\{f^3\mid\ f\in K{\langle}x_1,\ldots,x_d{\rangle}^{\#}\}$, satisfying $$T_1(a)=a^3=0,\;a\in K{\langle}x_1,\ldots,x_d{\rangle}^{\#}.$$ We call $x_i$ letters, and monomials in $x_i$ words. By $x,y,z$ we denote any triple of pairwise distinct letters. Throughout this section, all considered elements of $N_{3,d}$ are meant to be non-empty words, and all words are meant to belong to $N_{3,d}$, if we do not explicitly write otherwise. Small Greek letters (possibly with index) denote elements of $K$. Denote by $p$ ($p=0,2,3,\ldots$) the characteristic of the field $K$.
Since the ideal $I$ is homogeneous, $N_{3,d}$ possesses natural $N_0$- and $N_0^d$-gradings by degrees and multidegrees, respectively, for which we use the same notations as in Introduction. The degree of a word $u$ in a letter $x$ we denote by $\deg_x(u)$. The multidegree ${({\alpha},\ldots,{\alpha})}$ ($d$ times) will also be denoted by ${\alpha}^{(d)}$.
Partial and complete linearization of $a^3=0$ gives the identities $$\begin{array}{c}
T_2(a,b)=a^2b+aba+ba^2=0.\\
T_3(a,b,c)=abc+acb+bac+bca+cab+cba=0.
\end{array}$$ Denote by ${{{\mathcal{S}} }}$ the system $$\left\{
\begin{array}{ccl}
g_1T_1(f)g_2&=&0\\
g_1T_2(f_1,f_2)g_2&=&0\\
g_1T_3(f_1,f_2,f_3)g_2&=&0,
\end{array}\right.\eqno({{\mathcal{S}} })$$ where $f$, $f_i$ are non-empty words $(i=1,2,3)$, words $g_1$, $g_2$ can be empty, and equalities are meant to hold modulo ideal $I$. Let ${{\mathcal{S}} }_{\Lambda}$ be the subsystem of ${{\mathcal{S}} }$ which consists of equations of multidegree $\Lambda$. For each word $u$ of multidegree $\Lambda$, introduce a variable $x_u$, and regard system ${{\mathcal{S}} }_{\Lambda}$ as a homogeneous system of linear equations in $\{x_u\}$ over $K$. Clearly, if ${\mathop{\rm mdeg}}(u)=\Lambda$, then $u=0$ in $N_{3,d}$ iff $x_u=0$ for each solution of ${{\mathcal{S}} }_{\Lambda}$. If $h=0$ is an equation from ${{\mathcal{S}} }_{\Lambda}$, by $h|_{\{a_u\}}$ we denote the result of substitution $\{x_u=a_u\}$ in $h=0$, where $a_u\in K$.
We call a word [*canonical*]{} with respect to $x_i$, if it has one of the following forms: $w_1$, $w_1x_iw_2$, $w_1x_i^2w_2$, $w_1x_i^2ux_iw_2$, where subwords $w_1$, $u$, $w_2$ do not contain $x_i$, and subwords $w_1$, $w_2$ can be empty. If a word is canonical with respect to each $x_i$, we call it [*canonical*]{}.
\[canon\]An arbitrary word $w\in N_{3,d}$ is equal to a sum of canonical words which belong to the same homogeneous component as $w$.
$T_2(x_i,w)=0$ implies
\[a1\]x\_iwx\_i=-x\_i\^2w-wx\_i\^2.
Since $T_2(x,xw)=0$, it follows that
\[a\]xwx\^2=-x\^2wx.
Applying to each letter [(\[a1\])]{} and then [(\[a\])]{}, we obtain the required.
The presentation of a word from Statement \[canon\] does not have to be unique.
If a word $w \in N_{3,d}$ contains more than $4$ occurrences of some letter, then $w=0$. In particular, the length of a non-zero word does not exceed $3d$.
Hereafter, to specify the subword to which the identity is applied, we sometimes put it in parentheses. Also, if we need to split a word into a product of subwords, we insert dots in it. (For example, see the deduction of [(\[5.1\])]{} from [(\[f3\])]{}.) Moreover, we will apply Statement \[canon\] to all words without reference.
Let us obtain some identities. Applying [(\[a1\])]{}, we get
\[1p1\] (xy)\^2=(xyx)y=-x\^2y\^2-(yx\^2y)=y\^2x\^2.
Further, we apply [(\[1p1\])]{} to all subwords equal to $xyxy$ without reference. Besides that, [(\[a1\])]{} implies $(xayx)y=-x^2ayy-a(yx^2y)=-x^2ay^2+ay^2x^2+ax^2y^2$, and $xa(yxy)=-(xay^2x)-(xax)y^2=x^2ay^2+ay^2x^2+x^2ay^2+ax^2y^2$. Hence
\[f2\] x\^2ay\^2=0, p3.
By separate linearization of [(\[f2\])]{} with respect to $x$ and with respect to $y$, we obtain
\[f3\]x\^2abc+x\^2acb=0,abcx\^2+bacx\^2=0, p3.
Applying [(\[a1\])]{}, we get $(xux)vx=-x^2uvx-ux^2vx$, $xu(xvx)=-xux^2v-xuvx^2=x^2uxv+x^2uvx$. Hence
\[Azzz\] -2x\^2uvx=x\^2uxv+ux\^2vx.
The case of $N_{3,2}$ in characteristic different from $3$
----------------------------------------------------------
\[A2\]If $p\neq3$, then $C(3,2,K)=6$.
Applying [(\[a\])]{} and [(\[f2\])]{} to $x^2y^2xy$, we obtain that $p\neq3$ implies $x^2y^2xy=0$. Statement \[prop3\] concludes the proof.
\[prop3\] $x_1^2x_2^2x_1\neq0$ for each $p$.
Let us find a solution for ${{\mathcal{S}} }_{(3,2)}$ for which $x_{x_1^2x_2^2x_1}\neq0$. Let $x_{x_1^2x_2^2x_1}=1$, $x_{x_1x_2^2x_1^2}=-1$, $x_{x_1^2x_2x_1x_2}=-1$, $x_{x_2x_1x_2x_1^2}=1$, $x_{x_1x_2x_1^2x_2}=1$, $x_{x_2x_1^2x_2x_1}=-1$, $x_{x_1x_2x_1x_2x_1}=0$ and $x_u=0$ for any other word $u$ of multidegree $(3,2)$. It is easy to see that this is indeed a solution for every equation from ${{\mathcal{S}} }_{(3,2)}$.
The case of characteristic equal to $0$ or greater than $3$
-----------------------------------------------------------
If $p=0$ or $p>3$, $d>1$, then $C(3,d,K)=6$.
Equality $x_1x_2\cdots x_5=0$ implies $x^2y^2x=0$, which is a contradiction to Statement [\[A2\]]{}.
Applying [(\[f3\])]{}, we get $x^2\cdot a\cdot b\cdot cd=-x^2\cdot
a\cdot cd\cdot b$ and $(x^2abc)d=-(x^2acb)d=-x^2\cdot ac\cdot
b\cdot d=x^2\cdot ac\cdot d\cdot b$. Hence
\[5.1\]x\^2abcd=0, abcdx\^2=0.
It follows that $x^2y^2ab=0,abx^2y^2=0$. Linearization of these identities with respect to $x$ gives
\[5.24\] abx\^2cd+bax\^2cd=0, abx\^2cd+abx\^2dc=0.
Further, [(\[f3\])]{} and [(\[5.24\])]{} imply $T_3(x^2ab,c,d) =
cx^2abd+dx^2abc = 0$ and $T_3(x^2,a,b)cd = ax^2bcd+bx^2acd=0$. These two identities together with [(\[f3\])]{} imply that
\[5.4\] a\_1x\^2a\_2a\_3a\_4=a\_[(1)]{}x\^2a\_[(2)]{}a\_[(3)]{}a\_[(4)]{}S\_4.
Note that the same is true for $abcx^2d$. Further, $T_3(ax^2b,c,d)
= cax^2bd+dax^2bc=0$ (see [(\[5.4\])]{}). This identity together with [(\[5.24\])]{} imply
\[5.5\] a\_1a\_2x\^2a\_3a\_4=a\_[(1)]{}a\_[(2)]{}x\^2a\_[(3)]{}a\_[(4)]{}S\_4.
Let $A=ax^2bcd$, $B=abx^2cd$, $C=abcx^2d$. Then [(\[5.1\])]{}, [(\[5.4\])]{}, [(\[5.5\])]{} imply $T_3(x^2,a,bc)d=A+B+2C=0$, $dT_3(x^2,a,bc) = -2A-B-C=0$, $T_3(x^2a,bc,d)=-A+B-2C=0$. Hence $A=B=C=0$. Linearization of [(\[5.1\])]{} and $A=B=C=0$ gives $a_1\cdots a_6={\mathop{\rm{sgn }}}{\sigma}\cdot a_{{\sigma}(1)}\cdots a_{{\sigma}(6)}$, ${\sigma}\in
S_6$. It follows that $T_3(ab,cd,ef)=0$ implies $abcdef=0$.
The case of characteristic $2$ {#case_p_2}
------------------------------
If $p=2$, then $C(3,d,K)=\left\{
If $d=2$, see Statement [\[A2\]]{}.
A word of multidegree $\Lambda=({\lambda}_1,\ldots,{\lambda}_d)$, where ${\lambda}_i>1$ $(i=\overline{1,3})$, is equal to $0$ by [(\[f2\])]{}. Let us show that a word $u$ of multid¥gree $\Lambda$, where ${\lambda}_1=3,{\lambda}_2>1$, ${\lambda}_3>0$, is equal to $0$. Applying Statement \[canon\], we represent $u$ as a sum of words containing subwords $x^2y^2xz$ (see [(\[f2\])]{},[(\[a\])]{}). But $x^2\cdot y^2\cdot x\cdot z=/\mbox{see }
{(\ref{f3})}/=x^2y^2zx=/\mbox{see } {(\ref{a})}/=xy^2zx^2= /\mbox{see }
{(\ref{f2})}/=0$.
Let $d=3$. We have $x^2y^2x\neq0$ (by Statement \[prop3\]), and all words of degree $6$ are equal to $0$. Hence, the nilpotency degree is equal to $6$.
Let $d\geq4$. The longest words which can be non-zero are words of multidegrees $(2,2,1,\ldots,1)$ and $\Theta=(3,1,1,\ldots,1)$. Below we prove the existence of a non-zero word of multidegree $\Theta$.
\[predl\_p2\_1\] $x_1^2x_2\cdots x_dx_1\neq0$, where $d\geq2$.
Let $V=x_1^2x_2\cdots x_{d}x_1$, $d\geq2$. First let us show that $V\neq0$ when $d\geq4$, which will imply that if $x_1^2x_2x_1=0$ or $x_1^2x_2x_3x_1=0$, then the substitution $x_2\rightarrow
x_2x_3x_4$ or $x_3\rightarrow x_3x_4$, respectively, leads to required contradiction.
Let $d\geq4$. There exists a solution for ${{{\mathcal{S}} }}_{\Theta}$ for which $V\neq0$, namely, take $\{x_u=F(u)| {\mathop{\rm mdeg}}(u)=\Theta\}$, where $F(u)$ is equal to the number of all subwords $x_1^2$ in $u$. For example, if $\deg_{x_1}(u)=\deg_{x_1}(v)=0$, then $F(ux_1^3v)=0$. Let $$F(v,w)=\left\{
\begin{array}{ccl}
1&,&\mbox{if } v=v'x_1, w=x_1w'\\
0&,&\mbox{otherwise }\\
\end{array}
\right..$$ Here subwords $v'$, $u'$ can be empty. We have $F(v_1\cdots
v_l)=\sum\nolimits_{i=1}^{l} F(v_i) + \sum\nolimits_{i=1}^{l-1}
F(v_i,v_{i+1})$. Hence $g_1T_3(f_1,f_2,f_3)g_2|_{\{F(u)\}}=0$. Let $g_1T_2(x_1,f)g_2=0$ and $g_1T_1(f)g_2=0$ be equations from ${{{\mathcal{S}} }}_{\Theta}$. As one can see $g_1T_2(x_1,f)g_2|_{\{F(u)\}} =
F(g_1)+F(f)+F(g_2)+F(g_1,f)+F(f,g_2)$. We have $\deg_{x_1}(g_1fg_2)=1$, so $F(g_1)=F(f)=F(g_2)=F(g_1,f)=F(f,g_2)=0$. Hence, $g_1T_2(x_1,f)g_2|_{\{F(u)\}}=0$. Clearly, $g_1T_1(f)g_2|_{\{F(u)\}}=0$. So $\{x_u=F(u)\}$ is a solution for ${{{\mathcal{S}} }}_{\Theta}$.
\[note\_p2\] One can show that there exist non-zero words of multidegree $(2,2,1,\ldots,1)$ (namely, $x_1^2x_2^2x_3\cdots x_d\neq0$, where $d\geq2$).
The case of characteristic $3$ {#case_p_3}
------------------------------
\[prop6\] If $p=3$, then $C(3,d,K)=\left\{
$
The proof will follow from Statement \[predl3\] and Corollary \[predl3\_1\].
\[predl2\] Let $\sum{\alpha}_iu_i=0$ be a homogeneous identity of degree $1$ or $2$ in $x_k$, $k\in\overline{1,d}$, which contains some other letters. Then the result of substitution $x_k=1$ in $\sum{\alpha}_iu_i=0$ is an identity.
Let $M$ be the set of all identities from system ${{\mathcal{S}} }$ of degree $1$ or $2$ in $x_k$. The identity $\sum{\alpha}_iu_i=0$ is a consequence of identities from $M$. Set $M$ does not contain identities $g_1T_1(f)g_2=0$, where $\deg_{x_k}(f)\neq0$. Hence the result of substitution $x_k=1$ in any identity from $M$ is an identity.
Consider a word $x^2ux$, where $\deg_x(u)=0$. Replacing $x$ with $x+y$, where $\deg_y(u)=0$, and taking the homogeneous component of degree $1$ in $x$ and $2$ in $y$, we get $y^2ux+yxuy+xyuy$. Substitution $y=1$ gives $ux-xu$. This reasoning shows that linear function $\Pi_{x}(v_1x^2uxv_2)=v_1uxv_2-v_1xuv_2$, where $v_1$, $v_2$ are any words, is defined correctly on all homogeneous components of $N_{3,d}$ of degree $3$ in $x$. Let $W_{xy}=x^2y^2xy$. We will shorten $W_{x_ix_j}$ to $W_{ij}$, and $\Pi_{x_i}$ to $\Pi_i$. We have
\[q1\] \_[i]{}\_[j]{}(W\_[ij]{})=x\_ix\_j-x\_jx\_i.
The element $u=x_{\pi(1)}\cdots x_{\pi(t)}\in K{\langle}x_1,\ldots,x_t{\rangle}$, $\pi\in S_t$, is called even if permutation $\pi$ is even, and odd otherwise. Define ${\mathop{\rm{sgn }}}u=1$ for even $u$ and ${\mathop{\rm{sgn }}}u=-1$ for odd $u$. Denote by $|u|$ the length of $u$.
\[lemma\_q4\] If $|v_1|$ and $|v_2|$ are both odd or both even, then $${\mathop{\rm{sgn }}}uv_1u'v_2u''=(-1)^{|v_1|\cdot|v_2|}{\mathop{\rm{sgn }}}uv_2u'v_1u'',$$where words $u$, $u'$, $u''$ can be empty.
The statement follows from ${\mathop{\rm{sgn }}}uw_1w_2u''=(-1)^{|w_1|\cdot|w_2|}{\mathop{\rm{sgn }}}uw_2w_1u''$, where words $u$, $u''$ can be empty.
\[predl3\] The word $w_{2k}=W_{12}W_{34}\cdots
W_{2k-1,2k}$ is not equal to $0$, if $k\geq1$.
Assume that, on the contrary, $w_{2k}=0$. Then let $$h_{2k}=\Pi_{1}\Pi_{2}\cdots\Pi_{2k-1}\Pi_{2k}(w_{2k})=(x_1x_2-x_2x_1)\cdots(x_
{2k-1}x_{2k}-x_{2k}x_{2k-1})=0.$$ If a word $u\in K{\langle}x_1,\ldots,x_t{\rangle}$ of multidegree $1^{(2t)}$ is even, let $N_{+}(u)=1$ and $N_{-}(u)=0$; if it is odd, let $N_{+}(u)=0$ and $N_{-}(u)=1$. Let us show that for every equation $h=g_1T_3(f_1,f_2,f_3)g_2=0$ from ${{{\mathcal{S}} }}_{\Lambda}$ (where $\Lambda=1^{(2k)}$) it is true that
\[q2\] h|\_[{N\_[+]{}(u)}]{}=h|\_[{N\_[-]{}(u)}]{}=0.
It is enough to consider equations with $g_1=g_2=1$, because for words $uv_1$, $uv_2$ of multidegree $\Lambda$ if ${\mathop{\rm{sgn }}}v_1={\mathop{\rm{sgn }}}v_2$, then ${\mathop{\rm{sgn }}}uv_1={\mathop{\rm{sgn }}}uv_2$. There are two possibilities:
[$1)$]{} Among $f_1$, $f_2$, $f_3$ there are two words of odd length, for example, $f_2$ and $f_3$. Then by Lemma \[lemma\_q4\], ${\mathop{\rm{sgn }}}f_1f_2f_3=-{\mathop{\rm{sgn }}}f_1f_3f_2$, ${\mathop{\rm{sgn }}}f_2f_1f_3=-{\mathop{\rm{sgn }}}f_3f_1f_2$, ${\mathop{\rm{sgn }}}f_2f_3f_1=-{\mathop{\rm{sgn }}}f_3f_2f_1$. Hence [(\[q2\])]{} is true.
[$2)$]{} Among $f_1$, $f_2$, $f_3$ there are two words of even length, for example, $f_2$ and $f_3$. Then by Lemma \[lemma\_q4\], words $f_1f_2f_3$, $f_1f_3f_2$, $f_2f_1f_3$, $f_2f_3f_1$, $f_3f_1f_2$, $f_3f_2f_1$ are all even or all odd, hence [(\[q2\])]{} is true.
Prove by induction on $t$ that ${h_{2t}}|_{\{N_{+}(u)\}}=(-1)^{t+1}$, ${h_{2t}}|_{\{N_{-}(u)\}}=(-1)^{t}$. For $h_2$ it is obvious. Since $h_{2t}=h_{2(t-1)}(x_{2t-1}x_{2t}-x_{2t}x_{2t-1})$, we have ${h_{2t}}|_{\{N_{+}(u)\}} =h_{2(t-1)}|_{\{N_{+}(u)\}}
-{h_{2(t-1)}}|_{\{N_{-}(u)\}}$ and ${h_{2t}}|_{\{N_{-}(u)\}} =
{h_{2(t-1)}}|_{\{N_{-}(u)\}} -{h_{2(t-1)}}|_{\{N_{+}(u)\}}$. By induction hypothesis, we get what is required.
We found a solution for ${{\mathcal{S}} }_{\Lambda}$ on which $h_{2k}$ is not equal to zero, which is a contradiction.
\[predl3\_1\] The word $W_{12}W_{34}\cdots W_{2k-1,2k}x_{2k+1}^2$ is not equal to zero if $k>0$.
The proof follows from Statements \[predl2\] and \[predl3\].
In Section 3 we will need Statement \[predl2.p3\], which is formulated below. We have $0=(xy)^3=(xyx)(yxy)= /\mbox{see }
{(\ref{a1})}/=(x^2y+yx^2)(y^2x+xy^2)=/\mbox{see
}{(\ref{a})}/=-x^2y^2xy-y^2x^2yx$. Hence
\[1p3\]W\_[xy]{}=-W\_[yx]{}.
We will shorten $W_{xy}$ to $W$.
\[predl1\] Any word of degree $3$ with respect to $x$ and $y$ is equal to $\sum \alpha_iu_iWw_i$, where subwords $u_i$, $w_i$ do not contain $x$ and $y$.
By Statement \[canon\], it is enough to consider canonical words. For words of multidegree $(3,3)$, Statement \[predl1\] follows from [(\[1p3\])]{}. Let us prove it for words of multidegree $(3,3,1)$. $$\begin{array}{rcl}
T_3(x^2y^2,a,xy)=0&\Rightarrow &x^2y^2axy=-aW-Wa.\\
T_2(xy,ayx)=0&\Rightarrow &x^2y^2ayx=aW-Wa.\\
T_3(x^2,ay^2x,y)=0&\Rightarrow &x^2ay^2xy=aW.\\
T_3(y^2,yx^2a,x)=0&\Rightarrow &x^2y^2xay = Wa.\\
\end{array}$$
Consider identities of multidegree $(3,3,1,1)$. Identity $T_3(x^2a,xy^2,by)=0$ implies $x^2axy^2by=abW+Wab-baW-Wba$. The latter identity, together with $T_3(a,b,W)=0$, implies $$x^2axy^2by=-abW-Wab+aWb+bWa.$$ We apply [(\[Azzz\])]{} to subwords which are put into parentheses. $$\begin{array}{l}
x^2ay^2bxy=(x^2\cdot a\cdot y^2b\cdot x)y=abW-Wab+bWa.\\
x^2ay^2xby=(x^2\cdot a\cdot y^2\cdot x)by=-abW-Wab-aWb+bWa.\\
x^2y^2axby=x^2(y^2\cdot ax\cdot b\cdot y)=-abW+Wab+bWa.\\
x^2ay^2byx=(x^2\cdot a\cdot y^2by\cdot x)=-Wab+bWa.\\
x^2y^2aybx=(x^2\cdot y^2ay\cdot b\cdot x)=abW-bWa.\\
\end{array}$$
Likewise we obtain identities of multidegree $(3,3,1,1,1)$: $$\begin{array}{l}
x^2ay^2bxcy=(x^2\cdot a\cdot y^2b\cdot x)cy=abcW+acWb+bcWa-aWbc-Wabc.\\
x^2ay^2bycx=(x^2\cdot ay^2\cdot byc\cdot
x)=abcW-abWc-acWb+aWbc+bWac-Wabc.\\
T_3(x^2axby^2,c,y)=0\Rightarrow\\
x^2axby^2cy=cabW-abWc+caWb-cbWa-aWcb+bWac-cWab+Wcab.
\end{array}$$
Modulo the identities which we obtained, each word is equivalent to an element of the required form.
\[predl1.1\] Let $w$ have degree $3$ in $x$ and $y$. Then the result of substitution $\{x\rightarrow y,\;y\rightarrow x\}$ is $-w$.
Let us denote the result of substitution by $u$. Statement \[predl1\] implies $w=\sum\alpha_iu_iW_{xy}w_i=/{\rm
see~{(\ref{1p3})}}/=-\sum\alpha_iu_iW_{yx}w_i=-u$.
By Corollary \[predl1.1\] we have for any word $u$
\[0www\] W\_[ij]{}uW\_[kl]{}=W\_[kl]{}uW\_[ij]{}.
Thus every permutation of subwords of the form $W_{ij}$, $i\neq
j$, does not change a word. So with abuse of notation we denote all such words by one symbol $W$, i.e. $uWv$ equals $uW_{ij}v$ for some $i\neq j$ such that letters $x_i,x_j$ are not contained in $u,v$.
\[predl1.2\] Every word of multidegree $3^{(2k)}$ equals $\alpha W^k$.
See Statement \[predl1\].
\[predl1.3\] Every word of multidegree $3^{(2k+1)}$ equals $\alpha
x^2WxW^{k-1}$, $k>0$.
Identity $T_2(W,x)=0$ implies $W^2x+WxW+xW^2=0$. Multiplying the latter identity first from the left and then from the right by $x^2$, we get
\[bwww\] x\^2W\^2x=-x\^2WxW, x\^2W\^2x=-Wx\^2Wx
(see [(\[a\])]{}). Thus
\[bwww1\] Wx\^2Wx=x\^2WxW.
Identities $T_2(W,xW)=xW^3+W^2xW+WxW^2=0$ and $T_2(W,Wx)=W^3x+W^2xW+WxW^2=0$ imply that
\[cwww\] xW\^3=W\^3x.
Let $r\in\{0,1,2\}$, $s\geq0$. Identities [(\[cwww\])]{}, [(\[bwww\])]{} imply $x^2W^{3s+r}x=x^2W^rxW^{3s}=r\cdot x^2WxW^{3s+r-1}$, since $p=3$. Owing to [(\[bwww1\])]{}, we have
\[dwww\] W\^ix\^2W\^lxW\^j=lx\^2WxW\^[i+j+l-1]{},i,j,k0.
This formula and Statement \[predl1\] conclude the proof.
\[predl2.p3\] If ${\mathop{\rm mdeg}}(uv)=3^{(d)}$, $d=2k$ or $d=6m+1$ ($k,m>0$), then $uv=vu$.
Owing to Statement \[canon\], we may assume that the words $u$, $v$ are canonical. We will prove the Statement by ’decreasing’ induction on $s$, where $s$ is the number of subwords of the form $W$ in words $u$ and $v$.
[**Induction base.**]{} Let $d=2k$. If $s=k$, then $u=W^l$, $v=W^{k-l}$ $(0<l<k)$, and Statement \[predl2.p3\] follows from [(\[0www\])]{}.
Let $d=6m+1$. If $s=3k$, then $uv=W^ix^2W^lxW^j$, where $i+j+l=3m$, and both subwords $u$ and $v$ are products of elements of the set $\{x^2,x,W,\ldots,W\}$. Consider all possibilities:
1\) $uv=W^ix^2W^{l_1}\cdot W^{l_2}xW^j$. Identities [(\[dwww\])]{} and [(\[a\])]{} imply $uv=(l_1+l_2)x^2WxW^{3m-1}$, $vu=-(j+i)x^2WxW^{3m-1}$. Since $i+j+l_1+l_2=3m$, words $u$ and $v$ commute.
2\) $uv=W^ix^2W^lxW^{j_1}\cdot W^{j_2}$.
3\) $uv=W^{i_1}\cdot W^{i_2}x^2W^lxW^j$.
The last two cases are similar to the first one.
[**Induction step.**]{} Assume that $x$ and $y$ are not contained in any of the subwords $W$ of words $u$ and $v$. Up to change of notations, all possibilities can be reduced, by means of [(\[a\])]{}, to the following:
1\) $u$ contains $x^2$, $x$, $y^2$, $y$; $v$ does not contain letters $x$, $y$.
2\) $u=ax^2by^2c$, $v=dxeyf$.
3\) $u=ax^2by^2c$, $v=dyexf$.
4\) $u=ax^2bxc$, $v=dy^2eyf$.
5\) $u=ax^2bxcy^2d$, $v=eyf$.
6\) $u=ax^2by^2cxd$, $v=eyf$.
7\) $u=ay^2bx^2cxd$, $v=eyf$.
Here words $a,\ldots,f$ can be empty. Consider these cases:
1\) is obvious.
2\) Identity $uv=vu$ is equivalent to $a(x^2by^2c\cdot
dxey)f=d(xeyf\cdot ax^2by^2)c$. Applying Statement \[predl1\] to the subwords in parentheses, we can see that the previous identity is equivalent to $abcdeWf+abeWcdf+acdeWbf-abWcdef-aWbcdef =
defabWc+debWfac+ dfabWec- deWfabc-dWefabc$. By induction hypothesis, $-abcdeWf+ abeWcdf+acdeWbf+ abWcdef-aWbcdef -acdebWf
-abWecdf +abcdWef = 0$. Changing notations $b\rightarrow a$, $cd\rightarrow b$, $e\rightarrow c$, we can see that the latter identity follows from $-abcW-bcaW+abWc+acWb+bcWa+aWbc -aWcb-Wabc =
0$. The last identity was verified by means of a computer programme, which was written by means of Borland C++ Builder (version 5.0). The programme is available upon request from the author.
The rest of the possibilities can be treated likewise.
Matrix invariant algebra {#chapter_matr}
========================
Auxiliary results {#technik}
-----------------
Similarly to the definition of $R_d$ in terms of projective limits, let ${\overline{R_d}}=\bigoplus_{r\geq0}{\mathop{\rm{projlim }}}_n{\overline{R_{n,d}}}(r)$, or, equivalently, ${\overline{R_d}}=R_d/(R_d^{+})^2$. The algebras $R_{n,d}$, ${\overline{R_{n,d}}}$, $R_d$, $K\mbox{-}{\mathop{\rm alg}}\{X_1,\ldots,X_d\}\subset
C_{n,d}$ possess the natural $N_0$-grading by degrees and $N_0^d$-grading by multidegrees, for which we use the same notations as in Introduction. If elements $r_1,r_2$ of $R_{n,d}$ (of $R_d$, respectively) are equal modulo the ideal $(R_{n,d}^{+})^2$ ($(R_d^{+})^2$, respectively), we write $r_1\equiv r_2$. Since the ideal $(R_{n,d}^{+})^2$ is homogeneous with respect to the $N_0^d$-grading, one can see that for every equality of the form $r\equiv0$, $r\in R_{n,d}$, and $N_0^d$-homogeneous component $r^\prime$ of $r$, $r^\prime\equiv0$ is also true. As in Section 2, monomials in the generic matrices $X_i\in C_{n,d}$ are called words, and $X_i$ — letters. The same terminology is used for elements of $C_d$. By letters $U,V,W$, possibly, with indices, we denote non-empty words in the generic matrices, if we do not explicitly write otherwise.
\[lemma2\] $$\frac{C_{n,d}}{\mbox{\rm id}\{ R_{n,d}^{+}\}} \simeq N_{n,d}.$$
**Proof**. As we mentioned in Introduction, $$C_{n,d}\simeq \frac{C_d}{J_{n,d}}\simeq \frac{R_d{\langle}x_1,\ldots,x_d{\rangle}}{\mbox{\rm id}\{\chi_k(f)| k\geq
n,\;f\in R_d{\langle}x_1,\ldots,x_d{\rangle}^{\#}\}}.$$ Let $f\in C_d^{\#}$ and $f=f'+f''$, where $f'\in K{\langle}x_1,\ldots,x_d{\rangle}^{\#}$, $f''\in R_{d}^{+}C_d^{\#}$. Then $\chi_k(f)\in C_d$ is equal to $f'^k$ modulo the ideal ${{{\rm id}\{{R_{d}^{+}}\}}}\triangleleft C_d$, because $\sigma_j(g)\in
R_d^{+}$ for every $g\in C_{d}^{\#}$, $j>0$. Thus the ideal $J_{n,d}$ is equal to $\mbox{\rm id}\{f^n| f\in K{\langle}x_1,\ldots,x_d{\rangle}^{\#}\}\triangleleft C_d$ modulo the ideal $\mbox{\rm id}\{R_{d}^{+}\}$. It is easy to see that the preimage of the ideal $\mbox{\rm id}\{R_{n,d}^{+}\}\triangleleft C_{n,d}$ in $C_d$ is equal to $\mbox{\rm id}\{R_{d}^{+}\}+J_{n,d}$. By the Theorem on Homomorphism and the two preceding remarks, we have
$$\frac{C_{n,d}}{\mbox{\rm id}\{ R_{n,d}^{+}\}} \simeq
\left.{\frac{C_d}{J_{n,d}}}\right/\frac{\mbox{\rm id}\{
R_d^{+}\}+J_{n,d}}{J_{n,d}}\simeq\frac{C_d}{\mbox{\rm id}\{ R_d^{+}\}+J_{n,d}}\simeq$$
$$\simeq\frac{C_{d}}{\mbox{\rm id}\{ R_d^{+}\}+\mbox{\rm id}\{ f^n|
f\in K{\langle}x_1,\ldots,x_d{\rangle}^{\#}\}}\simeq N_{n,d}. \bigtriangleup$$ The image of $G\in C_{n,d}$ in $N_{n,d}$ we denote by ${\overline{G}}$. We denote any triple of pairwise distinct generic matrices by $X,Y,Z$, and their images we denote by $x,y,z$. We assume that ${\sigma}_k(f)$, where $f\in C_d^{\#}$, is an element of $R_{n,d}$, unless it is stated otherwise.
We will use the fact that ${{\rm tr}}(XY)$ is a nongenerate bilinear form, namely, if ${{\rm tr}}(GX_d)=0$, where $G\in M_n(K_{n,d-1})$, then $G=0$.
\[cr\_1\] Suppose that $G\in K\mbox{-}{\mathop{\rm alg}}\{X_1,\ldots,X_d\}^{\#}$. Then
1\) If ${\overline{G}}=0$ in $N_{n,d}$ then ${\sigma}_k(GX)$ is decomposable, where $k>0$.
2\) If $G$ does not contain $X$ and ${{\rm tr}}(GX)$ is decomposable, then ${\overline{G}}=0$ in $N_{n,d}$.
1\) Owing to Lemma \[lemma2\], the identity ${\overline{G}}=0$ implies $G=\sum_i r_iU_i$, where $r_i\in R_{n,d}^{+}$, $\deg(U_i)\geq0$. Thus ${\sigma}_k(GX)={\sigma}_k(\sum_{i} r_iU_iX)$ is decomposable (see [(\[amiss\])]{}).
2\) Let ${{\rm tr}}(GX)$ be decomposable. Since $R_{n,d}$ is homogeneous, we have ${{\rm tr}}(GX)=\sum{{\rm tr}}(U_iX)r_i$, where words $U_i$ may be empty, $\deg_X(U_i)=0$ and $r\in R_{n,d}^{+}$. Hence ${{\rm tr}}((G-\sum
r_iU_i)X)=0$. Since the trace form is nongenerate, we have $G=\sum
r_iU_i\in \mbox{id}\{R_{n,d}^{+}\}$. Therefore ${\overline{G}}=0.$
Further, we assume $n=3$. Word $U$ is called [*canonical*]{}, if $\overline{U}\in N_{3,d}$ is canonical.
\[can\] For every non-empty word $U$ there exist decompositions $${{\rm tr}}(U)\equiv\sum\alpha_i{{\rm tr}}(W_i),\;\;{\sigma_2}(U)\equiv\sum\beta_j{\sigma_2}(U_j)+\sum
\gamma_l{{\rm tr}}(V_l),$$ where $W_i,U_j,V_l$ are canonical words. Moreover, homogeneity of ideal $(R_{3,d}^{+})^2$ implies that multidegrees of ${{\rm tr}}(U)$ and ${{\rm tr}}(W_i)$ are all equal, and also that multidegrees of ${\sigma}_2(U)$, ${\sigma}_2(U_j)$ and ${{\rm tr}}(V_l)$ are all equal.
First we will prove the Lemma for the trace. Owing to Lemma \[cr\_1\] and linearity of the trace, one can prove formulas analogous to [(\[a1\])]{} and [(\[a\])]{}, namely, for $i={\overline{1,d}}$ we have ${{\rm tr}}(V_1X_iVX_iV_2) \equiv -{{\rm tr}}(V_1X_i^2VV_2) -
{{\rm tr}}(V_1VX_i^2V_2)$,
\[can\_id2\] [[tr]{}]{}(V\_1X\_iVX\_i\^2V\_2)-[[tr]{}]{}(V\_1X\_i\^2VX\_iV\_2).
Here one of words $V_1$, $V_2$ can be empty. Hence the Lemma is proved for the trace.
The proof for ${\sigma_2}(U)$ is similar, except that instead of the trace linearity we apply consequence of Amitsur’s formula for ${\sigma_2}$: ${\sigma_2}(V_1+V_2)\equiv{\sigma_2}(V_1)+{\sigma_2}(V_2)-{{\rm tr}}(V_1V_2)$, and then we apply the proved part of the Lemma to ${{\rm tr}}(V_1V_2)$.
\[cr\_2\] Suppose that $G\in K\mbox{-}{\mathop{\rm alg}}\{X_1,\ldots,X_d\}$, $G$ does not contain $X$. Then
1)If ${{\rm tr}}(GX^2)$ is decomposable then $gx+xg=0$ in $N_{3,d}$, where $g={\overline{G}}$.
2)In the case $p\neq2$, the converse is also valid.
1\) Substituting $X+Y$ for $X$, where $X$, $Y$ are not contained in $G$, and taking the homogeneous component of degree $1$ in $X$ and in $Y$, we get ${{\rm tr}}(GXY)+{{\rm tr}}(GYX)\equiv0$. Hence ${{\rm tr}}((GX+XG)Y)\equiv0$. Lemma \[cr\_1\] concludes the proof.
2\) By Lemma \[cr\_1\], we have ${{\rm tr}}((GX+XG)X)\equiv0$. Hence, $2{{\rm tr}}(GX^2)\equiv0$.
\[cr\_3\] Let $\deg_X(U)=\deg_X(V)=0$ and $u={\overline{U}}$, $v={\overline{V}}$.
1)If ${{\rm tr}}(X^2UXV)\equiv0$ then $ux^2v-2vx^2u-x^2uv-uvx^2=0$ in $N_{3,d}$.
2)In the case $p\neq3$, the converse is also valid.
1\) Substituting $X+Y$ for $X$ in ${{\rm tr}}(X^2UXV)\equiv0$, and taking the homogeneous component of degree $2$ in $X$ and of degree $1$ in $Y$, we get ${{\rm tr}}(VX^2UY)+{{\rm tr}}(UXVXY)+{{\rm tr}}(XUXVY)\equiv0$. Here words $U$, $V$ do not contain $X$, $Y$. By Lemma \[cr\_1\], we have $vx^2u+uxvx+xuxv=0\;\;\mbox{in } N_{3,d}$. This, together with identity [(\[a1\])]{}, yields the required equality.
2\) By Lemma \[cr\_1\], we have ${{\rm tr}}(UX^2VX)-2{{\rm tr}}(VX^2UX)\equiv0$. The identity [(\[can\_id2\])]{} gives $3{{\rm tr}}(X^2UXV)\equiv0$.
Applying Amitsur’s formula to ${\sigma}_2(U+V)$ and letting $V=U$, obtain
\[q0\] 2[\_2]{}(U)=[[tr]{}]{}\^2(U)-[[tr]{}]{}(U\^2).
\[predl\_si\] $a$) ${\sigma_2}(X)$, $\det(X)$ are indecomposable. In particular, $D_{\det}(3,d,K)=3$ and $D(3,1,K)=3$.
$b$) ${{\rm tr}}(X^2)$ is decomposable $\Leftrightarrow$ $p=2$.
$c$) ${{\rm tr}}(X^3)$ is decomposable $\Leftrightarrow$ $p=3$.
$a)$ Let ${\sigma}_k(X)$ be decomposable ($k=2,3$). Then, by $D)$, ${\sigma}_k(X)$ can be expressed in terms of ${\sigma}_l(X)$, $l<k$. Substitution $X={\mathop{\rm diag}}(x_1,x_2,x_3)$ yields a contradiction to the fact that an elementary symmetric polynomial can not be expressed in terms of other elementary symmetric polynomials.
Lemma \[cr\_1\] implies ${{\rm tr}}(X^k)\equiv0$, $k>3$, and $D)$ implies ${\sigma}_2(X^k)\equiv0$, $k>1$.
$b)$ For $p=2$, by [(\[q0\])]{}, ${{\rm tr}}(X^2)\equiv0$. For $p\neq2$, if ${{\rm tr}}(X^2)\equiv0$, then $2x=0$ in $N_{3,d}$ (see Lemma \[cr\_2\]), which is false.
$c)$ If ${{\rm tr}}(\chi_3(X))=0$, then ${{\rm tr}}(X^3)\equiv3\det(X)$.
The case of characteristic equal to $0$ or greater than $3$
-----------------------------------------------------------
If $p=0$ or $p>3$, $d>1$, then $D(3,d,K)=6$.
Element ${{\rm tr}}(X_1\cdots X_7)$ is decomposable by Lemma \[cr\_1\] and identity $x_1\cdots x_6=$ $0$ in $N_{3,d}$. Hence ${{\rm tr}}(U)\equiv0$ for every $U$ with $\deg(U)>6$.
Let us prove that ${{\rm tr}}(X^2Y^2XY)$ is indecomposable. Assume that it is decomposable. Letting $U=X^2$, $V=X$ and applying Lemma \[cr\_3\], we obtain $x^2y^2x-2xy^2x^2=0$ in $N_{3,d}$. Then $x^2y^2x=0$ (see [(\[a\])]{}). But this yields a contradiction (see Statement \[prop3\]).
Formula [(\[q0\])]{} concludes the proof.
The case of characteristic equal to $2$
---------------------------------------
If $p=2$, then $D(3,d,K)=\left\{
\begin{array}{ccl}
d+2&,&d\geq4\\
6&,&d=2\;{\rm or}\; 3\\
\end{array} \right..
$
The proof is a consequence of the following two statements.
\[predl\_p2\_tr\] If $p=2$, then $D_{{{\rm tr}}}(3,d,K)=\left\{
$
By Lemma \[can\], it is sufficient to consider ${{\rm tr}}(U)$, where $U$ is canonical.
First we point out some restrictions on the multidegree of an indecomposable invariant, namely, ${{\rm tr}}(U)$ is decomposable if multidegree of $U$ is equal to
$a)$ $\Delta_1=(2,2,2,i_4,\ldots,i_d)$, where $i_4+\cdots+i_d\geq
1$.
$b)$ $\Delta_2=(3,2,i_3,i_4,\ldots,i_d)$, where $i_3+\cdots+i_d\geq 2$.
Let us prove it. Every canonical word of multidegree $\Delta_1$ is equal to\
$U_1X_{\pi(1)}^2U_2X_{\pi(2)}^2U_3X_{\pi(3)}^2U_4$, $\pi\in
S_3$, where some words $U_1,\ldots,U_4$ (but not all of them) can be empty. Formula [(\[f2\])]{} and Lemma \[cr\_1\] yield ${{\rm tr}}(X^2V_1Z^2V_2)\equiv0$. Hence, decomposability is established for $a)$.
Let the multidegree of $U$ be equal to $(3,2,1,1,i_5,\ldots,i_d)$. Then ${{\rm tr}}(U)$ is decomposable, because each word from $N_{3,d}$ of multidegree $(3,2,1,j_4,\ldots,j_d)$ is equal to $0$ (see Section \[case\_p\_2\]); then we apply Lemma \[cr\_1\], which gives decomposability for $b)$.
Let $d=2$. Then ${{\rm tr}}(X^2Y^2XY)$ is a maximal indecomposable element (otherwise $y^2x^2y=0$ in $N_{3,d}$, by Lemma \[cr\_3\], but this is a contradiction, by Statement \[prop3\]). Invariants of greater degree are, evidently, decomposable.
Let $d=3$. Then ${{\rm tr}}(X^2Y^2Z^2)$ is a maximal indecomposable element (otherwise Lemma \[cr\_2\] implies $x^2y^2z+zx^2y^2=0$ in $N_{3,d}$, thus $x^2y^2x=xx^2y^2=0$ in $N_{3,d}$, by [(\[a\])]{}, but $x^2y^2x\neq0$ — see Statement \[prop3\]). All invariants of greater degree are decomposable by $b)$. Also note that ${{\rm tr}}(X^2Y^2XZ)$ is indecomposable, because, assuming that it is decomposable and letting $Z=Y$, we get that ${{\rm tr}}(X^2Y^2XY)$ is decomposable.
Let $d\geq4$. Invariant ${{\rm tr}}(X_1^2X_2X_1X_3\cdots X_d)$ is a maximal indecomposable element, because $x_1^2x_2x_1x_3\cdots
x_{d-1}\neq0$ in $N_{3,d}$ (see Statement \[predl\_p2\_1\] and Lemma \[cr\_1\]). All words of greater degree are decomposable by $a)$ and $b)$. Note that ${{\rm tr}}(X_1^2X_2X_1X_3\cdots X_d)$ is indecomposable (see Remark \[note\_p2\] and Lemma \[cr\_1\]).
\[predl\_p2\_sigma\] If $p=2$, then $D_{{\sigma}_2}(3,d,K)=\left\{
\begin{array}{ccc}
6&,&d\geq3\\
4&,&d=2\\
\end{array} \right..
$
Applying Amitsur’s formula to ${\sigma}_4(u+v)=0$, where $u,v\in K{\langle}x_1,\ldots,x_d{\rangle}^{\#}$ are words, and considering the result modulo the ideal $(R_{3,d}^{+})^2$, we obtain ${\sigma}_2(UV)+{{\rm tr}}(U^3V)+{{\rm tr}}(V^3U)+{{\rm tr}}(U^2V^2)\equiv0$, where $U,V$ are non-empty words in the generic matrices. Since ${{\rm tr}}(U^3V)$ is decomposable (see Lemma \[cr\_1\]), we have
\[m\_q2\] \_2(UV)[[tr]{}]{}(U\^2V\^2).
Letting $U=X^2$, we obtain ${\sigma_2}(X^2V)\equiv0$ (see Lemma \[cr\_1\]).
Let $U=X_1$, $V=X_2\cdots X_d$. Then [(\[m\_q2\])]{}, together with the identity of $N_{3,d}$ $(x_2\cdots x_d)^2-x_d^2\cdots x_2^2=0$ (which is a consequence of [(\[1p1\])]{}), to which we apply Lemma \[cr\_1\], yields ${\sigma_2}(X_1\cdots X_d)\equiv {{\rm tr}}(X_1^2(X_2\cdots
X_d)^2)\equiv {{\rm tr}}(X_1^2X_d^2\cdots X_2^2)$. Element ${{\rm tr}}(X^2Y^2)$ is indecomposable (otherwise Lemma \[cr\_2\] implies $x^2y+yx^2=0$ in $N_{3,d}$, thus $x^2y^2x=-y^2x^2x=0$, but the last identity contradicts Statement \[prop3\]). This reasoning and Statement \[predl\_p2\_tr\] imply that ${\sigma_2}(X_1\cdots X_d)$ is decomposable iff $d\geq 4$. By Lemma \[can\], the statement \[predl\_p2\_sigma\] is proved.
The case of characteristic equal to $3$
---------------------------------------
\[p3\] If $p=3$, then $D(3,d,K)= \left\{
\begin{array}{ccl}
3d&,&d\;{\rm \ is\ even}\\
3d-1&,&d\equiv 3,5\;({\mathop{\rm{mod }}}6) \\
3d-1 \;{\rm or}\; 3d&,& d\equiv 1\;({\mathop{\rm{mod }}}6). \\
\end{array} \right.$
To prove the proposition, we need more detailed study of identities of ${\overline{R_{3,d}}}$.
\[pr3\] If $\sum\alpha_iu_i=0$ in $N_{3,d}$, where $u_i$ are words, then $\sum\alpha_i{{\rm tr}}(U_i)\equiv0$ in ${\overline{R_{3,d}}}$, where ${\overline{U_i}}=u_i$. Note that this identity is a consequence of $${{\rm tr}}(dT_1(a)e)\equiv0,\;{{\rm tr}}(dT_2(a,b)e)\equiv0,\;{{\rm tr}}(dT_3(a,b,c)e)\equiv0,$$ where words $a,b,c\in K{\langle}x_1,\ldots,x_d{\rangle}^{\#}$, and words $d,e\in K{\langle}x_1,\ldots,x_d{\rangle}$.
Denote by $A,B,C,D,E$ words in the generic matrices, where $D$ and $E$ can be empty. Owing to Lemmas \[predl\_si\] and \[cr\_1\], ${{\rm tr}}(DA^3E)$ is decomposable. Linearization yields ${{\rm tr}}(DT_2(A,B)E)\equiv0,\;\;{{\rm tr}}(DT_3(A,B,C)E)\equiv0$.
Hence, if $g=0$ is an identity from ${{{\mathcal{S}} }}$, then ${{\rm tr}}(G)=0$ holds in ${\overline{R_{3,d}}}$, where ${\overline{G}}=g$ (see Section \[intro\]). Since all identities of $N_{3,d}$ are consequences of system ${{{\mathcal{S}} }}$, every identity of $N_{3,d}$ has a counterpart in $R_{3,d}$.
\[m\_lemma1\] All identities of the algebra ${\overline{R_{3,d}}}=R_{3,d}/(R_{3,d}^{+})^2$ are consequences of
\(a) ${{\rm tr}}(dT_1(a)e)\equiv0,\;{{\rm tr}}(dT_2(a,b)e)\equiv0$, ${{\rm tr}}(dT_3(a,b,c)e)\equiv0$.
\(b) ${{\rm tr}}(ab)\equiv{{\rm tr}}(ba)$.
\(c) ${\sigma}_2(a)\equiv {{\rm tr}}(a^2)$.
\(d) $\det(ab)\equiv0$.
\(e) ${\sigma}_k(a)\equiv0$, $k>3$.
Here words $a,b,c\in K{\langle}x_1,\ldots,x_d{\rangle}^{\#}$, and words $d,e\in K{\langle}x_1,\ldots,x_d{\rangle}$.
For $I\in\{A,B,C,D,E\}$ let $({\overline{I}})$ be the identity obtained by factorization of $(I)$ modulo the ideal $(R_{3,d}^{+})^2$. Denote by $(I_w)$, $({\overline{I_w}})$, respectively, those identities of type $(I)$, $({\overline{I}})$, respectively, in which $g,h\in K{\langle}x_1,\ldots,x_d{\rangle}^{\#}$ are words. Throughout this proof we denote by letters $u,v$, possibly with indices, non-empty words from $K{\langle}x_1,\ldots,x_d{\rangle}$. The ideal of relations of $R_d$ is generated by $(A_w)$ and $(D_w)$ (see [@Zub2]). Thus for the proof it is sufficient to show that $({\overline{A_w}})$, $({\overline{D_w}})$, $({\overline{E}})$ can be deduced from $(a)$–$(e)$. For $({\overline{A_w}})$ it is obvious. Consider $({\overline{D_w}})$: ${\sigma}_k(u^t)\equiv \alpha_{k,t}{\sigma}_{kt}(u)$, where $k\geq1$, $t\geq2$.
Let $k=1$, $t=2$. Since ${\sigma}_2(u)$ is indecomposable (Lemma \[predl\_si\]), we have ${\alpha}_{1,2}=1$, and $({\overline{D_w}})$ follows from $(c)$.
Let $k=1$, $t=3$. Since ${{\rm tr}}(u^3)$ is decomposable and $\det(u)$ is indecomposable (Lemma \[predl\_si\]), we have ${\alpha}_{1,3}=0$, and $({\overline{D_w}})$ follows from $(a)$.
If $k=1$, $t\geq4$, then $({\overline{D_w}})$ follows from $(a)$, $(e)$.
If $k=2$, then $({\overline{D_w}})$ follows from $(c)$ and $(a)$, $(e)$.
If $k=3$, then $({\overline{D_w}})$ follows from $(d)$, $(e)$.
If $k\geq4$, then $({\overline{D_w}})$ follows from $(e)$.
For the proof of deducibility of $({\overline{E}})$ we need some properties of identities of ${\overline{R_{3,d}}}$.
1. If an identity of ${\overline{R_{3,d}}}$ $t(x_1,\ldots,x_d)\equiv0$ can be deduced from $(a)$–$(e)$, then the identity $t(r_1u_1,\ldots,r_du_d)\equiv0$, where $r_i\in R_{3,d}$, can be deduced from $(a)$–$(e)$.
Let us prove $1)$. By homogeneity of $(a)$–$(e)$ we may assume $t(x_1,\ldots,x_d)\equiv0$ to be $N_0^d$-homogeneous. Then the identity $t(r_1u_1,\ldots,r_du_d)\equiv0$ has the form $r\cdot
t(u_1,\ldots,u_d)\equiv0$, $r\in R_{3,d}$. Clearly the latter identity is a consequence of $(a)$–$(e)$.
1. Let $u_i$ be words such that $\deg_{x_1}(u_i)\in\{1,2\}$, and let
\[to1\] \_i[[tr]{}]{}(u\_i)0
be an identity of ${\overline{R_{3,d}}}$. Then [(\[to1\])]{} follows from $(a)$, $(b)$. In particular, if [(\[to1\])]{} is an identity of ${\overline{R_{3,d}}}$ and $\deg(u_i)\neq3s$, then [(\[to1\])]{} follows from $(a)$, $(b)$.
Let us prove $2)$. Identity [(\[to1\])]{} can be assumed to be homogeneous. Let $\deg_{x_1}(u_i)= 1$. Rewrite identity [(\[to1\])]{} in the form $\sum{\alpha}_i{{\rm tr}}(v_ix_1)\equiv0$, where words $v_i$ can be assumed to be non-empty. By Lemma \[cr\_1\], $\sum {\alpha}_iv_i=0$ in $N_{3,d}$. But then $\sum {\alpha}_i v_ix_1=0$ in $N_{3,d}$, and Lemma \[pr3\] concludes the proof.
Let $\deg_{x_1}(u_i)=2$. Identity [(\[to1\])]{} can be deduced from an identity $\sum\beta_i{{\rm tr}}(v_ix_1^2)\equiv0$ by $(a)$ (see Lemma \[can\]), where words $v_i$ can be assumed to be non-empty. By Lemma \[cr\_2\], we have $\sum
\beta_i(x_1v_i+v_ix_1)=0$ in $N_{3,d}$. Substituting $x_1^2$ for $x_1$, applying Lemma \[pr3\] and using $(b)$, we get the required.
1. Denote by $(a_{*})$, $(b_{*})$, $(c_{*})$, $(d_{*})$ identities of ${\overline{R_{3,d}}}$ of the type $(a)$–$(d)$, respectively, in which $a,b,c\in K{\langle}x_1,\ldots,x_d{\rangle}^{\#}$ and $d,e\in K{\langle}x_1,\ldots,x_d{\rangle}$ (here $a,b,c,d,e$ are not necessarily words). Thus $(a_{*})$–$(d_{*})$ follow from $(a)$–$(d)$.
Let us prove $3)$. Deducibility of $(a_{*})$, $(b_{*})$ from $(a)$, $(b)$ is obvious. Owing to property $1)$, we can assume that $a=\sum\nolimits_{i=1}^s x_i$, $b=\sum\nolimits_{i=s+1}^t
x_i$ in $(c_{*})$, $(d_{*})$.
Consider $(c_{*})$: ${\sigma}_2(\sum x_i)\equiv {{\rm tr}}((\sum x_i)^2)$. Owing to $(c)$, identity $(c_{*})$ follows from some identity of ${\overline{R_{3,d}}}$ of the type $\sum\beta_i{{\rm tr}}(v_i)\equiv0$, where $v_i$ are words of degree $2$. The latter identity follows from $(a)$, $(b)$ by property $2)$.
Consider $(d_{*})$: $\det((\sum_{i=1}^{s} x_i)(\sum_{i=s+1}^{t}
x_i))\equiv0$. By $(d)$, identity $(d_{*})$ follows from some identity of ${\overline{R_{3,d}}}$ of the type $\sum
\gamma_l{{\rm tr}}(w_l)\equiv0$, where $w_l$ are products of words $x_ix_j$ ($i={\overline{1,s}}$, $j={\overline{s+1,t}}$) and $\deg(w_l)=6$. Taking homogeneous components, we may assume that this identity is homogeneous of multidegree $\Theta$.
Let $\Theta\neq(3,3)$. Then all words $w_l$ have degree $1$ or $2$ in some letter $x_r$. Applying property $2)$, we conclude the proof for this case.
Let $\Theta=(3,3)$. Then for each $l$ for some $r,q$ we have $w_l=(x_rx_q)^3$, and the identity follows from $(a)$. Thus $3)$ is proved.
Now we can show that $({\overline{E}})$: ${\sigma}_k(h)\equiv0$, where $k\geq4$, $h=\sum_{i=1}^{m} r_iu_i$, $r_i\in R_d$, follows from $(a)$–$(e)$. By property $1)$, we can assume $r_i=1$, $u_i=x_i$. Our proof is by induction on $k\geq4$, and for a fixed $k$ — by induction on $m$.
[**Induction base**]{}. Let us show that $(a)$–$(e)$ imply ${\sigma}_k(x_1+x_2)\equiv0$. Owing to $(c)$–$(e)$, this identity is a consequence of some identity of ${\overline{R_{3,d}}}$ of the form $\sum{\alpha}_i{{\rm tr}}(v_i)\equiv0$.
If $k=4,5$, then $\deg(v_i)=4$ or $5$. The proof is concluded, by property $2)$.
If $k=6$, then, by $(d)$ and $(e)$, the considered identity follows from $-{\sigma}_2(x_1^2x_2) -{\sigma}_2(x_1x_2^2)+
{{\rm tr}}(x_1^2x_2^2x_1x_2)+ {{\rm tr}}(x_2^2x_1^2x_2x_1) \equiv0$. Identities $(c)$ and $(a)$ imply ${\sigma}_2(x_1^2x_2)\equiv0$, ${\sigma}_2(x_1x_2^2)\equiv0$. Identity ${{\rm tr}}(x_1^2x_2^2x_1x_2)+{{\rm tr}}(x_2^2x_1^2x_2x_1)\equiv0$ follows from $(a)$, by Lemma \[pr3\] applied to $x_1^2x_2^2x_1x_2+x_2^2x_1^2x_2x_1=0$ in $N_{3,d}$ (see [(\[1p3\])]{}).
If $k\geq7$, then for every $i$ we have $\deg_{x_1}(v_i)>3$ or $\deg_{x_2}(v_i)>3$, thus $v_i=0$ in $N_{3,d}$. Hence ${{\rm tr}}(v_i)\equiv0$ follows from $(a)$ (see Lemma \[pr3\]).
[**Induction step**]{}. Consider identity of ${\overline{R_{3,d}}}$ ${\sigma}_k(x_1+x_2) = {\sigma}_k(x_1)
+{\sigma}_k(x_2) + \sum_j{\alpha}_{j}{\sigma}_{k_j}(u_j)\equiv0$, where $k_j<k$. Let $g=\sum_{i=2}^m x_i$. The induction hypothesis yields ${\sigma}_k(x_2|_{x_2\rightarrow g})\equiv0$, ${\sigma}_{k_j}(u_j|_{x_2\rightarrow g})\equiv0$ $(k_j>3)$ follow from $(a)$–$(e)$. Because ${\sigma}_k(x_1+x_2)\equiv0$ is a consequence of $(a)$–$(e)$, we have $\sum_{k_j\leq3} {\alpha}_j{\sigma}_{k_j} (u_j)
\equiv0$ follows from $(a)$–$(d)$. Hence $\sum_{k_j\leq3}
{\alpha}_j{\sigma}_{k_j} (u_j|_{x_2\rightarrow g}) \equiv0$ follows from $(a)$–$(d)$, by property $3)$. The lemma is proved.
\[pr4\] Let $U_i$ be words of equal multidegree $\Theta$. Then
\[x1\] \_i[[tr]{}]{}(U\_i)0
is an identity of ${\overline{R_{3,d}}}$ if and only if system ${{{\mathcal{S}} }_{\Theta}}$ and identities $uv=vu$, where $u,v\in K{\langle}x_1,\ldots,x_d{\rangle}^{\#}$ are words and ${\mathop{\rm mdeg}}(uv)=\Theta$, imply that $\sum\limits \alpha_i{\overline{U_i}}=0$.
$\Leftarrow$ Apply Lemma \[pr3\].
$\Rightarrow$ By Lemma \[m\_lemma1\], identity [(\[x1\])]{} follows from $(a)$–$(e)$. Identities [(\[x1\])]{}, $(a)$, $(b)$ do not contain ${\sigma}_k(a)$, $k\geq2$, while identities $(c)$–$(e)$ contain them. Every ’symbolic’ element ${\sigma}_k(a)$, where $k\geq2$, occurs in exactly one identity from $(c)$–$(e)$. Then the derivation of [(\[x1\])]{} from $(a)$–$(e)$ can be transformed into a derivation of [(\[x1\])]{} from $(a)$, $(b)$. The identities [(\[x1\])]{}, $(a)$, $(b)$ are homogeneous, thus for derivation of [(\[x1\])]{} we only need identities $(a)$, $(b)$ of multidegree $\Theta$.
Now we can prove Proposition \[p3\].
By Lemma \[can\] and formula [(\[q0\])]{}, it is sufficient to consider invariants of the form ${{\rm tr}}(U)$, where word $U$ is canonical. All words of the form $X_i^2X_j^2X_iX_j$, $i\neq j$, are denoted by the same symbol $W$, and let $w={\overline{W}}$ (see Section \[case\_p\_3\] for details).
Let $d=2k$, $k>0$. In $N_{3,d}$ $w^k\neq0$, and also $uv=vu$, where ${\mathop{\rm mdeg}}(uv)=3^{(2k)}$ (Statement \[predl2.p3\]). Statement \[pr4\] yields the indecomposability of ${{\rm tr}}(W^{k})$.
Let $d=2k+1$, $k>0$. Invariant ${{\rm tr}}(X^2W^{k})$ is indecomposable, because otherwise Lemma \[cr\_2\] implies that $x_1w^k+w^kx_1=0$ in $N_{3,d}$. Substitution $x_1=1$ (see Statement \[predl2\]) yields $w^{k}=0$, which is a contradiction to Statement \[predl3\].
Let $d=6m+r$, $r\in\{3,5\}$, $m>0$. Let us show that if ${\mathop{\rm mdeg}}(U)=3^{(d)}$, then ${{\rm tr}}(U)\equiv0$. For $u={\overline{U}}$ we have $u={\alpha}v_d$, where $v_d=x^2wxw^{k-1}$, $d=2k+1$ (Corollary \[predl1.3\]). Hence ${{\rm tr}}(U)\equiv{\alpha}{{\rm tr}}(V_d)$, where ${\overline{V_d}}=v_d$ (see Lemma \[pr3\]). If $r=3$, then [(\[cwww\])]{} implies ${{\rm tr}}(V_d) \equiv {{\rm tr}}(X^2WW^{3m}X) \equiv0$. If $r=5$, then it is easy to see that ${{\rm tr}}(V_d) ={{\rm tr}}(X^2WXW^{3m+1})=
{{\rm tr}}(XWW^{3m}X^2W)\equiv{{\rm tr}}(XWX^2W^{3m}W) \equiv /{\rm
see}~{(\ref{a})}/\equiv- {{\rm tr}}(X^2WXW^{3m+1})$. Hence ${{\rm tr}}(V_d)\equiv0$.
[ ACKNOWLEDGEMENTS]{}
The author is grateful to A.N.Zubkov for helpful advices and constant attention, to G.A.Bazhenova for help with the translation. The author is also grateful to the referee whose comments considerably improved the paper.
[99]{} S.A. Amitsur, [*On the characteristic polynomial of a sum of matrices*]{}, Linear and Multilinear Algebra 8(1980), 177–182.
M. Domokos, S.G. Kuzmin, A.N. Zubkov, [*Rings of matrix invariants in positive characteristic*]{}, J.Pure Appl.Algebra 176(2002), 61–80. M. Domokos, [*Finite generating system of matrix invariants*]{}, Math.Pannon. 13(2002), N2, 175–181.
S. Donkin, [*Invariants of several matrices*]{}, Invent. Math. 110(1992), 389–401.
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A.A. Klein, [*Bounds for indices of nilpotency and nility*]{}, Arch.Math.(Basel) 76(2000), 6–10.
E.N. Kuzmin, [*On the Nagata–Higman theorem*]{}, (Russian), in: Mathematical Structures — Computational Mathematics — Mathematical Modeling, Proceedings Dedicated to the 60th Birthday of Academician L.Iliev, Sofia, 1975, 101–107.
V.L. Popov, [*The constructive theory of invariants*]{}, (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 45(1981), N5, 1100–1120. C. Procesi, [*The invariant theory of $n\times n$ matrices*]{}, Adv.Math. 19(1976), 306–381.
Yu.P. Razmyslov, [*Trace identities of full matrix algebras over a field of characteristic 0*]{}, (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 38(1974), N4, 723–756.
Yu.P. Razmyslov, [*Identities of algebras and their representations*]{}, Translations of Mathematical Monographs, 138, American Math.Soc., Providence, RI, 1994.
K.S. Sibirskii, [*Algebraic invariants of a set of matrices*]{}, (Russian), Sibirsk. Mat. Zh. 9(1968), N1, 152–164.
M.R. Vaughan–Lee, [*An algorithm for computing graded algebras*]{}, J.Symbolic Comput., 16(1993), 345–354.
A.N. Zubkov, [*Endomorphisms of tensor products of exterior powers and Procesi hypothesis*]{}, Comm. Algebra 22(1994), N15, 6385–6399.
A.N. Zubkov, [*On a generalization of the Razmyslov–Procesi theorem*]{}, (Russian), Algebra i Logika 35(1996), N4, 433–457. A.N. Zubkov, [*The Razmyslov-Procesi theorem for quiver representations*]{}, Fundamentalnaya i Prikladnaya matematika, (Russian), 7(2001), N2, 387–421.
[^1]: Supported by RFFI (grant 01.01.00674).
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What made you become a chef?
I have had a strong passion for food for as long as I can remember. I guess it started in childhood where I would always help mum cook. I first remember helping my mum baking, we used to make cupcakes, and then as I got older I used to help with the Sunday roast.
What is your previous experience in kitchens?
I took food-tech at school. This is where I really started to put my passion into practice. I went onto further develop my skill-set at Westminster Kingsway College in their culinary department where in my final year, I specialised in kitchen larder. I was fortunate enough to have great work experience at Claridges. I started washing dishes and doing prep-jobs and worked my up from there.
When I started to work at One Moorgate Place, I was lucky enough to work with a professional chef and personal friend Adam Daniels who really allowed me to experiment with food and a variety of dish compositions. I have worked for OMP for a year now and have just been promoted to Junior Sous Chef, which means I now do a bit of everything.
How would you describe your cooking style and what are your influences?
There is nothing I don't like cooking! If I had to choose a cooking style I would say I prefer fine-dining. I like exploring a variety of flavours and making a beautiful dish that has taken a lot of thought and time to prepare. I do prefer kitchen as opposed to pastry. I prefer cooking refined dishes because I feel it showcases my skills, both in terms of culinary creativity and plating-up.
What does a mid-week meal look like for you?
Well, it could be anything really. I have a very large family with 4 brothers so there is a lot of cooking to be done! Growing up, a normal mid-week meal would be consist of dishes such as: lasagne, Sheperd’s pie, Sausage and Mash, all of which cooked fresh by my mum with the gradual help from me as I got older.
Who would your dream dinner guests be and what would you cook for them?
My granddad. Unfortunately, I never got the chance to cook for him. He has been an inspiration for me throughout my career so far, it all started from him working as a fruit & veg merchant and him growing vegetables at home. I obviously took some of this on, but If I had the chance to cook for anyone, it would be him.
What would you like to get out of the Great City Chefs Competition?
Experience. I haven't done anything like this before so this is a fresh, new challenge and an opportunity to see other ideas from great chefs. I don't think it's going to be easy. I had a glimpse at the final dishes last year so I know the standards expected at the final banquet.
What would you say is your inspiration?
I have had various people who have really inspired me throughout my career – my first cooking inspiration would be my mum. Coming from such a large family, meant she had a hard task of catering from all of needs growing up, and she did a great job of it. At college, we were lucky enough to have a range of guest-chefs come into college to teach us about their experience in the food industry. They acted as key role models and influencers so I would say they definitely had something to do with it! I also follow key chefs on Instagram which always keeps me up to date!
How involved are you with regards to the design of the menu?
For my dishes, my concept is using the whole of the animal or a part that isn't widely used. I believe discarded parts of an animal can have great or even better flavour if cooked correctly in comparison to traditional cuts of meat. I chose this with the centralised theme of sustainability in mind. Plus, more chefs moving towards this way or working and are conscious of food waste so I thought that it would go down well with the judges!
When are you happiest at work?
I am happiest when I am producing something that I have created from scratch, whether at it's for an event or when doing prep. I thrive when using my ideas and when I have made other people happy with my food. I am always looking for ways to improve so I can make a dish the best it can be.
What is your favourite comfort food?
Proper cottage pie in the winter, with crispy mash and lots of gravy, but it has to be Bisto!
What restaurant did you last eat at?
Blacklock in Soho, it’s a meat heavy restaurant. They do an ‘all in’ dish which you get lots of different cuts / chops of meat, and it’s all served on top of a flatbread which soaks up all the meat juices. It was amazing. | https://www.onemoorgateplace.com/an-interview-from-great-city-chef-2019-contestant-alfie-cobley/ |
Lobster diver swallowed by humpback whale survives after it spat him out
Michael Packard, a lobster diver, was swallowed by a whale off the coast of Provincetown in Massachusetts, US, on Friday.
Lobster diver swallowed by humpback whale 
Key Highlights
A lobster diver was swallowed by a humpback whale off the coast of Cape Cod in Massachusetts on Friday
The survived to share si experience after the whale spat him out after about 30 seconds
A lobster diver who was swallowed by a humpback whale off the coast of Provincetown in the US state of Massachusetts on Friday morning survived after the mammal spat him out after 30 seconds.
Michael Packard, 56, of Wellfleet, was about 45 feet (14 meters) deep in the waters off Provincetown when he was attacked by the humpback whale. He initially thought that he was attacked by a shark, as they are common in the area, however, he soon realised that it was a whale.
"All of a sudden I felt this huge bump, and everything went dark. And I could sense that I was moving, and I was like, 'Oh, my God, did I just get bit by a shark?'" he told WBZ-TV.
He recalled, "Then I felt around, and I realized there was no teeth and I had felt, really, no great pain. And then I realized, 'Oh, my God, I'm in a whale's mouth. I'm in a whale's mouth, and he's trying to swallow me.'"
"This is it, I’m gonna die," he thought to himself.
Packard then thought about his wife and children and felt that there was no way of escaping.
"Then all of a sudden he went up to the surface and just erupted and started shaking his head. I just got thrown in the air and landed in the water. I was free and I just floated there. I couldn’t believe... I’m here to tell it," he said.
Packard estimates that he was in the mammal's mandibles for about 30 seconds.
He was pulled out of the water by crewmate Captain Joe Francis. "I jumped aboard the boat. We got him up, got his tank off. Got him on the deck and calmed him down and he goes, ‘Joe, I was in the mouth of a whale’ he goes ‘I can’t believe it, I was in the mouth of a whale Joe!’"
Packard feard that he broke his legs. He was rushed to a nearby hospital and discharged a day later. He could walk with a limp.
Peter Corkeron, a senior scientist at the New England Aquarium, said that when humpback whales feed, "they do what we call gulp feeding, and they can open their mouths up incredibly widely."
He added, "It’s a very unusual accident. . . this is a one in a — goodness knows what — trillion chance. He was just unlucky enough to be in the wrong place at the wrong time." | |
Vegan Spaghetti Bolognese
- Total time:
- 40 min
- Preparation:
- 10 min
- Cooking:
- 30 min
- Serves:
- 6
- Created by:
- QAST
- Category:
- Hot Meals
- Level:
- Easy
Ingredients
1 each Brown Onion, diced
2 each Garlic Cloves, crushed
3 cup Finely Chopped & Grated Vegetables *(see notes)
1 cup Vegan Beef Stock Liquid e.g. Massels
1 unit Tomatoes, canned
0.3 cup Tomato Paste
1 tsp Paprika
1 tsp Dried Rosemary
1 tsp Dried Thyme
1 tsp Dried Basil
5 each Dried Bay Leaves
2 tbsp Soy Sauce or Tamari
1 tbsp Vegan Worcestershire Sauce e.g. Woolworths or Spring Gully
1 tbsp Maple Syrup or Brown Sugar
1 cup Lentils, canned, drained & rinsed
0.5 cup Textured Vegetable Protein (TVP), dry
1 unit Spaghetti, packet
1 unit Vegan Parmesan or Fresh Herbs e.g. basil to serve
1 tbsp Olive Oil
Recipe
- Boil the jug, add dry TVP to a medium sized bowl, cover with boiling water and set aside.
- Dice onion and fry in a small amount of oil (e.g. olive oil)in a large, non-stick pan until translucent, on medium to hot heat. Add minced garlic and fry for 30 sec.
- Add in the finely chopped and grated vegetables and beef stock. Cook for 3-5 minutes.
- Add in the remaining ingredients, along with salt & pepper. Mix & reduce heat to a simmer for 15 - 20 minutes, mixing often.
- Once reduced, cook the spaghetti according to the packet instructions.
- Pick out the 5 bay leaves from the sauce, taste sauce and add in additional seasoning if required.
- Serve the bolognese sauce over the spaghetti and top with vegan parmesan or fresh herbs if desired.
Full description
A twist on a classic recipe kids love, with a few hidden extra veggies. The vegan protein source is textured vegetable protein (tvp, soy) or/& lentils (canned). Thanks to Peace with Plants for the recipe: https://peacewithplants.com/vegan-spaghetti-bolognese/
Variations
Finely Chopped & Grated Vegetables: e.g. 1 carrot, 1 zucchini, finely chopped broccoli and cauliflower. | http://emenu.qast.org.au/recipes/10782 |
[From Manx Quarterly, #11 Oct 1912]
Valuable Work by Archaeologists.
Professor Herdman, the well-known biologist and archaeologist, and Mr Philip M. C. Kermode, who is the principal authority on Manx antiquities, have of late been conducting excavations at Fairy Hill, Rushen. with a view to determining the nature of the mound, and the character of the artificial works on its summit and at its base. A very interesting communication from Prof. Herdman upon the subject of the excavations appeared the " Liverpool Daily Post and Mercury" of Monday, Feb. 5th, 1912, and we take the liberty of reproducing as follows:
In the " Chronicon Manniae," under the year 1249 it is recorded that Reginald II., King of Man was slain on May 30th, by the Knight Ivar in a meadow near the Church of the Holy Trinity at Rushen." It is also stated that his body was taken for burial to Rushen Abbey a very natural and probable proceeding, as Reginald was a Christian King, and Rushen Abbey was the chief ecclesiastical establishment: in the Island and the burial place of several previous kings of Man. But local tradition in the south of the Island has it that Reginald was buried in his armour, standing erect in a great tumulus-like mound near Port Erin. This is the mound known to English visitors as "The Fairy Hill." It is marked as "Cronk Mooar" on the ordinance maps, but most of the natives living around call it "Cronkey-moo." which is nearer to what is there is reason to believe is the ancient Manx viz.. Cronk-Howe-Mooar cronk and howe the Celtic and Norse respectively for "hill" mooar being either the Celtic word for "large," or possibly that for "marsh." The early invaders have each named it "hill" in their own tongues, and the later Manx, adopting both these, have. added the final term. making the whole the " large hill, hill," or the " hill hill in the marsh." The surrounding meadows are still marshy, and were, no doubt, more so in earlier times. The old farm on a rocky ridge to the west is called Rowany, a modern form of the older Edremony, which means "between the marshes."
The great mound lying thus on the low ground behind Port Erin and in a line between Fleshwick and Port St Mary Bays and about one mile from each is a conspicuous object from all directions. The suddenness with which it rises from the level field and its regularity or shape, with circular base and conical form, suggests that the whole mound is artificial, and this, along with, or apart from the tradition of Reginald's burial, has caused many archaeologists visiting the place to regard it as being probably a tumulus, and to compare it with the celebrated Maes-Howe in the Orkneys. For example, Mr Arthur Moore, the late Speaker of the House of Keys, author of the "History of the Isle of Man," refers to this similarity to Maes-Howe. and urges that the Cronk-Howe-Mooar should be investigated. The view has also been pretty generally held by visiting antiquaries that the top of the mound, whether natural or artificial, had been subsequently used as a fort and shaped for that purpose; and finally, an obvious trench or moat encircles the base.
There were thus various possibilities, and two or three rival theories in connection with the mound, and for nearly thirty years my friend Mr Philip Kermode and I have been anxious to dig into the top and the base of the hill and set these doubts at rest. It has, however, been impossible, on account of the strong feeling locally against examining or interfering in any way with any pre-historic monuments, to obtain the necessary permission until late in the present winter; but that difficulty has now, happily, been overcome, and within a few hours of making final arrangements with the three persons concerned (the two separate owners and the tenant), we had our men with pick and spade on the ground and the work was started forthwith, and was carried to a finish without mishap or interruption save for the wet, the cold, and the darkness incidental to mid-winter days.
The mound is approximately 30 feet in height, and about 500 feet in circumference, and the distance from the base to the centre is about 84 feet. The moat encircling it is, on the average, 20 feet across. The irregular top of the hill measures about 40 feet by 30 feet, and has a depressed central area of 30 feet by 25 feet, surrounded by raised edges, or earthen ramparts, 7 feet or 8 feet in height,
We cut a trench from the base of the hill at the S.S.W. point, leading inwards towards the centre, and rising step by step as we came upon measured and traced definite natural bands of gravel, sand and clay. Eventually this trench reached about twenty-seven feet horizontally inwards, and the floor had risen about six feet from the base of the hill; and throughout, so far as we had seen, the sections had showed natural stratified beds of sand, gravel and clay along with layers of earth and stones, all evidently bedded and having every appearance of having been naturally deposited.
There seemed no reason to believe that any other part of the hill itself would show any different structure, so we next turned our attention to the artificial-looking earthworks on the summit, and first cut a trench six feet deep through the raised edge or rampart on the western side. The section showed a well-marked core of grey clay under the surface soil and over the undisturbed bed of stony earth forming the top of the hill. and it seems probable that this wall of clay has been brought up from the moat or some other part of the surrounding marsh to steepen and stiffen the top edge of the hill. Another small trench through the opposite rampart showed much the same structure.
The depression in the centre of the top now engaged our attention. One small conical knob of stone was seen sticking up for a few inches from the grass, and on digging down along its inner edge, it was found, as we nad expected, that this knob was the top of a large stone about 4 feet high, standing on end and forming part of a wall, which we then traced east and west for 18 feet. This wall, or rather revetment, for it was merely a stone facing to the earthen ramparts, was rudely built of unshaped stones, some of which were long slabs of the local metamorphic rock. and others were water-worn boulders of glacial origin. The largest stones were placed upright, and the smaller ones filled in between; but as a more detailed description with measurements and photographs of the wall and of the sections, is in preparation, it will suffice now to say that we excavated a rectangular area of about 18 feet by 10 feet, surrounded by the revetment and extending to about 4 feet below the present surface of the ground evidently the inside of a small fort or primitive defensive work on the summit of this strongly-placed mound in the marsh.
From the floor-level inside the wall it is impossible to see over the surrounding earthen ramparts, so the defence of the hill top was no doubt carried on from the shelf of level ground outside and above the wall, with the rampart rising still for a few feet in front, and giving good protection. The walled area in the centre may have been roofed over with branches and turf as a shelter and store; and it is not difficult to imagine that in the days of bows and arrows, javelins and swords, a party of about twenty or thirty fighting men might hold the little hill fort indefinitely while raiding the surrounding country for their supplies. It is not large enough to be regarded as a place of refuge for the inhabitants of the countryside in time of invasion, but might well be a position seized and fortified by a small party of Norse raiders who were cut off, had lost their ships, or were otherwise prevented from returning north for the winter. We have found little in the digging that gives any definite clue to the period and the race, and further remarks on these points are postponed until we have identified some doubtful objects.
We have made, then, in all, a complete excavation of the artificial works on the top of the " Cronkey-Moo," a deep trench for 30 feet up the south side of the hill, two sections east and west through the earthen ramparts, and two trial pits in the moat. The digging occupied the first week of 1912, and now the earth and stones have been filled in again and the turf restored, and by next tourist season the favourite "Fairy Hill" of Port Erin, will, we trust, have its normal regularly-rounded green surface for the trippers to climb up and the children to roll down. But there need be no doubts in future as to the origin and use of the mound, and no superstitious dread of King Reginald's ghost. Our results, with photographic and other illustrations and details of the sections, will be published by Mr Kermode and myself in due course; but I may now give the following as a brief preliminary statement of what our investigation showed
l. The greater part of the hill is a natural mound of sand and gravel, with thin layers of grey clay. It is probably to be regarded as a small rounded "esker" or kame of fluvio-glacial origin, piled up by the torrential floods which must have swept over the Isle of Man during the final melting, of the confluent glaciers.
2. We found no evidence of any burials or internal chambers in that part of the mound which we examined.
3. The base of the mound may have been shaped to some extent by those who used it as a fort, and has certainly been surrounded by a moat separating the hill on the east side from an elongated ridge of sand and gravel, which was, no doubt, originally continuous with it.
4. The top of the hill has also been shaped artificially and converted into a small fort, surrounded by earthen ramparts strengthened by a rudely-built stone revetment, enclosing a sunken quadrangular area about 18 feet by 10 feet. This may originally have been roofed in as a shelter, and as it is too small to have served as a place of refuge for many people, the suggestion is made that it may have been a position with natural advantages seized and fortified by a small body of Norsemen wrecked storm-stayed, or otherwise isolated on the Isle of Man at the time of the Viking raids in the ninth and tenth centuries. | http://www.isle-of-man.com/manxnotebook/mquart/mq11983.htm |
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method for feeding concrete or other thick materials from a container into a feeding pipe by means of two feeding cylinders which are alternately connectable by a switching device to the container or the feeding pipe, with the feeding pistons of the feeding cylinders alternately performing a suction stroke and a pressure stroke, and the average piston speed during the suction stroke being at least temporarily greater than during the pressure stroke, and to an apparatus for performing the method.
2. Description of the Related Art
A corresponding method and a corresponding apparatus are known from German patent specification 3525003. The gist of the known method consists in the feature that the first feeding cylinder has not yet finished its pressure stroke, while the second feeding cylinder already starts with its pressure stroke at a lower feeding speed. After the first feeding cylinder has finished its pressure stroke, the switching operation of the switching device is started, while the second feeding cylinder continues its feeding operation at a lower feeding speed. Such a procedure has the effect that the concrete in the second feeding cylinder is already advanced, so that after the switching operation of the switching device the concrete column in the feeding pipe has no chance to perform an excessive rebound movement. This method, and the apparatus used therefor, have proved to be successful in general. However, in the present technical field, demands for more and more efficient methods for concrete feeding machines have been made recently. For instance, serious attempts have been made to increase the length of the feeding pipe and thus, in particular, the feeding height. Since in the known method the pumping operation is carried out at a reduced feeding speed during the switching period, a small pulsation is created in the feeding flow. Such a pulsation could be disregarded under the feeding conditions which have so far prevailed, but will lead at the feeding heights that are now demanded, and thus at the great lengths, for instance in the case of an arm of a concrete conveying vehicle, to vibrations at the feeding pipe end.
OBJECTS AND SUMMARY OF THE INVENTION
It is therefore the object of the present invention to provide a method and an apparatus for feeding concrete from a container into a feeding pipe, whereby irregularities in the feeding flow are further reduced.
According to the present invention such an object is achieved by a generic method in which during the switching period t.sub.u of the switching device the two feeding cylinders are substantially separated from the container at least temporarily and are short-circuited together to form a joint connection with the feeding pipe, and in this state the one feeding piston is still finishing its pressure stroke and the other feeding piston already starts its pressure stroke at the same time, with the corresponding feeding piston performing its suction stroke not before the short circuit has substantially been cancelled again and the associated feeding cylinder has been connected to the container.
A mere feeding at a reduced feeding rate is avoided by the inventive method during the switching period t.sub.u. This is accomplished by short- circuiting the two feeding cylinders which in the short-circuited state can alternate during the feeding operation at a full feeding speed without any losses in the switching period. As a result of the short- circuiting operation, the concrete column is automatically compressed in the feeding cylinder which starts the pressure stroke. Pulsation impacts are avoided in this method by the continuous feeding flow provided for. The method of the invention is suited in a particularly advantageous manner for concrete pumps having a single switching device (for instance a single pivot pipe) which cooperates with the two feeding cylinders at the same time.
In an advantageous variant of the method, even more attention is paid to the characteristics of the material to be pumped. Such attention is paid in that the feeding piston which has terminated its suction stroke already starts with its pressure stroke during a time interval . DELTA.t of the switching period t.sub.u while the other feeding piston has not yet finished its pressure stroke. A precompression of the concrete column in one of the feeding cylinders is already made possible by this measure, so that, for instance, gas inclusions or not fully filled feeding cylinders do not lead to unintended feeding variations. In a further variant it certainly suffices when the speed of the feeding cylinder which begins the pressure stroke within time interval &Dgr;t is smaller than the average speed during the remaining pressure stroke. The beginning of the pressure stroke of the one feeding cylinder can be chosen with respect to its start time and its speed in such a manner that all of the losses to be taken into account and thus all variations caused for, e.g., by the material to be fed can be compensated for. In a further variant of the present method, the two feeding pistons can substantially be moved at half the average speed V. sub.1 of the remaining pressure stroke during the time interval. This has the advantage that switching from one feeding piston to the other one can be carried out almost stepwise, since the partial feeding flows add up to the continuous total feeding flow.
The method of the invention is advantageously performed with an apparatus which comprises at least two feeding cylinders that are alternately connectable by a switching device to a container or a feeding pipe, with the feeding pistons of the feeding cylinders alternately performing a suction stroke and a pressure stroke, and the switching device being a pivot pipe which is pivotable with its inlet opening along the open end portions of the feeding cylinders. The apparatus is particularly characterized in that the inlet opening and the surrounding closing regions of the pivot pipe are designed such that during a switching operation the feeding cylinders are substantially short- circuited with the feeding pipe, but are substantially separated from the container.
This apparatus has the advantage that use can be made of apparatuses which are known in principle and in the case of which the switching device must just be designed differently in the form of a pivot pipe. This pivot pipe must ensure with its inlet opening according to the invention that a short-circuit of the two feeding cylinders is established at least temporarily during the pivoting operation or switching operation.
Advantageously, the inlet opening may be designed in the form of an elongated hole which is substantially bent around the pivot axis of the pivot pipe and has a length which corresponds approximately to the outer distance of the two feeding cylinder openings. To achieve a reliable separation of the feeding cylinders from the container, the closing regions may be arranged in extension of the elongated hole and have a width which corresponds substantially to the diameter of the feeding cylinder openings. Any short-circuiting between a feeding cylinder which performs the pressure stroke and the container is thereby avoided.
Preferably, the apparatus is controlled hydraulically; to this end there may be provided in a first embodiment a respective cylinder/piston unit in which a selectively switchable line leads into the chamber of each cylinder at the piston side, with an additional pump being arranged for further supply of pressurized fluid to the two pressure chambers of the second cylinder/piston unit, with the pressure chambers of the cylinder/piston unit at the front side of the piston having extended thereinbetween a connecting line of the hydraulic system in which a line ends that is selectively connectable via a switching valve to the additional pump or to a pressurized-fluid return means, with the sections of the line between each cylinder and the mouth of the line respectively containing a check valve which is closable by the pressure of the cylinder, and the cylinders of the cylinder/piston units in the end portion of their piston rod side comprising a line which connects the cylinders and which is also connectable via the switching valve selectively to the pressurized-fluid return means or the additional pump. The additional pump for supplying pressure to the cylinder/piston unit which starts the piston stroke ensures that no drive energy has to be taken away from the feeding piston which still performs a pressing operation. The energy supply to the piston which is to move can be started in a simple manner in due time and in an exact amount. Since the pressure of the hydraulic pump which exceeds the pressure from the additional pump is present at the cylinder/piston unit in the pressure stroke mode, and is thus present at the check valve associated with said unit, it is only the other piston to be moved that can be activated thereby. This is also true for the standstill time of the piston which has completed the pressure stroke. Furthermore, the additional pump provides for a speed of the piston in the suction stroke mode which is higher than the one in the pressure stroke mode.
In a second embodiment, the cylinder/piston units can be actuated independently in that the cylinder/piston units are each supplied with pressurized fluid via a separate pump. With such a design, speed and switching cycles can be provided in response to the respective actuation of the pumps.
In a third embodiment of the apparatus, the sequence of the method according to the invention can be achieved by providing a respective cylinder/piston unit for driving the feeding pistons, in which unit a selectively switchable line of a first pump is connectable to or separable from the chamber of each cylinder at the piston rod side, that a second pump for supplying pressurized fluid to the two pressure chambers at the front side of the piston is connectable via a switchable line either individually or jointly to the pressure chambers, and that the chambers of each cylinder at the piston rod side are jointly connectable to a pressurized-fluid return means. The different piston speeds are achieved through the pump control and the surface ratio of piston to piston rod. Furthermore, according to this embodiment the two pistons move at the same speed during the pressure stroke, the control operation being normally performed such that in this state the one piston finishes its pressure stroke and the other one begins said stroke. When the second pump provides for a constant feeding flow, the flow of pressurized fluid is halved and distributed over the two cylinders, so that these will move at half the speed, but nevertheless will jointly generate a constant feeding flow.
In a third embodiment, there is respectively provided a cylinder/piston unit for driving the feeding piston, wherein a selectively switchable line of a first pump is respectively connectable via a controllable flow divider jointly to the pressure chamber of each cylinder at the front side of the piston and to the chamber of each other cylinder at the piston rod side and is separable therefrom, with a second pump for supplying pressurized fluid to the pressure chambers at the front side of the piston being connectable via a switchable line either individually or jointly to the pressure chambers, the lines of the flow dividers which lead to the pressure chambers of the cylinders at the front side of the piston being respectively connectable jointly with the pressure chambers or can be blocked together, and wherein the flow dividers are jointly connectable to a pressurized-fluid return means when these are separated from the first pump. The different actuation is substantially to be controlled by the pumps in this arrangement. This apparatus is finely adjusted by the second pump.
To dispense with a second pump in a fifth embodiment, there is respectively provided a cylinder/piston unit for driving the feeding pistons wherein a selectively switchable line of a pump is connectable to or separable from the chamber of each cylinder at the piston rod side, wherein a second selectively switchable line of this pump is jointly connectable to or separable from the pressure chambers of the cylinders at the front side of the piston, and wherein the pressure chambers of the cylinders at the front side of the piston are jointly connectable to a line and wherein the pressure chambers at the front side of the piston are jointly connectable to or separable from a pressurized-fluid return means via a selectively switchable line. In this hydraulic circuit the volume displaced in the pressure chamber at the front side of the piston ensures that the other piston is moved accordingly. Since the line is selectively connectable to the pressurized-fluid return means, it is possible to influence the volume flow pressed through the line.
Furthermore, a respective cylinder is advantageously connected at its end at the front side of the piston via a control line to the control connection side of the check valve which is assigned to the other cylinder. The pivot pipe can be operated by means of a slide via a controlled two-way valve which is connected to a pump and/or an accumulator.
BRIEF DESCRIPTION OF THE DRAWINGS
An embodiment of the present invention will now be explained in more detail in the following text with reference to a drawing, in which:
FIG. 1 is a diagrammatic, partly cut-away view of a feeding apparatus for feeding concrete;
FIG. 2 shows a first embodiment of a simplified hydraulic connection diagram for the drive means of the apparatus;
FIG. 3 shows a schematic connection diagram showing the front side of the pivot pipe which faces the feeding cylinder;
FIG. 4 shows a displacement/time diagram of the two feeding cylinders according to a first variant of the method of the present invention;
FIG. 5 shows five operative positions of the piston/cylinder units according to the diagram of FIG. 4;
FIG. 6 is a displacement/time diagram of a second variant of the method according to the present invention;
FIG. 7 shows five operative positions of the piston/cylinder units according to the second method variant of FIG. 6;
FIG. 8 shows a second embodiment of a simplified hydraulic connection diagram for the drive means of the apparatus;
FIG. 9 shows a third embodiment of a simplified hydraulic connection diagram for the drive means of the apparatus;
FIG. 10 shows a fourth embodiment of a simplified hydraulic connection diagram for the drive means of the apparatus; and
FIG. 11 shows a fifth embodiment of a simplified hydraulic connection diagram for the drive means of the apparatus.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
The feeding device which is shown in FIG. 1 is a top view on an approximately funnel-shaped container 1 for receiving concrete, for instance, from concrete mixer trucks. Concrete is fed into a supply pipe 2 (not shown in more detail) via a pivot pipe 3 and an elbow 4. This feeding operation is performed by means of two feeding cylinders 5 whose feeding pistons 6 alternately perform a respective suction stroke and a respective pressure stroke. The pivot pipe 3 is hydraulically pivotable via a slide 7 into its respectively desired position with respect to the mouth of the two feeding cylinders 5. In FIG. 1, the mouth of the sucking feeding cylinder 5 is open towards container 1, so that the cylinder is filled from the direction of said mouth (see the arrow shown in broken line).
The feeding pistons 6 are moved by means of cylinder/piston units 8, of which only cylinders 9 are schematically shown in FIG. 1. Housings 10 are arranged at the junction point between the feeding cylinders 5 and the cylinder/piston units 8. As will still be described further below, the pivot pipe 3 is funnel-shaped in this embodiment, so that the two feeding cylinders 5 are simultaneously connectable to feeding pipe 2 at least temporarily.
FIG. 2 shows a first embodiment of a simplified diagram of a hydraulic system for operating the cylinder/piston units 8 and the feeding pistons 6 coupled therewith. A feeding cylinder 5 and a feeding piston 6 are shown in a fragmentary and schematic manner in combination with one of the cylinder/piston units 8. Slide 7, which is also operated by the hydraulic system, is shown in a schematic manner as well.
Each cylinder/piston unit 8 comprises a piston 11 whose motional sequence is transmitted via its piston rod 12 to the feeding piston 6.
The drive means for the cylinder/piston units during the pressure stroke is substantially implemented by a hydraulic pump 13. An additional pump 14 supplies additional feeding flow for specific motional phases of the pistons. The hydraulic network comprises the following sections:
A line 15 leads from the hydraulic pump 13 to a junction point 16, and a line 17 extends from said point to a two-way valve 18, and a line 19 to a switching valve 20. A line 21 leads from the two-way valve 18 into the portion of a cylinder 9.sub.1 which is at the front side of the piston (the indices 1 and 2 will be used hereinafter for the two piston/cylinder units whenever the motional sequences of the two units are described).
A line 22 leads from the two-way valve 18 into the pressure chamber of cylinder 9.sub.2 which is at the front side of the piston. Lines 21 and 22 are thus connectable by the two-way valve 18 to the hydraulic pump 13 in a selective manner.
A line 23 leads from the switching valve 20 to the one side and a line 24 to the other side of a piston 7a in slide 7. Moreover, a line 25 leads from the switching valve 20 to the return means 26 in such a manner that in response to the respective valve position, one side of slide 7 is connected to the hydraulic pump 13 and the respectively other side to the return means 26.
A line 27 connects the two piston face portions of cylinders 9. sub.1 and 9.sub.2 each other. A line 28 is branched off between the two members to a switching valve 29. In front of the mouth of line 28 which leads into cylinders 9.sub.1 and 9.sub.2, line 27 includes a check valve 30 and 31, respectively, each having its closing direction towards line 28.
A line 32 leads from switching valve 29 to return means 26, and a line 33 to the additional pump 14. Moreover, a line 34 leads from switching valve 29 into the area of the cylinder/piston units where it terminates in a line 35 which connects the portions of cylinders 9.sub.1 and 9.sub.2 at the rod side. This line does not contain any valves.
A control ine 36 extends between the portion of cylinder 9.sub. 1 at the piston side and the control connection side of the check valve 31. Likewise, cylinder 9.sub.2 is connected via a control line 37 to the check valve 30.
A pressure control valve 38 is assigned to the hydraulic pump 13, and a pressure control valve 39 to the additional pump 14.
With the above-described apparatus and with an additional controlled switching system for the switching valves 20, 29 and the two- way valve 18, it is possible to obtain a motional sequence of the pistons 11 which will be described hereinafter with reference to FIGS. 3- 7. The motional sequence is analogously applicable to the feeding pistons 6, thereby defining the supply of concrete from the container 1 into the supply pipe 2.
A first variant of the method according to the present invention will now be described in more detail with reference to FIGS. 3 to 5 using the above-described apparatus.
As can specifically be seen in FIG. 3, the front side 40 of the pivot pipe 3 which faces the feeding cylinders 5 is substantially kidney- shaped. The front side 40 includes a bow-shaped inlet opening 41 whose width B corresponds substantially to the diameter D of the mouth openings 42, 43 of the feeding cylinders 5. The length L of the inlet opening 41 corresponds to the outer distance A of the two mouth openings 42, 43. Hence, the inlet opening 41 has the shape of a bent elongated hole whose bow center is located in the pivot axis 44 of pivot pipe 3. Furthermore, the front side 40 is respectively provided at the end of inlet opening 41 with closing regions 45, 46 whose minimum distance C from the inlet opening 41 to the outer edge corresponds to the diameter D of the mouth openings 42, 43. Starting from the front side 40 of the pivot pipe 3, the pipe extends in funnel-shaped fashion towards its second end which is connected to feeding pipe 2. The inlet opening 41 is here also reduced in funnel-shaped fashion towards the corresponding opening at the opposite end. Apart from the transition states, it is substantially possible, thanks to the inventive design of pivot pipe 3, to achieve the five states shown in FIG. 3, which are of decisive importance to the control of the system.
In the following description, the corresponding positions of pistons 11.sub.1 and 11.sub.2 will be assigned to the respective position of the pivot pipe 3 with reference to FIGS. 3 to 5.
The initial position for phase I is the position of the pistons and the pivot pipe, as shown in FIGS. 3 and 5. The hydraulic pump 13 acts on cylinder 9.sub.1 with a pressure P.sub.1 via line 15, valve 18 and line 21. At the same time, the hydraulic pump 13 keeps the slide 7 in a position which is at the right side in the figure, namely via lines 15, 19 and 23 and via valve 20. The right side of the slide is connected to the outlet 26 via switching valve 20. The portions of cylinders 9.sub. 1 and 9.sub.2 at the rod sides are connected via lines 35, 34 and via switching valve 29 to the return means 26. The additional pump 14 is connected via lines 33, 34 and 35 and via valve 29 to the end of pistons 11.sub.1, 11.sub.2 at the piston rod side. The additional pump 14 will act with a pressure P.sub.2 on cylinders 9.sub.1 and 9.sub.2 in the respective portions thereof at the piston rod side by switching switching valve 29. Pressure P.sub.2 is smaller than pressure P.sub.1.
Therefore, piston 11.sub.1 will press the liquid to be displaced by it upon pressure into line 35 against pressure P.sub.2. At the rod side, piston 11.sub.1 is acted upon by pressure in addition to the effect of pump 14. Its return stroke is carried out at speed V.sub.3. This stroke movement corresponds to the suction stroke of the associated feeding piston 6.
Since speed V.sub.3 is higher than speed V.sub.1, piston 11.sub. 1 has not yet finished its pressure stroke upon entry into phase II, while piston 11.sub.2 has already finished its suction stroke. As can be seen in the corresponding time/displacement diagram in FIG. 4, the switching period t.sub.u starts with the beginning of phase II. During a time interval &Dgr;t of the switching period t.sub.u, piston 11.sub.2 and thus the corresponding feeding piston 6 are at a standstill. An advantage must particularly be seen in the fact that the closing region 45 of the front side 40 is not unnecessarily subjected to a high pressure. In phase II, pivot pipe 3 already pivots due to the switching of valve 20 to such an extent that the mouth opening 42 is separated from container 1.
As soon as phase II has been reached, the two mouth openings 42, 43 and thus the two feeding cylinders 5 are short-circuited with the inlet opening 41 and thus with the feeding pipe 2. In this state, the two- way valve 18 performs its switching operation. As a result, the hydraulic pump 13 is connected to the portion of cylinder 9.sub.2 which is at the front side of the piston. Piston 11.sub.2 will now perform a pressure stroke at speed V.sub.1 until the end of phase IV has been reached. In phase IV, the pivot pipe 3 is pivoted further in such a manner that the closing region 45 will gradually sweep over the mouth opening 43. During this time, piston 11.sub.1 is at a standstill.
When the mouth opening 43 is entirely separated from inlet opening 41 and a connection is again established with container 1, the additional pump 14 is now in communication with the portions of cylinders 9.sub.1 and 9.sub.2 at the piston rod side via lines 33, 34, 35 and via switching valve 29, so that the piston 11.sub.2 presses the liquid to be displaced by it during the pressure stroke against pressure P.sub.2 into line 35, whereby the piston 11.sub.1 has thus pressure applied to it at the rod side in addition to the effect of pump 14. Its return stroke will take place at speed V.sub.3 ; see phase V. This stroke movement corresponds to the suction stroke of the associated feeding piston 6. At the end of phase III, i.e. at the beginning of phase IV, pistons 11.sub.1 and 11.sub. 2 will have exactly interchanged their initial positions. The further sequence will correspond to the sequence described above, only with correspondingly interchanged pistons and a correspondingly interchanged pressure application.
Thus, the motional sequence of the pivot pipe 3 as shown in FIG. 3 takes place between the end of phase I and the beginning of phase V, i. e. , during the switching period t.sub.u. The switching positions assigned to the displacement/time diagram during the pivotal movement of the pivot pipe 3, see FIG. 3, are configured to be variable and need not exactly comply with this embodiment. Overlapping phases might even be desired, depending on the operational conditions. As can clearly be gathered from FIG. 4, the pressure strokes of cylinders 9.sub.1 and 9. sub.2 alternate without any time loss at the end of the time interval . DELTA.t at the same feeding speed V.sub.1, thereby providing a continuous feed flow. According to the invention it is here important that the mouth openings 42, 43 of the feeding cylinder 6 are short- circuited with the inlet opening 41 and thus with the feeding pipe 2 in this state. Another important point is that both mouth openings 42, 43 are separated from container 1 and will therefore not start their suction stroke before the short-circuit has been cancelled again.
As becomes apparent from the displacement/time diagram for the pistons of the hydraulic device, which substantially corresponds to the stroke sequence of the feeding pistons for the delivery of concrete, the whole pessure stroke of a feeding piston takes more time, namely t.sub.1, than the suction stroke with period t.sub.3. However, the time sum of suction stroke and pressure stroke, t.sub.1 +t.sub.3, will always be the same, so that the opposite directions of the piston movements at the two sides will be maintained.
A second variant of the method according to the present invention will now be described in more detail, in particular with reference to FIGS. 3, 6, and 7. Only the essential differences with respect to the preceding embodiment will be discussed in more detail in the following text. Like reference numerals will therefore be used for like or similar method sequences and for like or similar components.
The apparatus shown in FIG. 2 is in a position, in particular due to the switching valve 29, the check valves 30, 31 and their control lines 36, 37, to prompt one of the cylinders 9 to start its pressure stroke already at a time at which the other cylinder 9 has not yet finished its pressure stroke. This is of particular advantage in cases where possible losses, for instance, caused by an inadequate filling or by air inclusions in the concrete, must be compensated for.
Starting from the end of phase I, i.e. at the beginning of phase II, the additional pump 14 is connected via lines 33, 28, 27 and valves 29, 31 to the face end of piston 9.sub.2. Hence, the additional pump 14 acts on piston 11.sub.2 at a pressure P.sub.2 from the beginning of phase II during period &Dgr;t until the beginning of phase III. Piston 11.sub.1 terminates its pressure stroke at speed V.sub.1. Under the action of pressure P.sub.2, piston 11.sub.2 will already start its pressure stroke at a speed V.sub.2 which is smaller than speed V.sub.1. As soon as phase III has been reached, the switching valve 29 will switch over, thereby separating the additional pump 14 from the face end of piston 11.sub.2. As a result of the pressure stroke at the reduced speed V.sub.2 during the time interval &Dgr;t, the concrete column is already precompressed in this feeding cylinder, so that, for instance, pressure losses caused by the material can be compensated for. As a consequence, both pistons perform a pressing operation during period . DELTA.t. The one feeding piston, which is still connected via pivot pipe 3 to feeding pipe 2, completes its pressure stroke during this period and will then remain at a standstill during switching period t.sub.u. Immediately at the end of its suction stroke, the other feeding piston is already moved again at a slow pace towards the pressure stroke with the aid of the additional pump 14. The concrete which has just been sucked into the cylinder in the opposite direction is thus already given an initial movement towards the mouth opening 42. After the end of time interval &Dgr;t, i.e. after short-circuiting the two mouth openings 42, 43 and after simultaneous switching to an increased oil delivery amount by the hydraulic pump 13, the speed of the feeding piston will change. Concrete is pressed from the feeding cylinder into the feeding pipe 2 without any risk of a sudden transition, an interruption or even a return movement caused by poor filling. After the end of the switching operation, i.e. after the end of time t.sub.u, the other feeding piston is moved towards its suction stroke, i.e. at a faster pace than during the pressure stroke. The increase in speed is made possible by the additional pump 14. It ensures that the suction stroke is terminated at the moment at which a new pressure stroke is started by performing corresponding switching operations, i.e., before the other piston has completely finished its pressure stroke.
An important aspect of the present invention is that the described speed differences between suction stroke and pressure stroke of each piston and the adjustment in time with respect to the stroke sequence of the other feeding piston, as well as the position of the front side of the suction pipe required at the corresponding times must be matched with one another.
Further embodiments of simplified schemes of a hydraulic system will now be described in more detail with reference to FIGS. 8 to 11. However, only essential differences with respect to the scheme shown in FIG. 2 shall be discussed hereinafter; that is why like reference numerals are used for like or similar components.
It should here be noted that the schemes just cover the most important components required for fulfilling the present function.
The diagram shown in FIG. 8 shows two substantially equivalent displacement pumps 13, 14 for the control operation. The first displacement pump 13 communicates via line 15, a 4/2-port directional control valve 45 and a line 21 with the pressure chamber of cylinder 9. sub.1 which is at the front side of the piston. In its other switching position, the directional control valve 45 ensures that the displacement pump 13 communicates via line 15 and line 46 with the chamber of cylinder 9.sub.1 which is at the piston rod side. Likewise, the displacement pump 14 communicates via line 33, a 4/2-port directional control valve 47 and line 22 with the pressure chamber of cylinder 9.sub. 2 which is at the front side of the piston. In the other switching position of the directional control valve 47, the displacement pump 14 communicates via line 48 with the chamber of cylinder 9.sub.2 which is at the piston rod side. The displacement pumps 13, 14 are adjusted to each other. As becomes apparent from the circuit, each cylinder 9.sub.1, 9.sub.2 can be controlled and operated separately via the associated displacement pump 13, 14. As a consequence, it is solely the actuation of the displacement pumps 13, 14 and the directional control valves 45, 47 which is responsible for the extension and retraction of the cylinders 9.sub.1, 9. sub.2, and the actuation thereof must be performed accordingly. Furthermore, an additional pump 49 is provided with a downstream accumulator 50 and communicates via line 19 and the 4/2-port directional control valve 20 with slide 7. The accumulator 50 ensures that pump 49 need not be operated permanently. However, an embodiment would here also be possible in which the accumulator 50 is filled by one of the displacement pumps 13, 14 during the standstill period of one of the pistons 11.sub.1, 11.sub.2.
The diagram shown in FIG. 9 comprises a displacement pump 13 which communicates via a line 15, a 4/3-port directional control valve 51 and lines 46, 48 with the chambers of cylinders 9.sub.1, 9.sub.2 which are at the piston rod side. The directional control valve 51 has a position in which the lines 46, 48 are separated from pump 13 and connected via line 25 to the pressurized-fluid return means 26. Furthermore, there is provided a second displacement pump 14 which selectively communicates via line 33, a 4/3-port directional control valve 52 and lines 53, 54 with the pressure chambers of cylinders 9.sub. 1 and 9.sub.2 at the piston rod side. In the position shown in FIG. 9, the directional control valve 52 connects the two pressure chambers of cylinders 9.sub.1 and 9.sub.2 to pump 14. Thanks to the control operation via the two displacement pumps 13, 14, with the one pump effecting the pressure stroke, and the second one the respective suction stroke, the speed ratio between pressure stroke and suction stroke can be kept at a constant level by accurately activating the directional control valves 51, 52 and pumps 13, 14. In the present embodiment this is especially the case when the two cylinders 9. sub.1 and 9.sub.2 perform a pressure stroke for a short period of time (see valve position in FIG. 9) and the two piston rod sides of cylinders 9.sub.1 and 9.sub.2 are connected to the tank during this period.
At the same time, slide 7 is activated. This means that, when the short-circuit is established on pivot pipe 3, the two feeding cylinders 5 are in the pressure stroke mode at substantially half the average speed V. sub.1. The stepwise switching from one to the other cylinder 9. sub.1 and 9.sub.2 had no influence on the total feeding flow due to the adaptation of the speeds.
The embodiment shown in FIG. 10 differs from the preceding one in that lines 46, 48 have respectively disposed therein after the 4/3- port directional control valve 51 an adjustable flow divider 55, 56 from which lines 46, 48 are respectively continued to the chambers of cylinders 9. sub.1 and 9.sub.2 at the piston rod side and a second line 57, 58 communicates via a 4/2-port directional control valve 59 with the pressure chambers of cylinders 9.sub.1 and 9.sub.2 at the piston rod side. In this embodiment, the pressure and suction strokes can each be produced by the displacement pump 13. During switching of the pivot pipe 3, however, the 4/3-port directional control valve 51 connects the lines 46, 48 to the pressurized-fluid return means 26, and the 4/2-port directional control valve 49 blocks the lines 57, 58, so that no oil volume can escape from the pressure chambers of cylinders 9.sub.1 and 9. sub.2 at the piston rod side. In this state, the displacement pump 14 is simultaneously connected to the two pressure chambers of cylinder 9.sub. 1 and 9.sub.2 at the piston rod side. In response to the delivery volume of the displacement pump 14, these cylinders will then perform a pressure stroke at the same speed. Normally, the one cylinder is positioned shortly before its end position during this process, and the other one is at the beginning of its pressure stroke. The delivery volume of the displacement pump 14 is normally selected such that there are no variations in the feeding flow. During this process the dividing ratio of the flow dividers 55, 56 and the surface ratio of the piston face and of the piston rod side of cylinders 9.sub.1 and 9.sub.2 must be designed to obtain a reasonable ratio between pressure stroke speed and suction stroke speed. A fine adjustment of the apparatus is possible through the displacement pump 14 which can be adjusted accordingly for producing higher or smaller speeds.
Finally, FIG. 11 shows a fifth embodiment of a hydraulic scheme for driving the feeding cylinders 5. The line 15 leading away from the displacement pump 13 is again connected via a 4/3-port directional control valve 51 and lines 46, 48 to the chambers of cylinders 9.sub.1 and 9.sub.2 which are at the piston rod side. Moreover, a line 59 is branched off from line 15 in front of the directional control valve 51. Line 59 connects line 15 and thus pump 13 to a line 61 via a 3/2-port directional control valve 60. Line 61 is directly connected to the two pressure chambers 9.sub.1 and 9.sub.2 which are provided at the front side of the piston. A line 62 which is also connected to the 3/2-port directional control valve 60 leads via a further 3/2-port directional control valve to the pressurized-fluid return means 26. At the beginning of the suction stroke of the one cylinder, a small amount of oil is passed from line 61 via the directional control valves 60, 63 to the pressurized-fluid return means 26. The chamber of this cylinder which is at the piston rod side is then in communication with the pump 13. The oil volume from the cylinder starting the suction stroke is now pressed, minus the small anount of hydraulic fluid, via the line 61 into the pressure chamber of the other cylinder at the front side of the piston. The small amount of hydraulic fluid which is discharged through the directional control valves 62, 63 provides for a temporary speed difference between the suction stroke and the pressure stroke. Following the closing of the directional control valve 63, the two cylinders 9.sub. 1 and 9.sub.2 will move at the same speed until the cylinder in the suction stroke mode reaches its final position. The cylinder which is in the pressure stroke mode has not yet reached its final position, due to the above-mentioned speed differences at the beginning of the movement. At this time, the 4/3-port directional control valve switches into the position shown in FIG. 11, and the 3/2-port directional control valve 60 also into the position shown in FIG. 11. Hence, pump 13 is connected via line 15, line 59 and line 61 to the pressure chambers of cylinders 9.sub. 1 and 9.sub.2 which are provided at the front side of the piston. As a result, both pistons 11.sub.1 and 11.sub.2 will perform a pressure stroke at the same speed until the cylinder which has been in the pressure stroke mode right from the beginning has reached its final position. During this time, the slide 7 is also operated via the directional control valve 20. The counter-stroke is then performed in the reverse order. The embodiment shown in FIG. 11 makes it possible to control the whole process with only one single pump 13. | |
Create a document sequence to uniquely number each document generated by an Oracle application. In General Ledger, you can use document sequences to number journal entries, enabling you to account for every journal entry.
Attention: Once you define a document sequence, you can change the Effective To date and message notification as long as the document sequence is not assigned. You cannot change a document sequence that is assigned.
1. Enter a unique Name for your document sequence.
2. Select Oracle General Ledger as the Application to associate with the document sequence. Audit records for your sequence are stored in the application’s audit table.
3. Enter the Effective From and To dates for your document sequence. If there is no end date defined and there are no assignments for a sequence, you can disable the sequence by entering the current date as the end date. Once disabled, you cannot reactivate a sequence.
4. Select the Type of numbering you want your documents to have.
Automatic: General Ledger sequentially assigns a unique number to each document as it is created. Documents are numbered in order by date and time of creation. Numbers are in sequential order, with no gaps or omissions.
Manual: The user must assign a number to each document when it is created. You must enter unique values. Sequential ordering and completeness are not enforced.
5. For an automatic sequence, choose whether to display a Message to inform the user of the sequence name and number.
6. For an automatic sequence, enter an Initial Value for the first document in your sequence.
7. Grant Access to your document sequence from General Ledger by selecting Oracle Usernames (ORACLE IDs). The additional applications may use the sequence to number their own documents. Extending access to your document sequence from more than one ORACLE ID is especially useful when there is more than one installation of a given product, for example, when there are multiple sets of books.
8. Save your work. General Ledger launches a concurrent process to create the document sequence.
9. When the concurrent process is completed, assign the sequence to an application and category, and optionally to a set of books and method.
Assigning Document Sequences
After defining document sequences, you must assign a specific sequence to an application and category. If you enabled the Set of Books and/or Method Document Flexfield segments, you can also assign sequences based on the set of books and/or creation method of the document.
You can assign sequence numbers to journal entries, but only to those journals created for actual transactions. You can choose to assign sequence numbers to journal entries that General Ledger automatically creates, or to journal entries you enter manually in the Enter Journals window. General Ledger automatically creates journal entries for actual transactions when you perform the following tasks:
- Import Journals
- Reverse Journals
- Revalue Balances
- Generate Recurring Journals
- Generate MassAllocation Journals
- Consolidate Sets of Books
You can assign only one active document sequence scheme to each unique combination of Application, Category, Set of Books, and Method. However, you can assign the same document sequence to more than one combination of Application, Category, Set of Books, and Method. | http://oracleug.com/user-guide/general-ledger/document-sequences |
The Classic Greek Ladder and Newton's Method
Introduction
For many students in early mathematics courses, their familiarity with approximations is limited to \( \sqrt{2}\approx{1.414} \), \( \sqrt{3}\approx{1.732} \), \( \pi\approx{\frac{22}{7}} \), and maybe a few more. But a topic of number theory, Diophantine Approximations (honoring Diophantus, a mathematician of Alexandria who lived circa 207 - 291 AD and wrote books called Arithmetica), involves approximating irrational numbers by ordinary reduced fractions. One of the approximation "tools" of ancient mathematicians is a construct called Greek ladders. Maybe Greek ladders will ignite your interest in approximations by ordinary fractions.
This article uses jsMath, which requires JavaScript, to process the mathematics expressions. If your browser supports JavaScript, be sure it is enabled. Once the jsMath scripts are running, clicking the "jsMath" button in the lower right corner of the browser window brings up a panel with configuration options and links to documentation and download pages, including instructions for installing missing mathematics fonts.
| |
Learning Objectives: Students will learn about the mechanics of a drone and how to code a drone.
Materials Needed: One computer, one Micro or Micro+ 3D printer, motors, wires, and at least one 1000ft 3D Ink filament spool (ABS-R is recommended) per 2-5 students.
Brief Description: Students will print and assemble a drone, add motors and wires, and then code the drone.
To Prepare: Students will need a computer that has the M3D software on it. We recommend one printer per every 2-5 students. The Micro or Micro+ 3D printer will need to be plugged into both the wall and the computer. Each printer will need to have a spool of 3D Ink feeding into the external port. A spool holder is also recommended.
If you need assistance with any of the above please see our guides at support.printm3d.com.
Lesson Plan:
1. Divide students into small groups.
2. Students will go online to thingiverse and find models of a quad rotor robot (drone). Here is an example: https://www.thingiverse.com/thing:267008
3. Each group should print out and assemble one drone. The group will need to add a motor and wires to make the drone fly.
4. Each group will need to code their drone.
5. After the robots are complete, the groups can compete their robots against each other. | https://support.printm3d.com/182952-Build-A-Drone |
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On Oct. 12, 2005 Lt. Cmdr. Mark Effer was called up and would be sent to Afghanistan for at least six months. What would his responsibilities be there? What about his job at home? What about his wife, Alice? Mark’s request to get back into the Reserves failed, so off to war! His goal was to be a commander on the next board or he’d not make retirement. What could he do to keep from being deployed? Was this order a mistake? Mark had only 16 days to prepare legal documents, POA, wills, bank accounts, and Alice’s spousal active duty ID card. Mark’s deployment was unusual for the Navy receiving and accepting a Request for Forces from the Army. Mark’s team was a guinea pig in a real life experiment by the Army! After eight weeks of training, the unit came home for Christmas for eight days. Then off to Kandahar, where the story of Mark and Cinnamon began.
Cinnamon was a 3-month-old puppy who brought much happiness to the military men when she wandered onto their base. Mark was just one of many individuals who showed compassion for this puppy. Cinnamon’s story is an emotional journey filled with many challenges and obstacles. When Mark was about to return to the United States he planned to bring the puppy along for his wife, Alice, who had rescued many dogs in the past. Recently she grieved over the loss of a longtime dog and companion. The colonel had granted Mark’s wish for taking the puppy home, but how would this take place? At what cost?
Dog Handlers Incorporated entrusted Matt Roberts to bring the puppy home to Maryland and to Alice, but things turned out to be a horrible experience for Cinnamon, Mark, Alice, Mark’s sister Christine and all the organizations involved in helping to arrange the necessary transport for the dog. Matt had abandoned the puppy at an airport. Why? Who did he give the puppy to? Would he claim her later? Why did Matt lie, saying the dog was in Turkey when all along the puppy was in Bishkek? Now a long search began and Mark’s sister, Christine, had a major part in the investigation and search. Because Cinnamon was not a military dog she was not allowed to fly on military planes and some airlines simply refused. Cinnamon’s story of life on the base in Afghanistan and being abandoned was known worldwide. With several animal groups, the Department of Defense, animal shelters and animal rescue teams, the search was intense and long. Who was caring for the puppy? Was she OK? After a long heart-breaking search and no good results or answers, Mark gave up, but his sister, Chris, continued. She contacted the Turkish Airways, the Red Cross, Noah’s Wish, World Society for Protection of Animals, the American embassy, Animal Transport Companies, Yulia Ten the head of Animal Welfare Society of Kyrgyzstan, and finally CNN and FOX. Should Chris tell her brother and Alice of her attempts? Should she wait to be sure Cinnamon was found? Through a series of very frustrating events, Yulia was the last hope in finding Cinnamon and getting her to Mark and Alice who lived in Maryland. How did they learn the puppy was never in Turkey? Why didn’t the dog handler Matt cooperate? Was Cinnamon taken care of in Beshkek? Would the caretaker there be willing to give her up? Mark offered a reward for finding and getting Cinnamon home. Who would receive the reward?
Emails from all around the world came to Chris as people heard Cinnamon’s story and wanted to help. They offered support, prayers and hope! Should the puppy stay in Beshkek? If found, would the trip be too hard on the puppy? Could another trusted dog handler travel with Cinnamon? Very confusing for many because of obstacles, challenges and a multitude of details that needed to be worked out once Cinnamon was found. Who was Mike Thomsen? What was his part in all this search and rescue? It took three weeks to find Cinnamon and then a 26-hour flight from Beshkek, to the base, to Moscow, New York and finally home to Maryland. The 44 long days were over now, but how would Cinnamon adapt to life with Alice and Mark? How would she adapt with another puppy recently taken in by Alice? Christine shared so many details on the rescue of Cinnamon, making this a story to be read by all animal lovers. | |
TECHNICAL FIELD
The present invention relates to a lever-type connector.
BACKGROUND
JP 2018-41627
A conventional lever-type connector includes a housing and a lever. The housing can be fitted with a mating housing. The lever is pivotably mounted to the housing, and is configured to fit the housing with the mating housing by pivoting. There is also a lever-type connector with a cover mounted to the housing. The cover is configured to cover an outer periphery of an electric cable drawn out from the housing (see ).
In the lever-type connector, the housing is provided with a deflectable lock member. The lock member has as a base end, a root part that is integrally mounted to the housing, and functions as a lock arm that holds the lever at a pivoting completion position of the lever.
Such a lever-type connector retains a fitting state of the housing and the mating housing by holding the lever at the pivoting completion position using the lock member.
SUMMARY
JP 2018-41627
In the lever-type connector as described in , the root part of the lock arm, which is the base end (deflection support end) of the lock arm, is covered and protected with the lever at a pivoting initial position of the lever
However, the root part of the lock arm is exposed to the outside at the pivoting completion position of the lever. Due to this, there is a possibility that an external force such as an interference with a peripheral member will be applied to the root part of the lock arm at the pivoting completion position.
It is concerned that a damage such as a plastic deformation or a fracture occurs in the root part of the lock arm when the external force is applied to the root part. If the damage occurs in the root part, the lock arm cannot hold the lever at the pivoting completion position. In this case, there is a possibility that the lever-type connector cannot retain the fitting state of the housing and the mating housing
The present invention has been made in view of such a conventional problem, and it is an object of the present invention to provide a lever-type connector capable of stably retaining a fitting state of a housing and a mating housing.
According to the invention, there is provided a lever-type connector including: a housing to be fitted with a mating housing; a lever pivotably mounted to the housing and fitting the housing with the mating housing by pivoting; and a cover mounted to the housing to cover an outer periphery of an electric cable drawn out from the housing, wherein the housing is provide with a deflectable lock arm, the lock arm having as a base end, a root part integrally mounted to the housing at a side where the housing faces the cover and holding the lever at a pivoting completion position of the lever, and the cover is provided with a protective wall arranged opposite to the root part of the lock arm.
It is preferred that the cover is provided with an upper protective wall arranged opposite to the root part of the lock arm above the root part of the lock arm.
According to the invention, it is possible to provide a lever-type connector capable of stably retaining a fitting state of a housing and a mating housing.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1
is a disassembled perspective view of a lever-type connector according to a first embodiment of the present invention.
FIG. 2
is a side view illustrating a state before the lever-type connector according to the first embodiment is fitted with a mating housing.
FIG. 3
is a side view illustrating a state where a lever of the lever-type connector according to the first embodiment is located at a pivoting initial position.
FIG. 4
is a side view illustrating a state where the lever of the lever-type connector according to the first embodiment pivots from the pivoting initial position.
FIG. 5
is a cross-sectional view illustrating a state where the lever-type connector according to the first embodiment is fitted with the mating housing.
FIG. 6
is a cross-sectional view illustrating a state where holding of the lever by a lock arm of the lever-type connector according to the first embodiment is released.
FIG. 7
is a cross-sectional view illustrating a state where a lever-type connector according to a second embodiment is fitted with the mating housing.
FIG. 8
is a perspective view of a cover of the lever-type connector according to the second embodiment.
DETAILED DESCRIPTION
(First embodiment)
(Second embodiment)
A lever-type connector according to exemplary embodiments will be described in detail below with reference to drawings. Note that since a dimensional ratio of each element is exaggerated in the drawings for convenience of explanation, there is a case where the dimensional ratio in the drawings differs from an actual dimensional ratio.
FIG. 1 to FIG. 6
FIG. 1 to FIG. 6
A first embodiment will be described with reference to . Note that in , an X-axis is defined as longitudinal directions of a mating housing 3, and a housing 5 and a cover 11 of a lever-type connector 1, a Y-axis is defined as width directions of the mating housing 3, the housing 5 and the cover 11, and a Z-axis is defined as height directions of the mating housing 3, the housing 5 and the cover 11. The X-axis, the Y-axis and the Z-axis are perpendicular to one another. In the lever-type connector 1, a side of the mating housing 3 in the housing 5 and a side of the housing 5 in the cover 11 are defined as +X side, and a side of the cover 11 in the housing 5 is defined as -X side.
The lever-type connector 1 according to the present embodiment includes the housing 5 and the lever 7. The housing 5 can be fitted with the mating housing 3. The lever 7 is pivotably mounted to the housing 5, and is configured to fit the housing 5 with the mating housing 3 by pivoting. The lever-type connector 1 also includes the cover 11 mounted to the housing 5. The cover 11 is configured to cover an outer periphery of an electric cable 9 drawn out from the housing 5.
The housing 5 is provided with a deflectable lock arm 15. The lock arm 15 has as a base end, a root part 13 that is integrally mounted to the housing 5 at a side (-X side) where the housing 5 faces the cover 11, and holds the lever 7 at a pivoting completion position of the lever 7.
The cover 11 is provided with a protective wall 17. The protective wall 17 is arranged opposite to the root part 13 of the lock arm 15. More specifically, the protective wall 17 is arranged opposite to a side surface of the root part 13.
FIG. 1 to FIG. 6
As illustrated in , the housing 5 includes an inner housing 19 and an outer housing 21. The inner housing 19 is made of an insulating material such as a synthetic resin. The inner housing 19 is formed into a casing-like shape such that the inner housing 19 can be fitted to the mating housing 3. The inner housing 19 includes a plurality of terminal receiving chambers 23.
Each of the terminal receiving chambers 23 is extended in the inner housing 19, in a direction (X-axis direction) where the housing 5 is fitted with the mating housing 3. The terminal receiving chambers 23 are arranged in a line in a width direction (Y-axis direction) of the inner housing 19 and in a line a height direction (Z-axis direction) of the inner housing 19. In each of the terminal receiving chambers 23, a locking lance 25 is deflectably mounted.
The locking lance 25 is locked to a terminal 29 received in the corresponding terminal receiving chamber 23 to prevent the terminal 29 from coming off from the corresponding terminal receiving chamber 23. A regulating member 27 is inserted into a space within the corresponding terminal receiving chamber 23 formed in a deflection direction of the locking lance 25. In a state where the locking lance 25 is locked to the terminal 29, the regulating member 27 regulates a deflection of the locking lance 25.
FIG. 5
FIG. 6
As illustrated in and , the terminal 29 is a female-type terminal having a connection part formed into a box-like shape. The terminal 29 is electrically connected to a terminal part of an electric cable 9. The electric cable 9 is electrically connected to a power source, a device or the like. In a state where the terminal 29 is electrically connected to the terminal part of the electric cable 9, the terminal 29 is introduced in the corresponding terminal receiving chamber 23 through an opening of the corresponding terminal receiving chamber 23, and then received in the corresponding terminal receiving chamber 23. In the corresponding terminal receiving chamber 23, the opening is formed at a side (-X side) opposite to a fitting surface of the inner housing 19 where the inner housing 19 is fitted to the mating housing 3.
In a state where the terminal 29 is received in the corresponding terminal receiving chamber 23, the electric cable 9 is drawn out to the outside of the housing 5 through the opening of the corresponding terminal receiving chamber 23 The electric cable 9 is provided with a rubber stopper 31. The rubber stopper 31 adheres to an outer periphery of the electric cable 9 and an inner periphery of the corresponding terminal receiving chamber 23, between the electric cable 9 and the corresponding terminal receiving chamber 23 to prevent water from entering the inner housing 19.
FIG. 1 to FIG. 6
As illustrated in , the outer housing 21 is made of an insulating material such as a synthetic resin. The outer housing 21 can accommodate the inner housing 19. The outer housing 21 is formed into a casing-like shape such that the mating housing 3 can be inserted in the outer housing 21. The outer housing 21 accommodates the inner housing 19 and holds the inner housing 19 by using a locking part 33 deflectably mounted to the outer housing 21. A spring S intervenes between the outer housing 21 and the inner housing 19 and allows the outer housing 21 and the inner housing 19 to relatively slide.
A packing 35 is arranged between the outer housing 21 and the inner housing 19. The packing 35 prevents water from entering between the outer housing 21 and the inner housing 19. In a state where the outer housing 21 accommodates the inner housing 19, the mating housing 3 is inserted in the outer housing 21 to be fitted to the inner housing 19.
FIG. 1 to FIG. 6
As illustrated in , the mating housing 3 is made of an insulating material such as a synthetic resin. The mating housing 3 is formed into a casing-like shape such that the mating housing 3 can be inserted in the outer housing 21 and the inner housing 19 can be fitted to the mating housing 3 within the mating housing 3. In the mating housing 3, a plurality of mating terminals 37 is received. Each of the mating terminals 37 is a male-type terminal having a connection part formed into a tab shape by an insert molding, a press fitting or the like.
The mating housing 3 is fitted with the inner housing 19 such that each of the mating terminals 37 is electrically connected to the corresponding terminal 29 in the corresponding terminal receiving chamber 23. Such a fitting of the mating housing 3 and the housing 5 is performed by pivoting of the lever 7 pivotably mounted to the housing 5.
FIG. 1 to FIG. 6
As illustrated in , the lever 7 is mainly made of a metal material. For example, parts made of an insulating material such as a synthetic resin, are mounted to a part of each of sidewalls 39, 39 and a part of a linking part 41 of the lever 7. Note that the lever 7 may be made of only an insulating material such as a synthetic resin. The lever 7 includes a pair of the sidewalls 39, 39 and the linking part 41 linking the sidewalls 39, 39 to each other. The lever 7 is formed to have a width larger than that of the housing 5 by the sidewalls 39, 39 and the linking part 41. The lever 7 is provided with shaft holes 43, 43 and cam grooves 45, 45.
The shaft holes 43, 43 penetrate the sidewalls 39, 39 of the lever 7 respectively. Shaft parts 47, 47 projected from both side surfaces of the outer housing 21, are engaged to the shaft holes 43, 43. By such an engaging of the shaft parts 47, 47 and the shaft holes 43, 43, the lever 7 is pivotably mounted to the outer periphery of the housing 5.
The cam grooves 45, 45 penetrate the sidewalls 39, 39 of the lever 7 respectively. Each of the cam grooves 45, 45 opens at a side of a fitting surface (+X side) of the housing 5 where the housing 5 is fitted with the mating housing 3. When the housing 5 starts to be fitted with the mating housing 3, cam pins 49, 49 projected from both side surfaces of the mating housing 3, are respectively inserted in the cam grooves 45, 45 from the openings of the cam grooves 45, 45, by pivoting of the lever 7.
FIG. 3
FIG. 5
In a state where the housing 5 is fitted with the mating housing 3, the lever 7 can pivot between the pivoting initial position (see ) and the pivoting completion position (see ). When the lever 7 pivots from the pivoting initial position toward the pivoting completion position, the cam pins 49, 49 of the mating housing 3 are respectively inserted in the cam grooves 45, 45 of the lever 7.
In this state, when the lever 7 pivots to the pivoting completion position, the cam pins 49, 49 move along the cam grooves 45, 45 and pull the mating housing 3 in the housing 5 to fit the mating housing 3 to the housing 5. By the fitting of the mating housing 3 and the housing 5, each of the mating terminals 37 is electrically connected to the corresponding terminal 29 in the corresponding terminal receiving chamber 23. At the pivoting completion position, the lock arm 15 mounted to the housing 5, holds the pivoting position of the lever 7.
The lock arm 15 is deflectably mounted to the housing 5. The lock arm 15 has as the base end, the root part 13 that is formed by a single member continuously connected to the housing 5, at a side (-X side) where the cover 11 is mounted to the housing 5, on an upper surface of the housing 5. An engaging part 51 is formed in a stepped shape near the center of the lock arm 15. The engaging part 51 is engaged with an engaged part 53 mounted to the linking part 41 of the lever 7 at the pivoting completion position of the lever 7. By the engagement of the engaging part 51 and the engaged part 53, the lever 7 is held at the pivoting completion position of the lever 7 to retain the fitting state of the mating housing 3 and the housing 5.
FIG. 1
A recessed part 52 is formed at a side of the root part 13 (-X side) in the lock arm 15 (see ). The recessed part 52 has an opened upper surface and an opened rear surface. An upper surface of the root part 13 is continuously connected to a bottom surface of the recessed part 52.
FIG. 6
A release operation part 55 is mounted to the lock arm 15 at a side of a free end (+X side) of the lock arm 15. When the release operation part 55 is pressed downward, the release operation part 55 deflects the lock arm 15 downward. By the deflection of the lock arm 15, the engagement of the engaging part 51 and the engaged part 53 is released (see ). When the engagement of the engaging part 51 and the engaged part 53 is released, the lever can pivot from the pivoting completion position toward the pivoting initial position.
When the lever 7 pivots from the pivoting completion position toward the pivoting initial position, the cam pins 49, 49 move along the cam grooves 45, 45 to release the fitting of the mating housing 3 and the housing 5. The cover 11 is mounted to the housing 5 at a side of the root part 13 (-X side) of the lock arm 15.
FIG. 1 to FIG. 6
As illustrated in , the cover 11 is made of an insulating material such as a synthetic resin, and includes an upper cover part 57 and a lower cover part 59. The upper cover part 57 is provided with engaging parts 61, 61 on both sidewalls of the upper cover part 57. By engaging the engaging parts 61, 61 to the lower cover part 59, the upper cover part 57 and the lower cover part 59 are assembled in a unified manner. The upper cover part 57 and the lower cover part 59 are respectively provided with electric cable leading parts 63, 63 each of which is formed into a semicircular shape. In a state where the upper cover part 57 and the lower cover part 59 are assembled in a unified manner and the cover 11 is mounted to the housing 5, the electric cable 9 drawn out from the housing 5 is inserted in a space surround by the electric cable leading parts 63,63.
The upper cover part 57 and the lower cover part 59 are respectively provided with engaging parts 65, 67. By engaging the engaging parts 65, 67 to the housing 5, the cover 11 is mounted to the housing 5 in a unified manner. Since the cover 11 configured to cover the electric cable 9 drawn out from the housing 5, is divided the upper cover part 57 and the lower cover part 59, the cover 11 is easily mounted to the housing 5. The upper cover part 57 of the cover 11 is provided with a protective wall 17 at a side of the lock arm 15 (+X side) in the cover 11.
The protective wall 17 is formed by a single member continuously connected to the upper cover part 57 and stands upward on an upper surface of the upper cover part 57. In a state where the cover 11 is mounted to the housing 5, the protective wall 17 is arranged opposite to the root part 13 of the lock arm 15. By arranging the protective wall 17 such that the protective wall 17 faces the root part 13 of the lock arm 15, the electric cable 9 drawn out from the housing 5, a peripheral member or the like can be prevented from interfering with the root part 13.
As described above, by protecting the root part 13 of the lock arm 15 using the protective wall 17, it is possible to prevent the root part 13 from being damaged due to an external force. Due to this, the lock arm 15 can stably hold the lever 7 at the pivoting completion position, which stably retains a fitting state of the mating housing 3 and the housing 5.
Thus, in the lever-type connector 1, since the cover 11 is provided with the protective wall 17 arranged opposite to the root part 13 of the lock arm 15, it is possible to prevent an external force from being applied to the root part 13 using the protective wall 17. This prevents the occurrence of damage in the root part 13 of the lock arm 15.
Therefore, the lever-type connector 1 can stably hold the lever 7 at the pivoting completion position using the lock arm 15, which stably retains a fitting state of the mating housing 3 and the housing 5.
FIG. 7
FIG. 8
FIG. 7
FIG. 8
A second embodiment will be described with reference to and . Note that in and , an X-axis is defined as the longitudinal directions of the mating housing 3, and the housing 5 and the cover 11 of a lever-type connector 101, a Y-axis is defined as the width directions of the mating housing 3, the housing 5 and the cover 11, and the Z-axis is defined as the height directions of the mating housing 3, the housing 5 and the cover 11. The X-axis, the Y-axis and the Z-axis are perpendicular to one another. In the lever-type connector 101, a side of the mating housing 3 in the housing 5 and a side of the housing 5 in the cover 11 are defined as +X side, and a side of the cover 11 in the housing 5 is defined as -X side.
In the lever-type connector 101 according to the present embodiment, the cover 11 is provided with an upper protective wall 103 arranged opposite to the root part 13 of the lock arm 15 above the root part 13 of the lock arm 15. More specifically, the upper protective wall 103 is arranged opposite to the upper surface of the root part 13.
Note that the same reference numerals are given to the same components as those of the lever-type connector 1 according to the first embodiment. Although description of the same components as those of the lever-type connector 1 is omitted, these components have the same effects as those of the lever-type connector 1.
FIG. 7
FIG. 8
As illustrated in and , the upper cover part 57 of the cover 11 is provided with the upper protective wall 103. The upper protective wall 103 is formed by a single member continuously connected to the protective wall 17. The upper protective wall 103 extends toward a side of the housing 5 (+X side) from an upper end of the protective wall 17. In a state where the cover 11 is mounted to the housing 5, the upper protective wall 103 is arranged opposite to the root part 13 of the lock arm 15 above the root part 13 of the lock arm 15.
By arranging the upper protective wall 103 such that the upper protective wall 103 faces the root part 13 of the lock arm 15 above the root part 13 of the lock arm 15, it is possible to protect the root part 13 of the lock arm 15 using the protective wall 17 and the upper protective wall 103. Due to this, the electric cable 9 drawn out from the housing 5, a peripheral member or the like can be further prevented from interfering with the root part 13.
In the lever-type connector 101, since the cover 11 is provided with the upper protective wall 103 arranged opposite to the root part 13 of the lock arm 15 above the root part 13 of the lock arm 15, it is possible to prevent an external force from being applied to the root part 13 using the protective wall 17 and the upper protective wall 103. This further prevents the occurrence of damage in the root part 13 of the lock arm 15.
Although the present embodiments has been described above, the invention is not limited to the present embodiment, and various modifications can be made.
Although the upper protective wall 103 is integrally mounted to the protective wall 17 and extends from an upper end of the protective wall 17 in the second embodiment, the invention is not limited to this. The upper protective wall 103 may be extend from another part of the protective wall 17. Although the upper protective wall 103 is formed by a single member continuously connected to the protective wall 17, the invention is not limited this. The upper protective wall 103 may be formed by a member independent of the protective wall 17. For example, the upper protective wall 103 may extend from a different position from the position where the protective wall 17 is provided, in the cover 11.
Although the present invention has been described above by reference to the embodiment, the present invention is not limited to those and the configuration of parts can be replaced with any configuration having a similar function, as long as they lie within the scope of the claims. | |
NATIONAL EMISSION STANDARDS FOR HAZARDOUS IR
or to a coal mill and exhausted through a separate stack, determine kiln specific THC limit. 10 30-day rolling emission rate of mercury, lb/MM tons clinker Calculate the 30-day rolling average using concentration of mercury, volumetric flow rate, number of kiln operating hour and production data from the 30 days of clinker production.
WebFire Search US EPA
For example, selecting "Bituminous and Subbituminous Coal Combustion" will retrieve only the emissions factors corresponding to AP-42 Chapter 1 (External Combustion Sources), Section 1.1 (Bituminous and Subbituminous Coal Combustion). You can select multiple AP-42 sections by holding down the "Ctrl" button on your keyboard.
Emission Factors for Greenhouse Gas Inventories
Coal and Coke: Anthracite Coal: 25.09 103.69 11 1.6 2,602 276 40 Emission Factors for Greenhouse Gas Inventories Typically, greenhouse gas emissions are reported in units of carbon dioxide equivalent (CO 2e). Gases are converted to CO 2e by multiplying by their global warming potential (GWP). The emission factors listed in this document
Carbon Dioxide Emission Factors for Coal
The high carbon dioxide emission factor for anthracite reflects the coal's relatively small hydrogen content, which lowers its heating value. (11) In pounds of carbon dioxide per million Btu, U.S. average factors are 227.4 for anthracite, 216.3 for lignite, 211.9 for subbituminous coal, and 205.3 for bituminous coal. Table FE4.
Coal and the environment U.S. Energy Information
In 2018, methane emissions from coal mining and abandoned coal mines accounted for about 11% of total U.S. methane emissions and about 1% of total U.S. greenhouse gas emissions (based on global warming potential). Some mines capture and use or sell the coalbed methane extracted from mines.
Estimating carbon dioxide emissions from coal plants
Nov 24, 2020 Formula. The CO 2 emissions from a proposed coal plant can be calculated with the following formula: . annual CO 2 (in million tonnes) = capacity * capacity factor * heat rate * emission factor * 9.2427 x 10^-12 . Example for a typical coal plant Size: 1,000 MW; Capacity factor: 80%; Supercritical combustion heat rate: 8863 Btu/kWh; Sub-bituminous coal emission factor: 96,100 kg
Coal Mill an overview ScienceDirect Topics
These factors cause a significant decrease in mill efficiency. The study In China and India in particular, coastal power stations tend to mill coal more finely, use superior emissions to control technologies, and have a tendency to use higher-quality coal blends. The result is higher quality and greater consistency in fly ash chemical
WebFire Search US EPA
Emission Factor-- 1.900E-3 mg per Megagrams Coal Burned; Quality -- U Emissions Factors Applicability: SCC: 10100202 : Details Emission Factor-- 6.950E-7 1.620E-6 Lb per Million Btus Heat Input; Quality -- U Emissions Factors Applicability Duplicate factor
Emission Estimation Technique Manual
Emission Factors for Kraft Pulping a Pulp and paper mills generate a range of emissions of listed substances from pulping processes and power generation. Major sources of emissions Fly ash from wood waste and coal fired boilers Particulate matter (PM 10) Sulphite mill operations Sulphur oxides
CHAPTER 4 METAL INDUSTRY EMISSIONS IGES
Chapter 4: Metal Industry Emissions 2006 IPCC Guidelines for National Greenhouse Gas Inventories 4.1 CHAPTER 4 METAL INDUSTRY EMISSIONS
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Emission Factor. An emission factor is a representative value that attempts to relate the quantity of a pollutant released to the atmosphere with an activity associated with the release of that pollutant. These factors are usually expressed as the weight of pollutant divided by a unit weight, volume, distance, or duration of the activity
EMISSION FACTORS 2020 DATABASE DOCUMENTATION
2020 edition of the Emission factors data package. This excel file includes 10 sheets with a set of carbon emission factors for electricity and electricity/heat generation. The factors are described below: CO2 emission factors for electricity and heat generation for world countries (in CO2 per kWh, 1990 to 2018). (Sheet CO2 KWH ELE & HEAT)
40 CFR Appendix F to Part 75 Conversion Procedures CFR
3.3.6 Equations F-7a and F-7b may be used in lieu of the F or F c factors specified in Section 3.3.5 of this appendix to calculate a site-specific dry-basis F factor (dscf/mmBtu) or a site-specific F c factor (scf CO 2 /mmBtu), on either a dry or wet basis. At a minimum, the site-specific F or F c factor must be based on 9 samples of the fuel. Fuel samples taken during each run of a RATA are
1.1 Bituminous And Subbituminous Coal Combustion
1.1-2 EMISSION FACTORS 9/98 categorized as PC-fired systems even though the coal is crushed to a maximum size of about 4-mesh. The coal is fed tangentially, with primary air, into a horizonal cylindrical furnace. Smaller coal particles are burned in suspension while larger particles adhere to the molten layer of slag on the combustion chamber wall.
Mercury enrichment and its effects on atmospheric
Aug 01, 2014 Other studies used an emission factor of 0.04 g Hg/t cement, which excluded the contribution of coal combustion in cement plants (Streets et al., 2005, Wu et al., 2006). However, recently Won and Lee estimated the emission factor for a precalciner process to be 0.026–0.034 g/t clinker, much lower than the previous values (Won and Lee, 2012).
CO2 Emission Factors for Fossil Fuels Umweltbundesamt
from statistics, by the applicable emission factors. The emission factors for this purpose depend pri-marily on the carbon content and net calorific value of the fuels involved. Over 80 % of all German greenhouse-gas emissions are calculated in this manner. For this reason, the quality of the factors is of central importance.
India Energy Outlook 2021 Analysis IEA
India’s building spree will shape its energy use for years to come. In the STEPS, India exceeds the goals set out in its Nationally Determined Contribution (NDC) under the Paris Agreement. The emissions intensity of India’s economy improves by 40% from 2005
Carbon Dioxide Emission Factors for Coal
Carbon Dioxide Emission Factors by Coal Rank and State of Origin. The (arithmetic) average emission factors obtained from the individual samples (assuming complete combustion) (Table FE4) (10) confirm the long-recognized finding that anthracite emits the largest amount of carbon dioxide per million Btu, followed by lignite, subbituminous coal, and bituminous coal.
NPI Emission Estimation Technique Manual for Mining
approaches for estimating emissions from facilities engaged in the mining of coal and metalliferous minerals. The mining industries covered in this manual are: coal, iron ore, bauxite, copper ore, gold ore,
Sulfur dioxide and nitrogen oxides emissions from U.S
The downward emission trends resulted from a combination of factors, including reductions in oil and coal use, steadily declining fuel sulfur content, lower pulp and paper production in recent years, increased use of flue gas desulfurization systems on boilers, growing use of combustion modifications and add-on control systems to reduce boiler
WebFire Search US EPA
Emission Factor-- 1.900E-3 mg per Megagrams Coal Burned; Quality -- U Emissions Factors Applicability: SCC: 10100202 : Details Emission Factor-- 6.950E-7 1.620E-6 Lb per Million Btus Heat Input; Quality -- U Emissions Factors Applicability Duplicate factor
The Calculation of Country Specific Emission Factors for
Figure 4.3: Results of uncertainty analysis for coal-based CO 2 emission factor (Secunda) 32. The Calculation of Country Specific Emission Factors for the Stationary Combustion of Fuels in the Electricity Generation Sector South Africa 5 LIST OF TABLES Table 2.1: Estimation of CO 2
Choice of emission factors tier 1 method Emission Factors
Feb 03, 2021 The emission factor would vary depending upon whether coal, natural gas, or coke oven gas was used as the primary fuel. The 'default' emission factor provided is at the high end of the range, 30 kg CO2 per tonne product, and should be used if the inventory compiler does not know anything about the fuels or raw materials used. | https://delforno.pl/sand/Dec_4786/ |
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SPRUCE PINE — Due to the recent large rain falls in Western NC, there will be a break from the Changing Forests Toe Talk article series to discuss stormwater.
Stormwater runoff is water after precipitation (rain, snow, sleet) that flows over the ground directly into streams and other bodies of water. Impervious, hard, and compacted surfaces (roofs, roads, etc) increase the amount of stormwater runoff, and prevent runoff from entering the ground and from recharging the groundwater. In forested settings there is little to no runoff, while in urban, residential, and developed areas there is a lot. Because stormwater runoff does not have the opportunity to infiltrate or enter the ground and quickly enters water bodies it causes flash flooding. Stormwater also causes erosion, habitat loss and destabilization of land and property. In urban, developed, agricultural, and residential areas, stormwater runoff collects pollutants including sediment, trash, debris, oils, chemicals, and fertilizers into our waterways.
Unlike groundwater which is cooled by being under ground and enters bodies of water through springs, runoff never enters the ground and is often heated by surfaces such as pavement. In Western NC, ground and spring water is about 56°F all year, even in summer. Surface temperatures can be much higher than the air or underground (think of a parking lot on a sunny day, versus the temperatures of local rivers and streams). When heated stormwater runoff enters a body of water it is known as “thermal shock,” and is detrimental to aquatic organisms that depend on cool water, such as trout. Because of all these factors, stormwater runoff greatly diminishes water quality and aquatic habitats. Stormwater runoff is rarely treated and enters streams directly or through storm drains/sewers.
There are simple techniques to treat or greatly reduce the impacts of stormwater such as Stormwater Control Measures (SCMs), also called Best Management Practices (BMPs), which are used to protect and improve our surface and groundwater. SCMs are structural, vegetative, or management practices installed to treat, slow, and reduce stormwater runoff.
Phytotechnology is a fancy word that combines “phyto,” meaning plants, and technology. It means technologies or structures that use plants to remove and/or contain pollutants in soils and water. This can even be a small rain garden in a residential front yard. Phytotechnologies are very applicable to SCMs. Phytotech systems use plants because of the chemical reactions that occur in between the roots of plants, microbes, water, and soil. The atomic compounds from photosynthesis (how plants breath) and oxygen released around the root zone of plants help to transform and breakdown pollutants contained in stormwater runoff. These compounds also promote microorganism growth which breakdown pollutants even faster and more effectively. Essentially phytotech SCMs are relatively simple infrastructure that often model a natural forested wetland, and create an effective ecological system that cleans stormwater runoff.
Some types of SCMs include:
Extended detention basin - its main function is to hold back large flushes of stormwater, and release it at a slow rate. This protects river and stream banks from erosion, and greatly reduces the temperature of stormwater, reducing thermal shock to the river. Sediment also settles in the basin, reducing the amount of sediment that enters water bodies.
Silt fence - often seen on construction sites, black fabric that serves as filter to let the water escape, but traps the sediment.
Cisterns - a method of collecting and storing rainwater for future use. It reduces the amount of runoff leaving a site.
A bioretention area or cell - a type of SCM that uses phytotechnology. A bioretention area is a large, engineered rain garden. Bioretention uses plants and soil for removal of pollutants from stormwater runoff and contains or prevents pollutants such as sediment, heavy metals, gas, oil, and pathogens from entering water bodies. A bioretention area consists of a depression in the ground filled with a soil mixture that supports various water-tolerant plants and allows for stormwater to enter.
Vegetative swales, or bioswales - SCM drainage structures that also use phytotechnology. They are planted with grasses which slow the water, allowing it to enter the ground, and filter pollutants before the water leaves the site.
The Pinebridge Coliseum Campus (future Three Peaks Enrichment Center) in Spruce Pine is comprised of a large building and large parking area. Pinebridge was previously an ice hockey and multipurpose arena. The Pinebridge Campus is currently being renovated and is under new ownership of Mayland Community College. It will include a restaurant, bar, cosmetology department, event space, and a living learning campus that showcases sustainability.
Previously at Pinebridge most of the runoff was captured in storm pipes and removed from the sites without treatment and with high velocities. This was a large source of heated, polluted water for the North Toe River, and caused erosion and long term land stability issues. Because of these issues, SCMs, phytotechnology stormwater treatment, and rainwater harvesting are being applied as part of the Pinebridge Campus renovation. A variety of partners are working together to achieve this goal including Blue Ridge Resource Conservation & Development (RC&D), Mayland Community College and Mitchell Soil and Water Conservation District.
A bioretention area within the parking area is being installed to capture and treat stormwater runoff at the source. The bioretention area will be planted with native plants that help slow the water, remove pollutants, and provide landscaping and habitat enhancement. An extended detention basin, vegetative swale, and cistern are also being added on site to reduce, cool, and treat the stormwater runoff before it reaches the North Toe River. Plants are also being used on site in a soil phytoremediation process, in which the plants will remediate the soil by taking up heavy metals and other pollutants. As phytotechnologies are leading SCM infrastructure advances, the site design and installation will be used as a model of how to enhance SCMs and implement pythotech systems within mountainous regions nationwide.
Blue Ridge RC&D is involved in many waterway projects to improve water quality and prevent property loss and damage from erosion and flooding. The Pinebridge Coliseum renovation is a very large scale project, but projects that relate to stormwater runoff, erosion, and water quality can be done on much smaller scales, even down to planting a flower or shrub along a streambank. In recent years, Blue Ridge RC&D has implemented other water resource related projects including an artificial wetland at Avery High School, Alleghany County High School bioretention cell, Grassy Creek stream restoration and Overmountain Victory National Historic trail construction, Todd Island Park restoration, Cane River dam removal, Middle Fork Greenway restoration, among others.
Many water resource projects relate to riparian zones, the area next to streams and rivers, and the interface between land and water. A riparian zone that has plants can remove pollutants, and will slow down or prevent stormwater runoff from directly entering a stream, and prevent property damage, loss, and effects from flooding. Improving riparian zones is often cheap and easy.
Where does the water go from your driveway or street when it rains? Does it run directly into a drain or stream, or does the water enter an area with plants that allows the water to slow down? If it runs directly into a stream, maybe consider installing water bars on the driveway to divert the water before it reaches the stream. Or plant some flowers, shrubs, live stakes, or trees to form a buffer or riparian zone. Not mowing or weed-eating along streams (something that requires no work or money!) is a very effective technique that allows a natural riparian zone to occur. This may appear “grown-up,” but drastically improves wildlife habitat, water quality, and benefits the landowner as it reduces erosion, property loss, and flood damage.
It is easy to forget about water, but each time it rains or snows, water hits the earth and begins a long course to the ocean. Rain is usually clean, without sediment, trash, debris, oils, chemicals, and fertilizers in it, but when rain reaches the surface as stormwater runoff, it can quickly collect these pollutants. The short lived first part of water’s course, as stormwater runoff, is often the most impactful and harmful to water quality. Once the water is polluted and enters a stream or river, it will remain polluted all the way to the ocean, and will continue to remain polluted once in the ocean. It is important to remember our downstream neighbors. Our headwaters in Western NC high the mountains will travel down rivers that serve as millions of people’s drinking water sources before passing through New Orleans, LA and entering the ocean.
Toe Talk is a monthly article series supported by local watershed partners highlighting watershed and community news. The Toe-Cane Watershed Coordinator position is working to improve water quality and gain associated economic benefits in the watershed by providing education and technical resources and implementing on-the-ground projects. Please see our website for updates on projects, and helpful documents for addressing water related issues: http://www.blueridgercd.com/ or contact Felix Stith, Toe-Cane Watershed Coordinator, Blue Ridge Resource Conservation & Development at [email protected] of (828) 279-2453.
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A SUCCESSFUL PROJECT has many components. While use of a project management tool is only one critical success factor in most projects, its importance cannot be diminished. However, bridging the gap between risk reduction techniques and using the project management tool for those techniques is either never done or quickly abandoned. The Plan Contingency Allowance (PCA) technique can identify and measure both schedule risk and cost risk.
The Contingency Problem
If contingency time is to be planned, then it should be separate and distinct to allow measurement. (“If it can't be measured, it can't be managed.”) Most project managers include some contingency factor in the task's duration and work effort. For example, Exhibit 1 shows a 180-hour/12.5-day phase of a project. Each task has incorporated a 20 percent contingency factor, which produced the 216-hour/15-day project shown. Specifically, Task A is a 100-hour/2.5-week task requiring a 20 percent contingency factor. It is represented as requiring 120 hours and 3 weeks.
We have all experienced the weaknesses in this approach. For example, if Jane is assigned to Task A, she would see her assignment requiring 120 hours and 3 weeks. Unfortunately, the original estimate is still 100 hours and 2.5 weeks. Further, questions related to the cost and duration of the project's contingency cannot be answered easily.
These situations highlight the need for identifying and measuring contingency in the project management tool. The desired approach would keep each team member's tasks separate from contingency requirements and allow easy measurement of planned, earned and consumed contingency. It should be scalable, to work on small projects through megaprojects, and relatively simple to administer.
The PCA technique creates a separate contingency task for each group of related tasks, adds appropriate dependency links to the work effort, creates fictional resources and assigns those resources to the new tasks. We will look at each of these steps separately to understand how to use and implement them in any tool.
The PCA Technique
The new tasks representing the Plan Contingency Allowance are associated with a set of activities (phase) with contingency to be measured. Using a software development example, there would be five PCA tasks—one for each of the major phases (Requirements Analysis, Design, Development, Testing, and Implementation). This allows for the measurement of contingency by major phase. It also allows for each phase to have separate contingency factors. For example, a software project may use a 20 percent contingency factor. However, one particular project may be the first attempt to use a new programming language. Therefore, the Design and Development phases could have a 30 percent or 40 percent contingency factor, with the remaining phases staying at 20 percent.
The PCA technique creates a separate contingency task for each group of related tasks, adds appropriate dependency links to the work effort, creates fictional resources and assigns those resources to the new tasks.
These PCA tasks are placed in the work breakdown structure such that it follows each of the phase's tasks directly or indirectly. This is accomplished by the tool's dependency links. The phase's milestone indicating completion follows the PCA task by also using a dependency link. These links ensure that the plan's indicated completion is dependent not only on each of the detailed tasks but also on the contingency's work and duration. As one or more changes are made to tasks through the project's execution, the phase's completion milestone adjusts appropriately.
One or more new resource(s) are added to the project plan to represent the staff “assigned” to contingency tasks. The hourly rate for these new resources should represent the blended rate of the staff assigned to tasks in the corresponding phase. These fictional team members are then assigned to the PCA tasks. “Real” team members are not assigned to contingency tasks. This is necessary since an accurate resource assignment is not possible for such tasks. Further, it ensures that each team member only sees his or her assigned tasks, thereby avoiding Parkinson's Law—“work expands to fill the available time.”
Performing these steps creates the new project plan represented in Exhibit 2. Notice that it has the same total work hours and the same duration as the original project plan in Exhibit 1. This new plan has all of the benefits deemed necessary for measurable contingency. (The PCA task's hours and duration are each 20 percent of the original plan. This will often generate an overloaded PCA resource due to parallel tasks within the phase, as in this example.)
Having separate PCA tasks increases the ability to report contingency time and cost. These PCA tasks should be baselined along with the rest of the project plan. This will allow time and cost variance analysis for the project's contingency.
Now that we have these new tasks and resource assignments in the project plan, we need to administer the project plan to take advantage of this data. Here are some general guidelines that address PCA task administration.
Managing Contingency Time
Project tasks are adjusted to reflect the task status until that task is completed. The adjustable fields include the actual start date, percent complete, revised estimate to complete figures and the actual finish date. The PCA tasks are also adjusted to reflect changes in the phase's contingency measurements. However, PCA tasks are never actually “performed”—they exist to represent the remaining contingency cost in time and dollars. (The only tasks that have work performed are the original tasks.) Therefore, the PCA task's percentage complete figure will always remain zero. It will have its work effort and duration adjusted to reflect the changing project status.
On Time Scenario. There are specific situations that will be reviewed to clarify PCA task administration. The first scenario to be studied is a project that is basically on time. If every task is completed nearly on time and on budget, then at the midway point of that phase's completion, the remaining contingency would be 50 percent of the original contingency. From our original example, the PCA task would be reduced to 18 hours, 1.25 days and 0 percent complete. At 75 percent completion of the phase, the PCA task should be set to 9 hours, .6 days and still 0 percent complete. This process will move the completion milestone closer to the predicted completion date.
Ahead of Schedule Scenario. A project performing ahead of schedule has PCA tasks adjusted similarly to the project that is basically on time. However, the original estimates for the project were apparently conservative. If a phase of a project is 15 percent ahead of schedule, then there may be justification to reduce the contingency factor for the remaining time by up to that same 15 percent. Using our example, the contingency factor would become 17 percent (15 percent below the original 20 percent). At the midway point of this phase, the PCA would be only 15.3 hours (17 percent of 90) with a duration of 1.1 days. This process will move the completion milestone even closer to the predicted completion date.
Behind Schedule Scenario. The project falling behind schedule needs to use a different process for adjusting Plan Contingency Allowance. The original project plan documented a particular completion date. Since we are assuming there has been no Project Change Request to account for a delayed completion, we need to “consume” the planned contingency to keep the project on schedule. If the team members are now giving an estimate to complete date of 3 days and 10 hours greater than originally planned for Task A, the PCA task should be reduced by 3 days and 10 hours. (If the task requiring greater time does not lie on the phase's critical path, such as Tasks B and C, then the PCA task's duration does not have to be reduced, only the PCA task work hours.)
The result is a phase with a completion date that still matches the original plan, task work effort that indicates an unfavorable variance of 10 hours, and reduced contingency available for other tasks in that phase. Note that a project phase running significantly late will consume all of the available contingency time. However, remember that contingency exists to cushion the effect of errors and problems. This method of tracking Plan Contingency Allowance will quickly highlight this situation and allow an early resolution to the problem.
When the phase's tasks are completed in each scenario, the PCA task is updated so that its work hours equal zero, the duration equals zero and the percent complete is 100 percent. This technique will facilitate cost calculations that reflect contingency variances and place the phase's completion milestone on the actual completion date.
Managing Cost Risk
The discussion so far has related to managing schedule risk. The measurement of cost risk follows in a similar manner. Earned value analysis (EVA) will include the time and cost of contingency throughout the project even as the contingency is adjusted—whether favorable or unfavorable. Periodic adjustments to PCA tasks will improve EVA's forecasting accuracy.
Exhibit 1. These 180 hours of project activities have 36 hours of embedded contingency time. However, the contingency time cannot be properly managed since it is not visible and may not be assigned to the proper resource.
Exhibit 2. The revised project plan clearly identifies contingency time and duration and provides for separate resource assignment. Further, it allows for accurate variance calculations of the project tasks and the opportunity to baseline plan contingency allowance time and duration for variance calculations.
The dollar cost of contingency can be measured in real terms and as a variance from the baselined project. These variances are also expressed in dollars since each PCA resource was assigned a blended rate of the corresponding staff.
“Earned contingency” is observed when the actual work hours for the phase are less than the baselined work hours. Therefore it is important to set the PCA task's actual work hours to zero when the phase completes. (Some professionals will argue that the “earned contingency” only occurs when the total actual work hours are less than the baseline plan, excluding the PCA work hours. These can be lively debates. However, regardless of your particular definition, this process will provide the data for whatever calculation is deemed appropriate.)
Similarly, contingency is “consumed” when the actual work hours for the phase are greater than the baselined work hours. Information on contingency variances, earned or consumed, is valuable for the next project planning effort since it provides feedback on the estimation process.
Miscellaneous Items
There are a few miscellaneous topics to be considered. It is possible to micromanage the PCA tasks by recalculating their work effort and duration with every update to the project plan. The PCA technique is a risk identification and measurement tool and should not require significant effort to administer. Biweekly PCA calculations should be sufficient for project accuracy. Additional recalculations would be warranted only if there are significant changes to the project plan. Also, the data should represent the risk level. In other words, focus on the order of magnitude of the PCA work and duration, not the fourth significant digit of the calculations.
Special circumstances may benefit from having multiple PCA resources. One large program required three PCA resources—one for each of the two major subcontractors and one for the internal staff. The PCA work effort was allocated to each of the PCA resources proportionate to that vendor's activity in each phase. This helped manage costs and helped each subcontractor anticipate resource requirements that included their planned contingency. Another example of needing multiple PCA resources is if there is a need to track contingency by resource skill set. Be wary of the trap exposed in the previous paragraph—that of making the precision gained too expensive to implement and administer by creating too many PCA resources.
Date-constrained projects (such as those that must meet regulatory dates or Year 2000 projects) have a unique characteristic. There may be recognition of a certain level of risk but insufficient calendar time to be feasible. This can be demonstrated by PCA tasks with significant work effort given the task's duration. The PCA technique allows the project manager a visible way to demonstrate the schedule risk.
Some organizations may manage two completion dates on projects. The “internal date” is calculated by setting the PCA durations to zero days, whereas the “external date” is calculated using the agreed-upon PCA durations.
Finally, large projects may use Monte Carlo analysis to identify more probable completion dates and costs. The PCA work effort and duration variables can be studied separately to determine their impact to the project's risk.
ONCE UNDERSTOOD, the PCA technique for risk identification and measurement will take a small percentage of project management time to implement and administer, but the benefits significantly outweigh the costs. ■
Bradford R. Eichhorn, senior manager with Claremont Technology Group, Inc., has 21 years in information technology experience, both as a consultant and in diverse industries. | https://www.pmi.org/learning/library/manage-contingencies-reduce-risk-pca-technique-3655 |
Third penny has provided funding for public safety and infrastructure since 1978
On Tuesday, February 11, City of Claremore residents will vote on the extension of a one penny sales tax, which has been in place since 1978. It provides funding for police, fire, parks and capital equipment expenditures.
Revenues from the penny accounts for approximately $3.9 million in sales tax revenue in the current fiscal year. Funds are allocated as follows: 20% for the Claremore Police Department, 20% for the Claremore Fire Department, 20% for the Claremore Parks & Recreation Department and 40% for capital expenditures, which has included equipment for police and fire, as well as community projects such as splash pads and the new dog park.
Revenue from the City’s three-cent sales tax is restricted and allocated as follows: one penny for streets and infrastructure, one penny for the Claremore Expo Center, wastewater treatment plant and Recreation Center and one penny for public safety, parks and capital needs. The third penny is the only one up for renewal, and if approved, will be extended for 10 years.
Residents who are registered voters within the Claremore city limits are eligible to vote. Polls will be open on Feb. 11 from 7 a.m. to 7 p.m., and early voting begins Feb. 6 at the Rogers County Election Board at 415 West 1st Street in Claremore.
More information can be found here. | http://moreclaremore.com/2020/02/03/claremore-residents-set-to-vote-on-penny-sales-extension-feb-11/ |
Winter weather closes several Southern Oregon roadways
Oregon Department of Transportation crews are working to get several highways reopened in the Southern Oregon Cascades after severe winter weather prompted road closures.
Weather hazards such as heavy snow, downed trees and mudslides prompted multiple roadway closures late Monday, according to ODOT. Some portions of Southern Oregon received as much as four feet of snow.
ODOT crews are focusing on Highway 62 near Prospect, Highway 138E near Glide and Highway 230 near Crater Lake National Park by deploying three snow blowers to help clear a path for vehicles with a goal of reopening the roads possibly as soon as the end of the day. ODOT is also working with Oregon Department of Forestry and contract crews to remove snow-laden trees and branches leaning over roads.
As of 11 a.m. Tuesday, here’s where roads remain closed:
Jackson County
- Highway 62 between mileposts 46 and 65, from Prospect north to the Highway 230 intersection.
- Highway 273, between mileposts 0 through 12, up to the intersection with Green Springs Highway
- Highway 66, between mileposts 2 and 45 between Highway 273 and Clover Creek Road in Klamath County
- Dead Indian Memorial Road, closed to all but local traffic due to weather hazards, and semitrailer traffic is “strongly not advised”
Josephine County
- Highway 46, between mileposts 16 and 19.3 — about three miles west of Oregon Caves National Monument
Douglas County
- Highway 138, roughly 11 miles east of Glide, between mileposts 16 and 61.
- Highway 230, the entirety between mileposts zero through 23.8
For the latest road conditions from ODOT, check TripCheck.com. | https://www.mailtribune.com/happening-now/2022/01/04/winter-weather-closes-several-southern-oregon-roadways/ |
---
abstract: 'In this article, we present a new analytical formulation for calculation of the mutual inductance between two circular filaments arbitrarily oriented with respect to each other, as an alternative to Grover [@Grover1944] and Babič [@BabicSiroisAkyelEtAl2010] expressions reported in 1944 and 2010, respectively. The formula is derived via a generalisation of the Kalantarov-Zeitlin method, which showed that the calculation of mutual inductance between a circular primary filament and any other secondary filament having an arbitrary shape and any desired position with respect to the primary filament is reduced to a line integral. In particular, the obtained formula provides a solution for the singularity issue arising in the Grover and Babič formulas for the case when the planes of the primary and secondary circular filaments are mutually perpendicular. The efficiency and flexibility of the Kalantarov-Zeitlin method allow us to extend immediately the application of the obtained result to a case of the calculation of the mutual inductance between a primary circular filament and its projection on a tilted plane. Newly developed formulas have been successfully validated through a number of examples available in the literature, and by a direct comparison with the results of calculation performed by the *FastHenry* software.'
address: 'The Institute of Microstructure Technology, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany'
author:
- 'Kirill V. Poletkin'
- 'Jan G. Korvink'
bibliography:
- 'References.bib'
title: 'Efficient calculation of the mutual inductance of arbitrarily oriented circular filaments via a generalisation of the Kalantarov-Zeitlin method '
---
Inductance,circular filaments,coils,line integral,electromagnetic system,electromagnetic levitation
Introduction
============
Analytical and semi-analytical methods in the calculation of [inductances]{}, and in particular the mutual inductances of filament wires and their loops, play an important role in power transfer, wireless communication, and sensing and actuation, and is applied in different fields of science, including electrical and electronic engineering, medicine, physics, nuclear magnetic resonance, mechatronics and robotics, to name the most prominent. Collections of formulas for the calculation of mutual inductance between filaments of different geometrical shapes covering a wide spectrum of practical arrangements have variously been presented in classical handbooks by Rosa [@Rosa1908], Grover [@Grover2004], Dwight [@Dwight1945], Snow [@Snow1954], Zeitlin [@Zeitlin1950], Kalantarov [@Kalantarov1986], among others.
The availability of efficient numerical methods such as *FastHenry* [@KamonTsukWhite1994] (based on the multipole expansion) currently provides an accurate and fast solution for the calculation of mutual and self-inductance for any circumstance, including the use of arbitrary materials, conductor cross-sections, loop shapes, and arrangements. However, analytical methods allow to obtain the result in the form of a final formula with a finite number of input parameters, which when applicable may significantly reduce computation effort. It will also facilitate mathematical analysis, for example when derivatives of the mutual inductance w.r.t. one or more parameters are required to evaluate electromagnetic forces via the stored magnetic energy, or when optimization is performed.
Analytical methods applied to the calculation of the mutual inductance between two circular filaments is a prime example, and has been successfully used in an increasing number of applications, including electromagnetic levitation [@OkressWroughtonComenetzEtAl1952], superconducting levitation , , wireless power transfer [@JowGhovanloo2007; @SuLiuHui2009; @ChuAvestruz2017], electromagnetic actuation [@ShiriShoulaie2009; @RavaudLemarquandLemarquand2009; @Obata2013; @ShalatiPoletkinKorvinkEtAl2018], micro-machined contactless inductive suspensions [@Poletkin2013; @Poletkin2014a; @Lu2014; @PoletkinLuWallrabeEtAl2017b] and hybrid suspensions [@Poletkin2012; @PoletkinShalatiKorvinkEtAl2018; @PoletkinKorvink2018], biomedical applications [@TheodoulidisDitchburn2007; @SawanHashemiSehilEtAl2009], topology optimization [@KuznetsovGuest2017], nuclear magnetic resonance [@D.I.B.2002; @SpenglerWhileMeissnerEtAl2017], indoor positioning systems [@AngelisPaskuAngelisEtAl2015], navigation sensors [@WuJeonMoonEtAl2016], and magneto-inductive wireless communications [@Gulbahar2017].
The original formula of the mutual inductance between two coaxial circular filaments was derived by Maxwell [@Maxwell1954 page 340, Art. 701] and expressed in terms of elliptic integrals. Butterworth obtained a formula covering the case of circular filaments with parallel axes [@ButterworthM.Sc.1916]. Then, a general formal expression made for cases where the axes of the circles are parallel, and where their axes intersect, was derived by Snow [@Snow1928]. However, the Butterworth and Snow expressions suffer from a low rate of convergence. This issue was recognized and solved by Grover, who developed the most general method in the form of a single integral [@Grover1944]. Using the vector potential method, as opposed to the Grover means, the general case for calculating the mutual inductance between inclined circular filaments arbitrarily positioned with respect to each other was subsequently obtained by Babič et al. [@BabicSiroisAkyelEtAl2010].
Kalantarov and Zeitlin showed that the calculation of mutual inductance between a circular primary filament and any other secondary filament having an arbitrary shape and any desired position with respect to the primary filament can be reduced to a line integral [@Kalantarov1986 Sec. 1-12, page 49]. In the present paper, we report an adaptation of this method to the case of two circular filaments and then derive a new analytical formula for calculating the mutual inductance between two circular filaments having any desired position with respect to each other as an alternative to the Grover and Babič expressions.
![General scheme of arbitrarily positioning two circular filaments with respect to each other: $P$ is an arbitrary point on the secondary filament. []{data-label="fig:scheme"}](fig//General_Scheme.pdf){width="2.7in"}
In particular, the obtained formula provides a solution for the singularity issue arising in the Grover and Babič formulas for the case when the planes of the primary and secondary circular filaments are mutually perpendicular. The efficiency and flexibility of the Kalantarov-Zeitlin method allow us to extend immediately the application of the obtained result to a case of the calculation of the mutual inductance between a primary circular filament and its projection on a tilted plane. For instance, this particular case appears in micro-machined inductive suspensions and has a direct practical application in studying their stability [@PoletkinLuWallrabeEtAl2017b] and pull-in dynamics [@PoletkinShalatiKorvinkEtAl2018; @PoletkinKorvink2018]. The new analytical formulae were verified by comparison with series of reference examples covering all cases given by Grover[@Grover2004], Kalantarov and Zeitlin [@Kalantarov1986], and using direct numerical calculations performed by the Babič Matlab function [@BabicSiroisAkyelEtAl2010] and the *FastHenry* software [@KamonTsukWhite1994].
Preliminary discussion {#sec:Pleliminary}
======================
Two circular filaments having radii of $R_p$ and $R_s$ for the primary circular filament (the primary circle) and the secondary circular filament (the secondary circle), respectively are considered to be arbitrarily positioned in space, namely, they have a linear and angular misalignment, as is shown in Figure \[fig:scheme\]. Let us assign a coordinate frame (CF) denoted as $XYZ$ to the primary circle in a such way that the $Z$ axis is coincident with the circle axis and the $XOY$ plane of the CF lies on the circle’s plane, where the origin $O$ corresponds to the centre of primary circle. In turn, the $xyz$ CF is assigned to the secondary circle in a similar way so that its origin $B$ is coincident with the centre of the secondary circle.
The linear position of the secondary circle with respect to the primary one is defined by the coordinates of the centre $B$ ($x_B,y_B,z_B$). The angular position of the secondary circle can be defined in two ways. Firstly, the angular position is defined by the angle $\theta$ and $\eta$ corresponding to the angular rotation around an axis passing through the diameter of the secondary circle, and then the rotation of this axis lying on the surface $x'By'$ around the vertical $z'$ axis, respectively, as it is shown in Figure \[fig:angular position\](a). These angles for determination of angular position of the secondary circle was proposed by Grover and used in his formula numbered by (179) in [@Grover2004 page 207] addressing the general case for calculation of the mutual inductance between two circular filaments.
The same angular position can be determined through the $\alpha$ and $\beta$ angle, which corresponds to the angular rotation around the $x'$ axis and then around the $y''$ axis, respectively, as it is shown in Figure \[fig:angular position\](b). This additional second manner is more convenient in a case of study dynamics and stability issues, for instance, applying to axially symmetric inductive levitation systems [@Poletkin2014a; @PoletkinLuWallrabeEtAl2017b] in compared with the Grover manner. These two pairs of angles have the following relationship with respect to each other such as: $$\label{eq:angles}
\left\{\begin{array}{l}
\sin\beta=\sin\eta\sin\theta;\\
\cos\beta\sin\alpha=\cos\eta\sin\theta.
\end{array}\right.$$
The details of the derivation of this set presented above are shown in \[app:determination\].
![Two manners for determining the angular position of the secondary circle with respect to the primary one: $x'y'z'$ is the auxiliary CF the axes of which are parallel to the axes of $XYZ$, respectively; $x''y''z''$ is the auxiliary CF defined in such a way that the $x'$ and $x''$ are coincide, but the $z''$ and $y''$ axis is rotated by the $\alpha$ angle with respect to the $z'$ and $y'$ axis, respectively. []{data-label="fig:angular position"}](fig//ang_position_theta_alpha.pdf){width="3.3in"}
![The Kalantarov-Zeitlin method: $s=\sqrt{x_B^2+y_B^2}$ is the distance to the centre $B$ on the $XOY$ plane. []{data-label="fig:KZ_method"}](fig//General_SchemeII.pdf){width="2.8in"}
The Kalantarov-Zeitlin method
=============================
Using the general scheme for two circular filaments shown in Figure \[fig:scheme\] as an illustrative one, the Kalantarov-Zeitlin method is presented. The method reduces the calculation of mutual inductance between a circular primary filament and any other secondary filament having an arbitrary shape and any desired position with respect to the primary circular filament to a line integral [@Kalantarov1986 Sec. 1-12, page 49].
Indeed, let us choose an arbitrary point $P$ of the secondary filament (as it has been mentioned above the filament can have any shape), as shown in Figure \[fig:scheme\]. An element of length $d\ell''$ of the secondary filament at the point $P$ is considered. Also, the point $P$ is connected the point $Q$ lying on the $Z$ axis by a line, which is perpendicular to the $Z$ axis and has a length of $\rho$, as shown in Figure \[fig:KZ\_method\]. Then the element $d\ell''$ can be decomposed on $dz$ along the $Z$ axis and on $d\rho$ along the $\rho$ line and $d\lambda$ along the $\lambda$-circle having radius of $\rho$ (see, Figure \[fig:KZ\_method plane\]). It is obvious that the mutual inductance between $dz$ and the primary circular filament is equal to zero because $dz$ is perpendicular to a plane of primary circle. But the mutual inductance between $d\rho$ and the primary circular filament is also equal to zero because of the symmetry of the primary circle relative to the $d\rho$ direction.
Thus, the mutual inductance $dM$ between element $d\ell''$ and the primary circle is equal to the mutual inductance $dM_{\lambda}$ between element $d\lambda$ and the primary circle. Moreover, due to the fact that the primary and the $\lambda$-circle are coaxial and, consequently, symmetric then we can write: $$\label{eq:KZ_method}
\frac{dM_{\lambda}}{M_{\lambda}}=\frac{d\lambda}{\lambda}=\frac{d\lambda}{2\pi\rho},$$ where $M_\lambda$ is the mutual inductance of the primary and $\lambda$-circle.
![The Kalantarov-Zeitlin method: projection of the secondary filament on the $\rho$-plane passed through the point $P$ and parallel to the plane of the primary circular filament; $d\ell$ is the projection of the element $d\ell''$ on the $\rho$-plane. []{data-label="fig:KZ_method plane"}](fig//KZ_method.pdf){width="1.8in"}
From Figure \[fig:KZ\_method plane\], it is directly seen that $$\label{eq:KZ_lambda}
d\lambda=dy\cos\varphi-dx\sin\varphi=(\cos\zeta\cos\varphi-\cos\varepsilon\sin\varphi)d\ell,$$ where $\cos\varepsilon$ and $\cos\zeta$ are the direction cosines of element $d\ell$ relative to the $X$ and $Y$ axis, respectively. Hence, accounting for (\[eq:KZ\_method\]) and (\[eq:KZ\_lambda\]), we can write: $$\label{eq:dM}
dM=dM_{\lambda}=M_{\lambda}\frac{\cos\zeta\cos\varphi-\cos\varepsilon\sin\varphi}{2\pi\rho}d\ell,$$ and as a result, a line integral for calculation mutual inductance between the primary circle and a filament is $$\label{eq:M}
M=\frac{1}{2\pi}\int_{\ell}M_{\lambda}\frac{\cos\zeta\cos\varphi-\cos\varepsilon\sin\varphi}{\rho}d\ell,$$ where $M_\lambda$ is defined by the Maxwell formula for mutual inductance between two coaxial circles [@Maxwell1954 page 340, Art. 701]. Note that during integrating, the $Z$ coordinate of the element $d\ell$ is also changing and this dependency is taken into account by the $M_\lambda$ function directly.
![Determination of the position of the point $P$ on the $\rho$-plane through the fixed parameter $s$ and the distance $r$. []{data-label="fig:derivation plane"}](fig//General_SchemeIII.pdf){width="2.5in"}
![The relationship between $d\lambda$ and $d\varphi$. []{data-label="fig:lambda and phi"}](fig//General_SchemeIII_zoom.pdf){width="2.0in"}
Derivation of Formulas
======================
Due to the particular geometry of secondary filament under consideration, its projection on the $\rho$-plane (the $\rho$-plane is parallel to the primary circle plane and passed through the point $P$) is an ellipse, which can be defined in a polar coordinate by a function $r=r(\varphi)$ with the origin at the point $B$ as it is shown in Figure \[fig:derivation plane\]. Hence, the distance $\rho$ can be expressed in terms of the parameter $s$, which is fixed, and the distance $r$ from the origin $B$, which is varied with the angular variable $\varphi$. Introducing the angle $\gamma$ as shown in Figure \[fig:lambda and phi\], for the distance $\rho$ the following equations can be written: $$\label{eq:rho cos}
\begin{array}{l}
\rho \cos\gamma=r+s\cos(\xi-\varphi), \\
\rho \sin\gamma=s\sin(\xi-\varphi).
\end{array}$$ Due to (\[eq:rho cos\]), we have: $$\label{eq:rho sq}
\rho^2 =r^2+r\cdot s\cos(\xi-\varphi)+s^2,$$ where the function $r=r(\varphi)$ can be defined as [@SpiegelLipschutzLiu2009]: $$\label{eq:r}
r=\frac{R_s\cos\theta}{\sqrt{\sin^2(\varphi-\eta)+\cos^2\theta\cos^2(\varphi-\eta)}}.$$ The angle $\theta$ and $\eta$ defines the angular position of the secondary circle with respect to the primary one according to manner I considered in Sec. \[sec:Pleliminary\]. Note that the function $r$ can be also defined via the angles $\alpha$ and $\beta$ of manner II also considered in Sec. \[sec:Pleliminary\] as it is shown in \[app:formulas\]. However, for the further derivation, the angular position of the secondary circle is defined through manner I, since it is convenient for the direct comparison with Grover’s and Babič’ results.
According to Figure \[fig:lambda and phi\], the relationship between the element $d\lambda$ of the $\lambda$-circle and an increment of the angle $\varphi$ is as follows: $$\label{eq:d_lambda and d_vi}
d\lambda=r\cdot d\varphi\cos\gamma-dr\sin\gamma=\left(r\cos\gamma-\frac{dr}{d\varphi}\sin\gamma\right)d\varphi.$$
Then, accounting for (\[eq:d\_lambda and d\_vi\]), (\[eq:rho sq\]) and (\[eq:rho cos\]), line integral (\[eq:M\]) can be replaced by a definite integral for the calculation of mutual inductance as follows: $$\label{eq:def integral}
M=\frac{1}{2\pi}\int_{0}^{2\pi}M_{\lambda}\frac{r^2+r\cdot s\cos(\xi-\varphi)-\frac{dr}{d\varphi}s\sin(\xi-\varphi)}{\rho^2}d\varphi.$$
![The special case: the two filament circles are mutually perpendicular to each other. []{data-label="fig:special case"}](fig//KZ_method_special_case.pdf){width="2.0in"}
Now, let us introduce the following dimensionless parameters such as: $$\label{eq:dimensionless_par}
\begin{array}{l}
{\displaystyle \bar{x}_B=\frac{x_B}{R_s};\; \bar{y}_B=\frac{y_B}{R_s};\; \bar{z}_B=\frac{z_B}{R_s};\;\bar{r}=\frac{r}{R_s};} \\
{\displaystyle \bar{\rho}=\frac{\rho}{R_s};\bar{s}=\sqrt{\bar{x}_B^2+\bar{y}_B^2}.}
\end{array}$$ The $\varphi$-derivative of $\bar{r}$ is $$\label{eq:derivative}
\frac{d\bar{r}}{d\varphi}=\frac{1}{2}\bar{r}^3\tan^2\theta\sin(2(\varphi-\eta)),$$ The mutual inductance $M_{\lambda}$ is $$\label{eq:M_lambda}
M_{\lambda}=\mu_0\frac{2}{k} \Psi(k)\sqrt{R_pR_s\bar{\rho}},$$ where $\mu_0$ is the magnetic permeability of free space, and $$\label{eq:Maxell}
\Psi(k)=\left(1-\frac{k^2}{2}\right)K(k)-E(k),$$ where $K(k)$ and $E(k)$ are the complete elliptic functions of the first and second kind, respectively, and $$\label{eq:k}
k^2=\frac{4\nu\bar{\rho}}{(\nu\bar{\rho}+1)^2+\nu^2\bar{z}_{\lambda}^2},$$ where $\nu=R_s/R_p$ and $\bar{z}_{\lambda}=\bar{z}_B+\bar{r}\tan\theta\sin(\varphi-\eta)$. Accounting for dimensionless parameters (\[eq:dimensionless\_par\]) and substituting (\[eq:derivative\]) and (\[eq:Maxell\]) into integral (\[eq:def integral\]), the new formula to calculate the mutual inductance between two circular filaments having any desired position with respect to each other becomes $$\label{eq:NEW FORMULA}
M=\frac{\mu_0\sqrt{R_pR_s}}{\pi}\int_{0}^{2\pi}\frac{\bar{r}+t_1\cdot\cos\varphi+t_2\cdot\sin\varphi}{k\bar{\rho}^{1.5}}\cdot\bar{r}\cdot\Psi(k)d\varphi,$$ where terms $t_1$ and $t_2$ are defined as $$\label{eq:t}
\begin{array}{l}
t_1=\bar{x}_B+0.5\bar{r}^2\tan^2\theta\sin(2(\varphi-\eta))\cdot\bar{y}_B; \\
t_2=\bar{y}_B-0.5\bar{r}^2\tan^2\theta\sin(2(\varphi-\eta))\cdot\bar{x}_B,
\end{array}$$ and $\bar{\rho} =\sqrt{\bar{r}^2+2\bar{r}\cdot \bar{s}\cos(\xi-\varphi)+\bar{s}^2}$.
Formula (\[eq:NEW FORMULA\]) can be applied to any possible cases, but one is excluded when the two filament circles are mutually perpendicular to each other. In this case the projection of the secondary circle onto the $\rho$-plane becomes simply a line as it is shown in Fig. \[fig:special case\] and as a result to integrate with respect to $\varphi$ is no longer possible.
For the treatment of this case, the Kalantarov-Zeitlin formula (\[eq:M\]) is directly used. Let us introduce the dimensionless variable $\bar{\ell}=\ell/R_s$ and then the integration of (\[eq:M\]) is preformed with respect to this dimensionless variable $\bar{\ell}$ within interval $-1\leq\bar{\ell}\leq1$. The direction cosines $\cos\zeta$ and $\cos\varepsilon$ become as $\sin\eta$ and $\cos\eta$, respectively (see, Fig. \[fig:special case\]). Accounting for $$\label{eq: varphi}
\begin{array}{l}
\rho \cos\varphi=s\cos\xi+\ell\cos\eta, \\
\rho \sin\varphi=s\sin\xi +\ell\sin\eta,
\end{array}$$ and the Maxwell formula (\[eq:Maxell\]) and (\[eq:k\]), where the $Z$-coordinate of the element $d\bar{\ell}$ is defined as $$\label{eq: Z}
\bar{z}_{\lambda}=\bar{z}_B\pm\sqrt{1-\bar{\ell}^2},$$ then the formula to calculate the mutual inductance between two filament circles, which are mutually perpendicular to each other, becomes as follows: $$\label{eq:Singular case}
\begin{array}{l}
{\displaystyle M=\frac{\mu_0\sqrt{R_pR_s}}{\pi}\left[\int_{-1}^{1}\frac{t_1-t_2}{k\bar{\rho}^{1.5}}\cdot\Psi(k)d\bar{\ell}\right.}\\
{\displaystyle \left.+\int_{1}^{-1}\frac{t_1-t_2}{k\bar{\rho}^{1.5}}\cdot\Psi(k)d\bar{\ell}\right]},
\end{array}$$ where terms $t_1$ and $t_2$ are defined as $$\label{eq:t for singular case}
\begin{array}{l}
t_1=\sin\eta(\bar{x}_B+\bar{\ell}\cos\eta); \\
t_2=\cos\eta(\bar{y}_B+\bar{\ell}\sin\eta),
\end{array}$$ and $\bar{\rho} =\sqrt{\bar{s}^2+2\bar{\ell}\cdot \bar{s}\cos(\xi-\eta)+\bar{\ell}^2}$. Note that integrating (\[eq:Singular case\]) between $-1$ and $1$ equation (\[eq: Z\]) is calculated with the positive sign and for the other direction the negative sign is taken.
In order to demonstrate the efficiency and flexibility of the Kalantarov-Zeitlin method, a formula for the calculation of the mutual inductance between the primary circular filament and its projection on a tilted plane is obtained as follows. In this case, the function of $r=r(\varphi)$ is constant and defined through the radius of primary coil as $r=R_p$. Since the centre of the projection is coincide with the $Z$-axis, thus $s=0$. Then, the formula is derived from (\[eq:NEW FORMULA\]) as its particular case ($\bar{s}=0$ and $\bar{r}=\bar{\rho}=1$) and becomes, simply, $$\label{eq:PROJECTOIN FORMULA}
M=\frac{\mu_0{R_p}}{\pi}\int_{0}^{2\pi}\frac{1}{k}\cdot\Psi(k)d\varphi.$$ The obtained formulas can be easily programmed, they are intuitively understandable for application. Also, the singularity arises in Grover’s and Babič’s formula for the calculate of the mutual inductance between two filament circles, which are mutually perpendicular to each other, is solved in developed formula (\[eq:Singular case\]). The *Matlab* files with the implemented formulas (\[eq:NEW FORMULA\]), (\[eq:Singular case\]) and (\[eq:PROJECTOIN FORMULA\]) are available from the authors as supplementary materials to this article. Also, in \[app:formulas\] the the developed formulas can be rewritten through the pair of the angle $\alpha$ and $\beta$.
Examples of Calculation. Numerical Verification
=================================================
In this section, developed new formulas (\[eq:NEW FORMULA\]), (\[eq:Singular case\]) and (\[eq:PROJECTOIN FORMULA\]) are verified by the examples taken from Grover [@Grover2004] and Kalantarov [@Kalantarov1986] books and Babič article [@BabicSiroisAkyelEtAl2010]. The special attention was addressed to the singularity case arisen when the two filament circles are mutually perpendicular to each other. Then, formula (\[eq:PROJECTOIN FORMULA\]) was validated with the *FastHenry* software [@KamonTsukWhite1994]. All calculations for considered cases proved the robustness and efficiency of developed formulas.
Note that the notation proposed in Grover’s and Kalantarov’s books in order to define the linear misalignment of the secondary coil is different from the notation used in the Babič article and in our article as well. Also, the angular misalignment in the Babič formula must be defined through the parameters of the secondary coil plane. These particularities of the notation will be discussed specifically for each case. For all calculation, the primary coil is located on the plane $XOY$ and its centre at the origin $O$(0,0,0).
![Geometrical scheme of coaxial circular filaments denoted via Grover’s notation: radii $a$ and $A$ of secondary and primary coils, respectively; $d$ is the distance between the planes of circles. []{data-label="fig:coaxial filaments"}](fig//coaxial_filaments.pdf){width="1.45in"}
Mutual inductance of coaxial circular filaments {#sec:coaxial circular}
------------------------------------------------
Let us consider the circular filaments, which are coaxial and have a distance between their centres, as shown in Fig. \[fig:coaxial filaments\]. Then, this case in the notation proposed in this article is defined as $R_p=A$, $R_s=a$, the linear misalignment is $z_B=d$, $x_B=y_B=0$, the angular misalignment (manner I, Sec. \[sec:Pleliminary\]) is $\theta=0$ and $\eta=0$. For the Babič formula the linear misalignment is defined in the same way, but for angular one the parameters of the secondary circle plane must be calculated and becomes $a=0$, $b=0$ and $c=1$ (the Babič notation). These parameters have the following relationship with the angle $\theta$ and $\eta$: $a=\sin\eta\sin\theta$; $b=-\cos\eta\sin\theta$ and $c=\cos\theta$ [@BabicSiroisAkyelEtAl2010 Eq. (27), page 3597].
### Example 1 (Example 24, page 78 in Grover’s book [@Grover2004]) {#example-1-example-24-page-78-in-grovers-book .unnumbered}
Let us suppose that two circles of radii $a$= and $A$= with their planes $d$= apart are given. The results of calculation are
Grover’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------ --------------- ------------------- -------------------------------------
$M$, nH 248.79 248.7874 248.7874
\[tab:example1\]
### Example 2 (Example 25, page 78 in Grover’s book [@Grover2004]) {#example-2-example-25-page-78-in-grovers-book .unnumbered}
Two circles of radii $a$== and $A$== with their planes $d$== apart, the results become
Grover’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------ --------------- ------------------- -------------------------------------
$M$, nH 18.38 18.3811 18.3811
\[tab:example2\]
### Example 3 (Example 5-4, page 215 in Kalantarov’s book [@Kalantarov1986]) {#sec:example3 .unnumbered}
For two circles having the same radii of with their planes $d$= apart, the calculation shows the following
Kalantarov’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------ ------------------- ------------------- -------------------------------------
$M$, nH 135.1 135.0739 135.0739
\[tab:example3\]
### Example 4 (Example 5-5, page 215 in Kalantarov’s book [@Kalantarov1986]) {#example-4-example-5-5-page-215-in-kalantarovs-book .unnumbered}
Circles having the same radii as in *Example 3*, but their planes $d$= apart are given. The results are
Kalantarov’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------ ------------------- ------------------- -------------------------------------
$M$, nH 1.41 1.4106 1.4106
\[tab:example3\]
### Example 5 (Example 5-6, page 224 in Kalantarov’s book [@Kalantarov1986]) {#example-5-example-5-6-page-224-in-kalantarovs-book .unnumbered}
Two circular coaxial filaments, radii of which are $A$= and $a$=, with their planes $d$= apart are given. The results are as follows
Kalantarov’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------ ------------------- ------------------- -------------------------------------
$M$, nH 289.11 289.0404 289.0404
\[tab:example3\]
![Geometrical scheme of circular filaments with parallel axes denoted via Grover’s notation: $\rho$ is the distance between axes; $r$ is the distance between the centres; $\varphi$ is the angle between the $Z$-axis and the radius vector $r$. []{data-label="fig:filaments parallel axes"}](fig//filaments_parallel_axes.pdf){width="1.8in"}
Mutual inductance of circular filaments with parallel axes
-----------------------------------------------------------
The scheme for calculation of the mutual inductance between circular filaments with parallel axes is shown in Fig. \[fig:filaments parallel axes\]. The linear misalignment in the Grover notation can be defined by $d$ is the distance between the planes of circles (the same parameter as in Sec. \[sec:coaxial circular\]) and $\rho$ is the distance between axes or via $r$ is the distance between the centres and $\varphi$ is the angle between the $Z$-axis and the radius vector $r$. These parameters have the following relationship to the notation defined in this article, namely, $z_B=d=r\cos\varphi$ and $\rho=\sqrt{x_B^2+y_B^2}=r\sin\varphi$. The angular misalignment is defined in the same way as described in Sec. \[sec:coaxial circular\]).
### Example 6 (Example 62, page 178 in Grover’s book [@Grover2004])) {#example-6-example-62-page-178-in-grovers-book .unnumbered}
Two circles of radii $a=A=$ have a distance between their centres $r=$ and an angle $\varphi=\cos^{-1}0.8$ between the $Z$-axis and the radius vector $r$ (please, see Fig. \[fig:filaments parallel axes\]). Assuming that $y_B=\rho=r\sin\varphi=$ and $z_B=r\cos\varphi=$, the results of calculation are as follows
Grover’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------ --------------- ------------------- -------------------------------------
$M$, nH 45.31 45.3342 45.3342
\[tab:example6\]
### Example 7 (Example 63, page 178 in Grover’s book [@Grover2004]) {#example-7-example-63-page-178-in-grovers-book .unnumbered}
Two circles of the same diameter of $2a=2A=$$=$ are arranged so that the distance between their planes $d=$$=$ and the distance between their axes is $\rho=$$=$ (please, see Fig. \[fig:filaments parallel axes\]). Thus, we have $R_p=R_s=$, $y_B=\rho$ and $z_B=d$, the results of calculation are as follows
Grover’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------ --------------- ------------------- -------------------------------------
$M$, nH $-24.56$ $-24.5728$ $-24.5728$
\[tab:example7\]
### Example 8 (Example 65, page 183 in Grover’s book [@Grover2004]) {#example-8-example-65-page-183-in-grovers-book .unnumbered}
Two circles with radii of $A=$ and $a=$ have the distance between their centres $r=$ and an angle of $\cos\varphi=0.4$ (please, see Fig. \[fig:filaments parallel axes\]). Hence, we have $R_p=A$ and $R_s=a$, assuming that $y_B=r\sin\varphi=$ and $z_B=r\cos\varphi=$, the results of calculation are as follows
Grover’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------ --------------- ------------------- -------------------------------------
$M$, nH $-0.2480$ $-0.24828$ $-0.24828$
\[tab:example8\]
### Example 9 (Example 66, page 184 in Grover’s book [@Grover2004]) {#example-9-example-66-page-184-in-grovers-book .unnumbered}
Two circles with radii of $A=$ and $a=$ have the distance between their centres $r=$ and an angle of $\cos\varphi=0.6$ (please, see Fig. \[fig:filaments parallel axes\]), to find the mutual inductance between these circles. Hence, we have $R_p=A$ and $R_s=a$, assuming that $y_B=r\sin\varphi=$ and $z_B=r\cos\varphi=$, the results of calculation are as follows
Grover’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------ --------------- ------------------- -------------------------------------
$M$, nH $4.405$ $4.465$ $4.465$
\[tab:example9\]
### Example 10 (Example 5-8, page 231 in Kalantarov’s book [@Kalantarov1986]) {#example-10-example-5-8-page-231-in-kalantarovs-book .unnumbered}
Two circular filaments of the same radius of $A=a=$ are arranged that the distance between their centres is $r$= and an angle of $\cos\varphi=0.4$. Hence, we have $R_p=R_s=$, assuming that $y_B=r\sin\varphi=$ and $z_B=r\cos\varphi=$, the results are as follows
Kalantarov’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------- ------------------- ------------------- -------------------------------------
$M$, nH $-0.049$ $-0.048963$ $-0.048963$
\[tab:example10\]
### Example 11 (Example 5-9, page 233 in Kalantarov’s book [@Kalantarov1986]) {#example-11-example-5-9-page-233-in-kalantarovs-book .unnumbered}
Two circular filaments of radii of $A=$ and $a=$ are arranged that the distance between their centres is $r=$ and an angle of $\cos\varphi=0.8$. Hence, we have $R_p=$ and $R_s=$, assuming that $y_B=r\sin\varphi=$ and $z_B=r\cos\varphi=$, the results are as follows
Kalantarov’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------- ------------------- ------------------- -------------------------------------
$M$, nH $2.95$ $3.0672$ $3.0672$
\[tab:example11\]
### Example 12 (Example 5-10, page 234 in Kalantarov’s book [@Kalantarov1986]) {#example-12-example-5-10-page-234-in-kalantarovs-book .unnumbered}
Two circular filaments of radii of $A=$ and $a=$ are arranged that the distance between their centres is $r=$ and an angle of $\cos\varphi=0.66$. Hence, we have $R_p=$ and $R_s=$, assuming that $y_B=r\sin\varphi=$ and $z_B=r\cos\varphi=$, the results become as follows
Kalantarov’s book The Babič formula This work,Eq. (\[eq:NEW FORMULA\])
------------------- ------------------- ------------------- ------------------------------------
$M$, nH $15.99$ $15.9936$ $15.9936$
\[tab:example12\]
![Geometrical scheme of inclined circular filaments with intersect axes denoted via Grover’s notation: $x_1$ and $x_2$ are the distances from $S$, $\theta$ is the angle of inclination of the axes. []{data-label="fig:filaments intersect axes"}](fig//intersect.pdf){width="1.8in"}
Mutual inductance of inclined circular filaments with intersect axes
---------------------------------------------------------------------
The general scheme of the arrangement of two inclined circular filaments whose axes intersect for calculation of mutual inductance is shown in Fig. \[fig:filaments intersect axes\]. In Grover’s notation, we have $A$ and $a$ are radii of circular filaments and $S$ is the point of intersection of the circles axes. The centres of circles are at the distances $x_1$ and $x_2$ from $S$ of the primary and secondary circle, respectively. $\theta$ is the angle of inclination of the axes. Also, the following relationships are true, namely, $d=x_1-x_2\cos\theta$ and $\rho=x_2\sin\theta$. Thus, the linear misalignment in the notation of this paper is defined again through $z_B=d$, $\rho=\sqrt{x_B^2+y_B^2}$ and the angular misalignment is defined by the angle $\theta$, but $\eta$ is equal to zero. For the Babič formula, the angular misalignment is defined by the parameters of the secondary circle plane as follows: $a=0$; $b=-\sin\theta$ and $c=\cos\theta$.
From the general scheme shown in Fig. \[fig:filaments intersect axes\], two particular cases can be recognized. Namely, the first case is corresponded to concentric circles, when $x_1=x_2=0$ and the second case is corresponded to circular filaments whose axes intersect at the centre of one of the circle, when $x_2=0$. For the first case, to calculate the mutual inductance, the angle $\theta$ and radii of circles must be known. For the second particular case, in addition to the distance $d$ between the centre $B$ of the secondary circle and the plane of the primary circle must be given.
### Example 13 (Example 5-7, page 227 in Kalantarov’s book [@Kalantarov1986]) {#example-13-example-5-7-page-227-in-kalantarovs-book .unnumbered}
Two circular filaments of radii of $A=$ and $a=$ are concentric and an angle of inclination of the plane of the secondary circle is $\theta=$. Hence, assuming that $x_B=y_B=z_B=0$, the calculation of mutual inductance shows
Kalantarov’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------- ------------------- ------------------- -------------------------------------
$M$, nH $6.044$ $6.0431$ $6.0431$
\[tab:example13\]
### Example 14 (Example 69, page 194 in Grover’s book [@Grover2004]) {#example-14-example-69-page-194-in-grovers-book .unnumbered}
Two concentric circles with radii of $A=$ and $a=$ are arranged that an angle of inclination of the plane of the secondary circle is $\cos\theta=0.3$. Hence, assuming that $x_B=y_B=z_B=0$ and $\theta=$, the results of calculation are as follows
Grover’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------- --------------- ------------------- -------------------------------------
$M$, nH $47.44$ $47.4431$ $47.4431$
\[tab:example14\]
### Example 15 (Example 70, page 194 in Grover’s book [@Grover2004]) {#example-15-example-70-page-194-in-grovers-book .unnumbered}
Two circles with radii of $A=$= and $a=$= are arranged that an angle of inclination of the plane of the secondary circle is $\cos\theta=0.4$ and a distance $d=$=. Hence, assuming that $x_B=y_B=0$, $z_B=d$ and $\theta=$, the results of calculation are as follows
Grover’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------- --------------- ------------------- -------------------------------------
$M$, nH $15.543$ $15.5435$ $15.5435$
\[tab:example15\]
### Example 16 (Example 71, page 201 in Grover’s book [@Grover2004]) {#example-16-example-71-page-201-in-grovers-book .unnumbered}
Two circles of radii $A=$ and $a=$ are considered with the centre of one on the axis of the other and a distance, $d$, of between the centres. The axes are to be inclined at an angle, $\theta$, of . The results of calculation show
Grover’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------- --------------- ------------------- -------------------------------------
$M$, nH $29.436$ $29.4365$ $29.4365$
\[tab:example16\]
### Example 17 (Example 5-11, page 235 in Kalantarov’s book [@Kalantarov1986]) {#example-17-example-5-11-page-235-in-kalantarovs-book .unnumbered}
Two circular filaments have radii of $A=$ and $a=$. The axis the primary circle is crossed through the centre of the secondary circle at a distance $d$ of between their centres. The axes are to be inclined at an angle, $\cos\theta=0.7$. Hence, assuming that $x_B=y_B=0$, $z_B=d$ and an angle of , the results of calculation are
Kalantarov’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------- ------------------- ------------------- -------------------------------------
$M$, nH $23.2$ $24.3794$ $24.3794$
\[tab:example17\]
### Example 18 (Example 73, page 204 in Grover’s book [@Grover2004]) {#example-18-example-73-page-204-in-grovers-book .unnumbered}
Two circles of radii $A=$ and $a=$ are considered to be intersect the axes at point $S$ in such a way that distances $x_1$ and $x_2$ are to be and , respectively. An angle of inclination between axes is $\cos\theta=0.5$. Hence, assuming that $x_B=0$, $y_B=$, $z_B=$ and an angle of , we have
Grover’s book The Babič formula This work, Eq. (\[eq:NEW FORMULA\])
------------------- --------------- ------------------- -------------------------------------
$M$, nH $13.612$ $13.6113$ $13.6113$
\[tab:example18\]
----------- ------------------------- ----------------------------------------------- --------------------------
$\eta$ The Grover formula, The Babič This work,
[@Grover2004 Eq. (179)] formula, [@BabicSiroisAkyelEtAl2010 Eq. (24)] Eq. (\[eq:NEW FORMULA\])
$M$, nH $M$, nH $M$, nH
0 13.6113 13.6113 13.6113
$\pi/6$ 14.4688 14.4688 14.4688
$\pi/4$ 15.4877 15.4877 15.4877
$\pi/4$ 16.8189 16.8189 16.819
$\pi/2$ 20.0534 20.0534 20.0534
$2\pi/3$ 23.3252 23.3252 23.3252
$3\pi/4$ 24.6936 24.6936 24.6936
$5\pi/6$ 25.7493 25.7493 25.7493
$\pi$ 26.6433 26.6433 26.6433
$7\pi/6$ 25.7493 25.7493 25.7493
$5\pi/4$ 24.6936 24.6936 24.6936
$4\pi/3$ 23.3253 23.3253 23.3252
$3\pi/2$ 20.0534 20.0534 20.0534
$5\pi/3$ 16.8189 16.8189 16.819
$7\pi/4$ 15.4877 15.4877 15.4877
$11\pi/6$ 14.4688 14.4688 14.4688
$2\pi$ 13.6113 13.6113 13.6113
----------- ------------------------- ----------------------------------------------- --------------------------
: Calculation of mutual inductance for Example 19 []{data-label="tab:Example19"}
Mutual inductance of circular filaments arbitrarily positioned in the space
----------------------------------------------------------------------------
The validation of the developed formulas (\[eq:NEW FORMULA\]) and (\[eq:Singular case\]) for the general case, when the angular misalignment is defined through the angle $\theta$ and $\eta$ as shown in Fig. \[fig:angular position\](a) in an range from 0 to 360, the examples from the Babič article [@BabicSiroisAkyelEtAl2010] were used. Also, we utilized the Matlab functions with the Grover formula [@Grover2004 page 207, Eq. (179)] and the Babič formula [@BabicSiroisAkyelEtAl2010 page 3593, Eq. (24)] implemented by F. Sirois and S. Babič.
### Example 19 (Example 12, page 3597 in the Babič article [@BabicSiroisAkyelEtAl2010]) {#example-19-example-12-page-3597-in-the-babič-article .unnumbered}
Using the geometrical arrangement as in Example 18 (two circles with radii $A=$ and $a=$ and the centre of the secondary circle is located at $x_B=0$, $y_B=$, $z_B=$ and the angle, $\theta$ of ), but the angle $\eta$ is varied in a range from 0 to 360. The results of calculation are summed up in Table \[tab:Example19\]. Analysis of Table \[tab:Example19\] shows that the developed formula (\[eq:NEW FORMULA\]) works identically to the Grover and Babič formula.
### Example 20 (Example 11, page 3596 in the Babič article [@BabicSiroisAkyelEtAl2010]) {#example-20-example-11-page-3596-in-the-babič-article .unnumbered}
Let us consider two circular filaments having radii of $R_p=$ and $R_s=$, which are mutually perpendicular to each other that angles of $\eta=$ and $\theta=$. The centre of the secondary circle has the following coordinates: $x_B=0$, $y_B=$, and $z_B=$. The problem illustrates the application of new formula (\[eq:Singular case\]). The results are
The Grover formula The Babič formula This work,Eq. (\[eq:Singular case\])
------------------- -------------------- ------------------- --------------------------------------
$M$, nH $-10.73$ $-10.73$ $-10.7272$
\[tab:example20\]
![Distribution of the error of the Babič formula in dependent on changing the $\eta$-angle within a range $0<\eta\leq360^{o}$ for Example 21 ($x_B=y_B=z_B=0$). []{data-label="fig:Babic error in origin"}](fig//Badic_error_in_origin.pdf){width="3.0in"}
### Example 21 {#example-21 .unnumbered}
Now we again apply formula (\[eq:Singular case\]) to the problem considered in Example 20, but in this case the centre of the secondary coil is located at origin, thus $x_B=y_B=z_B=0$. Hence, we have
The Grover formula The Babič formula This work, Eq. (\[eq:Singular case\])
------------------- -------------------- ------------------- ---------------------------------------
$M$, nH $NaN$ $NaN$ $0$
\[tab:example21\]
Thus, the calculation shows that the Babič and Grover formula gives an indeterminate results, but developed formula (\[eq:Singular case\]) equals explicitly zero as expected for this case. Then, rotating the angle $\eta$ in a range $0<\eta\leq360^{o}$, we reveal that the calculation of mutual inductance performed by developed formula (\[eq:Singular case\]) shows zero within this range of the $\eta$-angle, but the Babič formula demonstrates a small error, which is not exceeded $M=$ and distributed with the $\eta$-angle as shown in Figure \[fig:Babic error in origin\].
![Chaotic distribution of the error of the Babič formula in dependent on changing the $\eta$-angle within a range $0<\eta\leq360^{o}$ for Example 22 ($x_B=y_B=$ and $z_B=0$): the scaled-up images show the interruption of continuity of the curve at $\eta=$ and . []{data-label="fig:Babic error in x y"}](fig//Badic_error_in_x_y.pdf){width="2.8in"}
### Example 22 {#example-22 .unnumbered}
Let us consider mutually perpendicular circles (angles of $\theta=$ and $\eta=$) having the same radii as in Example 20, but the centre of the secondary coil occupies a position on the $XOY$-surface with the following coordinates $x_B=y_B=$ and $z_B=0$. Results of calculation are
The Grover formula The Babič formula This work, Eq. (\[eq:Singular case\])
------------------- ----------------------- ----------------------- ---------------------------------------
$M$, nH $4.013\times10^{-15}$ $2.416\times10^{-15}$ $0$
\[tab:example21\]
![Geometrical scheme for calculation of mutual inductance between a primary circular filament and its projection. The angular misalignment is given by an angle of $\theta$, while the linear misalignment by the coordinate $z_B$.[]{data-label="fig:projection"}](fig//Projection.pdf){width="2.8in"}
Thus, the calculation expresses that the Babič and Grover formula gives the small errors, but developed formula (\[eq:Singular case\]) shows, explicitly, zero. Then, again let us rotate the angle $\eta$ in a range $0<\eta\leq360^{o}$, the calculation of mutual inductance performed by developed formula (\[eq:Singular case\]) reveals zero within this range of the $\eta$-angle, but the Babič formula demonstrates the chaotic distribution of the small error of calculation as shown in Fig. \[fig:Babic error in x y\], which is in a range from to and at the $\eta$-angle of and the calculation of mutual inductance is indeterminate (see, the scaled-up images of Fig. \[fig:Babic error in x y\], which present the interruption of continuity at $\eta=$ and ).
Mutual inductance between a primary circular filament and its projection on a tilted plane
-------------------------------------------------------------------------------------------
In this section new formula (\[eq:PROJECTOIN FORMULA\]) for calculation of mutual inductance between a primary circular filament and its projection on a tilted plane is validated by comparison with the calculation performed via the *FastHenry* software [@KamonTsukWhite1994]. The angular misalignment is given by the angle $\theta$ and $\eta$, while the linear misalignment is defined by the coordinate $z_B$ of the point $B$ crossing the tilted plane and the $Z$-axis. Fig. \[fig:projection\] shows a geometrical scheme for the calculation. The shown arrangement of the primary circle and its projection on the tilted plane corresponds to a particular case, when $\eta=0$. Worth noting that the $\eta$-angle has no effect on the result of the calculation of the mutual inductance.
---------- -------------------------------------------- -----------------------------------
$\theta$ This work, Eq. (\[eq:PROJECTOIN FORMULA\]) *FastHenry* [@KamonTsukWhite1994]
$M$, nH $M$, nH
0 135.0739 135.076
142.0736 142.086
153.3233 153.298
---------- -------------------------------------------- -----------------------------------
: Calculation of mutual inductance for Example 23 []{data-label="tab:Example23"}
### Example 23 {#sec:example23 .unnumbered}
Let us consider primary circle having a radius of and a tilting plane crosses the $Z$-axis at the point $z_B$=. When a tilting angle of zero, then the geometry and arrangement corresponds to Example 3 (Example 5-4, page 215 in Kalantarov’s book) for the case of two coaxial circles with the same radii. We calculate the mutual inductance for three values of a tilted angle at , and . The results of calculation are shown in Table \[tab:Example23\].
Although, there is the small deviation between results obtained with the *FastHenry* software and analytical formula (\[eq:PROJECTOIN FORMULA\]), but this deviation is not significant and can be explained by the fact that the circles in the *FastHenry* software are divided into straight segments with a finite cross section in comparing with the analytical formula where the circles have no segments and a cross section. We are concluding the validity of developed formula (\[eq:PROJECTOIN FORMULA\]).
---------- -------------------------------------------- -----------------------------------
$\theta$ This work, Eq. (\[eq:PROJECTOIN FORMULA\]) *FastHenry* [@KamonTsukWhite1994]
$M$, nH $M$, nH
0 1.4106 1.3761
1.4117 1.3844
1.4151 1.3933
1.421 1.4031
1.4298 1.4120
1.4422 1.4202
1.4594 1.4268
1.4831 1.4336
1.5161 1.4574
1.5631 1.5230
1.6329 1.6180
1.7425 1.7273
1.9299 1.8765
2.2971 2.2416
3.2127 3.1806
7.1274 7.1679
---------- -------------------------------------------- -----------------------------------
: Calculation of mutual inductance for Example 24 []{data-label="tab:Example24"}
### Example 24 {#sec:example24 .unnumbered}
In this last example, we increase a distance between the centre of the primary circle with a radius of and a tilting plane to $z_B$=. Hence, a range of the tilted angle becomes larger then in example 23. Note that for zero tilting angle the geometry of the considered problem corresponds to example 4 (Example 5-5, page 215 in Kalantarov’s book). The results of calculation are shown in Table \[tab:Example24\]. Analysis of Table \[tab:Example24\] shows a good agreement between the calculations, which confirms the validity of developed formula (\[eq:PROJECTOIN FORMULA\]).
Conclusion
==========
We derived and validated new formulas (\[eq:NEW FORMULA\]) and (\[eq:Singular case\]) for calculation of the mutual inductance between two circular filaments arbitrarily oriented with respect to each other. These analytic formulas have been developed based on the Kalantarov-Zeitlin method, which showed that the calculation of mutual inductance between a circular primary filament and any other secondary filament having an arbitrary shape and any desired position with respect to the primary filament is reduced to a line integral. In particular, the developed formula (\[eq:Singular case\]) provides a solution for the singularity issue arising in Grover’s and Babič’ formulas for the case when the planes of the primary and secondary circular filaments are mutually perpendicular.
Moreover, a curious reader can already recognize that formula (\[eq:Singular case\]) can be applied for calculation of the mutual inductance between the circular filament and a line, position of which with respect to the circle is defined through the linear and angular misalignment. For this reason, in Eq. (\[eq: Z\]) we assume that $\bar{z}_{\lambda}=\bar{z}_B$ and formula (\[eq:Singular case\]) is integrated only from $-1$ to $1$. This fact proves again the efficiency and flexibility of the Kalantarov-Zeitlin method.
The advantages of the Kalantarov-Zeitlin method allow us to extend immediately the application of the obtained result to a case of the calculation of the mutual inductance between a primary circular filament and its projection on a tilted plane and to furnish this case via formula (\[eq:PROJECTOIN FORMULA\]). For instance, this particular case appears in micro-machined inductive suspensions and has a direct practical application in studying their stability and pull-in dynamics.
New developed formulas have been successfully validated through a number of examples available in the literature. Also, the direct comparison the results of calculation with the numerical results obtained by utilizing the *FastHenry* software shows a good agreement. Besides, the obtained formulas can be easily programmed, they are intuitively understandable for application.
Acknowledgment {#acknowledgment .unnumbered}
==============
Kirill Poletkin acknowledges with thanks to Prof. Ulrike Wallrabe for the continued support of his research. Also, Kirill Poletkin acknowledges with thanks the support from German Research Foundation (Grant KO 1883/26-1).
![The relationship between the angles of two manners for determining angular misalignment of the secondary circle: I and II are denoted for two spherical triangles highlighted by arcs in red color. []{data-label="fig:angular misalignment"}](fig//ang_position_theta_alpha_app.pdf){width="2.5in"}
Determination of angular position of the secondary circular filament {#app:determination}
====================================================================
The angular position of the secondary circle can be defined through the pair of angle $\theta$ and $\eta$ corresponding to manner I and the angle $\alpha$ and $\beta$ manner II. The relationship between two pairs of angles can be determined via two spherical triangles denoted in Roman number I and II as shown in Fig. \[fig:angular misalignment\]. According to the law of sines, for spherical triangle I we can write the following relationship: $$\label{eq: triangleI}
\frac{\sin\eta}{\sin\pi/2}=\frac{\sin\beta}{\sin\theta}.$$ For spherical triangle II, we have $$\label{eq: triangleII}
\frac{\sin(\pi/2-\eta)}{\sin(\pi/2-\beta)}=\frac{\sin\alpha}{\sin\theta}.$$ Accounting for (\[eq: triangleI\]) and (\[eq: triangleII\]), the final set determining the relationship between two pairs of angles becomes as $$\label{eq:angles pair}
Presentation of developed formulas via the pair of angles $\alpha$ and $\beta$ {#app:formulas}
==============================================================================
Using set (\[eq:angles pair\]), we can write the following equations: $$\label{eq:new pair}
\left\{\begin{array}{l}
\cos^2\theta=\cos^2\beta(1+\sin^2\alpha);\\
\sin^2\theta=\sin^2\beta+\cos^2\beta\sin^2\alpha;\\
{\displaystyle \tan^2\theta=\frac{\sin^2\beta+\cos^2\beta\sin^2\alpha}{\cos^2\beta(1+\sin^2\alpha)};}\\
{\displaystyle \cos^2\eta=\cos^2\beta\sin^2\alpha/{\sin^2\theta}};\\
{\displaystyle \sin^2\eta={\sin^2\beta}/{\sin^2\theta}}.
\end{array}\right.$$ Now, applying set (\[eq:new pair\]) to (\[eq:r\]), the square of the dimensionless function $\bar{r}$ becomes as $$\label{eq:square of r}
\bar{r}^2=\frac{\cos^2\beta(1+\sin^2\alpha)(\sin^2\beta+\cos^2\beta\sin^2\alpha)}{{\begin{array}{l}
(\sin\varphi\cos\beta\sin\alpha- \cos\varphi\sin\beta)^2+\\
\cos^2\beta(1+\sin^2\alpha)(\cos\varphi\cos\beta\sin\alpha+\sin\varphi\sin\beta)^2
\end{array}}}.$$ Then, for the dimensionless parameter $ \bar{z}_{\lambda}$, we have $$\label{eq:z_lambda}
\bar{z}_{\lambda}=\bar{z}_B+\bar{r}\frac{\sin\varphi\cos\beta\sin\alpha- \cos\varphi\sin\beta}{\sqrt{\cos^2\beta(1+\sin^2\alpha)}}.$$
Substituting (\[eq:square of r\]), (\[eq:z\_lambda\]) and $$\label{eq:terms}
\begin{array}{l}
{\displaystyle t_1=\bar{x}_B+\bar{y}_B\cdot\bar{r}^2\frac{\sin^2\beta+\cos^2\beta\sin^2\alpha}{\cos^2\beta(1+\sin^2\alpha)}\times}\\
{\displaystyle \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(\sin\varphi\cos\beta\sin\alpha- \cos\varphi\sin\beta)\times}\\
{\displaystyle\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; (\cos\varphi\cos\beta\sin\alpha+\sin\varphi\sin\beta);}\\
{\displaystyle t_2=\bar{y}_B-\bar{x}_B\cdot\bar{r}^2\frac{\sin^2\beta+\cos^2\beta\sin^2\alpha}{\cos^2\beta(1+\sin^2\alpha)}\times}\\
{\displaystyle \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(\sin\varphi\cos\beta\sin\alpha- \cos\varphi\sin\beta)\times}\\
{\displaystyle\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; (\cos\varphi\cos\beta\sin\alpha+\sin\varphi\sin\beta),}
\end{array}$$ into Eq. (\[eq:NEW FORMULA\]), the angular misalignment of the secondary circle are defined through the pair of angle $\alpha$ and $\beta$ corresponding to the manner II.
For the case when the two circles are mutually perpendicular to each other, assuming that $\alpha=\pi/2$ then just replacing the angle $\eta$ by $\beta$ in formula (\[eq:Singular case\]), it can be used for calculation with new pair of angle $\alpha$ and $\beta$.
Since formula (\[eq:PROJECTOIN FORMULA\]) is a particular case of (\[eq:NEW FORMULA\]), when $\bar{s}=0$ and $\bar{r}=\bar{\rho}=1$. Hence, substituting $\bar{r}=1$ into (\[eq:z\_lambda\]) and using this modified equation for formula (\[eq:PROJECTOIN FORMULA\]), it can be used for calculation of mutual inductance between the primary circle and its projection on a tilted plane, an angular position of which is defined by the pair of angle $\alpha$ and $\beta$.
References {#references .unnumbered}
==========
| |
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The X Factor was devised as a replacement for the highly successful Pop Idol, which was put on indefinite hiatus after its second series, largely because Simon Cowell wished to launch a show that he owned the television rights to. The perceived similarity between the shows later became the subject of a legal dispute. The X Factor winner receives a recording contract with record label Syco with a stated value of £1,000,000. This includes a cash payment to the winner, but the majority is allocated to marketing and recording costs. The show is the biggest television talent competition in Europe and has proved hugely popular with the public. Series 6 attracted 200,000 auditionees and peaked at 19.7 million UK viewers (a 63.2% audience share). 10 million votes were cast in the series 6 final.
In the initial televised audition phase of the show, contestants sing in front of the judges – currently Simon Cowell Louis Walsh Cheryl Cole and a guest judge – and, from series 6, a live audience, in the hope of getting through to the "boot camp" round. After a further selection process, the judges are each given a category to mentor and the chosen finalists then progress to the final phase of the competition, during which the public vote for their favourite act following weekly live performances by the contestants. There have been six winners to date: Steve Brookstein, Shayne Ward, Leona Lewis, Leon Jackson, Alexandra Burke and Joe McElderry. The winning contestant's single is released in time for the end of year chart battle for the UK's Christmas number one, a spot which it gained in four successive years from 2005 to 2008. In total, 14 number one singles have been released by artists who have appeared on the show.
The X Factor format has been adopted in a number of other countries. Local versions of the format have become successful throughout the world, most notably in Denmark and the Netherlands, where two series have been shown and a third is expected, as well as in Italy, Spain, Colombia, Portugal and India. However, the original British version has not been broadcast in any other country (except Ireland) due to unresolved rights issues. Television stations in the Scandinavian countries have expressed an interest in showing the UK version but not been able to acquire the rights.
To date, six series have aired, as summarised below.
a. ^ In series 1 to 3 the category was contestants aged 16 to 24; this was then split into girls and boys from series 4.
b. ^ In series 4 and 5 the age limit was lowered to 14. From series 6 the age limit returned to 16.
A celebrity special edition, The X Factor: Battle of the Stars, aired from 29 May to 5 June 2006. It was won by actress Lucy Benjamin.
The first appeal for contestants to take part in series 7 aired on Saturday 5 December 2009. However, in the series 6 pre-finale press conference Cowell confirmed that there was no deal in place for The X Factor in 2010. He said "We've got to get that sorted out [...] That's a conversation we'll be having next year with ITV." He also pointed out that any changes to the format would not be decided until the deal is agreed.
The show is primarily concerned with identifying singing talent, though appearance, personality, stage presence and dance routines are also an important element of many performances. The single most important attribute that the judges are seeking, however, is the ability to appeal to a mass market of pop fans.
A round of first auditions is held in front of producers months before the show is aired, either by application and appointment, or at "open" auditions that anyone can attend. These auditions, held at various venues around the UK, attract very large crowds. The auditions themselves are not televised, but shots of crowds waving and "judges' cars" arriving are filmed and later spliced in with the televised auditions shot later in the year. The production team supply the crowds with "home-made" signs. After waiting at the venue for hours and filming more inserts of screaming and waving, candidates are given a brief audition by someone from the production team. Should they pass that audition (either for reasons of talent or for the potential of making entertaining television) they are given a "golden ticket" allowing them to sing to a more senior production member. Only candidates who successfully pass that second audition are invited to perform to the judges. The televised version misrepresents the process by implying that the entire huge crowds are all interviewed by the judges.
A selection of the auditions in front of the judges – usually the best, the worst and the most bizarre (described by judge Louis Walsh as "the good, the bad and the ugly") – are broadcast over the first few weeks of the show. In the first five series, each act entered the audition room and delivered a stand-up unaccompanied performance of their chosen song to the judges. In series 6 (2009), the judges' auditions were held in front of a live audience – following the format of ITV's other talent show, Britain's Got Talent – and the acts sang over a backing track. If a majority of the judges (two in series 1–3 or three in series 4–6) say "yes" then the act goes through to the next stage, otherwise the act is sent home.
Over 50,000 people auditioned for series 1, around 75,000 for series 2 and around 100,000 for series 3. The number of applicants for series 4 reached 150,000, 182,000 people auditioned for series 5, and a record 200,000 people applied for series 6.
In 2010, applicants for the seventh series were given the opportunity to apply by uploading a video audition to the Internet.
The contestants selected at audition are further refined through a series of performances at "boot camp" (held at a venue such as a country hotel or an arena), and then at the "judges' houses", until a small number eventually progress to the live finals (nine in series 1 and twelve from series 2 onwards). Judge Louis Walsh revealed in November 2007 that the houses the contestants visit do not actually belong to the judges, but are rented for the purpose.
The finals consist of a series of two live shows, the first featuring the contestants' performances and the second revealing the results of the public voting, culminating in one or more acts being eliminated. Celebrity guest performers also feature regularly. These live shows are filmed at The Fountain Studios in Wembley, London. In series 1–5, both live shows aired on Saturday nights. In series 6, the results show moved to Sunday nights.
In the first few weeks of the finals, each act performs once in the first show in front of a studio audience and the judges. Acts usually sing over a pre-recorded backing track, though sometimes live musicians and backing singers are featured. Dancers are also commonly featured. Acts occasionally accompany themselves on guitar or piano (or mime an accompaniment), though almost always over a backing track.
In the first two series, acts usually chose a cover of a pop standard or contemporary hit. In the third series an innovation was introduced whereby each live show had a different theme (for example, Motown), thus increasing the show's similarity to Pop Idol. The contestants' songs are chosen according to the theme. This format has continued in subsequent series. A celebrity guest connected to the theme is often invited onto the show, and clips are shown of the guest conversing with the contestants at rehearsal. In series 1, much was made of the idea that each performer/mentor combination was free to present the performance however they wanted, including the performer playing live instruments, or the addition of choirs, backing bands, and dancers. Future series placed less emphasis on this element.
After each act has performed, the judges comment on their performance, usually focusing on vocal ability, image and stage presence. Heated disagreements, usually involving judges defending their contestants against criticism, are a regular feature of the show. Once all the acts have appeared, the phone lines open and the viewing public vote on which act they want to keep.
Before the results are announced, there are live or pre-recorded performances from one or more invited celebrities – often major international pop stars. Sometimes these performers are connected with the week's theme and featured in the earlier show; other times they are unconnected. In series 6, the results show began with a group performance from the remaining contestants. This performance is not judged or voted on and does not count towards the result.
After all the build-up performances have taken place, the two acts polling the fewest votes are revealed. Both these acts perform again in a "final showdown", and the judges vote on which of the two to send home. In earlier series the bottom two contestants reprised their earlier song, but from series 5 they were able to pick new songs. Ties became possible with the introduction of a fourth judge in series 4. In the event of a tie the show goes to deadlock, and the act who came last in the public vote is sent home. The actual number of votes cast for each act is not revealed, nor even the order; according to a spokesman, "We would never reveal the voting figures during the competition as it could give contestants an unfair advantage and spoil the competition for viewers". In series 3, a twist was introduced in one of the live shows where the act with the fewest votes was automatically eliminated, and the two with the next fewest votes performed in the "final showdown" as normal.
Once the number of contestants has been reduced to four (series 1 and 3) or five (series 2, 4, 5 and 6), the format changes. Each act performs twice in the first show, with the public vote opening after the first performance. The second show reveals which act polled the fewest votes, and they are automatically eliminated from the competition (the judges do not have a vote; their only role is to comment on the performances). In series 1 the acts also reprised one of their songs in the second show.
This continues until only two (series 1 and 3) or three (series 2, 4, 5 and 6) acts remain. These acts go on to appear in the grand final which decides the overall winner by public vote. In past series some of the more memorable failed auditionees from the early rounds have also returned for a special appearance in the final.
The winner of the competition is awarded a recording contract, stated to be worth £1 million, with Syco in association with Sony Music Entertainment. In series 5, this deal consisted of a £150,000 cash advance with the balance covering the costs of recording and marketing. Other highly placed contestants may also be offered recording deals, but this is not guaranteed.
In series 1–3, the premise of The X Factor was that the winner would be managed in the industry by their mentor on the show. With music executive Cowell and managers Osbourne and Walsh as judges/mentors, any of the three would be qualified to do so. Following the appointment of singer Dannii Minogue as a judge in series 4, the same principle could not universally apply. In fact, when Minogue won series 4 with Leon Jackson, a new, outside manager was appointed. It is still believed that if Cowell or Walsh win a future series then they are entitled to manage their act in the industry.
From series 1 to 3, the X Factor judges were music executive and TV producer Simon Cowell, music manager and TV personality Sharon Osbourne and music manager Louis Walsh. Pop singer, dancer and TV personality Paula Abdul was a special guest judge at the series 3 London auditions.
After the third series, Walsh was dropped from the show, being replaced by American choreographer Brian Friedman and Australian singer and actress Dannii Minogue. After a week, however, Friedman was re-assigned the role of Creative Director because Simon Cowell believed the judging panel was not working. Walsh then resumed his place on the panel, and the series 4 judging lineup was finally confirmed in June 2007 as Simon Cowell, Sharon Osbourne, Louis Walsh and Dannii Minogue. On 15 December 2007, Dannii Minogue became the first female judge to win after her series 4 victory with Leon Jackson.
Speculation surrounded judging lineup changes for series 5, centring on whether or not Sharon Osbourne would return. On 6 June 2008 (six days before filming for series 5 was due to begin), ITV confirmed that Osbourne had left the show, and Girls Aloud singer Cheryl Cole was confirmed as her replacement four days later. It was confirmed that a number of other artists and producers had been approached regarding Osbourne's replacement, including former Spice Girl Melanie Brown, Paula Abdul, Sinitta, and former Pop Idol judge Pete Waterman. Osbourne stated that she left The X Factor because she did not enjoy working with Dannii Minogue.
During series 5 it was rumoured that judge Dannii Minogue would leave the show after the series' conclusion, and that Sharon Osbourne would return to replace her in series 6. These rumours continued during the lead-up to series 6. Others tipped to replace Minogue included Robbie Williams, Victoria Beckham, Charlotte Church, Lily Allen, Sinitta and Randy Jackson. Simon Cowell reportedly held discussions about model Kate Moss joining the show as the contestants' "stylist". However, Minogue did not leave and all four judges from series 5 returned for series 6. On 13 December 2009, Cheryl Cole became the first judge to win two series in a row after her victories in series 5 with Alexandra Burke and series 6 with Joe McElderry.
The judges' appearance on screen is accompanied by several pieces of music including Tomoyasu Hotei's Battle Without Honor Or Humanity, Craig Armstrong's O Verona, O Fortuna from Carl Orff's Carmina Burana and Come With Me by Puff Daddy and Jimmy Page.
The show was hosted up to series 3 by Kate Thornton. Thornton was replaced from series 4 by Dermot O'Leary who signed a contract worth £1 million to present two series of the programme on ITV1. O'Leary was not forced to leave the Big Brother franchise and continued to present Big Brother sister shows during summer 2007. However, Dermot announced that Big Brother: Celebrity Hijack was to be his last Big Brother hosting role so he could focus on presenting The X Factor.
Brian Friedman has continued in his role as performance coach and choreographer (billed as "Creative Director") since series 4. Yvie Burnett has been X Factor vocal coach since series 2. Voice-overs are provided by Peter Dickson and Enn Reitel.
For information about The Xtra Factor presenters, see The Xtra Factor below.
In each series, each judge is allocated a category to mentor and chooses a small number of acts (three or four, depending on the series) to progress to the live finals. This table shows, for each series, which category each judge was allocated and which acts he or she put through to the live finals.
– Winning judge/category. Winners are in bold, other contestants in small font.
Viewing figures of around 10 million were claimed for series 2 and 4, and 11 to 12 million for series 5. Over three million public votes were cast in the series 2 semi-final, and six million in the first part of the final. The series 3 final attracted eight million votes and 12.6 million viewers. The series 4 final drew 12.7 million viewers – a 55% share of the terrestrial TV audience. In series 5, 12.8 million tuned in to see the 29 November 2008 show featuring guest Britney Spears, a new X Factor record. The series 5 final peaked with 14.6 million viewers, and the series 6 final topped this with 19.7 million viewers (a 63.2% audience share) and 10 million votes cast.
At the British Comedy Awards 2005, The X Factor beat Friday Night with Jonathan Ross and Ant & Dec's Saturday Night Takeaway to take the award for Best Comedy Entertainment Programme, prompting Simon Cowell to remark "We're not a comedy programme, we're a serious factual drama". In both 2005 and 2006, The X Factor won the award for "Most Popular Entertainment Programme" at the National Television Awards. At the same awards in 2007 the show won the "Most Popular Talent Show" category. In 2008 it lost out to Strictly Come Dancing at the TV Quick Awards, TRIC Awards and National Television Awards, despite beating it in the ratings. In 2009, The X Factor won "Best Talent Show" at the National Television Awards.
The BBC's rival talent show Strictly Come Dancing initially beat The X Factor in viewing figures, although in recent years The X Factor has reversed this trend, and when the shows went head-to-head for the first time The X Factor attracted a larger audience share. It rates as ITV's most popular programme whilst it airs, and is the first format (along with Britain's Got Talent) in years to knock Coronation Street off the top.
The show's viewing figures have generally trended up each series. However, this was not the case for series 2 and 3, when the former attracted more viewers than the latter.
All information in this table comes from BARB.
The X Factor has, from the outset, attracted its fair share of criticism. Recurring allegations are: that the excessive commercialism of the show detracts from of its supposed purpose of unearthing musical talent and even actively damages and distorts the UK music industry; that auditionees at mass auditions are shabbily treated; that controversy is deliberately courted and orchestrated, and supposedly spontaneous scenes are staged and scripted; that problems with phone lines leave members of the public unable to vote for their favourite acts; and that contestants are manipulated and unfairly edited.
This criticism became very public in 2009 when an internet campaign targeted against The X Factor and its effect on British music took Rage Against the Machine to the Christmas number one spot at the expense of the X Factor winner's single by Joe McElderry.
The first series was available to viewers only through the Northern Ireland-based ITV station UTV which is widely available in the Republic, but subsequent series have also been shown on Ireland's terrestrial TV station TV3.
Series 1–4 of the "UK" version of The X Factor effectively included Irish viewers on an equal footing, and Irish viewers were able to vote in these series via SMS or telephone. However for series 5 in 2008, the decision was made to discontinue Irish voting, with the decision being blamed on new regulations introduced regarding phone competitions in the UK.
The show has held auditions in Dublin and Belfast for only the first 3 series, with Belfast auditions continuing for series 4 before being dropped.
Irish acts have reached the finals in series 1 (Tabby Callaghan and Roberta Howett), series 2 (The Conway Sisters) and in series 6 (John and Edward Grimes). Northern Irish finalists have included Phillip Magee (series 2) and Eoghan Quigg (series 5). Irish singers can still audition, as shown when Dublin twins John & Edward made the live finals of series 6, but had to audition in Glasgow.
The Xtra Factor is a companion show that airs on digital channel ITV2 and on TV3 Ireland on Saturday and Sunday nights after the main ITV1 show. It features behind-the-scenes footage of The X Factor and shows the emotional responses of the contestants after the judges comment on their performances. The commissioning of The Xtra Factor was prompted by the success of Big Brother's Little Brother, a Big Brother companion show screened on E4.
The Xtra Factor was hosted up to series 3 by Ben Shephard. The voiceover on series 1 to 3 was Peter Dickson. Shephard did not return for series 4 after being upset at not getting the main ITV presenting job, and Fearne Cotton took over as host, for the fourth series only, before leaving the show to concentrate on her career in the US. Allegations of a falling-out with Simon Cowell were also reported. For series 5, Cotton was replaced by presenter and close friend, Holly Willoughby. Willoughby first presented The Xtra Factor on 9 August 2008, a week before series 5 began airing. The first show recapped on series 4 of The X Factor and revisited the series 4 finalists.
Cameras follow the finalists during their day, and in early series some of the footage was aired in a spin-off show The Xtra Factor: The Aftermath, which was broadcast in the middle of the week on ITV2. The Xtra Factor: Xcess All Areas was a live show in which there were interviews, games and trips around the contestants' homes. The show also let viewers know which songs the contestants would be singing in the next live show. Both shows were axed after series 3 due to ITV2 cutting back on spin-off programing.
Each year after the series has come to an end, The Xtra Factor has a week of special programmes titled Best and Worst, featuring the best and worst auditions from the previous series, ranging from 2 to 5 episodes each year.
A 60-minute special titled The Winner's Story airs each year over the festive period, featuring the winner of that year's X Factor. Cameras follow the winner from the announcement of the result through the lead-up to the Christmas No. 1.
The X Factor Live is a live show that tours the UK and Ireland in the new year, following the conclusion of the TV series. It features an array of finalists and other memorable contestants from the most recent X Factor series.
The X Factor: Battle of the Stars was a celebrity special edition of The X Factor, which screened on ITV, starting on 29 May 2006 and lasting for eight consecutive nights. Pop Idol was meant to air in its place as Celebrity Pop Idol but was stopped shortly before transmission, when ITV picked The X Factor over it.
Nine celebrity acts participated, singing live in front of the nation and facing the judges of the previous The X Factor series, Simon Cowell, Sharon Osbourne and Louis Walsh. Voting revenues were donated to the celebrities' chosen charities.
The contestants were Michelle Marsh, Nikki Sanderson, Matt Stevens, Lucy Benjamin, Gillian McKeith, Chris Moyles, Paul Daniels and Debbie McGee, James Hewitt and Rebecca Loos, and "The Chefs", a quartet of celebrity chefs comprising Jean-Christophe Novelli, Aldo Zilli, Paul Rankin and Ross Burden.
The winner of the show was Lucy Benjamin, mentored by Louis Walsh.
It was reported on 26 August 2006 that Simon Cowell had axed the show, describing it as "pointless" and adding "we are never going to do it again".
So far the show has spawned six number one winners' singles (four of which have been the Christmas number one), two number one charity singles, and a total of 14 number one singles by contestants who have appeared on the show (including winners and runners-up).
By series 6 (2009) it had seemingly become such a certainty that the X Factor winner would gain the Christmas number one slot every year that bookmakers William Hill were considering withdrawing from the 30-year tradition of betting on the outcome. However, hostility to the show from some quarters had prompted attempts to propel an alternative song to the 2008 Christmas number one spot, and in 2009 a similar internet-led campaign was successful, taking Rage Against the Machine's "Killing in the Name" to Christmas number one at the expense of X Factor winner Joe McElderry.
In series 1–2, the winner's debut album would be released a few months after their victory in the show. The album would contain some new material but would consist largely of cover versions. This format changed with series 3 winner Leona Lewis. Simon Cowell, Lewis's X Factor mentor and newly-appointed manager, said: "We could have gone into the studio for a month, made the record quick, and thrown it out. It would have been the wrong thing to do." The success of Lewis's debut album Spirit ensured that the debut albums of future series winners (with Jackson as an example) would consist more of new material than of cover versions.
The 2009 single was a cover of the Michael Jackson song You Are Not Alone which was released in aid of Great Ormond Street Hospital and reached number one in its first week.
^ "Official X Factor (series 6) Final - Press Conference (video sequence at around 02:00)". Digital Spy. 10 December 2009. http://www.digitalspy.co.uk/xfactor/news/a190864/watch-the-x-factor-final-press-conference.html.
^ a b c d e Genevieve Hassan (21 August 2009). "What happens at an X Factor audition?". BBC News. http://news.bbc.co.uk/1/hi/entertainment/8209429.stm.
^ "All change as The X Factor returns". BBC News. 17 August 2007. http://news.bbc.co.uk/1/hi/entertainment/6951467.stm. Retrieved 18 August 2007.
^ "X Factor wannabes given opportunity to post audition videos online". Daily Mail. Associated Newspapers. 26 February 2010. http://www.dailymail.co.uk/tvshowbiz/article-1254077/X-Factor-wannabes-given-opportunity-post-audition-videos-online.html. Retrieved 27 February 2010.
^ "The X Factor - About the show". The X Factor. 17 August 2007. http://www.xfactor.tv/information/about-the-show/. Retrieved 17 August 2007.
^ "Cowell: 'X Factor' judges are out of sync'". Digital Spy. 16 August 2007. http://www.digitalspy.co.uk/xfactor/a71993/cowell-x-factor-judges-are-out-of-sync.html. Retrieved 16 August 2007.
^ "Sharon leaves The X Factor". ITV. 6 June 2008. http://www.itv.com/Entertainment/celebrity/CelebrityNewsHoldingFolder/SharonleavesTheXFactor/default.html. Retrieved 6 June 2008.
^ "Cheryl joins The X Factor". ITV. 10 June 2008. http://www.itv.com/Entertainment/Music/MusicNews/News/CheryljoinsTheXFactor/default.html. Retrieved 10 June 2008.
^ "Cheryl is the new judge!". ITV. 10 June 2008. http://www.xfactor.tv/news/article/?scid=349. Retrieved 10 June 2008.
^ "X Factor: Secrets of the new show revealed as bosses promise it will be bigger and better". The Mirror. 13 August 2009. http://www.mirror.co.uk/celebs/news/2009/08/13/no-expense-spared-for-x-factor-as-the-show-promises-to-be-even-bigger-and-better-115875-21592793/. Retrieved 14 August 2009.
^ "The Factor Uprising, New Music Transmission"
^ "Find out all about GMTV presenter Ben Shephard | Presenters | GMTV"
^ "Ben Shephard Exits X Factor". The Sun. 2 May 2007. http://www.thesun.co.uk/article/0,,11050-2007200238,00.html. Retrieved 2 May 2007.
^ "Ben Shephard leaves Xtra Factor". The Daily Mirror. 2 May 2007. http://www.mirror.co.uk/showbiz/latest/tm_headline=x-factor-ben-quits%26method=full%26objectid=19031113%26siteid=89520-name_page.html. Retrieved 2 May 2007.
^ "Cotton quits X Factor role for US". Digital Spy. 6 February 2008. http://www.digitalspy.co.uk/xfactor/a88719/cotton-quits-x-factor-role-for-us.html. Retrieved 9 May 2007.
^ "Fearne Cotton to host Xtra Factor". The Sun. 9 May 2007. http://www.thesun.co.uk/article/0,,2001320029-2007210332,00.html. Retrieved 9 May 2007.
^ "Holly to host ITV2's Xtra Factor". Daily Mirror. 4 June 2008. http://www.mirror.co.uk/showbiz/2008/06/04/holly-willoughby-to-host-itv2-s-xtra-factor-89520-20594247/. Retrieved 4 June 2008.
^ "Holly has Xtra Factor". The Sun. 4 June 2008. http://www.thesun.co.uk/sol/homepage/showbiz/tv/article1245716.ece. Retrieved 4 June 2008.
^ "Holly Willoughby to present 'Xtra Factor'". Digital Spy. 4 June 2008. http://www.digitalspy.co.uk/xfactor/a97366/holly-willoughby-to-present-xtra-factor.html. Retrieved 4 June 2008.
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title=Dannii - YouTube - Broadcast Yourself. | http://www.thefullwiki.org/The_X_Factor_(UK) |
The PSAT 8/9 is the first test in the College Board’s SAT Suite of Assessments. It’s given to eighth and ninth graders and can be administered in the fall or spring. The PSAT 8/9 is designed to set a baseline for students at the beginning of their high school career so educators can measure progress over the following years.
Here are some reasons for schools to give their students the PSAT 8/9:
- It gives educators an acccurate way to predict performance on the PSAT/NMSQT and the SAT, and an opportunity to intervene early if necessary.
- Students can use their PSAT 8/9 scores to get free personalized practice for the SAT.
- PSAT 8/9 scores give students and their teachers information on whether they’ll likely do well in AP World History and AP European History.
Learn more about the PSAT 8/9. | https://counselors.collegeboard.org/programs/psat-8-9 |
Spellcasting is easily the most complex part of The Dresden Files RPG. This should come as no surprise; the game is based on a series of books about Wizard, and the books are full of all the cool things Harry does with magic. To be true to the source material, the game needs to model that kind of play.
The complexity arises from the flexibility of the system. If you want to be able to do everything that Harry does in the books, you need a system that can be twisted and bent to accomplish anything. That means it needs a robust backbone, so it can bend without breaking, and components that can be adapted to any situation the players come up with. This means that designers are left with a limited range of choices in how to implement the system:
- Come up with sub-systems for each possible application of magic.
- Use a very high-level system, where the GM and the players make all the calls with minimal rules.
- Find a middle ground, where there’s enough mechanical support to let the GM and players share an understanding of the capabilities of the system, but few enough rules that they can be mastered.
Evil Hat went with the third option, using a mechanic that can be adapted to a wide variety of situations, and tons of examples to help show how to do that. I think it was a good choice, and it results in a good mechanic.
But it also results in a lot of reading for spellcasting types. And while the language they use is very precise, the distinctions between some of the terms can get lost in the fog.
Over the next few posts, I’m going to talk extensively about spellcasting in this game, with the goal of demystifying the concepts, process, and mechanics. I’m going to start talking about theory, both in-world and in-game, so that the terms are clearly defined. Then, I’m going to move on to evocation, and finally thaumaturgy. At the end of those three topics, I may post a few spells, showing how they were created and what decisions were made along the way, but only if there’s a demand for it.
So. Let’s get going with theory.
In-World Magic Theory
Magic in the Harry Dresden books is structured and codified – that’s how you get Wizards. Jim Butcher does a good job of laying out the ideas behind spellcasting, so that you can get a solid grip on what magic does and doesn’t do, and the mechanism behind it. I’m starting with looking at this in-world theory of magic, because it’s important to know what the system is trying to model before we start looking at the model.
Note that I’m using a number of terms in this section that will show up in the in-game section, but the definitions in the in-game section are far more precise than the usage in-world. So, in this section, when I’m talking about complexity, I’m talking about how complicated something is. In the next section, when I’m talking about complexity, I’m talking about a very specific game term.
All magic in the game is basically shaping energy to work your will. That means you need two things to work magic: energy, and your will. You use them in concert to create a change in the world that you want to see*.
The high-level process is the same for all types of spells, as follows:
- Form the spell construct.
- Summon the energy into the spell construct.
- Release the spell construct.
Wizards break down spellcasting into two categories – evocation and thaumaturgy – but really, casting both has the same high-level process. It’s just the details that differ, and that’s really the function of the complexity of the spell construct.
Forming the spell construct
A spell construct is a pattern that will produce a change in the world in accordance with the spellcaster’s will once it has been empowered. It is a pattern of thought and symbolism bolstered by the spellcaster’s will that serves as a receptacle and template for the energy that will be used. Simple spell constructs can be held in the Wizard’s mind, enhanced by simple tools such as words, gestures, wands, rings, etc. More complex ones are too difficult to be held internally, so they rely on more symbolic tools, like magic circles, candles, lengthy chants, ritual dances, external power sources, and the like.
The simple spell constructs that can be contained within the Wizard’s mind entirely are generally evocations: they are quick, use minimal tools, and accomplish a very simple thing, which is pushing raw energy around. More complex spell constructs are generally thaumaturgy: they require more time, rituals, and special components, but can accomplish more varied effects, and more powerful ones.
Building a spell construct is half of what spellcasting training is about. Whether it’s being able to hold a simple form in the mind to channel a blast of fire through, or knowing the elemental correspondences of different colours and gemstones, these are the tools the caster learned in training, and the pieces that he or she uses to build the spell construct. Some simple constructs, called rotes, are so well-practiced that the spellcaster can form them with hardly any thought at all, while more more complex constructs may require research and preparation to assemble properly.
The more complex the spell construct, the more energy is required to fully activate it, and the more far-reaching effects it can have.
Summoning the energy into the spell construct
Once the spellcaster has created the spell construct, it must be empowered with energy for it to have an effect. Energy has to come from somewhere, and calling in and controlling energy from various sources is what the other half of spellcasting training is about. If the caster is in a hurry, he or she can use his or her own energy, but this can exhaust the caster in short order. The energy of a single human body is generally all needed to keep the body functioning properly*, so using too much is not a good thing. This is why fast evocations tend to be so tiring for the spellcaster.
With more time, the spellcaster can draw in energy from other sources: the environments, special components, ley lines, energy from other living beings*, or even just trickle his or her own energy in at a speed that allows it to replenish itself without so rapidly depleting the caster. Complex, external spell constructs can contain the energy as it comes in over time, often within a magic circle, allowing the spellcaster to take longer to supply the requisite energy.
This is another place where the difference between evocation and thaumaturgy differ. The simple spell construct of an evocation doesn’t require a lot of energy to empower, but you can funnel as much energy as you care to risk through it and out into the world. Complex spell constructs, like thaumaturgy rituals, are so precise that they need a very specific amount of energy to enact, calculated by the spellcaster when he or she creates the construct.
Drawing and controlling energy can be tricky, and this is where Wizards can wind up blowing themselves (and their surroundings) right to hell*. If the spellcaster’s concentration falters, or if he or she has tried to use too much energy too quickly, he or she can lose control. The caster can then either let the energy escape into the world, usually with destructive (or at least inconvenient) consequences, or they can try and contain it, letting it tear through their body and mind. Neither one is a very welcoming prospect, so most spellcasters are careful about how much energy they try to handle at one time.
Releasing the spell construct
Once the construct is fully empowered, the spellcaster releases it out into the world and it does what it was designed to do. The construct is shattered by this release – not necessarily destructively, but mystically, meaning that a new spell construct needs to be created if the spellcaster intends to cast the same spell a second time.
Quick and dirty spell constructs, such as those used in combat evocations, are not very precise, and the target of such a spell usually has a chance to avoid the effects, even if it’s simply by diving for cover. However, a more carefully designed and thoroughly researched construct, like a thaumaturgic ritual, usually takes effect without giving the target any chance to avoid it, as long as the assumptions made by the caster at the time of casting are accurate. If he or she has misjudged some aspect of the situation, such as not having a strong enough symbolic link to the target, or not knowing that the caster has some level of magical protection, the spell will have a diminished effect, possibly failing entirely.
And that’s a basic run-down of how magic works in the Dresdenverse.
In-Game Magic Theory
The game system models this style of magic with two similar systems: one for thaumaturgy and one for evocation. The high-level basics of both systems are the same, so that’s what I’m going to deal with in this post. Subsequent posts will look at each style individually and in more detail.
First, though, let’s define the terms we’re using.
Terminology
- Spell. A magical effect created by a spellcaster.
- Spellcaster. Someone who uses magical spells.
- Evocation. Quick combat magic involving only the spellcaster’s own energy and simple effects that are produced by pushing power around with a brute-force approach.
- Thaumaturgy. Ritual magic involving creating more elaborate, elegant, precise, or powerful effects. Takes a longer time to perform, and has a much broader range of possible effects.
- Power. The energy needed to make a spell work, measured in shifts.
- Complexity. An abstract measure of how difficult a thaumaturgical spell is to cast, measured in shifts.
- Control. The effort of the spellcaster to keep the power focused on the spell and doing what he or she wants. This is a roll using Discipline.
- Targeting. The Discipline roll the spellcaster makes to control the power serves as the targeting roll to hit the target. It sets the difficulty for the target to avoid the spell. This applies only to evocation.
- Conviction. A skill. Governs how much power the spellcaster can draw on a single turn.
- Lore. A skill. Governs how complex a spell the spellcaster can cast.
- Discipline. A skill. Rolled against a target of the shifts of power drawn in a single turn to see if the caster can focus it on the spell.
- Backlash. Damage taken as a result of a failed control roll, either as physical or mental stress and/or consequences. Does not reduce the power in the spell.
- Fallout. The effect of a failed control roll on the environment, based on how many shifts of power the spellcaster chooses not to take as backlash. This reduces the power of the spell.
Whether you’re using evocation or thaumaturgy, the high-level process is the same:
- Decide what you want to do.
- Determine the complexity/power requirements.
- Draw power.
- Control the power/target the spell.
Deciding what you want to do
On the surface, this step can look like the easiest part of the process, but it can quickly become the most daunting. In other games, you have lists of spells to choose from, each one doing something very specific. In DFRPG, magic can accomplish pretty much anything you can imagine, which can lead to a little bit of paralysis from too much choice.
There’s also more than one way to do pretty much anything you can imagine. Want to protect yourself while you sleep? Well, you can make a force field over your house, or rig a fire trap to go off if something evil crosses your threshold, or bind some spirits to keep watch for you. Want to hurt an enemy? You can blast him with fire, or buffet him with air, or cause the ground to swallow him, or even just give him a fatal disease. Not only do you need to decide what you want to do, you have to decide how you want to do it – what mechanism you’re going to use to accomplish your goal.
This is very much effects-based magic. Picking what you want to do and how you want to do it is fundamental to everything that comes afterward. Mechanically, you need to figure out what you want to do and how you want to do it first because that lets you figure out how complex the thaumaturgic ritual is and how much power you’re going to need to pull off your spell*.
With thaumaturgy, the field here is wide open. Basically, if you can imagine it, there’s a chance that you can pull it off. No guarantees, of course; some things you want to attempt will wind up being beyond the capabilities of your character, or beyond the resources of the situation. With evocations, you have a much more limited range of options: attack, block, maneuver, counterspell*.
Determining complexity/power requirements
Once you know what you’re doing, you’ve got to figure out how much power you’re going to need.
For evocations, this is pretty straightforward: decide how big a hammer you want to hit your target with, and that’s the number of shifts of power you need.
For thaumaturgy, you need to figure out complexity. Complexity is kind of a slippery concept in the game, and I’m going to talk at length about it when I get to the post on thaumaturgy. For now, let’s just say it’s a pretty arbitrary number based on how difficult the spell is to cast. There are guidelines of how to determine complexity, but in the end, you’re going to be eyeballing what you want to do and setting the complexity in negotiation with the GM.
The power you need to perform a thaumaturgic ritual is a number a shifts equal to the complexity.
Aside from power, complexity also determines how much preparation you need to do to set up a thaumaturgic ritual. Compare the complexity to your Lore skill. If your Lore is equal to or higher than the complexity, you know what you need to do and have everything you need to get started right away. If the complexity is higher than your Lore, then you need to prepare for the ritual, using maneuvers from your skills to add Aspects to the spell that you can tag for a Lore bonus*. Once you’ve made up the deficit, you’re good to go.
In terms of the in-world rationale for what you’re doing at this point, consider this the part of the spellcasting process where you are creating the spell construct, either by holding it in your mind (evocations) or by assembling the ritual components and preparations for the casting (thaumaturgy).
Once you’re ready to cast the spell, you need to power it.
Drawing power
Now you need to empower your spell construct. The amount of power you can safely draw on in a single turn is equal to your Conviction skill. You can draw more than that, but you take stress for doing it, so it can wear you out pretty quickly. If you need more, it’s safer to draw it in smaller amounts over a number of turns.
Unfortunately for the Wizard in the midst of a battle, you may not have time to draw power in slowly. For evocations, which are quick and dirty, you are drawing on your own power, and you need the whole amount of power you’ve decided to put into the spell right now to get the shield up before the ogre takes your head off. Working under pressure like that is tough; any evocations do a single point of stress, plus an extra point of stress for every shift of power you draw over and above your Conviction skill rating. You can, of course, offset this stress by taking consequences, as usual. Try and draw too much and you risk blinding headaches, nosebleeds, exhaustion, and your eyes exploding.
That sets a practical limit on evocation power levels, especially when you also need to control all that power, as outlined in the step below. Thaumaturgy doesn’t have that sort of limit on it. The main limitations on thaumaturgic power is time and creativity.
The elaborate spell construct of a thaumaturgic working and the reduced time pressure* allows the spellcaster to summon the power needed slowly, over a number of turns. Each turn, the spellcaster decides how much power to summon, rolls to control it as described below, and adds it to the total amount of power accumulated for the ritual.
Controlling the power/targeting
Every turn you summon power, whether it’s to store in a thaumaturgic ritual or unleash in an evocation, you need to roll to control the power summoned. This is a Discipline roll, with a difficulty equal to the number of shifts of power you’ve summoned this turn. If you succeed, everything is peachy-keen. Failure means you have some pain coming to you in the very near future.
Failing to control your power means that the power is uncontrolled. It’s going to do some damage to someone or something, and you get to decide whether that someone or something is you. You can decide to take some or all of the shifts of uncontrolled power as backlash, meaning that you clamp your sovereign will down on the chaotic, elemental energies of the universe and force them to do your will. As you may have guessed from the description, it’s gonna hurt, either in your brain or in your body. You take a stress hit equal to the number of shifts of uncontrolled power in either your Physical or Mental stress tracks, but you can’t split the stress. It’s all got to go to one stress track.
Good news is that you get to keep those shifts of power in your spell. Bad news is that you might die if you you’re dealing with too much power.
If you don’t want all that primal force echoing around inside you, messing the place up, you can let it out to run rampant through the area around you, messing the place up. This is called fallout. Basically, what you’re doing here is handing the shifts of uncontrolled power to the GM and saying, “Here. Use this to mess me up.”* This is how houses get burned down, and friends get blasted, and people wind up with donkey heads, and so forth.
Good news is that you don’t take any direct damage. Bad news is that the spell’s power is reduced by the number of shifts of uncontrolled power that you let free as fallout. Really bad news is that you might still die if you’re dealing with a lot of power, as the building collapses around you.
You get to decide how much uncontrolled power you’re taking as backlash and how much you let loose as fallout. This can be a very important decision to make, so consider the upside and downside of it carefully.
There’s an extra little wrinkle for thaumaturgy with control rolls. Because you’re adding power a little at a time to the spell construct, doing a delicate balancing act turn-by-turn, holding the power and the spell construct together with your will, failing a control roll can be worse than with evocation. If you fail your Discipline roll, all the shifts of power you’ve gathered over all the turns of casting this given ritual become uncontrolled, and you have to choose how much to take as backlash and how much to let go as fallout. If any is loosed as fallout, it destroys the fragile spell construct, and the spell fails. So, you may be tempted to take everything as backlash, but keep in mind that with thaumaturgy, you may wind up dealing with ten or more shifts of power. That’s gonna leave a mark no matter what.
This is why it’s a good idea, if there is no time pressure, to draw the power for a thaumaturgic ritual a single shift at a time. It takes much more game time, and more time rolling, but it can prevent exploding heads and burning forests.
There’s also an extra little wrinkle for evocation with control rolls. Just because you managed to successfully control the raging torrent of flame that you’ve focused into a lance with the force of your will, it doesn’t mean you hit your target. Your Discipline roll also determines the difficulty for the target to avoid your spell. This is the targeting roll. The target can take normal defensive actions to avoid the spell with a contested roll on an appropriate skill.
And that sums up the process of casting a spell, both in-world and in-game. Next time, I’m going to take a detailed look at evocation, talking about the little twists and turns of that system. | http://www.rickneal.ca/?p=628 |
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Salesforce Business Analyst
RM 16/9/22
My client is a leading education company seeking a salesforce BA to join their diverse team.
You'll have the opportunity to lead projects with bigger organizational impact at an earlier stage in your career with the client than you would get elsewhere.
As CRM Business Analyst, a member of the MAC function, you'll be supporting the CRM team to deliver solutions that will optimize performance and the family experience throughout the admissions journey using the client's unified global CRM.
Role & Responsibilities
Work with the CRM team to ensure all requirements are validated and documented to support the execution of the global roll out plan, including gathering requirements for the online inquiry and application form and any other component of the CRM roll out.
Provide support to CRM project manager, data analyst, and dev team to ensure all tasks are done to roll out to a school.
Contribute regularly to team discussions and work with regions and schools to gather requirements used to deliver CRM roadmap features across the regions. | https://www.masonfrank.com/de/job/RM%2016%2F9%2F22/salesforce-business-analyst |
Amber is fossilized tree resin, which has been appreciated for its color and natural beauty since Neolithic times.
Ukrainian rovno amber stone with fossil inclusions, trapped 34-56 million years ago - Leaf, Gnat with Mites, Spider and More.
It weighs 15.7 g. Measurements of stone 63x34x16mm, length of leaf ~3.4mm, gnat ~1.5mm, spider ~3.5mm.
Geological Period: Eocene.
Color: Honey.
Please be aware that picture is enlarged to show a better view of the inclusion, therefore please check the description of size, weight, inclusion quality before buying!
At the request of the buyer we can send high resolution photos.
All products in our store are real authentic amber, therefore all of them are certified. | https://www.amberinclusions.eu/leaf-gnat-with-mites-spider-and-more-fossil-inclusions-in-ukrainian-rovno-amber-10909 |
Step one of every counted canvas project is preparing the canvas to stitch. In this lesson you’ll learn how to bind the edges of the canvas, assemble stretcher bars and mount the canvas to the bars.
Begin by binding the edges of the canvas. Covering the edges of the canvas is important because canvas is rough and can catch on the threads as you stitch. It also provides a measure of strengthening the edges for attaching to the stretcher bars.
I use artist’s tape, 3/4″ wide, available at art supply stores and general craft stores (Michael’s, Hobby Lobby). Masking tape would also work; the edges of the canvas are cut away for finishing or framing, so don’t worry about sticky residue. If you have a sewing machine you could also cover the edges with seam binding if you prefer. As long as the rough edges of the canvas are covered, use the method you prefer. Squeeze the tape with your fingers down the edge to make sure it adheres well. Cover the other three sides in the same way. Set the prepared canvas to one side and assemble the stretcher bars.
Stretcher bars have lap joints at the ends. Put the lap joints together so that the bars form a smooth surface. I put two bars together in an “L” shape, then fit the remaining two bars to the “L”. Use a small hammer or mallet if the joints need coaxing. When assembled the stretcher bars should form a square or rectangle, depending on the size of the canvas.
Lay the prepared canvas on top of the stretcher bars. Use tacks or staples to secure the canvas to the bars. Begin in the center of each side, placing a single tack/staple in the top, then bottom, then left and right sides. Work out from the center tacks/staples, placing a fastener about 1/4″ to 1/2″ on each side of the center. Work alternate sides – top then bottom, left then right, pulling the canvas tight as you work.
Continue placing fasteners until you reach the corners, and place a fastener at each corner. Some specialized stretcher bars like Evertites do not require a fastener at the corners, so read the manufacturer’s directions if you are in doubt. But regular stretcher bars need a tack at each corner.
It may seem like a lot of fasteners, but a tight well mounted canvas is easier to stitch because the canvas is not moving up and down with the stitchers. Also, there will be less distortion in the canvas that will need to be corrected for framing/finishing. So take a little time to place adequate fasteners no more than 1/4″ to 1/2″ apart on all four sides of the canvas. Preparation at the beginning saves time during and at the end.
Now the canvas is ready to stitch. You may stitch with the canvas on top of the bars as you mounted it, or turn it over and stitch “in the well”, with the canvas under the bars. It is a personal preference, no absolute way you must stitch. I prefer the canvas on top of the bars because reaching over the bars to stitch induces wrist fatigue for me. But however you feel comfortable will be fine. | https://debbeesdesigns.com/lessons/preparing-the-canvas/ |
Job Summary:
Overall responsibilities include leading the formulation of product line vision and strategy across the patient monitoring product line, championship of the overall product vision and development portfolio for his/her team’s product areas, overseeing the development of product specifications and managing product roadmaps and portfolios through the product lifecycle.
Essential Functions:
- Patient Monitoring Portfolio Management:
- Develop and champion a product area vision and product area strategy in support of corporate goals and objectives
- Evangelize patient monitoring product strategy and vision to the product management and company leadership team
- Research and recommend new products, tools and applications
- Identify and conduct internal and external customer, competitor and industry research to uncover latent customer needs, competitive threats, and emerging trends
- Develop clear and complete business cases and present to senior management the information necessary to make informed approval, prioritization and tradeoff decisions
- Provide accurate and robust financial modeling and scenario analysis for all major initiatives
- Product Management:
- Lead global product management activities for patient monitoring portfolio and specifically assigned products
- Drive development of market requirements, product strategies, and programs to deliver profitable business growth
- Constantly question and clarify the cross-functional implications of all product decisions and ensure that critical business issues are surfaced and considered
- Serve as a voice of the customer and act as a customer experience advocate in considering product decisions that will impact the customer
- Ensure that product specifications meet high standards for quality before approval
- Champion a point-of-view to product management leadership regarding the relative importance of various initiatives that are ready to move to the development phase
- Balance scope of development projects against one another to determine how to make the most efficient use of resources to create the greatest level of value for the company
- Ensure the product specifications are well understood by engineering
- Support team members as they provide product requirements clarification and reply to implementation considerations raised by the development team
- Oversee pilot testing/validation of new product and proof of concept initiatives
- Understand global customer and market needs
- Analyze market segmentation and competitive environment
- Champion new product ideas and gain cross-business, multi-disciplinary support for advancing new ideas to the next stage for the patient monitoring portfolio
- Develop relationships with Channel Marketing & Sales and inspire their interest for in patient monitoring
- Develop and present market opportunity assessments, strategies, tactics and collateral content for the purpose of increasing revenue, margin and market share
- Demonstrate the ability to influence important key stakeholders in coordinating cross-team or work groups to achieve product goals
- or failure to properly asses the client requirements may cause serious delivery delays or substantially increase costs, which may result in poor customer relationshipd
- People Leadership:
- Develop, lead and inspire team members, each responsible for managing patient monitoring product roadmaps
- Create and foster career development and growth paths for team members in alignment with company, product and personal objectives
- Create clear and measurable goals and objectives for the team related to the creation and enhancement of timely, high-quality products that support critical business objectives
- Raise awareness of team’s plans, insights and accomplishments in order to facilitate cooperation across departments and to build a highly performing, highly motivated team
- Assist direct reports with ongoing prioritization and resource allocation to ensure that the crucial business initiatives are delivered
- Direct hiring, retention, and succession planning
- Coach Product Managers as they respond to project escalations with an assessment of the business implications of changes to project scope, timeline, or resources
- Comply with company policies and procedures regarding Employee health, safety and conduct.
Skills Requirements:
- Previous experience with medical device marketing or product management preferred
- Candidate must have excellent documentation, communication, and presentation skills
- Must have experience working across all layers of organizations, including the executive team, remote sales representatives, customer management personnel and project management
- Excellent analytical and problem-solving skills
Required/Preferred Education and Experience:
- Minimum of 7+ years work experience in product management, technical sales or product development related roles
- Minimum of 3+ years people management
- Bachelor of Science or Engineering or equivalent
Other Duties:
Please note this job description is not designed to cover or contain a comprehensive listing of activities, duties, or responsibilities that are required of the employee for this job. Duties, responsibilities, and activities will be reviewed periodically as duties and responsibilities change with business necessity. Essential and marginal job functions are subject to modification.
ZOLL Medical Corporation appreciates and values diversity. We are an Equal Opportunity Employer M/F/D/V. | https://www.zoll.com/contact/careers-at-zoll/careers-search?rid=3162 |
Selecting the Text tile will add a text block to the report.
To move a tile up, down, and side to side, hover over the header of the tile, which will illuminate light blue, and click and drag to drop the tile above, below, or next to another tile.
Drag/drop the tile on the screen and resize it by dragging your mouse from the bottom-right corner of the tile.
Click on the default "Text Block" title and start typing to enter a new title. Click the action list bar icon in the top-right corner of the tile to show/hide the header.
As you start typing, you'll notice a text-editor menu appear above. You can adjust the font size, color, style, and insert bulleted or numbered lists. To delete a tile you've added, click delete tile at the bottom of the list. To duplicate a tile, select Duplicate Tile.
To duplicate the tile, click the duplicate icon in the top-right corner. | https://support.fastmodelsports.com/support/solutions/articles/9000159181-text-tile-adjusting-and-moving-tiles |
Three people were injured in a two vehicle collision Wednesday morning in Byrneville.
The crash happened about 11:20 a.m. at the intersection of West Highway 4 and Byrneville Road. A pickup truck and a passenger car collided, and the pickup truck hit a concrete traffic signal pole.
None of the injuries were considered life threatening.
The Florida Highway Patrol is investigating. Escambia County EMS, the Century Station of Escambia Fire Rescue and the Escambia County Sheriff’s Office responded.
NorthEscambia.com photos, click to enlarge.
Comments
4 Responses to “Three People Injured In Highway 4 Byrneville Wreck”
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Bagger on
May 20th, 2020 6:12 pm
The trucks air bags may not have gone off because of something as simple as a sensor being bad disabling that system. Probably not the trucks fault, most folks never care to fix things like that.
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Carlos E McGugin on
May 20th, 2020 6:10 pm
CW, sometimes glancing blows do not trigger the Air Bags. Rapid deceleration is needed to deploy them.
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catman on
May 20th, 2020 5:28 pm
CW I have a 2001 Ford F-150 and it has a place on the console to turn off the airbags. Not sure about this one. Hope all are OK.
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CW on
May 20th, 2020 3:54 pm
If I were the owner of that truck I’d be wanting to know why the airbags didn’t work. | http://www.northescambia.com/2020/05/three-people-injured-in-highway-4-byrneville-wreck |
In this paper, we study the fuzzy multi attribute decision making problems with preference information on alternatives, in which the attribute values and the preference values given by the decision maker(s) are in the form of triangular fuzzy numbers, and the information about attribute weights is incomplete. We follow fuzzy multi-attribute decision making problems for online match making process. Many online systems that are available in Internet are lacking many features for match making process. Many of the online match making websites couldn't select a perfect match because they follow simple DSS (Decision Support System). In order to overcome this problem, we propose the fuzzy logic based multi attribute decision making process for the online match making process, which is based on fuzzy set theory. First of all, various criteria are considered for online match making process. Second, the different criteria will be given fuzzy weight terms such as very low, low, medium, high, very high depending upon the importance given by the user.
[...] Online FDM System model is explained in the following figure. (Fig. fuzzy query processing techniques for fuzzy database systems, International Journal of Fuzzy systems, Vol.5, pp. 161-170,2003. K. Zhang and R. Needham. A Private Matchmaking Protocol. http://citeseer.nj.nec.com/71955.html Figure 2.Screen for setting ideal partner criteria REFERENCES L.A.Zadeh, Fuzzy Sets, Information and Control, Vol.8, pp. 338-353,1965. Baldwin and Gramlich ,Cryptographic Protocol for Trustable Match [...]
[...] Using the sets of the preference ratings, certain ratings are assigned to the decision criteria respectively by the decision-maker. After the assignment of the ratings, the membership function will be matched to each rating for the fuzzy arithmetic operation In our method, the triangular fuzzy numbers are used as membership functions corresponding to the elements in term set. The reason of using triangular fuzzy number is that it is easy to be used by the decision-maker. The triangular fuzzy number is denoted as follows: membership set for the criterion C1 be Fi, Fi) of any applicant, FSW value Xi for the criterion C1 is calculated as the following: Xi = b1, c1) ( Fi, Fi, Fi b1, c1) For finding out the CFV for n criteria, the following formula can be applied CFV = F i i n i i n i Substituting Fi and Wi with triangular fuzzy numbers, we can calculate CFV triangular value all the applicants for the particular post they applied. [...]
[...] In Baldwin and Gramlich provided a solution for on-line matchmaking intended to support anonymity of users (i.e., protecting KeyWords: Fuzzy decision making method; linguistic variables; fuzzy set. I.INTRODUCTION Decision Support Systems (DSS) are a specific class of computerized information system that supports business and organizational decisionmaking activities. company and job seekers' identities), authentication of matches, and joint notification to users only in the event of a positive match (i.e., a male's identity is authenticated to the female's identity and viceversa only when both the opposite sex users agree). [...]
[...] The applicability of this method was demonstrated through the Fuzzy Decision Making model to select the most appropriate match for the specific registered users. In this proposed FDM system, there is no limit on the number of the decision criteria and the complexity of the analysis is not greatly affected by the numbers of the decision criteria. Moreover, evaluation of the decision criteria is generally easier than other method since the linguistic variables that are similar to everyday words are used. [...]
[...] But we propose the fuzzy logic based multi-attribute decision making process for the online match making process, which is based on fuzzy set theory. III. BASIC CONCEPTS OF A FUZZY SETS The theory of fuzzy sets was proposed by Zadeh in 1965 Let U be the universe of discourse, U = u un A fuzzy set N in the universe of discourse U can be represented by N = fN (ui ) i n A fuzzy number is a fuzzy subset in the universe of discourse U that is both convex and normal In the following, I introduce the simplified arithmetic operations of triangular fuzzy numbers Let E and L be two triangular fuzzy numbers, where E = b1, c1) L = ( a b c 2 ) Fuzzy Numbers Addition : E L = b1, c1) b c = (a1 + a b1 + b c1 + c 2). [...]
using our reader. | https://www.oboolo.com/scientific-and-technologic-subjects/computer-science/term-papers/online-match-making-process-using-fuzzy-multi-attribute-decision-making-606167.html |
Find out what makes us such a unique institution and discover the vibrant student life that is at the heart of our community.
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We are currently in the process of reviewing our approach to contextual admissions for undergraduate courses, from 2021 entry onwards. Please email us to register your interest in being notified when our approach for 2021 onwards is confirmed.
For 2020 entry we are using our Adjusted Criteria scheme for all undergraduate courses.
Candidates from eligible schools applying for courses which are part of our Adjusted Criteria scheme automatically have their conditional offer set at two grades lower than our standard conditional offer (even if their predicated grades are higher).
By considering the context in which an applicant achieved their educational qualifications, rather than against a national average, we are better able to identify potential. This means that students from poorer performing schools who are towards the top of their class are given due consideration in the admissions process for some of our courses and can enter St George’s, University of London with lower grades. Research has shown that our Adjusted Criteria students are successful in Medicine and we have expanded the scheme across other undergraduate courses including Biomedical Science, Clinical Pharmacology, Physiotherapy and Healthcare Science.
Students who apply to an eligible course from a non-selective state school in England with an average A-level grade of D+ or below, or one that is in the bottom 20 per cent in England for progression to Higher Education, are automatically eligible for consideration under our Adjusted Criteria scheme. Students do not need to fill out an additional form or provide any extra information at the point of application.
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The scheme is reviewed annually, so may change scope in future years. A list of eligible schools and colleges for 2021 entry will be posted here no later than 1 September 2020.
The Adjusted Criteria scheme is applied to the following undergraduate courses:
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As well as applying to us from a school which is eligible for the Adjusted Criteria scheme, applicants must meet all other course-specific academic and non-academic entry requirements:
minimum GCSE requirements
minimum non-academic requirements
course-specific A-level subject requirements
course-specific interview or assessment requirements
UCAT requirements (for MBBS5 only)
achieve a minimum of grade B in Chemistry A-level (for MBBS5 only).
Browser does not support script. | https://www.sgul.ac.uk/study/widening-participation/ensuring-a-fair-application-process |
What are spider mites?
Spider mites are often thought of as insects, but they are not. They have eight legs instead of six, thus they are more closely related to spiders than insects. There is typically three life stages to spider mite: eggs, immatures that look like adults but are smaller and adults. There several types of spider mites, but here we will only address boxwood two-spotted spider mites.
The boxwood spider mite is about the size of a period and is yellow-tan. Their eggs overwinter on leaves and twigs. They prefer English boxwoods and sometimes American, but rarely Japanese ones.
The boxwood spider mite feeding causes a yellow stippling of leaves. In heavy infestations, entire leaves may turn mostly yellowish-white, and leaves may prematurely drop.
In the winter, look at the bottom of leaves showing stippling from the previous season for yellow eggs. In spring and early summer, look on the leaf top and bottom of new growth for yellowish mites. One way to monitor is to place a white sheet of paper under some branches and then beat on it a few times. Pull the paper out and allow any debris to fall off the paper due to gravity, then swipe your hand across the paper. If any smears appear, then you most likely have mites and the boxwoods should be treated. Their monitoring process is called “the beat test”.
The two-spotted spider mites are bigger than the boxwood spider mites. They are bigger than a period or about 1/2 mm long. They are greenish-yellow with a black spot on each side of the body in the growing season. The eggs are white to yellow. They are known to attack annual and perennial flowers, many deciduous shrubs and some trees. One of their favorite shrubs is the burning bush euonymus.
Spider mites suck the leaf juices, causing white-to-yellow stipples to appear. When there are large infestations, the stippling may turn the leaves white to yellow to grayish brown and die.
The two-spotted spider mite likes the weather hot and humid. They often start on the inside of a plant that is dense from many years of shearing. Examine the plant for stippling and any signs of mites on the bottom of the leaves. Also, use “the beat test” to determine if spider mites are present. Webbing may appear, but may not be as visible as real spider webs usually are.
How are spider mites controlled? We here at Virginia Green use a dormant oil in late fall and winter to control overwintering stages of this pest. During the rest of the year, we use a miticide and/or a summer oil to control the active stages. These sprays help to control the spider mites and are less harmful to benefit such as lady beetles and phytoseiid mites.
If you have boxwoods, burning bush euonymus and other plants you suspect have mite problems, allow us here at Virginia Green to help you monitor and care for them. | https://virginiagreen.com/news/what-are-spider-mites/ |
People initiate, develop, implement, monitor and adjust strategy; people create and promote brands; people manage finance; people understand markets, and people communicate. In short, successful organisations are a result of people, individually or in teams, interacting and communicating clearly and taking appropriate, well reasoned action.
It holds true then, that successful organisations must identify, attract, employ, motivate, reward and retain the best people, and must develop the right mix of people.
Getting it right requires what appears to be a complex fusion of strategies that need not be complex at all. The solutions are often simple and obvious; but many business owners and senior managers are too close and emotionally bound to the business to be able to identify and articulate the issues.
Dunbar Executive helps clients to identify and address people issues - individually and in teams -to facilitate individual and organisational success; and works with individuals to assist with and facilitate the management of their careers. | http://dunbarexecutive.com/welcome.html |
211 Ontario and its affiliates collect, maintain and disseminate human service information that enables people to make informed choices to improve their quality of life.
Inclusion in the database of human services listed on the Website is free and is not dependent upon the purchase of a membership, products or separate advertising space from 211 Ontario or any of its affiliates.
Subject to the priorities detailed in the next section, the database includes organizations or programs primarily located in or serving the area that:
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Organizations must demonstrate the ability to provide ongoing reliable services and have an established funding base or the support of an established parent organization. Exceptions may be made in emerging or underfunded service areas.
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211 Ontario gives second priority to the following quality of life services, unless they are for people who may experience barriers to service:
- Education
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- Exclusion
211 Ontario reserves the right to exclude from the database any organization that it has, in its own discretion, adequate reason to believe may spread hatred or have a philosophy that could be hurtful to the well-being of individuals, groups or the community as a whole.
Potential grounds for exclusion or removal from the database may include, but is not limited to, service non-delivery, fraud, misrepresentation, discrimination, criminal activities, or operating outside licensing mandates.
211 Ontario reserves the right to refuse to list or to discontinue listings for organizations that have had serious complaints lodged against them with any regulatory body or with other organizations in the database providing similar services, or with 211 Ontario itself.
Decisions to include, exclude, or remove a service listing may be appealed by writing to 211 Ontario or its affiliates after a reasonable attempt has been made to resolve the issue with the editorial staff. | https://211southwest.ca/inclusion-policy/ |
I wonder how many countries have public institutions that usually use mediation services to resolve disputes in which they are parties. I am not referring primarily to disputes between investors and states, but to any dispute where a public institution is a party that eventually reaches litigation with high financial costs, even and in situations where it is evident that the solution will be negative. Why? Because the legislation is such that the negotiation and conclusion of agreements are more associated with the idea of corruption rather than with risk management and creative, win-win solutions. Even if the benefits of mediation are recognized and much acclaimed by policymakers, it seems that the legislation is adopted instead for citizens and the private sector, with few exceptions, the disputes with public institutions not being taken into account. There seems to be something missing.
Adoption of the legal framework for mediation
Many countries have created a legal framework for mediation to ensure the quality of mediation services and institutions responsible for managing mediator accreditation systems. With a few exceptions (i.e. Italy), the legal framework in most countries is oriented more towards the “supply” side and less towards the “demand” side, but this is not the main topic of this post (obviously, the comments are good -come on this topic as well).
The main reasons stated by policymakers in adopting mediation legislation are promoting a culture of dialogue, decongesting the role of courts, and shifting the focus from the number of cases resolved to the quality of solutions adopted. In general, the potential benefits of mediation are appreciated by the public sector, as related to the high possibility of settling the dispute more efficiently with less financial costs and time resources compared to other means of resolution, such as arbitration or the traditional court litigation.
The reasons why mediation is not on the “menu” of public disputes
However, if we look closely, it seems that mediation is not used by public institutions in many countries, even if its benefits are recognized. For example, the Romanian Parliament adopted the mediation legislation in 2006 because from January 1st 2007, Romania became a European Union Member State, and many conditions for accession had to be met. Meanwhile, it is challenging to identify situations where the public sector uses mediation. There is not an explicit, coherent, and favourable public policy.
The reduced use of mediation by the public sector may also discourage citizens and the private sector. But what are the reasons why mediation is not among the preferred dispute resolution methods by central and local public institutions in many countries? A discussion of these reasons would help understand how governments and public institutions may be encouraged to mediate. I open the conversation with three possible causes, which I briefly describe below – the fear of corruption, the financial audit of public institutions and the unfavourable legal framework.
Corruption
For mediation to be accepted by the public sector, a lot of integrity and transparency is needed. We need to remember that mediation happens in a confidential setting, which runs counter to the transparency necessary for the public sector. Moreover, in countries where the Corruption Perceptions Index (CPI) has a low value, as is the case of Romania compared with the other Member States of the European Union, without a favourable legal framework and an express mandate from the institution it represents, the civil servant will avoid at all costs the participation in “closed door” discussions to eliminate the risk of being accused of acts of corruption. Often, to avoid taking responsibility for deciding on using mediation, the civil servant prefers to be bound by the court, even if this practice is done at the expense of those who pay taxes.
Public financial audit
But not only the fear of corruption can be a contributing factor to the reduced use of mediation by public institutions. The fear of not being investigated by the authorities responsible for the financial audit of institutions and civil servants may be another factor that, again, in the absence of a coherent and favourable legal framework for mediation, generates a phenomenon of non-responsibility in decision-making on dispute resolution. This way, the courts take these decisions binding on all parties involved, the real loser being the taxpayer, as this process carries court taxes and other litigation costs.
Policies that establish that the courts have authority
Perhaps one of the most important reasons for the minimal number of public disputes resolved through mediation is the lack of a favourable policy and a legal framework to encourage public institutions to use mediation services. We are referring to the facts that the public sector does not usually initiate or accept mediation and do not include a mediation clause in public contracts. Often, the amicable settlement clause in these contracts is mostly a theoretical possibility. As an example of good practice, we mention here the opt-out model successfully implemented for several years in Italy, creating a mediation culture for the public sector. Last but not least, effective public policies start from the establishment of effective mechanisms for data collection and monitoring of mediation quality.
Conclusion
Indeed, much can be said about this subject. Certainly, the adoption of laws does not create realities. Instead of adopting laws focused mainly on the “development of the mediation offer”, it would be helpful to lay the necessary foundations for encouraging the use of mediation, primarily by the public sector, which, through its attitude, will send a powerful signal to citizens and the private sector. Finally, effective mediation promotion will occur when governments significantly improve the conditions for mediating disputes to which public institutions are parties.
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Winner of 2014 Supreme Award for Structural Engineering Excellence
This latest iteration of structural glass design provides the purest form possible within the limits of current material fabrication. Clear glazed single panel walls with no connections to distract the eye, 10m long by 3m high on four sides, provide an efficient structural form capable of resisting seismic loads, while providing total transparency and architectural purity.
The lightweight ultra-thin roof made of CFRP panels (carbon fibre reinforced plastic) seamlessly joined on site, provides a completely smooth uniform soffit while also improving the seismic performance of the whole structure. In such a minimalist project the detailing required particular attention, the result being a total absence of fixings, with the five panels being held together by structural silicone.
Judge's comment:
The judges found this to be a supreme example of collaboration between engineer and fabricator to achieve an outstanding, architecturally minimalist structure. The use of single panes of toughened laminated glass to support a lightweight ultra-thin CFRP roof without connections other than structural silicone, takes structural glass technology into a new dimension. A project where only engineering excellence and attention to detail can produce a result of such simplicity and purity of expression. | http://www.pct.ae/composite_projects.php?project=49 |
Despite steps by some chain restaurants to offer healthier kids' meals, most still aren't very nutritious, according to a new report.
Of the 3,500 meals from 41 top chain restaurants that were analyzed, just 3 percent met the nutrition standards set by the Center for Science in the Public Interest (CSPI), the advocacy organization that conducted the report.
Fifty percent of the meals had more than 600 calories, 78 percent offered soft drinks as a beverage option and 73 percent offered fries as a side.
The report named several meals as particularly egregious examples of unhealthy offerings, including the following:
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Applebee's: Grilled-cheese sandwich with fries and chocolate milk, which together contain 1,210 calories, 62 grams of fat and 2,340 milligrams (mg) of sodium — nearly three times the daily amount of sodium recommended by the CSPI.
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Chili's: Pepperoni Pizza with fries and soda, which total 1,010 calories, 45 grams of fat and 2,020 mg of sodium.
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Dairy Queen: Chicken strips, fries, sauce, an Arctic Rush (frozen drink) and a Dilly Bar (ice cream bar), which add up 1,030 calories, 45 grams of fat and 1,730 mg of sodium.
In order to meet CSPI's standards, kids' meals cannot have more than 430 calories (including no more than 35 percent of calories from fat, and 10 percent of calories from saturated and trans fats), 35 percent added sugars by weight and 770 mg of sodium. Additionally, CSPI-approved meals need to offer one of the following nutritious items: at least a half-serving of fruit or vegetables, an item made from at least 51 percent whole grains, or a specified level of vitamins or fiber.
The standards from the National Restaurant Association, an industry group, are similar but allow more calories.
At 19 chains, including Popeyes and Carl's Jr., not a single combination of the items offered for kids met CSPI’s standards, and nine chains met the National Restaurant Association's criteria.
Nonetheless, there has been some improvement in kids' meals over the years. In 2008, just 1 percent of meals met the CSPI's nutrition standards, and the percentage of meals that met the CSPI's criteria for sodium has increased from 15 percent in 2008 to 34 percent in 2012.
To make meals more nutritious, the CSPI recommended that restaurants offer kids meals with more fruit and vegetable options (making these default sides) and more whole-grain items, as well as remove soda and other sugary drinks from the meals.
Follow Rachael Rettner @RachaelRettner. Follow MyHealthNewsDaily @MyHealth_MHND, Facebook & Google+.
Related on MyHealthNewsDaily and MNN: | https://www.mnn.com/food/healthy-eating/stories/97-of-kids-meals-are-unhealthy-group-says |
The most common types of POV are:
First Person - The I, we, me, my, mine, us narrator.
I find that I am drawn to books written in first person more than others. I like being inside the MC's head, feeling their emotions. Also, aside from short story expiriments, everything I've written has ended up first person, even if I originally tried it in third. Apparently in the same way I'm drawn to reading first person, I'm also drawn to exploring my own characters the same way. Both of my WIPs, Anemone and Still Loving Ghosts, are written in first person, but the chapters alternate characters.
Second Person - The you narrator.
I've only tried to write in first person once, and because it really does come across as humorous, I made it a funny "short short story". Any longer than a few pages and I would have gone crazy... along with whoever ended up reading it.
Third Person - The he, she, it, they, them narrator.
Some writers are really good at this POV. I am not one of them. I've tried... oh how I've tried. I just can't pull it off. It just doesn't feel personal enough when I write this POV. I always want more. I want to actually feel like I'm inside the character's head, not just writing or reading about it. I've written one or two short stories in third person, but every time I start a novel in it, I end up reworking it into first.
Which POV do you write in most or exclusively? Do you like to read one over another?
(Check out the latest issue of Writer's Digest for an article by James V. Smith Jr. that analyzes the pros and cons of each POV. It's good.)
Happy Monday!
20 comments:
I like to switch it up, so I have short stories and novels written in various POVs (with the exception of Second Person which, while fun to experiment with, has never really worked for me in anything longer than flash fiction). For me, I like to let the story dictate what POV to tell it in, and there have been a number of times where I've gone back afterwards and changed point of views because something about a story just didn't feel right.ReplyDelete
almost exclusively in 3rd POV. Though i'm considering shaking it up a bit and trying first person for my YA sea sperent idea...ReplyDelete
I've never done second person. It's hard to get it right and maintain interest, I think.ReplyDelete
Mostly I write 3rd person, close. I've got a few things that are 1st, but haven't ever finished a manuscript with that point of view. Maybe I'll like it more when I get there.
I don't have a preference reading. 1st and 3rd are both fun.
My first novel was third-person, but everything since has been first person. I think it's easier that way for me to sink into the MC's personality while writing. At some point, I'll probably try another third-person novel, but for now I'm loving first :)ReplyDelete
I've only written in third person, but I think I'll try first with my next project.ReplyDelete
I've written in both. When I'm reading, if it is written in third person I want my narrator to get into the main characters' heads for me.ReplyDelete
I write in all third person for my fiction books, and I prefer to read from that POV as well.ReplyDelete
I'm not a huge fan of anything 2nd person. Ever. Not even mentioned in passing in papers. It causes physical pain to me. Almost. lolReplyDelete
I think writing 1st person is the easiest, actually, because you don't have to worry as much about POV issues. You're only in your MC's head, and it's easy to figure out whether you're head-hopping or not.
I go back and forth from 1st to 3rd limited. I used to actually like 3rd omniscient, but it's so hard to find now, I tend to be surprised and a little jolted when I see it at this point.
- AnonymousApril 12, 2010 at 3:10 PM
I'm pretty devoted to third person. But I have written in first and second. They just didn't click as much with me as third.ReplyDelete
I have noticed, though, that some ideas formulate in my mind and can only be pulled off with a specific POV. Those are the ones I tend to go after; I'm not a fan of variables.
I write in both 1st and 3rd (but not at the same time ;)). My story just seems to dictate to me what POV is wants to be written in.ReplyDelete
First person POV for me. I love reading it and writing it and don't know why! LOL. :)ReplyDelete
My first book was in First. Which I loved and was so right for that book. Second book, Third. I'm not so sure which I like best, both have their advantages, are able to free up some writing. I'll keep you posted on where third book goes. For sure, not second person. That one is a no-go for me.ReplyDelete
Falen - sea serpent!? can't wait to read that!ReplyDelete
KM - I accidentally tried writing in third person omniscient once. I say accidentally because I was writing with one person's thoughts in mind, but then randomly included other's here and there. It was a mess. I switched the whole thing to first person. LOL.
Southpaw - LOL!
Kim - I'm with you, sister! | http://www.kristinrae.com/2010/04/point-of-view.html |
This is an outrageous statement, and the truth is, I only really mean it when compared with the other languages I’ve spoken in their countries of origin: French, Thai, Korea, Peruvian Spanish, English, and Chinese. Although many people who have never spoken or even started studying Japanese make complaints like “it’s too hard!”, they have never had the opportunity to put it into practice in a convenience store in Hokkaido, a train station in Kyushu, or a school in Hiroshima.
The truth is, it’s remarkably easy to get through most day-by-day situations in Japan without speaking at all. One reason foreign visitors tend to complain about the language barrier is simply because they aren’t experiencing what most locals are, e.g. finding the bus to a random corner of the country, asking about the history of a shrine, deciding what to order in a restaurant when they don’t know the food.
Consider the last scenario, and assume you can read everything on the menu. Without fail, waiters and waitresses across Japan aren’t going to throw you off by starting with small talk. They’re going to greet you entering their establishment with a customary irasshaimase and wait until you press the button at the table before even approaching you… with the exception of water and oshibori. When it comes time to order, there’s no fanciful talk like “Yes, I believe we’d like to try the lobster, assuming it’s in season”, only “One of these, please, and one of these, and two of these. That’s all.”
It’s not as though you can’t chat someone up on the streets and be thrown by the difficulty of the conversation in Japanese, but to get you through the intricacies of daily life, long conversations aren’t necessary to survive in the modern world. In Japan, the language makes it even easier to function as an adult without knowing everything:
– In a convenience store, they don’t ask you if you want a bag or chopsticks; that’s a given. The only question is whether you want something heated up.
– In a train station, you don’t even have to speak to anyone if you know where you’re going. Tokyo’s trains can be confusing even for experienced city dwellers, but most locals wouldn’t need to ask the station attendants directions to the right platform, the time the train leaves, or if it makes a particular stop.
– Even in a professional setting like an office, stock phrases reign supreme, from a standard “good morning” (おはようございます) to “thank you for your hard work” (お疲れ様です). Certain protocol is to be followed when addressing superiors, I hear the same sentences of acknowledgement over and over again.
There are many reasons why the language is structured this way. Personally, I happen to think it makes Japanese even easier for the listener than the speaker, because there’s an intuition that comes from knowing the language. Japanese, in contrast to English, has a subject-object-verb sentence structure, versus the subject-verb-object ones we enjoy as English speakers. As a result, native speakers can often see where the sentence is going by knowing the subject and object without even considering the action. However, English speakers get the action out of the way so quickly it’s impossible to understand the full meaning without every word, e.g. “the cat ate the mouse”… the cat could be eating anything; in Japanese, “cat mouse ate” can make you guess what the cat did to that mouse before the word is spoken. | http://www.onceatraveler.com/why-japanese-is-the-easiest-functional-language |
What is an appraisal?
A real estate appraisal is an independent opinion of the estimated Market Value of real property. The appraisal should be prepared by a trained State Certified or State Licensed Appraiser who is familiar with the local market and with the type of property being appraised.
The appraisal process is an orderly procedure wherein the data utilized in estimating the value of the subject property is acquired, classified, analyzed, and presented. The first step in this process involves defining the appraisal problem as to the identification of the real estate, effective date of the value estimate, the identification of the property rights being appraised, and the type of value being sought. Once this has been accomplished, the appraiser embarks upon a collection of data and analysis of factors which affect the market value of the subject property. This includes area and neighborhood analysis, site and improvement analysis, highest and best use analysis, and the application of the available approaches to value, i.e., the Cost Approach, the Sales Comparison Approach, and the Income Capitalization Approach. Finally, the approaches utilized are combined in the reconciliation to determine the final value estimate.
The Inspection
An appraiser's duty is to inspect the property being appraised to ascertain the true status of that property. He or she must actually see features, such as the number of bedrooms, bathrooms, the location, and so on, to ensure that they really exist and are in the condition a reasonable buyer would expect them to be. The inspection often includes a sketch of the property, ensuring the proper square footage and conveying the layout of the property. Most importantly, the appraiser looks for any obvious features - or defects - that would affect the value of the house.
Cost Approach
The Cost Approachis based on the proposition that an informed purchaser would pay no more than the cost of producing a property with the same utility as the subject property. In this approach, the site is valued as though vacant by analyzing sales of similar sites on the market. The cost of replacing the subject's improvements is estimated at current cost. From this replacement cost new is subtracted the estimated accrued depreciation, or diminished utility. The estimated site improvements are then combined as an indication of value.
Sales Comparison Approach
The Sales Comparison Approachis based on the proposition that an informed purchaser would pay no more for a property than the cost of acquiring a property with the same utility. This approach involves the analysis and comparison of market transactions; i.e., the prices being paid for similar properties, prices asked by owners, and offers made on prospective comparable properties to arrive at an indication of what the property would have sold for had it been identical to the subject. Typically, a common denominator or unit of comparison is found such as the sale price per square foot or a gross rent multiplier, which is the relationship between the sale price and the gross rental income. The adjusted sale prices are then correlated into an indication of value for the subject.
Income Capitalization Approach
The Income Capitalization Approachis based on the assumption that there is a definite relationship between the amount of income a property will earn and its value. A number of appraisal principles form the basis of this approach with the principle of anticipation being particularly applicable. This principle affirms that value is created by the expectation of benefits to be derived in the future.
The Income Capitalization Approach is an appraisal technique in which the anticipated annual net income of the subject property is processed in order to arrive at an indication of value. Net income in the appraisal process is that income generated before payment of any debt service, and the technique of converting it to value is a form of discounting called capitalization. Capitalization involves dividing the net income by a rate which weighs such considerations as risk, time, interest on the capital investment, and recapture of the depreciating asset. The appropriateness of this rate is critical, and there are a number of techniques by which it may be developed.
Reconciliation
Reconciliation is the final step in the appraisal process. In the reconciliation, the appraiser considers the relative applicability of each of the approaches utilized, examines the range between value indications, and places emphasis on the approaches which appear to produce the most reliable and applicable solution to the specific appraisal problem. The purpose of the appraisal, the type of property, and the adequacy and reliability of the data is analyzed and these considerations influence the weight to be given to each of the approaches to value. | https://swansonappraisal.com/AppraisalInfo |
Abstract. By the Chinese room thought experiment, John Searle (1980) advocates the thesis that it is impossible for computers to think in the same way that human beings do. This article intends firstly to show that the Chinese room does not justify or even test this thesis and secondly to describe exactly how the person in the Chinese room can learn Chinese. Regarding this learning process, Searle ignores the relevance of an individual’s pattern recognition capacity for understanding. To counter Searle’s claim, this paper, via examining a series of thought experiments inspired by the Chinese room, aims to underline the importance of pattern recognition for understanding to emerge.
Keywords: Artificial intelligence, Chinese room, Turing test, understanding, pattern recognition
Teisingesnė „kinų kambario“ versija
Santrauka. Naudodamasis „kinų kambario“ mintiniu eksperimentu, Johnas Searle’as (1980) gina teiginį, jog kompiuteriai negali mąstyti taip, kaip mąsto žmonės. Šiame straipsnyje pirmiausia ketinama parodyti, kad „kinų kambario“ eksperimentas ne tik kad nepagrindžia, bet net ir neišbando šios tezės, o, antra, paaiškinama, kaip kinų kambaryje sėdintis žmogus gali išmokti kinų kalbos. Kalbėdamas apie šį mokymosi procesą Searle’as ignoruoja tai, kokią svarbą supratimui turi asmens gebėjimas atpažinti struktūras. Nesutikdami su Searle’o teze, šiame straipsnyje nagrinėjame keletą kitų, kinų kambario įkvėptų, mintinių eksperimentų ir pabrėžiame struktūros atpažinimo svarbą supratimui atsirasti.
Pagrindiniai žodžiai: dirbtinis intelektas, kinų kambarys, Turingo testas, supratimas, struktūros atpažinimas
Acknowledgments. I would like to thank Dr. Gürol Baba for his helpful comments and suggestions to improve this paper.
Received: 04/03/2018. Accepted: 01/10/2018
Copyright © Hasan Çağatay, 2019. Published by Vilnius University Press.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Searle, the Turing Test and Strong AI
After almost four decades of its publication, John Searle’s Chinese room thought experiment (1980) still puzzles the field of artificial intelligence (AI). Using this thought experiment, Searle convincingly – but mistakenly in my opinion – defended that no matter how complex and well programmed a computer performing symbol manipulation is at present, and could be in the future, it cannot think in the manner human beings do. He also rejected Alan Turing’s (1964) claim that the Turing test is a sufficient condition for determining whether an AI system really thinks. Although the specifics of how the Turing test should be performed remains a controversial topic (Traiger 2000), the test can roughly be described as follows:
There is a computer and two humans. One human is the interrogator. She or he communicates with the computer and the other human using a teletype or computer terminal. The interrogator is told that one of the two individuals it is communicating with is a computer, and that the other is a human. The computer’s goal is to fool the interrogator into thinking that it is the human. The other human’s goal is to convince the interrogator that he or she is the human. The computer attempts to achieve the deception by imitating human verbal behavior. If an interrogator does not make the right identification, where a “right identification” is identifying the computer as a computer, then the computer passes the test. (Traiger 2000: 561)
According to Turing, if a computer can convince an interrogator that it is a human being as frequently as a human being can, the computer should be considered to be a thinking being or to possess human-like cognitive capacity. He further asserts that the other philosophically complicated concepts of thinking are vague and useless because they are not testable or verifiable, and that there is no acceptable concept of thinking to replace his behavioristic concept of thinking based on Turing test results (Turing 1964).
After a decade, Roger C. Schank and Robert P. Abelson (1975) were working on a computer program (script applier mechanism [SAM]) capable of inferring implicit propositions in natural-language stories. The implicit propositions, which could be inferred by a human quite easily, were not logically necessary conclusions of the explicit statements in the stories. The following story is an example that SAM analyzed and answered the questions about: “John went to a restaurant. The hostess seated John. The waiter came to the table. John ordered lobster. John was served quickly. John left a large tip. John left the restaurant” (Schank and Abelson 1975: 153). Although the reason why John left a large tip is not explicitly stated, SAM was able to deduce that the probable reason was the quick service (Schank and Abelson 1975: 154). At the time, Schank and Abelson (1975: 155) estimated that with some improvement, their program (SAM) could understand simple stories about a range of domains.
In response to Turing (1964), Schank, and Ableson (1975); Searle (1980) posited that in the absence of a foundational scientific and/or engineering revolution that enables computers to perform tasks beyond symbol manipulation, no computer including ones that would pass Turing test can perform human-like thinking. He claims that insignificant developments, like coding a software aiming to pass behavioral tests like the one Turing proposed, overlook one of the core concepts of the philosophy of mind: intentionality.
In the Chinese room thought experiment, Searle imagines himself acting as a computer that is trying to understand Chinese stories, where Searle has no knowledge of the Chinese language. He is placed in a room with some syntactic instructions (algorithm) in English that will help him to manipulate Chinese symbols properly. Next, some Chinese stories and Chinese questions about these stories are passed to Searle from outside the room and he tries to answer the questions in Chinese with the help of English instructions. The algorithm is so comprehensive and Searle is so skillful in applying it that he manages to prepare correct Chinese-language answers to the questions quickly, although he does not know the language. If all these are true, a Chinese-speaking individual who does not know what is happening in the Chinese room could possibly think that the person in the room understands Chinese. That is to say, Searle would be able to pass the Turing test in Chinese, without understanding anything about the stories, questions and his answers to the questions. In brief, this thought experiment shows that a person or a computer with no understanding, can manipulate symbols (Chinese letters) meaningfully, with the help of an algorithm. Accordingly, it is possible to pass the Turing test without understanding or thinking like a human being.
This is a sound argument: The Turing test does not account for phenomenological, or at least the intentional aspect of thinking. Nevertheless, Searle bases a stronger and controversial conclusion on the Chinese room: no machine based on computational symbol manipulation can perform human-like thinking. Needless to say, this is a negative existential statement, proof of which is more demanding than the one above. After all, in the Chinese room, Searle tests only a particular kind of algorithm for a particular kind of problem.1 Searle would not make the mistake of relying on the following invalid argument in reaching his stronger and much more controversial conclusion:2
1) In the room Searle acts as a computer that manipulates symbols in order to communicate in Chinese.
2) Searle does not understand or think about content of Chinese symbols.
3) No computer using pure symbol manipulation can understand or think (which does not follow from 1 and 2).
Apparently, Searle uses at least one additional premise to show that (3) is true. One such premise that leads Searle to conclude (3) is that the person in the Chinese room has access to all the necessary tools that can be used by a computer for the task of understanding. Another of Searle’s additional premises is that there exists no better algorithm for understanding Chinese than the one the person in the Chinese room is given. And finally, no matter how long Searle stayed in the room, he could not start to understand Chinese. Without these additional premises, the Chinese room thought experiment cannot derive his controversial conclusion that no computer can perform human-like thinking. Unless he justifies these additional premises, a natural objection to Searle could be that even if the person in the room did not understand Chinese, if he used a better algorithm to communicate and understand Chinese, or if he had access to other tools a computer could, or if he had some more time experiencing symbol manipulation, he might have very well been able to understand Chinese. To prevent this objection, his argument suggesting that a computer cannot perform human-like thinking should be in the following form:
1) In the room Searle acted as a computer that manipulates symbols in order to communicate in Chinese.
2) (No matter how long Searle stayed in the room) Searle cannot understand or think about content of Chinese symbols.
3) No computer could have a better algorithm or access to more useful tools for understanding or thinking about content of Chinese symbols than Searle in the Chinese room.
4) No computer can understand or think (from 1, 2 and 3).
Intuitively, Searle seems correct in that the person in the Chinese room would not have accurate intentional states related to Chinese symbols at least in a short while. That is to say, the person would be unaware of how the symbols are connected to the world outside the room. On the contrary, this paper argues that (2) and (3) are false. That is to say, given enough time, Searle in the room could actually understand Chinese stories to some extent. Moreover, if he were given access to some additional tools which a computer could have access to, he would understand Chinese stories much easier, faster and more in depth.
As Searle points out, at the beginning, the person in the room would lack intentionality in the sense of directedness. Directedness, in its broadest definition, is the ability to establish relationships between mental and external objects. Both a standard computer and I may express the sentence, “The Moon is Earth’s natural satellite;” however, unlike me, a standard computer does not associate this statement with the two celestial objects. As far as a standard computer is concerned, the word Moon does not refer to a celestial body; therefore, it would be erroneous to assume that the computer understands that the Moon is Earth’s satellite. This problem is related to the difference between sentence and proposition or content and symbols. The central question concerning understanding is whether it is possible for semantics to emerge only from syntactical manipulation. Searle thinks it is not:
Computation is defined purely formally or syntactically, whereas minds have actual mental or semantic contents, and we cannot get from syntactical to the semantic just by having the syntactical operations and nothing else. To put this point slightly more technically, the notion “same implemented program” defines an equivalence class that is specified independently of any specific physical realization. But such a specification necessarily leaves out the biologically specific powers of the brain to cause cognitive processes (Searle 2010: 17).
Could Searle be correct in his claim that there are some biological/physical causal properties of the human brain that render it something more than a computational symbol manipulator? In this paper, the puzzling concepts of “meaning,” “reference,” “intentionality” and relations between them are not investigated thoroughly, therefore this question is not answered conclusively. This paper mainly aims to show that Searle’s Chinese room did not succeed to show that a computer cannot think, functionalism is false and semantics cannot emerge on syntactical operations. To do that, first I will modify the Chinese room thought experiment in a way that the person in the room is given more data and a proper algorithm for decoding Chinese, and consequently, these modifications will enable the person in the room to start understanding Chinese.
An Unfair Version of the Chinese Room (UVCR)
Proponents of robot reply underline the fact that in the Chinese room thought experiment, the person in the room does not have access to the external sensory data that a computer may have via a camera and/or a microphone and defends that this is the main reason why Searle in the room does not understand Chinese (Searle 1980: 431). The unfair version of the thought experiment (UVCR) that I will describe in this section, will intuitively support that robot reply is correct in that some set of relations between sensory data and syntax could help to bridge the gap between syntax and semantics. However, as its name suggests, this version of the Chinese room cannot be conclusive, as it gives the person in the room an unfair advantage that a computer does not possess.
In UVCR a person enters the room with English-language instructions (algorithm), as in Searle’s version, but now the algorithm, the Chinese stories and questions he receives are accompanied by visual data concerning the meaning of the Chinese characters. For example, for the Chinese sentence, “苹果 是 红色 的,” which means “the apple is red,” some additional data are provided, such that:
1. Pictures of apple in different color accompany the syntax “苹果” (apple);
2. The expression 红色 (red) is accompanied by examples of red objects;
3. Finally, the sentence “苹果 是 红色 的” is accompanied by a picture of a red apple and graphical data indicating the subject of the sentence is the apple and predicate is to be red.
Provided these additional data, Searle (a person) in the room would not only pass the Turing test, but would also begin to understand Chinese. This time, the person in the room would have accurate intentional states about the given Chinese symbols. In other words, when the person in the room reads the sentence “苹果 是 红色 的” they would associate it with an object (the apple) and a predicate (to be red).
It is now clear that if the person in the room were provided some additional tools or data that a computer could have, they could understand Chinese. At first glance, providing some visual data about the world to the person in the room may not seem unfair (despite the fact this paper argues otherwise), since, via a camera, a computer can also collect data about the world. If UVCR were to be fair, it would show that there is no sound argument put forward by Searle to believe that a properly programmed and adequately configured computer identifying relationships between syntax and the world cannot think. On the other hand, UVCR provides an unfair advantage to the person in the room: After all for the person in the room, the pictures that are associated with Chinese words are not mere symbols to be manipulated; they are symbols with content. That is to say, before entering the room, Searle already possessed the idea of what an apple is and how it seems. He simply associated the content of “apple,” which he had already possessed, with the syntax of “苹果,” as opposed to building the content of “apple” via mere symbol manipulation. Searle’s main conclusion that semantics cannot emerge through symbol manipulation cannot be debunked by UVCR as it is. However, this paper argues that the original version of the thought experiment is also unfair to the person in the room, as it did not allow Searle to perceive the outside world, which is crucial for the efficiency and quality of understanding the process as UVCR suggests. The bottom line is that Searle’s preference to hypothesize a person with a semantic history in the room to test strong AI creates a dilemma. If we were to allow the person in the room to access perceptual data about the Chinese symbols, we fail to test whether semantics can emerge through mere symbols; and, if we do not, we are unfair to the person in the room (or computers), since perceptual data is an important (although, not necessary, as it will be defended later) component of understanding in an ordinary sense.
The common sense concept of understanding requires an accurate establishment of relationships between syntax and the world, i.e., the meanings of words. Individuals learn the meaning of a word by interacting with the external world and constructing relationships between words and their correspondences in the world. A person or computer manipulating syntax in the absence of sense data cannot establish these substantial relationships, therefore lacks intentionality and understanding in an ordinary sense. This is one of the reasons why I conclude that Searle’s original Chinese room thought experiment is set up in a way that is unfair to the person in the room, computers, and strong AI. It does not allow the person in the room to perceive the world. On the other hand, modifying his thought experiment as it is done in this section, only makes it unfair in the opposite sense, as UVCR lets the person in the room use their semantic background to make sense of Chinese symbols. The next section constructs a conclusive version of the thought experiment, which decisively proves that Searle’s argument against strong AI is not valid.
As a final remark, notwithstanding sense data’s help for fast, intuitive and in depth understanding, this paper defends that availability of sense data is not a necessary condition for understanding, which will also be defended in the following section.
A Fair Version of the Chinese Room (FVCR)
Before presenting the fair version of the Chinese room, human capacity of pattern recognition will be elaborated briefly. Humans cope with an incredibly complex world. According to Claude Edward Shannon’s (1988) conservative calculations, in a chess game, there are 10120 variations (each variation is a complete possible chess game) to deduce the best possible starting move. “A machine operating at the rate of one variation per micro-second would require over 1090 years to calculate the first move! (Shannon 1988: 4)” It is practically impossible even for computers to process these data deductively. On the other hand, we humans do not have to deduce all variations to make a “good” decision, thanks to our pattern recognition ability. Human players categorizes chess entities like open file, fork, pin, mid-game, end-game, Slav formation, etc. and learn or discover advantageous chess moves in this conceptual space, which is much less complex than the well-defined variation space. In short, instead of processing all variations, humans categorize them and act according to which category they fall under. Recognizing patterns and making inferences about categories is more economical, and mostly only possible option with respect to cognitive resources. Now the question is, how do computers play chess if the game is incredibly complex? They also use pattern recognition techniques and they can be comparable to (and even better than) humans recognizing patterns at least in the domain they are designed for (Rasekhschaffe and Jones 2019). Cristopher M. Bishop (2006: 1) describes the aim of computational pattern recognition as the “discovery of regularities in data through the use of computer algorithms and with the use of these regularities to take actions such as classifying the data into different categories,” and underlines the fact that humans also have that capacity.
Even if chess is one of paradigmatic examples of complex systems, need and use of pattern recognition ability is not limited to challenging practices like playing chess or doing science. Apparently simple tasks, like perceiving the environment, walking, speaking, reading, driving, and so on, take place in complex systems, and human beings use their ability to recognize patterns in these domains too. To illustrate, while driving, an expert driver tend to recognize patterns of the engine sound and act accordingly, without following well-defined rules like “shift to 2nd gear when the speedometer needle points to 10 (Dreyfus 2004: 177).”3
Why Searle holds the view that the person in the Chinese room or a properly programmed computer would not be able to understand is his overlooking this essential capacity of pattern recognition and this paper will clarify how it is possible for the person in the Chinese room to understand Chinese, given that s/he has a moderate capacity to recognize patterns in the following thought experiment.
In the final, fair version of the Chinese room (FVCR) the person entering the room is an alien, unfamiliar with Earth or any other planet. She has always lived in a starship with no windows that would have allowed her to see the space. The starship is governed by artificial laws of physics which are different than ours. The alien has never seen an apple, a car, the Sun, the Moon, and so on. The alien lives in an environment which possesses entirely different characteristics than Earth. Naturally, she is wholly unfamiliar with the English language. Then she enters the “English room” in her starship. Needless to say, she is provided with certain instructions in her native language that will enable her to manipulate English letters correctly. In FVCR the alien is provided with English stories, questions and simple pictures associated with the given English words from the stories and questions, and she manipulates English symbols to write down reasonable answers to the questions. Let us assume that these stories focus extensively on simple information about the Solar System. For the alien, these pictures and letters are nothing more than meaningless symbols, as she is wholly ignorant of the referent of pictures and English words. With the help of instructions she is given, the alien is able to manipulate the English symbols accurately without any understanding about the content of the sentences she reads or writes. However, in this thought experiment, the alien enjoys manipulating symbols to the extent that she remains in the room for months.
The diligence of the alien brings about a twist in the thought experiment: After seeing thousands of texts about the Solar System, she begins to realize that there are certain patterns in the strings of symbols in the English stories. She discovers, for example, that while the string of “Venus,” “Earth” or “Saturn” concludes with “is a planet;” the string of “the Moon,” depicted in a similar way to these planets, concludes with “is not a planet.” or “is a satellite of the Earth” After investigating hundreds of sentences related to planets and natural satellites, she creates two concepts one corresponding with our concept of “planet,” and a second corresponding to our concept of “satellite”. It cannot be easily be claimed that it would be possible for her to construct a concept of planet or satellite that is similar to ours. After all, her concepts, let us call them “planet′” and “satellite′” are constructed in the absence of detailed information concerning planets or natural satellites. She knows, on the other hand, that planets′ or satellites′ are in some way related to circular shapes in different sizes and surfaces. Another thing she notices is that circular shape a satellite′ is associated with is always smaller than that of the planet′ it orbits′ and mostly those of other planets′. She further discovers that every string that accurately concludes with “is a satellite.” also concludes with “is satellite of [a planet].” In other words, every satellite′ has a certain relationship with a planet′. In the same way, she understands that there is a relation, namely “orbiting around” between planets′ and the Sun′, and satellites′ and planets′. Moreover, she notices that every satellite′ is a satellite′ of the planet that it is “orbiting around′.” She suspects that being satellite of′ is equivalent to orbiting around′. Finally, she discovers that whatever the relation of “being bigger than” is, it is an order relation. That is to say, for A, B and C are different from one another, if A is bigger than B and B is bigger than C, then A is bigger than C. Consequently, upon reading that the Sun is bigger than Mars and that Mars is bigger than a meteor, she can now conclude that Sun is bigger′ than a meteor. She does not stop there, and sees that if A is bigger than′ B, the circular shapes provided for the strings representing A is bigger than those of B. Now, she accurately believes that she understands the meaning of “being bigger than”. She understands the meaning of “bigger than” as a human being would do in their childhood and she has the appropriate intentional states concerning this concept. She understands the meaning of “being bigger than” and this understanding does not stem from past experiences collected outside the English room. Note that some of the understandings provided above does not require simple pictures associated with English words. The pictures which are analogous to sense data are not a necessary condition for understanding but a helpful tool for faster, more comprehensive and deeper understanding.
Now in FVCR has the alien begun to understand English? Apparently, she has a degree, scope and depth of understanding of English texts like any of us. For now, the alien’s understanding is limited to a very small domain but whatever she understands, she understands in the same way we do.
Note that FVCR reveals only one possible outcome about the English room. Therefore, FVCR does not show that any alien would start understanding in the English room. It is true that depending on the instructions the alien is given and pattern recognition capabilities and cognitive tendencies of her, she could get confused in the room and may not understand anything about English symbols, no matter how long she stays. To illustrate, she may wrongly assume that pictures associated with English words are not representations of sense data signified by the words but they themselves are some additional signifiers, or her memory or pattern recognition capability may not be enough to see the relationships in complex texts. On the other hand, FVCR shows that some aliens which have necessary pattern recognition capabilities and motivation would start understanding in the room. Demonstration of this possibility is enough to negate Searle’s view that strong AI is false.
It may be claimed, on the other hand, that what the alien learnt and understood in the English room is all about the Latin symbols and syntax of English language, not about the world. Assuming that she does not have access to pictures associated with English words, this claim would be even more appealing. After all, for the alien, the string of “planet” does not signify the celestial objects we call “planets”. Yet, this is not because she does not construct concepts about the entities in the world, which strings of Latin symbols could possibly refer to but because her concept of planet′ is much less complete than that of ours. Throughout the time the alien spent in the room, she has been constructing a concept of planet′ reference of which she has very little knowledge, just as we do when we clumsily construct a concept of a “wave function” while reading an advanced article in quantum physics with almost no prerequisite knowledge. In short, I assume that the alien in the English room knows that these Latin symbols are meant to express propositions about the world, just as the Searle in the Chinese room does know that Chinese symbols are related to the world. Someday, let us say she arrives on Earth and begins to perceive our world including the planets, the satellites and the Sun within our solar-system. In this case, she would start to deepen her understanding of the English language and our world far more progressively and convergent to our understanding. This article defends that FVCR shows that Searle is mistaken in that he would not understand Chinese in the room. Moreover, I suspect that FVCR may not be necessary to show that Searle is mistaken. It can be argued that with or without English instructions, the person in the original Chinese room could, in principle, understand Chinese, if they are given enough time and, hence, the necessary experience about meaningful Chinese texts. This conclusion is evident in the fact that while new-born babies perceive the world via meaningless symbols, they somehow make sense of the world without instructions on how to manipulate them. They naturally experience reality, recognize discernible patterns in it and map the meaningless symbols onto the world. If a new-born baby can understand a new language without any instructions, then it should be possible for Searle in the Chinese room to understand Chinese with or without instructions.
Another question in need of an answer is how is the task assigned to the person in the Chinese room related to the strong AI, which is the thesis that a properly configured and programmed computer can think in the same way we do? This article defends that a person’s success in understanding Chinese in the Chinese room is neither a necessary, nor a sufficient condition for strong AI: It is not a sufficient condition: In this section it is shown that a person with human cognitive capacities could pass the English-room-test (or the Chinese-room-test); yet, this does not conclusively show that a computer could accomplish the same task by using pure symbol-manipulation, since we do not agree on the premise that all cognitive capacities of humans are based on computational symbol manipulation. To clarify, an alien could learn a language solely by manipulating symbols; but while she is doing so, she is using various cognitive processes (consciousness, various reasoning methods, experiencing qualia, pattern recognition, and so on) and it is not obvious that these cognitive skills could all be replicated by algorithms on symbol manipulation. Assuming that all of a person’s cognitive capacities are based on symbol manipulation to show that a computer working on symbol manipulation can think in the same way a human does, would suffer from a circularity problem.
On the other hand, a person’s success in understanding Chinese in the room is certainly not a necessary condition for strong AI either: There are numerous ways (algorithms) of manipulating symbols, and the person in the Chinese room uses only one particular way of it, which is defined by “the instructions in English.” Even if we agreed that it is impossible for an ordinary person in the Chinese room to understand Chinese with one specific algorithm and one set of cognitive skills s/he possess, this does not provide conclusive evidence that no person in the room can understand Chinese regardless of the instructions s/he follows or the cognitive skills s/he possesses. Accordingly, Searle’s version of the Chinese room, and his premise that the person in the room could no way understand Chinese, does not show that no computer can think no matter what algorithm it uses and how it is configured. After all, a person in a “Fibonacci room” with no knowledge of Fibonacci numbers cannot calculate Fibonacci numbers, if s/he is given an inaccurate set of instructions but this does not show that no computer can calculate Fibonacci numbers, no matter which algorithm it uses. Just like it is still possible that a properly programmed computer can calculate Fibonacci numbers, it can still be possible that properly programmed computer can understand just as humans do.4
Therefore, the Chinese room thought experiment is not directly related to strong AI thesis. The Chinese shows only that a computer’s passing the Turing test does not guarantee that it thinks and understands in the way humans do.
Searle’s Response to the Robot Reply
I defend that even without perceptual data, a person with pattern recognition capability, could, in principle, begin to understand a foreign language that they are manipulating. This is where the position of this paper differs from “robot reply,” or any understanding which holds the view that perceptual (sense) data is necessary for understanding. However, the availability of perceptual data would enormously boost degree, scope and depth of their understanding. This is why, in this section, I will discuss “Robot Reply” in relation with human/computer capacity of pattern recognition.
Like Jerry Fodor5, I find Searle’s response to robot reply unconvincing (Searle 1980: 431):
[T]he addition of such “perceptual” and “motor” capacities adds nothing by way of understanding, in particular, or intentionality, in general, to Schank’s original program. To see this, notice that the same thought experiment applies to the robot case. Suppose that instead of the computer inside the robot, you put me inside the room and, as in the original Chinese case, you give me more Chinese symbols with more instructions in English for matching Chinese symbols to Chinese symbols and feeding back Chinese symbols to the outside. Suppose, unknown to me, some of the Chinese symbols that come to me come from a television camera attached to the robot and other Chinese symbols that I am giving out serve to make the motors inside the robot move the robot’s legs or arms. It is important to emphasize that all I am doing is manipulating formal symbols: I know none of these other facts. I am receiving “information” from the robot’s “perceptual” apparatus, and I am giving out “instructions” to its motor apparatus without knowing either of these facts. I am the robot’s homunculus, but unlike the traditional homunculus, I don’t know what’s going on. I don’t understand anything except the rules for symbol manipulation. Now in this case I want to say that the robot has no intentional states at all; it is simply moving about as a result of its electrical wiring and its program. And furthermore, by instantiating the program I have no intentional states of the relevant type. All I do is follow formal instructions about manipulating formal symbols (Searle 1980: 420).
First, I agree with Searle in that the robot version is not fundamentally different from the original thought experiment; but, unlike Searle, I defend that in both versions, given enough time, a human being would begin to make sense of the symbols. More precisely, with the lines of thinking in the FVCR, Searle in the Chinese room would begin to. It is evident, with the line of thinking in the FVRC, Searle in the Chinese room connected to a robot or Searle in my skull connected to my nerves could begin to recognize patterns in the symbols he is manipulating, discover relationships in them and consequently understand the meaning of symbols (or signals.) Even though Searle, when in the room connected to the robot does not perceive the outside world directly, he is fed by Chinese characters representing the sensory data coming from the camera attached to the robot. After processing these symbols, Searle sends back Chinese characters that manipulate the motors which move the robot. As far as we know, this is remarkably similar to how a human brain works. It perceives the world by electrical signals (symbols) and acts on outside signals by again using electrical signals. When the Searle in the Chinese room receives the Chinese characters representing the sensory data of an apple (without knowing that the syntax represents the apple), he might question whether this representation has a certain relationship (being in color) with syntax representing sense data of “red” or “green”. After all, Searle has previously manipulated and recognized patterns in countless texts containing Chinese symbols representing sense data of red and green apples that the robot he is connected interacted with. So, Searle by sending certain symbols to the robots visual components, may check if it is red or green (more precisely, if it has certain relationship with symbol patterns representing red or green)If the apple is green, Searle (ignorant about the real nature of apple, green or red), might decide to send certain symbols to obtain a (metaphorically speaking) pleasurable string of symbols, and this way, would cause the robot to eat the green apple and direct the robot to enter into a goal state.
It is true that Searle in the Chinese room connected to a robot would also be unaware what he is doing in an ordinary sense at least, at the beginning. He would be unaware that the apple is something to be eaten and its color is an electromagnetic property of the apple. He would be unaware of many things that we know about apples, because he is not receiving the same symbols that we do, and he is not manipulating the symbols via a similar mechanism that a human brain does. However, he would begin to understand symbols he is manipulating. and by time, in the same way as the alien in the English room, his understanding would be sharpened And after a while, perhaps, he would be aware of some facts that we are not aware about apples, the color of green and red (again because he is not fed by the same data we are fed with and algorithm he follows is different from the one our brains does). Moreover, I admittingly speculate that if the Searle’s mechanism of manipulating the symbols were similar to that of a brain, how he understands the world would eventually converge with our way of understanding.
Conclusion
In essence, Searle’s argument against functionalism, the robot reply and strong AI ignores a capability that both human beings and properly programmed computers share: pattern recognition. Human beings are capable of capturing patterns in complex inputs, consciously and unconsciously. In recognizing patterns, our nervous systems (mostly unconsciously) filter insignificant variables and allow us to make sense of complex electronic impulses that represent the world. Accordingly, pattern recognition is one of the tools we use to invent or discover meaningful higher-order concepts hidden in meaningless symbols (like Chinese letters or electrical signals). Meaning and understanding concerns these patterns hidden in these incredibly complex electrical signals (or Chinese letters in the Chinese room) coming from our sense organs.
The Chinese room, as it is, does not disprove strong AI, as shown in the fair version of the Chinese room: it is possible for the person in the room to understand Chinese if they are provided with enough time and possess a moderate capacity to recognize patterns emerging in the symbols they manipulate. Understanding Chinese in the room would be even easier and faster if the person in the room were fed by (familiar or alien) audiovisual data coming from outside, since our brains have specifically evolved to recognize patterns in these kinds of sensory data. Arguably, two of the “mysterious” causal powers of the brain that puzzles Searle are 1) the brain’s pattern recognition capacity and 2) the brain’s capacity to construct relationships between sets of symbols (as our brains do when we relate the word “table” to some visual data belonging to a table).
Intentionality, artificial pattern recognition and artificial concept creation are central issues for strong AI. Mechanism(s) by which meaningless sensory data result(s) in human-like understanding/thinking continue to remain a mystery; however, Searle fails to provide any convincing evidence that the brain is the only physical structure capable of human-like thinking or that the causal relationships formed by the brain are the only possible relationships that could provide the foundation for thinking to emerge. I believe that intentionality can be reduced to a set of well-defined functions, which can be realized in various types of hardware composed of different materials, including the brain, computer hardware or any other structure providing the opportunity to represent and manipulate dynamic complex relationships. Provided that algorithms that efficiently recognize patterns, create concept, and bind the concepts to the world could be constructed, I do not see why computers categorically may not think.
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Turing, A. M., 1964. Computing machinery and intelligence. In A. R. Anderson (ed.), Minds and machines, New Jersey: Prentice Hall, pp. 4–30.
1 See Jerry Fodor’s comment in Searle 1980.
2 Searle seems to base his thesis on a clearly invalid argument in the following passage: “[…] I offer an argument that is very simple: instantiating a program could not be constitutive of intentionality, because it would be possible for an agent to instantiate the program and still not have the right kind of intentionality (Searle 1980: 450-451).” I certainly do not see how the possibility of an agent’s instantiating a program that does not have the right kind of intentionality show the impossibility of an agent’s instantiating a program that does have the right kind of intentionality.
3 For a comprehensive discussion of human ability to cope with complex environments, see Dreyfus 1972; Dreyfus and Dreyfus 2000; Dreyfus 2004. On the other hand, note that I do not agree Dreyfuses in that non-representational learning cannot be simulated by computers.
4 See Churchlands’ (1990: 35) luminous room argument in response to the Chinese room.
5 I do not agree with Fodor’s initial comment on the Chinese room stating that “[I]nstantiating the same program that the brain does is not, in and of itself, a sufficient condition for having those propositional attitudes characteristic of the organism that has the brain. If some people in Al think that it is, they’re wrong (Searle 1980: 431).” See also Fodor 1991. | https://www.journals.vu.lt/problemos/article/view/14615/13578 |
Q:
Is likelihood calculated over the whole training set or a single example?
Suppose I have a training set of (x, y) pairs, where x is the input example and y is the corresponding target and y is a value (1 ... k) (k is the number of classes).
When calculating the likelihood of the training set, should it be calculated for the whole training set (all of the examples), that is:
L = P(y | x) = p(y1 | x1) * p(y2 | x2) * ...
Or is the likelihood computed for a specific training example (x, y)?
I'm asking because I saw these lecture notes (page 2), where he seems to calculate L_i, that is the likelihood for every training example separately.
A:
The likelihood function describes the probability of generating a set of training data given some parameters and can be used to find those parameters which generate the training data with maximum probability. You can create the likelihood function for a subset of the training data, but that wouldn't be represent the likelihood of the whole data. What you can do however (and what is apparently silently done in the lecture notes) is to assume that your data is independent and identically distributed (iid). Therefore, you can split the joint probability function into smaller pieces, i.e. p(x|theta) = p(x1|theta) * p(x2|theta) * ... (based on the independence assumption), and you can use the same function with the same parameters (theta) for each of these pieces, e.g. a normal distribution (based on the identicality assumption). You can then use the logarithm to turn the product into a sum, i.e. p(x|theta) = p(x1|theta) + p(x2|theta) + .... That function can be maximized by setting its derivative to zero. The resulting maximum is the theta which creates your x with maximum probability, i.e. your maximum likelihood estimator.
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The Communications and Information Technology Commission (CITC) is the information and communications technology sector (ICT) regulator in the Kingdom of Saudi Arabia (SA).
Amongst its roles and responsibilities include:
• Granting licenses in the ICT sector
• Protection of users’ rights
• Setting service quality standards
• Preparation of policies, regulatory frameworks and studies of ICT sector in SA
• domain name administration in SA
• Increasing the information security awareness level in SA
• Supervision of the National Committee for Information Society in SA
This application is sensitive as the applied-for gTLD/IDN string represents the Arabic word for Catholic.
The term .كاثوليك (.Catholic) has been incorporated into the name of the largest Christian communion, the Catholic Church (also called the Roman Catholic Church). However, many other Christians use the term "Catholic" to refer more broadly to the whole Christian Church regardless of denominational affiliation. Other Christian communions lay claim to the term "Catholic" such as the Eastern Orthodox Church and the Oriental Orthodox Church.
We do not believe that the applied-for gTLD/IDN string (.كاثوليك or .Catholic) should be under the control of one church which cannot, and does not, represent every Catholic communion.
Further, we believe that any and all gTLD/IDN applications for any name in relation to religion or a specific community or religion should be presented to the whole of that community for evaluation before an application is denied or granted. If this cannot be accomplished then such names should be restricted completely from being used as gTLDs/IDNs.
Failure to do so would give the use and control of an important religious name to one group, unjustly elevating its influence above others and permit that group to solely represent a spectrum of different churches.
The current applicant cannot demonstrate that it possesses a monopoly over the term "Catholic" nor can it demonstrate that its intended ownership of that term is accepted by Catholics around the world.
To allow this string to be registered may be offensive to many people and societies on religious grounds.
Therefore, we respectfully request that ICANN not award this gTLD/IDN string.
We have updated our privacy policies and certain website terms of service to provide greater transparency, promote simplification, and align with recent changes in
privacy laws applicable to us.
Learn more.
more. | https://gtldcomment.icann.org/applicationcomment/commentdetails/6032 |
A Chief Technology Officer is essential to startups, growing businesses, and large companies for ensuring their technology is inline with day-to-day operations and long-term goals of the company. CTO duties, although well defined, cover a range of needs, and the CTO is expected to wear many hats as different challenges and demands develop.
In short, a CTO is someone who focuses on the scientific and technological operations of a business from an executive-level position.
While that’s a concise description of the role, let’s take a closer look at some of the finer notes of the role. CTO roles and responsibilities can be broken down into two main parts: short term and long term.
Short term CTO job duties include making sure their team is finishing daily and weekly tasks, ensuring the company is hitting tech dependent deadlines, delegating duties related to short and long term technology goals, reviewing lower level management decisions, and stepping in to do the “dirty work” when needed.
Long term CTO job responsibilities include assessing the company’s technology and business strategies, providing tech-focused solutions for their CEO and stakeholder to achieve corporate goals, evaluating new technologies to see if they fit into the company’s future plans, and leading innovative projects to drive company performance.
A lot of what will be required and asked of a CTO depends on the size and scale of the business they’re working for, but these descriptions and our example job description later in this post will cover the major CTO roles and responsibilities in today’s business environment.
Regardless of their company’s scale, a successful CTO will need to utilize their experience, business insight, and creative skills to solve problems and overcome challenges as they appear in the many phases of corporate development.
Traits of a Great CTO
Before you write your CTO job description, you should become familiar with the traits of a great CTO and decide which traits will be most important in your CTO role.
To Code or Not to Code
Although not all CTOs have a background in coding, many come from a background in Computer Science and code writing. Knowing when to get your hands dirty on a project and when to delegate is a balancing act that any great CTO will need to master.
Even if unable to provide direct assistance on a project, a great CTO should know when to relegate more support to a specific department and when to let the cogs keep turning.
Business Acumen
An acute eye for technological necessities isn’t enough for a CTO if they want to drive company performance with their initiatives.
Technologies come and go quicker than the seasons pass. Having the business insight to know which innovations will be short-lived trends and which ones are there to stay will make all the difference when making executive decisions about the company’s future.
Jack of all Trades
A CTO’s responsibilities can change from day to day. Having the ability to shift gears and maintain flexibility is an essential trait for any great CTO.
First, this means assessing what processes, tools, etc. need the most the attention to align the company’s technology with their business strategy. Second, flexibility means efficiently making decisions and executing changes based on your assessment.
Additionally, the CTO must understand they are one of many faces of the company. They represent the company’s tech aptitude to the press, business partners, and listeners at conferences, and should be able to communicate eloquently when speaking on behalf of the company.
CTO Job Description & CTO Role Description Sample
Use this sample CTO Job Description to help you write your own job description for your next CTO.
Chief Technology Officer Jobs London is looking for a highly qualified Chief Technology Officer with an accomplished background in both technology and business. You must determine day-to-day operations of the technology team, delegate roles and responsibilities to meet deadlines, make executive decisions that support the company’s vision, introduce new tech platforms and channels when necessary, and ensure that tech teams and technology systems/infrastructure are in-line with the company’s greater business strategy.
The CTO will be required to function and act as both a business and technology expert. Strong business acumen, an understanding of the latest technology trends and innovations, and a mind for strategic thinking will all be essential to fit this role. CTO benefits will be competitive and comparable to CTO salary in Boston and other major cities.
Chief Technology Officer Responsibilities
- Develop a vision for technologies used in the company that are in line with the company’s business strategy and that drive greater performance at all levels.
- Implement benchmarks to measure progress toward both short and long-term goals, and ensure that the company’s technological resources meet those benchmarks.
- Develop timelines and chart the deployment dates of all technology services.
- Communicate and maintain all regulatory standards for technological practices.
- Oversee system infrastructure in ensuring efficiency and performance across and between all systems.
- Make executive decisions that support the needs of the company and the technological requirements that will help fulfill those needs.
- Advise and mentor team members.
- Monitor and maintain technology budgets.
- Be up to date with tech trends and the newest innovations relevant to the company’s goals and competitor actions.
- Ensure that all departments understand how to use technologies correctly, efficiently, and in a way that maximizes usage and profitability.
- Use feedback from stakeholders in making necessary technological improvements and adjustments.
- Appropriately represent the company’s public image as an executive when speaking on behalf of the company.
CTO Job Spec
- Bachelor’s degree in Engineering, Computer Science, or related field; Master’s degree or MBA.
- Proven and extensive experience in technology, leadership, and business management roles; more than 5 years VP or C-Level experience recommended.
- Must be able to demonstrate advanced technological skills.
- Must have excellent team management skills.
- Excellent communication skills; written and verbal skills required.
- Must be flexible and aware of what duties need the most attention to meet company goals at any given point.
- Must not only have industry knowledge but an extensive understanding of the future of the industry and which technologies will be a part of that future.
This job description is a great starting point for your company’s CTO job ad, but don’t forget to customize it so that it reflects your company’s or your client company’s culture and mission. This way, you can attract a CTO who is engaged with your job description, not someone who just wants a high paying job.
For recruiters searching for great CTO talent, Loxo is an all-in-one executive recruiting software platform that uses AI to source technology executives and automatically gathers their contact info in our CRM + ATS. This way, you can spend your time building relationships with great CTOs instead of scouring the internet for their contact info.
To see how Loxo can put you in touch with more technology executives, schedule a demo here. | https://loxo.co/blog/job-description-cto/ |
The Data analyst will be involved in providing ad hoc analysis, insights, and building and maintaining machine learning solutions. Should have ability to use different analytics tools and platforms like SAS, SQL, Python, R. etc.
Data analyst with basic proficiency in statistical analysis, data mining, machine learning and working with large scale datasets
Requirements:
- B.S. or Masters or equivalent degree in Statistics, Analytics, Applied Mathematics, Operation Research, or equivalent quantitative fields preferred. Strong mathematical and statistics background.
- 0-3 years ( CAN CONSIDER FRESHERS )of experience in industry (ideally ecommerce, technology, consumer banking, telecoms, retail) and/or academia with demonstrated track record of innovative research and insight generation and implementation of insights into tools/processes delivering front end business results.
- Should have a basic understanding of using data mining, machine learning techniques and recommendation Engines on large amount of data, building and implementing various statistical models.
- Good written and oral communication skills.
Key skill sets required
Statistical Programming Tool Skills : Programming experience in SAS (Base, Stats, Macro, EG, EM), R, Python, Spark or other statistical programing software.
Platform and Database skills : Familiarity with Hadoop, Hive, and Pig. Proficient in using databases like Teradata, Oracle, SQL Server, Neo4J etc.. | https://www.experdex.io/jobs/data-analyst/ |
New Delhi: Within 20 days, Haryana’s para javelin thrower Sumit Antil has broken the world record twice in the F-64 category.
On Friday, in his sixth and last attempt he hurled the javelin to a distance of 66.90 metres at the 19th Para-Athletics Championships at Bengaluru’s Vidyanagar Stadium.
The effort bettered his own world record of 66.43 metres, set during the third leg of the Indian Grand Prix on March 5 in Patiala.
By virtue of winning a silver medal at the 2019 World Para-Athletics, Antil became eligible to compete at the Tokyo Paralympic Games.
As per policy of the world governing body, the International Paralympic Committee (IPC), the top four athletes in each of the events at the World Para-Athletics were allotted Tokyo Paralympics berths.
But the final selection for the Tokyo Paralympic will be conducted by the Paralympic Committee of India (PCI) three months before the main competition in Japan.
Antil’s goal has been to consistently stay in the 66-plus metres zone in the competition. “Good performance will add to my confidence,” he said.
Earlier, in the first week of March he had competed with India’s top javelin throwers, including Asian Games champion and national record holder Neeraj Chopra, and recorded a throw of 66.43m to break the previous record of 66.18m set by India’s para-javelin thrower Sandeep Chaudhary at 2019 World Para Athletics Championship.
Sandeep Chaudhary, former world record holder finished second with a throw of 60.90m. | https://sportslounge.co.in/para-javelin-thrower-antil-breaks-own-world-record/ |
I love carrot cake, and I’ve quickly learned that it’s actually a very popular cake flavor. How did I learn that? Well, a lot of people have been asking for carrot cake lately!!
Since I’ve been making it so much, I decided to add a twist this time– cheesecake!
There’s a thick layer of carrot cake, topped with a layer of cheesecake.
and then…
frosted with creeeeeamy cream cheese frosting!
I made regular sized cupcakes as well as minis. I find the minis very popular; the perfect size when you just want a little something sweet! And/or you can eat more than 1 🙂
The carrot cake recipe, which I’ve made many times, is amazingly moist; the cheesecake is smooth and heavenly; and the frosting is finger-licking fantastic.
Make these. You’ll like ’em.
Carrot Cake Cheesecake Cupcakes!
Made 20 regular-sized cupcakes + 48 minis.
Ingredients:
For Cake:
2 cups all-purpose flour
2 tsp baking powder
2 tsp baking soda
1/2 tsp salt
3 tsp cinnamon
1/2 tsp nutmeg
4 eggs
3/4 cup vegetable oil
3/4 cup applesauce
1 cup granulated sugar
1 cup light brown sugar
2 tsp vanilla
3 cups baby carrots, cooked and mashed (measure raw, then cook them)
For Cheesecake:
2 8-oz blocks of cream cheese, room temperature
1/2 cup sugar
1 tsp vanilla
2 eggs
For Frosting:
2 8 oz cream cheese
2 stick butter
7 cups powdered sugar
1 Tablespoon vanilla
Directions:
1) Preheat the oven to 375 degrees. Line cupcakes pans with foil liners (should make about 30-35 regular-sized cupcakes).
2) Carrot Cake: In a medium-sized bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Set aside.
3) In a large bowl, whisk together the applesauce, oil, and sugars. Add in the eggs and vanilla and beat well. Then, switch to a spatula and alternate folding in the flour mixture and the mashed carrots. (NOTE: I usually cook the carrots– steam them– and then put them in a blender to basically make carrot baby food. Allow them to cool before mixing them into the batter.)
4) Mix just until flour streaks no longer remain. Now, make the cheesecake part!
5) Cheesecake: Beat together the cream cheese, 1/2 cup sugar, 2 eggs, and 1 tsp vanilla. Now you’re ready to assemble the cupcakes for baking.
6) Scoop about 1/2 cup of carrot cake batter into each cupcake cavity, filling until 1/2-2/3 full. Then top with 2 big tablespoons-full of the cheesecake batter. Honestly, next time, I’ll probably make more cheesecake and put more in each cupcake. It’s just so tasty!
7) Bake the cupcakes in the preheated oven about 20 minutes, or until the cheesecake topping is juuuust starting to turn golden brown on the edges, and a toothpick inserted into the center comes out not-gooey. (It won’t necessarily be clean because it’s a very moist cake! But shouldn’t be totally gooey)
8) Cool the cupcakes on a wire baking rack until completely cooled. Then frost with cream cheese frosting!
9) Frosting: Beat together the cream cheese and butter. Add in the powdered sugar and vanilla. Beat until fully combined and creamy.
10) Spread on top of the cake! Eat! | https://thefetchingfoodie.com/carrot-cake-cheesecake-cupcakes/ |
Today is the 50th anniversary of Title IX. The importance and impact of this law cannot be understated, and while Title IX has a long way to go, I believe that the experience of students (especially feminine students) in school today is incomparable to that of 1972.
Bernice Sandler is one of my biggest feminist inspirations, a woman whose name is hidden in far too much obscurity relative to her impact on the United States. Sandler, often known as the “godmother” of Title IX, worked diligently to pass Title IX. She herself had experienced hiring discrimination in higher education for simply having children, and her lobbying efforts would result in one of the largest education overhauls in the history of gender equity.
All the way up until the early 1970s, the words “sexual harassment” or “gender discrimination” were not used, for sexual harassment and gender discrimination were both considered commonplace in far too many instances. As an 18-year-old student, I think of all the sexual harassment I’ve experienced and witnessed in education, knowing that it is only a fraction of what likely occurred for years. When Title IX was passed by Congress and subsequently signed into law by President Nixon, there wasn’t even much ‘buzz’ about it in the news.
No one—as Bernice Sandler herself admitted—knew that Title IX would become a gender equity giant in fighting all kinds of gender discrimination.
In the years following the passage of Title IX, women’s sports teams began to receive funding proportionate to that of men’s teams. Title IX had become a legal giant in the sports arena, and women were leading the charge. When people hear “Title IX,” however, I fear it is far too often in an athletic context, but it is so much more than that.
Title IX is also known for its role in sexual assault on college campuses, with lawsuits across different colleges occurring across the country due to a cover-up of a sexual assault incident or failure to adequately support a survivor. There are two key cases to know here: Gebser v. Lago Vista Independent School District, which established liability for institutions that failed to adequately respond to teacher-student sexual harassment, and Davis v. Monroe County Board of Education, which established the same liability for student-student sexual harassment. Both of these cases have been instrumental in building the legal framework for Title IX to support sexual harassment survivors.
Feminists and education experts alike have been concerned about the impact of Betsy DeVos’s (Former Department of Education secretary under President Trump) restrictions put on Title IX guidelines. In these changes, survivors had fewer rights under Title IX, Transgender students were denied coverage under Title IX, and more rights were awarded to those accused of sexual harassment/assault. These guidelines were destructive to the rights of students, and we are overjoyed to see them revised in the Biden administration’s new proposed guidelines, announced today—on the 50th anniversary of Title IX.
But lacking in these regulations was something glaringly obvious to those of us here at the Ruth Project: dress codes. Title IX has increasingly, through the work of many of our initiatives, been utilized in cases of sexist dress codes. We’ve argued Title IX discrimination to school boards, district attorneys, and school officials all over the country in regards to dress codes that discriminate on the basis of sex. To truly begin an overhaul of dress codes that discriminate against LGBTQIA+ and feminine students, we need Title IX guidelines that make clear what a dress code can and cannot do under Title IX.
Just last year, in August 2021, a federal judge declared that Title IX applies to school dress codes in Peltier v. Charter Day School. The dress code at Charter Day School forced girls to wear skirts, in a particularly discriminatory use of a uniform policy. This dress code policy is deeply inequitable and pushes feminine students into archaic gender stereotypes that are harmful. Recently, a federal judge ruled that the very same dress code that forced girls to wear skirts also violated the Equal Protection Clause, and we hope that the coming additions to the case will also find it in violation of Title IX.
It is necessary that the Department of Education include dress codes in Title IX guidelines. For far too long, Title IX has been ignored in K-12 schools, and excluding dress codes from Title IX guidelines only continues this issue. Students deserve far better than for Title IX to abandon them when they are being pulled out of class for exposed cleavage or shoulders. We must act, and today on the 50th anniversary of Title IX, we are setting our eyes forward to ensure that younger students are never left behind by Title IX. | https://ruthproj.org/blog/title-ix-turns-50-today-50-steps-towards-equity/ |
Jeruzalemska 2,
Prague
110 00
No one has favorited this theater yet
Housed in an Art Deco style building in the city centre. Opened at the end of May 2019, the Edison Filmhub is a modern art-house cinema with a cafe bar. Seating is provided for 75, but can be expanded to 90 with additional seats. It offers screenings of premier titles, reruns of European art-house films and also special film introductions and debates. The films are carefully selected. The main focus of programming is influenced by the awarded films from the largest film festivals - Berlin, Venice, Cannes - Be2Can. There is also a yearly festival of Scandinavian cinema - Scandi - besides other events - Movie Barf Monday or Mental Hygien of Ales Stuchly. The programme includes at least one English friendly screening per day.
Edison Filmhub is the space where film professionals and enthusiasts can meet. Also it is a place to just relax over a drink or cup of speciality coffee where you can immerse yourself in the middle of the city bustle. | http://cinematreasures.org/theaters/61930 |
CMCG worked with a provider of healthcare services for children to update and streamline the hospital network Code White (Winter Weather) protocols. Serving a major metropolitan area with over 20 neighborhood locations, including five Urgent Care Centers, it was critical for the client to establish deployment for nursing a physician staffing ahead of inclement weather while keeping personnel safe. Our team assisted the client to incorporate NOAA’s winter weather reporting into the existing decision-making structure, updated the Code White protocols, brief hospital executives and trained staff responsible for implementing the Code White across the network.
Radiological Training and Workshops
CMCG assisted several hospitals in the State of New York develop procedures to receive, process and treat patients potentially contaminated by radioactive materials. Our team also trained hospital staff on the new protocols.
CMCG aided a major healthcare provider in Grand Rapids, Michigan with the development and conduct of a pandemic influenza and medical surge workshop (including a tabletop exercise and emergency medical services dispatcher drill). The goal of the workshop was to validate tools developed by the client under a CDC public health demonstration project for the provision of essential services during an influenza pandemic in Michigan Health Region 6. CMCG developed all workshop materials, facilitated the sessions, provided recorders to capture minutes and lessons learned; and assisted in assembling workshop documentation.
Spectrum Health
For Spectrum Health System and a regional emergency medical coordinating agency, CMCG developed and conducted a pandemic tabletop exercise as well as multiple functional exercises to validate mass casualty response capabilities.
Research Facilities
Our team has developed emergency procedures for animal research laboratories for several clients conducting research on small mammals and primates. We are very familiar with the Association for Assessment and Accreditation of Laboratory Animal Care (AAALAC) International and Public Health Service (PHS) guidelines in the area of emergency response planning for animal laboratories. We have trained Institutional Animal Care and Use Committees (IACUC) in their roles and responsibilities under response plans. Most recently, CMCG created a response plan for a state-of-the-art Vivarium. Our consultants understand the interconnection between the vivarium operations and a client’s overarching crisis, emergency and business continuity strategy. We also are all-hazards experts enabling us to document risks for external first responders, such as local fire and police departments. | http://cmcgllc.com/our-services/energy-oil-and-gas-telecommunications-crisis-emergency-hazmat-planning/healthcare/ |
Daniel Stein is President of the Stewards of Change Institute (SOCI), a unique not-for-profit think tank and advocacy/implementation organization. He is also Co-Principal Investigator for the National Interoperability Collaborative (NIC), a new “Community of Networks” initiative led by SOCI and AcademyHealth. SOCI is built on the foundational belief that responsible, systemic information-sharing is the key to achieving enduring advancements in the health and wellness of children, adults and communities. SOCI’s mission is to improve lives by initiating, inspiring and implementing transformational change in Health and Human Services at all levels of government, industry and the nonprofit sector. For over a decade, Stein has been a thought-leader, educator and advocate in promoting and implementing “interoperability” by working nationally in the private and public sectors – at the local, state and federal levels – to instigate systemic change. Through the Stewards of Change Consultancy, which is the implementation arm of SOCI, Stein also has provided his expertise and experience nationally to create the strategies, operational regimes, tools, trainings and materials needed to achieve tangible results and fulfill the Institute’s mission. | http://stewardsofchange.org/author/daniel-stein/ |
JOIN ISACS AT CORK MIDSUMMER FESTIVAL!
2017/06/17
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Join the Irish Street Arts, Circus & Spectacle Network for an afternoon discussion about collaboration & the rise of interdisciplinary arts.
Hear from a range of artists, practitioners and projects which have specialized in emerging art forms in new and unusual ways; uncovering new styles, new techniques, new circus, new theater, new stories and new ways of telling them, merging the old and the new, the traditional with the contemporary, the audience and the performer, the digital and the physical, the inside with the outside.
"Blurring the lines", Saturday 17th June from 2 to 4pm, at Circus Factory, Cork (IE), in association with the Circus Factory Cork and Cork Midsummer Festival. | https://www.circostrada.org/en/news/join-isacs-cork-midsummer-festival |
Regarding inoculation, Dr Hopkins said the vaccine produces a "strong immune response and it's broad and acts against lots of variation in the virus", adding that there is "no evidence at the moment that the vaccine will not work".
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How contagious is the new variant?
Mr Hancock said: "This new variant is highly concerning because it is yet more transmissible and it appears to have mutated further than the new variant that has been discovered in the UK."
The new strain is "shortly to be analysed at Porton Down", the health secretary added.
There are immediate restrictions on travelling from South Africa. Sky News understands incoming flights from the country will be stopped.
In addition, people who have been in contact with anyone who has been in South Africa in the last fortnight have been told they must quarantine.
Mr Hancock said ministers are "incredibly grateful to the South African government for the rigour of their science and the openness and the transparency with which they have rightly acted as we did when we discovered a new variant here".
Analysis: South African variant 'seems to have a higher viral load'
Thomas Moore, science correspondent
The new South African strain of the virus is a significant worry and the government has moved swiftly to shut it down.
Health authorities in the country believe the 501.V2 variant is more common in younger adults.
It also seems to have a higher viral load and as a result spreads more easily from person to person.
It's thought it could partly explain the recent surge of infections in South Africa.
Genetic analysis shows that it shares some of the mutations of the new strain already widespread in the UK, but the two viruses have evolved separately.
The health secretary has ordered anyone who has been to South Africa, or been in contact with someone who has, in the last two weeks to self-isolate immediately.
Once again the rapid genetic analysis of strains in the UK has picked up a mutant virus at an early stage - but has it been soon enough? | |
You’re seeing ladybugs (Coccinellidae) everywhere and you’re curious about them? When you just take a look at ladybug it makes you smile and at the moment wakes up child in you. Did you ever ask yourself does seeing these magnificent beings have some deeper meaning? Do you know what does it mean when you see a ladybug?
Ladybugs are considered a symbol of good luck and happiness. When you see a ladybug it could be a sign of change and an announcement of good fortune and true love. This magical creature is a messenger and bearer of the best news and gives blessing to those that see it.
This article will help you to better understand the spiritual meanings of ladybugs. Together we’re going to find out what does it mean when you see a ladybug in most common cases. You’ve been in some of these situations and surely asked yourself about its significance. Let’s see!
Contents
- 1 What does it mean when a ladybug lands on you?
- 2 What does it mean to find a dead ladybug?
- 3 What do ladybugs symbolize in dreams?
- 4 Do ladybugs have a spiritual meaning?
- 5 What is ladybug spiritual meaning?
- 6 Ladybug spots symbolism
- 7 Orange ladybug spiritual meaning
- 8 Yellow ladybug spiritual meaning
- 9 What do ladybugs symbolize in Christianity?
- 10 Do ladybugs symbolize pregnancy?
- 11 Conclusion
Too much to read? Watch the “What does it mean when you see a ladybug?” video instead
What does it mean when a ladybug lands on you?
Every time a ladybug would land on me, I felt special for a brief moment, almost like it was a stroke of good luck. It’s believed when a ladybug gets down on you, you’re going to gain some luck and your wish will come true. Also, very important is to count the spots before it goes.
These are the number of years or months that you will have to wait until the wish is fulfilled. Some people believe that ladybug land on a person announces that it will bring him good fortune and more spots mean a bigger sum of money.
Very special is the belief that an ill person will be healed when a ladybug lands on the patient. That belief was so strong in the past that doctors in the 1800s used this insect to cure measles.
If a newly married woman spots a ladybug on her that announces future pregnancy. And guess what? The number of spots means the number of children she’ll have.
Other recourses indicate that those spots represent the happy months that the relationship will have.
What does it mean when a ladybug is in your house?
Probably you’re at least once found a ladybug in your home. Don’t worry it’s a sign of good luck. Great things are going to happen to you. Also, there is a belief that it signals the coming of a newborn baby. That’s why the most common toys for newborns are ladybugs.
What does it mean to find a dead ladybug?
Seeing a dead ladybug doesn’t necessarily mean the absence of positive vibes that ladybugs usually bring. Spirit animals from time to time show up in unusual forms in our lives. They equally give us their blessing, whether they show up in our lives alive, dead, or even in dreams.
It is important to listen to your feelings when encountering this extraordinary spirit animal. What is your first reaction? Are you overwhelmed with a sense of joy and light or your main feeling is sadness and fear?
Seeing a ladybug could be like a mirror of what’s happening in your life. Your feeling would tell you to think about some questions. Maybe you’ve been experiencing a lot of pressure lately?
When you across the ladybug that’s already dead then there is no special meaning, it could represent simply a circle of life. But, if you kill a ladybug you are invoking a period of bad luck for nine days.
You need to know that ladybug, no matter in what shape appears always brings positive change and good luck.
What do ladybugs symbolize in dreams?
Dreaming ladybugs can have many different meanings. When a ladybug appears in your dream it could be a signal of good or bad news, often from a source least expected. Often ladybug in dreams announces good news, a pleasant change, an awakening, and the end of isolation.
Sometimes, ladybug sightings in dreams can also indicate problem areas, and some believe that the size of the ladybug can be an indication of the size of the problem. Often the symbolism of certain things in life has the direct opposite meaning in the dream world.
There is a belief that when a ladybug is flying away it’s a sign that you’ve let your dream go and if this extraordinary insect is flying towards you it indicates that better times are yet to come for you and you should not miss opportunities.
And if you are dreaming of a ladybug that’s rising high in the sky your dream promises you the opening of your horizon.
Seeing a lot of Ladybugs in a dream can point out that things are somewhat out of control and that a lot of small things are going wrong. So you can see it as advice to take one step at a time to feel more in control of your life and your work.
It’s not rare to see monstrous ladybugs in dreams. Your spirit animal advises you through nightmares to open your eyes, be brave, and struggle with your problems.
Do ladybugs have a spiritual meaning?
Ladybugs are animals with deep spiritual meaning. Depending on where you see a ladybug and the context that you see it in, there could be different meanings for your ladybug sighting. This article will help you to better understand its meaning.
What is ladybug spiritual meaning?
This extraordinary insect, which flies high, we can behold as a bridge between the earthly and celestial energies. There is a belief that the ladybugs, just like birds have a strong association with the divine.
Depending on the situation we see ladybugs there is a lot of different spiritual meanings. However, their deeper meaning often relates to inner peace, security, happiness, and good health. Also, colors red and black are associated with the root chakra, which is the energy that a ladybug represents.
It’s believed that one of the main meanings of ladybug is change, even metamorphosis. Insects from the beetle family, where ladybug belongs, evolve from an ugly larva to a beautiful, colorful creature. This transformation is something that’s not an ‘overnight’ change, it lasts and needs time.
This can be a reminder that all changes are going slow and gradually, so patience is the key thing. If this spirit animal visits you keep in mind that it means you are in a process of transformation and you need to stay determined and focused on your goals.
Ladybug spots symbolism
The number of spots on ladybugs is very important, so take note of the spots and their level of darkness. It’s believed that the darker color of the spots means greater fortune for you.
Numerology is a science that can help us to understand the meaning of the spots. The spots may tell us a lot about the ladybug’s symbolic meaning. If you see one spot on ladybug it represents union, just like two spots mean duality.
Three dots can mark transcending opposites and if you notice four spots on its wings it has a symbolic meaning of cardinal directions, elements. Number five means center, six gives love and perfection, seven, this magical number gives the symbolic meaning of eternal life.
The most beautiful belief is that seeing the spots on the Ladybug is a reminder the Universe is telling you it’s time to count the blessing you already have around you. Take a moment and think of as many ways you are blessed as the number of spots on the Ladybug. It’s good to be aware of the beautiful things we already have in life.
For young married couples ladybug’s spots can predict the number of babies they’ll have. Also, spots can indicate how many months a new couple would spend in happiness. So if you are a young spouse count carefully, you can find out valuable info.
Orange ladybug spiritual meaning
Depending on what color is ladybug there could be different meanings for your ladybug observing. For example, an orange ladybug represents creativity and innovative expression.
If you encounter an orange ladybug, it is a sign that your imagination will bring you prosperity in the future. You have individuality and inspiration that you should use more often.
Yellow ladybug spiritual meaning
There is a belief that yellow ladybugs carry a lot of masculine energy and you are on your way to take action on your plans. In case you are having a project that’s slipping out of your hands, this is an ideal time to move forward with it.
Don’t forget if you see a yellow ladybug, it means adventure, new love, or a new chapter in your life!
What do ladybugs symbolize in Christianity?
In ancient times, times before Christianity, the ladybug had other meanings concerning a multitude of deities. However, during the time ancient beliefs morphed into Christianity and since then in even more modern themes.
The most known story is a legend of two farmers, during the middle ages, whose crops were blighted with aphids. Farmers prayed to the Virgin Mary to save their crops from aphids. Then, one day the Virgin Mary sent a miracle.
You’re guessing well! She sent them a horde of Ladybugs who proceeded to feast on all the aphids. The crop was saved, the farmers shared their tale and the ladybug name was forever linked with the name of ‘The Beetle of Our Lady’.
Do ladybugs symbolize pregnancy?
Seeing a ladybug is definitely a sign that a new baby is on its way! This rule especially applies to encounter with a brown ladybug. It is a sign of fertility and possible pregnancy.
It represents a special connection between mother and child so if you have issues with your mother, this may be a good time to reach out and to resolve any hurt from the past.
Conclusion
Through this article, we’ve learned what does it mean when you see a ladybug. Now we know that seeing a ladybug is a small but powerful dose of optimism you need in an everyday struggle. It sends us a message to believe in ourselves and good luck. It’s a call for you to open your wings. Don’t be afraid to expose yourself to others.
Write to us about your ladybug experiences and don’t be afraid to make questions. We’ll provide you with additional info. | https://aboutspiritual.com/what-does-it-mean-when-you-see-a-ladybug/ |
I have been re-reading “Finality, Love, and Marriage” written by Lonergan in 1943. It is quite an interesting piece once you explore the details and interconnections of the work. Given the upcoming Synod of the Family in Rome, I would like to begin exploring what Lonergan might contribute to a deeper understanding of family life. Just to get started here are a few of the terms in the piece that I would like to begin commenting upon though not necessarily in the order given,
- fecundity,
- semi-fecundity,
- the passive aspect of love,
- the immanent aspect of love,
- the active aspect of love,
- natural law,
- statistics,
- concrete plurality,
- horizontal and vertical finality,
- hierarchy,
- organistic spontaneity,
- friendship,
- charity,
- projection,
- transference,
- the three ends of life,
- three levels of life,
- grace,
- reason,
- sexual differentiation.
I will start with fecundity since it is crucial for developing a “viewpoint of marriage.” More specifically, I would like to start with the horizontal finality of fecundity to adult offspring at the organistic level and its differentiation into two sexes, what Lonergan symbolizes as; Z–> Z’ –> Z”.
…. As far as human operation is concerned, [fecundity] is primarily on the level of nature, and its ultimate term is the repetitive emergence of adult offspring. but sex is more complex. Not only is it not a substance but it is not even an accidental potency as intellect or sense. Rather, it is a bias and orientation in a large number of potencies, a typical and complementary differentiation within the species, with a material basis in the difference in the number of chromosomes, with a regulator in the secretions of the endocrinal glands, with manifestations not only in anatomical structure and physiological function but also in the totality of vital, psychic, sensitive, emotional characters and consequently, though not formally, in the higher nonorganic activities of reason and rational appetite. But for all its complexity sex remains on the level of spontaneous nature, and there, clearly, one may easily recognize that in all its aspects it definitely, if not exclusively, has a role in the process from fecundity to adult offspring. For elementally sex is a difference added to fecundity, dividing it into two complementary semi-fecundities.
Fecundity is the real capacity to generate a new central potency-form-act of the same species. And because fecundity involves activation of the fecundity to effect the emergence of a new thing of the same species, and that new emergence has to undergo development from an indeterminate but directed dynamism to a determinate mature adult offspring, the fecundity has a horizontal finality to adult offspring. And in human beings, like all higher level organic creatures, this fecundity is differentiated into two semi-fecundities or “sexes” which then need to come together in “organistic union” in order to activate the realization of fecundity.
In all organisms that have sexual differentiation, the differentiation involves the creation of complementary gametes that then need to be united to form some kind of a seedling or egg, and then this seedling or egg needs to develop into a mature adult. Thus, there are a number of steps along the way by which fecundity is both real and then by which it is realized. It is real if it has formed gametes and there exists a way for the unification of those gametes and this unification can then grow into an adult offspring. In plants, sexual reproduction involves the formation of pollen and ovules. It is quite a beautiful process to learn about. Fecundity is partially realized once these gametes are united. In plants, these gametes can be united in a variety of ways, through the wind for example (grasses) or through water currents (seaweed) or through animal vectors (bees). As well, the “parents” might help to facilitate that unity, such as do the stigma and style in plants. Following the formation of the seed, it then needs to be formed until it is ready to be released. And the release of the seed may make use of wind or animals for dispersal. Think of the exciting helicopter seeds that float down from maple trees or the pine cones that fall from pine trees. Once that seed is “planted” and then grows and differentiate into a mature adult, fecundity has been fully realized. With animals, the process is improved and differentiated because of motor-sensory operations. The chaos of the wind and water is reduced by the motor-sensory union that takes place through mating schemes that involve “attraction and locomotion” as Lonergan noted in order to enhance the effectiveness of reproduction and thus reducing the amounts of bio-energy needed while increasing the collaborative unity between the parents that works toward the successful generation of adult offspring. After mating, in the simple animals, the formation of the egg is usually the end of the parent’s role. The process of development is short, and a simple egg is sufficient to provide the “womb” needed for maturity (many fish leave the eggs hidden in the rocks). But in more differentiated organisms, the development following the formation of the egg is more complex just as it was with the union of the parents in mating schemes or ritual. And so more help is needed. A simple unattended egg is not sufficient. Parents may need to be present not only to protect the egg (or warm it if they are warm blooded) but to be presented after being hatched in order to feed and, in higher animals (including birds), train their young in basic skills. In general, as one moves to higher and more differentiated organisms, one has to introduce more elaborate schemes for the unfolding of fecundity to adult progeny, from mating rituals to raising the young.
|Stage||Simple organisms – single celled||Plants||Simple animals||More differentiated animals|
|Pre-conception interactions||Not really relevant.||May grow flowers to help attract carriers but no interaction of parents.||Simple mating rituals with little to no connection formed between the parents.||More elaborate mating rituals that involve a more vibrant union of the parents.|
|Post-conception interactions||Not really relevant.||None.||Very little if any post-conception protection or care.||More elaborate post-conception protection and care with a differentiation of parental roles and tasks.|
In short, the more developed the organism, the more elaborate the process from fecundity to adult offspring, and the more differentiated the roles of the parents in mediating that movement from its beginnings to its end. A rich and differentiated fecundity sets up different roles and tasks in the parents who produced the complementary gametes. And as one thinks about it for a minute, Lonergan could not be more right in saying that with sex (as in gender–a semifecundity–not the act) “one may easily recognize that in all its (gender sex) aspects it definitely, if not exclusively, has a role in the process from fecundity to adult offspring.”
My next commentary will be one week from now, Thursday, May 28,2015.
Bernard Lonergan, Collected Works of Bernard Lonergan, volume 4, Collection, University of Toronto Press, 1988, 17 – 52.
Finality, Love, Marriage, 42.
Finality, Love, Marriage, 41.
Finality, Love, Marriage 42.
Central potency, form, and act are the metaphysical formulation of the notion of a thing (a unity, identity, whole). Lonergan argues as well that this notion is one of the most development and principle meanings of substance. See Insight: A Study of Human Understanding, chapter 8 and chapter 15, sections 1 – 2.
. | http://lonergan.org/2015/05/21/finality-love-and-marriage-fecundity/ |
- This event has passed.
Lunch & Learn: Conservation Blueprint in Action
March 15, 2018 @ 12:30 pm - 1:30 pm
Bring your lunch and get to know your local Land Trust! We will be featuring a variety of speakers and topics on the 3rd Thursday of the month from 12:30-1:30 pm. Free and open to the public, 1528 Chapala Street, 3rd Floor Conference Room. Contact the office to reserve your seat as space is limited: (805) 966-4520 or [email protected].
Join Dustin Pearce of Conservation Biology Institute for the first public opportunity to see the Conservation Blueprint in action.
More About the Conservation Blueprint
With increasing pressure to accommodate population growth on open space and agricultural lands, along with the new realities of climate change, it is critical to develop a collective vision for the future of our community’s landscapes, and tools and strategies for how to move toward that vision.
After nearly two years of research and public data collection guided by a Steering Committee representing agriculture, conservation, resource management and natural science, the Santa Barbara County Conservation Blueprint and Atlas are available as a resource for everyone to learn more about the region’s land and natural resources and gain a common understanding about what is needed to create a landscape of opportunity for generations to come.
Together, the Blueprint report and online Atlas offer a first step toward a common understanding of Santa Barbara County’s
current environmental conditions, the impacts of human interaction with the land, and the conscious tradeoffs required
to create a landscape of opportunity for generations to come. | https://www.sblandtrust.org/event/lunch-learn-conservation-blueprint/ |
Text description provided by the architects. In a new integrated child centre in Leeuwarden, primary school Prins Constantijn and children’s daycare centre Sinne come together under one roof. The project consists of adapting and expanding an existing school building to meet contemporary requirements, fit to house over 200 children throughout the day. Blending existing physical qualities with progressive pedagogical principles, the new building is organised around a number of learning clusters, with spaces for cooperation, play, concentration, and peace.
A clear differentiation has been made between fixed and flexible structural and mechanical components, making the building easily adaptable. Due to the ever-changing nature of education, this level of flexibility is key in future proofing the school in a sustainable manner.
Concrete bands mark the volume's edges and openings, with daylight falling deep into the building through its atrium and a palette of natural woods and hand-formed masonry used throughout. The design of the façades uses the historic building from 1929 as a springboard for a new tectonic language that seeks to form a complementary relation, rather than a contrasting one, between old and new. The renewal of this locally important building looks to establish the new children’s centre at the heart of its local community. | |
Nonprofit organizations — broadly described — operate to achieve missions that serve the common good. A grad degree in nonprofit management focuses on the development of leadership skills for nonprofit managers and provides education in areas such as general operations, human resources, strategies, and fund development.
Students of nonprofit management also develop proficiency in other matters such as nonprofit legal issues, organizational development, donor relations, financial management and fundraising, volunteer and human resource management, and program evaluation, to name a few competencies. Many nonprofit management programs have a theoretical component, and most programs also rely on experiential learning as a vital element of a graduate student’s education.
Why a graduate degree in nonprofit management?
With a plethora of graduate disciplines available to you—business administration with a nonprofit management specialization, public administration/affairs, even international affairs if you want to work internationally—you may be wondering, why should I go for a specialized degree in nonprofit management?
When you enroll in a specialized degree in nonprofit management you gain the skills and knowledge specific to and necessary for leadership in this growing and dynamic sector. The sheer diversity of nonprofit organizations and the issues they work on means that nonprofits require leaders with a thorough understanding of the complex nonprofit landscape.
Furthermore, your classmates will be very likely to share your interest in and knowledge of nonprofits. Your studies will emphasize nonprofit concerns as a default (whereas most business administration programs emphasize for-profit business, and public administration programs emphasize government administration).
As Rebecca Zirm, Director of Recruitment for Case Western Reserve University’s Mandel Center for Nonprofit Organizations, shares, “Unlike an MBA with a concentration in nonprofit management, every course you take in our program deals with nonprofit theory and practice and all of the work that the students do, whether papers, projects, or the strategic plan that is developed in our year-long strategic planning course, involve nonprofit organizations.
Students who want to study nonprofit management at an advanced level may choose from a great variety of program designs and offerings.
Several universities offer a specialized graduate degree in nonprofit management, each with its own unique title and most of which are master level courses. Because of the relative newness of this field, there are very few dedicated doctoral level programs. There are also concentrations in nonprofit management offered under other umbrella masters degree programs such as the Master of Business Administration or Master in Public Administration. Several universities that offer graduate degrees also offer certificate programs.
In addition to a variety of program concentrations, universities vary greatly in the formats and timelines for education.
Programs at the University of San Diego, University of San Francisco, and others are almost entirely populated with students who pursue their studies part-time while working full-time in nonprofit organizations. Thus these programs hold their classes in the evenings and weekends to accommodate their professional students and usually operate on a cohort model, where students are grouped together for the duration of the program. More traditional full-time graduate programs are offered at a variety of universities as well.
Nonprofit management graduate degree programs place a strong emphasis on connecting the theoretical with the practical. Experiential learning is usually accomplished through work with real clients in the community for courses or through internships.
Many nonprofit management programs offer their students a lot of flexibility to explore and cultivate intellectual and professional interests within the degree. Students may develop individual concentrations within the degree through elective coursework. If the program is part of a larger grad school, students can often fulfill electives in other departments or schools for an interdisciplinary curriculum.
You may also consider obtaining a dual or joint degree. Some common dual degree options include law and a specialty field such as social work or public health.
In order to complete your degree, nonprofit management graduate degree students may be required to complete a capstone project or thesis. A capstone project is an opportunity for you to apply the education you’ve received throughout the program by addressing a real issue and need in the community. It usually culminates in a written report and presentation. A thesis, on the other hand, is a written paper based on research that you have conducted on a topic relevant to nonprofit management and your area of interest.
Programs may differ with regards to the students that matriculate. Your classmates may be relatively new to or transitioning into the field, with some experience volunteering, working with a nonprofit, or participating in a national service program. The majority, hopefully, will have at least a few years of work experience, whether in the private, public, or nonprofit sectors, and bring varied perspectives and skills to the classroom.
Your faculty will have extensive knowledge of and experience in nonprofits and a variety of issue areas with individual areas of expertise and research interests. Many will also be very active in nonprofit organizations as consultants to, board members of, or even current staff.
Most graduate schools in nonprofit management strongly recommend, and some require, at least two years of management, professional work, or significant volunteer experience in nonprofits before applying to their graduate program. “A graduate program will be more meaningful with work experience, particularly if cases or projects involving actual management situations are used in coursework,” according to Michael Bisesi, Seattle University’s Director of the Center for Nonprofit and Social Enterprise Management.
Participating in a national service program such as AmeriCorps*VISTA or Public Allies, or taking a Peace Corps assignment in a nongovernmental organization (NGO) in a developing country. Full-time service is a good way to develop professional skills while gaining experience in nonprofits.
Sitting on the board of a nonprofit is an opportunity for professionals from the private or public sector to share their expertise with an organization and gain management skills in a nonprofit organization.
Volunteering your skills for special projects is another way to explore nonprofit work, e.g., helping to write a grant if you are a good writer or maintaining a website and its content for a nonprofit.
Others find that their education qualifies them for philanthropic work in the private sector or as consultants to nonprofits. The diversity of career opportunities is limited only by your own goals and interests.
Excellent leadership, interpersonal, problem solving, communication, and organizational skills.
Manage and develop an exceptional local team including the Program Director, and Program Associate, and ensure the team’s growth and success in meeting local goals.
Seek out and create opportunities to engage with the local education community to share the organization’s national and local vision and serve as the primary spokesperson for the organization within the local community in formal and informal settings including networking opportunities, conferences, panels, individual meetings with education stakeholders, etc.
What should I know about admissions?
Admissions staff recommend that prospective graduate students have a distinct vision of career goals before applying to a nonprofit management program. Applications require a personal statement or essay to describe these goals precisely. It is crucial that an applicant prepare essays and application materials meticulously, proving to the review committees that they can follow instructions and express their motivations to attend graduate school. Each program has its own requirements—many of the programs designed for working professionals do not require a graduate admissions test score if the minimum undergraduate GPA and years of work experience are met. More traditional programs for full-time students require either the GMAT or GRE.
Certificate program admissions are usually (but not always) less stringent than for the degree program, and often do not require a graduate admissions test score. Be sure to check with the programs you are interested in for specific instructions.
Universities themselves often offer scholarships and graduate assistantships that help cover the cost of tuition, fees, and expenses. | https://idealistgradschool.org/degree-overview-nonprofit-management/ |
When exporting, specifying the output image in megapixels, it produces bad numbers for width and height.
- Chose 3.84 (to have 2400 x 1600) it is changed to 3.8, results in totally other width/height numbers.
The input field should allow numbers up to 4 digits in precision.
Moreover the resulting image dimensions should be calculated with more precision, then rounded, to avoid unexpected numbers.
It all depends on the exact dimensions (exact aspect ratio) of the image you started with. If I export a Sony A7R Mk III image and resize it to 6 Mpixel, I get 2999 x 2000 pixels. If I export a Canon EOS-1D X image it becomes 2999 x 1999. My other Canon cameras produce the same 2999 x 2000, but if I export a Sony A7R image it becomes 2998 x 2001.
I'm not sure exactly what you're after here, Jozsef. Even simple math runs into precision & rounding issues for numbers that don't divide evenly.
Take a 3:2 ratio image with dimensions of 9000x6000. Making that fit your 6MP definition means you'd have to multiply each dimension by 0.333333. Using the full precision, you'll get your perfect 3000x2000, but reduce the precision by a few decimal places to 0.333 and you'll get 2997x1998.
If you want exact sizes, I think you're better off specifying the dimensions rather than relying on the MP math.
That's what I was thinking. Why go to all that trouble when the easy solution is right in front of you?
The issue is not one of numerical precision. Rather, as Johan said, the 6 MP 2999 x 1999 issue is caused by the aspect ratio of the original image -- some cameras have ratios that are close to but not exactly 3:2.
For example, the Sony A7R III produces images of size 7952 x 5304. These have an aspect ratio of approximately 1.49924585, not 1.5. When you ask LR to export such an image at 6 megapixels, you're asking it to export it at the same aspect ratio as the original (1.49924585). Thus, the exported image is 2999 x 2000, which is the largest size at that aspect ratio that's no larger than 6 MP (*).
Two other cameras with "close" aspect ratios are the the Sony A7R and Pentax K-1 II, which are both 7360 x 4912 (1.49837134).
If you want to export at exactly 3:2 with these cameras, you'll have to first crop the image to that ratio in Develop or Library's Quick Develop. You can't do this in Export, which never changes aspect ratio (crops).
LR appears to use these formulas.
I still maintain that if you're looking for exact dimensions you shouldn't be relying on the MP setting, making the rest of this more academic than anything, but I don't see your explanation panning out.
Try creating a solid color 9000x6000 image (or 6000x4000 or any dimensions with a 1.5 aspect ratio, for that matter) in Photoshop, import that image into Lightroom and then export with the 6.0 MP setting in the Image sizing section and I'll bet you get a 2999x1999 image.
According to your explanation & formulas, it should come out to be exactly 3000x2000, but it doesn't. Even though they all start out with an aspect ratio of 1.5, the exported image is 2999x1999, which is an aspect ratio of 1.50025.
I certainly could be wrong, but it still seems like precision/rounding is coming into play somewhere.
It’s both. Like I said, my Sony A7R gives a 2998*2001 image in case you export as 6MP. That means that you also won’t get a 3000*2000 image if you use that as export setting. You will get an image that is 2000 pixels on the shortest side, so it will be 2998 (or 2997, I didn’t try it) on the longest side. So I think it is both the aspect ratio as well as rounding errors. The Sony A7R will never produce 2000*3000 pixels, unless you crop first. Other cameras could produce 2000*3000 exactly, but a rounding error makes it 1999*2999.
Right Tom, I mistakenly focused just on the cameras whose aspect ratio was not exactly 1.5.
- Some cameras (e.g. the Sony A7R III) have aspect ratios that are close to but not exactly 1.5. Exporting such images will generally (and correclty) yield sizes that don't have ratio 1.5, since the originals don't have that ratio. | https://feedback.photoshop.com/photoshop_family/topics/export-image-sizing-megapixels-isnt-precise-it-produces-weird-image-dimensions |
Department of Chemistry, Sri Krishnadevaraya University, Ananthapuramu-515003 A.P, India.
A simple, accurate, economical, rapid, selective, reverse phase high performance liquid chromatography (RP-HPLC) was developed for simultaneous estimation of Meropenem and Vaborbactam in its tablet dosage form. The separation was carried out using a mobile phase of buffer and acetonitrile in the ratio of 50:50 pumped at a flow rate of 1 ml/min along with 250nm as a UV detection wavelength. The stationary phase used was column Kromasil 250 x 4.6 mm, 5m. Meropenem and Vaborbactam were eluted at a retention time of Meropenem 2.47min and Vaborbactam 3.31 min. The method was developed and validated as per ICH guidelines by considering the parameters such as precision, accuracy, linearity, specificity, robustness and degradation studies. The developed RP-HPLC method can be used for routine analysis of Meropenem and Vaborbactam in combinational dosage form.
RP-HPLC method development, Validation, Meropenem, Vaborbactam.
B. Balaswami, P. Venkata Ramana, B. Subba Rao, P. Sanjeeva. A New Simple RP – HPLC Method for Simultaneous Estimation of Meropenem and Vaborbactam in Tablet Dosage Form. Asian J. Research Chem. 2018; 11(1):111-116. | http://ajrconline.org/AbstractView.aspx?PID=2018-11-1-23 |
As the next At-Large Councilmember, I will do everything possible to make DC the safest and most inclusive city in the nation. I will address the structural inequities that impact our systematically marginalized neighbors.
I would prioritize the following actions to protect our systematically marginalized communities:
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Identify funding, and prioritize the development of communities that provide permanent supportive housing for LGBTQIA+ individuals, with a unique focus on the needs of seniors and youth.
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Ensure that the Office of Human Rights is both funded and statutorily authorized to affirmatively pursue suspected instances of systematic discrimination.
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Provide administrative cost-sharing tools and reduce overhead costs to enable LGBTQIA+-serving nonprofits to spend a larger portion of their grant funding on full-time staff salaries instead of overhead.
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Improve oversight of the DC Jail and the treatment of LGBTQIA+ incarcerated members and more aggressively monitor the performance of programs that exist to provide reentry services.
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Expand workforce and entrepreneurial opportunities for LGBTQIA+ youth and adults.
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Expand free and low-cost HIV/AIDS health prevention and protection.
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Authorize multi-year performance-based contracts to provide funding stability for high-performing community partners who provide services to vulnerable communities so they can predictably mobilize, serve, and expand to cover more service areas. | https://www.marshallfordc.com/lgbtqia-plus-rights |
Child Care Center, Inc.
At Child Care Center, Inc. we believe that infants, toddlers and young children need a safe, comfortable, and developmentally appropriate environment. This would include positive teacher/child interactions, developing peer relationships, emotional, social and cognitive development and meeting the individual curriculum needs of each child.
Children need a comfortable place to grow and learn. We provide a nurturing home-like environment that stimulates each child’s interests to help them grow and develop to their fullest potential.
Our comfortable environment includes a mixture of hard and soft textures and materials (soft pillows and chairs, tumbling mats, dress-up clothes and blankets, hard chairs, tables, and trucks.) We provide a mixture of open spaces (playroom and playground) and closed spaces (quiet reading area and small cubbies). We respect the privacy of each child. Each child has his or her own cot, his or her own space for belongings, and privacy in the bathroom. Comfort also means feeling secure. Security is provided by sensitive and caring teachers that view each child’s needs individually and who teach understanding and acceptance of all children.
At Child Care Center, Inc. we feel that relationships with peers are important. These relationships are as natural and essential for young children as they are for adults. From these relationships children will experience friendship, security, and a sense of belonging.
The curriculum at the Child Care Center, Inc. is developed and geared toward the interests and ages of the children. We provide a rich sensory environment with a lot to look at, touch, hear, taste, smell, try, and learn! We use a hands-on approach where the children learn from doing and trying new things. | http://childcarecenterinc.com/philosophy.php |
RELATED DOCUMENTS
1. FIELD OF USE
2. BACKGROUND OF THE DISCLOSURE
SUMMARY OF THE DISCLOSURE
DETAILED DESCRIPTION AND SPECIFIC EMBODIMENTS
This application claims the benefit and priority to provisional application entitled “Berm or Levee Expansion System and Method, Application No. 62/008,662 filed Jun. 6, 2014. This provisional application is incorporated herein by reference in its entirety.
The method and system of this disclosure pertains to economical expansion of capacity of liquid retention structures such as levees, retention ponds and similar structures. The expansion of capacity can be achieved with an expedited construction schedule.
Embankments are widely used in civil, industrial, and municipal applications for reservoirs for the retention and storage of fluids. As used in this disclosure, embankments, levees, retention dikes, dams and berms will collectively be referred to as berms. The fluids stored by these berms can range from storm water to hazardous materials such as fracing water or industrial process by-products. Industrial reservoirs are typically land-locked within existing facilities with little or no room to expand the reservoir in a horizontal direction due to adjacent structures, property owners, buried utilizes, etc. The need for additional reservoir volume capacity may occur for multiple reasons, including but not limited to expansions in process or treatment requirements. For the reasons described above, facility owners are faced with limited options to increase reservoir capacity.
One application of industrial reservoirs is the surface storage of brine solution at salt dome storage facilities. These facilities store hydrocarbon products in underground caverns that have been formed by dissolving salt deposits from naturally occurring salt dome formations. The brine solution is pumped underground to displace the hydrocarbon products out of the storage and into the facility for distribution to downstream facilities. When new product is pumped into the cavern, the brine is displaced through pipe systems to the surface storage reservoirs.
In the State of Texas, for example, regulations require an operating freeboard of 2 to 3 feet between the maximum operating fluid elevation and the top of the berm. Because this freeboard is by nature at the top of the berm and at the widest part of the levee (due to the sloping berm walls as described below), the storage lost to the freeboard requirement can be over 13% of the total available capacity of the reservoir. These reservoir are typically installed to utilize the maximum available footprint and cannot be easily expanded. Land restrictions make it difficult or impossible to add additional reservoirs. It is also expensive to remove and build a new berm wall constructed of soil.
Berms are also common in stationary flood control structures such as levees and dams. There are an estimated 100,000 miles of levees in the United States alone. It is sometimes necessary to raise the effective fluid retention height of these levees due to increases in upstream development that lead to increased runoff and therefore increased flood elevations. This is traditionally done by adding soil to the levee, constructing concrete barrier walls, or adding a gravity fill structure to the crest of the levee. These gravity fill systems rely on the weight of the added structure to resist the fluid pressures from the contained fluid.
This disclosure teaches a method and system that can regain the pond storage lost by adding berm height and therefore the required freeboard capacity. In this regard, this disclosure can directly help America's energy delivery and storage systems. By simply adding 3-4 feet of berm height to multiple existing ponds, a significant increase in storage capacity can be realized.
In a broad aspect, the disclosure is directed to a fluid retention method and system. In one specific sense, the disclosure relates to raising the height of new or existing berms by installation of the proposed structure/system on top of an existing engineered berm. The method and apparatus of the disclosure pertains to erecting a structure consisting of a unique combination of lightweight fill material at least partially enclosed by an impervious fluid liner material. The fluid liner material will be attached to a new or existing liner positioned on the face of the berm, or otherwise be made impervious by anchoring into or against the existing structure. The proposed structure has no length limit. The lightweight fill structure can be installed around the full perimeter of the berm crest ground surface (the top of the berm surrounding an enclosed pond) or along the full length of a levee. The proposed system (impervious fluid liner and lightweight fill structure) effectively increases the height of the inner sidewall of a levee. This increased height may comprise a regulatory required freeboard for the berm structure, i.e., acting as a barrier only during temporary elevation of the fluid level in the retention pond, etc.
The unique combination of materials creates a system that can be installed where traditional earthen, sheetpile, or concrete structures are not feasible or cannot be constructed due to physical limitations such as equipment access, geotechnical concerns, or other constraints.
The lightweight fill material may be comprised of Expanded Polystyrene (EPS), commonly referred to as Geofoam®, or a similar lightweight rigid foam plastic material. Geofoam is a registered trademark of Minova International Limited United Kingdom. Materials having physical characteristics of: density less than 5 pounds per cubic foot, compressive strength greater than 2 psi, and a flexural strength greater than 10 psi can be utilized. These materials will hereinafter be referred to as “lightweight fill material”. The liner will typically be High Density Polypropylene (HDPE), although other liner materials such as LDPE, PVC, and polyurea composites (e.g. geotextiles coated with polyurea) are commercially available. HDPE liner thicknesses of 30-120 mils would be typically used for the fluid impermeable liner. These materials may be referred to as liner materials or as fluid impermeable liner material. These materials typically have physical characteristics of: yield strength greater than 60 pounds per inch (per ASTM D 6693), puncture resistance greater than 45 pounds (per ASTM D 4833), and are stabilized for protection against ultraviolet sun damage. A textured surface is available on many liner products and would be desirable in this application, specifically as the textured surface increases the coefficient of friction against any surface the liner is in contact with.
The lightweight fill material has a structure. The structure's cross sectional shape would typically be triangular, with approximately 45 degree interior slope and a vertical face on the exterior face. Other shapes, however, are not excluded. The height and width of the structure can vary to fit the physical limitations of the specific installation and are limited by the physical strength of the liner and lightweight fill material, the fluid being contained, and the characteristic of the underlying berm. It will be appreciated that berms are engineered structures with load limits. A typical installation would be no more than 6 feet tall although taller installations are possible.
1. Excavation of an anchor trench at the berm crest (or ground surface) for the new liner that will enclose the Light weight fill material
2. Cleaning the existing primary liner.
3. Temporarily placing the new liner along the berm crest.
4. Attach the new liner to the existing liner by extrusion weld or other adhesive or mechanical methods.
5. Layback new liner to allow placement of Light weight fill material.
6. Placing Light weight fill material along the berm crest (ground surface).
7. Flip liner over the light weight fill material and install outside edge into anchor trench.
8. Backfill anchor trench.
The basic installation on an existing earthen berm with an existing impervious HDPE liner system would entail the following activities.
Another aspect of the disclosure relates to partially enclosing the lightweight material with a liner material that is embedded and anchored into natural grade (ground surface) or an existing earthen berm. In this case the earthen anchor trench will provide the required tensile connection to the liner that is required to prevent movement or overturning of the lightweight fill material. The anchor trench can be specifically designed to optimize the liner embedment into the existing soils in order to maximize the impervious characteristics of the subgrade portion of the assembly. The liner can partially act as an embedded cutoff wall when installed vertically into an anchor trench.
Another aspect of the disclosure is that it provides flexibility in the application of the liner material. Any material that provides the necessary strength to resist overturning and movement of the lightweight fill material (hereinafter “lightweight fill material”) could be utilized in order to vary the durability, appearance, and design life of the system. One embodiment of this flexibility would be the application of shotcrete over an impervious HDPE liner. Shotcrete is concrete conveyed through a hose and pneumatically projected at high velocity onto a surface. Shotcrete undergoes placement and compaction at the same time due to the force with which it is projected from the nozzle. It can be impacted onto any type or shape of surface, including vertical or overhead areas
The shotcrete would provide a concrete protective layer to protect the assembly from vandalism, accidental impacts, and prevent UV damage to the HDPE liner. This level of protection would be desirable in publicly accessible areas or areas without controlled access, such as public flood control levees. Traditional cast in place concrete or precast concrete panels could also be utilized to provide alternate armoring systems and vary the visual appearance of the system.
Another aspect of the disclosure relates to its minimal weight when compared to traditional methods of constructing berms or raising berms. Traditional methods of raising berms require the addition of structural fill, construction of concrete foundations and wall systems, or the installation of a container to hold a material of sufficient weight to resist the lateral fluid pressures imposed by the retained fluid. This additional weight, in some instances could not be supported by the underlying foundation soils, e.g., the load exceeds the engineered limits of the existing. This makes traditional methods impossible to implement. The disclosed structure and method eliminates these weight concerns as the liner material provides the structural capacity required to resist the lateral fluid pressures. The system does not rely on fluid pressure or the weight of the fill material or contained fluid to seal the liner to the existing soil or to other sections of the liner.
It will be appreciated that not all embodiments of the disclosure can be disclosed within the scope of this document and that additional embodiments of the disclosure will become apparent to persons skilled in the technology after reading this disclosure. These additional embodiments are claimed within the scope of this disclosure.
It should be noted that each installation of this system will present unique engineering challenges that will require customization of the system. These may include, but are not limited to, provision of personnel access routes, pipe penetrations, and custom fitting around existing structures. These are impossible to predict and will vary with the existing conditions and equipment at the individual installation locations. The scope of the Applicant's disclosure is adaptable to each unique engineering challenge by combination of the disclosed systems.
FIG. 8
FIG. 7
It will be appreciated that retention ponds do not experience a fluid current. The disclosure, however, is also applicable to levees retaining flowing fluid, e.g. water. A current creates a force parallel with the face of the lightweight fill material, i.e., the surface of the lightweight fill material facing the fluid. A current may also be experienced at the inlet or outfall of a retention pond. In such applications, it may be advantageous to utilize anchors that penetrate the lightweight fill materials and extend into the soil comprising the berm. An example of this is shown in . In another embodiment, shows a concrete layer in front of the lightweight fill material. In one embodiment, the concrete layer faces only the fluid.
FIG. 1
FIG. 4
Figure 4
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is a cross section of an existing reservoir that demonstrates a potential application of the system. This type of reservoir is typically constructed by excavating an area , below the existing ground surface of the site. This excavated material may be utilized to construct the berm , if it is of suitable geotechnical characteristics, or may be disposed of in another location. The berm , may also be constructed of imported fill material of suitable characteristics. The fluid surface , is shown for reference. The fluid surface , cannot become higher than the top elevation of berm . If fluid surface overtops berm , significant damage and potential catastrophic failure of the berm can result. Existing surface grade surrounding the berm , is shown for reference. Dimension represents the total footprint of the reservoir formed by the berm. This dimension is often constrained by adjacent structures, utilities, or property lines and cannot be increased. It is also expensive to construct earthen berms. In a scenario where dimension is constrained, there are limited options to raise the height of berm as the berms have been designed per specific slope stability calculations and an increase of weight caused by adding fill or heavy barriers to the crest of berm to increase the berm height could affect the slope stability or the underlying existing surface to create an unstable geotechnical condition. (See also and the paragraph within the DETAILED DESCRIPTION AND SPECIFIC EMBODIMENTS beginning with the text stating “ shows a cross section of a typical earthen perm”.)
FIG. 2
FIG. 3
2
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shows a typical cross section of a berm crest that has a double liner system installed. The fluid surface is shown for reference. The distance between the fluid surface and the crest of the berm is shown as dimension , commonly referred to as freeboard. Freeboard heights are sometimes regulated by government agencies to provide additional storage capacity for extreme rainfall events, system failures, or other events that could quickly increase the elevation of the fluid surface and result in overtopping of the berm . In an embodiment, the lightweight fill material subject of this disclosure (positioned on top of the berm) may comprise the required freeboard. (See )
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The double liner is typically installed in instances where little or no leakage of the fluid is desired or permitted by law. The double liner consists of a Primary Liner, that is the primary impervious layer in the system. Liner is typically terminated in an anchor trench A, placed along the berm crest. The anchor trenches A and B are engineered to provide adequate soil mass to prevent pullout or displacement of the respective liners and and can also anchor the drainage layer . The Primary Liner may be the top liner of the double liner system. Two anchor trenches A and B are shown. One anchor trench B may be used to secure the Secondary Liner. The anchor trench stabilizes the liner against displacement and is typically backfilled with compacted soil. Secondary Liner , provides a backup impervious liner and enables installation of leak detections systems to determine the quantity of leakage through the primary liner. A drainage layer , is typically installed between liners & to cushion and protect the primary liner and to provide means for leakage through the primary liner to be directed and collected in a leak detection system. The drainage layer can be constructed of a sand layer or a synthetic material such as a geonet.
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Liners & are typically constructed of High Density Polypropylene (HDPE), Low Density Polypropylene (LDPE), Polyvinyl Chloride (PVC), poly urea composites, or polyethylene. They are installed to form a continuous liner in the reservoir.
This double liner system presents challenges to any attempt to raise the height of the existing levee as the integrity of the anchor trenches and liners must be preserved to maintain the system.
FIG. 3
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shows Embodiment A of the proposed system. The drainage layer is omitted from this view for clarity. A new anchor trench , is shown along the exterior edge of the proposed system. The new anchor trench is installed along the existing berm crest in a manner that does not disturb (or minimally disturbs) the existing anchor trench, A. A lightweight fill material , is shown placed along the berm crest. This lightweight fill material forms the structural core of the extended berm height system. The lightweight fill material is typically installed in lengths that are 8-10 feet long (sections) and do not require direct attachment to each other. The light weight fill material may be constructed of a foam type material as described previously. A new liner , partially encloses the fill , and is attached to the existing liner , by mechanical bonding, welding, adhesives or mechanical fastening at point . The attachment must provide sufficient strength to join the two liners and secure the position of the lightweight fill material. The attachment must also be fluid impervious to maintain the integrity of the liner system. The combination of liner , and the attachment point , and anchor trench , form the structural anchor system that enables the lightweight fill to adequately resist the fluid pressure , which results from the fluid elevation acting upon the structure. Items 7, 13, and 14 (liner, liner attachment point, and anchor trench) also form the means of joining the system into a continuous structure. The system eliminates the need for directly connecting the lightweight fill material sections. This method does not disturb the secondary liner or its anchor trench B.
FIG. 4
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shows a cross section of a typical earthen berm. Berms are commonly constructed of compacted earth fill . The compacted earth fill is of suitable geotechnical characteristics to contain the fluid and maintain the structural integrity of the berm against hydrostatic pressures. These berms may be constrained by the underlying foundation soils. There may be instances where the bearing capacity of the foundation soils limits the weight (and therefore the height) of the levee to be constructed on top of the foundation soils. The height can also be constrained by the available footprint of the berm, shown as dimension . The interior slope A and exterior slopes B of the berm, are limited in their degree of steepness by the soil characteristics of the earth fill . This slope limits the height within the footprint . The berm crest , is typically limited to how narrow it can be due to constructability of the berm itself as related to equipment access during construction. The berm crest may also facilitate installation of equipment, roadways, pedestrian paths, or routes for inspection of the berm.
FIG. 5
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shows Embodiment B of the disclosure. In this version, the new anchor trenches A and B, are utilized to anchor the impervious liner, into the existing soil. Note that this existing soil (compacted earth fill ) may be part of an existing berm or could be natural grade in instances where a berm does not exist. The lightweight fill material , forms the structural core of the system while the liner , and anchor trenches form the system that anchors the system and provides the impervious nature of the system. This embodiment could provide economical means of effectively raising the height of an existing berm, or facilitate the construction of a levee where none existed previously. This embodiment is unique in that it does not require an existing impervious liner to be present. In this embodiment, the liner could be, but is not limited to the materials discussed above such as HDPE, LDPE, PVC, poly urea, or polyethylene. In one embodiment, the impervious liner has tensile strength of 168 pounds per inch and puncture resistance of 90 lbs.
FIG. 6
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shows a version of embodiment B with the addition of an armored facing (protective structure ). This version would be desirable for use in areas where protection against fluid flow, vandalism, impact, or UV degradation of the liner material was desirable. In this version the anchor trenches A and B, lightweight fill , and impervious liner , are installed in the same manner as above. A protective structure could be installed by placement of a reinforcing steel (Welded Wire Fabric or Rebar) along the liner . Concrete could then be placed over the liner and enclosing the reinforcing by means of shotcrete placement, where concrete is sprayed onto a structure. Shotcrete is, in effect, a version of a cast-in-place concrete wall. Rather than placing concrete into forms, however, a fresh mix is sprayed onto wall panels that have been erected in the shape of the structure. Concrete is applied from a pressurized hose to encompass the reinforcement and build up the wall thickness, forming structural shapes that include structural shape or assemblies. These can be constructed over the lightweight fill material. Polystyrene is a common surface for accepting fresh concrete. This method of concrete placement is well known in the industry, and is only one example of how concrete could be placed for protection of the system. The concrete structure , would ideally extend below grade to provide additional protection.
FIG. 7
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shows embodiment C of the system in which the protective structure A, B, and C would be installed in sections and joined sealed together at the joints with sealant A and B, to form the impervious liner. This method demonstrates the use of an alternate material to anchor the lightweight fill and provide the impermeable liner. As it would require the installation of foundations A and B, and either the fabrication of the armor panels A-C or the utilization of cast in place concrete, it is envisaged that this embodiment would not be as economical as other embodiments. In this embodiment, the protective armor could feasibly be any material which would be of impervious nature, of sufficient structural strength, and incorporate the ability to be joined together to create impervious joints.
FIG. 8
FIG. 3
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shows Embodiment D of the system in which the impervious liner , is extended to the interior of the berm and is continuous with, and acts as the primary liner for the entire pond. This embodiment would be typical of using the system in a newly constructed pond, without the need to bond or join the liner to an existing liner , as shown in . In this embodiment, the addition of a mechanical anchor , would be desirable to anchor the lightweight fill , in instances where the reservoir was empty and the liner would have no fluid pressure acting to prevent movement of the system towards the pond interior.
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FIG. 9
As an alternate to the mechanical anchor, the foam could be bonded adhesively or mechanically to a concrete foundation or other rigid material as a means of anchoring the system against movement towards the interior. This detail is shown in . The rigid material , would lock the lightweight fill into place and prevent movement towards the pond interior as a result of an external force such as wind or impact. This configuration would also provide additional resistance to overturning due to the weight of the rigid material. The rigid material could be buried and mechanically anchored to the lightweight fill.
FIG. 12
FIGS. 8 and 9
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shows a further embodiment of , wherein an arrangement with a soil anchor point is created, on both sides of the lightweight fill . This detail shows the soil on the inner face of the lightweight fill extending along the face of the lightweight fill to anchor the block and to provide a continuous interior slope , against which to place the impervious liner . This arrangement may be desirable to better anchor the lightweight fill in Embodiment D of the system. The soil anchor point , could be installed on one side only, and the cross section and shape of the soil anchor could vary according to the unique properties of each installation.
FIG. 13
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shows another arrangement of Embodiment D, in which an anchor trench A and B, is installed on both sides of the lightweight fill material, . This arrangement would fully anchor the lightweight fill against lateral movement. It would also provide the benefit of a traditional anchor trench for the impervious liner . This may be desirable in instances where the forces exerted by the liner (due to thermal expansion/contraction) may be greater than the resistance available by the lightweight fill , and the previously mentioned mechanical anchors, . An anchor trench cover may be desirable to prevent erosion and saturation of the interior anchor trench by the contained fluid. The anchor trench cover could be constructed from the same material as the liner and attached by mechanical, welding, or adhesive means to the liner . The anchor trench cover could be an alternate type of liner or a thinner section of liner, as it will likely not function as a structural member.
FIG. 14
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In another embodiment illustrated in , the system may be installed on an interior berm. An interior berm is defined a berm with contained fluids on each side, as would be the case in a berm dividing a larger basin into two separate basins. This situation could present a situation that would require bonding of the new liner to an existing liner on each side of the lightweight fill and introduce unique structural load situations or constructability requirements. One alternative in this situation is to install the primary liner embedded into anchor trenches A and B in order to provide structural integrity to the system. A containment liner , would then be bonded (adhesively or mechanically) to the existing liner on either side of the system. This liner , could also be bonded to the liner in order to provide additional strength and prevent liner movement in the wind. The new anchor trenches A and B may need to be constructed in a way to minimally disturb existing anchor trenches A and B.
FIG. 10
FIG. 3
FIG. 8
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shows Embodiment E of the system that incorporates a multitude of individual lightweight fill block sections to form a singular larger block. The individual blocks , would be joined via mechanical anchors , which are commercially available and typical to the installation of multiple layers of Light weight fill material blocks. The height of this system would be limited by the strength of the liner material , the strength of the anchor trenches A and B, and potentially the strength of the lightweight fill material. This embodiment could also be utilized as in , where the liner is connected to an existing liner , or as shown in where utilized with a continuous liner. The downward force applied by the liner material will act to compress the blocks together and cause them to act as a singular block in conjunction with the mechanical anchors. As an alternative to the mechanical anchors , the blocks , could be joined together with a compatible adhesive. This adhesive would cause the individual blocks to act as a singular block. In another embodiment, (not shown) the individual block sections could be over lapped across the lower joints of two separate section, thereby increasing the structural unity of the length of multiple block sections comprising the lightweight fill material.
FIG. 3
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Embodiment A () could be constructed to allow the addition of a leak collection and detection system in between the existing primary liner and the new liner . This could be required to satisfy certain regulatory requirements or provide a means of monitoring the integrity of the attachment point . A leak detection system could be provided for any of the embodiments. A leak detection system is traditionally constructed of perforated pipe (typically PVC or HDPE) installed to collect any fluid that leaks from the containment system, in this case, through liner or attachment point . The collected fluid is routed to a collection sump where it can be monitored or pumped back into the containment area.
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Embodiment A could also be constructed by adding a second impervious liner over liner and providing an additional attachment point to the existing liner and an installing the second liner into the anchor trench .
FIG. 10 or 5
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Embodiment E or B () could be constructed also with the addition of a second impervious liner over liner and the addition of a new anchor trench on each side of the system. This would provide a secondary liner and provide additional safety factor into the strength of the system against overturning.
FIG. 11
shows Embodiment F of the system that incorporates a high mass insert to provide additional resistance to horizontal displacement and overturning of the system.
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In this embodiment the weight of the light weight fill material structure is supplemented by the addition of more dense material. The high mass insert , could be constructed of any material of sufficient density to provide the required resistance to displacement or overturning. This supplemental mass can be concrete poured and cured in a mold wherein the shape of the mold is complementary to an indentation formed within the structure of the lightweight fill material. Materials such as sand bags, geo-tubes, and steel shapes, would be examples of materials also available. As this method would require the use of additional materials, it is envisaged that this embodiment would not be as economical as other embodiments. It will be appreciated that the lightweight fill material is transported and positioned at the berm crest without the supplemental weight. The weight can be added after the structure is in position. In one embodiment, the weight may be less than 100 lbs. and manually positioned into the structure. It will be appreciated that a structure can have multiple indentations to receive the supplemental weight. The advantage of this system will be to allow the structure to have increased mass without requiring mechanical equipment, e.g., mechanical lifting equipment or carrying equipment, to be brought to the site. (The supplemental mass may be manually placed within the structure.) It will be appreciated that access to the site of the berm may be restricted. Illustrated is the lightweight fill material structure and the supplemental mass fitting into an indenture of the fill structure. The high mass insert , could be anchored or bonded to the lightweight fill material . Also illustrated is the anchoring trench containing the end of the liner that is placed over the fill structure and continues to cover the inner surface of the berm.
In another embodiment, the lightweight fill sections can be joined together end to end. This is particularly useful when the lightweight fill material comprise sections of expanded polystyrene (EPS) or a similar lightweight rigid foam plastic material. The lightweight fill material (components or sections) are prefabricated offsite into selected shapes. Each section can be between 6 and 30 feet in length. Other dimensions are possible. The sections can be variable in height. The lower portion of the section can be broader than the upper section to enhance stability. The sections can be placed end to end on the berm crest.
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The ends of the lightweight fill material sections can be joined together. This can be accomplished by inserting rebar into each end or using commercially available anchors as in embodiment E. In one embodiment, the length of rebar inserted into each section can be 4 to 24 inches. The rebar can be precut, thereby facilitating prompt assembly in the field. Each juncture can be linked together by multiple sections of rebar. It will be appreciated that the linking together of each component will prevent one component or section of lightweight fill material from being pushed out of line, causing a gap to form in the extended height berm subject of this disclosure. The rebar can be fitted into indentations or holes within section ends of the lightweight fill material. It will be appreciated that the length of the rebar section, preferably greater than 20 inches, will improve the stability of the junction between two sections of the lightweight fill material. The greater unified length of the lightweight fill sections will protect against a localized surge in fluid level and help to facilitate construction by anchoring the lightweight fill material sections together prior to anchoring them by enclosing them with the liner . Multiple lightweight fill sections could also be joined together using continuous steel cables inserted lengthwise through preformed penetrations in each section of the lightweight fill material. This steel cable could be mechanically anchored to the existing berm to provide additional structural stability. The cable diameter, material of construction and spacing of the mechanical anchors would depend on the specific design parameter of each installation.
In another embodiment, the ends of each lightweight fill material are modified in the manufacturing process to create male and female protrusions and indentations at each end. Therefore one end of the lightweight fill component would contain a male protrusion and the other end would contain a female indentation. The indentations and protrusions would be complementary dimensioned to allow the male end of a first component to fit into the female end of a second component. As with the joining the ends with rebar, the joined sections of lightweight fill material would prevent one section from being pushed back. In both cases (rebar linkage or male/female end coupling), the series of lightweight fill material would act as a unified structure or barrier.
Figure 12
Figures 8 and 9
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In another embodiment the lightweight fill materials completely surround a retention pond. Therefore the ends of each section of lightweight fill material abut the end of another section. In another embodiment where the lightweight fill material forms a levee structure, the series of sections of lightweight fill material may end where the ground level exceeds a specified elevation. The end section may be dug into the ground at the point that the ground level exceeds the specified elevation. This would serve to anchor the end of the section linked in accordance with a preceding paragraph beginning with the text stating “ shows a further embodiment of , wherein an arrangement with a soil anchor point is created, on both sides of the lightweight fill ”.
This specification is to be construed as illustrative only and is for the purpose of teaching those skilled in the art the manner of carrying out the disclosure. It is to be understood that the forms of the disclosure herein shown and described are to be taken as the presently preferred embodiments. As already stated, various changes may be made in the shape, size and arrangement of components or adjustments made in the steps of the method without departing from the scope of this disclosure. For example, equivalent elements may be substituted for those illustrated and described herein and certain features of the disclosure may be utilized independently of the use of other features, all as would be apparent to one skilled in the art after having the benefit of this description of the disclosure.
While specific embodiments have been illustrated and described, numerous modifications are possible without departing from the spirit of the disclosure, and the scope of protection is only limited by the scope of the accompanying claims.
BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate preferred embodiments of the disclosure. These drawings, together with the general description of the disclosure given above and the detailed description of the preferred embodiments given below, serve to explain the principles of the disclosure.
FIG. 1
FIG. 2
is a typical cross section of a reservoir constructed by excavating the inner portion of the pond below natural grade and utilizing the excavated material to construct earth embankments. The top of the embankment is shown in .
FIG. 2
is a typical cross section of an embankment with two layers of impervious liners (double lined levee). Also shown are two anchor structures for retain the flexible impervious liners.
FIG. 3
shows Embodiment A of the disclosure where the new impervious liner is joined to an existing liner. A former anchor is illustrated with two additional anchors. The anchors may be trenches dug in the top of the ground berm and filled with additional earth, gravel or concrete.
FIG. 4
shows a typical cross section of an existing earthen levee (berm) constructed of compacted soil material.
FIG. 5
shows Embodiment B of the disclosure where the new impervious liner is anchored into existing soil. In this embodiment, the liner may be buried in one or more trenches dug in the top of the earthen berm.
FIG. 6
shows a typical cross section of Embodiment B, with the addition of an armored surface composed of concrete placed over the added berm material.
FIG. 7
shows a typical section of Embodiment C, where the armored surface acts as the impervious liner. The armored surface contains the added shaped berm layer. Footers may also be installed to support the armored layer.
FIG. 8
11
shows Embodiment D of the system in which the impervious liner , is extended to the interior of the berm and is continuous with, and acts as the primary liner for the entire pond. Also shown is a mechanical anchor to secure the added berm material to the earthen berm surface.
FIG. 9
shows the light weight fill material bonded to a concrete foundation as a means of anchoring the system (added berm material and imperious liner) against lateral movement towards the interior (fluid side of the berm surface).
FIG. 10
shows Embodiment E of the system which incorporates a multitude of individual lightweight fill blocks to form a singular larger block. The embodiment shows multiple mechanical anchors assisting in securing the fill blocks together. Trenches are shown for anchoring the impervious liner.
FIG. 11
illustrates an embodiment wherein the lightweight fill material is supplemented with a preformed higher density mass that fits within an indentation of the fill material structure. The higher density mass may extend across a plurality of light weight material sections.
FIG. 12
illustrates an embodiment wherein the lightweight fill material is anchored by soil or other fill material on both sides of the structure. Also the slope of the berm is extended at at least a portion of the material structure. An anchor structure is also shown on the back side (non fluid side) of the berm.
FIG. 13
illustrates an embodiment where the lightweight fill material is anchored by the impervious liner and the liner is anchored by a trench constructed on both sides of the lightweight fill material structure.
FIG. 14
illustrates a cross section of an interior berm, i.e., a berm with contained fluids on each side. Elevation of this structure requires bonding of the new liner to an existing liner on each side of the lightweight fill and introduces unique structural load situations and/or constructability requirements. In this embodiment a double layers of a fluid impervious liner may be used with the inner anchored in a trench dug in the top of the berm surface and the outer liner layer covering the trench surface. | |
BISMARCK, N.D. (KFYR) - North Dakota confirmed a positive rate of 10.5%* Saturday. There are 148 currently hospitalized (+0 change) with 31 ICU beds occupied due to COVID. Out of 7,596 tests, 760 were positive. There were 11 new deaths (399 total). 5,370 active cases.
BY THE NUMBERS
7,596 – Total Tests from Yesterday*
754,769 – Total tests completed since the pandemic began
760 – Positive Individuals from Yesterday*****
31,261 – Total positive individuals since the pandemic began
10.50% – Daily Positivity Rate**
5,370 Total Active Cases
+123 Individuals from yesterday
610 – Individuals Recovered from Yesterday (501 with a recovery date of yesterday****)
25,492 – Total recovered since the pandemic began
148 – Currently Hospitalized
+0 - Individuals from yesterday
11 – New Deaths*** (399 total deaths since the pandemic began)
INDIVIDUALS WHO DIED WITH COVID-19
Man in his 70s from Burleigh County with underlying health conditions.
Woman in her 70s from Dunn County with underlying health conditions.
Man in his 90s from Foster County with underlying health conditions.
Man in his 80s from Grant County with underlying health conditions.
Woman in her 70s from McHenry County with underlying health conditions.
Woman in her 90s from McLean County with underlying health conditions.
Woman in her 90s from Morton County with underlying health conditions.
Man in his 90s from Morton County with underlying health conditions.
Woman in her 90s from Stark County with underlying health conditions.
Man in his 90s from Stutsman County with underlying health conditions.
Woman in her 70s from Traill County with underlying health conditions.
COUNTIES WITH NEW POSITIVE CASES REPORTED TODAY
Adams County - 2
Barnes County - 9
Benson County – 9
Bottineau County – 13
Bowman County – 1
Burleigh County - 151
Cass County – 181
Cavalier County – 1
Dickey County - 3
Divide County - 4
Eddy County – 8
Emmons County - 3
Foster County – 9
Grand Forks County – 54
Hettinger County - 6
Kidder County – 1
LaMoure County – 5
Logan County – 4
McHenry County – 3
McIntosh County - 3
McKenzie County – 14
McLean County - 12
Mercer County - 21
Morton County – 49
Mountrail County – 11
Oliver County – 2
Pembina County - 3
Pierce County - 6
Ramsey County – 1
Ransom County – 3
Renville County - 1
Richland County – 10
Rolette County - 4
Sargent County – 1
Sheridan County - 1
Sioux County – 2
Stark County – 38
Steele County - 3
Stutsman County – 12
Towner County - 2
Traill County - 17
Walsh County - 13
Ward County – 21
Wells County - 8
Williams County – 35
* Note that this does not include individuals from out of state and has been updated to reflect the most recent information discovered after cases were investigated.
*Rate based on ‘susceptible test encounters.’ True rate based on all testing = 10.0%.
**Individuals who tested positive divided by the total number of people tested who have not previously tested positive (susceptible encounters).
*** Number of individuals who tested positive and died from any cause while infected with COVID-19. There is a lag in the time deaths are reported to the NDDoH.****The actual date individuals are officially out of isolation and no longer contagious.
*****Totals may be adjusted as individuals are found to live out of state, in another county, or as other information is found during investigation. | |
It was my intention from the start of this blog not to review the sort of movie which dictates to people whether they will run back to pack theaters to see parts 2 through 27, or whatever. Honestly, Warcraft is not my type of movie. I’m not really into the fantasy genre (which capitalizes most often from franchises/sequels) as a rule, but of course there are exceptions (like Mad Max: Fury Road (2015), which I cannot rave enough about and absolutely loved, if you hadn’t heard). People generally already have their minds made up as to whether they do or do not enjoy these types of movies. I don’t believe anything I write will change their minds, and there is nothing exceptional about this one to report, so why waste everyone’s time?
What compelled me to see this movie is that I had no idea what I was about to watch. I did not know that it’s the first in a series based on the video game, World of Warcraft. I have heard of the game, but never played nor laid eyes on one character from the game. Ever. I was not concerned about what was changed, added or left out from the game.
Watching the previews for Warcraft, the 3D looked like it was going to be pretty cool. And it was. As with most 3D movies, there are never enough 3D effects featured to satisfy me. I want to see things coming at me constantly. I want to be ducking in my seat with my forearm over my face. That never gets old for me. There was none of that here, but the effects were well executed and kept the movie much more interesting than it would have been without the 3D. I won’t say the movie relied on the effects, but as someone who is not a fan, without the 3D I don’t think I could have made it through.
As for the story, it is what it is: mythical creatures, aliens, kingdoms, clans, flying beasts of all sorts, oversized – seemingly prehistoric animals, portals, hybrid species, love, deception, betrayal, war featuring primitive weapons and epic battles, several underdogs. There is really nothing new to see here, with the exception of some outstanding makeup and special effects. As a person who doesn’t generally watch fantasy franchises (The Hobbit, Harry Potter, Avatar, Star Wars, those pirate movies… and I mean, I’ve seen none of these. Ever.), I enjoyed it. I didn’t want to walk out, fall asleep, throw popcorn at the screen or demand my money back.
What I absolutely hated, as I always do, was the sequel set up. There will be a Part 2 (at least) to Warcraft as there were enough loose ends to quilt a blanket with at the end of this movie. They could release another installment almost immediately (that is, if this installment does well enough financially at the box office), just in case there was any doubt about Universal Picture’s intentions to develop a franchise.
I still will not rate Warcraft: The story is not original at all; you cannot tell who half the actors are for the makeup; actual “acting” becomes secondary to makeup and effects – so there really is no point. I suppose it is the type of movie that isn’t really meant to be rated, just enjoyed. Or not. If you enjoy this genre, I think you should enjoy this movie. If you generally do not enjoy this genre much, you may enjoy it for the effects, and it is something you should be able to get through with the kids if you must – at the very least. So… Enjoy! Or don’t. | https://bloopbymimi.com/2016/06/10/warcraft-pg-13/ |
Trump Believes Universal Health Coverage Is Better Than U.S. Current Health Care System
Dear Friends & Neighbors,
(Please click on red links & note magenta)
Note: as of 2008, Australia was spending less than 9% of GDP in health care, Canada was spending 10% in health care, whereas U.S. was spending 15.5% GDP (by 2012, U.S. was spending 17.6% of GDP in health care.). Both Australia and Canada had/has universal health coverage, but not U.S.
Health care in the United States:
Health care in the United States is provided by many distinct organizations. Health care facilities are largely owned and operated by private sector businesses. 58% of US community hospitals are non-profit, 21% are government owned, and 21% are for-profit. According to the World Health Organization (WHO), the United States spent more on health care per capita ($8,608), and more on health care as percentage of its GDP (17%), than any other nation in 2011.
64% of health spending was paid for by the government in 2013, funded via programs such as Medicare, Medicaid, the Children’s Health Insurance Program, and the Veterans Health Administration. People aged under 67 acquire insurance via their or a family member’s employer, by purchasing health insurance on their own, or are uninsured. Health insurance for public sector employees is primarily provided by the government.
The United States life expectancy of 79.8 years at birth, up from 75.2 years in 1990, ranks it 42nd among 224 nations, and 22th out of the 35 industrialized OECD countries, down from 20th in 1990. Of 17 high-income countries studied by the National Institutes of Health in 2013, the United States had the highest or near-highest prevalence of obesity, car accidents, infant mortality, heart and lung disease, sexually transmitted infections, adolescent pregnancies, injuries, and homicides. On average, a U.S. male can be expected to live almost four fewer years than those in the top-ranked country, though notably Americans aged 75 live longer than those who reach that age in other developed nations. A 2014 survey of the healthcare systems of 11 developed countries found the US healthcare system to be the most expensive and worst-performing in terms of health access, efficiency, and equity.
Americans undergo cancer screenings at significantly higher rates than people in other developed countries, and access MRI and CT scans at the highest rate of any OECD nation. Diabetics are more likely to receive treatment and meet treatment targets in the U.S. than in Canada, England, or Scotland.
Gallup recorded that the uninsured rate among U.S. adults was 11.9% for the first quarter of 2015, continuing the decline of the uninsured rate outset by the Patient Protection and Affordable Care Act (PPACA). A 2012 study for the years 2002–2008 found that about 25% of all senior citizens declared bankruptcy due to medical expenses, and 43% were forced to mortgage or sell their primary residence.
In 2010 the Patient Protection and Affordable Care Act (PPACA) became law, providing for major changes in health insurance. Under the act, hospitals and primary physicians would change their practices financially, technologically, and clinically to drive better health outcomes, lower costs, and improve their methods of distribution and accessibility. The Supreme Court upheld the constitutionality of most of the law in June 2012 and affirmed insurance exchange subsidies in all states in June 2015.
At the moment, much of the future of American Healthcare is in limbo, for the House (May 4, 2017) has recently passed a bill to repeal and replace the ACA (Affordable Care Act, aka Obamacare), and this is the post on the analysis of the current state of this bill.
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Healthcare in Australia:
Health care in Australia is provided by both private and government institutions. The federal Minister for Health, currently Greg Hunt, administers national health policy, and state and territory governments administer elements of health care within their jurisdictions, such as the operation of hospitals.
Medicare, administered by the federal government, is the publicly funded universal health care system in Australia which was instituted in 1984. It coexists with a private health system. Medicare is funded partly by a 2% Medicare levy (with exceptions for low-income earners), with the balance being provided by government from general revenue. An additional levy of 1% is imposed on high-income earners without private health insurance. As well as Medicare, there is a separate Pharmaceutical Benefits Scheme also funded by the federal government which considerably subsidizes a range of prescription medications.
The funding model for health care in Australia has seen political polarisation, with governments being crucial in shaping national health care policy.
Australia has a universal health care structure, with the federal government paying a large part of the cost of health services, including those in public hospitals. The amount paid by the federal government includes:
- patient health costs based on the Medicare benefits schedule. Typically, Medicare covers 75% of general practitioner, 85% of specialist and 100% of public in-hospital costs.
- patients may be entitled to other concessions or benefits.
- patients may be entitled to further benefits once they have crossed a so-called safety net threshold, based on total health expenditure for the year.
Government expenditure on healthcare is about 67% of the total, below the OECD average of 72%.
The remainder of health costs (called out of pocket costs or the copayment) are paid by the patient, unless the provider of the service chooses to use bulk billing, charging only the scheduled fee, leaving the patient with no out of pocket costs. Where a particular service is not covered, such as dentistry, optometry, and ambulance transport, patients must pay the full amount, unless they hold a Health Care card, which may entitle them to subsidized access.
Individuals can take out private health insurance to cover out-of-pocket costs, with either a plan that covers just selected services, to a full coverage plan. In practice, a person with private insurance may still be left with out-of-pocket payments, as services in private hospitals often cost more than the insurance payment.
The government encourages individuals with income above a set level to privately insure. This is done by charging these (higher income) individuals a surcharge of 1% to 1.5% of income if they do not take out private health insurance, and a means-tested rebate. This is to encourage individuals who are perceived as able to afford private insurance not to resort to the public health system, even though people with valid private health insurance may still elect to use the public system if they wish.
Insurance
Private health insurance, funds private health and is provided by a number of private health insurance organizations, called health funds. The largest health fund with a 30% market share is Medibank. Medibank was set up to provide competition to private “for-profit” health funds. Although government owned, the fund has operated as a government business enterprise since 2009, operating as a fully commercialized business paying tax and dividends under the same regulatory regime as do all other registered private health funds. Highly regulated regarding the premiums it can set, the fund was designed to put pressure on other health funds to keep premiums at a reasonable level. The Coalition Howard Government had announced that Medibank would be sold in a public float if it won the 2007 election , however they were defeated by the Australian Labor Party under Kevin Rudd which had already pledged that it would remain in government ownership. The Coalition under Tony Abbott made the same pledge to privatize Medibank if it won the 2010 election but was again defeated by Labor. Privatization was again a Coalition policy for the 2013 election, which the Coalition won. However, public perception that privatization would lead to reduced services and increased costs makes privatizing Medibank a “political hard sell.
Some private health insurers are “for profit” enterprises, and some are non-profit organizations such as HCF Health Insurance and CBHS Health Fund. Some have membership restricted to particular groups, some focus on specific regions – like HBF which centres on Western Australia, but the majority have open membership as set out in the PHIAC annual report. Membership to most of these funds is also accessible using a comparison websites or the decision assistance sites. These sites operate on a commission-basis by agreement with their participating health funds and allow consumers to compare policies before joining online.
Most aspects of private health insurance in Australia are regulated by the Private Health Insurance Act 2007. Complaints and reporting of the private health industry is carried out by an independent government agency, the Private Health Insurance Ombudsman. The ombudsman publishes an annual report that outlines the number and nature of complaints per health fund compared to their market share.
The private health system in Australia operates on a “community rating” basis, whereby premiums do not vary solely because of a person’s previous medical history, current state of health, or (generally speaking) their age (but see Lifetime Health Cover below). Balancing this are waiting periods, in particular for pre-existing conditions (usually referred to within the industry as PEA, which stands for “pre-existing ailment”). Funds are entitled to impose a waiting period of up to 12 months on benefits for any medical condition the signs and symptoms of which existed during the six months ending on the day the person first took out insurance. They are also entitled to impose a 12-month waiting period for benefits for treatment relating to an obstetric condition, and a 2-month waiting period for all other benefits when a person first takes out private insurance. Funds have the discretion to reduce or remove such waiting periods in individual cases. They are also free not to impose them to begin with, but this would place such a fund at risk of “adverse selection“, attracting a disproportionate number of members from other funds, or from the pool of intending members who might otherwise have joined other funds. It would also attract people with existing medical conditions, who might not otherwise have taken out insurance at all because of the denial of benefits for 12 months due to the PEA Rule. The benefits paid out for these conditions would create pressure on premiums for all the fund’s members, causing some to drop their membership, which would lead to further rises, and a vicious cycle would ensue.
There are a number of other matters about which funds are not permitted to discriminate between members in terms of premiums, benefits or membership – these include racial origin, religion, sex, sexual orientation, nature of employment, and leisure activities. Premiums for a fund’s product that is sold in more than one state can vary from state to state, but not within the same state.
The Australian government has introduced a number of incentives to encourage adults to take out private hospital insurance. These include:
- Lifetime Health Cover: If a person has not taken out private hospital cover by 1 July after their 31st birthday, then when (and if) they do so after this time, their premiums must include a loading of 2% per annum. Thus, a person taking out private cover for the first time at age 40 will pay a 20 per cent loading. The loading continues for 10 years. The loading applies only to premiums for hospital cover, not to ancillary (extras) cover.
- Medicare Levy Surcharge: People whose taxable income is greater than a specified amount (in the 2011/12 financial year $80,000 for singles and $168,000 for couples) and who do not have an adequate level of private hospital cover must pay a 1% surcharge on top of the standard 1.5% Medicare Levy. The rationale is that if the people in this income group are forced to pay more money one way or another, most would choose to purchase hospital insurance with it, with the possibility of a benefit in the event that they need private hospital treatment – rather than pay it in the form of extra tax as well as having to meet their own private hospital costs.
- The Australian government announced in May 2008 that it proposes to increase the thresholds, to $100,000 for singles and $150,000 for families. These changes require legislative approval. A bill to change the law has been introduced but was not passed by the Senate. A changed version was passed on 16 October 2008. There have been criticisms that the changes will cause many people to drop their private health insurance, causing a further burden on the public hospital system, and a rise in premiums for those who stay with the private system. Other commentators believe the effect will be minimal.
- Private Health Insurance Rebate: The government subsidises the premiums for all private health insurance cover, including hospital and ancillary (extras), by 10%, 20% or 30%. In May 2009, The Labor Government under Kevin Rudd announced that as of June 2010, the Rebate would become means-tested and offered on a sliding scale.
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Healthcare in Canada:
Health care in Canada is delivered through a publicly funded health care system, informally called Medicare, which is mostly free at the point of use and has most services provided by private entities. It is guided by the provisions of the Canada Health Act of 1984.
Canada has a publicly funded medicare system, with most services provided by the private sector. Each province may opt out, though none currently do. Canada’s system is known as a single payer system, where basic services are provided by private doctors (since 2002 they have been allowed to incorporate), with the entire fee paid for by the government at the same rate. Most government funding (94%) comes from the provincial level. Most family doctors receive a fee per visit. These rates are negotiated between the provincial governments and the province’s medical associations, usually on an annual basis. Pharmaceutical costs are set at a global median by government price controls.
Hospital care is delivered by publicly funded hospitals in Canada. Most of the public hospitals, each of which are independent institutions incorporated under provincial Corporations Acts, are required by law to operate within their budget. Amalgamation of hospitals in the 1990s has reduced competition between hospitals. As the cost of patient care has increased, hospitals have been forced to cut costs or reduce services. Applying perspective (pharmacoeconomic) to analyze cost reduction, it has been shown that savings made by individual hospitals result in actual cost increases to the Provinces.
In 2009, the government funded about 70% of Canadians’ healthcare costs. This is slightly below the OECD average of public health spending. This covered most hospital and physician cost while the dental and pharmaceutical costs were primarily paid for by individuals. Half of private health expenditure comes from private insurance and the remaining half is supplied by out-of-pocket payments. Under the terms of the Canada Health Act, public funding is required to pay for medically necessary care, but only if it is delivered in hospitals or by physicians. There is considerable variation across the provinces/territories as to the extent to which such costs as out of hospital prescription medications, physical therapy, long-term care, dental care and ambulance services are covered.
Healthcare spending in Canada (in 1997 dollars) has increased each year between 1975 and 2009, from $39.7 billion to $137.3 billion, or per capita spending from $1,715 to $4089. In 2013 the total reached $211 billion, averaging $5,988 per person. Figures in National Health Expenditure Trends, 1975 to 2012, show that the pace of growth is slowing. Modest economic growth and budgetary deficits are having a moderating effect. For the third straight year, growth in healthcare spending will be less than that in the overall economy. The proportion of Canada’s gross domestic product will reach 11.6% in 2012 down from 11.7% in 2011 and the all-time high of 11.9% in 2010. Total spending in 2007 was equivalent to 10.1% of the gross domestic product which was slightly above the average for OECD countries, and below the 16.0% of GDP spent in the United States.
In 2009, the greatest proportion of this money went to hospitals ($51B), followed by pharmaceuticals ($30B), and physicians ($26B). The proportion spent on hospitals and physicians has declined between 1975 and 2009 while the amount spent on pharmaceuticals has increased. Of the three biggest health care expenses, the amount spent on pharmaceuticals has increased the most. In 1997 the total price of drugs surpassed that of doctors. In 1975 the three biggest health costs were hospitals ($5.5B/44.7%), physicians ($1.8B/15.1%), and medications ($1.1B/8.8% ) while in 2007 the three biggest costs were hospitals ($45.4B/28.2% ), medications ($26.5B/16.5%), and physicians ($21.5B/13.4%).
Healthcare costs per capita vary across Canada with Quebec ($4,891) and British Columbia ($5,254) at the lowest level and Alberta ($6,072) and Newfoundland ($5,970) at the highest. It is also the greatest at the extremes of age at a cost of $17,469 per capita in those older than 80 and $8,239 for those less than 1 year old in comparison to $3,809 for those between 1 and 64 years old in 2007.
According to Lightman, “In-kind delivery in Canada is superior to the American market approach in its efficiency of delivery.” In the USA, 13.6 per cent of GNP is used on medical care. By contrast, in Canada, only 9.5 per cent of GNP is used on the medicare system, “in part because there is no profit incentive for private insurers.” Lightman also notes that the in-kind delivery system eliminates much of the advertising that is prominent in the USA, and the low overall administrative costs in the in-kind delivery system. Since there are no means tests and no bad-debt problems for doctors under the Canadian in-kind system, doctors billing and collection costs are reduced to almost zero.
Current status
The government attempts to ensure the quality of care through federal standards. The government does not participate in day-to-day care or collect any information about an individual’s health, which remains confidential between a person and their physician. Canada’s provincially based Medicare systems are cost-effective partly because of their administrative simplicity. In each province, each doctor handles the insurance claim against the provincial insurer. There is no need for the person who accesses healthcare to be involved in billing and reclaim. Private health expenditure accounts for 30% of health care financing. The Canada Health Act does not cover prescription drugs, home care or long-term care, prescription glasses or dental care, which means most Canadians pay out-of-pocket for these services or rely on private insurance. Provinces provide partial coverage for some of these items for vulnerable populations (children, those living in poverty and seniors). Limited coverage is provided for mental health care.
Competitive practices such as advertising are kept to a minimum, thus maximizing the percentage of revenues that go directly towards care. In general, costs are paid through funding from income taxes. In British Columbia, taxation-based funding is supplemented by a fixed monthly premium which is waived or reduced for those on low incomes. There are no deductibles on basic health care and co-pays are extremely low or non-existent (supplemental insurance such as Fair Pharmacare may have deductibles, depending on income). In general, user fees are not permitted by the Canada Health Act, though some physicians get around this by charging annual fees for services which include non-essential health options, or items which are not covered by the public plan, such as doctors notes, or prescription refills over the phone.
Benefits and features
A health card is issued by the Provincial Ministry of Health to each individual who enrolls for the program and everyone receives the same level of care. There is no need for a variety of plans because virtually all essential basic care is covered, including maternity but excluding mental health and home care. Infertility costs are not covered fully in any province other than Quebec, though they are now partially covered in some other provinces. In some provinces, private supplemental plans are available for those who desire private rooms if they are hospitalized. Cosmetic surgery and some forms of elective surgery are not considered essential care and are generally not covered. For example, Canadian health insurance plans do not cover non-therapeutic circumcision. These can be paid out-of-pocket or through private insurers. Health coverage is not affected by loss or change of jobs, health care cannot be denied due to unpaid premiums (in BC), and there are no lifetime limits or exclusions for pre-existing conditions. The Canada Health Act deems that essential physician and hospital care be covered by the publicly funded system, but each province has some license to determine what is considered essential, and where, how and who should provide the services. The result is that there is a wide variance in what is covered across the country by the public health system, particularly in more controversial areas, such as midwifery or autism treatments.
All of Canada (except the province of Quebec) is one of the few countries with a universal healthcare system that does not include coverage of prescription medication (other such countries are Russia and some of the former USSR republics even though Russia is considering a switch to full coverage of many prescription medications). Quebec citizens who are covered by the province’s public prescription drug plan pay an annual premium of $0 to $660 when they file their Quebec income tax return. Pharmaceutical medications are covered by public funds in some provinces for the elderly or indigent, or through employment-based private insurance or paid for out-of-pocket. Most drug prices are negotiated with suppliers by each provincial government to control costs but more recently, the Council of the Federation announced an initiative for select provinces to work together to create a larger buying block for more leverage to control costs. More than 60 percent of prescription medications are paid for privately in Canada. Family physicians (often known as general practitioners or GPs in Canada) are chosen by individuals. If a patient wishes to see a specialist or is counseled to see a specialist, a referral can be made by a GP. Preventive care and early detection are considered important and yearly checkups are encouraged.
Statistics
2012 saw a record year for number of doctors with 75,142. The gross average salary was $328,000. Out of the gross amount, doctors pay for taxes, rent, staff salaries and equipment. Recent reports indicate that Canada may be heading toward an excess of doctors, though communities in rural, remote and northern regions, and some specialties, may still experience a shortage.
Public opinion
Canadians strongly support the health system’s public rather than for-profit private basis, and a 2009 poll by Nanos Research found 86.2% of Canadians surveyed supported or strongly supported “public solutions to make our public health care stronger.” A Strategic Counsel survey found 91% of Canadians prefer their healthcare system instead of a U.S. style system.
A 2009 Harris-Decima poll found 82% of Canadians preferred their healthcare system to the one in the United States.
A 2003 Gallup poll found 25% of Americans are either “very” or “somewhat” satisfied with “the availability of affordable healthcare in the nation”, versus 50% of those in the UK and 57% of Canadians. Those “very dissatisfied” made up 44% of Americans, 25% of respondents of Britons, and 17% of Canadians. Regarding quality, 48% of Americans, 52% of Canadians, and 42% of Britons say they are satisfied.
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I am not kidding: Over the years, I have already seen some Americans who sought after citizenship of other countries purely due to health care. As of 2009, 58 countries on planet earth have already adopted Universal Health Coverage. Allow me to explain:
Universal health coverage is a broad concept that has been implemented in several ways. The common denominator for all such programs is some form of government action aimed at extending access to health care as widely as possible and setting minimum standards. Most implement universal health care through legislation, regulation and taxation. Legislation and regulation direct what care must be provided, to whom, and on what basis. Usually some costs are borne by the patient at the time of consumption but the bulk of costs come from a combination of compulsory insurance and tax revenues. Some programs are paid for entirely out of tax revenues. In others tax revenues are used either to fund insurance for the very poor or for those needing long term chronic care. In some cases, government involvement also includes directly managing the health care system, but many countries use mixed public-private systems to deliver universal health care.
The UN has adopted a resolution on universal health care. It may be the next stage after the Millennium Development Goals
Please refer to the list of (click–>) Countries with universal health care
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Frequently raised issues, below:
- Q: Why should I pay for some one else’s problem? A: When your neighbors are ill, you are more likely to come down with the illness also. When 58+ countries on earth already have universal health coverage and U.S. does not, what does that say about U.S.
- Q: It would cost too much to have Universal Health Coverage. A: U.S. is spending more than any other country on earth, without universal health coverage, and getting lower result. Something is not working right in U.S. health care system that needs to be modified or addressed. Ultimately, with more effective measures, after U.S. health care would be paying more attention to preventive medicine, gearing medical training toward treating the root cause of the problem rather than treating symptoms, and utilizing non-profit motivation rather than for-profit motivation behind the system of health care, will the U.S. health care system be able to measure up to the rest of the world. Perhaps then we will be able to implement Universal health coverage.
Perhaps our Senate would consider taking a look at the Australian and Canadian Healthcare Systems for ideas.
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Due to the topic/title of this post, I’ve received some reader (who may not have read our previous posts on health care issues), wondering if I know what the current bill that’s recently passed the House is all about. My response: yes, I am quite aware. Please refer to our earlier posts regarding this health care bill, below:
- Health Care Bill That Is Not For Health Care….Time To Contact Your Senators
- Rally at Rubio’s Office on Tuesday, May 9, 2017, at Noon, for Health Care
- Floridians’ Grass-Root Response To House Passing Health Care Bill
I am simply trying to make a point. As of 2017, between 1/4 to 1/3 of the nations on earth have universal health coverage. All developed nations (except USA) have universal health coverage. 11 African nations had universal health coverage in 2009. Once again, I’d like to invite you to review the list of countries that had universal health coverage by 2009 by clicking HERE.
Gathered, written, and posted by Windermere Sun-Susan Sun Nunamaker
More about the community at www.WindermereSun.com
Any comments, suggestions, concerns regarding this post will be welcomed at [email protected]
We Need Fair Value of Solar
~Let’s Help One Another~
Please also get into the habit of checking at these sites below for more on solar energy topics: | https://www.windermeresun.com/2017/05/12/trump-believes-universal-health-coverage-is-better-than-u-s-current-health-care-system/ |
A year ago this week, our team at Experiences Canada was furiously rebooking flights to secure the safe travel home of four youth groups still in the middle of an Exchange as the pandemic shut down took effect. We also started the process of postponing (and later cancelling) travel plans for more than 2000 youth involved in our programs. Who imagined that a year later, we would still be anxiously wondering when it would once again be safe to travel? While the warm weather and arrival of vaccines have given us reason to be optimistic, we’re still wistful for the time when we once again receive the social media posts, the photos and videos, and other reports from our participants as they discover another part of Canada for themselves. As we continue to wait, here is a compilation of some virtual tours of our most popular exchange destinations:
Even when the pandemic is declared over – it will be another decade before anyone can visit the #1 travel destination for Experiences Canada participants, so this virtual tour will have to do
Almost half our exchanges are arranged to support second language learning, mostly pairing Quebec francophone schools with other schools across the country. A visit to Valcartier Park and to Carnaval are always on the itinerary!
We always have more demand for exchanges to the North than we can accommodate each year.
Exploring Canada’s natural environment is another popular theme for exchanges, with Alberta and BC being top destinations for the rest of Canada eager to see the Rockies and Coastal Mountains.
Google Street Views offer a growing number of walk-through tours of Canadian museums and art galleries for those missing cultural excursions!
Presently, nearly 10% of our exchanges involve Indigenous communities. We’re continually working to build relationships with more Indigenous communities to support opportunities for them to build connections with other Indigenous as well as non-Indigenous youth across the country.
Opportunities to explore the East Coast are also very popular, and it is always a thrill if they can catch a glimpse of an iceberg while they are there!
Outdoor Education and exploring history and heritage are two other popular themes for exchanges – all the better when you can do both at the same time!
We count this as a future top destination since the Centre isn’t open yet – but we wanted to share this sneak peak of Winnipeg’s newest cultural attraction
We do a lot of sports exchanges including ski groups, but to be honest, no youth we know of have been on this kind of trip!
There are so many amazing places to discover in Canada. This year, since were all sticking around in our own neighborhoods, we’re inviting youth to take a closer look and share the stories about what makes their home so special – creating photo galleries, videos, and other multi-media presentations to highlight the history, geography, art, culture and heritage of their communities. At the end of the school year, we’ll share their work of all the youth participating in our Virtual Exchange program on an Interactive map of Canada. So stay tuned and join us this summer for a virtual tour across Canada as seen through the eyes of our youth! | https://experiencescanada.ca/a-pand-epic-tour-of-canada/ |
The popularity of physical training and even sports competitions among middle-age and older adults has increased dramatically since the late 1960's. Though it is generally agreed that such activity has a positive influence on endurance and physical well-being , little information is available to describe the orthopaedic and clinical impact of intense athletic training on the health of this older population. Thus, the intent of the present study will be to examine (1) the effects of 20-30 years of intense training on the rate of decline in aerobic endurance capacity, the influence of endurance training on muscle fiber composition, enzyme activities, strength, and mass in middle aged men, (3) the orthopaedic complications associated with 20-30 years of intense endurance training and competition (4) the incidence of clinical pathology with aging and its relationship to endurance running and (5) the effects of aging and training on the biomechanics of running. This study offers a unique opportunity to reexamine a group of middle-aged men who have continued to train intensely for the past 20-30 years. Three groups of men who originally competed in distance running and were studied in the late 1960's and early 1970's will serve as subject for this investigation. One group of these subjects (TR group) have continued to train for competitive running, whereas the other men now only train for general fitness and occasional competition (RR group) or have ceased to engage in any regular physical activity (UR group). In addition a group of sedentary non-runners will be tested for comparison (UT group). All participants will be examined for orthopaedic and clinical abnormalities, prior to all exercise testing. In addition to resting measurements of blood lipids, electrocardiogram, and muscle biopsies, the men will perform submaximal and a maximal treadmill tests to determine their running economy and aerobic capacities. Strength will be measured in the arms and legs of each subject. X-rays of the knees and nuclear magnetic resonance imaging of the thigh and upper arm will also be performed on subgroups of these men. These observations will provide information relative to both the positive and negative aspects of intense sports training in aging men. | https://grantome.com/grant/NIH/R15-AG010576-01 |
This Genetically Modified Rice Could Make More Food and Reduce Greenhouse Gases
Scientists at the Swedish University of Agricultural Sciences are working on a genetically modified strain of rice that combines barley genes with rice genes.The result would be a high-yielding, starchy rice plant that produces less methane gases than regular rice paddies. This plant, which pumps much less gas into the atmosphere, could have an impact on the severity of the greenhouse effect.
According to Ars Technica, methane gas emissions are the natural result of humidity in rice paddies; the wetlands where rich is cultivated emit methane gas in low-oxygen conditions. It is estimated that more than 25 million metric tons of methane enter the atmosphere every year as a result of the demand for rice worldwide. The Intergovernmental Panel on Climate Change estimates that methane is 84 times more potent than carbon dioxide as a greenhouse gas. However, this new GMO rice could pose a solution: the Swedish rice produces 90 to 99 percent fewer emissions than traditional rice.
The research development would provide “a tremendous opportunity for more-sustainable rice cultivation,” the researchers wrote in the accompanying essay. | https://www.thedailymeal.com/news/eat/genetically-modified-rice-could-make-more-food-and-reduce-greenhouse-gases/080415 |
Today in 2019: Two suspects arrested over ‘contract killing’ of Otumfuo’s Asamponhene
The Ashanti Regional Police on August 19, 2019, confirmed the arrest of two suspects in connection to the death of Oheneba Kwadwo Fodour, the Asamponhene of Kumasi.
The police described his death as a contract killing.
Oheneba Kwadwo Fodour was found stabbed by some unknown persons on the Ejura–Nkoranza road.
“So far we suspect contract killing but as at now we don’t know the motive but preliminary investigations suspect contract killing. At the right time, there will be update," confirmed DSP Godwin Ahianyo.
The Ashanti Regional Police Command has picked up two suspects in connection with what the Police suspect to be contract killing of the Asamponhene of Kumasi Oheneba Kwadwo Fodour.
The Police for security reasons has declined to reveal the identity of the suspects.
The chief, Oheneba Kwadwo Fodour, 46, was said to have been stabbed by unidentified persons while traveling on the Ejura–Nkoranza road in the Ashanti Region on Sunday, August 18, 2019.
Police officers who received information of a vehicle having been involved in an accident on the road went to the scene only to realize that the victim who had rather been stabbed in the back seat of the car was actually Oheneba Kwadwo Fodour.
The body of the deceased has since been sent to the Komfo Anokye Teaching Hospital (KATH) in Kumasi.
Confirming the incident to Kasapafmonline.com, the PRO of the Ashanti Regional Police Command DSP Godwin Ahianyo urged the public to remain calm and volunteer information as the Police have picked important leads that will lead to the arrest of anyone involved in the gruesome murder.
“So far we suspect contract killing but as at now we don’t know the motive but preliminary investigations suspect contract killing. At the right time, there will be update. We’ve picked one or two persons but for security reasons, we wouldn’t want to mention their names.” | |
I have always loved to cook: for family, friends, for friends of friends. And I believe that every time you prepare a meal for people, you give a part of yourself to them. My passion for cooking is rooted in the Italian tradition of cooking together with family in the home. When I was a child in my house in Umbria, there was always “profumo di cucinato”, the smell of cooking in the air. I have fond memories of helping my mother and grandmothers in the kitchen, learning their simple techniques for preparing fine, tasty meals. This all happened in my grandparents’ home in Umbria.
That humble tiny house, in the outskirt of Assisi, Umbria where I spent all my childhood summers, surrounded by my grandparents' love, is currently under restoration and I am thrilled to announce that it will be ready at the end of 2020 to host cooking lessons!
I can’t wait to welcome you into my family Umbrian country side kitchen where all began!
Umbria is called the green heart of Italy. Nestled in the right center of Italy are miscellaneous artistic, natural, and spiritual treasures. Etruscan, Roman, Medieval, and Renaissance historic layers shape its landscape, architecture, traditions, and gastronomy.
By car, by train, and by plane, here are the nearest airports: | https://www.pastaalpesto.com/cooking-lessons-in-umbria.php |
A skilled accomplished charge nurse with fifteen years of experience in implementing and developing nursing care plans, assessing patient's requirements and maintaining medical report.
Seeking for a Clinical Supervisor position to utilize my nursing and leadership experience in a reputable hospital.
Possess excellent communication and interpersonal skills
Advocate for patients, strive to understand patients' needs and concerns
Team leader with ability to create a positive working environment that uplifts staff and patients' spirits.
Goal oriented and excellent team player.
Positive qualities in developing and implementing quality patient care.
Experienced in medical surgical nursing, Hematology and Oncology.
Chemotherapy certified.
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Assist in coordinating daily operations for the department.
Collaborate with department coordinator to ensure smooth flow of patients to the unit by assigning beds. Determined patient care assignments in accordance with patient's requirements.
Keeps department coordinator informed as work related issues arise.
Intervene to resolve patient and family complaints.
Provide guidance to families and patients with long term illness.
Handled supervision of staffs, and conduct training for new nurses, serve as preceptor to nursing students and new nurses.
Collaborate with Clinical Nurse Specialist and Clinician to ensure a well plannned orientation and training program for new employees.
Demonstrates the ability to solve problems logically and independently as a Charge Nurse.
Evaluate and make clinical decisions on assigned patients.
Motivate staff in delivering effective and high quality patient care.
Assess, plan, evaluate and coordinate nursing and medical care, and collaborate with other disciplines to improve clinical care.
Educate assigned patients relating to condition and care.
Prioritized and delegate assignments, as a relief charge nurse on 36 beds medical surgical unit, contributed to a higher standard of patient care.
Coordinated with staffing office and identified staffing need for the unit.
Companies Worked For:
School Attended
Job Titles Held:
Degrees
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© 2019, Bold Limited. All rights reserved. | https://www.livecareer.com/resume-search/r/charge-nurse-preceptor-984c9faf2813403281380fb079df352e |
Ethan Clark Joins Property Subrogation Practice
Keis George LLP has named Ethan Clark an associate in the firm’s property subrogation practice. Clark will focus on large property losses involving product liability, fire and water damage, and construction defect matters. Clark will also litigate negligent workmanship matters involving utility company errors, general and subcontractor liability, and other types of deficiencies. Clark will assist in the firm’s defense practice, defending our insureds in bodily injury and contractual claims, including bad faith.
Ethan Clark Joins Property Subrogation Practice
Clark is at the forefront of his peers as his understanding of the changing nature of litigation allow him to be a reliable resource to those within the firm. He is often approached to discuss various legal theories and tasked with identifying ways to counter strategies used by opposing counsel.
Warren S. George, managing litigation partner, commends Clark’s litigation methodology. “Ethan energizes the litigation department. He has many good ideas and he is not afraid to challenge former procedures. That’s where his creativity will benefit our clients.”
Clark is a welcome addition to the firm’s property subrogation practice. A partner oversees each file to recovery with the support of firm associates and paralegals. The firm’s managing litigation partner encourages each partner and their respective associates to roundtable files so that every large loss is guided toward the best result.
Learn More About Ethan Here.
As a law clerk at Sprague Law, LLC, Clark participated in the Litigation Clinic at Wake Forest University School of Law, where he earned his juris doctor. Prior to law school Clark earned his bachelor’s degree in sociology from The Ohio State University.
Clark is a member of the Ohio State Bar Association, the Cleveland Metropolitan Bar Association, and the Federal Bar Association, which allows him to both integrate himself in the legal community and stay up to date on what is happening in the world of law. Clark works with the Legal Aid Society of Cleveland, bridging the gap between attorneys and those who need quality legal assistance. | https://www.keisgeorge.com/news/2019/01/23/ethan-clark-joins-property-subrogation-practice/ |
Here are some reminders in terms of content and format.
Remember, Besides including the works citation material, the annotation requires that you review the source for the following information:
Summarize: What are the main details or arguments? What is the point of this book or video or article or interview? What topics are covered? If someone asked what this source is about, what would you say? This may include both paraphrase and direct quotation (in either case, you should use parenthetical citation for facts/quotes/details).
Assess: After summarizing the source, evaluate it. How does it compare with other sources or your prior knowledge? Is the information reliable? Is this source biased or objective? What is the goal of this source?What are the author’s/speaker’s credentials or expertise?
Reflect: Once you've summarized and assessed a source, you need to ask yourself how it fits into your research. How was this source helpful or useful to you? How does it help you shape your argument or thinking? How has it changed how you think about the topic? What makes this source’s perspective special or significant?
CHECK that your Critical Annotation includes the following:
- MLA Heading and Header
- complete bibliographic information without hanging indent, single paragraph is preferred
- qualifications of author, his or her bias, point of view
- scope and purpose of the work, summary
- audience, or intended readership
- usefulness of the source, comparison to other sources or prior knowledge
STUDENT SAMPLE:
Lange, Dorothea. Tribute to Dorothea Lange. Flickr. 2007. Web. 21 September 2013.
Dorothea Lange is one of the most lauded Great Depression photographers of all time. Her pictures captured the ordeals of people throughout the country, and influenced even the government in providing aid. The photo shows a long line of people standing in front of a large sign. This sign, claiming, “There’s no way like the American Way," is juxtaposed with the poor and needy people in front of it. Lange published this work in order to give proof of the struggle endured by the American people, who did not get to experience the “American Way." Lange has an obvious bias towards the poor Americans; she publishes her work partially in the hope that they will be provided with aid. On the simplest level, the photo is appropriate for any audience, but only an older viewer would understand the implications of the photo. Lange’s photography is unlike any other attempt at capturing the Great Depression, which made her so successful.
Note: Though variance does occur in whether or not one should single or double space, indent or not indent, the majority of the content requirements are uniform. | http://www.stevensap.com/2015/03/then-and-now-critical-annotations.html |
While this quote from the 6th President of the United States, John Quincy Adams, was penned almost 200 years ago, his words have as much impact today as they did in the early 19th century. Indeed, this practice of inspiring others to dream more, learn more and do more captures the very type of leadership we are building in PSD – with parents, students, staff, administrators, and community partners.
In PSD, we believe that leadership has more to do with the actions you inspire than the position that you hold. As our values and beliefs statements highlights, “We value leadership in all places – everyone in our Division has the potential to be a leader.” For me personally, I believe it is incredibly important for PSD to build capacity and provide leadership opportunities for all staff, students, and parents and to provide encouragement along the way. Our success as a school division is dependent upon us working together in moving our vision and mission forward. We all have a meaningful role to play in these exciting times for PSD.
For those of you who might be wondering about the leadership and engagement opportunities that I’m referring to, here are but a few.
Student representatives from grades 9-12 meet with the PSD Board of Trustees throughout the year. The purpose of the Student Advisory Committee is to have direct conversation with the Trustees about any matters related to education in Parkland. Schools Councils play a significant role in advising administration at each school and their collective organization, the Council of School Councils (COSC), is a voice focused on the bigger picture of the School Division and provincial initiatives. Exploring Leadership is a cohort group of teachers who are participating in a program that provides opportunity to learn and reflect on their own professional journeys and the multitude of leadership situations that arise for teachers. And finally we have many staff, students and parents who participate in presentations and activities that teach others. In Parkland School Division we are very public about our learning and very generous in sharing and so we are called upon regularly to celebrate our successes and to assist other school divisions and organizations. Some recent examples include presentations at Teacher’s Convention and at the Shaping the Future – Engaging Healthy School Communities Conference.
I’m not saying that building leadership has to be a formal process – through a program, course, or committee. While we do have a number of quality opportunities like this, building leadership can be as simple as teachers collaborating with grade-level colleagues, students leading fundraising or awareness initiatives, or school council members working with community partners to build a playground or coordinate school lunch and snack programs.
We are incredibly fortunate in PSD to have so many talented leaders helping us become a place where exploration, creativity, and imagination make learning exciting and where all learners aspire to reach their dreams. Your actions are inspiring others to dream more, learn more, and do more. While we still have more to achieve in moving our new vision forward, it is inspiring to see so many leaders emerging throughout our division.
This entry was posted in Messages from the Superintendent and tagged leadership, leadership initiatives, PSD70. Bookmark the permalink. | http://www.psdblogs.ca/archives/618 |
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