text:
Researchers Find That a Family's Preference For Sons Results in Low Math Scores For Girl Children in Same Family
A group of researchers from the London School of Economics, the University of California Los Angeles, and Northwestern University has found in a new study that a family's preference towards boys can have a negative affect on their daughters' math achievement in school.
In order to determine if the family preferred boy children, the researchers used an approach called "fertility stopping rules," which is when a family continues to have children until they produce a boy. The researchers believed that while this is an imperfect sign of bias, it could be a sign that the family prefers boys.
In the researcher's first experiment, they analyzed families in Florida who expressed a preference for boys and who had children between 1994 and 2002 and sent them to public schools between 2002 and 2012. Even when accounting for economic and educational levels, girls in boy-favoring families did worse on math tests. Additionally, the wealthier the family and the more educated the mother, the worse the daughter performed on math tests. The boys from these families did not do better or worse in math than boys raised in other families.
In a second experiment, the researchers analyzed data from a 1979 Bureau of Labor Statistics survey that tracked people between ages 14 and 22. The researchers found about 5,000 women in that survey that had at least one child by 2014 and assessed their children's performance in math. The women in the survey were asked on multiple occasions if they agreed or disagreed with various statements about women being homemakers and caretakers.
The researchers found that the more the women believed a woman's place was in the home, the lower their daughters scored on math exams. There was no connection between the mother's attitudes and their sons' math performance.
In order to combat this phenomena, the researchers belief that both educators and parents need to set an example and undermine the stereotypes of women in STEM.
"When a mom says, 'I hate math,' that's reinforcing the stereotype that women hate math," said author David Figlio, dean of the School of Education at Northwestern University. "A really good thing to do, if you want your daughters to consider math, is to work extra hard to undermine that stereotype."
The full study, "Born in the Family: Preferences for Boys and the Gender Gap in Math," was published by the National Bureau of Economic Research. It can be accessed here.
Filed Under: Research/Study
Tags: London School of Economics • Northwestern University • University of California Los Angeles


text:
Astyanax jordani — вид лучепёрых рыб, обитающих в мексиканских пещерах. Не следует путать его со слепой пещерной формой другого вида — Astyanax mexicanus. При этом виды родственны и есть мнение, что Astyanax jordani всё же младший синоним или подвид Astyanax mexicanus.

Слепая пещерная рыба длиной до 10 см. Самки мечут икру в случайных местах, поэтому на дне пещеры должны быть щели и углубления, в которых клейкие икринки будут скрыты до вылупления мальков, чтобы избежать полного поедания обитателями пещерного водоёма, включая родителей.

Примечания

Харациновые
Рыбы Северной Америки
Троглобионты
Животные, описанные в 1936 году

redpajama_set_name: RedPajamaWikipedia


text:
"""Module for the Jax tracer functionality for tags."""
import functools
from typing import Any, Callable, Sequence, Tuple

import jax
from jax import core
from jax import util as jax_util
import jax.numpy as jnp

from kfac_ferminet_alpha import layers_and_loss_tags as tags
from kfac_ferminet_alpha import tag_graph_matcher as tgm
from kfac_ferminet_alpha import utils

_Function = Callable[[Any], Any]
_Loss = tags.LossTag

def extract_tags(
    jaxpr: core.Jaxpr
) -> Tuple[Sequence[core.JaxprEqn], Sequence[core.JaxprEqn]]:
  """Extracts all of the tag equations."""
  # Loop through equations and evaluate primitives using `bind`
  layer_tags = []
  loss_tags = []
  for eqn in jaxpr.eqns:
    if isinstance(eqn.primitive, tags.LossTag):
      loss_tags.append(eqn)
    elif isinstance(eqn.primitive, tags.LayerTag):
      layer_tags.append(eqn)
  return tuple(layer_tags), tuple(loss_tags)

def construct_compute_losses_inputs(
    jaxpr: core.Jaxpr,
    consts: Tuple[Any],
    num_losses: int,
    primals: Any,
    params_index: int) -> Callable[[Any], Sequence[Sequence[jnp.ndarray]]]:
  """Constructs a function that computes all of the inputs to all losses."""
  primals_ = list(primals)

  def forward_compute_losses(
      params_primals: Any,
  ) -> Sequence[Sequence[jnp.ndarray]]:
    primals_[params_index] = params_primals
    flat_args = jax.tree_flatten(primals_)[0]
    # Mapping from variable -> value
    env = dict()
    read = functools.partial(tgm.read_env, env)
    write = functools.partial(tgm.write_env, env)

    # Bind args and consts to environment
    write(jax.core.unitvar, jax.core.unit)
    jax_util.safe_map(write, jaxpr.invars, flat_args)
    jax_util.safe_map(write, jaxpr.constvars, consts)

    # Loop through equations and evaluate primitives using `bind`
    losses_so_far = 0
    loss_tags = []
    for eqn in jaxpr.eqns:
      tgm.evaluate_eqn(eqn, jax_util.safe_map(read, eqn.invars), write)
      if isinstance(eqn.primitive, tags.LossTag):
        loss_tags.append(eqn)
        losses_so_far += 1
      if num_losses is not None and losses_so_far == num_losses:
        break
    return tuple(tuple(read(v) for v in tag.invars) for tag in loss_tags)
    # return tuple(jax_util.safe_map(read, tag.invars) for tag in loss_tags)
  return forward_compute_losses

# We know when `.primitive` will be either a `LossTag` or a `LayerTag`, however
# pytype cannot infer its subclass, so we need to unbox it.

def _unbox_loss_tag(jaxpr_eqn: core.JaxprEqn) -> tags.LossTag:
  assert isinstance(jaxpr_eqn.primitive, tags.LossTag)
  return jaxpr_eqn.primitive

def _unbox_layer_tag(jaxpr_eqn: core.JaxprEqn) -> tags.LayerTag:
  assert isinstance(jaxpr_eqn.primitive, tags.LayerTag)
  return jaxpr_eqn.primitive

def trace_losses_matrix_vector_vjp(tagged_func: _Function,
                                   params_index: int = 0):
  """Returns the Jacobian-transposed vector product (backward mode) function in equivalent form to jax.vjp."""
  def vjp(*primals):
    typed_jaxpr = jax.make_jaxpr(tagged_func)(*primals)
    jaxpr, consts = typed_jaxpr.jaxpr, typed_jaxpr.literals
    _, loss_jaxpr_eqns = extract_tags(jaxpr)
    n = len(loss_jaxpr_eqns)
    losses_func = construct_compute_losses_inputs(
        jaxpr, consts, n, primals, params_index)
    losses_inputs, full_vjp_func = jax.vjp(losses_func, primals[params_index])
    losses = []
    for jaxpr_eqn, inputs in zip(loss_jaxpr_eqns, losses_inputs):
      loss_tag = _unbox_loss_tag(jaxpr_eqn)
      losses.append(loss_tag.loss(*inputs, weight=jaxpr_eqn.params["weight"]))
    losses = tuple(losses)

    def vjp_func(tangents):
      flat_tangents = jax.tree_flatten(tangents)[0]
      loss_invars = []
      loss_targets = []
      for jaxpr_eqn, inputs in zip(loss_jaxpr_eqns, losses_inputs):
        num_inputs = _unbox_loss_tag(jaxpr_eqn).num_inputs
        loss_invars.append(tuple(jaxpr_eqn.invars[:num_inputs]))
        loss_targets.append(inputs[num_inputs:])
      treedef = jax.tree_structure(loss_invars)
      tangents = jax.tree_unflatten(treedef, flat_tangents)
      # Since the losses could also take and targets as inputs and we don't want
      # this function to computes vjp w.r.t to those (e.g. the user should not
      # be providing tangent vectors for the targets, only for inputs) we have
      # to manually fill in these "extra" tangents with zeros.
      targets_tangents = jax.tree_map(jnp.zeros_like, loss_targets)
      tangents = tuple(ti + tti for ti, tti in zip(tangents, targets_tangents))
      input_tangents = full_vjp_func(tangents)[0]
      return input_tangents,
    return losses, vjp_func
  return vjp

def trace_losses_matrix_vector_jvp(
    tagged_func: _Function,
    params_index: int = 0):
  """Returns the Jacobian vector product (forward mode) function in equivalent form to jax.jvp."""
  def jvp(primals, params_tangents):
    typed_jaxpr = jax.make_jaxpr(tagged_func)(*primals)
    jaxpr, consts = typed_jaxpr.jaxpr, typed_jaxpr.literals
    _, loss_tags = extract_tags(jaxpr)
    n = len(loss_tags)
    losses_func = construct_compute_losses_inputs(jaxpr, consts, n,
                                                  primals, params_index)
    primals = (primals[params_index],)
    tangents = (params_tangents,)
    (primals_out, tangents_out) = jax.jvp(losses_func, primals, tangents)
    tangents_out = tuple(tuple(t[:tag.primitive.num_inputs])
                         for t, tag in zip(tangents_out, loss_tags))
    losses = tuple(tag.primitive.loss(*inputs, weight=tag.params["weight"])
                   for tag, inputs in zip(loss_tags, primals_out))
    return losses, tangents_out
  return jvp

def trace_losses_matrix_vector_hvp(tagged_func, params_index=0):
  """Returns the Hessian vector product function of **the tagged losses**, rather than the output value of `tagged_func`."""
  # The function uses backward-over-forward mode.

  def hvp(primals, params_tangents):
    typed_jaxpr = jax.make_jaxpr(tagged_func)(*primals)
    jaxpr, consts = typed_jaxpr.jaxpr, typed_jaxpr.literals
    _, loss_tags = extract_tags(jaxpr)
    n = len(loss_tags)
    losses_func = construct_compute_losses_inputs(
        jaxpr, consts, n, primals, params_index)

    def losses_sum(param_primals):
      loss_inputs = losses_func(param_primals)
      losses = [
          _unbox_loss_tag(jaxpr_eqn).loss(
              *inputs, weight=jaxpr_eqn.params["weight"])
          for jaxpr_eqn, inputs in zip(loss_tags, loss_inputs)
      ]
      # This computes the sum of losses evaluated. Makes it easier as we can
      # now use jax.grad rather than jax.vjp for taking derivatives.
      return sum(jnp.sum(loss.evaluate(None)) for loss in losses)

    def grads_times_tangents(params_primals):
      grads = jax.grad(losses_sum)(params_primals)
      return utils.inner_product(grads, params_tangents)

    return jax.grad(grads_times_tangents)(primals[params_index])
  return hvp

def trace_estimator_vjp(tagged_func: _Function) -> _Function:
  """Creates the function needed for an estimator of curvature matrices.

  Args:
    tagged_func: An function that has been annotated with tags both for layers
      and losses.

  Returns:
    A function with the same signatures as `tagged_func`, which when provided
    with inputs returns two things:
    1. The instances of all losses objected that are tagged.
    2. A second function, which when provide with tangent vectors for each
      of the loss instances' parameters, returns for every tagged layer a
      dictionary containing the following elements:
        inputs - The primal values of the inputs to the layer.
        outputs - The primal values of the outputs to the layer.
        params - The primal values of the layer.
        inputs_tangent - The tangent value of layer, given the provided
          tangents of the losses.
        inputs_tangent - The tangent value of layer, given the provided
          tangents of the losses.
        inputs_tangent - The tangent value of layer, given the provided
          tangents of the losses.
  """
  def full_vjp_func(func_args):
    # Trace the tagged function
    typed_jaxpr = jax.make_jaxpr(tagged_func)(*func_args)
    jaxpr, consts = typed_jaxpr.jaxpr, typed_jaxpr.literals
    layer_tags, loss_tags = extract_tags(jaxpr)

    layer_vars_flat = jax.tree_flatten([tag.invars for tag in layer_tags])[0]
    layer_input_vars = tuple(set(layer_vars_flat))

    def forward():
      own_func_args = func_args
      # Mapping from variable -> value
      env = dict()
      read = functools.partial(tgm.read_env, env)
      write = functools.partial(tgm.write_env, env)

      # Bind args and consts to environment
      write(jax.core.unitvar, jax.core.unit)
      jax_util.safe_map(write, jaxpr.invars, jax.tree_flatten(own_func_args)[0])
      jax_util.safe_map(write, jaxpr.constvars, consts)

      # Loop through equations and evaluate primitives using `bind`
      num_losses_passed = 0
      for eqn in jaxpr.eqns:
        tgm.evaluate_eqn(eqn, jax_util.safe_map(read, eqn.invars), write)
        if isinstance(eqn.primitive, tags.LossTag):
          num_losses_passed += 1
          if num_losses_passed == len(loss_tags):
            break
      if num_losses_passed != len(loss_tags):
        raise ValueError("This should be unreachable.")

      return jax_util.safe_map(read, layer_input_vars)

    def forward_aux(aux):
      own_func_args = func_args
      # Mapping from variable -> value
      env = dict()
      read = functools.partial(tgm.read_env, env)
      def write(var, val):
        if not isinstance(var, (jax.core.Literal, jax.core.UnitVar)):
          val = val + aux[var] if var in aux else val
        env[var] = val

      # Bind args and consts to environment
      write(jax.core.unitvar, jax.core.unit)
      jax_util.safe_map(write, jaxpr.invars, jax.tree_flatten(own_func_args)[0])
      jax_util.safe_map(write, jaxpr.constvars, consts)

      # Loop through equations and evaluate primitives using `bind`
      num_losses_passed = 0
      losses_inputs_values = []
      losses_kwargs_values = []
      for eqn in jaxpr.eqns:
        input_values = jax_util.safe_map(read, eqn.invars)
        tgm.evaluate_eqn(eqn, input_values, write)
        if isinstance(eqn.primitive, tags.LossTag):
          loss = eqn.primitive.loss(*input_values, weight=eqn.params["weight"])
          losses_inputs_values.append(loss.inputs)
          losses_kwargs_values.append(dict(
              targets=loss.targets,
              weight=eqn.params["weight"]
          ))
          num_losses_passed += 1
          if num_losses_passed == len(loss_tags):
            break
      if num_losses_passed != len(loss_tags):
        raise ValueError("This should be unreachable.")
      # Read the inputs to the loss functions, but also return the target values
      return tuple(losses_inputs_values), tuple(losses_kwargs_values)

    layer_input_values = forward()
    primals_dict = dict(zip(layer_input_vars, layer_input_values))
    primals_dict.update(zip(jaxpr.invars, jax.tree_flatten(func_args)[0]))
    aux_values = jax.tree_map(jnp.zeros_like, layer_input_values)
    aux_dict = dict(zip(layer_input_vars, aux_values))

    losses_args, aux_vjp, losses_kwargs = jax.vjp(forward_aux, aux_dict,
                                                  has_aux=True)
    losses = tuple(tag.primitive.loss(*inputs, **kwargs)
                   for tag, inputs, kwargs in
                   zip(loss_tags, losses_args, losses_kwargs))

    def vjp_func(tangents):
      all_tangents = aux_vjp(tangents)
      tangents_dict, inputs_tangents = all_tangents[0], all_tangents[1:]
      inputs_tangents = jax.tree_flatten(inputs_tangents)[0]
      tangents_dict.update(zip(jaxpr.invars, inputs_tangents))

      read_primals = functools.partial(tgm.read_env, primals_dict)
      read_tangents = functools.partial(tgm.read_env, tangents_dict)
      layers_info = []
      for jaxpr_eqn in layer_tags:
        layer_tag = _unbox_layer_tag(jaxpr_eqn)
        info = dict()
        primals = jax_util.safe_map(read_primals, tuple(jaxpr_eqn.invars))
        (
            info["outputs"],
            info["inputs"],
            info["params"],
        ) = layer_tag.split_all_inputs(primals)
        tangents = jax_util.safe_map(read_tangents, tuple(jaxpr_eqn.invars))
        (
            info["outputs_tangent"],
            info["inputs_tangent"],
            info["params_tangent"],
        ) = layer_tag.split_all_inputs(tangents)
        layers_info.append(info)
      return tuple(layers_info)

    return losses, vjp_func
  return full_vjp_func

redpajama_set_name: RedPajamaGithub


text:
So, as all know that now most populated cars are Tesla and the more the Tesla models 3. So, you should know about and know about the Tesla model 3 self-driving car. You will be able to know more about cars.
Now before starting to the topic, I would like to say that when reading and learning something from this don't quit in the middle. So, just because that every new feature is more important than the other. So, let us cover the topic now:
Trailers For Sale Victoria
Toyota Self Driving Car
Best Toyota Vehicles Car
Tesla model 3 self-driving car
So, all know that the owner of the Tesla company is the Elon Musk. So, as Elon Musk has just put a message on his twitter about the Tesla model 3 that Model 3 motor & gearbox still in good condition after driving 1M miles. Designed for ultra high endurance and he did it. So, let us start the Tesla model 3 self-driving car.
Things that you want to know about
About the hardware 1
Design of the Tesla model 3
Reception of the Tesla model 3
Autopilot of the Tesla model 3
The Tesla model 3 vehicles was manufactured after the late September 2014 are equipped with the camera mounted at the top of the windshield and forward-looking at the radar (supplied by the Bosch) in the lower grille and the ultrasonic acoustic location sensors in the front and rear bumpers that provide about 360-degree view around that car.
In 2013 the chief Franz von Holzhausen said that the Model 3 will "be an Audi A4. BMW 3 Series and Mercedes-Benz C-Class type of the vehicle. There will be offering them everything range, affordability, and the performance" which is targeted toward the mass market. While the technology from Tesla's Model S will be used at the Model 3 it will be 20% smaller than the Model S and have the own unique design.
So, the car-design the columnist and former car designer for the GM Robert Cumberford said that the Model 3 "is having an excellent design" and praised to the front fascia skin that he thinks is the superior to the black plastic simulated grille of the pre-refresh of the Model S. Cumberford praised the Model 3's minimalist design, and the "elegant simplicity" akin to Apple products. Now you had been known about the Tesla model 3 self-driving.
So, now coming to the last one which is the feature of the autopilot. So, Tesla model has a self-driving car features that help the rider that should be ok at the time of the emergence and automatically it wants to be autopilot. Autopilot advanced safety and it's convenience features are designed to it's assist you with the most burdensome parts of driving. So, it was about the Tesla model 3 self-driving car autopilot.
Top 5 BMW Autonomous Self Driving Cars
So, now coming to the conclusion and knowing more about the Tesla Model 3. Remember that performing anything with the zilch amount of knowledge is dangerous. However, even a little knowledge aids in perfrming to the next level. So does know about your car. So, hope you get something from this I hope that now you will be able to define the Tela model 3 to others.

redpajama_set_name: RedPajamaCommonCrawl


text:
India has a spirit where nation is above self: PM Modi
Prime Minister Narendra Modi on Sunday said that India is an idea, a family that stands for protecting the interests of humanity. Addressing a gathering at Dr Shyama Prasad Mukherjee Stadium here on the Goa Liberation Day celebrations, PM Modi said, "India has a spirit where the nation is above the 'self' and is paramount. Where there is only one mantra, nation first. Where there is only one resolve, Ek Bharat, Shreshtha Bharat." "The land of Goa, the air of Goa, the sea of Goa, have been blessed with a wonderful gift of nature. And today, this enthusiasm of the people of Goa, is adding to the pride of liberation," the Prime Minister said.
"I also had the privilege of paying homage to the martyrs at the Shaheed Memorial at Azad Maidan. After paying homage to the martyrs, I also witnessed the cell parade and fly past in Miramar. I got an opportunity to honour the veterans of Operation Vijay," the Prime Minister said.
The Prime Minister said that Goa came under Portugal at a time when other major parts of the country were ruled by the Mughals. "Countless political storms and turbulence has been witnessed by Goans. But even after centuries of distance between time and the upheaval of power, neither Goa has forgotten its Indianness, nor has India forgotten its Goa. This is a relationship that has only grown stronger with time."
"The people of Goa also did not allow the movements for liberation and Swaraj to stop. They kept the flame of freedom burning for the longest time in the history of India. This is because India is not just political power. India is an idea, a family that stands for protecting interests of humanity," PM Modi said.
On the occasion of Goa Liberation Day celebrations, Prime Minister Narendra Modi inaugurated development projects worth Rs 600 cr here on Sunday.
The Prime Minister felicitated the freedom fighters and veterans of "Operation Vijay" at the function. Goa Liberation Day is celebrated on 19 December every year to mark the success of "Operation Vijay" undertaken by the Indian Armed Forces that liberated Goa from Portuguese rule.
He inaugurated multiple development projects including the renovated Fort Aguada Jail Museum, Super Speciality Block at Goa Medical College, New South Goa District Hospital, Aviation Skill Development Center at Mopa Airport and the Gas insulated Substation at Dabolim-Navelim, Margao. He laid the foundation stone for India International University of Legal Education and Research of Bar Council of India Trust at Goa.
The Prime Minister released a Special Cover and Special Cancellation to mark the commemoration of the Indian Armed Forces freeing Goa from Portuguese rule. This special episode of history is shown on the special cover, whereas the special cancellation depicts the war memorial at Indian Naval Ship Gomantak, constructed in memory of seven young gallant sailors and other personnel who laid down their lives in "Operation Vijay".
Pak terrorist killed by security forces in Kashmir
With 107 cases, Delhi witnesses highest single-day spike in 6 months


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Natasha Devon- Support and Guidance
We are pleased to announce that we will be launching a series of Parent Support Groups from February 2021.
The groups are for parents living in Gloucestershire who are worried about the mental health and emotional wellbeing of their child or young person (between the ages of 11-18).
Groups will take place initially by Zoom on a variety of days and times. We aim to run groups face-to-face from April 2021 (providing COVID restrictions allow for this) at Gloucester, Forest of Dean and Cheltenham venues.
Further details can be found on the new Parent Support Group page of our website. Below are electronic versions of the information leaflet and diary listing all groups.
Parents will need to self-refer by completing the Online Referral Form accessed from the Parent Support Group page of our website. Telephone self-referrals are also accepted.
Please do contact Judith if you'd like to find out more information Judith Bell judith@ticplus.org.uk
If your child needs counselling, it doesn't mean you've failed.
Life is a struggle for many children and young people in today's world. Thousands of parents and carers contact us to get support for their child. You're not alone.
Many children and young people find that being able to speak confidentially to a counsellor who isn't in their close circle of friends and family, can really help. This is where TIC+ comes in. Our counsellors are qualified professionals who are experienced at working with children and young people. They care about what they do and want the best outcome for your child. They will not judge you or anyone in your family. Click on the logo for more
A Parents Guide to Depression; contains a summarised list of warning signs, advice and links to agencies for further support if you suspect that your child may be suffering from depression. The information explains how a referral should progress from initial enquiry to treatment. It is important to note that isolated symptoms or signs should not be taken out of context. If you have any concerns please call 111.
As part of our 'You're never too young to talk mental health' campaign we have produced a new resource for parents and carers to help start the difficult conversation.
Click on the image to access these resources.
There is more related content and a fantastic video halfway down the page! MindEd - click for a comprehensive resource centre aimed at parents coping with their children in all walks of their lives.
My Mum's got a Dodgy Brain from ForMed Films on Vimeo.
A film for children made by children who have a parent with a mental health problem, made in collaboration with Devon Partnership NHS trust.
Duchess of Cambridge to launch pilot mental health website to help primary schools support pupils Kate will give the green light to the initiative during a visit to a London primary school helping to trial the online portal coordinated and financed by the duchess' Royal Foundation. Click this link to find out more http://www.headstogether.org.uk/schools
& follow @heads_together on Instagram for live updates
Having a conversation with parents and carers about mental health
A Beginner's Guide for Schools. Developed with YoungMinds', Teachers' Insight Group (May 2019)
Mental health is a very emotional subject to talk about. This is especially true of conversations between teachers and parents and carers, whether they have approached you, or you have encouraged them to think about their family's mental health yourself. Click here to view the full resource.
Coping with Self-Harm - A Guide for Parents and Carers developed by researchers at the University of Oxford. Includes information on the nature and causes of self-harm, how to support a young person when facing this problem and what help is available.
Young people who self-harm- A Guide for School Staff developed by researchers at the University of Oxford.
Family Lives offers a guide to understanding self-harm, practical suggestions and links to further support.
The NSPCC's guide to self-harm find out how to spot the signs and what you can do to help.
Understanding Young Minds is a free resource pack which includes a poster, an infographic, an email footer, an image to share on social media and a website banner.
Know the Signs: information on suicide and self-harm for parents from the Samaritans
Papyrus is a national charity for the prevention of young suicide.
A registered charity which has been running a crisis centre since 2013. Providing face to face support to people who are at risk of suicide, we are totally independent. We know from speaking with families that the inquest can be a daunting prospect. Families can get support on how to cope after suicide, when it can get very confusing with so many unanswered questions.
The Staying Safe website is a potentially life-saving resource developed by 4 Mental Health, with invaluable with invaluable input from our Expert Reference Group of international academics, people with lived experience (including of surviving a suicide attempt, self-harm, supporting a friend or family member or bereavement by suicide), suicide prevention experts, mental health practitioners, general practitioners, policy makers, public health experts, sector experts, educationalists and concerned citizens.
StayingSafe.net offers compassion, kindness and easy ways to help keep people safer from thoughts of harm and suicide, seek support and discover hope of recovery through powerful videos from people with personal experience.
The website provides vital 'Safety Plan' guidance tools jointly funded by NHS England, with easy to print / online templates and guidance video tutorials purposefully designed to help people through the process of writing their own Safety Plan to build hope, identify actions and strategies to resist suicidal thoughts and develop positive ways to cope with stress and emotional distress.
Tragically, suicide takes far too many lives, yet suicide is preventable. Anyone struggling to cope or experiencing deep distress may begin to think about harming themselves and consider suicide as a means to escape their emotional pain. It can be incredibly difficult to think clearly during these times. Everyone is encouraged to PREPARE for possible difficult times ahead BEFORE they happen, by completing a Safety Plan.
Staying safe - safety plan template
Helplines for young people
How to talk about suicide sensitively Happiful Magazine October 2019
Talking about suicide is tough. It's also incredibly important. But, what's even more important is how we talk about it
If you know someone who might be feeling suicidal, you can find information on what to do, what to say and how to help them on Counselling Directory. Alternatively, the Samaritans have some really helpful advice on how to have a difficult conversation. Take a look at their website for guidance on how to help someone you're worried about open up about their feelings
At Girl Rising, stories inspire us. They encourage us to see the world differently. They show us what is possible. We have put together the Girl Rising Family Guide to help bring these stories and conversations into your homes. It includes links to the film chapters, additional supporting short videos, discussion guides, and more.
The Girl Rising message has always been one of resilience and courage, of hope in the face of challenge. Those values have never felt more important than they do today. (April 20)
Anxiety Affirmations
Anxiety can often take us by surprise, throwing us off course and preventing us from going about our normal lives. But repeating affirmations can help us take back control, and vocalise our intentions. Next time you feel overpowered by anxiety, stop for a moment, take a deep breath, and repeat one of these affirmations firmly to yourself. You may be surprised at the effect such simple, reassuring words can have
What is mean world syndrome?
Right now, perhaps more than ever before, it's easy to feel overwhelmed by the news cycle. But have you ever stopped to consider how the bad news that we're consuming could be seeping into the rest of our lives? It turns out that what we see and hear being reported, could be negatively impacting how we view the world. Find out more about mean world syndrome and how to tackle it.
How to overcome Sunday night anxiety
The weekend is just about to begin, but something that a lot of people will be familiar with is a sense of dread that winds its way up inside you on Sunday night. Whether you have a busy week of work ahead of you, or you feel overwhelmed by your job, don't let anxiety about the week ahead disturb your weekend. Learn how to tackle Sunday night anxiety, for good.
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The Culture of Bruising: Essays on Prizefighting.
Selected as one of the Best American Essays of the Century, Gerald Early's Life With Daughters: Watching the Miss America Pageant is a profoundly perceptive examination of America's beauty complex, and its effects on young Black women, as seen through the eyes of his ten- and seven-year-old daughters who, like their mother, have become avid fans of televised beauty pageants. Life With.
This week, I finished The Best American Essays of the Century (Joyce Carol Oates ed) and found Gerald Early's essay, "Life with Daughters: Watching the Miss America Pageant." Just another humbling and soaring moment in the learning curve for me, specifically on how to breach the cozy family wall of the personal essay into the wide cultural, political, and racial world we all stem from.
Tuxedo Junction Essays on American Culture by Gerald Early.
In his first new collection of sports essays since Tuxedo Junction (1989), the noted cultural critic Gerald Early investigates these contradictions as they play out in the sports world and in our deeper attitudes toward the athletes we glorify. Early addresses a half-century of heated cultural issues ranging from integration to the use of performance-enhancing drugs. Writing about Jackie.The Culture of Bruising is Gerald Early's long-awaited sequel to his award-winning first volume of essays Tuxedo Junction and, in the same spirit, he explores not only a variety of subjects but the form of the essay itself. Early's cultural ruminations on the sport of prize-fighting form the intellectual core and central metaphor of this book. That is to say, his subject, when writing about.Gerald Early has 39 books on Goodreads with 2135 ratings. Gerald Early's most popular book is Satchel Paige: Striking Out Jim Crow.
Tuxedo Junction: Essays on American Culture by Early, Gerald. Ecco Pr. Hardcover. 0880012323 Student Edition. No apparent missing pages. Light wear, fading or curling of cover or spine. May have used stickers or residue. Good binding with NO apparent loose or torn pages. Moderate writing, highlighting and marker. Supplemental materials are not guaranteed with used books.Gerald Early is the Merle Kling Professor of Modern Letters in the Department of English at Washington University in St. Louis, where he joined the faculty in 1982. He is the author of several books, including The Culture of Bruising: Essays on Prizefighting, Literature, and Modern American Culture (1994), for which he won the 1994 National Book Critics Circle Award for Criticism; This is.
Gerald Early is the Merle Kling Professor of Modern Letters at Washington University in St. Louis. He is the series editor of Best African American Essays and Best African American Fiction.He was a Fellow at the National Humanities Center in 2001-02. To cite this essay: Early, Gerald. "Jazz and the African American Literary Tradition.".
Here's a 1990 essay by Gerald Early about watching the Miss America contest with is family. As African-Americans, Early and his wife are conflicted about the messages in such a contest. But Vanessa Williams had won the contest a few years back, and then there was a little scandal. Even more conflicted thoughts. The daughters though, fascinated by the pageant, but not at all conflicted, love.
Gerald Early's second collection of essays features several of his characteristic themes and subjects: black identity, boxing, jazz, movies, material culture, masculinity and femininity, and.
Gerald Early Quotes. facebook; twitter; googleplus; I think there are only three things that America will be known for 2,000 years from now when they study this civilization: the Constitution, jazz music and baseball. They're the three most beautifully designed things this culture has ever produced. Gerald Early. Music, Baseball, Thinking. 6 Copy quote. It was common practice for me to take my.
The Culture of Bruising: Essays on Prizefighting, Literature, and Modern American Culture by Early, Gerald Book condition: Used - Good Book Description. Ecco Pr. Used - Good. Ships from the UK. Former Library book. Shows some signs of wear, and may have some markings on the i. Title: The Culture of Bruising: Essays on Prizefighting, Literature, and Modern American Culture; Author: Early.
Tuxedo Junction builds a theoretical framework that inv Ranging from presidential politics, literature, and cinema, to sports, jazz, and the Miss America contest, these essays serve simultaneously as intellectual autobiography and intellectual manifesto.
Gerald Early. Contributor. BIOGRAPHY. Merle Kling Professor of Modern Letters, Washington University, St. Louis, Missouri. Author of Tuxedo Junction: Essays on American Culture; The Culture of Bruising: Essays on Prizefighting, Literature, and American Culture. Primary Contributions (2) Articles; Motown. Motown, recording company founded by Berry Gordy, Jr., in Detroit, Michigan, U.S., in.
Tuxedo Junction: Essays on American Culture by Gerald Early A copy that has been read, but remains in clean condition. All pages are intact, and the cover is intact. The spine may show signs of wear. Pages can include limited notes and highlighting, and the copy can include previous owner inscriptions. At ThriftBooks, our motto is: Read More, Spend Less. See details - Tuxedo Junction: Essays.
Cornell University graduate Gerald Early is an essayist and professor at Washington University. Early was the director of African and Afro-American studies at Washington University and the director of the American Culture Studies Program.
Gerald early essays on the great. 5 stars based on 84 reviews kalamlakapp.com Essay. Prakritik aapda essay help first person interview essay birmingham dissertation. Abstract of prospectus for research paper outlining an argumentative essay on euthanasia. Fight club ending analysis essay schulterklopfen essay cornell johnson mba essays 2016 camaro masters dissertation timetable for roasting.
Gerald Lyn Early (born April 21, 1952) is an American essayist and American culture critic. He is currently the Merle Kling Professor of Modern letters, of English, African studies, African American studies, American culture studies, and Director, Center for Joint Projects in the Humanities and Social Sciences at Washington University in St. Louis, Missouri.
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Gerald Early: The Roosevelts: An Intimate History. Gerald Early was born as Gerald Lyn Early. He is known for his work on The Roosevelts: An Intimate History (2014), The War (2007) and Baseball (1994). He has been married to Ida Haynes since August 27, 1977. They have two children.
The first half is a series of scholarly lectures Early gave at Harvard University, the second half a group of essays commissioned by less academic venues. He adds an introduction that presents the.


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gui2de's Response to COVID-19
gui2de has been working with our partners in India, Pakistan, Kenya, and Tanzania to quickly respond to the challenges posed by COVID-19 in developing countries by adapting our ongoing projects, initiating new research and data collection, and disseminating evidence-based policy guidance for governments, NGOs, and the private sector.
A collection of the ongoing work for our affiliate researchers is provided on this page.
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How can India address big surge for health care after coronavirus lockdown?
"India's COVID-19 lockdown bought valuable time. Infection rates are only now starting to increase, and case fatality rates have remained lower than in many other countries. But how the health crisis plays out in the future depends critically on what is done with this borrowed time — and how effectively planning is done for the future…"
By Jishnu Das – June 3, 2020
The COVID-19 Development Innovation Agenda: An Economic and Financial Lens
"A successful response to both the coronavirus's health and economic costs in less developed countries requires that we move quickly to accelerate innovation and learning. The innovation agenda comes from the uncertainty associated with any emergent crisis. To support the public health response, innovation is needed to make behavior change easier to adopt and sustain. To meet the needs of firms working to rebuild markets, impact investors should be seeking to create innovative financial products and vehicles to avoid a liquidity crunch that could wipe out decades of investing for social impact."
By James Habyarimana – May 27, 2020
Smart Containment: How Low-Income Countries Can Tailor Their COVID-19 Response
"Low-income countries will have a much harder time putting their economies in a "medically induced coma" in response to the coronavirus pandemic (COVID-19). They are home to many of the extreme poor, who, for the most part, have no option but to live in overcrowded conditions with limited access to clean water and sanitation. They work in the informal sector, often for a daily wage, depend heavily on public service provision, and have limited savings and no access to credit. For many, staying at home is not a viable option, and not working comes at the expense of food and other necessities…"
With Jishnu Das – May 15, 2020
"Low-income countries will have a much harder time putting their economies in the "medically induced coma" of a full lockdown in response to the coronavirus (COVID-19) pandemic. They are home to many of the extreme poor, who, for the most part, have no option but to live in overcrowded conditions with limited access to clean water and sanitation. They work in the informal sector, often for a daily wage, depend heavily on public services, and have limited savings and no access to credit. For many, staying at home is not a viable option, and not working comes at the expense of food and other necessities…"
By Jishnu Das – May 14, 2020
Covid-19 Diaries: Early Impressions from an Online Questionnaire 1
We launched an online questionnaire for students to voice their experiences in the light of the Covid-19 pandemic. This note, submitted to American Ethnologist, is based on the first 516 responses and highlights a significant worsening of psychological well-being as home lives are now intertwined with academic pursuits at a time of considerable anxiety and stress.
By Benjamin Daniels, Ali Hamza, Beatrice Leydier, and Jishnu Das – May 1, 2020
Ask a Political Scientist: What makes a good democracy? Lessons from research in India
We all think democracy is good for us (well, many of us think that), but what makes for a "good" democracy? Is it as simple as fair and free elections, or something more? (hint: it's probably more.) This week we are joined by Irfan Nooruddin, professor and chair of Indian politics at the Georgetown School of Foreign Service to discuss what makes for good democratic governance, with lessons learned from his research in India! We'll also explore whether, given recent events, the 21st century is likely to be American, Chinese, Indian … or something else?
With Irfan Nooruddin – May 11, 2020
See gui2de's earlier work on COVID-19 here.
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Q: Python - AttributeError: index I am stuck here...
Connecting to t3://localhost:7001 with userid weblogic ...
Successfully connected to Admin Server 'examplesServer' that belongs to domain 'wl_server'.
Warning: An insecure protocol was used to connect to the
server. To ensure on-the-wire security, the SSL port or
Admin port should be used instead.

[MBeanServerInvocationHandler]com.bea:Name=mainWebApp,Type=AppDeployment
ParcelLienData.war
ParcelLienData
P
Problem invoking WLST - Traceback (innermost last):
  File "D:\RM-Share\RM-Scripts\wl_deploy_localhost-WC.py", line 30, in ?
AttributeError: index
My code looks like:
import sys
import getopt
import os

loadProperties(sys.argv[1] +".props")
connect(username,password,adminUrl)

cmd = "awk -F'Name=' '{print $2}' | awk -F',' '{print $1}'"

f = open(r'./applicationsList.txt','r')
#In Above line you can specify the Complete Path of the "applications.txt" as well

print f
for i in range(5):
       line=f.readline()
       line1=line[:-4]
       line2=line1[:1]
       #check if the service or application is already present on the server...
       cd('AppDeployments')
       myapps=cmo.getAppDeployments()
       for dep_file in myapps:
          print depfile
          print line
          print line1
          print line2
          num1=depfile.index(line2)
          print num1
          num2=depfile.index(",", num1)
          print num2
          appName=depfile[num1:num2]
          print appName

          if appName == "line1":
             print Redeploy
          elif appName != "line1":
             print "Not deploying"
             continue
          else:
             print Deploying

Please advice, where am I going wrong....
Thanks....

A: The error tells you that this line:
appName=dep_file[num1:num2]

Is wrong. Are you sure the dep_file object can be indexed with a slice?
Maybe you should call  getName() on dep_name first?

redpajama_set_name: RedPajamaStackExchange


To increase efficiency and to improve democratic and economic processes in Southeast Europe (SEE) by building an open Information Society.
To support the eGovernance programs of the participants in the eSEE (Electronic SEE) and bSEE (Broadband SEE) initiatives.
To serve a single regional coordination point and build a network of programs and training nodes in the field of eGovernance.
To disseminate the information and good practices by facilitating training and advising leaders and regional governments in the use of ICT.
To encourage regional ownership and be closely coordinated with those regional initiatives that would benefit from SEE eGovernance initiatives.
To enable strong participation and benefits for regional governments that support monitoring, design and implementation of policy-related elements of the modern Information Society.


text:
Where You Can Watch Japan's Highest Grossing Film "Demon Slayer"
ByCan Kay Posted on December 28, 2020 May 11, 2021 Updated on May 11, 2021
Demon Slayer: Kimetsu No Yaiba: Mugen Train surpassed Spirited Away and became Japan's #1 movie! 19 years of Spirited Away reign is over! Spirited Away, the successful film by Studio Ghibli and Hayao Miyazaki, was Japan's #1 film for 19 years. However, as of today, Demon Slayer has taken the lead. Demon Slayer: Mugen Train began staging in Japan's IMAX theaters on October 16 and it has so far made 32,478,895,850 yen (the US $ 313,513,909) in 73 days.
劇場版「鬼滅の刃」無限列車編、公開73日間で観客動員 2404万9907人(興行収入 324億7889万5850円)となりました。2020年、映画と共に、様々な形で本作に触れていただいたお一人お一人に心より御礼申し上げます。皆様のご健勝とご多幸をお祈りしております。良いお年をお迎えください。#鬼滅の刃
— 鬼滅の刃公式 (@kimetsu_off) December 28, 2020
Of course, when Spirited Away aired at the box office, technologies like IMAX or 4DX were absent and ticket prices were lower. That's why we have to take these details into consideration while examining these sales. However, there is an important detail that Mugen Train has not been released anywhere outside of Japan yet. If we add the earnings from major markets such as America, Europe, and China, Mugen Train seems to continue to break revenue records. It is one of the most popular anime series in the world. Now, it's breaking records with the movie Demon Slayer: Mugen Train.
When is the Demon Slayer: Kimetsu no Yaiba the Movie: Mugen Train release date?
The film aired in Japan on October 19. However, there is no official statement yet for the rest of the world. There are rumors circulating for North America and China. It looks like we will be able to watch Mugen Train in 2021.
Where will Demon Slayer: Kimetsu no Yaiba the Movie: Mugen Train be available to watch?
Unfortunately, just like the release date, where the movie will be streamed has not been published by official sources. Its anime series is now available on Hulu. It is a question mark that Demon Slayer's movie will be released on Hulu.
Demon Slayer: Kimetsu no Yaiba the Movie: Mugen Train about what?
The movie is based on Koyuharu Gotoge's manga of the same name. The manga is currently published in the Weekly Shonen Jump comic anthology, with more than 14 million prints at a time. The story begins like this; One day, Tanjiro learns that his fond family was murdered by a demon, that only his sister Nezuko survived, but that he had actually turned into a demon. Tanjiro becomes a demon hunter in order to save his sister and turn her back into a human. You can watch the official trailer below!
About Demon Slayer (Via Wikipedia)
Demon Slayer: Kimetsu no Yaiba (鬼滅の刃, Kimetsu no Yaiba, lit. "Blade of Demon Destruction"[4]) is a Japanese manga series written and illustrated by Koyoharu Gotouge. It follows Tanjiro Kamado, a young boy who wants to become a demon slayer after his family is slaughtered and his younger sister Nezuko is turned into a demon. It was serialized in Shueisha's shōnen manga magazine Weekly Shōnen Jump from February 2016 to May 2020, with its chapters collected in 23 tankōbon volumes. It has been published in English by Viz Media and simulpublished by Shueisha on their Manga Plus platform.
A 26-episode anime television series adaptation produced by Ufotable aired in Japan from April to September 2019. A sequel film, Demon Slayer: Kimetsu no Yaiba the Movie: Mugen Train, premiered in October 2020 and became the highest-grossing anime film and Japanese film of all time. Meanwhile, the second season will premiere in 2021.
As of February 2021, the manga had over 150 million copies in circulation, including digital versions, making it one of the best-selling manga series of all time. Meanwhile, the anime series has received critical acclaim, with critics praising the animation and fight sequences. It has received numerous awards and is considered one of the best anime of the 2010s. As of December 2020, the Demon Slayer franchise is estimated to have generated total sales of at least ¥270 billion ($2.6 billion) in Japan.
Can Kay
THE BEATLES Fan Solve Which Baseball Movie Inspired John Lennon Song
ByYunus Emre Özdiyar October 4, 2020
THE BEATLES expert Kenneth Womack discover which baseball film inspired John Lennon's love song. Before a month ago he was shot dead in 1980, released the new song "Grow Old With Me" and lyrics from…
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Miley Cyrus Reveals Inspired by METALLICA for Her New Album
ByYunus Emre Özdiyar September 14, 2020
Miley Cyrus reveals METALLICA and Britney Spears are inspirations for her new album. She already released the first song, 'Midnight Sky' from the seventh studio album. So you think how Miley Cyrus inspired by METALLICA….
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When is the release date of 'In the Dark' season 4?
BySimge Yıldırımkaya February 7, 2021
In the Dark, which is about a young, blind woman who tries to solve her friend's murder is now renewed for its 4th season! In The Dark was first released on April 4, 2019. It…
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My Chemical Romance Launches Charity Collaboration With Soundwaves Art
ByBen Hestad May 6, 2021 May 23, 2021
My Chemical Romance has partnered with Soundwaves Art to produce several pieces of wave form art, with frontman Gerard Way signing select pieces to raise money for both The Trevor Project and KultureCity. The Trevor…
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The Witcher: Netflix Shares Behind-the-Scenes Look as Wraps Production on Season 2
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Netflix has released a behind-the-scenes video for The Witcher season 2 and announced that the production phase of The Witcher season 2 is finally completed. To celebrate the moment, Netflix shared a new teaser of…
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The First Official Trailer for Elle Fanning's Teen Spirit Film: Watch
Bleecker Street and LD Entertainment released the official trailer for Elle Fanning's musical drama Teen Spirit. We will see Fanning (Maleficent, The Beguiled) in her quest to be a pop star in the new film….
Read More The First Official Trailer for Elle Fanning's Teen Spirit Film: WatchContinue


One afternoon late in the summer of 1956, I spoke my first words. "Down water," I told my parents, and that terse announcement meant that I wanted to toddle along the path from our rented summer cabin in upstate New York to the glistening shoreline of Lake George.
I know of those words and that incident not because I remember them. My own recollections don't begin till I am three-years-old and sitting on my paternal grandmother's ample lap in the Jewish anarchist colony where she raised my father and his siblings.
Rather, the story of 10-month-old me at Lake George is embossed into my psyche by a particular article of clothing. It was a sweatshirt my father had worn that summer, with a zipper from the neckline to the sternum, and the resort's logo stenciled in thick green ink on the left breast.
By the time I received that sweatshirt as a hand-me-down when I was in my teens, my father had worn it so often and my mother had washed it so often that the cotton on the inside had pilled up and the green ink was crusty and cracking.
For that matter, the sweatshirt barely fit me. My father stood a sturdy 5 foot 8 inches, and I, entering my junior year of high school, had barely cracked 5 feet. The sweatshirt that my father's muscles filled out hung sacklike over my skinny frame and halfway down my thighs.
But I inordinately, disproportionately adored wearing the sweatshirt, as if in tugging it on I was donning some kind of generational continuity, too. That garment seemed to carry my father's sweat, his scent, his very cells, the manliness for which I yearned.
The sweatshirt never made it to college with me in the fall of 1973. By then, at least, I had outgrown my father by several inches. I did, however, bring another piece of his clothing to my dorm at the University of Wisconsin. This was a short-sleeve button-down shirt in a black-and-white Tattersall pattern.
On the hottest days, I wore that checked shirt for the way it admitted the breeze. And also for the mental snapshot it conjured, of my father clad in it as he piloted the small boat we used for those Lake George vacations and summer weekends on the murky waters of the Raritan Bay. My father seemed the vision of capability at the steering wheel of that little boat, a master of mechanical things beyond my ken.
So I wore the Tattersall shirt even though it barely reached my adult waist. In a favorite photograph of me, taken by a long-ago girlfriend — at an afternoon picnic in a forest preserve near Chicago, several hours after I'd run a personal-best in a half-marathon — I am wearing it. When I traveled to Egypt in 1982, I brought it along. And when the arid desert air and unrelenting sun conspired to blister the skin on my ears, I fashioned the shirt into a kind of protective headdress.
My father was a man indifferent to clothes as a matter of political principle, and there was nothing aesthetically special about the sweatshirt and the Tattersall. His elder brother Ziggy, a Manhattanite and compulsive shopper, was the relative who regularly bestowed on me barely used dress shirts from his Saturday pilgrimages to Saks and Bloomingdale's.
Indeed, Ziggy was a bit taller than my father, and a long-sleeve shirt from him could just about cover my 35-inch sleeves. Ziggy also took it as a mission, I think, to compensate for my father's willful inability to teach me how to dress for dates.
Even so, none of the Ziggy shirts exert any particular hold on my heart all these decades later, whereas the sweatshirt and the Tattersall fill me with sweet melancholy, especially at this time of year, as Father's Day approaches. It falls, as always, on the third Sunday of June, near the longest day of the year, that summer solstice when life feels as endless as the sunlight.
My father is by now seven years in his grave, and I remember vividly the last time I wore his sweatshirt. It was an August twilight in the early 1970s, and I was tossing around a football in a vacant lot in my Central Jersey hometown with one of my best friends.
We were in a jocular mood together, savoring the remaining week or two of summer vacation. Then, in the midst of our tosses and our chatter, I realized it was getting dark, even though it was barely past 7 p.m. I heard leaves rustle and felt a surprisingly cool burst of wind, the first presentiment of autumn. It promised golden-hued days of October and the turning of the leaves.
Yet it also augured the end of things, the certainty of death. By that time I was in my mid-teens, and my mother had been diagnosed with the breast cancer that would soon kill her. My father had spent an unexplained several days in the hospital, presumably for a heart attack. Such an attack had recently killed my best friend's father, who had lived across the street.
So I felt an awareness of mortality that set me apart from most of my peers. And that awareness was mystically conflated with the sweatshirt, which was inexorably aging in its own ways. As for the Tattersall shirt, not long after my Egypt trip its decades-old fabric began to tear, and not even my capacious nostalgia was enough to save it from the Salvation Army bin.
A couple of years ago, though, I was browsing a website, looking for a few lightweight shirts, and there I saw a button-down short-sleeve with the exact same pattern. I bought it in my size, and I have worn it a few times each summer. If I take care of it, it should last a number of years.
Nearing 62, I cherish my health. I've survived prostate cancer and have the luxury of fretting about things like a receding hairline and tendinitis. My father lived until 89. And maybe, just perhaps, my son or daughter will, some distant day in the future, ask for that Tattersall shirt.
Samuel G. Freedman is a contributing editor to the Forward. His most recent book is "Breaking the Line: The Season in Black College Football That Transformed the Sport and Changed the Course of Civil Rights" (Simon & Schuster, 2013).
This story "On Father's Day, I Reminisce About My Dad's Sweatshirt" was written by Samuel G. Freedman.


text:
\section{Introduction and statement of results}
The structure of group algebras and restricted enveloping algebras,
over a field $K$ of characteristic $p>0$, that are Lie nilpotent,
Lie solvable ($p\neq2$) or satisfy the Engel condition has been
completely determined in \cite{passi-passman-sehgal, riley-shalev:lie_structure,
sehgal:topics}.   Integral to the proof of these results was the fact that each of these
conditions corresponds to a particular {\em nonmatrix identity},  which is to say,
a polynomial identity not also satisfied by the algebra $M_2(K)$ of all $2\times 2$
matrices.

Nonmatrix identities in characteristic zero were studied  by Kemer
in \cite{kemer:nonmatrix},
 who showed, in particular, that nonmatrix varieties are Lie solvable. The situation in
positive characteristic is more complicated. More recently, the existence of an arbitrary
nonmatrix identity was shown in \cite{billig-riley-tasic} to be intimately related to the
existence of a group identity in the group of units of a certain class of associative
algebras, which includes group algebras of periodic groups and  restricted enveloping
algebras of $p$-nil restricted Lie algebras.

In this first half of this paper we completely describe enveloping algebras and group
algebras which satisfy a nonmatrix identity. In the results below, $K[G]$ and
$u(L)$ denote, respectively, the group algebra of a group $G$  and the
restricted universal enveloping algebra of the restricted Lie algebra $L$. In
addition, $\omega(R)$ represents the augmentation ideal of
$R=u(L)$ or $K[G]$,  while $\gamma^2(R)$ denotes its (associative) commutator ideal.

\begin{theorem}
\label{nonmatrix-u(L)}
The following statements are equivalent for a restricted Lie
algebra $L$ over a field of characteristic $p>0\mathrm{:}$

\begin{enumerate}
\romenumi

\item $u(L)$ satisfies a nonmatrix identity\textup{;}
\item $\omega(u(L))$ satisfies a nonmatrix identity\textup{;}
\item $L$ contains a restricted ideal $A$ such that both $L/A$ and $A'$
 are finite-dimensional, and  $L'$ is $p$-nil of bounded index\textup{;}
\item $\gamma^2(u(L))$ is nil of bounded index.

\end{enumerate}
\end{theorem}

\begin{theorem}
\label{nonmatrix-K[G]}
The following statements are equivalent for a group $G$ and
a field $K$ of characteristic $p>0\mathrm{:}$

\begin{enumerate}
\romenumi

\item $K[G]$ satisfies a nonmatrix identity\textup{;}
\item $\omega(K[G])$ satisfies a nonmatrix identity\textup{;}
\item $G$ has a normal subgroup $A$ such that both $A'$ and $G/A$ are
finite, and $G'$ is a $p$-group of finite exponent\textup{;}
\item $\gamma^2(K[G])$ is nil of bounded index.
\end{enumerate}

\end{theorem}

It was conjectured in \cite{riley:boundednil} and \cite{riley:tensor},
respectively, that if $R$ and $S$ are arbitrary algebras over a
field of characteristic $p>0$ satisfying nonmatrix identities, then
$\gamma^2(R)$ is nil of bounded index  and the tensor product $R\otimes_K S$
also satisfies some nonmatrix identity. The corresponding results were shown
to fail in characteristic 0.  Theorems~\ref{nonmatrix-u(L)} and~\ref{nonmatrix-K[G]}
verify both these conjectures for  the class of restricted enveloping algebras,
since $u(L)\otimes_Ku(M)\cong u(L\times M)$, and the class of group algebras,  since
$K[G]\otimes_KK[H]\cong K[G\times H]$.

It will become apparent in the next section (see the paragraph after
Proposition~\ref{nonmatrix}) that if $R$ is either an  ordinary enveloping algebra over an
arbitrary field, or a group algebra over a field of  characteristic zero, and $R$
satisfies a nonmatrix identity, then
$R$ must be commutative.

In the second half of this article we look at  restricted
enveloping algebras and group algebras which satisfy a semigroup identity.
A {\em semigroup identity} is a polynomial identity of the form
$$f(x_1,\dots,x_n)=w_1(x_1,\dots,x_n)-w_2(x_1,\dots,x_n)=0,$$
where $w_1$ and $w_2$ are monomials.
It follows from well-known results that  a semigroup
identity is a nonmatrix identity precisely  when the base field $K$ is infinite. In fact,
by a result of Jones \cite{jones:varieties}, every proper variety of groups can contain
only finitely many simple groups. Hence the general linear group $GL_2(K)$ does not
satisfy any group identity unless $K$ is finite. This last fact is also a special case of
\cite[Theorem 1.2]{billig-riley-tasic}. The present authors studied arbitrary algebras
$R$ over an infinite field that satisfy a semigroup identity in
\cite{riley-wilson:semigroup}.   In particular, we proved that if $R$ is unital then $R$
satisfies a semigroup  identity if and only if $R$ satisfies the Engel condition:
$$[x, _my]=[x,\underbrace{y,\dots,y}_m]=0,$$
for some $m$.
Hence, using the characterization of the Engel condition in restricted enveloping
algebras and group algebras in \cite{riley-shalev:lie_structure} and \cite{sehgal:topics},
respectively, we immediately obtain the equivalence of the first three conditions
in each of the following two theorems:

\begin{theorem}
\label{semigroup-u(L)}
The following statements are equivalent for a restricted Lie algebra $L$
over an infinite field of characteristic $p>0\mathrm{:}$
\begin{enumerate}
\romenumi

\item $u(L)$ satisfies a semigroup identity\textup{;}
\item $u(L)$ satisfies the Engel condition\textup{;}
\item $L$ is nilpotent, $L'$ is $p$-nil of bounded
index, and $L$ contains a restricted ideal $A$
such that both $L/A$ and $A'$ are finite-dimensional\textup{;}
\item $L'$ and $L/Z(L)$ are $p$-nil of bounded index
and $L$ contains a restricted ideal $A$ such that both $L/A$ and
$L'$  are finite-dimensional.

\end{enumerate}
\end{theorem}

\begin{theorem}
\label{semigroup-K[G]}
The following statements are equivalent for a group $G$
and an infinite field $K$ of characteristic $p>0\mathrm{:}$
\begin{enumerate}
\romenumi

\item $K[G]$ satisfies a semigroup identity\textup{;}
\item $K[G]$ satisfies the Engel condition\textup{;}
\item $G$ is nilpotent and contains a normal subgroup $A$ such that both
$G/A$ and $A'$ are finite $p$-groups\textup{;}
\item $G'$ and $G/Z(G)$ are $p$-groups of finite exponent and
$G$ contains a normal subgroup $A$ such that both $G/A$ and $A'$ are finite.

\end{enumerate}
\end{theorem}

Note that since every finite ring satisfies an identity of the form
$x^k-x^l=0$, these results do not hold when $K$ is finite.
Observe also that the corresponding conditions (iv) provide an exact
analogue between the group algebra and restricted enveloping algebra cases.
These alternate characterizations will prove useful below.
The proof of their equivalence requires some work and will be given later.

For nonunital algebras, semigroup identities are more difficult to
classify. In particular, the existence of a semigroup identity does not generally imply
the Engel condition. In fact, this implication does not even hold for augmentation
ideals:

\begin{example}
\label{e:2-D}
 Let $K$ be a field of characteristic 2, and let $L$
be the 2-dimensional restricted Lie algebra over $K$ generated by
$a,b$ with relations $[a,b]=a$, $a^2=0$, $b^2=b$.
Then $\omega(u(L))$ satisfies the semigroup identity
$$wxyz-wyxz=0,$$
despite the fact that $\omega(u(L))$ does not satisfy the Engel
condition.
\end{example}

\begin{example}
\label{e:dihedral} Let $K$ be a field of characteristic 3, and let $G$ be
the dihedral group of order 6.  Then $\omega(K[G])$ satisfies the
semigroup identity
$$yxy^2-y^2xy=0,$$
and yet $\omega(K[G])$ does not satisfy the Engel condition.
\end{example}

We shall see in Section~\ref{s:semigroup} though, that these two examples are in some
sense canonical.

\begin{theorem}
\label{semigroup-omega(u(L))}

Let $L$ be a restricted Lie algebra over an infinite field
of characteristic $p>2$.
Then the following statements are equivalent\textup{:}
\begin{enumerate}
\romenumi

\item $\omega(u(L))$ satisfies a semigroup identity\textup{;}
\item $\omega(u(L))$ satisfies an identity of the form $y^m[x, _my]y^m=0$\textup{;}
\item $L'$ and $L/Z(L)$ are both $p$-nil of bounded index and
$L$ contains a restricted ideal $A$ of finite codimension such that $L'$ is
finite-dimensional\textup{;}
\item $u(L)$ satisfies the Engel condition.

\end{enumerate}
\end{theorem}

\begin{theorem}
\label{semigroup-omega(K[G])}
Let $K$ be an infinite field of characteristic $p>0$, and suppose that $p=2$ or $G$ is a
group with no $2$-torsion. Then the following statements are equivalent\textup{:}
\begin{enumerate}
\romenumi

\item $\omega(K[G])$ satisfies a semigroup identity\textup{;}
\item $\omega(K[G])$ satisfies an identity of the form $y^m[x, _my]y^m=0$\textup{;}
\item $G'$ and $G/Z(G)$ are $p$-groups of finite exponent and $G$ contains a
normal subgroup $A$ of finite index such that $A'$ is finite\textup{;}
\item $K[G]$ satisfies the Engel condition.

\end{enumerate}
\end{theorem}

\section{Nonmatrix identities}
In this section we prove Theorems~\ref{nonmatrix-u(L)} and~\ref{nonmatrix-K[G]}.
Throughout, $K$ is a field, $G$ a group and $L$ a restricted Lie
$K$-algebra. For each (ordinary) subalgebra $H$ of $L$, $H_p$ denotes its $p$-hull
inside $L$.

We begin by collecting some important facts about algebras  satisfying a
nonmatrix identity.

\begin{proposition}
\label{nonmatrix}
Let $R$ be an algebra over a field $K$.
If $R$ satisfies a nonmatrix identity then the following statements hold\textup{:}
\begin{enumerate}
\romenumi
\item The unital hull of $R$ also satisfies a nonmatrix identity.

\item $\gamma^2(R)$ is nil, and is nilpotent if $R$ is finitely
generated over $K$.

\item If $\ch K=p>0$ then $R$ satisfies an identity of the form
$([x,y]z)^{p^t}=0$, so that $\gamma^2(R)$ is generated by nilpotent
elements of bounded index.

\item If $\ch K=p>0$ and  $R=\omega(K[G])$ then $G'$
is a $p$-group generated by elements of bounded $p$-power order.

\item If $\ch K=p>0$ and $R=\omega(u(L))$ then $(L')_p$ is a $p$-nil
restricted Lie algebra generated by $p$-nilpotent elements of bounded index.
\end{enumerate}

\end{proposition}

\begin{proof}

Let $S$ be the unital hull of $R$, that is, $S=R$ if $R$ is unital and $S=R\oplus
K\cdot 1$ otherwise. Then $R$ is an associative ideal of $S$ such that$[S,S]S\subseteq R$.
 Let $f(x_1,\dots ,x_n)=0$ be a nonmatrix identity satisfied by $R$. It follows that $S$
satisfies the identity
$$f([x_1,y_1]z_1,\dots ,[x_n,y_n]z_n)=0.$$
Now this last identity is also nonmatrix, since
$$a=[e_{12},e_{21}](e_{11}-e_{22})a$$
for every $a\in M_2(K)$, and this proves (i).

Henceforth, we assume that $R$ is unital.

Let $f$ be the given nonmatrix identity, and $J(R)$ the
Jacobson radical of $R$. We first show that $R/J(R)$ is commutative. Now
$R/J(R)$ is a semiprimitive PI-algebra, and hence a subdirect product of
primitive PI-algebras, each of which satisfies $f$.  By a theorem of
Kaplansky, a primitive PI-algebra is simple and finite-dimensional over
its centre, and thus has the form $M_n(D)$ where $D$ is a division algebra
finite-dimensional over its centre $F$. Since $M_2(F)$ does not satisfy
$f$, $n=1$. If $D$ is finite then $D=F$, while if $D$ is infinite then
$D$ satisfies the same identities as some $M_m(F)$. The nonmatrix
condition gives $m=1$ and so either way $D=F$. Thus $R/J(R)$ is a
subdirect product of fields and hence commutative. It
follows that $\gamma^2(R)\subseteq J(R)$.

By a theorem of Braun \cite{braun:nilpotency}, if $A$ is a finitely
generated PI-algebra then $J(A)$ is nilpotent. Let $A$ be the relatively
free algebra on 3 generators in the variety defined by the given
nonmatrix identity $f$.  Then  $\gamma^2(A)\subseteq J(A)$ is nilpotent
and so $A$ satisfies an identity of the form $([x,y]z)^{m}=0$. It
follows that $R$ also satisfies this same identity. This yields (ii) and
(iii). If $R=u(L)$ then $L'\subseteq \gamma^2(R)$, whereas if $R=K[G]$ then
$G'\subseteq 1+\gamma^2(R)$, yielding (iv) and (v).

\end{proof}

If an ordinary enveloping algebra $U(L)$ satisfies a nonmatrix identity
then $L'$ is nil. By the Poincar\'{e}-Birkhoff-Witt (PBW) theorem, $L'=0$
and $L$ is abelian. For similar reasons, $K[G]$ satisfies a nonmatrix
identity in characteristic $0$ if and only if $G$ is abelian.
Thus we shall focus on modular group algebras and restricted enveloping algebras from now
on. Because of the strong parallels between the group algebra and restricted
enveloping algebra cases, we prove only the restricted enveloping algebra
case in detail.

For the rest of this section, $K$ will be assumed to be of characteristic $p>0$.
\subsection*{Enveloping algebras}

We adapt a lemma of Passman \cite[Lemma 3.2]{passman:units2} to
the enveloping algebra situation.

\begin{lemma}
\label{expand}
Let $A$ be a restricted ideal of an abelian restricted Lie
algebra $L$ such that $\dim L/A$ is finite. If $I$ is an $L$-stable
ideal of $u(A)$ then the ideal $J=Iu(L)=u(L)I$ of $u(L)$
generated by $I$ is  nil of bounded index if (and only if) $I$ is.

\end{lemma}

\begin{proof} Let $n=\dim L/A$. Jacobson's theorem (the analogue of the
PBW theorem for restricted Lie algebras) implies
that as a left $u(A)$-module, $u(L)$ is free of rank $q=p^n$.
Indeed, if $\{x_1,\dots ,x_n\}$ is an ordered basis for a vector space
complement for $A$ in $L$, the monomials $x_1^{i_1}\cdots x_n^{i_n}$
form a basis for $u(L)$ over $u(A)$.

The right regular representation of $u(L)$ embeds $u(L)$ into $M_q(u(A))$
in such a way that for all  basis monomials $\nu$, $\nu
x=\sum_{\mu}x_{\nu\mu}\mu$ for $x\in u(L)$. If
$x\in J$ then also $\nu x\in J$.  Since $J=\bigoplus_{\mu} I\mu$ we have
$\sum_{\mu}x_{\nu\mu}\mu\in \bigoplus_{\mu} I\mu$.  Since all
$x_{\nu\mu}\in u(A)$, freeness yields
$x_{\nu\mu}\in I$ and so $J$ embeds in $M_q(I)$.

If $I$ is nil of bounded degree $p^t$, then since every element of
$M_q(I)$ is algebraic of degree at most $q$ over the central
subalgebra $I$, it follows easily that $M_q(I)$ is nil of bounded
index at most $qp^t$.

\end{proof}

\begin{proof}[Proof of Theorem~\ref{nonmatrix-u(L)}]
Clearly (i) is equivalent to (ii) by Proposition~\ref{nonmatrix}, while the fact that (iv)
implies (i) is immediate.

Recall that for an (ordinary) ideal $J$ of $L$, the ideal generated by
$J$ in $u(L)$ is $\omega(u(J_p))u(L)=u(L)\omega(u(J_p))$.
By Jacobson's theorem, this ideal is nilpotent if and only if
$J_p$ is finite-dimensional and $p$-nil.

Results of Passman \cite{passman:u(L)-PI} and Petrogradski \cite{petrogradski},
yield that $u(L)$ satisfies a polynomial identity if and only if
$L$ contains a restricted ideal $A$ such that $\dim L/A<\infty$,
$\dim A'<\infty$ and $(A')_p$ is $p$-nil.
Suppose that condition (i) holds, so that $L$ has a restricted ideal
$A$ with these basic properties.  In particular, $A$ is solvable
since by Engel's theorem it is nilpotent-by-abelian.
To show (i) implies (iii), it remains to show that $(L')_p$ is $p$-nil of bounded
index. Certainly $(L')_p$ is $p$-nil and generated by $p$-nilpotent elements of
bounded index by Proposition~\ref{nonmatrix}.
Thus $(L')_p/(A\cap (L')_p)$ is  finite-dimensional and $p$-nil,
so that $(L')_p$ is solvable. Consequently, $L$ is solvable.
Now arguing by induction on the derived length of $L$ enables
us to reduce to the case when $L'$ is abelian.
But in this case $(L')_p$ is clearly $p$-nil of bounded index,
since it is generated by elements with that property.

Finally, suppose that (iii) holds. We show that $\gamma^2(u(L))$ is nil
of bounded index. We make a series of reductions based on the
fact that the class of algebras which are nil of bounded index is closed
under extensions.
Because $A'$ generates a nilpotent ideal in $u(L)$, it suffices for us to
assume $A$ is abelian. Now put $B=[A,L]$. Then $B$ is an ideal of $L$
contained in $A\cap L'$ and so $B_p$ is $p$-nil of bounded index.
Since $A$ is abelian, it follows that $B$ generates an ideal $I$ of
$u(A)$ which is $L$-stable and nil of bounded index. By Lemma~\ref{expand} the same
is true of the expanded ideal $Iu(L)$ of $u(L)$. Thus we may assume that $B=0$ and
hence that $A$ is central in $L$. This implies that $L'$ is finite-dimensional
and so $L'$ generates a nilpotent ideal of $u(L)$. Finally, we can assume
that $L$ is abelian and the result follows immediately.
\end{proof}

\begin{uncorollary}
$u(L)$ satisfies a nonmatrix identity if and only if it satisfies some polynomial identity
and $L'$ is $p$-nil of bounded index.
\hfill\qedsymbol
\end{uncorollary}

\subsection*{Group algebras}

\begin{proof}[Proof of Theorem~\ref{nonmatrix-K[G]}]
The proof is entirely analogous to the restricted enveloping algebra case, and is in
fact simpler since there  is no need to trouble ourselves with any analogue of the
$p$-hull.

The main ingredients are:
\begin{itemize}
\item By a result of Passman \cite[Corollary 5.3.10]{passman:asgr}, $K[G]$
satisfies a polynomial identity if and only if $G$ has a subgroup
$A$ such that $G/A$ is finite and $A'$ is a finite $p$-group.
\item A normal subgroup $H$ of $G$ generates a nilpotent ideal of
$K[G]$ if and only if $H$ is a finite $p$-group.
\item In place of Lemma~\ref{expand}, we use the group algebra
analogue \cite[Lemma 3.2]{passman:units2}.
\end{itemize}
\end{proof}

\begin{uncorollary}
$K[G]$ satisfies a nonmatrix identity if and only if it satisfies some polynomial identity
and $G'$ is a $p$-group of finite exponent.
\hfill\qedsymbol
\end{uncorollary}

\section{Semigroup identities}
\label{s:semigroup}
In this section we prove Theorems~\ref{semigroup-u(L)}, \ref{semigroup-K[G]},
\ref{semigroup-omega(u(L))} and \ref{semigroup-omega(K[G])}, and justify
Examples~\ref{e:2-D} and \ref{e:dihedral}. The same notational hypotheses as in the
previous section are in force throughout. In addition, the field $K$ is assumed to be
infinite of characteristic $p>0$.

\subsection*{Enveloping algebras}

\begin{proof}[Proof of Theorem~\ref{semigroup-u(L)}]
It remains to prove the equivalence of condition (iv) and condition (iii), say.
That (iii) implies (iv) is obvious.  Conversely, assume that
(iv) holds.  Replacing $A$ by the centralizer of $A'$ in $A$,
we may assume that $A$ is a nilpotent restricted
ideal of $L$ containing $Z(L)$.  But then $L$ is
nilpotent-by-(finite-dimensional and $p$-nil), and hence
nilpotent by \cite{shalev:PI-grK[G]}.
\end{proof}

\begin{proposition}
\label{2-D} Let $p=2$ and let $D$ be the $2$-dimensional restricted
Lie algebra over $K$ generated by
$a,b$ with relations $[a,b]=a$, $a^2=0$, $b^2=b$.
Then $\omega(u(D))$ satisfies the semigroup identity
$$wxyz-wyxz=0.$$
\end{proposition}

\begin{proof} By Jacobson's theorem, $\omega(u(D))$ has $K$-basis
$$\{a,b,ab\}.$$
Because the given semigroup identity is multilinear, it suffices to
show that it holds on basis elements.
Observe
$$[a,b]=a,\quad [a,ab]=a^2=0,\quad [ab,b]=ab=(1+b)a,$$
each of which is annihilated by $a$ on the right and left.
The remaining possibilities are:
$$bab=b(1+b)a=2ba=0,\quad b[(1+b)a]b=2bab=0.$$
\end{proof}

\begin{proposition} If $\omega(u(L))$ satisfies an identity of the form
$y^m[x, _m y]y^m=0$ then either $u(L)$ satisfies the Engel condition or
$p=2$ and $L$ contains a restricted subalgebra isomorphic to $D$.
\end{proposition}
\begin{proof} Since $y^m[x, _m y]y^m=0$ is a nonmatrix identity,
it is clear from Theorems~\ref{nonmatrix-u(L)} and \ref{semigroup-u(L)} that
$u(L)$ satisfies the Engel condition as soon as $L/Z(L)$ is
$p$-nil of bounded exponent.   Because
$$y^m[x, _{m+1}y]y^m=[y^m[x, _m y]y^m,y]=0$$
is also an identity for $\omega(u(L))$, we may
assume that $m=p^t$ for some $t$.
Then $\omega(u(L))$ satisfies the identity
$$y^{p^t}[x,y^{p^t}]y^{p^t}=y^{p^t}[x, _{p^t} y]y^{p^t}=0.$$
Suppose now that $a,c$ are arbitrary elements in $L$ and put
$b=c^{p^t}$.
Then
$$[a,b]b^2-[a,b,b]b=b[a,b]b=0.$$
Assume, for the moment, that $p>2$.
Then it follows easily using Jacobson's theorem that $[a,b,b]=0$\textup{;}
hence, $L^{p^{t+1}}\subseteq Z(L)$, as required.

Assume, finally, that $p=2$ and, without loss of generality,
$[a,_3 b]\neq0$ for some $a,c$ as above.
Then, by Jacobson's theorem, there exist
$\lambda,\mu,\nu\in K$ such that
$[a,b,b]=\lambda [a,b]+\mu b+\nu b^2.$
It follows that $[a,b,b,b]=\lambda [a,b,b]$, where $\lambda\neq0$.
Replacing $a$ by $[a,b,b]$ and subsequently $b$ by $\lambda^{-1} b$,
we can assume $[a,b]=a$.  Therefore
$$a(b^2-b)=[a,b]b^2-[a,b,b]b=0,$$
so that $b^2=b$.
Clearly now, $a$ and $b$ generate a restricted subalgebra of
$L$ isomorphic to $D$, as required.
\end{proof}

\begin{proof}[Proof of Theorem~\ref{semigroup-omega(u(L))}]
According to
\cite{riley-wilson:semigroup}, if an algebra over an infinite field
satisfies a semigroup identity then it satisfies an identity
of the form $$y^m[x,_m y]y^m=0,$$
for some $m$.  Now combining the preceding
proposition with Theorem~\ref{semigroup-u(L)} readily yields the result.
\end{proof}

\subsection*{Group algebras}

\begin{proof}[Proof of Theorem~\ref{semigroup-K[G]}]
It remains to prove the
equivalence of condition (iv) and conditions (i)-(iii).
That  condition (ii) implies (iv) is clear from Theorem~\ref{nonmatrix-K[G]}
since if $g,h\in G$ then
$$gh^{p^t}-h^{p^t}g=[g,h^{p^t}]=[g, _{p^t}h].$$
Assume now that only (iv) holds.  Replacing $A$ by the centralizer
of $A'$ in $A$, we may assume that $A$ is a nilpotent normal
subgroup of $G$ containing $Z(G)$.  But then $G/Z(G)$
is  a $p$-group of finite exponent that is an extension of a
nilpotent group by a finite $p$-group.
Such a group is nilpotent by \cite{baumslag}.  Hence,
$G$ itself is nilpotent and (iii) holds.
\end{proof}

\begin{proposition}
\label{dihedral}
Let $p=3$ and let $G$ be the dihedral group of order $6$. Then $\omega(K[G])$ satisfies
the identity $yxy^2=y^2xy$.
\end{proposition}

\begin{proof}
Write $R=\omega(K[G])$. We use the presentation $G=\langle a,b | a^2=b^3=aba=1\rangle$.
Let $d=b-b^{-1}\in R$ and let $e=(1-a)/2\in R$. It is easy to see that $e^2=e, d^3=0$ and
$d^2$ is central in $R$. Furthermore, $ed=d(1-e)$. A $K$-basis for $R$ is $\{e,d^2,
ed^2,d,ed\}$. Let $R_0$ be the span of $e, d ^2, ed^2$ and let $R_1$ be the span of $d,
ed$. Then $R=R_0\dotplus R_1$ is a superalgebra and the following basic properties hold:
\begin{itemize}
\item $R_0$ is commutative;
\item $(R_1)^3=0$;
\item $R_0R_1R_0=0$.
\end{itemize}

Consider the given identity in the form $y[x,y]y=0$. Since the identity is linear in $x$
it suffices to assume that $x\in R_0$ or $x\in R_1$. Fix $y=s_0+s_1\in R_0\dotplus R_1$.

Suppose that $0\neq x=r_0\in R_0$. Then using the above properties we obtain
$$
y[x,y]y=s_0[r_0,s_1]s_1+s_1[r_0,s_1]s_0.
$$
Since $d^2$ kills all basis elements except $e$, and the last expression is homogeneous
in $r_0$ and $s_0$, without loss of generality we may assume that $r_0=s_0=e$. Then the
above simplifies to
$$
y[x,y]y=e[e,s_1]s_1+s_1[e,s_1]e=es_1^2-s_1^2e=0.
$$

Suppose that $0\neq x=r_1\in R_1$. Then the basic properties above yield
$$
y[x,y]y=[r_1,s_1]s_0^2+s_0[r_1,s_0]s_1+s_1[r_1,s_0]s_0.
$$

Since $x$ has degree 1 in $d$ we may again assume that $s_0=e$, which yields
$$
y[x,y]y=[r_1,s_1]e+e[r_1,e]s_1+s_1[r_1,e]e=r_1s_1e-s_1r_1e-er_1s_1+s_1r_1e=0.
$$
\end{proof}

\begin{proposition} If $\omega(K[G])$ satisfies an identity of the form
$y^m[x,_m y]y^m=0$ then either $K[G]$ satisfies the Engel condition or $p>2$ and $G$
contains a subgroup isomorphic to the dihedral group $D_{2p}$ of order $2p$.
\end{proposition}
\begin{proof} As above, if $G/Z(G)$ is a $p$-group of bounded
exponent, then the assumption on $\omega(K[G])$ forces $K[G]$ to satisfy
the Engel condition.

Assume $m=p^t$.  We claim that given $h\in G$, either $h^{p^{t+1}}\in Z(G)$ or
$h^{2p^t}=1$.  Let $g,h\in G$.  Substituting $x=1-g,y=1-h$ into the  polynomial
identity yields
$$(1-h^{p^t})[h^{p^t},g](1-h^{p^t})=(1-h)^{p^t}[g,(1-h)^{p^t}](1-h)^{p^t}=0.$$
Expanding, we obtain
$$h^{p^t}g-gh^{p^t}-h^{2p^t}g+gh^{2p^t}+h^{2p^t}gh^{p^t}-h^{p^t}gh^{2p^t}=0.$$

Consider first the case when $p>5$.  Then by the linear independence of group
elements we have:
$$\{h^{p^t}g,gh^{2p^t},h^{2p^t}gh^{p^t}\}=\{gh^{p^t},h^{2p^t}g,h^{p^t}gh^{2p^t}\}.$$
By inspection, it follows that either $h^{p^t}$ commutes with $g$ or $h^{2p^t}=1$,
as claimed.

Next assume $p=3$.  One additional possibility can occur:
$$h^{3^t}g=gh^{2\cdot3^t}=h^{2\cdot3^t}gh^{3^t},
\quad gh^{3^t}=h^{2\cdot3^t}g=h^{3^t}gh^{2\cdot3^t}.$$
But then $h^{3^t}g=h^{2\cdot3^t}gh^{3^t}$ implies $g=h^{3^t}gh^{3^t}$, so that
$g=(h^{3^t}g)h^{3^t}=(gh^{2\cdot3^t})h^{3^t}$ implies that $h^{3^{t+1}}=1$.

Finally, in the $p=2$ case the fact that the group element terms above must cancel
pairwise eventually shows that $h^{2^{t+1}}$ commutes with $g$, thus establishing
the claim for all characteristics.  This also completes the proof in the
case $p=2$\textup{;} henceforth, we assume $p>2$.

Now let $P$ denote the set of $p$-elements in $G$.  Since $\omega(K[G])$
satisfies a nonmatrix identity, $G'$ is a $p$-group by Theorem~\ref{nonmatrix-K[G]}.
It follows immediately that $P$ is a normal subgroup of $G$.

According to the claim above, either $G/Z(G)$ is a $p$-group of
finite exponent or $G$ contains an element $\sigma$ of order $2$.
Consider the case that $\sigma$ centralizes $P$.
We claim that $\sigma$ must be central.
Indeed, let $\tau\in G$. Then since $G'$ is a $p$-group,
$\sigma^\tau=\sigma g$ for some $p$-element $g$.  Thus
$$g^2=\sigma^2 g^2=(\sigma g)^2=(\sigma^\tau)^2=1,$$
so that $g=1$ since $p$ is odd.

Now consider the case when $\sigma$ does not centralize $P$.
Then there is some $p$-element $g$ in $G$ such that
$g^\sigma\neq g$.  Put $h=g^{-1}g^\sigma$, another
$p$-element in $G$.  Then
$$h^\sigma h=(g^{-1}g^\sigma)^\sigma g^{-1}g^\sigma=(g^\sigma)^{-1}gg^{-1}g^\sigma=1.$$
If the order of $h$ is $p^n$ and $n\ge2$, then replacing
$h$ by $h^{p^{n-1}}$ we may assume $h$ has order exactly
$p$ and $h^\sigma=h^{-1}$.  Consequently, the subgroup
$G$ generated by $\sigma$ and $h$ is isomorphic to $D_{2p}$.
\end{proof}

\begin{proof}[Proof of Theorem~\ref{semigroup-omega(K[G])}]
According to
\cite{riley-wilson:semigroup}, if an algebra over an infinite field
satisfies a semigroup identity then it satisfies an identity
of the form $$y^m[x,_m y]y^m=0,$$ for some $m$.  Now combining the preceding proposition
with Theorem~\ref{semigroup-K[G]} readily yields the result.
\end{proof}

\section{Further comments}
The complete analogy between Theorems~\ref{nonmatrix-u(L)} and \ref{nonmatrix-K[G]}
suggests that a more general result may be possible, perhaps in some class of Hopf
algebras containing both examples.

We strongly suspect that $\omega(K[D_{2p}])$ satisfies a semigroup identity for fields
$K$ of arbitrary prime characteristic $p$, but do not have a general proof. The
difficulties encountered in even this seemingly simple case lead us to believe that the
full characterization of augmentation ideals satisfying a semigroup identity will require
considerable additional effort.

\bibliographystyle{amsalpha}

redpajama_set_name: RedPajamaArXiv


text:
Now I want to dancing and singing in films: Nawazuddin Siddiqui
By Varun Kumar August 12, 2019 Entertainment 1 Comment
In addition to the Tamil film 'Petta' this year, the films 'Photograph' and 'Thackeray' based on the life of Shiv Sena founder Balasaheb Thackeray, Nawazuddin Siddiqui's were also released. In the second season of the web show 'Sacred Games', he will be seen in a serious character, after which he will not be seen in serious roles for some time. Excerpts from the conversation with Nawaz:
In serious characters, 'Sacred Games' should now be considered as the last episode, because now you are doing romantic films 'Bole Chudiyan', 'Raat Akeli Hai'?
Yes, I am doing love stories now. I also feel that love should be loved. Nowadays I am doing all the movies like that. For some time I will stay away from serious and dark characters. Now I want to dancing and singing in films.
When you came to films, did you ever think that you will become a hero in romantic films?
I thought, but the characters were not found in them. In my part those characters have come now.
Wouldn't it be risky to switch to positive characters after negative characters?
There is nothing negative and positive. No human is perfect in real life. There are some bad things in it. These things make him a human being. I myself do not like perfect characters. There are many such things in the character of Ganesh Gaitonde, which are not even among the good people.
How stubborn is the character of Ganesh Gaitonde going to be this time?
His stubbornness moves a bit in this series. In addition to the stubbornness, the spirit of survival emerges, which is focused in the second season.
When you thought of coming to digital, you were doing films like Raees and Manto. Didn't it feel that the decision could be wrong?
I didn't think that this character would become so big. I wasn't even going to do this role. I even rotated the makers first, then Anurag Kashyap and Vikramaditya sat down and explained.
There must have been a lot of time to understand a character in two series of 16 hours. Do not get much opportunity to work on characters in films?
Yes, that's why it was easy for me to understand the character even after a year's break in the second season. But there is also the fear that such a famous character will not get over the top or be a little bit underdressed. The character you have to play has to follow the same edge.
How much does the character's popularity mean to you?
I enjoy the process between preparing and playing the character. Even if my character is not popular, I do not mind. I should get creative satisfaction. This satisfaction was found in the movie Manto, but the film did not work. But I found that character happy during the process of living.
Tags:Bole Chudiyan Nawazuddin Siddiqui Raat Akeli Hai Sacred Games 2
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Hello, My name is Varun Kumar. My age is 27 years. I hold a Bachelor of Arts degree from IGNOU. I am from Delhi, India & I enjoy the great pleasure of blogging. I also read blogs as well. This is my blog, which I tell you about latest news from the World. If you would like to contact me see below.


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