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How often do you take a good look at your gutters? You may clean them out when they get clogged but most homeowners don't take the time to really inspect their gutters for damage. Leaky gutters can be a result of rust spots. If you have traditional gutters installed with nails, your leaky gutters can cause water to seep around the nail hole where the gutters are installed. This will lead to your fascia board rotting and it can cause your gutters to pull away or fall off of your home. Gutter repairs may help, but ultimately you will have to say goodbye to your old gutters and invest in replacement gutters.
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Capital spending for vehicle assembly has averaged just $1.2 billion a year since 2010.
TORONTO — Capital investment in the Canadian auto assembly sector since the financial crisis and recession has been nearly cut in half compared with the period before the downturn, a new report says.
DesRosiers Automotive Consultants said capital spending for Canada's motor vehicle assembly industry has averaged $1.2 billion a year for 2010-17.
That's down from $2.3 billion annually on average from 2000 through 2009.
Meanwhile, the average new capital expenditures for the parts and accessories industry dropped to $565.9 million from $887.7 million for the same time periods.
"Despite small occasional increases in the period between 2008 and 2017 there has been no sustained indication of a return to the heights recorded in the mid to late 90s and late 2000's," DesRosiers said.
However, DesRosiers noted that investments by truck body and trailer manufacturers have increased on average from $52.7 million for 2000 to 2009 to $82.7 million since 2010.
Securing new investments in Canada was a key goal for Unifor during its negotiations with the big U.S. automakers last year.
Ford, General Motors and Fiat Chrysler all pledged to invest hundreds of millions in their Canadian operations as part of their agreements with the union.
Meanwhile, Unifor members remain on strike at GM's CAMI assembly plant in Ingersoll, Ont., where the union is seeking to have the location designated the lead producer of the Chevrolet Equinox.
Job security at the plant is a key issue, with Unifor seeking to prevent work from being moved to Mexico, where GM also produces the popular sport utility vehicle.
The plant saw the loss of hundreds of jobs when GM shifted production of its GMC Terrain from Ingersoll to Mexico earlier this year.


Along the bend of the Yarra River lies the Children's Farm with hectares of land with farm animals for those wanting a bit of the country life within the city. Visitors can milk cows, feed animals and go into paddocks with sheep, goats and more. Perfect for families, animal lovers and kids at heart.


A game created for the Engine001 Contest.
In this game, you play as a ball getting from the start to finish.
This is my entry into the 001 Arcade Contest.
A meteor hits the earth. Soon he discovers that they are actually alien spacecraft, they want to invade the planet to get natural resources.
Did it as an english assignment, but decided to submit it as a contest game (just to see how it'd do). It has no menu, game launches from beginning. It is automatically 2-player.
You are a black blob of slime that has recently escaped from a science laboratory. You a tyring to get back to the toxic waste dump where your DNA was first discovered.


By M.-E. Héroux et al.
World Health Organization (WHO) published the Guidelines for Community Noise in 1999 and the Night Noise Guidelines for Europe in 2009.
Significant new research in the area of environmental noise and health has taken place since then.
As well, new noise sources of concern for public health, such as wind turbines, were not addressed in previous guidelines.
For these reasons, WHO is currently engaged in the revision of all pertinent literature and will provide recommendations for the protection of public health as part of WHO Environmental Noise Guidelines for the European Region.
The guidelines will focus on the WHO European Region and provide guidance to its Member States that is compatible with the noise indicators used in the European Union (EU) Directive on Environmental Noise.
We systematically review the effects of noise on the following health outcomes: effects on sleep, annoyance, cognitive impairment, cardiovascular disease, hearing impairment, tinnitus, adverse birth outcomes, and mental health and wellbeing.
The guidelines will consider the evidence on health effects of environmental noise related to the following various sources: aircraft, railway, road traffic, wind turbines and leisure noise.
They will address exposure to noise in such relevant settings as residences, hospitals, learning establishments and public venues.
Additionally, they will review the potential health benefits from noise mitigation and interventions to decrease noise levels.
The process of developing the guidelines involves the synthesis and interpretation of the available evidence by a large group of scientists from across the world under the coordination of WHO.
The Guidelines will provide up-to-date information on the health risks from environmental noise and evidence-based recommendations in order to support WHO Member States in their efforts to prevent and control exposure to excessive environmental noise.


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by gary from abingdon va.
My sales person was Stephanie, it is an understatement to say she was great. She stayed on top of the sale from start to finish. She had the right mix of professionalism and friendliness. Mike in finance was also very helpful and good at the job he performs. Overall this buying experience with Apple Tree Honda was a positive experience.
We really appreciate the quick and helpful service we received from Ed & Travis at Skye Auto Haus in Weaverville, NC. We would highly recommend them !!!
Ready to cruise the USA!
A friend recommended Skye Autohaus to me and I am so thankful I reached out to them first before a big dealership. It was an easy process and I wasn't sitting in there all day. Love my new Crosstrek!


Download the mother of all questions further reports from the feminist revolutions in pdf or read the mother of all questions further reports from the feminist revolutions in pdf online books in PDF, EPUB and Mobi Format. Click Download or Read Online button to get the mother of all questions further reports from the feminist revolutions in pdf book now. This site is like a library, Use search box in the widget to get ebook that you want.


text:
Senate amends Firearms Act
UK PM fires Conservative chairman after tax probe
Russian president, Vladimir Putin, has ordered strippers and pole dancers to be sent to the front line in a move to cheer up his troops and boost morale. The move comes as the Kremlin announces a meda...
The Socio-Economic Rights and Accountability Project has urged the President, Major General Muhammadu Buhari (retd.), "to direct the Inspector-General of Police Usman Baba to promptly, thoroughly, a...
The Chinese embassy in Tokyo announced Sunday that it would resume issuing visas to Japanese citizens. The move ends a retaliatory step against Japan's decision to require Covid testing for trav...
…Security outfit denies allegations An All Progressives Grand Alliance supporter in Ebonyi State, Amobi Ujar, was on Saturday allegedly beaten to a pulp by members of the state's security ...

redpajama_set_name: RedPajamaCommonCrawl


Schools and churches are always in need of signage. Whether the signs are used on a permanent basis (wall signs, monument signs, dimensional lettering and others) or are temporary by design (event signs, posters, banner), schools and churches by their very nature are in the business to inform, communicate and help. These are what signs essentially do. Blend the right type of sign with the right message and you have a winning combination.
Building Signs – From illuminated channel letters to formed plastic letters, we are a licensed California electrical sign contractor. Also, we can help you refurbish your existing entrance and building signs.
ADA Compliant Signs – Required for all public buildings, be sure your facility is up to date with the latest California ADA compliant signage, including exit signs, EVAC maps, classroom numbers, handicap and restroom signs, to just name a few.
Changeable Reader-Boards – Often illuminated, changeable reader boards are made with easily changeable inserts to announce your upcoming events, along with changeable letters that keep your school or church members informed.
Digital Banners – Advertise an event, speaker or sports activity with an inexpensive, full color banner.
Directional or Way-Finding signs – Need help directing your students and parishioners around campus? Post and panel signs, fence or stake signs are a great solution.
Event Signs – Post yard signs at your entrances or in your parking lot to advertise fundraisers and events.
LED Message Boards – The cutting edge way to communicate your messages, announce activities, and post information for your students, parents and parishioners is the use of LED message boards. At the click of your keyboard, new messages are created and old ones deleted.
Safety and Parking Signs – Whenever there are busy parking lots, you need safety signs! "Stop" and "Slow" signs are a must. Regulatory signs must be posted to be able to tow away improperly parked cars.
Donor Recognition Panels – Looking for a way to thank your school or church donors? Honor them with a series of acrylic panels that "float off the wall" with their names proudly listed. Larger panels can hold a list of names and smaller panels can feature one donor name…so they stand out!


Take your food and drinks with you in style with the Ice Box 20 litre cooler, comfortable grip handle , snap on lid, perfect for road trips in the car, picnics and parties. Able to hold 30 cans. 52-29-29cm. 2.5 kg.


Props shot out to Cam "Shaft," assistant sys/admin at www.midcoast.com. He upgraded the server I'm on to the very newest WordPress release–the one just release on 12/10! The layout is much different than the old 2.0.5 version I had been using. This newer version allows me to do all kinds of new things. Let's see what wonderifics I'll install!


Emily Bett Rickards in Normal Doors . . HD Wallpaper and background images in the Emily Bett Rickards club tagged: photo.
This Emily Bett Rickards photo might contain attractiveness, appeal, hotness, bustier, portrait, headshot, and closeup.


text:
Tag education
Education Residence
Dec 8, 2021 By	Loki Uncategorized education, residence
UC lecturers have had enough, and that's why we now have called this strike to guard our collective bargaining rights," McIver added. UC-AFT, the union that represents more than 6,000 part-time lecturers across the system's 10 undergraduate and one graduate campuses, introduced its plan to strike Wednesday and Thursday. The union has filed seven costs throughout the past two years with California's Public Employment Relations Board and most lately has alleged that UC management has refused to discount over paid family leave and time to permit for bonding with a new baby. Other college districts, similar to Fremont Unified, have returned law enforcement officials to campuses shortly after eradicating them.
Mung Chiang, an electrical engineer who serves as the dean of the engineering college at Purdue University, said in a press release by way of the University of South Carolina that he was specializing in his family as an alternative.
Dec 2, 2021 By	Loki Education News education, newest, norfolk
Newest Norfolk Education News
Portions of the third-largest U.S. faculty district stay woefully undervaccinated. An inflow of students confirmed up in disaster at school in current months, and the trend continued into the school year. Providers are scheduling COVID vaccine appointments for kids ages 5 to 11.
Combined with cash the university already promised, Yale will contribute $135 million in lieu of property taxes.
He attended East Los Angeles College and Fullerton College before transferring to the University of California Irvine, where he earned his bachelor's degree in psychology and social behavior.
The curriculum includes basic subjects like spiritual education, national philosophy and civics, Indonesian, mathematics, science, social science, arts, and physical education.
Even though student-to-teacher ratios within the private sector are lower than within the public sector, private madrasahs, for instance, tend to have lower-qualified academics and insufficient amenities.
According to UIS information, the variety of Indonesian degree-seeking college students enrolled overseas has …
Oct 11, 2021 By	Loki Uncategorized education
ACE celebrates 4 members at the forefront of supporting first-gen students. ACE and 45 other greater education associations sent comments to the Department of Homeland Security at present on the draft guidelines launched in September to strengthen the Obama-era Deferred Action for Childhood Arrivals program. Children and their families all through British Columbia will proceed to learn from local literacy applications with assist from the annual Raise-a-Reader campaign Sept 17-24. Students, academics and workers at Shortreed Community Elementary will soon have a structurally safer school now that seismic upgrades are underway. Government is updating its K-12 education well being and security tips to require masks for kindergarten to Grade three students.
The Los Angeles Board of Education has chosen the longtime superintendent of Miami-Dade County Public Schools to be the subsequent superintendent of Los Angeles Unified School District, the second largest in the nation, officials stated Thursday.
Leung says school
Jul 1, 2021 By	Loki Uncategorized department, education, jersey, press, releases
Press Releases For The New Jersey Department Of Education
Good planning will cut the chance of "tremendous spreader occasions" in schools, ministry says. Response from ninety.8% of Northland colleges reveals 6.7% of lecturers have refused vaccination. Pandemic has seen an unprecedented "spike" in lecturers staying within the classroom. The California Department of Education needs to deliver as many as 10,000 extra psychological well being professionals to schools by providing scholarships, loan forgiveness and deferrals, and dashing the licensing course of. State Superintendent Tony Thurmond declares plan to transform California colleges, embarks on statewide listening tour.
Overall, there are 34 provinces that are additional subdivided into hundreds of districts, subdistricts, cities, and greater than 75,000 villages. Despite these marked variations, Indonesia is seen as having a promising financial future; it's certain to turn out to be a country of world significance in the 21st century. The island nation is at present transitioning from an agricultural economy pushed by commodity exports …
Jan 8, 2021 By	Loki Uncategorized education
Education News 2021
A paradigm shift is occurring in larger education with the emergence of recent methods, models and missions of studying. We will study how universities can remain important to a Covid-disrupted society and serve the wants of a rapidly altering world. The summit may also see the reveal of the THE Asia University Rankings 2022. Stephanie Parra, Governing Board Member at Phoenix Union School District and Executive Director of ALL in Education Arizona, sits for a portrait on the nonprofit's space at Galvanize Phoenix in downtown Phoenix, Ariz. on Nov. 15, 2021. [newline]Phoenix Union is majority BIPOC students Education Definition, however college board and educator demographics in Arizona lag behind in illustration and alternative. The return of in-person learning and up to date acts of violence have renewed debates over how to hold students protected. But the newest wave in Covid-19 instances may challenge the rickety infrastructure that has stored …
Dec 15, 2020 By	Loki Uncategorized childhood, early, education
Early Childhood Education News
So it's not surprising that many larger education institutions have began targeting their advertising towards this geographic market. Here are our prime suggestions for recruiting students from China to study abroad at your college. A dispute between the Chicago Teachers Union and the college district over in-person learning has resulted in classes being canceled. Several massive college methods are pivoting to distant learning as they steadiness well being considerations with preserving students on track academically.
Institutions spend millions on efforts like cluster hiring in an try to reply to protests and employ school who look more like the scholars on campus. To school, on-again off-again necessities on the University of Tennessee at Knoxville seemed like sinking time and sources into pleasing lawmakers. LAWRENCE, Kan. — The University of Kansas has suspended two fraternities for five years following an investigation that accused the clubs of fostering a culture of hazing. KU …
Dec 1, 2020 By	Loki Uncategorized education
Education Week
California Health and Human Services is constant to name on families to get their children vaccinated in opposition to Covid and to provide them with well-fitting, filtrated masks. Despite general hospitals nearing capability in California, pediatric hospitals and hospitals serving youngsters are "able to tackle the current demand," Ghaly mentioned. Many youngsters hospitalized with Covid usually are not being despatched to intensive care items and are not having to be put on ventilators, Ghaly added. Children who're hospitalized with Covid sometimes have other underlying health issues, he stated.
Kids tobogganing at Carlington Park in Ottawa through the Family Day long weekend 2021. The pandemic has offered vital new opportunities to maneuver society in a path that will increase out of doors lively play for kids. Washington Post columnist Marc Thiessen requires the firing of any teacher that refuses to return to the classroom. Only a small percentage of districts still …
Jul 15, 2020 By	Loki Uncategorized childhood, early, education
Click here to see how we work and discover out more about our priorities under. Staffing Shortages Are Hurting Students Who Need Extra Reading Support As colleges attempt to assist older college students who need studying assist, they're bumping up in opposition to personnel issues as a outcome of pandemic. LaGrange mentioned free online-tutoring assets shall be out there beginning next week for faculty kids in grades four to 9 who have to catch up on skills after falling behind due to the pandemic. School authorities may have flexibility to shift a category or an individual grade to short-term at-home learning if wanted to deal with operational challenges at a school, the province mentioned in a news release. "Given the present state of affairs, I additionally need to notice that I strongly suggest that college students in all grades put on masks, including kindergarten to Grade three," she mentioned.
However, …
Jan 13, 2020 By	Loki Uncategorized education, right
Education News Right Now
Graduates of this program earn an endorsement for the Connecticut Superintendent Certification and purchase the information necessary for successfully assembly the challenges of district leadership within the twenty first century. As UConn's assistant vp for scholar affairs and govt director of student actions, Joseph P. Briody '86 , '95 MA, '96 Ph.D. is a Husky through and through. It's one thing to attend knowledgeable improvement or instructional coaching session—but taking what you've discovered and putting it into motion is another.
BOSTON — Two dogs skilled to detect an odor distinct to people who find themselves sick with COVID-19 will go to three school districts in Bristol County this week. A black Labrador named Huntah and a golden Lab referred to as Duke can detect the odor of the virus on surfaces and can sit to point once they pick up the scent. — Teams from West Virginia high schools will …
Jan 31, 2019 By	Loki Uncategorized education, review
Their opponent, North Carolina State, expressed frustration on the late cancellation, based on ESPN. "A booster dose of the presently licensed vaccines might assist provide better protection in opposition to both the delta and omicron variants," Peter Marks, director of the FDA's Center for Biologics Evaluation and Research, stated. "In specific, the omicron variant appears to be slightly more proof against the antibody ranges produced in response" to the preliminary shot. The ruling, issued last week, allows Measure AA to pass with a easy majority, instead of a two-thirds majority. The measure, a charter amendment that establishes an education parcel tax, obtained 62% of the vote in 2018.
Wheelie bin stickers selling domestic recycling are about to be released to colleges, and the public. Almost 1200 Degree Colleges in Odisha are presently operating without regular Principals. Let that sink in because, as many as 49 government-run Degree faculties too need …


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Justia Dockets & Filings Eleventh Circuit U.S. Court of Appeals, Eleventh Circuit USA v. Steven Patrick Riffe Filing 1116135802
USA v. Steven Patrick Riffe
Opinion issued by court as to Appellant Steven Patrick Riffe. Decision: Affirmed. Opinion type: Non-Published. Opinion method: Per Curiam.
USA v. Steven Patrick Riffe Doc. 0 Case: 10-10330 Date Filed: 12/16/2010 Page: 1 of 3 [DO NOT PUBLISH] IN THE UNITED STATES COURT OF APPEALS FOR THE ELEVENTH CIRCUIT ________________________ FILED U.S. COURT OF APPEALS ELEVENTH CIRCUIT No. 10-10330 DECEMBER 16, 2010 Non-Argument Calendar JOHN LEY ________________________ CLERK D.C. Docket No. 7:09-cr-00273-CLS-HGD-1 UNITED STATES OF AMERICA, lllllllllllllllllllll versus STEVEN PATRICK RIFFE, lllllllllllllllllllll ________________________ Appeal from the United States District Court for the Northern District of Alabama ________________________ (December 16, 2010) Defendant-Appellant. Plaintiff-Appellee, Before BLACK, CARNES and MARCUS, Circuit Judges. PER CURIAM: Dockets.Justia.com Case: 10-10330 Date Filed: 12/16/2010 Page: 2 of 3 Steven Patrick Riffe appeals the 168-month total sentence he received after he pled guilty to one count of receiving child pornography, in violation of 18 U.S.C. � 2252A(a)(2)(A), one count of possession of child pornography, in violation of � 2252A(a)(5)(B), and one count of criminal forfeiture, pursuant to � 2253(a)(1), (a)(3). Riffe asserts he should not have received a two-level enhancement under U.S.S.G. � 2G2.2(b)(3)(F) because he was not convicted of distribution of child pornography. He further contends his sentence is procedurally and substantively unreasonable because the district court's explanation for his sentence was insufficient and the court failed to consider the factors listed in 18 U.S.C. � 3553(a). Lastly, Riffe argues the "amount of images" enhancement pursuant to U.S.S.G. � 2G2.2(b)(7)(D), violates the separation of powers doctrine. After review, we affirm Riffe's sentence. Prior to his sentencing hearing, Riffe filed a written objection to the presentence report specifically objecting to the legal conclusion that he had distributed child pornography. He did not, however, object to the facts in the PSI which showed he used Limewire, a peer-to-peer file-sharing program, to obtain and store child pornography images on his computer. Therefore, it is undisputed that Riffe obtained child pornography through the use of file-sharing software, stored such pornography in his shared folder, and the police downloaded 2 Case: 10-10330 Date Filed: 12/16/2010 Page: 3 of 3 pornography directly from that folder. We find no error in the district court's application of the � 2G2.2(b)(3)(F) distribution enhancement. Additionally, we conclude Riffe's 168-month total sentence was both procedurally and substantively reasonable. The district court correctly calculated the advisory guideline range and stated the range was advisory. The court made clear it had considered the � 3553(a) factors, and it emphasized the seriousness of the offense and the need for specific deterrence. The court's sentence of 168 months represented the lowest end of the applicable guideline range of 168-210 months, and we ordinarily expect such a sentence to be reasonable. See United States v. Talley, 431 F.3d 784,788 (11th Cir. 2005). Lastly, the district court did not commit plain error when it applied an "amount of images" enhancement pursuant to U.S.S.G. � 2G2.2(b)(7)(D). Although this Court nor the Supreme Court has previously addressed the constitutionality of the enhancement, other circuits have upheld the statute's constitutionality. See, e.g., United States v. Rogers, 610 F.3d 975, 977-78 (7th Cir. 2010); United States v. Bastian, 603 F.3d 460, 465 (8th Cir. 2010). AFFIRMED. 3


text:
\section{Introduction and main results}
\label{intro}

A gradient almost Ricci soliton \cite{pigola2010ricci} is a complete Riemannian manifold $(M^{n}, g)$ together with functions $ h,\rho:M\to\mathbb{R} $ satisfying the equation
\begin{equation}\label{1}Ric_{g}+Hess_{g}h=\rho g,
\end{equation}
where $Ric_{g}$ and $Hess_{g}h$ stand, respectively, for the Ricci tensor and the Hessian of $h$. The function $h:M\to\mathbb{R}$ is usually referred to as the potential function of the soliton in the literature. The quadruple $(M^{n},g,h,\rho)$ is classified into three types according to the sign of $\rho$: expanding if $\rho<0$, steady if $\rho=0$ and shrinking if $\rho>0$. If $\rho$ occurs as a constant, the soliton is usually referred to as a \textit{gradient Ricci soliton}.

From the above it is readily seen that Einstein manifolds, that is, those for which
\[Ric_{g}=\rho g,\]
trivially fulfill the requirement for a gradient almost Ricci soliton with a constant $\rho$ and Killing vector field $\nabla h$, not to exclude the possibility of an also constant $ h $.

Recent works like \cite{de2017gradient, feitosa2015gradient, feitosa2017construction, kim2013warped, pina2017invariant} exhibit the fact that warped product manifolds constitute a highly profitable ground for the construction of gradient almost Ricci solitons. It's worth noticing that [12] contain infinitely many solutions to (1) in closed form.

\begin{definition} Let $(B^{n}, g_{B})$ and $(F^{k}, g_{F})$ be two Riemannian manifolds and $f>0$ on $B$. The product manifold $B\times F$ furnished with metric tensor
	\begin{equation}\label{warped metric}
	g=\pi^{\ast}g_{B}+(f\circ\pi)^{2}\sigma^{\ast}g_{F},
	\end{equation}
	where $\pi:B\times F\rightarrow B$, $\sigma:B\times F\rightarrow F$ are the projections on the first and second factor, respectively, is called \textit{warped product manifold} and will be denote by $B\times_{f}F$. The function $f$ is called \textit{warping function}, $B$ is called the \textit{base} and $F$ the \textit{fiber}.
\end{definition}

In \cite{de2017gradient} the authors investigated warped product gradient Ricci solitons and proved that either the warping function $f$ is constant or the potential function satisfies
\begin{equation*}
 h=h_{B}\circ\pi,\hspace{0,5cm} h_{B}\in C^{\infty}(B).
\end{equation*}

In this very spirit the authors of \cite{feitosa2015gradient} studied warped product gradient almost Ricci solitons with the assumption that
\begin{equation}\label{3'}
\rho=\rho_{B}\circ\pi, \hspace{0,5cm} h=h_{B}\circ\pi,\hspace{0,7cm}\rho_{B},\hspace{.1cm} h_{B}\in C^{\infty}(B),
\end{equation}
and prove the following result:

\begin{proposition}\label{lemma1} Let
	$(B^{n}\times_{f}F^{k},g,h,\rho)$ be a \textbf{gradient almost Ricci soliton}, then the functions $f$, $h_{B}$ defined on $(B^{n},g_{B})$ satisfy
	\begin{equation}\label{111}
	Ric_{g_B}+Hess_{g_B}h_{B}=\rho_{B} g_{B}+\frac{k}{f}Hess_{g_B}f,
	\end{equation}
	and the fiber $(F^{k}, g_{F})$ is \textbf{Einstein} with $Ric_{g_{F}}=\theta g_{F}$, where

	\begin{equation}\label{nazareno1}
	\theta=\rho_{B} f^{2}+f\Delta f+(k-1)|\nabla f|^{2}-f\nabla h_{B}(f).
	\end{equation}
\end{proposition}

The authors make use of the equation \eqref{nazareno1} in combination with the maximum principle to provide triviality results for warping functions reaching a maximum. As a consequence one sees that it is impossible to achieve the structure of a gradient almost Ricci soliton on warped product manifolds possessing a compact base and $\rho_{B}f^2\geq\theta$.

Proposition \ref{lemma1} is known to be true for Einstein manifolds $(B^{n}\times_{f}F^{k},g)$ since \cite{kim2013warped}. Besides, with the change $f =\exp{(k^{-1}u)}$ in \eqref{111}, we get that
\begin{equation}\label{222}
Ric_{g_{B}}+Hess_{g_{B}}u-\frac{1}{k}du\otimes du=\rho_{B} g_{B}.
\end{equation}
Objects satisfying equation \eqref{222} are called \textit{quasi-Einstein manifold} \cite{case2011rigidity} and play an important role in the analysis of solutions for \eqref{nazareno1}. For instance, in \cite{case2010nonexistence}, by starting off with \eqref{222}, the author developed a gradient estimate for $u$ and concluded that there are no nonconstant solutions for \eqref{nazareno1} if $\rho_{B}=0$ and $\theta\leq0$. Therefore, there are no nontrivial Ricci flat warped products such that its fiber manifold has a nonpositive Einstein constant. In the same way, in \cite{mastrolia2014some} it's shown some triviality results for the warping function $f$ in terms of gradient estimates, however, in the case $\rho_{B}\leq0$.

By the above exposed it is interesting to investigate whether or not we have local gradient estimates for warping solutions of \eqref{nazareno1} in the general case. By the change $f=v^{\frac{1}{k}}$ in equation \eqref{nazareno1} we obtain that
\begin{equation}\label{9'}
\Delta_{h_{B}}v+\rho_{B} kv-\theta k v^{1-\frac{1}{k}}=0.
\end{equation}
where $\Delta_{w}=e^{w}div(e^{-w}\nabla w)$ is the so called drifting Laplacian on the Bakry-\'Emery geometry. In order to accomplish such a task, we focus our attention on gradient estimates for the positive solutions of the nonlinear equation \eqref{9'} that, in compliment to \cite{feitosa2015gradient}, are defined on a noncompact base. We mainly follow the lines of P. Li and S.T. Yau's proof in \cite{li1986parabolic}.

\begin{theorem}\label{gradient}Let $(B^{n}\times_{f}F^{k},g, h,\rho)$ be a complete gradient almost Ricci soliton with noncompact base satisfying
	$$Ric_{g_B}+Hess_{g_B}h_{B}-\frac{1}{m}dh_{B}\otimes dh_{B}\geq -K,\qquad\Delta_{h_{B}}\rho_{B}\geq0,\qquad|\nabla\rho_{B}|\leq\gamma(2R),$$
	for $K\geq0$ in the metric ball $B(p,2R)$ of the base. Then, for any $\beta\in(0,1)$ with $\beta>1-\frac{2}{k}$, the warping function $f$ satisfies the following gradient estimates:

	\begin{itemize}
		\item If $\theta<0$, we have

		$$\beta\frac{|\nabla f|^{2}}{f^{2}}+\frac{\rho_B}{k}-\frac{\theta}{kf^2}\leq \frac{(n+m)}{ k^{2}\beta}P+\sqrt{\frac{n+m}{2\beta k^{4}}}Q^{\frac{1}{2}}, \quad \text{in}\quad B(p,R),\hspace{2,5cm}$$

		\item If $\theta\geq0$, assume that $f$ is bounded in $B(p,2R)$, then we have

		$$\beta\frac{|\nabla f|^{2}}{f^{2}}+\frac{\rho_B}{k}-\frac{\theta}{kf^2}\leq \frac{(n+m)}{k^{2}\beta}\left[P+2\theta M\right]+\sqrt{\frac{n+m}{2\beta k^{4}}}(Q+S)^{\frac{1}{2}}, \quad \text{in}\quad B(p,R),$$

	\end{itemize}
	where

	\begin{eqnarray*}
		M&=&\displaystyle\sup_{B(p,2R)}f^{-2},\nonumber\\
		P&=&\frac{(n+m)c_{1}^{2}}{4R^{2}\beta(1-\beta)}+\frac{(n-1+R\sqrt{nK})c_{1}+c_{2}+2c_{1}^{2}}{R^2},\nonumber\\
		Q&=&\frac{3\beta}{2} \left[\frac{n+m}{4}(k\gamma)^{4}\frac{(1-\beta)^{2}}{\beta^{4}}\varepsilon^{-1}\right]^{\frac{1}{3}}+\frac{(n+m)}{2}\beta(1-\varepsilon)^{-1}(1-\beta)^{-2}K^{2}, \nonumber\\
		S&=&\frac{\beta(n+m)}{2(1-\varepsilon)(1-\beta)^{2}}\Bigg{\{}\left[\frac{M\theta }{\beta}\left(\beta-1+\frac{2}{k}\right)\right]^{2}
		+\frac{2KM\theta}{\beta}\left(\beta-1+\frac{2}{k}\right)\Bigg{\}},\nonumber
	\end{eqnarray*}
$c_{1}$, $c_{2}$ are positive constants and $\varepsilon\in(0,1)$.
\end{theorem}

By letting $R\to\infty$ we get the following global gradient estimates.

\begin{cor}Let $(B^{n}\times_{f}F^{k},g, h,\rho)$ be a complete gradient almost Ricci soliton with nocompact base satisfying
	$$Ric_{g_B}+Hess_{g_B}h_{B}-\frac{1}{m}dh_{B}\otimes dh_{B}\geq -K,\qquad\Delta_{h}\rho_{B}\geq0,\qquad|\nabla\rho_{B}|\leq\gamma,$$
	for $K\geq0$ on $B$. Then, for any $\beta\in(0,1)$ with $\beta>1-\frac{2}{k}$, the warping function $f$ satisfies the following gradient estimates:

	\begin{itemize}
		\item If $\theta<0$, we have
		$$\beta\frac{|\nabla f|^{2}}{f^{2}}+\frac{\rho_B}{k}-\frac{\theta}{kf^2}\leq \sqrt{\frac{n+m}{2\beta k^{4}}}Q^{\frac{1}{2}},\qquad \text{in}\quad  B^{n},$$

		\item If $\theta=0$, we have
		$$\beta\frac{|\nabla f|^{2}}{f^{2}}+\frac{\rho_B}{k}\leq \sqrt{\frac{n+m}{2\beta k^{4}}}Q^{\frac{1}{2}},\qquad \text{in}\quad  B^{n},$$

		\item If $\theta>0$, assume that $f$ is bounded, then we have
			$$\beta\frac{|\nabla f|^{2}}{f^{2}}+\frac{\rho_B}{k}-\frac{\theta}{kf^2}\leq \frac{2(n+m)\theta M'}{k^{2}\beta}+\sqrt{\frac{n+m}{2\beta k^{4}}}(Q+S)^{\frac{1}{2}},\qquad \text{in}\quad  B^{n},$$

	\end{itemize}
 where

	\begin{eqnarray*}
		M'&=&\displaystyle\sup_{B}f^{-2},\nonumber\\
		Q&=&\frac{3\beta}{2} \left[\frac{n+m}{4}(k\gamma)^{4}\frac{(1-\beta)^{2}}{\beta^{4}}\varepsilon^{-1}\right]^{\frac{1}{3}}+\frac{(n+m)}{2}\beta(1-\varepsilon)^{-1}(1-\beta)^{-2}K^{2}, \nonumber\\
		S&=&\frac{\beta(n+m)}{2(1-\varepsilon)(1-\beta)^{2}}\Bigg{\{}\left[\frac{M\theta }{\beta}\left(\beta-1+\frac{2}{k}\right)\right]^{2}
		+\frac{2KM\theta}{\beta}\left(\beta-1+\frac{2}{k}\right)\Bigg{\}},\nonumber
	\end{eqnarray*}
and $\varepsilon\in(0,1)$.
\end{cor}

As an application we obtain the following two results.

\begin{cor}\label{cor}There is no complete gradient Ricci soliton $(B^{n}\times_{f}F^{k},g, h,\rho)$ satisfying $$ Ric_{g_B}+Hess_{g_B}h_B-\frac{1}{m}dh_B\otimes dh_B\geq 0, $$ if either $\rho=0$, $\theta<0$ or $\rho=\text{cte}>0$, $\theta=0$.
\end{cor}

\begin{example}\label{ex:1}
	Let $(\mathbb{H}^{n},g_{-1})$, $(\mathbb{R}^{n},g_{0})$ and $(\mathbb{S}^{n},g_{1})$ be, in this order, the hyperbolic  and Euclidean spaces as well as the round sphere, all with standard metrics. Consider the manifolds $(B,g_B)=(\mathbb{S}^{n}\times \mathbb{R}^n, g_1+g_{0})$, $(F,g_F)=(\mathbb{H}^k,g_{-1})$ and define
	\[h_v:\mathbb{S}^n\to\mathbb{R},\quad p\mapsto g_1(p,v),\]
	for any given $v\in\mathbb{S}^n$. Then, it's readily seen that
	\[h_{B}: \mathbb{S}^{n}\times \mathbb{R}^n\to\mathbb{R},\quad(x,y)\mapsto -\log{\left(\frac{3-h_{v}(x)}{n}\right)},\]
	satisfies
	\[Ric_{g_B}+Hess_{g_B}h_B-dh_B\otimes dh_B\geq 0,\]
	and, therefore, by Corollary \ref{cor}, there cannot exist an $f:\mathbb{S}^n \times\mathbb{R}^n\to(0,\infty)$, not even a constant one, such that the warped product $ ((\mathbb{S}^n\times \mathbb{R}^n)\times_f\mathbb{H}^k,g) $ is a steady gradient Ricci soliton with potential $ h_B\circ\pi $.
\end{example}

Corollary \ref{cor} revels us that by starting with a quasi-Einstein manifold $(B,g_B)$ such that
\begin{equation*}
Ric_{g_B}+Hess_{g_B}h_B-\frac{1}{m}dh_B\otimes dh_B=0,
\end{equation*}
it is impossible to utilize such manifold as the base of a warped product gradient Ricci soliton $ (B^n\times F^k,g,h_B\circ\pi,\rho) $ with either a negative scalar curvature of the fiber manifold $ <0 $ and $ \rho=0 $ or null scalar curvature of the fiber manifold $ =0 $ and $ \rho>0 $.

In particular, for Einstein metrics, we foresee that

\begin{cor}
	\label{cor2}
	There is no Einstein warped product $(B^{n}\times_{f}F^{k},g)$ such that $\rho=0$ and $Ric_{g_B}\geq0$ with either $\theta<0$ or $ \theta=0 $ and $ f\neq constant $.
\end{cor}

\begin{example}
	By taking $ (B,g_B)=(\mathbb{R}^n,g_0) $ and $ (F,g_F)=(\mathbb{H}^k,g_{-1}) $ we see, now from Corollary \ref{cor2}, that none of the warped product manifolds $ (\mathbb{R}^n\times_f\mathbb{H}^k,g) $ are Ricci flat.
\end{example}

\section{Proofs}
\label{proofs}

\begin{myproof}{Theorem}{\ref{gradient}} Applying the change $f=v^{\frac{1}{k}}$ in equation \eqref{nazareno1} of Proposition \ref{lemma1} we obtain that
\begin{equation}\label{9}
\Delta_{h_{B}}v+\rho_{B} kv-\theta k v^{1-\frac{1}{k}}=0.
\end{equation}
Let $v$ a positive solution to \eqref{9}. Then, $u=\log v$ satisfies

\begin{equation*}
\Delta_{h_B}u=(\beta-1)|\nabla u|^{2}-L,\quad \text{where}\quad L:=\beta|\nabla u|^{2}+\rho_{B}k-\theta k e^{-\frac{2u}{k}},\quad \beta\in(0,1),\quad \beta>1-\frac{2}{k}.
\end{equation*}

Now, consider a cut-off function $\xi$ satisfying

\begin{equation*}
\xi(r)= \begin{cases} 1 &\text{if } r\in[0,1] \\[10pt]
0 & \text{if } r\in[2,\infty)
\end{cases},\qquad -c_{1}\leq\frac{\xi'(r)}{\xi^{\frac{1}{2}}(r)}\leq0,\qquad -c_{2}\leq\xi''(r),\qquad c_{1},c_{2}\in (0,\infty)
\end{equation*}
and define
\begin{equation*}
\psi(x)=\xi\left(\frac{r(x)}{R}\right),
\end{equation*}
where $r(x)$ is the distance function from $p$ to $x$.
Using an argument of Calabi \cite{calabi1958extension} (see also Cheng and Yau \cite{cheng1975differential}), we can assume without loss of generality that the function $\psi$ is smooth in $B(p,2R)$. Then, the function defined by $G=\psi L$ is smooth in $B(p,2R)$.

Let $x_{0}\in B(p,2R)$ be a point at which $G$ attains its maximum value $G_{max}$, and suppose that $G_{max}>0$ (otherwise the proof is trivial). At the point $x_{0}$, we have
\begin{equation*}
\nabla (G)=\psi\nabla L+L\nabla \psi=0.
\end{equation*}
Moreover,
\begin{equation}\label{general}
\begin{split}
0&\geq\Delta_{h_{B}}G,\\
&=\psi\Delta_{h_{B}}L+L\Delta_{h_{B}}\psi+2\langle\nabla \psi,\nabla L\rangle,\\
&=\psi\Delta_{h_B}L+L\Delta_{h_B}\psi-2L\frac{|\nabla\psi|^{2}}{\psi}.
\end{split}
\end{equation}
In order to estimate the right-hand side of \eqref{general} we prove the following lemma:

\begin{lema}\label{lemma2}Let $(B^{n},g_{B})$ be a complete noncompact Riemannian  manifold satisfying,

	\begin{equation}\label{m-Bakry}
	Ric_{g_B}+Hess_{g_B}h_B-\frac{1}{m}dh_{B}\otimes dh_{B}\geq -K,
	\end{equation}
	for $K\geq0$ in the metric ball $B(p,2R)\subset B$, and let $L$ and $\psi$ as above. Then, we have that

	\begin{equation}\label{a2'}
	\frac{|\nabla\psi|^{2}}{\psi}\leq\frac{c_{1}^{2}}{R^{2}},
	\end{equation}

	\begin{equation}\label{a3'}
	\Delta_{h_{B}}\psi\geq-\frac{(n-1+R\sqrt{nK})c_{1}+c_{2}}{R^2},
	\end{equation}

		\begin{equation}\label{a1}
		\begin{split}
		\Delta_{h_B}L\geq 2\beta\frac{(\Delta_{h_B}u)^{2}}{n+m}+2(1-\beta)k\langle\nabla u,\nabla \rho_{B}\rangle-2\langle\nabla u,\nabla L\rangle-2\beta K|\nabla u|^{2}
		+\\+k\Delta_{h_B}\rho_B-2\theta e^{-\frac{2u}{k}}\left(\big{(}\beta-1+\frac{2}{k}\big{)}|\nabla u|^{2}+L\right).
		\end{split}
	\end{equation}
\end{lema}

\begin{myproof}{Lemma}{\ref{lemma2}}
Equation \eqref{a2'} follows from the calculation

\begin{equation*}
\frac{|\nabla\psi|^{2}}{\psi}=\frac{1}{\xi}\left\langle \xi'\frac{\nabla r}{R}, \xi'\frac{\nabla r}{R}\right\rangle=\frac{(\xi')^2}{\xi}\frac{1}{R^2}\langle\nabla r,\nabla r\rangle\leq\frac{c_{1}^{2}}{R^{2}}.\\[10pt]
\end{equation*}

It has been shown by Qian \cite{qian1998comparison}, the following estimate

\begin{equation*}
\Delta_{h_{B}}r^{2}\leq n\left(1+\sqrt{1+\frac{4Kr^2}{n}}\right)
\end{equation*}
which implies
\begin{eqnarray}
\Delta_{h_B}r&=&\frac{1}{2r}\left(\Delta_{h_B}r^2-2|\nabla r|^{2}\right)\nonumber\\
&\leq&\frac{n-2}{2r}+\frac{n}{2r}\left(1+\sqrt{1+\frac{4Kr^2}{n}}\right)\nonumber\\
&=&\frac{n-1}{r}+\sqrt{nK}\nonumber.
\end{eqnarray}
Then, we obtain
\begin{equation*}
\Delta_{h_B}\psi=\frac{\xi''(r)|\nabla r|^{2}}{R^2}+\frac{\xi'(r)\Delta_{h_B}r}{R}\geq-\frac{(n-1+R\sqrt{nK})c_{1}+c_{2}}{R^2}.
\end{equation*}
which proves \eqref{a3'}.

From the Bochner formula for the $m$-Bakry-\'Emery Ricci tensor and
the lower bound hypothesis \eqref{m-Bakry}, we obtain

\begin{eqnarray*}
	\frac{1}{2}\Delta_{h_B}|\nabla u|^{2}\geq\frac{(\Delta_{h_B}u)^{2}}{n+m}+\langle\nabla u,\nabla\Delta_{h_B}u\rangle-K|\nabla u|^{2}.
\end{eqnarray*}
Therefore,
\begin{equation*}
\begin{split}
\Delta_{h_B}L&=\beta\Delta_{h_B}|\nabla u|^{2}+k\Delta_{h_B}\rho_B-k\theta\Delta_{h_B}e^{-\frac{2u}{k}}\\[5pt]
&\geq 2\beta\frac{(\Delta_{h_B}u)^{2}}{n+m}+2\beta\langle\nabla u,\nabla\Delta_{h_B}u\rangle-2\beta K|\nabla u|^{2}+k\Delta_{h_B}\rho_B-k\theta\Delta_{h_B}e^{-\frac{2u}{k}}.
\end{split}
\end{equation*}
Notice that

\begin{eqnarray}
2\beta\langle\nabla u,\nabla\Delta_{h_B}u\rangle&=&2\beta\langle\nabla u,\nabla\left[\left(1-\frac{1}{\beta}\right)\left(-k\rho_B+k\theta e^{-\frac{2u}{k}}\right)-\frac{L}{\beta}\right]\rangle\nonumber\\[5pt]
&=&2(1-\beta)k\langle\nabla u,\nabla \rho_{B}\rangle+2(\beta-1) k\theta\langle\nabla u,\nabla e^{-\frac{2u}{k}}\rangle-2\langle\nabla u,\nabla L\rangle\nonumber\\[5pt]
&=&2(1-\beta)k\langle\nabla u,\nabla \rho_{B}\rangle-4(\beta-1) \theta e^{-\frac{2u}{k}}|\nabla u|^{2}-2\langle\nabla u,\nabla F\rangle,\nonumber
\end{eqnarray}
and

\begin{eqnarray}
\Delta_{h_B}e^{-\frac{2u}{k}}&=&\frac{2}{k}e^{-\frac{2u}{k}}\left[\frac{2}{k}|\nabla u|^{2}-\Delta_{h_B}u\right]\nonumber\\
&=&\frac{2}{k}e^{-\frac{2u}{k}}\left[\frac{2}{k}|\nabla u|^{2}-(\beta-1)|\nabla u|^{2}+L\right]\nonumber\\
&=&\frac{2}{k}e^{-\frac{2u}{k}}\left[\left(\frac{2}{k}-\beta+1\right)|\nabla u|^{2}+L\right].\nonumber
\end{eqnarray}
It follows that

\begin{equation*}
\begin{split}
\Delta_{h_B}L\geq 2\beta\frac{(\Delta_{h_B}u)^{2}}{n+m}+2(1-\beta)k\langle\nabla u,\nabla \rho_{B}\rangle-2\langle\nabla u,\nabla L\rangle-2\beta K|\nabla u|^{2}
+\\+k\Delta_{h_B}\rho_B-2\theta e^{-\frac{2u}{k}}\left(\big{(}\beta-1+\frac{2}{k}\big{)}|\nabla u|^{2}+L\right),
\end{split}
\end{equation*}
which completes the proof of lemma.
\end{myproof}\\[1pt]

Continuing, by Lemma \ref{lemma2} and \eqref{general}, we obtain at the point $x_{0}$,

\begin{eqnarray*}
\psi\Bigg{\{}2\beta\frac{(\Delta_{h_B}u)^{2}}{n+m}+2(1-\beta)k\langle\nabla u,\nabla \rho_{B}\rangle-2\langle\nabla u,\nabla L\rangle-2\beta K|\nabla u|^{2}+k\Delta_{h_B}\rho_B+\\-2\theta e^{-\frac{2u}{k}}\left[\big{(}\beta-1+\frac{2}{k}\big{)}|\nabla u|^{2}+L\right]\Bigg{\}}\leq LH,
\end{eqnarray*}
where

\begin{equation*}
H=\left(\frac{(n-1+R\sqrt{nK})c_{1}+c_{2}+2c_{1}^{2}}{R^2}\right).
\end{equation*}

From the fact that $0\leq\psi\leq1$, we have
$$
-2\psi\langle\nabla u,\nabla L\rangle=2L\langle\nabla u, \nabla \psi\rangle\geq-2L|\nabla u||\nabla\psi|\geq-\frac{2c_{1}}{R}\psi^{\frac{1}{2}}L|\nabla u|.
$$
Then

\begin{equation}\label{final}
\begin{split}
	2\beta\psi\frac{(\Delta_{h_B}u)^{2}}{n+m}+2(1-\beta)k\psi\langle\nabla u,\nabla \rho_{B}\rangle
	-\frac{2c_{1}}{R}\psi^{\frac{1}{2}}L|\nabla u|
	-2\beta\psi K|\nabla u|^{2}+\\
	+k\psi\Delta_{h_B}\rho_B-2\theta e^{-\frac{2u}{k}}\psi\left[\big{(}\beta-1+\frac{2}{k}\big{)}|\nabla u|^{2}+L\right]\leq LH.
\end{split}
\end{equation}
In the sequel we distinguish between two cases: (a) $\theta<0$ and (b) $\theta\geq0$.

Case (a): $\theta<0$. Since

$$\Delta_{h_B}\rho_{B}\geq0,\qquad|\nabla \rho_{B}|\leq\gamma(2R),$$
then \eqref{final} yields

\begin{eqnarray*}
		2\beta\psi\frac{(\Delta_{h_B}u)^{2}}{n+m}-2(1-\beta)k\psi\gamma|\nabla u|
		-\frac{2c_{1}}{R}\psi^{\frac{1}{2}}L|\nabla u|
		-2\beta\psi K|\nabla u|^{2}\leq LH.
\end{eqnarray*}
Multiplying both sides of the above equation by $\psi$ and using the fact that $0\leq\psi\leq 1$, we obtain

\begin{eqnarray*}
	2\beta\frac{(\psi\Delta_{h_B}u)^{2}}{n+m}+2(\beta-1)k\psi^{\frac{1}{2}}\gamma|\nabla u|
	-\frac{2c_{1}}{R}\psi^{\frac{3}{2}}L|\nabla u|
	-2\beta\psi K|\nabla u|^{2}\leq \psi LH.
\end{eqnarray*}
Let

$$y=\psi|\nabla u|^{2},\qquad z=\psi(-k\rho_B+k\theta e^{-\frac{2u}{k}}).$$
Then we have

\begin{eqnarray*}
	\frac{2\beta}{n+m}\Big\{ (y-z)^{2}+\frac{(\beta-1)k\gamma(n+m)y^{\frac{1}{2}}}{\beta}-\frac{(n+m)c_{1}}{R}y^{\frac{1}{2}}\left(y-\frac{z}{\beta}\right)-(n+m)Ky\Big\}\leq \psi LH.
\end{eqnarray*}
From Li-Yau's arguments (\cite{li1986parabolic}, pg.161-162), we know that

\begin{eqnarray*}
(y-z)^{2}-(n+m)c_{1}R^{-1}y^{\frac{1}{2}}\left(y-\frac{z}{\beta}\right)-(n+m)Ky-(n+m)\left(\frac{1}{\beta}-1\right)\gamma y^{\frac{1}{2}}\geq\nonumber\\
\geq\left(\frac{1}{\beta}\right)^{-2}\left(y-\frac{z}{\beta}\right)^{2}-\frac{(n+m)^{2}}{8}c_{1}^{2}\left(\frac{1}{\beta}\right)^{2}\left(\frac{1}{\beta}-1\right)^{-1}R^{-2}\left(y-\frac{z}{\beta}\right)+\nonumber\\
-\frac{3}{4}4^{-\frac{1}{3}}(n+m)^{\frac{4}{3}}\left[\gamma^{4}\left(\frac{1}{\beta}-1\right)^{2}\left(\frac{1}{\beta}\right)^{2}\varepsilon^{-1}\right]^{\frac{1}{3}}-\frac{(n+m)^{2}}{4}(1-\varepsilon)^{-1}\left(\frac{1}{\beta}-1\right)^{-2}\left(\frac{1}{\beta}\right)^{2}K^{2}.
\end{eqnarray*}
for any $0<\varepsilon<1$.

Therefore in our context, we obtain
\begin{eqnarray*}
	\frac{2\beta}{n+m}\Bigg\{(\beta y-z)^{2}-\frac{(n+m)^{2}c_{1}^{2}}{8R^{2}\beta^{2}(1-\beta)}(\beta y-z)-\frac{3}{4}4^{-\frac{1}{3}}(n+m)^{\frac{4}{3}}\left[\left(k\gamma\right)^{4}\frac{(1-\beta)^{2}}{\beta^{4}}\varepsilon^{-1}\right]^{\frac{1}{3}}+\nonumber\\
	-\frac{(n+m)^{2}}{4}(1-\varepsilon)^{-1}(1-\beta)^{-2}K^{2}\Bigg\}
	\leq (\beta y-z)H.
\end{eqnarray*}
Hence,

\begin{equation*}
\frac{2\beta}{n+m}(\psi L)^{2}-P(\psi L)-Q\leq0,
\end{equation*}
where,

\begin{eqnarray*}
P&=&\frac{(n+m)c_{1}^{2}}{4R^{2}\beta(1-\beta)}+H,\nonumber\\
Q&=&\frac{3\beta}{2} \left[\frac{n+m}{4}\left(k\gamma\right)^{4}\frac{(1-\beta)^{2}}{\beta^{4}}\varepsilon^{-1}\right]^{\frac{1}{3}}+\frac{\beta(n+m)}{2}(1-\varepsilon)^{-1}(1-\beta)^{-2}K^{2}. \nonumber
\end{eqnarray*}

Using the inequality $az^{2}-bz\leq c$, one obtain $z\leq\frac{2b}{a}+\sqrt{\frac{c}{a}}$. Then

\begin{eqnarray*}
\sup_{x\in B(p,R)}L(x)\leq(\psi L)(x_{0})\leq \frac{n+m}{\beta}P+\sqrt{\frac{n+m}{2\beta}}Q^{\frac{1}{2}},
\end{eqnarray*}
and hence,

$$\beta|\nabla u|^{2}+k\rho_B-k\theta e^{-\frac{2u}{k}}\leq \frac{n+m}{\beta}P+\sqrt{\frac{n+m}{2\beta}}Q^{\frac{1}{2}}.$$

Replacing the function $u=\log f^{\frac{d+1}{2}}$ back into the above equation we obtain the desired estimate when $\theta<0$.

Case (b): $\theta\geq0$. Since
$$\Delta_{h_B}\rho_{B}\geq0,\qquad|\nabla \rho_{B}|\leq\gamma(2R),$$
then \eqref{final} yields

\begin{equation*}
\begin{split}
2\beta\psi\frac{(\Delta_{h_B}u)^{2}}{n+m}-2(1-\beta)k\psi|\nabla u|\gamma
-\frac{2c_{1}}{R}\psi^{\frac{1}{2}}L|\nabla u|
-2\beta\psi K|\nabla u|^{2}+\\
-2\theta e^{-\frac{2u}{k}}\psi\left[\big{(}\beta-1+\frac{2}{k}\big{)}|\nabla u|^{2}+L\right]\leq LH.
\end{split}
\end{equation*}
Multiplying both sides of the above equation by $\psi$, and using the fact that $0\leq\psi\leq 1$, we obtain

\begin{eqnarray*}
	2\beta\frac{(\psi\Delta_{h_B}u)^{2}}{n+m}+2(\beta-1)k\psi^{\frac{1}{2}}\gamma|\nabla u|-\frac{2c_{1}}{R}\psi^{\frac{3}{2}}L|\nabla u|-2\beta\psi K|\nabla u|^{2}+\\
	-2\theta M\psi\left[\big{(}\beta-1+\frac{2}{k}\big{)}|\nabla u|^{2}+L\right]\leq \psi LH,
\end{eqnarray*}
where $M=\sup_{B(p,2R)} e^{-\frac{2u}{k}}$.

Let
$$y=\psi|\nabla u|^{2},\qquad z=\psi(-k\rho_B+k\theta e^{-\frac{2u}{k}}).$$
Then we have

\begin{eqnarray*}
	\frac{2\beta}{n+m}\Bigg\{(y-z)^{2}-\frac{c_{1}(n+m)}{R}y^{\frac{1}{2}}\left(y-\frac{z}{\beta}\right)
	+(n+m)\frac{(\beta-1)}{\beta}k\gamma y^{\frac{1}{2}}+\nonumber\\
	-(n+m)\left[\frac{\theta M}{\beta}(\beta-1+\frac{2}{k})+K\right]y
	\Bigg\}\leq \psi L(H+2\theta M).
\end{eqnarray*}
Hence, again by the Li-Yau arguments, we get that

\begin{eqnarray*}
	\frac{2\beta}{n+m}\Bigg\{(\beta y-z)^{2}-\frac{(n+m)^{2}c_{1}^{2}}{8R^{2}\beta^{2}(1-\beta)}(\beta y-z)-\frac{3}{4}4^{-\frac{1}{3}}(n+m)^{\frac{4}{3}}\left[\left(k\gamma\right)^{4}\frac{(1-\beta)^{2}}{\beta^{4}}\varepsilon^{-1}\right]^{\frac{1}{3}}+\nonumber\\
	-\frac{(n+m)^{2}}{4}(1-\varepsilon)^{-1}(1-\beta)^{-2}\left[\frac{\theta M}{\beta}(\beta-1+\frac{2}{k})+K\right]^{2}\Bigg\}
	\leq (\beta y-z)H,
\end{eqnarray*}
which means that

\begin{eqnarray*}
	\frac{2\beta}{n+m}(\psi L)^{2}-\big\{P+2\theta M\big\}(\psi L)-(Q+S)\leq 0,
\end{eqnarray*}
where

\[S=\frac{\beta(n+m)}{2(1-\varepsilon)(1-\beta)^{2}}\Bigg{\{}\left[\frac{M\theta }{\beta}\left(\beta-1+\frac{2}{k}\right)\right]^{2}
+\frac{2KM\theta}{\beta}\left(\beta-1+\frac{2}{k}\right)\Bigg{\}}.\]
Therefore

\begin{eqnarray*}
	\beta|\nabla u|^{2}+k\rho_B-k\theta e^{-\frac{2u}{k}}\leq \frac{n+m}{\beta}(P+2\theta M)+\sqrt{\frac{n+m}{2\beta}}(Q+S)^{\frac{1}{2}}.
\end{eqnarray*}
Replacing the function $u=\log f^{\frac{d+1}{2}}$ back into the above equation we obtain the desired estimate when $\theta\geq0$.
\end{myproof}

redpajama_set_name: RedPajamaArXiv


IFE14 is an Integrated Field Exercise to simulate an almost entire on-site inspection (OSI) in Jordan from 3 November to 9 December 2014 organized by the Preparatory Commission for the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO).
"The Integrated Field Exercise 2014 in Jordan will prove to the world that CTBT on-site inspections are a viable deterrent against would-be nuclear testers. With a range of new techniques never used before in an on-site inspection context, IFE14 will take our capabilities to a new level." – CTBTO Executive Secretary Lassina Zerbo. Today, on 3 November 2014, the CTBTO is starting the Integrated Field Exercise 2014 (IFE14) with launch-phase activities in Vienna. The Jordan segment with field activities will run from 7 November to 9 December. The exercise will simulate an almost entire on-site inspection (OSI) in Jordan's Dead Sea area. During IFE14 the inspection team will conduct a meticulous search of a clearly defined inspection area to establish whether or not a nuclear explosion has been conducted. The exercise will be in response to a technically realistic and stimulating but fictional scenario.
This will be the CTBTO's second full-scale simulation of an on-site inspection after IFE08 in Kazakhstan and the most ambitious, realistic and challenging inspection simulation to date.
Hungary has provided experts and in-kind equipment contribution to aid the successful conduct of the exercise.


Dos Equis, home of the Most Interesting Man in the World, Beer Mixology and the Stay Thirsty Grant.The Most Interesting Man in the World in an advertising campaign for the Dos Equis brand of beer, produced by the marketing firm Euro RSCG for Cuauhtémoc Moctezuma Brewery.
Cuba imports cigars from him. Mosquitos refuse to bite him purely out of respect. In museums, he is allowed to touch the art.
He divorced his wife because he caught her littering.
He gave his father "the talk"
He has inside jokes with people he's never met.
His business card simply says 'I'll Call You"
His mother has a tattoo that says "Son"
His passport requires no photograph.
On every continent in the world, there is a sandwich named after him. His hands feel like rich brown suede.
Once he ran a marathon because it was "on the way"


Editor's note: For a related story, please see Marta Lane's Tastes of Kaua'i on page 8.
Last August, when I came home from an Africa mission trip, I stepped on the scales and discovered a 10-pound weight loss. Losing weight is usually met with, "Congratulations, how did you do it?" In my case, reaction to my new "look" was, "Have you been sick? You need to put on some weight." Thank you very much.
I really didn't feel well either, so my doctor and I went in search of answers. Sometimes people return from remote areas of Africa and other developing nations with intestinal parasites, but thankfully tests were negative. Still, two months passed and the weight didn't return. This would get expensive if I had to downsize my whole wardrobe, which was looking quite baggy.
More fun tests by a gastroenterologist that included what I call "organ spelunking" – little cameras exploring my gastro intestinal tract – ruled out any major diseases such as cancer (my grandfather died of stomach cancer in his mid-60s), diverticulosis and celiac disease. Aside from a little common acid reflux, I was healthy. I just didn't look it – or feel it.
Meanwhile, some friends suggested looking at gluten sensitivity. Huh? Celiac disease, a serious condition related to gluten intolerance, had already been ruled out, I assured them. Still, I agreed to consult with naturopathic doctor Laurie Steelsmith for other possibilities.
The definition of the word "gluten" on Wikipedia made me question why I'd ever eat it. "Gluten is the composite of a prolamin and a glutelin, which exist, conjoined with starch, in the endosperm of various grass-related grains." Yuch. But how I love my bread, rolls, pasta, biscuits, pizza dough, gravy and waffles – all of which contain gluten. I prayed gluten and I were compatible.
Dr. Steelsmith, author of Natural Choices for Women's Health (Three Rivers Press, 2005), wanted to help me further rule out things that could be causing my symptoms and suggested a test that would reveal whether I was in some way allergic to this binding material found in every grain except rice, millet, corn, buckwheat and a couple of others.
I was in denial, certain I didn't have this allergy, because a life without sourdough and Grapenuts just wasn't doable for me.
But the test results were clear. I have two of the anti-gluten (my term) genes, which means my children and my parents each have/had at least one. My parents never knew they had this gene, but Mother, poor thing, had gastrointestinal problems her whole life. No, mine isn't celiac disease, which makes a person obviously sick, but my genetic predisposition can disrupt the immune system possibly causing weight loss and other symptoms.
Steelsmith wasn't sure going off gluten would help my issue, but suggested I try it for a couple of months. Luckily, my good friend and doctor, who (unfortunately) has celiac disease, has guided my diet, suggesting brands of yummy gluten-free products. Food manufacturers are now producing ono gluten-free dessert mixes, breads, pastas and even pizza dough. Just in Austin, Texas, I ate at an upscale pizza restaurant, The Grove, that makes the best gluten-free pizza I've ever eaten, including regular pizza.
So after five months gluten-free, I've gained five pounds, feel great, and mostly don't pine for the old gluten foods. While I can't say with definitive medical certainty that gluten was the culprit, I know I discovered something important in the process.
I hope my story will help someone else.


In the past, we wrote about how the partial government shutdown is affecting the craft brewing industry. That was all about how breweries are unable to release new beer because they can't get the new labels approved. Well, as the shutdown nears 30 days, there are much more important things to worry about than beer. That's because over 800,00 federal workers are currently working without pay.
That means that many can't pay their mortgages, car payments, various bills, and even afford food. Just like us, Stephen Colbert, host of The Late Show has noticed this. That's why CBS is selling a special mug to help benefit the unpaid federal workers.
Click the link in our bio to purchase a mug! 100% of the proceeds go to Chef José Andrés and World Central Kitchen to help feed government workers impacted by the shutdown.
The Late Show with Stephen Colbert Shutdown Mug is available for purchase on at the CBS store online for $14.99. It's a simple white mug adorned with the phrase "Don't even talk to me until I've had my paycheck." Remove the word "paycheck" and insert "coffee" and you can see where the phrase originated. One-hundred percent of the profits go to Chef José Andrés' World Central Kitchen, the nonprofit that in the past was used to feed millions of Americans after natural disasters.
Now, the charity is being used to feed furloughed government workers and their families. Andrés took to Twitter recently to draw attention to this problem that doesn't seem like it will have a resolution any time soon.
"Today we face another type of disaster in the United States. More than 800,000 federal workers are without a job. Many millions of Americans are gonna go through hard times," the chef said in a video he shared on Twitter.
Beginning last Wednesday, Andrés' team opened a kitchen and café on Pennsylvania Avenue in Washington D.C. The restaurant will serve free hot meals for federal works with a valid ID from 11 a.m. to 6 p.m. every day.


It helped me tremendously to study up on OB– normals, a normals, complications: ie postpartum hemorrhage, and neonatal norms, care of epidural site, cesarean sections, coding adult women and neonate so, etc. I never worked OB, but after 5 years as RN, two of my own births, and strong lactation background with IBCLC underway, I got called to interview five months after I wondered on to the unit and the gracious nurse manager spoke with me for a few minutes. Dress very well and show up with up to date resume and cover letter. She gave me her email and I stayed in touch, finally hearing back. I wore my black BR power suit, answered all the questions like a seasoned OB nurse (studied for the couple weeks leading to the interview) and did not shy away from telling them I already had two offers for other units, but it was there on the mother-baby unit I wanted to work. Three days later I accepted the offer ?


[EF#4] I WANT DORAEMON'S ANYWHERE DOOR!
As travelers, if we want to go somewhere, we don't need to think twice about the cost of traveling anymore. No need to type "the budget hotel option in (let say) Bali" keyword in Google. Because, you already have Doraemon's Anywhere Door!
Let say, I want to go to Kenya! Then we only need to grab Anywhere Door from Doraemon's Pocket.
And voila! We are in Kenya in a minute. No need to long haul, no need to through the complex immigration rules, no need to pay visa, no need to buy a ticket, but still need to think about the hotel. But at least, we eliminate one important thing to do traveling: ticket.
Can you guess where my destination is if I have an Anywhere Door?
The answer is…I will go to Mecca to do pilgrim and invite my family to join. And when we were there, I want pilgrimage to the tomb of Rasulullah. I want to visit all the historic site in Mecca.
Yes, Mecca is my number one place that I want to visit before die.
This blog entry makes up a collection of writing by fellow bloggers, who joined [EF#4 Challenge] Grab A Tool From Doraemon's Magic Pocket! Let's write your idea!
Previous postTella: Untuk Sampai di Titik ini Bersyukur Banget!
Tapi ada batas atasnya juga kan, jadi pas high season dari maskapai jg gak boleh sembarangan naikin harga….
duh, ini pintu sih impian semua orng deh kyknya. ahhaha.
Wohoooo Masjid Nabawi…why I am not thingking that amazing idea, Nad?
And yes, I need you to go with me because you have that translator tool.
Two thumbs up, Mbak Mikan!!! Aku juga mikirnya gitu. Klo mimpi aja gak berani, gimana mau berani untuk mewujudkannya?
Haha, to me this still does not solve the problem Dev because we do still need to prepare for a visa if our destination requires us one, no? Otherwise we will be like illegal aliens in that country 😛 .
Tinggal taruh di kamar, tapi bisa ke mana-mana. 🙂 Great!
Deva… so sorry for late stopping by on this post of yours.


It is actually possible that the next few days will offer more locations in the forecast area without rain than with rain!
Today and Tonight: A continued trend of fewer showers and thunderstorms is expected this afternoon. Rain coverage will be in the 30 percent range. Most of the activity that can develop should remain south of I-10. High temperatures will eclipse 90 degrees with plenty of early sun. Overnight lows will remain in the 70s beneath mostly clear skies.
Up Next: Pretty typical July weather is in store for the remainder of the week. Days will be partly sunny and hot with highs near 93 and a few pop-up showers during the afternoon hours. On any given day, most locations will stay dry, but that isolated activity will bring an afternoon cool down to a few spots. Nights will be quiet and muggy with lows near 75. Expect an upper level disturbance to provide another uptick in afternoon activity Saturday through Monday.
The Tropics: Don has degenerated into a remnant low with a minimum pressure of 1012mb and 40mph winds. Across the Windward Islands, the system will continue westward at 20mph before fully dissipating in the southern Caribbean Sea. A trailing tropical wave in the Eastern Atlantic has a 30 percent chance of development before conditions become unfavorable.
An upper level ridge will begin to build southeastward from the Midwest through Thursday. In response to this atmospheric warming, instability will decrease. At the same time, forecast models are showing a bit less moisture available as well. This combination will result in fewer showers and thunderstorms each afternoon; though it looks as though daytime heating and marine breezes will still be able to spark an isolated shower or thunderstorm. For Wednesday, water vapor imagery shows a much drier mid-level air mass stretching across the Gulf Coast. The HRRR Model seems to be resolving this trend well, holding any shower and thunderstorm development near the coast. While rain coverage goes down this week, the mid-level dry air may mean intensity on the few storms that do develop may increase with gusty winds and frequent lightning possible. The upper ridge will not last long though. It appears as through an easterly wave in the mid-levels will traverse the Gulf Coast Saturday and Sunday before washing out into an open trough early next week. The return of upper low pressure will result in more ascent and the return of scattered to widespread convection. With regard to temperatures, highs will generally stick to the 90 to 95 degree range—lower on days with greater rain coverage and higher on days with lower rain coverage. Particularly on the drier days, heat indices will climb into the 100 to 105 range for an extended period of the afternoons. Lows will be consistently in the middle 70s.


Hoka's roots are in the mountains, designing shoes that allowed athletes to run faster, safer and farther downhill. The result are a range of trail and road shoes that puts performance and comfort first. With Hoka, your feet feel light gliding above the earth. Don't run, fly.
The Hoka "One One" maximum cushioning provides premium shock absorption and superior comfort for those long runs. Their unique "Meta-Rocker" enhances a runners' natural running gait and delivers a smooth roll from the impact phase through to toe off.
In summary, it is designed to increase running efficiency and performance.


It doesn't matter if you're driving a brand-new luxury model or an old favorite, sooner or later you're going to need maintenance to keep your car on the road. That's why finding a service center you can trust is so essential. With so much riding on your vehicle's wheels, it only makes sense to put your car in the hands of an expert service team.
That's exactly what you'll find when you when you come to Capitaland Subaru in Glenville, NY. Our dealership maintains an onsite service center staffed by technicians with years of shared experience. They possess everything needed to diagnose and repair any issues your vehicle might be experiencing. We work hard to be a superior source of vehicle maintenance for drivers of all sorts in Schenectady and Clifton Park.
Why Seek Service at Capitaland Subaru?
When you bring your vehicle to our dealership, you'll find a service center staffed by a team of factory-trained professionals. Our technicians have the skills, tools, and experience to handle a wide array of jobs and tasks. These could be as simple as routine inspections or oil changes to more complicated repairs.
To help guarantee the best service, we also use OEM-supplied parts. Provided by the same manufacturers that build our top-rated Subaru cars, our replacement parts are designed to be durable and long-lasting. These parts allow us to make sure your car can return to the road in the best condition possible. That way you can drive home to Ballston Lake or Burnt Hills with the peace of mind that you deserve.
When you bring your vehicle to us, we understand that you might have other things to do. That's why we offer the option to drop off your vehicle while you leave to run other errands. Our convenient shuttle service can take you where you need to go while your car's out of commission. We can even come and pick you up when your vehicle's ready.
And if you decide to stay and wait? You'll find a range of amenities waiting to keep you comfortable. Our waiting area has comfortable places to sit, a nice TV, and, of course, complimentary Wi-Fi. You'll have everything you need to sit back and relax while we take care of your car.
If you're ready to get your vehicle maintenance taken care of, give us a call at (888) 443-5384. Our friendly service team will ask you questions about what's going on so we can better understand your needs. Once we've done that, we'll help you find a convenient time to bring your car in for an appointment to get the issue taken care of.
If you'd prefer to schedule your appointment online, that's an option too. All you need to do is go to our online scheduling page and provide the requested information. Once you've submitted the online form, a representative from our dealership will get in touch with you to finalize the details.


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Q: Problems determining similarity of angles I'm working on implementing Context Steering movement for the enemy AI in my unity project and running into problems when it comes to determining the interest of each angle.
I have two classes: ContextMap and DirectionContext.
DirectionContext is a data storage class. It contains an angle, a Vector3 that relates that angle into a direction to move in, and a float ranging from 0 to 1 depending on how interesting that angle is to move in.
ContextMap contains a list of DirectionContext depending on the "detail" of the contextmap. So if I set the detail to 4, it will generate 4 DirectionContexts, and if I set the detail to 8, it will generate 8 DirectionContexts. The angles go from -180, to +180.
What I want to do is write a function that determins the angle between the enemy gameobject and the player gameobject, then compare it to each DirectionContext in the context map. I want it to set the interest float for each DirectionContext depending on the similarity of the angle between the objects and the DirectionContexts angle. I want it to set interest to 1 if the directions are identical, and to set interest to 0 if the difference between the angles is a high as they can be (360.)
The issue I'm having, is my scripts aren't setting the interest for the angles correctly. If the Player is directly above the enemy, it works as expected, but if the player is to the diagonals or sides it starts working opposite.
Here's a picture of what's happening: The black object is the enemy, the red is the human. The lines are longer depending on how high the interest is.
Link to the image
As you can see in the image, if the directions are up/down then it works fine, but things get weird when it goes diagonal or to the sides.
Here's what I've come up with in code:
    public class DirectionContext
    {
        [SerializeField] private Vector3 direction;
        [SerializeField] private float interest;
        [SerializeField] private float angle;
        [SerializeField] private bool isExcluded = false;
        public Vector3 GetDirection() { return direction; }
        public float GetInterest() { return interest; }
        public void SetInterest(float value) { interest = value; }
        public void CheckInterestAndSet(float newInterest)
        {
            if (newInterest > interest)
                interest = newInterest;
        }

        public float GetAngle() { return angle; }

        public DirectionContext(float angle)
        {
            this.angle = angle;
            this.direction = new Vector3(Mathf.Sin(angle * Mathf.Deg2Rad), Mathf.Cos(angle * Mathf.Deg2Rad), 0).normalized;
        }
}

Context map:
    public class ContextMap
    {
        [SerializeField] private List<DirectionContext> contextMap = new List<DirectionContext>();
        public List<DirectionContext> GetContext()
        {
            return contextMap;
        }

        public void GenerateMap(int detail)
        {
            contextMap.Clear();

            for (int i = 0; i < detail; i++)
            {
                float angle = (360 / detail * i) - 180;
                contextMap.Add(new DirectionContext(angle));
            }
        }

        public void UpdateContext(int index, float interest)
        {
            contextMap[index].CheckInterestAndSet(interest);
        }

        public void DebugDrawMap(Vector3 position, Color color)
        {
            foreach (DirectionContext direction in contextMap)
            {
                Debug.DrawLine(position, (position + direction.GetDirection()).normalized * direction.GetInterest());
            }
        }

        public void Clear()
        {
            foreach (DirectionContext dir in contextMap)
                dir.Clear();
        }
    }

Seek: (I left out SteeringContext as it's a super simple class. It just contains variables that may be interesting. The two used in seek are parent and targetDestination. TargetDestination is the players location, and parent is a reference to the enemy.
    public class Seek : SteeringBehavior
    {
        public override ContextMap AddContext(ContextMap contextMap, SteeringContext steeringContext)
        {
            float angleToTarget = AngleBetween(Vector3.up, steeringContext.targetDestination - steeringContext.parent.transform.position);
            //Debug.Log(angleToTarget);

            for (int i = 0; i < contextMap.GetContext().Count; i++)
            {

                float delta = Mathf.Abs(Mathf.Max(angleToTarget, contextMap.GetContext()[i].GetAngle()) - Mathf.Min(angleToTarget, contextMap.GetContext()[i].GetAngle()));
                if (delta > 180)
                {
                    delta = 360f - delta;
                }
                float interest = 1f - delta / 180f;

                contextMap.UpdateContext(i, interest);
            }

            return contextMap;
        }

        private float AngleBetween(Vector3 vector1, Vector3 vector2)
        {
            float sin = vector1.x * vector2.y - vector2.x * vector1.y;
            float cos = vector1.x * vector2.x + vector1.y * vector2.y;
            return Mathf.Atan2(sin, cos) * (180) / Mathf.PI;
        }
    }

And I make the call to Seek using this function:
        private void PopulateInterestMap()
        {
            interestMap.Clear();

            foreach (SteeringBehavior behavior in interestBehaviors)
            {
                interestMap = behavior.AddContext(interestMap, steeringContext);
            }
        }

Thank you for any help!

A: I solved it. I'm going to answer my own question as there's no source code online that really goes into Context Steering behaviors, so maybe the code posted here will save somebody else the trouble I went through.
Now that I have it up and working, anybody messing around with steering behaviors I highly recommend looking into Context Steering (If you google there's some good blog posts and papers about it's benefits.) It totally fixed the jitter issues with my steering behaviors, and fixed all of the issues of blended behaviors cancelling themselves out in oddball situations.
The problem wasn't in determining the weight, but the part of DirectionContext where I convert the angle into a direction vector.
        this.direction = new Vector3(Mathf.Sin(angle * Mathf.Deg2Rad), Mathf.Cos(angle * Mathf.Deg2Rad), 0).normalized;

Should have been
        this.direction = new Vector3(Mathf.Cos(angle * Mathf.Deg2Rad), Mathf.Sin(angle * Mathf.Deg2Rad), 0);

The normalized isn't what ruined it, it was Cos vs Sin. Normalized was just unneccessary.

redpajama_set_name: RedPajamaStackExchange


text:
Bradley Cooper Impresses Prince William With His Singing Skills At BAFTAs
Tim IrelandGetty Images
On Sunday evening, celebrities and royals alike attended the British Academy Film and Television Awards to celebrate the past year's on-screen successes. Prince William and Kate Middleton, the Duke and Duchess of Cambridge, were among the list of guests, as well as stars like Bradley Cooper. Following the awards show, the royals mingled with Hollywood celebrities behind the scenes, particularly hitting it off with Cooper as they discussed his direction and leading role in A Star is Born.
William happily approached and greeted Cooper after the actor won the award for Original Music, People reported. He congratulated Cooper on the success of the film and admitted that he didn't even know the actor could sing.
"I didn't either," Cooper quickly joked back, causing the royal to chuckle.
Cooper not only made his directorial debut with A Star is Born, but also appeared as the leading man Jackson Maine, a talented musician struggling with alcoholism and drug addiction.
William and Cooper also discussed Lady Gaga, the film's leading lady, who opted to attend the Grammys on Sunday evening instead.
"Did you always have her in mind when you wanted to do this?" the duke asked.
"Not originally," Cooper replied. "But then it was dormant for a while, and I saw her perform and that was it."
This evening The Duke and Duchess of Cambridge attended the @BAFTA Awards at the Royal Albert Hall. The Duke, BAFTA President, presented the Fellowship to Thelma Schoonmaker at the Awards Ceremony. Swipe to see The Duke and Duchess congratulating some of tonight's #BAFTA Award winners, including Rising Star Award winner @letitiawright and @officialspikelee, Director of BlacKkKlansman, winner of Best Adapted Screenplay. Congratulations to all of tonight's #EEBAFTAs Award Winners! ???? PA / ???? Kensington Palace
A post shared by Kensington Palace (@kensingtonroyal) on Feb 10, 2019 at 2:53pm PST
In addition to Cooper, the duke and duchess also chatted with the star of Bohemian Rhapsody Rami Malek, BlacKkKlansman director Spike Lee, and Black Panther star Letitia Wright. Malek, who had just won the award for Best Leading Actor, reportedly shared a few kind words about London with William, according to Express.
"I don't know if you caught my speech but this country and city have embraced me like no other and I couldn't think of a better place to shoot with a better crew," Malek told the prince.
Prince William not only sat in the audience for the awards show with his wife, but also presented a prestigious honor to film editor Thelma Schoonmaker–the Fellowship award for an outstanding contribution to film, games, or television, according to BAFTA's website.
As a huge supporter of the arts, Prince William has been the president of BAFTA since February 2010. His presidency follows a tradition of royal involvement in the organization. In fact, the majority of BAFTA leaders have been members of the royal family.
Prince Philip became the first president in 1959 not long after the British Film Academy merged with the Guild of Television Producers and Directors.
William has made a strong effort to tie charitable activity to BAFTA, hosting several forums and events as well as creating scholarships to benefit young artists.


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Q: AWS/Ansible - How to access facts across roles/hosts from host defined in dynamic-inventory? I am currently setting up a number of Ansible roles to setup a Kubernetes cluster. So far I have a role to provision idempotent EC2s (1x Master / 2x Worker) and subsequent roles to setup these master/worker nodes with Docker/Kubernetes dependencies. I am using AWS ec2.ini/.py dynamic-inventory to discover IPs of the instances provisioned by my create_ec2 role.
I have encountered an issue when trying to join my workers to the cluster with the join command I am retrieving from the master node. I have 2 seperate roles for the master & worker provisioning. In the tasks for the master, I get the join command with:
kubeadm token create --print-join-command

and then register a variable which I then use to set a host fact:
set_fact:
  join_command: "{{ join_command_stdout.stdout_lines[0] }}"

The issue I am having is when I try to access this fact on my worker nodes when running my worker role. I am trying to access the fact with:
"{{ hostvars['tag_Type_master'].join_command }} --ignore-preflight-errors all  >> node_joined.txt"

However it is failing as the host I am providing for the hostvars is apparently undefined..
For reference, I have this value held in my dynamic-inventory (IP omitted):
  "tag_Type_master": [
    "1.2.3.4"

The error I am receiving is:
"{"msg": "The task includes an option with an undefined variable. The error was: \"hostvars['tag_Type_master']\" is undefined"

I am struggling to figure out how I access the host facts of an EC2 instance defined in my dynamic-inventory.
I have tried supplementing the EC2 IP directly into the hostvars (hostvars['1.2.3.4'].join_command), however the task just hangs and does nothing.
I have also tried putting in a Magic variable (hostvars['inventory_hostname].join_command) to no avail.
It seems that people have had success with accessing host facts from hosts defined in a static inventory file, however due to the dynamic nature of the EC2 servers the cluster will be created on I am unable to use this approach.
run.yml:
  name: Setup K8s master node
  hosts: tag_Name_kube_master
  gather_facts: true
  roles:
  - setup_kube_master

  name: Setup K8s worker nodes
  hosts: tag_Name_kube_worker
  gather_facts: true
  roles:
  - setup_kube_worker

setup_kube_master/tasks/set_fact.yml:
  name: Get join command for workers
  shell: kubeadm token create --print-join-command
  register: join_command_stdout
  name: Persist variable for workers
  set_fact:
   join_command: "{{ join_command_stdout.stdout_lines[0] }}"

setup_kube_worker/tasks/get_fact.yml:
  name: join cluster
  shell: "{{ hostvars['tag_Type_master'].join_command }} --ignore-preflight-errors all  >> node_joined.txt"
  args:
   chdir: $HOME
   creates: node_joined.txt

A: So the way you would troubleshoot this for yourself is to use the debug: task to show the entire fact cache and find the relationship for yourself:
- name: show the state of affairs
  debug: var=hostvars verbosity=0

However, having said that, I'm pretty sure that tag_Type_master is defined as a group and thus will not show up in hostvars since -- as its name implies -- it is vars for hosts not vars for groups
You have to do one level of indirection to obtain a host that is a member of that group:
- hosts: tag_Name_kube_worker
  tasks:
  - name: promote the "join_command" fact from the masters group
    set_fact:
      join_command: '{{ some_master.join_command }}'
    vars:
      some_master: '{{ hostvars[groups["tag_Type_master"][0]] }}'

I took some liberties with that some_master definition for the sake of brevity -- in production code you would want to actually check that that group exists and its contents are not empty, etc, etc, but I'm about 80% sure it will work even as written
You would want that to appear in run.yml in between the hosts: tag_Type_master and hosts: tag_Type_worker to bridge the fact-gap between the two groups and make it appear as if the workers had that join_command fact the whole time

Separately, while this isn't what you asked, if you were to tag those instances with "kubernetes.io/role/master": "" and/or "kubernetes.io/role": "master" you would benefit by already having the tags that the cloud-provider is expecting. I have no idea what that would look like in ec2.py, but I'm sure it would be cheap to find out using ansible-inventory -i ec2.py --list
I tag the workers with the corresponding kubernetes.io/role: worker even though I'm pretty sure the AWS cloud-provider doesn't care about it, choosing instead to just use the metadata.labels on the existing Nodes for doing ELB registration et al.


As of this year, Translas opens its third division. The new entity, officially called Translas Canada Industries Ltd., is located in Woodstock, Canada and aims to serve the whole Canadian market.
Manufacturing environments will become cleaner and safer throughout Canada with Translas' new Woodstock division. Serving the single welder to hundreds of welders, Translas Canada Industries has a comprehensive line of products and services to improve air quality and plant productivity. These include compact mobile units and welding torches with integrated fume extraction to complete fixed solutions for your plant, creating a safer environment for any workforce.
Speaking about Translas' growth, Jelmer Wolleswinkel, Commercial Director: "Businesses that bring new ideas and innovative solutions to the market are growing. We identified a few markets where we know Translas can make an important contribution to the success of key manufacturing segments. Canada fits our growth and strategic plans perfectly so we're happy to be a part of the manufacturing community here".
Duncan Beaumont is the new Executive Director for Translas Canada Industries, serving the Canadian market. He brings more than 15 years project management, sales and leadership experience in the Canadian industrial sector and over eight years in the welding, fabrication and fume extraction industry. In his current role at TCI, he helps the welding & fabrication sector select and implement air quality solutions to mitigate health and safety risks and ensure regulatory compliance. With a deep understanding of evolving regulations and Hi-Vac collection technologies, he works with companies to balance regulatory, economic and health and safety needs and design the best overall system for their goals.
Translas Canada Industries is a problem-solving company for the welding & fabrication industry. They supply welding torches and fume extraction torches with highly efficient, reliable and cost-effective systems. Applications include mild steel, stainless steel, aluminum, MIG & TIG manual and robotic welding. Their expertise and resources can be applied to almost any welding process in the manufacturing environment.
Translas is at the finals of the Accenture Innovation Awards!


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Mr T V Narendran
Vice President, CII (2019-20)
CEO & Managing Director, Tata Steel Limited
Mr T V Narendran is a Mechanical Engineer from NIT Trichy (class of 1986). He joined Tata Steel after completing his MBA from IIM Calcutta in 1988. He is a Chevening Scholar and has also attended the Advanced Management Programme in CEDEP-INSEAD, Fontainebleau, France. He is a Fellow of The Indian National Academy of Engineering (INAE), and is a recipient of Distinguished Alumnus Awards from both NIT Trichy and IIM Calcutta. He has more than 30 years of experience in the Mining and Metals industry.
As the CEO & Managing Director of Tata Steel Limited, Mr Narendran oversaw the successful acquisition of Bhushan Steel Limited, and is currently actively involved in the acquisition of the steel business of Usha Martin Limited and in the discussions with Thyssenkrupp for formation of the "Thyssenkrupp Tata Steel" Joint Venture which would be the second largest steel maker in Europe.
Mr Narendran was the Managing Director of Tata Steel (India & South East Asia) before he was elevated as the CEO & Managing Director, Tata Steel Limited on 31st October, 2017. As the MD of Tata Steel (India & South East Asia), he successfully executed and commissioned one of the largest greenfield projects in India, the Kalinganagar Steel Plant in Odisha, which achieved its rated capacity within a very short span of time. It also enhanced Tata Steel's ability to deliver steel to higher value segments like the automotive and the oil & gas industries.
Mr Narendran's career in Tata Steel spanned many areas in India and overseas, including Marketing & Sales, International Trade, Supply Chain & Planning, Operations and General Management and includes stints at Jamshedpur, Kolkata, Dubai and Singapore. Before becoming the MD of Tata Steel in November 2013, Mr Narendran was the Vice President - Safety, Flat Products & Long Products from 2010.
Mr Narendran was actively involved in Tata Steel's first overseas acquisition, NatSteel, and was seconded there as an Executive Vice President in 2005. He took over as the President & CEO of NatSteel from January 2008.
Mr Narendran is currently on the Boards of Tata Steel Limited and Tata Steel Europe. He is the Chairman of Tata Steel BSL Limited, Tata Sponge Iron Limited, and the Board of Governors of XLRI Jamshedpur.
He is a member on the Board of the World Steel Association and is a member of its Executive Committee. He was the co-chair of the Mining & Metals Governors Council of the World Economic Forum from 2016 to 2018. He is also a member from Indian side in BRICS Business Council and is a member of the Indo-French CEO council. He is a member of the National Council of CII, and is the former Chairman of CII Eastern Region and the Jharkhand State Council of CII. He is also currently the President of the Indian Steel Association.
DG's Quotes
We are happy to see that Ministry of Defence has taken cognizance of CII's recommendations to prune the list and keeping it to the bare minimum…..We are also hopeful that the delays in granting / renewing Industrial Licensing would also be addressed at the earliest.
Budget and the Building Blocks of Growth
Don't Undermine the Sector
Redefining MSMEs will give the sector a boost
Spending the lone remedy: CII President
"Infra spend has to grow, fiscal deficit can be ...


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Cover Mockups Received
Following Tuesday's teleconference, today the design coordinator at iUniverse sent me three different cover mockups for The Earthworm That Blows No Trumpet. That was quick: They said within two weeks, and here I have it within two days. Not bad, iUniverse.
Unfortunately, I'm not entirely happy with any of them. One of them, at least, is closer to what I want than the other two. All three feature the same setting sun, chalice, flame, and earthworm, but each has the chalice placed differently and different fonts for the title and author's name.
The main main [sic] problem is that the chalice is not a standard UU chalice. It's a regular silver goblet. The novel centers around a UU church in a fictitious university town in Central Texas. Given the role that the large Catholic church in this town plays, it might be appropriate to have a standard Holy Eucharist chalice with flames coming out of it. Sigh. There just isn't much in the way of UU chalice representations on thinkstockphotos.com, which iUniverse uses for assembling book covers. Even a look at uua.org didn't produce the chalice I was hoping to find.
The other main problem is that the sun is setting over a darkened ridge, but there's no landscape that one would recognize as Texas. I asked for a sunset over a prairie, and if there's a prairie in the photo it is obscured by everything else. It's the same problem I had with A Small Town for Its Size, which takes place in Houston—in fact, Houston is as much a major character as a setting—but has nothing on the cover that one would recognize as Houston.
To get in all the elements I originally wanted would cost more, because it requires paying fees for multiple stock photos. I understand that too many elements makes the cover too busy, but I think we can do this with a picture that spans the front and back covers.
Oh, here's the other thing: This is a comic/satiric novel. The sun setting (truthfully, it looks to be rising) over a darkened ridge lends an air of mystery and menace. There's plenty of mystery and menace in the book, but it's played for laughs. It needs to be lighter.
Despite all this, it brings this work another step closer to publication. I'm pleased. It's making me start the planning process for author events. "Plan" has always been a four-letter word for me, but it has to be done.
Jill Rolls through Houston, I Roll Blogs
Most folks who bother to read this blog know who Jill Stein is. The 2012 Green nominee for president is considering another run in 2016. Her candidacy, currently in the exploratory phase, is not a foregone conclusion. She seems to make no presumptions about whether the Greens will nominate her again.
All that said, you won't find many Greens in the US who will tell her, "No, Dr. Stein, please don't!"
Here's the blog roll promised in the title of this entry: fellow UU Dan Rigney on his Salon blog Danagram. Dan writes about Jill's appearance at Trinity Episcopal Church for the monthly meeting of the Harris County Green Party.
Earlier yesterday, Jill visited KPFT-FM Pacifica Radio (having appeared by phone on George Reiter's program Thresholds last Thursday. She also made it in for Houston Matters on KUHF-FM Houston Public Media. Then she went out to Refinery Row to meet with striking workers at the Lyondell and Shell plants.
Today she visited College Station, home of Texas A&M University—a school not known as a hotbed of Greendom, but with a fairly active and vocal progressive community. This evening she returned to the Houston area to speak at Lone Star College's Kingwood campus. Tomorrow, it's on to Laredo, about which I have spoken elsewhere in this blog.
My impression, in a nutshell: I was looking for Jill to talk about topics beyond those in her 2012 stump speech, and she did. She also addressed a lot of the same topics. The policy prescriptions outlined in her Green New Deal have not changed much, because the problems still exist. She is still, as I noted on Facebook, "her serene and brilliant self." If she runs and is nominated, she will very likely improve greatly on her 0.3% nationwide showing from 2012. She will be a known quantity, and name recognition is important. I'm psyched and pumping up for 2016.
Earthworm Reaches the Design Stage
This will be much shorter than my other post for today, I promise.
My novel has reached the design stage. In this case, "design" refers to the exterior, not the content. I have an appointment next Tuesday afternoon for a telephone conference with my Publishing Services Associate. (I had to go back to the email and look up the title. All these friendly helpers at iUniverse are hard to keep track of, even harder when they change in the middle of the process.) We'll be discussing and choosing a cover illustration, the content and placement of the blurbs on the back, and other packaging decisions.
The cover design service is included in the package that I purchased from iUniverse, as is cover copy polishing. CCP involves examining the promotional text I submitted for the back cover and injecting enough zing to make it even more enticing to a reader in my target audience.
We're still looking at a March release date for The Earthworm That Blows No Trumpet, but I'm thinking April is more likely. Stay tuned.
Geeking Out on Public Transit
I'm falling into old habits of neglecting the blog for long periods of time. Ah well. Today I'll do two entries—how-d'ya-like-them-apples?
In April 2015, the East End and Southeast MetroRail lines are due to open here in Houston. In August, after decades of small, incremental adjustments, the whole network of bus routes will change dramatically. This fall I plan to ride every single bus route and blog about the experience.
I have ridden Houston's Metro buses almost as long as Metro has existed. In 1970, years before the birth of Metro, I remember a few times paying a dime to ride the 82 Westheimer with a friend from St. John's School to somewhere near Woodlake Square. In 1983, I remember taking the new Park & Ride service from Seton Lake to Downtown, transferring to a bus to the Medical Center.
These days I seldom use a personal motor vehicle, opting to avoid traffic and parking hassles by riding buses or MetroRail. Sometimes I go multi-modal, with the help of the bike racks on the fronts of all local buses and special accommodations on the rail cars.
Since 1979, Metro has grown and evolved in some interesting ways, not always good ways. Due to legal and financial constraints, our transit authority has not been able to focus properly on its main mission of getting people to their destinations quickly and conveniently. Its hands have been tied by operating in a city that has traditionally been hostile to public transit. People of means perceive that local buses are just for minorities, the poor, and people with profound mental problems. The news has trumpeted tales of mismanagement by directors and board members using the agency as their personal cash cow, or violating federal law by procuring rail cars made outside the US.
Despite the difficulties, Metro provides local bus rides for a basic fare of $1.25, far less than other cities. Students and seniors can ride for 50 cents. That fare hasn't increased since 2005. Now that gasoline is less than two dollars a gallon, it's less of a bargain, and people have gone back to driving their gas-guzzlers.
Houston Access to Urban Sustainability (HAUS) is the housing cooperative in which I have dwelt for the past two years and five months. Co-op living, in and of itself, is more ecologically sustainable than living alone, with a housemate, or in a nuclear family. But we take it further with gardening, composting, recycling, reduced water and electricity use per person, and living inside Loop 610 near almost everything we need. We have space to accommodate 26 resident members in two large, refurbished houses in Old Third Ward. Rosalie HAUS is in what we now call Midtown, and uRth HAUS (where I live) is on Ruth Street in Museum Park. (Yes, we currently have some vacancies too!)
Yesterday I posted the following in the News section of hausproject.org; this morning I determined that it was worth reposting here, with some adjustments, rather than just linking to it.
Back from Seattle
Let's see if I can sum up my recent Seattle mini-vacation experience. Highlights:
Friday dinner: Treated Kate "Bionic Dance" Fahr to a reasonably priced dinner at Charlie's on Broadway. After that, I caught up with traveling buddy Kevin and the Martins, a couple of friends who are "Houston expats" now living in Portland OR.
Saturday's visit to the EMP Museum: The Sci-Fi/Fantasy portion had costumery from the Star Wars movies, and the Experience Music Project featured an exhibit on Jimi Hendrix's time in London. There was also an excellent and tasteful history of music video on multiple screens. From EMP I went to Pike Place Market, which can be overwhelming on a Saturday.
Sunday's expedition to Fremont: After brunch with the aforementioned couple, I walked to, around, and from the Fremont district, including one stop at Theo for some fair trade chocolate treats and at the Dubliner to sip some Harp and read some Ulysses.
There was also plenty of time spent chilling in the rental apartment, which had a state-of-the-art hot tub in back. There was also plenty of walking down Queen Anne Hill for meals and shopping, followed by walking back up the hill afterward.
Scribbling in Seattle
In August of 1998, I visited Seattle and Washington State for the first time. I have so many pleasant memories of that trip that they consistently outshine the unpleasant ones.
Traveling long distances via Amtrak can be an adventure, and this trip definitely was, especially the first leg between Houston and Los Angeles. Tropical Storm Charley had dumped so much rain on the Rio Grande Valley that the train station in Del Rio was washed out and inaccessible.
After our Sunset Limited train sat in San Antonio a bit longer than scheduled, and the Texas Eagle finally arrived to meet it, those of us continuing west had to be herded onto motor coaches. There was one for all the Sul Ross State students and others heading back to Alpine, and a few other coaches to take the rest of us to El Paso. A train would be waiting in El Paso to take us across the vast southwestern deserts to LA.
Not far from Palm Springs, we encountered more delays, mostly from yielding the right of way to freight trains. I remember the train sitting motionless on the track for about an hour within sight of a wind farm, the AC system bravely staving off 105-degree heat. Due to the delays, we would have arrived in LA too late to catch the Coast Starlight bound for Seattle. So those of us going north got off the train at Pomona and boarded a coach to Oxnard, where we waited a little longer for the train.
If your keeping score, that's a train to a coach to a train to a coach to a train. Fortunately there were no similar mishaps en route to Seattle, and none on my return trip. I had booked the return trip on the Empire Builder to Chicago and the Eagle to Longview, which requires transferring to a motor coach to get back to Houston. (That's right, civilized world: There is no train directly connecting the 3rd and 4th largest cities in the United States.)