text:
Wind propulsion a realistic choice toward decarbonisation
20:1431 August 2018
In an exclusive interview with SAFETY4SEA, Mr. Gavin Allwright, Secretary of the International Windship Association (IWSA), mentions that industry has realized wind propulsion is a realistic choice for a more sustainable future and refers to the existing
Although the viability of these installations is starting to be proved, there are still barriers for the industry to overcome with perception being on top of these. Nonetheless, the industry is setting the ground to adopt more wind propulsion installations; namely the aim of IWSA since its foundation in 2014 has been toward that end. After explaining how industry can embrace decarbonisation, Mr Allwright concludes that we need to change mindset and think about the long term. In this context, industry should advocate for clear regulatory framework, new technologies, alternative fuel development and a more standardized circular economy approach.
SAFETY4SEA: What should be the top priorities for the shipping industry stakeholders towards a more sustainable future for the shipping industry?
Gavin Allwright: Sustainability is often used very narrowly in the industry to mean, 'will I still be in business next month, next year or in 2023', rather than looking at the triple bottom line of social, environmental and economic benefits. That is understandable; however it has also led the industry down the efficiency pathway without much of a focus on resilience. The ships we are designing and building today will be operating in a net zero-emissions world by the end of their lifetime, meaning that every ton emitted will need to be offset or paid for.
So what are the top priorities to make the industry more efficient and resilient? First and foremost, the largest cost in shipping is fuel, the supply and price are volatile and will increasingly be regulated, therefore the search for a low-cost, low-carbon, compliant and viable solution to this problem is top priority. Our members are delivering an important option for the technology toolbox; wind propulsion can deliver between 10-30% fuel savings retrofit and up to 50% for optimized new builds, meaning a renewable energy source, free and abundant delivery at the point of use.
If we link this to a circular economy focus, increased investment in technology innovation in general and investment in the human resources in the industry, we have a clear set of priorities for sustainable shipping in the future.
S4S: Do you think that the industry is ready for a more low-carbon future? What may be the biggest challenges to prepare?
G.A.: This is a challenging question with different sectors moving in different directions and at varying speeds, but overall the answer would have to be 'No' or 'Not Yet'. Having said that, the foundations and preparations to embrace change are starting to be laid. The biggest challenges will be finding ways to very quickly and deeply cut CO2 emissions while maintaining the profitability of the sector, this has to be in line with a 1.5C global warming target if we are to avoid dramatic impacts and resultant adaptation costs further down the line – therefore the 'at least' part of the 'at least 50%' reduction in carbon emissions by 2050 outlined in the IMO Initial Strategy in April has to be the main focus going forward.
In the past, the industry has often relied on regulation to produce a perceived level playing field and most companies would be driven by that lowest common denominator. However, while tighter regulation is coming, the challenge is for the commercial operators to move in front of that, decarbonize now using existing technology and fuel options. Industry groups are working on these areas, and last year's Ambition 1.5C: Global Shipping Action Plan conference showed very clearly that this is not a technology issue; it is a systems issue and an overhaul of how we retrofit and redesign vessels quickly and efficiently is much needed.
The industry is facing huge challenges, but what an exciting time to be in shipping. These challengers are going to be attracting new industry participants, young engineers and other sustainability change advocates, and that disruption in itself will be one of the biggest challenges the industry faces going forward.
S4S: Which are the key drivers and barriers towards investing in wind propulsion projects?
G.A.: There are a number of quite diverse drivers that are generating the current interest in wind propulsion solutions but the key ones are credibility, viability, affordability and the need to make vessels future ready. These are not new, they are the main drivers for all innovation, but we have seen significant changes over the past 12 months around wind as a primary renewable energy source for ship propulsion.
There is an increasing understanding in the industry that wind-assist and primary wind vessels are a credible and realistic choice when it comes to new technology, with class, policy makers, engineers, designers and increasingly commercial shipping companies testing installations. The viability of these installations is starting to be proved, with increasing data and more points of reference allowing for comparison.
Finally, the economics are starting to align, increasing fuel prices, low Sulphur, NOx and carbon regulations on the horizon are pushing up the forecast prices of fuel and thus ROI's will drop significantly, also leasing or rental options for rigs will lead to a further reduction in CAPEX expenditure.
As for barriers, there are still a number of impactful ones whether these are from the split incentive when it comes to who pays the fuel and who bears the installation cost and there are other market and non-market failures that effect uptake, however the main barrier is perception, and changing that comes down to having more rigs installed on more vessels, demonstrator vessels and market-ready technologies, all of which are starting to come through the pipeline.
S4S: What could be the right environmental and financial incentives to facilitate wind propulsion from your perspective?
G.A.: On financial incentives, it is more a removal of financial barriers, enabling access to funding for innovation, R&D work and the difficult transition from late stage R&D to market-ready. This is an area the industry should support more in a pre-competitive fashion, sharing the benefits of systematic and integrated system developments rather than the current piecemeal approach.
Another area that will be critical in the longer term is a form of carbon levy on marine fuel and we all know that some form of this is coming, but leaving that until 2023 and beyond is a very serious mistake if we are to incentivize all of the first movers and early adopters and support innovative technology companies.
A substantial, annually tightened levy on bunker fuel, based on the hypothecated Norwegian NOx fund model would be good for all low carbon innovation, including wind. This would keep all funds within the industry and strengthen the virtuous circle – we have a model, so let's use it.
Environmentally, a holistic approach to dealing with the challenge of shipping and the logistics chain that shipping is a single but important link in. This means that we approach the challenges in a systematic way, not transferring pollution from air to water, or from sea to land. It will also entail using the total carbon footprint of a technology or alternative fuel option, not from bunker-to-funnel or factory gate to breaking yard, but well-to-wake and cradle to cradle.
This will mean that there needs to be a truly 'level playing field' between renewables and fossil fuels, putting a stop to the externalizing of costs and internalizing profit is a critical change required – the polluter pays and we can clearly compare the total costs involved with every technology decision we make. Under these conditions, wind propulsion will always be a first stop option, the challenge will be what auxiliary propulsion option do you go for.
S4S: What types of solid developments (i.e. projects completed) have been realized in Europe/ worldwide concerning wind propulsion applications?
G.A.: Wind propulsion developments have started to pick up pace, from early Flettner rotor and kites installations in the 2000's, we then saw a growth of wind propulsion projects under development and when the fuel price nosedived in 2014-15, the pace of new wind propulsion technologies and development actually increased. This growth precipitated the development of IWSA in late 2014, and we are now seeing the fruit of the last four years of concerted development.
Over the last 12 months we have seen a threefold increase in rotor sail installations, now with six vessels with 14 rotors installed by Norsepower, Anemoi and MariGreen and a number of other projects and installations in the works. More importantly for further growth, these are installation cut across all major segments; bulker (64,000dwt), tanker (109,000dwt), roro, ferry/cruise, general cargo, with some major companies embracing the technology, including Maersk tankers and Viking Lines.
In the cruise sector, along with the rotor sail installation on the Viking Grace, STX France has launched a new line of specialist primary wind propulsion expedition cruise vessels, the largest being the 190m, Silenseas 190, carrying 300 passengers and 80 crew. Peace Boat's Ecoship design has also been completed for a 2,000 passenger, 55,000t wind-assist vessel and we are awaiting confirmation for the build schedule in a contracted Finnish yard.
In the US, Wind+Wing Technologies have successfully tested their wingsail designs on small catamarans and are moving towards installations on commercial ferries. Solarsailor developed and built a number of small combined solar and hardsail ferries operating in Sydney, Hong Kong and Shanghai harbours.
Other key developments have been seen in the development of rigid sails, MOL and University of Tokyo have completed land trials of their retractable rig and will retrofit in late 2019/2020, Bound4Blue will be retrofitting two newly designed wing sails to vessels at the end of this year.
The large scale dynarig sail system has now been extensively tested on large mega-yachts with the Maltese Falcon (2008) and now the Black Pearl (2017) and work is continuing to adapt these to commercial use. We are also expecting announcements this year from other hardsail, soft sail and suction wing developers on sea trials, demonstrator vessels and commercial builds.
Last year, a EU commissioned report on the market potential for wind propulsion was released stating, "In 2030, the market potential could amount to 3,700–10,700 installed systems on bulkers & tankers, associated with approx. 3.5–7.5 Mt CO2 savings…', this is a sizeable market size and the forecast was made prior to the increase in industry focus on decarbonisation we have seen this year.
S4S: Do you think that the industry is ready for these applications in terms of technology, installation and operation?
G.A.: From a technology standpoint, most of the wind propulsion systems are straightforward and class are involved with the certification of all of the solutions, so this is preparing the industry to adopt wind technology. With installation, it depends upon the scale of the rigs that are chose, in the case of a basic rotor retrofit installation, there is a minimal level of preparation, a base plate is put in place over a couple of days and then the fitting of the actual rotor is a matter of hours along with the rig testing etc.
As for operation, the industry expects a turnkey solution, automated, that is safe, has minimal maintenance and doesn't require any significant additional training to operate, and modern wind propulsion technologies are being designed to deliver on all of those aspects.
S4S: How your organization may contribute towards sustainability? What are your plans/ incentives / initiatives to move forward?
G.A.: The International Windship Association (IWSA) is a member-driven not-for-profit organization with over 100 technology, design, research, ship building and operator members and registered supporters. Our collective aim is to provide information to the market and policy makers of wind propulsion developments and advocate for the removal of barriers to the development of wind, but also support other low carbon technology and alternative fuel developments.
To strengthen and develop this further, this year we have adopted three tier strategy, firstly we will continue with our successful wind propulsion communication, advocacy, market support and education programs.
Secondly we are continuing to develop our network, functioning as the maritime shipping organization in close cooperation with the World Wind Energy Association (WWEA), we are liaising the IMO & EU MTCC program in the 5 centers around the world and working with industry bodies developing third party verification tools for wind technology uptake. IWSA is also actively engaged with the development of small sail cargo vessel projects through EU Interreg programs.
Thirdly, we're developing wind propulsion hubs, clustering together wind propulsion technology developers, engineering companies, research institutes, shipping companies, ship builders, etc. to further collaborate and drive project development and the sector as a whole. The first active hub is IWSA Europe Atlantique based in Nantes, with 60+ participants, and this will be followed soon by North Europe, South Pacific, Asia and the US
S4S: If you could change one thing about the shipping industry, what would it be and why?
G.A.: As with any industry there are always areas that need to change, can be optimized or simply discarded, and I have highlighted a few of those in earlier questions, but if I need to select one it would be the creation of a clear, understandable, stable playing field or pathway forward for the industry. Work has been done on this, but we still make decision based on today or tomorrows compliance requirements rather than 2040 or 2050.
That requires clear regulatory framework, pre-competitive investment and support for new technologies and alternative fuel development, a standardized circular economy approach to ship building and breaking, a carbon levy that incentivizes low carbon investment and helps protect first movers.
I fear that without that clear pathway to effectively zero-emissions by 2050 (or before) we will not meet our obligations to deliver on a 2C global warming target, let alone the 1.5C target that we really have to be aiming at.
Welcome to the Future of Shipping – Follow the Wind at SMM 2018 New Liebherr offshore crane counters requirements for operations with limited space on deck


In our new rank based on the most recent short interest data from NASDAQ, Zimmer Holdings, Inc. ( ZMH has taken over the position of #188 most shorted S&P 500 component, from Estee Lauder Cos., Inc. ( EL which is now in the #149 spot. The "days to cover" at 06/15/2015 was 4.59 for ZMH, and 5.25 for EL; this compares to the average across all S&P 500 components of 4.78 (up from the average back on the 05/29/2015 settlement date of 4.41). The chart below shows the movement over time of the "days to cover" values of both ZMH and EL, versus the average S&P 500 component.


USCIS released a notice confirming that international students on F1 who are beneficiaries of H1B applications filed in April 2018 and are still waiting for adjudication, will start to accrue unlawful presence if they work beyond September 30th.
If you or anyone you know is waiting for H1B adjudication and your OPT has expired, you must stop working. Please speak to your international department personnel to ensure you are up to speed on the rules and how it affects you.


I want to know which one of you is responsible for this. You've clearly hurt Quebec filmmaker, Xavier Dolan's feelings, and I for one am not going to stand for it. He is only 21 years old and already he knows what it is to be tossed aside by critics who once purported to be his biggest fans. You built him up, and just because he didn't do exactly what you wanted him to do, you declared him a disappointment and your earlier proclamations of genius to be premature. While I applaud your ability to admit your faults (even though the point was to highlight another's), I'm not sure you realize just how much damage you've done. You should be fostering genius, not trying to kill its spirit.
When I met Dolan at the 2010 Toronto International Film Festival, I expected him to sit with me and speak fondly of his second feature, LES AMOURS IMAGINAIRES (HEARTBEATS), which he wrote while attending the festival the year before. I had just seen the film, a cynical yet optimistic exploration of the ridiculousness we all put ourselves through when we think we're in love. Cynical because we look like idiots; optimistic because we still put ourselves through it regardless. And even though I gushed about how much I admire him as a filmmaker right at the top of our chat, I was not met with fondness; I was met with skepticism. Friendly and polite but skeptical nonetheless.
"It is a movie about the various steps of the love downfall," Dolan proclaims, without necessarily seeing what a downer his statement truly is. "It is literally a condensed journey through typical, impossible love." The kind of love Dolan is talking about, the same kind of love that comes across on screen, isn't real but rather imagined (which is more evident in the film's original French title, which directly translates to "Imagined Loves")."The movie ought to be as shallow and as empty as the encounter they have." HEARTBEATS does just this but it does so with sumptuous imagery and romantic grandness. It is a farce after all.
I admire Dolan. Both of his films, regardless of how they compare with each other, are devoid of ego, an incredible accomplishment considering he wrote them both, directed them both and stars in both of them as well. His choices in all three of his roles on each film could easily serve his own self-interests, but instead serve only the story and the overall success of the film itself. This requires skill and dedication that I would never imagine a 21-year-old to have but yet here we are. And at 21, he has also learned a couple of other hard lessons he didn't need to know right away. He now knows how it feels to be criticized on an international level and he clearly knows a thing or two about love.
For further HEARTBEATS reading, be sure to check Black Sheep's 4-star review. Click here.


text:
Police plea after flasher exposes himself outside Metro Bank in Reading town centre
Appeal for witnesses as man indecently exposed himself at a time when St Mary's Butts was busy
Raina Wilson
(Image: Google)
Police are appealing for witnesses after a man exposed himself in Reading town centre.
At 4pm yesterday (Thursday, June 18), a man exposed himself outside the Metro Bank on St Mary's Butts.
Pc Mark Skeavington, the investigating officer with Thames Valley Police, said: "I am appealing to anyone who has any information about this incident to come forward.
"The town centre was busy at this time and members of the public, including children, were present."
A 25-year-old man from Reading was arrested on suspicion of outraging public decency. He has been released under investigation.
Mystery continues over cause of Reading sinkhole
Latest update on Berkshire's coronavirus cases and death toll
The officer, who is based at Reading police station, added: "I am appealing particularly to any motorists who were passing through the area at the time to check their dash-cam footage, as well as any nearby businesses to review their CCTV footage.
"You can contact us using our online reporting form, quoting reference number 43200182790. If you cannot report online, call the non-emergency number 101.
Rules B&Q, Homebase, Wilko, Wickes and Home Bargains customers must follow as supermarkets enforce mask wearing
UK & World NewsIt comes as five supermarkets announced earlier this week that they would refuse entry to customers who do not wear a face mask, without a valid exemption

redpajama_set_name: RedPajamaCommonCrawl


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Adorable bungalow style home. Move-in ready. Cathedral ceilings in the living room. Tile back splash in kitchen. Stainless steel appliances. Built in microwave, dishwasher. New flooring in living room. Located on the outskirts of the city limits, in a quiet area. Great for a starter home or those looking to downsize.
Listing provided courtesy of Kendal Edmondson of Roanoke Realty Team.


Famous Impressionists Start Their Training By Making Fun Of Family Members.
Drunken Human Impression: Nailed It!
I'm REALLY good at impressions, you know.
What udder pop culture icons can ai use dis fing to be?


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\begin{document}
\title {\bf Weighted sum formulas of multiple $t$-values with even arguments}
\author{
{ Zhonghua Li$^{a,}$\thanks{Email:  zhonghua\_li@tongji.edu.cn}\quad Ce Xu$^{b,c,}$\thanks{Email: 19020170155420@stu.xmu.edu.cn; 9ma18001g@math.kyushu-u.ac.jp}}\\[1mm]
\small a. School of Mathematical Sciences, Tongji University\\
 \small Shanghai 200092, P.R. China\\
\small b. Multiple Zeta Research Center, Kyushu University \\
\small  Motooka, Nishi-ku, Fukuoka 819-0389, Japan\\
\small c. School of Mathematical Sciences, Xiamen University\\
\small Xiamen
361005, P.R. China}

\date{}
\maketitle \noindent{\bf Abstract} In this paper, we study the weighted sums of multiple $t$-values and of multiple $t$-star values at even arguments. Some general weighted sum formulas are given, where the weight coefficients are given by (symmetric) polynomials of the arguments.
\\[2mm]
\noindent{\bf Keywords}: Multiple $t$-values, Multiple $t$-star values, Multiple zeta values, Multiple zeta-star values, Bernoulli numbers, Weighted sum formulas.

\noindent{\bf AMS Subject Classifications (2010):} 11M32, 11B68.

\section{Introduction}

We begin with some basic notation. A finite sequence ${\bf k} = (k_1,\ldots, k_n)$ of positive integers is called an index. We
put
\[|{\bf k}|:=k_1+\cdots+k_n,\quad d({\bf k}):=n,\]
and call them the weight and the depth of ${\bf k}$, respectively. If $k_1>1$, ${\bf k}$ is called admissible. Let $I(k,n)$ be the set of all indices of weight $k$ and depth $n$.

For an admissible index ${\bf k}=(k_1,\ldots,k_n)$, the multiple zeta value and the multiple zeta-star value are defined by
\begin{align*}
\zeta({\bf k})\equiv\zeta(k_1,k_2,\ldots,k_n):=\sum\limits_{m_1>m_2>\cdots>m_n>0 } \frac{1}{m_1^{k_1}m_2^{k_2}\cdots m_n^{k_n}}
\end{align*}
and
\begin{align*}
\zeta^\star({\bf k})\equiv\zeta^\star(k_1,k_2,\ldots,k_n):=\sum\limits_{m_1\geqslant m_2\geqslant \cdots\geqslant m_n\geqslant 1 } \frac{1}{m_1^{k_1}m_2^{k_2}\cdots m_n^{k_n}},
\end{align*}
respectively. The systematic study of multiple zeta values began in the early 1990s with the works of Hoffman \cite{H1992} and Zagier \cite{DZ1994}. After that it has been attracted a lot of research on them in the last three decades (see, for example, the book of Zhao \cite{Z2016}).

Let $m,k,n$  be positive integers with $k\geqslant n$, and let $f(x_1,\ldots,x_n)\in \mathbb{Q}[x_1,\ldots,x_n]$ be a symmetric polynomial. Set
\[E_f(2m,k,n):=\sum\limits_{(k_1,k_2,\ldots,k_n)\in I(k,n)}f(k_1,k_2,\ldots,k_n)\zeta(2mk_1,2mk_2,\ldots,2mk_n),\]
which is a weighted sum of multiple zeta values with even arguments of weight $2mk$ and depth $n$. If $f(x_1,\ldots,x_n)=1$, we denote $E_f(2m,k,n)$ by $E(2m,k,n)$. The evaluations of these weighted sums $E_f(2m,k,n)$ have been attracted the attention of many researches. In \cite{GKZ2006}, Gangl, Kaneko and Zagier proved that $E(2,k,2)=\frac{3}{4} \z(2k)$. Later, Nakamura gave a different proof of this result in \cite{N2009}. Shen and Cai \cite{SC2012} studied the sums $E(2,k,3)$ and $E(2,k,4)$, and evaluated them in terms of $\z(2k)$ and $\z(2)\z(2k-2)$.  Using different methods, Hoffman \cite{H2017} and Gen${\check{\rm c}}$ev \cite{G2016} gave the explicit formula of $E(2,k,n)$. Furthermore,  Gen${\check{\rm c}}$ev \cite{G2016} proposed a conjecture on the weighted sum $E(4,k,n)$. More general sums $E(2m,k,n)$ with $m\geqslant 2$ have been considered by Komori, Matsumoto and Tsumura \cite{KMT2014}. And the explicit evaluation formula of $E(2m,k,n)$ was obtained just recently in \cite{ELO2017,ELO2018} and \cite{LQ2016}. Later in \cite{GL2015}, Guo, Lei and Zhao considered the weighted sums $E_f(2,k,2)$ and $E_f(2,k,3)$, and found that they can be evaluated by zeta values at even arguments. Moreover, they conjectured that
\begin{align*}
E_f(2,k,n)=\sum\limits_{l=0}^T c_{f,l}(k)\z(2l)\z(2k-2l),
\end{align*}
where $T={\rm max}\{[r+n-2]/2,[(n-1)/2]\}$, $c_{f,l}(x)\in \mathbb{Q}[x]$ depends only on $l$ and $f$, and with $\deg c_{f,l}(x)\leqslant \deg_{x_1}f(x_1,\ldots,x_n)$. Here $r=\deg f(x_1,\ldots,x_n)$ and for a real number $\alpha$, we denote by $[\alpha]$ the greatest integer that not exceeding $\alpha$. Recently, this conjecture was proved by the first author and Qin in \cite{LQ2019} with restriction $\deg c_{f,l}(x)\leqslant r+n-2l-1$. A similar weighted sum formula of the multiple zeta-star values with even arguments was simultaneously obtained by the first author and Qin in \cite{LQ2019}.

In a recent paper \cite{H2016}, Hoffman introduced and studied an odd variant of multiple zeta values,  which is defined for an admissible index ${\bf k}=(k_1,k_2,\ldots,k_n)$ as
\begin{align*}
t({\bf k})\equiv t(k_1,k_2,\ldots,k_n):=\sum\limits_{m_1>m_2>\cdots>m_n>0\atop m_i:\text{odd}} \frac{1}{m_1^{k_1}m_2^{k_2}\cdots m_n^{k_n}},
\end{align*}
and is called a multiple $t$-zeta value. Similarly, one can define a multiple $t$-star value by
\begin{align*}
t^\star({\bf k})\equiv t^\star(k_1,k_2,\ldots,k_n):=\sum\limits_{m_1\geqslant m_2\geqslant\cdots\geqslant m_n\geqslant 1\atop m_i:\text{odd}} \frac{1}{m_1^{k_1}m_2^{k_2}\cdots m_n^{k_n}}.
\end{align*}
Then similar as multiple zeta values, for any positive integers $m,k,n$ with $k\geqslant n$ and any symmetric
polynomial $f(x_1,\ldots,x_n)\in\mathbb{Q}[x_1,\ldots,x_n]$, we define the weighted sums of multiple $t$-values and of multiple $t$-star values by
\[T_f(2m,k,n):=\sum\limits_{(k_1,k_2,\ldots,k_n)\in I(k,n)}f(k_1,k_2,\ldots,k_n)t(2mk_1,2mk_2,\ldots,2mk_n)\]
and
\[T_f^\star(2m,k,n):=\sum\limits_{(k_1,k_2,\ldots,k_n)\in I(k,n)}f(k_1,k_2,\ldots,k_n)t^\star(2mk_1,2mk_2,\ldots,2mk_n).\]
If $f(x_1,\ldots,x_n)=1$, we set
\[T(2m,k,n)=T_f(2m,k,n),\qquad T^{\star}(2m,k,n)=T^\star_f (2m,k,n).\]
There are some work on the evaluations of the sums $T(2m,k,n)$. For example, using similar but more complicated ideas from \cite{SC2012} Shen and Cai gave a few sum formulas of $T(2,k,n)$ for $n\leqslant 5$ in \cite{SC2011}.
In \cite{Z2015}, Zhao gave two explicit formulas of $T(2,k,n)$. Furthermore, Shen and Jia \cite{SJ2017} gave some explicit evaluation formulas of $T(2m,k,n)$. We remark that as for multiple zeta values, one can obtain the evaluation formulas of $T(2m,k,n)$ and $T^{\star}(2m,k,n)$ algebraically. In fact, using \cite[Theorem 2.3]{H2016} and \cite[Proposition 3.26]{LQ2016}, one can express $T(2m,k,n)$ and $T^{\star}(2m,k,n)$ in terms of $t(2m,\ldots,2m)$ and $t^{\star}(2m,\ldots,2m)$. Then one gets evaluation formulas of $T(2m,k,n)$ and $T^{\star}(2m,k,n)$ from that of multiple $t$ and $t$-star values with all arguments equal to the same even number $2m$.

In this paper, using a similar method as in \cite{LQ2019}, we study the weighted sums $T_f(2,k,n)$ and $T_f^\star(2,k,n)$.  Our main result is the following theorem.

\begin{thm}\label{thm2}
Let $n,k$ be positive integers with $k\geqslant n$. Let $f(x_1,\ldots,x_n)\in \mathbb{Q}[x_1,\ldots,x_n]$ be a symmetric polynomial of degree $r$. Then we have
\begin{align}\label{1.2}
T_f(2,k,n)=\sum\limits_{l=0}^{{\rm min}\{T,k\}} c_{f,l}(k)\z(2l)t(2k-2l)
\end{align}
and
\begin{align}\label{1.3}
T_f^\star(2,k,n)=\sum\limits_{l=0}^{{\rm min}\{T,k\}} c_{f,l}^\star(k)\z(2l)t(2k-2l),
\end{align}
where $T={\rm max}\{[(r+n-2)/2],[(n-1)/2]\}$, $c_{f,l}(x),c_{f,l}^\star(x)\in \mathbb{Q}[x]$ depend only on $l$ and $f$, and with $\deg c_{f,l}(x), \deg c_{f,l}^\star(x)\leqslant r+n-2l-1$.
\end{thm}

To prove Theorem \ref{thm2}, we use the symmetric sum formulas of multiple $t$-values and of multiple $t$-star values \cite[Theorems 2.5 and 2.8]{H2016}. Then we find it is sufficient to study the weighted sums of the products of $t$-values at even integers and prove the following theorem.

\begin{thm}\label{thm1}
Let $n,k$ be positive integers with $k\geqslant n$. Let $f(x_1,\ldots,x_n)\in\mathbb{Q}[x_1,\ldots,x_n]$ be a polynomial of degree $r$. Then we have
\begin{align}\label{1.1}
\sum\limits_{k_1+\cdots+k_n=k\atop k_j\geqslant 1}f(k_1,\ldots,k_n)t(2k_1)\cdots t(2k_n)=\sum\limits_{l=0}^{\min\{T,k\}}e_{f,l}(k)\zeta(2l)t(2k-2l),
\end{align}
where $T=\max\{[(r+n-2)/2],[(n-1)/2]\}$, $e_{f,l}(x)\in\mathbb{Q}[x]$ depends only on $l$ and $f$, and with $\deg e_{f,l}(x)\leqslant r+n-2l-1$.
\end{thm}

Note that the polynomial $f(x_1,\ldots,x_n)$ in Theorem \ref{thm1} is not necessarily symmetric.

To prove Theorem \ref{thm1}, we use Euler's formula \cite[Eq. (1.4)]{H2016}, which expresses $t(2k)$ by the Bernoulli numbers. Then it is enough to treat the weighted sums of products of the Bernoulli numbers. And we do this by using the generating function of the Bernoulli numbers. We give the proofs of Theorem \ref{thm1} and Theorem \ref{thm2} in Section \ref{Sec:Proof}.

Although the weighted sum formulas \eqref{1.2}-\eqref{1.1} are not so concrete, one can get the explicit formulas for given positive integers $n,k$ and a given polynomial $f$ according to the procedure of our proof. We list some weighted sum formulas as examples in Appendix \ref{Sec:Example}.

\section{Proofs}\label{Sec:Proof}

\subsection{Preliminary knowledge}

We begin with the definition of the Bernoulli numbers. The generating function of the Bernoulli numbers $\{B_i\}$ is
$$\sum\limits_{i=0}^{\infty} \frac{B_i}{i!}x^i=\frac{x}{e^x-1}.$$
Let $\beta_i:=(2^i-1)B_i$ and
\begin{align*}
&F(x):=\frac{x}{2}-\frac{x}{e^x+1}.
\end{align*}
Then since $B_0=1$, $B_1=-\frac{1}{2}$ and $B_i=0$ for odd $i\geqslant 3$, we find that
\begin{align*}
&F(x)=\sum\limits_{i=1}^\infty\frac{\beta_{2i}}{(2i)!}x^{2i}=\sum\limits_{i=0}^\infty\frac{\beta_{2i}}{(2i)!}x^{2i}.
\end{align*}
Hence, $F(x)$ is an even function.

Let $D:=x\frac{d}{dx}$ and $H(x):=\frac{x}{e^x+1}$. Then we have
 $$D H(x)=(1-x)H(x)+H(x)^2.$$
Therefore, one can get the following theorem without difficulty.

\begin{thm}\label{thm2.1}
For any nonnegative integer $m$,
\begin{align}
D^mF(x)=\sum\limits_{i=0}^{m+1}F_{mi}(x)H(x)^i.
\label{Eq:Diff-f}
\end{align}
Here $F_{mi}(x)$ are polynomials determined by $F_{00}(x)=\frac{x}{2}$, $F_{01}(x)=-1$ and the recurrence relations
\begin{align}
\begin{cases}
F_{m0}(x)=xF_{m-1,0}'(x) & \text{for\;} m\geqslant 1,\\
F_{m,m+1}(x)=mF_{m-1,m}(x) & \text{for\;} m\geqslant 1,\\
F_{mi}(x)=xF'_{m-1,i}(x)+i(1-x)F_{m-1,i}(x)+(i-1)F_{m-1,i-1}(x) & \text{for\;} 1\leqslant i\leqslant m.
\end{cases}
\label{Eq:Recursive-fmi}
\end{align}
\end{thm}

In particular, for any integers $m,i$ with $1\leqslant i\leqslant m+1$, we have $F_{mi}(x)\in\mathbb{Z}[x]$.
From \eqref{Eq:Recursive-fmi}, we deduce that for any nonnegative integer $m$,
$$F_{m0}(x)=\frac{x}{2},\quad F_{m,m+1}(x)=-m!.$$
In general, we have the following result.

\begin{pro}
For any integers $m,i$ with $1\leqslant i\leqslant m+1$, we have $\deg F_{mi}(x)=m+1-i$, and the leading coefficient $c_{mi}$ of $F_{mi}(x)$ satisfies  $(-1)^{m+i}c_{mi}>0$.
\end{pro}

\pf We prove this result by induction on $m$. Assume that $m\geqslant 1$. The result for $i=m+1$ follows from $F_{m,m+1}(x)=-m!$. Now assume $1\leqslant i\leqslant m$, and
$$F_{m-1,i}(x)=c_{m-1,i}x^{m-i}+\text{lower degree terms}$$
with $(-1)^{m-1+i}c_{m-1,i}>0$.
Let $c_{m0}=\frac{1}{2}$. Then we obtain
$$F_{mi}(x)=(-ic_{m-1,i}+(i-1)c_{m-1,i-1})x^{m+1-i}+\text{lower degree terms},$$
and
\begin{align*}
&(-1)^{m+i}(-ic_{m-1,i}+(i-1)c_{m-1,i-1})\\
=&i(-1)^{m-1+i}c_{m-1,i}+(i-1)(-1)^{m-1+i-1}c_{m-1,i-1}>0,
\end{align*}
from which one can deduce the desired result. \hfill$\square$

Now we have
$$F_{m0}(x)=c_{m0}x$$
with $c_{m0}=\frac{1}{2}$, and for any integers $m,i$ with the condition $1\leqslant i\leqslant m+1$, we have
$$F_{mi}(x)=c_{mi}x^{m+1-i}+\text{lower degree terms},$$
with the recurrence relation
$$c_{mi}=-ic_{m-1,i}+(i-1)c_{m-1,i-1},\quad (1\leqslant i\leqslant m)$$
and $c_{m,m+1}=-m!$. In particular, according to the recurrence relation above, we deduce that if $m$ is a nonnegative integer, then $c_{m1}=(-1)^{m+1}$.

The following result will be used later.

\begin{pro}
For any nonnegative integer $m$, we have
\begin{align}
\sum\limits_{i=1}^{m+1}F_{mi}(x)x^{i-1}=-1,
\label{Eq:Sum-fmi}
\end{align}
and
\begin{align}
\sum\limits_{i=1}^{m+1}c_{mi}=-\delta_{m,0},
\label{Eq:Sum-cmi}
\end{align}
where $\delta_{i,j}$ is Kronecker's delta.
\end{pro}

\pf
We prove \eqref{Eq:Sum-fmi} by induction on $m$. The case of $m=0$ follows from the fact $F_{01}(t)=-1$. Now assume that $m\geqslant 1$, using the recurrence formula \eqref{Eq:Recursive-fmi}, we arrive at
\begin{align*}
\sum\limits_{i=1}^{m+1}F_{mi}(x)x^{i-1}=&\sum\limits_{i=1}^mF_{m-1,i}'(x)x^{i}+\sum\limits_{i=1}^{m}iF_{m-1,i}(x)x^{i-1}\\
&-\sum\limits_{i=1}^miF_{m-1,i}(x)x^i+\sum\limits_{i=1}^m(i-1)F_{m-1,i-1}(x)x^{i-1}-m!x^m\\
=&\sum\limits_{i=1}^m(F_{m-1,i}(x)x^{i})'-mF_{m-1,m}(x)x^m-m!x^m\\
=&\frac{d}{dx}\sum\limits_{i=1}^mF_{m-1,i}(x)x^{i}.
\end{align*}
Then we get \eqref{Eq:Sum-fmi} from the inductive hypothesis. Thus, comparing the coefficients of $x^m$ of both sides of \eqref{Eq:Sum-fmi}, we obtain the desired result \eqref{Eq:Sum-cmi}. \hfill$\square$

Now we use matrix computations to express $H(x)^i$ by $D^m F(x)$. First, for any nonnegative integer $m$, we define a $(m+1)\times (m+1)$ matrix $A_m(x)$ by
$$A_m(x)=\begin{pmatrix}
F_{01}(x) & &&\\
F_{11}(x) & F_{12}(x) &&\\
\vdots & \vdots & \ddots &\\
F_{m1}(x) & F_{m2}(x) & \cdots & F_{m,m+1}(x)
\end{pmatrix}.$$
It is clear that for $m\geqslant 1$, we have
$$A_m(x)=\begin{pmatrix}
A_{m-1}(x) & 0\\
\alpha_m(x) & -m!
\end{pmatrix}$$
with $\alpha_m(x)=(F_{m1}(x),\ldots,F_{mm}(x))$. Hence, the identity \eqref{Eq:Diff-f} can be rewritten as
\begin{align}
\begin{pmatrix}
F(x)\\
DF(x)\\
\vdots\\
D^mF(x)
\end{pmatrix}-\frac{1}{2}x\begin{pmatrix}
1\\
1\\
\vdots\\
1
\end{pmatrix}=A_m(x)\begin{pmatrix}
H(x)\\
H(x)^2\\
\vdots\\
H(x)^{m+1}
\end{pmatrix},
\label{Eq:G-h-Matrix}
\end{align}
and the identity \eqref{Eq:Sum-fmi} can be rewritten as
$$A_{m}(x)\begin{pmatrix}
1\\
x\\
x^2\\
\vdots\\
x^m
\end{pmatrix}=-\begin{pmatrix}
1\\
1\\
\vdots\\
1
\end{pmatrix}.$$
Since the matrix $A_m(x)$ is invertible, we find
\begin{align}
\begin{pmatrix}
H(x)\\
H(x)^2\\
\vdots\\
H(x)^{m+1}
\end{pmatrix}=A_m(x)^{-1}\begin{pmatrix}
F(x)\\
DF(x)\\
\vdots\\
D^mF(x)
\end{pmatrix}+\frac{1}{2}x\begin{pmatrix}
1\\
x\\
x^2\\
\vdots\\
x^m
\end{pmatrix}.\label{2.6}
\end{align}
Therefore, we need to obtain a description of $A_m(x)^{-1}$. From linear algebra, we know that the matrix $\begin{pmatrix}
A & 0\\
C & B
\end{pmatrix}$ is invertible with
$$\begin{pmatrix}
A & 0\\
C & B
\end{pmatrix}^{-1}=\begin{pmatrix}
A^{-1} & 0\\
-B^{-1}CA^{-1} & B^{-1}
\end{pmatrix},$$
provided that $A$ and $B$ are invertible square matrices. Hence by induction on $m$, we find that the inverses $A_m(x)^{-1}$ satisfy the recursive formula
\begin{align}
A_m(x)^{-1}=\begin{pmatrix}
A_{m-1}(x)^{-1} & 0\\
\frac{1}{m!}\alpha_m(x)A_{m-1}(x)^{-1} & \frac{-1}{m!}
\end{pmatrix},\quad (m\geqslant 1).
\label{Eq:Recursive-AmInverse}
\end{align}

For any nonnegative integer $m$, set
$$A_m(x)^{-1}=\begin{pmatrix}
G_{01}(x) & &&\\
G_{11}(x) & G_{12}(x) &&\\
\vdots & \vdots & \ddots &\\
G_{m1}(x) & G_{m2}(x) & \cdots & G_{m,m+1}(x)
\end{pmatrix}.$$
Then from (\ref{2.6}), for any positive integer $i$, we get
\begin{align}
H(x)^i=\sum\limits_{j=1}^iG_{i-1,j}(x)D^{j-1}F(x)+\frac{1}{2}x^i.
\label{Eq:h-i}
\end{align}
Moreover, it is easy to prove that for a nonnegative integer $m$, the functions $$1,F(x),D F(x),\ldots,D^m F(x)$$ are linearly independent over the rational function field $\mathbb{Q}(x)$. For a proof one can refer to \cite[Lemma 2.6]{LQ2019}.

Next, we give some properties of the polynomials  $G_{ij}(x)$.

\begin{pro} Let $m$ and $i$ be integers.
\begin{itemize}
  \item [(1)] For any $m\geqslant 0$, we have $G_{m,m+1}(x)=-\frac{1}{m!}$;
  \item [(2)] For $1\leqslant i\leqslant m$, we have the recursive formula
  \begin{align}
  G_{mi}(x)=\frac{1}{m!}\sum\limits_{j=i}^{m}F_{mj}(x)G_{j-1,i}(x);
  \label{Eq:Recursive-gmi}
  \end{align}
  \item [(3)] For $1\leqslant i\leqslant m+1$, we have $G_{mi}(x)\in\mathbb{Q}[x]$ with $\deg G_{mi}(x)\leqslant m+1-i$;
  \item [(4)] For $1\leqslant i\leqslant m+1$, set
  $$G_{mi}(x)=d_{mi}x^{m+1-i}+\text{lower degree terms}.$$
  Then we have $d_{m,m+1}=-\frac{1}{m!}$ and
   \begin{align}
  d_{mi}=\frac{1}{m!}\sum\limits_{j=i}^{m}c_{mj}d_{j-1,i}
  \label{Eq:Recursive-dmi}
  \end{align}
  for $1\leqslant i\leqslant m$.
\end{itemize}
\end{pro}

\pf The assertions in items (1) and (2) follow from \eqref{Eq:Recursive-AmInverse}. To prove the item (3), we proceed by induction on $m$. For the case of $m=0$, we get the result from $G_{01}(t)=-1$. Assume that $m\geqslant 1$, then $G_{m,m+1}(x)=-\frac{1}{m!}\in\mathbb{Q}[x]$ with degree zero. For $1\leqslant i\leqslant j\leqslant m$, by the induction assumption, we may set
$$G_{j-1,i}(x)=d_{j-1,i}x^{j-i}+\text{lower degree terms}\in\mathbb{Q}[x].$$
Since
$$F_{mj}(x)=c_{mj}x^{m+1-j}+\text{lower degree terms}\in\mathbb{Z}[x],$$
we get
$$F_{mj}(x)G_{j-1,i}(x)=c_{mj}d_{j-1,i}x^{m+1-i}+\text{lower degree terms}\in\mathbb{Q}[x].$$
Using \eqref{Eq:Recursive-gmi}, we finally get
$$G_{mi}(x)=\left(\frac{1}{m!}\sum\limits_{j=i}^{m}c_{mj}d_{j-1,i}\right)x^{m+1-i}+\text{lower degree terms}\in\mathbb{Q}[x].$$
The item (4) follows from the above proof.\hfill$\square$
\begin{cor}
For any nonnegative integer $m$, we have $d_{m1}=-1$.
\end{cor}
\pf
We use induction on $m$. If $m\geqslant 1$, using \eqref{Eq:Recursive-dmi} and the induction assumption, we get
$$d_{m1}=-\frac{1}{m!}\sum\limits_{j=1}^mc_{mj}.$$
By \eqref{Eq:Sum-cmi}, we have
$$d_{m1}=-\frac{1}{m!}(-\delta_{m,0}-c_{m,m+1}),$$
which implies the result.\hfill$\square$

\subsection{A weighted sum formula of the Bernoulli numbers}

Let $n$ be a fixed positive integer, and $m_1,\ldots,m_n$ be fixed nonnegative integers. Set $|{\mathbf{m}}|_n:=m_1+m_2+\cdots+m_n+n$. Now, we evaluate $D^{m_1}F(x)\cdots D^{m_n}F(x)$. First, using the fact that
$$D^mF(x)=\sum\limits_{i=1}^{\infty}(2i)^m\frac{\beta_{2i}}{(2i)!}x^{2i}=\sum\limits_{i=0}^{\infty}(2i)^m\frac{\beta_{2i}}{(2i)!}x^{2i},$$
we get
\begin{align*}
D^{m_1}F(x)\cdots D^{m_n}F(x)=\sum\limits_{k=n}^\infty \left( \sum\limits_{(k_1,\ldots,k_n)\in I(k,n)} (2k_1)^{m_1}\cdots (2k_n)^{m_n} \frac{\beta_{2k_1}\cdots \beta_{2k_n}}{(2k_1)!\cdots (2k_n)!}\right)x^{2k}.
\end{align*}
Therefore, for any positive integer $k$ with $k\geqslant n$, the coefficient of $x^{2k}$ in $D^{m_1}F(x)\cdots D^{m_n}F(x)$ is
\begin{align}
\sum\limits_{(k_1,\ldots,k_n)\in I(k,n)}(2k_1)^{m_1}\cdots(2k_n)^{m_n}\frac{\beta_{2k_1}\cdots \beta_{2k_n}}{(2k_1)!\cdots(2k_n)!}.
\label{Eq:Coeff-Left}
\end{align}

Next, using \eqref{Eq:Diff-f}, we have
$$D^{m_1}F(x)\cdots D^{m_n}F(x)=\sum\limits_{i=0}^{|\mathbf{m}|_n}F_i(x)H(x)^i,$$
with
$$F_i(x)=\sum\limits_{i_1+\cdots+i_n=i\atop 0\leqslant i_j\leqslant m_j+1}F_{m_1i_1}(x)\cdots F_{m_ni_n}(x).$$

\begin{pro}
We have
$$F_0(x)=\left(\frac{x}{2}\right)^n,$$
and $\deg F_i(x)\leqslant |\mathbf{m}|_n-i$ for any nonnegative integer $i$.
\end{pro}

\pf
For integers $i_1,\ldots,i_n$ with the conditions $i_1+\cdots+i_n=i$ and $0\leqslant i_j\leqslant m_j+1$, we have
$$\deg(F_{m_1i_1}(x)\cdots F_{m_ni_n}(x))\leqslant \sum\limits_{j=1}^n(m_j+1-i_j)=|\mathbf{m}|_n-i,$$
which implies that $\deg F_i(x)\leqslant|\mathbf{m}|_n-i$.\hfill$\square$

Then using \eqref{Eq:h-i}, we get
\begin{align*}
&D^{m_1}F(x)\cdots D^{m_n}F(x)\\
=&\sum\limits_{i=1}^{|\mathbf{m}|_n}F_i(x)\left(\sum\limits_{j=1}^iG_{i-1,j}(x)D^{j-1}F(x)+\frac{1}{2}x^i\right)+R_0(x)\\
=&\sum\limits_{j=1}^{|\mathbf{m}|_n}R_j(x)D^{j-1}F(x)+R_0(x)
\end{align*}
with
$$R_0(x):=F_0(x)+\frac{1}{2}\sum\limits_{i=1}^{|\mathbf{m}|_n}F_i(x)x^i$$
and
$$R_j(x):=\sum\limits_{i=j}^{|\mathbf{m}|_n}F_i(x)G_{i-1,j}(x),\quad (1\leqslant j\leqslant |\mathbf{m}|_n).$$

\begin{pro}\label{pro7}
Let $j$ be a nonnegative integer with $j\leqslant |\mathbf{m}|_n$. Then
\begin{itemize}
  \item [(1)] the function $R_j(x)$ is even;
  \item [(2)] we have
  $$R_0(x)=\frac{1}{2^{n+1}}\left(x^n+(-x)^n \right).$$
In particular, $\deg R_0(x)\leqslant n$;
  \item [(3)] for $j>0$, we have $\deg R_j(x)\leqslant |\mathbf{m}|_n-j$.
Moreover, we have $\deg R_1(x)\leqslant |\mathbf{m}|_n-2$ provided that $n$ is even or $m_1,\ldots,m_n$ are not all zero.
\end{itemize}
\end{pro}

\pf
Since $D^{m}F(x)$ is even, we have
$$\sum\limits_{j=1}^{|\mathbf{m}|_n}R_j(x)D^{j-1}F(x)+R_0(x)=\sum\limits_{j=1}^{|\mathbf{m}|_n}R_j(-x)D^{j-1}F(x)+R_0(-x).$$
Using the fact that the functions $1,F(x),D F(x),\ldots,D^m F(x)$ are linearly independent over the rational function field $\mathbb{Q}(x)$, we know all $R_j(x)$ are even functions.

By the definition of $F_i(x)$, we have
$$\sum\limits_{i=0}^{|\mathbf{m}|_n}F_i(x)x^i=\prod\limits_{j=1}^n\sum\limits_{i_j=0}^{m_j+1}F_{m_ji_j}(x)x^{i_j}.$$
Using \eqref{Eq:Sum-fmi}, we find
$$\sum\limits_{i=0}^{|\mathbf{m}|_n}F_i(x)x^i=\prod\limits_{j=1}^n(F_{m_j0}(x)-x).$$
Then we get (2) from the fact that $F_{m0}(x)=\frac{1}{2}x$ and the expression of $F_0(x)$.

Since
$$\deg F_i(x)G_{i-1,j}(x)\leqslant (|\mathbf{m}|_n-i)+(i-j)=|\mathbf{m}|_n-j,$$
we get $\deg R_j(x)\leqslant |\mathbf{m}|-j$.

If we set
$$\widetilde{c}_{mi}=\begin{cases}
\frac{1}{2}\delta_{m,0} & \text{if\;} i=0,\\
c_{mi} & \text{if\;} i\neq 0,
\end{cases}$$
then the coefficient of $x^{m+1-i}$ in $F_{mi}(x)$ is $\widetilde{c}_{mi}$ for any integers $m,i$ with the condition $0\leqslant i\leqslant m+1$.
Since
$$R_1(x)=\sum\limits_{i=1}^{|\mathbf{m}|_n}\sum\limits_{i_1+\cdots+i_n=i\atop 0\leqslant i_j\leqslant m_j+1}F_{m_1i_1}(x)\cdots F_{m_ni_n}(t)G_{i-1,1}(x),$$
and $d_{i-1,1}=-1$, we find the coefficient of $x^{|\mathbf{m}|-1}$ in $R_1(x)$ is
\begin{align*}
&-\sum\limits_{i=1}^{|\mathbf{m}|_n}\sum\limits_{i_1+\cdots+i_n=i\atop 0\leqslant i_j\leqslant m_j+1}\widetilde{c}_{m_1i_1}\cdots \widetilde{c}_{m_ni_n}
=\widetilde{c}_{m_10}\cdots \widetilde{c}_{m_n0}-\prod\limits_{j=1}^n\sum\limits_{i_j=0}^{m_j+1}\widetilde{c}_{m_ji_j},
\end{align*}
more precisely which equals
$$\widetilde{c}_{m_10}\cdots \widetilde{c}_{m_n0}-\prod\limits_{j=1}^n(\widetilde{c}_{m_j0}-\delta_{m_j,0})$$
by \eqref{Eq:Sum-cmi}. Then the coefficient of $x^{|\mathbf{m}|_n-1}$ in $R_1(x)$ is
$$\left(\frac{1}{2}\right)^n(1-(-1)^n)\delta_{m_1,0}\cdots\delta_{m_n,0},$$
which is zero if $n$ is even or at least one $m_i$ is not zero. \hfill$\square$

Let $a_{jl}\in \mathbb{Q}$ be the coefficient of $x^{2l}$ in the even polynomial $R_j(x)$, then we have
\begin{align}
R_j(x)=\sum\limits_{l\geqslant 0}a_{jl}x^{2l}=\sum\limits_{l=0}^{\left[(|\mathbf{m}|_n-j)/{2}\right]}a_{jl}x^{2l}.
\label{Eq:Fj}
\end{align}
Moreover, from Proposition \ref{pro7}, it is clear that if
$n$ is even or $m_1,\ldots,m_n$ are not all zero, then
$$R_1(x)=\sum\limits_{l=0}^{\left[(|\mathbf{m}|_n-2)/{2}\right]}a_{1l}x^{2l}.$$
Hence we have
$$D^{m_1}F(x)\cdots D^{m_n}F(x)=\sum\limits_{j=1}^{|\mathbf{m}|_n}\sum\limits_{l=0}^{\left[(|\mathbf{m}|_n-j)/{2}\right]}a_{jl}x^{2l}D^{j-1}F(x)+R_0(x).$$
Changing the order of the summation yields
$$D^{m_1}F(x)\cdots D^{m_n}F(x)=\sum\limits_{l=0}^{T}\sum\limits_{j=1}^{|\mathbf{m}|_n-2l}a_{jl}x^{2l}D^{j-1}F(x)+R_0(x),$$
where
$$T=\begin{cases}
\left[\frac{n-1}{2}\right] & \text{if\;} m_1=\cdots=m_n=0,\\
&\\
\left[\frac{|\mathbf{m}|_n-2}{2}\right] & \text{otherwise}.
\end{cases}$$
Since
$$D^{j-1}F(x)=\sum\limits_{i=0}^\infty(2i)^{j-1}\frac{\beta_{2i}}{(2i)!}x^{2i},$$
we get
\begin{align*}
&D^{m_1}F(x)\cdots D^{m_n}F(x)
=&\sum\limits_{k=0}^\infty\sum\limits_{l=0}^{\min\{T,k\}}\left(\sum\limits_{j=1}^{|\mathbf{m}|_n-2l}a_{jl}(2k-2l)^{j-1}\right)\frac{\beta_{2k-2l}}{(2k-2l)!}x^{2k}+R_0(x).
\end{align*}
Then the coefficient of $x^{2k}$ in $D^{m_1}F(x)\cdots D^{m_n}F(x)$ is
\begin{align}
\sum\limits_{l=0}^{\min\{T,k\}}\left(\sum\limits_{j=1}^{|\mathbf{m}|_n-2l}2^{j-1}a_{jl}(k-l)^{j-1}\right)\frac{\beta_{2k-2l}}{(2k-2l)!},
\label{Eq:Coeff-Right}
\end{align}
provided that $k\geqslant n$.

Finally, comparing \eqref{Eq:Coeff-Right} with \eqref{Eq:Coeff-Left}, we get a weighted sum formula of the Bernoulli numbers.

\begin{thm}\label{Thm:WeightedSum-Bernoulli}
Let $n,k$ be positive integers with $k\geqslant n$. Then for any nonnegative integers $m_1,\ldots,m_n$, we have
\begin{align}
&\sum\limits_{k_1+\cdots+k_n=k\atop k_j\geqslant 1}k_1^{m_1}\cdots k_n^{m_n}\frac{\beta_{2k_1}\cdots \beta_{2k_n}}{(2k_1)!\cdots(2k_n)!}
=&\sum\limits_{l=0}^{\min\{T,k\}}\left(\sum\limits_{j=1}^{|\mathbf{m}|_n-2l}\frac{a_{jl}(k-l)^{j-1}}{2^{m_1+\cdots+m_n-j+1}}\right)\frac{\beta_{2k-2l}}{(2k-2l)!},
\label{Eq:WeightedSum-Bernoulli}
\end{align}
where $T=\max\{[(|\mathbf{m}|_n-2)/2],[(n-1)/2]\}$ and $a_{jl}$ are determined by \eqref{Eq:Fj}.
\end{thm}

\subsection{Proof of Theorem \ref{thm1}}

Now, we prove the weighted sum formula \eqref{1.1} of $t$-values at even arguments. Using Euler's formula of $\zeta(2k)$, we have
\begin{align}
t(2k)=(-1)^{k+1}\frac{\beta_{2k}}{2(2k)!}\pi^{2k}.
\label{Eq:Euler-Formula}
\end{align}
Then from Theorem \ref{Thm:WeightedSum-Bernoulli}, we get the following weighted sum formula of $t$-values at even arguments.

\begin{thm}\label{Thm:WeightedSum-Zeta}
Let $n,k$ be positive integers with $k\geqslant n$. Then for any nonnegative integers $m_1,\ldots,m_n$, we have
\begin{align}
&\sum\limits_{k_1+\cdots+k_n=k\atop k_j\geqslant 1}k_1^{m_1}\cdots k_n^{m_n}t(2k_1)\cdots t(2k_n)\nonumber\\ &=(-1)^n\sum\limits_{l=0}^{\min\{T,k\}}\frac{(2l)!}{B_{2l}}\left(\sum\limits_{j=1}^{|\mathbf{m}|_n-2l}\frac{a_{jl}(k-l)^{j-1}}{2^{|\mathbf{m}|_n+2l-j-1}}\right)\zeta(2l)t(2k-2l),
\label{Eq:WeightedSum-Zeta}
\end{align}
where $\zeta(0)=-1/2$ and $t(0)=0$, $T=\max\{[(|\mathbf{m}|_n-2)/2],[(n-1)/2]\}$ and $a_{jl}$ are determined by \eqref{Eq:Fj}.
\end{thm}

Finally, from Theorem \ref{Thm:WeightedSum-Zeta}, we prove Theorem \ref{thm1}.\hfill$\square$

\subsection{Proof of Theorem \ref{thm2}}

Next, we use the symmetric sum formulas of Hoffman \cite[Theorems 2.5 and 2.8]{H2016} to prove Theorem \ref{thm2}. For a partition $\Pi=\{P_1,P_2,\ldots,P_i\}$ of the set $\{1,2,\ldots,n\}$, let $l_j=\sharp P_j$ and
$$c(\Pi)=\prod\limits_{j=1}^i (l_j-1)!,\quad \tilde{c}(\Pi)=(-1)^{n-i}c(\Pi).$$
We also denote by $\mathcal{P}_n$ the set of all partitions of the set $\{1,2,\ldots,n\}$. Then the symmetric sum formulas of multiple $t$-values are
\begin{align}
\sum\limits_{\sigma\in S_n}t(k_{\sigma(1)},\ldots,k_{\sigma(n)})=\sum\limits_{\Pi\in\mathcal{P}_n}\tilde{c}(\Pi)t(\mathbf{k},\Pi)
\label{Eq:SymSum-MZV}
\end{align}
and
\begin{align}
\sum\limits_{\sigma\in S_n}t^{\star}(k_{\sigma(1)},\ldots,k_{\sigma(n)})=\sum\limits_{\Pi\in\mathcal{P}_n}c(\Pi)t(\mathbf{k},\Pi),
\label{Eq:SymSum-MZSV}
\end{align}
where $\mathbf{k}=(k_1,\ldots,k_n)$ is an index with all $k_i>1$, $S_n$ is the symmetric group of degree $n$ and for a partition $\Pi=\{P_1,\ldots,P_i\}\in\mathcal{P}_n$,
$$t(\mathbf{k},\Pi)=\prod\limits_{j=1}^i t\left(\sum\limits_{l\in P_j}k_l\right).$$
Now let $\mathbf{k}=(2k_1,\ldots,2k_n)$ with all $k_i$ positive integers. Using \eqref{Eq:SymSum-MZV} and \eqref{Eq:SymSum-MZSV}, we have
\begin{align}
&\sum\limits_{\sigma\in S_n}t(2k_{\sigma(1)},\ldots,2k_{\sigma(n)})\nonumber\\
=&\sum\limits_{i=1}^n(-1)^{n-i}\sum\limits_{l_1+\cdots+l_i=n\atop l_1\geqslant \cdots\geqslant l_i\geqslant 1}\prod\limits_{j=1}^i(l_j-1)!\sum\limits_{\Pi=\{P_1,\ldots,P_i\}\in\mathcal{P}_n\atop \sharp{P_j}=l_j}t(\mathbf{k},\Pi)
\label{Eq:SymSum-2-MZV}
\end{align}
and
\begin{align}
&\sum\limits_{\sigma\in S_n}t^{\star}(2k_{\sigma(1)},\ldots,2k_{\sigma(n)})\nonumber\\
=&\sum\limits_{i=1}^n\sum\limits_{l_1+\cdots+l_i=n\atop l_1\geqslant \cdots\geqslant l_i\geqslant 1 }\prod\limits_{j=1}^i(l_j-1)!\sum\limits_{\Pi=\{P_1,\ldots,P_i\}\in\mathcal{P}_n\atop \sharp{P_j}=l_j}t(\mathbf{k},\Pi).
\label{Eq:SymSum-2-MZSV}
\end{align}

From now on, let $k,n$ be fixed positive integers with $k\geqslant n$, and let $f(x_1,\ldots,x_n)$ be a fixed symmetric polynomial with rational coefficients. It is easy to see that
\begin{align*}
&\sum\limits_{(k_1,\ldots,k_n)\in I(k,n)}f(k_1,\ldots,k_n)\sum\limits_{\sigma\in S_n}t(2k_{\sigma(1)},\ldots,2k_{\sigma(n)})\\
=&n!\sum\limits_{(k_1,\ldots,k_n)\in I(k,n)}f(k_1,\ldots,k_n)t(2k_1,\ldots,2k_n)=n!T_f(2,k,n)
\end{align*}
and
\begin{align*}
&\sum\limits_{(k_1,\ldots,k_n)\in I(k,n)}f(k_1,\ldots,k_n)\sum\limits_{\sigma\in S_n}t^{\star}(2k_{\sigma(1)},\ldots,2k_{\sigma(n)})\\
=&n!\sum\limits_{(k_1,\ldots,k_n)\in I(k,n)}f(k_1,\ldots,k_n)t^{\star}(2k_1,\ldots,2k_n)=n!T_f^\star(2,k,n).
\end{align*}
On the other hand, for a partition $\Pi=\{P_1,\ldots,P_i\}\in\mathcal{P}_n$ with $\sharp P_j=l_j$, we have
\begin{align}
&\sum\limits_{(k_1,\ldots,k_n)\in I(k,n)}f(k_1,\ldots,k_n)t(\mathbf{k},\Pi)\nonumber\\
=&\sum\limits_{s_1+\cdots+s_i=k\atop s_j\geqslant 1}\sum\limits_{{{k_1+\cdots+k_{l_1}=s_1\atop\vdots}\atop k_{l_1+\cdots+l_{i-1}+1}+\cdots+k_n=s_i}\atop k_j\geqslant 1}f(k_1,\ldots,k_n)t(2s_1)\cdots t(2s_i).
\label{Eq:F-times-zeta}
\end{align}
To treat the inner sum about $f(k_1,\ldots,k_n)$ in the right-hand side of \eqref{Eq:F-times-zeta}, we need the following lemma.

\begin{lem}[{\cite[Lemma 4.2]{LQ2019}}]\label{Lem:PowerSum}
Let $k$ and $n$ be integers with $k\geqslant n\geqslant 1$, and let $p_1,\ldots,p_n$ be nonnegative integers.  Then there exists a polynomial $g(x)\in\mathbb{Q}[x]$ of degree $p_1+\cdots+p_n+n-1$, such that
$$\sum\limits_{k_1+\cdots+k_n=k\atop k_j\geqslant 1}k_1^{p_1}\cdots k_n^{p_n}=g(k).$$
\end{lem}

 Using Lemma \ref{Lem:PowerSum}, there exists a polynomial $g_{s_1,\ldots,s_i}(x_1,\ldots,x_i)\in\mathbb{Q}[x_1,\ldots,x_i]$ of degree $\deg f+n-i$, such that
\begin{align*}
&\sum\limits_{(k_1,\ldots,k_n)\in I(k,n)}f(k_1,\ldots,k_n)t(\mathbf{k},\Pi)\\
=&\sum\limits_{s_1+\cdots+s_i=k\atop s_j\geqslant 1}g_{s_1,\ldots,s_i}(s_1,\ldots,s_i)t(2s_1)\cdots t(2s_i).
\end{align*}
Therefore  we get
\begin{align*}
T_f(2,k,n)=&\frac{1}{n!}\sum\limits_{i=1}^n(-1)^{n-i}\sum\limits_{l_1+\cdots+l_i=n\atop l_1\geqslant\cdots \geqslant l_i\geqslant 1}\prod\limits_{j=1}^i(l_j-1)!n(l_1,\ldots,l_i)\\
&\times\sum\limits_{s_1+\cdots+s_i=k\atop s_j\geqslant 1}g_{s_1,\ldots,s_i}(s_1,\ldots,s_i)t(2s_1)\cdots t(2s_i)
\end{align*}
and
\begin{align*}
T^{\star}_f(2,k,n)=&\frac{1}{n!}\sum\limits_{i=1}^n\sum\limits_{l_1+\cdots+l_i=n\atop l_1\geqslant\cdots\geqslant l_i\geqslant 1}\prod\limits_{j=1}^i(l_j-1)!n(l_1,\ldots,l_i)\\
&\times\sum\limits_{s_1+\cdots+s_i=k\atop s_j\geqslant 1}g_{s_1,\ldots,s_i}(s_1,\ldots,s_i)t(2s_1)\cdots t(2s_i),
\end{align*}
where
$$n(l_1,\ldots,l_i)=\frac{n!}{\prod\limits_{j=1}^il_j!\prod\limits_{j=1}^n\sharp\{m\mid 1\leqslant m\leqslant i,k_m=j\}!}$$
is the number of partitions $\Pi=\{P_1,\ldots,P_i\}\in\mathcal{P}_n$ with the conditions $\sharp P_j=l_j$ for $j=1,2,\ldots,i$.

Thus, applying Theorem \ref{thm1}, we prove the weighted sum formulas (\ref{1.2}) and (\ref{1.3}). \hfill$\square$

redpajama_set_name: RedPajamaArXiv


text:
Urartu (Greek Ararat)
Urartu was an ancient country of southwest Asia centered in the mountainous region southeast of the Black Sea and southwest of the Caspian Sea in the Lake Van (Sevan) area. Today the region is divided among Armenia, eastern Turkey and northwestern Iran (A).
For three centuries Urartu was a formidable rival to Assyria. Though twice defeated by the Assyrians the Urartians several times prevailed in this contest and indeed --- though only by a few decades --- outlasted their rivals. But posterity dealt harshly with the memory of Urartu. The name was preserved in the Old Testament in the corrupted form Ararat (1).
Genesis 8:4 And the ark rested in the seventh month on the seventeenth day
of the month upon the mountains of Ararat
Ararat: sacred land or high land; the name of a country on one of the mountains of which the ark rested after the Biblical Flood subsided. The mountains mentioned were probably the Kurdish range of South Armenia. The word is rendered Armenia in the Authorized Version but in the Revised Version Land of Ararat. In Jeremiah 51:27 the name denotes the central or southern portion of Armenia. It is however generally applied to a high and almost inaccessible mountain which rises majestically from the plain of the Araxes (Aras River). This part of Armenia was inhabited by a people who spoke a language unlike any other now known though it may have been related to the modern Georgian. About 900 BC they borrowed the cuneiform characters of Nineveh and from this time we have inscriptions of a line of kings who at times contended with Assyria. At the close of the seventh century BC the kingdom of Ararat came to an end and the country was occupied by a people who are ancestors of the present day Armenians (2).
Landscape Illustrations of the Bible --- Publisher : John Murray (1836)
(1) The Ancient Civilization of Urartu by Boris B. Piotrovsky (1969)
(2) Ararat in the Easton Illustrated Bible Dictionary (1897)
(A) Urartu ©2018 Encyclopædia Britannica
Urartu in WikiPedia


text:
Obręcz – jeden z obowiązkowych przyrządów, z jakimi występują zawodniczki w gimnastyce artystycznej. Wykorzystywana jest zarówno w układach indywidualnych, jak i zbiorowych. Jeden z pierwszych przyrządów, z jakim zaczynają naukę dyscypliny przyszłe gimnastyczki.

Obręcz może być plastikowa lub drewniana, o średnicy od 51 do 90 cm. Musi ważyć przynajmniej 300 g. Może być naturalnego, jednolitego koloru bądź oklejana jedną lub kilkoma kolorowymi taśmami.

Do obowiązkowych ćwiczeń wykonywanych z obręczą należą m.in. kręcenie nią wokół różnych części (partii) ciała, podrzuty i łapania, toczenie i inne.

Linki zewnętrzne

Przyrządy w gimnastyce artystycznej

redpajama_set_name: RedPajamaWikipedia


text:
Home/Music/COVID Can't Stop Latitude28
COVID Can't Stop Latitude28
RJ Frometa August 27, 2020 Music, Other Stuff Leave a comment
The pandemic has taken a tremendous toll on the entertainment industry, but few have been impacted more than businesses operating in the live entertainment space. Since COVID, live performances across the US have been minimized, pushed-back, or ended indefinitely.
But not everything, in fact; one band has made it their mission to bring live entertainment back to the masses in full force.
Latitude28 is a Lake Nona-based performance group that covers
popular songs in diverse styles ranging from pop, rock, and hip hop to country, alternative, and dance. Founded in 2018, the dynamic band consists of four core musicians and three to four vocalists.
The band has managed to make headlines with their Drive-In and Fireworks Extravaganza Tour. The tour was uniquely designed to enable people to experience live show entertainment, while following all necessary social distancing protocols — an ideal solution in the age of COVID. So far, the group has hit cities throughout central and southeast United States, with new dates being booked across the country.
According to the band founder Avinash Singh, the inspiration for the tour came after watching churches do drive-in sermons. After finding a prototype, the entire team got working on further developing and launching the concept. But just performing wasn't enough, Singh wanted to bring people an unforgettable experience. As a result, he added top-tier production that includes lasers, LED panels, sparklers, CO2 jets, and more. Each show takes place at drive-in parking lots where viewers have the ability to watch from their cars or a designated area outside their vehicles.
Event-goers and critics alike are raving about the innovative and entertaining concert. At the same time, the band is airing its own reality show on Amazon Prime Video and Facebook. If you'd like to learn more, check out their website. Latitude28 Band may be coming to a town
near you.
https://www.instagram.com/latitude28band/
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Online slot games have drastically changed since their beginnings in the 1990s, and their variety …


Asia meets Latin America in this Balinese-style bungalow in Manuel Antonio. Tucked away in a secluded spot, Royale Palm exudes an old-world charm right garden entrance and the porch swing to the glazed earthenware in the bathrooms. Thee villa provides 3 air conditioned bedrooms, 2 in the main house, with extra sleeping space for a king-size bed. There is a separate house with a trundle bed that can sleep two and a full bath. Both homes share a private plunge pool with lounge chairs to stretch out with a book. A full kitchen, WiFi, private parking, and security are other essentials this villa offers.


So the next game Nadeo will release is Trackmania: United.
Here's almost all information released this far.
Those of you who have the beta, are not allowed to post info or screenshots that are not official.
Last edited by Acegikmo on 09 Oct 2006 18:33, edited 13 times in total.
I'd suggest to make this for EVERY TMU news that comes out, counting pics, vids, dates, interviews, etc.. Then it could be a sticky.
I'll update this thread as more TMU media releases.
Baboy's got a point though.
I'll update and add TMU info soon.
Florent Castelnerac is project director at Nadeo. After showing us the next TrackMania, he accepted answering our questions about this new version.
jeuxvideo.com: How would you define TMU in a few words?
Florent Castelnerac: United gathers and fits the needs of everyone. Each player will play at the level of this 'county', share his creations, aso.
jeuxvideo.com: During the presentation you said United needed a huge amount of work. What kind of work was it?
Florent Castelnerac: First at all, United represents the biggest budget for Nadeo and people we're showing it to can't really see this point. That's why we take the time to explain everything we did. Everyone thinks that the graphic card is a really great advantage to make nice games but there's also other things. There is the network card which allows players to be together and we worked at Nadeo a lot with people outside to be able to realize this project. Saying this is for sure less easy-selling than a beautiful trailer but we have made a huge number of efforts as we worked hours and hours very hard to be as convincant as we were in our first days.
jeuxvideo.com: Should United be seen as an add-on or as a full game?
Florent Castelnerac: It's a full game. Once more it's difficult to say it like that because our buyers are not very sensitive to this argument but it's our 2.0 engine, so it's a brand new game.
jeuxvideo.com: As a developper, how do you manage this new beginning? Do you know when there will be other ones? Do you regret beggining earlier and not in 2006, and not using today's tools?
Florent Castelnerac: It's much hard in fact. A games studio has to success in all creation steps. We got our dedicated server last year, aso. We don't regret all the steps that allowed us to progress, but it's sure that today's tools allow doing much more innovant things as before.
Florent Castelnerac: I don't think so. You shouldn't stop to the first idea but find the second, the third one... At the end of the time, you get a kind of monsters fight in which only one idea will surpass the other ones. And it's probably our better strength: being in a permanent debate.
jeuxvideo.com: Games remain incredible freedom places. Aren't you afraid of cheating?
Florent Castelnerac: Until now we're lucky as we never discovered cheating in three years, and it's some kind of hard thing when your game is mostly online. Never any cheat has been proved in TM. But it's true that we made a great work making everything we could about preventing any kind of cheat we thought possible. It's a continue fight against cheaters, but cheaters themselves has not begun this fight against us. We still have a few safety fences.
jeuxvideo.com: And could it change with the new coppers system? Can you imagine what could happen?
Florent Castelnerac: You can't cheat on your coppers account. It's persistant and directly managed by the server. The only cheat we can imagine, it's some private stories between friends in order to steal some coppers. We'll wait to see what will happen for a few time before acting against it. TM still requests no subscription. Coppers are a currency "to make like" as Monopoly's banknotes and if you give wrongly the money back while doing the bank, we can't be held for responsible.
jeuxvideo.com: It's OK but for example WoW's money is not "real money". Nevertheless there's a gargantious underground economy that requests centains of account deletions. Don't you find that it makes the game spirit a bit rotten?
Florent Castelnerac: TM differs from WoW by 2 essential points. First of all, there's no subscription, so we can relativize. In TM you don't lose 10 months of subscription if you have a problem with coppers. But WoW is overall based on time: if I spend months and months to make a character grow up and offer him powerful objects, I'll be very angry if someone beats me with a cheat. But TM is also based on the player's qualities and skills: if I break my account down and have a lot of difficulties, I restart from nothing and find my performences back as it only depends on my driver's skill. In TMN, if you're much good, you don't need more than a dizain of hours to reach the worldwide top 1000.
jeuxvideo.com: You can very easily change the music of the maps. It's an open door for the copyright violation, isn't it?
Florent Castelnerac: Yes, but it's everywhere like that. If you put on the net a link to a copyrighted music, the owner can ask you to delete it. For us it's the same thing.
jeuxvideo.com: The game is still very arcade-styled. Could the next TM evolution be about the physics, with cars destroying or mechanical problems? What's your mind on it?
Florent Castelnerac: I don't know if it could ever happen. Anyway, now we don't want this. I know this could be fun. If TM would take more distance from other games, we could make it. Why so? It's because this change could be benefic to people who'd like it. Today, we think that other games, like FlatOut or Burnout, are still doing it and it's important that each one keeps its own personality. But it's not impossible to plan: we could give to our players the network, the P2P, the local ladder and the features of the other games. But I would do it against my purpose because, for me, it would concurrence some other games.
jeuxvideo.com: Thank you, Mr Castelnerac.
Last edited by Daiima on 03 Oct 2006 15:04, edited 1 time in total.


text:
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What You Don't Know About History of Computers
History of Computers
What You Don't Know About History of Computers
By administrator on September 2, 2018
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The Good, the Bad and History of Computers
As computers are offered in several configurations, some PC games may not operate on regular computers. The spare pieces of a desktop computer are easily obtainable at relatively lower costs. Desktop computers are commonly popular for everyday use at work and households. The computer is getting to be one of the most crucial sections of normal life today. It's possible to receive a fantastic gaming computer for a small percent of the total cost of the next-gen consoles in the industry.
Terminal Emulator software replicates the functionality and behavior of multiple terminal types and is offered in versions which run an assortment of devices found in today's workplace, for instance a hand held computer, a cell phone or even through an internet browser. Dependent on the operational principle, computers can be categorized as analog and digital. Computers of the previous times were of the extent of a huge room and required to consume tremendous amounts of electric power. A computer is just one of the most brilliant inventions of mankind. General purpose computers, as their name implies, are created for particular types of information processing while general purpose computers are intended for general use.
The Key to Successful History of Computers
With the aid of computer software, you may use your PC as an intelligent typewriter. The way a PC works with unique gadgets is only amazing. It takes care of all your personal things. The most significant thing is to consider what they do with the PC and what you can do in order to provide help. Most modern PCs are lightweight and they are able to perform just about any function.
Facts, Fiction and History of Computers
There are a lot of unique kinds of games being invented every single day. The game is quite easy and simple to play. The games are rated accordingly and just then they're permitted to enter the marketplace. The game is timed so you must work fast and make sure the chaos meter" doesn't escape from control. It can be really addictive. It takes place in the world of Neopia. Since a lengthy time, video games are blamed for a great deal of things.
Computer styles and types covered so many distinctive functions and actions, that it was challenging to name all of them. One of the simplest and popular forms of animations, clay animation also referred to as claymation is done with the assistance of an animated piece. A missile simulator game, it was made by using analog circuitry. Users can make Neopoints by playing games of unique genres like puzzle, action, and luck with distinctive users.
The 30-Second Trick for History of Computers
The late 90's computer training was much enjoy the computer classes that we can take today for a large selection of things. Military and wellness professionals have incorporated wearable computers in their everyday routine, as part of such studies. Your business could be part of your loved ones and part of your life, but it's not a kid! There are many reasons why folks wish to put up there own businesses like computer cleaning support. It isn't hard to calculate that a company with the ideal tools can be twice as powerful.
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You might have talk to lots of people about your idea of putting up a computer cleaning assistance, but at the conclusion of the day, you've got to decide for yourself what you would like to do and what you must do. In addition, the topic has to be appropriate for the kind of audience you are going to be addressing to. Having said this, here are a few subjects on science it's possible to pull out information about, and provide your speech on… Health is the secret to delight in life, and all that includes it.
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Christopher's poetry has been published in blazeVOX, The Aura, Danse Macabre, Drunk Monkeys, Poetry Super Highway and Rufous City Review. Christopher is currently a twenty-four year old undergraduate at the University of Alabama at Birmingham. He is a musician involved in three current projects: Philos Moore (singer-songwriter) In Snow (Instrumental), and Loveislight (Experimental Hip-Hop).
These relics weren't always disguised by sleet.
a fable, the garden in her mind consumed.
a red sky against her stale bones and the year's cracked lips.
my boyhood began lapping me again.
the relief of the land rising and drowning behind me.


text:
Hyosung Group delivered 1 billion won in donations for needy neighbors to the Community Chest of Korea on December 7.
The donations raised on the occasion of the year-end by five companies -- Hyosung Co., Hyosung TNC., Hyosung Heavy Industries, Hyosung Advanced Materials, and Hyosung Chemical -- will be used to support Korean War veterans′ housing, employment of women whose careers were interrupted, and self-reliance and daily livelihood of underprivileged people.
Hyosung Chairman Cho Hyun-jun said, "We hope that warmth will be delivered so that our neighbors suffering from the COVID-19 crisis can have hope."
Under the social contribution slogan "We will be together with sharing," Hyosung has been actively carrying out social contribution programs and sustainable management, focusing on three themes: support for the vulnerable, support for culture and arts, and reward for veterans and patriots.
Recently, Hyosung was designated as an "Excellent Enterprise for Social Contribution to Cultural Heritage" by the Cultural Heritage Administration for contributing to preservation of cultural properties by supporting the restoration work for Daejojeon Hall and Huijeongdang at Changdeokgung Palace. It also became the single company to receive the ″Culture for Rewarding Veterans and Patriots Award″ from the Ministry of Veterans and Patriots Affairs for supporting war veterans and families.


The Alliance is currently made up of a distinctive group of innovative property enterprises with offices in the UK, USA, Hong Kong and Australia. Together this creates a comprehensive fund and asset management capability.
St. Bride's Managers LLC is headquartered in Greenwich, Connecticut, US.
They represent Alliance investors from the UK, Europe, China and Africa in implementing their global investment strategies, in addition to working with domestic investors. With over 125 years of experience among the four senior members, SBM LLC are sure of their ability to identify, qualify, underwrite and execute on behalf of their clients.
EG is a specialist Australian real estate fund manager, with over AU$2.40 billion in assets under management with offices in Sydney, Austin (USA) and Manila (Philippines).
Since establishing in 2000, EG has invested on behalf of many of Australia's largest industry and public sector superannuation funds and in turn gained an outstanding reputation particularly for investing / developing in commercial assets linked to urban renewal, new transport and community infrastructure.
BEI is an Asian based global real estate and alternative investment company headquartered in Hong Kong.
Backed by major institutional investors, BEI's focus is to create and implement investment strategies for the leading global sovereign wealth funds, pensions, insurance companies and reputable family offices. Founded in 2012, BEI has an experienced team of 15, of which the senior management has been investing since the late-1980s.
Oxygen has developed a global reputation for providing a tailored service to investors who are seeking to invest in commercial real estate. They have expertise that spans all core commercial property sectors, allowing them to provide innovative ways to invest and proactively enhance the value of their portfolios both in the UK and overseas.
Morgan Capital was established in 2010 as a platform for its investment partners to access and profit from the London property market. They invest in and develop Central London Real Estate managing the full range of asset management and construction activities. Morgan Capital has a strong track record for performance.


Fipra Korea is the only integrated communications service provider in South Korea that embraces public affairs, crisis and conflict management and reputation management. Our team combines political and regulatory activities at both national and local levels to achieve our clients' goals and objectives.
Our 120-strong team offers more than 30 senior advisers. All our consultants have experience in their respective fields including industry, government, parliament, media and consultancy. Fipra Korea experts deliver effective and insightful advice to clients, built upon an in-depth understanding of the dynamics of the political and policy-making processes.
Priding ourselves on our tailored services, Fipra Korea conducts risk assessment, stakeholder analysis and regulatory analysis using our own laboratory, a research institute certified by the government.
In order to ensure that our consultants uphold the highest degree of business standards and ethics, all members of Fipra Korea sign our code of conduct. This code reflects our belief in, and strict adherence to, our industry's best practice and ethical standards.


text:
life at H2M
H2M's moments
why join H2M
public agency
doing business with H2M
Design That Save Lives
H2M's Fire Protection team offers comprehensive knowledge of fire protection and life safety requirements that can impact the preservation of life and property in a fire event. Our integrated knowledge of fire-rated construction and assemblies, egress requirements, and fire protection systems help protect building occupants, assist owners in helping to prevent and extinguish fires, and evacuate occupants in a fire emergency. We work directly with our clients to provide design, third-party review or existing conditions assessments to plan for building fire safety.
Jonathan R. Muratore, P.E., CPD
Senior Project Engineer – Mechanical Engineering
Mr. Muratore has over a decade of experience in Fire Protection and Plumbing Engineering services. His expertise ranges across many markets, including higher education, government installation, and real estate, just to name a few.
Mr. Muratore is skilled in the design of fire suppression systems and he currently supervises the design of these systems at H2M. His responsibilities include detailing design concepts, development of bid documents, and overseeing projects through construction. Furthermore, he performs internal coordination reviews of fire protection and MEP designs.
Life Safety Review and Consulting
Means of Egress Evaluation
Code Analysis
Third-party Plan Review
Hazard and Risk Analysis
Emergency Communication System Design: Fire Alarm and Detection Systems and Mass Notification Systems
Water-Based Suppression System Design: Sprinkler and Standpipe Systems
Fire Pump Design
Special Hazard Suppression System Design
Smoke Control Design
Review of Calculations, Shop Drawings, and Equipment Submittals
FIRE SAFETY PLANS AND PUBLIC SAFETY PLANS FOR LOCUST VALLEY CENTRAL SCHOOL DISTRICT
Project Info: (Waiting on official purchase order, but this project increases our range of services dramatically and should be included); PM: Renee Marcus/Maria di Natale Scotto Client: Locust Valley Central School District Location: Locust Valley, New York Scope: H2M has been engaged to provide fire safety plans and public safety plans for Locust Valley Central School District, including the high school, two intermediate school and two primary schools. The scope of work will include working closely with the District to provide emergency response plans to assist the District's personnel and students for identification, reporting and evacuation to maintain fire safety in an emergency. Additionally, H2M will assist the District in providing crowd management plans for procedures and protocols during large gatherings and events.
FIRE SUPPRESSION DESIGN FOR A HIGH-RISE, ASSISTED-LIVING FACILITY
Project Info: ENBU 1802; PM: David Mammina/Joseph Ciserano Client: Engel Burman Location: New York, New York Scope: Services include the design of fire pump systems, an automatic standpipe system and automatic sprinkler systems for a new 14-story high-rise in Manhattan. H2M provided complete piping and equipment layouts including hydraulic calculations and design to improve the water supply to meet all system demand requirements in according with the New York City Building Code and its amended, referenced standards.
THIRD PARTY PLAN REVIEW FOR HONDA OF VALLEY STREAM
Project Info: VASV 1701; PM: Rob Ikes Client: The Incorporated Village of Valley Stream Location: Valley Stream, New York Scope: H2M conducted a third-party review of the engineering design for the fire suppression systems at a new Honda car dealership. Design documentation was reviewed for conformance with the requirements of the Uniform Fire Prevention and Building Code of New York State, as well as the Nassau County Fire Prevention Ordinance.
FIRE ALARM SYSTEM DESIGN AT HARRISON HIGH SCHOOL
Project Info: HCSD 1706; PM: Kelly Finzel Client: Harrison Central School District Location: Harrison, New York Scope: Provided design services for the expansion of an existing fire alarm and detection system at Harrison High School. The scope of services included surveying 150,000 square feet of existing fire alarm systems. The design included system upgrades and modifications to provide voice messaging, expanded occupant signaling and fire detection, and carbon monoxide detection layouts design for compliance with New York State laws and NFPA 72-2013.
DRY CHEMICAL SYSTEM DESIGN AT PUBLIC WORKS FUEL ISLAND
Project Info: HEMV 1601; PM: Brian Leger Client: Incorporated Village of Hempstead Location: Hempstead, New York Scope: Provided a design for the installation of a dry-chemical, fire-extinguishing system for a new fueling station at the Public Works Facility in Hempstead, New York. H2M's design incorporated fire alarm requirements for the system actuation and emergency shut offs in accordance with the Nassau County Fire Prevention Ordinance and Fire Marshals' standards.
RETROFIT DESIGN FOR A NEW SPRINKLER SYSTEM AND FIRE PUMP DESIGN AT JAMAICA MAIN POST OFFICE
Project Info: USPS 1610 and USPS 1701; PM: Kelly Finzel Client: United States Postal Service Location: Queens, New York Scope: H2M conducted an investigation of the existing fire sprinkler, standpipe and fire pump equipment at the Jamaica Main Post Office. Based on the condition of the existing system, piping sizing and coverage H2M provided short-term and long-term recommendations to the US Postal Service, including a recommendation to replace the existing systems and equipment. Subsequently, H2M was engaged to provide the design to retrofit new suppression systems in approximately 90,000 square feet of existing building space and provide a design and layout for a new fire pump.
CODE REVIEW FOR A NEW, MIXED-USE, HIGH-RISE BUILDING
Project Info: ECDC 1601; PM: Rob Ikes Client: Erin Construction Development Corporation Location: Yonkers, New York Scope: Performed a life safety analysis and code review for conformance with the 2015 Uniform Fire Prevention and Building Code of New York State. Services included a review of building height and area, construction fire-rating requirements and review of the preliminary egress layout, with specific attention to high-rise building requirements. Performed additional review for coordination with building utility services and life safety systems requirements as related to building layout and egress requirements.
SUPPRESSION SYSTEM INVESTIGATION AT THE YONKERS JOINT WASTEWATER TREATMENT PLANT
Project Info: WCPW 1601; PM: David Leun Client: Westchester County Department of Public Works and Transportation Location: Yonkers, New York Scope: Performed an on-site evaluation of an existing foam-water fire suppression system for protection of chemical storage areas used in water treatment process. H2M evaluated the condition of the existing system installation including piping, bladder tanks and associated controls in order to provide recommendations as to the re-use or replacement of the existing systems.
H2M's fire protection engineering service covers the following markets listed below, please click "learn more" to view each market.
H2M designs bright, engaging spaces that foster collaboration, encourage discovery, and inspire learners of all ages.
H2M's architects and engineers apply their experiences as emergency service personnel to envision how a facility will be used on a day-to-day basis.
Forensic industry professionals count on H2M engineers and consultants to service both residential and commercial claims.
With deep roots in all of our local communities, H2M designs creative, environmentally responsible projects tailored to each of our client's needs.
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From the due diligence to the grand opening, H2M helps make visions a reality.
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I never received an invoice when we picked it up. We did not know what it said so when we returned the truck, we got charged for refueling when we should not have. When we picked it up it was half full.
Communication between the employees was not great but the unit we rented was ready and in great shape.
The service was very friendly (better than most other locations), but was slow (similar to many locations); fortunately, I was not in a hurry this time around.
Amber at Sonoita Auto was friendly, professional and wonderfully efficient. I'd recommend them wholeheartedly. 5 star experience.
The truck was full of blankets and boxes and plastic from the previous user, and I was charged 50 dollars for it, after the clerk had told me it would be cleaned out when I picked it up. There was also a trailer attached to the truck that I had to remove myself as the location was closed the day I picked up the truck. I was told that would also be removed and was not.
The employees where very friendly and helpful. Excelent service.
The manager knew her business and was prompt and friendly. all went well!
The location was great, but we had a flat tire , no spare is provided so we had to return it. Could not use it our second day.
This location was great to do business with.


Becky Lynch proved why she is indisputably one of the most must-watch WWE Superstars today by leading a stunning SmackDown Live women's charge on the RAW Women's roster on RAW.
And what was even more entertaining was that she went straight for Ronda Rousey first, taking the Rowdy out of the equation after locking in a Disarm-Her in the lockerroom.
She then led the charge into the ring to do battle with the remainder of the RAW women's lockerroom, during which she ended up possibly breaking and bloodying her nose.
However, she still continued inflicting punishment, taking out Rousey again, this time with a steel chair.
And while she came across as a star throughout the whole segment, her post RAW reaction to her bloody nose is one of the reasons why Becky Lynch has become such a hot favourite of the WWE Universe of late.
There's the face of the Women's Revolution, right there.


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Problematic pop stars: M.I.A.
INTERVIEW! Controversial pop star M.I.A. has always flipped negatives to positives. Can she do the same for the documentary she initially lambasted? Steve Loveridge's Matangi / Maya / M.I.A. hits Berlin cinemas November 22.
Controversial pop star M.I.A. has always flipped negatives to positives. Can she do the same for the documentary she initially lambasted? Steve Loveridge's Matangi / Maya / M.I.A. hits Berlin cinemas November 22.
Matangi / Maya / M.I.A. sees filmmaker Steve Loveridge condense around 700 hours of personal footage belonging to pop provocateur M.I.A. into a brisk feature documentary chronicling the early days of her career, her background as a Sri Lankan refugee in London and the media establishment's hounding of a controversial pop star.
The film had garnered controversy ahead of its Berlinale debut, as M.I.A. herself openly criticised it on numerous fronts at its Sundance world premiere. I sat down with the filmmaker and its subject, keeping my fingers crossed that the pair would still be on speaking terms.
M.I.A: I warn you, I'm a bit hungover. I needed a drink after seeing the film again last night…
About that… You've openly said that this isn't the film you would have made. After seeing it again, has that opinion changed at all?
M: From the last time I saw the film at Sundance to yesterday, I haven't seen Steve. He's clearly been avoiding me! And I get it – he's made a film and people like it, and I'm not going to come and stomp all over it and hijack the film, which I think he's really scared of. He went to New York and made the film and I didn't know what it was going to be. He hasn't given me the opportunity to make a few edits or even see the film before it premiered. I'm just bitching at this point… [Laughs]
Why did you give Steve all this footage in the first place?
M: I was going through a very difficult time in 2010 and 2011, and the tour I did, which was the same year I left America and came back to Europe, was crazy. The shows were intense, difficult and interesting and important for me. Creatively, I was going through so many things and what I had was a lot of show footage from around the world. I was really embraced and really rejected, and there was a love/hate thing going on. The footage was insane and I told Steve that he should cut a tour documentary of the Maya album because people hate this album so much. I did so much work around that album that nobody had seen. So, I gave all that to Steve and never really thought about it. Then Steve wanted more and more stuff. I sporadically gave him more, and then he changed things without telling me.
The reaction towards the film has been very positive though – do you feel happier now?
M: It's very weird, you know? My entire life has been so compartmentalised and I've got to show this to my parents and family.
Have they seen it yet?
M: No, not yet.
Steve: Some of your cousins were there last night and they seemed to respond really well to it…
M: Yeah… And my aunty was crying.
S: And you were crying…
M: And I was crying too. It's going to be a lot of that, and I was never given the time to digest things before this all happened.
You both met at St. Martins art college in London, and you, Maya, wanted to be a filmmaker. After this experience, would you consider going into moviemaking?
M: I would, yeah, but even that's hard because right now everyone's saying that smart people don't make movies, they make TV series, and it seems that even moviemaking is quite an endangered art form!
You sound very pessimistic…
M: Yeah, sorry – Iike I said, I'm hungover! (Laughs). I'm writing movies all the time, but I know they're all going to be problematic and so no one will give me any money to make them. When Steve and I were students, I was always writing scripts and he would say: "You're on the dole, you can't do this". So then I was like: "Fine, I'm going to get a record deal, and then I'm going to make a movie with it" and years later, I still haven't achieved that. Steve has… I'm going to do it, but I need to make it less problematic … which is problematic for me.
You're called a "problematic pop star" a lot…
M: Yeah, it's fashionable now to be an activist in your music, but even then, there are codes, and when I tried to touch on that a few years ago, I got ambushed by the press and banned from festivals. But that conversation was never had about what "problematic" actually means. What makes a person or an issue problematic or not? Also, can you talk about two issues at once or do you have to talk about one issue at a time? There's a queue now. Before, we never had to be picking and choosing. But now, between September and November, we're going to be talking about what it's like being a woman; between November and April, we're going to talk about being gay… You know what I mean? Now there's just a timescale and you get slotted in.
Do you think it's more a burden or a gift to be in the public eye and to be so influential?
M: I don't know. When I came to England as a refugee, everyone said that the best thing you could possibly do is become a pop star, and then I did it in 15 years and then was like: "OK, this is it, what now?" And then someone said that you go to the ball and marry the prince and be Cinderella, and I did that and moved to Beverly Hills. And that wasn't really it… Ultimately, it's always about work. I like working and I like making work, and I think that's a common thread. No matter what happens in your personal life and what the issues are – whether you're an immigrant, a refugee, a woman, a single parent, poor – no matter what, you're just making work.
S: At the beginning of the film, Maya's making music on a $300 keyboard, cutting up cereal packets and spraying stuff, and I think that work is just as good as expensive music videos. To me, they're just the same, and I hope people watch the film and get inspired, that kids see it and then try with whatever they have in front of them. Work, make stuff and definitely document yourself! That's another message: don't think that filming your dinner and Instagramming and all that is documenting your life. It's not. Remember to buy a proper video camera and stick it on a sideboard and film the important moments if you really want to document things. All these 10 second little clips do not add up to stories.
M: In the end, I like making work and then shit comes at you because you did, and then you've got to handle it. There are real consequences: you have to get fired and hired, or go to court and get dropped, blocked, hacked… It all happens, but those things teach me about society and then feeds into the work I make.
You come across in this film as a real voice for so many dispossessed people – and you can see that you've taken a load of flack over the years…
M: Yes! Thank you! There's been a lot of flack and when you get to address it, they make it about something else…
S: I think one of the nice things about the documentary is that we managed to take that flack and turn it into something interesting and positive, showing Maya doing that thing she does, which is taking negative experiences and flipping it and processing it to get stories and work out of it, and see a positive however difficult the obstacle is. When we first met, I came to her and she asked me: "What's your problem? Why are you always so sad?" And I was like: "Oh, I'm really awkward, I'm gay, I'm not good looking and I don't know what to do and I don't fit in". And her reply was: "Just stick a fucking wig on and you're Andy Warhol! You're weird and people would die to be as weird as you. People are dying their hair purple and getting piercings but you're actually really weird – use it! " She always does that and I hope it comes across in the film.
Another filmmaker could have made something more sensational with the material…
S: Yeah, but I've been to Maya's house, I've met her family and so there was a trust there when it came to handing over the tapes. Because it doesn't just affect Maya, it affects her whole family and we knew that we would never put something out there that would in any way hurt them or make them feel vulnerable. So, yeah, another filmmaker would probably have made a very different film.
M: I think there's also the fact that there's loads of other people going through this…
S: Yeah – I just saw that BBC strand on Syrian refugees coming over, and it ends with someone getting a job in a petrol station or just getting their council house and this feels like it's stage B to C. I mean, don't limit your expectations and your hopes for these people. Within one generation, Maya got pop stardom and magazine covers, and you can open your mind to them having the same dreams and aspirations and achievements as everybody else has. It doesn't have to be: "Well done, you got off the boat and you get to work in a shop."
M: I think it's more universal than that. It's not just about refugees. It's about taking negatives and turning them into positives. Shit happens and it's about your ability to turn it around and how quickly you do. And I get it that we're in this Instagram phase of people putting up positive quotes and feeling like they've achieved that thing because they've read something for that day; but it's about the persistence of needing that ability throughout your life, and hopefully that's applicable to more people than just those who are coming from a war zone.
Finally, which part of the film did you like the most?
M: There are a few moments. I saw stuff in it yesterday that I didn't see before. I liked the "Born Free" section because those were the only two clips Steve used of the initial idea… before he changed the narrative!
by David Mouriquand
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