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12.) Communications Manager, Rugmark, Washington, D.C.
34.) Public Relations Manager, Produce Marketing Association, Newark, Del.
Great! Any chance I can ask you to post this updated version instead?
Freelance B2B marketing writer: Stephanie Tilton is an expert case study and white paper writer who crafts compelling, persuasive copy that inspires decision makers to buy. Drawing upon nearly 20 years in the world of B2B marketing, she helps technology companies advance the sales cycle. Stephanie's finely honed project management and interviewing skills enable her to solve clients' workload and time-crunch problems – and quickly produce powerful marketing tools. Harnessing her unique blend of technical knowledge, marketing savvy, and writing skills, Stephanie has crafted over 50 case studies and dozens of white papers for leading brands including Akamai Technologies, EMC, Macromedia, Novell, SAP, and Symantec.
Stephanie's best-practice marketing articles have appeared in productmarketing.com magazine, and on sites such as the American Marketing Association, BNET, eZineArticles, and SalesVantage.
To find out more about how she can help you produce case studies and white papers that educate prospects, demonstrate thought leadership, and ratchet up the results of lead campaigns, email her at stilton@tentonmarketing.com or visit her site: http://www.tentonmarketing.com.
Salsaros and salsaras! Come join a gathering of the finest artistes, performers, instructors and DJ's for workshops, shows and parties in Abu Dhabi.
*** Ned enjoyed meeting with fellow communicators at the Intercontinental Hotel Yacht Club in Abu Dhabi yesterday. See the photo at www.nedsjotw.com.
What about the rescue of our Captain and the role of the Navy Seals? I am sure you have an opinion.
*** Ned: I am in Abu Dhabi.
Mike: Hey, on the way home can you pick up some milk?
Which Metro station is this near?
percentage of junior level and internship positions now appears to dominate.
I also want to acknowledge your attention to pirating activities over the years. As a military dude it's obvious that the crime draws your interest, but apparently Americans have to be intricately involved before the whole nation pays attention.
Leads highly complex communications and/or relations with the public, the media, and the community. Be able analyze mission, goals and objectives of the organizations involved in the programs about which the strategies and plans are being developed; identify audiences for the communications; assess reputation risk; develop objectives themes and messages; synchronize related communication events across command, echelon agency and governmental lines; establish measures of performance and measures of effectiveness; develop strategies, plans and tactics; monitor implementation of strategic communication plans and make assessments of strategy, plan and effectiveness.
Leads the planning and implementing of marketing communications projects in support of advertising product promotion, public relations and trade shows.
Develops materials for internal and external multi-media presentations of CHINFO products, services and business plans.
Participates in planning and executing marketing events.
Provides work leadership to less experienced Communications Specialists.
Public Affairs position to be established as part of a contract to be awarded by Navy Chief of Information (CHINFO).
Requires Bachelor's degree in related discipline plus 8 to 10 years of directly related experience. Master's degree preferred, as well as, professional accreditation. In some cases, educational requirements may be adjusted or waived for more than 10 years applicable work experience. Work experience may be adjusted for highly specialized knowledge or uniquely applicable experience.
Proficient with Microsoft Excel, Word, Outlook and Power Point programs.
In concert with other CHINFO team members, conceptualize, design and create informational materials to support strategic communications plans. This includes, but is not limited to, web-based materials, brochures, posters, large convention displays, fact sheets and direct marketing materials.
Capable of developing plans and implementing marketing communications projects in support of advertising, product promotion, pubic relations and trade shows.
Prepares materials for internal and external multi-media presentations of CHINFO products, services and business plans to include navy Rhumblines, a weekly update for Flag and General Officers providing situational awareness and factual information to communicate navy priorities.
Public Affairs position to be established as part of a contract to be awarded by Navy Chief of Information (CHINFO). Under general supervision, handles moderately complex communications and/or relations with the public, the media and the community. Prepares promotional materials for CHINFO and prepares articles and releases for electronic and print media consumption.
Requires Bachelor's degree in related discipline plus 2 to 4 years of directly related experience. In some cases, educational requirements may be adjusted or waived for more than 7 years applicable work experience. Work experience may be adjusted for highly specialized knowledge or uniquely applicable experience. Professional accreditation a plus.
Please add the attached to your weekly job listings.
Minimum Education and Experience: Bachelor's degree in a discipline related to the area of assignment; or equivalent combination of training and experience. All degrees must be received from appropriately accredited institutions.
Essential Skills, Knowledge and Abilities: PLEASE NOTE: All positions have moved to a new Career Banding Compensation Program.
Selected candidate should have the skills, knowledge, and ability to develop and implement a strategic communications plan; considerable knowledge and ability to prepare and disseminate information about FPG to the public through a variety of methods, techniques, and media including newspapers, periodicals, television, radio, and especially internet-based media; ability to work collaboratively with IT and others at FPG to prepare, edit, and manage content on the FPG web site; knowledge of and skills in planning, writing, and editing print and online publications for lay and professional audiences; ability to write according to accepted standards for magazine and press publications; ability to edit and analyze informational material prepared by others; ability to establish and maintain effective working relationships with representatives of the press, radio, and television and others contacted in the course of work; and ability to effectively work with a team.
Preferred Qualifications: FPG Child Development Institute (FPG) is an internationally recognized early childhood development institute that conducts research and provides technical assistance. The Director of Public Relations position is responsible for communicating the work of FPG to key stakeholders, including policymakers, practitioners, the media, and colleagues who do research and technical assistance. The Director creates local, state, and national exposure for FPG's work by developing and implementing a strategic communications plan, writing and producing a national magazine, partnering with IT to create an effective organizational website, and working effectively with both traditional and new media outlets. The Director also works with individual grant-funded projects on a variety of communications activities. The selected candidate should possess excellent writing skills, including the ability to write in a variety of media (magazines, websites, brochures, blogs, etc.); thorough knowledge of social marketing strategies; and experience in podcast production, media relations, message development, social media engagement, and materials development.
Candidates with some knowledge of early childhood or educational issues will receive priority. FPG is moving towards using internet-based media to communicate its messages. Preference will be given to candidates who have experience using modern internet tools and networks for strategic communication. Preferred candidates also will have experience working with nonprofit organizations and will be able to demonstrate their ability to think strategically about communicating messages to the broader professional and lay communities.
For additional information, please refer to our website at http://hr.unc.edu/Data/SPA/paysystems/careerbanding/. Specific competencies are required for the different banded levels and roles. This position is being recruited for at the Advanced competency level under this Career Banding Program. The hiring range for this position is $48,633-$61,764. The salary grade equivalent for this position is 76.
Special Physical/Mental Requirements: None Listed.
The Web-based Communications Specialist works as a member of the Communications Team and reports to the Manager, Web-based Communications. This specialist will be responsible for supporting multiple, concurrent Web-based initiatives for Ascension Health. This includes the external Web site, the Board site, the internal knowledge sharing site, and the Ascension Health portal.
Candidate qualifications: Exemplary writing, communication and interpersonal skills; experience with design software and media planning/buying; demonstrated research abilities; agency experience preferred and franchise experience a plus; college degree; experience with MS Word, Excel, PowerPoint, Outlook, Adobe Creative Suite, and both the PC and Mac platforms.
Our competitive compensation package includes: Health care benefits, 401k matching, Life insurance, and more. Join a fast growing company with 27 years of stability. Please email your cover letter and resume in confidence to careers@kiddieacademy.com, Attention Marketing.
Please post this opening in next week's JOTW.
Vice President-Group Manager opportunity in a DC Public Affairs agency Ketchum is a global leader in public relations and we are currently searching for a Vice President-Group Manager to play a lead role in our growing Public Affairs practice.
The ideal candidate would have experience managing large public affairs campaigns within a large agency. A mastery of public affairs capabilities, i.e. strategic client counsel & planning, third party/influence outreach, media relations. Strong people/team management skill, strong financial management skills, and a demonstrated new business track record and/or experience responding to RFP's and pitching. Experience with the finance industry, specifically with credit cards is helpful.
Please contact me at andrea.maurey@ketchum.com if you are interested in learning more.
Please post this job posting.
The National Headquarters of the American Lung Association is seeking a Manager, Learning & Member Services. This position is the lead staff member for CLAS learning and professional development-related programs and services. Works collaboratively with national and field staff to develop and manage effective learning and career advancement activities. Collaborates with the CLAS Executive Director and Governing Council to support all CLAS member services. Responsible for duties to accomplish the annual PBMS targets and as directed by the CLAS Executive Director.
Directs all aspects of the CLAS learning and professional development program to ensure all activities are coordinated and effective for CLAS members. Researches, identifies and introduces emerging eLearning strategies, tools and solutions that enhance face-to-face and distance learning. Researches, identifies and manages web-based registration process of new and existing learning opportunities. Serves as the lead staff to the CLAS Learning and Professional Development Committee and Committee sub-groups. Directs CLAS Assemblies; collaborates with CLAS President-elect, Assembly co-chairs and CLAS staff to assure robust networking, collaboration and learning activities. Researches, analyzes, identifies and initiates new technology-based systems in collaboration with national and field staff to build strong collaboration and networking. Collaborates with CLAS staff and Governing Council with membership recruitment, renewal and retention for Active and Associate members. Builds and monitors e-commerce fundraising events. Raises funds to help support the CLAS Dearholt Scholarship Program and other initiatives that support the CLAS membership activities Collaborates with CLAS staff team to develop the CLAS PBMS targets, annual operational plan and budget. Assists the CLAS Executive Director in evaluating the degree to which CLAS annual performance based management targets have been achieved. Assists the CLAS Executive Director in the preparation of CLAS Governing Council meetings and CLAS President and President-elect responsibilities to the National Board and Nationwide Assembly. Maintains the CLAS membership databases, financial records and historical electronic data for all CLAS activities. Creates and maintains a directory of all CLAS members. Supervises volunteers, interns, temporary employees and vendors.
Bachelor's degree, preferably in Education (technology-focus); Organizational Development or related field. Minimum three to five years' experience in Learning or Organizational Development preferably in a not-for-profit voluntary agency setting. Computer proficiency in MS Office (Word, Excel, Access), web-based and electronic communication skills essential. Comprehensive database experience. Knowledge and skills in Learning or Organizational Development, e.g., adult learning theories and practices, instructional development, design and evaluation. Specific experience in developing and implementing conferences, workshops, seminars in a variety of learning formats. Experience in fundraising. Excellent interpersonal skills. Experience providing staff leadership to volunteer committees, including conference planning committees. Ability to take initiative and work independently with minimal supervision as well as part of a team. Willingness to learn and to assume greater responsibilities. Excellent written and verbal communication skills. Ability and willingness to travel.
Edward, attached is a job posting for your next edition. Thank you!
Advancement Project, a Washington DC-based public policy and racial justice action group, seeks a highly creative and skilled communications specialist to join its communications team. This is a senior position on the team and reports directly to the Director of Communications.
The ideal candidate has significant (at least 6 years) experience in advocacy, campaign, social justice, and/or political communications work, outstanding strategic instincts, excellent writing skills, a proven track record of successful media relations and broader communications initiatives for a diverse array of audiences. Knowledge of the legislative process/public affairs is helpful; experience in the civil rights community and fluency in Spanish is desirable. A strong interest in racial justice issues is essential. The ability to lead initiatives, juggle competing priorities and work effectively within teams and coalitions is important.
The position is fast-paced and challenging, and offers a wealth of opportunity to increase and diversify skills and experience, exercise leadership and fuel creativity.
	Play a leadership role in broader departmental and organizational identity initiatives.
A bachelor's degree in communications/journalism or equivalent experience is required.
Ned – Here's two more from DePaul.
Relations Specialist supports the university's strategic communication objectives by maximizing positive media coverage in traditional and new media to enhance DePaul's competitive market position and prominence.
The successful candidate will work about 25 hours per week at the Loop office with a 10 a.m. to 4 p.m. Monday – Friday schedule (negotiable).
through journalism and public relations experience.
media in a PR context.
and contribute to team efforts.
professional with outstanding portfolio of media placements.
and deadline management of each project.
publications (brochures, direct mail and other marketing collateral).
Proof read and edit enrollment communications collateral.
the university, ensuring recruitment materials are brand compliant.
consumer product, services firm, or non-profit organization.
response, print, electronic production, and project management.
Must have previous client service experience.
inception to completion. Must be accountable for his/her work.
player with a cooperative spirit and a sense of humor.
Proficiency in Word, Excel and PowerPoint required.
news media in a new direction.
lead our project from prototype to business case and beyond.
digital media is a necessity.
* Sourcing and sub-edition news content.
* Initiating contractual relationships with major news providers.
* Writing and sub-editing original content.
* Working with management to complete a business case for the system.
The position is based in Manukau.
Remuera 1541 or nznewmedia@gmail.com by 1st May 2009.
reliably meet the needs of our esteemed clients.
content, etc.) for US R&D employees.
departments for site-specific communications, events and projects.
site design or administration a plus.
– Working knowledge of French is a plus.
position reports into the Wound Therapeutics Business Unit.
effectiveness, PR, medical communications, education and tradeshows.
collaborate cross-functionally, globally and across the organization.
your experience and realize tremendous success.
through the real estate course if necessary.
rbednash@pma.com. No calls please. EOE.
Ned — Here's some leads I stumbled across. FYI — IBM seems to have a lot of openings for summer interns. I didn't want to list them all, so if your readers have any interest, they might want to check the careers site of IBM.
freelancers and a PR agency.
relations, corporate branding and shareholder communication.
content and digital media including intranet, internet and elec.
communication integrated timely and engaging.
communication programs and makes suggestions for improvement.
BIOLOGICAL FIELD TECHNICIANS AND INTERNS NEEDED (10) by the Rocky Mountain Bird Observatory (RMBO) to conduct bird surveys for our Regional Monitoring Program that includes surveys in Wyoming, Arizona, Colorado, South Dakota, North Dakota, New Mexico, Nebraska, Texas, Montana, Oklahoma, and Kansas. RMBO is committed to the conservation of birds and their habitats. Technicians will be expected to attend one of the training workshops in late April through mid May and work through the end of July. The training workshops consist of a 5-day comprehensive training on the protocols conducted by RMBO. The workshops will take place throughout the study area, after which technicians will be required to work independently the majority of the time to conduct bird surveys and complete data entry. The standard work week will be ten days on/four days off. Technicians should be able to identify all western and some eastern birds by sight and sound, and should expect to hike off-trail regularly in steep, rugged terrain, sometimes under difficult conditions. Applications will be accepted through 15 April 2009 but positions will be filled as suitable applicants are found.
Qualifications: Experience with point-counts, western tree and shrub ID, backcountry hiking/backpacking, and navigation (w/ maps, compass, and GPS) is preferred. Primitive camping, often without phone service or facilities, will be required. A valid driver's license, personal vehicle, proof of auto insurance, binoculars, camping gear, a strong work ethic, and enthusiasm are required. Monthly salary of $1700-$2400, plus mileage and some lodging will be reimbursed. Internships are also available for those looking to gain experience.
14.04.2009: 0200 LT: Posn: 12:51N – 048:11E: Gulf of Aden.
Pirates in a skiff armed with automatic weapons chased a bulk carrier and opened fire on it. Pirates boarded and hijacked it with the 21 crew members as hostage and are now proceeding to an undisclosed location in Somalia.
14.04.2009: 1400 UTC: Posn: 02:16N – 047:37E, Off Somalia.
Pirates in three skiffs chased a general cargo ship underway and successfully boarded it. They hijacked the vessel and sailed to an undisclosed location in Somalia.
14.04.2009: 1300 LT: Posn: 03:45S – 048:20E, About 380 nm SE Mogadishu, Somalia.
Two speed boats approached a container ship underway from the stbd bow at a distance of 4 nm. The pirates were armed with automatic weapons and RPG. One speed boat with six pirates attempted to board but vessel took evasive manoeuvres and boat retreated. The speed boats attacked the vessel again and fired RPG, which resulted in slight damage to the vessel.
12.04.2009: 0400 UTC: Posn: 13:03N – 048:49E, Gulf of Aden.
Six pirates armed with guns in a skiff fired upon a bulk carrier underway. Vessel sent distress messages and took evasive manoeuvres and prevented the boarding. Vessel sustained slight damage to the bridge.
12.04.2009: 1625 UTC: Manila, Philippines.
While waiting for pilot, AB on routine rounds noticed robbers on the forecastle of a container ship. Alarm raised and crew mustered and proceeded to forecastle to prevent any theft. Noticing the alert crew the robbers jumped overboard and escaped with ship's properties.
11.04.2009: 1104 UTC: Posn 12:24N – 046:19E, Gulf of Aden.
Pirates fired upon and attacked an offshore tug towing two barges. Further report are awaited.
11.04.2009: 0415 UTC: Posn 12:16.0N – 046:23E, Gulf of Aden.
Eight pirates armed with guns in a speed boat (blue colour, plastic hull, 12m length) attacked a bulk carrier underway. Vessel took evasive manoeuvres and contacted coalition warship. A coalition warship acknowledged and came to the location. The pirates approached at a distance of 100m and aborted the attack.
11.04.2009: 1240 UTC: Posn: 00:18.2N – 051:44.3E, About 285 nm east of Mogadishu, Somalia.
Eight pirates armed with guns and RPG in two skiffs, launched by a pirate mother vessel, attacked a container ship underway. Master increased speed to 22.8 knots and the skiffs followed at 23.5 knots. They approach very close and fired upon the ship. Master made evasive manoeuvers and prevented the boarding.
10.04.2009: In the vicinity of Ras Kampomi off Bossaso, Gulf of Aden.
Pirates attacked and hijacked a blue and white hull, length 36 meters, fishing vessel with 18 crew members. It is suspected the pirates may be using the fishing vessel as a pirate mother vessel to attack and hijack other vessels.
09.04.2009: 0210 UTC: Posn: 06:44.85S – 039:20.06E: Dar es Salaam anchorage, Tanzania.
While the crew kept a vigilant anti piracy watch onboard a container ship, robbers boarded her and succeeded in throwing one life raft into the sea. The crew raised alarm, mustered and reported to the authorities. Vessel did not attempt to recover the life raft due to the large number of robbers.
09.04.2009: 0020 UTC: Posn: 13:08N – 049:13E: Gulf of Aden.
Pirates in a skiff chased and fired upon a bulk carrier underway. The vessel commenced evasive manoeuvres and contacted the coalition naval forces for assistance. A military helicopter arrived and upon sighting the aircraft, the pirates aborted the attempt.
09.04.2009: 1807 LT: Posn: 14:08N – 051:28E, Gulf of Aden.
A general cargo ship underway sighted a suspicious mother vessel which later launched two skiffs. The boats chased the vessel and opened fire with guns and RPG. Master raised alarm, carried out evasive manoeuvers and succeeded in deterring the pirates.
08.04.2009: 0200 LT: Posn: 03:49.5N – 077:10.0W, Buenaventura anchorage, Colombia.
Seven robbers armed with long knives boarded a bulk carrier at anchor during heavy rain. Duty crew saw movements at bosun store and raised alarm. Crew mustered and rushed to the location. The robbers escaped with ship's properties.
07.04.2009: 1140 UTC: Posn: 02:25N – 051:40E: Off Somalia.
Pirates in skiffs, armed with automatic weapons chased and fired upon a container ship underway. Pirates eventually managed to board and hijacked her.
April 16-17, New York City: Experts on the use of intranets, Enterprise 2.0 and social media for internal communication and teaming – blogs, wikis, social networks, RSS, podcasts and video – are meeting at Con Edison Headquarters, New York City. INTRANET INSIDER WORLD TOUR LIVE 2009 delivers best practices on enhancing business success using intranets in a focused and interactive format. Don't miss this mash-up of Enterprise/Web 2.0 featuring tours of the best intranets including IBM, IKEA, Siemens, Deloitte, Thomson Financial, Sprint Nextel, Watson Wyatt, Con Ed and Others. Register today – use code "nedspecial" to receive $100 off registration.


text:
\section{Introduction}

A notion of security named physical layer security defined by Wyner established an area of research in the world \cite{wyn75}. It uses the channel for its purpose by coding and other techniques in communication. Wyner's initial work assumes sender wants to send a confidential message to receiver without adversary being able to decode it. It was shown that if the channel from sender to receiver is statistically better than the channel from sender to adversary, secure and reliable communication is possible\cite{wyn75}.

\textit{M} is the \textit{k-bit} message that is supposed to be sent. Encoder maps \textit{M} to codeword \textit{X} and sends it on the channel. Bob receives sequence \textit{Y} on the main channel $W_m$ and Eve receives sequence \textit{Z} on the wiretap channel $W_w$. Finally decoder maps \textit{Y} to an estimate of message $\hat M $. The main purpose is to design a system for sending message reliably and secure on the channel when message length tends to infinity. Reliably is measured in terms of probability of error in rebuilding message. For a reliable system the following condition should be satisfied:
\begin{eqnarray}
\textbf{Reliability}: \mathop {\lim }\limits_{k \to \infty } \Pr (M \ne \hat M) = 0\
\end{eqnarray}

 Security is usually measured in terms of the normalized mutual information between the message \textit{M} and Eve's observations \textit{Z}. Encoding algorithms should satisfy the following to be called as secure:
 \begin{eqnarray}
\textbf{Weak Security}: \mathop {\lim }\limits_{k \to \infty } \frac{{I(M;Z)}}{k} = 0\
\end{eqnarray}

 Intuitively, (2) means that observing \textit{Z} does not provide much information about \textit{M}. Maurer discussed in \cite{mau94}, \cite{mau20} that the conventional notion of security (2) is a weak notion. Indeed, it is easy to construct examples where ${k^{1 - \varepsilon }}$ out of the \textit{k} message bits are disclosed to Eve while still satisfying (2). So Maurer defined another condition in \cite{mau94}:
 \begin{eqnarray}
\textbf{Strong Security}: \mathop {\lim }\limits_{k \to \infty } I(M;Z) = 0
\end{eqnarray}

Notice that both security conditions (2) and (3) are information-theoretic not computational: there is not any limitation for computational power of adversary, and security does not depend on computational complexity of algorithm. Basically the leakage of the information must be prevented and it is unlike the other works like \cite{vapnik15}, \cite{moti16} and \cite{lampert13} in which the marginal information is leveraged as auxiliary information for reasoning.

\subsection{Assumptions and Settings}
Our coding scheme is based on polar coding presented in\cite{ari09}. Polar codes achieve the capacity of binary-input DMCs. It is shown in \cite{ari09} that for sufficiently large block length the channel turn into a perfect channel or a complete noisy one. Noiseless channels are called good channels and the other ones are called bad channels.

Main idea of our construction is as following: Random symbols are transmitted over those channels that are good for both Eve and Bob. Information symbols are transmitted over those channels that are good for Bob but bad for Eve, and a fixed vector is transmitted over those channels that are bad for both Bob and Eve which is defined over all possible choices using polar coding ensemble. We prove that there exist a sequence of frozen symbols that our coding scheme satisfies the reliability and security condition. In our proposed coding scheme we consider asymmetric settings and wiretap channel $W_w$ is degraded with respect to $W_m$ and both have nonbinary-input alphabet.

\subsection{Backgrounds and Related Works}
Wyner considered a condition in which both main and wiretap channels are discrete memoryless channels and wiretap channel, is degraded with respect to main channel. He proved that for rates lower than a constant number he called secrecy capacity, reliable and secure transfer of data is possible \cite{wyn75}.\\
After Wyner, some works fulfilled in this area like \cite{che78} and \cite{csi78}. In some of them like \cite{che09}, \cite{oza84} a constraint is assumed on the computational power of eavesdropper.

 A large number of works in information-theoretic security, prove the existence of a code sequences which using them leads to achieving secrecy capacity, but a few number of them design explicit encoding-decoding algorithms. Explicit algorithms was presented in \cite{sur10} and \cite{tha07} and led to achieving secrecy capacity. In \cite{oza84} a situation is studied that assume a computational power constraint on adversary.

  There are other works similar to ours like \cite{mah11},\cite{hof10} and \cite{koy12} but main differences should be mentioned. \cite{hof10} and \cite{mah11} considered binary-input channels for symmetric setting but our contributions is for asymmetric nonbinary-input channels. Moreover the focus of \cite{koy12} is on utilizing privacy amplification protocol and information distillation for key agreement but we only consider pure information-theoretic security. In \cite{hof10} the distribution of message is assumed to be uniform But we don't consider any specific distribution on the message which is a fair assumption on message \textit{M}.

\subsection*{Organization}
In Section II, relevant concepts related to wiretap channels, in order to show an expression for the secrecy capacity  is represented in the setting where $W_m$ and $W_w$ are DMC and $W_w$ is degraded with respect to $W_m$. Also the notion of symmetric channels and secrecy capacity has been defined.
Section III is devoted to polar codes and important theorems that are necessary for our proofs.
We present the proposed coding scheme in Section IV and proofs show the security and reliability of proposed scheme and also the code rate approached to secrecy capacity while the message distribution is uniform.
We conclude the paper in Section VI with a brief discussion of further results.
\subsection*{Notation definition}
 We denote random variables (RVs) by upper case letters, such as \textit{X}, \textit{Y} and their sample values by the corresponding lower case letters, such as $x,y$ and calligraphic font shows the alphabet set of related random variable. For example, ${\cal X}$ shows the alphabet set of \textit{X} and $|{\cal X}|$ demonstrates the alphabet size. $P_X$ is the distribution of \textit{X}. If $f(x)$ and $g(x)$ are defined on a subset of real numbers then we write
$f(x) = O(g(x))$ if for large $x$ there exists a constant number \textit{M} for which the inequality
$f(x) \le M(g(x))$ holds. Notation $a_1^N$ is used instead of row vector $({a_1},{a_2},...,{a_N})$ and notation ${a_A}$ is used for representing the sub vector $\left( {{a_i}:{\rm{ }}i \in A} \right)$.
$C_W$ is the capacity of the channel W and defined as :
\begin{eqnarray}
C = \mathop {\max }\limits_{{P_X}} I(X;Y)
\end{eqnarray}
$I_W$ is the symmetric capacity of the channel W and for general channels defined as below:
\begin{eqnarray}
I(W) = \sum\limits_{y \in {\cal Y}} {\sum\limits_{x \in {\cal X}} {\frac{1}{{|{\cal X}|}}} } W(y|x)\log \frac{{W(y|x)}}{{{\textstyle{1 \over {|{\cal X}|}}}\sum\limits_{x' \in {\cal X}} {W(y|x')} }}
\end{eqnarray}

This is the mutual information when the input distribution
$P_X$ is uniform.

$[N]$ stands for $\{ 1,...,N\}$. $log(.)$ is based on 2 in the rest of the paper.
\vspace{-3mm}
\section{Secrecy Capacity}
In this section we review the prior works in \cite{csi78} and \cite{s77}. Our discussion is about nonbinary discrete memoryless channels. Such channel has the transition probability of $W(y|x)$ and ${\cal X}$,${\cal Y}$ as input and output alphabets of channel.

Assume there exists a channel $W_b$ with input alphabet ${\cal Y}$ that holds following equation:
\begin{eqnarray}
{W_w}(z|x) = \sum\limits_{y' \in {\cal Y}} {{W_m}(y'|x)} {W_b}(z|y'){\rm{   }}\forall x,z
\end{eqnarray}

In this case, the wiretapper's channel is stochastically degraded with respect to the main channel. According to \cite{csi78} the secrecy capacity is:
\begin{eqnarray}
{C_s} = \mathop {\max }\limits_{{P_X}} \{ I(X;Y) - I(X;Z)\}
\end{eqnarray}
\vspace{-3mm}

According to the concept of symmetric capacity and equation (7), by assuming uniform input distribution $P_X$, the capacity-equivocation region is given by:
\begin{eqnarray}
{R_e} \le R \le {I_{{W_m}}},0 \le {R_e} \le {I_{{W_m}}} - {I_{{W_w}}}
\end{eqnarray}
 In this case the secrecy capacity define as:
\begin{eqnarray}
{C_s} = {I_{{W_m}}} - {I_{{W_w}}}
\end{eqnarray}
\vspace{-5mm}

\vspace{-5mm}
\section{Polar Coding}
In this section important notion of polar coding is defined which is used in our designs and proofs.
\subsection{Primitive Definitions}
Consider we have a binary-input DMC which its transition probabilities are $W(y|x)$ . \textit{N} transition over the channel is shown by ${W^N}(y_1^N|x_1^N)$.
 The Bhattacharyya for nonbinary input DMCs with alphabet size q is defined as one of the two following forms\cite{sas09}:
    \begin{align}
    Z(W) = \frac{1}{{1 - q}}\sum\limits_{x,x' \in {\cal X}:x \ne x'} {\sum\limits_y {\sqrt {W(x,y)W(x',y)} } }
\end{align}

  \begin{align}
    Z(W) = \frac{1}{{1 - q}}\sum\limits_{x,x' \in {\cal X}:x \ne x'} {\sum\limits_y {\sqrt {W(y|x)W(y|x')p(x)p(x')} } }
\end{align}

If uniform input distribution is assumed we have:
\begin{align}
    Z(W) = \frac{1}{{q(1 - q)}}\sum\limits_{x,x' \in {\cal X}:x \ne x'} {\sum\limits_y {\sqrt {W(y|x)W(y|x')} } }
\end{align}

 Channel polarization has two phases: channel combining and channel splitting. $u_1^N$ is the transformed vector. The combined channel is formed by :
\begin{eqnarray}
{W_N}(y_1^N|u_1^N)  \equiv  {W^N}(y_1^N|u_1^N{G_N})
\end{eqnarray}
$G_N$ is the generator matrix of the polar code.
In the channel splitting phase, channels formed by:
\begin{eqnarray}
W_N^{(i)}(y_1^N,u_1^{i - 1}|{u_i}) \equiv \frac{1}{{{2^{N - 1}}}}\sum\limits_{u_{i + 1}^N \in {X^{N - i}}} {{W_N}(y_1^N|u_1^N)} {\rm{ }}
\end{eqnarray}
The idea of polar coding is utilizing the polarization phenomenon and transmitting data using the channels for which $I(W_N^{(i)})$ is approximately 1.

 In \cite{ari09} the notation ${\cal P}(N,K,{\cal A},{u_{{{\cal A}^c}}})$ is defined for polar code. ${u_{{{\cal A}^c}}}$ is the frozen vector . Information set (${\cal A}$) is chosen such that it satisfies two conditions :first $|{\cal A}| = K$ and second $Z(W_N^{(i)}) \le Z(W_N^{(j)})$ for all $i \in {\cal A},j \in {{\cal A}^c}$. The decode has the knowledge of frozen vector. Decoder(Successive cancellation decoder) derive an estimation of the input :for frozen indexes put ${u_{{A^c}}} = {{\hat u}_{{A^c}}}$ and For other indexes which satisfying $i \in {\cal A}$ it puts ${{\hat u}_i} = 0$ if ${\mathop W\nolimits_N^{(i)} (y_1^N,\hat u_1^{i - 1}|1) \le \mathop W\nolimits_N^{(i)} (y_1^N,\hat u_1^{i - 1}|0)}$ and otherwise ${{\hat u}_i} = 1$.

  Recently, the results of \cite{ari09} has extended to general DMCs in \cite{sas09}. These results show polar coding usage for achieving the symmetric capacity of the DMC channels with alphabet of size q given by (2) in which $|{\cal X}| = q$.

  Channel polarization, from the early stage proposed for binary-input settings,and now has been generalized to arbitrary DMCs. It is proved that when the size of input alphabet is prime, a similar method to binary-input case leads to polarizing the channels. This method extended to channels of not-prime input sizes by splitting these channels to a subset of channels that have prime input alphabet size. The extending of polarization for channels with input alphabet of arbitrary sizes leads to polar coding for achieving the real capacity of arbitrary channels\cite{sas09}.

 In this paper we skip further details of polar coding for nonbinary input channels and use the results. For more details, see \cite{ari09} and \cite{sas09}.

For the rest of the paper Z(W) means equation (12).
\subsection{Polar Coding Ensemble}
Now, polar code notation is represented which is implemented for defining polar coding ensemble and is used for the rest of the paper.

\textbf{Definition 1} (\textit{Polar Coding\cite{ari09}}):
Polar code ${{\cal P}}(N,{{\cal A}},{u_{{\cal F}}})$ for every ${{\cal A}} \subseteq \{ 1,...,N\} $ and ${u_{{\cal F}}} \in {{{\cal X}}^{|{{\cal F}}|}}$ is a linear code according to the following notation:
\begin{eqnarray}
{{\cal P}}(N,{{\cal A}},{u_{{\cal F}}}) = \{ x_1^N = u_1^N{G_N}:{u_{{{{\cal F}}^c}}} \in {{{\cal X}}^{|{{{\cal F}}^c}|}}\}
\end{eqnarray}

${{\cal F}}$ is frozen set and its indexes are called forzen indexes. Also ${{\cal A}}$ is information set and its indexes are called information indexes.

\textbf{Definition 2} (\textit{Polar Coding Ensemble\cite{kor09}}):Polar code Ensemble ${{\cal P}}(N,{{\cal A}})$ for every ${{\cal A}} \subseteq \{ 1,...,N\} $ represents the Ensemble below:
\begin{eqnarray}
{{\cal P}}(N,{{\cal A}}) = \{ {{\cal P}}(N,{{\cal A}},{u_{{\cal F}}}):\forall {u_{{\cal F}}} \in {{{\cal X}}^{|{{\cal F}}|}}\}
\end{eqnarray}
${P_{B,e}}({{\cal A}},{u_{{\cal F}}})$ represents the block error probability ${{\cal P}}(N,{{\cal A}},{u_{{\cal F}}})$ with uniform distribution assumption on all codewords. ${P_{B,e}}({{\cal A}})$ is average block error probability of ensemble ${{\cal P}}(N,{{\cal A}})$ means averaging ${P_{B,e}}({{\cal A}},{u_{{\cal F}}})$ on all possible choices of ${u_{{\cal F}}} \in {{{\cal X}}^{|{{\cal F}}|}}$ with equal probability.

\textbf{Lemma 1} (\textit{Averaged Block Error Probability Upper Bound}\cite{kor09}): for a B-DMC W and information set ${{\cal A}}$, averaged error probability of block (over all possible choices of frozen vectors) can be bounded as follows:
\begin{eqnarray}
{P_{B,e}}({{\cal A}}) \le \sum\limits_{i \in {{\cal A}}} {Z(W_N^{(i)})}
\end{eqnarray}

\subsection{Rate of Polarization}
following theorem shows the concept of polarization :\\
\textbf{Theorem 1} (\textit{Rate of Convergence\cite{ari09}}):for any binary discrete memoryless channel W, for $N = {2^n}$ and $\delta  \in (0,1)$ :
\begin{eqnarray}
\mathop {\lim }\limits_{N \to \infty } \frac{{|i \in [N] :I(W_N^{(i)}) \in (1 - \delta ,1)|}}{N} = I(W)
\end{eqnarray}
\vspace{-5mm}
\begin{eqnarray}
\mathop {\lim }\limits_{N \to \infty } \frac{{|i \in [N] :I(W_N^{(i)}) \in (0,\delta )|}}{N} = 1 - I(W)
\end{eqnarray}

\textbf{Theorem 2} (\textit{\cite{sas09}}): For any DMC W in which $ R < I(W)$, parameter $\beta \in (0,1/2)$ is considered to be fixed. Averaged Block error probability of polar coding satisfy the following equality:
\begin{eqnarray}
{P_{B,e}}({{\cal A}}) \le (q-1)*{2^{ - {N^\beta }}}
\end{eqnarray}
In which q is the input alphabet size.
Now we propose a lemma which is an extention of lemma 4.7 from \cite{kor09} that used for realizing good channels and bad channels from each other.

\textbf{Lemma 2}:
if $W:{\cal X} \to {\cal Y}$ and ${W_d}:{\cal X} \to {{\cal Y}_d}$ are two DMC W with nonbinary input alphabet size and $W_d$ is degraded with respect to $W$ then there exists a channel like ${W_b}:{\cal Y} \to {{\cal Y}_d}$ that ${W_d}({y_d}|x) = \sum\limits_{y \in {\cal Y}} {W(y|x){W_b}({y_d}|y)} $. In this condition ${W_d}_N^{(i)}$ is degraded with respect to ${W}_N^{(i)}$ and $Z({W_d}_N^{(i)}) \ge Z(W_N^{(i)})$.
\begin{proof}
now we should prove that inequality $Z({W_d}_N^{(i)}) \ge Z(W_N^{(i)})$ holds:\\
\begin{flalign}
&Z({W_d}_N^{(i)}) = \frac{1}{{1 - q}}\sum\limits_{x,x' \in {\cal X}:x \ne x'} \nonumber\\&{\sum\limits_{{y_d} \in {{\cal Y}_d}} {\sqrt {{W_d}_N^{(i)}({y_d}|x){W_d}_N^{(i)}({y_d}|x')p(x)p(x')} } }\nonumber&
\end{flalign}
\vspace{-5mm}
\begin{flalign}
& = \frac{1}{{1 - q}}\sum\limits_{x,x' \in {\cal X}:x \ne x'} {\sqrt {p(x)p(x')}} \nonumber\\ & \times \sum\limits_{{y_d} \in {{\cal Y}_d}} {\sqrt {{W_d}_N^{(i)}({y_d}|x){W_d}_N^{(i)}({y_d}|x')} } \nonumber &
\end{flalign}
\vspace{-5mm}
\begin{flalign}
& = \frac{1}{{1 - q}}\sum\limits_{x,x' \in {\cal X}:x \ne x'} {\sqrt {p(x)p(x')} }  \times \nonumber\\ & \sum\limits_{{y_d} \in {{\cal Y}_d}} {\sqrt {\sum\limits_{y \in {\cal Y}} {W_N^{(i)}(y|x){W_b}_N^{(i)}({y_d}|y)} \sum\limits_{y \in {\cal Y}} {W_N^{(i)}(y|x'){W_b}_N^{(i)}({y_d}|y)} } } \nonumber &
\end{flalign}
\vspace{-5mm}
\begin{flalign}
&\mathop  \ge \limits^{(a)} \frac{1}{{1 - q}}\sum\limits_{x,x' \in {\cal X}:x \ne x'} {\sqrt {p(x)p(x')} } \nonumber\\& \times \sum\limits_{{y_d} \in {{\cal Y}_d}} {\sum\limits_{y \in {\cal Y}} {\sqrt {W_N^{(i)}(y|x){W_b}_N^{(i)}({y_d}|y)W_N^{(i)}(y|x'){W_b}_N^{(i)}({y_d}|y)} } } \nonumber&
\end{flalign}
\vspace{-5mm}
\begin{flalign}
& = \frac{1}{{1 - q}}\sum\limits_{x,x' \in {\cal X}:x \ne x'} {\sqrt {p(x)p(x')}} \nonumber\\ & \times \sum\limits_{{y_d} \in {{\cal Y}_d}} {\sum\limits_{y \in {\cal Y}} {{W_b}_N^{(i)}({y_d}|y)\sqrt {W_N^{(i)}(y|x)W_N^{(i)}(y|x')} }  } \nonumber &
\end{flalign}
\vspace{-5mm}
\begin{flalign}
& = \frac{1}{{1 - q}}\sum\limits_{x,x' \in {\cal X}:x \ne x'} {\sqrt {p(x)p(x')} }\nonumber\\ & \times  \sum\limits_{y \in {\cal Y}} {\sqrt {W_N^{(i)}(y|x)W_N^{(i)}(y|x')} \sum\limits_{{y_d} \in {{\cal Y}_d}} {{W_b}_N^{(i)}({y_d}|y)} }  = Z(W_N^{(i)})&
\end{flalign}

(a) follows from Cauchy-Schwartz inequality.
\end{proof}
This lemma implies that with assumption of degradation of wiretap channel with respect to main channel if a channel is good to Eve it is good for Bob, conversely if a channel is bad for Bob, it is Bad for Eve too.
\vspace{-5mm}
\section{Proposed Coding Scheme}
In this section we represent a coding scheme and prove its security and reliability . Also we show that it achieves the rate of secrecy capacity.
\subsection{Secret Codebook}

Assume that Alice has a confidential message \textit{M} which is to be transmitted to Bob and should be hidden from the Eve.
Reliable and secure communication is possible, if the following conditions for any given $\varepsilon  > 0$ be satisfied:
\begin{eqnarray}
Reliability :{P_{B,e}}({{{\cal A}}_m}) \le \varepsilon
\end{eqnarray}
\vspace{-5mm}
\begin{eqnarray}
Security :\frac{1}{N} I(M;Z_1^N) \le \varepsilon
\end{eqnarray}
Wiretap channel is degraded with respect to the main channel. We have the following Markov chain:
\begin{eqnarray}
U \to X \to (Y,Z)
\end{eqnarray}
for sufficiently large N and $0 < \beta  < 1/2$ following sets are defined:
\begin{eqnarray}
{{{\cal A}}_m} = \{ i \in [N] :Z({W_m}_N^{(i)}) \le \frac{q-1}{N}{2^{ - {2^{n\beta} }}}\}
\end{eqnarray}
\vspace{-5mm}
\begin{eqnarray}
{{{\cal F}}_m} = \{ i \in [N] :Z({W_w}_N^{(i)}) \ge \frac{q-1}{N}{2^{ - {2^{n\beta} }}}\}
\end{eqnarray}
According to the defined sets, ${{{\cal A}}_m}$ is the good channel indexes for the main channel and ${{{\cal F}}_m}$ is the bad channel indexes for the wiretap channel.
According to polar coding definition and lemma 2 it is concluded that ${{\cal F}_m} \subseteq {{\cal F}_w},{{\cal A}_w} \subseteq {{\cal A}_m}$. The main task is to form $u_1^N$ based on defined indexes sets.
$u_1^N$ is the vector that multiplied by generator matrix and forms transmitted codeword. Fig.1 demonstrates the relation between defined indexes.
 \begin{figure}[h!]
  \centering
           \includegraphics[width=0.4\textwidth]{2}
           \centering
  \caption{the relation between main channel and wiretap channel indexes}
\end{figure}
In the following part the coding scheme has been proposed. According to definition 2 we define our proposed coding scheme by defining frozen symbols over all possible choices.
\subsection{Encoding Algorithm}
Secret message is mapped on the vector $V_m$ and random vector $V_r$ is generated with uniformly random distribution. Now the vector $u_1^N$ is formed as below:
\begin{enumerate}
\item Information symbols are sent over the indexes which are good for the main channel and bad for the wiretap channel. This concept could be shown by ${u_{{{\cal A}_m}\backslash {{\cal A}_w}}} = {u_{{{\cal F}_w}\backslash {{\cal F}_m}}} = {u_I}$
message length is k and $|{V_m}| = |{{\cal A}_m}| - |{{\cal A}_w}| = k$.
\item We send random symbols over indexes that belong to good channel for both main and wiretap channels as ${u_{{{\cal A}_w}}} = {u_R}$.
\item Over bad channels for both equal ${u_{{{\cal F}_m}}}$ we send a frozen vector assumed to be chosen from all possible choices ${u_{{{\cal F}_m}}} \in {{{\cal X}}^{|{{{\cal F}}_m}|}}$ and given to decoder of Bob and Eve. Polar coding ensemble is used, it meants coding scheme is built over $\forall {u_{{{\cal F}_m}}} \in {{{\cal X}}^{|{{{\cal F}}_m}|}}$.

\end{enumerate}
Encoding is defined as the following function:
\begin{align}
&encod:{\{ 0,...,q - 1\} ^k} \times {\{ 0,...,q - 1\} ^r} \to {\{ 0,...,q - 1\} ^N}&
\end{align}
Input contains a secret message $m \in {\{ 0,1,...,q - 1\} ^k}$ and a random vector ${u_R} \in {\{ 0,1,...,q - 1\} ^r}$. There is no assumption on the message distribution but $u_R$ assumed to be choosen randomly from ${\{ 0,1,...,q - 1\} ^r}$ with uniform distribution.
\subsection{Decoding}
Decoding is divided into two subsection. Reliability satisfaction and coding rate.
\subsubsection{Reliability}
Both $V_m$ and $V_r$ has been defined over good indexes of main channel, thus according to theorem 3, both of them could be decoded using SC decoding with probability of error as ${P_{B,e}}({{{\cal A}}_m}) = O((q-1)*{2^{ - {N^\beta }}})$ \cite{sas09}(averaging over all possible choices of ${u_{{{\cal F}_m}}}$). So the reliability condition is satisfied.
\subsection{Security Proof}
In this part we prove the security of the coding scheme.
Since the scheme is formed over all possible choices of frozen symbols(polar coding ensemble), mutual information between message and Eve evaluated using one random chosen vector ${u_{{{\cal F}_m}}}$ over the whole set ${u_{{{\cal F}_m}}} \in {{{\cal X}}^{|{{{\cal F}}_m}|}}$. After choosing ${u_{{{\cal F}_m}}}$ we fix it and ultimately we should prove that there exists such ${u_{{{\cal F}_m}}}$ for our purpose. The decoding error probability of Eve has been evaluated over the ensemble in average sense. Now we have the following equations:
\begin{align}
&I(M;Z|{U_F}) = I(U;Z) - I({U_R};Z|{U_F},{U_I})\nonumber\\
&\mathop  = \limits^{(a)} I(U;Z) - H({U_R}|{U_F},{U_I}) + H({U_R}|{U_I},{U_F},Z)\nonumber\\
&\mathop  = \limits^{(b)} I(U;Z) - H({U_R}) + H({U_R}|{U_I},{u_F},Z)\nonumber\\
&\mathop  \le \limits^{(c)} I(X;Z) - H({U_R}) + H({U_R}|{U_I},{U_F},Z)\nonumber\\
&\mathop  \le \limits^{(d)} NI({W_w}) - H({U_R}) + H({U_R}|{U_I},{U_F},Z)
&
\end{align}
Equation (a) follows from the chain rule of mutual information and a consequence of the following:
\begin{align}
&I(U;Z) = I({U_{{I} \cup {R} \cup {{{{ F}}}}}};Z)\nonumber\\&
 = I({U_I},{U_R},{U_{{{F}}}};Z)\nonumber\\&
 = I({U_{{{ F}}}};Z) + I({U_I},{U_R};Z|{U_{{{ F}}}})\nonumber\\&
 = I({U_I},{U_R};Z|{U_{{{F}}}})&
\end{align}
The last equality in (29) derived from the fact that $I({U_{{{\cal F}_m}}};Z_1^N)$ equals to zero because ${u_{{{\cal F}_m}}}$ has been sent over bad channels for both main and wiretap channels.
(b) follows form the independence of ${U_R},{U_I},{U_{{{ F}}}}$.(c) is the result of applying the data processing inequality because of the Markov chain $M \to U \to X \to (Y,Z)$. Below operations lead to (d):
\begin{align}
&I(X_1^N;Z_1^N) = H(Z_1^N) - H(Z_1^N|X_1^N)\nonumber\\&
 = H(Z_1^N) - \sum\limits_{i = 1}^N {H({Z_i}|{X_i})}
 \le \sum {(H({Z_i})}  - H({Z_i}|{X_i})) \nonumber\\&
 = \sum\limits_{i = 1}^N {I({X_i};{Z_i})}  \le NI({W_w})&
\end{align}
According to (d) for finding an upper bound for $I(M;Z|{U_{{{ F}}}})$ an upper bound for $H({U_R}|{U_I},{U_{{{F}}}},Z)$ should be found. For the upper bound of $H({U_R}|{U_I},{U_{{{F}}}},Z)$ we propose the following lemma:

\textbf{Lemma 3}: For a asymmetric binary-input channel the Ensemble of polar code was defined which means defining polar code over all possible choices of frozen symbols. For proposed coding scheme defined over the ensemble there exists a sequence ${u_{{{F}}}}$, which with utilizing it as frozen vector, the following inequality will be satisfied:
\begin{align}
 &H({U_R}|Z,{U_I},{U_F}) \nonumber\\
 &\le H((q - 1){2^{ - {N^\beta }}}) + (r{\log _2}q) \times (q - 1){2^{ - {N^\beta }}}&
\end{align}
\vspace{-5mm}
\begin{proof}
we define an error event as following:
\begin{eqnarray}
 E = \left\{ {\begin{array}{*{20}{c}}
{\textbf{1          } {{\hat U}_R} \ne {U_R}}\\
{\textbf{0          } {{\hat U}_R} = {U_R}}
\end{array}} \right.
\end{eqnarray}
random vector is sent over good channels for both main channel and wiretap channel so we can write ${P_e} = {P_{B,e}}({{\cal A}_w})$ and:
\begin{align}
&{P_e} = P(E = 1) \nonumber\\& =  \Pr ({{\hat U}_R} \ne {U_R})
 \le \sum\limits_{i \in {{\cal A}_w}} {Z({W_w}_N^{(i)})}  \le {(q-1)*2^{ - {N^\beta }}}
\end{align}
Because coding scheme is defined over all possible choices of ${u_{{{\cal F}_m}}} \in {{{\cal X}}^{|{{{\cal F}}_m}|}}$ and the error probability in average sense is smaller than its upper bound,it means that there exists a specific frozen vector  ${u_{{\cal F}_m}}$ which is in set ${{{\cal X}}^{|{{{\cal F}}_m}|}}$
and with choosing it the error probability does not exceed the upper bound $(q-1)*{2^{ - {N^\beta }}}$.
Now the term $H(E,{U_R}|{U_I},{U_{{{F}}}},Z)$ is expanded in two ways:
\begin{align}
&H(E,{U_R}|{U_I},{U_{{{F}}}},Z) = \nonumber\\&
H({U_R}|{U_I},{U_{{{F}}}},Z) + H(E|{U_R},{U_I},{U_{{{F}}}},Z) =\nonumber\\&
 H({U_R}|E,{U_I},{U_{{{F}}}},Z) + H(E|{U_I},{U_{{{F}}}},Z)&
\end{align}
obviously the term $H(E|{U_R},{U_I},{U_{{{F}}}},Z)$ equals zero because with having $U_R$ there is no equivocation on Error, consequently:
\begin{align}
&H({U_R}|{U_I},{U_{{{F}}}},Z) =\nonumber\\&
H({U_R}|E,{U_I},{U_{{{F}}}},Z) + H(E|{U_I},{U_{{{F}}}},Z)&
\end{align}
clearly eliminating the condition of entropy function do not decrease the entropy so:
\begin{align}
 & H({U_R}|{U_I},{U_{{{F}}}},Z)\nonumber\\&
 \le H({U_R}|E,{U_I},{U_{{{F}}}},Z) + H(E)&
\end{align}

a new task is to find an upper bound for the right hand side of (36):
\begin{align}
&H({U_R}|E,{U_I},{U_{{{F}}}},Z) = \nonumber\\&
\sum\limits_{i = 0}^1 {P(E = i)H({U_R}|E = i,{U_I},{U_{{{F}}}},Z)}\nonumber\\ &
 = P(E = 1)H({U_R}|E = 1,{U_I},{U_{{{F}}}},Z)
 + (1 - P(E = 1)) \times 0 \nonumber\\&
 = P(E = 1)H({U_R}|E = 1,{U_I},{U_{{{F}}}},Z)\nonumber\\&
 \le P(E = 1)H({U_R}) = {P_e}*r{log_2}q&
\end{align}

according to (36) and (37):
\begin{flalign}
&H({U_R}|{U_I},{U_{{{F}}}},Z) \le H(E) + {P_e}*r{log_2}q\nonumber\\
&\le H((q - 1){2^{ - {N^\beta }}}) + (r{\log _2}q) \times (q - 1){2^{ - {N^\beta }}} &
\end{flalign}
\vspace{-5mm}
\end{proof}
according to lemma 3 and (28):
\begin{align}
&\mathop {\lim }\limits_{N \to \infty } I(M;Z|{U_F})/N = \mathop {\lim }\limits_{N \to \infty } \{ I({W_w}) - r{\log _2}q/N + \nonumber\\
& \{ H((q - 1){2^{ - {N^\beta }}}) + r{\log _2}q*(q - 1){2^{ - {N^\beta }}}\} /N\}&\nonumber\\
&= \mathop {\lim }\limits_{N \to \infty } \{ I({W_w}) - r{\log _2}q/N\}
\nonumber\\
&= {\log _2}q*\mathop {\lim }\limits_{N \to \infty } \{ {I_q}({W_w}) - {H_q}({U_R})\}\nonumber\\
&\approx \mathop {\lim }\limits_{N \to \infty } \{ {I_q}({W_w}) - r/N\}  = 0
\end{align}
${I_q}({W_w})$ is symmetric capacity of wiretap channel if in equation (2), the base of logarithm be q and ${H_q}({U_R})$ is q-based logarithmic entropy function.
If $R$ is the rate of coding then:
\vspace{-3mm}
\begin{align}
\frac{{H(M)}}{N} \le R \le \frac{{k{{\log }_2}q}}{N} &= \frac{{{{\log }_2}|q{|^{k + r}} - {{\log }_2}|q{|^r}}}{N} \nonumber\\
&= I({W_m}) - I({W_w}) = {C_S}
\end{align}

It concludes that for achieving secrecy capacity the distribution of message should be uniform, otherwise there exists a code such that its rate $R$ satisfy the following inequality :

\begin{align}
\frac{{H(M)}}{N} < R < \frac{{k{{\log }_2}q}}{N}
\end{align}
And the code rate doesn't achieve secrecy capacity. Inequality $H(M)/N \le R$ derives from source coding theorem.
So the security of coding scheme is proved because $\mathop {\lim }\limits_{N \to \infty } I(M;Z)/N$ is equivalent to $\mathop {\lim }\limits_{k \to \infty } I(M;Z)/k$. Equation (39) holds because according to the definition of polar coding $I({W_w})\mathop  \equiv \limits^{N \to \infty } |{{\cal A}_w}|/N$.

\section{Conclusion and discussion}
We briefly mention our results and certain extensions of them. So far, nonbinary-input asymmetric wiretap channels have been considered in this paper. We proved that there exists some choices of frozen symbols for which coding scheme satisfies reliability and security conditions. Also it has been proved that the necessary condition for achieving secrecy capacity is uniform distribution of the message set.
An open problem is to construct codes for the situation where the wiretap channel is not degraded with respect to the main channel.for example if Eve has just a less noisy channel than Bob.
 Our coding scheme is not totally explicit because only existence of a frozen vector that is suitable for our setting has been proven.
Another problem is successive cancellation decoding depends on the past estimates of itself that should be correct otherwise that will propagate error. Implementing another decoder for overcoming this setback is of great interest.
Recently in \cite{hon13} a method has been suggested for overcoming the polarization limitation. The method is based on defining pseudorandom frozen bits and extent to all kind of channels. Using results in \cite{hon13} to extend our results to arbitrary discrete memolyless channels is a thrilling task.
It was shown by Maurer-Wolf \cite{mau20} that any coding scheme that satisfies the "weak" security condition can be converted to a coding scheme that satisfies the stronger condition (3). This has been accomplished using information reconciliation and privacy amplification protocol \cite{ben95}. So the results of this paper could be extented to strong security using results of privacy amplification protocol.
\bibliographystyle{elsarticle-harv}

redpajama_set_name: RedPajamaArXiv


text:
Forest Service Fills Two Key Positions At Its Headquarters
U.S. Department of Agriculture Forest Service Chief Dale Bosworth today announced the selections for two national leadership positions at its headquarters office here. Kent Connaughton has been selected as associate deputy chief of state and private forestry and Greg Smith has been named as director of the lands staff.
This additional associate deputy chief position in state and private forestry was created for expanded executive leadership capability because of our increased hazardous forest restoration goals associated with the National Fire Plan, the Healthy Forests Initiative and the challenges facing our fire and aviation management programs. "Kent has the background and experience to help with these growing challenges and responsibilities and look forward to his arrival," said Bosworth.
In his new position, Connaughton will help to oversee the state and private forestry organization, which is a leader in providing technical and financial assistance to landowners and resource managers to help sustain the nation's forests and protect communities and the environment from wildland fires. Connaughton, a second generation Forest Service employee, currently serves as deputy regional forester for state and private forestry for the Pacific Southwest Region based out of Vallejo, Calf., where he has helped direct forest health, urban and community forestry, landowner assistance and economic action programs, as well as forest fuels reduction, fire suppression, recreation and wilderness management and tribal relations since 2001. As associate deputy chief for state and private forestry in Washington, he will have oversight and management direction for some of these same programs at the national level.
"I'm honored to have been selected as associate deputy chief for state and private forestry and I'm thrilled that I will be working on such a challenging array of issues affecting our nation's forests," said Connaughton. "It will be my privilege to be able to work with so many fine people in our national headquarters and I also look forward to forging strong working relationships with the many non-federal partners involved in our national state and private forestry programs."
Prior to 2001, Connaughton served as project manager for the Sierra Nevada Forest Plan Amendment, which amended management plans for national forests in the Sierra Nevada Mountain range. He was also forest supervisor on the Lassen National Forest in California. In addition, he served as assistant director of the U.S. Office of Forestry and Economic Development with responsibilities for coordination and implementation of 18 economic development and watershed restoration programs established by the Northwest Forest Plan and as a research scientist for the Pacific Northwest Research Station in Portland, Ore.
The lands office resides in the agency's National Forest System deputy area. The lands staff oversees a number of activities for the 155 national forests and 20 grasslands, including land acquisitions, land exchanges, title claims and treaty rights. Smith has served as acting director of the lands staff since December 2003. Prior to the assignment, he held the deputy director position for the office.
"I am really appreciative of the great job Greg has done in lands for the past year and a half as acting director," said Bosworth. "Greg is uniquely qualified to manage and direct the program—one that is becoming increasingly complex—with his legal training and background of the agency's program."
Over his career with the Forest Service, Smith has held positions with the communications staff here in Washington as well as a public involvement officer for the Bridger-Teton National Forest in the Greater Yellowstone Area. Prior to joining the Forest Service, Smith worked as a staff attorney for the Colorado General Assembly and served as the assistant to the vice chancellor of the University of Colorado's Health Sciences Center. He also worked as a civil rights mediator and assistant county attorney in Polk County, Iowa.
"I am humbled and excited for the opportunity to lead the challenging and complex lands and realty management program for the Forest Service," said Smith. "My primary objective will be to develop a greater understanding among agency managers and staff regarding the role of land and realty management in achieving excellence in overall natural resources management."
Connaughton holds a bachelor's in biological sciences from Stanford University, a master's in forest management from Oregon State University and a doctorate in forest economics from the University of California.
Smith graduated from Bethune-Cookman College in Florida with a bachelor's in history and political science. He also holds a master's in public administration from Iowa State University and a juris doctorate from Drake University.
A reporting date for Connaughton has not yet been established. Smith's position is effective immediately.
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Descubre el Bosque
¡Es todo tuyo!
https://www.fs.usda.gov/news/releases/forest-service-fills-two-key-positions-its-headquarters

redpajama_set_name: RedPajamaCommonCrawl


Discussion in 'Provincial Nomination Program Immigration' started by ashuindian, Jul 27, 2017.
On July 27, the popular International Skilled Worker – Express Entry sub-category of the Saskatchewan Immigrant Nominee Program (SINP) reopened for 600 new applications. This was the fifth such reopening this year, and the application intake typically fills within days, benefiting candidates who have prepared thoroughly in advance. Historically, intake periods do not come with prior notice.
At the time of writing, the sub-category remains open. If the intake is reached and the program subsequently closes for a period, it may reopen again later in 2017.
Try through different ways like Net Banking etc. Their payment gateway is very easy going. So try carefully, repeatedly. But Debit card and Credit card options are the best.
Jimmy V and Canada 2017 like this.
As for me, this is not surprising! I'm from Russia. )))))) but you, Ashu, are so funny! I do love your optimism!
Wow. Siberia or Cyberia is the coldest in the world.
what time for next scheduled opening please?
There is no fix time to die and SINP Intake opening.
Yes, will open this month certain. Keep checking every 1 hour.
what about the translation affidavit, is it required for some governmental papers like birth certificate knowing that it is written by the ministry in my native language and in English?
If written in English also then it is all right.


Purchasers of a new home often question whether or not mortgage insurance is a worthwhile endeavor. I suggest that you take the time to speak to the numerous providers about the various products available to you. Mortgage insurance can sure make dealing with an unforeseen tragedy a lot less stressful. To know that your home ownership is secure removes a tremendous burden.
As I mentioned earlier investigate the various products available to you. There is mortgage insurance that is relatively inexpensive and that will keep its full payout value to the end of your mortgage term no matter how soon you pay off your mortgage. The policy is than convertible to whole life insurance with a cash value. Avoid the mortgage insurance with a reducing payout based on the remaining value of the mortgage. This insurance can have a little less expensive premium but has no cash value and over time ends up costing you much more money.
Take your time and do your research before purchasing this much needed product.


text:
\section{Introduction}
Tempered ultrahyperfunctions were introduced in papers of {\sc Sebasti\~ao e
Silva}~\cite{T} and {\sc Hasumi}~\cite{H}, under the name of tempered
ultradistributions, as the strong dual of the space of test functions
of rapidly decreasing entire functions in any horizontal strip.
Recently, aside from the mathematical interest of the
results presented in Refs.~\cite{T}-\cite{DH}, {\sc Br\"uning--Nagamachi}~\cite{BN}
have conjectured that the properties of tempered
ultrahyperfunctions are well adapted for their use in quantum field
theory with a {\em fundamental length}, while {\sc Bollini--Rocca}~\cite{BR}
have given a general definition of convolution between two arbitrary tempered
ultrahyperfunctions in order to treat the problem of singular pro\-du\-cts
of functions Green also in quantum field theory. The present contribution
contains a brief statement of the results obtained in Ref.~\cite{DH}, where the principal
problem studied was the generalization of Paley-Wiener-Schwartz theorem for the
setting of tempered ultradistributions corresponding to a convex cone and its connection
with the microlocal analysis.

\section{Tempered Ultrahyperfunctions Corresponding to a Convex Cone}
An open set $C \subset {\mathbb R}^n$ is called a cone if
$x \in C$ implies $\lambda x \in C$ for all $\lambda > 0$. Moreover,
$C$ is an open connected cone if $C$ is a cone and if $C$ is an open connected set.
In the sequel, it will be sufficient to assume for our purposes
that the open connected cone $C$ in ${\mathbb R}^n$ is an open convex cone
with vertex at the origin. A cone $C^\prime$ is called compact in $C$ --
we write $C^\prime \Subset C$ -- if the projection ${\sf pr}{\overline C^{\,\prime}}
\overset{\text{def}}{=}{\overline C^{\,\prime}} \cap S^{n-1} \subset
{\sf pr}C\overset{\text{def}}{=}C \cap S^{n-1}$, where $S^{n-1}$ is the unit
sphere in ${\mathbb R}^n$. Being given a cone $C$ in $x$-space, we associate with $C$ a
closed convex cone $C^*$ in $\xi$-space which is the set $C^*=\bigl\{\xi \in {\mathbb R}^n
\mid \langle \xi,x \rangle \geq 0, \forall x \in C \bigr\}$.
The cone $C^*$ is called the {\em dual cone} of $C$.

By $T(C)$ we will denote the set ${\mathbb R}^n+iC \subset {\mathbb C}^n$. If $C$ is
open and connected, $T(C)$ is called the tubular radial domain in ${\mathbb C}^n$,
while if $C$ is only open $T(C)$ is referred to as a tubular cone. An
important example of tubular radial domain in quantum field theory
is the {\em forward light-cone}
\[
V_+=\Bigl\{z \in {\mathbb C}^n \mid {\rm Im}\,z_1 >
\Bigl(\sum_{i=2}^n {\rm Im}^2\,z_i \Bigr)^{\frac{1}{2}}, {\rm Im}\,z_1 > 0 \Bigr\}\,\,.
\]

We will deal with tubes defined as the set of all points $z \in {\mathbb C}^n$
such that
\[
T(C)=\Bigl\{x+iy \in {\mathbb C}^n \mid
x \in {\mathbb R}^n, y \in C, |y| < \delta \Bigr\}\,\,,
\]
where $\delta > 0$ is an arbitrary number.

Let $C$ be an open convex cone and let $C^\prime$ be an arbitrary
compact cone of $C$. Let $B[0;r]$ denote a closed ball of the
origin in ${\mathbb R}^n$ of radius $r$, where $r$ is an arbitrary positive
real number. Denote $T(C^\prime;r)={\mathbb R}^n+i\bigl(C^\prime \setminus
\bigl(C^\prime \cap B[0;r]\bigr)\bigr)$. We want to consider the space
consisting of holomorphic functions $f(z)$ such that
\begin{equation}
\bigl|f(z)\bigr|\leq K(C^\prime)(1+|z|)^N e^{h_{C^*}(y)}\,\,,\quad
z=x+iy \in T(C^\prime;r)\,\,,
\tag{{\bf 1}}
\end{equation}
where $h_{C^*}(y)=\sup_{\xi \in C^*}|\langle \xi,y \rangle|$
is the indicator of $C^*$, $K(C^\prime)$ is a constant that depends
on an arbitrary compact cone $C^\prime$ and $N$ is a non-negative real number.
The set of all functions $f(z)$ which are holomorphic in $T(C^\prime;r)$ and
satisfy the estimate ({\bf 1}) will be denoted by $\boldsymbol{{\mathscr H}^o_c}$.
In what follows, we shall prove two lemmas which will be important for our
extension of Paley-Wiener-Schwartz theorem for the setting of tempered ultrahyperfunctions.

\begin{lemma}
Let $C$ be an open convex cone, and let $C^\prime$ be an arbitrary compact
cone contained in $C$. Let $h(\xi)=e^{k|\xi|}g(\xi)$, $\xi \in {\mathbb R}^n$, be
a function with support in $C^*$, where $g(\xi)$ is a bounded continuous
function on ${\mathbb R}^n$. Let $y$ be an arbitrary but fixed point of
$C^\prime \setminus \bigl(C^\prime \cap B[0;r]\bigr)$. Then
$e^{-\langle \xi,y \rangle}h(\xi) \in L^2$, as a function of $\xi \in {\mathbb R}^n$.
\label{lemma0}
\end{lemma}

\begin{proof}
For details see Ref.~\cite{DH}.
\end{proof}

\begin{definition}
We denote by $H^\prime_{C^*}({\mathbb R}^n;O)$ the subspace of $H^\prime({\mathbb R}^n;O)$
of distributions of exponential growth with support in the cone $C^*$:
\begin{equation*}
H^\prime_{C^*}({\mathbb R}^n;O)=\Bigl\{V \in H^\prime({\mathbb R}^n;O) \mid
\mathrm{supp}(V) \subseteq C^* \Bigr\}\,\,.
\end{equation*}
\end{definition}

\begin{lemma}
Let $C$ be an open convex cone, and let $C^\prime$ be an arbitrary compact
cone contained in $C$. Let $V=D^\gamma_\xi[e^{h_K(\xi)}g(\xi)]$, where
$g(\xi)$ is a bounded continuous function on ${\mathbb R}^n$ and $h_K(\xi)=k|\xi|$
for a convex compact set $K=\bigl[-k,k\bigr]^n$. Consider
$V \in H^\prime_{C^*}({\mathbb R}^n;O)$. Then $f(z)=(2\pi)^{-n}
(V,e^{-i\langle \xi,z \rangle})$ is an element of
$\boldsymbol{{\mathscr H}^o_c}$.
\label{lemma1}
\end{lemma}

\begin{proof}
For details see Ref.~\cite{DH}.
\end{proof}

We define ${\mathscr U}_c=\boldsymbol{{\mathscr H}^o_c}/\boldsymbol{\Pi}$ as
being the quotient space of $\boldsymbol{{\mathscr H}^o_c}$ by set of pseudo-polynomials.
Here the set ${\mathscr U}_c$ is the space of tempered ultrahyperfunctions corresponding
to the open convex cone $C \subset {\mathbb R}^n$. The space ${\mathscr U}_c$ is algebraically
isomorphic to the space of generalized functions ${\mathfrak H}^\prime$. This
result, which represents a generalization of {\sc Hasumi}~\cite[Proposition 5]{H},
was obtained by {\sc Carmichael}~\cite[Theorem 5]{C} in the case where $C$ is an
open cone, but not necessarily connected.

\section{A Generalization of the Paley-Wiener-Schwartz Theorem}
More can be said concerning the functions $f(z) \in \boldsymbol{{\mathscr H}^o_c}$.
It is shown that $f(z) \in \boldsymbol{{\mathscr H}^o_c}$ can be recovered as the
(inverse) Fourier-Laplace transform\footnote{The convention of signs in the Fourier
transform which is used in Ref.~\cite{DH} one leads us to consider the inverse
Fourier-Laplace transform.} of the constructed distribution $V \in H^\prime_{C^*}({\mathbb R}^n;O)$.
This result is a generalization of the Paley-Wiener-Schwartz theorem.

\begin{theorem}[PWS-Type Theorem]
Let $f(z) \in \boldsymbol{{\mathscr H}^o_c}$, where $C$ is an open convex cone.
Then the Fourier ultrahyperfunction $V \in H^\prime_{C^*}({\mathbb R}^n;O)$ has a uniquely
determined inverse Fourier-Laplace transform $f(z)=(2\pi)^{-n}
(V,e^{-i\langle \xi,z \rangle})$ which is holomorphic in
$T(C^\prime;r)$ and satisfies the estimate
\begin{equation*}
\bigl|f(z)\bigr|\leq K(C^\prime)(1+|z|)^N e^{h_{C^*}(y)}\,\,,\quad
z=x+iy \in T(C^\prime;r)\,\,.
\end{equation*}
\label{PWSTheo}
\end{theorem}

\begin{proof}
For details see Ref.~\cite{DH}.
\end{proof}

\section{Analytic Wave Front Set of Tempered Ultrahyperfunctions}
We shall characterize the spectrum of singularities of tempered ultrahyperfunctions
via the notion of analytic wave front set~\cite{Hor2}. Let us now consider the consequences
of Theorem \ref{PWSTheo}.

\begin{theorem}
If $u \in {\mathscr U}_c({\mathbb R}^n)$ and $V \in H^\prime_{C^*}({\mathbb R}^n;O)$
$({\mbox{with}}\,\,\,O \subseteq {\mathbb R}^n)$, then $WF_A(u) \subset {\mathbb R}^n \times C^*$.
\end{theorem}

\begin{proof}
Let $\{C^*_j\}_{j \in L}$ be a finite covering of closed properly convex
cones of $C^*$. Decompose $V \in H^\prime_{C^*}({\mathbb R}^n;O)$ as follows:
\begin{equation}
V=\sum\,V_j\,,\quad{\mbox{such that}}\,\, V_j \in H^\prime_{C_j^*}({\mathbb R}^n;O)=
\Bigl\{V_j \in H^\prime({\mathbb R}^n;O) \mid \mathrm{supp}(V_j) \subseteq C_j^* \Bigr\}\,\,.
\label{decomp}
\end{equation}
Next apply the Theorem \ref{PWSTheo} for each $V_j$.
Then the decomposition (\ref{decomp}) will induce a representation of
$u$ in the form of a sum of boundary values of functions $f_j(z)\in
\boldsymbol{{\mathscr H}^o_{c_j}}$, such that $f_j(z) \rightarrow
{\mathscr F}^{-1}[V_j] \in {\mathfrak H}^\prime$ in the strong topology of
${\mathfrak H}^\prime$ as $y={\rm Im}\,z \rightarrow 0$, $y \in C_j^\prime
\subset C_j$. According to Theorem \ref{PWSTheo}, the family of functions
$f_j(z)$ satisfy the estimate
\begin{equation*}
\bigl|f_j(z)\bigr|\leq K(C^\prime)(1+|z|)^N e^{h_{C^*}(y)}\,\,,\quad
z=x+iy \in T(C_j^\prime;r)\,\,.
\end{equation*}
unless $\langle \xi,Y \rangle \geq 0$ for $\xi \in C_j^*$ and $Y \in C_j^\prime$, with
$|Y| < \delta$. Then the cones of ``bad'' directions
responsible for the singularities of these boundary values are contained in
the dual cones of the base cones. So, we have the inclusion
\begin{equation}
WF_A(u) \subset {\mathbb R}^n \times \bigcup_j\,C_j^*\,\,.
\label{inclusion}
\end{equation}
Then, by making a refinement of the covering and shrinking it to $C^*$,
we obtain the desired result.
\end{proof}

\section{Physical Applications of the Results Obtained}
The Paley-Wiener-Schwartz theorem has a conceptual significance for QFT since
it determines the analytic structure of $n$-point correlations functions of the
fields, relating this structure to the support properties implied by the
basic physical notions of causa\-li\-ty and spectral condition. This theorem
underlines the derivation of the main results of the axiomatic QFT, such as
PCT theorem.

In its standard form, the Paley-Wiener-Schwartz theorem deals with the
Fourier-Laplace transform of {\it tempered} distributions and so with
analytic functions which have {\em polynomial growth} at infinity. It enters
in some way or other in the perturbative framework to QFT due to the {\it temperedness}
of the free propagators. However, the
behavior of the fields in a QFT with a fundamental length (as the non-commuta\-ti\-ve
quantum field theories (NCQFT)) can be appreciably {\em more singular}.
This implies that the Wightman framework of local QFT turned out to be too narrow for
theoretical physicists, who are interested in handling situations involving
a QFT with a fundamental length. In particular, for NCQFT some very important evidences
to expect that the traditional Wightman axioms must be somewhat modified are:

\,\,\,

\begin{itemize}

\item {\sl NCQFT are {\bf nonlocal}.}

\,\,\,
\item {\sl The existence of hard infrared singularities in the non-planar sector
of the theory can destroy the {\bf tempered} nature of the Wightman functions}.

\,\,\,
\item {\sl The commutation relations $[x_\mu,x_\nu]=i \theta_{\mu\nu}$
also imply uncertainty relations for space-time coordinates
$\Delta x_\mu \Delta x_\nu \sim \bigl|\theta_{\mu\nu}\bigr|$, indicating that the
notion of space-time point loses its meaning. Space-time points are replaced by cells
of area of size $\bigl|\theta_{\mu\nu}\bigr|$. This suggests the existence of
a finite lower limit to the possible resolution of distance. The {\bf nonlocal}
structure of NCQFT manifests itself in a indeterminacy of the interaction regions,
which spread over a space-time domain whose size is determined by
the existence of a {\bf fundamental length} $\ell$ related to the scale of nonlocality
$\ell \sim \sqrt{\bigl|\theta_{\mu\nu}\bigr|}$}.

\end{itemize}

\,\,\,Our aim is to apply the results obtained here in the extension of the Wightman
axiomatic approach to NCQFT in terms of tempered ultrahyperfunctions (for details see~\cite{DZH}).
We note that the class of NCQFT in terms of ultrahyperfunctions allows for the possibility
that the off-mass-shell amplitudes can grow at large energies faster than any polynomial
(such behavior {\bf is not possible} if fields are assumed to be tempered only). This fact
is relevant since NCQFT stands as an intermediate framework between string theory and the
usual quantum field theory.


text:
Your 5-year-old: Getting enough sleep
While it may seem like 5-year-olds never stop, stop they eventually must – and ideally for at least 10 to 13 hours.That's the amount of shuteye the average 5-year-old needs.
It's true that some people, including some children, seem to require less sleep than others. But it's generally wise to err on the side of ensuring plenty of zz's. If a 5-year-old doesn't sleep long enough, he may be cranky or have trouble staying focused during the daytime.
Even though your child seems like a "big kid" compared to just a year ago, he needs a bedtime routine now as much as ever. Familiar rituals soothe and relax your child and prepare him for sleep.
It will help to remove any electronics from his bedroom, as well. Kids who are plugged in have a harder time falling and staying asleep. (Not to mention a litany of other problems, including a higher risk of obesity.)
Five marks the beginning of the school years for most children. It's easy to get drawn into a busy whirl of school, play, and activities. But take time for one throwback: updating his baby book or website.
Some parents write an annual letter to their child, to be opened on his eighteenth birthday. In it, you could jot down amazing highlights of the previous year, observations about personality and character, and your hopes for the future. If you didn't start doing this from birth, now's a great time to start.
Watch the video: How to help your child get a good sleep (January 2023).
Copyright 2023 \ Your 5-year-old: Getting enough sleep...


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text:
Fräulein Wunder é uma banda alemã de pop rock de Friedberg, Hesse.

História
O quarteto se encontrou em 2006 em um lugar onde seus ídolos musicais regularmente vão. Em 2007, elas escreveram suas primeiras músicas, e mais tarde, seguida com suas primeiras aparições. Inicialmente, o grupo foi formado sob o nome de "Puppenblut", mas elas trocaram para sHERO até 2008. Em um de seus concertos, elas foram descobertas por uma gravadora. A banda brevemente publicou seu primeiro álbum em 29 de Agosto de 2008. Elas rapidamente lançaram seu primeiro single, Wenn ich ein Junge wär, que ficou em #16 na parada de singles alemã.  Em Agosto e Julho de 2008, a banda foi ao ar no "Band Diaries" no canal de TV VIVA. Em 2009, a banda representou Hesse em no concurso Bundesvision Song Contest e alacançaram o sexto lugar com sua música Sternradio.

Integrantes
 Vocal: Chanty (Jana Chantal Franziska) Loch
 Guitarra: Kerstin Klein
 Baixo: Steffy (Stefanie) Spänkuch
 bateria: Pia Gottwals

Discografia

Álbuns
 Fräulein Wunder (2008)

Singles
 Wenn ich ein Junge wär
 Mein Herz ist Gift für Dich

Ligações externas

Bandas da Alemanha
Bandas formadas em 2006
Girl bands

redpajama_set_name: RedPajamaWikipedia


The Secretariat of the ICC International Court of Arbitration® periodically issues documents for the information of parties and arbitrators, as well as to aid in the conduct of proceedings under the ICC Rules. These notes, forms and checklists, which deal with various aspects of practice and procedure, are sent to participants at the relevant stages of the proceedings and are updated in accordance with changes in the Rules or developments in practice and procedure.
Below is a list of the Secretariat's principal notes, forms and checklists, copies of which can be found here.


The Flip Trap give you a convenient yet still portable place to set your tools while weaving. The Flip Trap installs into the ends of the loom sides, using the same holes as the clamps. We use it to hold our shuttles, threading hook, yarn and more. We love the trap and so will you!


Seagrass coffins have a light brown and beige hue with a subtle hint of green. They are suitable for burial or cremation. Each coffin will carry up to 159kg.
Sizes: 5'6" x 18", 5'8" x 20", 5'10" x 20", 6'0 x 22" all with a depth of 14" and 6'2" x 22", 6'2" x 24, 6'4" x 24" all with a depth of 15" and 6'8" x 26" with a depth of 16".


text:
Q: Prove that $M/N$ and $N$ are finitely generated $\Rightarrow M$ is finitely generated. Let $M$ be an $R$-module, and $N$ be it's submodule.
I need to prove that if both $M/N$ and $N$ are finitely generated, then so is $M$.
How to prove it? Don't have any ideas at the moment.

A: Suppose
$$N=\langle n_1,...,n_k\rangle\;,\;\;M/N=\langle m_1+N,...,m_r+N\rangle$$
Observe then that if we take any element $\;x\in M\;$ then exists $\;1\le i\le r\;$ and $\;n\in N\;$ with $\;x=m_i+n\;$ . But you can write that $\;n\;$ as $\;n=a_1n_1+\ldots+a_kn_k\;$ ....complete now.

A: Finite generation is the existence of something (do you know what ?).
This something for $N$ and $M/N$ gives a something for $M$. Do you see how ?

redpajama_set_name: RedPajamaStackExchange


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Andis 26700 Styliner II Trimmer. Features T-blade design, ideal for trimming around ears, beard and mustache. Powerful and very quiet. Contoured housing design, fits any hand comfortably. Perfect for all around shaping and trimming. Convenient thumb-controlled switch.