Reevaluation Phase €" in B2B sales it's common for offerings to involve contracts which will need to be renewed. As a customer becomes familiar with an offering, and notably as a contract draws to a close, a client will enter a reevaluation phase during which they will decide whether or not to renew their contract.
Sales funnels are the pathway that captures earnings prospects and moves from awareness of your product to interest, want and ultimately the sale. Here is how to make sales funnel to drive sales for your company. Creating sales funnel is one of the most essential things you will have to do as a company owner, and sadly one of these things that many small business owners neglect.|} If you are unfamiliar with this particular phrase, the sales funnel is a company' strategy for best prospects from the"I don't know you" stage to the"let us do business" stage. It does not just happen. You need to determine how to identify prospects, qualify themand then lead them in the purchase. Consider how the sales funnel is shaped. It is wide on one side and narrow on the other. The wide end"grabs" the liquid you pour into it and then gravity pulls the liquid through the thin end, leaving behind the residue of unqualified particles. The purpose is to drive interested parties into the wide end of your sales funnel so that you can qualify them as great prospects or identify them as"unwanted residue." To begin with, begin with defining your perfect customer. Create a questionnaire for your self that identifies the topics that your perfect customer has.
You'll need to create your own collection of qualifying questions. You are not going to explore this questionnaire with anyone; it's merely for your planning benefit. The goal here is to work out of your perfect client's wants and desires. Some people purchase flowers for weddings, so you might opt to identify people who are getting married or know someone who's getting married. Odds are, your company has a lot of different sorts of perfect clients, or prospects. You are going to want to identify all them. Just because a person fits into your perfect client demographic doesn't mean they are always an perfect client. Perhaps Bob and Jane are arranging a marriage but don't care about flower structures. They certainly wouldn't be on your potential range if this is the case.
The main thing is to understand what your client needs and what you have to do in order to deliver those benefits. To get to the first phase in your sales process, you have to believe backward from the point you want your client to end up. That is how you create your sales funnel.
ClickFunnels, sales funnel building software, gives businesses an easier way to sell and deliver their products and services. ClickFunnels makes the process far simpler for a company to market, by offering pre constructed attachment choices for services and products.
With ClickFunnels, it is simple to make a marketing and sales funnel from the ground as it incorporates all of the core components necessary to possess a practical and effective sales funnel. Typically using the older more traditional revenue funneling softwares, you might want to worry about all of the components. Together with ClickFunnels, this really is all in 1 spot, which makes it much simpler and cheaper than traditional funnels. ClickFunnels incorporates these and more, offering them at a comprehensive, unified bundle so you won't have to handle them one by one. Provided that you have a company, ClickFunnels has that funnel that is excellent for you.
ClickFunnels is our favorite tool, as|since} it simplifies the whole sales and marketing funnel process for businesses.There are so many different kinds of revenue funnels. Each of those needing to be created specifically for a specific client. Consequently, they ought to be assembled in a manner that they attract your preferred customer. There are funnels for webinars, earnings, membership sites, and contributor listing and each 1 is quite different from another. The wonderful thing is that ClickFunnels has you covered. Within ClickFunnels, users may select from many different pre-built attachment options. It's as straightforward as picking the one that aligns best with your organization. If you are trying to push an e-book, the approach should be much different than if you are hoping to sell a subscription. Even if the final effect of trying to make a sale is identical. ClickFunnels saves you time and attempt to start organizing your sales funnels from scratch and also accelerate your sales funnel installment. At any time you've selected your funnel, then you need to obtain a template. With ClickFunnels, you're treated to many different templates and all of these are tested and proven to work. With a throng of tested and proven templates available, ClickFunnels accelerates your A/B testing period since you don't need to weed out templates which are not performing. You may easily integrate videos, videos or animations in your template utilizing ClickFunnels easy to use interface. Then you can start performing your A/B testing to determine what works and what does not.


text:
Бомилькар (финик. 12px|דַ12px|ל12px|רְ) — мужское имя финикийского происхождения. Известные носители:
 Бомилькар (казнён в 308 году до н. э) — карфагенский военачальник и государственный деятель
 Бомилькар (упоминается в 210-х до н. э.) — военачальник карфагенян во время Второй Пунической войны
 Бомилькар (III век до н. э.) — карфагенский политический деятель (суффет)
 Бомилькар (II век до н. э.) — соратник нумидийского царя Югурты

redpajama_set_name: RedPajamaWikipedia


Bosch HC8510 SDS-max Rotary Hammer Core Concrete Bit 2" x 12". New w/ Tags.
Bosch HC8540 3-9/16" x 12" SDS-max Rotary Hammer Core Bit- Concrete. New.
Bosch SDS-max Rotary Hammer Core Concrete Bit 3-1/8'' x 12".
BOSCH 2608578765 SDS Plus Mixed Set In Aluminium Case 11 pics.
BOSCH HCSTP2061 SDS-plus Stop Bit 3/8 x 1-1/16"


First edition. Fine in price-clipped dust jacket. Short stories by the author known as "the Texan with the Mencken touch." A collection of pieces the author wrote for the Atlantic Monthly, Holiday, Life, and Harper's.The down home touch of a Texas boy surprised he really made it in the world of big names comes through in most of his articles, be they about politicians, football heroes, fading comics, country-western singers, lawyers, his father, being a Nieman Fellow at Harvard. An old-fashioned liberal rather sentimental about the passing of the good old days." Two especially fine stories are The Old Man and A Country Lawyer and How He Grew. Each of the stories is particularly good because of the author's close personal involvement with the subjects: his late father and an old dear friend named Warren Burnett. Splendid reading.


text:
Better Buy: Bellicum Pharmaceuticals, Inc. vs. bluebird bio
There's more than meets the eye to both of these CAR-T biotechs.
Brian Orelli
(TMFBiologyFool)
This version of our ongoing better buy series pits two development-stage biotechs, Bellicum Pharmaceuticals (NASDAQ:BLCM) and bluebird bio (NASDAQ:BLUE), against each other. The companies have something in common -- they're both developing chimeric antigen receptor T-cell (CAR-T) therapies to treat cancer -- but they've both got something else up their sleeves.
CAR-T technology and the related T cell receptor (TCR) technology both involve taking immune cells out of patients, inserting DNA that trains the immune cells to attack cancer cells expressing a certain protein, and then putting the cells back into the patient to do their work.
While both Bellicum Pharmaceuticals and Bluebird have therapies using CAR-T/TCR, they're not currently competing with each other directly because their respective CAR-T therapies train the immune cells against different targets expressed on different types of tumors.
CAR-T/TCR Therapy
Initial Disease(s)
BCMA
Bellicum
BPX-601
PSCA
PRAME
AML and MDS
Data sources: Company websites. BCMA = B-cell maturation antigen, PSCA = prostate stem cell antigen, PRAME = preferentially expressed antigen in melanoma, AML = acute myeloid leukemia, MDS = myelodysplastic syndromes.
The chart is a little bit of an alphabet soup with all the acronyms, but it's clear that there isn't much overlap between the two companies' strategies for now.
Image source: Getty Images.
Bellicum secret sauce
One of the problems with activating the immune system to attack a cancer is there are positive feedback loops through signaling molecules called cytokines that the immune system sends out to recruit additional cells. If CAR-T/TCR enabled cells get too overactive, they can create what's called a cytokine storm, which, if not stopped in time, can kill a patient.
Bellicum has developed a safety switch incorporated into the immune cells that can, depending on the construct, turn on or off the immune cells when the switch is activated by a drug called rimiducid, which otherwise has no effect on humans.
The biotech is actually using the safety switch in its lead product BPX-501, which uses immune cells to treat cancer but isn't a CAR-T. Instead, the switch is used to avoid a side effect of a treatment.
Many patients with blood cancers are given hematopoietic stem cell transplantation -- essentially, a patient's cancer and healthy cells are killed and replaced with a donor's immune cells -- but the transplant only works well when there's a perfect match between the donor and the patient. Otherwise, there's a chance of developing graft versus host disease (GVHD) when the donor's immune cells recognize the patient's cells as foreign and start attacking their host.
BPX-501 avoids the side effects of GVHD, which can be life-threatening, by using rimiducid to kill the donor cells, keeping them from further attacking the host. Initial results look promising, but the drug still needs to pass its pivotal clinical trial, which should read out in the second half of 2018 to gain approval in the EU. A separate trial will be required to gain approval in the U.S.
Here's Why Bellicum Pharmaceuticals Lost 13.8% in July
Better Buy: Bellicum Pharmaceuticals, Inc. vs. Alnylam Pharmaceuticals, Inc.
Here's Why Bellicum Pharmaceuticals Is Jumping Higher Today
Bluebird's (sort of) unrelated technology
CAR-T/TCR is a remarkable technology, and developing the DNA constructs that could be inserted into immune cells to train them to attack cancerous cells was pretty ingenious, but the technology still requires a key step: getting the DNA into the immune cells.
Bluebird has been working on that technical problem for a while in its gene therapy programs, which seek to express a protein in cells to replace a mutant or missing protein. The company has a couple of gene therapies, including Lenti-D for cerebral adrenoleukodystrophy and LentiGlobin, which treats beta thalassemia and sickle cell disease. The former is further along, but LentiGlobin, especially to treat sickle cell disease, is likely to be a better seller given the larger market.
Bluebird has run into some potency issues with LentiGlobin -- the gene therapy seems to work, but not for every patient -- so the company made some manufacturing changes that it believes will increase expression of the protein responsible for making the cells normal. Investors will get to hear about how the new manufacturing procedure is helping patients at the American Society of Hematology meeting in December.
Better buy?
There's certainly nothing keeping investors from buying both biotechs. Despite the CAR-T/TCR connection, there isn't enough overlap to really worry about one company hurting sales of the other.
But if I had to pick one based on current valuations, I'd give Bellicum the edge on a risk-reward basis given its smaller size. I like Bluebird's gene therapy programs, and its CAR-T is a nice bonus, albeit still early in development, but at a market cap of more than $6 billion, there's a lot of success already priced into the valuation. Bellicum is the riskier of the two, but the potential payoff is also greater.
BLCM
Bellicum Pharmaceuticals
NASDAQ:BLCM
Bluebird Bio
NASDAQ:BLUE
Is Bellicum Pharmaceuticals, Inc. a Buy?
Here's Why Bellicum Pharmaceuticals Dropped as Much as 14.6% Today
Better Buy: Bellicum Pharmaceuticals, Inc. vs. bluebird bio @themotleyfool #stocks $BLCM $BLUE Next Article

redpajama_set_name: RedPajamaCommonCrawl


text:
Article| May 01 1915
THE WIDE-SPREAD DISTRIBUTION OF DIPHTHEROIDS AND THEIR OCCURRENCE IN VARIOUS LESIONS OF HUMAN TISSUES
William H. Harris,
William H. Harris
From the Laboratories of Pathology and Bacteriology of Tulane University of Louisiana, and the Charity Hospital, New Orleans.
H. Windsor Wade
Received: January 14 1915
Copyright, 1915, by The Rockefeller Institute for Medical Research New York
J Exp Med (1915) 21 (5): 493–508.
https://doi.org/10.1084/jem.21.5.493
William H. Harris, H. Windsor Wade; THE WIDE-SPREAD DISTRIBUTION OF DIPHTHEROIDS AND THEIR OCCURRENCE IN VARIOUS LESIONS OF HUMAN TISSUES . J Exp Med 1 May 1915; 21 (5): 493–508. doi: https://doi.org/10.1084/jem.21.5.493
It is evident from this work and from the work of others that organisms having diphtheroidal morphology are wide-spread in their distribution in the human body. They are readily isolated from miscellaneous skin lesions, probably thriving better in pathological soils as saprophytes than in normal skin, although they can be obtained quite easily from the latter. Various strains can also be cultivated from the air, at least in this environment.
Aside from the air and superficial parts of the human body, diphtheroids have frequently been isolated from the deeper regions. Hoag, working on general paresis and certain conditions of the lung, cultivated 199 diphtheroids, the majority of which were from the lungs and respiratory tract, also in some instances from the liver and spleen. He considered 146 of these isolations to be identical and classified them as organism x. Robertson, McRae, and Jeffry likewise in cases of dementia paralytica isolated what they considered an identical strain which was closely related to the Klebs-Loeffler bacillus, from the inflamed ileum, stomach, tonsils or pharynx, bronchi, lung, and brain. They differentiated their organism from Bacillus hoffmanni and Bacillus xerosis.
The fact that these organisms have a somewhat unusual morphology, resembling as they do an organism of known pathogenicity, namely. Bacillus diphtheriœ, should form no basis for assuming that they, too, are apt to possess these qualities. When we consider the number of simple bacillary contaminators analogous to such organisms as Bacillus anthracis, Bacillus typhosus, etc., we can readily see how frequently this occurs.
The majority of the diphtheroids isolated by us stai??? by Gram's method; nearly all fail to resist the standard acid-fast methods, although use of the very low strengths of mineral acids allows the fixed stain to remain in whole or in part. There is consequently nothing unique in their tinctorial properties.
These bacillary strains differ considerably in their powers of cultivation. While the majority grow readily upon the ordinary laboratory foodstuffs, others require special products for their growth and still others cannot be grown even where special effort has been made. The fact that many strains grow slowly no doubt enhances their consideration as disease producers, as it seems to argue their difficult adaptation from their preëxisting site to an artificial environment. This reasoning does not apply when we consider the numerous causal agents that can so readily be cultivated directly from the diseased tissue, and again the fact that many saprophytes in their natural habitat are incapable of growth in vitro (figure 1).
The most striking of the biological features of these cultures is their wide range of pigment production. While many are white or creamy white, the majority range from a canary yellow to a distinct crimson, and one of the cultures recovered from a leper was a very deep dusky red or garnet. Numerous combined shades of yellow and pink, including such colors as salmon and orange, were present. Some cultures were distinctly pink, others varied in depth of color to a crimson. While many cultures of identical colors were obtained, the majority of strains showed some slight variance of shade.
While, of course, the inoculation of diphtheroidal cultures produces varying degrees of localized inflammation if employed in sufficient dosage, probably for the two-fold reason of acting as a foreign body and liberating proteolytic substances, still the diphtheroids isolated in the past have never been able to reproduce the clinical picture of the various diseases from which they were cultivated. The apparent reproduction of lesions in general paresis, in hepatic cirrhosis, and in leprosy does not form an ultimate postulate for the acceptance of organisms as specific etiological entities. This is evidenced by the fact that certain known saprophytic organisms when used as controls are capable of producing the same results.
It seems clear that organisms as broadly distributed as the diphtheroids should be suspected as contaminators when met in experiments bearing upon etiology. They should be viewed primarily in the same light as the staphylococcus and the various known contaminating bacteria. It is apparent that this type of organism has been regarded too much from the standpoint of pathogenicity. It is, of course, probable that among this large group there may be a few pathogenic types.
A CONTRIBUTION TO THE BACTERIOLOGY OF ACUTE ANTERIOR POLIOMYELITIS
NASOPHARYNGEAL FLORA IN HEALTH AND DURING RESPIRATORY DISEASE IN ISOLATED COMMUNITIES IN ALABAMA AND LABRADOR
STREPTOCOCCI IN INFECTIOUS (ATROPHIC) ARTHRITIS AND RHEUMATIC FEVER


Prominent artists, art collectors, curators, gallery owners, celebrities, and philanthropists from around the world gather in Aspen every year during the first week in August to celebrate ArtCrush, the Aspen Art Museum's annual summer benefit.
ArtCrush has evolved into a week full of social events aimed at engaging the arts community here in Aspen and around the globe. An eagerly anticipated event that quickly sells out, the benefit features a remarkable wine tasting and auction, seated dinner for 350 guests, and both a live and silent auction of major works of contemporary art. The live auction will once again be conducted by Tobias Meyer, Sotheby's Europe Deputy Chairman, Worldwide Head of Contemporary Art and Principal Auctioneer.
This extremely limited attendance event features amazing and rare vintages paired with gourmet delights. Dine with world-renowned master sommeliers as they guide guests through a remarkable evening of wine and food.
This event is 100% underwritten—every dollar goes directly to the AAM.
A cocktail reception at Aspen's Baldwin Gallery to preview fabulous ArtCrush live auction artworks.
ArtCrush, Aspen's premier summer event benefiting the Aspen Art Museum features the 2011 Aspen Award for Art presentation to Roni Horn. The evening features a wine tasting of rare vintages, a silent auction, an elegant multicourse dinner, and a live auction hosted by Sotheby's world-renowned auctioneer, Tobias Meyer.
Join us immediately after the main event for an incredible dance party at Syzygy City! Features a hosted full bar and musical entertainment by celebrity DJ Samantha Ronson.
ArtAspen 2011 opens the day following the conclusion of ArtCrush, enabling guests and AAM members to attend with the museum's full endorsement.
In addition to the gala and auction, each year the AAM presents the Aspen Award for Art to an important contemporary artist. This year's celebration culminates with the Friday, August 5, presentation of the 2011 Aspen Award for Art to renowned artist Roni Horn. Distinguished artists such as Richard Tuttle, Tony Feher, Jim Hodges, Ed Ruscha, Fred Tomaselli, and Marilyn Minter have been honored in the past.
For more than thirty years, artist Roni Horn has made work that combines conceptual rigor and formal beauty, often exploring issues of gender, identity, and the complex relationship between object and subject. Horn works in a variety of media, including photography and sculpture, creating intricate relationships between the viewer and her work by installing a single piece on opposing walls, in adjoining rooms, or throughout a series of buildings. Many works are composed of pairs, multisided parts, or series that invite comparison between their elements. The diversity of Horn's works reflects her ongoing exploration of how one's identity and memory can be as changeable and fleeting as flowing water, weather, and time.
Roni Horn was born in New York in 1955, and lives and works in New York. She received a BFA from the Rhode Island School of Design and an MFA from Yale University. She received the CalArts/Alpert Award in the Arts, several NEA fellowships, and a Guggenheim fellowship. She has had one-person exhibitions at the Art Institute of Chicago; Centre Georges Pompidou, Paris; Dia Center for the Arts, New York; and Whitney Museum of American Art, New York, among others. Group exhibitions include the Whitney Biennial (1991, 2004); Documenta (1992); and Venice Biennale (1997), among others.
Seating at a Connoisseur Table for two (2). Includes two (2) tickets to AfterPartyCrush.
Seating at a Connoisseur Table for one (1). Includes one (1) ticket to AfterPartyCrush.
Join us at 10 p.m. for an incredible dance party at Syzygy City featuring a hosted full bar and musical entertainment by celebrity DJ Samantha Ronson.
This wine tasting and gourmet dinner hosted by John and Amy Phelan is sponsored by Sotheby's and is limited to 150 guests.


text:
Q: Route User Role Laravel 5.4 I'm very confused on this situation. I have two routes with on resource name.
Route::resource('product', 'Product\AreaManagerProductController');
Route::resource('product', 'Product\SystemAdminProductController');

I need to make it as one because I have a contextual binding.
$this->app->when(AreaManagerProductController::class)
          ->needs(ProductInterface::class)
          ->give(AreaManagerProductRepository::class);

           $this->app->when(SystemAdminProductController::class)
          ->needs(ProductInterface::class)
          ->give(SystemAdminProductRepository::class);

The contextual binding works fine... but I need to change my route like this.
Route::resource('product_area_manager', 'Product\AreaManagerProductController');
Route::resource('product_system_admin', 'Product\SystemAdminProductController');

I created ProductController and some kind of weird solution.
public function index(){

        //Create a conditional statement base on user

        return app('App\Http\Controllers\Product\AreaManagerProductController')->index();

    }

It may work but it doesn't trigger the middleware... What could be the best practice on this situation. TY

A: You can have your Route like this
Route::group(['prefix' => 'product', 'namespace' => 'Product', 'middleware' => '<your middleware>'], function() {

        Route::resource('area_manager', 'AreaManagerController');
        Route::resource('system_admin', 'SystemAdminController');
});

The reason I grouped the route is to reduce redundancy, and the reason i removed Product from the controller name is, as there is a namespace Product already, there is no need of long Class names.
If you wan to access some methods in the AreaManagerController and SystemAdminController just extend the ProductController to these Controllers.
If you want to add some specific middleware for the actions inside these controllers, I have added a middleware clause in the route group which will affect to these controllers, if not needed just remove it.
Hope this helps you.

redpajama_set_name: RedPajamaStackExchange


Lynn Tredeau is an American musician who lives and performs in the Pacific Northwest. She got an early start in music and by the time she was six, her parents arranged for a surprise delivery of her first piano.
The surprise part was ruined when Lynn took the call from the delivery company confirming the arrival of her piano, but that didn't dampen her enthusiasm for playing. She was a natural musician and by the time she was sixteen, Lynn had mastered classical music on her piano, played guitar for her school's jazz band, flute and clarinet in the orchestra, saxophone in the marching band, and played hymns on the pipe organ at church. Early musical influences range from artists like Nate King Cole to bands like Creedence Clearwater Revival.
After discovering the music of Michele McLaughlin on Pandora, Lynn found her calling in the world of New Age music. She released her debut album, Echoes of Life, in January, 2015, which led to her nomination of Best New Artist 2015 by Enlightened Piano. Echoes climbed to #1 on Spa Channel & #2 on One World Music Radio top 100 and this debut album was nominated for Best Solo Piano Album on One World Music Radio. Lynn's second album, SnowLight (A Christmas Memory), was released in September 2015 and it quickly went to #1 on OWMR. This holiday album was nominated for Album of the Year on SoloPiano.com, One World Music Radio and won Best Holiday Album 2016 at Enlightened Piano Radio. In April of 2016, A New Dream became her third release. A New Dream has nominations for Album of the Year at SoloPiano.com, Best Solo Piano Album and Album of the Year at One World Music Radio and has charted in the top 10 for 8 months at OWMR. She has received glowing reviews: Kathy Parsons of Mainly Piano wrote, "Her music is gentle, melodic and very accessible. Many of her pieces have a quiet hymn-like quality" and Steve Sheppard from One World Music Radio said, "She has a style that is both gentle and artistically clever…" Dana Wright at New Age Music Reviews noted, "The art of sharing emotion through music has to be one of this artist's greatest talents...." Lynn's eagerly anticipated fourth album will be released in spring 2017 and is promising to be her best work yet.
Listen to Lynn Tredeau now.


Wisdom is the knowledge that allows people to live truly and happily, to experience inner stillness and greater depth of being.
Join like-minded people in exploring how to apply this knowledge to your life. Evolve your understanding and experience of this timeless wisdom through guided discussion and practical exercises in a supportive group setting.
Welcome to the School of Philosophy, Melbourne!
Practical Philosophy explores the meaning of wisdom, truth and consciousness and the real nature of the human being.
It draws from the great philosophical teachings of the East and West to help us enjoy a deeper understanding of ourselves, our world and our fellow mankind.
Practical Philosophy offers students an effective and novel approach to the great questions of life: Who am I? How can I be truly happy? How can I be at peace? What is the purpose of my life? How may I realise my full potential?
The School of Philosophy, Melbourne, has been offering courses in practical philosophy since 1977.
The School began in London in 1936 when a small group of people came together to study economics, seeking an understanding of the universal laws that govern the relations between people in society. They hoped to discover principles that would help to eliminate the social ills prevailing at that time.
This inquiry soon led to the study of Philosophy, and the School's philosophy courses are now widely available.
Take a look around the School of Philosophy's Hawthorn premises in this 360° tour. You can click the toggle icon (top right) to view full screen. Take more tours here.
In addition to the regular Philosophy classes and classes on a range of other subjects, the School regularly hosts events—one-off talks, lectures and gatherings in good company—for the enjoyment of students and their family and friends.
Upcoming events are listed here, and also on our dedicated Events page. Some of our most popular featured events also have their own pages, so that you can learn more about them.
Details of scheduled events are yet to be finalised, but will be coming soon!
The Lifestyle & Culture Lecture Series presents unique and exciting talks that explore issues of health and well-being, the arts and society, and the quest for happiness and self-knowledge.
An informative, experiential and interactive course, exploring not just the theory, philosophy and science of mindfulness but also how to apply it to all aspects of life.
The Cultural Day is a wonderful opportunity for 1st, 2nd and 3rd year students—along with family and friends—to take part in a range of workshops spanning the arts and sciences.
Erasmus Primary School was established in 1996 with the support of the School of Philosophy, and is now a thriving concern in the heart of Hawthorn, with nine sister schools around the world.


The Bachelor's degree programs in Marine Sciences at UConn are designed to inspire you intellectually and challenge you academically. The core of the curriculum integrates courses in marine biology, chemistry, geology, and physics. Students specialize in a subdiscipline of the marine sciences through upper level Marine Sciences electives and through independent study with Marine Sciences faculty. Student's scientific training is bolstered with courses in policy, law, economics, and resource management of the oceans. The program is quantitative, practical, and experiential in nature. Starting the first semester, most of the courses in the major include work in many of the region's various marine habitats. Learning through hands-on experiences, you'll get your feet wet and your hands dirty. The program is analogous to a rigorous environmental sciences degree, but focused on the environment that covers more than two-thirds of the planet….the oceans.
Students may pursue either a Bachelors of Science (BS) or Bachelors of Arts (BA) major in Marine Sciences. A number of our graduates have gone on to a variety of occupations with either the BS or the BA. Although there are no hard and fast rules about the BS vs BA, Students who elect the BS track typically want careers doing science and/or choose to continue on to graduate school in the sciences. Students in the BA track are typically interested in applying the marine sciences to management, or policy efforts. In practical terms, the BS requires more quantitative classes and the BA requires more social science courses focused on the oceans.
Either degree can be started at the Avery Point or Storrs campuses. Students who elect to begin at Storrs typically transition to Avery Point campus to complete the final two years of their Marine Sciences degree. Avery Point, UConn's marine and maritime campus, is located on the shores of Long Island Sound. It is an environment immersed in research, outreach, and marine education. It is home to UConn's fleet of research vessels, state-of-the art laboratories, and oceanographic support facilities in the Department of Marine Sciences.
To view our brochure please click here!


text:
\section{Introduction}
\ \ \ Let $\Sigma_{g,b}$ be an closed orientable surface of genus $g\geq 1$ with arbitrarily chosen $b$ points (which we call punctures). Let $\rm Mod(\Sigma_{\textit{g,b}})$ be the mapping class group of $\Sigma_{g,b}$, which is the group of homotopy classes of
orientation-preserving homeomorphisms preserving the set of punctures. Let $\rm Mod^{\pm}(\Sigma_{\textit{g,b}})$ be the extended mapping class group of $\Sigma_{g,b}$, which is the group of homotopy class of all
(including orientation-reversing) homeomorphisms preserving the set of punctures. By $\rm Mod_{\textit{g,b}}^{0}$ we will denote  the subgroup of $\rm Mod_{\textit{g,b}}$ which fixes the punctures pointwise. It is clear that we have
the exact sequence:
\begin{center}
$1 \rightarrow  \rm Mod_{\textit{g,b}}^{0} \rightarrow \rm Mod_{\textit{g,b}} \rightarrow Sym_{\textit{b}} \rightarrow 1,$
\end{center}
where the last projection is given by the restriction of a homeomorphism to its action on the puncture points.\\
\ \ \ The study of the generators for the mapping class group of a closed surface was first considered by Dehn. He proved in [De] that $\rm Mod(\Sigma_{\textit{g},0})$ is generated by a finite set of Dehn twists.
Thirty years later, Lickorish [Li] showed that $3\textit{g}-1$ Dehn twists generate $\rm Mod_{\textit{g},0}$. This number was improved to $2\textit{g}+1$ by Humphries [Hu]. Humphries proved, moreover, that in fact the number $2\textit{g}+1$ is minimal;
i.e. $\rm Mod(\Sigma_{\textit{g},0})$ cannot be generated by $2g$ (or less) Dehn twists. Johnson [Jo] proved that the $2g+1$ Dehn twists also generate $\rm Mod(\Sigma_{\textit{g},1})$.
In the case of multiple punctures the mapping class group can be generated by $2g+b$ Dehn twists for $b\geq 1$ (see [Ge]).\\
\ \ \ It is possible to obtain smaller generating sets of $\rm Mod(\Sigma_{\textit{g,b}})$ by using elements other than twists. N.Lu (see [Lu]) constructed a generated  set of
$\rm Mod(\Sigma_{\textit{g},0})$ consisting of 3 elements. This result was improved by Wajnryb who found the smallest possible generating set of $\rm Mod(\Sigma_{\textit{g},0})$
consisting of 2 elements (see [Wa]). Korkmaz proved in [Ko] that one of these generators can be taken as a Dehn twist. It is also known that in the case of $b=0$ the mapping class group
can be generated by 3 torsion elements (see [BF]). More, Korkmaz showed in [Ko] that the mapping class group can be generated by 2 tosion elements (also in the case of $b=0,1$).
In [Ma], Maclachlan proved that the moduli space is simply connected as a topological space by showing that $\rm Mod(\Sigma_{\textit{g},0})$ is generated by torsion elements.
Several years later Patterson generalized these results to $\rm Mod(\Sigma_{\textit{g,b}})$ for $g\geq 3, b\geq 1$ (see [Pa]).\\
\ \ \ In [MP], McCarthy and Papadopoulos proved that $\rm Mod(\Sigma_{\textit{g},0})$ is generated by infinitely
many conjugetes of a single involution for $g\geq 3$. Luo, see [Luo], described the finite set of involutions which generate $\rm Mod(\Sigma_{\textit{g,b}})$ for $g\geq 3$.
He also proved that $\rm Mod(\Sigma_{\textit{g,b}})$ is generated by torsion elements in all cases except $g=2$ and $b=5k+4$, but this group is not generated by involutions if $g\leq 2$.
Brendle and Farb proved that $\rm Mod(\Sigma_{\textit{g,b}})$ can be generated by 6involutions for $g\geq 3,b=0$ and $g\geq 4,b\leq 1$ (see [BF]). In [Ka], Kassabov proved that for every $b$
$\rm Mod(\Sigma_{\textit{g,b}})$ can be generated by 4 involutions if $g\geq 8$, 5 involutions if $g\geq 6$ and 6 involutions if $g\geq 4$. He also proved in the case of $\rm Mod^{\pm}(\Sigma_{\textit{g,b}})$.\\
Our main result is stronger than [Ka].
\begin{maintheorem}
For all $g\geq 3$ and $b\geq 0$, the mapping class group $\rm Mod({\Sigma_{\textit{g,b}}})$ can be generated by:\\
\ \ \ $(a)$ $4$ involutions if $g\geq 7$;\\
\ \ \ $(b)$ $5$ involutions if $g\geq 5$.
\end{maintheorem}

\section{Preliminaries}
\ \ \ Let $c$ be a simple closed curve on $\Sigma_{g,b}$.
Then the (right hand) Dehn twist $T_{c}$ about $c$ is the homotopy class of the homeomorphism obtained
by cutting $\Sigma_{\textit{g,p}}$ along $c$, twisting one of the side by $360^{\circ}$ to the right and gluing two sides of a back to each ohter. Figure 1 shows the Dehn twist about the curve $c$.
\begin{figure}[htbp]
 \begin{center}
  \includegraphics*[width=10cm]{T.eps}
 \end{center}
 \caption{The Dehn twist}
 \label{fig:one}
\end{figure}
We will denote by $T_{c}$ the Dehn twist around the curve $c$. \\
\ \ \ We record the following lemmas.
\begin{lemma}
For any homeomorphism $h$ of the surface
$\Sigma_{g,b}$ the twists around the curves $c$ and $h(c)$ are conjugate in the mapping class group $\rm Mod(\Sigma_{\textit{g,b}})$,
\begin{eqnarray*}
T_{h(\textit{c})}&=&hT_{\textit{c}}h^{-1}.
\end{eqnarray*}
\end{lemma}
\begin{lemma}
Let $c$ and $d$ be two simple closed curves on $\Sigma_{g,b}$. If $c$ is disjoint from $d$, then
\begin{eqnarray*}
T_{c}T_{d}=T_{d}T_{c}
\end{eqnarray*}
\end{lemma}

\section{Proof of main theorem}
In this section we proof maintheorem. The keypoints of proof are to generate $T_{\alpha}$ in 4 involutions by using lantern relation.

\subsection{The policy of proof}
We give the policy of proof of maintheorem.
\begin{lemma}
Let $G$, $Q$ denote the groups and let $N, H$ denote the subgroups of $G$. Suppose that the group $G$ has the following exact sequence;
\begin{eqnarray*}
1 \rightarrow N \xrightarrow[]{i} G \xrightarrow[]{\pi} Q \rightarrow 1.
\end{eqnarray*}
If $H$ contains $i(N)$ and has a surjection to $Q$ then we have that $H=G$.
\end{lemma}
\begin{proof}
We suppose that there exists some $g\in G-H$. By the existence of surjection from $H$ to $Q$, we can see that there exists some $h\in H$ such that $\pi(h)=\pi(g)$.
Therefore, since $\pi(g^{-1}h)=\pi(g)^{-1}\pi(h)=1$, we can see that $g^{-1}h\in \rm Ker \ \pi= Im \ \textit{i}$. Then there exists some $n\in N$ such that $i(n)=g^{-1}h$.
By $i(N)\subset H$, since $i(n)\in H$ and $h\in H$, we have
\begin{eqnarray*}
g=h\cdot i(n)^{-1}\in H.
\end{eqnarray*}
This is contradiction in $g\notin H$. Therefore, we can prove that $H=G$.
\end{proof}
It is clear that we have the exact sequence:
\begin{eqnarray*}
1 \rightarrow  \rm Mod_{\textit{g,b}}^{0} \rightarrow \rm Mod_{\textit{g,b}} \rightarrow Sym_{\textit{b}} \rightarrow 1.
\end{eqnarray*}
Therefore, we can see the following corollary;
\begin{corollary}
Let $H$ denote the subgroup of $\rm Mod(\Sigma_{\textit{g,b}})$, which contains $\rm Mod^{0}(\Sigma_{\textit{g,b}})$ and has a surjection to $\rm Sym_{\textit{b}}$. Then H is equal to $\rm Mod(\Sigma_{\textit{g,b}})$.
\end{corollary}
We generate the subgroup $H$ which has the condition of corollary 4 by involutions.\\
\ \ \ \ Let us embed our surface $\Sigma_{g,b}$ in the Euclidian space in two different ways as shown on Figure 2. (In these pictures we will assume that
genus $g=2k+1$ is odd and the number of punctures $b=2l+1$ is odd. In the case of even genus we only have to swap the top parts of the pictures, and in the case of even
number of punctures we have to remove the last point.)\\
\ \ \ In Figure 2 we have also marked the puncture points as $x_{1},\ldots,x_{b}$ and we have the curves $\alpha_{i}$, $\beta_{i}$, $\gamma_{i}$ and $\delta$.
The curve $\alpha_{i}$, $\beta_{i}$, $\gamma_{i}$ are non separating curve and $\delta$ is separating curve.\\
\ \ \ Each embedding gives a natural involution of the surface---the half turn rotation around its axis of symmetry. Let us call these involutions $\rho_{1}$
and $\rho_{2}$.\\
\begin{figure}[htbp]
 \begin{center}
  \includegraphics*[width=13cm]{f1plus.eps}
 \end{center}
 \caption{The embeddings of the surface $\Sigma_{g,b}$ in Euclidian space used to define the involutions $\rho_{1}$ and $\rho_{2}$.}
 \label{fig:one}
\end{figure}
\ \ \ Then we can get following lemma;
\begin{lemma}
The subgroup of the mapping class group be generated by $\rho_{1}$, $\rho_{2}$ and 3 Dehn twists $T_{\alpha}$, $T_{\beta}$ and $T_{\gamma}$ around one
of the curve in each family contains the subgroup $\rm Mod^{0}(\Sigma_{\textit{g,b}})$.
\end{lemma}
We postopne the proof of lemma 5 until Section 5.\\
\ \ \ The existence a surjection from the subgroup $H$ of $\rm Mod(\Sigma_{\textit{g,b}})$ to $\rm Sym_{\textit{b}}$ is equivalent to showing taht the $\rm Sym_{\textit{b}}$
can be generated by involutions;
\begin{eqnarray*}
r_{1}&=&(1,\textit{b}-1)(2,\textit{b}-2)\cdots (\textit{l},\textit{l}+1)(\textit{b}) \\
r_{2}&=&(2,\textit{b}-1)(3,\textit{b}-2)\cdots (\textit{l},\textit{l}+2)(1)(\textit{l}+1)(\textit{b}) \\
r_{3}&=&(1,\textit{b})(2,\textit{b}-1)(3,\textit{b}-2)\cdots (\textit{l},\textit{l}+2)(\textit{l}+1)
\end{eqnarray*}
corresponding to 3 involutions in $H$.
\begin{lemma}
The symmetric group $\rm Sym_{\textit{b}}$ is generated by $r_{1}, r_{2}$ and $r_{3}$.
\end{lemma}
\begin{proof}
The group generated by $r_{i}$ contains the long cycle $r_{3}r_{1}=(1,2,\ldots,\textit{b})$ and transposition $r_{3}r_{2}=(1,\textit{b})$. These two elements generate the whole symmetric group, therefore
the involutions $r_{i}$ generate $\rm Sym_{\textit{b}}$.
\end{proof}
We note that the images of $\rho_{1}$ and $\rho_{2}$ to $\rm Sym_{\textit{b}}$ are $r_{1}$ and $r_{2}$.\\
\ \ \ Therefore, by Lemma 1, Corollary 4, Lemma 5 and Lemma 6 we sufficient to generate $H$ by $\rho_{1}$, $\rho_{2}$ and involutions which have the following conditions;
\begin{description}
\item[$\langle 1 \rangle$] involutions which genarate the Dehn twist around $\gamma$,
\item[$\langle 2 \rangle$] two of each involutions which exchange $\alpha$ and $\beta$, $\beta$ and $\gamma$, $\gamma$ and $\alpha$,
\item[$\langle 3 \rangle$] involution whose image is $r_{3}$.
\end{description}

\subsection{Generating Dehn twists by 4 involutions}
\ \ \ In this subsection, we argue about $\langle 1 \rangle$. Moreover, we generate Dehn twists by 4 involutions. The basic idea is to use the lantern relation.\\
\ \ \ We begin by recalling the lantern relation in the mapping class group. This relation was first discovered by Dehn and later
rediscovered by Johnson. \\

\begin{figure}[htbp]
 \begin{center}
  \includegraphics*[width=4.5cm]{lan.eps}
 \end{center}
 \caption{Lantern}
 \label{fig:one}
\end{figure}
From now on we will assume that the genus $g$ of the surface is at least 5.\\
\ \ \ Let the $S_{0,4}$ be a surface of genus 0 with 4 boundary components. Denote by $a_{1}, a_{2}, a_{3}$ and $a_{4}$ the four boundary
curves of the surface $S_{0,4}$ and let the interior curves $y_{1}, y_{2}$ and $y_{3}$ be as shown in Figure 3.\\
\ \ \ The following relation:
\begin{eqnarray}
T_{y_{1}}T_{y_{2}}T_{y_{3}}=T_{a_{1}}T_{a_{2}}T_{a_{3}}T_{a_{4}}.
\end{eqnarray}
among the Dehn twists around the curves $a_{i}$ and $y_{i}$ is known as the lantern relation. Notice that the curves $a_{i}$ do not
intersect any other curve and that the Dehn twists $T_{a_{i}}$ commute with every twists in this relation. This allows us to
rewrite the lantern relation as follows
\begin{eqnarray}
T_{a_{4}}=(T_{y_{1}}T_{a_{1}}^{-1})(T_{y_{2}}T_{a_{2}}^{-1})(T_{y_{3}}T_{a_{3}}^{-1}).
\end{eqnarray}
\ \ \ Let $R$ denote the product $\rho_{2}\rho_{1}$. By Figure 2 we can see that $R=\rho_{2}\rho_{1}$ acts as follows:
\begin{eqnarray}
 R\alpha_{\textit{i}}&=&\alpha_{\textit{i}+1},  \ (1\leq \textit{i}<\textit{g})\nonumber \\
 R\beta_{\textit{i}}&=&\beta_{\textit{i}+1},   \ (1\leq \textit{i}<\textit{g})\\
 R\gamma_{\textit{i}}&=&\gamma_{\textit{i}+1},  \ (1\leq \textit{i}<\textit{g}-1).\nonumber
\end{eqnarray}
\ \ \ The lanterns $S$ and $R^{-2}S$ have a common boundary component $a_{1}=R^{-2}a_{2}$ and their union is a surface $S_{2}$ homeomorphic to a sphere with 6 boundary components. By Figure 4 we can see that there exists an involution $\bar{J}$ of $S_{2}$ which takes $S$ to $R^{-2}S$.\\
\ \ \ Let us embed the surface $S_{2}$ in $\Sigma_{g,b}$ as shown on Figure 5. The boundary components of $S_{2}$ are $a_{1}=\alpha_{k}$, $a_{2}=\alpha_{k+2}$, $a_{3}=\gamma_{k+1}$, $a_{4}=\gamma_{k}$, $R^{-2}a_{1}=\alpha_{k-2}$, $R^{-2}a_{2}=\alpha_{k}$, $R^{-2}a_{3}=\gamma_{k-1}$ and $R^{-2}a_{4}=\gamma_{k-2}$; and the middle curve $y_{1}=\alpha_{k+1}$.
The Figure 5 shows the existence of the involution $\tilde{J}$ on the complement of $S_{2}$ which is a surface of genus $g-5$ with 6 boundary components. Gluing together $\bar{J}$ and $\tilde{J}$ gives us the involution $J$ of the surface $\Sigma_{g,b}$. By Figure 4 $J$ acts as follows
\begin{eqnarray*}
J(a_{1})=R^{-2}a_{2}, \ J(a_{3})=R^{-2}a_{1}, \ J(y_{1})=R^{-2}y_{2}, \ J(y_{3})=R^{-2}y_{1}.
\end{eqnarray*}
Therefore, we have
\begin{eqnarray}
R^{2}J(a_{1})=a_{2}, \ R^{2}J(y_{1})=y_{2} \nonumber \\
JR^{-2}(a_{1})=a_{3}, \ JR^{-2}(y_{1})=y_{3}.
\end{eqnarray}
Let $\rho_{3}$ denote $T_{a_{1}}\rho_{2}T^{-1}_{a_{1}}$.\\
By Lemma 1, (4) and that $\rho_{2}$ sends $a_{1}=\alpha_{k}$ to $y_{1}=\alpha_{k+1}$, we have
\begin{eqnarray}
T_{y_{1}}T_{a_{1}}^{-1}=\rho_{2}T_{a_{1}}\rho_{2}T^{-1}_{a_{1}}=\rho_{2}\rho_{3},\nonumber \\
T_{y_{2}}T^{-1}_{a_{2}}=R^{2}J\rho_{2}\rho_{3}JR^{-2}, \ T_{y_{3}}T^{-1}_{a_{3}}=JR^{-2}\rho_{2}\rho_{3}R^{2}J.
\end{eqnarray}
By (2) and (5) we have
\begin{eqnarray}
T_{\gamma_{\textit{k}}}=(\rho_{2}\rho_{3})(R^{2}J\rho_{2}\rho_{3}JR^{-2})(JR^{-2}\rho_{2}\rho_{3}R^{2}J).
\end{eqnarray}
\begin{figure}[htbp]
 \begin{center}
  \includegraphics*[width=7cm]{f10.eps}
 \end{center}
 \caption{$S_{2}$ and the involution $\bar{J}$}
 \label{fig:one}
\end{figure}
\begin{figure}[htbp]
 \begin{center}
  \includegraphics*[width=12cm]{f11plus.eps}
 \end{center}
 \caption{The involution $J$ on $\Sigma_{g,b}$}
 \label{fig:one}
\end{figure}

\subsection{Genus at least 5}
\ \ \ We proof that the mapping class group is generated by 5 involutions.\\
\ \ \ The five involutions are $\rho_{1}, \rho_{2}, \rho_{3}, J$ and another involution $I$. We construct involution $I$ in the same way as involution $J$ like Figure 6.
\begin{figure}[h]
 \begin{center}
  \includegraphics*[width=8cm]{f9plus.eps}
 \end{center}
 \caption{The involution $I$ on $\Sigma_{g,b}$}
 \label{fig:one}
\end{figure}
\begin{theorem}
If $g\geq 5$, the group $G_{3}$ generated by $\rho_{1}$, $\rho_{2}$, $\rho_{3}$, $I$ and $J$ is the whole mapping class group $\rm Mod(\Sigma_{\textit{g,b}})$.
\end{theorem}
\begin{proof}
By the relation (6) we satisfy the condition $\langle 1 \rangle$. Since $J$ sends $\alpha_{k-2}$ to $\gamma_{k+1}$ and $I$ sends $\alpha_{k}$ to $\beta_{k+1}$, we consist the condition $\langle 2 \rangle$.
We can also see that we satisfy the condition $\langle 3 \rangle$ from a way to the construction of the involution $J$.\\
\ \ \ Therefore, we can finish the proof of the theorem because we can satisfy the conditions in 3.1.
\end{proof}

\subsection{Genus at least 7}

\begin{figure}[htbp]
 \begin{center}
  \includegraphics*[width=12cm]{f13.eps}
 \end{center}
 \caption{The involution $J^{\prime}$ on $\Sigma_{g,b}$}
 \label{fig:one}
\end{figure}

\ \ \ We want to improve the above argument and show that for the genus $g\geq 7$ we do not need the involution $I$ in order to generate the mapping class group.
Assume that the genus of the surface is at least 7.\\
\ \ \ The $S_{2}$ and two pairs of pants have common boundary components $R^{-2}a_{1}$ and $a_{3}$ and their union is a surface $S_{3}$ homeomorphic to a sphere with 8 boundary components.
Figure 7 shows the existence of the involution $\bar{J^{\prime}}$ on $S_{3}$ which extends the involution $\bar{J}$ on $S_{2}$. \\
\ \ \ Let us embed $S_{3}$ in the $\Sigma_{g,b}$ as shown on Figure 7. From Figure 7 we can find the involution $\tilde{J^{\prime}}$ of the complement of $S_{3}$. Let $J^{\prime}$ be
the involution obtained by gluing together $\bar{J^{\prime}}$ and $\tilde{J^{\prime}}$. Moreover, from Figure 7 we can construct $J^{\prime}$ which acts on the punctures as the involution $r_{3}$.

\begin{theorem}
If $g\geq 7$, the group $G_{4}$ generated by $\rho_{1}$, $\rho_{2}$, $\rho_{3}$ and $J^{\prime}$ is the whole mapping class group $\rm Mod(\Sigma_{\textit{g,b}})$.
\end{theorem}

\begin{proof}
From the construction of $J^{\prime}$ we have
\begin{eqnarray*}
T_{\gamma_{\textit{k}}}=(\rho_{2}\rho_{3})(R^{2}J^{\prime}\rho_{2}\rho_{3}J^{\prime}R^{-2})(J^{\prime}R^{-2}\rho_{2}\rho_{3}R^{2}J^{\prime}) \in G_{4}.
\end{eqnarray*}
Therefore, we can see that we satisfy the condition $\langle 1 \rangle$. Since $J^{\prime}$ can send $\alpha_{k-2}$ to $\gamma_{k+1}$ and $\beta_{k+3}$ to $\gamma_{k-3}$, we can satisfy the condition $\langle 2 \rangle$ only in $J^{\prime}$.
Moreover, By that $J^{\prime}$ acts as $r_{3}$, we consist the condition $\langle 3 \rangle$. Therefore, the group $G_{4}$ is the whole mapping class group.
\end{proof}

\section{The subgroup generated by 2 involutions and 3 Dehn twists, which contains $\rm Mod^{0}(\Sigma_{\textit{g,b}})$}
\ \ \ In this section we prove Lemma 5 (i.e. we construct the subgroup of the mapping class group $\rm Mod(\Sigma_{\textit{g,b}})$ by 2 involutions and 3 Dehn twists, which contains the pure mapping class group $\rm Mod^{0}(\Sigma_{\textit{g,b}})$).\\
\ \ \ We recall that $R=\rho_{2}\rho_{1}$. By Lemma 1 and (3), we get following relation;
\begin{eqnarray}
T_{\alpha_{\textit{i}+1}}&=&RT_{\alpha_{\textit{i}}}R^{-1} \nonumber \\
T_{\beta_{\textit{i}+1}}&=&RT_{\beta_{\textit{i}}}R^{-1}\\
T_{\gamma_{\textit{i}+1}}&=&RT_{\gamma_{\textit{i}}}R^{-1}. \nonumber
\end{eqnarray}
\ \ \ Let the subgroup $G$ of the mapping class group be generated by $\rho_{1}$, $\rho_{2}$ and 3 Dehn twists $T_{\alpha}$, $T_{\beta}$ and $T_{\gamma}$ around one
of the curve in each family. By relation (7), $T_{\alpha_{i}}, T_{\beta_{i}}, T_{\gamma_{i}} \in G$ for all $i$.\\
\ \ \ Our next step is to show that $G$ contains $\rm Mod^{0}(\Sigma_{\textit{g,b}})$.
Let denote the curves $\delta^{\prime},\eta^{\prime},\delta^{\prime\prime},\eta^{\prime\prime},\delta_{\textit{j}},\eta_{\textit{j}} (\textit{j}=1,\ldots,\textit{l}-1,\textit{l}+1,\ldots,\textit{b}-2)$ in Figure 8.
In [Ge] it is shown that $\rm Mod^{0}(\Sigma_{\textit{g,b}})$ is generated by Dehn twists around the curves $\alpha_{i}$-es, $\beta_{i}$-es, $\gamma_{i}$-es, $\delta^{\prime}$, $\delta^{\prime\prime}$ and $\delta_{j}$-es, for $j=1,\ldots, l-1, l+1,\ldots ,b-2$.
\begin{figure}[htbp]
 \begin{center}
  \includegraphics*[width=13cm]{f4.eps}
 \end{center}
 \caption{The curves $\delta_{i}$-es, $\eta_{i}$-es.}
 \label{fig:one}
\end{figure}
\begin{lemma}
$R^{-1}(\delta_{\textit{j}})=\eta_{\textit{j}-1} \ (\textit{l}+2\leq \textit{j}\leq \textit{b}-1)$, \ $R^{-1}(\delta_{\textit{l}+1})=\eta^{\prime}$.
\end{lemma}
\begin{proof}
Figure 9 and Figure 10 shows the action of $\rho_{1}$ and $\rho_{2}$ on the curve $\delta^{\prime}$ and $\delta_{j}$ $(j=l-1,\ldots ,b-1)$. It is clear from the picture that $\eta_{j-1}=\rho_{1}\rho_{2}(\delta_{j})=R^{-1}(\delta_{j})$. It is also showed that $R^{-1}(\delta_{l+1})=\eta^{\prime}$.
\end{proof}
\begin{figure}[htbp]
 \begin{center}
  \includegraphics*[width=13cm]{f2.eps}
 \end{center}
 \caption{The action of $R$ on the curve $\delta_{j}$ \ $(l+2\leq j\leq b-1)$}
 \label{fig:one}
\end{figure}
\begin{figure}[htbp]
 \begin{center}
  \includegraphics*[width=13cm]{f3.eps}
 \end{center}
 \caption{The action of $R$ on the curve $\delta_{l+1}$}
 \label{fig:one}
\end{figure}
\begin{figure}[htbp]
 \begin{center}
  \includegraphics*[width=13cm]{f5.eps}
 \end{center}
 \caption{The action of $U$ on the curve $\delta_{i}$.}
 \label{fig:one}
\end{figure}
\begin{lemma}
$T_{\delta_{\textit{j}}}, T_{\delta^{\prime}}, T_{\delta^{\prime\prime}}\in G \ \ (\textit{j}=1,\ldots ,\textit{l}-1,\textit{l}+1,\ldots,\textit{b}-2)$.
\end{lemma}
\begin{proof}
At first, we prove $T_{\delta_{j}}\in G$ using induction $j$ $(j=l+2,\ldots ,b-1)$ and $T_{\delta^{\prime}}\in G$, then we prove that $T_{j}\in G$ $(j=0,\ldots ,l-1)$ and $T_{\delta^{\prime\prime}}\in G$.\\
\ \ \ The base case, $j=b-1$, is clear because by construction $G$ contains $T_{\delta_{b-1}}=T_{\alpha_{1}}$. Suppose that $G$ contains the twist $T_{\delta_{j}}$. Using Lemma 1 and Lemma 8 we can see that the twists
$T_{\eta_{j-1}}$ and $T_{\eta^{\prime}}$ also lies in $G$, since it is conjugate to $T_{\delta_{j}}$ and $T_{\delta_{l+1}}$
\begin{eqnarray}
T_{\eta_{\textit{j}-1}}=R^{-1}T_{\delta_{\textit{j}}}R\in G.
\end{eqnarray}
Let $U$ denote the product
\begin{eqnarray*}
U= T_{\beta_{1}}^{-1}T_{\gamma_{1}}^{-1}T_{\beta_{2}}^{-1}\cdots T_{\beta_{\textit{g}-1}}^{-1}T_{\gamma_{\textit{g}-1}}^{-1}T_{\beta_{\textit{g}}}^{-1}T_{\alpha_{\textit{g}}}^{-1}T_{\alpha_{1}}T_{\beta_{1}}T_{\gamma_{1}}T_{\beta_{2}}\cdots T_{\beta_{\textit{g}-1}}T_{\gamma_{\textit{g}-1}}T_{\beta_{\textit{g}}} \in G.
\end{eqnarray*}
The Figure 11 shows that
\begin{eqnarray}
 U(\eta^{\prime})&=&\delta^{\prime} \nonumber \\
 U(\eta^{\prime\prime})&=&\delta^{\prime\prime}  \\
 U(\eta_{k})&=&\delta_{j} \ (j=1,\ldots,l-1,l+1,\ldots,b-2). \nonumber
\end{eqnarray}
By Lemma 1, Lemma 10 and (9) we can see that $T_{\delta_{j-1}}=UT_{\eta_{j-1}}U^{-1} \in G$.
Thus $T_{\delta_{j}} \in G$ \ $(j=l+2,\ldots ,b-1)$. Moreover, we can see that
\begin{eqnarray*}
R^{-1}(\delta_{l+2})=\eta_{l+1},
U(\eta_{l+1})=\delta_{l+1},
R^{-1}(\delta_{l+1})=\eta^{\prime},
U(\eta^{\prime})=\delta^{\prime}.
\end{eqnarray*}
Therefore, we have that $T_{\delta_{l+1}}, T_{\delta^{\prime}}\in G$.\\
\ \ \ The next step we will prove that $T_{\delta^{\prime\prime}},T_{\delta_{\textit{j}}} \in G \ (\textit{j}=1,\ldots,\textit{l}-1)$.\\
\ \ \ By Figure 3 we can see that $\rho_{1}(\delta^{\prime\prime})=\eta^{\prime}, \rho_{1}(\delta_{\textit{j}})=\eta_{\textit{b}-1-j} \ (1 \leq \textit{j} \leq l-1)$.
By (9) we can understand that $T_{\delta_{j}}=U^{-1}T_{\eta_{b-1-j}}U, T_{\delta^{\prime\prime}}=U^{-1}T_{\eta^{\prime\prime}}U \in G$. We finished proving Lemma 10.
\end{proof}
\begin{corollary}
The group $G$ contains the subgroup $\rm Mod^{0}(\Sigma_{\textit{g,b}})$.
\end{corollary}
Therefore, we can prove Lemma 5.
\begin{remark}
The group $G$ is not the whole group $\rm Mod^{0}(\Sigma_{\textit{g,b}})$ (if $b>3$), because its image in the symmetric group $\rm Sym_{\textit{b}}$ is generated by two involutions
and therefore is a dihedral group. It is easy see that this image is the group $D_{2b}$ which is a proper subgroup of $\rm Sym_{\textit{b}}$.
\end{remark}

\section{Remark}
\ \ \ Clearly $\rm Mod(\Sigma_{\textit{g,b}})$ is never generated by two involutions, for then it would be a quotient of the infinite dihedral group, and so would be virtually abelian.
Since the current known bounds are so close to being sharp, it is natural to ask for the sharpest bounds.
\begin{problem}
For each $g\geq 3$, prove sharp bounds for the minimal number of involutions required to generate $\rm Mod(\Sigma_{\textit{g,b}})$. In particular, for $g\geq 7$ determine whether or not $\rm Mod(\Sigma_{g,b})$ is generated by 3 involutions.
\end{problem}
In order to generate the extended mapping class group $\rm Mod^{\pm}(\Sigma_{\textit{g,b}})$, it suffices to add one more generator, namely the isotopy class of any orientation-reversing diffeomorphism. Therefore, by replacing the involution $\rho_{1}$ with the reflection, we can get following result;
\begin{corollary}
For all $g\geq 3$ and $b\geq 0$, the extended mapping class group $\rm Mod^{\pm}({\Sigma_{\textit{g,b}}})$ can be generated by:\\
\ \ \ $(a)$ $4$ involutions if $g\geq 7$;\\
\ \ \ $(b)$ $5$ involutions if $g\geq 5$.
\end{corollary}
But in the case of $b=0$, Stukow showed the result that was stronger than Corollary 12. He proved that $\rm Mod^{\pm}(\Sigma_{\textit{g},0})$ is generated by three involutions. Then, we can consider following problem;
\begin{problem}
Can the extended mapping class group $\rm Mod^{\pm}(\Sigma_{\textit{g,b}})$ be generated by 3 involutions ?
\end{problem}

\section{Acknowledgement}
\ \ \ I would like to thank Professor Hisaaki Endo for careful readings and for many helpful suggestions
and comments. And I would like to thank Hitomi Fukushima, Yeonhee Jang and Kouki Masumoto for many advices.

redpajama_set_name: RedPajamaArXiv


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Home All OSF Bear's Sonic Journals: Tim Buckley Live at the Carousel Ballroom San Francisco, California CD
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Never-before-released original compositions and rare covers
28-Page Booklet
This is the most important Tim Buckley release since Dream Letter, featuring a singular performance with a jazz-rock lineup that calls to mind Van Morrison's Astral Weeks. Buckley, father of Jeff Buckley, made his mark with his Southern California folk-rock sound and four-octave vocal range. But this rich weave of accessible, warm, improvisational music reveals Buckley in a light never before captured on tape, including two newly discovered songs ("Blues, Love" and "The Lonely Life"), early drafts of Buckley classics, and a stunning cover of Fred Neil's "Merry-Go-Round." Recorded by the Grateful Dead's legendary soundman Owsley "Bear" Stanley, the infamous LSD chemist, this is one of the treasures of his Sonic Journal archive. Buckley's performance is incredible and Bear's thumbprint on the sonics is part of the magic!
Featuring nearly 80 minutes of live performances from June 15 & 16, 1968 at the Carousel Ballroom in San Francisco, CA.
This is a significant and rare addition to Tim Buckley's musical legacy for both the performance and excellent sound quality.
A 28-page booklet includes original cover art by Dennis Larkins and liner notes featuring new interviews with bassist John Miller, lyricist Larry Beckett, and Buckley scholar Pat Thomas.
With Tim Buckley on vocals and 12-string guitar, John Miller on bass, David Friedman on vibraphone, and Carter C.C. Collins on percussion.
These tapes were transferred and mastered by Jeffrey Norman (Mockingbird Mastering), long-time collaborator with the Grateful Dead and Owsley Stanley.
"This is the follow-up to Dream Letter. Between the sonics and the songs, this is a major moment in Buckley land."
—Pat Thomas, Tim Buckley scholar
"A great discovery! … Even though tracks here appear elsewhere in studio albums or other concert recordings, they are not the same at all. They are reinvented. And that's why every single [release] is worth listening to."—Larry Beckett, Tim Buckley lyricist
Recommended for the OSF Bear's Sonic Journals: Tim Buckley Live at the Carousel Ballroom San Francisco, California CD


ST. GEORGE – A winter weather advisory for snow in parts of six southern Utah counties has been extended in both time and area.
The National Weather Service in Salt Lake City has issued a Winter Weather Advisory for snow which is in effect from 5 a.m. Wednesday to midnight Wednesday night.
The advisory affects Garfield, Piute, Kane, Washington, Iron and Beaver counties.
The Southern Utah mountains including Loa, Panguitch and Bryce Canyon.
Generally 2-5 inches with locally higher amounts of up to 12 inches in the Tushar Mountains by late Wednesday evening.
A band of heavy snow will accompany a cold front Wednesday morning across the mountains of Southern Utah. Snowfall may taper briefly midday but snow showers and higher intensity squalls will redevelop Wednesday afternoon into Wednesday evening.
Falling to between 6,500 and 7,000 feet.
Accumulating snow is expected on all roadways above 8,000 feet early Wednesday morning.
Visibility will be reduced in areas of intense snowfall. Roads are expected to be mostly wet through Wednesday afternoon, though higher intensity snow showers will still have the capability to produce brief accumulations of slush on road surfaces.


To enable message tracing, select the Tracing → Trace messages checkbox.
If message tracing is enabled, each Modbus message sent or received is logged as two lines.
The first line begins with the time that the message was sent or received. This is followed by the character '<' for an incoming message or the character '>' for an outgoing message. The '<' or '>' is followed by the transaction identifier (only for TCP packets), slave identifier, PDU length (in bytes), function code, and then the first few bytes of the body of the message (in hex).
The second line of a message trace provides an interpretation of the main fields in the message. This line also begins with the time. After the time is the word "Request" for a request message, or "Response" for a normal response message. "Request" or "Response" is followed by the function code (expressed in words) and the main fields of the message (address, count, etc.).
Troubleshooting help is available for the "Error response" and "Discarded" lines. Click on the line in the log window (or move to it with the keyboard and press space) to display the help.


Educational Qualification – Candidates should have completed CA / ICWA / MBA (Finance) or its equivalent qualification from a recognised university. However for further details see the detailed advertisement.
Age Limit – Candidates age should not exceed 45 years (for Post 1) & 35 years (for Post 2) as on 01/12/2016. However for age relaxations see the detailed advertisement.
How to Apply – All interested and eligible candidates are required to visit Gujarat Mineral Development Corporation Limited (GMDC) Official Website http://www.gmdcltd.com/ and fill the On-line Application Form.


Auction season in Arizona may be over, but that doesn't mean you missed your chance to experience the World's Greatest Collector Car Auction. Barrett-Jackson will head to Palm Beach, Fla., April 4-6, with the opening night gala on April 3. Just as in Arizona, thousands of spectators and collectors from around the world are expected to participate in the world-class automotive lifestyle event to witness hundreds of classics, exotics, muscle cars, Hot Rods, Resto-Mods and contemporary collectibles, as they cross the auction block at No Reserve.
Thursday, April 4 and Friday, April 5: 11 a.m. to 5 p.m.
Saturday, April 6: 8 a.m. to 11 a.m. and 1 p.m to 5:30 p.m.
If you decide to make the trip, tickets can be purchased online. Barrett-Jackson will also head to Reno-Tahoe for Hot August Nights, August 8-10, 2013.


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HomeMinistriesMissions
And he came and preached peace to you who were far off and peace to those who were near.
Ephesians Chapter 2 Verse 17
Funding and Outreach Mission Team
Trinity Church has received of God's grace, and so we choose to give five percent of all church income for furthering God's Kingdom on Earth. The Funding and Outreach Mission Team ('FOMT') oversees this charitable giving of Trinity Church as a sub-committee of the church Council. FOMT is made up of Council and non-council Trinity Church members. Other TCE members with a heart for outreach and mission are invited to join us in discernment and prayer for this important work.
FOMT Distribution Policy
The distribution of funds allocated to mission beyond Trinity Church is orientated to four categories. These categories provide a framework through which to review our allocation of funds.
Evangelism: Frontline, active presentation of the Gospel.
Mercy: A response of gracious kindness to those who need help. Disaster relief is a typical example. It is difficult to budget for or anticipate as pleas for help come unexpected.
Awareness / Discipleship: This area is focused on the development of people for distant mission, particularly younger people from within our own church community. It is seeding and nurturing mission hearted people.
Justice: Involves putting things right, especially where structural injustice needs to be challenged.
Maintaining a set distribution pattern is not a hard policy. The total mix needs to include all four categories but allocation remains flexible.
Current Mission Distribution
Andrew and Ruth Garvey-Williams in Buncrana, Republic of Ireland
Aphrezo and Sylvia Kroze in Ulaanbaatar, Mongolia
Allston and Sherene Olive in Pondicherry, India
More information on each of the mission partners' projects can be found on the FOMT information board near the coffee table at church.
FOMT also currently supports the Gill family, which lives in exile in Sri Lanka as they had to flee their home country because of Christian activities they were involved in. This support consists of the rental payment for their temporary home and a cash collection in the church for basic food staples and children's education costs for their family — 2 adults and 4 children.
Ongoing support to The Mission to Seafarers located in Rotterdam harbour.
Support for Hwee Chong as a member of Trinity Church on mission with OM.
Traditionally, during Advent, FOMT has also organised a 'Missions Market' of food and crafts in church after a Sunday service to raise funds for mission projects. This is always a successful event and a wonderful time of fellowship amongst church members and local visitors.
Donate to FOMT Online Now
If you would like to support Trinity Church's missions outreach you can now directly and immediately donate to FOMT using the secure online donation below. The donation form has a suggested amount which you can change as you wish. Your donation will be automatically labelled as being a donation to FOMT, so you can be assured that your giving will go 100% to supporting Trinity's mission outreach work.
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Suggested Donation:
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This form is secured by digital certificate and utilises end-to-end encryption. Convenient payment methods such as iDEAL, bank transfer and other options are available.
When you click the button above you will be transferred to the website of our secure payment processor Mollie B.V., located in the Netherlands, to process the transaction. No financial data (e.g. card numbers, bank account details) are stored on the Trinity Church website and/or systems.


Objectives: A naturalistic study on the use of aripiprazole long-acting injectable (LAI) in acute inpatients with schizophrenia of two hospitals is presented. Methods: In this study, 51 inpatients (30 men, 21 women) with schizophrenia were treated with aripiprazole LAI; in 1 patient this treatment was removed before discharge because of lack of efficacy. 49% of patients had a damaging drug consumption (56% of them consumed cannabis). Results: The average hospital stay (HS) was 21 days. The HS was smaller when the dose of aripiprazole LAI was administered earlier (linear regression; r<.0001). When the dose of aripiprazole LAI was administered in the first week of admission the HS was 16.3 days, in comparition when administered over a week, 28.4 days (t test; p<.0001). At discharge, mean dose of aripiprazole LAI was 404 mg. Conclusions: In this sample, aripiprazole LAI is a effective treatment for acute inpatients with schizophrenia and a short average HS is observed. The early use of aripiprazole LAI, in the first week of admission, reduces HS.


Here are a couple of useful functions to have handy when working with html forms.
Sometimes it is useful to set some default text in an input text box, to provide extra information to the user. This function automatically removes this text when the user moves the focus of their browser to the text field in question. If they fail to enter any text, the default text is re-inserted when they move away from the input box. If they do enter their own information, this behaviour is removed.
It would be a fairly simple task to expand upon the default text checker. One useful extension would be to have it automatically check for fields with default text defined, without having to be set explicitly.


Pre-order for Thirstin Howl the 3rd latest album Survival of the Skillest.
Add Thirstin Howl the 3rd's l Survival of the Skillest, to your collection of skill. This album features Talib Kweli, Shabam Sahdeeq, Black Rob, The Liknuts, Umi selah, Brother J of XClan and Lo-Life members Unique London, Richie Balance, Sadat X, Master Fuol and Big Boo. Skillionaire Music's own Anger Bangers lay down most of the production with additional tracks by Psycho Les of the Beatnuts, Domingo, Will Tell, DJ Heron and more.
This version is a digital download. For a physical copy, purchase the CD.