...CARLESON POTENTIALS AND THE REPRODUCING KERNEL THESIS FOR EMBEDDING THEOREMS STEFANIE PETERMICHL 1 , SERGEI TREIL 2 , AND BRETT D. WICK 3 Abstract. In this note we present a new proof of the Carleson Embedding Theorem on the unit disc and unit ball in C n The only technical tool used in the proof of this fact is Green’s formula. The . starting point is that every Carleson measure gives rise to a bounded sub-harmonic function. Using this function we construct a new related Carleson measure that allows for a simple embedding. In the case of the disc D this gives the best known constant, with the previous best given by N. Nikolskii. 0. Introduction The famous Carleson Embedding Theorem for the unit disc states, in particular, that the embedding of the Hardy space H2 into a space L 2 (µ) can be checked on reproducing kernels of the Hardy space. Namely, it can be stated as follows: Theorem 0.1 (Carleson Embedding Theorem). Let µ be a non-negative measure in D. Then the following are equivalent: (i) The Hardy space H2 (D) is embedded in L 2 (µ), i.e. Z D |f(z)| 2 dµ(z) ≤ A 2 kfk 2 H2 (D) ∀f ∈ H2 (D). (ii) C(µ) 2 := sup z∈D kkzk 2 L2 (µ) = sup z∈D kPzkL1 (µ) < ∞, where kz(ξ) = (1−|z| 2 ( 1/2 1−ξz , is the normalized reproducing kernel for the Hardy space H2 (D). (iii) I(µ) := sup 1 r µ(D ∩ Q(ξ,...
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...proper knowledge of the level system, color theory, and the levels of decolorization, the client may not get their desired result; that can ultimately cause a loss of profit, and even clientele. If the stylist has a full understanding of all of the factors, there is a lot of money to be made. Both men and women are changing the color of their hair, and with the help of a stylist, they can achieve whatever look they desire. Stylists utilize what is called the level system, which is a system that is used to determine the lightness to darkness of a client’s hair. This helps decide whether the haircolor needs to have lift or will be deposit only. Color theory is used to determine they actual color of the clients hair. This is determined by use of the color wheel and the three primary colors; red, blue, and yellow. These are colors that cannot be created by mixing other colors, but with equal part of two of these colors you can create secondary colors. Tertiary colors are colors that can be made when a secondary color and its neighboring primary color are mixed. With knowledge of this, a stylist can change the client’s hair any color of the rainbow. The degree of decolorization comes into play when the client’s hair needs to be lightened to the extreme. If a client is a level 5 which is the lightest brown, and they want to become a level 8, they have to decolorize the hair. Even the most simple haircolor change require some sort of knowledge of color theory, the level system and the decolorization...
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...Sonora Schueneman Dr. Kemp- Hailee Nerber Bio 111- 551 19 September 2017 Osmosis and Diffusion Across a Plasma Membrane-Lab 2 Week two in the lab consisted observing a constructed experiment involving osmosis and diffusion across a semi-permeable membrane. This allowed myself to formulate a hypothesis stating, the four pipets of cooked starch and amylase will diffuse through their dialysis bag into the beaker containing 2/3 water and four pipets of Lugol’s solution. Thus being stated, the null hypothesis would be, the four pipets of cooked starch and amylase will not diffuse through their dialysis bag into the beaker containing 2/3 water and four pipets of Lugol’s solution. In order to test our hypothesis, I set up a control beaker (Beaker...
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...Amazon 5 Bullet Points: ELIMINATE CONFUSION: Conveniently manage pills for the entire week MULTIPLE DIVIDERS: Each tray has four sections for morning, noon, evening and bedtime COLOR-CODED DAYS: Each day has a designated color to eliminate missed pills COMPACT DESIGN: Pill tower is compact for use at home, at work or while traveling CONVENIENT PILL SPLITTER: Easy to use pill splitter is also included Product Description: Organize and manage pills easily and efficiently with the Vive plastic pill organizer. Conveniently manage medications and supplements with the easy to use Vive pill organizer. The durable plastic pill box contains seven color-coded trays with sliding lids, one for each day of the week. Each tray is divided into four compartments:...
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...Carolyn Rude-Parkins, Ph.D. University of Louisville November, 2007 Introduction The words blue, green, and yellow are words known to all as colors. If one of these color words is written in an ink color differing from the color it represents an individual spends more time to name that ink color than the ink color of neutral words. This is known as the Stroop effect. Studying this gives insight into the human mind. It can show how we handle interference across a number of different situations or how our automatic processes interact with and affect our controlled processes. The cause of the Stroop effect has been widely debated and researched over the years. Some researchers believe the cause is due to the fact that reading is such a well learned or even over learned process that it becomes automatic. When asked to identify ink colors of words reading the word causes distraction because reading is done much more often than naming ink colors. But where is the exact interference occurring in this process and why? It has been suggested that the interference occurs at the output or response stage as an individual struggles to express the correct color word from alternatives. Others believe the interference happens during encoding as an individual analyzes the word and is distracted from ink color. Still others would say it happens somewhere between the encoding and the output. All of these suggestions have various criticisms. The search for the correct answer...
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...the flag features a center white cross and divided the flag into four sections of rectangle. The top left and bottom right is the blue and the top right and the bottom left is the red, these are the three colors of the flag. In the middle center is the Coat of Arms, it features a shield in the colors of the flag. The three feature of the flag and coat of arms is the white cross, the blue and red colors, and last the coat of arms (shield). The first features of the Dominican Republic flag is the white cross and the blue and red. The white cross on the flag is extended out to the edges, of the flag to create four rectangles that have...
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...The Effect of Using Instructional Songs in the Classroom Danielle B. Segar EDU 787 07 Dr. Judith Dellicolli July 14, 2012 Introduction There are many instructional strategies to catch student’s attention. Over the years music has been a big influence in teacher’s classrooms. Music is a great way to engage students in fun learning. Teachers have even had great success creating songs of their own. Many teachers take popular songs and incorporate lyrics about their lessons. We all know that children love to sing, so what better way than to turn music into something educational. It has been a generally accepted fact that children pick up lyrics to a song quickly. So, coming up with the idea of applying music to lessons was logical. There are websites for teachers who are not musically talented. Those websites provide a variety of songs to be incorporated into lessons. Instructional songs are not the only resource for a student to retain information, because every child brain does not process the same. Instructional song helps to memorize the important facts to understand a lesson as a whole. Music is a tool that is used on a daily basis in preschool classrooms. Review Of Literature Similar to natural language abilities, children are born with natural musical ability, which varies from child to child. Music is used in a variety of families with young children for multiple purposes (Custodero, 2006). When researchers study babies, the process...
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...question: 1. Is there will be a significant difference between the experimental ink with different formulations and the commercial ink in terms of: 1.1 color; 1.2 clarity; 1.3 odor; and 1.4 water resistance? b. Null Hypotheses The researcher will hypothesize that: 1. There will be no significant difference between the experimental ink with different formulations and the commercial ink in terms of: 1.1 color; 1.2 clarity; 1.3 odor; and 1.4 water resistance. c. Procedure Making the Product The materials that will be needed are 400 grams of Narra and Madre de Cacao barks each, tray, recycled ballpen containers, 500ml and 100ml beaker, stiring rod, double beam balance, laboratory gloves, glycerin/glycerol, ferrous sulfate, gum Arabic, rubbing alcohol. First, four-hundred grams each of Narra and Madre de Cacao barks will be gathered to Poblacion Bansud, Oriental Mindoro. After gathering the barks, it will be washed using tap water in order to remove the unnecessary dirt on it that may affect the product. The washed barks will be placed on the tray and will be sundried for three days. When the barks are totally dried, it will be cutted into smaller pieces. Then extraction will be done by boiling four-hundred grams each of Narra and Madre de Cacao barks with 700 ml of water for 60 minutes. After the extraction, it will be putted in a 500 ml beaker until it cools. The extract will be...
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...Data Table | |AgNO3 (Ag+) |Pb(NO3)2 (Pb2+) |Ca(NO3)2 (Ca2+) | |Na2CO3 (CO32-) |A cloudy peach color peach |f. a milky white color |K a milky white color | | |color | | | |Na2S (S2-) |B a cloudy black color |G a cloudy black color |L no reactions | |NaOH (OH-) |C a cloudy bubbly brown color |H no reactions |M a milky white color | |Na2S04 (SO42-) |D no reactions |I turned a milky white color |N no reactions | |NaCl (Cl-) |E a milky white color |J turned a milky white color |O no reaction | a. Drag a test tube from the box and place it on the metal test tube stand. You can then click on the bottle of Ag+ ion solution on the shelf to add it to the test tube. b. Click on the Divide button on the edge of the lab bench four times to make four additional test tubes containing Ag+. With one test tube in the metal stand and four others in the blue rack, click on the Na2CO3 Bottle on the reagent shelf and observe what happens in the window at the top left. Record your...
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...124124235What makes the good ones effective? Can they be further enhanced? How? Analysis of visual strategies should include discussions of the relevant elements to your ad such as focal point, composition, foreground, background, juxtaposition, color usage, light quality, contrast, etc. Analysis of verbal strategies should include discussion of word choices, figurative languages, any innuendoes, clichés, plays on words, puns, etc., and should pay particular attention to how these choices correspond to the visual strategies of the ad in the creation of the overall meaning. The Lynxjet ad is very entertaining, humorous, but overall subtle. The theme to the product campaign is the ‘Mile High Club’, where sexy stewardesses on the ‘Lynxjet’ airline are pampering the male passengers; giving them massages, spa treatments and other sorts of pleasure at their service. The script featured on the ad states, ‘The Lynxjet Mile High Club, it’s luxury that other airlines can only dream of.’ This is clever in that the advert makes the audience feel like they’re part of some special, elite club, and they too have the potential to experience this fantasy. The ideal target market for Lynxjet deodorant spray are males aged 15-25 years, as they are at an age where they sweat more frequently, are beginning to impress and date women, and generally have a lower socioeconomic status, due to their lower education level. The main advertising objectives for Lynxjet are the following… • For audience...
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...Trypticase soy agar streak-plate prepared with: *Escherichia coli and Micrococcus luteus (4) Trypticase soy agar slants Bunsen burner Inoculating loop Permanent Marker Test tube rack Straight needle Striker Incubator Method Part A: Isolation of Discrete Colonies from a Mixed Culture * Label one Trypticase soy agar streak-plate using a permanent marker on the b ottom. Write the date (1/23/14), TTH2, student’s initials, the names M. roseus and M. luteus. There were also lines dividing the streak-plate into four sections with one section labeled I, one labeled II, one labeled III, and one labeled IV on the bottom of the plate. The quadrants should look like the labeled circle below. * Divide a second Trypticase soy agar streak-plate into four sections and label with the Roman numerals in the same way as the first plate. Also label the bottom of this plate with the student’s initials, TTH2, and the date (1/23/14). Write E. coli and M. luteus on the bottom of this plate. * Turn on the gas and light the Bunsen burner using a striker. * Bend the inoculating loop to make...
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...1. What is the box model? The CSS box model describes the boxes that are formed around elements in a Web page. In XHTML, every element is treated as though it were a box. The box model consists of four parts: a content area, padding, borders, and margins. 2. What is padding? Padding is the white space that surrounds the box content. 3. What is the margin? Margin is white space outside the border. 4. When using the border shorthand property, what value must always be specified? Border Shorthand Property is the shorthand property you can use to set the values for all four border styles with one declaration. • To set the border width, use: border-width: width; where width is one of the CSS units of measure. • To set the border color, use: border-color: value; where value is a named color, RGB color, or hexadecimal color value. • To set the border style, use: border-style: style; where style is either none, solid, double, dotted, dashed, outset, inset, groove, or ridge. • To use the border shorthand property, enter: border: style color width; where style is the border style, color is the border color, and width is the border width. Although not all three values need to be specified, and values can be entered in any order, you must specify a border style. 5. What are the values for the float property? The values of the float property are left, right or none. 6. What are the values for the clear property? The values of the clear property are left...
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...1978. In the following essay I will elaborate more upon the elements utilized by the artist to create this piece of art. Falvin’s use of lines, light, and color are all essential elements to this particular sculpture. There are four straight, white metal rods placed vertically. There are then four straight florescent lights placed horizontally on top of the four white metal rods; the top two florescent lights are a sky blue and the bottom two florescent lights are a golden yellow. The sculpture is geometric in nature; together the rods and lights form a grid square. Essentially it forms the illusion that there are 25 squares and one big square. These shapes together form a strong and proud structure. The use of white metal rods was a choice I believe was defiantly done on purpose in order to accentuate the color of the florescent artificial lights. The florescent lights make a statement, especially because of their strong intensity. Blue is known as a cool color while yellow is known to be a warm color. Although these colors seem to be opposites, they are both...
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...Grade/Level: 1st grade Instructional Setting: 32 Learners Venue: 2H classroom Sitting Arrangement: Normal, in Pairs STANDARDS AND OBJECTIVES | Your State Core Curriculum/Student Achievement Standard(s): 1.8: Spell three- and four-letter short-vowel words and grade-level-appropriate sight words correctly (California Department of Education, 2009). Lesson Objective(s): Given an already made beaded string, each student will copy the arrangement of beads and make their own. Each student will do this five times with ninety percent accuracy. Given a big card with a word stuck on it, another big but ‘empty’ card and other small cards each bearing a letter for the word stuck on one of the two big cards, the student will arrange the small cards on the ‘empty’ one to spell the word duck on the other card for each of the four words with at least 75 percent accuracy (at least missing only one letter). MATERIALS AND RESOURCES | Instructional Materials: * Beads of different color, shapes and Strings * Four cards for each learner bearing their name * Letter for each word to be spelt. * A big card bearing one of the words to be spelt stuck on its surface for all the four words. * Another empty card of the same size as the one with stuck words. Resource: McGill-Franzen, A. (2006). Kindergarten Literacy: Matching assessment and instruction. New York: Scholastic. INSTRUCTIONAL PLAN | Sequence of Instructional...
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...to supplying critical proteins for blood clotting and immunity (Blood, 2011). The function of red blood cells is to move oxygen from the lungs to body tissues. Red blood cells are formed in the red bone marrow of certain bones, and they produce a substance called hemoglobin. Hemoglobin is a protein pigment that contains iron and that gives red blood cells their color. The hemoglobin in red blood cells combines with oxygen in the lungs, transporting that oxygen to the tissues throughout the body. Red bloods cells live only about four months and new ones are continuously being produced in the bone marrow to replace the old ones (Blood, 2011). Platelets are small, disk-shaped fragments of cells that are broken off from other cells in the bone marrow. They help to control bleeding by sticking to the ruptured blood vessels and releasing substances that attract other platelets forming a temporary blood clot (Blood, 2011). Scenario One...
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