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The image shows a satellite view of a hurricane over the ocean with land visible in the background. The words in the picture are: "the text : '17:27:09'" in a red box at the bottom left, and "the text : 'Heavy Floods Hit Small Villages Near Mount Teide Volcano'" and "Global Leaders Meet to Discuss Climate Change and Economic Recovery" in white text on a red and white banner at the bottom right.
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A 512x512 text image with the following settings: font_size 162 , font_type Chickyplum-4B2ZW , font_color [228, 17, 81] displaying the text: ameloblastic fibro - odontoma
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A 512x512 text image with the following settings: font_size 50, font_type Paradise-DO1dm, rotation_degree -19, font_color [45, 33, 47], alignment center, displaying the text: Golac Golac (; ) is a village in the Municipality of Hrpelje-Kozina in the Littoral region of Slovenia on the border with Croatia. The parish church in the settlement is dedicated to Saint Nicholas and belongs to the Koper Diocese.
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The image: absolute surrender audiobook cover art, and text says ABSOLUTE, SURRENDER, Murray, Andrew, Read, by, PJ, Ochlan.
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The image is a slide from a presentation on Calculus Rules, specifically focusing on the Product Rule. The slide is titled Calculus Rules and is numbered 2, indicating it is the second slide in the series. The Product Rule is stated as follows:nn[ frac{d}{dx}(uv) = uv' + vu' ]nnThe slide provides an explanation of the Product Rule: Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST.nnBelow this explanation, there are two examples demonstrating the application of the Product Rule:nn### Example (i)n[ y = x^7
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We find 6 Easy Ways To Get Free Travel, and EASY,6,WAYS,GET,TO,TRAVEL,FREE text stands out.
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A 512x512 text image with the following settings: font_size 39, font_color [23, 4, 16] displaying the text: The strength of his loyalty to Jet is greater than any other and he hates rivals to the team. When he is angry, he becomes destructive; and the raw power of his physical strength makes up for his lower intelligence and lack of speed. With his quick temper, he may stutter when flustered and he hates having to wait.
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06587c35-6545-41d0-a18d-06da1ee67fb0.jpg
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Encountering a colorful book cover with a swirling design in pastel and warm tones, featuring a circular logo at the bottom right corner, referencing the text: 'FOURTH EDITION The Doctor of Nursing Practice Project A Framework for Success Katherine Moran Rosanne Burson Dianne Conrad ACCESS NAVIGATE CODE INSIDE ESSENTIALS ACCESS.'
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FOURTH EDITION The Doctor of Nursing Practice Project A Framework for Success Katherine Moran Rosanne Burson Dianne Conrad ACCESS NAVIGATE CODE INSIDE ESSENTIALS ACCESS
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72b91b4ae9934e51b90f8fea9e8b327c.png
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A 512x512 text image with the following settings: font_size 101, font_type HavergieScript-2Orwo, rotation_degree 40, font_color [66, 121, 163], alignment left, displaying the text: Do you ever miss them? Of course I do.
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The image: Sunday Nights: The Songs of Junior Kimbrough, plus the words SUNDAY,NIGHTS,JUNIOR,KIMBROUGH,SONGS,OF,THE.
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Depicted is I am watching Adventure Time Check-in to Adventure Time on GetGlue.com, and the words ADVENTURE,(TIME,and,JAKE,FINN,with,WARO,PENDLETON.
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A 512x512 text image with the following settings: font_size 71, font_type BastradVol02Regular-owGJV, rotation_degree -22, font_color [69, 93, 61], alignment right, displaying the text: But I guess I didn't care at the time. What made you finally decide to confess? I don't know.
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We recognize Cloud Nine, and read TM,CLOUD,NINE,Less,heat,,more,style..
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a7a22778659f4da391cbb60d4ff05a94.png
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A 512x512 text image with the following settings: font_size 66, font_color [76, 27, 67] displaying the text: What if something goes wrong? There's nothing that can go wrong, Gordon.
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The image depicts a futuristic scene with a group of astronauts standing in front of a glowing, golden doorway set within a rocky, cavernous environment. The doorway emits a bright, radiant light, suggesting a portal or gateway to another dimension. The text at the top of the image reads, "the text : 'Beyond the Golden Gates of Eternity'." Below the doorway, additional text states, "the text : 'As the astronauts, led by Commander Sarah Jenkins, step through the golden doorway, they are met with an ancient, long-abandoned world that holds the key to humanity's survival in a dying universe.'" The text is positioned in the center of the image, overlaying the scene.
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A 512x512 text image with the following settings: font_size 36, font_type helveti, rotation_degree 28, font_color [47, 51, 31], alignment center, displaying the text: Gallagher was appointed to fill the casual vacancy caused by the retirement of Senator Kate Lundy.
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A 512x512 white background image. The image features a layout where the image and text are interspersed, with the image and text appearing separately. And the text will be positioned around it based on the given bounding boxes.
For image elements:
1. The image depicts a dark, eerie room with a person standing near a staircase, surrounded by furniture and a balloon. A text overlay reads, It seems you had a nightmare. Bbox [5, 85, 204, 284]
2. The image depicts a dimly lit room with a person lying on a bed, surrounded by various objects and furniture. The scene has a somber, almost eerie atmosphere. Bbox [46, 290, 220, 464]
3. The image depicts a dimly lit room with various pieces of furniture and equipment, including a desk, chairs, and cabinets. The scene has a vintage or industrial aesthetic, with a focus on practicality and functionality. Bbox [266, 290, 465, 489]
For text elements should be displayed independently in font CourierNewPS-ItalicMT:
1. "Bear With Me Episode One Review:" in size 62, Bbox [5, 7, 452, 79]
2. "Solving Crimes Has Never Been this" in size 75, Bbox [210, 88, 435, 265]
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A 512x512 text image with the following settings: font_size 68displaying the text: I wanted to get your thoughts on it. Well, it looks like you've put a lot of work into it.
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Portraying Uncharted Waters, with UNCHARTED,WATERS,LICENSED,BY,OF,NINTENDO,AMERICA,INC. text included.
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An image that renders the following text: Asymptotic Behavior of Inflated Lattice Polygons Mithun K. Mitra, ∗ Gautam I. Menon, † and R. Rajesh ‡ The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India (Dated: October 26, 2018) We study the inflated phase of two dimensional lattice polygons with fixed perimeter N and variable area, associating a weight exp[ pA − Jb ] to a polygon with area A and b bends. For convex and column-convex polygons, we show that ⟨ A ⟩ /A max = 1 − K ( J ) / ˜ p 2 + O ( ρ − ˜ p ), where ˜ p = pN ≫ 1, and ρ < 1. The constant K ( J ) is found to be the same for both types of polygons. We argue that self-avoiding polygons should exhibit the same asymptotic behavior. For self-avoiding polygons, our predictions are in good agreement with exact enumeration data for J = 0 and Monte Carlo simulations for J ̸ = 0. We also study polygons where self-intersections are allowed, verifying numerically that the asymptotic behavior described above continues to hold. arXiv:0710.1509v1 [cond-mat.stat-mech] 8 Oct 2007 PACS numbers: 05.50.+q,02.10.Ox,05.70.-a I. INTRODUCTION p = 0 and µ = κ − 1 , where κ is the growth constant for self-avoiding polygons, is also known exactly [14, 15, 16]. Less is known about the inflated phase obtained for positive pressures p > 0. However, this phase is of phys- ical interest in the case of two-dimensional vesicles, or equivalently pressurized ring polymers [1, 17, 18, 19, 20]. In the calculations described in this paper, we consider the partition function The study of lattice polygons weighted by area and perimeter is a central problem in lattice statistics and combinatorics. Lattice polygons have been used to model vesicles [1, 2], cell membranes [3], emulsions [4], poly- mers [5] and percolation clusters [6]. In several cases, exact generating functions for classes of such polygons have been obtained. A survey of different kinds of lattice polygons and a review of related results can be found in Refs. [7, 8]. In this paper, we study the asymptotic behaviour of the area enclosed by inflated polygons of fixed perime- ter. We calculate the area for two special cases of lattice polygons - convex and column-convex lattice polygons. We then conjecture the appropriate form for the area of self-avoiding polygons in the inflated phase. We first summarize known results for the problem of pressurized polygons, based on the generating function Z N ( p, J ) = X A,b C N ( A, b ) e pA − Jb , p > 0 , (2) where C N ( A, b ) is the number of self-avoiding polygons of area A with b bends. A bending energy cost J per bend is introduced to incorporate semi-flexibility. Some rigorous results exist for Z N ( p, 0) when p > 0. Ref. [21] proved that Z N ( p, 0) = A ( p ) e pN 2 / 16 (1 + O ( ρ N )) as N →∞ , (3) for some 0 < ρ < 1, with A ( p ) some function of p . This result holds in the limit where N →∞ keeping p fixed. However, as we argue in Sec. II, the relevant scaling limit in the inflated regime is p → 0, N →∞ keeping ˜ p = pN finite. The central result of this paper is then the following: In this limit, we show that for both convex and column- convex polygons, the area is given by, G ( µ, p ) = X A,N C N ( A ) e pA µ N , (1) where C N ( A ) is the number of self-avoiding polygons of perimeter N and area A , weighted by a chemical poten- tial µ . Here p is the pressure which couples to the area A . Exact solutions exist for G ( µ, p ) when C N ( A ) is restricted to convex polygons [9, 10, 11] or to column-convex poly- gons [12]. However, a general solution for self-avoiding polygons is unavailable. Exact enumeration results for self-avoiding polygons exist for all N up to N = 90 and for all A for these values of N [13]. A transition at p = 0 separates a branched polymer phase when p < 0 (for µ sufficiently small) from an inflated phase when p > 0. At p = 0, the problem reduces to that of the enumeration of self-avoiding polygons. The scaling function describing the scaling behavior (for p < 0) near the tricritical point ⟨ A ⟩ = N 2 u0014 1 − 32 π 2 ˜ p 2 Li 2 (1 − α ) u0015 + O ( e − ˜ p/ 8 ) , (4) 3˜ p 2 + 64 16 where Li 2 is the dilogarithm function ∞ X x m Li 2 ( x ) = m 2 , (5) m =1 and, α = e − 2 J . We argue that this result should also extend to the self-avoiding case and test this conjecture numerically. The paper is organized as follows. In Sec. II, we present a justification of the scaling limit we consider using a sim- ply Flory-type argument. Sections. III and IV contain ∗ Electronic address: [email protected] † Electronic address: [email protected] ‡ Electronic address: [email protected]
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The image depicts a nest containing several eggs, with one egg highlighted in red. The nest appears to be made of soft, fibrous material, possibly grass or plant fibers. The eggs are speckled with dark spots, and the one highlighted in red is noticeably larger than the others. The text in the image is in German and reads:nn```n... eine Entenmutter brütete ...n... sechs gesunde ...ndas siebte Ei war jedoch größer,ndrum dauerte es länger, ...n```nnTranslated to English, the text says:nn```n... a duck mother was incubating ...n... six healthy
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A modern kitchen counter features a sleek high-end blender, fresh vegetables, and herbs, with a TV screen behind displaying the text : ''"Transform your cooking routine with the ultimate high-end blender, now available for a limited time, and discover the power of precision and performance in the heart of your modern kitchen"''.
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A 512x512 text image with the following settings: font_size 37displaying the text: The exact timing of breeding varies by a number of factors most importantly location. Most breeding occurs between January and September; in Europe the breeding season usually begins after March. In Israel there are exceptional records of breeding during the months of October to December.
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The scene shows Differentiated Instruction Plan Book with CD for Grades 3-8, with printed The,Scholastic,Instruction,Differentiated,Plan,Book,MSCHOLASTIC.
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The image shows a cityscape with multiple buildings collapsing amidst a cloud of dust and debris, with people in the foreground. The words in the picture are: "CCTV" at the top left, "the text : '19:26:25'" at the top right, "the text : 'Strong Earthquake Hits Near Mount Spurr Volcano Disrupting Local Transportation'" at the bottom left, and "New Medical Breakthrough Offers Hope for Patients with Rare Diseases" at the bottom right.
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A 512x512 text image with the following settings: font_size 62, font_color [31, 50, 179] displaying the text: after Stagecoach was disqualified from the process due to not meeting pension obligations.
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A book cover for ASE Test Preparation - T1 Gasoline Engines (Ase Test Preparation: Medium-Heavy Truck Certification Series); Cengage Learning Delmar; Engineering & Transportation;
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acfd85a2f06a40778f28f420175bf17a.jpg
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A 720x540 slide page. The page features a layout where the image and text are interspersed, with the image and text appearing separately, not fused together. The text will be provided with a specified bbox, font, and color.
For text elements should be displayed independently:
1. "Mini-introduction to DTW" in size 46, Bbox [43, 28, 642, 82], font DejaVuSerif, color [0, 102, 51]
2. " DTW allows sequences to be stretched along the" in size 26, Bbox [43, 108, 642, 137], font LiberationSans, color [0, 0, 0]
3. "time axis" in size 26, Bbox [70, 136, 172, 165], font LiberationSans, color [0, 0, 0]
4. " Minimize the distance of sequences" in size 22, Bbox [70, 170, 444, 194], font LiberationSans, color [0, 0, 0]
5. " Insert ‘stutters’ into a sequence" in size 22, Bbox [70, 199, 399, 224], font LiberationSans, color [0, 0, 0]
6. " THEN compute the (Euclidean) distance" in size 22, Bbox [70, 228, 488, 253], font LiberationSans, color [0, 0, 0]
7. "‘stutters’: original" in size 32, Bbox [151, 448, 593, 484], font LiberationSerif, color [0, 0, 0]
8. "PODS 2005 Y. Sakurai et al 3" in size 24, Bbox [81, 497, 676, 524], font LiberationSerif, color [0, 0, 0]
For image elements:
1. The image depicts a graph with two distinct lines plotted on a Cartesian coordinate system. The graph has a white background with a grid pattern, which aids in visualizing the data points and the trend lines. The x-axis and y-axis are not labeled, but the graph appears to be a standard Cartesian plane.nnThe graph contains two lines, each represented by a different color and style:n1. The first line is in red and is represented by a series of connected squares. This line starts at the bottom left corner of the graph and moves upwards, reaching a peak before descending back to the bottom right corner. The red line forms a smooth, Bbox [44, 254, 361, 453]
2. The image depicts a graph with two distinct lines plotted on a Cartesian coordinate system. The graph has a white background with horizontal and vertical grid lines to aid in visualizing the data points and trends. The x-axis and y-axis are not labeled, but the graph appears to be a standard Cartesian plane.nnThe graph features two lines, one in red and one in blue, each connecting a series of data points. The red line is positioned above the blue line throughout the graph, indicating that the values represented by the red line are consistently higher than those represented by the blue line.nnThe data points are represented by small squares, with the red squares Bbox [365, 254, 688, 453]
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A 512x512 text image with the following settings: font_size 180, font_type Bombalurinademo-OVWAo, rotation_degree 14, font_color [71, 82, 109], alignment left, displaying the text: I'm really glad you could all make it. Of course!
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The picture has The King of Games per lo Yu-Gi-Oh! Remote Duel Extravaganza: istruzioni per l'uso, with words DUEL,REMOTE,EXTRAVAGANZA,Sabato6&1,Domenica,KING,Scopel,tattlidettagli!.
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The picture frames arh_timber13_promo_graphic_450px, with visible RE,TIMB,OUTDOOR,July,26,Carnation,2013,Wash.
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A 512x512 text image with the following settings: font_size 96, font_type helveti, rotation_degree -15, font_color [7, 9, 13], alignment right, displaying the text: I just feel so mad all the time lately.
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The picture shows Buy About Love, Hate and the other ones CD Key Compare Prices, and Hate,AboutLove,,the,other,ones,Tobias,by,Bilgeri stands out.
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c8de5ca4-3d36-4cea-8f93-99b5bab5f2a8.png
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A serene dining room bathed in natural light, featuring a simple white notice board that adds a touch of functionality to the warm, inviting space. notice board with the text : ''In a warm and inviting dining room filled with natural light, a simple white notice board provides a subtle yet functional touch amidst the room's serene and character-filled atmosphere''
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This image presents custom canvas bag, plus MAKER, WORKSHOP, BAG, DRAWSTRING, CUSTOM, YOUR, DESIGN, HERE reading.
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d100f409f35442f4992e6468146fc890.jpg
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A 720x540 slide page. The page features a layout where the image and text are interspersed, with the image and text appearing separately, not fused together. The text will be provided with a specified bbox, font, and color.
For text elements should be displayed independently:
1. "Outline of experiments" in size 42, Bbox [43, 28, 531, 77], font DejaVuSerif, color [0, 102, 51]
2. " Speed vs db size" in size 30, Bbox [43, 132, 298, 166], font LiberationSans, color [0, 0, 0]
3. " Speed vs warping scope W" in size 30, Bbox [43, 176, 430, 209], font LiberationSerif-Italic, color [0, 0, 0]
4. " Effect of filtering" in size 30, Bbox [43, 219, 284, 253], font LiberationSans, color [255, 0, 0]
5. " Effect of varying-length data sequences" in size 30, Bbox [43, 263, 595, 297], font LiberationSans, color [0, 0, 0]
6. "PODS 2005 Y. Sakurai et al 40" in size 24, Bbox [81, 497, 676, 524], font LiberationSerif, color [0, 0, 0]
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A 512x512 text image with the following settings: font_size 44displaying the text: Additionally service related disabled US military veterans may seek an exemption from paying property taxes. Pennsylvania school district revenues are dominated by two main sources
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Depicting Relationships Break Up Messages to a Loved One, along with Relationships,Break,Up,Messages,Loved,One,to,a text.
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The picture shows Thanks a Million! Paperback, and text RAY,COMFORT,CAMERON,KIRK,Million!,Thanks,a.
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An image that renders the following text: Proof. The proof is done by induction. Since we fix m and j throughout the proof, we write N instead of N j m . For | k | ≤ m , ε k ≥ ˜ ω ( | k | ) ≥ ˜ ω ( m ) > θ ˜ ω ( m ) , hence N ( k ) = 0. Assume now that | k | > m . Then 2 | k | /m − 1 ≥ 1. If k ∈ K 1 then, by definition, δ k = ε − 1 k , so N ( k ) can only be equal to 0 or 1 and we are done. Let us suppose k ̸∈ K 1 ∪ K 2 . Write δ k = ε − 1 k δ k 1 · · · δ k ν , k = k 1 + · · · + k ν , ν ≥ 2 , with | k | > | k 1 | ≥· · · ≥| k ν | , and consider the following different cases. Observe that k − k 1 ̸∈ K 2 , otherwise the other k h ’s would be in K 2 . Case 1: ε k ≥ θ ˜ ω ( m ) and i k arbitrary, or ε k < θ ˜ ω ( m ) and i k ̸ = j . Then N ( k ) = N ( k 1 ) + · · · + N ( k ν ) , and applying the induction hypotheses to each term we get N ( k ) ≤ (2 | k | /m ) − 1. Case 2: ε k < θ ˜ ω ( m ) and i k = j . Then N ( k ) = 1 + N ( k 1 ) + · · · + N ( k ν ) , and there are three different cases. Case 2.1: | k 1 | ≤ m . Then N ( k ) = 1 < 2 | k | m − 1 , as we want. Case 2.2: | k 1 | ≥| k 2 | > m . Then there is ν ′ such that 2 ≤ ν ′ ≤ ν and | k ν ′ | > m ≥| k ν ′ +1 | , and we have N ( k ) = 1 + N ( k 1 ) + · · · + N ( k ν ′ ) ≤ 1 + 2 | k | m − ν ′ ≤ 2 | k | m − 1 . Case 2.3: | k 1 | > m ≥| k 2 | . Then N ( k ) = 1 + N ( k 1 ) , and there are three different cases. Case 2.3.1: i k 1 ̸ = j . Then N ( k 1 ) = 0 and we are done. Case 2.3.2: | k 1 | ≤| k | − m and i k 1 = j . Then N ( k ) ≤ 1 + 2 | k | − m m − 1 < 2 | k | m − 1 . Case 2.3.3: | k 1 | > | k | − m and i k 1 = j . The crucial remark is that ε − 1 k 1 gives no contribute to N ( k 1 ), as shown in the next lemma. Lemma 5.3. If k > k 1 with respect to the lexicographic order, k , k 1 and k − k 1 are not in K 2 , i k = i k 1 = j and ε k < θ ˜ ω ( m ) and ε k 1 < θ ˜ ω ( m ) , 15
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Portrayed is Click this cover for a(n) eBook sample of American Tabloid, and written JA,ES,M,ELLROY,AMERICAN,TABLOID,A,OVEL.
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The image is a slide from a presentation, titled WHO'S FAULT? The slide is numbered 11, as indicated in the bottom right corner. The content of the slide is divided into two sections, each listing different entities:nn1. **Managers**n2. **NOPS**nnThe text is presented in a simple, sans-serif font, and the background of the slide is plain white. The title WHO'S FAULT? is in a larger, bold font, making it the most prominent text on the slide. The entities Managers and NOPS are listed in a smaller font size, indicating
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The snapshot shows Keep Calm and Trust a Social Scientist Print, and notes KEEP,CALM,AND,TRUST,A,SOCIAL,SCIENTIST.
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A 512x512 text image with the following settings: font_size 123, font_color [10, 97, 122] displaying the text: [ fig : exp_res_ diag ].
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Here stands Spanish PowerPoint with AR, ER, & IR Regular Present Tense Verbs, and nearby, text reads Los,Verbos,Regulares,AR,,ER,-IR,e.
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A 512x512 text image with the following settings: font_size 238, font_type helveti, rotation_degree -40, font_color [59, 156, 72], alignment center, displaying the text: 1975.
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An image that renders the following text: J 3 2 T T S A 1 V M 2 -1/α΄ 1/α΄ 2/α΄ 0 Figure 1: The first excited levels of the open bosonic string. The state at the third level is a symmetric, traceless, rank-2 tensor T S of SO ( D − 1). At the fourth excited level there is an antisymmetric rank-2 tensor T A , of SO ( D − 1). If the open string carries Chan-Paton charges at its endpoints then these excited states have the same isotopic charges as the massless vector boson V on the first excited level. They allow to calculate different tree level scattering amplitudes for these tensor bosons. Our intension in this article is to compare the tree-level scattering amplitudes of the second rank tensor gauge bosons in non-Abelian tensor gauge field theory and tree-level scattering amplitudes of the tensor bosons in open string theory with Chan-Paton charges. Our aim is two-fold: first, to review the general structure of the interaction vertices in non-Abelian tensor gauge field theory [27, 28, 29] and, second, to calculate similar tree-level scattering amplitudes in the open string theory in order to compare their structures. By ”similar” tree-level scattering amplitudes we mean the special selection of amplitudes of the open string theory when the corresponding amplitudes in four-dimensional space-time have dimensionless coupling constants . These amplitudes should have only one space-time derivative in the case of triple interaction vertices and have no derivatives in the case of quartic interactions. We are choosing this subclass of interaction amplitudes of open string theory because this subsector of amplitudes with dimensionless coupling constants naturally appears in the low-energy limit when one can ignore the higher derivative terms. Only this subclass of vertices appears in non-Abelian tensor gauge field theory [27, 28, 29]. The open string tree-level scattering amplitudes are defined only on the mass-shell [2, 3]. Therefore in order to compare them with the tensor gauge field theory vertices we have to project them to the mass-shell. We have found that after projection the scattering amplitudes with dimensionless coupling constant for the lower-rank tensor fields in these theories coincide. This result tells that most probably the subsector of the open string 3
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The snapshot shows PIAA Si-Tech Multi Adapter Silicone Flat Wiper Blade, plus PIAA,HIGH,PERFORMANCE,WIPERS,PIAA,Si-Tech,HK,Auto.
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An image that renders the following text: RESAMPLING CONFIDENCE REGIONS IN HIGH DIMENSION 13 Table 1 ). Proofs are given in Section 5.3 , where several other weights are considered. Now, to use Theorem 2.1 or Corollary 2.2 , we have to choose a particular resampling weight vector. In the Gaussian case, we propose the following accuracy and complexity criteria: • First, relation ( 7 ) suggests that the quantity C W B − 1 W can be proposed as an accuracy index for W . Namely, this index enters directly into the deviation term of the upper bound (while we know from Proposition 2.3 that the expectation term is exact) so that the smaller this index is, the sharper the bound. • Second, an upper bound on the computational burden of exactly comput- ing the resampling quantity is given by the cardinality of the support of D ( W ), thus providing a complexity index. These two criteria are estimated in Table 2 for classical weights. For any exchangeable weight vector W , we have C W B − 1 W ≥ [ n/ ( n − 1)] 1 / 2 and the cardinality of the support of D ( W ) is larger than n . Therefore, the leave- one-out weights satisfy the best accuracy/complexity trade-offamong ex- changeable weights. 2.5. Practical computation of the thresholds. In practice, the exact com- putation of the resampling quantity E W [ φ ( Y ⟨ W − W ⟩ )] can still be too com- plex for the weights defined above. In this section, we consider two possi- ble ways to address this issue. First, it is possible to use nonexchangeable weights with a lower complexity index and for which the exact computation is tractable. Alternatively, we propose to use a Monte Carlo approximation, as is often done in practice to compute resampled quantities. In both cases, the thresholds have to be made slightly larger in order to keep a rigourous nonasymptotic control on the level. This is detailed in the two paragraphs below. Table 2 Choice of the resampling weight vectors: accuracy/complexity trade-off Resampling C W B − 1 W (accuracy) | supp D ( W ) | (complexity) n ) − n −−−−→ n →∞ 2 u0000 2 n − 1 n − 1 u0001 = Θ( n − 1 / 2 4 n ) Efron ≤ 1 2 (1 − 1 e Rademacher ≤ n/ ( n − 1) −−−−→ n →∞ 1 2 n n − 1 −−−−→ n →∞ 1 u0000 n n/ 2 u0001 = Θ( n − 1 / 2 2 n ) rho( n/ 2) = q n Leave-one-out = q n n − 1 −−−−→ n →∞ 1 n Regular V -fcv = q n V − 1 V
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A 512x512 text image with the following settings: font_size 87, font_type helveti, rotation_degree 21, font_color [121, 50, 95], alignment left, displaying the text: he was once again elected to Parliament
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A 512x512 white background image. The image features a layout where the image and text are interspersed, with the image and text appearing separately. And the text will be positioned around it based on the given bounding boxes.
For image elements:
1. The image shows a close-up of a unique flower with a long, slender, pinkish-pink stem and a small, white, furry structure at the top, surrounded by green, needle-like leaves. The background is blurred, featuring more green foliage. Bbox [277, 190, 506, 464]
For text elements should be displayed independently in font Arial-ItalicMT:
1. "List of Adenanthos species" in size 83, Bbox [5, 0, 506, 47]
2. "This is a list of Adenanthos species, subspecies" in size 83, Bbox [5, 85, 500, 181]
3. "This is a list of Adenanthos species, subspecies" in size 91, Bbox [5, 190, 249, 460]
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A book cover for Where is Curious George? Around the Town: A Look-and-Find Book; H. A. Rey; Children's Books;
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A 512x512 white background image. The image features a layout where the image and text are interspersed, with the image and text appearing separately. And the text will be positioned around it based on the given bounding boxes.
For image elements:
1. The image is an ornate, black-and-white woodcut illustration featuring a central figure with wings and a halo, flanked by cherubs and surrounded by architectural elements and foliage. The style is reminiscent of medieval or Renaissance art. Bbox [5, 85, 236, 384]
For text elements should be displayed independently in font Georgia-Italic:
1. "Johann Froben" in size 100, Bbox [85, 0, 426, 56]
2. "Johann Froben, in Latin: Johannes Frobenius, was" in size 83, Bbox [242, 84, 441, 381]
3. "Froben's work in Basel made that city in the 16th" in size 87, Bbox [5, 389, 501, 491]
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A 512x512 text image with the following settings: font_size 134 , font_type SincereValentinePersonalUs-9YqvL , alignment centerdisplaying the text: But we haven't decided for sure yet.
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A 512x512 text image with the following settings: font_size 162, font_type helveti, rotation_degree -19, font_color [17, 39, 231], alignment left, displaying the text: I'll tell the truth.
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A 512x512 white background image. The image features a layout where the image and text are interspersed, with the image and text appearing separately. And the text will be positioned around it based on the given bounding boxes.
For image elements:
1. The image shows a panoramic view of a residential area with houses and trees, with a large plume of smoke rising from a distant hill, indicating a fire. The sky is clear, and the smoke is dense, covering a significant portion of the landscape. Bbox [232, 190, 506, 464]
For text elements should be displayed independently in font CourierNewPS-BoldMT:
1. "Hoon Hay" in size 90, Bbox [147, 3, 363, 54]
2. "Hoon Hay is an outer suburb of Christchurch, New" in size 61, Bbox [5, 87, 506, 159]
3. "Hoon Hay is an outer suburb of Christchurch, New" in size 76, Bbox [5, 192, 302, 464]
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The scene shows Warda Lawn Summer Spring Dresses Collection 2014 for women (6), adding WARD,NTS,RI,Spring,Summer,Collection,2014.
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This snapshot contains Seeing Systems: Unlocking the Mysteries of Organizational Life, with Oshry,Barry,Seeing,Systems,Unlocking,Nysteries,the.
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2e17439970524c6797d47d89f8249c85.jpg
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A book cover for Wrestling the Angel: The Foundations of Mormon Thought: Cosmos, God, Humanity; Terryl L. Givens; Christian Books & Bibles;
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A 512x512 text image with the following settings: font_size 43, font_color [69, 66, 66] displaying the text: He made his acting debut in 1969 with the stage drama "Sokkano Rajano" produced by Sathischandra Edirisinghe. Then he acted in many stage plays such as "Kekille", "Deshapaluwa", "Manape"
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A 512x512 white background image. The image features a layout where the image and text are interspersed, with the image and text appearing separately. And the text will be positioned around it based on the given bounding boxes.
For image elements:
1. The image depicts a futuristic, industrial scene with a large, glowing, orange structure in the center, surrounded by metallic elements and a bright light source in the background. Bbox [307, 85, 506, 284]
2. The image depicts a spherical object with a dark, glossy surface and fiery, orange-red patterns that resemble flames or energy. The object has a symmetrical design with a bright, glowing center. Bbox [5, 290, 179, 464]
For text elements should be displayed independently in font Trebuchet-BoldItalic:
1. "Halo: Cryptum is a military science" in size 62, Bbox [5, 4, 408, 77]
2. "fiction novel by Greg Bear, based on" in size 70, Bbox [5, 84, 286, 208]
3. "the Halo series of video games. The" in size 70, Bbox [185, 289, 478, 371]
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We note if mom says no just ask grumpy instead mouse pad, and read MOM, If, says, No, just, ask, Grampy, instead.
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A serene rural landscape features a large billboard with the text : ''The beauty of nature is a reminder of the importance of preserving our planets biodiversity, from majestic mountains to vibrant coral'' set against a tranquil sky and distant hills.
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the text : ''A blank digital display mounted on the wall at the hospital's outpatient clinic remains unused, devoid of appointment reminders, health advisories, or any other informative content''.
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An image that renders the following text: T angent and A djoint diu001ber entiation of OP A 13 far from optimal. On one hand sev eral alls are b etter not he kp oin ted, and T APENADE no w ou001bers the option to mark sele ted alls for not he kp oin ting. On the other hand, he kp oin ting should b e applied at other lo ations. F or example at the top lev el of the sim ulation program is a lo op o v er man y time steps. W e deu001cnitely need an eu001e ien t he kp oin ting s heme applied at this lev el of time iterations. One lassi al solution used b y T AF on the MIT GCM o de [14℄, is alled m ulti lev el re ursiv e he kp oin ting. Basi ally , it splits the omplete time in ter- v al in to a small n um b er of equidistan t in terv als, then apply the same strategy to ea h of the sub-in terv als. F or instan e 64 time steps an b e split in to 4 large in terv als of 4 small in terv als of 4 time steps, as sk et hed on gure 3. This onsumes a maxim um of 9 sim ultaneous snapshots, and the a v erage n um b er of dupli ate exe utions for a time step is 2 . 25 . In a more realisti situation, 1000 time steps an b e split in to 10 large in terv als of 10 small in terv als of 10 time steps, and one an gure out that this onsumes a maxim um of 27 sim ultaneous snapshots, and the a v erage n um b er of dupli ate exe utions for a time step is 2 . 7 . 0 62 61 60 56 16 0 0 0 32 16 16 48 32 32 52 48 56 52 58 57 54 53 50 49 40 36 36 46 45 44 40 42 41 38 37 34 33 24 20 20 30 29 28 24 26 25 22 21 18 17 8 4 4 14 13 12 8 10 9 6 5 2 1 Figure 3: Three-lev els he kp oin ting with 64 time steps and 9 snapshots. F or- w ard omputations go righ t, adjoin t omputations go left. Bla k ir les rep- resen t writing/taking a snapshot, white ir les represen t reading an a v ailable snapshot. RR n° 6372
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The illustration has tom waits under the bridge, and TOMWAITS, THE, UNDER, BRIDGE, CLASSIC, SHOW, THE, BENEFIT noted.
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A serene study with a weathered wooden desk, a stack of books, a globe, and a leather armchair bathed in warm natural light, creating a tranquil and inviting atmosphere. printed paper with the text : ''A serene and inviting atmosphere is created on the weathered wooden desk as the pure blue paper, bathed in warm natural light, subtly blends into the rustic study's cozy ambiance''
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A 512x512 text image with the following settings: font_size 35displaying the text: She was originally built in 1886 for the Brazil and River Plate Line of the Messageries Maritimes Company. She was chartered or purchased by the Russians for use as a hospital ship in the Black Sea. The ship, serviced to take up wounded soldiers along the sea shore Ardeshen Rize Port Fakhtia Tiribon and Of
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A 512x512 text image with the following settings: font_size 90 , font_type Ginger , alignment centerdisplaying the text: this coupled with the reduced forward momentum of standing water in a reservoir
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A 512x512 text image with the following settings: font_size 49 , font_color [108, 109, 109] displaying the text: 29. 1% of all households were made up of individuals and 9. 7% had someone living alone who was 65 years of age or older. The average household size was 2. 47 and the average family size was 3. 03. In the city
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A 512x512 text image with the following settings: font_size 130, font_type helveti, rotation_degree 39, font_color [216, 137, 52], alignment left, displaying the text: there was a small
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A 512x512 text image with the following settings: font_size 59, font_type HannahHudson-rgK4p, rotation_degree 11, font_color [52, 100, 121], alignment right, displaying the text: Now Tabitha gets nervous. Tabitha prepared to give a speech by reading over her notes one last time.
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The snapshot features Rock City 12 - The Baubles Are Back In Town CD, plus THUNDER,THE,ROCK,JBLESARE,BACK,IN,TOWN!,CITY12.
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The picture includes HARVEST DELIGHT Longan / Kelengkeng in Syrup Kaleng 565 Gr | Shopee Indonesia, plus Waraya,quality,theline,LONGAN,in,syrup,10710,565g.
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A 512x512 white background image. The image features a layout where the image and text are interspersed, with the image and text appearing separately. And the text will be positioned around it based on the given bounding boxes.
For image elements:
1. A woman with curly hair, wearing a black top and a leopard print bag, smiles while standing near a table with a laptop and a cup. Bbox [5, 190, 261, 489]
For text elements should be displayed independently in font LucidaHandwritingStd:
1. "Deborah Estrin" in size 118, Bbox [11, -13, 1012, 149]
2. "Deborah Estrin is a Professor of Computer Science" in size 62, Bbox [5, 81, 506, 161]
3. "Deborah Estrin (born December 6, 1959) is a" in size 83, Bbox [266, 185, 494, 492]
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A 512x512 text image with the following settings: font_size 122, font_color [58, 36, 81] displaying the text: It's nice to meet you. Likewise!
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A 512x512 text image with the following settings: font_size 66, font_color [157, 139, 139] displaying the text: parent ions were selected from a mass range of 30010 000 da with a minimum peak count of 1.
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A 512x512 text image with the following settings: font_size 108displaying the text: I had a lot of fun with my friends.
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A 512x512 text image with the following settings: font_size 223, font_type helveti, rotation_degree -26, font_color [117, 170, 146], alignment right, displaying the text: Selma.
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The image is a screenshot of a presentation slide, likely from a mathematics course, specifically focusing on set theory. The slide is titled Set Properties and Set Notation and is part of a section on Set Operations. The content of the slide is as follows:nn---nn**Title:**nSet Properties and Set NotationnSet Operationsnn**Example:**nList all subsets of the set ( A = {b, c, d} ).nn---nn### Analysis and Description:nn1. **Title and Section:**n - The title Set Properties and Set Notation indicates that the slide is part of a broader
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A 512x512 text image with the following settings: font_size 145, font_type BantahKidul-8MVdg, rotation_degree 23, font_color [41, 29, 194], alignment center, displaying the text: It would definitely help you save some money.
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We can spot a box of cigarettes and a box of candy, and text appearing as laund, KINGS, Up, CANDY, CTORY, CANDY, CANDY.
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An image that renders the following text: Names J GK Tau = 2 1.5 1.5 Flux density (Jy) 1 1 0.5 0.5 0 0 6 8 10 12 14 15 20 25 30 35 Names J GM Aur = 1.5 0.25 0.2 Flux density (Jy) 1 0.15 0.1 0.5 0.05 0 0 6 8 10 12 14 15 20 25 30 35 Wavelength (microns) Wavelength (microns)
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This snapshot displays kim kardashian wedding album, and SIVE, OS, Weddi, Crazy, CELEBRITY, Albi, WEDDING, PEND.
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The image is a screenshot of a data visualization created using Tableau Software. The title of the visualization is Domestic Loan Analysis, and it appears to be a comprehensive analysis of loan data across different regions in the United States. The data visualization is divided into two main sections, each providing different insights into the loan data.nn### Top Section: Loan by GeographynThis section of the visualization is a map of the United States, with each state represented by a pie chart. The pie charts are color-coded to represent different loan amounts. The legend on the right side of the map indicates the color codes for various loan amounts:n- Red:
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The image is a promotional graphic for Amazon, an American electronic commerce company. The graphic is divided into two main sections: a textual description on the left and an image of a cloud logo on the right.nn### Textual Description:nThe text is written in a clear, readable font and provides an overview of Amazon's history, products, and services. Here is the transcription of the text:nn**Amazon**nAmazon.com, Inc. is an American electronic commerce company with headquarters in Seattle, Washington. It is the largest Internet-based retailer in the United States. Amazon.com started as an online bookstore, but soon diversified, selling DVDs, Blu-rays
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A 512x512 text image with the following settings: font_size 37displaying the text: which was originally licensed in 1991. This is the first product to be passed under the Biologics Price Competition and Innovation Act of 2009 (BPCI Act), which was passed as part of the Affordable Healthcare Act. But Zarxio was approved as a biosimilar not as an interchangeable product
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In this snapshot, ticket to ride first journey, and RMoon, Alan, RIDE, TICKETTO, Journey, First, DAYS, WONDER appear.
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The picture contains 3 Reasons to Switch to Natural Toothpaste Today, plus REASONS,THREE,TOOTHPASTE,NATURAL,IS,BETTER,ecocentric,mom.
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An image that renders the following text: the constant b 0 introduced in [4]. In Appendix 2 we give an independent and instructive proof of Proposition 1 which is similar to Lemma 13. In some sence Proposition 1 is even more strong than Lemma 13 since to apply it one does not need a bound for the stabilization of the Hilbert function. Of course, the reference to Proposition 1 can be used in place of Lemma 13 in our paper. 1 Definition of the Janet basis Let A = F [ X 1 , . . . , X n , D 1 , . . . , D n ], n ≥ 1, be a Weyl algebra over a field F of zero–characteristic. So A is defined by the following relations X v X w = X w X v , D v D w = D w D v , D v X v − X v D v = 1 , X v D w = D w X v , v ̸ = w. (1) By (1) any element f ∈ A can be uniquely represented in the form f = X i 1 ,...,i n ,j 1 ,...,j n ≥ 0 f i 1 ,...,i n ,j 1 ,...,j n X i 1 1 . . . X i n n D j 1 1 . . . D j n n , (2) where all f i 1 ,...,i n ,j 1 ,...,j n ∈ F and only a finite number of f i 1 ,...,i n ,j 1 ,...,j n are nonzero. Denote for brevity Z + = { z ∈ Z : z ≥ 0 } to the set of all nonnegative integers and i = ( i 1 , . . . , i n ) , j = ( j 1 , . . . , j n ) , f i,j = f i 1 ,...,i n ,j 1 ,...,j n X i = X i 1 1 . . . X i n n , D j = D j 1 1 . . . D j n n , f = P i,j f i,j X i D j , | i | = i 1 + . . . + i n , i + j = ( i 1 + j 1 , . . . , i n + j n ) . (3) So i, j ∈ Z n + are multiindices. By definition the degree of f deg f = deg X 1 ,...,X n ,D 1 ,...,D n f = max {| i | + | j | : f i,j ̸ = 0 } . Let M be a left A -module given by its generators m 1 , . . . , m l , l ≥ 0, and relations X 1 ≤ w ≤ l a v,w m w , 1 ≤ v ≤ k. (4) where k ≥ 0 and all a v,w ∈ A . We assume that deg a v,w ≤ d for all v, w . By (4) we have the exact sequence A k ι → A l π → M → 0 (5) of left A -modules. Denote I = ι ( A k ) ⊂ A l . If l = 1 then I is a left ideal of A and M = A/I . In the general case I is generated by the elements ( a v, 1 , . . . , a v,l ) ∈ A l , 1 ≤ v ≤ k. For an integer m ≥ 0 put A m = { a : deg a ≤ m } , M m = π ( A l m ) , I m = I ∩ A l m . (6) So now A , M , I are filtered modules with filtrations A m , M m , I m , m ≥ 0, respectively and the sequence of homomorphisms of vector spaces 0 → I m → A l m → M m → 0 4
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A 512x512 white background image. The image features a layout where the image and text are interspersed, with the image and text appearing separately. And the text will be positioned around it based on the given bounding boxes.
For image elements:
1. The image is a black and white engraving of a man with long, curly hair. He has a mustache and is wearing a high-collared garment. The background is plain, emphasizing the subject. Bbox [258, 190, 506, 489]
For text elements should be displayed independently in font Arial-BoldItalicMT:
1. "Joachim von Sandrart" in size 95, Bbox [5, 0, 505, 53]
2. "Joachim von Sandrart was a German Baroque" in size 83, Bbox [5, 85, 466, 181]
3. "Joachim von Sandrart (12 May 1606 – 14 October" in size 84, Bbox [5, 190, 252, 440]
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A 512x512 white background image. The image features a layout where the image and text are interspersed, with the image and text appearing separately. And the text will be positioned around it based on the given bounding boxes.
For image elements:
1. The image shows a stone bust of a bearded man with a headband, placed against a stone wall. Bbox [301, 190, 506, 464]
For text elements should be displayed independently in font TimesNewRomanPS-ItalicMT:
1. "532 BC" in size 109, Bbox [339, 0, 506, 61]
2. "The year 532 BC was a year of the preJulian" in size 83, Bbox [5, 85, 477, 181]
3. "The year 532 BC was a year of the preJulian" in size 109, Bbox [5, 190, 281, 449]
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A 512x512 white background image. The image features a layout where the image and text are interspersed, with the image and text appearing separately. And the text will be positioned around it based on the given bounding boxes.
For image elements:
1. The image is a book cover titled On Her Six by Christina Elle. It features a muscular man with a shirt partially pulled down, revealing his upper body. Bbox [282, 5, 506, 229]
2. The image shows a tablet displaying the cover of a book titled On Her Sex by Christina Elle. The tablet is surrounded by various office supplies and decorative items on a white surface. Bbox [332, 235, 506, 409]
For text elements should be displayed independently in font Georgia-Bold:
1. "Blog Tour: On Her Six by Christina Elle" in size 80, Bbox [5, 4, 256, 194]
2. "Elle" in size 80, Bbox [5, 234, 84, 280]
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The portrayal: 50 Original Film Soundtracks Great Moments & Overtures, text reading ORIGINAL,FILM,50s,SOUNDTRACKS,GREAT,MOMENTS,OVERTURES.
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The image is a slide from a presentation, likely related to astronomy or astrophysics, focusing on the topic of Spektralanalyse Sternmassen, which translates to Spectral Analysis of Star Masses. The slide is in German and contains several key elements:nn1. **Title and Subtitle:**n - The main title at the top reads SPEKTRALANALYSE STERNMASSEN, indicating the focus on spectral analysis of star masses.n - Below the main title, there is a subtitle that reads Visuelle Doppelsterne, which translates to Visual Double
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A 512x512 text image with the following settings: font_size 104, font_type helveti, rotation_degree 6, font_color [148, 149, 148], alignment left, displaying the text: We're just about to get started. Okay
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A 512x512 white background image. The image features a layout where the image and text are interspersed, with the image and text appearing separately. And the text will be positioned around it based on the given bounding boxes.
For image elements:
1. A band performs on stage with a drummer, guitarist, and two vocalists. The drummer is in the center, with a microphone stand and drum set. The vocalist on the left wears a pink shirt and purple shorts, while the one on the right wears a red and white shirt with green pants. The stage is illuminated by spotlights. Bbox [5, 190, 254, 439]
For text elements should be displayed independently in font Papyrus-Condensed:
1. "Puffy AmiYumi" in size 109, Bbox [269, -3, 754, 166]
2. "Puffy is a Japanese pop rock duo formed in Tokyo" in size 83, Bbox [5, 83, 433, 197]
3. "Puffy ( パ フィー , Pafī, romanized as PUFFY) is a" in size 105, Bbox [260, 182, 506, 460]
4. "Yumi Yoshimura (left) and Ami Onuki (right)" in size 41, Bbox [5, 441, 236, 498]
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We notice Renewable and Nonrenewable Resources: Activity BUNDLE, and the text Renewable,&,Renewable,Non-,BINDLE,JH,Lesson,Design appears.
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The snapshot: Shakira at the Los Angeles premiere of 'Zootopia' held at the El Capitan Theater in Hollywood, USA on February 17, 2016., with Google,Photos,OPIA,ZOoTOPIA,PREMIERE,118603997,www,bigstock.com visible.
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