The AnglE model introduces angle optimization to address common challenges like vanishing gradients and underutilization of supervised negatives in Large Language Models (LLMs). By enhancing the gradient and optimization processes, this novel approach improves text embedding learning effectiveness.

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Discover how to solve right triangles using trigonometric ratios and angle measures. Explore examples and real-world applications, such as calculating street grades in San Francisco. Learn how to identify angles using sine, cosine, and tangent ratios, and use inverse trigonometric functions to find

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Prisms are optical devices that deviate light without changing its vergence. This module explores the various terminology associated with prisms, including Apex, Base, Refracting Angle, and Angle of Deviation. The passage of light through a prism follows Snell's Law, where the ray is deviated toward

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Fresnel prisms, a type of prism where the angle of refraction only depends on the surface angle and material's refractive index, offer advantages such as thinness, lightweight, and flexibility but have disadvantages like cosmetic differences and reduced visual performance. They find applications in

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Explore key geometry vocabulary such as congruent, vertical, adjacent, complementary, and supplementary angles. Learn how to identify different types of angle pairs and calculate unknown angle measures using angle relationships. Visual examples and explanations enhance understanding.

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Detailed instructions on how to operate a Kruss goniometer contact angle analyzer. Learn how to set up the equipment, prepare the sample, adjust camera focus, measure contact angle, and analyze the results. Follow each step carefully to achieve accurate measurements.

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Glaucoma, the 3rd leading cause of blindness in Uganda, is primarily managed by General Ophthalmologists across 20 hospitals in the country. Uganda lacks Glaucoma subspecialists and specialized nurses. Equipment availability varies among hospitals. Cases in Uganda are typically identified through re

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Learn how to rotate shapes around a center by a specified angle and describe the resulting transformation. Explore concepts like center of rotation, angle, and sense of rotation. Practice rotations with various examples and understand the process step by step.

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In this educational material, students will learn to differentiate between acute, right, and obtuse angles. They will practice identifying angles, ordering them from smallest to largest, and determining angles within various shapes. The content also includes reasoning exercises to enhance understand

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This strand delves into trigonometric problems focusing on triangles with mixed information, exploring side lengths and angle measurements beyond right-angled triangles. It covers mixed problems, sine and cosine rules, applying area of any triangle, and Heron's formula. Engage in various exercises i

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Explore the Vocabulary of Exterior Angle Inequality Theorem, Angle-Side Relationship Theorems 5.9 and 5.10. Understand how to order triangel angle measures and side lengths from smallest to largest through examples. Discover the principles governing triangles in terms of angles and side lengths.

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This content explains the concept of exterior angles in polygons and the Exterior Angle Theorem. It covers how exterior angles are formed when the sides of a polygon are extended, their relationship with interior angles, and how to calculate their measures using the Exterior Angle Theorem. Various e

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Explore the EmPower Oarlock and SpeedCoach GPS systems for rowing, providing real-time feedback on stroke metrics like length, blade engagement, and force. Customize your display with various metrics and receive technical feedback on improving catch angle, finish angle, blade engagement, and more. E

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Lorentz transformations have profound consequences in the realm of special relativity. Length contraction results in objects appearing shorter in the direction of motion, with the amount of contraction determined by the Lorentz transformation. Time dilation causes clocks in moving frames to run slow

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Photography is a form of art that involves various creative expressions, including the use of different camera angles to capture unique perspectives. This content explores different camera angles such as high-angle shot, low-angle shot, Dutch angle, and straight angle, each offering a distinct visua

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This supplemental content presents comparisons of dyslipidaemia, final minimal luminal diameter (MLD), distance between ostium of the LAD and proximal edge of the stent, lesion length, and various angle measurements in different restenosis groups. The findings highlight significant differences in dy

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Explore advanced calibration and alignment techniques in CGEM technology, including Lorentz angle correction, spatial resolution analysis, drift velocity computation, time-related calibration, and alignment methods. Learn about misalignment motivations and strategies to improve track reconstruction

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This project focuses on calculating modifications to the Newtonian gravitational force through experimental short-range tests of gravity. Utilizing the Standard-Model Extension (SME) test framework to search for potential violations of General Relativity and Newtonian Gravity. Key objectives include

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This briefing delves into the potential physical and infrastructure effects of an impact event with an asteroid of up to 400 meters in diameter, traveling at a speed of 16 km/s. The simulation highlights the significant threat of tsunamis resulting from such an impact, with tsunami strength varying

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Explore the concept of four-vectors in four-dimensional space, covering topics such as radius vectors, general 4-vectors, contravariant and covariant components, summation conventions, scalar products, and the components of a general 4-vector. Learn how these vectors transform under rotations and Lo

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Delve into the principles of congruent triangles by exploring the properties of side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), and right-angle-hypotenuse-side (RHS) congruence. Visual explanations help clarify how these properties determine if triangles are congruent.

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Explore concepts such as light polarization angles, resonance frequency of LRC circuits, Lorentz Force Law, Gauss Law, Faraday's Law, and Ampere-Maxwell Law in Physics 213. Delve into the interplay between electric and magnetic fields, and their effects on charged particles such as electrons and pro

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Delve into the world of quantum field theory, gauge symmetry, Higgs mechanism, electroweak theory, and more with this detailed overview of the Standard Model. Explore classical mechanics, Noether's theorem, relativistic mechanics, quantum mechanics, and quantum field theory concepts. Discover how th

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This discussion covers various topics such as tents (or Carleson boxes), outer measures on the open upper half-plane, sizes of functions on tents, outer essential supremum on subsets, outer Lp spaces, embedding theorems, and estimates related to Linfity-Sinfty and weak L1-Sinfty. The content delves

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Polar coordinates define the location of a point in terms of distance and angle from an origin. The distance is denoted by "r" and the angle by "?". However, the angle is not unique for a point. The concept involves fixing an origin and an initial ray, with positive angles measured counterclockwise.

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In this lesson on additive angle measures, students learn how to find missing angle measures when two non-overlapping angles combine to form a larger angle. Essential questions are posed, and students are guided through solving problems involving angle decomposition and measurement. Practical activi

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Explore the concepts of equidistance and angle bisectors in geometry through practical examples like determining the path for John to walk equidistant from a hedge and a wall, understanding the ideal flight path for a plane to land, constructing angle bisectors, and verifying constructions for accur

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Dive into the world of geometry with various diagrams and scenarios focusing on angle sums, concave and convex polygons, and angle measurements. Learn about properties of polygons and test your skills in identifying different shapes and their classifications based on their properties. Explore angles

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This analysis focuses on the magnetic model of a 20T hybrid block-coil V5.8 system, including modifications to incorporate ribs, iron components, rigid boundaries, component bonding, sliding and separating configurations, and stress evaluations. The study explores the layout adjustments, peak magnet

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The Hall effect, discovered by Edwin Hall in 1879, is utilized in magnetic sensors to detect magnetic fields by measuring the Lorentz force on moving charges. Hall sensors generate a Hall voltage based on the positive and negative charge carriers present. Integrated Hall sensors provide detailed spe

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Explore the application of angle-pair theorems in finding missing angle measures using properties of parallel lines. Learn about different types of angle pairs such as vertical angles, corresponding angles, same-side interior angles, alternate exterior angles, and more through engaging activities an

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Explore the world of angles with definitions of angle parts, types of angles, angle pairs, Angle Addition Postulate, and more. Dive into examples and classwork exercises to enhance your understanding of angles in geometry.

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Learn how to apply angle pair theorems using properties of parallel lines to find missing angle measures. Explore concepts like corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles through visual aids and practice problems.

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Explore the Polygon Angle-Sum Theorems that determine the sum of interior angle measures in polygons. Learn about the Polygon Angle-Sum Theorem, number of sides in polygons, finding angle sums, and the corollary for regular polygons. Practice using the theorems to calculate interior angle measures i

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This content delves into understanding triangle congruence and similarity through various scenarios and visual representations. It discusses how to determine congruence using side-side-side, side-angle-side, and angle-side-angle criteria, and explores the concept of similarity in triangles based on

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Explore the essential concepts of relativity, mathematics, statistics, and lab methods crucial for the GRE. Delve into special relativity, reference frames, velocity addition, Lorentz transformations, and relativistic collisions. Gain insights into key relationships, relativistic mass, momentum, kin

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Learning about parallel lines involves using angle facts like those on a straight line or around a point. By interpreting what a transversal is, you can apply angle relationships such as corresponding, alternate, co-interior, and vertically opposite angles. Practice finding unknown angles and identi

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Glaucoma is a group of eye conditions that can lead to irreversible vision loss. There are different types such as open-angle, closed-angle, secondary, and normal-tension glaucoma, each with unique characteristics and causes. Symptoms vary from rapid damage in closed-angle glaucoma to gradual periph

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Exploring the Dirac equation for spin particles within the framework of special theory of relativity. Topics covered include energy-momentum relationships, basics of special relativity, Lorentz transformations, and relativistic effects on particles. The lecture delves into the interplay between quan

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Framing Riemannian Geometry as a Generalized Lie Algebra to combine General Relativity with Quantum Theory. The proposal extends Heisenberg Algebra to incorporate a more general geometry, allowing for a function of position in commutator relationships. The discussion covers historical developments,

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