At Least One Symbol Assignment Changed Tramaine

UDL Guidelines - Version 2.0: Principle I. Provide Multiple Means of Representation

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Learners differ in the ways that they perceive and comprehend information that is presented to them. For example, those with sensory disabilities (e.g., blindness or deafness); learning disabilities (e.g., dyslexia); language or cultural differences, and so forth may all require different ways of approaching content. Others may simply grasp information quicker or more efficiently through visual or auditory means rather than printed text. Also learning, and transfer of learning, occurs when multiple representations are used, because they allow students to make connections within, as well as between, concepts. In short, there is not one means of representation that will be optimal for all learners; providing options for representation is essential.

Guideline 1: Provide options for perception

PerceptionLanguage, expressions, and symbolsComprehension

Learning is impossible if information is imperceptible to the learner, and difficult when information is presented in formats that require extraordinary effort or assistance. To reduce barriers to learning, it is important to ensure that key information is equally perceptible to all learners by: 1) providing the same information through different modalities (e.g., through vision, hearing, or touch); 2) providing information in a format that will allow for adjustability by the user (e.g., text that can be enlarged, sounds that can be amplified). Such multiple representations not only ensure that information is accessible to learners with particular sensory and perceptual disabilities, but also easier to access and comprehend for many others.

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Checkpoint 1.1 Offer ways of customizing the display of information

In print materials, the display of information is fixed and permanent.  In properly prepared digital materials, the display of the same information is very malleable and customizable.  For example, a call-out box of background information may be displayed in a different location, or enlarged, or emphasized by the use of color, or deleted entirely. Such malleability provides options for increasing the perceptual clarity and salience of information for a wide range of learners and adjustments for preferences of others. While these customizations are difficult with print materials. They are commonly available automatically in digital materials, though it cannot be assumed that because it is digital it is accessible as many digital materials are equally inaccessible. Educators and learners should work together to attain the best match of features to learning needs.

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  • Display information in a flexible format so that the following perceptual features can be varied:
    • The size of text, images, graphs, tables, or other visual content
    • The contrast between background and text or image
    • The color used for information or emphasis
    • The volume or rate of speech or sound
    • The speed or timing of video, animation, sound, simulations, etc.
    • The layout of visual or other elements
    • The font used for print materials 

Checkpoint 1.1: View examples and resources

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Checkpoint 1.2 Offer alternatives for auditory information

Sound is a particularly effective way to convey the impact of information, which is why sound design is so important in movies and why the human voice is particularly effective for conveying emotion and significance. However, information conveyed solely through sound is not equally accessible to all learners and is especially inaccessible for learners with hearing disabilities, for learners who need more time to process information, or for learners who have memory difficulties. In addition, listening itself is a complex strategic skill that must be learned. To ensure that all learners have access to learning, options should be available for any information, including emphasis, presented aurally.  

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  • Use text equivalents in the form of captions or automated speech-to-text (voice recognition) for spoken language
  • Provide visual diagrams, charts, notations of music or sound 
  • Provide written transcripts for videos or auditory clips
  • Provide American Sign Language (ASL) for spoken English
  • Use visual analogues to represent emphasis and prosody (e.g., emoticons, symbols, or images)
  • Provide visual or tactile (e.g., vibrations) equivalents for sound effects or alerts 
  • Provide visual and/or emotional description for musical interpretation 

Checkpoint 1.2: View examples and resources

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Checkpoint 1.3 Offer alternatives for visual information

Images, Graphics, Animations, Video, or Text (see below) are often the optimal way to present information, especially when the information is about the relationships between objects, actions, numbers, or events.  But such visual representations are not equally accessible to all learners, especially learners with visual disabilities or those who are not familiar with the type of graphic being used. Visual information can be quite dense, particularly with visual art, which can have multiple complex meanings and interpretations depending on contextual factors and the viewer’s knowledge base. To ensure that all learners have equal access to information, it is essential to provide non-visual alternatives.

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  • Provide descriptions (text or spoken) for all images, graphics, video, or animations
  • Use touch equivalents (tactile graphics or objects of reference) for key visuals that represent concepts
  • Provide physical objects and spatial models to convey perspective or interaction
  • Provide auditory cues for key concepts and transitions in visual information

Checkpoint 1.3: View examples and resources

Text is a special case of visual information. The transformation from text into audio is among the most easily accomplished methods for increasing accessibility.  The advantage of text over audio is its permanence, but providing text that is easily transformable into audio accomplishes that permanence without sacrificing the advantages of audio.  Digital synthetic Text-To-Speech is increasingly effective but still disappoints in its ability to carry the valuable information in prosody.

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  • Follow accessibility standards (NIMAS, DAISY, etc.) when creating digital text
  • Allow for a competent aide, partner, or “intervener” to read text aloud
  • Provide access to text-to-Speech software

Checkpoint 1.3: View examples and resources

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Guideline 2: Provide options for language, mathematical expressions, and symbols

PerceptionLanguage, expressions, and symbolsComprehension

Learners vary in their facility with different forms of representation – both linguistic and non-linguistic. Vocabulary that may sharpen and clarify concepts for one learner may be opaque and foreign to another. An equals sign (=) might help some learners understand that the two sides of the equation need to be balanced, but might cause confusion to a student who does not understand what it means. A graph that illustrates the relationship between two variables may be informative to one learner and inaccessible or puzzling to another. A picture or image that carries meaning for some learners may carry very different meanings for learners from differing cultural or familial backgrounds. As a result, inequalities arise when information is presented to all learners through a single form of representation.  An important instructional strategy is to ensure that alternative representations are provided not only for accessibility, but for clarity and comprehensibility across all learners.

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Checkpoint 2.1 Clarify vocabulary and symbols

The semantic elements through which information is presented – the words, symbols, numbers, and icons – are differentially accessible to learners with varying backgrounds, languages, and lexical knowledge. To ensure accessibility for all, key vocabulary, labels, icons, and symbols should be linked to, or associated with, alternate representations of their meaning (e.g., an embedded glossary or definition, a graphic equivalent, a chart or map).  Idioms, archaic expressions, culturally exclusive phrases, and slang, should be translated.

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  • Pre-teach vocabulary and symbols, especially in ways that promote connection to the learners’ experience and prior knowledge
  • Provide graphic symbols with alternative text descriptions
  • Highlight how complex terms, expressions, or equations are composed of simpler words or symbols
  • Embed support for vocabulary and symbols within the text (e.g., hyperlinks or footnotes to definitions, explanations, illustrations, previous coverage, translations)
  • Embed support for unfamiliar references within the text (e.g., domain specific notation, lesser known properties and theorems, idioms, academic language, figurative language, mathematical language, jargon, archaic language, colloquialism, and dialect)

Checkpoint 2.1: View examples and resources

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Checkpoint 2.2 Clarify syntax and structure

Single elements of meaning (like words or numbers) can be combined to make new meanings.  Those new meanings, however, depend upon understanding the rules or structures (like syntax in a sentence or the properties of equations) of how those elements are combined.  When the syntax of a sentence or the structure of a graphical representation is not obvious or familiar to learners, comprehension suffers. To ensure that all learners have equal access to information, provide alternative representations that clarify, or make more explicit, the syntactic or structural relationships between elements of meaning.

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  • Clarify unfamiliar syntax (in language or in math formulas) or underlying structure (in diagrams, graphs, illustrations, extended expositions or narratives) through alternatives that:
    • Highlight structural relations or make them more explicit
    • Make connections to previously learned structures
    • Make relationships between elements explicit (e.g., highlighting the transition words in an essay, links between ideas in a concept map, etc.)

Checkpoint 2.2: View examples and resources

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Checkpoint 2.3 Support decoding text, mathematical notation, and symbols

The ability to fluently decode words, numbers or symbols that have been presented in an encoded format (e.g., visual symbols for text, haptic symbols for Braille, algebraic expressions for relationships) takes practice for any learner, but some learners will reach automaticity more quickly than others. Learners need consistent and meaningful exposure to symbols so that they can comprehend and use them effectively. Lack of fluency or automaticity greatly increases the cognitive load of decoding, thereby reducing the capacity for information processing and comprehension.  To ensure that all learners have equal access to knowledge, at least when the ability to decode is not the focus of instruction, it is important to provide options that reduce the barriers that decoding raises for learners who are unfamiliar or dysfluent with the symbols.

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  • Allow the use of Text-to-Speech
  • Use automatic voicing with digital mathematical notation (Math ML)
  • Use digital text with an accompanying human voice recording (e.g., Daisy Talking Books)
  • Allow for flexibility and easy access to multiple representations of notationwhere appropriate (e.g., formulas, word problems, graphs)
  • Offer clarification of notation through lists of key terms  

Checkpoint 2.3: View examples and resources

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Checkpoint 2.4 Promote understanding across languages

The language of curricular materials is usually monolingual, but often the learners in the classroom are not, so the promotion of cross-linguistic understanding is especially important. For new learners of the dominant language (e.g., English in American schools) or for learners of academic language (the dominate discourse in school), the accessibility of information is greatly reduced when no linguistic alternatives are available. Providing alternatives, especially for key information or vocabulary is an important aspect of accessibility.

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  • Make all key information in the dominant language (e.g., English) also available in first languages (e.g., Spanish) for learners with limited-English proficiency and in ASL for learners who are deaf
  • Link key vocabulary words to definitions and pronunciations in both dominant and heritage languages
  • Define domain-specific vocabulary (e.g., “map key” in social studies) using both domain-specific and common terms
  • Provide electronic translation tools or links to multilingual glossaries on the web 
  • Embed visual, non-linguistic supports for vocabulary clarification (pictures, videos, etc) 

Checkpoint 2.4: View examples and resources

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Checkpoint 2.5 Illustrate through multiple media

Classroom materials are often dominated by information in text.  But text is a weak format for presenting many concepts and for explicating most processes. Furthermore, text is a particularly weak form of presentation for learners who have text- or language-related disabilities. Providing alternatives - especially illustrations, simulations, images or interactive graphics – can make the information in text more comprehensible for any learner and accessible for some who would find it completely inaccessible in text.

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  • Present key concepts in one form of symbolic representation (e.g., an expository text or a math equation) with an alternative form  (e.g., an illustration, dance/movement, diagram, table, model, video, comic strip, storyboard, photograph, animation, physical or virtual manipulative) 
  • Make explicit links between information provided in texts and any accompanying representation of that information in illustrations, equations, charts, or diagrams

Checkpoint 2.5: View examples and resources

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Guideline 3: Provide options for comprehension

PerceptionLanguage, expressions, and symbolsComprehension

The purpose of education is not to make information accessible, but rather to teach learners how to transform accessible information into useable knowledge. Decades of cognitive science research have demonstrated that the capability to transform accessible information into useable knowledge is not a passive process but an active one. Constructing useable knowledge, knowledge that is accessible for future decision-making, depends not upon merely perceiving information, but upon active “information processing skills” like selective attending, integrating new information with prior knowledge, strategic categorization, and active memorization. Individuals differ greatly in their skills in information processing and in their access to prior knowledge through which they can assimilate new information. Proper design and presentation of information – the responsibility of any curriculum or instructional methodology - can provide the scaffolds necessary to ensure that all learners have access to knowledge.

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Checkpoint 3.1 Activate or supply background knowledge

Information is more accessible and likely to be assimilated by learners when it is presented in a way that primes, activates, or provides any pre-requisite knowledge. Barriers and inequities exist when some learners lack the background knowledge that is critical to assimilating or using new information. However, there are also barriers for learners who have the necessary background knowledge, but might not know it is relevant. Those barriers can be reduced when options are available that supply or activate relevant prior knowledge, or link to the pre-requisite information elsewhere.

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  • Anchor instruction by linking to and activating relevant prior knowledge (e.g., using visual imagery, concept anchoring, or concept mastery routines)
  • Use advanced organizers (e.g., KWL methods, concept maps)
  • Pre-teach critical prerequisite concepts through demonstration or models
  • Bridge concepts with relevant analogies and metaphors
  • Make explicit cross-curricular connections (e.g., teaching literacy strategies in the social studies classroom)

Checkpoint 3.1: View examples and resources

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Checkpoint 3.2 Highlight patterns, critical features, big ideas, and relationships

One of the big differences between experts and novices in any domain is the facility with which they distinguish what is critical from what is unimportant or irrelevant.  Since experts quickly recognize the most important features in information, they allocate their time efficiently, quickly identifying what is valuable and finding the right “hooks” with which to assimilate the most valuable information into existing knowledge. As a consequence, one of the most effective ways to make information more accessible is to provide explicit cues or prompts that assist individuals in attending to those features that matter most while avoiding those that matter least.

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  • Highlight or emphasize key elements in text, graphics, diagrams, formulas 
  • Use outlines, graphic organizers, unit organizer routines, concept organizer routines, and concept mastery routines to emphasize key ideas and relationships  
  • Use multiple examples and non-examples to emphasize critical features 
  • Use cues and prompts to draw attention to critical features
  • Highlight previously learned skills that can be used to solve unfamiliar problems

Checkpoint 3.2: View examples and resources

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Checkpoint 3.3 Guide information processing, visualization, and manipulation

Successful transformation of information into useable knowledge often requires the application of mental strategies and skills for “processing” information. These cognitive, or meta-cognitive, strategies involve the selection and manipulation of information so that it can be better summarized, categorized, prioritized, contextualized and remembered. While some learners in any classroom may have a full repertoire of these strategies, along with the knowledge of when to apply them, most learners do not. Well-designed materials can provide customized and embedded models, scaffolds, and feedback to assist learners who have very diverse abilities in using those strategies effectively.

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  • Give explicit prompts for each step in a sequential process
  • Provide options for organizational methods and approaches (tables and algorithms for processing mathematical operations)
  • Provide interactive models that guide exploration and new understandings
  • Introduce graduated scaffolds that support information processing strategies
  • Provide multiple entry points to a lesson and optional pathways through content (e.g., exploring big ideas through dramatic works, arts and literature, film and media)
  • “Chunk” information into smaller elements
  • Progressively release information (e.g., sequential highlighting)
  • Remove unnecessary distractions unless they are essential to the instructional goal 

Checkpoint 3.3: View examples and resources

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Checkpoint 3.4 Maximize transfer and generalization

All learners need to be able to generalize and transfer their learning to new contexts. Students vary in the amount of scaffolding they need for memory and transfer in order to improve their ability to access their prior learning. Of course, all learners can benefit from assistance in how to transfer the information they have to other situations, as learning is not about individual facts in isolation, and students need multiple representations for this to occur. Without this support and the use of multiple representations, information might be learned, but is inaccessible in new situations. Supports for memory, generalization, and transfer include techniques that are designed to heighten the memorability of the information, as well as those that prompt and guide learners to employ explicit strategies.

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  • Provide checklists, organizers, sticky notes, electronic reminders
  • Prompt the use of mnemonic strategies and devices (e.g., visual imagery, paraphrasing strategies, method of loci, etc.)
  • Incorporate explicit opportunities for review and practice
  • Provide templates, graphic organizers, concept maps to support note-taking
  • Provide scaffolds that connect new information to prior knowledge (e.g., word webs, half-full concept maps)
  • Embed new ideas in familiar ideas and contexts (e.g., use of analogy, metaphor, drama, music, film, etc.)
  • Provide explicit, supported opportunities to generalize learning to new situations (e.g., different types of problems that can be solved with linear equations, using physics principles to build a playground)
  • Offer opportunities over time to revisit key ideas and linkages between ideas


Checkpoint 3.4: View examples and resources

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Suggested citation

CAST (2011). Universal Design for Learning Guidelines version 2.0. Wakefield, MA: Author.


The UDL Guidelines began as a project of the National Center on Accessing the General Curriculum (NCAC), a cooperative agreement between the Center for Applied Special Technology (CAST) and the U.S. Department of Education, Office of Special Education Programs (OSEP), Cooperative Agreement No. h424H990004. The contents of this document do not necessarily reflect the views or policies of the U.S. Department of Education, nor does this acknowledgement imply endorsement by the U.S. Government.

The UDL Guidelines were compiled by David H. Rose, Ed.D., Co-Founder and Chief Education Officer at CAST, and Jenna Gravel, M.Ed., doctoral student at Harvard. They have received extensive review and comments from: colleagues at CAST; teachers at the elementary, secondary, and postsecondary levels; researchers; and other practitioners. As with Guidelines 1.0 we will be inviting peer review and comments from individuals throughout the field.


We present 31 bright eclipsing contact and semidetached binaries that showed high period change rates (HPCRs) in a 5-yr interval in observations by the All-Sky Automated Survey. The time-scales of these changes range from only 50 up to 400 kyr. The orbital periods of 10 binaries are increasing and of 21 are decreasing, and even a larger excess is seen in contact binaries, where the numbers are 5 and 17, respectively. Period change has previously been noticed for only two of these binaries; our observations confirmed a secular period drift for SV Cen and period oscillations for VY Cet. The spectroscopic quadruple system V1084 Sco shows both period change and brightness modulation. According to our results, the incidence of asymmetry in the brightness at maximum light in the HPCR domain may be different from the incidence in the general population. All investigated binaries were selected from a sample of 1711 (1135 contact and 576 semidetached) that fulfilled all criteria of data quality. We also introduce a ‘branch’ test to check if luminosity changes on part of the binary's photosphere have led to a spurious or poorly characterized period change detection.

binaries: close, binaries: eclipsing, stars: evolution, stars: individual: SV Cen, stars: individual: VY Cet, stars: individual: V1084 Sco


There are various reasons for an observed period change of an eclipsing binary star.

  • During conservative mass exchange, the period decreases if the mass loser is currently more massive than the gainer and increases if the opposite is true.

  • Mass lost from the system in a rather isotropic wind causes the period to increase as the specific angular momentum increases.

  • Mass lost in a flattened configuration may carry away angular momentum, causing the period to decrease.

  • By tidal dissipation the orbital angular momentum may be transferred to or drawn from the spin motion of a star, causing the period to either decrease or increase until a spin equilibrium is reached in which the tidal torque vanishes.

  • Period oscillations are also possible, caused by oblateness changes during magnetic cycles as proposed by Applegate (1992).

However, apparent orbital period change is not always an intrinsic phenomenon and sometimes is not even physical. Virtual oscillations of period are observed due to the light–time effect (LITE) caused by the displacement induced by one or more additional companions (Irwin 1959; Mayer 1990; Pribulla et al. 2005). Also, for a minority of stars, surface activity resulting in apparent phase shift of parts of the light curve may be misinterpreted as a period change. This phase shift is, however, generally smaller than 0.02 of a period and does not accumulate (Kalimeris, Rovithis-Livanou & Rovithis 2002).

The Algol paradox, in which the less massive component of a binary is more evolved, seems to be resolved (see Pustylnik 1998, for a review), but the structure and evolution of close interacting binaries still hide some mysteries (Webbink 2003; Ibanoglu et al. 2006). The origin of contact binaries is still being debated (Yakut & Eggleton 2005; Eker et al. 2006; Pribulla & Rucinski 2006; Stȩpień 2006; Van Hamme 2006). It is also unclear whether close binaries evolve through angular momentum loss (van't Veer 1979; Rahunen 1981; Vilhu 1982; Stȩpień 1995, and others), which requires mass-loss in magnetized winds, or thermal relaxation oscillations (TRO) (Flannery 1976; Lucy 1976; Robertson & Eggleton 1977; Wang 1999; Webbink 2003), which requires mass exchange between components, or a mixture of both (Qian 2003). TRO predicts that contact binaries can even become semidetached for periods of time.

A large sample of stars with swift period changes can therefore shed light on the evolution of interacting binaries, give information about stellar structure and magnetic fields involved in the Applegate mechanism, or signal the presence of a multiple system in LITE.

Recently, Paczyński et al. (2006) (hereafter Paper I) has brought attention to a great number of eclipsing binaries from the All-Sky Automated Survey (ASAS) Catalogue (Pojmański, Pilecki & Szczygiel 2005). The variable stars were discovered quasi-uniformly for declination < +28°, covering almost 3/4 of the full sky. For brightness within 8 < V < 12 mag nearly all the variable stars with the amplitude ΔV > 0.1 mag have been found (see Paper I for details). There are 5384 eclipsing contact binaries (EC), 2957 semidetached binaries (ESD) and 2758 detached binaries (ED) in the catalogue.

The precision of a period change rate measurement of a binary with strictly sinusoidal variation is


where P is the orbital period and A is the full amplitude of the variation, N is the number of data points (roughly uniformly spread over a duration of T) and σ is the photometric precision of each data point. This estimate comes from a Fisher-matrix analysis in which the second derivative matrix of the sinusoid model with respect to its parameters is inverted to find the errors on those parameters. Typical numbers for ASAS light curves are P= 0.4 d, A= 0.4 mag, N= 400, T= 1900 d, σ= 0.02 mag. Therefore for a typical curve an optimistic 3σ detection of period change is ∼7 × 10−7 d yr−1, comparable to period changes discovered through observed minus calculated (O − C) diagrams spanning many decades obtained by literature searches (e.g. Qian 2001a,b).

In our examinations we consider only EC and ESD binaries (i.e. we neglect ED). We require more than 300 observation points, randomly distributed in time, and a binary period shorter than 10 d (see Section 2 for details). Section 3 describes the methods used to find period changes. The 31 binaries with high period change rates (HPCRs) are presented in Section 4. For discussion of results see Section 5.


In this section we will focus only on the selection criteria. For detailed information on data statistics and quality please refer to Paper I.

Good coverage of the phase with observations is essential to get reliable results, therefore, we have selected only stars that have no fewer than Nobs= 300 observations with acceptable quality flags (A or B). Moreover, while examining light curves of ASAS eclipsing binaries we found that some of the stars (even with a large number of points) have most observations concentrated around specific HJD (Heliocentric Julian Date). This situation is not good for a period change study, as the T−2 factor in equation (1) attests. Therefore, we required the observation time s.d.,


where is the average of all observation times, be greater than 500 d, which corresponds to about 1750 d of uniform observations. A larger value of σHJD gives a better constraint on period changes as observation times are less concentrated. All binaries in the parameter space (Nobs, σHJD) are presented in Fig. 1. We analysed the binaries enclosed with a dashed line. These selection criteria reduced the number of stars from 8333 to 4252.

Figure 1

This diagram shows the number of points (Nobs) and time-scatter of observations (σHJD) for all 8333 EC and ESD binaries. Low σHJD means that observation points are too highly concentrated. Stars selected for analysis (4252) are enclosed with a dashed line. Triangles mark detected HPCR stars.

Figure 1

This diagram shows the number of points (Nobs) and time-scatter of observations (σHJD) for all 8333 EC and ESD binaries. Low σHJD means that observation points are too highly concentrated. Stars selected for analysis (4252) are enclosed with a dashed line. Triangles mark detected HPCR stars.

An upper period limit was set to 10 d to cover at least 200 orbital cycles, while the maximum is about 10 000 cycles. The quality of period change determination, however, progressively diminishes with increasing period (equation 1). This is illustrated by Table 1, where we present stars for which the highest accuracy period changes were obtained: the longest period there is only 1.658 d. There are fewer long period systems, so this criterion reduced the number of binaries only by 272 to 3980 systems (2573 contact, 1407 semidetached). To make sure that the period change analysis would give reliable results this set was further reduced to 1711 (1135 EC, 576 ESD) stars with highest signal-to-noise ratio. This step is described in the next section.

Table 1

We list here 31 HPCR stars with their time of first minimum after HJD = 245 1868 (HJD0), orbital period (P), period change rate (; error in the last one or two digits is quoted in parentheses, ‘b’ marks failed branch test), corresponding time-scale (), V-band maximum brightness (Vmax; followed by ‘↑’ if rising, ‘↓’ if descending) and amplitude (Amp – a primary minimum depth; with ‘⇓’ if third light is present), minima depth ratio (dS/dP), O'Connell effect (Δmax; if greater than 2 per cent of Amp), spectral type (Sp), status (St; ‘X’ means this is also a ROSAT X-ray source while ‘3’ or ‘4’ denotes number of known components if more than 2, ‘s’ marks spectroscopic multiple) and cross-identification (GCVS name if available, other if not; was known as variable if shown in bold font). First column is ASAS identification (was not known as variable if shown in bold font).

ID HJD0 (d) P (d) [10−5 d yr−1 (kyr) Vmax (mag) Amp (mag) dS/dPΔ max (mmag) Sp St Other ID 
114757−6034.0 1.030 1.657 589 −2.50(35) 66 8.67 1.30 0.58 65 B2 – SV Cen 
113333−6353.70.478 0.991 121 1.67(23)b59 9.23 0.29⇓ 0.90 – B8 HD 100530 
184110−7229.7 0.391 0.710 832 1.29(27) 55 11.60 0.73 0.36 – – – NSV 11124
071225−2530.0 0.346 0.720 825 0.85(11)b85 9.41 0.40 0.73 – – – VW CMa
074537−3109.60.398 0.602 926 −0.77(19) 78 10.73↓ 0.27 0.80 41 – – GSC 07106−00494 
144910−4424.30.191 0.446 193 −0.61(11) 74 10.37↓ 0.19⇓ 0.86 −11 – DON 684 
231524−5018.4 0.152 0.418 344 0.55(10) 76 11.48 0.43 0.99 – – – NSV 14467
173758−3911.4 0.293 0.303 315 −0.54(5) 56 8.93 0.14⇓ 0.79 – G6V X4sV1084 Sco
062426−2044.90.231 0.384 692 −0.47(7) 82 10.64↑ 0.34 0.96 – – – GSC 05959−01748 
102014−1351.60.285 0.381 025 −0.45(9) 85 10.28 0.12 0.97 −11 – – BD-13 3091 
082456−4833.60.180 0.364 875 −0.44(7) 84 11.63 0.34 0.96 – – – –— 
160302−3749.40.354 0.363 239 −0.40(9)b90 10.92↑ 0.38 0.91 27 – GSC 07851−01451 
004717−1941.60.031 0.488 810 −0.39(13) 130 11.21 0.38 0.69 – – – CPD-20 88 
060557−5342.90.137 0.463 634 0.38(9) 120 10.82 0.32 0.89 – – – GSC 08521−01468 
231603−1553.50.143 0.470 110 −0.37(12)b130 9.98↑ 0.27 0.93 −11 G0 – HD 219462 
070959−3639.50.165 0.371 829 −0.28(7) 130 9.66↓ 0.18⇓ 0.92 – F5V X3 HD 55100 
065232−2533.50.247 0.418 639 0.27(5)b160 8.61↓ 0.38 0.87 15 F6V HD 50494 
004430−3606.50.064 0.246 537 0.26(4) 96 9.58 0.13⇓ 0.80 −11 G5 X3 HD 4227 
014933−1937.6 0.145 0.340 809 −0.25(4) 130 11.00 0.64 0.93 – G5V – VY Cet
135243−5532.5 0.112 0.580 784 −0.25(9) 230 9.44 0.53 0.57 27 B9IV – V758 Cen
072729−5056.50.317 0.330 557 0.24(6) 140 11.89 0.37 0.97 18 – –— 
002449−2744.30.265 0.313 661 −0.23(5)b140 12.39 0.76 0.82 – – – –— 
002821−2904.10.195 0.269 892 −0.23(5) 120 11.97 0.54 0.80 −37 – – –— 
062254−7502.00.148 0.257 707 0.21(4)b130 11.40 0.43 0.92 – – – –— 
025016−4649.20.139 0.271 753 −0.20(4) 140 12.44 0.51 0.95 −12 – – –— 
093312−8028.50.118 0.406 067 −0.20(6) 200 10.64 0.33 0.94 – – – GSC 09404−00233 
144047−3725.30.276 0.353 410 0.19(6) 180 9.25 0.28⇓ 0.93 G2V X3 HD 128910 
195350−5003.5 0.110 0.286 827 −0.18(3)b160 11.25 0.99 0.69 – – NSV 12502
052851−3010.20.153 0.302 101 −0.17(4) 180 11.30 0.36 0.96 – – – –— 
071727−4007.7 0.144 0.320 265 −0.11(3) 300 11.14 0.66 0.85 – – GZ Pup
095048−6723.3 0.235 0.276 943 −0.07(2)b430 11.15 0.79 0.92 −17 – – NSV 4657
ID HJD0 (d) P (d) [10

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