DOCSLIB.ORG

Early Stages of 1,2-Dimethylliydrazine-Induced Colon Carcinogenesis Suppress Immune-Regulated Ion Transport of Mouse Distal Colon1

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Early Stages of 1,2-Dimethylliydrazine-Induced Colon Carcinogenesis Suppress Immune-Regulated Ion Transport of Mouse Distal Colon1 [CANCER RESEARCH54, 5930—5936,November15, 19941 Early Stages of 1,2-Dimethylliydrazine-induced Colon Carcinogenesis Suppress Immune-regulated Ion Transport of Mouse Distal Colon1 Russell R. Broaddus, Michael J. Wargovich, and Gilbert A. Castro2 Departments of Physiology and Cell Biology (R. R. B., G. A. C.] and Medical Oncology [M. J. WI, University of Texas Medical School [R. R. B., G. A. C.] and University of Texas M. D. Anderson Cancer Center [M. .1. WI, Houston, Texas 77225 ABSTRACT then to adenocarcinoma. In addition to these genetic events, epige netic and microenvironmental changes also contribute to the devel Genetic events, such as gene deletion, mutation, and amplification, are opment of neoplasia (3). For colon cancer, these latter changes have involved in the development and progression of colonic neoplasia The importance of interactions between immune cells and neoplastlc cells in been much less intensively studied. influencing the pathogenesis of colon cancer is suggested by the clinical Compelling results suggest that local mucosal immunity is one such efficacy of levamisole, an immunostimulant, in the treatment of colon microenvironmental factor important in the pathogenesis of colorectal cancer and by the association of local lymphocytic infiltration with Im carcinoma. Colon adenocarcinomas often contain an inflammatory proved prognosis. Thus, the immune cell-neoplastic cell interaction can be infiltrate, typically consisting of T lymphocytes with some macro viewed as being analogous to various host-parasite relationships that phages and B lymphocytes (4). The presence of lymphocytic infiltra involve the immune system attempting to contain the intruding parasite tion or of lymphoid follicles near resected colon cancers is associated on the one hand and the parasite attempting to escape detection and with an increased patient survival rate (5, 6). Levamisole, a nonspe rejection on the other. This study is an attempt to gain a better under standing ofsuch interactions by examining possible effects ofa developing cific stimulator of many different arms of the immune system, in tumor on the immune system. Colon cancer was experimentally induced in combination with 5-fluorouracil significantly improves disease-free mice to examine potential effects of carcinogenesis in the colon on local survival and overall survival in patients with Stage C resected colon mucosal immune function in situ, using the expression of type I hyper cancer (7). These observations underscore a delicate modulatory role sensitivity as an index of immune function. Antigen-induced changes in of the immune system, especially the mucosal immune system of the net ion transport, a quantifiable correlate of type I hypersensitivity, were colon, in colonic neoplasia. To enhance an understanding of the measured in the colon of mice following the administration of the procar interaction between the mucosal immune system and neoplastic tissue, cinogen 1,2-dimethyihydrazine (DM11).Segments of colon and small in we investigated the effects of experimental colon carcinogenesis on testine from mice immunized by infection with Trichinella spiralir secrete immunity in the colon and small intestine. ions, manifested as a rise in transmural short-circuit current, when dial lenged with T. spiralis antigen in Ussing chambers. Antigen-induced rise in Systemic administration of the procarcinogen DMH3 to CF-i mice transmural short-circuit current Is mast cell dependent and occurs only in is a well-established laboratory model of colon carcinogenesis. DMH immunized mice. To determine the effects of early stages of colon card selectively induces colonic adenomas and adenocarcinomas (8, 9) nogenesis on this mucosal immune response, mice were immunized with T. while only rarely causing liver or small intestine tumors (10). Admin spiralis prior to and after 6 weekly injections of DM11. Responsiveness to istration of DMH causes a continuum of morphological changes from antigenic challenge was suppressed in the distal colon 4—6weeks after the normal colonic epithelium to carcinoma. One injection of DMH final injection of DMH. Although responsiveness to antigen was sup causes the development of aberrant crypts within 2 weeks (11), while pruned, the colonic epithelium remained sensitive to direct stimulation by 6 injections of DMH, 1 per week for 6 weeks, typically causes grossly exogenous secretagogues. Decreased antigen responsiveness observed In visible adenomas and carcinomas of the colon within 4—6months (8, the distal colon was not due to generalized Immunesuppression by DM11, because the proximal colon and thejejunum retained their responsiveness 9). Within the same time frame as the histological development of to antigen, and immune rejection of a secondary T.spiralis infection from aberrant crypts, there is electrophysiological evidence of inhibition of the small Intestinewas not altered. Visible tumors eventually developed 30 the Na@-K@-ATPase(12) and stimulation of Na@-H@exchange (13) in weeks after the final Injection of DM11 only in the distal portions of the the distal colon. These changes in ion transport are important, because colon. These results suggest that early stages of DM11-induced carcino Na@influx into the cell (14) and increased intracellular pH (15) are genesis are associated with the suppression of mucosal immune function, early events in mitogenesis and may, at least partially, be the basis for as measured by Immune-regulatedion secretion, in the distal colon but not the hyperproliferation observed in aberrant crypts (16). in the proximal colon or jejunum. Future eluddation of the mechanisms The hyperproliferative lesions, aberrant crypts, adenomas, and ad by which this localized hnmunosuppression occurs may provide clues to enocarcinomas of the colon induced by DMH are biologically and the microenvironmental changes necessary for tumor progression in the histologically quite similar to those seen in humans (17). Importantly, distal colon. there is pathological evidence that DMH-induced colon tumors (18) resemble human tumors (2) in that both follow an adenoma-to INTRODUCTION carcinoma sequence. Because of the potential progression of early Recent molecular biological evidence (1) supports histological ev changes to malignancy, the study of the premalignant hyperprolifera idence (2) indicating an adenoma-to-carcinoma sequence in the de tive lesions and aberrant crypts is crucial in understanding the patho velopment of colon cancer. The accumulation of mutations in onco genesis of colon cancer. genes and deletions and mutations of tumor suppressor genes allows Immunity in the small intestine and colon of DMH-treated mice for the progression of hyperproliferative epithelium to adenoma and was measured by quantifying a vital physiological function, ion trans port, that is regulated by the mucosal immune system (19). Immune Received 6/14/94; accepted 9/20/94. regulated intestinal ion transport has been described for a variety of The costs of publication of this article were defrayed in part by the payment of page host-antigen systems. Antigenic challenge of intestinal segments from charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. 1 This work was supported by NIH Grant P01-DK37260 and the University of 3 The abbreviations used are: DMH, 1,2-dimethylhydrazine; PGE@, prostaglandin E@; Texas-Houston Health Science Center Mucosal Biology Program. 5-rn,,5-hydroxytryptamine;L@short-circuitcurrent;KRBbuffer,Krebs-Ringerbicar 2 To whom requests for reprints should be addressed, at Department of Physiology and bonate buffer; TGF-@, transforming growth factor @;cAMP, cyclic AMP; cGMP, cyclic Cell Biology, University of Texas Medical School, P.O. Box 20708, Houston, TX 77225. GMP. 5930 Downloaded from cancerres.aacrjournals.org on September 26, 2021. © 1994 American Association for Cancer Research. COLONCARCINOGENESISSUPPRESSESMUt@OSALIMMUNEFUNCI1ON laboratory rodents sensitized to dietary proteins (20, 21) or parasites Segments of intestine were allowed to stabilize for 30 mm after @ (2Z 23) resultsin an immediate(typeI) hypersensitivityreaction, mounting in the chambers to obtain a steady-state [email protected] basal is expressed as net epitheial anion secretion. In Ussing chambers, net an index of net active ion transport across the serosal and mucosal anion secretion is manifested electrophysiologically as a rise in trans surfaces. The tissues were stimulated with antigen or secretagogues mural I.e. Applying similar principles, we have recently described a added to the serosal bathing fluid. T. spiralis antigen was added at a method to quantify colonic mucosal immune function in situ (24). concentration of 50 ,.agprotein/mi of Ussing chamber fluid. PGE@and Briefly, segments ofcolon from mice immunized by infection with the 5-HT were added at final chamber concentrations of iO@ M and 10@ intestinal nematode parasite Trichinella spiralis undergo an increase M, respectively. After addition of antigen or secretagogue, the maxi in Inc (biI,,@)after challenge with T. spiralis-derived antigen in Ussing mum change in I@ (@M@)from the basal state was calculated and chambers. The antigen-induced AL@is inhibited by furosemide, indi expressed as @ eating that the is most likely due to net Cl@secretion by the colon. T.spiralisantigenbridges1gBboundto mucosalmastcells,triggering Histology the release of anaphylactic mediators that stimulate epitheial ion secretion. Ion secretion
Load more

Recommended publications
  • An Overview of Gut Microbiota and Colon Diseases with a Focus on Adenomatous Colon Polyps
    International Journal of Molecular Sciences Review An Overview of Gut Microbiota and Colon Diseases with a Focus on Adenomatous Colon Polyps Oana Lelia Pop 1 , Dan Cristian Vodnar 1 , Zorita Diaconeasa 1 , Magdalena Istrati 2, 3 4 1, Adriana Bint, int, an , Vasile Virgil Bint, int, an , Ramona Suharoschi * and Rosita Gabbianelli 5,* 1 Department of Food Science, University of Agricultural Sciences and Veterinary Medicine, 400372 Cluj-Napoca, Romania; [email protected] (O.L.P.); [email protected] (D.C.V.); [email protected] (Z.D.) 2 Regional Institute of Gastroenterology and Hepatology “Prof. Dr. Octavian Fodor”, 400158 Cluj-Napoca, Romania; [email protected] 3 1st Medical Clinic, Department of Gastroenterology, Emergency County Hospital, 400006 Cluj Napoca, Romania; [email protected] 4 1st Surgical Clinic, Department of Surgery, University of Medicine and Pharmacy Cluj Napoca, 400006 Cluj Napoca, Romania; [email protected] 5 Unit of Molecular Biology, School of Pharmacy, University of Camerino, Via Gentile III da Varano, 62032 Camerino, Italy * Correspondence: [email protected] (R.S.); [email protected] (R.G.) Received: 6 August 2020; Accepted: 2 October 2020; Published: 5 October 2020 Abstract: It is known and accepted that the gut microbiota composition of an organism has an impact on its health. Many studies deal with this topic, the majority discussing gastrointestinal health. Adenomatous colon polyps have a high prevalence as colon cancer precursors, but in many cases, they are hard to diagnose in their early stages. Gut microbiota composition correlated with the presence of adenomatous colon polyps may be a noninvasive and efficient tool for diagnosis with a high impact on human wellbeing and favorable health care costs.
    [Show full text]
  • Punctuation Guide
    Punctuation guide 1. The uses of punctuation Punctuation is an art, not a science, and a sentence can often be punctuated correctly in more than one way. It may also vary according to style: formal academic prose, for instance, might make more use of colons, semicolons, and brackets and less of full stops, commas, and dashes than conversational or journalistic prose. But there are some conventions you will need to follow if you are to write clear and elegant English. In earlier periods of English, punctuation was often used rhetorically—that is, to represent the rhythms of the speaking voice. The main function of modern English punctuation, however, is logical: it is used to make clear the grammatical structure of the sentence, linking or separating groups of ideas and distinguishing what is important in the sentence from what is subordinate. It can also be used to break up a long sentence into more manageable units, but this may only be done where a logical break occurs; Jane Austen's sentence ‗No one who had ever seen Catherine Morland in her infancy, would ever have supposed her born to be a heroine‘ would now lose its comma, since there is no logical break between subject and verb (compare: ‗No one would have supposed …‘). 2. The main stops and their functions The full stop, exclamation mark, and question mark are used to mark off separate sentences. Within the sentence, the colon (:) and semicolon (;) are stronger marks of division than the comma, brackets, and the dash. Properly used, the stops can be a very effective method of marking off the divisions and subdivisions of your argument; misused, they can make it barely intelligible, as in this example: ‗Donne starts the poem by poking fun at the Petrarchan convention; the belief that one's mistress's scorn could make one physically ill, he carries this one step further…‘.
    [Show full text]
  • Punctuation: Program 8-- the Semicolon, Colon, and Dash
    C a p t i o n e d M e d i a P r o g r a m #9994 PUNCTUATION: PROGRAM 8-- THE SEMICOLON, COLON, AND DASH FILMS FOR THE HUMANITIES & SCIENCES, 2000 Grade Level: 8-13+ 22 mins. DESCRIPTION How does a writer use a semicolon, colon, or dash? A semicolon is a bridge that joins two independent clauses with the same basic idea or joins phrases in a series. To elaborate a sentence with further information, use a colon to imply “and here it is!” The dash has no specific rules for use; it generally introduces some dramatic element into the sentence or interrupts its smooth flow. Clear examples given. ACADEMIC STANDARDS Subject Area: Language Arts–Writing • Standard: Uses grammatical and mechanical conventions in written compositions Benchmark: Uses conventions of punctuation in written compositions (e.g., uses commas with nonrestrictive clauses and contrasting expressions, uses quotation marks with ending punctuation, uses colons before extended quotations, uses hyphens for compound adjectives, uses semicolons between independent clauses, uses dashes to break continuity of thought) (See INSTRUCTIONAL GOALS 1-4.) INSTRUCTIONAL GOALS 1. To explain the proper use of a semicolon to combine independent clauses and in lists with commas. 2. To show the correct use of colons for combining information and in sentence fragments. 3. To illustrate the use of a dash in sentences. 4. To show some misuses of the semicolon, colon, and dash. BACKGROUND INFORMATION The semicolon, colon, and dash are among the punctuation marks most neglected by students and, sad to say, teachers. However, professional writers—and proficient writers in business—use them all to good effect.
    [Show full text]
  • Review of Set-Theoretic Notations and Terminology A.J
    Math 347 Review of Set-theoretic Notations and Terminology A.J. Hildebrand Review of Set-theoretic Notations and Terminology • Sets: A set is an unordered collection of objects, called the elements of the set. The standard notation for a set is the brace notation f::: g, with the elements of the set listed inside the pair of braces. • Set builder notation: Notation of the form f::: : ::: g, where the colon (:) has the meaning of \such that", the dots to the left of the colon indicate the generic form of the element in the set and the dots to 2 the right of the colon denote any constraints on the element. E.g., fx 2 R : x < 4g stands for \the set of 2 all x 2 R such that x < 4"; this is the same as the interval (−2; 2). Other examples of this notation are f2k : k 2 Zg (set of all even integers), fx : x 2 A and x 2 Bg (intersection of A and B, A \ B). 2 Note: Instead of a colon (:), one can also use a vertical bar (j) as a separator; e.g., fx 2 R j x < 4g. Both notations are equally acceptable. • Equality of sets: Two sets are equal if they contain the same elements. E.g., the sets f3; 4; 7g, f4; 3; 7g, f3; 3; 4; 7g are all equal since they contain the same three elements, namely 3, 4, 7. • Some special sets: • Empty set: ; (or fg) • \Double bar" sets: 1 ∗ Natural numbers: N = f1; 2;::: g (note that 0 is not an element of N) ∗ Integers: Z = f:::; −2; −1; 0; 1; 2;::: g ∗ Rational numbers: Q = fp=q : p; q 2 Z; q 6= 0g ∗ Real numbers: R • Intervals: ∗ Open interval: (a; b) = fx 2 R : a < x < bg ∗ Closed interval: [a; b] = fx 2 R : a ≤ x ≤ bg ∗ Half-open interval: [a; b) = fx 2 R : a ≤ x < bg • Universe: U (\universe", a \superset" of which all sets under consideration are assumed to be a subset).
    [Show full text]
  • International Language Environments Guide
    International Language Environments Guide Sun Microsystems, Inc. 4150 Network Circle Santa Clara, CA 95054 U.S.A. Part No: 806–6642–10 May, 2002 Copyright 2002 Sun Microsystems, Inc. 4150 Network Circle, Santa Clara, CA 95054 U.S.A. All rights reserved. This product or document is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation. No part of this product or document may be reproduced in any form by any means without prior written authorization of Sun and its licensors, if any. Third-party software, including font technology, is copyrighted and licensed from Sun suppliers. Parts of the product may be derived from Berkeley BSD systems, licensed from the University of California. UNIX is a registered trademark in the U.S. and other countries, exclusively licensed through X/Open Company, Ltd. Sun, Sun Microsystems, the Sun logo, docs.sun.com, AnswerBook, AnswerBook2, Java, XView, ToolTalk, Solstice AdminTools, SunVideo and Solaris are trademarks, registered trademarks, or service marks of Sun Microsystems, Inc. in the U.S. and other countries. All SPARC trademarks are used under license and are trademarks or registered trademarks of SPARC International, Inc. in the U.S. and other countries. Products bearing SPARC trademarks are based upon an architecture developed by Sun Microsystems, Inc. SunOS, Solaris, X11, SPARC, UNIX, PostScript, OpenWindows, AnswerBook, SunExpress, SPARCprinter, JumpStart, Xlib The OPEN LOOK and Sun™ Graphical User Interface was developed by Sun Microsystems, Inc. for its users and licensees. Sun acknowledges the pioneering efforts of Xerox in researching and developing the concept of visual or graphical user interfaces for the computer industry.
    [Show full text]
  • List of Approved Special Characters
    List of Approved Special Characters The following list represents the Graduate Division's approved character list for display of dissertation titles in the Hooding Booklet. Please note these characters will not display when your dissertation is published on ProQuest's site. To insert a special character, simply hold the ALT key on your keyboard and enter in the corresponding code. This is only for entering in a special character for your title or your name. The abstract section has different requirements. See abstract for more details. Special Character Alt+ Description 0032 Space ! 0033 Exclamation mark '" 0034 Double quotes (or speech marks) # 0035 Number $ 0036 Dollar % 0037 Procenttecken & 0038 Ampersand '' 0039 Single quote ( 0040 Open parenthesis (or open bracket) ) 0041 Close parenthesis (or close bracket) * 0042 Asterisk + 0043 Plus , 0044 Comma ‐ 0045 Hyphen . 0046 Period, dot or full stop / 0047 Slash or divide 0 0048 Zero 1 0049 One 2 0050 Two 3 0051 Three 4 0052 Four 5 0053 Five 6 0054 Six 7 0055 Seven 8 0056 Eight 9 0057 Nine : 0058 Colon ; 0059 Semicolon < 0060 Less than (or open angled bracket) = 0061 Equals > 0062 Greater than (or close angled bracket) ? 0063 Question mark @ 0064 At symbol A 0065 Uppercase A B 0066 Uppercase B C 0067 Uppercase C D 0068 Uppercase D E 0069 Uppercase E List of Approved Special Characters F 0070 Uppercase F G 0071 Uppercase G H 0072 Uppercase H I 0073 Uppercase I J 0074 Uppercase J K 0075 Uppercase K L 0076 Uppercase L M 0077 Uppercase M N 0078 Uppercase N O 0079 Uppercase O P 0080 Uppercase
    [Show full text]
  • Top Ten Tips for Effective Punctuation in Legal Writing
    TIPS FOR EFFECTIVE PUNCTUATION IN LEGAL WRITING* © 2005 The Writing Center at GULC. All Rights Reserved. Punctuation can be either your friend or your enemy. A typical reader will seldom notice good punctuation (though some readers do appreciate truly excellent punctuation). However, problematic punctuation will stand out to your reader and ultimately damage your credibility as a writer. The tips below are intended to help you reap the benefits of sophisticated punctuation while avoiding common pitfalls. But remember, if a sentence presents a particularly thorny punctuation problem, you may want to consider rephrasing for greater clarity. This handout addresses the following topics: THE COMMA (,)........................................................................................................................... 2 PUNCTUATING QUOTATIONS ................................................................................................. 4 THE ELLIPSIS (. .) ..................................................................................................................... 4 THE APOSTROPHE (’) ................................................................................................................ 7 THE HYPHEN (-).......................................................................................................................... 8 THE DASH (—) .......................................................................................................................... 10 THE SEMICOLON (;) ................................................................................................................
    [Show full text]
  • Colon Warnings Everything You Need 1
    5. Colon Warnings Everything You Need 1. Do not use a colon after a verb. Wrong—The topic of the pamphlet is: the colon. to Know about Right—The topic of the pamphlet is the colon. 2. Do not use a colon after consists of or such as. the Colon Wrong—Pack useful items such as: an MLA guide, . Right—Pack useful items such as an MLA guide, . 3. Do not capitalize the first item in a list included in a sentence. Right—Learn how to use the following machines: computer, printer, . WANTED Do capitalize the first item in a list in a column. Right—Learn how to use the following machines: ● Computer ● Printer 4. You do not have to capitalize the first word in a complete │ thought after a colon, but you may. Right—I was disappointed: misspelling spoiled my essay. Right—I was disappointed: Misspelling spoiled my essay. │ : 6. An Exit Exam on the Colon Front View Side View Place a colon in each of the following: Description of suspect: 1. Dear Professor 1. Fearful Colon Facts: Of Greek origin 2. On Mondays through Thursdays The Writing Center opens 2. The Top Six Excuses Used by a Colon at 9 00 a.m., but on Fridays it opens at 1 00 p.m. 3. Who can forget the Center's slogan “We'll help you write.” 3. Sometimes Mistaken for a Semicolon 4. After weeks of research, she wanted just one thing MLA 4. Sometimes Incorrectly Used as a Dash guidelines. 5. He knew it was important to revise his paper a good 5.
    [Show full text]
  • Set (Mathematics) from Wikipedia, the Free Encyclopedia
    Set (mathematics) From Wikipedia, the free encyclopedia A set in mathematics is a collection of well defined and distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics. Developed at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. In mathematics education, elementary topics such as Venn diagrams are taught at a young age, while more advanced concepts are taught as part of a university degree. Contents The intersection of two sets is made up of the objects contained in 1 Definition both sets, shown in a Venn 2 Describing sets diagram. 3 Membership 3.1 Subsets 3.2 Power sets 4 Cardinality 5 Special sets 6 Basic operations 6.1 Unions 6.2 Intersections 6.3 Complements 6.4 Cartesian product 7 Applications 8 Axiomatic set theory 9 Principle of inclusion and exclusion 10 See also 11 Notes 12 References 13 External links Definition A set is a well defined collection of objects. Georg Cantor, the founder of set theory, gave the following definition of a set at the beginning of his Beiträge zur Begründung der transfiniten Mengenlehre:[1] A set is a gathering together into a whole of definite, distinct objects of our perception [Anschauung] and of our thought – which are called elements of the set. The elements or members of a set can be anything: numbers, people, letters of the alphabet, other sets, and so on.
    [Show full text]
  • Commonly Misused Punctuation: Colons And
    COMMONLY MISUSED PUNCTUATION: COLONS AND DASHES Center for Writing and Speaking Colons and dashes are two of the most mysterious and misunderstood marks of punctuation. This handout is meant to demystify and clarify the function of these forms of punctuation, so that you can use them more accurately. Colon Colons are used after an independent clause. What is an independent clause? It is a sentence that can stand alone as a complete thought. The colon is often used for listing things, before quotations that are three or more lines, and in place of a semicolon between two related independent clauses. Example A: You may need the following items to go camping: a sleeping bag, a tent, a blanket, clean undies, and marshmallows. Example B: This is best described by Maslow in his paper “A Theory of Human Motivation”: What a man can be, he must be. This need we may call self-actualization…It refers to the desire for self-fulfillment, namely, to the tendency for him to become actualized in what he is potentially. This tendency might be phrased as the desire to become more and more what one is, to become everything that one is capable of becoming. Example C: It’s been snowing for three days straight: The roads around here aren’t very safe for driving. How not to use a colon Incorrect example: The grocery list included: apples, grapes, milk, bread, and eggs. “The grocery list included” is not an independent clause, so it cannot be used with a colon—even if it is listing something after! Quick Tip: To make a dash in Microsoft Word, type two hypens Dashes (--) directly after a word, then type Dashes replace commas, semicolons, colons, and parentheses for the next word right after the two added emphasis, or an interruption/abrupt change of thought.
    [Show full text]
  • Math Symbol Tables
    APPENDIX A Math symbol tables A.1 Hebrew and Greek letters Hebrew letters Type Typeset \aleph ℵ \beth ℶ \daleth ℸ \gimel ℷ © Springer International Publishing AG 2016 481 G. Grätzer, More Math Into LATEX, DOI 10.1007/978-3-319-23796-1 482 Appendix A Math symbol tables Greek letters Lowercase Type Typeset Type Typeset Type Typeset \alpha \iota \sigma \beta \kappa \tau \gamma \lambda \upsilon \delta \mu \phi \epsilon \nu \chi \zeta \xi \psi \eta \pi \omega \theta \rho \varepsilon \varpi \varsigma \vartheta \varrho \varphi \digamma ϝ \varkappa Uppercase Type Typeset Type Typeset Type Typeset \Gamma Γ \Xi Ξ \Phi Φ \Delta Δ \Pi Π \Psi Ψ \Theta Θ \Sigma Σ \Omega Ω \Lambda Λ \Upsilon Υ \varGamma \varXi \varPhi \varDelta \varPi \varPsi \varTheta \varSigma \varOmega \varLambda \varUpsilon A.2 Binary relations 483 A.2 Binary relations Type Typeset Type Typeset < < > > = = : ∶ \in ∈ \ni or \owns ∋ \leq or \le ≤ \geq or \ge ≥ \ll ≪ \gg ≫ \prec ≺ \succ ≻ \preceq ⪯ \succeq ⪰ \sim ∼ \approx ≈ \simeq ≃ \cong ≅ \equiv ≡ \doteq ≐ \subset ⊂ \supset ⊃ \subseteq ⊆ \supseteq ⊇ \sqsubseteq ⊑ \sqsupseteq ⊒ \smile ⌣ \frown ⌢ \perp ⟂ \models ⊧ \mid ∣ \parallel ∥ \vdash ⊢ \dashv ⊣ \propto ∝ \asymp ≍ \bowtie ⋈ \sqsubset ⊏ \sqsupset ⊐ \Join ⨝ Note the \colon command used in ∶ → 2, typed as f \colon x \to x^2 484 Appendix A Math symbol tables More binary relations Type Typeset Type Typeset \leqq ≦ \geqq ≧ \leqslant ⩽ \geqslant ⩾ \eqslantless ⪕ \eqslantgtr ⪖ \lesssim ≲ \gtrsim ≳ \lessapprox ⪅ \gtrapprox ⪆ \approxeq ≊ \lessdot
    [Show full text]
  • Effective Punctuation
    Effective Punctuation Contents: 1. Oxford commas 2. Parenthetic phrases 3. Independent clauses 4. Punctuation before or after quotation marks 5. Ellipses in quotations 6. Em dashes 7. One or two spaces after periods 8. When to capitalize after colons 1. Oxford Comma Writers disagree on whether lists of three or more should include a comma before the “and” (or “or”) and the last item in the list. Above all, consistency is key. If you do not know your reader's preference, choose one method and stick to it. Commas before the last “and” must be used when the final item in the list itself contains a conjunction (e.g., “He was charged with assault, battery, and breaking and entering.”) Option 1 Option 2 When the “Oxford Comma” is required The American flag is red, The American flag is red, You are charged with white and blue. white, and blue. trespassing, burglary, and assault and battery. 2. Parenthetic phrases Use commas to set off words and phrases that do not neatly fit into the main grammatical structure of the sentence. Nonrestrictive clauses are examples of parenthetic phrases. Unless the parenthetic phrase ends the sentence, there should always be a comma at the end of the parenthetic phrase. Do not use commas to set off phrases that, if removed, would change the meaning of the sentence, i.e., a restrictive clause. • Examples: o The Constitution, which was signed in 1787, is the supreme law of the land. o The Constitution, signed in 1787, is the supreme law of the land. o The judge, however, was not amused.
    [Show full text]