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a triangular number or triangle number counts the objects that can form an equilateral triangle, as in the diagram on the right.
בתורת המספרים, מספר טבעי formula_1 נקרא מספר משולשי אם אפשר לסדר formula_1 עצמים בצורת משולש שווה-צלעות.
given a commutative diagram, a proof by diagram chasing involves the formal use of the properties of the diagram, such as injective or surjective maps, or exact sequences.
"מרדף בדיאגרמה" (מקובל הביטוי האנגלי - diagram chase) =הוכחה מקובלת באלגברה הומולוגית, במקרה שבו מבקשים להוכיח קיומו של חץ בדיאגרמה, או תכונות שלו.
after recognizing any malfunction related to the fuses, determine the location of the corresponding fuse by checking the fuse charts pro- vided in the wiring diagram docu- mentation.
לאחר זיהוי תקלה כלשהי הקשורה לנתיכים, קבע את מיקום הנתיך המתאים על-ידי בדיקת תרשימי הנתיכים בתרשימי החיווט.
when observed from the perspective of the subsystem which is being integrated, the connections are reminiscent of a star, but when the overall diagram of the system is presented, the connections look like spaghetti, hence the name of this method.
שיטה זו נקראת כך משום שאם מסתכלים על גרף המערכת מנקודת מבט של אחת מתתי-המערכת, הקשרים מזכירים כוכב, אבל אם מסתכלים על הדיאגרמה הכוללת של המערכת, הקשרים נראים כמו ספגטי.
effect of biological pretreatment on biomass characteristics biological pretreatment of lignocellulosic biomass using white-rot fungi changes the biochemical and physical characteristic of the biomass (fig. 2). lignin degradation is the point of interest in many studies. for examples, lignin loss of corn straw was up to 54.6% after 30 days pretreatment with t. versicolor (yu et al. 2010b); bamboo culm was > 20% after 4 weeks pretreatment with echinodontium taxodii 2538 and t. versicolor g20 (zhang et al. 2007b); and wheat straw was 39.7% decreased after pretreatment with p. ostreatus (zadražil and puniya 1994). the degradation of lignin by white-rot fungi is a non-specific oxidative process that finally results in complete degradation of the lignin. peer-reviewed review article bioresources.com isroi et. al. (2011). “biological pretreatment: review,” bioresources 6(4), 5224-5259. 5232 fig. 2. schematic diagram of biological pretreatment of lignocelluloses. white-rot fungi decrease lignin content and alter chemical and physical structures of lignocelluloses that make biodegradation of lignocelluloses more efficient. white-rot fungi have unique capability to depolymerise, cleave carbon-carbon linkages, and mineralize lignin by ligninolytic enzymes. studies with 14c labeled lignin showed that white-rot fungi degraded them into 14co2 (lundquist et al. 1977; agosin, daudin and odier 1985; pérez and jeffries 1990; hofrichter et al. 1999). pleurotus ostreatus and b. adusta are highly specific lignin degraders based on 14c-lignin-labeled degradation analysis (agosin, daudin and odier 1985). changes in the ratio between phydroxyphenyl (h), guaiacyl (g), and syringyl (s) lignin units were analysed using pyrolysis-gas chromatography-mass spectrometry. it was shown that 10 u of peroxidase per mg of straw decreased the proportion of phenolic h units from 31% in the control to 3% in the treated straw, the g units from 40 to 4%, and completely removed the small amount of phenolic s units present in wheat straw (camarero et al. 2001). it is proposed that the susceptibility of the lignin units are in the following order: s>g>h. in general, biomass with s-rich lignins is more susceptible to fungal degradation than other lignin units (valmaseda et al. 1991). hemicellulose is easier to degrade than other components in lignocellulosic biomass. white-rot fungus such as p. chrysosporium (kirk and cullen 1998), phlebia floridensis (sharma and arora 2010), c. subvermispora (mendonça et al. 2008), pleurotus ostreatus (baldrian et al. 2005), and pleurotus dryinus (kachlishvili et al. 2005) were shown to produce multiple endoxylanases. compositional analyses of corn stover showed that during the 30 days biodegradation, white-rot fungi mainly degraded hemicellulose by 24.4 to 34.9% (yang et al. 2010). corn stover pretreated using c. subvermispora for 18 days lost up to 22.5% of hemicelluloses, and chinese-willow pretreated using echinodontium taxodii 2538 for 120 days lost 54.8% of its hemicellulose (yu et al. 2009a). degradation of hemicellulose combined with degradation of lignin may decrease recalcitration of lignocelluloses to enzymatic hydrolysis, but xylan loss increases the risk of lowering all sugar recovery in the bioconversion process (yu et al. 2010a).
ההשפעה של טיפול מקדים ביולוגי על מאפייני ביומסה טיפול מקדים ביולוגי של ביומסה ליגנוצלולוזית באמצעות פטריות ריקבון לבנות משנה את המאפיין הביוכימי והפיזי של הביומסה (איור 2). השפלת ליגנין היא נקודת העניין במחקרים רבים. לדוגמה, אובדן ליגנין של קש תירס היה עד 54.6% לאחר 30 ימים לפני הטיפול עם t. versicolor (yu et al. 2010b); אשמת במבוק היה 20% לאחר 4 שבועות לפני הטיפול עם echinodontium taxodii 2538 ו - t. versicolor g2
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