Im Rahmen dieser Arbeit wurde versucht, die A1AO ATP-Synthase von I. hospitalis zu reinigen und die Untereinheitenzusammensetzung des Komplexes zu bestimmen. Obwohl der gekoppelte Komplex erfolgreich durch das Detergenz DDM (n-Dodecyl-β-D-Maltopyranosid) aus der Membran herausgelöst werden konnte, war eine Reinigung des Gesamtkomplexes bisher nicht möglich. Zahlreiche Versuche, das Enzym über säulenchromatographische Verfahren zu reinigen, führten lediglich zu einer Anreicherung der dissoziierten A1- und AO-Subkomplexe der ATP-Synthase. Eine Identifizierung der Untereinheiten war durch eine Kombination von 2D-Native/SDS-PAGE, Western-Blot-Analysen und MALDI-TOF MS/MS möglich. So konnte die in vivo Expression von acht annotierten Untereinheiten der ATP-Synthase (A, B, C, D, E, F, a(I) und c(K)) bestätigt und das Protein Igni1215 als Bestandteil der ATP-Synthase (Untereinheit H) identifiziert werden. Die beiden erhaltenen Subkomplexe bestanden aus A, B, E und F (A1) und aus C, D, H und a ...

Of all the Megavirales members, faustovirus shared the largest number of orthologs, as defined by the bidirectional best-hit strategy (45), with ASFV. Thus, the faustovirus and ASFV protein sequences comprised 52 pairs of orthologs that shared 21 to 50% identity; 13 of these 52 genes were not found in any other members of the Megavirales. In addition, phylogenies of several conserved genes of Megavirales, including that encoding the family B DNA polymerase, showed that faustovirus E12 and other faustovirus isolates were distantly related to ASFV (Fig. 3; see Fig. S5 at http://www.mediterranee-infection.com/article.php?laref=373&titer=faustovirus). Nevertheless, this evolutionary relationship was supported only by analysis of a relatively small number of shared genes, constituting only ≈12% of the faustovirus gene complement. In addition, several features were found to differ significantly between faustovirus and ASFV. They included an ≈3 times larger genome in faustovirus and a G+C content ...

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Que la Chambre: a) déplore les pertes de vies humaines suite à lexplosion tragique survenue à Beyrouth le 4 août 2020; b) exprime sa solidarité avec le peuple libanais, en particulier avec les familles des plus de 150 personnes décédées, des plus de 6 000 personnes hospitalisées et des quelque 300 000 personnes qui se sont retrouvées sans abri à la suite de lexplosion; c) sengage à aider et à soutenir le peuple libanais dans son désir de réforme et de reconstruction durable et continue à soutenir la communauté libanaise, tant au Liban quici au Canada, en ces temps très difficiles ...

Rationnelle. La ventilation mécanique invasive (VI) saccompagne lorsquelle se prolonge, dune augmentation de la morbimortalité. Jusquà 64% des enfants hospitalisés aux soins intensifs sont ventilés et peu de données épidémiologiques existent afin destimer précocement la durée du support ventilatoire. Objectifs. Déterminer lincidence et les facteurs de risque précoces de ventilation mécanique invasive prolongée aux soins intensifs pédiatriques. Méthode. Nous avons conduit une étude descriptive rétroélective sur un an. Tous les épisodes de VI aux soins intensifs du Centre hospitalier universitaire Sainte Justine de Montréal ont été inclus. Les facteurs de risque de VI prolongée (≥ 96 heures) ont été déterminés par régression logistique. Résultats. Parmi les 360 épisodes de VI, 36% ont duré ≥ 96 heures. Les facteurs de risques de ventilation prolongée en analyse multivariée sont : âge ,12 mois, score de PRISM ≥ 15 à ladmission, pression moyenne dans ...

Gregory Hampton et sa compagne, Monica Roberts, son hospitalisés à la suite de ce qui semble être une intoxication au monoxyde de carbone. Monica succombe…. ...

Une épidémie de salmonellose à Salmonella Enteridis lysotype PT4 dorigine alimentaire a eu lieu en Cumbria, au nord-ouest de lAngleterre, durant lété 2006. Quinze personnes, dont les échantillons de selles étaient positifs, correspondaient à la définition du cas ; trois dentre elles ont été hospitalisées, et lune de ces trois personnes est décédée.

Le bilan lavallois est désormais de 612 cas actifs selon les données émises par le Centre intégré de santé et de services sociaux (CISSS) de Laval. Cela signifie que le territoire connait une hausse de 12 cas actifs par rapport à la veille. Le total de décès augmente à 719 (+1) depuis le début de la pandémie. 90 tests positifs ont été effectués dans les 24 dernières heures. Ainsi, depuis le mois de mars, 10 580 citoyens lavallois ont été affectés par le virus. Parmi les personnes touchées par la COVID-19, 18 sont présentement hospitalisées, dont 2 aux soins intensifs. 34 employés de lorganisation de santé sont toujours absents du travail en raison de la COVID-19. Fabreville-Est/Sainte-Rose connait encore la plus forte augmentation du dernier bilan avec 19 nouveaux cas confirmés. Ce secteur est désormais le deuxième plus affecté de lîle Jésus avec un taux dinfection de 260 cas par 100 000 habitants sur les deux dernières semaines. Il est devancé par Pont-Viau/Renaud

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Consider the following experiment.. We throw a three-sided die with sides $1$, $2$ and $3$ infinitely many times. Let $T_i$ denote the outcome of the $i$th throw. Define $N:=\min\{i:T_i\neq1\}$. Let $X$ be the event that $T_N=2$ and let $Y$ be the event that $T_N=3$.. Some calculation (*) leads to the result that $\mathbb{E}(N)=\mathbb{E}(N,X)=\mathbb{E}(N,Y)=3/2$.. Let $Z$ be the event that $T_i\neq3$ for all $i$. Some calculation (**) leads to the result that $\mathbb{E}(N,Z)=2$.. I find it very unintuitive that $\mathbb{E}(N,X)\neq\mathbb{E}(N,Z)$. Obviously we have $Z\subsetneq X$. However, the information $Z$ gives, which $X$ does not give, intuitively only affects what comes after the $N$th throw. So how is it possible that the probability distribution of $N$ is different when conditioning on $X$ or $Z$?. (*) We have $\mathbb{P}(X)=\mathbb{P}(Y)$ and $\mathbb{E}(N,X)=\mathbb{E}(N,Y)$ by symmetry. Also notice that $X$ and $Y$ partition the event space, so $\mathbb{P}(X)+\mathbb{P}(Y)=1$, ...

转运核糖核酸（Transfer RNA），又称传送核糖核酸、转移核糖核酸，通常简称为tRNA，是一种由76-90个核苷酸所组成的RNA[1]，其3端可以在氨酰-tRNA合成酶催化之下，接附特定种类的氨基酸。转译的过程中，tRNA可借由自身的反密码子识别mRNA上的密码子，将该密码子对应的氨基酸转运至核糖体合成中的多肽链上。每个tRNA分子理论上只能与一种氨基酸接附，但是遗传密码有简并性（degeneracy），使得有多于一个以上的tRNA可以跟一种氨基酸接附。

Let f(x,y) = \begin{array}{cc} \frac{xy}{\sqrt{x^2 + y^2}} &, (x,y) \neq(0,0) \\ 0 & ,(x,y) = (0,0) \\ \end{array} Show that the directional...

We learned to factor complex trinomials today (of the form $latex ax^2+bx+c $ where $latex a \neq 1 $). Its more challenging than factoring simple trinomials (hence the name!). Important tip: always look to see if there is a common factor that you can remove first. If there is, you can factor it out and have…

But I cant do this equation backwards, Im missing a step. I would think if Im converting g/mol to mol, I would divide by how many grams I have (1000 in this case), but 78.074g/mol CaF2 / 1000g [tex]\neq[/tex] ~13mol ...

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tRFs & tiRNAs: small RNAs with distinct and varied functions tRNA is known to be an adaptor molecule to decode and translate mRNA into protein. However, recent studies have discovered tRNAs to be a major source of small non-coding RNAs, with their abundance levels often higher than microRNAs. tRNA derived fragments (tRF) and tRNA halves (tiRNA) are generated from tRNAs by precise biogenesis processes (Fig. 1), having distinct and varied functions to [1-3]:. ...

The main reason for posting this was to answer it, thus collecting all this stuff in a single place for future reference -- and present too.. The first item on this proof is that a linear operator on a finite-dimensional complex vector space admits an upper triangular representation. This is proved by induction on $n:=\dim V$, $V$ being the vector space. If it is 1D, the proof is trivial. Suppose $\dim V=n,1$ and the theorem holds for dimensions up to $n-1$. We know our operator $T$ has an eigenvalue. Indeed, consider $v,Tv,T^2v,T^3v,\dotsc,T^nv$. Those cannot be linearly independent if $v\neq0$, since they are $n+1$ and $\dim V=n$. So there exist $a_i\in\mathbb{C}$ such that: $$\sum_{i=1}^nT^iva_i=0.$$ Let $m$ be the largest index such that $a_m\neq0$. THis is not 0, since $v\neq0$. Factor the polynomial: $$a_0+a_1z+\dotso+a_mz^m=c(z-\lambda_1)\cdot\dotso\cdot(z-\lambda_m).$$ Substituting $T$ for $z$, and applying to $v$, we find: ...

Definition: Let $f_n = a_1f_{n-1} + a_2f_{n-2} + ... + a_kf_{n-k}$ for $n \geq k$ be a linear homogeneous recurrence relation of order $k$, i.e., $a_1, a_2, ..., a_k$ are constants and $a_k \neq 0$. Then this recurrence relation can be rewritten as $f_n - a_1f_{n-1} - a_2f_{n-2} - ... - a_kf_{n-k} = 0$ and the Character Equation for the linear homogeneous recurrence relation with constant coefficients is the polynomial $x^k - a_1x^{k-1} - a_2x^{k-2} - ... - a_k = 0$ ...

Unsubscribe from Ikeda Spa? JS - nca Nosema ceranae - nce Nitrosomonas communis - nco Neurospora crassa - ncr Naumovozyma castellii - ncs Nocardia cyriacigeorgica - ncy Nocardiopsis dassonvillei - nda Nitrospira defluvii - nde Naumovozyma dairenensis - ndi Candidatus Nasuia deltocephalinicola - ndl Nonlabens dokdonensis - ndo Neisseria elongata - nel Nanoarchaeum equitans - neq Nitrosomonas eutropha - net Nitrosomonas europaea - neu Candidatus Nitrososphaera evergladensis - nev Nocardia farcinica - nfa Neosartorya fischeri - nfi Candidatus Nitrososphaera gargensis - nga Nannochloropsis gaditana - ngd Natronobacterium gregoryi - nge Neorhizobium galegae bv.. CC - syd Synechococcus sp. Lost your model?. ...

Staphylothermus marinus is a marine organism that was isolated from hydrothermal sediment off the the coast of Vulcano Island in Italy. It can also be found from black smokers on the ocean floor. In a rich medium, Staphylothermus marinus grows in an optimum temperature of 92 degrees Celsius, but when nutrients are sparce, the optimum temperature drops to 85 degrees Celsius. For growth in a lab, a complex nutrient source is needed for optimum growth. The morphology of the Staphylothermus marinus can differ depending on the nutrients available. When nutrients are plentiful, Staphylothermus marinus grow as giant cells in a slightly irregular coccus shape with diameters up to 15 mm. Low nutrient concentrations produce little cells with diameters ranging from 0.5 to 1.0 mm. Up to 100 of these cells can cluster together to form grape-like groups. S. marinus is related to Aeropyrum pernix, Hyperthermus butylicus, and Ignicoccus hospitalis. (5) Describe the appearance, habitat, etc. of the organism, ...

The Genome Analysis Core conducts several RT-PCR platforms plus single cell encapsulation for RNA Seq 3 library production.. The BioMark Genetic Analysis Platform is a system that is a fully integrated system enabling analysis of gene expression, genotyping, mutant detection, and absolute quantization of nucleic-acid sequences utilizing Dynamic Array Integrated Fluidic Chip (IFC) technology which provides high-throughput real-time qPCR.. The BioRad QX200 Droplet Digital PCR (ddPCR) provides absolute quantification of target DNA or RNA molecules for EvaGreen or probe-based digital PCR applications.. ...

displaystyle {\begin{aligned}{\frac {d}{dx}}\sinh x&=\cosh x\\{\frac {d}{dx}}\cosh x&=\sinh x\\{\frac {d}{dx}}\tanh x&=1-\tanh ^{2}x=\operatorname {sech} ^{2}x={\frac {1}{\cosh ^{2}x}}\\{\frac {d}{dx}}\coth x&=1-\coth ^{2}x=-\operatorname {csch} ^{2}x=-{\frac {1}{\sinh ^{2}x}}&&x\neq 0\\{\frac {d}{dx}}\operatorname {sech} x&=-\tanh x\operatorname {sech} x\\{\frac {d}{dx}}\operatorname {csch} x&=-\coth x\operatorname {csch} x&&x\neq 0\\{\frac {d}{dx}}\operatorname {arsinh} x&={\frac {1}{\sqrt {x^{2}+1}}}\\{\frac {d}{dx}}\operatorname {arcosh} x&={\frac {1}{\sqrt {x^{2}-1}}}&&1,x\\{\frac {d}{dx}}\operatorname {artanh} x&={\frac {1}{1-x^{2}}}&&,x,,1\\{\frac {d}{dx}}\operatorname {arcoth} x&={\frac {1}{1-x^{2}}}&&1,,x,\\{\frac {d}{dx}}\operatorname {arsech} x&=-{\frac {1}{x{\sqrt {1-x^{2}}}}}&&0,x,1\\{\frac {d}{dx}}\operatorname {arcsch} x&=-{\frac {1}{,x,{\sqrt {1+x^{2}}}}}&&x\neq 0\end{aligned ...

Were trying to invert a function $latex f:X\rightarrow\mathbb{R}^n$ which is continuously differentiable on some region $latex X\subseteq\mathbb{R}^n$. That is we know that if $latex a$ is a point where $latex J_f(a)\neq0$, then there is a ball $latex N$ around $latex a$ where $latex f$ is one-to-one onto some neighborhood $latex f(N)$ around $latex f(a)$. Then…

Let $N_n$ be a sequence of natural numbers increasing to infinity, and suppose we have a sequence of finite sets of distinct points $X_n = \{x_1^{n},x_2^{n},\ldots,x^{n}_{N_n}\} \subset[0,1] \subset \mathbb{R}$. Consider the discrete probability measure $$ \rho_n = \frac{1}{N_n}\sum_{i=1}^{N_n}\delta_{x^{n}_i}, $$ a normalized sum of delta functions centered at the points $x^{n}_i$. Being bounded as a linear operator on $C([0,1])$, there exists a vaguely convergent subsequence of the $\rho_n$ i.e. there exists a probability measure $\rho$ on [0,1] such that $$ \int_0^1fd\rho_{n_k} \to_{k\to \infty} \int_0^1 fd\rho $$ for all $f \in C([0,1])$. Let me further impose a spacing condition that if $$ r_n := \inf_{i\neq j} ,x^n_i - x^n_j, $$ is the minimum distance between distinct pairs of the $x^n_i$, then $$ \inf_n N_n r_n , 0. $$ (in particular, this implies $x^n_i$ are distinct). This loosely can be interpreted as enforcing that the $X_n$ not accumulate too much on 0-dimensional sets (or perhaps I ...

It sounds weird. You essentially only care about the finitely many $x_i$ for which $c_i \neq 0$. But the constraints involving those variables you like might involves lots of variables you dont care about. Ultimately, this seems equivalent to a finite linear program in the sense that as far as you care, the matrix $Ax = b$ could be replaced by some finite matrix equation $A x = b.$ whose solution set is the projection of $\{x \ : \ Ax =b\}$ onto the variables you actually care about.. But Im not sure to what extent that even makes sense since for instance we could have the equations $x_0 = x_1$ and for all $n \geq 1$ $$ x_{n+1} - x_{n} + \frac{(-1)^{n}}{n} = 0. $$ This matrix would have the finite row condition you want (and a finite column condition), but its not at all clear how to solve it. One would be tempted to sum all the equations together yielding the telescoping $$ x_0 = x_1 + \sum_{n\geq 1} \left [x_{n+1} - x_{n} + \frac{(-1)^{n}}{n} \right ] = \sum_{n\geq 1} \frac{(-1)^{n}}{n}, ...

Based on our previous study [1], we tested the null hypothesis that during the 2 weeks after the NEQ there was a compensation for the excess of deaths due to IHD and ASCVD on the day of the NEQ. This was tested against the alternative hypothesis that during the 2 weeks after the NEQ there was an overcompensation for the excess IHD and ASCVD deaths on the day of the NEQ. Plots of deaths due to IHD and ASCVD per day during January of 1992, 1993 and 1994 (Fig. 2) suggested that the slopes for the control years and that part of the quake year (1994) before the NEQ were not different, although the intercepts were different. This was confirmed by statistical analysis (p = 0.6789 for a test of slopes, p = 0.0006 for a test of intercepts). In choosing a model that assumes equal slopes and different intercepts for the relation between IHD and ASCVD versus time, we determined that the best model was a simple linear model in which the slope was −0.36764 and the intercepts in 1992, 1993 and 1994 were ...

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Comment on attachment 667931 [details] [diff] [review] Tests for the debugging server profiler actor Review of attachment 667931 [details] [diff] [review]: ----------------------------------------------------------------- Nice! One check is failing for me locally, but Im sure you can fix that. ::: toolkit/devtools/debugger/tests/unit/test_profiler_actor.js @@ +119,5 @@ , + var sample = aResponse.profile.threads[0].samples[Math.floor(aResponse.profile.threads[0].samples.length / 2)]; , + do_check_eq(sample.name, (root)); , + do_check_eq(typeof sample.frames, object); , + do_check_neq(sample.frames.length, 0); , + do_check_true(sample.frames.some(function(f) { This check fails locally on OS X 10.8 debug. I added some dumps and I get this: 0.70 f.line == stack.lineNumber: false 0.70 f.line: undefined 0.70 stack.lineNumber: 107 0.70 f.location == stack.name + etc.: false 0.70 f.location: 0x101e96441 0.70 stack.name + etc.: test_profile ...

chains in the Genus database with same CATH superfamily 4AEA A; 2LA1 A; 2JQP A; 1KFH A; 1PLO A; 4QTI U; 1BTE A; 1IDG A; 1W6B A; 1MR6 A; 1TGX A; 2CRT A; 1FSS B; 2QC1 A; 3FEV A; 3PLC A; 2HLR A; 2CTX A; 2QJ9 C; 1RGJ A; 5DU1 A; 2MUO A; 1MAH F; 2UWR A; 6EBX A; 1KBS A; 2H5F A; 3U74 U; 1IDH A; 1V6P A; 1FFJ A; 1KS6 A; 2X8B B; 4LFT A; 1FSC A; 1JGK A; 1HAJ A; 2ABX A; 1F8U B; 1ABT A; 3BT1 U; 4IYE A; 4BDT B; 1H0J A; 3BT2 U; 2HLQ A; 2CDX A; 1F94 A; 3QB4 B; 1CDR A; 3EBX A; 1JBD A; 1KBT A; 3NH7 A; 2GOO C; 1CHV S; 1NTN A; 1KTZ B; 1IJC A; 3HH7 A; 1CDT A; 2N99 A; 1ERG A; 1NYS A; 2H8U A; 2H7Z A; 1LJZ A; 1NXB A; 1HC9 A; 1NTX A; 4OM5 A; 1COE A; 4P7U A; 1IK8 A; 1VB0 A; 5DZ5 A; 1TXA A; 4UY2 C; 2CRS A; 1TXB A; 5IMY C; 1IQ9 A; 1NEA A; 2MHY A; 1CDQ A; 1ONJ A; 3U73 U; 1RL5 A; 2ERA A; 1NOR A; 2UX2 A; 3NEQ A; 1JE9 A; 2GOO B; 2L5S A; 1CVO A; 5DO6 A; 1M9Z A; 2MJY A; 4RUD A; 2MUP A; 2FD6 U; 1CCQ A; 1QKD A; 2QJB C; 1HOY A; 1KXI A; 1CXN A; 2H7Z B; 2H62 D; 2MJ4 A; 4DO8 A; 2BTX A; 4FAO E; 1HC9 B; 3LAQ U; 2PJY B; 2H64 C; 2J8B A; ...

The result (1) is a lower bound of the degree of Galois orbits of special subvarieties computed against the automorphic line bundle on \(S\), i.e., the line bundle defining the Baily-Borel compactification of \(S\). Here the Galois orbits is taken with respect to the canonical model of \(S\) over its reflex field \(E({\mathbf{G}},X)\). The bound given in Section 2 of the paper (cf. Theorem 2.19 and Remark 2-20 formula (8)) actually only involves the counting of connected components in the Galois orbits, generalizing the case of special points treated in [Zbl 1097.11032]: \[ \deg_{\mathcal{L}}(\text{Gal}(\overline{\mathbb{Q}}/E)\cdot V)\geq c_N\prod_{p:K^{\mathrm{max}}_{{\mathbf{T}},p}\neq K_{{\mathbf{T}},p}}\max(1,B,K_{{\mathbf{T}},p}^{\mathrm{max}}/K_{{\mathbf{T}},p},)\cdot(\log,\mathrm{disc}(L_{\mathbf{T}}),)^N \] where \(N\) is any prescribed integer, \(c_N,0\) is an absolute constant that only depends on \(N\), and \(B,0\) is an absolute constant independent of \(N\) (lying in \((0,1)\)). ...

NovaTaq DNA Polymerase from Novagen,NovaTaq DNA Polymerase is a premium quality recombinant form of Thermus aquaticus DNA polymerase. This thermostable enzyme is suitable for a wide range of PCR applications. To ensure the highest purity and reproducible performance, each preparation is extensively tested in a variety of quality cont,biological,biology supply,biology supplies,biology product

The replicating polymerase scans the template, ahead of the replication fork, for the presence of uracil and halts polymerisation on detecting this base.

Euryarchaeota (es); Euryarchaeota (hu); Euryarchaeota (is); Euryarchaeota (ast); Euryarchaeota (nds); Euryarchaeota (de); Euryarchaeota (ga); پهن‌باستانیان (fa); 廣古菌門 (zh); Euryarchaeota (tr); ユリアーキオータ門 (ja); Euryarchaeota (ia); Euryarchaeota (sv); Евріархеоти (uk); Euryarchaeota (la); 유리고세균 (ko); Eŭriarkeoto (eo); Euryarchaeota (cs); Euryarchaeota (bs); Euryarchaeota (it); Euryarchaeota (fr); Euryarchaeota (jv); Euryarchaeota (et); Euryarchaeota (vi); Euriarqueotas (gl); Euryarchaeota (pt); Euryarchaeota (lt); Euryarchaeota (war); Euryarchaeota (tl); Euryarchaeota (id); Euriarqueot (ca); Euryarchaeota (ceb); Euryarchaeota (pl); Euryarchaeota (bg); Euryarchaeota (nl); эвриархеоты (ru); Euryarchaeota (sr); Euryarchaeota (ro); Euryarchaeota (nn); Euryarchaeota (en); عتائق عريضة (ar); Euryarchaeota (sq); Euryarchaeota (fi) тип архей (ru); archaea törzse, ország (hu); Stamm der Archaeen (Archaea) (de); ...

Dr. Jason Russ, MD is a hospital medicine specialist in Indianapolis, IN. Dr. Russ completed a residency at Indiana University / School of Medicine. He currently practices at IU Health Physicians Hospitalis and is affiliated with IU Health Methodist Hospital.

Presenter: Gudrun Vogeser, PIKA Weihenstephan GmbH, Pfaffenhofen/Ilm, Germany.. During beer production, the growth of several microorganisms can cause spoilage. Well known are some representatives of the genera Lactobacillus and Pediococcus, in addition to anaerobic Megasphaera and Pectinatus species. Different bacteria species inherit different capabilities for spoilage. Besides generating turbidity by growing to high numbers, they may cause off-flavors such as diacetyl, acetic, lactic or propionic acid, hydrogen sulfide, etc. The brewer not only needs to detect these spoilers at a very early stage, but also has to know about their spoilage potential as soon as possible. By application of the PCR method it is possible to receive knowledge about the appearance of a spoiling microorganism at a very early stage and to identify the species. The microbiological flora in different breweries have been monitored with PCR applications, and the data from 2010 and 2011 (as far as available) will be shown. ...

The PDB archive contains information about experimentally-determined structures of proteins, nucleic acids, and complex assemblies. As a member of the wwPDB, the RCSB PDB curates and annotates PDB data according to agreed upon standards. The RCSB PDB also provides a variety of tools and resources. Users can perform simple and advanced searches based on annotations relating to sequence, structure and function. These molecules are visualized, downloaded, and analyzed by users who range from students to specialized scientists.

The difficult case is $f(x) \in B$. Fortunately, since $B$ is in P, we can test whether this case happens. When it does, we would like to output something which is not in $A \cup B$. Here it is helpful (and necessary!) that $A \cup B \neq \Sigma^*$. Indeed, we can pick some arbitrary $z \notin A \cup B$, and choose this as our output when $f(x) \in B$.. Here is what the updated reduction looks like: $$ g(x) = \begin{cases} z & \text{if } f(x) \in B, \\ f(x) & \text{otherwise}. \end{cases} $$ Does this work? Let us prove that it does.. If $f(x) \in B$, then since $A$ and $B$ are disjoint, we are guaranteed that $f(x) \notin A$, and so $x \notin L$. In this case $g(x) = z \notin A \cup B$, as needed.. If $f(x) \notin B$ then $g(x) = f(x)$, and moreover $g(x) = f(x) \in A \cup B$ iff $f(x) \in A$ iff $x \in L$, again as needed.. Finally, note that $g$ can be implemented in polynomial time, since $f$ can be so implemented, and $B$ is in P.. ...

The CONVERT_ADD spreadsheet function (known as CONVERT in other applications) has many more conversion factors implemented, as defined in OASIS ODFF/OpenFormula, for details see http://www.oasis-open.org/committees/documents.php?wg_abbrev=office-formula The full list is: SI prefix: unit may be prefixed by one SI prefix, supported prefixes are: y Yocto 1.00E-24 z Zepto 1.00E-21 a Atto 1.00E-18 f Femto 1.00E-15 p Pico 1.00E-12 n Nano 1.00E-09 u Micro 1.00E-06 m Milli 1.00E-03 c Centi 1.00E-02 d Deci 1.00E-01 1.00E+00 e Deca 1.00E+01 h Hecto 1.00E+02 k Kilo 1.00E+03 M Mega 1.00E+06 G Giga 1.00E+09 T Tera 1.00E+12 P Peta 1.00E+15 E Exa 1.00E+18 Z Zetta 1.00E+21 Y Yotta 1.00E+24 Information units bit and byte may also be prefixed by one IEC 60027-2 / IEEE 1541 prefix, supported prefixes are: 1 ki kibi 1024 Mi mebi 1048576 Gi gibi 1073741824 Ti tebi 1099511627776 Pi pebi 1125899906842620 Ei exbi 1152921504606850000 Zi zebi 1180591620717410000000 Yi yobi 1208925819614630000000000 // MASS: 1 Gram ...