Topology - Imbeddings of Manifolds Prove that every manifold is regu.pdf

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There are two Chevrolet dealers in Jamestown, New York. The mean monthly sales at Sharkey Chevy and Dave White Chevrolet are about the same. However, Tom Sharkey, the owner of Sharkey Chevy, believes his sales are more consistent. Below are the numbers of new cars sold at Sharkey in the last 7 months and for the last 8 months at Dave White. Do you agree with Mr. Sharkey? Use the 0.01 significance level. 101 State the decision rule for 0.01 significance level What is the value of F? There is more variation of the monthly sales True/FalseSharkey98785457686470Dave White75818130824658 101 State the decision rule for 0.01 significance level What is the value of F? There is more variation of the monthly sales True/False Solution State the decision rule for 0.01 significance level It is a one-tailed test. The degree of freedom df1=n1-1=7-1=6 The degree of freedom df2=n2-1=8-1=7 Given a=0.01, the critical value isF(0.99, df1=6, df2=7) =7.19 (from F table) The rejection region is if F>7.19, we reject the null hypothesis. -------------------------------------------------------------------------------------------------------------------- What is the value of F? F= s1^2/s2^2 =14.79^2/22.95^2 =0.42 -------------------------------------------------------------------------------------------------------------------- There is more variation of the monthly sales True/False Since F=0.42 is less than 7.19, we do not reject the null hypothesis. So answer is FalseSharkeyDave White69.8669.25mean14.7922.95std. dev.78n.

Topology - Imbeddings of Manifolds Prove that every manifold is regular and hence
memorizable. Where do you use the Hausdorff condition?
Solution
Let X be a space.
X is called regular if and only if for each point x in X and U a neighbourhood of x, there is an
open set V such that
xVclVUxVclVU
Also we have that a manifold is locally Euclidean. (A topological manifold is a locally Euclidean
Hausdorff space)
In mathematics, a completely metrizable space(metrically topologically complete space) is a
topological space (X, T) for which there exists at least one metric d on Xsuch that (X, d) is a
complete metric space and d induces the topology
Thus here to prove that is it metrizable we use the Hausdorff space that distinct points have
distinct neighbourhoods.

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Assume a disease is dominant, indicated by shading. Based on the pedigree (click to enlarge), which parent determines whether the child indicated by the question mark will have the disease? Female parent. Male parent. Either parent. Solution Male Parent Because it shows in the pedigree that it is a X-linked disorder. If the child is female definitly she will be diseased getting both the diseased X allele from both the parents. Whereas when the child is male he will get one diseased X allele from mother and normal Y allele from father making him a carrier..

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Chorismate 3-glycero phosphate Relying on the above pathway for bil of tryptophan, fii in the table below to osynthesis predict growth or failure to grow When defective in each of the are placed on media supplemented with the Dom Mutant trpA trpB trpC trpD trpE Supplement Anthranilic acid Tryptophan and indole (Graded as right minus wrong) Solution Suppliment/Mutant trpA trpB trpC trpD trpE None -ve -ve -ve -ve -ve Anthranilic acid -ve - ve -ve -ve +ve Indole -ve +ve +ve +ve +ve tryptophan +ve +ve +ve +ve +ve tryptophan and Indole +ve +ve +ve +ve +ve.

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A form of favoritism where you give preferential treatment to your family members is called Solution This kind of favoritism is referred to as Nepotism.This term finds its origin back to the catholic popes and bishops who used to to put their nephews on important tasks and dignified positions. Broadly speaking, this kind of favoritism is favored upon close and dear relatives, family members in various fields like politics, sports, organisations and particularly in employement..

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2.Describe a technique that would allow a developmental biologist to visualize the expression of developmental genes in space and time. Be sure to describe how it works in as much information as you can remember or give an example. 3.Describe (briefly) ONE historical experiment provided by Hans Driesch which refuted the most accepted cell specification mechanism of the time period (1800s). 4.In developmental biology researchers often want to ‘drive’ gene expression within developing tissues – sometimes expressing genes in different locations or at different times of development so as to demonstrate the gene’s role during normal development. What research tools could you use to ‘drive’gene expression of Your Gene of Interest (YGI)? Explain. 5.What does it mean to be genetically equivalent? Describe how cloning demonstrates this? 6.Experiments with Xenopus (frog) in the late 1950s demonstrated that cells within the 3 germ layers had an affinity for each other and thus indicated that they had differentiated enough to be “biased” toward a specific cell layer (endoderm, mesoderm, ectoderm). Describe an experiment that demonstrated how the 3 different layers of the gastrula have an affinity for each other. 7.Morphogenesis involves the orchestration of Cell Affinity, Cell Adhesion, and Cell Migration. How do the adhesive molecules play a role as cells of the embryo change their affinity for one another? please help... Solution The best technique developed to visualise the expression of developmental genes is OPT ( OPTICAL PROJECTION TOMOGRAPHY). It has the ability to generate 3d images of non floroscent signals which helps to capture the expression of gene and histology using traditional tissue strains upto the resolution of 5 um×5um×5um within the 3d context of whole embryo between 0.5 to 15mm in depth. It is quite inexpensive technique , even cheaper than confocal microscopes..

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Write an essay on the Chernobyl nuclear accident, explaining why such an accident is unlikely to happen to a power plant in the United States. Solution The nuclear power plant disaster in the town of Chernobyl in 1986 came to have major impact on the environment and the population of the European continent. Due to the lack of security and financial resources, the Chernobyl plant was considered unsafe before the accident; one was able to prevent the accident from happening, as the old Soviet regime would not let any nuclear specialists from the west into the country. As a result, current winds following the disaster brought radioactive particles to Scandinavia and northwestern Europe, which came to have much greater impact than if the winds would have been blowing in another direction. According to De Boer and Catsburg (1997), the Chernobyl accident was not the first incident at a nuclear plant. In 1979, the nuclear plant at Three Mile Island in Pennsylvania had troubles, as well as the nuclear plant at Sellafield in Great Britain 1985. The accident in Chernobyl concerned people’s opinion about safety issues related to nuclear plants (Catsburg, De Boer 254). Much of the information about the Chernobyl disaster has been kept secret from people outside the former republic of Russia, but since the breakdown of the Soviet Union, a lot of information has become available to the west. Nuclear power is a fantastic energy source as it is efficient and leaves minimal chemical pollution, which can be minimized if it is done right. It is extremely effective and consistent, but what if something goes wrong? The oppositional forces to nuclear power received free advertising due to the disaster and the question about nuclear power was once again a subject for discussion..

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A living plant leaf is an open system that exchanges energy (sunlight and thermal flows) + matter (O2, CO2, water vapor, etc.) with the surroundings (the exterior). Even with irreversible processes (energy dissipation) we find that the net entropy change for the system + surroundings can decrease; i.e. dS < 0. Using equations and your own critical thinking: a) Explain how this is possible in terms of deS and diS. b) Explain how the Second Law remains valid for this case. Solution Kindly go through below details for entropy to clear concepts about entropy. According to the principle of entropy , the entropy change of the universe i.e system + surroundings can never have a negative value. i.e [(dS ) system + (dS) surroundings] >or = 0 always (dS) universe > 0 => Irreversible process (dS) universe = 0 => reversible process (dS) universe < 0 => Impossible So, it is impossible to have dS<0 for system and universe unlike mentioned by you in the question. Now let us analyse entropy change of system Entropy change of the system is summation of entropy change due to internal irreversibilty and entropy change due to external interaction. i.e dS = (dS) iir +(dS) ei = S gen (entopy generation) + dQ/T CASE I : If sytem is reversible than value of entropy generation is zero and Entropy change of system is given by dS= dQ/T ( A ) if heat is supplied to system then dQ/T >0 and hence entropy change of system is having positive value i.e dS >0 (B)if heat is rejected from system then dQ/T <0 and hence entropy change of system is having negative value i.e dS <0 (C) if system is adiabatic or well insulated system then dQ/T =0 and hence entropy change of system is having zero value i.e dS =0 NOTE : ENTROPY CHANGE OF THE SYSTEM MAY HAVE +VE, -VE OR ZERO VALUE BUT ENTROPY CHANGE OF THE UNIVERSE CAN NEVER HAVE NEGATIVE VALUE. CASE II :IF system is irreversible than the entropy change is given by dS = (dS)iir + (dS) ei or dS = S (gen ) + dQ/T (A) if the system is adibatic then dQ=0 therefore dS = (dS)iir =S (gen) and we know that the value of entropy generation can never be negative. (B) If the system is not adiabatic and the increase in internal ireversibilty is compensated by decrease in external interaction than the value of entropy changes can be zero i.e iscentropic dS = (dS)iir { increases) + (dQ/T)ei { decreases} e.g. 0 = 5 - 5 Now after discussing you must be clear that what is being wrongly/ mistakenly mentioned in the question. Consider the leaf as an irreversible sytem due to various process occuring for the conversion for one form of energy into another and also the transfer of heat occurs between systen ( leaf here) and surroundings and we can say heat is absorbed by the system here therefore entropy change of the system, dS > 0 since {(dS)iir >0 and also (dQ/T) ei >0 } and (dS) system + surrunding > 0 always for an irreversible process.

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our original model was pv^n =C where n is an exponent and C is a constant use the p and V data sent to you Previous it was shown that, if using log-log paper, a straight line could be drawn showing the relationship between volume and pressure A regression analysis will do even a better job of analysis But keep in mind that bo is in terms of a log. So taking the antilog of bo will give the real value for Bo where your Bo is really C Show your work in determining Bo and B1 Solution we have logP=logC-n*logV and -n = B1,logC=B0 then logP=B0-B1logV logP=B0-2B1 (answer).

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