Production_of_plaques_in_monolayer_tissue_culture- Dulbecco

Production_of_plaques_in_monolayer_tissue_culture- Dulbecco...

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Unformatted text preview: PA THOLOG Y: RENA TO D ULBECCO (1) The coefficients of the rth derivatives for r< m are O(1/rIm-r+ ) forsome e> 0. (2) For r> m, j < r- m, thejth derivatives ofthe coefficients ofthe rthderivativetermsinA are0(1/r mti-r)forsome e> 0. Then iftheDirichletproblemfor K onD with zero boundary values has only thezero solution, theDirichletproblemforK on D has a solutionfor everyboundaryvaluefunctiongpermissiblewithrespecttoL. 1 Browder, F.E.,"The DirichletProblem forLinearEllipticEquationsofArbitrary Even Order withVariable Coefficients," PROC. NATL. AcAD. ScI.,38,230-235 (1952). 2 The definition ofpositivityused here isstronger than theusual form inL2(D). I Courant-Hilbert, MethodenderMathematischenPhysik,Vol.II,Berlin,1937;p.489. 4 Condition (b)forellipticityofour previousnoteissuperfluoussinceevery elliptic differentialoperator can be writtenasthesum ofa positiveoperatorand one oflower order. Thisfactwas observedby L.Girdingwhohasannounced thesemi-boundedness ofthehomogeneous operatorL definedintheproofofTheorem 1aswellasresultson the Dirichlet problem forequations with infinitelydifferentiablecoefficientssimilarto thoseofourpreviousnote; Compt. rend.,253, 1554-1556(1951). 6The results of (b) contain similar results obtained,for the general second-order equation by Carleman, "Uber dieasymptotische Verteilung der Eigenwerte partieller Differentialgleichungen," Ber. Sachs,Akad., 88, 128-129(1936),SatzV. 6 John, F., "General Properties of Solutions of Linear EllipticPartial Differential Equations," Proceedings oftheSymposium on SpectralTheory and DifferentialProb- lems,Stillwater,Okla.(1951),Chap. III. 7 Cf.reference 1,p.232. 8Bergman, S., "The Kernel Function and Conformal Mapping," Mathematical SurveySeries,1950. 9Courant-Hilbert, Vol. II,p.511. 10 A sufficientcondition forg to be permissible with respect to L isthat (f,g) < K!IfJIm forall fe Cc"'(D). PRODUCTION OF PLAQUES IN MONOLA YER TISSUE CUL- TURES B Y SINGLE PARTICLES OF AN ANIMAL VIRUS By RENATO DULBECCO CALIFORNIA INSTITUTE OFTECHNOLOGY, PASADENA, CALIFORNIA Read beforetheAcademy, April29,1952 Researchon thegrowth characteristicsand geneticpropertiesofanimal viruseshasstood greatlyin needof improvedquantitativetechniques,such asthoseusedin the' relatedfieldof bacteriophage studies. The requirements fora quantitativevirustechniqueare asfollows: (1) The use ofa uniform type ofhost cell; (2) an accurate assay technique; (3) the isolation of the progeny of a single virus particle; and (4) the separateisolationofeachofthevirus particlesproducedby a singleinfected VOL. 38,1952 747 PA THOLOG Y: RENA TO D ULBECCO cell. In bacterial virus work, production of plaques by single virus particleson a uniform bacterial layerfulfillsthe firstthreerequirements....
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Production_of_plaques_in_monolayer_tissue_culture- Dulbecco...

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