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Sufficient conditions for univalence of a general integral operator
Chellian Selvaraj,Kadhavoor Ragavan Karthikeyan 대한수학회 2009 대한수학회보 Vol.46 No.2
In this paper, univalence of a certain integral operator and some interesting properties involving the integral operators on the classes of complex order are obtained. Relevant connections of the results, which are presented in this paper, with various other known results are also pointed out. In this paper, univalence of a certain integral operator and some interesting properties involving the integral operators on the classes of complex order are obtained. Relevant connections of the results, which are presented in this paper, with various other known results are also pointed out.
On certain classes of multivalent functions involving a generalized differential operator
Chellian Selvaraj,Kuppathai A. Selvakumaran 대한수학회 2009 대한수학회보 Vol.46 No.5
Making use of a generalized differential operator we introduce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships. Some integral preserving properties of these subclasses are also discussed. Making use of a generalized differential operator we introduce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships. Some integral preserving properties of these subclasses are also discussed.
ON CERTAIN CLASSES OF MULTIVALENT FUNCTIONS INVOLVING A GENERALIZED DIFFERENTIAL OPERATOR
Selvaraj, Chellian,Selvakumaran, Kuppathai A. Korean Mathematical Society 2009 대한수학회보 Vol.46 No.5
Making use of a generalized differential operator we introduce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships. Some integral preserving properties of these subclasses are also discussed.
SUFFICIENT CONDITIONS FOR UNIVALENCE OF A GENERAL INTEGRAL OPERATOR
Selvaraj, Chellian,Karthikeyan, Kadhavoor Ragavan Korean Mathematical Society 2009 대한수학회보 Vol.46 No.2
In this paper, univalence of a certain integral operator and some interesting properties involving the integral operators on the classes of complex order are obtained. Relevant connections of the results, which are presented in this paper, with various other known results are also pointed out.
Ngnitcho, Paul-Franç,ois Kounkeu,Tango, Charles Nkufi,Khan, Imran,Daliri, Eric Banan- Mwine,Chellian, Ramachandran,Oh, Deog Hwan Elsevier 2018 FOOD SCIENCE AND TECHNOLOGY -ZURICH- Vol.91 No.-
<P><B>Abstract</B></P> <P>This research was performed to evaluate the inactivation kinetics of slightly acidic electrolyzed water (SAEW), fumaric acid (FA) and their combination simultaneous with ultrasound (US) at a mild temperature against <I>L.monocytogenes</I> and <I>E.coli</I> O157:H7 on sprouts. The effects of combined treatments on sensory quality of sprouts were also examined. A t<SUB>4D</SUB> equal to 10 min was needed for the combined SAEW with FA (SAEW + FA) at 40 °C to reach 4 log reduction of <I>L.monocytogenes;</I> while the same combination simultaneous with ultrasound (SAEW + FA + US) provided the t<SUB>4D</SUB> value of 12; 7 and 3 min for <I>L.monocytogenes</I> at 23°, 30° and 40 °C respectively. For <I>E.coli</I> O157:H7, only (SAEW + FA + US) gave the t<SUB>4D</SUB> of 14; 9 and 3 min at 23°, 30°, and 40 °C respectively. The Weibull model provided a good fit with R<SUP>2</SUP> ≥ 0.9 for both bacteria and the root mean square errors (RMSEs) were in the range of 0.01–0.48 for <I>L.monocytogenes</I> and 0.02–0.54 for <I>E.coli</I> O157:H7. The samples submitted to both combined treatments remained in good quality at the end of storage with slight deterioration due to ultrasound usage. This study suggests that the Weibull model could successfully be used to determine exact contact time for inactivating foodborne pathogens on food.</P> <P><B>Highlights</B></P> <P> <UL> <LI> SAEW+FA and SAEW+FA+US treatments were more effective compared to single treatments. </LI> <LI> Increasing temperature in combined treatment decreases the time required to inactivate 4 log (t<SUB>4D</SUB>). </LI> <LI> Quality of SAEW+FA and SAEW+FA+US treated samples remained acceptable at the end of storage. </LI> </UL> </P>