SUFFICIENT CONDITIONS FOR STARLIKENESS

RAVICHANDRAN, V.,SHARMA, KANIKA Korean Mathematical Society 2015 대한수학회지 Vol.52 No.4

We obtain the conditions on ${\beta}$ so that $1+{\beta}zp^{\prime}(z){\prec}1+4z/3+2z^2/3$ implies p(z) ${\prec}$ (2+z)/(2-z), $1+(1-{\alpha})z$, $(1+(1-2{\alpha})z)/(1-z)$, ($0{\leq}{\alpha}$<1), exp(z) or ${\sqrt{1+z}}$. Similar results are obtained by considering the expressions $1+{\beta}zp^{\prime}(z)/p(z)$, $1+{\beta}zp^{\prime}(z)/p^2(z)$ and $p(z)+{\beta}zp^{\prime}(z)/p(z)$. These results are applied to obtain sufficient conditions for normalized analytic function f to belong to various subclasses of starlike functions, or to satisfy the condition ${\mid}log(zf^{\prime}(z)/f(z)){\mid}$ < 1 or ${\mid}(zf^{\prime}(z)/f(z))^2-1{\mid}$ < 1 or zf'(z)/f(z) lying in the region bounded by the cardioid $(9x^2+9y^2-18x+5)^2-16(9x^2+9y^2-6x+1)=0$.

SUFFICIENT CONDITIONS FOR STARLIKENESS

V. Ravichandran,Kanika Sharma 대한수학회 2015 대한수학회지 Vol.52 No.4

We obtain the conditions on β so that 1+βzp′(z) ≺ 1+4z/3+ 2z2/3 implies p(z) ≺ (2+z)/(2−z), 1+(1−α)z, (1+(1−2α)z)/(1−z), (0 ≤ α < 1), exp(z) or √1 + z. Similar results are obtained by considering the expressions 1+βzp′(z)/p(z), 1+βzp′(z)/p2(z) and p(z)+βzp′(z)/p(z). These results are applied to obtain sufficient conditions for normalized analytic function f to belong to various subclasses of starlike functions, or to satisfy the condition | log(zf′(z)/f(z))| < 1 or |(zf′(z)/f(z))2 −1| < 1 or zf′(z)/f(z) lying in the region bounded by the cardioid (9x2 + 9y2 − 18x + 5)2 − 16(9x2 + 9y2 − 6x + 1) = 0.

Mixed Layer Variability in Northern Arabian Sea as Detected by an Argo Float

T.V.S. Udaya Bhaskar,D. Swain,M. Ravichandran 한국해양과학기술원 2007 Ocean science journal Vol.42 No.4

Seasonal evolution of surface mixed layer in the Northern Arabian Sea (NAS) between 17° N–20.5° N and 59° E–69° E was observed by using Argo float daily data for about 9 months, from April 2002 through December 2002. Results showed that during April - May mixed layer shoaled due to light winds, clear sky and intense solar insolation. Sea surface temperature (SST) rose by 2.3 oC and ocean gained an average of 99.8 Wm-2. Mixed layer reached maximum depth of about 71 m during June - September owing to strong winds and cloudy skies. Ocean gained abnormally low ~18 Wm-2 and SST dropped by 3.4 oC. During the inter monsoon period, October, mixed layer shoaled and maintained a depth of 20 to 30 m. November - December was accompanied by moderate winds, dropping of SST by 1.5 oC and ocean lost an average of 52.5 Wm-2. Mixed layer deepened gradually reaching a maximum of 62 m in December. Analysis of surface fluxes and winds suggested that winds and fluxes are the dominating factors causing deepening of mixed layer during summer and winter monsoon periods respectively. Relatively high correlation between MLD, net heat flux and wind speed revealed that short term variability of MLD coincided well with short term variability of surface forcing.

Effect of Food Seasoning Spices Mixture on Biomarkers of Oxidative Stress in Tissues of Fructose-Fed Insulin-Resistant Rats

C.V. Anuradha,R. Suganthi,S. Rajamani,M.K. Ravichandran 한국식품영양과학회 2007 Journal of medicinal food Vol.10 No.1

High fructose feeding in normal rats induces insulin resistance and also facilitates oxidative damage. The pre-sent study examines the effects of a spices mixture (SM) on oxidative stress markers and antioxidant potential in tissues ofhigh fructose-fed insulin-resistant rats. Male Wistar rats received a semisynthetic diet containing either 60% fructose or 60%starch. SM administration at three different doses (10, 30, and 50 mg/day per rat) was initiated orally 15 days later and con-tinued for the next 30 days. After the total experimental period of 45 days, peroxidation of lipids and antioxidant status inliver and kidney were quantified. Fructose-treated rats showed increased levels of peroxidation indices such as thiobarbituricacid-reactive substances and lipid hydroperoxides in tissues. The condition was associated with an inadequate antioxidant sys-tem. Administration of SM along with fructose diet reduced the levels of peroxidation markers in tissues and improved theantioxidant status. The positive effect of SM on the oxidantantioxidant balance could be attributed to the active constituentsof the different spices present in the mixture.

Food Seasoning Spices Mixture Improves Glucose Metabolism and Lipid Profile in Fructose-Fed Hyperinsulinemic Rats

C.V. Anuradha,S. Rajamani,R. Suganthi,M.K. Ravichandran 한국식품영양과학회 2005 Journal of medicinal food Vol.8 No.4

Fructose feeding has been shown to induce insulin resistance in rats, associated with hyperinsulinemia, hy-perglycemia, and hypertriglyceridemia. We have investigated the effect of administering food seasoning spices mixture (SM)on glucose, insulin, and lipids in circulation and carbohydrate enzymes in the erythrocytes of high fructose-fed rats. Addi-tionally, we also measured the protein glycation status by assaying the levels of glycated hemoglobin, fructosamine, and plasmaprotein glycation. Male Wistar rats received a daily diet containing either 60% fructose or 60% starch (control). The rats wereadministered SM at three different doses (10, 30, or 50 mg/day per rat) orally 15 days later. At the end of the 45-day exper-imental period, fructose-fed rats showed significantly higher levels of plasma glucose and insulin, dyslipidemia, and alter-ations in enzyme activities. Treatment with SM significantly reduced plasma glucose and insulin levels and brought about afavorable lipid profile. In these rats, the activities of enzymes of glucose metabolism were normal. These effects were ob-served at all three doses of SM. High homeostasis model assessment (HOMA) values indicated insulin resistance in fructose-fed rats, while the HOMA values in SM-treated fructose-fed rats were comparable to those of control rats. We conclude thatadministration of SM improves glucose metabolism and plasma lipid profile in fructose-fed rats, possibly through improvedinsulin-sensitizing actions of the active constituents.

CONSTRUCTION OF SUBCLASSES OF UNIVALENT HARMONIC MAPPINGS

Nagpal, Sumit,Ravichandran, V. Korean Mathematical Society 2014 대한수학회지 Vol.51 No.3

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notions of harmonic Alexander operator and harmonic Libera operator are introduced and their properties are investigated.

CONSTRUCTION OF SUBCLASSES OF UNIVALENT HARMONIC MAPPINGS

Sumit Nagpal,V. Ravichandran 대한수학회 2014 대한수학회지 Vol.51 No.3

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new method- ology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notions of harmonic Alexander operator and harmonic Libera operator are intro- duced and their properties are investigated.

SUFFICIENT CONDITIONS FOR ANALYTIC FUNCTIONS TO BE STARLIKE OF RECIPROCAL ORDER

( Shalu Yadav ),( V. Ravichandran ) 호남수학회 2024 호남수학학술지 Vol.46 No.1

A normalized analytic function f, defined on the unit disk D, is starlike of reciprocal order α > 1 if the real part of f(z)/(zf′(z)) is less than α for all z ∈ D. By utilizing the theory of differential subordination, we establish several sufficient conditions for analytic functions defined on D to be starlike of reciprocal order. Additionally, we investigate the conditions under which the function f(z)/(zf′(z)) is subordinate to the function 1 + (α - 1)z. This subordination, in turn, is sufficient for the function f to be starlike of reciprocal order α > 1.

Mixed Layer Variability in Northern Arabian Sea as Detected by an Argo Float

Bhaskar, T.V.S. Udaya,Swain, D.,Ravichandran, M. The Korean Society of Oceanography 2007 Ocean science journal Vol.42 No.4

Northern Arabian Sea (NAS) between $17^{\circ}N-20.5^{\circ}N$ and $59^{\circ}E-69^{\circ}E$ was observed by using Argo float daily data fur about 9 months, from April 2002 through December 2002. Results showed that during April - May mixed layer shoaled due to light winds, clear sky and intense solar insolation. Sea surface temperature (SST) rose by $2.3^{\circ}C$ and ocean gained an average of 99.8 $Wm^{-2}$. Mixed layer reached maximum depth of about 71 m during June - September owing to strong winds and cloudy skies. Ocean gained abnormally low $\sim18Wm^{-2}$ and SST dropped by $3.4^{\circ}C$. During the inter monsoon period, October, mixed layer shoaled and maintained a depth of 20 to 30 m. November - December was accompanied by moderate winds, dropping of SST by $1.5^{\circ}C$ and ocean lost an average of 52.5 $Wm^{-2}$. Mixed layer deepened gradually reaching a maximum of 62 m in December. Analysis of surface fluxes and winds suggested that winds and fluxes are the dominating factors causing deepening of mixed layer during summer and winter monsoon periods respectively. Relatively big]h correlation between MLD, net heat flux and wind speed revealed that short term variability of MLD coincided well with short term variability of surface forcing.

JANOWSKI STARLIKENESS AND CONVEXITY

KANIKA KHATTER,V. Ravichandran,S. SIVAPRASAD KUMAR 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.4

Certain necessary and sufficient conditions are determined for the functions f(z) = z - P1 n=2 anzn, an ≥ 0, defined on the open unit disk, to belong to various subclasses of starlike and convex func- tions. Also discussed are certain sufficient conditions for the normalised analytic functions f of the form (z=f(z))μ = 1 + P1 n=1 bnzn, μ ∈ C to belong to the class of Janowski starlike functions.