Entire functions of locally slow growth

Fricke, Gerd H.

doi:10.1007/bf02786809

Cited by 26 publications

(16 citation statements)

References 4 publications

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“…As sufficient conditions of boundedness of index or l-index they improve corresponding results of G. H. Fricke (see Theorem 5 in [3] and Theorem 2 in [4]) and M. M. Sheremeta, A. D. Kuzyk (see Theorems 1 and 6 in [5]). …”

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confidence: 69%

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Some improvements of criteria of $L$-index boundedness in direction

Bandura

2016

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supporting

confidence: 69%

“…[3], [4], [5]). We remind some definitions of the theory of entire functions (more details are in [16]).…”

mentioning

confidence: 99%

Some improvements of criteria of $L$-index boundedness in direction

Bandura

2016

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“…The eggs were then suspended in 20 ml of sea water containing 10 mM Tris (pH 8.0), 0.2 mg of soybean trypsin inhibitor per ml (Sigma), and 0.2 ml of dimethyl sulfoxide containing 2 mg of ionophore A23187 per ml (Eli Lilly, final concentration 38 ,uM), a known parthenogenetic activator of sea urchin eggs (14). The eggs were stirred gently by hand for 1 (15). Radioactivity was determined by scintillation counting.…”

Section: And Methodsmentioning

confidence: 99%

Egg surface glycoprotein receptor for sea urchin sperm bindin.

Glabe¹,

Vacquier²

1978

Proc. Natl. Acad. Sci. U.S.A.

130

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Bindin is an insoluble protein coating the sperm acrosome process and mediating the adhesion of sperm to sea urchin eggs. Milligrams of bindin have been isolated. Here we report the identification, isolation, and partial characterization of a high molecular weight, trypsin-sensitive glycoprotein fraction from the sea urchin egg surface having species-specific affinity for bindin. This glycoprotein may be the egg surface receptor for bindin. The bindin receptor was released from 125I-labeled eggs by parthenogenetic activation of eggs with ionophore A23187 in the presence of soybean trypsin inhibitor. The receptor has an isoelectric point of 4.02 and a molecular weight in sea water >5 X 106, suggesting that it is an aggregate. It contains 34% neutral sugars, which are galactose and mannose.Attachment of spermatozoa to the egg surface occurs in many animal species, including mammals (1). In sea urchins, gamete adhesion is between the sperm acrosome process and the egg vitelline layer (2). An insoluble protein, named bindin, has been isolated from acrosome granules of sea urchin sperm. Peroxidase-conjugated antibody to bindin localizes bindin on the acrosome process'membrane and on the vitelline layer adjacent to the point of adhesion of the acrosome process (3). Bindin is a species-specific agglutinin of unfertilized eggs (4, 5). Trypsin-generated glycopeptides from egg surfaces block the eggagglutinating property of bindin and periodate oxidation of eggs renders them nonagglutinable by bindin. These data are evidence that bindin mediates sperm adhesion to eggs.The presence of species-specific glycoprotein "sperm receptors" on sea urchin eggs has been inferred for several years (6-12). Here we present the direct demonstration and isolation of a large, protease-sensitive egg surface glycoprotein having specific affinity for bindin. MATERIALS AND METHODSGametes and Bindin Isolation. Gametes of Strongylocentrotus purpuratus were obtained by pouring 0.5 M KCI into opened body cavities. Egg jelly coats were dissolved by 2-min exposure to pH 4.7 sea water, followed by settling and resuspension in pH 8.0 sea water. The pH 4.7 treatment was repeated and the washed eggs were stored at 4°. Bindin was isolated as described (4). After the final sea water wash the insoluble bindin pellet was resuspended in sea water by mild sonication, the protein concentration was determined (13), and 1-ml portions were stored at -700.125I Labeling of Egg Surfaces. Twenty milliliters of 50% (vol/vol) suspension of dejellied eggs in sea water containing 10 mM Tris (pH 8.0) was placed in a 50-ml conical tube. Two-tenths milliliter of 125I (carrier-free, 2.0 mCi/ml in 10 mM NaOH, Amersham) was added, followed by 0.1 ml of chloramine-T (10 mg/ml in sea water) at 15-sec intervals for 5 min. The reaction was stopped by adding 2.0 ml of sodium metabisulfite (10 mg/ml in sea water). The labeled eggs were washed a minimum of five times by settling through fresh sea water. 52I-Labeled eggs developed to the gastrula stage.Isolation of 125I-Label...

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“…Meanwhile, in corresponding theorem from [26,27] the circle ( 0 , 0 ) is chosen such that ( ) ̸ = 0 for all ∈ ( 0 , 0 ).…”

Section: Then the Function Has Bounded -Index (Here Meas Means The Lementioning

confidence: 99%

Entire Functions of Bounded L-Index: Its Zeros and Behavior of Partial Logarithmic Derivatives

Bandura

Скасків

2017

Journal of Complex Analysis

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In this paper, we obtain new sufficient conditions of boundedness of L-index in joint variables for entire function in C functions. They give an estimate of maximum modulus of an entire function by its minimum modulus on a skeleton in a polydisc and describe the behavior of all partial logarithmic derivatives and the distribution of zeros. In some sense, the obtained results are new for entire functions of bounded index and -index in C too. They generalize known results of Fricke, Sheremeta, and Kuzyk.

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Entire functions of locally slow growth

Cited by 26 publications

References 4 publications

Some improvements of criteria of $L$-index boundedness in direction

Some improvements of criteria of $L$-index boundedness in direction

Egg surface glycoprotein receptor for sea urchin sperm bindin.

Entire Functions of Bounded L-Index: Its Zeros and Behavior of Partial Logarithmic Derivatives

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