scholarly journals Schwarz lemma and Kobayashi metrics for holomorphic functions

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3253-3262 ◽  
Author(s):  
Miodrag Mateljevic
Keyword(s):  
Holomorphic Functions ◽  
Schwarz Lemma ◽  
The Subject ◽  
Kobayashi Metrics

In this paper, we mainly consider Schwarz lemma for holomorphic functions and contraction properties of holomorphic functions with respect to Kobayashi distances. We also review some results related to the subject using some novelty and announce a few new results.

scholarly journals Foundations of Fatou Theory and a Tribute to the Work of E. M. Stein on Boundary Behavior of Holomorphic Functions

2021 ◽  
Author(s):  
Fausto Di Biase ◽  
Steven G. Krantz
Keyword(s):  
Harmonic Functions ◽  
Boundary Behavior ◽  
Holomorphic Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Several Variables ◽  
The Subject ◽  
Differentiation Of Integrals ◽  
Fatou Theory

AbstractWe lay the foundations of Fatou theory in one and several complex variables. We describe the main contributions contained in E. M. Stein’s book Boundary Behavior of Holomorphic Functions, published in 1972 and still a source of inspiration. We also give an account of his contributions to the study of the boundary behavior of harmonic functions. The point of this paper is not simply to exposit well-known ideas. Rather, we completely reorganize the subject in order to bring out the profound contributions of E. M. Stein to the study of the boundary behavior both of holomorphic and harmonic functions in one and several variables. In an appendix, we provide a self-contained proof of a new result which is relevant to the differentiation of integrals, a topic which, as witnessed in Stein’s work, and especially by the aforementioned book, has deep connections with the boundary behavior of harmonic and holomorphic functions.

Dissipative holomorphic functions, Bloch radii, and the Schwarz Lemma

2000 ◽  
Vol 82 (1) ◽  
pp. 221-232 ◽  
Author(s):  
Lawrence A. Harris ◽  
Simeon Reich ◽  
David Shoikhet
Keyword(s):  
Holomorphic Functions ◽  
Schwarz Lemma ◽  
The Schwarz Lemma

scholarly journals Boundary Schwarz lemma for holomorphic functions

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5553-5565
Author(s):  
Nafi Örnek ◽  
Burcu Gök
Keyword(s):  
Boundary Point ◽  
Unit Disc ◽  
Holomorphic Functions ◽  
Schwarz Lemma ◽  
Angular Derivative ◽  
Taylor Coefficient ◽  
Boundary Schwarz Lemma ◽  
Boundary Version

In this paper, a boundary version of Schwarz lemma is investigated. We take into consideration a function f (z) holomorphic in the unit disc and f (0) = 0 such that ?Rf? < 1 for ?z? < 1, we estimate a modulus of angular derivative of f (z) function at the boundary point b with f (b) = 1, by taking into account their first nonzero two Maclaurin coefficients. Also, we shall give an estimate below ?f'(b)? according to the first nonzero Taylor coefficient of about two zeros, namely z=0 and z0 ? 0. Moreover, two examples for our results are considered.

Words

PMLA ◽  
1935 ◽  
Vol 50 (4) ◽  
pp. 1320-1327
Author(s):  
Colbert Searles
Keyword(s):  
Subject Matter ◽  
Assistant Professor ◽  
The Subject

THE germ of that which follows came into being many years ago in the days of my youth as a university instructor and assistant professor. It was generated by the then quite outspoken attitude of colleagues in the “exact sciences”; the sciences of which the subject-matter can be exactly weighed and measured and the force of its movements mathematically demonstrated. They assured us that the study of languages and literature had little or nothing scientific about it because: “It had no domain of concrete fact in which to work.” Ergo, the scientific spirit was theirs by a stroke of “efficacious grace” as it were. Ours was at best only a kind of “sufficient grace,” pleasant and even necessary to have, but which could, by no means ensure a reception among the elected.

Artificial satellite orbit computations

1966 ◽  
Vol 25 ◽  
pp. 363-371
Author(s):  
P. Sconzo
Keyword(s):  
Artificial Satellite ◽  
Satellite Orbit ◽  
Artificial Satellites ◽  
Orbital Elements ◽  
Differential Correction ◽  
Gravitational Effects ◽  
Short Intervals ◽  
The Subject ◽  
Introductory Discussion ◽  
Orbit Computation

In this paper an orbit computation program for artificial satellites is presented. This program is operational and it has already been used to compute the orbits of several satellites.After an introductory discussion on the subject of artificial satellite orbit computations, the features of this program are thoroughly explained. In order to achieve the representation of the orbital elements over short intervals of time a drag-free perturbation theory coupled with a differential correction procedure is used, while the long range behavior is obtained empirically. The empirical treatment of the non-gravitational effects upon the satellite motion seems to be very satisfactory. Numerical analysis procedures supporting this treatment and experience gained in using our program are also objects of discussion.

C. Wire Cabling for Telescope Systems

1966 ◽  
Vol 27 ◽  
pp. 159-161
Keyword(s):  
The Subject ◽  
Data Multiplexing

Rule: I'd like at this point to bring up the subject of cables and wireways around the telescope. We've touched upon this twice during previous sessions: the cable wrap up problem, the communications problem, and data multiplexing problem. I think we'll ask Bill Baustian if he will give us a brief run down on what the electrical run problems are, besides doubling the system every year.

The relationship of the scleractinian corals to the rugose corals

Paleobiology ◽  
1980 ◽  
Vol 6 (02) ◽  
pp. 146-160 ◽  
Author(s):  
William A. Oliver
Keyword(s):  
Critical Points ◽  
Scleractinian Corals ◽  
Convincing Evidence ◽  
Early Triassic ◽  
Rugose Corals ◽  
History Of ◽  
The Subject ◽  
Relationship Of ◽  
The Relationship ◽  
Biologic Factors

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.

Direct Observations of the Epitaxial Growth of Sputtered Ag on Si

1973 ◽  
Vol 31 ◽  
pp. 122-123
Author(s):  
J. S. Maa ◽  
Thos. E. Hutchinson
Keyword(s):  
Epitaxial Growth ◽  
Film Growth ◽  
Ion Beam ◽  
Ion Beam Sputtering ◽  
Microscopy Technique ◽  
Direct Observations ◽  
In Situ Electron Microscopy ◽  
Beam Sputtering ◽  
The Subject

The growth of Ag films deposited on various substrate materials such as MoS2, mica, graphite, and MgO has been investigated extensively using the in situ electron microscopy technique. The three stages of film growth, namely, the nucleation, growth of islands followed by liquid-like coalescence have been observed in both the vacuum vapor deposited and ion beam sputtered thin films. The mechanisms of nucleation and growth of silver films formed by ion beam sputtering on the (111) plane of silicon comprise the subject of this paper. A novel mode of epitaxial growth is observed to that seen previously.The experimental arrangement for the present study is the same as previous experiments, and the preparation procedure for obtaining thin silicon substrate is presented in a separate paper.

Effects of Hyperoxia on Lung Utrastructure

1970 ◽  
Vol 28 ◽  
pp. 26-27
Author(s):  
Gladys Harrison
Keyword(s):  
Central Nervous System ◽  
Nervous System ◽  
Light Microscopy ◽  
Oxygen Effects ◽  
Age Dependent ◽  
The Central Nervous System ◽  
The Subject ◽  
Space Age ◽  
Alveolar Septa ◽  
Extensive Damage

With the advent of the space age and the need to determine the requirements for a space cabin atmosphere, oxygen effects came into increased importance, even though these effects have been the subject of continuous research for many years. In fact, Priestly initiated oxygen research when in 1775 he published his results of isolating oxygen and described the effects of breathing it on himself and two mice, the only creatures to have had the “privilege” of breathing this “pure air”.Early studies had demonstrated the central nervous system effects at pressures above one atmosphere. Light microscopy revealed extensive damage to the lungs at one atmosphere. These changes which included perivascular and peribronchial edema, focal hemorrhage, rupture of the alveolar septa, and widespread edema, resulted in death of the animal in less than one week. The severity of the symptoms differed between species and was age dependent, with young animals being more resistant.

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