Gap series and normal functions

1979 ◽  
Vol 166 (1) ◽  
pp. 93-101
Author(s):  
Linda R. Sons
Keyword(s):  
Gap Series ◽  
Normal Functions

scholarly journals Hadamard Gap Series and Normal Functions

1980 ◽  
Vol 12 (2) ◽  
pp. 115-118 ◽  
Author(s):  
L. R. Sons ◽  
D. M. Campbell
Keyword(s):  
Gap Series ◽  
Normal Functions

Functions in All Hp Spaces, p < ∞

1982 ◽  
Vol 25 (1) ◽  
pp. 110-113 ◽  
Author(s):  
Douglas M. Campbell
Keyword(s):  
Bloch Functions ◽  
Gap Series ◽  
Normal Functions ◽  
Geometric Conditions ◽  
Hp Spaces ◽  
Class Of Functions

AbstractLet Ĥ denote the class of functions analytic in |z| < 1 which are in every Hp class, 0 < p < ∞. The class Ĥ strictly contains H∞ and consists of those functions that are ‘almost in H∞’ in the sense of integration. L. Hansen and W. Hayman have given simple geometric conditions for a function to belong to Ĥ. The purpose of this note is to show that Hansen and Hayman's conditions are far from necessary. Using techniques from normal functions, gap series, characterizations of BMOA, subordination, Bloch functions, and VMOA, six completely different examples of functions in Ĥ are given which ‘fill the plane’.

FR-IR Molecular Microanalysis System

1990 ◽  
Vol 48 (2) ◽  
pp. 270-271
Author(s):  
John A. Reffner ◽  
William T. Wihlborg
Keyword(s):  
Fourier Transform ◽  
Fourier Transform Infrared ◽  
Integrated System ◽  
Morphological Examination ◽  
Fully Integrated ◽  
Ir Microscopy ◽  
Normal Functions ◽  
Infrared Microspectroscopy ◽  
Infrared Spectral ◽  
Ft Ir

The IRμs™ is the first fully integrated system for Fourier transform infrared (FT-IR) microscopy. FT-IR microscopy combines light microscopy for morphological examination with infrared spectroscopy for chemical identification of microscopic samples or domains. Because the IRμs system is a new tool for molecular microanalysis, its optical, mechanical and system design are described to illustrate the state of development of molecular microanalysis. Applications of infrared microspectroscopy are reviewed by Messerschmidt and Harthcock.Infrared spectral analysis of microscopic samples is not a new idea, it dates back to 1949, with the first commercial instrument being offered by Perkin-Elmer Co. Inc. in 1953. These early efforts showed promise but failed the test of practically. It was not until the advances in computer science were applied did infrared microspectroscopy emerge as a useful technique. Microscopes designed as accessories for Fourier transform infrared spectrometers have been commercially available since 1983. These accessory microscopes provide the best means for analytical spectroscopists to analyze microscopic samples, while not interfering with the FT-IR spectrometer’s normal functions.

Evaluation of positive and negative symptoms in schizophrenia

1986 ◽  
Vol 1 (2) ◽  
pp. 108-122 ◽  
Author(s):  
Nancy C. Andreasen ◽  
William M. Grove
Keyword(s):  
Negative Symptoms ◽  
The United States ◽  
Psychotic Symptoms ◽  
Positive Symptoms ◽  
University Of Iowa ◽  
Normal Functions ◽  
Subsequent Investigation ◽  
The University ◽  
The Relationship ◽  
Positive And Negative Symptoms

SummaryMost investigators concur that schizophrenia is probably a heterogeneous group of disorders that share the common features of psychotic symptoms, partial response to neuroleptics, and a relatively poor outcome. The subdivision of schizophrenia into two subtypes, positive versus negative, has achieved wide acceptance throughout the world during recent years. This distinction has heuristic and theoretical appeal because it unites phenomenology, pathophysiology, and etiology into a single comprehensive hypothesis.In spite of its wide appeal, the distinction has a number of problems. These include the failure to distinguish between symptom syndromes and diseases; failure to deal with the mixed patient; failure to take longitudinal course into account; and failure to address conceptually and methodologically the distinction between positive and negative symptoms.This paper focuses primarily on the conceptual basis for two instruments designed to measure positive and negative symptoms, the Scale for the Assessment of Negative Symptoms (SANS) and the Scale for the Assessment of Positive Symptoms (SAPS), originally described in 1982. Since their description, these scales have been used in a variety of other centers. These scales are based on the hypothesis that negative symptoms represent a deficit or diminution in normal psychological functions wliile positive symptoms represent an excess or distortion of normal functions. Reliability data are now available from Italy, Spain, and Japan which suggest that these scales can be used reliably in cultural settings outside the United States. The results of these studies are summarized in this paper. In addition, a replication study involving a new sample of 117 schizophrenics collected at the University of Iowa is described. In this second study of the SANS and SAPS, internal consistency is found to be quite high in the SANS. Thus negative symptoms appear to be more internally correlated with one another than are positive symptoms. The implications of this result are discussed. A principal components analysis is used to explore the relationship between positive and negative symptoms. While the study reported in 1982 suggested that positive and negative symptoms are negatively correlated, in the present study they appear to be uncorrelated. Overall, the results suggest that the SANS and SAPS are useful comprehensive instruments for the evaluation of positive and negative symptoms. The relationship between these symptoms and external validators such as cognitive functioning or CT scan abnormalities will be reported in a subsequent investigation.

scholarly journals Hadamard gap series in weighted-type spaces on the unit ball

2017 ◽  
Vol 8 (2) ◽  
pp. 259-269 ◽  
Author(s):  
Bingyang Hu ◽  
Songxiao Li
Keyword(s):  
Unit Ball ◽  
Gap Series ◽  
Type Spaces ◽  
Weighted Type

Normal Functions and Their Applications

2017 ◽  
pp. 255-271
Author(s):  
James Carlson ◽  
Stefan Muller-Stach ◽  
Chris Peters
Keyword(s):  
Normal Functions

The Range of a Gap Series

1975 ◽  
Vol 18 (5) ◽  
pp. 753-754
Author(s):  
J. S. Hwang
Keyword(s):  
Natural Number ◽  
Gap Series ◽  
Image Position

Theorem. Letbe a function holomorphic in the disk, wherep is a natural number andIfthen then f(z) assumes every complex value infinitely often in every sector.The purpose of this note is to prove the above result. To do this, we first observe that from the condition a<∞, we can easily show that the derivative f′(z) satisfying

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