scholarly journals A Theorem of Galambos-Bojanić-Seneta Type

2009 ◽  
Vol 2009 ◽  
pp. 1-6 ◽  
Author(s):  
Dragan Djurčić ◽  
Aleksandar Torgašev
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Condition ◽  
The Given

In the theorems of Galambos-Bojanić-Seneta's type, the asymptotic behavior of the functions , for , is investigated by the asymptotic behavior of the given sequence of positive numbers , as and vice versa. The main result of this paper is one theorem of such a type for sequences of positive numbers which satisfy an asymptotic condition of the Karamata type  , for .

scholarly journals Asymptotic Behaviors of Wronskians and Finite Asymptotic Expansions in the Real Domain - Part I: Scales of Regularly- or Rapidly-Varying Functions

2017 ◽  
Vol 9 ◽  
pp. 1-33 ◽  
Author(s):  
Antonio Granata
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Expansions ◽  
Higher Order ◽  
Weight Functions ◽  
Asymptotic Behaviors ◽  
The Real ◽  
Special Cases ◽  
Real Domain ◽  
The Given ◽  
Rapidly Varying Functions

In a previous series of papers we established a general theory of finite asymptotic expansions in the real domain for functions f of one real variable sufficiently-regular on a deleted neighborhood of a point x0 ∈ R, a theory based on the use of a uniquely-determined linear differential operator L associated to the given asymptotic scale and wherein various sets of asymptotic expansions are characterized by the convergence of improper integrals involving both the operator L applied to f and certain weight functions constructed by means of Wronskians of the given scale. Very special cases apart, Wronskians have quite complicated expressions and unrecognizable asymptotic behaviors; however in the present work, split in two parts, we highlight some approaches for determining the exact asymptotic behavior of a Wronskian when the involved functions are regularly- or rapidly-varying functions of higher order. This first part contains: (i) some preliminary results on the asymptotic behavior of a determinant whose entries are asymptotically equivalent to the entries of a Vandermonde determinant; (ii) the fundamental results about the asymptotic behaviors of Wronskians involving scales of functions all of which are either regularly (or, more generally, smoothly) varying or rapidly varying of a suitable higher order. A lot of examples and applications to the theory of asymptotic expansions in the real domain are given.

Detecting and Locating a Changed Segment in a Binomial Sequence: Comparison

2005 ◽  
Vol 10 (2) ◽  
pp. 171-192 ◽  
Author(s):  
D. Zuokas
Keyword(s):  
Monte Carlo ◽  
Asymptotic Behavior ◽  
Sequence Analysis ◽  
Monte Carlo Simulations ◽  
Dna Sequence ◽  
Sequence Comparison ◽  
Deoxyribonucleic Acid ◽  
Dna Sequence Analysis ◽  
Changed Segment ◽  
The Given

A class of tests for testing a changed segment in a binomial sequence is proposed and an asymptotic behavior is established. A consistent procedure of estimating the length of a changed segment is proposed. The performance of two tests from the given class is compared by Monte-Carlo simulations. The results are applied for the non-coding deoxyribonucleic acid (DNA) sequence analysis.

scholarly journals A Construction of Meromorphic Functions with Prescribed Asymptotic Behavior

1971 ◽  
Vol 41 ◽  
pp. 75-87 ◽  
Author(s):  
J.L. Stebbins
Keyword(s):  
Asymptotic Behavior ◽  
Complex Plane ◽  
Meromorphic Functions ◽  
The Other ◽  
Asymptotic Values ◽  
Other Hand ◽  
Extended Complex ◽  
The Given ◽  
Prescribed Asymptotic Behavior ◽  
Extended Complex Plane

Although there are several constructions of meromorphic functions with prescribed asymptotic sets [e.g., 5,6], it is usually difficult to determine or prescribe the nature of the asymptotic paths used in these constructions. On the other hand, there are several other constructions of meromorphic functions with prescribed asymptotic paths [e.g., 1, 10, 12], but the extent of the asymptotic values for these functions cannot always be restricted to the values approached along the given paths. Gross [3] has accomplished both results by prescribing paths for every value in the extended complex plane.

On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle

1991 ◽  
Vol 7 (3) ◽  
pp. 269-306 ◽  
Author(s):  
P. Jeganathan
Keyword(s):  
Time Series ◽  
Asymptotic Behavior ◽  
Least Squares ◽  
Unit Circle ◽  
Asymptotic Expansions ◽  
Asymptotic Properties ◽  
Ar Model ◽  
Convergence In Distribution ◽  
Least Squares Estimators ◽  
The Given

Some asymptotic properties of the least-squares estimator of the parameters of an AR model of order p, p ≥ 1, are studied when the roots of the characteristic polynomial of the given AR model are on or near the unit circle. Specifically, the convergence in distribution is established and the corresponding limiting random variables are represented in terms of functionals of suitable Brownian motions.Further, the preceding convergence in distribution is strengthened to that of convergence uniformly over all Borel subsets. It is indicated that the method employed for this purpose has the potential of being applicable in the wider context of obtaining suitable asymptotic expansions of the distributions of leastsquares estimators.

scholarly journals On asymptotic behavior of solutions of discrete systems

2009 ◽  
Vol 43 (1) ◽  
pp. 99-108
Author(s):  
Irena Hlavičková
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equations ◽  
Discrete Systems ◽  
Asymptotic Behavior Of Solutions ◽  
Discrete Equations ◽  
Nonlinear Anal ◽  
The Given

Abstract This contribution concerns the asymptotic behavior of solutions of systems of difference equations. It reassumes paper [J. Dibl´ık: Anti-Lyapunovmethod for systems of discrete equations, Nonlinear Anal. 57 (2004), 1043-1057], where conditions are described which ensure that the graph of at least one solution of the studied system stays in a prescribed domain. Those conditions include the existence of a so called connecting function for the sets forming the given domain. The connecting function must have certain properties which enable the use of the retract method for the proof of the main result of the cited work. We show that the conditions can be made simpler, without the need to introduce the connecting function.

MASS PROBLEMS AND INITIAL SEGMENT COMPLEXITY

2014 ◽  
Vol 79 (01) ◽  
pp. 20-44 ◽  
Author(s):  
W. M. PHILLIP HUDELSON
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bound ◽  
Lower Bounds ◽  
Kolmogorov Complexity ◽  
Initial Segment ◽  
Infinite Sequence ◽  
Finite Sequence ◽  
Randomness Extraction ◽  
The Given ◽  
Infinite Sequences

Abstract By the complexity of a finite sequence of 0’s and 1’s we mean the Kolmogorov complexity, that is the length of the shortest input to a universal recursive function which returns the given sequence as output. By initial segment complexity of an infinite sequence of 0’s and 1’s we mean the asymptotic behavior of the complexity of its finite initial segments. In this paper, we construct infinite sequences of 0’s and 1’s with given recursive lower bounds on initial segment complexity which do not compute any infinite sequences of 0’s and 1’s with a significantly larger recursive lower bound on initial segment complexity. This improves several known results about randomness extraction and separates many natural degrees in the lattice of Muchnik degrees.

Personal Problem Solving of Partners in Divorce Proceedings

2015 ◽  
Vol 36 (1) ◽  
pp. 82-103 ◽  
Author(s):  
Tereza Soukupova ◽  
Petr Goldmann
Keyword(s):  
Gender Differences ◽  
Problem Solving ◽  
Thematic Apperception Test ◽  
Scoring Systems ◽  
Personal Control ◽  
Personality Characteristics ◽  
Personal Problem ◽  
Thematic Apperception ◽  
And Gender ◽  
The Given

Abstract. The Thematic Apperception Test is one of the most frequently administered apperceptive techniques. Formal scoring systems are helpful in evaluating story responses. TAT stories, made by 20 males and 20 females in the situation of legal divorce proceedings, were coded for detection and comparison of their personal problem solving ability. The evaluating instrument utilized was the Personal Problem Solving System-Revised (PPSS-R) as developed by G. F. Ronan. The results indicate that in relation to card 1, men more often than women saw the cause of the problem as removable. With card 6GF, women were more motivated to resolve the given problem than were men, women had a higher personal control and their stories contained more optimism compared to men’s stories. In relation to card 6BM women, more often than men, used emotions generated from the problem to orient themselves within the problem. With card 13MF, the men’s level of stress was less compared to that of the women, and men were more able to plan within the context of problem-solving. Significant differences in the examined groups were found in those cards which depicted significant gender and parental potentials. The TAT can be used to help identify personality characteristics and gender differences.

Pattern Recognition in Histo-Pathology: Basic Considerations

1982 ◽  
Vol 21 (01) ◽  
pp. 15-22 ◽  
Author(s):  
W. Schlegel ◽  
K. Kayser
Keyword(s):  
Pattern Recognition ◽  
Graph Theory ◽  
Normal Tissue ◽  
Diagnostic Procedures ◽  
Minimal Distance ◽  
Malignant Growth ◽  
Colon Tissue ◽  
First Results ◽  
Tissue Structures ◽  
The Given

A basic concept for the automatic diagnosis of histo-pathological specimen is presented. The algorithm is based on tissue structures of the original organ. Low power magnification was used to inspect the specimens. The form of the given tissue structures, e. g. diameter, distance, shape factor and number of neighbours, is measured. Graph theory is applied by using the center of structures as vertices and the shortest connection of neighbours as edges. The algorithm leads to two independent sets of parameters which can be used for diagnostic procedures. First results with colon tissue show significant differences between normal tissue, benign and malignant growth. Polyps form glands that are twice as wide as normal and carcinomatous tissue. Carcinomas can be separated by the minimal distance of the glands formed. First results of pattern recognition using graph theory are discussed.

Coordinating Medical Literature with Patient Care

1977 ◽  
Vol 16 (04) ◽  
pp. 234-240 ◽  
Author(s):  
Joann Gustafson ◽  
J. Nelson ◽  
Ann Buller
Keyword(s):  
Health Care ◽  
Medical Staff ◽  
Medical Information ◽  
Medical Literature ◽  
Medical Information System ◽  
Staff Members ◽  
Information Displays ◽  
Medical Displays ◽  
Computerized Medical Information ◽  
The Given

The contribution of a special library project to a computerized problem-oriented medical information system (PROMIS) is discussed. Medical information displays developed by the PROMIS medical staff are accessible to the health care provider via touch screen cathode terminals. Under PROMIS, members of the library project developed two information services, one concerned with the initial building of the medical displays and the other with the updating of this information. Information from 88 medical journals is disseminated to physicians involved in the building of the medical displays. Articles meeting predetermined selection criteria are abstracted and the abstracts are made available by direct selective dissemination or via a problem-oriented abstract file. The updating service involves comparing the information contained in the selected articles with the computerized medical displays on the given topic. Discrepancies are brought to the attention of PROMIS medical staff members who evaluate the information and make appropriate changes in the displays. Thus a feedback loop is maintained which assures the completeness, accuracy, and currency of the computerized medical information. The development of this library project and its interface with the computerized health care system thus attempts to deal with the problems in the generation, validation, dissemination, and application of medical literature.

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