COMPLEX ARITHMETIC FUNCTIONS

2021 ◽

pp. 55-71

Author(s):

Yuriy Zack

Keyword(s):

Expert Systems ◽

Correct Diagnosis ◽

Signs And Symptoms ◽

Medical Diagnostics ◽

Arithmetic Functions ◽

Characteristic Functions ◽

Complex Arithmetic ◽

Methodological Aspects ◽

First Time ◽

Fuzzy Logical

The main problems in making a correct diagnosis are: subjectivity and insufficient qualifications of the doctor, difficulties in correctly assessing the patient’s complaints, signs and symptoms of the disease observed in the patient, as well as individual manifestations of the symptoms of the disease. In publications on the use of expert systems for medical diagnostics using fuzzy logic, the main attention was paid to the medical features of the problem. In this work, for the first time, general methodological aspects of building such systems, creating databases, representing by fuzzy sets of real numbers, digital scales, linguistic and Boolean data of symptom values are formulated. The types of membership functions that are advisable to use to represent the symptoms of diseases are proposed. In fuzzy-logical conclusions, not only the values of the characteristic functions of the logical terms of individual symptoms, but also complex arithmetic functions of their values are used.

Download Full-text

Analysis of observability of model parameters for physical absorption of poorly soluble gases in packed beds

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19822639 ◽

1982 ◽

Vol 47 (10) ◽

pp. 2639-2653 ◽

Cited By ~ 2

Author(s):

Pavel Moravec ◽

Vladimír Staněk

Keyword(s):

Transfer Functions ◽

Plug Flow ◽

Packed Bed ◽

Model Parameters ◽

Packed Bed Column ◽

Interfacial Transport ◽

Complex Arithmetic ◽

Physical Absorption ◽

Poorly Soluble ◽

Phase Lags

Expressions have been derived for four possible transfer functions of a model of physical absorption of a poorly soluble gas in a packed bed column. The model has been based on axially dispersed flow of gas, plug flow of liquid through stagnant and dynamic regions and interfacial transport of the absorbed component. The obtained transfer functions have been transformed into the frequency domain and their amplitude ratios and phase lags have been evaluated using the complex arithmetic feature of the EC-1033 computer. Two of the derived transfer functions have been found directly applicable for processing of experimental data. Of the remaining two one is useable with the limitations to absorption on a shallow layer of packing, the other is entirely worthless for the case of poorly soluble gases.

Download Full-text

The Multi-Dimensional Local Theorem for Additive Arithmetic Functions

Analytic and Probabilistic Methods in Number Theory ◽

10.1515/9783112314234-029 ◽

1992 ◽

pp. 285-292

Keyword(s):

Arithmetic Functions ◽

Additive Arithmetic ◽

Local Theorem

Download Full-text

On the growth and zeros of polynomials attached to arithmetic functions

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg ◽

10.1007/s12188-021-00241-3 ◽

2021 ◽

Author(s):

Bernhard Heim ◽

Markus Neuhauser

Keyword(s):

Lie Algebras ◽

Chebyshev Polynomials ◽

Fourier Coefficients ◽

Arithmetic Functions ◽

Zeros Of Polynomials ◽

Simple Complex ◽

Hook Length ◽

Moderate Growth ◽

Growth Properties ◽

Sum Of Divisors

AbstractIn this paper we investigate growth properties and the zero distribution of polynomials attached to arithmetic functions g and h, where g is normalized, of moderate growth, and $$0<h(n) \le h(n+1)$$ 0 < h ( n ) ≤ h ( n + 1 ) . We put $$P_0^{g,h}(x)=1$$ P 0 g , h ( x ) = 1 and $$\begin{aligned} P_n^{g,h}(x) := \frac{x}{h(n)} \sum _{k=1}^{n} g(k) \, P_{n-k}^{g,h}(x). \end{aligned}$$ P n g , h ( x ) : = x h ( n ) ∑ k = 1 n g ( k ) P n - k g , h ( x ) . As an application we obtain the best known result on the domain of the non-vanishing of the Fourier coefficients of powers of the Dedekind $$\eta $$ η -function. Here, g is the sum of divisors and h the identity function. Kostant’s result on the representation of simple complex Lie algebras and Han’s results on the Nekrasov–Okounkov hook length formula are extended. The polynomials are related to reciprocals of Eisenstein series, Klein’s j-invariant, and Chebyshev polynomials of the second kind.

Download Full-text