Evaluation of Hessenberg determinants via generating function approach

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4945-4962 ◽  
Author(s):  
Emrah Kılıç ◽  
Talha Arıkan
Keyword(s):  
Generating Function ◽  
Arbitrary Constant ◽  
Function Method ◽  
Higher Order ◽  
Function Approach ◽  
New Method ◽  
Factor Matrix ◽  
New Approach ◽  
Constant Coefficients ◽  
The Subject

In this paper, we will present various results on computing of wide classes of Hessenberg matrices whose entries are the terms of any sequence. We present many new results on the subject as well as our results will cover and generalize earlier many results by using generating function method. Moreover, we will present a new approach on computing Hessenberg determinants, whose entries are general higher order linear recursions with arbitrary constant coefficients, based on finding an adjacency-factor matrix. We will give some interesting showcases to show how to use our new method.

The completeness of the first-order functional calculus

1949 ◽  
Vol 14 (3) ◽  
pp. 159-166 ◽  
Author(s):  
Leon Henkin
Keyword(s):  
Functional Calculus ◽  
Propositional Calculus ◽  
Higher Order ◽  
New Method ◽  
Completeness Proof ◽  
New Approach ◽  
First Order ◽  
Formal Systems ◽  
The Subject ◽  
Image Position

Although several proofs have been published showing the completeness of the propositional calculus (cf. Quine (1)), for the first-order functional calculus only the original completeness proof of Gödel (2) and a variant due to Hilbert and Bernays have appeared. Aside from novelty and the fact that it requires less formal development of the system from the axioms, the new method of proof which is the subject of this paper possesses two advantages. In the first place an important property of formal systems which is associated with completeness can now be generalized to systems containing a non-denumerable infinity of primitive symbols. While this is not of especial interest when formal systems are considered as logics—i.e., as means for analyzing the structure of languages—it leads to interesting applications in the field of abstract algebra. In the second place the proof suggests a new approach to the problem of completeness for functional calculi of higher order. Both of these matters will be taken up in future papers.The system with which we shall deal here will contain as primitive symbolsand certain sets of symbols as follows:(i) propositional symbols (some of which may be classed as variables, others as constants), and among which the symbol “f” above is to be included as a constant;(ii) for each number n = 1, 2, … a set of functional symbols of degree n (which again may be separated into variables and constants); and(iii) individual symbols among which variables must be distinguished from constants. The set of variables must be infinite.

scholarly journals The quantum geometric tensor from generating functions

2019 ◽  
Vol 17 (02) ◽  
pp. 1950017 ◽  
Author(s):  
Javier Alvarez-Jimenez ◽  
J. David Vergara
Keyword(s):  
Quantum Information ◽  
Harmonic Oscillator ◽  
Generating Function ◽  
Generating Functions ◽  
Function Method ◽  
New Method ◽  
Berry Curvature ◽  
Information Metric

We introduce a new method to compute the Quantum Geometric Tensor, this procedure allows us to compute the Quantum Information Metric and the Berry curvature perturbatively for a theory with an arbitrary interaction Hamiltonian. The calculation uses the generating function method, and it is illustrated with the harmonic oscillator with a linear and a quartic perturbation.

Positive Reintegration as a Way of Small and Medium-Sized Business Development

2012 ◽  
pp. 83-88
Author(s):  
A. Zolotov ◽  
M. Mukhanov
Keyword(s):  
Policy Implementation ◽  
Policy Making ◽  
Economic Reforms ◽  
Alternative Possibility ◽  
New Approach ◽  
Compensation Mechanisms ◽  
Policy Making Process ◽  
Monitoring And Enforcement ◽  
The Subject ◽  
Modernization Process

А new approach to policy-making in the field of economic reforms in modernizing countries (on the sample of SME promotion) is the subject of this article. Based on summarizing the ten-year experience of de-bureaucratization policy implementation to reduce the administrative pressure on SME, the conclusion of its insufficient efficiency and sustainability is made. The alternative possibility is the positive reintegration approach, which provides multiparty policy-making process, special compensation mechanisms for the losing sides, monitoring and enforcement operations. In conclusion matching between positive reintegration principles and socio-cultural factors inherent in modernization process is provided.

Social organization in the Orcadian Neolithic: identification of elite domestic structures and settlements through analysis of excavation data

2018 ◽  
Vol 40 (1) ◽  
pp. 25-53 ◽  
Author(s):  
David MacInnes
Keyword(s):  
Social Organization ◽  
Qualitative Data ◽  
Social Hierarchy ◽  
Published Data ◽  
Early Neolithic ◽  
Late Neolithic ◽  
New Approach ◽  
Qualitative Evidence ◽  
Methods Of Analysis ◽  
The Subject

The nature of social organization during the Orcadian Neolithic has been the subject of discussion for several decades with much of the debate focused on answering an insightful question posed by Colin Renfrew in 1979. He asked, how was society organised to construct the larger, innovative monuments of the Orcadian Late Neolithic that were centralised in the western Mainland? There are many possible answers to the question but little evidence pointing to a probable solution, so the discussion has continued for many years. This paper takes a new approach by asking a different question: what can be learned about Orcadian Neolithic social organization from the quantitative and qualitative evidence accumulating from excavated domestic structures and settlements?In an attempt to answer this question, quantitative and qualitative data about domestic structures and about settlements was collected from published reports on 15 Orcadian Neolithic excavated sites. The published data is less extensive than hoped but is sufficient to support a provisional answer: a social hierarchy probably did not develop in the Early Neolithic but almost certainly did in the Late Neolithic, for which the data is more comprehensive.While this is only one approach of several possible ways to consider the question, it is by exploring different methods of analysis and comparing them that an understanding of the Orcadian Neolithic can move forward.

A New Approach for the Analysis of Mixture Toxicity Data

1992 ◽  
Vol 26 (9-11) ◽  
pp. 2345-2348 ◽  
Author(s):  
C. N. Haas
Keyword(s):  
Quantitative Analysis ◽  
Mixture Toxicity ◽  
New Method ◽  
Metal Exposure ◽  
Positive Interactions ◽  
Toxicity Data ◽  
Data Set ◽  
New Approach ◽  
Negative Interactions

A new method for the quantitative analysis of multiple toxicity data is described and illustrated using a data set on metal exposure to copepods. Positive interactions are observed for Ni-Pb and Pb-Cr, with weak negative interactions observed for Ni-Cr.

scholarly journals Innovative Method for Calculating the Break-Even for Multi-Assortment Production

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4213
Author(s):  
Dariusz Fuksa
Keyword(s):  
Coal Mines ◽  
New Method ◽  
Hard Coal ◽  
Customer Demand ◽  
Innovative Method ◽  
The Subject ◽  
Economic Health ◽  
Production Plans ◽  
A Company ◽  
A Current

The subject of the article is a new method that I have developed for calculating a multi-asset break-even for multi-assortment production, extended by a percentage threshold and a current sales ratio (which was missing in previously published methods). The percentage threshold provides unambiguous information about the economic health of a company. As a result, it became possible to use it in practice to evaluate the activities of economic entities (mines) and to perform modelling and optimisation of production plans based on different variants of customer demand scenarios. The publication addresses the complexity of the problem of determining the break-even in multi-assortment production. Moreover, it discusses the practical limitations of previous methods and demonstrates the usefulness of the proposed method on the example of hard coal mines.

scholarly journals New Method for Generating New Families of Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 726
Author(s):  
Lamya A. Baharith ◽  
Wedad H. Aljuhani
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Rate Function ◽  
New Method ◽  
Likelihood Method ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Failure Rate Function ◽  
New Approach ◽  
Numerical Studies

This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis.

scholarly journals A New Class of Higher-Order Hypergeometric Bernoulli Polynomials Associated with Lagrange–Hermite Polynomials

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 648
Author(s):  
Ghulam Muhiuddin ◽  
Waseem Ahmad Khan ◽  
Ugur Duran ◽  
Deena Al-Kadi
Keyword(s):  
Generating Function ◽  
Functional Equations ◽  
Laguerre Polynomials ◽  
Hermite Polynomials ◽  
Bernoulli Polynomials ◽  
Higher Order ◽  
New Class

The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using the generating function and their functional equations, we investigate some properties of these polynomials. Moreover, we derive several connected formulas and relations including the Miller–Lee polynomials, the Laguerre polynomials, and the Lagrange Hermite–Miller–Lee polynomials.

scholarly journals New type of degenerate Daehee polynomials of the second kind

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sunil Kumar Sharma ◽  
Waseem A. Khan ◽  
Serkan Araci ◽  
Sameh S. Ahmed
Keyword(s):  
Generating Function ◽  
Special Class ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Higher Order ◽  
Bernoulli Numbers And Polynomials ◽  
New Type ◽  
Order Degenerate ◽  
Math Phys

Abstract Recently, Kim and Kim (Russ. J. Math. Phys. 27(2):227–235, 2020) have studied new type degenerate Bernoulli numbers and polynomials by making use of degenerate logarithm. Motivated by (Kim and Kim in Russ. J. Math. Phys. 27(2):227–235, 2020), we consider a special class of polynomials, which we call a new type of degenerate Daehee numbers and polynomials of the second kind. By using their generating function, we derive some new relations including the degenerate Stirling numbers of the first and second kinds. Moreover, we introduce a new type of higher-order degenerate Daehee polynomials of the second kind. We also derive some new identities and properties of this type of polynomials.

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