scholarly journals Exponents of Diophantine Approximation in Dimension Two

2009 ◽  
Vol 61 (1) ◽  
pp. 165-189 ◽  
Author(s):  
Michel Laurent
Keyword(s):  
Diophantine Approximation ◽  
Necessary Conditions ◽  
Rational Points ◽  
Transference Principle ◽  
Linearly Independent ◽  
Quality Of Approximation

Abstract. Let Θ = (α, β) be a point in R2, with 1, α, β linearly independent over Q. We attach to Θ a quadruple Ω (Θ) of exponents that measure the quality of approximation to Θ both by rational points and by rational lines. The two “uniform” components of Ω (Θ) are related by an equation due to Jarník, and the four exponents satisfy two inequalities that refine Khintchine's transference principle. Conversely, we show that for any quadruple Ω fulfilling these necessary conditions, there exists a point Θ ∈ R2 for which Ω (Θ) = Ω.

scholarly journals KHINTCHINE'S THEOREM AND TRANSFERENCE PRINCIPLE FOR STAR BODIES

2006 ◽  
Vol 02 (03) ◽  
pp. 431-453
Author(s):  
M. M. DODSON ◽  
S. KRISTENSEN
Keyword(s):  
Distance Function ◽  
Diophantine Approximation ◽  
Direct Proof ◽  
Distance Functions ◽  
Transference Principle ◽  
Simultaneous Diophantine Approximation ◽  
Star Bodies

Analogues of Khintchine's Theorem in simultaneous Diophantine approximation in the plane are proved with the classical height replaced by fairly general planar distance functions or equivalently star bodies. Khintchine's transference principle is discussed for distance functions and a direct proof for the multiplicative version is given. A transference principle is also established for a different distance function.

scholarly journals EU Postal Directives and Croatian Regulatory Frame

2012 ◽  
Vol 22 (4) ◽  
pp. 309-317
Author(s):  
Pero Tabak ◽  
Slobodan Kaštela
Keyword(s):  
Necessary Conditions ◽  
Market Competition ◽  
Accounting System ◽  
Comparison Analysis ◽  
Technical Standards ◽  
Provision Of Services ◽  
Postal Services ◽  
Reserved Area ◽  
The Eu

The paper compares the EU Postal Directives (97/67/EZ and 2002/39/EZ) in a consolidated text and the respective parts of the Croatian legislative frame with the aim of harmonising the national postal system with EU. Both regulatory frames are presented, as well as objectives and scopes, types of postal services (particularly the universal ones), reserved area, necessary conditions governing the provision of services, tariff principles, insurance of market competition through transparency of financing and separation of the accounting system, desired quality of universal services, harmonisation of technical standards and obligations of national regulatory authorities. By presenting individual chapters of the Post Directives, some specific solutions of the Croatian regulatory framework have been indicated and uncertainties which result from the comparison analysis of the European Postal Directives and the Croatian legislation as well as the influence of these documents on the postal traffic technology. KEY WORDS: EU Postal Directives, Croatian postal regulatory frame, universal services

CONTINUOUS TIME RANDOM WALK AND TIME FRACTIONAL DIFFUSION: A NUMERICAL COMPARISON BETWEEN THE FUNDAMENTAL SOLUTIONS

2005 ◽  
Vol 05 (02) ◽  
pp. L291-L297 ◽  
Author(s):  
FRANCESCO MAINARDI ◽  
ALESSANDRO VIVOLI ◽  
RUDOLF GORENFLO
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Fundamental Solutions ◽  
Fractional Diffusion ◽  
Continuous Time Random Walk ◽  
Diffusion Limit ◽  
Numerical Comparison ◽  
Time Fractional Diffusion Equation ◽  
Quality Of Approximation

We consider the basic models for anomalous transport provided by the integral equation for continuous time random walk (CTRW) and by the time fractional diffusion equation to which the previous equation is known to reduce in the diffusion limit. We compare the corresponding fundamental solutions of these equations, in order to investigate numerically the increasing quality of approximation with advancing time.

A Conceptual Model of Wellness Destination Characteristics That Contribute to Psychological Well-Being

2017 ◽  
Vol 43 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Karen Irene Thal ◽  
Simon Hudson
Keyword(s):  
Conceptual Model ◽  
Necessary Conditions ◽  
Well Being ◽  
Self Determination Theory ◽  
Voluntary Participation ◽  
Subjective Well Being ◽  
Psychological Well Being ◽  
Daily Schedule ◽  
Mindfulness Practices

This study considered the characteristics of a stay at a wellness destination that enhance psychological well-being. Self-determination theory (SDT) was used to identify the necessary conditions to promote subjective well-being, and focus group sessions were then conducted to evaluate the SDT constructs in the context of a wellness facility. A conceptual model articulating characteristics of the external environment or wellness facility as well as ideal guest experiences, to ensure enhanced well-being as the outcome of a stay at a wellness facility, was then proposed. These conditions included the quality of staff–guest interactions, voluntary participation in novel and engaging activities in the context of a structured daily schedule, encouraging mindfulness practices, guest camaraderie, and enhanced competence or confidence overall.

scholarly journals A mass transference principle for systems of linear forms and its applications

2018 ◽  
Vol 154 (5) ◽  
pp. 1014-1047 ◽  
Author(s):  
Demi Allen ◽  
Victor Beresnevich
Keyword(s):  
Lebesgue Measure ◽  
Diophantine Approximation ◽  
Hausdorff Measure ◽  
Linear Forms ◽  
Transference Principle ◽  
Integer Points ◽  
Additional Constraints

In this paper we establish a general form of the mass transference principle for systems of linear forms conjectured in 2009. We also present a number of applications of this result to problems in Diophantine approximation. These include a general transference of Lebesgue measure Khintchine–Groshev type theorems to Hausdorff measure statements. The statements we obtain are applicable in both the homogeneous and inhomogeneous settings as well as allowing transference under any additional constraints on approximating integer points. In particular, we establish Hausdorff measure counterparts of some Khintchine–Groshev type theorems with primitivity constraints recently proved by Dani, Laurent and Nogueira.

scholarly journals DIOPHANTINE APPROXIMATION BY PRIMES

2009 ◽  
Vol 52 (1) ◽  
pp. 87-106 ◽  
Author(s):  
KAISA MATOMÄKI
Keyword(s):  
Diophantine Approximation ◽  
Necessary Conditions ◽  
Circle Method ◽  
Sieve Method

AbstractWe show that whenever δ > 0 and constants λi satisfy some necessary conditions, there are infinitely many prime triples p1, p2, p3 satisfying the inequality |λ0 + λ1p1 + λ2p2 + λ3p3| < (max pj)−2/9+δ. The proof uses Davenport–Heilbronn adaption of the circle method together with a vector sieve method.

scholarly journals “SPOCU”: scaled polynomial constant unit activation function

2020 ◽  
Author(s):  
Jozef Kiseľák ◽  
Ying Lu ◽  
Ján Švihra ◽  
Peter Szépe ◽  
Milan Stehlík
Keyword(s):  
Activation Function ◽  
Tissue Growth ◽  
Breast Cancer Dataset ◽  
Large Dataset ◽  
Cancer Dataset ◽  
Nonlinear Networks ◽  
Quality Of Approximation ◽  
Constant Unit ◽  
Polynomial Constant

AbstractWe address the following problem: given a set of complex images or a large database, the numerical and computational complexity and quality of approximation for neural network may drastically differ from one activation function to another. A general novel methodology, scaled polynomial constant unit activation function “SPOCU,” is introduced and shown to work satisfactorily on a variety of problems. Moreover, we show that SPOCU can overcome already introduced activation functions with good properties, e.g., SELU and ReLU, on generic problems. In order to explain the good properties of SPOCU, we provide several theoretical and practical motivations, including tissue growth model and memristive cellular nonlinear networks. We also provide estimation strategy for SPOCU parameters and its relation to generation of random type of Sierpinski carpet, related to the [pppq] model. One of the attractive properties of SPOCU is its genuine normalization of the output of layers. We illustrate SPOCU methodology on cancer discrimination, including mammary and prostate cancer and data from Wisconsin Diagnostic Breast Cancer dataset. Moreover, we compared SPOCU with SELU and ReLU on large dataset MNIST, which justifies usefulness of SPOCU by its very good performance.

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