Compound Invariants and Mixed F-, DF-Power Spaces

1998 ◽  
Vol 50 (6) ◽  
pp. 1138-1162 ◽  
Author(s):  
P. A. Chalov ◽  
T. Terzioğlu ◽  
V. P. Zahariuta
Keyword(s):  
Power Series ◽  
Tensor Products ◽  
Main Tool ◽  
Proper Definition ◽  
Definition Of ◽  
Image Position ◽  
Isomorphic Classification

AbstractThe problems on isomorphic classification and quasiequivalence of bases are studied for the class of mixed F-, DF-power series spaces, i.e. the spaces of the following kind where ai (p, q) = exp((p - λiq)ai), p,q ∈ ℕ, and λ = (λi)i∈ℕ, a = (ai)i∈ℕ are some sequences of positive numbers. These spaces, up to isomorphisms, are basis subspaces of tensor products of power series spaces of F- and DF-types, respectively. The mrectangle characteristic of the space G(λ a) is defined as the number of members of the sequence (ïiÒ ai)i2N which are contained in the union of m rectangles Pk = (δk, εk] ✗ (τk, tk], k = 1, 2 , . . . , m. It is shown that each m-rectangle characteristic is an invariant on the considered class under some proper definition of an equivalency relation. The main tool are new compound invariants, which combine some version of the classical approximative dimensions (Kolmogorov, Pełczynski) with appropriate geometrical and interpolational operations under neighborhoods of the origin (taken from a given basis).

The Structure of the Algebra of Hankel Transforms and the Algebra of Hankel-Stieltjes Transforms

1971 ◽  
Vol 23 (2) ◽  
pp. 236-246 ◽  
Author(s):  
Alan Schwartz
Keyword(s):  
Banach Space ◽  
Entire Function ◽  
Power Series ◽  
Real Number ◽  
Stieltjes Transform ◽  
Borel Measures ◽  
Definition Of ◽  
Image Position ◽  
Complex Valued ◽  
Stieltjes Transforms

Let M be the space of all bounded regular complex-valued Borel measures defined on I = [0, ∞). M is a Banach space with ‖μ‖ = ∫d|μ|(x) (μ ∈ M). (Integrals in this paper extend over all of I unless otherwise specified.) Let v be a fixed real number no smaller than and let if z ≠ 0 and , where Jv, is the Bessel function of the first kind of order v and cv =[2vΓ(v + 1)]–1; is an entire function, as can be seen from the power series definition ofThe Hankel-Stieltjes transform of order v is given by .

Simultaneous heat and mass transfer during evaporation from a film of liquid into the turbulent gas

1982 ◽  
Vol 47 (3) ◽  
pp. 766-775 ◽  
Author(s):  
Václav Kolář ◽  
Jan Červenka
Keyword(s):  
Experimental Data ◽  
Mass Transfer ◽  
Liquid Film ◽  
Heat And Mass Transfer ◽  
Driving Forces ◽  
Proper Definition ◽  
Definition Of ◽  
Simultaneous Heat ◽  
Theory And Experiment

The paper presents results obtained by processing a series of published experimental data on heat and mass transfer during evaporation of pure liquids from the free board of a liquid film into the turbulent gas phone. The data has been processed on the basis of the earlier theory of mechanism of heat and mass transfer. In spite of the fact that this process exhibits a strong Stefan's flow, the results indicate that with a proper definition of the driving forces the agreement between theory and experiment is very good.

WoCoVA consensus on the clinical use of in-line filtration during intravenous infusions: Current evidence and recommendations for future research

2021 ◽  
pp. 112972982198916
Author(s):  
Ton Van Boxtel ◽  
Mauro Pittiruti ◽  
Annemarie Arkema ◽  
Patrick Ball ◽  
Giovanni Barone ◽  
...  
Keyword(s):  
Potential Benefit ◽  
Scientific Evidence ◽  
Venous Access ◽  
Current Evidence ◽  
Future Research ◽  
Global Awareness ◽  
Current State ◽  
Intravenous Infusions ◽  
Proper Definition ◽  
Definition Of

The need for filtering intravenous infusions has long been recognized in the field of venous access, though hard scientific evidence about the actual indications for in-line filters has been scarce. In the last few years, several papers and a few clinical studies have raised again this issue, suggesting that the time has come for a proper definition of the type of filtration, of its potential benefit, and of its proper indications in clinical practice. The WoCoVA Foundation, whose goal is to increase the global awareness on the risk of intravenous access and on patients’ safety, developed the project of a consensus on intravenous filtration. A panel of experts in different aspects of intravenous infusion was chosen to express the current state of knowledge about filtration and to indicate the direction of future research in this field. The present document reports the final conclusions of the panel.

Pascal's Prism

2012 ◽  
Vol 96 (536) ◽  
pp. 213-220
Author(s):  
Harlan J. Brothers
Keyword(s):  
Probability Theory ◽  
Fractal Geometry ◽  
Euclidean Geometry ◽  
Fibonacci Series ◽  
Pascal’S Triangle ◽  
Number Sequences ◽  
Definition Of ◽  
Image Position ◽  
Pascal's Triangle

Pascal's triangle is well known for its numerous connections to probability theory [1], combinatorics, Euclidean geometry, fractal geometry, and many number sequences including the Fibonacci series [2,3,4]. It also has a deep connection to the base of natural logarithms, e [5]. This link to e can be used as a springboard for generating a family of related triangles that together create a rich combinatoric object.2. From Pascal to LeibnizIn Brothers [5], the author shows that the growth of Pascal's triangle is related to the limit definition of e.Specifically, we define the sequence sn; as follows [6]:

Analogue of a theorem of Khintchine in fields of formal power series

1966 ◽  
Vol 62 (4) ◽  
pp. 637-642 ◽  
Author(s):  
T. W. Cusick
Keyword(s):  
Power Series ◽  
Positive Constant ◽  
Classical Result ◽  
Real Numbers ◽  
Linear Forms ◽  
Absolute Value ◽  
The Difference ◽  
Image Position ◽  
Formal Power ◽  
Positive Integers

For a real number λ, ‖λ‖ is the absolute value of the difference between λ and the nearest integer. Let X represent the m-tuple (x1, x2, … xm) and letbe any n linear forms in m variables, where the Θij are real numbers. The following is a classical result of Khintchine (1):For all pairs of positive integers m, n there is a positive constant Г(m, n) with the property that for any forms Lj(X) there exist real numbers α1, α2, …, αn such thatfor all integers x1, x2, …, xm not all zero.

Artificially making Lifeform

2021 ◽  
Vol 9 (10) ◽  
pp. 1290-1295
Author(s):  
Souvik Das
Keyword(s):  
Medical Community ◽  
Programming Algorithm ◽  
The Public ◽  
For Profit ◽  
Not For Profit ◽  
Funding Agencies ◽  
Proper Definition ◽  
Inanimate Matter ◽  
Living Organisms ◽  
Definition Of

Abstract: The word ‘life’ is a mysterious word with a chart of attributes that have neither been completed nor has been agreed upon by the race of humans. Probably the proper definition of life is impossible to identify for humans (the proof for this claim is given later) but the handbook to the secret shall be updated till the end, thanks to the inquisitive attitude of humans. For this piece, we shall adopt the description from the professional medical community of today. Though this topic falls midway between science and philosophy, this project is strictly technical. To quote dictionary.com, Life is the condition that distinguishes organisms from inorganic objects and dead organisms, being manifested by growth through metabolism, reproduction and the power of adaptation to environment- through changes originating internally; cambridge.com teaches Life is the period between birth and death, or the experience or state of being alive; medicaldictionary.thefreedictionary.com states Life is the property or quality that distinguishes living organisms from dead organisms and inanimate matter, manifested in functions such as metabolism, growth, reproduction and response to stimuli or adaptation to the environment originating from within the organisms. There are several other definitions but to summarize, we can safely state that though the concept is somewhat vague, we could indeed point out some common principles. We shall, in this project, try to replicate the characteristics so as to attain life in medical terms. (The order does not base upon importance of the listed character since the characters, all of them are absolute essentials and cannot possibly be categorized as more or less important). 1) Metabolism 2) Growth 3) Adaptability 4) Birth 5) Death 6) Self-stimulated response to environment 7) Reproduction 8) Can sustain self without foreign intervention Keywords: artificial, life, intelligence, computer, programming, algorithm This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

scholarly journals An algebraically closed field

1968 ◽  
Vol 9 (2) ◽  
pp. 146-151 ◽  
Author(s):  
F. J. Rayner
Keyword(s):  
Positive Integer ◽  
Power Series ◽  
Formal Power Series ◽  
Characteristic Zero ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Zero Characteristic ◽  
Image Position ◽  
Formal Power ◽  
Puiseux Expansions

Letkbe any algebraically closed field, and denote byk((t)) the field of formal power series in one indeterminatetoverk. Letso thatKis the field of Puiseux expansions with coefficients ink(each element ofKis a formal power series intl/rfor some positive integerr). It is well-known thatKis algebraically closed if and only ifkis of characteristic zero [1, p. 61]. For examples relating to ramified extensions of fields with valuation [9, §6] it is useful to have a field analogous toKwhich is algebraically closed whenkhas non-zero characteristicp. In this paper, I prove that the setLof all formal power series of the form Σaitei(where (ei) is well-ordered,ei=mi|nprt,n∈ Ζ,mi∈ Ζ,ai∈k,ri∈ Ν) forms an algebraically closed field.

Analytic functions of finite dimensional linear transformations

1959 ◽  
Vol 55 (1) ◽  
pp. 51-61 ◽  
Author(s):  
S. N. Afriat
Keyword(s):  
Power Series ◽  
Integral Formula ◽  
Characteristic Root ◽  
Interpolation Formula ◽  
General Function ◽  
Linear Transformations ◽  
Multiple Characteristic ◽  
Characteristic Roots ◽  
Image Position ◽  
Necessary And Sufficient

Since the first introduction of the concept of a matrix, questions about functions of matrices have had the attention of many writers, starting with Cayley(i) in 1858, and Laguerre(2) in 1867. In 1883, Sylvester(3) defined a general function φ(a) of a matrix a with simple characteristic roots, by use of Lagrange's interpolation formula, and Buchheim (4), in 1886, extended his definition to the case of multiple characteristic roots. Then Weyr(5) showed in 1887 that, for a matrix a with characteristic roots lying inside the circle of convergence of a power series φ(ζ), the power series φ(a) is convergent; and in 1900 Poincaré (6) obtained the formulaefor the sum, where C is a circle lying in and concentric with the circle of convergence, and containing all the characteristic roots in its ulterior, such a formula having effectively been suggested by Frobenius(7) in 1896 for defining a general function of a matrix. Phillips (8), in 1919, discovered the analogue, for power series in matrices, of Taylor's theorem. In 1926 Hensel(9) completed the result of Weyr by showing that a necessary and sufficient condition for the convergence of φ(a) is the convergence of the derived series φ(r)(α) (0 ≼ r < mα; α) at each characteristic root α of a, of order r at most the multiplicity mα of α. In 1928 Giorgi(10) gave a definition, depending on the classical canonical decomposition of a matrix, which is equivalent to the contour integral formula, and Fantappie (11) developed the theory of this formula, and obtained the expressionfor the characteristic projectors.

scholarly journals Lean & Green on Industry 4.0 Context – Contribution to Understand L&G Drivers and Design Principles

2021 ◽  
Vol 6 (5) ◽  
pp. 1214-1229
Author(s):  
Lenin John ◽  
Manuel Sampayo ◽  
Paulo Peças
Keyword(s):  
Industry 4.0 ◽  
Research Work ◽  
Design Principles ◽  
Manufacturing Companies ◽  
Bottom Line ◽  
Industrial Firms ◽  
Systems Implementation ◽  
Sustainability Concept ◽  
Proper Definition ◽  
Definition Of

The purpose of this paper is to demonstrate how the implementation of Lean & Green (L&G) in an Industry 4.0 (I4.0) environment can enhance the potential impact of the L&G approach and help manufacturing companies moving towards higher operational and sustainable performances. The research work developed here shows that although a proper definition of L&G is neither exposed worldwide nor explicitly implemented under that name, the current industrial firms are deeply concerned about the demanding challenge of keeping businesses flexible and agile without forgetting strategies to minimize the acceleration of climate change. So, one contribution of this paper is the identification and characterization of L&G drivers and design principles, supporting a robust and well-informed L&G systems implementation. As inferred from the research work, this challenge demands high quality and updated data together with assertive information. Thus, the implementation of L&G in I4.0 contexts is the answer to overcome the identified barriers. Likewise, an L&G system contributes to overcoming the challenges of I4.0 implementation regarding the triple bottom line sustainability concept. Consequently, another contribution of this paper is to depict why an L&G system performs better in the I4.0 context.

scholarly journals Reconstructing the Contours of the Copyright Originality and Idea- Expression Doctrines Regarding the Right to Deny Access to Works

2014 ◽  
Vol 1 (4) ◽  
pp. 921-940
Author(s):  
Michael D. Murray
Keyword(s):  
First Amendment ◽  
Freedom Of Expression ◽  
Cultural Knowledge ◽  
Fair Use ◽  
Digital Revolution ◽  
Content Development ◽  
Proper Definition ◽  
Definition Of ◽  
Access To Knowledge ◽  
The Right

ccess to innovative scientific, literary, and artistic content has never been more important to the public than now, in the digital age. Thanks to the digital revolution carried out through such means as super-computational power at super-affordable prices, the Internet, broadband penetration, and contemporary computer science and technology, the global, national, and local public finds itself at the convergence of unprecedented scientific and cultural knowledge and content development, along with unprecedented means to distribute, communicate, and access that knowledge. This Article joins the conversation on the Access-to-Knowledge, Access-to- Medicine, and Access-to-Art movements by asserting that the copyright restrictions affecting knowledge, innovation, and original thought implicate copyright’s originality and idea-expression doctrines first and fair use doctrine second. The parallel conversation in copyright law that focuses on the proper definition of the contours of copyright as described in the U.S. Supreme Court’s most recent constitutional law cases on copyright—Feist, Eldred, Golan, and Kirtsaeng—interprets the originality and idea-expression doctrines as being necessary for the proper balance between copyright protection and First Amendment freedom of expression. This Article seeks to join together the two conversations by focusing attention on the right to access published works under both copyright and First Amendment law. Access to works is part and parcel of the copyright contours debate. It is a “first principles” question to be answered before the question of manipulation, appropriation, or fair use is contemplated. The original intent of the Copyright Clause and its need to accommodate the First Amendment freedom of expression support the construction of the contours of copyright to include a right to access knowledge and information. Therefore, the originality and idea-expression doctrines should be reconstructed to recognize that the right to deny access to published works is extremely limited if not non-existent within the properly constructed contours of copyright.

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