To the definition of operators , which are performed IN Kaluzhnin’s graph-schems with parafractal characteristics

2020 ◽  
pp. 98-104
Author(s):  
V.M. Simonov
Keyword(s):  
Standard Procedure ◽  
Principal Result ◽  
Operator Equations ◽  
Definition Of ◽  
System Of Operator Equations

The regular formula of operator, which is performed in given Kaluzhnin’s graph-scheme with parafractal characteristics, can be definded by two procedures. The standard procedure is based on the solution of system of operator equations, which is given birth by this graph-scheme. The modified procedure is based on the solution of several lesser-scale systems of operator equations, which are given birth by parafractals. The modified procedure is simpler than the standard one, but it is not evident identity of the results of both procedures. The principal result of this article is the theorem about this identity.

scholarly journals Unveiling the Link between the Third Law of Comminution and the Grinding Kinetics Behaviour of Several Ores

Metals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1079
Author(s):  
Victor Ciribeni ◽  
Juan M. Menéndez-Aguado ◽  
Regina Bertero ◽  
Andrea Tello ◽  
Enzo Avellá ◽  
...  
Keyword(s):  
Standard Procedure ◽  
Research Work ◽  
Excellent Correlation ◽  
The Third ◽  
Work Index ◽  
Bond Work Index ◽  
Laboratory Procedures ◽  
Grinding Kinetics ◽  
Definition Of ◽  
Index Estimation

As a continuation of a previous research work carried out to estimate the Bond work index (wi) by using a simulator based on the cumulative kinetic model (CKM), a deeper analysis was carried out to determine the link between the kinetic and energy parameters in the case of metalliferous and non-metallic ore samples. The results evidenced a relationship between the CKM kinetic parameter k and the grindability index gbp; and also with the wi, obtained following the standard procedure. An excellent correlation was obtained in both cases, posing the definition of alternative work index estimation tests with the advantages of more straightforward and quicker laboratory procedures.

scholarly journals Comparison of Quantitative PCR (qPCR) Paenibacillus larvae Targeted Assays and Definition of Optimal Conditions for Its Detection/Quantification in Honey and Hive Debris

2018 ◽  
Author(s):  
Franca Rossi ◽  
Carmela Amadoro ◽  
Addolorato Ruberto ◽  
Luciano Ricchiuti
Keyword(s):  
Quantitative Pcr ◽  
Clinical Symptoms ◽  
Sequence Data ◽  
Standard Procedure ◽  
Paenibacillus Larvae ◽  
Optimal Conditions ◽  
Target Species ◽  
Speed Up ◽  
Definition Of ◽  
Culture Dependent

The application of quantitative PCR (qPCR) as a routine method to detect and enumerate Paenibacillus larvae in honey and hive debris could greatly speed up the estimation of prevalence and outbreak risk of the American foulbrood (AFB) disease of Apis mellifera. However, none of the qPCR tests described so far has been officially proposed as a standard procedure for P. larvae detection and enumeration for surveillance purposes. Therefore, in this study inclusivity, exclusivity and sensitivity in detection of P. larvae spores directly in samples of honey and hive debris were re-evaluated for the previously published qPCR methods. To this aim recently acquired P. larvae sequence data were considered to assess inclusivity in silico and more appropriate non-target species were used to verify exclusivity experimentally. This led to the modification of one of the previously described methods resulting in a new test capable to allow the detection of P. larvae spores in honey and hive debris down to 1 CFU/g. The application of the qPCR test optimized in this study can allow to reliably detect and quantify P. larvae in honey and hive debris, thus circumventing the disadvantages of late AFB diagnosis based on clinical symptoms and possible underestimation of spore numbers that is the main drawback of culture-dependent procedures.

scholarly journals A saddle point type solution for a system of operator equations

2021 ◽  
pp. 1-12
Author(s):  
Piotr Kowalski
Keyword(s):  
Saddle Point ◽  
Minimax Theorem ◽  
Dirichlet Problems ◽  
Type Solution ◽  
Operator Equations ◽  
Potential Operators ◽  
System Of Operator Equations ◽  
Ky Fan ◽  
Point Type

Let Ω⊂Rn n>1 and let p,q≥2. We consider the system of nonlinear Dirichlet problems equation* brace(Au)(x)=Nu′(x,u(x),v(x)),x∈Ω,r-(Bv)(x)=Nv′(x,u(x),v(x)),x∈Ω,ru(x)=0,x∈∂Ω,rv(x)=0,x∈∂Ω,endequation* where N:R×R→R is C1 and is partially convex-concave and A:W01,p(Ω)→(W01,p(Ω))* B:W01,p(Ω)→(W01,p(Ω))* are monotone and potential operators. The solvability of this system is reached via the Ky–Fan minimax theorem.

On the “Third Definition” of the Topology on the Spectrum of a C*-Algebra

1971 ◽  
Vol 23 (3) ◽  
pp. 445-450 ◽  
Author(s):  
L. Terrell Gardner
Keyword(s):  
Hilbert Space ◽  
Quotient Space ◽  
Principal Result ◽  
Irreducible Representations ◽  
C Algebra ◽  
Fell Topology ◽  
The Third ◽  
Definition Of ◽  
Image Position

0. In [3], Fell introduced a topology on Rep (A,H), the collection of all non-null but possibly degenerate *-representations of the C*-algebra A on the Hilbert space H. This topology, which we will call the Fell topology, can be described by giving, as basic open neighbourhoods of π0 ∈ Rep(A, H), sets of the formwhere the ai ∈ A, and the ξj ∈ H(π0), the essential space of π0 [4].A principal result of [3, Theorem 3.1] is that if the Hilbert dimension of H is large enough to admit all irreducible representations of A, then the quotient space Irr(A, H)/∼ can be identified with the spectrum (or “dual“) Â of A, in its hull-kernel topology.

MINIMAL AND STRANGE ATTRACTORS

1996 ◽  
Vol 06 (06) ◽  
pp. 1177-1183 ◽  
Author(s):  
A. GORODETSKI ◽  
Yu. ILYASHENKO
Keyword(s):  
Dynamical System ◽  
General Concept ◽  
Principal Result ◽  
Strange Attractors ◽  
Mild Form ◽  
Attracting Set ◽  
Probabilistic Character ◽  
A Chain ◽  
The One ◽  
Definition Of

A general concept going back to Kolmogorov claims that if a dynamical system has a complicated attracting set then its behavior has not a deterministic, but rather probabilistic character. This concept was not formalized up to now. Even the definition of attractor has a lot of different versions. This paper presents an attempt to give some definitions and results formalizing this heuristic ideas. It contains a definition of a minimal attractor, modifying the one given in Ilyashenko [1991]. The actual minimality of the attractor is discussed. The principal result is the Triple Choice Theorem. It claims that the existence of a strange minimal attractor implies some mild form of chaos for the map itself or for a nearby one. The program of further investigation is proposed as a chain of problems at the end of the paper.

scholarly journals Differential transcendence of solutions of systems of linear differential equations based on total reduction of the system

2020 ◽  
pp. 24-24
Author(s):  
Ivana Jovovic
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Complex Field ◽  
System Matrix ◽  
Operator Equations ◽  
Total Reduction ◽  
Commuting Operators ◽  
Constant Coefficients ◽  
Linear Differential ◽  
System Of Operator Equations

In this paper we consider total reduction of the nonhomogeneous linear system of operator equations with constant coefficients and commuting operators. The totally reduced system obtained in this manner is completely decoupled. All equations of the system differ only in the variables and in the nonhomogeneous terms. The homogeneous parts are obtained using the generalized characteristic polynomial of the system matrix. We also indicate how this technique may be used to examine differential transcendence of the solution of the linear system of the differential equations with constant coefficients over the complex field and meromorphic free terms.

Multivariate version of slant Toeplitz operators on the Lebesgue space

2021 ◽  
pp. 2150152
Author(s):  
Shesh Kumar Pandey ◽  
Gopal Datt
Keyword(s):  
Toeplitz Operator ◽  
Lebesgue Space ◽  
Spectral Properties ◽  
Toeplitz Operators ◽  
Operator Equations ◽  
System Of Operator Equations

The paper introduces the [Formula: see text]th-order slant Toeplitz operator on the Lebesgue space of [Formula: see text]-torus, where [Formula: see text] such that [Formula: see text] for all [Formula: see text]. It investigates certain properties of [Formula: see text]th-order slant Toeplitz operators on the Lebesgue space [Formula: see text]. The paper deals with a system of operator equations, characterizing the [Formula: see text]th-order slant Toeplitz operators. At the end, we discuss certain spectral properties of the considered operator.

The Future Neolithic

Early Farmers ◽  
2014 ◽  
Author(s):  
John Robb
Keyword(s):  
Principal Result ◽  
Specific Kind ◽  
Material World ◽  
Quiet Revolution ◽  
The Future ◽  
Definition Of ◽  
The Relationship

As for Shakespeare, every generation gets the Neolithic it deserves. This chapter discusses emerging views of what the Neolithic is and how to study it, with the thesis that recently there has been a quiet revolution in how we understand the Neolithic. A broad change in how Neolithic specialists understand the relationship between science and the humanities is envisioned, with the principal result that a new interpretive vocabulary, including a definition of the Neolithic, has arisen. This is illustrated with regard to changing understandings in the study of animals, plants, landscapes, things and monuments; for example, rather than being culture written on the material world, or material worlds determining culture, the practices of Neolithic life defined participation in a specific kind of historic process structured by these relations. The effects of changing perspectives are shown in, for example, multi-scalar approaches to both the origins and the end of the Neolithic.

scholarly journals Novel Procedure for Designing and 3D Printing a Customized Surgical Template for Arthrodesis Surgery on the Sacrum

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 334 ◽  
Author(s):  
Francesco Naddeo ◽  
Alessandro Naddeo ◽  
Nicola Cappetti ◽  
Emilio Cataldo ◽  
Riccardo Militio
Keyword(s):  
3D Printing ◽  
Computer Aided Design ◽  
Standard Procedure ◽  
Anatomical Landmarks ◽  
X Rays ◽  
Surgical Template ◽  
3D Printed ◽  
Definition Of ◽  
Aided Design

In this article, the authors propose a novel procedure for designing a customized 3D-printed surgical template to guide surgeons in inserting screws into the sacral zone during arthrodesis surgeries. The template is characterized by two cylindrical guides defined by means of trajectories identified, based on standard procedure, via an appropriate Computer-Aided-Design (CAD)-based procedure. The procedure is based on the definition of the insertion direction by means of anatomical landmarks that enable the screws to take advantage of the maximum available bone path. After 3D printing, the template adheres perfectly to the bone surface, showing univocal positioning by exploiting the foramina of the sacrum, great maneuverability due to the presence of an ergonomic handle, as well as a break system for the two independent guides. These features make the product innovative. Thanks to its small size and the easy anchoring, the surgeon can simply position the template on the insertion area and directly insert the screws, without alterations to standard surgical procedures. This has the effect of reducing the overall duration of the surgery and the patient’s exposure to X-rays, and increasing both the safety of the intervention and the quality of the results.

Sheaves and normal submodels

1977 ◽  
Vol 42 (2) ◽  
pp. 241-250 ◽  
Author(s):  
Richard Mansfield
Keyword(s):  
Model Theory ◽  
Heyting Algebra ◽  
Global Section ◽  
Principal Result ◽  
Traditional Model ◽  
Boolean Valued Model ◽  
Definition Of ◽  
Interesting Generalization ◽  
Horn Sentences

Ellerman, Comer, and Macintyre have all observed that sheaves are an interesting generalization of models and are deserving of model theoretic attention. Scott has pointed out that sheaves are Heyting algebra valued models. The reverse does not hold however since almost no genuine Boolean valued model is a sheaf.In §1 we shall review the definition of a sheaf and prove a theorem about Boolean valued models using the sheaf construction. In §2 we shall be concerned with the set of sentences preserved by global sections. Our principal result is that global section sentences are also normal submodel sentences. (We define as a normal submodel of if is a submodel of and every point of B − A can be moved by an automorphism of which fixes each point of A.) In §3 we prove that every normal submodel sentence is the negation of a disjunction of Horn sentences and that the set of normal submodel sentences is r.e. but not recursive. §3 involves only traditional model theory and can be read independently of the first two sections.

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