scholarly journals Fractal Behavior of a Ternary 4-Point Rational Interpolation Subdivision Scheme

2018 ◽  
Vol 23 (4) ◽  
pp. 65 ◽  
Author(s):  
Kaijun Peng ◽  
Jieqing Tan ◽  
Zhiming Li ◽  
Li Zhang
Keyword(s):  
Singular Point ◽  
Sufficient Conditions ◽  
Rational Interpolation ◽  
Subdivision Scheme ◽  
Fractal Curve ◽  
Rational Scheme ◽  
Special Cases ◽  
Necessary And Sufficient ◽  
Parameter Values ◽  
Selection Of

In this paper, a ternary 4-point rational interpolation subdivision scheme is presented, and the necessary and sufficient conditions of the continuity are analyzed. The generalization incorporates existing schemes as special cases: Hassan–Ivrissimtzis’s scheme, Siddiqi–Rehan’s scheme, and Siddiqi–Ahmad’s scheme. Furthermore, the fractal behavior of the scheme is investigated and analyzed, and the range of the parameter of the fractal curve is the neighborhood of the singular point of the rational scheme. When the fractal curve and surface are reconstructed, it is convenient for the selection of parameter values.

scholarly journals Системний підхід у дослідженні технологічного процесу збирання льону-довгунця

2013 ◽  
pp. 100-105
Author(s):  
О. А. Примаков
Keyword(s):  
New Technology ◽  
Rational Scheme ◽  
Wide Range ◽  
Necessary And Sufficient ◽  
Selection Of ◽  
Agricultural Machines

Розкривається питання обґрунтування раціональ-ної схеми збирання льону-довгунця із застосуван-ням сільськогосподарських машин загального при-значення. Проведено вибір необхідних та достат-ніх технологічних операцій для збирання льону-довгунця за новою технологією з аналізом кожного окремого елемента. При виборі технічних засобів для збирання льону акцент зроблено не на спеціа-льні льонозбиральні машини, а на техніку, що за-стосовується для збирання інших культур; це ро-бить технологію більш доступною для широкого кола сільгоспвиробників. На основі обґрунтування обраного комплексу технічних засобів складено первинну модель технологічної схеми збирання посіву льону-довгунця. The article reveals the issues of a rational scheme of harvesting flax with the use of agricultural machines for general use. The adequate selection of the necessary and sufficient technical operations for flax harvesting on new technology has been done. When choosing machines for the harvesting of flax a great attention is paid not to special flax pullers but to equipment that is used to harvest other crops, making the technology more accessible to a wide range of manufacturers.

scholarly journals Is there contextuality in behavioural and social systems?

2016 ◽  
Vol 374 (2058) ◽  
pp. 20150099 ◽  
Author(s):  
E. N. Dzhafarov ◽  
Ru Zhang ◽  
Janne Kujala
Keyword(s):  
Quantum Physics ◽  
Broad Class ◽  
Social Systems ◽  
Sufficient Conditions ◽  
Type Systems ◽  
Binary Outcomes ◽  
Special Cases ◽  
Einstein Podolsky Rosen ◽  
Cyclic Systems ◽  
Necessary And Sufficient

Most behavioural and social experiments aimed at revealing contextuality are confined to cyclic systems with binary outcomes. In quantum physics, this broad class of systems includes as special cases Klyachko–Can–Binicioglu–Shumovsky-type, Einstein–Podolsky–Rosen–Bell-type and Suppes–Zanotti–Leggett–Garg-type systems. The theory of contextuality known as contextuality-by-default allows one to define and measure contextuality in all such systems, even if there are context-dependent errors in measurements, or if something in the contexts directly interacts with the measurements. This makes the theory especially suitable for behavioural and social systems, where direct interactions of ‘everything with everything’ are ubiquitous. For cyclic systems with binary outcomes, the theory provides necessary and sufficient conditions for non-contextuality, and these conditions are known to be breached in certain quantum systems. We review several behavioural and social datasets (from polls of public opinion to visual illusions to conjoint choices to word combinations to psychophysical matching), and none of these data provides any evidence for contextuality. Our working hypothesis is that this may be a broadly applicable rule: behavioural and social systems are non-contextual, i.e. all ‘contextual effects’ in them result from the ubiquitous dependence of response distributions on the elements of contexts other than the ones to which the response is presumably or normatively directed.

Maximal and Minimal Ranks of the Common Solution of Some Linear Matrix Equations over an Arbitrary Division Ring with Applications

2009 ◽  
Vol 16 (02) ◽  
pp. 293-308 ◽  
Author(s):  
Qingwen Wang ◽  
Guangjing Song ◽  
Xin Liu
Keyword(s):  
Division Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Common Solution ◽  
Special Cases ◽  
The Common ◽  
Necessary And Sufficient ◽  
Linear Matrix Equations

We establish the formulas of the maximal and minimal ranks of the common solution of certain linear matrix equations A1X = C1, XB2 = C2, A3XB3 = C3 and A4XB4 = C4 over an arbitrary division ring. Corresponding results in some special cases are given. As an application, necessary and sufficient conditions for the invariance of the rank of the common solution mentioned above are presented. Some previously known results can be regarded as special cases of our results.

Planar Linkage Synthesis for Mixed Motion, Path and Function Generation Using Poles and Rotation Angles

2017 ◽  
Author(s):  
Ronald A. Zimmerman
Keyword(s):  
Sufficient Conditions ◽  
Motion Path ◽  
Engineering Practice ◽  
Function Generation ◽  
Problem Types ◽  
The Family ◽  
And Function ◽  
Necessary And Sufficient ◽  
Four Bar Linkage ◽  
Selection Of

The kinematic synthesis of planar linkage mechanisms has traditionally been broken into the categories of motion, path and function generation. Each of these categories of problems has been solved separately. Many problems in engineering practice require some combination of these problem types. For example, a problem requiring coupler points and/or poses in addition to specific input and/or output link angles that correspond to those positions. A limited amount of published work has addressed some specific underconstrained combinations of these problems. This paper presents a general graphical method for the synthesis of a four bar linkage to satisfy any combination of these exact synthesis problems that is not over constrained. The approach is to consider the constraints imposed by the target positions on the linkage through the poles and rotation angles. These pole and rotation angle constraints are necessary and sufficient conditions to meet the target positions. After the constraints are made, free choices which may remain can be explored by simply dragging a fixed pivot, a moving pivot or a pole in the plane. The designer can thus investigate the family of available solutions before making the selection of free choices to satisfy other criteria. The fully constrained combinations for a four bar linkage are given and sample problems are solved for several of them.

scholarly journals Injectivity of linear combinations in $\mathcal{B}(\mathcal{H})$

2021 ◽  
Vol 37 ◽  
pp. 359-369
Author(s):  
Marko Kostadinov
Keyword(s):  
Linear Combination ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Combinations ◽  
Special Cases ◽  
Sufficient And Necessary Conditions ◽  
Alpha Beta ◽  
Necessary And Sufficient

The aim of this paper is to provide sufficient and necessary conditions under which the linear combination $\alpha A + \beta B$, for given operators $A,B \in {\cal B}({\cal H})$ and $\alpha, \beta \in \mathbb{C}\setminus \lbrace 0 \rbrace$, is injective. Using these results, necessary and sufficient conditions for left (right) invertibility are given. Some special cases will be studied as well.

Planar Linkage Synthesis for Mixed Motion, Path, and Function Generation Using Poles and Rotation Angles1

2018 ◽  
Vol 10 (2) ◽  
Author(s):  
Ronald A. Zimmerman
Keyword(s):  
Sufficient Conditions ◽  
Motion Path ◽  
Engineering Practice ◽  
Function Generation ◽  
Problem Types ◽  
The Family ◽  
And Function ◽  
Necessary And Sufficient ◽  
Four Bar Linkage ◽  
Selection Of

The kinematic synthesis of planar linkage mechanisms has traditionally been broken into the categories of motion, path, and function generation. Each of these categories of problems has been solved separately. Many problems in engineering practice require some combination of these problem types. For example, a problem requiring coupler points and/or poses in addition to specific input and/or output link angles that correspond to those positions. A limited amount of published work has addressed some specific underconstrained combinations of these problems. This paper presents a general graphical method for the synthesis of a four bar linkage to satisfy any combination of these exact synthesis problems that is not overconstrained. The approach is to consider the constraints imposed by the target positions on the linkage through the poles and rotation angles. These pole and rotation angle constraints (PRCs) are necessary and sufficient conditions to meet the target positions. After the constraints are made, free choices which may remain can be explored by simply dragging a fixed pivot, a moving pivot, or a pole in the plane. The designer can thus investigate the family of available solutions before making the selection of free choices to satisfy other criteria. The fully constrained combinations for a four bar linkage are given and sample problems are solved for several of them.

The Projective Antecedent of the Three Reflection Theorem

1991 ◽  
Vol 34 (2) ◽  
pp. 265-274
Author(s):  
F. A. Sherk
Keyword(s):  
Projective Geometry ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Metric Geometry ◽  
Natural Question ◽  
Complete Answer ◽  
Special Cases ◽  
Reflection Theorem ◽  
Necessary And Sufficient

AbstractA complete answer is given to the question: Under what circumstances is the product of three harmonic homologies in PG(2, F) again a harmonic homology ? This is the natural question to ask in seeking a generalization to projective geometry of the Three Reflection Theorem of metric geometry. It is found that apart from two familiar special cases, and with one curious exception, the necessary and sufficient conditions on the harmonic homologies produce exactly the Three Reflection Theorem.

On the Preservation of Root Numbers and the Behavior of Weil Characters under Reciprocity Equivalence

1997 ◽  
Vol 40 (4) ◽  
pp. 402-415
Author(s):  
Jenna P. Carpenter
Keyword(s):  
Number Field ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Witt Ring ◽  
Root Numbers ◽  
Local Root ◽  
Necessary And Sufficient ◽  
Selection Of ◽  
Local Root Numbers

AbstractThis paper studies how the local root numbers and the Weil additive characters of the Witt ring of a number field behave under reciprocity equivalence. Given a reciprocity equivalence between two fields, at each place we define a local square class which vanishes if and only if the local root numbers are preserved. Thus this local square class serves as a local obstruction to the preservation of local root numbers. We establish a set of necessary and sufficient conditions for a selection of local square classes (one at each place) to represent a global square class. Then, given a reciprocity equivalence that has a finite wild set, we use these conditions to show that the local square classes combine to give a global square class which serves as a global obstruction to the preservation of all root numbers. Lastly, we use these results to study the behavior of Weil characters under reciprocity equivalence.

scholarly journals H-function with complex parameters I: existence

2001 ◽  
Vol 25 (9) ◽  
pp. 571-586
Author(s):  
Fadhel A. Al-Musallam ◽  
Vu Kim Tuan
Keyword(s):  
Sufficient Conditions ◽  
Integral Transforms ◽  
Necessary And Sufficient Conditions ◽  
Special Cases ◽  
Type Integral ◽  
Necessary And Sufficient

AnH-function with complex parameters is defined by a Mellin-Barnes type integral. Necessary and sufficient conditions under which the integral defining theH-function converges absolutely are established. Some properties, special cases, and an application to integral transforms are given.

THE QUASITRIANGULAR STRUCTURES FOR ω-SMASH COPRODUCT HOPF ALGEBRAS

2009 ◽  
Vol 08 (05) ◽  
pp. 673-687 ◽  
Author(s):  
ZHENGMING JIAO
Keyword(s):  
Hopf Algebras ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Special Cases ◽  
Necessary And Sufficient

In this paper, the quasitriangular structures of ω-smash coproduct Hopf algebras Bω ⋈ H as constructed by Caenepeel, Ion, Militaru and Zhu were studied. Necessary and sufficient conditions for ω-smash coproduct Hopf algebras to be quasitriangular Hopf algebras are given in terms of properties of their components. As applications of our results, some special cases are discussed. Especially, The quasitriangular structures for D(H)* and H4ω ⋈ kℤ2 are constructed.

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