Maximisation and minimisation on classes of rearrangements

1991 ◽  
Vol 119 (3-4) ◽  
pp. 287-300 ◽  
Author(s):  
G. R. Burton ◽  
J. B. McLeod
Keyword(s):  
Angular Momentum ◽  
Finite Number ◽  
Bounded Domain ◽  
Ideal Fluid ◽  
Fluid Flows ◽  
Linear Constraints ◽  
Dirichlet Integral ◽  
The One

SynopsisMaximisation and minimisation of the Dirichlet integral of a function vanishing on the boundary of a bounded domain are studied, subject to the constraint that the Laplacean be a rearrangement of a given function. When the Laplacean is two-signed, non-existence of minimisers is proved, and some information on the limits of minimising sequences obtained; this contrasts with the known existence of minimisers in the one-signed case. When the domain is a ball and the Laplacean is one-signed, maximisers and minimisers are shown to be radial and monotone. Existence of maximisers is proved subject additionally to a finite number of linear constraints, with particular reference to ideal fluid flows of prescribed angular momentum in a disc.

scholarly journals The Spin Structure of the Nucleon

2016 ◽  
Vol 40 ◽  
pp. 1660001
Author(s):  
Xiangdong Ji ◽  
Yong Zhao
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Deeply Virtual Compton Scattering ◽  
Virtual Compton Scattering ◽  
Proton Spin ◽  
Effective Theory ◽  
Large Momentum ◽  
Theory Approach ◽  
The One ◽  
The Relationship

We justify the physical meaning of the spin and orbital angular momentum of free partons in the infinite momentum frame, and discuss the relationship between the Jaffe-Manohar and Ji’s sum rules for proton spin. The parton orbital angular momentum in the Jaffe-Manohar sum rule can be measured through twist-three GPD’s in hard scattering processes such as deeply virtual Compton scattering. Furthermore, we propose that the paton orbital angular momentum as well as the gluon helicity can be calculated in lattice QCD through a large momentum effective theory approach, and provide all the one-loop matching conditions for the proton spin content in perturbative QCD.

scholarly journals The behavior of a gas–vapor system inside a cavitation bubble during axial valve operation

Vestnik IGEU ◽  
2020 ◽  
pp. 58-64 ◽  
Author(s):  
A.B. Kapranova ◽  
A.E. Lebedev ◽  
A.M. Melzer ◽  
S.V. Neklyudov
Keyword(s):  
Angular Momentum ◽  
Cavitation Bubble ◽  
Fluid Flows ◽  
Design Solution ◽  
Vapor Concentration ◽  
Random Component ◽  
Negative Consequences ◽  
Control Valves ◽  
Cavitation Bubbles ◽  
Working Volume

The energy industry needs reliable, environmentally friendly control valves, which include the category of control valves. The creation of conditions for reducing the intensity of cavitation effects at the initial stages of its development determines the main purpose of the study which aims to prevent possible negative consequences of developed cavitation, which in their turn include erosion of the flowing surfaces of the elements of the specified equipment and vibrations that go beyond operating standards. One of the possible ways to solve the problem is to use the process of throttling fluid flows in the working volume of the control device. The particular interest is paid to the mathematical description of the mechanism of formation of cavitation bubbles in terms of gas–vapor system. To obtain analytical results for describing the behavior of the gas–vapor system of the macro-system of cavitation bubbles, we used the authoring stochastic model of the cavitation bubbles formation process in the flow part of the axial valve. The model was constructed on the basis of the energy method in the framework of the equilibrium representation of states of an energetically closed macro-system. The dependence of the random component of the angular momentum of the cavitation bubble on the flow coefficient of the valve and the conditional diameter of its flow cross section for various ratios of gas and vapor concentration inside the bubbles has been analysed. The implementation of the process of throttling fluid flows in the control valve using the proposed design solution to the separator–external locking shell allows reducing the random component of the angular momentum of the cavitation bubble and increasing the valve throughput coefficient at various stages of the separator opening.

scholarly journals Axisymmetric simulation of viscoelastic filament thinning with the Oldroyd-B model

2018 ◽  
Vol 851 ◽  
Author(s):  
Emre Turkoz ◽  
Jose M. Lopez-Herrera ◽  
Jens Eggers ◽  
Craig B. Arnold ◽  
Luc Deike
Keyword(s):  
Stress Component ◽  
Fluid Flows ◽  
Theoretical Description ◽  
Slender Body ◽  
Complex Materials ◽  
Two Phase ◽  
Practical Applications ◽  
Numerical Studies ◽  
Fundamental Understanding ◽  
The One

A fundamental understanding of the filament thinning of viscoelastic fluids is important in practical applications such as spraying and printing of complex materials. Here, we present direct numerical simulations of the two-phase axisymmetric momentum equations using the volume-of-fluid technique for interface tracking and the log-conformation transformation to solve the viscoelastic constitutive equation. The numerical results for the filament thinning are in excellent agreement with the theoretical description developed with a slender body approximation. We show that the off-diagonal stress component of the polymeric stress tensor is important and should not be neglected when investigating the later stages of filament thinning. This demonstrates that such numerical methods can be used to study details not captured by the one-dimensional slender body approximation, and pave the way for numerical studies of viscoelastic fluid flows.

scholarly journals THE RELATIVE WEAK ASYMPTOTIC HOMOMORPHISM PROPERTY FOR INCLUSIONS OF FINITE VON NEUMANN ALGEBRAS

2011 ◽  
Vol 22 (07) ◽  
pp. 991-1011 ◽  
Author(s):  
JUNSHENG FANG ◽  
MINGCHU GAO ◽  
ROGER R. SMITH
Keyword(s):  
Finite Number ◽  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Unitary Operators ◽  
Von Neumann ◽  
The One ◽  
Finite Von Neumann Algebras

A triple of finite von Neumann algebras B ⊆ N ⊆ M is said to have the relative weak asymptotic homomorphism property if there exists a net of unitary operators {uλ}λ∈Λ in B such that [Formula: see text] for all x,y ∈ M. We prove that a triple of finite von Neumann algebras B ⊆ N ⊆ M has the relative weak asymptotic homomorphism property if and only if N contains the set of all x ∈ M such that [Formula: see text] for a finite number of elements x1, …, xn in M. Such an x is called a one-sided quasi-normalizer of B, and the von Neumann algebra generated by all one-sided quasi-normalizers of B is called the one-sided quasi-normalizer algebra of B. We characterize one-sided quasi-normalizer algebras for inclusions of group von Neumann algebras and use this to show that one-sided quasi-normalizer algebras and quasi-normalizer algebras are not equal in general. We also give some applications to inclusions L(H) ⊆ L(G) arising from containments of groups. For example, when L(H) is a masa we determine the unitary normalizer algebra as the von Neumann algebra generated by the normalizers of H in G.

scholarly journals On the One Extremal Problem on the Riemann Sphere

2016 ◽  
Vol 4 ◽  
pp. 1-7 ◽  
Author(s):  
Andrey L. Targonskii ◽  
Irina Targonskaya
Keyword(s):  
Finite Number ◽  
Extremal Problem ◽  
Pairwise Disjoint ◽  
Riemann Sphere ◽  
Sharp Estimates ◽  
The One ◽  
Disjoint Domains

Sharp estimates of product of inner radii for pairwise disjoint domains are obtained. In particular, we solve an extremal problem in the case of arbitrary finite number of rays containing arbitrary even number of free poles.

scholarly journals A priori aggregation multicriteria optimization of family business vitality through Likert scaling with price evaluation

2021 ◽  
Vol 92 ◽  
pp. 05022
Author(s):  
Lucia Orlovova ◽  
Lukas Pospisil
Keyword(s):  
Family Business ◽  
A Priori ◽  
Value Added ◽  
Optimal Investment ◽  
Linear Constraints ◽  
Equity Capital ◽  
Optimal Decision ◽  
Integer Linear Programming Problem ◽  
The Family ◽  
The One

Research background: In this work, we are dealing with the problem of the optimal decision for increasing the vitality of family business. This type of business is the global topic since the companies owned by the family members with the equity capital shared with family are widespread all around the world and belongs to the one of the most popular types. The field of family businesses is characterized by specific properties and therefore, we suggest the measure of the vitality based on Likert scaling. The variants of the possible improvement are weighted by the required time and money. Purpose of the article: By solving the presented corresponding optimization problem, we manage to obtain optimal investment to the improvement of vitality measured by Likert scaling. The proposed methodology aims to avoid the influence of emotional aspect of decision making and rather find the optimality based on financial and time costs. Methods: In our contribution, we propose and compare two different formulations: the problem with constrained budget and the multicriteria formulation of the problem of the vitality maximization with costs minimization using the aggregation with a priori known coefficients. The corresponding integer linear programming problem with linear constraints is solved in Microsoft Excel. Findings & Value added: We examine, compare, and discuss the proposed methodologies on the selected practical benchmark.

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