Injective stability for unitary K1, revisited

2013 ◽  
Vol 11 (2) ◽  
pp. 233-242 ◽  
Author(s):  
S. Sinchuk
Keyword(s):  
Stability Theorem ◽  
Stable Range ◽  
Range Condition ◽  
The Stability

AbstractWe prove the injective stability theorem for unitary K1 under the usual stable range condition on the ground ring. This improves the stability theorem of A. Bak, V. Petrov and G. Tang where a stronger Λ-stable range condition was used.

scholarly journals Injective stability for odd-dimensional unitary K1{K_{1}}

2020 ◽  
Vol 23 (2) ◽  
pp. 313-325 ◽  
Author(s):  
Weibo Yu
Keyword(s):  
Decomposition Theorem ◽  
Stability Theorem ◽  
Stable Range ◽  
Elementary Subgroup ◽  
Range Condition

AbstractIn this paper, under the usual stable range condition, a decomposition theorem for the elementary subgroup is obtained, and the injective stability theorem for odd-dimensional unitary {K_{1}} is proved.

Stability of elliptical horizontally inhomogeneous rodons

2000 ◽  
Vol 416 ◽  
pp. 29-43
Author(s):  
RENÉ PINET ◽  
E. G. PAVÍA
Keyword(s):  
Formal Analysis ◽  
Detailed Examination ◽  
Stability Theorem ◽  
Homogeneous Case ◽  
Density Distributions ◽  
Formal Stability ◽  
Inhomogeneous Density ◽  
Loss Of Mass ◽  
The Stability ◽  
Main Effects

The stability of one-layer vortices with inhomogeneous horizontal density distributions is examined both analytically and numerically. Attention is focused on elliptical vortices for which the formal stability theorem proved by Ochoa, Sheinbaum & Pavía (1988) does not apply. Our method closely follows that of Ripa (1987) developed for the homogeneous case; and indeed they yield the same results when inhomogenities vanish. It is shown that a criterion from the formal analysis – the necessity of a radial increase in density for instability – does not extend to elliptical vortices. In addition, a detailed examination of the evolution of the inhomogeneous density fields, provided by numerical simulations, shows that homogenization, axisymmetrization and loss of mass to the surroundings are the main effects of instability.

Evaluation of Non-Vibrating Utility Burner/Furnace Systems for Resistance to Thermoacoustic Oscillations

2006 ◽  
Author(s):  
Frantisek L. Eisinger ◽  
Robert E. Sullivan
Keyword(s):  
Design Process ◽  
Axial Direction ◽  
Stability Diagram ◽  
Stable Range ◽  
Design Engineers ◽  
Secondary Role ◽  
The Stability ◽  
Thermoacoustic Oscillations

Six burner/furnace systems which operated successfully without vibration are evaluated for resistance to thermoacoustic oscillations. The evaluation is based on the Rijke and Sondhauss models representing the combined burner/furnace (cold/hot) thermoacoustic systems. Frequency differences between the lowest vulnerable furnace acoustic frequencies in the burner axial direction and those of the systems’ Rijke and Sondhauss frequencies are evaluated to check for resonances. Most importantly, the stability of the Rijke and Sondhauss models is checked against the published design stability diagram of Eisinger [1] and Eisinger and Sullivan [2]. It is shown that the resistance to thermoacoustic oscillations is adequately defined by the published design stability diagram to which the evaluated cases generally adhere. Once the system falls into the stable range, the frequency differences or resonances appear to play only a secondary role. It is concluded, however, that in conjunction with stability, the primary criterion, sufficient frequency separations shall also be maintained in the design process to preclude resonances. The paper provides sufficient details to aid the design engineers.

scholarly journals HUR-approximation of an ELTA functional equation

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4311-4328
Author(s):  
A.R. Sharifi ◽  
Azadi Kenary ◽  
B. Yousefi ◽  
R. Soltani
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Linear Mapping ◽  
Stability Theorem ◽  
Normed Spaces ◽  
The Stability ◽  
Rassias Stability

The main goal of this paper is study of the Hyers-Ulam-Rassias stability (briefly HUR-approximation) of the following Euler-Lagrange type additive(briefly ELTA) functional equation ?nj=1f (1/2 ?1?i?n,i?j rixi- 1/2 rjxj) + ?ni=1 rif(xi)=nf (1/2 ?ni=1 rixi) where r1,..., rn ? R, ?ni=k rk?0, and ri,rj?0 for some 1? i < j ? n, in fuzzy normed spaces. The concept of HUR-approximation originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

The ?-stability theorem for flows

1970 ◽  
Vol 11 (2) ◽  
pp. 150-158 ◽  
Author(s):  
Charles Pugh ◽  
Michael Shub
Keyword(s):  
Stability Theorem ◽  
The Stability

scholarly journals Adhesion state estimation based on improved tire brush model

2018 ◽  
Vol 10 (1) ◽  
pp. 168781401774770
Author(s):  
Bei Shaoyi ◽  
Li Bo ◽  
Zhu Yanyan
Keyword(s):  
Lateral Force ◽  
Longitudinal Force ◽  
Lateral Acceleration ◽  
Stable Range ◽  
The Road ◽  
Nonlinear Compensation ◽  
The Stability ◽  
Standard Calculation ◽  
Double Nonlinear ◽  
Brush Model

On the basis of calculating the longitudinal force using the original brush model, we simplify the tire structure and consider the lateral force generated by the lateral elasticity of the tread. At the same time, the boundary conditions between the adhesion area and the slip zone in the contact area of the tire are fully discussed. By establishing an improved tire brush model, the error caused by neglecting the sideslip characteristics is avoided, and the adaptability of the tire model is improved. A double nonlinear compensation method based on the lateral acceleration deviation and the yaw rate deviation is employed to estimate the road adhesion coefficient, which is closer to the actual attachment situation than the standard calculation. Based on this model, the vehicle stability coefficient k is defined and calculated to describe the stability of the vehicle during the driving process. The modeling results show that the value of k is always in the stable range of [0, 1]. Therefore, the vehicle that utilizes the improved tire brush model is always within the controllable range in the driving process, which verifies the effectiveness of the model.

scholarly journals Generalized Hyers–Ulam Stability of the Additive Functional Equation

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 76 ◽  
Author(s):  
Yang-Hi Lee ◽  
Gwang Kim
Keyword(s):  
Functional Equation ◽  
Additive Function ◽  
Additive Functional ◽  
Stability Theorem ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Stability Theorems ◽  
The Stability

We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f(x1 + y1, x2 + y2, …, xn + yn) = f(x1, x2, … xn) + f(y1, y2, …, yn). By restricting the domain of a mapping f that satisfies the inequality condition used in the assumption part of the stability theorem, we partially generalize the results of the stability theorems of the additive function equations.

Stability theorems

1977 ◽  
Vol 9 (02) ◽  
pp. 336-361 ◽  
Author(s):  
Eugene Lukacs
Keyword(s):  
Stability Theorem ◽  
Stability Theorems ◽  
Primary Object ◽  
The Stability ◽  
Decomposition Theorems

A stability theorem determines the extent to which the conclusions of a given theorem are affected if the assumptions of the theorem are not exactly but only approximately satisfied. The meaning of the word ‘approximately’ has to be defined exactly. The stability of decomposition theorems, of characterizations by independence and by regression properties are the primary object of the paper.

The crystallography of calf rennin (chymosin)

1971 ◽  
Vol 178 (1052) ◽  
pp. 245-258 ◽  
Keyword(s):  
Degradation Products ◽  
Protein Solutions ◽  
Stable Range ◽  
X Ray Diffraction ◽  
Stable Species ◽  
Wide Range ◽  
Unit Cells ◽  
Diffraction Patterns ◽  
The Stability ◽  
Ph Range

The growth of crystals of calf rennin (chymosin, † EC 3.4.4.3) and the control of nucleation to produce crystals of desired size, are described. Only one stable species, orthorhombic rennin I, has been found, but a metastable monoclinic species, rennin II, appeared on one occasion in a solution nearly saturated with glycine. The morphology, optical characteristics and unit cells of these species are recorded. In rennin I, small differences in the properties of sectors built by deposition on the three types of crystal faces are attributed to differences in the proportions of either degradation products or of the slightly different isoenzymes known to be present in calf rennin. Rennin I crystals have been obtained only within the pH range of greatest stability of the protein, 5. 0 to 6. 2; but the crystals tolerate subsequent changes of pH down to 2. 0. The stability of crystals appears to be much greater than that of salt-free protein solutions. Rennin I may be crosslinked with glutaraldehyde with no loss of order, giving crystals stable over a wide range of solution conditions, including pH 2.0 to 10.0 and salt-free solutions. The remarkable swelling behaviour when the pH is raised beyond the stable range is described. Rennin II, though monoclinic in symmetry, shows in its X -ray diffraction patterns strong evidence of a pseudo-orthorhombic arrangement of molecules.

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