scholarly journals Shift invariant operators and a saturation theorem

2003 ◽  
Vol 30 (3) ◽  
pp. 267-286
Author(s):  
Karol Dziedziul
Keyword(s):  
Saturation Theorem

scholarly journals An Investigation Into The Effect Of Isothermal Annealing On Magnetic Properties In The Alloy: Fe64Co10Y6B20

2015 ◽  
Vol 60 (3) ◽  
pp. 1987-1992
Author(s):  
M. Nabiałek
Keyword(s):  
Magnetic Properties ◽  
Isothermal Annealing ◽  
Structural Defects ◽  
Bulk Amorphous Alloy ◽  
Cast State ◽  
Soft Magnetic ◽  
Scanning Calorimetry ◽  
Saturation Magnetisation ◽  
Crystallisation Temperature ◽  
Saturation Theorem

AbstractThis work presents the results of investigations into the structural and magnetic properties of the bulk amorphous alloy: Fe64Co10Y6B20. The structure, thermal stability and magnetic properties of the alloy were studied using: X-ray diffractometry, differential scanning calorimetry (DSC), and a vibrating sample magnetometer (VSM), respectively. The investigations were performed on samples of the alloy in both the ‘as-cast’ state, and the state resulting from a process of isothermal annealing at a temperature of 750 K for 30 minutes.The aim of the conducted studies was to relax the structure and improve the soft magnetic properties of the investigated alloy. The results show that annealing the alloy at a temperature well below its crystallisation temperature leads to an increase in the value of the saturation magnetisation and a decrease in the value of the coercivity. Utilising the ‘approach to the ferromagnetic saturation’ theorem, the nature of structural defects within the investigated material has been established. For both ‘as-cast’ and isothermally-annealed samples, the magnetisation process has been found to be connected with the existence of linear structural defects.

An Lp Saturation Theorem for Splines

1972 ◽  
Vol 24 (5) ◽  
pp. 957-966 ◽  
Author(s):  
G. J. Butler ◽  
F. B. Richards
Keyword(s):  
Lebesgue Measure ◽  
Measure Zero ◽  
Lebesgue Measure Zero ◽  
Usual Norm ◽  
Saturation Theorem ◽  
Image Position ◽  
Class Of Functions

Let 1 be a subdivision of [0, 1], and let denote the class of functions whose restriction to each sub-interval is a polynomial of degree at most k. Gaier [1] has shown that for uniform subdivisions △n (that is, subdivisions for which if and only if f is a polynomial of degree at most k. Here, and subsequently, denotes the usual norm in Lp[0, 1], 1 ≦ p ≦ ∞, and we should emphasize that functions differing only on a set of Lebesgue measure zero are identified.

SATURATED OUTPUTS FOR HIGH-GAIN, SELF-EXCITING NETWORKS

1991 ◽  
Vol 01 (01) ◽  
pp. 211-217 ◽  
Author(s):  
MORRIS W. HIRSCH
Keyword(s):  
Internal State ◽  
Broad Class ◽  
Stable Solution ◽  
Nondecreasing Function ◽  
High Gain ◽  
Internal State Variable ◽  
State Variable ◽  
Dynamical Systems Modeling ◽  
Saturation Theorem ◽  
Limiting Values

We consider a broad class of continuous time dynamical systems modeling a collection of processing units sending signals to each other. Each unit has an internal state variable xi and an output variable yi which is a nondecreasing function gi (xi). Certain outputs, called "forced", are of the form σj (Kxj) where σj is a sigmoid and K > 0 is a parameter called "gain". The dynamics is given by a system of differential equations of the form dx/dt = H (x, y, t). The system is self-exciting: ∂Hi/∂yi ≥ 0, and > 0 for the forced outputs. We show that for sufficiently high gain, the forced outputs are close to the asymptotic limiting values of the sigmoids along any stable solution x (t) defined on a finite interval J, for a proportion of t ∈ J that approaches 1 as K → ∞. This generalizes Hopfield's Saturation Theorem about additive neural networks with symmetric weight matrices.

scholarly journals Eigenvalues of Hermitian matrices and equivariant cohomology of Grassmannians

2013 ◽  
Vol 149 (9) ◽  
pp. 1569-1582 ◽  
Author(s):  
David Anderson ◽  
Edward Richmond ◽  
Alexander Yong
Keyword(s):  
Eigenvalue Problem ◽  
Recent Work ◽  
Equivariant Cohomology ◽  
Eigenvalue Problems ◽  
Schubert Calculus ◽  
Hermitian Matrices ◽  
Common Features ◽  
Saturation Theorem ◽  
The Common

AbstractThe saturation theorem of Knutson and Tao concerns the nonvanishing of Littlewood–Richardson coefficients. In combination with work of Klyachko, it implies Horn’s conjecture about eigenvalues of sums of Hermitian matrices. This eigenvalue problem has a generalization to majorized sums of Hermitian matrices, due to S. Friedland. We further illustrate the common features between these two eigenvalue problems and their connection to Schubert calculus of Grassmannians. Our main result gives a Schubert calculus interpretation of Friedland’s problem, via equivariant cohomology of Grassmannians. In particular, we prove a saturation theorem for this setting. Our arguments employ the aforementioned work together with recent work of H. Thomas and A. Yong.

SATURATION THEOREM FOR SZÁSZ-DURRMEYER OPERATORS

1996 ◽  
Vol 29 (1) ◽  
Author(s):  
Vijay Gupta ◽  
G. S. Srivastava
Keyword(s):  
Durrmeyer Operators ◽  
Saturation Theorem
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