scholarly journals The Burkill-Cesari Integral on Spaces of Absolutely Continuous Games

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
F. Centrone ◽  
A. Martellotti
Keyword(s):  
Existence Result ◽  
Lipschitz Norm ◽  
Absolutely Continuous ◽  
Lipschitz Continuous ◽  
A Value

We prove that the Burkill-Cesari integral is a value on a subspace ofACand then discuss its continuity with respect to both theBVand the Lipschitz norm. We provide an example of value on a subspace ofACstrictly containingpNAas well as an existence result of a Lipschitz continuous value, different from Aumann and Shapley’s one, on a subspace ofAC∞.

scholarly journals On a second-order functional evolution problem with time and state dependent maximal monotone operators

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Soumia Saïdi
Keyword(s):  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Uniqueness Result ◽  
Second Order ◽  
Absolutely Continuous ◽  
Lipschitz Continuous ◽  
State Dependent ◽  
Real Separable Hilbert Space ◽  
Order State

<p style='text-indent:20px;'>The present paper proposes, in a real separable Hilbert space, to analyze the existence of solutions for a class of perturbed second-order state-dependent maximal monotone operators with a finite delay. The dependence of the operators is -in some sense- absolutely continuous (or bounded continuous) variation in time, and Lipschitz continuous in state. The approach to solve our problem is based on a discretization scheme. The uniqueness result is applied to optimal control.</p>

scholarly journals Central limit theorem for generalized Weierstrass functions

2019 ◽  
Vol 19 (01) ◽  
pp. 1950002
Author(s):  
Amanda de Lima ◽  
Daniel Smania
Keyword(s):  
Limit Theorem ◽  
Bounded Solution ◽  
Positive Lebesgue Measure ◽  
Lipschitz Continuous Function ◽  
Absolutely Continuous ◽  
Lipschitz Continuous ◽  
Expanding Map ◽  
Cohomological Equation ◽  
Weierstrass Functions ◽  
Absolutely Continuous Invariant

Let [Formula: see text] be a [Formula: see text] expanding map of the circle and let [Formula: see text] be a [Formula: see text] function. Consider the twisted cohomological equation [Formula: see text] which has a unique bounded solution [Formula: see text]. We show that [Formula: see text] is either [Formula: see text] or continuous but nowhere differentiable. If [Formula: see text] is nowhere differentiable then the Newton quotients of [Formula: see text], after an appropriated normalization, converges in distribution (with respect to the unique absolutely continuous invariant probability of [Formula: see text]) to the normal distribution. In particular, [Formula: see text] is not a Lipschitz continuous function on any subset with positive Lebesgue measure.

scholarly journals On the Cauchy problem for the differential equation f(t, x, x′, …, x(k)) = 0

1991 ◽  
Vol 33 (3) ◽  
pp. 343-348 ◽  
Author(s):  
Biagio Ricceri
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Existence Result ◽  
Real Interval ◽  
Absolutely Continuous ◽  
The Cauchy Problem

In the sequel, given k, n ∈ ℕ, p ∈ [1, ∞] and a compact real interval I, we denote by Wk, p(I, ℝn) (simply by Wk,p(I if n = 1) the space of all functions u ∈ Ck−1(I, ℝn) such that uk−1 is absolutely continuous in I and u(k) ∈ Lp (I, ℝn).Very recently, in [11], J. R. L. Webb and S. C. Welsh obtained the following existence result.

scholarly journals Explicit and Implicit Non-convex Sweeping Processes in the Space of Absolutely Continuous Functions

2021 ◽  
Author(s):  
Pavel Krejčí ◽  
Giselle Antunes Monteiro ◽  
Vincenzo Recupero
Keyword(s):  
Continuous Functions ◽  
Input Output ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Lipschitz Continuous ◽  
State Dependent ◽  
Banach Contraction ◽  
Solution Mapping ◽  
Output Mapping ◽  
Sweeping Processes

AbstractWe show that sweeping processes with possibly non-convex prox-regular constraints generate a strongly continuous input-output mapping in the space of absolutely continuous functions. Under additional smoothness assumptions on the constraint we prove the local Lipschitz continuity of the input-output mapping. Using the Banach contraction principle, we subsequently prove that also the solution mapping associated with the state-dependent problem is locally Lipschitz continuous.

Observations of the Thermal Decomposition of Brucite

1968 ◽  
Vol 26 ◽  
pp. 446-447
Author(s):  
P. L. Burnett ◽  
W. R. Mitchell ◽  
C. L. Houck
Keyword(s):  
Thermal Decomposition ◽  
Magnesium Oxide ◽  
Basal Plane ◽  
Magnesium Ions ◽  
A Value ◽  
Reaction Proceeds

Natural Brucite (Mg(OH)2) decomposes on heating to form magnesium oxide (MgO) having its cubic ﹛110﹜ and ﹛111﹜ planes respectively parallel to the prism and basal planes of the hexagonal brucite lattice. Although the crystal-lographic relation between the parent brucite crystal and the resulting mag-nesium oxide crystallites is well known, the exact mechanism by which the reaction proceeds is still a matter of controversy. Goodman described the decomposition as an initial shrinkage in the brucite basal plane allowing magnesium ions to shift their original sites to the required magnesium oxide positions followed by a collapse of the planes along the original <0001> direction of the brucite crystal. He noted that the (110) diffraction spots of brucite immediately shifted to the positions required for the (220) reflections of magnesium oxide. Gordon observed separate diffraction spots for the (110) brucite and (220) magnesium oxide planes. The positions of the (110) and (100) brucite never changed but only diminished in intensity while the (220) planes of magnesium shifted from a value larger than the listed ASTM d spacing to the predicted value as the decomposition progressed.

Field-assisted ionization theory for microscopists

1994 ◽  
Vol 52 ◽  
pp. 820-821
Author(s):  
Patrick P. Camus
Keyword(s):  
Electric Field ◽  
Electron Tunneling ◽  
Ionization Probability ◽  
Critical Distance ◽  
Tunneling Probability ◽  
Field Ionization ◽  
Radius Of Curvature ◽  
Field Evaporation ◽  
A Value ◽  
Ion Emission

The theory of field ion emission is the study of electron tunneling probability enhanced by the application of a high electric field. At subnanometer distances and kilovolt potentials, the probability of tunneling of electrons increases markedly. Field ionization of gas atoms produce atomic resolution images of the surface of the specimen, while field evaporation of surface atoms sections the specimen. Details of emission theory may be found in monographs.Field ionization (FI) is the phenomena whereby an electric field assists in the ionization of gas atoms via tunneling. The tunneling probability is a maximum at a critical distance above the surface,xc, Fig. 1. Energy is required to ionize the gas atom at xc, I, but at a value reduced by the appliedelectric field, xcFe, while energy is recovered by placing the electron in the specimen, φ. The highest ionization probability occurs for those regions on the specimen that have the highest local electric field. Those atoms which protrude from the average surfacehave the smallest radius of curvature, the highest field and therefore produce the highest ionizationprobability and brightest spots on the imaging screen, Fig. 2. This technique is called field ion microscopy (FIM).

Vitamin A Value of Plant Food Provitamin A - Evaluated by the Stable Isotope Technologies

2014 ◽  
Vol 84 (Supplement 1) ◽  
pp. 25-29 ◽  
Author(s):  
Guangwen Tang
Keyword(s):  
Stable Isotope ◽  
Vitamin A ◽  
Provitamin A ◽  
Animal Origin ◽  
Plant Food ◽  
Plant Foods ◽  
A Value ◽  
Provitamin A Carotenoids ◽  
Β Carotene

Humans need vitamin A and obtain essential vitamin A by conversion of plant foods rich in provitamin A and/or absorption of preformed vitamin A from foods of animal origin. The determination of the vitamin A value of plant foods rich in provitamin A is important but has challenges. The aim of this paper is to review the progress over last 80 years following the discovery on the conversion of β-carotene to vitamin A and the various techniques including stable isotope technologies that have been developed to determine vitamin A values of plant provitamin A (mainly β-carotene). These include applications from using radioactive β-carotene and vitamin A, depletion-repletion with vitamin A and β-carotene, and measuring postprandial chylomicron fractions after feeding a β-carotene rich diet, to using stable isotopes as tracers to follow the absorption and conversion of plant food provitamin A carotenoids (mainly β-carotene) in humans. These approaches have greatly promoted our understanding of the absorption and conversion of β-carotene to vitamin A. Stable isotope labeled plant foods are useful for determining the overall bioavailability of provitamin A carotenoids from specific foods. Locally obtained plant foods can provide vitamin A and prevent deficiency of vitamin A, a remaining worldwide concern.

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