scholarly journals Rigorous numerics for nonlinear operators with tridiagonal dominant linear part

2015 ◽  
Vol 35 (10) ◽  
pp. 4765-4789 ◽  
Author(s):  
Maxime Breden ◽  
◽  
Laurent Desvillettes ◽  
Jean-Philippe Lessard ◽  
Keyword(s):  
Linear Part ◽  
Rigorous Numerics ◽  
Nonlinear Operators

In Vitro Incorporation of Sodium Acetate-l-C14 into Leukocyte Lipids of Normal and Leukaemic Subjects as a Function of Incubation Time

1962 ◽  
Vol 02 (02) ◽  
pp. 165-172
Author(s):  
C Miras ◽  
G Lewis ◽  
J Mantzos
Keyword(s):  
Sodium Acetate ◽  
Linear Part ◽  
Lipid Synthesis ◽  
Normal Subjects ◽  
Cytostatic Agents ◽  
Time Intervals ◽  
Total Blood ◽  
Effect Of Treatment ◽  
Product Relation

Summary1. Separated leukocytes or total blood from normal subjects, untreated leukaemic patients and from leukaemic patients treated with cytostatic agents were incubated with CH3COONa-l-C14. Radioactivity of mixed lipids was measured at standard time intervals.2. The time incorporation curve observed with leukocytes from treated leukaemic patients showed after an initial linear part, a more rapid levelling off than the curves observed with leukocytes from untreated and normal subjects.3. Therefore, an indirect effect of treatment on leukocyte lipid synthesis seems to be present.4. Phospholipid and neutral lipid synthesis by leukaemic leukocytes was also studied. The results give no evidence that these fractions as a whole have any precursor-product relation.

Forecasting of Summer Monsoon Rainfall over Gangetic West Bengal, India Utilising Intrinsic Mode Functions, Linear and Neural Regression

2020 ◽  
Vol 12 (1) ◽  
pp. 60-69 ◽  
Author(s):  
Pijush Basak
Keyword(s):  
Neural Network ◽  
West Bengal ◽  
Monsoon Rainfall ◽  
Linear Part ◽  
Intrinsic Mode Functions ◽  
Quasi Biennial Oscillation ◽  
Nonlinear Part ◽  
South West ◽  
South West Monsoon ◽  
West Monsoon

The South West Monsoon rainfall data of the meteorological subdivision number 6 of India enclosing Gangetic West Bengal is shown to be decomposable into eight empirical time series, namely Intrinsic Mode Functions. This leads one to identify the first empirical mode as a nonlinear part and the remaining modes as the linear part of the data. The nonlinear part is modeled with the technique Neural Network based Generalized Regression Neural Network model technique whereas the linear part is sensibly modeled through simple regression method. The different Intrinsic modes as verified are well connected with relevant atmospheric features, namely, El Nino, Quasi-biennial Oscillation, Sunspot cycle and others. It is observed that the proposed model explains around 75% of inter annual variability (IAV) of the rainfall series of Gangetic West Bengal. The model is efficient in statistical forecasting of South West Monsoon rainfall in the region as verified from independent part of the real data. The statistical forecasts of SWM rainfall for GWB for the years 2012 and 2013 are108.71 cm and 126.21 cm respectively, where as corresponding to the actual rainfall of 93.19 cm 115.20 cm respectively which are within one standard deviation of mean rainfall.

Recording of the Cavitation Phenomena when Modeling Flows in the Trunk Pipelines

2020 ◽  
pp. 7-14
Author(s):  
A.M. Sverchkov ◽  
◽  
S.I. Sumskoy ◽  
Keyword(s):  
Occupational Safety ◽  
Linear Part ◽  
Simple Wave ◽  
Pressure Profile ◽  
Real Problem ◽  
Flow Modeling ◽  
Oil Pipeline ◽  
Emergency Situations ◽  
Hydraulic Shocks ◽  
The Waves

In the article, it is proposed to use a numerical method based on the approach of S.K. Godunov to simulate boiling in a pipeline. The paper presents a statement of the real problem of modeling a water hammer, considering possible boiling of the transported liquid on a real object — an oil pipeline. When solving the problem, two variants of flow modeling when closing the valve installed at the end of the pipeline were carried out. In the first Наука и техника 14 Безопасность Труда в Промышленности • Occupational Safety in Industry • № 11'2020 • www.safety.ru case, the possibility of liquid boiling was not considered. In the second case, this opportunity was considered. The performed numerical simulation showed that in the pipeline in emergency situations, liquid columns can be formed, separated by the cavitation zones and oscillating in different phases, respectively, at the collapse of the cavitation zones, which serve as a kind of pressure dampers, the collisions of liquid columns occur, which can lead, depending on the ratio of velocities, to hydraulic shocks that occur not on the valves, but on the linear part of the pipeline (local hydraulic shocks). The waves from these collapses, interacting with each other, create the new pressure peaks that do not coincide with the pattern of simple wave circulation, which are predicted in the simulations that do not consider possible liquid boiling. As a resul t, the pressures reached in the pipeline during fluid hammer is significantly different from what it would be in the absence of boiling. When boiling is considered, the maximum reached pressures are 40 % higher. Moreover, this excess is repeated. The detailed analysis of the pressure profile in the pipeline is given in the article. Based on the results of solving this problem, it is concluded that when modeling pre–emergency and emergency situations in the pipeline, it is necessary to consider the process of possible liquid boiling, since sometimes, as in the presented case, the values of the pressure surges can be higher than the values of the pressure surges in the liquid without considering boiling, which increases the likelihood of emergency depressurization.

Solvability of a 2 x 2 block operator matrix of chandrasekhar type on a Bananch algebra

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5169-5175 ◽  
Author(s):  
H.H.G. Hashem
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Of Solutions ◽  
Banach Algebras ◽  
Operator Matrix ◽  
Nonlinear Operators ◽  
Block Operator Matrix ◽  
Block Operator ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

In this paper, we study the existence of solutions for a system of quadratic integral equations of Chandrasekhar type by applying fixed point theorem of a 2 x 2 block operator matrix defined on a nonempty bounded closed convex subsets of Banach algebras where the entries are nonlinear operators.

scholarly journals Discrete Nonlinear Schrödinger Systems for Periodic Media with Nonlocal Nonlinearity: The Case of Nematic Liquid Crystals

2021 ◽  
Vol 11 (10) ◽  
pp. 4420
Author(s):  
Panayotis Panayotaros
Keyword(s):  
Differential Equation ◽  
Infinite System ◽  
Linear Part ◽  
Optical Power ◽  
Explicit Construction ◽  
Translation Invariance ◽  
Nonlocal Nonlinearity ◽  
Wannier Functions ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger Systems

We study properties of an infinite system of discrete nonlinear Schrödinger equations that is equivalent to a coupled Schrödinger-elliptic differential equation with periodic coefficients. The differential equation was derived as a model for laser beam propagation in optical waveguide arrays in a nematic liquid crystal substrate and can be relevant to related systems with nonlocal nonlinearities. The infinite system is obtained by expanding the relevant physical quantities in a Wannier function basis associated to a periodic Schrödinger operator appearing in the problem. We show that the model can describe stable beams, and we estimate the optical power at different length scales. The main result of the paper is the Hamiltonian structure of the infinite system, assuming that the Wannier functions are real. We also give an explicit construction of real Wannier functions, and examine translation invariance properties of the linear part of the system in the Wannier basis.

scholarly journals A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds

2021 ◽  
Author(s):  
Alessandro Goffi ◽  
Francesco Pediconi
Keyword(s):  
Maximum Principle ◽  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Strong Maximum Principle ◽  
Second Order ◽  
Fully Nonlinear Equations ◽  
Nonlinear Operators ◽  
Fully Nonlinear ◽  
Second Order Equations ◽  
Curvature Type

AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

scholarly journals Existence results for some integro-differential equations with state-dependent nonlocal conditions in Fréchet Spaces

2020 ◽  
Vol 7 (1) ◽  
pp. 272-280
Author(s):  
Mamadou Abdoul Diop ◽  
Kora Hafiz Bete ◽  
Reine Kakpo ◽  
Carlos Ogouyandjou
Keyword(s):  
Differential Equations ◽  
Resolvent Operator ◽  
Mild Solutions ◽  
Linear Part ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Fréchet Spaces ◽  
Local Conditions ◽  
State Dependent ◽  
Darbo Fixed Point Theorem

AbstractIn this work, we present existence of mild solutions for partial integro-differential equations with state-dependent nonlocal local conditions. We assume that the linear part has a resolvent operator in the sense given by Grimmer. The existence of mild solutions is proved by means of Kuratowski’s measure of non-compactness and a generalized Darbo fixed point theorem in Fréchet space. Finally, an example is given for demonstration.

Coupled fixed points of nonlinear operators with applications

1987 ◽  
Vol 11 (5) ◽  
pp. 623-632 ◽  
Author(s):  
Dajun Guo ◽  
V. Lakshmikantham
Keyword(s):  
Fixed Points ◽  
Nonlinear Operators ◽  
Coupled Fixed Points
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