scholarly journals UNIPOTENT REDUCTION AND THE POINCARÉ PROBLEM

2006 ◽  
Vol 17 (08) ◽  
pp. 949-962
Author(s):  
ALEXIS G. ZAMORA
Keyword(s):  
Linear Part ◽  
General Fiber ◽  
Poincaré Problem

Given a fibration f : S → ℙ1, and the associated foliation [Formula: see text], the problem of bounding the genus of the general fiber of f in terms of the sheaf [Formula: see text] is studied. Using unipotent reduction of f, several bounds are obtained, under positivity assumptions on [Formula: see text]. In Sec.4, the Poincaré problem is solved, for non-degenerate [Formula: see text], assuming that all the eigenvalues of the linear part of [Formula: see text] near singularities are greater than 3.

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.

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 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.

scholarly journals Dispersive Estimates for Full Dispersion KP Equations

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Didier Pilod ◽  
Jean-Claude Saut ◽  
Sigmund Selberg ◽  
Achenef Tesfahun
Keyword(s):  
Stationary Phase ◽  
Initial Value Problem ◽  
Bessel Functions ◽  
Linear Part ◽  
Independent Interest ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Initial Value ◽  
Kp Equations ◽  
Well Posed

AbstractWe prove several dispersive estimates for the linear part of the Full Dispersion Kadomtsev–Petviashvili introduced by David Lannes to overcome some shortcomings of the classical Kadomtsev–Petviashvili equations. The proof of these estimates combines the stationary phase method with sharp asymptotics on asymmetric Bessel functions, which may be of independent interest. As a consequence, we prove that the initial value problem associated to the Full Dispersion Kadomtsev–Petviashvili is locally well-posed in $$H^s(\mathbb R^2)$$ H s ( R 2 ) , for $$s>\frac{7}{4}$$ s > 7 4 , in the capillary-gravity setting.

scholarly journals Tropical geometry and the motivic nearby fiber

2011 ◽  
Vol 148 (1) ◽  
pp. 269-294 ◽  
Author(s):  
Eric Katz ◽  
Alan Stapledon
Keyword(s):  
Euler Characteristic ◽  
Hodge Structure ◽  
Tropical Geometry ◽  
Mixed Hodge Structure ◽  
General Fiber ◽  
Algebraic Torus ◽  
Tropical Varieties

AbstractWe construct motivic invariants of a subvariety of an algebraic torus from its tropicalization and initial degenerations. More specifically, we introduce an invariant of a compactification of such a variety called the ‘tropical motivic nearby fiber’. This invariant specializes in the schön case to the Hodge–Deligne polynomial of the limit mixed Hodge structure of a corresponding degeneration. We give purely combinatorial expressions for this Hodge–Deligne polynomial in the cases of schön hypersurfaces and matroidal tropical varieties. We also deduce a formula for the Euler characteristic of a general fiber of the degeneration.

scholarly journals The diminished base locus is not always closed

2014 ◽  
Vol 150 (10) ◽  
pp. 1729-1741 ◽  
Author(s):  
John Lesieutre
Keyword(s):  
Blow Up ◽  
Weak Sense ◽  
Prime Divisors ◽  
General Fiber ◽  
Base Locus ◽  
The Family

AbstractWe exhibit a pseudoeffective $\mathbb{R}$-divisor ${D}_{\lambda }$ on the blow-up of ${\mathbb{P}}^{3}$ at nine very general points which lies in the closed movable cone and has negative intersections with a set of curves whose union is Zariski dense. It follows that the diminished base locus ${\boldsymbol{B}}_{-}({D}_{\lambda })={\bigcup }_{A\,\text{ample}}\boldsymbol{B}({D}_{\lambda }+A)$ is not closed and that ${D}_{\lambda }$ does not admit a Zariski decomposition in even a very weak sense. By a similar method, we construct an $\mathbb{R}$-divisor on the family of blow-ups of ${\mathbb{P}}^{2}$ at ten distinct points, which is nef on a very general fiber but fails to be nef over countably many prime divisors in the base.

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