Convergence of Ces�ro means of negative order of functions of bounded generalized second variation

1976 ◽  
Vol 20 (5) ◽  
pp. 914-922
Author(s):  
T. I. Akhobadze
Keyword(s):  
Second Variation ◽  
Negative Order

EPIZOOTOLOGICAL FEATURES OF MODERN CATTLE LEUKEMIA

1970 ◽  
pp. 53-58
Author(s):  
V. V. Makarov ◽  
D. A. Lozovoy
Keyword(s):  
Dairy Cattle ◽  
Western Europe ◽  
Control Programs ◽  
Foreign Countries ◽  
Negative Order ◽  
Dairy Cattle Breeding ◽  
The Usa ◽  
Epizootic Process ◽  
National Programs

  Enzootic bovine leucosis (EBL) has been known for more than a century and a half. Its occurrence and registration may have historically been associated with intensive breeding of dairy cattle in Western Europe to increase target productivity. It is known that any limiting intervention in the nature of the animal organism is always accompanied by an uncontrolled and unpredictable change in the genotype of a wider range than the required, particularly negative order. In particular, a decrease in the resistance to macroorganisms and the possibility of the new diseases emergence, including infectious ones (for example, immunodeficiencies such as BLAD syndrome of black-motley cattle and stress syndrome in pigs, the occurrence of scrapie and other slow sheep infections). In the last two decades of the last century, in many disadvantaged countries, primarily Western European, national programs for the eradication of EBL have been developed and subsequently successfully implemented. First of all the motivation was the economy of dairy cattle breeding (mainly the extension of productive age, as well as the tightening of requirements in international trade in cattle and bull products, breeding, pricing, etc.). In an analytical article are reviewed the elements of epizootology of EBL in the foreign countries with special attention to the situation in the USA, scenarios of various control programs, and promising methods for assessing the role of infected animals in the epizootic process. A critical assessment of the problem of EBL in the Russian Federation is given, the reasons for the ineffectiveness of against leucosis measures are discussed.

scholarly journals Lie Group Method for Solving the Negative-Order Kadomtsev–Petviashvili Equation (nKP)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 224
Author(s):  
Ghaylen Laouini ◽  
Amr M. Amin ◽  
Mohamed Moustafa
Keyword(s):  
Lie Group ◽  
Traveling Wave ◽  
Invariant Solution ◽  
Traveling Wave Solutions ◽  
Group Method ◽  
Lie Group Method ◽  
Reduced Equations ◽  
Wave Solutions ◽  
Negative Order ◽  
Petviashvili Equation

A comprehensive study of the negative-order Kadomtsev–Petviashvili (nKP) partial differential equation by Lie group method has been presented. Initially the infinitesimal generators and symmetry reduction, which were obtained by applying the Lie group method on the negative-order Kadomtsev–Petviashvili equation, have been used for constructing the reduced equations. In particular, the traveling wave solutions for the negative-order KP equation have been derived from the reduced equations as an invariant solution. Finally, the extended improved (G′/G) method and the extended tanh method are described and applied in constructing new explicit expressions for the traveling wave solutions. Many new and more general exact solutions are obtained.

scholarly journals Variational formulations of steady rotational equatorial waves

2020 ◽  
Vol 10 (1) ◽  
pp. 534-547
Author(s):  
Jifeng Chu ◽  
Joachim Escher
Keyword(s):  
Linear Stability ◽  
Stream Function ◽  
Water Waves ◽  
Variational Formulation ◽  
Energy Functional ◽  
Equatorial Waves ◽  
Second Variation ◽  
Governing Equations ◽  
The Second Variation ◽  
Variational Formulations

Abstract When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional 𝓗 in terms of the stream function and the thermocline. We also compute the second variation of the constrained energy functional, which is related to the linear stability of steady water waves.

The Einstein pseudo-tensor and the flux integral for perturbed static space-times

1991 ◽  
Vol 435 (1895) ◽  
pp. 645-657 ◽  
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Second Variation ◽  
Common Procedure ◽  
Static Vacuum ◽  
Linear Perturbations ◽  
Maxwell Space ◽  
The Common ◽  
Static Space

The flux integral for axisymmetric polar perturbations of static vacuum space-times, derived in an earlier paper directly from the relevant linearized Einstein equations, is rederived with the aid of the Einstein pseudo-tensor by a simple algorism. A similar earlier effort with the aid of the Landau–Lifshitz pseudo-tensor failed. The success with the Einstein pseudo-tensor is due to its special distinguishing feature that its second variation retains its divergence-free property provided only the equations governing the static space-time and its linear perturbations are satisfied. When one seeks the corresponding flux integral for Einstein‒Maxwell space-times, the common procedure of including, together with the pseudo-tensor, the energy‒momentum tensor of the prevailing electromagnetic field fails. But, a prescription due to R. Sorkin, of including instead a suitably defined ‘Noether operator’, succeeds.

scholarly journals Lp-Lq estimates off the line of duality

1995 ◽  
Vol 58 (2) ◽  
pp. 154-166 ◽  
Author(s):  
J.-G. Bak ◽  
D. McMichael ◽  
D. Oberlin
Keyword(s):  
Sobolev Inequalities ◽  
Riesz Means ◽  
Negative Order

AbstractTheorems 1 and 2 are known results concerning Lp–Lq estimates for certain operators wherein the point (1/p, 1/q) lies on the line of duality 1/p + 1/q = 1. In Theorems 1′ and 2′ we show that with mild additional hypotheses it is possible to prove Lp-Lq estimates for indices (1/p, 1/q) off the line of duality. Applications to Bochner-Riesz means of negative order and uniform Sobolev inequalities are given.

Second-variation methods in dynamic optimization

1969 ◽  
Vol 3 (3) ◽  
pp. 164-173 ◽  
Author(s):  
A. G. Longmuir ◽  
E. V. Bohn
Keyword(s):  
Dynamic Optimization ◽  
Second Variation
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