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On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation
M. Z. Rahman,
A.B.M. Shamim. Ul Hasan
Issue:
Volume 2, Issue 3, June 2013
Pages:
110-118
Received:
24 April 2013
Published:
30 May 2013
Abstract: In a beforehand paper they found some exact and explicit solutions for the standard Rossby form of the equation for the stream function for some specified and realistic wind stress. This equation, which is a third order linear partial differential equation for the stream function, relates the rate of change of vertical vortices to the curl of the applied wind stress. The equation involves the gradient of the Coriolis parameter and has particular relevance to the equatorial region, such as the North Indian Ocean. Some interesting physical properties of the solutions are considered. In this paper we find some more complicated but similar exact and explicit solutions. Some properties for these solutions are derived which are in some sense complementary to the kind of properties of the simpler solutions considered in advance.
Abstract: In a beforehand paper they found some exact and explicit solutions for the standard Rossby form of the equation for the stream function for some specified and realistic wind stress. This equation, which is a third order linear partial differential equation for the stream function, relates the rate of change of vertical vortices to the curl of the a...
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Strong Reflection Principles and Large Cardinal Axioms
J. Foukzon,
E. R Men’kova
Issue:
Volume 2, Issue 3, June 2013
Pages:
119-127
Received:
18 May 2013
Published:
10 June 2013
Abstract: In this article an possible generalization of the Löb’s theorem is considered. We proved so-called uniform strong reflection principle corresponding to formal theories which has ω-models.Main result is: let κ be an inaccessible cardinal and H_κ is a set of all sets having hereditary size less than κ,then:"¬Con" ("ZFC+" ("V=" "H" _"κ" ) )
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Refutation Of Hard-Determinable Formulas In The System “Resolution Over Linear Equations” And Its Generalization
Anahit Chubaryan,
Armine Chubaryan,
Arman Tshitoyan
Issue:
Volume 2, Issue 3, June 2013
Pages:
128-133
Received:
11 May 2013
Published:
20 June 2013
Abstract: We research the power of the propositional proof system R(lin) (Resolution over Linear Equations) described by Ran Raz and Iddo Tzameret. R (lin) is the generalization of R (Resolution System) and it is known that many tautologies, which require the exponential lower bounds of proof complexities in R, have polynomially bounded proofs in R (lin). We show that there are the sequences of unsatisfiable collections of disjuncts of linear equations, which require exponential lower bounds in R (lin). After adding the renaming rule, mentioned collections have polynomially bounded refutations.
Abstract: We research the power of the propositional proof system R(lin) (Resolution over Linear Equations) described by Ran Raz and Iddo Tzameret. R (lin) is the generalization of R (Resolution System) and it is known that many tautologies, which require the exponential lower bounds of proof complexities in R, have polynomially bounded proofs in R (lin). We...
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An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique
Bolujo Joseph Adegboyegun
Issue:
Volume 2, Issue 3, June 2013
Pages:
134-139
Received:
23 June 2013
Published:
10 July 2013
Abstract: In this article, Adomian’s Decomposition Method (ADM) is employed to approximate the solution of Burgers’ equationwhich is one-dimensional non-linear differential equations in fluid dynamics. The exact solution for Burger’s equation with low kinematic viscosity does not exist in the literatures.Thus, we obtained an explicit solution for this special case. We compared our solution using ADM with the exact solution and the existing numerical solution while .We found out that ADM converges very rapidly to the exact solution and performed better than the existing numerical method.
Abstract: In this article, Adomian’s Decomposition Method (ADM) is employed to approximate the solution of Burgers’ equationwhich is one-dimensional non-linear differential equations in fluid dynamics. The exact solution for Burger’s equation with low kinematic viscosity does not exist in the literatures.Thus, we obtained an explicit solution for this spec...
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