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11 
Tchebycheff type inequalitiesYalovsky, Morty January 1968 (has links)
No description available.

12 
Causes of gender differences in perceived mathematical abilityRindfleisch, Casie. January 2007 (has links) (PDF)
Thesis PlanB (M.S.)University of WisconsinStout, 2007. / Includes bibliographical references.

13 
Some inequalities with combinatorial applicationsGordon, William Robert January 1961 (has links)
Some inequalities of H. J. Ryser with combinatorial applications are generalized.
Let f be a nonnegative concave symmetric function on vtuples of nonnegative reals. If f has the property that when θa + (1 θ)b ∈ G[subscript f] = f[power 1] ({t:t > 0}), 0 < θ < 1, then f(θa + (1 θ)b) = θf(a) + (1θ)f(b), then we say that f is strictly concave. (Similarly, if f is convex and has the property just mentioned, then we say that f is strictly convex).
Let H be a nonnegative hermitian matrix with eigenvalues λ₁, ..., λ[subscript v], where λ₁ ≧ ... ≧λ[subscript e] > λ[subscript e+1] = … = λ[subscript v] = 0. Let h be an integer, 1 < h, such that e ≦h ≦ v and define k and λ by k = trace (H)/h, λ[subscript h] ≦k + (h1) λ ≦λ₁. Define the matrix B of order h by B = (k λ)I + λJ, where I is the identity matrix all of whose entries are 1's. Let B₀ = B ∔ 0, where the matrix B₀ of order v is the direct sum of the matrix B of order h and the (vh)order zero matrix. Let f(H) denote f(λ₁, … , λ[subscript v]). Then we prove theorems of the following nature.
THEOREM: The matrices H and B₀ satisfy
f(H) ≦ f(B₀).
If f is strictly concave and if (λ₁, ..., λ[subscript v]) ∈ G[subscript f] then equality holds if and only if H and B₀ have the same eigenvalues. If f is strictly concave and if for some integer z, G[subscript f] is the set of nonnegative vectors with at least z positive coordinates and if k + (h1) λ ≠ 0 and z ≦ h or k + (h1)λ = 0 and z < h, then f(H) = f(B₀) if and only if H and B₀ have the same eigenvalues.
If f is convex a similar theorem with the inequality reversed can be proved.
We discuss various choices of the function f and indicate some applications of the results to some combinatorial problems. / Science, Faculty of / Mathematics, Department of / Graduate

14 
A sharp inequality for Poisson's equation in arbitrary domains and its applications to Burgers' equationXie, Wenzheng January 1991 (has links)
Let Ω be an arbitrary open set in IR³. Let  •  denote the L²(Ω) norm, and let [formula omitted] denote the completion of [formula omitted] in the Dirichlet norm  ∇•. The pointwise bound [forumula omitted] is established for all functions [formula omitted] with Δ u є L² (Ω). The constant [formula omitted] is shown to be the best possible.
Previously, inequalities of this type were proven only for bounded smooth domains or convex domains, with constants depending on the regularity of the boundary.
A new method is employed to obtain this sharp inequality. The key idea is to estimate
the maximum value of the quotient ⃒u(x)⃒/  ∇u  ½  Δ u  ½, where the point x is fixed, and the function u varies in the span of a finite number of eigenfunctions of the Laplacian. This method admits generalizations to other elliptic operators and other domains.
The inequality is applied to study the initialboundary value problem for Burgers'
equation:
[formula omitted]
in arbitrary domains, with initial data in [formula omitted]. New a priori estimates are obtained. Adapting and refining known theory for NavierStokes equations, the existence
and uniqueness of bounded smooth solutions are established.
As corollaries of the inequality and its proof, pointwise bounds are given for eigenfunctions
of the Laplacian in terms of the corresponding eigenvalues in two and threedimensional domains. / Science, Faculty of / Mathematics, Department of / Graduate

15 
An inequality in generalized sobolev spacesKanigan, Lawrence Louis January 1967 (has links)
In the study of the spaces (formula omitted) of functions for which the pth powers of all the derivatives up to order ℓ are summable in the domain Ω⊂R, it has been found that there are mutual relations between various spaces. These relations were developed under the name "embedding theorems". The first embedding theorem (for spaces (formula omitted) were proved by Sobolev [3]*. Subsequently these spaces became known as Sobolev Spaces.
However, in the study of existence of solutions for wellposed boundary value problems, there arose the necessity to consider spaces of distributions: an example is the space dual to (formula omitted). For a thorough development of distributions see L. Schwarz's texts [4]. Furthermore, the classes of
Sobolev spaces had to be widened to fractional values of ℓ,
the latter spaces being particularly useful in the study of nonlinear problems.
This thesis follows the development of generalized Sobolev spaces as in Volevich and Panayakh [1]. In section I we prove the basic theorems in this formulation.
In section II, the existence of a function is proved using the formulation of section II. The proof of the
proposition in which a modification has been made was given by Agranovich and Vishik [2]. The proposition is essential to the applications of Sobolev spaces to differential operators. The result states that ll u ll µ ≤ constant ll u,Ω ll µ for (formula omitted) for the particular case when the weighting function is (formula omitted) and Ω is a halfline. (For definitions see section I).
Section III is devoted to a brief comparison of this formulation of Sobolev spaces to other approaches. / Science, Faculty of / Mathematics, Department of / Graduate

16 
On the stability and propagation of barotropic modons in slowly varying mediaSwaters, Gordon Edwin January 1985 (has links)
Two aspects of the theory of barotropic modons are examined in this thesis. First, sufficient neutral stability conditions are derived in the form of an integral constraint for westward and eastwardtravelling modons. It is shown that eastwardtravelling and westwardtravelling modons are neutrally stable to perturbations in which the energy is contained mainly in spectral components with wavenumber magnitudes (ƞ) satisfying ƞ<κ and ƞ>κ, respectively, where κ is the modon wavenumber. These results imply that when κ/ƞ>1 the slope of the neutral stability curve proposed by McWilliams et al.(l98l) for eastwardtravelling modons must begin to increase as κ/ƞ increases. The neutral stability condition is computed with mesoscale wavenumber eddy energy spectra representative of the atmosphere and ocean. Eastwardtravelling atmospheric modons are neutrally stable to the observed seasonally and annuallyaveraged atmospheric eddies. The neutral stability of westwardtravelling atmospheric modons and oceanic modons cannot be inferred on the basis of the observed wavenumber eddy energy spectra for the atmosphere and ocean.
Second, a leading order perturbation theory is developed to describe the propagation of barotropic modons in a slowly varying medium. Two problems are posed and solved. A perturbation solution is obtained describing the propagation of an eastwardtravelling modon modulated by a weak bottom Ekman boundary layer. The results predict that the modon radius and translation speed decay exponentially and that the modon wavenumber increases exponentially, resulting in an exponential amplitude decay in the streamfunction and vorticity. These results agree with the numerical solution of
McWilliams et al.(l98l). A leading order perturbation theory is also developed describing modon propagation over slowly varying topography. Nonlinear hyperbolic equations are derived to describe the evolution of the slowly varying modon radius, translation speed and wavenumber for arbitrary finiteamplitude topography. To leading order, the modon is unaffected by meridional gradients in topography. Analytical perturbation solutions for the modon radius, translation speed and wavenumber are obtained for smallamplitude topography. The perturbations take the form of westward and eastwardtravelling transients and a stationary component proportional to the topography. The general solution is applied to ridgelike and escarpmentlike topographic configurations. / Science, Faculty of / Mathematics, Department of / Graduate

17 
Systems of linear inequalities and equationsUnknown Date (has links)
"This paper is a study of finite systems of homogenous linear inequalities, homogeneous linear equations, and nonhomogeneous equations. To each inequality or equation in one system there corresponds a nonnegative or unrestricted variable in the other and conversely. The array of coefficients in one system is the negative transpose in the other system. This duality furnishes the foundation for the duality of matrix games and linear programming"Introduction. / Typescript. / "June, 1959." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Paul J. McCarthy, Professor Directing Paper. / Includes bibliographical references (leaves 3839).

18 
Tchebycheff type inequalitiesYalovsky, Morty January 1968 (has links)
No description available.

19 
Variational inequalities with the analytic center cutting plane methodDenault, M. (Michel) January 1998 (has links)
No description available.

20 
Best constants in Sobolev and related inequalities. / CUHK electronic theses & dissertations collectionJanuary 2013 (has links)
Chan, Chi Ming. / Thesis (M.Phil.)Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 123125). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

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