Conditionally Negative Definite Functions
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DOI: 10.1007/s00009-018-1239-0
Abstract: Let $$f:[0,\infty )\rightarrow [0,\infty )$$f:[0,∞)→[0,∞) be an operator monotone function and $$g: \mathbb {R}\rightarrow [0,\infty )$$g:R→[0,∞) be a conditionally negative definite(in short cnd) function. We obtain that $$f\circ g:\mathbb {R}\rightarrow [0,\infty )$$f∘g:R→[0,∞) is also conditionally… read more here.
Keywords: conditionally negative; negative definite; definite functions; rightarrow infty ... See more keywords
Asymptotic Behaviour of Cuboids Optimising Laplacian Eigenvalues
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DOI: 10.1007/s00020-017-2407-5
Abstract: We prove that in dimension $$n \ge 2$$n≥2, within the collection of unit-measure cuboids in $$\mathbb {R}^n$$Rn (i.e. domains of the form $$\prod _{i=1}^{n}(0, a_n)$$∏i=1n(0,an)), any sequence of minimising domains $$R_k^\mathcal {D}$$RkD for the Dirichlet… read more here.
Keywords: cuboids optimising; asymptotic behaviour; rightarrow infty; laplacian eigenvalues ... See more keywords
Global m-Equivariant Solutions of Nematic Liquid Crystal Flows in Dimension Two
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DOI: 10.1007/s00205-017-1144-x
Abstract: AbstractIn this article we construct a global solution of the simplified Ericksen-Leslie system. We show that the velocity of the solution can be decomposed into the sum of three parts. The main flow is governed… read more here.
Keywords: rightarrow infty; solutions nematic; global equivariant; equivariant solutions ... See more keywords
Tauberian theorems for iterations of weighted mean summable integrals
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DOI: 10.1007/s11117-018-0603-4
Abstract: Let p be a positive weight function on $$A:=[1, \infty )$$A:=[1,∞) which is integrable in Lebesgue’s sense over every finite interval (1, x) for $$11$$x>1, $$P(1)=0$$P(1)=0 and $$P(x) \rightarrow \infty $$P(x)→∞ as $$x \rightarrow \infty $$x→∞.… read more here.
Keywords: rightarrow infty; tauberian theorems; weighted mean; lim rightarrow ... See more keywords