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1.
This paper derives a new integral relationship between heat flux and temperature in a transient, two-dimensional heat conducting half space. A unified mathematical treatment is proposed that is extendable to higher-dimensional and finite-region geometries. The analytic expression provides the local heat flux perpendicular to the front surface solely based on an embedded line of temperature sensors parallel to the surface. The relationship does not require apriori knowledge of the surface boundary condition. A new sensor strategy is analytically conceived based on the integral relationship for estimating the local, in-depth heat flux without surface instrumentation. It should further be clarified that the integral relationship requires only knowledge of the local, in-depth temperature and heating/cooling rate (time rate of change of temperature). The resulting formulation is mildly ill-posed and either requires digital filtering of the temperature signal to remove high frequency components of noise or the development of direct heating/cooling rate sensors. This paper (a) develops the new mathematical relationship; (b) demonstrates that the proposed relationship reduces to well-known (i) one-dimensional results under the appropriate assumptions; and, (ii) two-dimensional surface results; and, (c) provides a simple numerical example validating the concept.  相似文献   

2.
We prove certain L p -estimates for Littlewood-Paley functions arising from rough kernels. The estimates are useful for extrapolation to prove L p -boundedness of the Littlewood-Paley functions under a sharp kernel condition.   相似文献   

3.
This paper considers a generalization of an integral introduced by S. Ramanujan in his third notebook. Ramanujan’s integral is itself a version of the dilogarithm,
We prove various functional equations and properties of the generalized integral. 2000 Mathematics Subject Classification Primary–33B30  相似文献   

4.
The free convection boundary-layer flow on a vertical surface in a porous medium with local heat generation proportional to (TT)p, where T is the local temperature and T is the ambient temperature, is considered when the surface is thermally insulated. The way in which the flow develops from the leading edge is seen to depend critically on the exponent p. For p ≤ 2 there is a boundary-layer flow for all x > 0, where x measures distance from the leading edge, with the internal heating having a significant effect at large x. For p ≥ 5 there is also a boundary-layer flow to large x but now the internal heating has an increasingly weaker effect as x increases. For 2 < p <  5 the boundary-layer solution breaks down at a finite x, with a singularity developing leading to thermal runaway at a finite distance along the surface.  相似文献   

5.
6.
We introduce a framework for studying differential operators which are invariant with respect to the real (complex) symplectic Lie algebra ( ), associated to a quaternionic structure on a vector space . To do so, these algebras are realized within the orthogonal Lie algebra . This leads in a natural way to a refinement of the recently introduced notion of complex Hermitean Clifford analysis, in which four variations of the classical Dirac operator play a dominant role. David Eelbode: Postdoctoral fellow supported by the F.W.O. Vlaanderen (Belgium).  相似文献   

7.
In this paper the invariance criterion is applied for the nonlinear equation
(0.1)
where g(u) is a smooth function on u. Some particular set of Lie generators are given. In the case of inviscid Burger’s equation [1]
(0.2)
the Lie projectable symmetry algebra is determined, and the inviscid Burger’s equation will be connected to some order differential equations. The obtained differential equations are solved and some exact solutions of (2) are found. E.H. El Kinani, Junior Associate at The Abdus Salam ICTP, Trieste, Italy.  相似文献   

8.
During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured p-adic analogues to such formulae. Using a combination of ordinary and Gaussian hypergeometric series, we prove one of these conjectures. Received: 11 April 2008  相似文献   

9.
We consider the existence, uniqueness and convergence for the long time solution to the harmonic map heat equation between two complete noncompact Riemannian manifolds, where the target manifold is assumed to have nonpositive curvature. As an application, we solve the Dirichlet problem at infinity for proper harmonic maps between two hyperbolic manifolds for a class of boundary maps. The boundary map under consideration has finite many points at which either it is not differentiable or has vanishing energy density.  相似文献   

10.
The steady mixed convection boundary layer flow over a vertical surface with prescribed heat flux is revisited in this Note. The subset of solutions which can be obtained with the aid of the Reynolds analogy is discussed in a close relationship with the dual solutions reported by Merkin and Mahmood [1] for impermeable, and more recently by Ishak et al. [2], for permeable surfaces.   相似文献   

11.
Let f be an integral homogeneous polynomial of degree d, and let be the level set for each . For a compact subset in ), set
We define the notion of Hardy-Littlewood system for the sequence {Vm}, according as the asymptotic of as coincides with the one predicted by Hardy-Littlewood circle method. Using a recent work of Eskin and Oh [EO], we then show for a large family of invariant polynomialsf, the level sets {Vm} are Hardy-Littlewood. In particular, our results yield a new proof of Siegel mass formula for quadratic forms.  相似文献   

12.
We identify the sporadic simple group M12 and the simple group SL3(3) from some part of their 3-local structure. We also present a graph theoretic analogue of our main theorem. Received: 6 October 2008, Revised: 25 October 2008  相似文献   

13.
We employ the notion of slice monogenic functions to define a new functional calculus for an n-tuple of not necessarily commuting operators. This calculus is consistent with the Riesz-Dunford calculus for a single operator. Received: October, 2007. Accepted: February, 2008.  相似文献   

14.
The rate of deformation for glassy (amorphous) matter confined in microscopic domain at very low temperature regime was investigated using a rate-state-dependent model considering the shear thinning behavior which means, once material being subjected to high shear rates, the viscosity diminishes with increasing shear rate. The preliminary results show that there might be the enhanced rate of deformation and (shear) yield stress due to the almost vanishing viscosity in micropores subjected to some surface conditions: The relatively larger roughness (compared to the macroscopic domain) inside micropores and the slip. As the pore size decreases, the surface-to-volume ratio increases and therefore, surface roughness will greatly affect the (plastic) flow in micropores. By using the boundary perturbation method, we obtained a class of microscopic fields for the rate of deformation and yield stress at low temperature regime with the presumed small wavy roughness distributed along the walls of an annular micropore.  相似文献   

15.
In this work we discuss Schmutz’s conjecture that in dimension 2 to 8 the distinct norms that occur in the lattices with the best known sphere packings are strictly greater than those in any other lattice of the same covolume. We see that the ternary conjecture is not true. However, it seems that there is but one exception: one lattice, where for one length the conjecture fails. Received: 11 February 2008, Revised: 20 May 2008  相似文献   

16.
For a group G, let M(G) denote the near-ring of functions on G. We characterize all maximal subnear-rings of M(G) and show that for many classes of groups, E(G), the near-ring generated by the semigroup, End(G) of G, is never maximal as a subnear-ring of M 0 (G). Received: 25 April 2008  相似文献   

17.
Flower snarks and Goldberg snarks are two infinite families of cyclically 5–edge–connected cubic graphs with girth at least five and chromatic index four. For any odd integer k, k > 3, there is a Flower snark, say J k , of order 4k and a Goldberg snark, say B k , of order 8k. We determine the automorphism groups of J k and B k for every k and prove that they are isomorphic to the dihedral group D 4k of order 4k. Research performed within the activity of INdAM–GNSAGA with the financial support of the Italian Ministry MIUR, project “Strutture Geometriche, Combinatoria e loro Applicazioni”.  相似文献   

18.
Suppose that is a 0-symmetric convex body which denes the usual norm
on . Let also be a measurable set of positive upper density . We show that if the body K is not a polytope, or if it is a polytope with many faces (depending on ), then the distance set
contains all points t t0 for some positive number t0 . This was proved by Furstenberg, Katznelson and Weiss, by Falconer and Marstrand and by Bourgain in the case where K is the Euclidean ball in any dimension greater than 1. As corollaries we obtain (a) an extension to any dimension of a theorem of Iosevich and Laba regarding distance sets with respect to convex bodies of well-distributed sets in the plane, and also (b) a new proof of a theorem of Iosevich, Katz and Tao about the nonexistence of Fourier spectra for smooth convex bodies with positive curvature.  相似文献   

19.
We discuss quadrature domains for subharmonic functions and prove the existence of core quadrature domains for certain positive measures. The core quadrature domains are the smallest quadrature domains as measures and inherit good properties from quadrature domains with finite volume. We next discuss new balayage for the class of harmonic functions integrable in a neighborhood of ∞. We give several estimates of balayage measures. The new balayage is introduced to construct quadrature domains for harmonic functions. Submitted: June 26, 2008. Accepted: July 24, 2008.  相似文献   

20.
We show that the operators of Read’s type on the Hilbert space constructed by Sophie Grivaux and Maria Roginskaya cannot be orbit-reflexive.   相似文献   

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