共查询到20条相似文献,搜索用时 15 毫秒
1.
Jay I. Frankel Majid Keyhani Rao V. Arimilli Jayne Wu 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,57(2):869-888
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.
Shuichi Sato 《Integral Equations and Operator Theory》2008,62(3):429-440
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.
Jeffrey L. Meyer 《The Ramanujan Journal》2007,14(1):79-88
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.
J. H. Merkin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(3):543-564
The free convection boundary-layer flow on a vertical surface in a porous medium with local heat generation proportional to
(T – T∞)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.
David Eelbode 《Advances in Applied Clifford Algebras》2007,17(4):635-649
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
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]
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
(0.1) |
(0.2) |
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.
Jiaping Wang 《Journal of Geometric Analysis》1998,8(3):485-514
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.
Fabrizio Colombo Irene Sabadini Daniele C. Struppa 《Advances in Applied Clifford Algebras》2009,19(2):225-236
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.
Z. Kwang-Hua Chu 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(3):529-542
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.
Thomas A. Willging 《Archiv der Mathematik》2008,91(4):323-329
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.
C. J. Maxson 《Archiv der Mathematik》2008,91(5):385-391
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.
Makoto Sakai 《Complex Analysis and Operator Theory》2009,3(2):525-549
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.
Jean Esterle 《Integral Equations and Operator Theory》2009,63(4):591-593
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