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131.
This paper is devoted to proving the existence and uniqueness of solutions to Cauchy type problems for fractional differential equations with composite fractional derivative operator on a finite interval of the real axis in spaces of summable functions. An approach based on the equivalence of the nonlinear Cauchy type problem to a nonlinear Volterra integral equation of the second kind and applying a variant of the Banach’s fixed point theorem to prove uniqueness and existence of the solution is presented. The Cauchy type problems for integro-differential equations of Volterra type with composite fractional derivative operator, which contain the generalized Mittag-Leffler function in the kernel, are considered. Using the method of successive approximation, and the Laplace transform method, explicit solutions of the open problem proposed by Srivastava and Tomovski (2009) [11] are established in terms of the multinomial Mittag-Leffler function. 相似文献
132.
Brahim Amaziane Mladen Jurak Ana Žgaljić Keko 《Journal of Computational and Applied Mathematics》2012
We present an approach and numerical results for a new formulation modeling immiscible compressible two-phase flow in heterogeneous porous media with discontinuous capillary pressures. The main feature of this model is the introduction of a new global pressure, and it is fully equivalent to the original equations. The resulting equations are written in a fractional flow formulation and lead to a coupled degenerate system which consists of a nonlinear parabolic (the global pressure) equation and a nonlinear diffusion–convection one (the saturation equation) with nonlinear transmission conditions at the interfaces that separate different media. The resulting system is discretized using a vertex-centred finite volume method combined with pressure and flux interface conditions for the treatment of heterogeneities. An implicit Euler approach is used for time discretization. A Godunov-type method is used to treat the convection terms, and the diffusion terms are discretized by piecewise linear conforming finite elements. We present numerical simulations for three one-dimensional benchmark tests to demonstrate the ability of the method to approximate solutions of water–gas equations efficiently and accurately in nuclear underground waste disposal situations. 相似文献
133.
Let K = {K
0
,... ,K
k
} be a family of convex bodies in R
n
, 1≤ k≤ n-1 . We prove, generalizing results from [9], [10], [13], and [14], that there always exists an affine k -dimensional plane A
k
(subset, dbl equals) R
n
, called a common maximal k-transversal of K , such that, for each i∈ {0,... ,k} and each x∈ R
n
, where V
k
is the k -dimensional Lebesgue measure in A
k
and A
k
+x . Given a family K = {K
i
}
i=0
l
of convex bodies in R
n
, l < k , the set C
k
( K ) of all common maximal k -transversals of K is not only nonempty but has to be ``large' both from the measure theoretic and the topological point of view. It is shown
that C
k
( K ) cannot be included in a ν -dimensional C
1
submanifold (or more generally in an ( H
ν
, ν) -rectifiable, H
ν
-measurable subset) of the affine Grassmannian AGr
n,k
of all affine k -dimensional planes of R
n
, of O(n+1) -invariant ν -dimensional (Hausdorff) measure less than some positive constant c
n,k,l
, where ν = (k-l)(n-k) . As usual, the ``affine' Grassmannian AGr
n,k
is viewed as a subspace of the Grassmannian Gr
n+1,k+1
of all linear (k+1) -dimensional subspaces of R
n+1
. On the topological side we show that there exists a nonzero cohomology class θ∈ H
n-k
(G
n+1,k+1
;Z
2
) such that the class θ
l+1
is concentrated in an arbitrarily small neighborhood of C
k
( K ) . As an immediate consequence we deduce that the Lyusternik—Shnirel'man category of the space C
k
( K ) relative to Gr
n+1,k+1
is ≥ k-l . Finally, we show that there exists a link between these two results by showing that a cohomologically ``big' subspace
of Gr
n+1,k+1
has to be large also in a measure theoretic sense.
Received May 22, 1998, and in revised form March 27, 2000. Online publication September 22, 2000. 相似文献
134.
Ivana Djurišić Dr. Miloš S. Dražić Dr. Aleksandar Ž. Tomović Dr. Marko Spasenović Dr. Željko Šljivančanin Dr. Vladimir P. Jovanović Dr. Radomir Zikic 《Chemphyschem》2021,22(3):336-341
Functionalization of electrodes is a wide-used strategy in various applications ranging from single-molecule sensing and protein sequencing, to ion trapping, to desalination. We demonstrate, employing non-equilibrium Green′s function formalism combined with density functional theory, that single-species (N, H, S, Cl, F) termination of graphene nanogap electrodes results in a strong in-gap electrostatic field, induced by species-dependent dipoles formed at the electrode ends. Consequently, the field increases or decreases electronic transport through a molecule (benzene) placed in the nanogap by shifting molecular levels by almost 2 eV in respect to the electrode Fermi level via a field effect akin to the one used for field-effect transistors. We also observed the local gating in graphene nanopores terminated with different single-species atoms. Nitrogen-terminated nanogaps (NtNGs) and nanopores (NtNPs) show the strongest effect. The in-gap potential can be transformed from a plateau-like to a saddle-like shape by tailoring NtNG and NtNP size and termination type. In particular, the saddle-like potential is applicable in single-ion trapping and desalination devices. 相似文献
135.
Foundations of Computational Mathematics - In 1995 Jean-Claude Hausmann proved that a compact Riemannian manifold X is homotopy equivalent to its Rips complex $${\text {Rips}}(X,r)$$ for small... 相似文献
136.
The (π ?,K +) reaction is proposed as an optimalσ-hypernuclear production process on nuclear tagets. Several ingredients of this process are discussed in connection with the choice of appropriate target nuclei. For demonstration, the excitation functions are calculated for the (π ?,K +) reaction on the56Fe and28Si targets by assuming a shallowσ well depth, varying the spin-orbit strength and smearing (conversion) widths. 相似文献
137.
138.
139.
The temperature dependences of the14N nuclear quadrupole resonance frequencies have been measured in phases II, III, IV and V of ammonium nitrate with the help of the1H–14H nuclear quadrupole double resonance technique. The experimental results are related to the proposed crystal structures and disorder in the various crystallographic phases. 相似文献
140.
This paper reports on the results attained in the determination of the mechanism of oxidation of molybdenum sulphide under
non-isothermal conditions in an air atmosphere. The mechanism of the process was determined by simultaneous DTA-TG-DTG, and
the kinetic parameters of the reactions involved were obtained according to the methods of Kissinger and Ozawa.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献