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By
Long, Jianren; Wu, Tingmi; Wu, Xiubi
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We study the growth of solutions of
$$f''+A(z)f'+B(z)f=0$$
, where A(z) and B(z) are nontrivial solutions of another secondorder complex differential equations. Some conditions guaranteeing that every nontrivial solution of the equation is of infinite order are obtained, in which the notion of accumulation rays of the zero sequence of entire functions is used.
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By
Klein, Nicolas
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The present article provides some additional results for the twoplayer game of strategic experimentation with threearmed exponential bandits analyzed in Klein (Games Econ Behav 82:636–657, 2013). Players play replica bandits, with one safe arm and two risky arms, which are known to be of opposite types. It is initially unknown, however, which risky arm is good and which is bad. A good risky arm yields lump sums at exponentially distributed times when pulled. A bad risky arm never yields any payoff. In this article, I give a necessary and sufficient condition for the state of the world eventually to be found out with probability 1 in any Markov perfect equilibrium in which at least one player’s value function is continuously differentiable. Furthermore, I provide closedform expressions for the players’ value function in a symmetric Markov perfect equilibrium for low and intermediate stakes.
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By
Belgacem, F. Ben; Girault, V.; Jelassi, F.
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The variational finite element solution of Cauchy’s problem, expressed in the Steklov–Poincaré framework and regularized by the Lavrentiev method, has been introduced and computationally assessed in Azaïez et al. (Inverse Probl Sci Eng 18:1063–1086, 2011). The present work concentrates on the numerical analysis of the semidiscrete problem. We perform the mathematical study of the error to rigorously establish the convergence of the global biasvariance error.
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By
Fortney, Jon Pierre
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The generalized version of Stokes’ theorem,
Stokes’ theorem
henceforth simply called Stokes’ theorem, is an extraordinarily powerful and useful tool in mathematics. We have already encountered it in Sect.
9.5
where we found a common way of writing the fundamental theorem of line integrals,
Fundamental theorem of line integrals
the vector calculus version of Stokes’ theorem,
Stokes’ theorem
vector calculus version
and the divergence theorem
Divergence theorem
as ∫_{M}dα =∫_{∂M}α. More precisely Stokes’ theorem can be stated as follows.
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By
Golasiński, Marek; Melo, Thiago; Santos, Edivaldo L.
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We estimate the number of homotopy types of pathcomponents of the mapping spaces
$$M(\mathbb {S}^m,\mathbb {F}P^n)$$
from the msphere
$$\mathbb {S}^m$$
to the projective space
$$\mathbb {F}P^n$$
for
$$\mathbb {F}$$
being the real numbers
$$\mathbb {R}$$
, the complex numbers
$$\mathbb {C}$$
, or the skew algebra
$$\mathbb {H}$$
of quaternions. Then, the homotopy types of pathcomponents of the mapping spaces
$$M(E\Sigma ^m,\mathbb {F}P^n)$$
for the suspension
$$E\Sigma ^m$$
of a homology msphere
$$\Sigma ^m$$
are studied as well.
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By
Du, Feng; Wang, Qiaoling; Adriano, Levi; Pereira, Rosane Gomes
Show all (4)
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In this paper, we investigate the eigenvalue problem of the Markov diffusion operator
$$\mathfrak {L}$$
and
$$\mathfrak {L}^2$$
, respectively. Firstly, we obtain some general inequalities for eigenvalues of the operator
$$\mathfrak {L}$$
and
$$\mathfrak {L}^2$$
on a diffusion Markov triple, respectively. By applying these inequalities, we then get some universal inequalities for eigenvalues of a special Markov diffusion operator
$$\mathfrak {L}$$
and
$$\mathfrak {L}^2$$
on bounded domains in a Euclidean space. Finally, we prove a Lichnerowicz type inequality for the Markov diffusion operator on a diffusion Markov triple.
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By
Botvinnik, Boris; Kazaras, Demetre
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Let (Y, g) be a compact Riemannian manifold of positive scalar curvature (psc). It is wellknown, due to Schoen–Yau, that any closed stable minimal hypersurface of Y also admits a pscmetric. We establish an analogous result for stable minimal hypersurfaces with free boundary. Furthermore, we combine this result with tools from geometric measure theory and conformal geometry to study pscbordism. For instance, assume
$$(Y_0,g_0)$$
and
$$(Y_1,g_1)$$
are closed pscmanifolds equipped with stable minimal hypersurfaces
$$X_0 \subset Y_0$$
and
$$X_1\subset Y_1$$
. Under natural topological conditions, we show that a pscbordism
$$(Z,{\bar{g}}) : (Y_0,g_0)\rightsquigarrow (Y_1,g_1)$$
gives rise to a pscbordism between
$$X_0$$
and
$$X_1$$
equipped with the pscmetrics given by the Schoen–Yau construction.
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By
Fuller, Jessica; Gould, Ronald J.
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1 Citations
Given a graph H, we say a graph G is Hsaturated if G does not contain H as a subgraph and the addition of any edge
$$e'\not \in E(G)$$
results in H as a subgraph. In this paper, we construct
$$(K_4e)$$
saturated graphs with E(G) either the size of a complete bipartite graph, a 3partite graph, or in the interval
$$\left[ 2n4, \left\lfloor \frac{n}{2}\right\rfloor \left\lceil \frac{n}{2}\right\rceil n+6\right] $$
. We then extend the
$$(K_4e)$$
saturated graphs to
$$(K_te)$$
saturated graphs.
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By
Jha, Navnit; Gopal, Venu; Singh, Bhagat
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In this article, a family of high order accurate compact finite difference scheme for obtaining the approximate solution values of mildly nonlinear elliptic boundary value problems in threespace dimensions has been developed. The discretization formula is developed on a nonuniform meshes, which helps in resolving boundary and/or interior layers. The scheme involves 27 points single computational cell to achieve high order truncation errors. The proposed scheme has been applied to solve convection–diffusion equation, Helmholtz equation and nonlinear Poisson’s equation. A detailed convergence theory for the new compact scheme has been proposed using irreducible and monotone property of the iteration matrix. Numerical results show that the new compact scheme exhibit better performance in terms of
$$l^\infty $$
 and
$$l^2$$
error of the exact and approximate solution values.
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