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This manuscript deals with the global existence and asymptotic behavior of solutions for a Kirchhoff beam equation with internal damping. The existence of solutions is obtained by using the Faedo-Galerkin method. Exponential stability is proved by applying Nakao’s theorem.
We consider hypersphere x = x(u, v, w) in the four dimensional Euclidean space. We calculate the Gauss map, and the curvatures of it. Moreover, we compute the second Laplace-Beltrami operator the hypersphere satisfying ΔIIx = Ax, where A ϵ Mat (4,4).
In this paper, we show a Marcinkiewicz type interpolation theorem for Orlicz spaces. As an application, we obtain an existence result for a parabolic equation in divergence form.
Extending Blaschke and Lebesgue’s classical result in the Euclidean plane, it has been recently proved in spherical and the hyperbolic cases, as well, that Reuleaux triangles have the minimal area among convex domains of constant width D. We prove an essentially optimal stability version of this statement in each of the three types of surfaces of constant curvature. In addition, we summarize the fundamental properties of convex bodies of constant width in spaces of constant curvature, and provide a characterization in the hyperbolic case in terms of horospheres.
Let P be a set of n points in general position in the plane. Let R be a set of points disjoint from P such that for every x, y € P the line through x and y contains a point in R. We show that if
We use the same approach to show a similar result in the case where each of B and G is a set of n points in general position in the plane and every line through a point in B and a point in G passes through a point in R. This provides a partial answer to a problem of Karasev.
The bound
Let E, G be Fréchet spaces and F be a complete locally convex space. It is observed that the existence of a continuous linear not almost bounded operator T on E into F factoring through G causes the existence of a common nuclear Köthe subspace of the triple (E, G, F). If, in addition, F has the property (y), then (E, G, F) has a common nuclear Köthe quotient.
In this paper we study the sum
In this paper we derive new inequalities involving the generalized Hardy operator. The obtained results generalized known inequalities involving the Hardy operator. We also get new inequalities involving the classical Hardy–Hilbert inequality.
The bipartite domination number of a graph is the minimum size of a dominating set that induces a bipartite subgraph. In this paper we initiate the study of this parameter, especially bounds involving the order, the ordinary domination number, and the chromatic number. For example, we show for an isolate-free graph that the bipartite domination number equals the domination number if the graph has maximum degree at most 3; and is at most half the order if the graph is regular, 4-colorable, or has maximum degree at most 5.
This study proposes a new family of continuous distributions, called the Gudermannian generated family of distributions, based on the Gudermannian function. The statistical properties, including moments, incomplete moments and generating functions, are studied in detail. Simulation studies are performed to discuss and evaluate the maximum likelihood estimations of the model parameters. The regression model of the proposed family considering the heteroscedastic structure of the scale parameter is defined. Three applications on real data sets are implemented to convince the readers in favour of the proposed models.
