Let $G=(V,E)$ be a connected finite graph. We investigate two Bogomol'nyi-Prased-Sommerfeld equations on $G$. We establish necessary and sufficient conditions for the existence and uniqueness of solutions to the two BPS equations.
The presented paper will be proved the necessary and sufficient conditions in order maximal operator of Walsh-Nörlund means with non-increasing weights to be bounded from the dyadic Hardy space $H_{p}(\mathbb{I})$\ to the space $% L_{p}(\mathbb{I})$.
AbstractMailing lists are a major communication channel for supporting developer coordination in open-source software projects. In a recent study, researchers explored temporal relationships (e.g., synchronization) between developer activities on source code and on the mailing list, relying on simple heuristics of developer collaboration (e.g., co-editing files) and developer communication (e.g., sending e-mails to the mailing list). We propose two methods for studying synchronization between collaboration and communication activities from a higher-level perspective, which captures the complex activities and views of developers more precisely than the rather technical perspective of previous work. On the one hand, we explore developer collaboration at the level of features (not files), which are higher-level concepts of the domain and not mere technical artifacts. On the other hand, we lift the view of developer communication from a message-based model, which treats each e-mail individually, to a conversation-based model, which is semantically richer due to grouping e-mails that represent conceptually related discussions. By means of an empirical study, we investigate whether the different abstraction levels affect the observed relationship between commit activity and e-mail communication using state-of-the-art time-series analysis. For this purpose, we analyze a combined history of 40 years of data for three highly active and widely deployed open-source projects:QEMU,BusyBox, andOpenSSL. Overall, we found evidence that a higher-level view on the coordination of developers leads to identifying a stronger statistical dependence between the technical activities of developers than a less abstract and rather technical view.
In the present paper, we investigate the regularity and symmetry properties of weak solutions to semilinear elliptic equations which are locally stable.
An obsession with origins is a hallmark of pseudoarchaeology, while the celebration of arbitrary anniversaries is one of the more meaningless conceits of the heritage industry. In that spirit, I would like to wish a happy tenth anniversary to AP: Online Journal in Public Archaeology, and to extend my warmest congratulations to the editorial team.
We consider the PDE $-Δ_pu=ρ$, where $ρ$ is a signed Borel measure on $\mathbb{R}^n$. For each $p>n$, we characterize solutions as extremals of a generalized Morrey inequality determined by $ρ$.
We consider the linear Zakharov-Kuznetsov equation on a rectangle with a left Dirich-let boundary control. Using the flatness approach, we prove the null controllability of this equation and provide a space of analytic reachable states.
We propose a time fractional extension of the Schr{ö}dinger equation that keeps the main mechanical and quantum properties of the classical Schr{ö}dinger equation. This extension is shown to be equivalent to another well identified time first order PDE with fractional hamiltonian.
Blowup analysis for solutions of a general evolution equation with nonlocal diffusion and localized source is performed. By comparison with recent results on global-in-time solutions, a dichotomy result is obtained.
We establish the existence and uniqueness of variational solution to the nonlinear Neumann boundary problem for the $p^{th}$-Sub-Laplacian associated to a system of Hörmander vector fields
We prove in this article that functions satisfying a dynamic programming principle have a local interior Lipschitz type regularity. This DPP is partly motivated by the connection to the normalized parabolic $p$-Laplace operator.
In this paper, we prove a time dependent lower bound on density in the optimal order $O(1/(1+t))$ for the general smooth nonisentropic flow of compressible Euler equations.
In this paper, we present a new argument (see Lemma 3.4) that allows us to simplify the proof of stability of peakons established in Lin and Liu (2009) (Theorem 1.1).
This paper studies the convergence rates in $L^2$ and $H^1$ of Dirichelt problems for Stokes systems with rapidly oscillating periodic coefficients, without any regularity assumptions on the coefficients.
We give the new connection formula for the divergent bilateral basic hypergeometric series ${}_2ψ_2(a_1,a_2;b_1;q,x)$ by the using of the $q$-Borel-Laplace resummation method and Slater's formula. The connection coefficients are given by elliptic functions.
An initial-boundary value in a strip with homogeneous Dirichlet boundary conditions for two-dimensional Zakharov-Kuznetsov-Burgers equation is considered. Results on global well-posedness and long-time decay of solutions in Sobolev spaces are established.