Inner boundary value problem with an integral condition for fractional diffusion equation

В данной работе рассматривается нелокальная внутреннекраевая задача для уравнения дробной диффузии с оператором дробного дифференцирования в смысле Римана-Лиувилля с интегральными условиями. Исследуемая задача эквиваленто сведена к системе двух интегральных уравнений Вольтерра второго рода. Доказана теорема существования и единственности решения поставленной задачи. In this paper, we consider a nonlocal interior boundary value problem for the fractional diffusion equation with a fractional differentiation operator in the sense of Riemann-Liouville with integral conditions. The problem under study is equivalently reduced to a system of two Volterra integral equations of the second kind. The theorem of existence and uniqueness of the solution of the posed problem is proved.

Why enterprise resource planning initiatives do succeed in the long run: A case-based causal network

Despite remarkable academic efforts, why Enterprise Resource Planning (ERP) post-implementation success occurs still remains elusive. A reason for this shortage may be the insufficient addressing of an ERP-specific interior boundary condition, i.e., the multi-stakeholder perspective, in explaining this phenomenon. This issue may entail a gap between how ERP success is supposed to occur and how ERP success may actually occur, leading to theoretical inconsistency when investigating its causal roots. Through a case-based, inductive approach, this manuscript presents an ERP success causal network that embeds the overlooked boundary condition and offers a theoretical explanation of why the most relevant observed causal relationships may occur. The results provide a deeper understanding of the ERP success causal mechanisms and informative managerial suggestions to steer ERP initiatives towards long-haul success.

Boundary Conditions that Remove Certain Ultraviolet Divergences

In quantum field theory, Hamiltonians contain particle creation and annihilation terms that are usually ultraviolet (UV) divergent. It is well known that these divergences can sometimes be removed by adding counter-terms and by taking limits in which a UV cutoff tends toward infinity. Here, I review a novel way of removing UV divergences: by imposing a type of boundary condition on the wave function. These conditions, called interior-boundary conditions (IBCs), relate the values of the wave function at two configurations linked by the creation or annihilation of a particle. They allow for a direct definition of the Hamiltonian without renormalization or limiting procedures. In the last section, I review another boundary condition that serves to determine the probability distribution of detection times and places on a time-like 3-surface.

Structural Changes of Circularly Defected Monolayer Circular Graphene Nanosheets Upon Mechanical Vibrations

As the strongest and toughest material known, graphene has found numerous applications in various types of sensors. Due to the great influences of the graphene sheet’s geometry on resonance frequency, circular defects could effect on expected results of sensors. Circular holes in circular graphene sheets (CGSs) have been modeled with molecular dynamics (MD) simulation in the present work. Then the vibration behavior of intact circular plate and circular sheet with the circular defect has been investigated using frequency-domain analysis (FDD). Furthermore, for validating the used method, the obtained natural frequencies for different graphene sheets have been compared with acquired data in former research. The result of validation showed the accuracy of the used method in this study. The results indicated that by increasing the hole size, the natural frequency of a defected sheet with free edges will be diminished, and with simply-supported interior boundary conditions typically went up. Also, by increasing the hole’s eccentricity, the natural frequency of the defected graphene sheet will be diminished when the hole boundary was subjected to simply-support or free condition.

Surface Wave Topography using The 4 Point FDM Simulator

The 2D topography proffers a new challenge of modeling surface waves with a 4-point finite difference (FDM) model. Topographic representation of wave propagation over a certain area will result in loss of accuracy of the numerical model. Then from this the need for appropriate modifications to reduce calculation errors. The existing approach requires value representation as an internal extrapolation solution for temporary exterior conditions. It is finally by providing boundary conditions and initial conditions in the system. However, the scheme sometimes becomes unstable for very irregular topography. 1D extrapolation along the parallel path is known to produce a simple and efficient scheme. During extrapolation, the stability of the 1D hyperbolic Schema improved by disregarding the nearest interior boundary point, which is less than half the lattice distance. Given the limited difference so that the stencils from both sides of the central evaluation point can be used as a 2D form modification if there are not enough inside points. So that in propagation space, waves that move and change according to changes in time. It will be following the wave nature of one source that travels in the x and y fields whose amplitude will change exponentially against propagation time. It is by the nature of surface wave motion.

Mass formulae and staticity condition for dark matter charged black holes

The Arnowitt–Deser–Misner formalism is used to derive variations of mass, angular momentum and canonical energy for Einstein–Maxwell dark matter gravity in which the auxiliary gauge field coupled via kinetic mixing term to the ordinary Maxwell one, which mimics properties of hidden sector. Inspection of the initial data for the manifold with an interior boundary, having topology of $$S^2$$ S 2 , enables us to find the generalised first law of black hole thermodynamics in the aforementioned theory. It has been revealed that the stationary black hole solution being subject to the condition of encompassing a bifurcate Killing horizon with a bifurcation sphere, which is non-rotating, must be static and has vanishing magnetic Maxwell and dark matter sector fields, on static slices of the spacetime under consideration.

Multi-time formulation of particle creation and annihilation via interior-boundary conditions

Interior-boundary conditions (IBCs) have been suggested as a possibility to circumvent the problem of ultraviolet divergences in quantum field theories. In the IBC approach, particle creation and annihilation is described with the help of linear conditions that relate the wave functions of two sectors of Fock space: [Formula: see text] at an interior point [Formula: see text] and [Formula: see text] at a boundary point [Formula: see text], typically a collision configuration. Here, we extend IBCs to the relativistic case. To do this, we make use of Dirac’s concept of multi-time wave functions, i.e. wave functions [Formula: see text] depending on [Formula: see text] space-time coordinates [Formula: see text] for [Formula: see text] particles. This provides the manifestly covariant particle-position representation that is required in the IBC approach. In order to obtain rigorous results, we construct a model for Dirac particles in 1+1 dimensions that can create or annihilate each other when they meet. Our main results are an existence and uniqueness theorem for that model, and the identification of a class of IBCs ensuring local probability conservation on all Cauchy surfaces. Furthermore, we explain how these IBCs relate to the usual formulation with creation and annihilation operators. The Lorentz invariance is discussed and it is found that, apart from a constant matrix (which is required to transform in a certain way), the model is manifestly Lorentz invariant. This makes it clear that the IBC approach can be made compatible with relativity.