It is well known that the supercritical state of a gas has great dissolving capacity. In this paper, the mathematical reason for this phenomenon is studied in great detail.
We consider interior and exterior initial boundary value problems for the three-dimensional wave (d’Alembert) equation. First, we reduce a given problem to an equivalent operator equation with respect to unknown sources deﬁned only at the boundary of the original domain. In doing so, the Huygens’ principle enables us to obtain the operator equation in a form that involves only ﬁnite and non-increasing pre-history of the solution in time. Next, we discretize the resulting boundary equation and solve it eﬃciently by the method of difference potentials (MDP). The overall numerical algorithm handles boundaries of general shape using regular structured grids with no deterioration of accuracy. For long simulation times it offers sub-linear complexity with respect to the grid dimension, i.e., is asymptotically cheaper than the cost of a typical explicit scheme. In addition, our algorithm allows one to share the computational cost between multiple similar problems. On multi- processor (multi-core) platforms, it beneﬁts from what can be considered an effective parallelization in time.
The independent set problem for a given simple graph is to determine the size of a maximal set of its pairwise non-adjacent vertices. We propose a new way of graph reduction leading to a new proof of the NP-completeness of the independent set problem in the class of planar graphs and to the proof of NPcompleteness of this problem in the class of planar graphs having only triangular internal facets of maximal vertex degree 18
What happens with Russian mathematics in terms of metric parameters? Where do Russian mathematicians work, where do they publish, how well are they cited?
For a semigroup $S(t):X\to X$ acting on a metric space $(X,\dist)$, we give a notion of global attractor based only on the minimality with respect to the attraction property. Such an attractor is shown to be invariant whenever $S(t)$ is asymptotically closed. As a byproduct, we generalize earlier results on the existence of global attractors in the classical sense.
Transportation discrete network design problem (DNDP) is about how to modify an existing network of roads and highways in order to improve its total system travel time, and the candidate road building or expansion plan can only be added as a whole. DNDP can be formulated into a bi-level problem with binary variables. An active set algorithm has been proposed to solve the bi-level discrete network design problem, while it made an assumption that the capacity increase and construction cost of each road are based on the number of lanes. This paper considers a more general case when the capacity increase and construction cost are specified for each candidate plan. This paper also uses numerical methods instead of solvers to solve each step, so it provides a more direct understanding and control of the algorithm and running procedure. By analyzing the differences and getting corresponding solving methods, a modified active set algorithm is proposed in the paper. In the implementation of the algorithm and the validation, we use binary numeral system and ternary numeral system to avoid too many layers of loop and save storage space. Numerical experiments show the correctness and efficiency of the proposed modified active set algorithm.
In this paper within a field-theoretical approach taking into account explicitly a cosolvent with a nonzero dipole and a polarizability tensor, we derive a modified Poisson-Boltzmann equation. Applying the modified Poisson-Boltzmann equation, we formulate a generalized Gouy- Chapman theory for the case when an electrolyte solution is mixed with a polar co-solvent having a large polarizability. We show that an increase of the co-solvent concentration as well as the co-solvent polarizability lead to a significant increase of differential capacitance at sufficiently high surface potentials of the electrode, whereas the profile of the electrostatic potential becomes considerably more long-ranged. On the contrary, an increase in the permanent dipole of the co-solvent only weakly affects the differential capacitance.
We show that under mild boundary conditions the moduli space of non-compact curves on a complex surface is (locally) an analytic subset of a ball in a Banach manifold, defined by finitely many holomorphic functions.
Background: Vectorial capacity and the basic reproductive number (R0) have been instrumental in structuring thinking about vector-borne pathogen transmission and how best to prevent the diseases they cause. One of the more important simplifying assumptions of these models is age-independent vector mortality. A growing body of evidence indicates that insect vectors exhibit age-dependent mortality, which can have strong and varied affects on pathogen transmission dynamics and strategies for disease prevention.
Methodology/Principal Findings: Based on survival analysis we derived new equations for vectorial capacity and R0 that are valid for any pattern of age-dependent (or age–independent) vector mortality and explore the behavior of the models across various mortality patterns. The framework we present (1) lays the groundwork for an extension and refinement of the vectorial capacity paradigm by introducing an age-structured extension to the model, (2) encourages further research on the actuarial dynamics of vectors in particular and the relationship of vector mortality to pathogen transmission in general, and (3) provides a detailed quantitative basis for understanding the relative impact of reductions in vector longevity compared to other vector-borne disease prevention strategies.
Conclusions/Significance: Accounting for age-dependent vector mortality in estimates of vectorial capacity and R0 was most important when (1) vector densities are relatively low and the pattern of mortality can determine whether pathogen transmission will persist; i.e., determines whether R0 is above or below 1, (2) vector population growth rate is relatively low and there are complex interactions between birth and death that differ fundamentally from birth-death relationships with age-independent mortality, and (3) the vector exhibits complex patterns of age-dependent mortality and R0,1. A limiting factor in the construction and evaluation of new age-dependent mortality models is the paucity of data characterizing vector mortality patterns, particularly for free ranging vectors in the field.