Observer design for open and closed trophic chains

Monitoring of ecological systems is one of the major issues in ecosystem research. The concepts and methodology of mathematical systems theory provide useful tools to face this problem. In many cases, state monitoring of a complex ecological system consists in observation (measurement) of certain state variables, and the whole state process has to be determined from the observed data. The solution proposed in the paper is the design of an observer system, which makes it possible to approximately recover the state process from its partial observation. Such systems-theoretical approach has been applied before by the authors to Lotka–Volterra type population systems. In the present paper this methodology is extended to a non-Lotka–Volterra type trophic chain of resource–producer–primary consumer type and numerical examples for different observation situations are also presented.     

On the equations for p-adic closed and open strings

A survey of several pure mathematical results concerning the boundary-value problems for nonlinear pseudo-differential equation for closed and open strings in d-dimensional flat spacetime is presented. We obtained some results on existence or nonexistence of solutions. In particular, the absence of almost-periodic solutions was shown. We consider also some numerical approaches to the problems. The text was submitted by the author in English.     

Arbitrary decompositions into open and closed trails

The problem of arbitrary decomposition of a graph G into closed trails i.e. a decomposition into closed trails of prescribed lengths summing up to the size of the graph G was first considered in the case of the complete graph G=K_n (for odd n) in connection with vertex-distinguishing coloring of the union of cycles.Next, the same problem was investigated for other families of graphs.In this paper we consider a more general problem: arbitrary decomposition of a graph into open and closed trails. Our results are based on and generalize known results on decomposition of a graph into closed trails. Our results also generalize some results concerning decomposition of a graph into open trails. We here emphasize that the known results on the closed case are basic ingredients for the proof of the open and closed case.     

Constructive closed range and open mapping theorems

We prove a version of the closed range theorem within Bishop's constructive mathematics. This is applied to show that if an operator T on a Hilbert space has an adjoint and a complete range, then both T and T^* are sequentially open.     

Nonlinear equations for p-adic open, closed, and open-closed strings

We investigate the structure of solutions of boundary value problems for a one-dimensional nonlinear system of pseudodifferential equations describing the dynamics (rolling) of p-adic open, closed, and open-closed strings for a scalar tachyon field using the method of successive approximations. For an open-closed string, we prove that the method converges for odd values of p of the form p = 4n+1 under the condition that the solution for the closed string is known. For p = 2, we discuss the questions of the existence and the nonexistence of solutions of boundary value problems and indicate the possibility of discontinuous solutions appearing. To Anatolii Alekseevich Logunov on his 80th birthday __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 3, pp. 354–367, December, 2006.     

Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves

Deckelnick and Dziuk (Math. Comput. 78(266):645–671, 2009) proved a stability bound for a continuous-in-time semidiscrete parametric finite element approximation of the elastic flow of closed curves in \mathbbR^d, d 3 2{\mathbb{R}^d, d\geq2} . We extend these ideas in considering an alternative finite element approximation of the same flow that retains some of the features of the formulations in Barrett et al. (J Comput Phys 222(1): 441–462, 2007; SIAM J Sci Comput 31(1):225–253, 2008; IMA J Numer Anal 30(1):4–60, 2010), in particular an equidistribution mesh property. For this new approximation, we obtain also a stability bound for a continuous-in-time semidiscrete scheme. Apart from the isotropic situation, we also consider the case of an anisotropic elastic energy. In addition to the evolution of closed curves, we also consider the isotropic and anisotropic elastic flow of a single open curve in the plane and in higher codimension that satisfies various boundary conditions.     

Categorical anatomy of closed graph and open mapping theorems

Recent development of the theory of general topological vector spaces (without local convexity, hence without duality theory), as in [1], has exposed more of the essential (distinctly topological) nature of a good deal of the locally convex theory, resulting in a remarkably high survival rate of theorems, with (it is claimed) greater simplicity and elegance of proofs. This is especially true of the closed graph theorem. Associated concepts, such as barrelledness and the various kinds of completeness, can be described and related in a manner which demands extension to uniform spaces and beyond. In the setting of categories and functors, we believe these ideas acquire an elegance and unity which considerably widens their scope while shedding light on their homeground in functional analysis. The aim of this paper, which takes a much broader perspective than Pelletier [10], is to distill some of this categorical essence, and to point out new problems, both topological and categorical, which present themselves along the way.     

Slow mode shocks propagating in open and closed magnetic fields

A 2-D MHD model is used to investigate the propagation of slow mode shocks in the open and closed magnetic fields of the meridional plane near the sun. The solutions demonstrate that a forward slow shock could retain its slow shock characteristics into interplanetary space in the magnetically open region; however, it can evolve into an intermediate shock through the helmet-type current sheet to the open magnetic field. Project supported by the National Natural Science Foundation of China and partially the SIGMA Weather Project.     

The 2-D Neumann problem in an exterior domain bounded by closed and open curves

The Neumann problem for the Laplace equation in an exterior connected plane region bounded by closed and open curves is studied. The existence of classical solution is proved by potential theory. The problem is reduced to the Fredholm equation of the second kind, which is uniquely solvable. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.     

The sequence of open and closed prefixes of a Sturmian word

A finite word is closed if it contains a factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We are interested in the oc-sequence of a word, which is the binary sequence whose n-th element is 0 if the prefix of length n of the word is open, or 1 if it is closed. We exhibit results showing that this sequence is deeply related to the combinatorial and periodic structure of a word. In the case of Sturmian words, we show that these are uniquely determined (up to renaming letters) by their oc-sequence. Moreover, we prove that the class of finite Sturmian words is a maximal element with this property in the class of binary factorial languages. We then discuss several aspects of Sturmian words that can be expressed through this sequence. Finally, we provide a linear-time algorithm that computes the oc-sequence of a finite word, and a linear-time algorithm that reconstructs a finite Sturmian word from its oc-sequence.     

Load balancing via random local search in closed and open systems

In this paper, we analyze the performance of random load resampling and migration strategies in parallel server systems. Clients initially attach themselves to an arbitrary server, but may switch servers independently at random instants of time in an attempt to improve their service rate. This approach to load balancing contrasts with traditional approaches where clients make smart server selections upon arrival (e.g., Join-the-Shortest-Queue policy and variants thereof). Load resampling is particularly relevant in scenarios where clients cannot predict the load of a server before being actually attached to it. An important example is in wireless spectrum sharing where clients try to share a set of frequency bands in a distributed manner. We first analyze the natural Random Local Search (RLS) strategy. Under this strategy, after sampling a new server randomly, clients only switch to it if their service rate is improved. In closed systems, where the client population is fixed, we derive tight estimates of the time it takes under RLS strategy to balance the load across servers. We then study open systems where clients arrive according to a random process and leave the system upon service completion. In this scenario, we analyze how client migrations within the system interact with the system dynamics induced by client arrivals and departures. We compare the load-aware RLS strategy to a load-oblivious strategy in which clients just randomly switch server without accounting for the server loads. Surprisingly, we show that both load-oblivious and load-aware strategies stabilize the system whenever this is at all possible. We use large-system asymptotics to characterize system performance, and augment this with simulations, which suggest that the average client sojourn time under the load-oblivious strategy is not considerably reduced when clients apply smarter load-aware strategies.     

Uniformization and performance sensitivity estimation in closed queueing networks

This paper proposes a single sample path-based sensitivity estimation method for discrete event systems. The method employs two major techniques: uniformization and importance sampling. By uniformization, steady-state performance measures can be estimated via the transition matrix of the embedded Markov chain in the uniformized process. The sensitivity of a transition matrix is obtained by applying importance sampling to an ensemble average of sample paths. The algorithm developed for this method is easy to be implemented; the method applies to more systems than infinitesimal perturbation analysis.     

Optimization and balancing of open,closed, and mixed multiclass queueing networks

Doklady Mathematics -     

A critical look at the kinematic‐wave theory for sedimentation–consolidation processes in closed vessels

The two‐phase flow of a flocculated suspension in a closed settling vessel with inclined walls is investigated within a consistent extension of the kinematic wave theory to sedimentation processes with compression. Wall boundary conditions are used to spatially derive one‐dimensional field equations for planar flows and flows which are symmetric with respect to the vertical axis. We analyse the special cases of a conical vessel and a roof‐shaped vessel. The case of a small initial time and a large time for the final consolidation state leads to explicit expressions for the flow fields, which constitute an important test of the theory. The resulting initial‐boundary value problems are well posed and can be solved numerically by a simple adaptation of one of the newly developed numerical schemes for strongly degenerate convection‐diffusion problems. However, from a physical point of view, both the analytical and numerical results reveal a deficiency of the general field equations. In particular, the strongly reduced form of the linear momentum balance turns out to be an oversimplification. Included in our discussion as a special case are the Kynch theory and the well‐known analyses of sedimentation in vessels with inclined walls within the framework of kinematic waves, which exhibit the same shortcomings. In order to formulate consistent boundary conditions for both phases in a closed vessel and in order to predict boundary layers in the presence of inclined walls, viscosity terms should be taken into account. Copyright © 2001 John Wiley & Sons, Ltd.     

Relatively weakly open sets in closed balls of Banach spaces,and the centralizer

Let f be a transcendental entire function and let I(f) denote the set of points that escape to infinity under iteration. We give conditions which ensure that, for certain functions, I(f) is connected. In particular, we show that I(f) is connected if f has order zero and sufficiently small growth or has order less than 1/2 and regular growth. This shows that, for these functions, Eremenko’s conjecture that I(f) has no bounded components is true. We also give a new criterion related to I(f) which is sufficient to ensure that f has no unbounded Fatou components.