Distributed computing viewed as a team problem with constraints

The optimal distribution of the workload in a system of interconnected computer units is considered. Formulated as a team decision problem with a singular cost criterion and with equality and inequality constraints, it is shown that the problem admits always a unique piecewise linear strategy which is globally optimal. Some interesting particular cases are studied.The research reported in this paper was made possible through support from the Office of Naval Research under the Joint Services Electronics Program by Contract No. N00014-75-C-0648 and Contract No. N00014-77-C-0531 and by the National Science Foundation, Grant No. ENG-76-11824.     

Convection caused by Radiation through the Layer

A nonlinear stability threshold is determined for the problemof convection in a layer of non-Boussinesq fluid with prescribedheat flux on the lower boundary and constant-temperature uppersurface. The convection problem is one in which motion can penetratefrom an unstable layer into a gravitationally stable one andthe unconditional nonlinear analysis necessitates utilizationof a spatially weighted energy.     

Cooperation by indirect revelation through strategic behavior

The paper deals with a one-shot prisoners' dilemma when the players have an option to go to court but cannot verify their testimonies. To solve the problem a second stage is added to a game. At the first stage the players are involved in the prisoners' dilemma and at the second stage they play another game in which their actions are verifiable. In such a setup the information about the actions chosen at the prisoners' dilemma stage can be revealed through strategic behavior of the players during second stage. A mechanism for such revelation in the extended game is described. It provides an existence of a unique sequential equilibrium, which may be obtained by an iterative elimination of dominated strategies and has a number of desirable properties.     

Strict Betweennesses Induced by Posets as well as by Graphs

For a finite poset P = (V, ≤ ), let _s(P){\cal B}_s(P) consist of all triples (x,y,z) ∈ V ³ such that either x < y < z or z < y < x. Similarly, for every finite, simple, and undirected graph G = (V,E), let B_s(G){\cal B}_s(G) consist of all triples (x,y,z) ∈ V ³ such that y is an internal vertex on an induced path in G between x and z. The ternary relations B_s(P){\cal B}_s(P) and B_s(G){\cal B}_s(G) are well-known examples of so-called strict betweennesses. We characterize the pairs (P,G) of posets P and graphs G on the same ground set V which induce the same strict betweenness relation B_s(P)=B_s(G){\cal B}_s(P)={\cal B}_s(G).     

Explication as a lens for the formalization of mathematical theory through guided reinvention

Realistic Mathematics Education supports students’ formalization of their mathematical activity through guided reinvention. To operationalize “formalization” in a proof-oriented instructional context, I adapt Sjogren's (2010) claim that formal proof explicates (Carnap, 1950) informal proof. Explication means replacing unscientific or informal concepts with scientific ones. I use Carnap's criteria for successful explication – similarity, exactness, and fruitfulness – to demonstrate how the elements of mathematical theory – definitions, axioms, theorems, proofs – can each explicate their less formal correlates. This lens supports an express goal of the instructional project, which is to help students coordinate semantic (informal) and syntactic (formal) mathematical activity. I demonstrate the analytical value of the explication lens by applying it to examples of students’ mathematical activity drawn from a design experiment in undergraduate, neutral axiomatic geometry. I analyze the chains of meanings (Thompson, 2013) that emerged when formal elements were presented readymade alongside those emerging from guided reinvention.     

Viscous flow through corrugated tube by boundary element method

Summary The creeping flow of a Newtonian fluid through a sinusoidally-corrugated tube is solved by the Boundary Element Method. Agreement with another numerical method is noted. In addition, it is shown that previous perturbation theory is valid only when the corrugation amplitude is small (<0.3a) and the wavelength of the corrugation is large (>3a), wherea is the mean radius of the tube.

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Zusammenfassung Das Problem der schleichenden Bewegung eines Newton'schen Fluids durch ein Rohr mit sinusförmig gewellter Wand wird mit Hilfe der Boundary Element-Methode gelöst. Übereinstimmung mit einer anderen numerischen Methode wird festestellt. Zudem wird gezeigt, daß eine früher gefundene Störungstheorie nur gültig ist wenn die Wellenamplitude klein (<0.3a) und die Wellenlänge groß (>3a) ist (a=mittlerer Rohrradius).

     

Geometry as seen by string theory

This is an introductory review of the topological string theory from physicist’s perspective. I start with the definition of the theory and describe its relation to the Gromov–Witten invariants. The BCOV holomorphic anomaly equations, which generalize the Quillen anomaly formula, can be used to compute higher genus partition functions of the theory. The open/closed string duality relates the closed topological string theory to the Chern–Simons gauge theory and the random matrix model. As an application of the topological string theory, I discuss the counting of bound states of D-branes.     

Flow through a channel bounded by two confocal porous elliptic walls

Steady flow of a viscous incompressible fluid through a channel bounded by two confocal elliptic walls have been discussed. A suitable velocity of suction and injection have been applied and skin friction has been calculated.     

A sphere can be characterized as a smooth ovaloid which contains one circle through each point

A sphere inE ³ can be characterized as a smooth ovaloid which contains one circle of an arbitrary but fixed radius through each point.Dedicated to Professor N. K. Stiphanidis on his 65th birthday     

On the Mathematical Simulation of the Measuring of the Intraocular Pressure by Applanation Method after Refractive Surgery

Applanation tonometry estimates intraocular pressure (IOP) by quantifying the force needed to create a defined amount of deformation of the cornea (Goldmann tonometer) or by estimating the diameter of the circular contact area of the cornea and flat tonometer of defined load (Maklakov tonometer). The first simplest models of the applanation method for measurement of the IOP were based on approach, in which an eyeball is modelled as a thin-walled spherical liquid-filled soft shell with corneal biomechanical properties. It was usually supposed that these properties were the same for all patients. In this work numerical simulation have been carried out using finite element code ANSYS. The eye shell is modeled as two joint shells (cornea and sclera) with different mechanical properties. The results are obtained for numerous sets of parameters and were compared to clinical data. For statistics the measurements of IOP for both eyes of 120 patients before and one month after refractive surgery are used. All parameter of refractive surgery (depth, the width and the place of ablation - refractive surgery for myopia or hypermetropia) have effect on IOP reading obtained with both Goldmann and Maklakov tonometry. The results obtained by Goldmann tonometer are significantly more sensitive to all parameters of refractive surgery than those found with Maklakov tonometer with load 10 g. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Density of the Semigroup Generated by Curves through Zero in a Banach Space

Mathematical Notes -     

Improved exploration in Hopfield network state-space through parameter perturbation driven by simulated annealing

An approach is presented for treating discrete optimization problems mapped on the architecture of the Hopfield neural network. The method constitutes a modification to the local minima escape (LME) algorithm which has been recently proposed as a method that uses perturbations in the network's parameter space in order to escape from local minimum states of the Hopfield network. Our approach (LMESA) adopts this perturbation mechanism but, in addition, introduces randomness in the selection of the next local minimum state to be visited in a manner analogous with the case of Simulated Annealing (SA). Experimental results using instances of the Weighted Maximum Independent Set (MIS) problem indicate that the proposed method leads to significant improvement over the conventional LME approach in terms of quality of the obtained solutions, while requirinŗ & g a comparable amount of computational effort.     

Magneto-hydrodynamic channel flow as influenced by wall conductance

Zusammenfassung Die Theorie vonHartmann undLazarus, Shercliff undChang sowieLundgren der magneto-hydrodynamischen Kanalströmung wird erweitert, indem der elektrische Leitungswiderstand von gegenüberliegenden Wänden als verschieden gross angenommen wird. Es zeigt sich merkwürdigerweise, dass die Geschwindigkeits- und Stromdichteverteilung nach wie vor symmetrisch bleibt. Beide Verteilungen hängen nur von der Summe der Wandleitungsfähigkeiten ab und von der Hartmann-Zahl.     

Tetrahedra passing through a triangular hole,and tetrahedra fixed by a planar frame

We show that a convex body can pass through a triangular hole iff it can do so by a translation along a line perpendicular to the hole. As an application, we determine the minimum size of an equilateral triangular hole through which a regular tetrahedron with unit edge can pass. The minimum edge length of the hole is $(1+\sqrt{2})/\sqrt{6}\approx 0.9856$. One of the key facts for the proof is that no triangular frame can hold a convex body. On the other hand, we also show that every non-triangular frame can fix some tetrahedron.