Optimal stability criterion for a wall in a ferromagnetic wire in a magnetic field

In this paper, we study a one dimensional asymptotic model of ferromagnetic nanowire submitted to a magnetic field. We address the stability of the wall configuration for the Landau-Lifschitz equation, thus we determine the stability domain improving a result of Carbou-Labbé.     

An interpolation scheme for designing rational rotation-minimizing camera motions

When a moving (real or virtual) camera images a stationary object, the use of a rotation-minimizing directed frame (RMDF) to specify the camera orientation along its path yields the least apparent rotation of the image. The construction of such motions, using curves that possess rational RMDFs, is considered herein. In particular, the construction entails interpolation of initial/final camera positions and orientations, together with an initial motion direction. To achieve this, the camera path is described by a rational space curve that has a rational RMDF and interpolates the prescribed data. Numerical experiments are used to illustrate implementation of the method, and sufficient conditions on the two end frame orientations are derived, to ensure the existence of exactly one interpolant. By specifiying a sequence of discrete camera positions/orientations and an initial motion direction, the method can be used to construct general rotation-minimizing camera motions.     

Approximate analytical solutions of Schnakenberg systems by homotopy analysis method

In this paper, the homotopy analysis method (HAM) has been employed to obtain analytical solution of a two reaction–diffusion systems of fractional order (fractional Schnakenberg systems) which has been modeling morphogen systems in developmental biology. Different from all other analytic methods, HAM provides us with a simple way to adjust and control the convergence region of solution series by choosing proper values for auxiliary parameter h. The fractional derivative is described in the Caputo sense. The reason of using fractional order differential equations (FOD) is that FOD are naturally related to systems with memory which exists in most biological systems. Also they are closely related to fractals which are abundant in biological systems. The results derived of the fractional system are of a more general nature. Respectively, solutions of FOD spread at a faster rate than the classical differential equations, and may exhibit asymmetry. However, the fundamental solutions of these equations still exhibit useful scaling properties that make them attractive for applications.     

Dynamic cruise ship revenue management

Recently, it has been recognized that revenue management of cruise ships is different from that of airlines or hotels. Among the main differences is the presence of multiple capacity constraints in cruise ships, i.e., the number of cabins in different categories and the number of lifeboat seats, versus a single constraint in airlines and hotels (i.e., number of seats or rooms). We develop a discrete-time dynamic capacity control model for a cruise ship characterized by multiple constraints on cabin and lifeboat capacities. Customers (families) arrive sequentially according to a stochastic process and request one cabin of a certain category and one or more lifeboat seats. The cruise ship revenue manager decides which requests to accept based on the remaining cabin and lifeboat capacities at the time of an arrival as well as the type of the arrival. We show that the opportunity cost of accepting a customer is not always monotone in the reservation levels or time. This non-monotone behavior implies that “conventional” booking limits or critical time periods capacity control policies are not optimal. We provide analysis and insights justifying the non-monotone behavior in our cruise ship context. In the absence of monotonicity, and with the optimal solution requiring heavy storage for “large” (industry-size) problems, we develop several heuristics and thoroughly test their performance, via simulation, against the optimal solution, well-crafted upper bounds, and a first-come first-served lower bound. Our heuristics are based on rolling-up the multi-dimensional state space into one or two dimensions and solving the resulting dynamic program (DP). This is a strength of our approach since our DP-based heuristics are easy to understand, solve and analyze. We find that single-dimensional heuristics based on decoupling the cabins and lifeboat problems perform quite well in most cases.     

Benzimidazole condensed ring systems,III . Synthesis of some substituted 2,3-dihydrocyclopenta-1H-[4′,5′: 2,3]pyrido[1,2-a]benzimidazole-11-carbonitriles

Summary The synthesis of compound3 by condensing 1H-benzimidazole-2-acetonitrile (1) with ethyl cyclopentanone-2-carboxylate (2) in the presence of ammonium acetate is described. Methylation of3 with trimethyl phosphate yielded the N-methyl derivative4. Methods for converting3 to some of its related derivatives in which the carbonyl function was replaced by Cl, N₃ and amines are also reported.

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Kondensierte Ringsysteme des Benzimidazols, 3. Mitt.. Synthese von substituierten 2,3-Dihydrocyclopenta[4,5:2,3]pyrido[1,2-a]benzimidazol-11-carbonitrilen

Zusammenfassung Die Synthese der tetracyclischen Verbindung3 durch Kondensation von 1H-Benzimidazol-2-acetonitril (1) mit Cyclopentanon-2-carbonsäureester (2) in Gegenwart von Ammonacetat wird beschrieben. Die Methylierung von3 mit Trimethylphosphat liefert das N-Methylderivat4. Die Sauerstoffunktion in3 kann durch Chlor, Azid und Aminogruppen ersetzt werden.

     

Condensed thiazoles,II: Synthesis of 7-substituted thiazolo[4,5-d]pyrimidines as possible anti-HIV,anticancer, and antimicrobial agents

Summary Some 3-substituted 2-thioxothiazolo[4,5-d]pyrimidin-7(6H)-ones (2a,b;4) have been synthesized and converted to their 7-chloro (3,5), 7-diethanolamino (6a,b), 7-bis(2-chloroethyl)amino (7), 7-azido (8), 7-amino (9), 7-hydrazino (16), 7-mercapto (11a,b), and 7-methylthio (12) derivatives. These compounds were evaluated for theirin vitro antimicrobial, anti-HIV; and anticancer activities.For part I of this series, see Monatsh Chem127: 1203     

Benzimidazole condensed ring systems,VI: Organic azides in heterocyclic synthesis,X: Synthesis of some substituted pyrimido[1,6-a]-benzimidazoles as potential antimicrobial agents

Summary The syntheses of 3-chloro derivatives of 2-alkyl-pyrimido[1,6-a]benzimidazol-1(2H)-ones2a, b as well as of 4,4-dichloro and 4,4-dibromo derivatives of 2-alkylpyrimido[1,6-a]benzimidazole-1,3(2H,4H)-diones3 a, b and4 are reported. Methods for converting some of the chloro compounds to azido (5, 6), amino (8), morpholino (9 a,10,11), piperidino (9 b), cyano (12), and methoxy (13) derivatives of the adopted tricyclic system are also described.

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Kondensierte Ringsysteme des Benzimidazols, 6. Mitt.: Organische Azide in der Heterocyclen-Synthese, 10. Mitt.: Synthese von substituierten Pyrimido[1,6-a]benzimidazolen als mögliche antimikrobielle Wirkstoffe

Zusammenfassung Die Synthese von 3-Chlor-2-alkyl-pyrimido[1,6-a]benzimidazol-1(2H)-onen (2 a, b) und von 4,4-Dichlor- und 4,4-dibrom-pyrimido[1,6-a]benzimidazol-1,3(2H,4H)-dionen (3 a, b, 4) wird beschrieben. Diese Verbindungen lassen sich zu den entsprechenden Azido- (5, 6), Amino- (8), Morpholino- (9 a, 10, 11), Piperidino- (9 b), Cyano- (12) und Methoxy- (13) Derivaten umwandeln.

     

Construction ofC 2 Pythagorean-hodograph interpolating splines by the homotopy method

The complex representation of polynomial Pythagorean-hodograph (PH) curves allows the problem of constructing aC ² PH quintic spline that interpolates a given sequence of pointsp ₀,p ₁,...,p _N and end-derivativesd ₀ andd _N to be reduced to solving a tridiagonal system ofN quadratic equations inN complex unknowns. The system can also be easily modified to incorporate PH-splineend conditions that bypass the need to specify end-derivatives. Homotopy methods have been employed to compute all solutions of this system, and hence to construct a total of 2 ^N+1 distinct interpolants for each of several different data sets. We observe empirically that all but one of these interpolants exhibits undesirable looping behavior (which may be quantified in terms of theelastic bending energy, i.e., the integral of the square of the curvature with respect to arc length). The remaining good interpolant, however, is invariably afairer curve-having a smaller energy and a more even curvature distribution over its extent-than the corresponding ordinaryC ₂ cubic spline. Moreover, the PH spline has the advantage that its offsets arerational curves and its arc length is apolynomial function of the curve parameter.     

Computation of Minkowski Values of Polynomials over Complex Sets

As a generalization of Minkowski sums, products, powers, and roots of complex sets, we consider the Minkowski value of a given polynomial P over a complex set X. Given any polynomial P(z) with prescribed coefficients in the complex variable z, the Minkowski value P(X) is defined to be the set of all complex values generated by evaluating P, through a specific algorithm, in such a manner that each instance of z in this algorithm varies independently over X. The specification of a particular algorithm is necessary, since Minkowski sums and products do not obey the distributive law, and hence different algorithms yield different Minkowski value sets P(X). When P is of degree n and X is a circular disk in the complex plane we study, as canonical cases, the Minkowski monomial value P _m (X), for which the monomial terms are evaluated separately (incurring n(n+1) independent values of z) and summed; the Minkowski factor value P _f (X), where P is represented as the product (z–r ₁)(z–r _n ) of n linear factors – each incurring an independent choice zX – and r ₁,...,r _n are the roots of P(z); and the Minkowski Horner value P _h (X), where the evaluation is performed by nested multiplication and incurs n independent values zX. A new algorithm for the evaluation of P _h (X), when 0X, is presented.