Oscillatory and Asymptotic Behavior of Damped Functional Differential Equations

New theorems on the oscillatory and asymptotic behavior of solutions of the damped differential equations with deviating arguments of the form are established.     

Crystal structures of dimethylsuccinate and dimethyloxalate: Carbonyl group orientation for C13 chemical shielding tensor studies

The crystal structures of dimethylsuccinate (DMS) and dimethyloxalate (DMO) have been determined to facilitate the determination of the C-13 chemical shielding tensors of the carbonyl carbon in esters. Crystals of DMS are monoclinic, space groupC2/c,Z=4,a=13.154(4),b=6.156(1),c=9.363(4)Å,=98.53(3)°. The structure was solved by direct methods and refined by leastsquares procedures to giveR=0.071 for 932 observed data. Crystals of DMO are monoclinic space group,P2₁/n,Z=2, witha=3.891(1),b=11.879(2),c=6.213(2) Å,=103.32(2)°. The structure is the same (within experimental error) as that reported by Dougill and Jeffrey (1953) and refined to giveR=0.074 for 395 observed data.     

Anticancer agent development: X-ray crystal structure and keto-enol tautomerism of dimethyl 1-hydroxy-6,7-methylenedioxy-4-(3′,4′,5′-trimethoxyphenyl-trans-3,4-dihydronaphthalene-2,3-dicarboxylate

Structural and conformational information obtained from the crystal structure and solution¹H nmr investigations of the title compound are compared. The 4-aryltetralone, C₂₄H₂₄O₁₀, crystallizes as a chloroform solvate in the monoclinic space group, P2₁/n, witha=12.519(4),b=17.938(6),c=12.534(9)Å,=111.90(5)°, and D_calc=1.51 g cm^–3 forZ=4. The data for this compound were collected at –150°C. Least-squares refinement of 2796 observed [F _o5(F _o)] reflections led to the final agreement index ofR=0.062. A threefold static disorder was observed for one of the carboxyl groups. The second carboxyl group participates in an intramolecular hydrogen bond and is thus ordered. The¹H nmr spectrum revealed the title compound to exist as a keto-enol tautomeric mixture in solution. Vicinal hydrogen coupling constant analysis proved reliable in ascertaining B-ring stereochemistry of 2,3-disubstituted-4-aryltetralones.     

A modified Tolman mass-energy formula

A modified Tolman mass (energy) formula is derived for spherically symmetric, time-independent systems. In the absence of surfaces of discontinuity, the modified formula has, in contradistinction to the original formula, the following desirable properties: (i) it always gives the correct mass of the system as a whole; (ii) it always gives the correct mass of any portion of the system which is surrounded by vacuum; and (iii) it remains invariant under a rescaling of the time coordinate of the formt Ct, C=constant. In the presence of surfaces of discontinuity the Tolman mass formula is further modified by the addition of the Israel mass associated with each surface. The resulting formula also has the above three properties. A new exact solution of Einstein's equations which is well behaved everywhere and is, in a sense, a generalization of Florides' new interior Schwarzschild solution is also presented.This result explains why, takingT ₁ ¹ =[C] in Section 2, we were able to obtain a solution free of surfaces of discontinuity.     

Pair formation in age-structured populations

The modelling problems associated with pair formation in age-structured populations are discussed in this paper. The author also formulates a class of models for pair formation in human populations and derives some results on persistent distributions.     

Weighted Voronoi tessellation with a poisson field of centroids

One considers a weighted Voronoi tessellation generated by a system of n Poisson fields of centroids. One investigates the composition and the boundary field of this structure. It is proved that the boundary field intensity between grains of types i and j (1ijn) is equal to where p_i is the volume part, _i>0 is the weight (for the comparison of distances) of the i-th component, c is a scaling factor. One obtains formulas for the boundary field intensities in plane and linear sections of the structure: . Estimators for the parameters p_i and _i from the observation of the linear section are proposed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 153, pp. 160–172, 1986.     

Quantum field theories of vortices and anyons

We develop the quantization of topological solitons (vortices) in three-dimensional quantum field theory, in terms of the Euclidean region functional integral. We analyze in some detail the vortices of the abelian Higgs model. If a Chern-Simons term is added to the action, the vortices turn out to be anyons, i.e. particles with arbitrary real spin and intermediate () statistics. Localization properties of the interpolating field, scattering theory and spin-statistics connection of anyons are discussed. Such analysis might be relevant in connection with the fractional quantum Hall effect and two-dimensional models of HighT _csuperconductors.     

Messung der Gewebetemperatur mit infrarotem Thermometer in einer Trockenanlage

Zusammenfassung Es wurde eine theoretische Analyse der kontaktlosen Temperaturmessung des an der Spann-, Trocken- und Fixiermaschine bearbeiteten Gewebes vorgenommen. Der Einfluß der Trocknerwand ist durch die Korrektive Funktion ausgedrückt, zu deren Festlegung ein allgemein anwendbares Diagramm zusammengestellt wurde. Dabei wird die Tatsache berücksichtigt, daß die Messung in einem beschränkten Teil des Spektrums durchgeführt wird, welcher außerhalb der Wasserdampfabsorptionsbänder liegt.

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Measuring temperature of textiles in driers with infrared thermometer

The paper undertakes a theoretical analysis of contactless temperature measurement of textiles processed on a stretching, drying and fixation machine. The effect of the drier wall is expressed through a corrective function for whose determination a universal diagram has been established. The measurements have been performed in a narrow part of the spectrum lying outside the water vapour absorption bands.

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Formelzeichen B W· m^–2 Effektive Wärmestromdichte durch Strahlung - K _i Radiationskoeffizient für Oberflächei - q W · m^–2 Wärmestromdichte durch Strahlung - T K Temperatur - t °C Temperatur - dtj Kroneckersches Symbol - Emissionsgrad der Oberfläche - m Wellenlänge - _ij Radiationskoeffizient - _T W·m ^–2 ·K ^–4 Koeffizient in der Gleichung (2) - Winkelkoeffizient für Strahlung zwischen Oberflächen 1, 2 - – Korrektionsfunktion - W·m ^–2 Wärmestromdichte des schwarzen Körpers Indizes c Gewebe - M Meßwert - w Trocknerwand     

Invariant submanifolds and properCR foliations on a para-coKählerian manifold with concircular structure vector field

After recalling the basic properties of para-coKählerian manifolds \(\tilde M\) with concircular structure vector field ξ, the infinitesimal auto morphismsX of the structure 1-form \(\tilde \eta \) are considered. One of the results is that the Lie derivative of all powers of the structure 2-form \(\tilde \Omega ,\) i.e. \(\mathcal{L}x\tilde \Omega ^p ;p = 1,...,m,\) is exterior recurrent. Further two types of horizontal distributionsD _n which are normal to ξ. IfD _t (resp.D _n ) is involutive, the corresponding leafM _t (resp.M _n ) is a minimal submanifold of \(\tilde M\) . FurtherM _n is a symplectic submanifold and ξ is an umbilical normal section ofM _n . Finally proper immersion \(M \to \tilde M\) are discussed, whereM is aCR-sub-manifold whose horizontal distribution isD _t . It is shown that the vertical distribution is involutive, and the restriction of ξ toM is an symptotic direction. Some interesting special cases are treated.     

Nonlinear void-fraction waves in two-phase bubbly flow

It is shown that nonlinear void-fraction waves constitute exact solutions of the two-fluid equations for bubbly flow, if and only if the virtual-mass coefficientm() is a definite function of the void fraction. In the case of spherical bubbles the functional dependence is given bym()=(1/2)(1–a)(1–3). A similar expression was obtained recently by means of an elaborate linear stability analysis of a uniform two-phase flow. It is remarkable that the greater part of the physical quantities of a nonlinear void-fraction wave depends linearly on. The virtual-mass coefficient may be derived directly from a special form of Hamilton's variational principle.

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Zusammenfassung Es wird gezeigt daß nichtlineare Konzentrationswellen exakte Lösungen der Zweifluiden Gleichungen einer Blasenströmung darstellen dann und nur dann, wenn der Koeffizientm() der virtuellen Masse eine bestimmte Funktion der Volumenkonzentration der Blasen ist. Die funktionelle Abhängigkeit ist im Falle kugelförmiger Blasen gegeben durchm()= (1/2)(1–) (1–3). Ein gleicher Ausdruck wurde neulich mittels einer umständlichen linearen Stabilitätsanalysis einer uniformen Zweiphasen-Strömung erhalten. Es ist bemerkenswert daß der größere Teil der physikalischen Größen einer nichtlinearen Konzentrationswelle in linearer Weise von abhängt. Der Koeffizient der virtuellen Masse kann in direkter Weise von einer speziellen Form des Hamiltonschen Variationsprinzips hergeleitet werden.