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71.
We study Sturm–Liouville differential operators on noncompact graphs without cycles (i.e., on trees) with standard matching
conditions in internal vertices. First we establish properties of the spectral characteristics and then we investigate the
inverse problem of recovering the operator from the so-called Weyl vector. For this inverse problem we prove a uniqueness
theorem and propose a procedure for constructing the solution using the method of spectral mappings.
Received: February 13, 2007. 相似文献
72.
V. A. Yurko 《Doklady Mathematics》2010,81(3):410-413
An inverse spectral problem is studied for Sturm-Liouville differential operators on arbitrary compact graphs (spatial networks).
A uniqueness theorem of recovering operators from their spectra is proved, and a constructive procedure for the solution of
the inverse problem is provided. 相似文献
73.
V. A. Yurko 《Differential Equations》2008,44(12):1721-1729
We study boundary value problems on noncompact cycle-free graphs (i.e., trees) for second-order ordinary differential equations with a nonlinear dependence on the spectral parameter. We establish properties of the spectrum and analyze the inverse problem of reconstructing the coefficients of a differential equation on the basis of the so-called Weyl functions. For this inverse problem, we prove a uniqueness theorem and obtain a procedure for constructing the solution by the method of spectral mapping. 相似文献
74.
75.
Composite latex particles have shown a great range of applications such as paint resins, varnishes, water borne adhesives, impact modifiers, etc. The high-performance properties of this kind of materials may be explained in terms of a synergistical combination of two different polymers (usually a rubber and a thermoplastic). A great variety of composite latex particles with very different morphologies may be obtained by two-step emulsion polymerization processes. The formation of specific particle morphology depends on the chemical and physical nature of the monomers used during the synthesis, the process temperature, the reaction initiator, the surfactants, etc. Only a few models have been proposed to explain the appearance of the composite particle morphologies. These models have been based on the change of the interfacial energies during the synthesis. In this work, we present a new three-component model: Polymer blend (flexible and rigid chain particles) is dispersed in water by forming spherical cavities. Monte Carlo simulations of the model in two dimensions are used to determine the density distribution of chains and water molecules inside the suspended particle. This approach allows us to study the dependence of the morphology of the composite latex particles on the relative hydrophilicity and flexibility of the chain molecules as well as on their density and composition. It has been shown that our simple model is capable of reproducing the main features of the various morphologies observed in synthesis experiments. 相似文献
76.
V. A. Yurko 《Mathematical Notes》1975,18(4):928-932
This paper is devoted to the proof of the unique solvability of the inverse problem for second-order differential operators with arbitrary regular nonseparable boundary conditions. It is shown that the operator can be recovered from three of its spectra. As a special case, the well-known reconstruction of the Sturm-Liouville operator is accomplished. 相似文献