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provide a procedure for constructing the solution of the inverse problem and prove its uniqueness. Keywords: Geometrical graphs, dierential operators, regular singularities, inverse spectral problems MSC 2010: 34A55, 34L05, 47E05 DOI: 10.1515/jiip-2014-0085 Received December 8, 2014; revised February 11, 2015; accepted February 20, 2015 1 Introduction We study inverse spectral problems for variable order dierential equations with regular singularities on compact star-type graphs. More precisely, dierential equations have dierent orders on dierent edges. Boundary value

spectral problems, method of spectral mappings. 2010 Mathematics Subject Classification. 34A55, 47E05. 1 Introduction In this paper, we consider the pencil L D L.`; U/ given by the differential expression `.Y / WD Y 00 C 2I C 2iQ1.x/CQ0.x/ Y; x > 0; (1) with the initial condition U.Y / WD Y 0.0/C .ih1 C h0/Y.0/ D 0: (2) Here Y.x/ D Œyk.x/kD1;:::;m is a column vector, is the spectral parameter, I is themm unit matrix,Qs.x/ D ŒQs;jk.x/j;kD1;:::;m aremmmatrix-functions, hs D Œhs;jkj;kD1;:::;m, where hs;jk are complex numbers. We assume that det.I ˙ h1/ ¤ 0. This

uniqueness theorem and provide a procedure for constructing its solution. Keywords. Geometrical graphs with a cycle, differential pencils, inverse spectral problems. 2010 Mathematics Subject Classification. Primary 34A55; secondary 34B45, 34B07, 47E05. 1 Introduction Analysis on graphs and other similar structures has been developed for quite some time due to various applications in applied sciences. In particular in recent years it has experienced a significant boost in terms of new applications arising and new methods were developed and studied. In this paper we study

spectral mappings. A constructive algorithm for the solution of the inverse problem is provided. Keywords:Matrix quadratic dierential pencils, spectral data, inverse spectral problems, method of spectral mappings MSC 2010: 34A55, 34B07, 34B24, 34L40, 47E05 || Natalia Bondarenko: Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia, e-mail: bondarenkonp@info.sgu.ru 1 Introduction In this paper, we consider the boundary value problem L = L(ℓ, U, V) for the equation ℓY := Y + (ñ2I + 2iñQ1(x) + Q0(x))Y = 0, x ∈ (0, ð

, heat and moisture transfer, particle swarm optimization, thickness-heat conductivity-porosity determination, weighted least-squares solution MSC 2010: 34A55, 65L08, 80A23 DOI: 10.1515/jiip-2013-0084 Received December 14, 2013; revised June 8, 2014; accepted April 5, 2015 1 Introduction Clothing does not only represent a nation, an era or a prevailing social climate with dierent characteristics, but it also reflects changes of human civilization. From an emphasis on the natural beauty of the classical style to themodern or smart clothing in the garment development

ofmodels that are not identiable only from forced responses. Explicit formulations and an algorithm are derived to identify model parameters from the combined data of forced and initial condition responses. Keywords: Linear time-invariant systems, parameter estimation, forced response, initial condition response MSC 2010: 34A30, 34A55, 93A30, 93B30, 93C05, 65F05 || Ya Guo, Jinglu Tan: Department of Bioengineering, University of Missouri, Columbia, MO 65211, USA, e-mail: guoy@missouri.edu, tanj@missouri.edu 1 Introduction Many systems in physics such as wave propagation

Abstract

Inverse problems for differential pencils with nonlocal conditions are considered. Uniqueness theorems of inverse problems from the Weyl-type function and spectra are proved, which are generalizations of the well-known Weyl function and Borg’s inverse problem for the classical Sturm–Liouville operators.

Abstract

We consider the boundary value problem $R⁢(a,q)$: $-y′′⁢(x)+q⁢(x)⁢y⁢(x)=λ⁢y⁢(x)$ with $y⁢(0)=0$ and $y⁢(1)⁢cos⁡(a⁢λ)=y′⁢(1)⁢sin⁡(a⁢λ)λ$. Motivated by the previous work [T. Aktosun and V. G. Papanicolaou, Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation, Inverse Problems 29 2013, 6, Article ID 065007], it is natural to consider the following interesting question: how does one characterize isospectral sets corresponding to problem $R⁢(1,q)$? In this paper applying constructive methods we answer the above question.

Abstract

We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.

Abstract

We give a short review of results on inverse spectral problems for second-order differential operators on an interval with non-separated boundary conditions. We pay the main attention to the most important nonlinear inverse problems of recovering coefficients of differential operators from given spectral characteristics. In the first part of the review, we provide the main results and methods related to inverse problems for Sturm–Liouville operators with non-separated boundary conditions: periodic, quasi-periodic and Robin-type boundary conditions. At the end, we present the main results on inverse problems for differential pencils with non-separated boundary conditions.