175 research outputs found
Singularly Perturbed Self-Adjoint Operators in Scales of Hilbert spaces
Finite rank perturbations of a semi-bounded self-adjoint operator A are
studied in the scale of Hilbert spaces associated with A. A concept of
quasi-boundary value space is used to describe self-adjoint operator
realizations of regular and singular perturbations of A by the same formula. As
an application the one-dimensional Schr\"{o}dinger operator with generalized
zero-range potential is considered in the Sobolev space W^p_2(\mathbb{R}),
p\in\mathbb{N}.Comment: 26 page
Singularly perturbed self-adjoint operators in scales of Hilbert spaces
Finite rank perturbations of a semi-bounded self-adjoint operator A are studied in the scale of Hilbert spaces
associated with A. A concept of quasi-boundary value space is used to describe self-adjoint operator realizations of regular and singular perturbations of A by the same formula. As an application the one-dimensional
Schrodinger operator with generalized zero-range potential is considered in the Sobolev space Wp₂(R), p ∈ N.У шкалі гільбертових просторів, асоційованих з A, вивчаються скінченного рангу збурення напівобме-женого самоспряженого оператора A. Поняття квазіпростору граничних значень використовується для опису однією формулою самоспряжених операторних реалізацій як регулярних, так і сингулярних збурень оператора A. Як застосування, розглядається одновимірний оператор Шредінгера з узагальненим потенціалом нульового радіуса у просторі Соболева Wp₂(R),p∈N
On the classification of scalar evolutionary integrable equations in dimensions
We consider evolutionary equations of the form where
is the nonlocality, and the right hand side is polynomial
in the derivatives of and . The recent paper \cite{FMN} provides a
complete list of integrable third order equations of this kind. Here we extend
the classification to fifth order equations. Besides the known examples of
Kadomtsev-Petviashvili (KP), Veselov-Novikov (VN) and Harry Dym (HD) equations,
as well as fifth order analogues and modifications thereof, our list contains a
number of equations which are apparently new. We conjecture that our examples
exhaust the list of scalar polynomial integrable equations with the nonlocality
. The classification procedure consists of two steps. First, we classify
quasilinear systems which may (potentially) occur as dispersionless limits of
integrable scalar evolutionary equations. After that we reconstruct dispersive
terms based on the requirement of the inheritance of hydrodynamic reductions of
the dispersionless limit by the full dispersive equation
A Standard CMOS Humidity Sensor without Post-Processing
A 2 μW power dissipation, voltage-output, humidity sensor accurate to 5% relative humidity was developed using the LFoundry 0.15 μm CMOS technology without post-processing. The sensor consists of a woven lateral array of electrodes implemented in CMOS top metal, a Intervia Photodielectric 8023–10 humidity-sensitive layer, and a CMOS capacitance to voltage converter
Inverse Eigenvalue Problems for Nonlocal Sturm-Liouville Operators
We solve the inverse spectral problem for a class of Sturm - Liouville operators with singular nonlocal potentials and nonlocal boundary conditions
Self-Calibrated Humidity Sensor in CMOS without Post-Processing
A 1.1 μW power dissipation, voltage-output humidity sensor with 10% relative humidity accuracy was developed in the LFoundry 0.15 μm CMOS technology without post-processing. The sensor consists of a woven lateral array of electrodes implemented in CMOS top metal, a humidity-sensitive layer of Intervia Photodielectric 8023D-10, a CMOS capacitance to voltage converter, and the self-calibration circuitry
Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies
Analytic-bilinear approach for construction and study of integrable
hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice
hierarchies are considered. This approach allows to represent generalized
hierarchies of integrable equations in a condensed form of finite functional
equations. Generalized hierarchy incorporates basic hierarchy, modified
hierarchy, singularity manifold equation hierarchy and corresponding linear
problems. Different levels of generalized hierarchy are connected via
invariants of Combescure symmetry transformation. Resolution of functional
equations also leads to the -function and addition formulae to it.Comment: 43 pages, Late
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