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  • Single-step template synthesis of mesoporous silicas containing thiourea functional groups 
    Zub, Yu.L.; Gona, O.I.; Chuiko, A.A.; Yaroshenko, N.A.; Dabrowski, A. (Functional Materials, 2006)
    Mesopo rous adsorbents co ntaining mono-(-(CH₂)₃NHC(=S)NHC₂H₅) or bi-(-(CH₂)₃NHC(=S)NHC₂H₅ / amino) functional surface layer have been synthesized in a single-step process using bi- or tricomponent (with respect to ...
  • Singular analysis of Jones-matrix images describing polycrystalline networks of biological crystals in diagnostics of cholelithiasis in its latent period 
    Balanetska, V.O.; Marchuk, Yu.; Karachevtsev, A.V.; Ushenko, V.O. (Semiconductor Physics Quantum Electronics & Optoelectronics, 2011)
    Determined in this work are analytical interrelations between orientations of optical axes and birefringence of biological crystals and characteristic values of Jonesmatrix elements corresponding to flat layers of ...
  • Singular beams with transverse electric and transverse magnetic fields 
    Fadeyeva, T.A. (Semiconductor Physics Quantum Electronics & Optoelectronics, 2013)
    We have obtained the solutions of the paraxial wave equation in free space and homogeneous media in the form of transverse electric (TE) and transverse magnetic (TM) fields with Laguerre-Gaussian (LG) and Hermite-Gaussian ...
  • Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones 
    Langmann, E. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    There exists a large class of quantum many-body systems of Calogero-Sutherland type where all particles can have different masses and coupling constants and which nevertheless are such that one can construct a complete (in ...
  • Singular Instantons and Painlevé VI 
    Muñiz Manasliski, R. (Symmetry, Integrability and Geometry: Methods and Applications, 2016)
    We consider a two parameter family of instantons, which is studied in [Sadun L., Comm. Math. Phys. 163 (1994), 257-291], invariant under the irreducible action of SU₂ on S⁴, but which are not globally defined. We will see ...
  • Singular integral inequalities with several nonlinearities and integral equations with singular kernels 
    Medveď, M. (Нелінійні коливання, 2008)
    We deal with an integral inequality with a power nonlinearity in its left-hand side, with n nonlinearities in its right-hand side, and weakly singular kernels. The obtained result is an extention of the Bihari, Henry, Pachpatte ...
  • Singular Isotonic Oscillator, Supersymmetry and Superintegrability 
    Marquette, I. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    In the case of a one-dimensional nonsingular Hamiltonian H and a singular supersymmetric partner Hα, the Darboux and factorization relations of supersymmetric quantum mechanics can be only formal relations. It was shown ...
  • Singularities of Affine Schubert Varieties 
    Kuttler, J.; Lakshmibai, V. (Symmetry, Integrability and Geometry: Methods and Applications, 2009)
    This paper studies the singularities of affine Schubert varieties in the affine Grassmannian (of type Al⁽¹⁾). For two classes of affine Schubert varieties, we determine the singular loci; and for one class, we also determine ...
  • Singularities of Type-Q ABS Equations 
    Atkinson, J. (Symmetry, Integrability and Geometry: Methods and Applications, 2011)
    The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS) in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what ...
  • Singularity Analysis and Integrability of a Burgers-Type System of Foursov 
    Sakovich, S. (Symmetry, Integrability and Geometry: Methods and Applications, 2011)
    We apply the Painlevé test for integrability of partial differential equations to a system of two coupled Burgers-type equations found by Foursov, which was recently shown by Sergyeyev to possess infinitely many commuting ...
  • Singularity Classes of Special 2-Flags 
    Mormul, P. (Symmetry, Integrability and Geometry: Methods and Applications, 2009)
    In the paper we discuss certain classes of vector distributions in the tangent bundles to manifolds, obtained by series of applications of the so-called generalized Cartan prolongations (gCp). The classical Cartan prolongations ...
  • Singularly perturbed linear boundary-value problems with pulse effects and the regular reduced problem 
    Karandjulov, L.I. (Український математичний журнал, 1995)
    A singularly perturbed linear boundary-value problem with pulse effect is considered. By using pseudo-inverse matrices, we construct an asymptotic solution with a single boundary layer.
  • Singularly perturbed periodic and semiperiodic differential operators 
    Mikhailets, V.A.; Molyboga, V.M. (Український математичний журнал, 2007)
  • Singularly perturbed problems of hyperbolic-parabolic type with lipschitzian nonlinearity 
    Perjan, A. (Нелинейные граничные задачи, 2005)
    We study the behavior of solutions of the Cauchy problem εu"(t)+u'(t) + Au(t)+B(u(t)) = f(t), u(0) = u₀, u'(0) = u₁ in the Hilbert space H as ε → 0, where A is a linear, self-adjoint, strong positive operator B is nonlinear ...
  • Singularly perturbed self-adjoint operators in scales of Hilbert spaces 
    Albeverio, S.; Kuzhel, S.; Nizhnik, L. (Український математичний журнал, 2007)
    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 ...
  • Singularly perturbed stochastic systems 
    Korolyuk, V.S. (Український математичний журнал, 1997)
    Problems of singular perturbation of reducible invertible operators are classified and their applications to the analysis of stochastic Markov systems represented by random evolutions are considered. The phase merging, ...
  • Singular nonlinear eigenvalue problem for second order differential equation with energy dissipation 
    Parasyuk, I.O.; Pozur, S.V. (Нелінійні коливання, 2002)
    An eigenvalue problem on the half line for a singular nonlinear ordinary differential operator of the second order is considered. We find sufficient conditions under which this problem has a solution which has a prescribed ...
  • Singular optics methods for analysis of spatial structure of diffraction field of optical elements 
    Budnyk, O.P.; Lymarenko, R.A. (Semiconductor Physics Quantum Electronics & Optoelectronics, 2003)
    The paper is devoted to developing methods of analytical and experimental investigations of diffraction and interference phenomena used in test systems for optical elements. The theoretical analysis and experimental results ...
  • Singular peculiarities of a plane wave diffracted on half-plane 
    Anokhov, S.; Khizhnyak, A.; Lymarenko, R.; Soskin, M. (Semiconductor Physics Quantum Electronics & Optoelectronics, 2001)
    We analyzed singular properties of edge dislocation waves («EDW») - the main information component of the field formed at plane wave diffraction on half-plane. It is shown that analytical structure of this wave is completely ...
  • Singular periodic impulse problems 
    Halas, Z.; Tvrdy, M. (Нелінійні коливання, 2008)
    We obtain an existence principle for the impulsive periodic boundary-value problem u’’ + cu’ = g(x) + e(t), u(ti+) = u(ti) + Ji(u, u’ ), u’(ti+) = u’(ti) + Mi(u, u’), i = 1, . . ., m, u(0) = u(T), u’(0) = u’(T), where g ∈ ...