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We prove that the problem of recognition of the existence of solutions as rational functions for linear homogeneous partial differential or difference equations with polynomial coefficients is algorithmically undecidable.
It is proved that the problem of checking the existence of solutions of linear partial differential equations with polynomial coefficients is algorithmically undecidable. Decidability of the problem of checking the existence of monomial solutions with real and complex exponents is established.
We consider the problem of testing the existence of a universal denominator for partial differential or difference equations with polynomial coefficients and prove its algorithmic undecidability. This problem is closely related to finding rational function solutions in that the construction of a universal denominator is a part of the algorithms for finding… (More)
The problem of checking existence of infinitely differentiable solutions of linear partial differential equations with zero boundary conditions is considered. The coefficients of the equations are assumed to be polynomials over Z in independent variables. It is proved that this problem is algorithmically undecidable. This result extends results of our… (More)
The photochromic properties of a chromene derivative, which contains a positively charged substituent, were investigated in the presence of ct DNA. Upon irradiation in the absence of DNA the colored quinoid open form is highly unstable and rapidly reverts back to the initial closed form (bleaching). In the presence of DNA the open form is significantly… (More)
The fluorescent properties of a recently synthesized photochromic naphthopyran containing a 1-aza-15-crown-5 moiety (1b) and its crownless analogue (1a) were studied. 1b emits fluorescence with a maximum at 528 nm, quantum yield 0.1 and characteristic lifetime 2.4 ns (in acetonitrile at room temperature). Its luminescence could be switched off… (More)
In this work, the interaction of protonated amino acids with a chromene bearing a fused 18-crown-6 ether moiety was studied by UV-vis and NMR spectroscopy. Initial closed forms of the chromene form monotopic 1 : 1 complexes, the ammonium group being localized inside the crown ether cavity. UV-irradiation leads to transformation of the ring-closed species… (More)
A macrocyclic benzo-15-crown-5 ether unit tethered to a photochromic naphthopyran by a styryl spacer (MEN) is shown to form a 1:1 complex with magnesium(II). The structure and dynamics of the specific host-metal interactions were investigated by PFG-NMR analysis. A combination of UV/Vis and variable temperature multi-dimensional (1)H NMR photokinetic… (More)