Response of portable gamma monitors for dose rate measurements under various radiation conditions

Journal of Radioanalytical and Nuclear Chemistry - Responses of the hand-held gamma monitors available for the ambient dose equivalent rate measurements in the Federation of Bosnia and Herzegovina...     

Existence of invariant manifolds for stochastic equations in infinite dimension

We provide a Frobenius type existence result for finite-dimensional invariant submanifolds for stochastic equations in infinite dimension, in the spirit of Da Prato and Zabczyk (Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, UK, 1992). We recapture and make use of the convenient calculus on Fréchet spaces, as developed by Kriegl and Michor (The Convenient Setting for Global Analysis, Surveys and Monographs, Vol. 53, Amer. Math. Soc., Providence, RI, 1997). Our main result is a weak version of the Frobenius theorem on Fréchet spaces. As an application, we characterize all finite-dimensional realizations for a stochastic equation which describes the evolution of the term structure of interest rates.     

Regularity of finite-dimensional realizations for evolution equations

We show that a continuous local semiflow of C^k-maps on a finite-dimensional C^k-manifold M with boundary is in fact a local C^k-semiflow on M and can be embedded into a local C^k-flow around interior points of M under some weak assumption. This result is applied to an open regularity problem for finite-dimensional realizations of stochastic interest rate models.     

Synthesis, structure and properties of novel N-thiophosphorylated derivatives of 1,3-dihydro-2H-benzimidazol-2-imine and imidazolidine-2-imine

The reaction of bis-thiourea o-C₆H₄[NHC(S)NHP(S)(Oi-Pr)₂]₂ (1) with iodine, KOH and ClCH₂C(O)OCH₃ leads to O,O′-diisopropyl-1,3-dihydro-2H-benzimidazol-2-ylideneamidothiophosphate (2) formation. The complex of the potassium salt of compound 2 with 18-crown-6, having the composition [K(18-crown-6)L], has been synthesized. Bis-thiourea [CH₂NHC(S)NHP(S)(Oi-Pr)₂]₂ (6) forms a stable potassium salt, which oxidation by iodine leads to a product of heterocyclization, O,O′-diisopropyl-(1-{[(diisopropoxyphosphorothio)amino]carbonothioyl}imidazolidine-2-ylidene)amidothiophosphate (8), in which one of the thiourea fragments is kept.     

Cobalt(II) Complexes with N‐Thioacylamidophosphates and 2,2′‐Bipyridyl and 1,10‐Phenathroline. Crystal Structures,Solution 1H NMR Spectral and Magnetic Properties

Structure and magnetic properties of N‐diisopropoxyphosphorylthiobenzamide PhC(S)‐N(H)‐P(O)(OiPr)₂ ( HL^I ) and N‐diisopropoxyphosphoryl‐N′‐phenylthiocarbamide PhN(H)‐C(S)‐N(H)‐P(O)(OiPr)₂ ( HL^II ) complexes with the Co^II cation of formulas [Co{PhC(S)‐N‐P(O)(OiPr)₂}₂] ( 1 ), [Co{PhN(H)‐C(S)‐N‐P(O)(OiPr)₂}₂] ( 2 ), [Co{PhC(S)‐N(H)‐P(O)(OiPr)₂}₂{PhC(S)‐N‐P(O)(OiPr)₂}₂] ( 1a ) and [Co{PhC(S)‐N‐P(O)(OiPr)₂}₂}(2,2′‐bipy)] ( 3 ), [Co{PhC(S)‐N‐P(O)(OiPr)₂}₂(1,10‐phen)] ( 4 ), [Co{PhN(H)‐C(S)‐N‐P(O)(OiPr)₂}₂(2,2′‐bipy)] ( 5 ), [Co{PhN(H)‐C(S)‐N‐P(O)(OiPr)₂}₂(1,10‐phen)] ( 6 ) were investigated. Paramagnetic shifts in the ¹H NMR spectrum were observed for high‐spin Co^II complexes with HL^I,II , incorporating the S‐C‐N‐P‐O chelate moiety and two aromatic chelate ligands. Investigation of the thermal dependence of the magnetic susceptibility has shown that the extended materials 1‐2 and 6 show ferromagnetic exchange between distorted tetrahedral ( 1 , 2 ) or octahedral ( 1a , 6 ) metal atoms whereas 3 and 5 show antiferromagnetic properties. Compound 4 behaves as a spin‐canted ferromagnet, an antiferromagnetic ordering taking place below a critical temperature, T_c = 115 K. Complexes 1 and 1a were investigated by single crystal X‐ray diffraction. The cobalt(II) atom in complex 1 resides a distorted tetrahedral O₂S₂ environment formed by the C=S sulfur atoms and the P=O oxygen atoms of two deprotonated ligands. Complex 1a has a tetragonal‐bipyramidal structure, Co(O^ax)₂(O^eq)₂(S^eq)₂, and two neutral ligand molecules are coordinated in the axial positions through the oxygen atoms of the P=O groups. The base of the bipyramid is formed by two anionic ligands in the typical 1,5‐O,S coordination mode. The ligands are in a trans configuration.     

Parseval frame wavelets with -dilations

We study Parseval frame wavelets in with matrix dilations of the form , where A is an arbitrary expanding n×n matrix with integer coefficients, such that |detA|=2. We show that each A-MRA admits either Parseval frame wavelets, or Parseval frame bi-wavelets. The minimal number of generators for a Parseval frame associated with an A-MRA (i.e. 1 or 2) is determined in terms of a scaling function. All Parseval frame (bi)wavelets associated with A-MRA's are described. We then introduce new classes of filter induced wavelets and bi-wavelets. It is proved that these new classes strictly contain the classes of all A-MRA Parseval frame wavelets and bi-wavelets, respectively. Finally, we demonstrate a method of constructing all filter induced Parseval frame (bi)wavelets from generalized low-pass filters.     

Optimization of the direct LSC method for determination of biogenic component in liquids by applying 14C

Journal of Radioanalytical and Nuclear Chemistry - Determination of fraction of biogenic component in liquid fuels by a direct radiocarbon measurement in liquid scintillation counter (direct-LSC...     

Variable neighborhood search for extremal graphs. 23. On the Randi? index and the chromatic number

Let G=(V,E) be a simple graph with vertex degrees d₁,d₂,…,d_n. The Randi? index R(G) is equal to the sum over all edges (i,j)∈E of weights . We prove several conjectures, obtained by the system AutoGraphiX, relating R(G) and the chromatic number χ(G). The main result is χ(G)≤2R(G). To prove it, we also show that if v∈V is a vertex of minimum degree δ of G, G−v the graph obtained from G by deleting v and all incident edges, and Δ the maximum degree of G, then .