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31.
Leszek Słomiński 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(5):275-293
The problem of approximation of a solution to a reflecting stochastic differential equation (SDE) with jumps by a sequence of solutions to SDEs with penalization terms is considered. The approximating sequence is not relatively compact in the Skorokhod topology J 1 and so the methods of approximation based on the J 1-topology break down. In the paper, we prove our convergence results in the S-topology on the Skorokhod space D(R+,?R d ) introduced recently by Jakubowski. The S-topology is weaker than J 1 but stronger than the Meyer-Zheng topology and shares many useful properties with J 1. 相似文献
32.
Normal modes of s-triazine and cyanuric acid were calculated at the DFT(B3LYP)/6-311++G(d,p) level. These modes were analyzed in terms of potential energy distribution (PED), computed using a specially designed set of symmetry coordinates. The normal-mode analysis was described in detail and the PED matrix definition used in the calculations was provided. Particular attention has been devoted to the degenerate vibrations. The experimental infrared spectra of s-triazine and cyanuric acid isolated in low-temperature Ar matrices have been recorded and interpreted by comparison with the theoretically predicted normal modes. In the spectrum of matrix-isolated s-triazine, the IR bands originating from 13C and 15N isotopologues with one of the ring atoms substituted by a rare isotope were detected. These bands were identified thanks to the excellent agreement between the experimentally observed and theoretically predicted isotope shifts. 相似文献
33.
Tertiary aliphatic β- and γ-nitro nitriles and ketones deuterated in (several) selected positions had been synthesized. The deuterated nitro compounds served as a starting material for the corresponding deuterium labeled nitrones or hydroxylamines (reducing with aluminum amalgam). Further oxidation of the last two groups of compounds with sodium periodate or m-CPBA afforded the relevant deuterated tertiary C-nitroso compounds. 相似文献
34.
Substituted five-membered cyclic nitrones (pyrroline N-oxides) have been obtained in good to high yields from tertiary γ-nitro ketones and nitriles employing aluminium amalgam as a reducing agent in moist diethyl ether or THF. Attempts to obtain cyclic amino nitrones from α- or β-nitro nitriles failed and only the corresponding hydroxylamines have been isolated. Both nitrones and hydroxylamines have been used for synthesis of tertiary C-nitroso nitriles or ketones. 相似文献
35.
We discuss the following problems, plaguing the present search for the “final theory”: (1) How to find a mathematical structure rich enough to be suitably approximated by the mathematical structures of general relativity and quantum mechanics? (2) How to reconcile nonlocal phenomena of quantum mechanics with time honored causality and reality postulates? (3) Does the collapse of the wave function contain some hints concerning the future quantum gravity theory? (4) It seems that the final theory cannot avoid the problem of dynamics, and consequently the problem of time. What kind of time, if this theory is supposed to be background free? (5) Will the dynamics of the “final theory” be probabilistic? Quantum probability exhibits some essential differences as compared with classical probability; are they but variations of some more general probabilistic measure theory? (6) Do we need a radically new interpretation of quantum mechanics, or rather an entirely new theory of which the present quantum mechanics is an approximation? (7) If the final theory is to be background free, it should provide a mechanism of space-time generation. Should we try to explain not only the generation of space-time, but also the generation of its material content? (8) As far as the existence of the initial singularity is concerned, one usually expects either “yes” or “not” answers from the final theory. However, if the mathematical structure of the future theory is supposed to be truly more general that the mathematical structures of the present general relativity and quantum mechanics, is a “third answer“ possible? Could this third answer be related to the probabilistic character of the final theory? We discuss these questions in the framework of a working model unifying gravity and quanta. The analysis reveals unexpected aspects of these rather wildly discussed issues. 相似文献
36.
Leszek Krzemień Krzysztof Brzozowski Marcin Witkowski Micha? Zawada 《Optics Communications》2011,284(5):1247-1253
We present a method of Doppler-free laser frequency stabilization based on magnetically assisted rotation spectroscopy (MARS) which combines the Doppler-free velocity-selective optical pumping (VSOP) and magnetic rotation spectroscopy. The stabilization is demonstrated for the atomic rubidium transitions at 780 nm. The proposed method is largely independent of stray magnetic fields and does not require any modulation of the laser frequency. Moreover, the discussed method allows one to choose between locking the laser exactly to the line center, or with a magnetically-controlled shift to an arbitrary frequency detuned by up to several natural linewidths. This feature is useful in many situations, e.g. for laser cooling experiments. In addition to presenting the principle of the method, its theoretical background and peculiarities inherent to the repopulation VSOP are discussed. 相似文献
37.
Leszek Olszowy 《Mediterranean Journal of Mathematics》2014,11(2):687-701
The aim of this paper is to study a new family of measures of noncompactness in the space ${L^1_{\text{loc}}(\mathbb{R}_+)}$ consisting of all real functions locally integrable on ${\mathbb{R}_+}$ , equipped with a suitable topology. As an example of applications of the technique associated with that family of measures of noncompactness, we study the existence of solutions of a nonlinear Volterra integral equation in the space ${L^1_{\text{loc}}(\mathbb{R}_+)}$ . The obtained result generalizes several ones obtained earlier with help of other methods. 相似文献
38.
Leszek Pazderski Tomasz Pawlak Jerzy Sitkowski Lech Kozerski Edward Szłyk 《Magnetic resonance in chemistry : MRC》2010,48(6):450-457
1H, 13C and 15N NMR studies of iron(II), ruthenium(II) and osmium(II) tris‐chelated cationic complexes with 2,2′‐bipyridine and 1,10‐phenanthroline of the general formula [M(LL)3]2+ (M = Fe, Ru, Os; LL = bpy, phen) were performed. Inconsistent literature 1H signal assignments were corrected. Significant shielding of nitrogen‐adjacent protons [H(6) in bpy, H(2) in phen] and metal‐bonded nitrogens was observed, being enhanced in the series Ru(II) → Os(II) → Fe(II) for 1H, Fe(II) → Ru(II) → Os(II) for 15N and bpy → phen for both nuclei. The carbons are deshielded, the effect increasing in the order Ru(II) → Os(II) → Fe(II). Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
39.
40.
The problem of characterizing the least expensive bond portfolio that enables one to meet his/her liability to pay C dollars
K years from now is dealt with in this article. Bond prices are allowed to be either overpriced or underpriced at the purchase
time, while at the sale time the bonds are suppose to be fairly priced. Assuming shifts in spot rates to occur instantly after
the acquisition of a bond portfolio Z and to follow fairly general type of behavior described by the condition (2), we give
both necessary and sufficient conditions for Z to solve the immunization problem above. Our model is general enough to cover
situations with twists in the yield curve. Making use of the K-T conditions, we explain in remark 7 why we focus on search
of an optimal portfolio in the class of barbell strategies. Finally, by means of the K-T conditions we find an optimal bond
portfolio which solves the immunization problem.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献