189 research outputs found
Motivic Milnor fibre for nondegenerate function germs on toric singularities
We study function germs on toric varieties which are nondegenerate for their
Newton diagram. We express their motivic Milnor fibre in terms of their Newton
diagram. We extend a formula for the motivic nearby fibre to the case of a
toroidal degeneration. We illustrate this by some examples.Comment: 14 page
The study of the canonical Watson-Crick DNA base pairs by Moller-Plesset perturbation method: the nature of their stability
Gas-phase gradient optimization was carried out on the canonical Watson-Crick DNA base pairs using the second-order Moller-Plesset (MP2) perturbation method at the 6-31G* and 6-31G*(0.25) basis sets. It is detected that full geometry optimization at the MP2 level leads to an intrinsically nonplanar propeller-twisted and buckled geometry of G-C and A-T base pairs. Morokuma-Kitaura (MK) and reduced variational space (RVS) methods of the decomposition for molecular Hartree-Fock interaction energies were used for the investigation of the hydrogen bonding in the Watson-Crick base pairs in question. It is shown that the stability of the hydrogen-bonded DNA base pairs originates mainly from electrostatic interactions. At the same time the polarization, charge transfer and dispersion interactions also make considerable contribution to the attraction energy of bases.Використовуючи теорію збурень Моллера-Плессета у другому порядку, проведено градієнтну оптимізацію канонічних уотсон-криківських пар основ у базисах 6-31G* і 6-31G*(0,25). Знайдено, що повна оптимізація геометрії на рівні МР2 спричинює внутрішньо неплоску пропелер-повернуту і вигнуту геометрію пар основ G-C і А-Т. Для дослідження водневих зв'язків в уотсон-криківських парах використано методи Мороку ми-Кітаури та зменшеного варіаційного простору для розкладу хартрі-фоківської енергії молекулярної взаємодії. Показано, що стабільність водневих зв'язків пар основ переважно з'являється за рахунок електростатичної взаємодії. В той же час поляризаційна і исперсійна компоненти та взаємодія з перенесенням заряду також роблять значний внесок в енергію притяжіння основ.Используя теорию возмущений Моллера-Плессета во втором порядке, проведена градиентная оптимизация канонических уотсон-криковских пар оснований в базисах 6-31G* и 6-31G* (0,25). Обнаружено, что полная оптимизация геометрии на уровне МР2 приводит к внутренне неплоской пропеллер-повернутой и изогнутой геометрии пар оснований G-C и А-Т. Для исследования водородных связей в уотсон-криковских парах оснований использованы методы Морокумы-Китауры и уменьшенного вариационного пространства для разложения хартри-фоковской энергии молекулярного взаимодействия. Показано, что стабильность водородно-связанных пар оснований возникает, как правило, благодаря электростатическим взаимодействиям. В то же время поляризационная и дисперсионная компоненты, а также взаимодействие с переносом заряда в свою очередь вносят значительный вклад в энергию притяжения оснований
Graph hypersurfaces and a dichotomy in the Grothendieck ring
The subring of the Grothendieck ring of varieties generated by the graph
hypersurfaces of quantum field theory maps to the monoid ring of stable
birational equivalence classes of varieties. We show that the image of this map
is the copy of Z generated by the class of a point. Thus, the span of the graph
hypersurfaces in the Grothendieck ring is nearly killed by setting the
Lefschetz motive L to zero, while it is known that graph hypersurfaces generate
the Grothendieck ring over a localization of Z[L] in which L becomes
invertible. In particular, this shows that the graph hypersurfaces do not
generate the Grothendieck ring prior to localization. The same result yields
some information on the mixed Hodge structures of graph hypersurfaces, in the
form of a constraint on the terms in their Deligne-Hodge polynomials.Comment: 8 pages, LaTe
The molecular mechanism of the spontaneous substitution mutations caused by tautomerism of bases: Post Hartree-Fock study of the DNA rare base pairs
Gas-phase gradient optimization of the DNA rare base pairs containing lactam-lactim and amino-imino tautomers was carried oat using the Hartree-Fock (HF), Density Functional Theory (DFT) and the second-order Moller-Plesset perturbation (MP2) methods at the 6-31G(d, p) basis set. It is shown that full geometry optimization at the MP2 level leads to an intrinsically nonplanar propeller-twisted and buckled geometry of G*-T and G-T* base pairs. The nonplanarity of the pairs is caused by pyramidalization of the amino nitrogen atoms, which is underestimated by the HF and DFT methods. This justifies the importance of geometry optimization at the MP2 level for obtaining reliable prediction of the charge distribution, molecular dipole moments and geometrical structure of the base pairs. The comparison of the formation energies for the rare base pairs shows the energetical preference of the G*-T and A-C* base pairs as compared with the G-T* and A*-C ones, respectively. It is detected that the stabilization energies of the G-T* and A*-C base pairs describing the interaction between monomers are essentially larger than those of the G*-T and A-C* base pairs, respectively. An analysis of the decomposition members for molecular HF interaction energies by Morokuma-Kitaura (MK) and the Reduced Variational Space (RVS) methods showed that the nature of a larger stability of the G-T* and A*-C base pairs as compared to the G*-T and A-C* ones is due to the electrostatic interactions by 60–65 % and the polarization and charge transfer interactions by 35–40 %.Здійснено газофазну градієнтну оптимізацію рідкісних пар основ ДНК, які включають у себе лактам-лактимні і аміно-імінні таутомери, за допомогою методу Хартрі-Фока (ХФ), теорії функціонала густини (ТФГ) та другого порядку теорії збурень Моллера-Плессета (МП2) у базисі 6-31G(d, р). Показано, що повна оптимізація геометрії на рівні МП2 веде до внутрішньо неплоскої пропелер-обертальної і вигнутої геометрії пар основ G*-T і G-T*. Неплощинність пар обумовлена пірамідалізацією атомів азоту аміногрупи, яка недооцінюється методами ХФ і ТФГ. Це виправдовує важливість оптимізації геометрії на рівні МП2 для отримання помірко ваного передбачення розподілу зарядів, молекулярних дипольних моментів і геометричної структури пар основ. Порівняння енергій формування рідкісних пар основ демонструє енергетичну перевагу пар основ G*-T і А-С* стосовно пар G-T* і А*-С. Виявлено, що величини енергій стабілізації пар основ G-T* і А*-С, які описують взаємодію між мономерами, значно більші за аналогічні значення пар основ G*-T і А-С* відповідно. Використовуючи аналіз членів розкладання ХФ енергій молекулярної взаємодії методами Морокуми-Кітаури і зменшеного варіаційного простору, знайдено, що природа більшої стабільності пар основ G-T* і А*-С порівняно з парами G*-T і А-С* на 60–65 % обумовлена електростатичними взаємодіями і на 35–40 % — поляризаційними взаємодіями і взаємодіями з перенесенням заряду відповідно.Gas-phase gradient optimization of the DNA rare base pairs containing lactam-lactim and amino-imino tautomers was carried oat using the Hartree-Fock (HF), Density Functional Theory (DFT) and the second-order Moller-Plesset perturbation (MP2) methods at the 6-31G(d, p) basis set. It is shown that full geometry optimization at the MP2 level leads to an intrinsically nonplanar propeller-twisted and buckled geometry of G*-T and G-T* base pairs. The nonplanarity of the pairs is caused by pyramidalization of the amino nitrogen atoms, which is underestimated by the HF and DFT methods. This justifies the importance of geometry optimization at the MP2 level for obtaining reliable prediction of the charge distribution, molecular dipole moments and geometrical structure of the base pairs. The comparison of the formation energies for the rare base pairs shows the energetical preference of the G*-T and A-C* base pairs as compared with the G-T* and A*-C ones, respectively. It is detected that the stabilization energies of the G-T* and A*-C base pairs describing the interaction between monomers are essentially larger than those of the G*-T and A-C* base pairs, respectively. An analysis of the decomposition members for molecular HF interaction energies by Morokuma-Kitaura (MK) and the Reduced Variational Space (RVS) methods showed that the nature of a larger stability of the G-T* and A*-C base pairs as compared to the G*-T and A-C* ones is due to the electrostatic interactions by 60–65 % and the polarization and charge transfer interactions by 35–40 %
Exceptional Sequences of Line Bundles and Spherical Twists - a Toric Example
Exceptional sequences of line bundles on a smooth projective toric surface
are automatically full when they can be constructed via augmentation. By using
spherical twists, we give examples that there are also exceptional sequences
which can not be constructed this way but are nevertheless full.Comment: 12 pages, 3 figure
A Quantum-Conceptual Explanation of Violations of Expected Utility in Economics
The expected utility hypothesis is one of the building blocks of classical
economic theory and founded on Savage's Sure-Thing Principle. It has been put
forward, e.g. by situations such as the Allais and Ellsberg paradoxes, that
real-life situations can violate Savage's Sure-Thing Principle and hence also
expected utility. We analyze how this violation is connected to the presence of
the 'disjunction effect' of decision theory and use our earlier study of this
effect in concept theory to put forward an explanation of the violation of
Savage's Sure-Thing Principle, namely the presence of 'quantum conceptual
thought' next to 'classical logical thought' within a double layer structure of
human thought during the decision process. Quantum conceptual thought can be
modeled mathematically by the quantum mechanical formalism, which we illustrate
by modeling the Hawaii problem situation, a well-known example of the
disjunction effect, and we show how the dynamics in the Hawaii problem
situation is generated by the whole conceptual landscape surrounding the
decision situation.Comment: 9 pages, no figure
Magnetic field effect on tunnel ionization of deep impurities by terahertz radiation
A suppression of tunnelling ionization of deep impurities in terahertz
frequency electric fields by a magnetic field is observed. It is shown that the
ionization probability at external magnetic field, B, oriented perpendicular to
the electric field of terahertz radiation, E, is substantially smaller than
that at B || E. The effect occurs at low temperatures and high magnetic fields
Kazan period of life-sustaining activity of professor V.I. Ra-zumovsky — a pioneer of Russian neurosurgery
There were presented historical data of life-sustaining activity of professor V. I. Razumovsky — a pioneer of Russian neurosurgery, who began to perform and then was performing systematically neurosurgical operations in the Kazan clinic under the guidance of outstanding neurologists V. M. Bekhterev and L. O. Darkshevich
The Hodge--Poincar\'e polynomial of the moduli spaces of stable vector bundles over an algebraic curve
Let X be a nonsingular complex projective variety that is acted on by a
reductive group and such that . We
give formulae for the Hodge--Poincar\'e series of the quotient .
We use these computations to obtain the corresponding formulae for the
Hodge--Poincar\'e polynomial of the moduli space of properly stable vector
bundles when the rank and the degree are not coprime. We compute explicitly the
case in which the rank equals 2 and the degree is even.Comment: Final published version. arXiv admin note: text overlap with
arXiv:math/0305346, arXiv:math/0305347 by other author
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