Stability of Landau-Ginzburg branes

We evaluate the ideas of Pi-stability at the Landau-Ginzburg point in moduli space of compact Calabi-Yau manifolds, using matrix factorizations to B-model the topological D-brane category. The standard requirement of unitarity at the IR fixed point is argued to lead to a notion of "R-stability" for matrix factorizations of quasi-homogeneous LG potentials. The D0-brane on the quintic at the Landau-Ginzburg point is not obviously unstable. Aiming to relate R-stability to a moduli space problem, we then study the action of the gauge group of similarity transformations on matrix factorizations. We define a naive moment map-like flow on the gauge orbits and use it to study boundary flows in several examples. Gauge transformations of non-zero degree play an interesting role for brane-antibrane annihilation. We also give a careful exposition of the grading of the Landau-Ginzburg category of B-branes, and prove an index theorem for matrix factorizations.Comment: 46 pages, LaTeX, summary adde

Single-electron latch with granular film charge leakage suppressor

A single-electron latch is a device that can be used as a building block for Quantum-dot Cellular Automata (QCA) circuits. It consists of three nanoscale metal "dots" connected in series by tunnel junctions; charging of the dots is controlled by three electrostatic gates. One very important feature of a single-electron latch is its ability to store ("latch") information represented by the location of a single electron within the three dots. To obtain latching, the undesired leakage of charge during the retention time must be suppressed. Previously, to achieve this goal, multiple tunnel junctions were used to connect the three dots. However, this method of charge leakage suppression requires an additional compensation of the background charges affecting each parasitic dot in the array of junctions. We report a single-electron latch where a granular metal film is used to fabricate the middle dot in the latch which concurrently acts as a charge leakage suppressor. This latch has no parasitic dots, therefore the background charge compensation procedure is greatly simplified. We discuss the origins of charge leakage suppression and possible applications of granular metal dots for various single-electron circuits.Comment: 21 pages, 4 figure

Semiorthogonal decompositions of derived categories of equivariant coherent sheaves

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of bounded derived category of G-equivariant coherent sheaves on X into components, equivalent to derived categories of twisted representations of the group. If the group is finite or reductive over the algebraically closed field of zero characteristic, this gives a full exceptional collection in the derived equivariant category. We apply our results to particular varieties such as projective spaces, quadrics, Grassmanians and Del Pezzo surfaces.Comment: 28 pages, uses XY-pi

Structure of 2-Methyl-5,6,7-triphenyl-6,7-dihydropyrazolo[2,3-\u3cem\u3ea\u3c/em\u3e]pyrimidine

C25H21N3, Mr = 363.46, monoclinic, P21/n, a = 9.245 (2), b = 23.502 (5), c = 9.340 (2) Å, β= 103.50(3)°, V=1973.3(2) Å3, Z=4, Dx= 1.220 (2) g cm-3, λ (Mo Kα )= 0.71069 Å, μ = 0.068 cm-1, F(000) = 768, T= 292 K, R = 0.091 for 1442 unique observed reflections. The dihydropyrimidine ring adopts a distorted sofa conformation. The aryl substituents on the saturated C atoms have an axial orientation

Bound, virtual and resonance SS-matrix poles from the Schr\"odinger equation

A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual and resonant states based on numerical solutions of the Schr\"odinger equation. This method is well-known for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when $r\to\infty$. Concrete calculations are performed for the $1^+$ ground and the $0^+$ first excited states of $^{14}\rm{N}$, the resonance $^{15}\rm{F}$ states ($1/2^+$, $5/2^+$), low-lying states of $^{11}\rm{Be}$ and $^{11}\rm{N}$, and the subthreshold resonances in the proton-proton system. We also demonstrate that in the case the broad resonances their energy and width can be found from the fitting of the experimental phase shifts using the analytical expression for the elastic scattering $S$-matrix. We compare the $S$-matrix pole and the $R$-matrix for broad $s_{1/2}$ resonance in ${}^{15}{\rm F}$Comment: 14 pages, 5 figures (figures 3 and 4 consist of two figures each) and 4 table

Синтез та N-алкілування діетил 4,7-дигідроазоло[1,5-a]піримідин-5,6-дикарбоксилатів

It has been shown that the ternary condensation of oxaloacetic ester (diethyl 2-oxosuccinate), aromatic aldehydes and 3-amino-1,2,4-triazole or 5-aminotetrazole in dimethylformamide results in formation of the corresponding diethyl 7-aryl-4,7-dihydroazolo[1,5-a]pyrimidin-5,6-dicarboxylates. By 1H NMR spectroscopy (according to the data of the chemical shifts of C(2)H-protons for the corresponding N(4)H- and N(4)-methylderivatives of 7-phenyl-4,7-dihydro[1,2,4]triazolo[1,5-a]pyrimidin-5,6-dicarboxylate) it has been found that alkylation of 4,7-dihydro[1,2,4]azolo[1,5-a]pyrimidin-5,6-dicarboxylates in the acetonitrile–saturated water alkali system leads selectively to formation of N(4)-alkyl derivatives. Both the starting compounds obtained and their N(4)-methylsubstituted analogues together with relative diethyl 4-aryl-3,4-dihydropyrimidin-2(1H)-on-5,6-dicarboxylates, 6-unsubstituted 4-aryl-3,4-dihydropyrimidin-2(1H)-on-5-dicarboxylates and the derivatives of 6-COR-7-aryl-4,7-dihydro[1,2,4] triazolo[1,5-a]pyrimidines are the promising objects for studying benzyl C(7)-functionalization of 4,7-dihydroazolo 1,5-a]pyrimidines, as well as of reactions associated with the presence of double C=C-bonds activated by two electron withdrawing groups. Obtaining of the key N(4)H- and N(4)Me-derivatives of 7-phenyl-4,7-dihydro[1,2,4] triazolo- and tetrazolo[1,5-a]pyrimidin-5,6-dicarboxylates also opens the way to the research of biological properties of the compounds of this class. It is noteworthy that being a three-component one the reaction studied, without any doubts, are appropriate for the synthesis of the derivatives of 7-aryl-4,7-dihydro[1,2,4]triazolo- and tetrazolo[1,5-a]pyrimidines containing two electron withdrawing substituents in positions 5 and 6.Показано, что трехкомпонентная конденсация щавелевоуксусного эфира (диэтил 2-оксосукцината), ароматических альдегидов и 3-амино-1,2,4-триазола или 5-аминотетразола в диметилформамиде приводит к образованию соответствующих диэтил 7-арил-4,7-дигидроазоло[1,5-a]пиримидин-5,6-дикарбоксилатов. С помощью 1Н ЯМР-спектроскопии (по данным химических сдвигов сигналов протонов С(2)H для соответствующих N(4)H- и N(4)Ме-производных диэтил 7-фенил-4,7-дигидро[1,2,4]триазоло[1,5-a] пиримидин-5,6-дикарбоксилата) установлено, что алкилирование 7-арил-4,7-дигидроазоло[1,5-a]пиримидин-5,6-дикарбоксилатов в системе ацетонитрил-насыщенная водная щелочь селективно приводит к образованию N(4)-алкилпроизводных. Как полученные исходные соединения, так и их N(4)-метилзамещенные аналоги наряду с родственными диэтил 4-арил-3,4-дигидропиримидин-2(1Н)-он-5,6-дикарбоксилатами, 6-незамещенными этил 4-арил-3,4-дигидропиримидин-2(1Н)-он-5-карбоксилатами и производными 6-COR-7-арил-4,7-дигидро[1,2,4]триазоло[1,5-a]пиримидинов являются перспективными объектами для изучения бензильной С(7)-функционализации 4,7-дигидроазоло[1,5-a]пиримидинов, а также реакций, связанных с наличием двойной C=C-связи, активированной двумя акцепторными группами. Получение ключевых N(4)H- и N(4)Ме-производных 7-фенил-4,7-дигидро[1,2,4]триазоло- и тетразоло[1,5-a]пиримидин-5,6-дикарбоксилатов также открывает путь к биологическим исследованиям соединений этого класса. Заметим, что исследованная реакция, являясь трехкомпонентной, безусловно подходит для синтеза и исследования комбинаторных библиотек производных 7-арил-4,7-дигидро[1,2,4]триазоло- и тетразоло[1,5-a]пиримидинов, содержащих два электроноакцепторных заместителя в положениях 5 и 6.Показано, що трикомпонентна конденсація щавлевооцтового естеру (діетил 2-оксосукцинату), ароматичних альдегідів та 3-аміно-1,2,4-триазолу або 5-амінотетразолу в диметилформаміді призводить до утворення відповідних діетил 4,7-дигідроазоло[1,5-a]піримідин-5,6-дикарбоксилатів. За допомогою 1Н ЯМР-спектроскопії (за даними про хімічні зсуви сигналів протонів С(2)Н для відповідних N(4)H- та N(4)Me-похідних діетил 7-феніл-4,7-дигідро[1,2,4]триазоло[1,5-a]піримідин-5,6-дикарбоксилатів) вста-новлено, що алкілування 4,7-дигідроазоло[1,5-a]піримідин-5,6-дикарбоксилатів у системі ацетонітрилнасичений водний луг селективно призводить до утворення N(4)-алкілпохідних. Як отримані вихідні сполуки, так і їхні N(4)-метилзаміщені аналоги поряд зі спорідненими діетил 4-арил-3,4-дигідропіримідин-2(1Н)-он-5,6-дикарбоксилатами, 6-незаміщеними етил 4-арил-3,4-дигідропіримідин-2(1Н)-он-5-карбоксилатами та похідними 6-COR-7-арил-4,7-дигідро[1,2,4]триазоло[1,5-a]піримідинів є перспективними об’єктами для вивчення бензильної С(7)-функціоналізації 4,7-дигідроазоло[1,5-a]піримідинів, а також реакцій, пов’язаних з наявністю подвійного C=C-зв’язку, активованого двома акцепторними групами. Отримання ключових N(4)H- і N(4)Ме-похідних 7-феніл-4,7-дигідро[1,2,4]триазоло- та тетразоло[1,5-a]піримідин-5,6-дикарбоксилатів також відкриває шлях до біологічних досліджень сполук цього класу. Відзначимо, що досліджена реакція, будучи трикомпонентною, безумовно підходить для синтезу та дослідження комбінаторних бібліотек похідних 7-арил-4,7-дигідро[1,2,4]триазоло- та тетразоло[1,5-a]піримідинів, що містять два електроноакцепторні замісники у положеннях 5 та 6

Anisotropic fragmentation in low-energy dissociative recombination

On a dense energy grid reaching up to 75 meV electron collision energy the fragmentation angle and the kinetic energy release of neutral dissociative recombination fragments have been studied in a twin merged beam experiment. The anisotropy described by Legendre polynomials and the extracted rotational state contributions were found to vary on a likewise narrow energy scale as the rotationally averaged rate coefficient. For the first time angular dependences higher than 2$^{nd}$ order could be deduced. Moreover, a slight anisotropy at zero collision energy was observed which is caused by the flattened velocity distribution of the electron beam.Comment: 8 pages, 4 figures; The Article will be published in the proceedings of DR 2007, a symposium on Dissociative Recombination held in Ameland, The Netherlands (18.-23. July 2008); Reference 19 has been published meanwhile in S. Novotny, PRL 100, 193201 (2008

Energy-sensitive imaging detector applied to the dissociative recombination of D2H+

We report on an energy-sensitive imaging detector for studying the fragmentation of polyatomic molecules in the dissociative recombination of fast molecular ions with electrons. The system is based on a large area (10 cm x 10 cm) position-sensitive, double-sided Si-strip detector with 128 horizontal and 128 vertical strips, whose pulse height information is read out individually. The setup allows to uniquely identify fragment masses and is thus capable of measuring branching ratios between different fragmentation channels, kinetic energy releases, as well as breakup geometries, as a function of the relative ion-electron energy. The properties of the detection system, which has been installed at the TSR storage ring facility of the Max-Planck Institute for Nuclear Physics in Heidelberg, is illustrated by an investigation of the dissociative recombination of the deuterated triatomic hydrogen cation D2H+. A huge isotope effect is observed when comparing the relative branching ratio between the D2+H and the HD+D channel; the ratio 2B(D2+H)/B(HD+D), which is measured to be 1.27 +/- 0.05 at relative electron-ion energies around 0 eV, is found to increase to 3.7 +/- 0.5 at ~5 eV.Comment: 11 pages, 12 figures, submitted to Physical Review

Equivalences between GIT quotients of Landau-Ginzburg B-models

We define the category of B-branes in a (not necessarily affine) Landau-Ginzburg B-model, incorporating the notion of R-charge. Our definition is a direct generalization of the category of perfect complexes. We then consider pairs of Landau-Ginzburg B-models that arise as different GIT quotients of a vector space by a one-dimensional torus, and show that for each such pair the two categories of B-branes are quasi-equivalent. In fact we produce a whole set of quasi-equivalences indexed by the integers, and show that the resulting auto-equivalences are all spherical twists.Comment: v3: Added two references. Final version, to appear in Comm. Math. Phy

The first data on the infestation of the parti-coloured bat, Vespertilio murinus (Chiroptera, Vespertilionidae), with gamasid mites, Steatonyssus spinosus (Mesostigmata, Gamasina, Macronyssidae)

This article presents one of the very few records of a macronyssid mite (Mesostigmata, Gamasina, Macronyssidae) infestation of vesper bats (Chiroptera, Vespertilionidae). It is the first report of the influence of host parameters on the infestation of the parti-coloured bat, Vespertilio murinus, by the mite Steatonyssus spinosus. It has been shown that the infestation varies considerably throughout the host's occupation of summer roosts and the highest infestation was observed in the post-lactation period. Female bats are infested significantly more intensively than male bats due to changes in their immune status during pregnancy and lactation. The infestation decreases in the period when the breeding colony disbands due to both roost switching and the intensification of grooming during this period. © Russian Journal Of Theriology, 2017