Spherical DG-functors

For two DG-categories A and B we define the notion of a spherical Morita quasi-functor A -> B. We construct its associated autoequivalences: the twist T of D(B) and the co-twist F of D(A). We give powerful sufficiency criteria for a quasi-functor to be spherical and for the twists associated to a collection of spherical quasi-functors to braid. Using the framework of DG-enhanced triangulated categories, we translate all of the above to Fourier-Mukai transforms between the derived categories of algebraic varieties. This is a broad generalisation of the results on spherical objects in [ST01] and on spherical functors in [Ann07]. In fact, this paper replaces [Ann07], which has a fatal gap in the proof of its main theorem. Though conceptually correct, the proof was impossible to fix within the framework of triangulated categories.Comment: 53 pages; v2: An inaccuracy in the definition of homotopy action maps fixed by tensoring everything in sight with bar-complexes; several twisted complex computations correcte

Orthogonally spherical objects and spherical fibrations

We introduce a relative version of the spherical objects of Seidel and Thomas. Define an object E in the derived category D(Z x X) to be spherical over Z if the corresponding functor from D(Z) to D(X) gives rise to autoequivalences of D(Z) and D(X) in a certain natural way. Most known examples come from subschemes of X fibred over Z. This categorifies to the notion of an object of D(Z x X) orthogonal over Z. We prove that such an object is spherical over Z if and only if it has certain cohomological properties similar to those in the original definition of a spherical object. We then interpret this geometrically in the case when our objects are actual flat fibrations in X over Z.Comment: 29 pages; v2: A missing assumption reinstated in Prop. 3.7, some notation cleaned up. The final version to appear in Adv. in Mat

Posteriori estimation of teaching and learning process

У статті розглядується питання застосування технології апостеріорного оцінювання навчально-пізнавальної діяльності студентів. Результати апостеріорного оцінювання надають важливу інформацію про ефективність викладання викладачеві та навчальному закладу.В статье рассматривается вопрос использования технологии апостериорного оценивания учебно-познавательной деятельности студентов. Результаты апостериорного оценивания предоставляют важную информацию об эффективности преподавания преподавателю и учебному заведению.The question about the development and application of technology posterior estimation of teaching and educational activity of the students, is considered at the article. Posteriori estimation results provide important information about the performance of teaching and teacher education institutions

Estimating individual cone fundamentals from their color-matching functions

Estimation of individual spectral cone fundamentals from color-matching functions is a classical and longstanding problem in color science. In this paper we propose a novel method to carry out this estimation based on a linear optimization technique, employing an assumption of a priori knowledge of the retinal absorptance functions. The result is an estimation of the combined lenticular and macular filtration for an individual, along with the nine coefficients in the linear combination that relates their color-matching functions to their estimated spectral-cone fundamentals. We test the method on the individual Stiles and Burch color-matching functions and derive cone-fundamental estimations for different viewing fields and matching experiment repetition. We obtain cone-fundamental estimations that are remarkably similar to those available in the literature. This suggests that the method yields results that are close to the true fundamentals

Luminescent coordination polymers based on Ca²⁺ and octahedral cluster anions [{M₆Clⁱ₈}Clᵃ₆}²⁻ (M = Mo, W) : synthesis and thermal stability studies

Luminescent coordination polymers (CPs) based of inexpensive stable precursors are attractive materials for applications. Here we report the synthesis and evaluation of the stability and photophysical characteristics of the first examples of phosphorescent CPs based on octahedral molybdenum and tungsten cluster anions. Specifically 1D CP trans-[{Ca(OPPh₃)₄}{{M₆Clⁱ₈}Clᵃ₆}]∞ (M = Mo, W) can be obtained either directly at increased temperature or via intermediate phases [cis-Ca(OPPh₃)₄(H₂O)₂][{M₆Clⁱ₈}Clᵃ₆]∙2CH₃CN that are stable at room-temperature, but convert to the titled CP at temperatures above 100 °C

Meteoprotective properties of melaxen in old and middle aged patients with ischemic heart disease in combination with arterial hypertension

We studied 102 patients (mean age 60.1±3.3 years) with arterial hypertension (AH) II-III stage, grade 2-3 and ischemic heart disease (exertional angina functional class (FC) I-II, postinfarction cardiosclerosis). The control group of patients received traditional therapy (TT): beta -blockers, calcium channel blockers, ACE inhibitors, antiplatelet agents, diuretics and nitrate

Empirical evidence for unique hues?

Red, green, blue, yellow, and white have been distinguished from other hues as unique. We present results from two experiments that undermine existing behavioral evidence to separate the unique hues from other colors. In Experiment 1 we used hue scaling, which has often been used to support the existence of unique hues, but has never been attempted with a set of non-unique primaries. Subjects were assigned to one of two experimental conditions. In the "unique" condition, they rated the proportions of red, yellow, blue, and green that they perceived in each of a series of test stimuli. In the "intermediate" condition, they rated the proportions of teal, purple, orange, and lime. We found, surprisingly, that results from the two conditions were largely equivalent. In Experiment 2, we investigated the effect of instruction on subjects' settings of unique hues. We found that altering the color terms given in the instructions to include intermediate hues led to significant shifts in the hue that subjects identified as unique. The results of both experiments question subjects' abilities to identify certain hues as unique