THE EFFECT OF SODIUM PYROPHOSPHATE IN CERTAIN CASES OF DEMORALIZATION

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THE RETAINING OF MICROORGANISMS ON SILICAGEL IN ELECTRICAL FIELD

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On Correlation Functions of BPS Operators in 3d N= 6 Superconformal Theories

We introduce a novel harmonic superspace for 3dN=6 superconformal field theories that is tailor made for the study of correlation functions of BPS operators. We calculate a host of two- and three-point functions in full generality and put strong constraints on the form of four-point functions of some selected BPS multiplets. For the four-point function of 12-BPS operators we obtain the associated Ward identities by imposing the absence of harmonic singularities. The latter imply the existence of a solvable subsector in which the correlator becomes topological. This mechanism can be explained by cohomological reduction with respect to a special nilpotent supercharge

ADSORPTION OF METHYLENE BLUE OVER SOME ACID AND THERMALLY ACTIVIED NATIVE SORBENTS IN ULTRASOUND FIELD

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Апробация усредненного метода цепных подстановок для трех- и четырехкратных и мультипликативно-кратных факторных моделей

The aim of the present study is to present the results of the approbation of the methodology of the averaged method of chain substitutions for three and four-multiple and multiplicative-multiple factor models and to systematize in tabular form all mathematical expressions developed so far to determine the individual factor influences by types of factor models. The relevance of the research is caused by the disadvantages and the limited applicability of the methods of deterministic factor analysis developed so far, which is one of the areas of financial and economic analysis. The scientific novelty of the research is the new mathematical expressions developed by the author for determining the individual factor influences according to the methodology of the averaged method of chain substitutions for three and four multiple and multiplicative-multiple factor models. Previous and new mathematical expressions according to the averaged method of chain substitutions are systematized by types of factor models in tabular form. The main conclusion is that the averaged method of chain substitutions has complete universality of application for all types of factor models and is characterized by accuracy and unambiguity of the results obtained for quantification of individual factor influences.Цель настоящего исследования – представить результаты апробации методологии усредненного метода цепных подстановок для трех-, четырехкратных и мультипликативно-кратных факторных моделей и систематизировать в табличной форме все разработанные к настоящему времени математические выражения для определения влияния отдельных факторов на различные типы факторных моделей. Актуальность исследования обусловлена недостатками и ограниченной применимостью разработанных к настоящему времени методов детерминированного факторного анализа, являющегося одним из направлений финансово-экономического анализа. Научная новизна исследования заключается в выведенных автором новых математических выражениях для определения индивидуальных факторных влияний по методике усредненного метода цепных подстановок для трех- и четырехкратных и мультипликативно-кратных факторных моделей. Предыдущие и новые математические выражения усредненным методом цепных подстановок систематизированы по видам факторных моделей в табличной форме. Основной вывод состоит в том, что усредненный метод цепных подстановок имеет полную универсальность применения для всех типов факторных моделей и характеризуется точностью и однозначностью результатов, получаемых при количественной оценке влияния отдельных факторов

CONCERNING METHYLENE BLUE SORPTION OVER ACID AND THERMALLY ACTIVIED KAOLIN IN ULTRASOUND FIELD

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Bootstrapping the half-BPS line defect

We use modern bootstrap techniques to study half-BPS line defects in 4dN= 4 superconformal theories. Specifically, we consider the 1d CFT with OSP(4∗|4) superconformal symmetry living on such a defect. Our analysis is general and based only on symmetries, it includes however important examples like Wilson and ’t Hooft lines in N= 4 super Yang-Mills. We present several numerical bounds on OPE coefficients and conformal dimensions. Of particular interest is a numerical island obtained from a mixed correlator bootstrap that seems to imply a unique solution to crossing. The island is obtained if some assumptions about the spectrum are made, and is consistent with Wilson lines in planar N= 4 super Yang-Mills at strong coupling. We further analyze the vicinity of the strong-coupling point by calculating perturbative corrections using analytic methods. This perturbative solution has the sparsest spectrum and is expected to saturate the numerical bounds, explaining some of the features of our numerical results

Bootstrapping N= 3 superconformal theories

We initiate the bootstrap program for N= 3 superconformal field theories (SCFTs) in four dimensions. The problem is considered from two fronts: the protected subsector described by a 2d chiral algebra, and crossing symmetry for half-BPS operators whose superconformal primaries parametrize the Coulomb branch of N= 3 theories. With the goal of describing a protected subsector of a family of N= 3 SCFTs, we propose a new 2d chiral algebra with super Virasoro symmetry that depends on an arbitrary parameter, identified with the central charge of the theory. Turning to the crossing equations, we work out the superconformal block expansion and apply standard numerical bootstrap techniques in order to constrain the CFT data. We obtain bounds valid for any theory but also, thanks to input from the chiral algebra results, we are able to exclude solutions with N= 4 supersymmetry,allowingustozoominonaspecific N= 3 SCFT