On unbalanced Boolean functions with best correlation immunity

It is known that the order of correlation immunity of a nonconstant unbalanced Boolean function in $n$ variables cannot exceed $2n/3-1$; moreover, it is $2n/3-1$ if and only if the function corresponds to an equitable $2$-partition of the $n$-cube with an eigenvalue $-n/3$ of the quotient matrix. The known series of such functions have proportion $1:3$, $3:5$, or $7:9$ of the number of ones and zeros. We prove that if a nonconstant unbalanced Boolean function attains the correlation-immunity bound and has ratio $C:B$ of the number of ones and zeros, then $CB$ is divisible by $3$. In particular, this proves the nonexistence of equitable partitions for an infinite series of putative quotient matrices. We also establish that there are exactly $2$ equivalence classes of the equitable partitions of the $12$-cube with quotient matrix $[[3,9],[7,5]]$ and $16$ classes, with $[[0,12],[4,8]]$. These parameters correspond to the Boolean functions in $12$ variables with correlation immunity $7$ and proportion $7:9$ and $1:3$, respectively (the case $3:5$ remains unsolved). This also implies the characterization of the orthogonal arrays OA$(1024,12,2,7)$ and OA$(512,11,2,6)$.Comment: v3: final; title changed; revised; OA(512,11,2,6) discusse

Characteristics of water and ion exchange of Elodea nuttallii cells at high concentrations of lanthanides

© 2016 Elsevier LtdChanges of diffusive permeability of membranes of Elodea nuttallii cells following a short-term (60 min) treatment with high concentrations of lanthanides were recorded by the 1H NMR-diffusometry and conductometry methods. The 1-h infiltration of segments of Elodea nuttallii internodes in 10 mM solutions of nitrates of La, Nd and Lu resulted in the increased leakage of electrolytes from cells, but has no effect on a water diffusive permeability of membranes. In samples subjected to a 30 min pretreatment with a water channel inhibitor HgCl2 the water diffusive permeability of membranes (Pd) drops down under the influence of lanthanides, as well as an outcome of electrolytes. To explain the observed effects the change of spontaneous curvature of membrane lipid layer has been taken into consideration. The interaction of lanthanides with lipids of plasmalemma leads to the negative spontaneous curvature of lipid layer at which membrane channels are unclosed. Blocking of the ionic and water channels by mercury ions compensate the effect of change of spontaneous curvature of lipid layer

Magneto-gyrotropic effects in semiconductor quantum wells (review)

Magneto-gyrotropic photogalvanic effects in quantum wells are reviewed. We discuss experimental data, results of phenomenological analysis and microscopic models of these effects. The current flow is driven by spin-dependent scattering in low-dimensional structures gyrotropic media resulted in asymmetry of photoexcitation and relaxation processes. Several applications of the effects are also considered.Comment: 28 pages, 13 figure

Case of insulinoma detected in a patient after bariatric operation for morbid obesity

The prevalence of insulinomas is 1–3 cases per million population per year of which 4–14% tumor is malignant. Weight gain is one of the symptoms of the disease, often resulting in morbid obesity with indications for surgical treatment. The presented clinical case demonstrates the successful treatment of malignant insulinoma with the manifestation of hypoglycemic syndrome after carrying out biliopancreatic bypass with longitudinal gastrectomy for morbid obesity

Gravitational Couplings of Intrinsic Spin

The gravitational couplings of intrinsic spin are briefly reviewed. A consequence of the Dirac equation in the exterior gravitational field of a rotating mass is considered in detail, namely, the difference in the energy of a spin-1/2 particle polarized vertically up and down near the surface of a rotating body is $\hbar\Omega\sin\theta$. Here $\theta$ is the latitude and $\Omega = 2GJ/(c^2 R^3)$, where $J$ and $R$ are, respectively, the angular momentum and radius of the body. It seems that this relativistic quantum gravitational effect could be measurable in the foreseeable future.Comment: LaTeX file, no figures, 16 page

Geoantineutrino Spectrum, 3He/4He-ratio Distribution in the Earth's Interior and Slow Nuclear Burning on the Boundary of the Liquid and Solid Phases of the Earth's Core

The description problem of geoantineutrino spectrum and reactor antineutrino experimental spectrum in KamLAND, which takes place for antineutrino energy \~2.8 MeV, and also the experimental results of the interaction of uranium dioxide and carbide with iron-nickel and silicaalumina melts at high pressure (5-10 GP?) and temperature (1600-2200C) have motivated us to consider the possible consequences of the assumption made by V.Anisichkin and coauthors that there is an actinid shell on boundary of liquid and solid phases of the Earth's core. We have shown that the activation of a natural nuclear reactor operating as the solitary waves of nuclear burning in 238U- and/or 232Th-medium (in particular, the neutron- fission progressive wave of Feoktistov and/or Teller-Ishikawa-Wood) can be such a physical consequence. The simplified model of the kinetics of accumulation and burnup in U-Pu fuel cycle of Feoktistov is developed. The results of the numerical simulation of neutron-fission wave in two-phase UO2/Fe medium on a surface of the Earth's solid core are presented. The georeactor model of 3He origin and the 3He/4He-ratio distribution in the Earth's interior is offered. It is shown that the 3He/4He ratio distribution can be the natural quantitative criterion of georeactor thermal power. On the basis of O'Nions-Evensen-Hamilton geochemical model of mantle differentiation and the crust growth supplied by actinid shell on the boundary of liquid and solid phases of the Earth's core as a nuclear energy source (georeactor with power of 30 TW), the tentative estimation of geoantineutrino intensity and geoantineutrino spectrum on the Earth surface are given.Comment: 28 pages, 12 figures. Added text, formulas, figures and references. Corrected equations. Changed content of some section

The Hamiltonian Structure of the Second Painleve Hierarchy

In this paper we study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear ODE of order 2n in the independent variable $z$ depending on n parameters denoted by ${t}_1,...,{t}_{n-1}$ and $\alpha_n$. We introduce new canonical coordinates and obtain Hamiltonians for the $z$ and $t_1,...,t_{n-1}$ evolutions. We give explicit formulae for these Hamiltonians showing that they are polynomials in our canonical coordinates

Non-invasive comprehensive laboratory and ultrasound method for the evaluation of the functional status of the liver in patients with type 2 diabetes mellitus

The article analyzes the methods of assessment of fatty infiltration of the liver in patients with type 2 diabetes and a new non-invasive method using laboratory, echohepatodensitographic and tomographic study options. Discriminant models are developed which are used as variables in the values activity of aspartate aminotransferase, gamma-glutamiltranspeptidase, coefficient of density of the tissue in the anterior surface of the liver in echohepatodensitographic study, the density of the liver in tomographic ones study. Using the model, you can define the degree of steatoinfiltration of the liver from minimal to marked. The greatest impact of the classification in the model had the density of the liver determined by tomographic ones and echohepatodensitographicstudy.В статье проанализированы методы оценки жировой инфильтрации печени у больных сахарным диабетом 2 типа и предложен новый неинвазивный метод на основе использования лабораторных, эхогепатоденситометрических и томографических параметров исследования. Разработаны дискриминантные модели, где в качестве переменных используются величины активности аспартатаминотрансферазы, гамма-глутамилтранспептидазы, коэффициента плотности ткани в области передней поверхности печени при эхогепатоденситометрическом исследовании,плотности печени при томографическом исследовании. Используя модели, можно определить степень жировой инфильтрации печени от минимальной до выраженной. Наибольшее классификационное влияние в модели имела величина плотности печени, определяемая при томографическом и зходенситографическом исследовании