Real Form Research Articles

Features and quantitative characteristics of the interaction of benzo[a]pyrene with fractions of the human blood plasma lipoproteins

The paper considers the features and quantitative characteristics of the interaction of human blood plasma low (LDL), very low (VLDL) and high density lipoproteins (HDL) with a polycyclic aromatic hydrocarbon benzo[a]pyrene (B[a]P). Material and methods. The studies were performed using preparative ultracentrifugation of human plasma lipoprotein fractions and fluorescence spectroscopy. Results. The spectral characteristics of tryptophan fluorescence of VLDL, LDL and HDL fractions during titration with B[a]P solution are presented. The interaction of LP fractions with B[a]P was accompanied by quenching of tryptophanil fluorescence: the greatest decrease in fluorescence at saturating concentrations of B[a]P was noted for the HDL fraction — over 80 %; the effect of B[a]P was weaker for LDL (65-74 %) and for VLDL (50-60 %) of the initial level. Based on the results of the tryptophan fluorescence quenching curves and taking into account the molecular weights, quantitative characteristics of the interaction of the LP fractions with B[a]P were obtained: the association constants were of the order of (1.3 - 2.5) × 10-6 M, and the number of binding sites for B[a] P on LP particles ranged from 19 for HDL and up to 43 for VLDL. Conclusion. The quantitative characteristics of the interaction obtained for the complexes of LP with B[a]P allow us to consider the LP of blood plasma as real transport forms for B[a]P and other hydrophobic compounds into the cells of organs and tissues of the body.

The Real Forms of the Fractional Supergroup SL(2,C)

The real forms of complex groups (or algebras) are important in physics and mathematics. The Lie group SL2,C is one of these important groups. There are real forms of the classical Lie group SL2,C and the quantum group SL2,C in the literature. Inspired by this, in our study, we obtain the real forms of the fractional supergroups shown with A3NSL2,C, for the non-trivial N = 1 and N = 2 cases, that is, the real forms of the fractional supergroups A31SL2,C and A32SL2,C.

A receptance method for robust and minimum norm partial quadratic eigenvalue assignment

This paper considers the partial quadratic eigenvalue assignment problem (PQEAP) in active vibration control using state feedback. A receptance method is proposed for PQEAP such that the norms of feedback matrices and the condition number of close-loop system are simultaneously minimized. The real form of the proposed method is developed. The proposed method only uses receptance matrices and the unwanted eigenpairs of open-loop system. The system matrices and the unchanged eigenpairs of open-loop system are not required. The efficiency of the proposed method is illustrated by some numerical examples.

A linearized energy-conservative scheme for two-dimensional nonlinear Schrödinger equation with wave operator

Based on the invariant energy quadratization approach, we propose a linear implicit and local energy preserving scheme for the nonlinear Schrödinger equation with wave operator, that describes the solitary waves in physics. In order to overcome the difficulty of designing an efficient scheme for the imaginary functions of the nonlinear Schrödinger equation with wave operator, we transform the original problem into its real form. By introducing some auxiliary variables, the real form of nonlinear Schrödinger equation with wave operator is reformulated into an equivalent system, which admits the modified local energy conservation law. Then the equivalent system is discretized by the finite difference method to yield a linear system at each time step, which can be efficiently solved. A numerical analysis of the proposed scheme is conducted to show its uniquely solvability and convergence. Our proposed method is validated by numerical simulations in terms of accuracy, energy conservation law and stability.

Absolute parallelism for 2-nondegenerate CR structures via bigraded Tanaka prolongation

Abstract This article is devoted to the local geometry of everywhere 2-nondegenerate CR manifolds M of hypersurface type. An absolute parallelism for such structures was recently constructed independently by Isaev and Zaitsev, Medori and Spiro, and Pocchiola in the minimal possible dimension ( dim ⁡ M = 5 {\dim M=5} ), and for dim ⁡ M = 7 {\dim M=7} in certain cases by the first author. In the present paper, we develop a bigraded (i.e., ℤ × ℤ {\mathbb{Z}\times\mathbb{Z}} -graded) analog of Tanaka’s prolongation procedure to construct an absolute parallelism for these CR structures in arbitrary (odd) dimension with Levi kernel of arbitrary admissible dimension. We introduce the notion of a bigraded Tanaka symbol – a complex bigraded vector space – containing all essential information about the CR structure. Under the additional regularity assumption that the symbol is a Lie algebra, we define a bigraded analog of the Tanaka universal algebraic prolongation, endowed with an anti-linear involution, and prove that for any CR structure with a given regular symbol there exists a canonical absolute parallelism on a bundle whose dimension is that of the bigraded universal algebraic prolongation. Moreover, we show that for each regular symbol there is a unique (up to local equivalence) such CR structure whose algebra of infinitesimal symmetries has maximal possible dimension, and the latter algebra is isomorphic to the real part of the bigraded universal algebraic prolongation of the symbol. In the case of 1-dimensional Levi kernel we classify all regular symbols and calculate their bigraded universal algebraic prolongations. In this case, the regular symbols can be subdivided into nilpotent, strongly non-nilpotent, and weakly non-nilpotent. The bigraded universal algebraic prolongation of strongly non-nilpotent regular symbols is isomorphic to the complex orthogonal algebra 𝔰 ⁢ 𝔬 ⁢ ( m , ℂ ) {\mathfrak{so}(m,\mathbb{C})} , where m = 1 2 ⁢ ( dim ⁡ M + 5 ) {m=\tfrac{1}{2}(\dim M+5)} . Any real form of this algebra – except 𝔰 ⁢ 𝔬 ⁢ ( m ) {\mathfrak{so}(m)} and 𝔰 ⁢ 𝔬 ⁢ ( m - 1 , 1 ) {\mathfrak{so}(m-1,1)} – corresponds to the real part of the bigraded universal algebraic prolongation of exactly one strongly non-nilpotent regular CR symbol. However, for a fixed dim ⁡ M ≥ 7 {\dim M\geq 7} the dimension of the bigraded universal algebraic prolongations of all possible regular CR symbols achieves its maximum on one of the nilpotent regular symbols, and this maximal dimension is 1 4 ⁢ ( dim ⁡ M - 1 ) 2 + 7 {\frac{1}{4}(\dim M-1)^{2}+7} .

GLOBAL ISSUES OF ENVIRONMENTAL LAW ENFORCEMENT IMPACTS ON SUSTAINABLE DEVELOPMENT

The global environmental crisis is caused by wrong and failed policies, low political commitment, deviant behavior from state actors ranging from trans-national corporations, consumerism and individualism culture, which ultimately harms the environment. The purpose of this research is to analyze environmental law, the form and importance of law enforcement in realizing sustainable development. The method used in this paper is to use a normative juridical approach. The results of the research show that currently environmental law is still weak in overcoming various environmental problems that occur. The cause of not optimal environmental law is the lack of a firm and real form of law enforcement. Therefore, law enforcement must be enforced for the realization of sustainable development

Semialgebraic sets and real binary forms decompositions

The Waring Problem over polynomial rings asks how to decompose a homogeneous polynomial p of degree d as a linear combination of d-th powers of linear forms. In this work we give an algorithm to obtain a real Waring decomposition of any given real binary form p of length at most its degree. In fact, we construct a semialgebraic family of Waring decompositions for p. We illustrate our results with some examples.

A comparison of positivity in complex and tropical toric geometry

Given a smooth complex toric variety we will compare real Lagerberg forms and currents on its tropicalization with invariant complex forms and currents on the toric variety. Our main result is a correspondence theorem which identifies the cone of invariant closed positive currents on the complex toric variety with closed positive currents on the tropicalization. In a subsequent paper, this correspondence will be used to develop a Bedford–Taylor theory of plurisubharmonic functions on the tropicalization.

Метафизическое пространство идентичности и идентичности личности, его границы в рамках цивилизационной парадигмы

The problem of identity and identity of the individual, which exists throughout human history, is particularly acute at the intersection of epochs, when existing knowledge and skills are not enough to understand the processes taking place in society, history, and nature, and new theories and tools have not yet been developed. When a civilization was faced with a paradox, when it was decided whether to live as before or accept a new one, it was individuals who were able to go beyond identity that showed a new path. It went against the existing dogmas, against identity. Moreover, over time, man had to accept many more rules and restrictions than at the beginning of his existence. At the intersection of epochs, there was an infusion of new ideas into society. This was done by people who did not just see the future in dreams or nightmares, but were able to imagine what the implementation of a particular postulate in the life of society entails. There was a crisis that literally buried all the old ideas about the world around us and other communities. It was then that the metaphysical perception of the world took on a real form, which, nevertheless, had to be worked out for the sake of the existence of society as a whole.

Development of digital animation as a learning media in primary schools

Digital animation is an example of a concrete manifestation of a copyrighted work that combines computer applications in the multimedia field by combining images, text, audio, animation, and video so that it can modify a series of photographic images in such a way that they appear as if they are moving and making sounds and can become interesting story setting, especially for elementary school children. Also in modern times, digital animation can attract students’ attention and help them develop their understanding of certain subjects. One of the most important theories that reflects how people learn through text and illustrations is the cognitive theory which states that people store more verbal and visual information than students do through words. Digital animation can be used as an alternative learning medium that can be used to bridge learning to be more interesting and to provide a new environment for students. Media is very important to be present in learning to produce stimulation, activeness, new skills for students, and understand the real form of learning applications.

Higher order Levi forms on homogeneous CR manifolds

We investigate the nondegeneracy of higher order Levi forms on weakly nondegenerate homogeneous CR manifolds. Improving previous results, we prove that general orbits of real forms in complex flag manifolds have order less or equal than 3 and the compact ones less or equal 2. Finally we construct by Lie extensions weakly nondegenerate CR vector bundles with arbitrary orders of nondegeneracy.

Kicked rotor with attosecond pulse train

The kicked rotor (KR) is one of the basic models in connection with chaos and quantum chaos. A possible application of an attosecond pulse train as a kicking field in the KR is theoretically examined for the first time. This version of the KR is denoted as an atto-KR. It seems to be the most realistic version of the KR because it takes into account the real form of the kicking field as it appears in the experiments. The atto-KR is investigated from the classical and the quantum aspects. In the classical case, a new map instead of the Chirikov standard map is proposed. It may be useful in appropriate experiments with the classical chaos. In the quantum case, the atto-KR gives satisfactory results. Phenomena such as dynamical localization and quantum resonances appear in the undisturbed form. It may be also used for examining the influence of the quantum effects on classical chaos and diffusion.

Wintgen ideal submanifolds: New examples, frame sequence and Möbius homogeneous classification

In real space forms, any submanifold must satisfy the so-called DDVV inequality which relates the scalar curvature, the mean curvature, and the scalar normal curvature pointwise. When the equality is attained at each point, it is called a Wintgen ideal submanifold. This property is invariant under the conformal transformations. So we try to give a complete classification of this class of submanifolds. This is done under the additional assumption of Möbius homogeneity in this paper. Some new interesting examples are constructed using the real representation of SU(2), which turn out to constitute the majority of Möbius homogeneous Wintgen ideal submanifolds. The classification follows by constructing a frame sequence. This reveals a wonderful connection with the classical harmonic sequence of Riemann surfaces.

On $$\mathrm {G}_2$$ and sub-Riemannian model spaces of step and rank three

We give the complete classification of all sub-Riemannian model spaces with both step and rank three. Model spaces in this context refer to spaces where any infinitesimal isometry between horizontal tangent spaces can be integrated to a full isometry. They will be divided into three families based on their nilpotentization. Each family will depend on a different number of parameters, making the result crucially different from the known case of step two model spaces. In particular, there are no nontrivial sub-Riemannian model spaces of step and rank three with free nilpotentization. We also realize both the compact real form $${\mathfrak {g}}_2^c$$ and the split real form $${\mathfrak {g}}_2^s$$ of the exceptional Lie algebra $${\mathfrak {g}}_2$$ as isometry algebras of different model spaces.

Orthogonality of bilinear forms and application to matrices

We characterize Birkhoff-James orthogonality of continuous vector-valued functions on a compact topological space. As an application of our investigation, Birkhoff-James orthogonality of real bilinear forms are studied. This allows us to present an elementary proof of the well-known Bhatia-Šemrl Theorem in the real case.

Memristor emulator – a nonlinear load for reduction of ferroresonance in a single-phase transformer

PurposeAn annual substation equipment failure report says 3/7 capacitive voltage transformer (CVT) got damaged because of ferroresonance overvoltage. The conventional mitigation circuit fails to protect the transformer as the overvoltage may fall in the range between 2 and 4 per unit. It is necessary to develop a device to suppress the overvoltage as well as overcurrent of the CVT. This study aims to propose the suitability of memristor emulator as a mitigation circuit for ferroresonance.Design/methodology/approachThe literature implies that a nonlinear circuit can protect the transformer against ferroresonance. An attempt is made with a memristor emulator using Operational Amplifier (OPAMP) for the mitigation of ferroresonance in a prototype transformer. The circuit is simulated using PSpice and validated for its ideal characteristics using hardware implementation. The nonlinear memductance is designed which is required to mitigate the ferroresonance. The mitigation performance has been compared with conventional method along with fast Fourier transform (FFT) analysis.FindingsWhile the linear resistor recovers the secondary voltage by 74.1%, the memristor emulator does it by 82.05% during ferroresonance. Also, the total harmonic distortion (THD) of ferroresonance signal found to be 22.06% got improved as 2.56% using memristor emulator.Research limitations/implicationsThe suitability of memristor emulator as a mitigation circuit for ferroresonance is proposed in this paper. As ferroresonance occurs in instrument transformers which have extra high voltage (EHV) rated primary windings and (110 V/[110 V/1.732]) rated secondary windings, the mitigation device is proposed to be connected as a nonlinear load across the secondary windings of the transformer. This paper discusses the preliminary work of ferroresonance mitigation in a prototype transformer. The mitigation circuit may have memristor or meminductor for ferroresonance mitigation when they are commercially available in future.Practical implicationsThe electronic component-based memristor emulator may not work at 110 V practically as they may be rated at low power. Hence, chemical component-based memristor emulator was developed to do the same. The authors like to clarify that the memristor will be a solution for ferroresonance in future not the memristor emulator circuit.Social implicationsWith the real form of memristor, the transistor world will be replaced by it and may have a revolution in the field of electronics, VLSI, etc. This contribution attempts to project the use of memristor in a smaller scale in high-voltage engineering.Originality/valueThe electronic component-based memristor emulator is proposed as a mitigation circuit for ferroresonance. The hypothesis has been verified successfully in a prototype transformer. Testing circuit of memristor emulator involves transformer, practically. The mitigation performance has been compared with conventional method technically and justified with FFT analysis.

Recursive formulation of the WKB solution for linear time-varying dynamic systems

This work proposes a new calculation algorithm of the Wentzel–Kramers–Brillouin (WKB) solution for slow linear time-varying (LTV) systems based on the recursive formulation. For a linear dynamic system with time-varying (TV) mass, damping or stiffness, the recursive relations in real function form among the components of the WKB solution are obtained. The integral terms within the sampling intervals that cannot be solved analytically are approximated by simple algebraic calculations with high precision. Thus, the conventional expression of the WKB solution involving complex numerical integral terms is reduced to an analytical recursive formulation. An explicit function relationship between the TV system parameters and the dynamic response can be obtained when the external excitation is given. In the premise of similar accuracy, the recursive formulation has much higher efficiency than the conventional calculation process, which is verified by applying the proposed method to a particular LTV dynamic system.

Real forms of the complex Neumann system: A method for finding real roots of polynomial [formula omitted

The topology of Arnold–Liouville level sets of the real forms of the complex generic Neumann system depends indirectly on the positions of the roots of the special polynomial US(λ). For certain polynomials, the existence and positions of the real roots, according to the suitable parameters of the system, is not obvious.In the paper, a method for checking the existence and positions of the real roots of the polynomials US(λ) is given. The method and algorithm are based on searching of a positive solution of a system of linear equations. In case n=2, we provide a complete solution to the problem of existence of real roots for all special polynomials and determine the topology of the Arnold–Liouville level sets.

Nonclassical vibrations of a monoclinic composite strip

A mathematical model of damped flexural-torsional vibrations of monoclinic composite strip of constant length rectangular cross section is proposed. The model is based on the refined bending theory Timoshenko beams, the theory of generalized Voigt — Lekhnitskii torsion and the elastic-viscoelastic correspondence principle in the linear theory of viscoelasticity. A two-stage method for solving a coupled system of differential equations is developed. First, using the Laplace transform in spatial variable, real natural frequencies and natural forms are found. To determine the complex natural frequencies of the strip in found real values are used as their initial values of natural frequencies, and then the complex frequencies are calculated by the method iterations of the third order. An assessment of the reliability of the mathematical model and method of numerical solution, performed by comparing calculated and experimental values of natural frequencies and loss factors is given. The results of a numerical study of the effect angles of orientation of reinforcing fibers and lengths by the values of natural frequencies and loss factors for free-free and cantilever monoclinic stripes are discussed. It is shown that for the free-free strip the region of mutual transformation eigenmodes of coupled vibration modes arise for quasi-bending and quasi-twisting vibrations of either even or odd tones. In the console strip of the region of mutual transformation of eigenforms of coupled modes vibrations occur for both even and odd tones.

Полиция в общественном мнении молодежи

On the basis of qualitative sociological surveys, the article presents certain aspects of public opinion of students of the Khabarovsk territory about the activities of the police, real and potential forms of interaction between the police officers and youth, directions of harmonizing relations between these social groups. The study showed that assessments of young people in these aspects are not uniform. In the collective consciousness of young people, the police mostly evoke positive associations. This is due, first of all, to the experience of personal positive interaction of students with the police officers, including as victims, or the experience of friends, acquaintances, relatives of respondents. Presence of similar experience, but substantively negative predetermined the spread of skeptical assessments of the activities of this law enforcement body in the student environment. The media, the Internet, and rumors also have a significant impact on the negative opinion of the police. Despite the presence of an unfavorable perception of the police, many respondents acted in cooperation with the police not only as victims or offenders, but, above all, in the role of those who assisted the police in solving the tasks facing it. The overwhelming majority of respondents expressed their readiness to help the police if necessary. The respondents see the main directions for optimizing interaction between young people and the police and increasing confidence in the latter in transforming the police as a social institution, but not in the society as a whole or Russian youth in particular.