Arbitrary Number Of Generations Research Articles

Optimizing the Operation Mode of an Autonomous Wind Power Plant with a Distributed Generation System

The article considers physical interactions and a mathematical model of a wind power plant consisting of separate wind turbines distributed over a large area, which generate electric energy to common buses and from them to a transformer and load. Induction generators are used as electromechanical converters, which differ from synchronous ones in having a simple design and featuring better operational reliability. In view of distributed location of wind turbines, each of them generally operates under different wind conditions; in addition, their interaction depends both on the length of cable routes to the busbars and on the parameters of transformers. Owing to these circumstances, it is of interest to study parallel operation of distributed induction generators and the possibility to optimize the wind power plant operation mode to ensure the required quality of the generated electricity in terms of power supply frequency and voltage. The operation mode of such wind power plant – taking as an example two induction generators operating in parallel on a common resistive-inductive load – is represented by a complex T-shaped equivalent circuit, the mathematical description of which is given by nonlinear complex homogeneous equations for nodal potentials. The magnetization inductances are nonlinear functions of the EMFs, which are analytically approximated by an inverse trigonometric function. The mechanical equilibrium equations include the wind turbine torques, the electromagnetic moments of generators, the rotating parts inertia moments, and resistance and friction moments. It should be noted that with a given wind turbine size, its torque depends on the angular rotation speed, wind velocity and blade angle, and is approximated by spline functions of the load impedance and wind turbine rotation speeds. The operating mode analysis is based on the numerical calculation of non-trivial solutions of nonlinear complex equations for the potentials of the equivalent circuit nodes, load voltage and frequency, and their subsequent approximation as a function of rotation speeds and load impedance at fixed values of load inductance, capacitances, ballast conductivity, and other parameters. On the example of a calculation performed for typical parameters of a small-capacity wind power plant with a real difference of wind velocities for individual wind turbines and variable load impedance, it is shown that by changing the blade angle alone, it is not possible to stabilize the voltage parameters on the load, while by simultaneously changing the capacitive and ballast conductivities, the frequency and voltage can be stabilized at the specified levels. In particular, with increasing the wind turbine rotation speeds, the capacitive and ballast conductivity should be increased, and with an increase in load resistance, the ballast conductivity should also increase, and capacitive conductivity should decrease. As a subsequent development of this method, ways to stabilize the operation of such wind power plant with an arbitrary number of generators can be analyzed.

The Superalgebras of Jordan Brackets Defined by the $ n $-Dimensional Sphere

We study the generalized Leibniz brackets on the coordinate algebra of the $ n $ -dimensional sphere. In the case of the one-dimensional sphere, we show that each of these is a bracket of vector type. Each Jordan bracket on the coordinate algebra of the two-dimensional sphere is a generalized Poisson bracket. We equip the coordinate algebra of a sphere of odd dimension with a Jordan bracket whose Kantor double is a simple Jordan superalgebra. Using such superalgebras, we provide some examples of the simple abelian Jordan superalgebras whose odd part is a finitely generated projective module of rank 1 in an arbitrary number of generators. An analogous result holds for the Cartesian product of the sphere of even dimension and the affine line. In particular, in the case of the 2-dimensional sphere we obtain the exceptional Jordan superalgebra. The superalgebras we constructed give new examples of simple Jordan superalgebras.

Left division in the free left distributive algebra on many generators

Left distributive algebras arise in the study of classical structures such as groups, knots, and braids, as well as more exotic objects like large cardinals. A long-standing open question is whether the set of left divisors of every term in the free left distributive algebra on any number of generators is well-ordered. A conjecture of J. Moody describes a halting condition for descending sequences of left divisors in the free left distributive algebra on an arbitrary number of generators. In this paper we present progress toward an affirmative answer to the open question mentioned above, namely we prove that the many generator form of Moody's conjecture holds if each member of the free left distributive algebra has a "division form" representation in an expanded algebra.

Brushes of Dendritically Branched Polyelectrolytes

We present an analytical theoretical framework to describe a polymer brush formed by dendritically branched polyions root-tethered to a planar inert surface. First, a mean-field boxlike model is used to obtain the average thickness of the dendron brush with arbitrary number of generations in branched macromolecules. Here, finite extensibility of dendrons with high degree of ionization is taken into account. Second, a more refined self-consistent field Poisson–Boltzmann formalism is developed to analyze the internal structure of the brushes formed by branched polyions with Gaussian elasticity. Brushes of first-generation ionic dendrons (arm-grafted starlike polymers) are considered in detail. Diagrams of states for such brushes are constructed in salt-free and salt-added solutions. The analytical dependences for the overall brush thickness in various regimes, the profiles of electrostatic potential, monomer units, and mobile ions are derived explicitly as a function of grafting density, branching functionality of macromolecules, and ionic strength in solution.

Study of Periodic Frames and Trivariate Tight Wavelet Frames and Applications in Materials Engineering

It is shown that there exists a frame wavelet with fast decay in the time domain and compact support in the frequency domain generating a wavelet system whose canonical dual frame cannot be generated by an arbitrary number of generators. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions.

An [formula omitted]-quotient algorithm for finitely presented groups on arbitrarily many generators

We generalize the Plesken–Fabiańska L2-quotient algorithm for finitely presented groups on two or three generators to allow an arbitrary number of generators. The main difficulty lies in a constructive description of the invariant ring of GL(2,K) on m copies of SL(2,K) by simultaneous conjugation. By giving this description, we generalize and simplify some of the known results in invariant theory. An implementation of the algorithm is available in the computer algebra system Magma.

The Golod-Shafarevich inequality for Hilbert series of quadratic algebras and the Anick conjecture

We study the question of whether the famous Golod-Shafarevich estimate, which gives a lower bound for the Hilbert series of a (non-commutative) algebra, is attained. This question was considered by Anick in his 1983 paper, ‘Generic algebras and CW-complexes’ (Princeton University Press), where he proved that the estimate is attained for the number of quadratic relations d ≤ ¼n2 and d ≥ ½n2, and conjectured that it is the case for any number of quadratic relations. The particular point where the number of relations is equal to ½n(n – 1) was addressed by Vershik. He conjectured that a generic algebra with this number of relations is finite dimensional.We prove that over any infinite field, the Anick conjecture holds for d ≥ (n2 + n) and an arbitrary number of generators n, and confirm the Vershik conjecture over any field of characteristic 0. We give also a series of related asymptotic results.

Shape minimization of the dissipated energy in dyadic trees

In this paper, we study the role of boundary conditions on the optimal shape of a dyadic tree in which flows a Newtonian fluid. Our optimization problem consists in finding the shape of the tree that minimizes the viscous energy dissipated by the fluid with a constrained volume, under the assumption that the total flow of the fluid is conserved throughout the structure. These hypotheses model situations where a fluid is transported from a source towards a 3D domain into which the transport network also spans. Such situations could be encountered in organs like for instance the lungs and the vascular networks. Two fluid regimes are studied: (i) low flow regime (Poiseuille) in trees with an arbitrary number of generations using a matricial approach and (ii) non linear flow regime (Navier-Stokes, moderate regime with a Reynolds number 100) in trees of two generations using shape derivatives in an augmented Lagrangian algorithm coupled with a 2D/3D finite elements code to solve Navier-Stokes equations. It relies on the study of a finite dimensional optimization problem in the case (i) and on a standard shape optimization problem in the case (ii). We show that the behaviours of both regimes are very similar and that the optimal shape is highly dependent on the boundary conditions of the fluid applied at the leaves of the tree.

Minimal Hilbert series for quadratic algebras and the Anick conjecture

We study the question on whether the famous Golod–Shafarevich estimate, which gives a lower bound for the Hilbert series of a (noncommutative) algebra, is attained. This question was considered by Anick in his 1983 paper ‘Generic algebras and CW-complexes’, Princeton Univ. Press, where he proved that the estimate is attained for the number of quadratic relations d 6 n2 4 and d > n2 2 , and conjectured that it is the case for any number of quadratic relations. The particular point where the number of relations is equal to n(n−1) 2 was addressed by Vershik. He conjectured that a generic algebra with this number of relations is finite dimensional. We announce here the result that over any infinite field, the Anick conjecture holds for d > 4(n 2+n) 9 and an arbitrary number of generators. We also discuss the result that confirms the Vershik conjecture over any field of characteristic 0, and a series of related asymptotic results.

Movement towards equilibrium in autotetraploid populations

With the assumptions of an effectively infinite population, panmixis, and discrete generations, it is shown that a population of autotetraploids is expected to move asymptotically towards a stable equilibrium, with respect to one locus. After three generations of panmixis the gamete frequencies deviate from their equilibrium frequencies with less than 4% of the initial deviation, and after four to five generations the deviations appear to be insignificant. It is demonstrated how the model can be used to predict genotypic compositon of synthetic populations an arbitrary number of generations with panmixis after synthesis. Observations of phenotypes from a natural 4x population are shown to be in close agreement with the expectations assuming equilibrium at one locus.

Weakly Confluent Quadratic Algebras

Any quadratic algebra endowed with an ordered set of generators can bedescribed by some linear map called a reduction operator. The general lineargroup naturally acts on reduction operators, which allows us to introduceweak and strong confluence. With respect to these notions, a completeclassification for two generators and complex coefficients is obtainedshowing that weak confluence is equivalent to Koszulity in this case. Bycontrast, some Sklyanin algebras with three generators fail to be weaklyconfluent. For an arbitrary number of generators and under some assumptionson the first terms of the Hilbert series, a weak confluence hypothesis isequivalent to some rather drastic conditions which determine the whole ofthe Hilbert series.

TERNARY GENERALIZATIONS OF GRASSMANN ALGEBRA

We propose the ternary generalization of the classical anti-commutativity and study the algebras whose generators are ternary anti-commutative. The integral over an algebra with an arbitrary number of generators N is defined and the formula of a change of variables is proved. In analogy with the fermion integral we define an analogue of the Pfaffian for a cubic matrix by means of Gaussian type integral and calculate its explicit form in the case of N = 3.

Majorana neutrinos and CP violation in the leptonic sector

A set of weak-basis-independent necessary conditions is derived for CP conservation in the leptonic sector of the SU(2) × U(1) gauge theory with an arbitrary number of generations, when both Majorana and Dirac neutrino mass terms are present. In the case of two and three generations of left-handed Majorana neutrinos, weak-basis-independent conditions are given which are necessary and sufficient for CP invariance in the leptonic sector. It is also shown that for three or more generations of Majorana neutrinos, there may be CP violation even in the limit of complete neutrino-mass degeneracy.

Weak-basis invariant conditions for CP conservation in SU(2) L X SU(2) R X U(1) B − L models

Weak-basis invariant necessary conditions are derived for CP conservation in the framework of SU(2) L X SU(2) R X U(1) B − L models, with an arbitrary number of generations. In the case of two and three generations, a set of conditions is selected which are both necessary and sufficient for CP invariance. The case of degenerate or vanishing fermion masses is also analyzed, with emphasis on some novel features which arise in left-right models.

Monopole-induced baryon decay with arbitrary number of generations and effects of fermion mass

Baryon number condensation around a monopole is estimated in the presence of N fermion generations. The massless fermion model is studied for arbitrary N, while the massive fermion model is analyzed in the large N limit. It is shown that in these cases ( N>1) the chiral anomaly does not contribute to baryon decay.

Radiative Corrections for W->e Formula Decay in the Weinberg-Salam Model

The one-loop corrections for the W→eν decay rate are calculated in the Weinberg-Salam model with arbitrary number of generations. The on-shell renormalization prescription and the 't Hooft-Feynman gauge are employed. Divergences are treated by the dimensional regularization method. Some numerical estimates for the decay rate are given in the three-generation model. It is found that there are significant corrections mainly owing to fermion-mass singularities.

A decomposition theorem for SU(n) and its application to CP-violation through quark mass diagonalisation

It is proved that the groupG=SU(n) has a decompositionG=FCF whereF is a maximal abelian subgroup andC is an (n − 1)2 parameter subset of matrices. The result is applied to the problem of absorbing the maximum possible number of phases in the mass-diagonalising matrix of the charged weak current into the quark fields; i.e., of determining the exact number of CP-violating phases for arbitrary number of generations. The inadequacies of the usual way of solving this problem are discussed. Then=3 case is worked out in detail as an example of the constructive procedure furnished by the proof of the decomposition theorem.

Identity coefficients and covariances between relatives in a parent-offspring inbreeding system

A one-locus "operator" for a younger parent-offspring inbreeding system is obtained by a generation matrix method in which 14 "classes" of matings are defined. The eigenvalues and a set of eigenvectors for the generation matrix and, also, the general solution for the frequencies of mating classes among descendants of an original mating of genotypes ab x cd are given. The operator gives the genotypic array of descendants of a given mating an arbitrary number of generations later. Using this operator, an algorithm is developed for calculating identity coefficients between any two relatives in a possibly branching younger parent-off spring mating system. Application to obtaining covariances between relatives for a one-locus model is illustrated.