Grid-Tied Distribution Static Synchronous Compensator for Power Quality Enhancement Using Combined-Step-Size Real-Coefficient Improved Proportionate Affine Projection Sign Algorithm

A control structure design of a three-phase three-leg four-wire grid-tied Distribution Static Synchronous Compensator (DSTATCOM) based on a combined-step-size real-coefficient improved proportionate affine projection sign algorithm (CSS-RIP-APSA) has been presented. The three-phase four-wire DSTATCOM is used for reactive power compensation along with harmonic current minimization. This strategy also helps in load balancing and neutral current compensation. The affine projection sign algorithm (APSA) is a member of the adaptive filter family, which has a slow convergence rate. The conventional adaptive filter deals with the trade-off between the convergence rate and the steady-state error. In the proposed algorithm, the RIP-APSA adaptive filter with two different step sizes has been designed to decrease the computational burden while achieving the advantages of a fast convergence rate and reduced steady-state error. The proposed controller also makes the inverter function a shunt compensator. The controller primarily evaluates the fundamental weight component of distorted load currents. The aim of the proposed system is to compensate for reactive power and to ensure unity power factor during the faulty conditions as well as for unbalancing grid conditions. The proposed control algorithm of the grid-tied DSTATCOM works effectively on the laboratory prototype as verified from the experimental results.

A note on the Kervaire semi-characteristic

We present a potential generalization of the Kervarie semi-characteristic (with real coefficient) to the case of non-orientable manifolds.

Rogue waves in the KdV-type models

<p>In this study, we investigate the rogue-wave-type phenomena in the physical systems described by the Korteweg-de Vries (KdV)-like equation in the form $ u_t + [u^m \sgn{u}]_x + u_{xxx} = 0 $ with the arbitrary real coefficient $m>0$. The periodic waves (sinusoidal or cnoidal) described by this equation have been shown to suffer from the modulational instability if $m \ge 3$; the modulational growth results in the formation of rogue waves similar to the Peregrine, Kuznetsov-Ma or Akhmediev breathers known for the nonlinear Schrodinger equation. In this work we focus on the rogue wave occurrence in ensembles of soliton-type waves. First of all, the characteristics of the solitary waves are investigated depending on the power $m$. The existence of solitary waves with exponential tails, as well as algebraic solitons and compactons has been shown for different ranges of the parameter $m$ values. Their energetic stability is discussed. Two solitary wave/breathers interactions are studied as elementary acts of the soliton/breather turbulence. It is demonstrated that the property of attracting solitons/breathers is a necessity condition for the formation of rogue waves. Rigorous results are obtained for the integrable versions of the KdV-type equations. Series of numerical simulations of the rogue wave generation has been conducted for different values of $m$. The obtained results are applied to the problems of surface and internal waves in the ocean, and to elastic waves in the solid medium.</p><p>The research is supported by the RNF grant 19-12-00253.</p>

Normalized Laplace operators for hypergraphs with real coefficients

Chemical hypergraphs and their associated normalized Laplace operators are generalized and studied in the case where each vertex–hyperedge incidence has a real coefficient. We systematically study the effect of symmetries of a hypergraph on the spectrum of the Laplacian.

Efficient Orthogonal Bicomplex Bilinear DSP Algorithm Design

The present paper describes the development of a new technique for designing orthogonal bicomplex Digital Signal Processing (DSP) algorithms. In contrast to those previously reported on, this novel method is of universal application while being unaffected by either the type or the order of the real digital processing algorithm employed as a prototype. The proposed technique builds on Watanabe and Nishihara’s complex orthogonal transformation, and converts real or complex orthogonal transfer functions into bicomplex orthogonal ones. In this study, the new technique is applied to the design and testing of orthogonal bilinear bicomplex filters with a canonical number of elements, the main advantage of which is that they are several times lower in order. In this way, bilinear bicomplex orthogonal transfer functions are made up of real coefficient ones of the fourth-order, thereby reducing the order of the filter by a factor of four. The experiments demonstrate that the properties of the prototype filter are acquired by the bicomplex orthogonal filters, irrespective of the prototype being complex or real in nature.

The Landau Hamiltonian with δ-potentials supported on curves

The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian [Formula: see text] in [Formula: see text] with a [Formula: see text]-potential supported on a finite [Formula: see text]-smooth curve [Formula: see text] are studied. Here [Formula: see text] is the vector potential, [Formula: see text] is the strength of the homogeneous magnetic field, and [Formula: see text] is a position-dependent real coefficient modeling the strength of the singular interaction on the curve [Formula: see text]. After a general discussion of the qualitative spectral properties of [Formula: see text] and its resolvent, one of the main objectives in the present paper is a local spectral analysis of [Formula: see text] near the Landau levels [Formula: see text], [Formula: see text]. Under various conditions on [Formula: see text], it is shown that the perturbation smears the Landau levels into eigenvalue clusters, and the accumulation rate of the eigenvalues within these clusters is determined in terms of the capacity of the support of [Formula: see text]. Furthermore, the use of Landau Hamiltonians with [Formula: see text]-perturbations as model operators for more realistic quantum systems is justified by showing that [Formula: see text] can be approximated in the norm resolvent sense by a family of Landau Hamiltonians with suitably scaled regular potentials.

Considerations in the study of trophies

Roe deer is Laurasiatherian mammal from the family of Cervidae. It is autochthonous and one of the most valued trophy game species in Croatia (Zorić 2014.). Antlers (left and right branch) with complete or part of the skull are regarded as trophy. Despite the fact that roe deer antlers are easily accessible trophies, formulas for their evaluations are still largely debated. It is a consequence of large number of elements that need to be evaluated, possible use of coefficient instead of measuring volume and mass, and potential differences in trophy preparation. Guidelines of the International Council for Game and Wildlife Conservation (CIC) instructs that skulls should be cut through the eye cavities leaving intact nasal bones on the trophy. If otherwise cut or left intact with maxillar teeth, deduction of 65 or 90g is foreseen. Considering the fact that weight and density of bones varies between populations, we hypothesize that above mentioned deductions do not represent real values. Therefore the aim of this research was to determine the deviations from actual mass. A total of 40 roe buck skulls originating from the area of Central Croatia were analysed. All skulls were weighed 3 times, initially when intact, after shallow cut and after proscribed cut. Obtained data were statistically analysed. Following the shallow cut, skull is lighter for 25 to 52 g, which is 11 g less than proscribed 65 g. In other words application of shallow cut will result in the loss in trophy value. In cases of intact skulls loss in weight is related to gross skull mass. In this case even 68 to 70% of variability are explained by gross skull mass (R²=0.680; p<0.0001 – linear function, or R²=0.699; p<0.01 – potency function). According to the intersection of the lines (obligate deduction of 90 g and dependence of mass loss due to the cutting) milestone in the mass is at 310 g gross. In other words trophies lighter than 310 g should be cut according to proscriptions as they will lose less than 90 g, while heavier skulls should be left intact as they will lose more than proscribed 90 g. Regardless of the skull preparation, all obtained masses show statistically significant relation to volume. With increase in volume density of trophies decreases (R²=0.813; p<0.001), with the fact that cutting of the skull results in removal of denser, heavier parts of the trophy. Application of the coefficient 0.23 depends on the density of the trophy, meaning that its application in the case of heavier antlers with lower volume will increase the trophy value. In the case of porous antlers the real coefficient should be higher, as application of 0.23 results in lower trophy values. In the case of intact skulls we do not advice application of 0.23 coefficient as this will decrease the trophy value.

Estimation of the Gruneisen parameter and an explicit measure of anharmonicity of dodecaborides

In previous works on the ratio (θД – the characteristic temperature of Debye, was calculated according to the Lindemann formula; V – molar volume of hypothetical lattice atoms; γ is the Gruneisen parameter) for the group of dodecaborides (TbB12, DyB12, HoB12, ErB12, TuB12, LaB12, UB12) the average value of γ = 1.3 was determined. However, due to the ambiguity of the coefficient of proportionality in the Lindemann formula by definition θD, the authors selected an independent high-temperature X-ray method for determining the dependence θr (T). Taking into account the immutability of the structure and type of interatomic connection in the temperature interval of the search (293–973 K), the authors evaluated the value and temperature dependence of γ (T) of each dodecaboride separately. The results of the search showed that the value of γ for each given dodecaboride is different, but practically independent from temperature. For some dodecaborides, the parameter γ is about 2–3 units, and for others it is overestimated. The values of γ made it possible to estimate the magnitude of the implicit γβ and the explicit parts of the universal measure of anharmonicity of dodecaborides , where β – real coefficient of volumetric expansion of the crystalline lattice. Because (n – dimensionless coefficient of proportionality), then the temperature change n(T) is also determined.

Polynomiality of Certain Average Weights for Oscillating Tableaux

We prove that a family of average weights for oscillating tableaux are polynomials in two variables, namely, the length of the oscillating tableau and the size of the ending partition, which generalizes a result of Hopkins and Zhang. Several explicit and asymptotic formulas for the average weights are also derived. The main idea in this paper is to translate the study of certain average weights for oscillating tableaux to the study of an operator $\Psi$ from the set of real coefficient polynomials with two parameters to itself.

Cohomology of Flat Principal Bundles

We invoke the classical fact that the algebra of bi-invariant forms on a compact connected Lie group G is naturally isomorphic to the de Rham cohomology H*dR(G) itself. Then, we show that when a flat connection A exists on a principal G-bundle P, we may construct a homomorphism EA: H*dR(G)→H*dR(P), which eventually shows that the bundle satisfies a condition for the Leray–Hirsch theorem. A similar argument is shown to apply to its adjoint bundle. As a corollary, we show that that both the flat principal bundle and its adjoint bundle have the real coefficient cohomology isomorphic to that of the trivial bundle.