Generalization Of Formula Research Articles

Jucys–Murphy elements and a presentation for partition algebras

We give a new presentation for the partition algebras. This presentation was discovered in the course of establishing an inductive formula for the partition algebra Jucys-Murphy elements defined by Halverson and Ram [European J. Combin. 26 (2005), 869-921]. Using Schur-Weyl duality we show that our recursive formula and the original definition of Jucys-Murphy elements given by Halverson and Ram are equivalent. The new presentation and inductive formula for the partition algebra Jucys-Murphy elements given in this paper are used to construct the seminormal representations for the partition algebras in a separate paper.

A New Low-Pass Filter in Asymmetrical Finline Topology Using Split-Ring Resonators

A variation of the quasi-static equivalent circuit model formulation of miniaturized magnetic resonant structures -i.e., split-ring resonator (SRR)- is presented. The validity of this model is verified by means of an analytical model that uses a new, simple and accurate analytical design formula for the SRRs inductance, full-wave simulations and measurements. These structures are inserted on the opposite side of a compact low-pass filter (LPF) in asymmetrical finline consisting of several notches alternating with a number of single-ridge finline sections. A soft transition from metal waveguide to finline is guaranteed by tapering the finline slot employing a numerically adjusted expression. Finally, experimental results of the filter are presented in order to demonstrate the feasibility of the proposed structure.

Poincaré series for maximal De Concini–Procesi models of root arrangements

In this paper we focus on maximal complex De Concini–Procesi models associated to root arrangements of types A, B, C, D and we compute inductive formulas for their Poincaré series.

The Ackermann approach for modal logic, correspondence theory and second-order reduction

The problem of eliminating second-order quantification over predicate symbols is in general undecidable. Since an application of second-order quantifier elimination is correspondence theory in modal logic, understanding when second-order quantifier elimination methods succeed is an important problem that sheds light on the kinds of axioms that are equivalent to first-order correspondence properties and can be used to obtain complete axiomatizations for modal logics. This paper introduces a substitution-rewrite approach based on Ackermannʼs Lemma to second-order quantifier elimination in modal logic. Compared to related approaches, the approach includes a number of enhancements: The quantified symbols that need to be eliminated can be flexibly specified. The inference rules are restricted by orderings compatible with the elimination order, which provides more control and reduces non-determinism in derivations thereby increasing the efficiency and success rate. The approach is equipped with a powerful notion of redundancy, allowing for the flexible definition of practical simplification and optimization techniques. We present correctness, termination and canonicity results, and consider two applications: (i) computing first-order frame correspondence properties for modal axioms and rules, and (ii) rewriting second-order modal problems to equivalent simpler forms. The approach allows us to define and characterize two new classes of formulae, which are elementary and canonical, and subsume the class of Sahlqvist formulae and the class of monadic inductive formulae.

Algorithmic correspondence and canonicity for distributive modal logic

We define the algorithm ALBA for the language of the same distributive modal logic (DML) for which a Sahlqvist theorem was proved by Gehrke, Nagahashi, and Venema. Successful executions of ALBA compute the local first-order correspondents of input DML inequalities, and also guarantee their canonicity. The class of inequalities on which ALBA is successful is strictly larger than the newly introduced class of inductive inequalities, which in its turn properly extends the Sahlqvist inequalities of Gehrke et al. Evidence is given to the effect that, as their name suggests, inductive inequalities are the distributive counterparts of the inductive formulas of Goranko and Vakarelov in the classical setting.

Computational proof of the Mackey formula for [formula omitted

Let G be a connected reductive group defined over a finite field with q elements. We prove that the Mackey formula for the Lusztig induction and restriction holds in G whenever q>2 or G does not have a component of type E.

항공기 투명체의 편각개념 설계 및 측정 시스템 개발

Angular Deviation(AD) on transparency applied to TA-50 Aircraft deteriorates armament system`s accuracy because it makes a difference in between actual and theoretical targets. In order to increase accuracy, therefore, TA-50 Aircraft measures AD on transparency and provide the measured values for the integrated mission display computer as a type of AD coefficients. This makes AD revised so that pilots can accurately see the actual target on their head-up display. In order to implement such mechanism into a real field, we develop a new device and system automatically measuring AD for the first time. We also deal with basic concept including AD induction formula as well as operating systems. As a consequence of testing the accuracy and precision for verifying reliability of the system, we got satisfactory results. In specific, the accuracy was within the resultant criterion of 1%. The precision was also satisfied with respect to the whole criteria. The system developed through this research is qualified as a military standard equipment for transparency of the canopy.

A Simple Innovative Method to Calculate the Magnetic Field Generated by Twisted Three-Phase Power Cables

This paper firstly examines the consolidated analytical methodologies available in literature for the calculation of the magnetic field generated by a twisted three-phase conductor arrangement carrying balanced three-phase currents. Such literature methodologies consist of an exact analytical expression of the RMS magnetic induction given in the form of complicated Bessel-function series and of an approximation of such exact expression where only the first term of the series is considered. Subsequently, a simple innovative approximated formula for the RMS magnetic induction generated by twisted three-phase power cables is obtained by means of an heuristic procedure. This formula results a good approximation of the rigorous analytical one and at the same time is much more accurate than the approximated formula found in literature, as demonstrated by the case of a twisted three-phase power cable used for power distribution at the medium voltage level.

Multiple Burnside rings and Brauer induction formulae

Let G be a finite group, and suppose that G is an operator group of a finite group A . Define S ( G , A ) = { ( H , σ ) | H ∈ S ( G ) and σ ∈ Z 1 ( H , A ) } , where S ( G ) is the set of subgroups of G and Z 1 ( H , A ) is the set of crossed homomorphisms from H to A . We view G as an operator group of the opposite group A ○ of A , and make S ( G , A ) into a left A ○ ⋊ G -set. The ring Ω ( G , A ) is defined to be a commutative ring consisting of all formal Z -linear combinations of A ○ ⋊ G -orbits in S ( G , A ) . Idempotent formulae for Q ⊗ Z Ω ( G , A ) not only imply a generalization of Dress' induction theorem but bring, in the case where Z 1 ( G , A ) is the set of linear C -characters of G , Boltje's explicit formula for Brauer's induction theorem and its hyperelementary version.

The negative answer to Kameko's conjecture on the hit problem

The goal of this paper is to give a negative answer to Kameko's conjecture on the hit problem stating that the cardinal of a minimal set of generators for the polynomial algebra P k , considered as a module over the Steenrod algebra A , is dominated by an explicit quantity depending on the number of the polynomial algebra's variables k. The conjecture was shown by Kameko himself for k ⩽ 3 in his PhD thesis in the Johns Hopkins University in 1990, and recently proved by us and Kameko for k = 4 . However, we claim that it turns out to be wrong for any k > 4 . In order to deny Kameko's conjecture we study a minimal set of generators for A -module P k in some so-call generic degrees. What we mean by generic degrees is a bit different from that of other authors in the fields such as Crabb–Hubbuck, Nam, Repka–Selick, Wood …We prove an inductive formula for the cardinal of the minimal set of generators in these generic degrees when the number of the variables, k, increases. As an immediate consequence of this inductive formula, we recognize that Kameko's conjecture is no longer true for any k > 4 .

Computation of Differential Inductance and Flux Linkage Positional Derivative by a Sensitivity Approach

The differential inductance and flux linkage positional derivative are important parameters in the analysis and simulation of electrical machines where saturation is nonnegligible. A new method for the computation of these quantities for devices with an arbitrary number of windings is presented. The method is based on the determination of the sensitivity of the magnetic vector potential to variations in the input current vector or the rotor position, in the context of finite-element formulations. The implementation of the proposed method for plane Cartesian and axisymmetric cases is considered in detail. The method and its implementation are verified by comparisons against known inductance formulas or results from other computational methods. In the case of the differential inductance, the proposed scheme is an alternative to energy perturbation methods, while the determination of the flux linkage positional derivative is made in one step for the first time.

A novel approach to calculate inductance and analyze magnetic flux density of helical toroidal coil applicable to Superconducting Magnetic Energy Storage systems (SMES)

Abstract In this paper, formulas are proposed for the self and mutual inductance calculations of the helical toroidal coil (HTC) by the direct and indirect methods at superconductivity conditions. The direct method is based on the Neumann’s equation and the indirect approach is based on the toroidal and the poloidal components of the magnetic flux density. Numerical calculations show that the direct method is more accurate than the indirect approach at the expense of its longer computational time. Implementation of some engineering assumptions in the indirect method is shown to reduce the computational time without loss of accuracy. Comparison between the experimental measurements and simulated results for inductance, using the direct and the indirect methods indicates that the proposed formulas have high reliability. It is also shown that the self inductance and the mutual inductance could be calculated in the same way, provided that the radius of curvature is >0.4 of the minor radius, and that the definition of the geometric mean radius in the superconductivity conditions is used. Plotting contours for the magnetic flux density and the inductance show that the inductance formulas of helical toroidal coil could be used as the basis for coil optimal design. Optimization target functions such as maximization of the ratio of stored magnetic energy with respect to the volume of the toroid or the conductor’s mass, the elimination or the balance of stress in some coordinate directions, and the attenuation of leakage flux could be considered. The finite element (FE) approach is employed to present an algorithm to study the three-dimensional leakage flux distribution pattern of the coil and to draw the magnetic flux density lines of the HTC. The presented algorithm, due to its simplicity in analysis and ease of implementation of the non-symmetrical and three-dimensional objects, is advantageous to the commercial software such as ANSYS, MAXWELL, and FLUX. Finally, using the presented algorithm, magnetic flux density lines in several examples are drawn.

A Novel Approach for Calculations of Helical Toroidal Coil Inductance Usable in Reactor Plasmas

In this paper, formulas are proposed for the self- and mutual-inductance calculations of a helical toroidal coil by direct and indirect methods at superconductivity conditions. The direct method is based on the Neumann's equation, and the indirect approach is based on the toroidal and the poloidal components of the magnetic flux density. Numerical calculations show that the direct method is more accurate than the indirect approach at the expense of its longer computational time. Implementation of some engineering assumptions in the indirect method is shown to reduce the computational time without loss of accuracy. Comparison between the experimental, empirical, and numerical results for inductance, using the direct and the indirect methods, indicates that the proposed formulas have high reliability. It is also shown that the self-inductance and mutual inductance could be calculated in the same way, provided that the radius of curvature is greater than 0.4 of the minor radius and that the definition of the geometric mean radius in the superconductivity conditions is used. Plotting contours for the magnetic flux density and the inductance show that the inductance formulas of the helical toroidal coil could be used as the basis for coil optimal design. Optimization target functions such as maximization of the ratio of stored magnetic energy with respect to the volume of the toroid or the conductor's mass, the elimination or the balance of stress in certain coordinate directions, and the attenuation of leakage flux could be considered.

Indecomposable permutations, hypermaps and labeled Dyck paths

Hypermaps were introduced as an algebraic tool for the representation of embeddings of graphs on an orientable surface. Recently a bijection was given between hypermaps and indecomposable permutations; this sheds new light on the subject by connecting a hypermap to a simpler object. In this paper, a bijection between indecomposable permutations and labeled Dyck paths is proposed, from which a few enumerative results concerning hypermaps and maps follow. We obtain for instance an inductive formula for the number of hypermaps with n darts, p vertices and q hyperedges; the latter is also the number of indecomposable permutations of S n with p cycles and q left-to-right maxima. The distribution of these parameters among all permutations is also considered.

Modeling and parametrization of DC motor winding inductances

PurposeThe purpose of this paper is to compare several methods to calculate solenoid inductances regarding their applicability to model the inductance of DC motor armature windings. Special attention is given to the influence of wiring insulation and current distribution and the axial length of the solenoid.Design/methodology/approachExpressions for the self‐ and mutual‐inductance of current filament and wire combinations are derived from basic inductance formulas. Combining these expressions allows expressing the inductance of arbitrary shaped solenoids (e.g. polygons).FindingsAccurately describing self‐ and mutual‐inductances is a very complex topic. However, in the case of motor armature windings, several simplifications can be applied to lower the calculation cost significantly. Plus, differences in inductances between regular polygonial solenoids and similar circular shapes were found to be rather small. Thus, many windings' inductances can well be approximated by using expressions for circular solenoids.Originality/valueA new way to calculate the inductance of arbitrary polygonial shapes is presented, and an example is given for hexagonal shapes.

MUTUAL INDUCTANCE CALCULATION FOR NON-COAXIAL CIRCULAR AIR COILS WITH PARALLEL AXES

We present a practical and simple method for calculating the mutual inductance between two non-coaxial circular coils with parallel axes. All possible circular coils such as coils of rectangular cross section, thin wall solenoids, thin disk coils (pancakes) and circular filamentary coils are taken into consideration. We use Grover’s formula for the mutual inductance between two filamentary circular coils with parallel axes. The filament method is applied for all coil combinations, for coils of the rectangular cross section and for thin coils. We consider that the proposed method is very simple, accurate and practical for engineering applications. Computed mutual inductance values obtained by the proposed method have been verified by previously published data and the software Fast-Henry. All results are in a very good agreement. This method can be used in various electromagnetic applications such as coil guns, tubular linear motors, transducers, actuators and biomedical implanted sensors.

Inductance Computation Consideration of Induction Coil Launcher

Inductance computation is an important issue for the design of the induction coil launcher (ICL). The self-inductance of the driving coil and the system equivalent inductance of ICL are investigated in the paper. Computation equations are presented. Both theoretical computation method and simulative computation method are employed for the inductance computation. Theoretical computation methods consider the influence of the per turn coil's distribution, and the simulative method doesn't consider the influence of per turn coil's distribution. Under the condition of static magnetic field, the deviation between the theoretical computation result ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> = 150.46 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mu</i> H) and the simulative result ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> = 147.22 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mu</i> H) is low, which shows that per turn coil's distribution has little influence on the self-inductance of the driving coil. The theoretical computation method for the system equivalent inductance is also presented. As for the system equivalent inductance, the simulative result is 83.69 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mu</i> H, and the theoretical result is 99.396 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mu</i> H. These mean that per turn coil's distribution has large influence on the system equivalent inductance under the condition of eddy current. The system equivalent inductance is much lower than the self-inductance of the driving coil. Therefore the system equivalent inductance should be employed to evaluate the factual working parameters of ICL In addition, computation formula for the mutual inductance between the driving coil and the armature are given out.

About the some conditions of the replaceability of the double induction

The provability of the axiom of double induction (ADI) with the open induction formula in the additive arithmetic is investigated. The system of additional axioms and theirs provability by ADI is presented.

Milne’s volume function and vector symmetric polynomials

The number of real roots of a system of polynomial equations fitting inside a given box can be counted using a vector symmetric polynomial introduced by P. Milne, the volume function. We provide the expansion of Milne’s volume function in the basis of monomial vector symmetric functions, and observe that only monomial functions of a particular kind appear in the expansion, the squarefree monomial functions. By means of an appropriate specialization of the vector symmetric Newton identities, we derive an inductive formula that expresses the squarefree monomial functions in the power sums basis. As a corollary, we obtain an inductive formula that writes Milne’s volume function in the power sums basis. The lattice of the sub-hypergraphs of a hypergraph appears in a natural way in this setting.

Calculating Mutual Inductance Between Circular Coils With Inclined Axes in Air

In this paper we present a lucid, easy, and accurate approach for calculation of the mutual inductance between all inclined circular coils with either rectangular cross section or negligible section. We use Grover's formula for the mutual inductance between two filamentary circular coils with inclined axes that lie in the same plane. Their centers are either displaced along the axis of one coil or displaced along one axis of the first coil and then displaced sideways in addition. We apply the filament method for coil combinations comprising circular coils of rectangular cross section, thin wall solenoids, thin disk coils (pancakes), and filamentary circular coils. In this approach we clarify how Grover's formulas have to be used for different coil combinations in the filament treatment. Thus, two well-known methods (Grover's formulas and the filament method) can be easily used to calculate the mutual inductance between all inclined circular coils, even though the problem is purely three-dimensional.