Type Formula Research Articles

Zonasi Bencana Abrasi Pantai Sappoang Kabupaten Polewali Mandar

This research uses a formula approach. In formula has several variables. The variables in this research are tidal, ocean current speed and direction, wave height and wave period, type of geological structure of the coast and sediment grain size materials, the slope of the beach and coastline direction, wind speed and direction. The number of samples or observation points at 27, with interval distance every point is 200 m. The results of the research were analyzed in the waves of the type formula and determinants of abrasion and sedimentation. Sappoang Beach is one of the marine landforms are more specifically known as a land form bar (deposition of sand along the coast). Conditions beach located around the mouth of the river to the beach physical differences that are in the basin area (central coast), where the force of the waves, and the flow velocity at the beach slope basin area beaches have greater value when compared to the coastal areas near the mouth river. The results showed that there are three conditions in Sappoang Beach beaches of different areas of research currently conducted (the west wind), like sedimentation area, balanced and abraded. Abraded zone and sedimentation zone is more dominant than the beaches that are stable. This is more significant because at the time of measurement, the wind is blowing west wind, given the quantity of variables measuring the higher the coast, so the coastal zone is increasing abraded.

Eigenstructure and Voronovskaja type formula for a sequence of integral operators

Abstract The composition ℱ n of Rathore and Gamma operators was considered in the literature. We introduce a generalization of ℱ n . For it we determine the eigenstructure and establish the corresponding Voronovskaja type formula.

Aldaz–Kounchev–Render Operators and Their Approximation Properties

The approximation properties of the Aldaz–Kounchev–Render (AKR) operators where investigated in several papers. We improve some existing quantitative results concerning these approximation properties. Moreover, we describe classes of functions for which these operators approximate better than the classical Bernstein operators and classes of functions for which Bernstein operators approximate better than AKR operators. The new results, in particular involving monotonic convergence and Voronovskaja type formulas, are then extended to the bivariate case on the square \([0,1]^2\) and compared with other existing results. Several numerical examples, illustrating the relevance and supporting the theoretical findings, are presented.

Density theorems for {textrm{GL}}(n)

Strong bounds—going beyond Sarnak’s density hypothesis—are obtained for the number of automorphic forms for the group Gamma _0(q) subseteq textrm{SL}(n, {mathbb {Z}}) violating the Ramanujan conjecture at any given unramified place. The proof is based on a relative trace formula of Kuznetsov type and best-possible bounds for certain Kloosterman sums for textrm{GL}(n). Further applications are given.

Comparing formulas for typeGLnMacdonald polynomials – Supplement

This paper is a supplement to Guo-Ram arXiv:2104.02942, containing examples, remarks and additional material that could be useful to researchers working with Type $GL_n$ Macdonald polynomials. In the course of our comparison of the alcove walk formula and the nonattacking fillings formulas for type $GL_n$ Macdonald polynomials we did many examples and significant analysis of the literature. In the preparation of Guo-Ram arXiv:2104.02942 it seemed sensible to produce a document with focus and this material was removed. This is paper resurrects and organizes that material, in hopes that others may also find it useful.

Exchange Option Pricing Under Variance Gamma-Like Models

In this article, we focus on the pricing of exchange options when the risk-neutral dynamic of log-prices follows either the well-known variance gamma or the recent variance gamma++ process introduced in Gardini et al. (2022. “The Variance Gamma++ Process and Applications to Energy Markets.” Applied Stochastic Models in Business and Industry 38 (2): 391–418. https://doi.org/10.1002/asmb.v38.2.). In particular, for the former model we can derive a Margrabe's type formula whereas for the latter one we can write an ‘integral free’ formula. Furthermore, we show how to construct a general multidimensional versions of the variance gamma++ processes preserving both the mathematical and numerical tractabilities. Finally we apply the derived models to German and French energy power markets: we calibrate their parameters using real market data and we accordingly evaluate exchange options with the derived closed formulas, Fourier based methods and Monte Carlo techniques.

Induced character in equivariant K-theory, wreath products and pullback of groups

Let G be a finite group and let X be a compact G-space. In this note we study the (Z+ × Z/2Z)-graded algebra
 FqG (X) = ⊕n ≤ 0 qn · KG∫Gn(Xn) ⊗ C,
 defined in terms of equivariant K-theory with respect to wreath products as a symmetric algebra, we review some properties of FqG (X) proved by Segal and Wang. We prove a Kunneth type formula for this graded algebras, more specifically, let H be another finite group and let Y be a compact H-space, we give a decomposition of FqG × H (X × Y) in terms of FqG (X) and FqH (Y). For this, we need to study the representation theory of pullbacks of groups. We discuss also some applications of the above result to equivariant connective K-homology.

On the ‘definability of definable’ problem of Alfred Tarski, Part II

Alfred Tarski [J. Symbolic Logic 13 (1948), pp. 107–111] defined D p m \mathbf {D}_{pm} to be the set of all sets of type p p , type-theoretically definable by parameterfree formulas of type ≤ m {\le m} , and asked whether it is true that D 1 m ∈ D 2 m \mathbf {D}_{1m}\in \mathbf {D}_{2m} for m ≥ 1 m\ge 1 . Tarski noted that the negative solution is consistent because the axiom of constructibility V = L \mathbf {V}=\mathbf {L} implies D 1 m ∉ D 2 m \mathbf {D}_{1m}\notin \mathbf {D}_{2m} for all m ≥ 1 m\ge 1 , and he left the consistency of the positive solution as a major open problem. This was solved in our recent paper [Mathematics 8 (2020), pp. 1–36], where it is established that for any m ≥ 1 m\ge 1 there is a generic extension of L \mathbf {L} , the constructible universe, in which it is true that D 1 m ∈ D 2 m \mathbf {D}_{1m}\in \mathbf {D}_{2m} . In continuation of this research, we prove here that Tarski’s sentences D 1 m ∈ D 2 m \mathbf {D}_{1m}\in \mathbf {D}_{2m} are not only consistent, but also independent of each other, in the sense that for any set Y ⊆ ω ∖ { 0 } Y\subseteq \omega \smallsetminus \{0\} in L \mathbf {L} there is a generic extension of L \mathbf {L} in which it is true that D 1 m ∈ D 2 m \mathbf {D}_{1m}\in \mathbf {D}_{2m} holds for all m ∈ Y m\in Y but fails for all m ≥ 1 m\ge 1 , m ∉ Y m\notin Y . This gives a full and conclusive solution of the Tarski problem. The other main result of this paper is the consistency of D 1 ∈ D 2 \mathbf {D}_{1}\in \mathbf {D}_{2} via another generic extension of L \mathbf {L} , where D p = ⋃ m D p m \mathbf {D}_{p}=\bigcup _m\mathbf {D}_{pm} , the set of all sets of type p p , type-theoretically definable by formulas of any type. Our methods are based on almost-disjoint forcing of Jensen and Solovay [Some applications of almost disjoint sets, North-Holland, Amsterdam, 1970, pp. 84–104].

Framed curves in three-dimensional Lie groups and a Berry phase model

In this study, we introduce framed curves which can have singular points in three-dimensional Lie groups. We give Frenet-Serret type formulas of framed curves with the help of a Lie curvature in three-dimensional Lie groups. Then, we define adapted frames of framed curves in three-dimensional Lie groups such that Frenet-Serret type frame and Bishop frame. Finally, as a physical application, we give Berry phase model of polarized light wave along an optical fiber in Lie groups.

Specializing Koornwinder polynomials to Macdonald polynomials of type B, C, D and BC

We study the specializations of parameters in Koornwinder polynomials to obtain Macdonald polynomials associated to the subsystems of the affine root system of type \((C_n^\vee ,C_n)\) in the sense of Macdonald (Affine Hecke algebras and orthogonal polynomials, Cambridge tracts in mathematics, Cambridge Univ Press, 2003), and summarize them in what we call the specialization table. As a verification of our argument, we check the specializations to type B, C and D via Ram–Yip type formulas of non-symmetric Koornwinder and Macdonald polynomials.

Comprehensive Investigation on the Influence of Magnetic Materials on the Weight and Performance of Onboard WPT Systems

In an inductive power transfer (IPT) system, the magnetic core is usually used to improve the coefficient between the primary and secondary coils. However, considering the iron losses on magnetic materials, the addition of magnetic core may affect the system efficiency and, at the same time, increase the weight of the IPT system significantly. Therefore, in this study, the aggregate influence of thickness, permeability, and iron losses of magnetic core on IPT system performance is comprehensively investigated. First, the equivalent circuit model of IPT system is established, and the formulas for different types of losses are analyzed. Then, the three-dimensional models of the IPT system with magnetic core in different shapes are established to simulate the aggregate influence of core thickness, permeability, and iron losses. The simulation results reveal that reducing the core thickness requires a larger saturation flux density of magnetic materials. In addition, only if the material losses below a certain value and an appropriate core shape are adopted, the addition of magnetic material can improve the system efficiency. Finally, experimental validation on a 3-kW IPT system is performed under the conditions of no magnetic core, using ferrite core in radial pattern and hollow square shapes, and using nanocrystalline core with the thickness of 22 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m and 16 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m in radial pattern and hollow square shapes, respectively. The results show that the high efficiency and lower overall weight of the IPT system can be achieved when nanocrystalline core with suitable permeability and shape is used.

Seifert-Torres type formulas for the Alexander polynomial from quantum [formula omitted

We develop a diagrammatic calculus for representations of unrolled quantum sl2 at a fourth root of unity. This allows us to prove Seifert-Torres type formulas for certain splice links using quantum algebraic methods, rather than topological methods. Other applications of this diagrammatic calculus given here are a skein relation for n-cabled double crossings and a simple proof that the quantum invariant associated with these representations determines the multivariable Alexander polynomial.

Feynman–Kac formula for perturbations of order le 1, and noncommutative geometry

Let Q be a differential operator of order le 1 on a complex metric vector bundle mathscr {E}rightarrow mathscr {M} with metric connection nabla over a possibly noncompact Riemannian manifold mathscr {M}. Under very mild regularity assumptions on Q that guarantee that nabla ^{dagger }nabla /2+Q canonically induces a holomorphic semigroup mathrm {e}^{-zH^{nabla }_{Q}} in Gamma _{L^2}(mathscr {M},mathscr {E}) (where z runs through a complex sector which contains [0,infty )), we prove an explicit Feynman–Kac type formula for mathrm {e}^{-tH^{nabla }_{Q}}, t>0, generalizing the standard self-adjoint theory where Q is a self-adjoint zeroth order operator. For compact mathscr {M}’s we combine this formula with Berezin integration to derive a Feynman–Kac type formula for an operator trace of the form TrV~∫0te-sHV∇Pe-(t-s)HV∇ds,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\mathrm {Tr}\\left( \\widetilde{V}\\int ^t_0\\mathrm {e}^{-sH^{\ abla }_{V}}P\\mathrm {e}^{-(t-s)H^{\ abla }_{V}}\\mathrm {d}s\\right) , \\end{aligned}$$\\end{document}where V,widetilde{V} are of zeroth order and P is of order le 1. These formulae are then used to obtain a probabilistic representations of the lower order terms of the equivariant Chern character (a differential graded extension of the JLO-cocycle) of a compact even-dimensional Riemannian spin manifold, which in combination with cyclic homology play a crucial role in the context of the Duistermaat–Heckmann localization formula on the loop space of such a manifold.

Chevalley formula for anti-dominant minuscule fundamental weights in the equivariant quantum K-group of partial flag manifolds

In this paper, we give an explicit formula of Chevalley type, in terms of the Bruhat graph, for the quantum multiplication with the class of the line bundle associated to an anti-dominant minuscule fundamental weight −ϖk in the torus-equivariant quantum K-group of the partial flag manifold G/PJ (where J=I∖{k}) corresponding to the maximal (standard) parabolic subgroup PJ of minuscule type in type A, D, E, or B. This result is obtained by proving a similar formula in a torus-equivariant K-group of the semi-infinite partial flag manifold QJ of minuscule type, and then by making use of the isomorphism between the torus-equivariant quantum K-group of G/PJ and the torus-equivariant K-group of QJ, recently established by Kato.

Jacobi-type functions defined by fractional Bessel derivatives

ABSTRACT For a class of even weight functions, generalizations of the classical Jacobi and Laguerre polynomials are defined via fractional Rodrigues' type formulas using the Bessel operators in the form . Their properties, including hypergeometric representation, differential recurrence relations and fractional boundary value problem, are investigated.

Bipartite graph search optimization for type II diabetes mellitus Jamu formulation using branch and bound algorithm.

Jamu is an Indonesian traditional herbal medicine that has been practiced for generations. Jamu is made from various medicinal plants. Each plant has several compounds directly related to the target protein that are directly associated with a disease. A pharmacological graph can form relationships between plants, compounds, and target proteins. Research related to the prediction of Jamu formulas for some diseases has been carried out, but there are problems in finding combinations or compositions of Jamu formulas because of the increase in search space size. Some studies adopted the drug–target interaction (DTI) implemented using machine learning or deep learning to predict the DTI for discovering the Jamu formula. However, this approach raises important issues, such as imbalanced and high-dimensional dataset, overfitting, and the need for more procedures to trace compounds to their plants. This study proposes an alternative approach by implementing bipartite graph search optimization using the branch and bound algorithm to discover the combination or composition of Jamu formulas by optimizing the search on a plant–protein bipartite graph. The branch and bound technique is implemented using the search strategy of breadth first search (BrFS), Depth First Search, and Best First Search. To show the performance of the proposed method, we compared our method with a complete search algorithm, searching all nodes in the tree without pruning. In this study, we specialize in applying the proposed method to search for the Jamu formula for type II diabetes mellitus (T2DM). The result shows that the bipartite graph search with the branch and bound algorithm reduces computation time up to 40 times faster than the complete search strategy to search for a composition of plants. The binary branching strategy is the best choice, whereas the BrFS strategy is the best option in this research. In addition, the the proposed method can suggest the composition of one to four plants for the T2DM Jamu formula. For a combination of four plants, we obtain Angelica Sinensis, Citrus aurantium, Glycyrrhiza uralensis, and Mangifera indica. This approach is expected to be an alternative way to discover the Jamu formula more accurately.

A fractional Borel–Pompeiu type formula and a related fractional ψ−$$ \psi - $$Fueter operator with respect to a vector‐valued function

In this paper, we combine the fractional hyperholomorphic function theory with the fractional calculus with respect to another function. As a main result, a fractional Borel–Pompeiu type formula related to a fractional Fueter operator with respect to a vector‐valued function is proved.

Optimal quadrature formulas for oscillatory integrals in the Sobolev space

This work studies the problem of construction of optimal quadrature formulas in the sense of Sard in the space L_{2}^{(m)}(0,1) for numerical calculation of Fourier coefficients. Using Sobolev’s method, we obtain new sine and cosine weighted optimal quadrature formulas of such type for N + 1geq m, where N + 1 is the number of nodes. Then, explicit formulas for the optimal coefficients of optimal quadrature formulas are obtained. The obtained optimal quadrature formulas in L_{2}^{(m)}(0,1) space are exact for algebraic polynomials of degree (m-1).

Anti-Gaussian quadrature formulae of Chebyshev type

We prove that there is no positive measure d σ d\sigma on the interval [ a , b ] [a,b] such that the corresponding anti-Gaussian quadrature formula is also a Chebyshev quadrature formula. We also show that the only positive and even measure d σ ( t ) = d σ ( − t ) d\sigma (t)=d\sigma (-t) on the symmetric interval [ − a , a ] [-a,a] , for which the anti-Gaussian formula has the form ∫ − a a f ( t ) d σ ( t ) = μ 0 2 [ f ( a ) + f ( − a ) ] + R 2 A G ( f ) \int _{-a}^{a}f(t)d\sigma (t)=\frac {\mu _{0}}{2}[f(a)+f(-a)]+R_{2}^{AG}(f) for n = 1 n=1 and ∫ − a a f ( t ) d σ ( t ) = w 1 f ( a ) + w ∑ μ = 2 n f ( t μ ) + w 1 f ( − a ) + R n + 1 A G ( f ) \int _{-a}^{a}f(t)d\sigma (t)=w_{1}f(a)+w\sum _{\mu =2}^{n}f(t_{\mu })+w_{1}f(-a)+R_{n+1}^{AG}(f) for all n ≥ 2 n\geq 2 , is the measure d σ ( t ) = ( a 2 − t 2 ) − 1 / 2 d t d\sigma (t)=(a^{2}-t^{2})^{-1/2}dt . It turns out that the formula for n ≥ 2 n\geq 2 is the ( n − 1 ) (n-1) -point Gauss-Lobatto quadrature formula for the measure d σ ( t ) = ( a 2 − t 2 ) − 1 / 2 d t d\sigma (t)=(a^{2}-t^{2})^{-1/2}dt , which is a generalization of what happens in the case of the Chebyshev measure of the first kind. Moreover, we compute the anti-Gaussian formulae for any one of the four Chebyshev measures.

Solving Fredholm Integro-Differential Equation of Fractional Order by Using Sawi Homotopy Perturbation Method

In our article, we develop an efficient compined method consisting of integral transform and Homotopy Perturbation Method for solving Fractional Integro-differential equations of Fredholm type. Sawi transformation formulas of fractional types are derived and used in the proposed method. The Caputo derivative is the fractional derivative type that we used. The results of numerical experiments show the efficiency of our newly developed method. Exact solution and the existing method Homotopy perturbation method is used in the comparison with our new results.