Finite Order Research Articles

Coupled thermal-mechanical analysis of power electronic modules with finite element method and parametric model order reduction

This work presents a new approach for performing a parametric study and examining nonlinear material behaviours of a coupled thermal-mechanical model of a Power Electronics Module (PEM) by integrating the Finite Element Method (ANSYS-FEM) with Parametric Model Order Reduction (pMOR). The considered coupling method solves the thermal and structural models concurrently compared to the widely practised sequential coupling method. Instead of constant parameter values, which are generally regarded for pMOR studies, the temperature-dependent material properties of the wire material have been parametrised in the work using the pMOR method. A generalised 2D model has been regarded here for thermal-mechanical analysis with the pMOR approach, parametrising temperature-dependent coefficient of thermal expansion (CTE) and Young’s modulus (E) of the wire material to explore their impact on wire bonds. The matrix interpolation method has been applied here for the pMOR study, and PRIMA, a Krylov subspace-based model order reduction (MOR) technique, has been exercised for local model order reductions. A new efficient process of matrix interpolation, based on the Lagrange interpolation technique, has been developed to implement matrix interpolation in the parametric reduced order model (pROM). The local reduced order models (ROMs) have a degree of freedom (DOF) of just 8, compared to the full-order models’ (FOMs) of 50,602. The pROM provides an excellent solution and reduces computational time by 84% for the presented case.

Pre-Leibniz algebras

The notion of pre-Leibniz algebras was recently introduced in the study of Rota-Baxter operators on Leibniz algebras. In this paper, we first construct a graded Lie algebra whose Maurer-Cartan elements are pre-Leibniz algebras. Using this characterization, we define the cohomology of a pre-Leibniz algebra with coefficients in a representation. This cohomology is shown to split the Loday-Pirashvili cohomology of Leibniz algebras. As applications of our cohomology, we study formal and finite order deformations of a pre-Leibniz algebra. Finally, we define homotopy pre-Leibniz algebras and classify some special types of homotopy pre-Leibniz algebras.

Existence of entire solutions for k-th derivative of certain type of non-linear differential-difference equations

The paper discusses the existence of entire solutions for k th derivative of certain type of non-linear differential-difference equations. In addition to, the paper evaluates some previous results for existence of finite order transcendental entiresolutions and extends to the higher order. Particularly, we obtain the conditions for occurrence and attainable forms of entire solutions.

Optimal finite-dimensional controller of the stochastic differential object’s state by its output II. Stochastic measurements and separation theorem

Consideration is continued of the problem of the inertial control law by the output synthesis of a continuous nonlinear stochastic plant, which is optimal on average and on a finite time interval, and works with the desired speed. An algorithm for synthesizing the optimal structure of a dynamic controller of a selected finite order, obtained in the first part of the article for the case of accurate measurements of a of the control object’s state variables part, is presented. Its application is demonstrated in detail for the case when the state variables of an object are measured with random errors. Using the example of a linear-quadratic-Gaussian problem, it is shown that the proposed controller of the corresponding order also satisfies the well-known separation theorem.

Nondefinability results with entire functions of finite order in polynomially bounded o-minimal structures

Nondefinability results with entire functions of finite order in polynomially bounded o-minimal structures

Consistency of averaged impulse response estimators in vector autoregressive models

We show root‐T consistency of the smoothed AIC and smoothed BIC model averaging estimators (sAIC, sBIC) of impulse response coefficients in stationary vector autoregressive models of finite lag order. We also show that there is not one unique way to define the sAIC and sBIC estimators, but that instead there is a whole class of each of these defined by a weight scaling factor that allows the averaging estimator to become more similar to either its model selection counterpart or the equal weights averaging estimator. We also show asymptotic validity of a bootstrap method for estimating the averaging estimators' distributions. Simulations illustrate the benefits of using sAIC instead of AIC estimators.

On polynomial solutions of certain finite order ordinary differential equations

Given a finite order differential operator, some properties and relations satisfied by its polynomial eigenfunctions are studied. Under certain restrictions, such eigenfunctions are explicitly obtained, as well as the corresponding eigenvalues. Also, some linear transformations are applied to sequences of eigenfunctions and a necessary condition for this to be a sequence of eigenfunctions of a new differential operator is obtained. These results are applied to the particular case of classical Hermite polynomials.

Twisted representations of ℕ-graded vertex algebras over a good field

Let [Formula: see text] be an [Formula: see text]-graded vertex algebra over a field [Formula: see text], and let [Formula: see text] be an automorphism of [Formula: see text] with a finite order [Formula: see text]. Assume that the field [Formula: see text] contains a [Formula: see text]th primitive root of unity. We construct two associative algebras, [Formula: see text] and [Formula: see text], and investigate their properties and interconnections. As applications, we establish the following results: (1) If [Formula: see text] is finite-dimensional, then [Formula: see text] is also finite-dimensional; (2) If [Formula: see text] is strongly finitely generated, then [Formula: see text] is stably noetherian; (3) If [Formula: see text] is strongly finitely generated and [Formula: see text] is an irreducible admissible [Formula: see text]-twisted [Formula: see text]-module, then the endomorphism algebra [Formula: see text] is finite-dimensional.

On the Characterization of Some m-Plithogenic Vector Spaces and Their AH-Substructures Under the Condition 6 ≤ dim SPV ≤10

This paper is concerned with studying symbolic m-plithogenic vector spaces with finite orders between 6 and 10, where it defines and characterizes the AH-subspaces, AH-kernels, and AH- linear transformations in five different symbolic m-plithogenic spaces (6-plithogenic, 7-plithogenic,10-plithogenic vector spaces). Also, we prove many theorems that describe the computation of the kernels and direct images of the plithogenic AH-linear transformations.

On Two-Dimensional Diffeomorphisms with Homoclinic Orbits to Nonhyperbolic Fixed Points

We consider two-dimensional diffeomorphisms with homoclinic orbits to nonhyperbolic fixed points. We assume that the point has arbitrary finite order degeneracy and is either of saddle-node or weak saddle type. We consider two cases when the homoclinic orbit is transversal and when a quadratic homoclinic tangency takes place. In the first case we give a complete description of orbits entirely lying in a small neighborhood of the homoclinic orbit. In the second case we study main bifurcations in one-parameter families that split generally the homoclinic tangency but retain the degeneracy type of the fixed point.

Pseudo-resolvent energy of weighted graphs

Let G be a finite order graph. Its resolvent matrix and its resolvent energy are respectively given by Rξ(A(G)) = (A(G) – ξI)–1 and ER(G) = Σn i = 1 (n – λi)–1. For some classes of weighted graphs, we know that λ1 = n which means that the formula for ER(G) is not applicable. In this work, the pseudo-resolvent energy for those classes of graphs are obtained where λ1 = n.

The Spaces of Delta-subharmonic Functions of Finite Order with Respect to the Model Function of Growth

The Spaces of Delta-subharmonic Functions of Finite Order with Respect to the Model Function of Growth

Mean of the product of derivatives of Hardy's Z-function with Dirichlet polynomial

Inspired by the work of Balasubramanian, Conrey and Heath-Brown [1], we obtain an asymptotic expression for the mean of the product of any two finite order derivatives of Hardy's Z-function times Dirichlet polynomials in short intervals.

Meridional rank and bridge number of knotted 2-spheres

Abstract The meridional rank conjecture asks whether the bridge number of a knot in $S^3$ is equal to the minimal number of meridians needed to generate the fundamental group of its complement. In this paper, we investigate the analogous conjecture for knotted spheres in $S^4$ . Towards this end, we give a construction to produce classical knots with quotients sending meridians to elements of any finite order in Coxeter groups and alternating groups, which detect their meridional ranks. We establish the equality of bridge number and meridional rank for these knots and knotted spheres obtained from them by twist-spinning. On the other hand, we show that the meridional rank of knotted spheres is not additive under connected sum, so that either bridge number also collapses, or meridional rank is not equal to bridge number for knotted spheres.

Uniqueness of Meromorphic Functions With Nonlinear Differential Polynomials Sharing a Small Function IM

In the paper, we discuss the distribution of uniqueness and its elements over the extended complex plane from different polynomials of view. We obtain some new results regarding the structure and position of uniqueness. These new results have immense applications like classifying different expressions to be or not to be unique. The principal objective of the paper is to study the uniqueness of meromorphic functions when sharing a small function $a(z)$ IM with restricted finite order and its nonlinear differential polynomials. The lemma on the logarithmic derivative by Halburb and Korhonen (Journal of Mathematical Analysis and Applications, \textbf{314} (2006), 477--87) is the starting point of this kind of research. In this direction, the current focus in this field involves exploring unique results for the differential-difference polynomials of meromorphic functions, covering both derivatives and differences. Liu et al. (Applied Mathematics A Journal of Chinese Universities, \textbf{27} (2012), 94--104) have notably contributed to this research. Their research establishes that when $n \leq k + 2$ for a finite-order transcendental entire function $f$ the differential-difference polynomial$[f^{n}f(z+c)]^{(k)} - \alpha(z)$ has infinitely many zeros. Here, $\alpha(z)$ is characterized by its smallness relatively to $f$. Additionally, for two distinct meromorphic functions $f$ and $g$, both of finite order, if the differential-difference polynomials $[f^{n}f(z+c)]^{(k)}$\ and\ $[g^{n}g(z+c)]^{(k)}$ share the value $1$ in the same set, then $f(z)=c_1e^{dz},$ $g(z)=c_2e^{-dz}.$ We prove two results, which significantly generalize the results of Dyavanal and Mathai (Ukrainian Math. J., \textbf{71} (2019), 1032--1042), and Zhang and Xu (Comput. Math. Appl., \textbf{61} (2011), 722-730) and citing a proper example we have shown that the result is true only for a particular case. Finally, we present the compact version of the same result as an improvement.

The Bohr radius and its modifications for linearly invariant families of analytic functions

In 1914, Harald Bohr published an article in which he considered the class B of all analytic functions in the unit disk |z|<1, bounded in absolute value by 1. The article contains proofs that for any function f(z)=∑n=0∞anzn from B, the inequality ∑n=0∞|anzn|≤1 holds in the disk of radius 1/3 centered at the origin, and the value 1/3 is optimal. Also, Bohr himself in this article proved the corresponding result in a circle of radius 1/6 and adds, following the request of Wiener, Wiener's later proof for the disk of radius 1/3. Since then, the constant 1/3 in this problem has been called the Bohr radius. This was followed by a series of papers dealing with analogues of the Bohr radius or its estimates in other classes of functions. In this article, we give estimates for the Bohr radius in some classes of analytic functions in D, associated with linearly invariant families of finite order.

Constructing copulas using corrected Hermite polynomial expansion for estimating cross foreign exchange volatility

A finite order multivariate Hermite polynomial expansion, as an approximation of a joint density function, can handle complex correlation structures. However, it does not construct copulas, because the density function can take negative values. In this study, we propose a formulation of multivariate Hermite polynomial expansion suitable for the application of correction that recovers non-negativity and construct a copula. Several useful expressions for integrals with the copula are derived from this formulation. We also apply this copula to estimate the volatility smile of cross-currency pairs in the foreign exchange option market. In the numerical experiments, we compare the estimation results of the volatility smile of EUR–JPY, GBP–JPY, and AUD–JPY for the proposed and other copulas to confirm the validity of the proposed copula.

Weak centers and local criticality on planar [formula omitted]-symmetric cubic differential systems

There exist the necessary and sufficient conditions for planar Z2-symmetric cubic differential systems with a bi-center and an isochronous bi-center in the existing literature. Based on these bi-center conditions, we give a complete discussion on the order of weak centers and the local criticality for planar Z2-symmetric cubic systems at the origin and the symmetric equilibria (±1,0) separately. More precisely, we first give the parametric conditions for the origin and the equilibria (±1,0) being weak centers of exact order separately. Then we prove that the local criticality from the weak centers of finite order at the origin is at most 4, and at each of symmetric equilibria (±1,0) is at most 3. Finally, we also obtain that the local criticality from the isochronous center at the origin is at most 3, and at each of equilibria (±1,0) is at least 2. More importantly, these numbers are reachable.

Composition closed premodel structures and the Kreweras lattice

We investigate the rich combinatorial structure of premodel structures on finite lattices whose weak equivalences are closed under composition. We prove that there is a natural refinement of the inclusion order of weak factorization systems so that the intervals detect these composition closed premodel structures. In the case that the lattice in question is a finite total order, this natural order retrieves the Kreweras lattice of noncrossing partitions as a refinement of the Tamari lattice, and model structures can be identified with certain tricolored trees.

Bochner Laplacian and Bergman kernel expansion of semipositive line bundles on a Riemann surface

We generalize the results of Montgomery (Commun Math Phys 168:651–675, 1995) for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel expansion for semipositive line bundles whose curvature vanishes at finite order. The proof exploits the relation of the Bochner Laplacian on tensor powers with the sub-Riemannian (sR) Laplacian.