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In this paper we study the probability that the commutator of a randomly chosen pair of elements, one from a subring of a finite ring and other from the ring itself is equal to a given element of the ring. [ABSTRACT FROM AUTHOR]

It has been recently reported that trapping problem can characterize various dynamical processes taking place on complex networks. However, most works focused on the case of binary networks, and dynamical processes on weighted networks are poorly understood. In this paper, we study two kinds of biased walks including standard weight-dependent walk and mixed weight-dependent walk on the weighted scale-free treelike networks with a trap at the central node. Mixed weight-dependent walk including non-nearest neighbor jump appears in many real situations, but related studies are much less. By the construction of studied networks in this paper, we determine all the eigenvalues of the fundamental matrix for two kinds of biased walks and show that the largest eigenvalue has an identical dominant scaling as that of the average trapping time (ATT). Thus, we can obtain the leading scaling of ATT by a more convenient method and avoid the tedious calculation. The obtained results show that the weight factor has a significant effect on the ATT, and the smaller the value of the weight factor, the more efficient the trapping process is. Comparing the standard weight-dependent walk with mixed weight-dependent walk, although next-nearest-neighbor jumps have no main effect on the trapping process, they can modify the coefficient of the dominant term for the ATT. [ABSTRACT FROM AUTHOR]

Let A = I − P Q T , where P and Q are two n × 2 complex matrices of full column rank and det ( Q T P ) ≠ 0 . All the commuting solutions with A of the quadratic matrix equation A X A = X A X have been founded. [ABSTRACT FROM AUTHOR]

We consider the problem of embedding eigenvalues into the essential spectrum of periodic Jacobi operators, using an oscillating, decreasing potential. To do this we employ a geometric method, previously used to embed eigenvalues into the essential spectrum of the discrete Schrödinger operator. For periodic Jacobi operators we relax the rational dependence conditions on the values of the quasi-momenta from this previous work. We then explore conditions that permit not just the existence of infinitely many subordinate solutions to the formal spectral equation but also the embedding of infinitely many eigenvalues. [ABSTRACT FROM AUTHOR]

Let 픤 be the super Galilean conformal algebra. In this paper, we first determine all the super-skewsymmetric super-biderivations of 픤. In particular, we find that there exist non-inner super-biderivations of 픤. Based on the result of super-biderivations, we show that all the linear super-commuting maps on 픤 are standard. [ABSTRACT FROM AUTHOR]

We derive the most general families of first- and second-order differential operators semicommuting with the Heun class differential operators. Among these families, we classify all the families that commute with the Heun class. In particular, we find that a certain generalized Heun equation commutes with the Heun differential operator, which allows constructing a general solution of a complicated fourth-order linear differential equation with variable coefficients whose solution cannot be obtained using Maple 16. [ABSTRACT FROM AUTHOR]

Let ∑ n = 1 ∞ ( ‖ A n h ‖ 2 + ‖ A n ⁎ h ‖ 2 + ‖ B n h ‖ 2 + ‖ B n ⁎ h ‖ 2 ) < + ∞ for all h in a Hilbert space H , for some families { A n } n = 1 ∞ and { B n } n = 1 ∞ of bounded operators on H , where at least one of them consists of mutually commuting normal operators. If p ⩾ 2 , Φ is a symmetrically normed (s.n.) function, Φ ( p ) is its p -modification, Φ ( p ) ⁎ is a s.n. function adjoint to Φ ( p ) and ‖ ⋅ ‖ Φ ( p ) ⁎ is a norm on the ideal Image 1 , associated to the s.n. function Φ ( p ) ⁎ , then for all Image 2 (1) ‖ ∑ n = 1 ∞ A n X B n ‖ Φ ( p ) ⁎ ⩽ ‖ ( ∑ n = 1 ∞ A n ⁎ A n ) 1 / 2 X ( ∑ n = 1 ∞ B n B n ⁎ ) 1 / 2 ‖ Φ ( p ) ⁎ . Amongst other applications, this new Cauchy–Schwarz type norm inequality was used to explore a class of elementary operators induced by an analytic functions with non-negative Taylor coefficients to prove that, under conditions required for (1) , ‖ f ( ∑ n = 1 ∞ A n ⊗ B n ) X ‖ Φ ( p ) ⁎ ⩽ ‖ f ( ∑ n = 1 ∞ A n ⁎ ⊗ A n ) ( I ) X f ( ∑ n = 1 ∞ B n ⊗ B n ⁎ ) ( I ) ‖ Φ ( p ) ⁎ , whenever ‖ ∑ n = 1 ∞ A n ⁎ A n ‖ , ‖ ∑ n = 1 ∞ A n A n ⁎ ‖ , ‖ ∑ n = 1 ∞ B n ⁎ B n ‖ and ‖ ∑ n = 1 ∞ B n B n ⁎ ‖ are smaller then the radius of convergence of an analytic function f , where A n ⊗ B n stands for the bilateral multipliers Image 3 . Different applications and examples for the obtained norm inequalities are also provided. [ABSTRACT FROM AUTHOR]

It is proved that the commutative algebra A of operators on a reflexive real Banach space has an invariant subspace if each operator T ∈ A satisfies the condition ‖1−εT2‖e≤1+o(ε)asε↘0, where ║ · ║e denotes the essential norm. This implies the existence of an invariant subspace for any commutative family of essentially self-adjoint operators on a real Hilbert space. [ABSTRACT FROM AUTHOR]

We establish a comprehensive stability theory for Feynman's operational calculus (informally, the forming of functions of several noncommuting operators) in the time-dependent setting. Indeed, the main theorem, Theorem 2, contains many of the current stability theorems for the operational calculus and allows the stability theory to be significantly extended. The assumptions needed for the main theorem, Theorem 2, are rather mild and fit in nicely with the current abstract theory of the operational calculus in the time-dependent setting. Moreover, Theorem 2 allows the use of arbitrary time-ordering measures, as long as the discrete parts of these measures are finitely supported. [ABSTRACT FROM AUTHOR]

Conditions for commuting a Toeplitz matrix and a Hankel matrix were obtained relatively recently (in 2015). The solution to the problem of describing all anti-commuting pairs ( T, H), where T is a Toeplitz matrix and H is a Hankel matrix, is sketched below. [ABSTRACT FROM AUTHOR]

Principal component analysis is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations. Theoretically, such extreme high dimensionality will cause biased or inconsistent eigenvector estimates, but in practice, the principal component scores are used for visualization with great success. In this paper, we explore when and why the classical principal component scores can be used to visualize structures in high-dimensional data, even when there are few observations compared with the number of variables. Our argument is twofold: First, we argue that eigenvectors related to pervasive signals will have eigenvalues scaling linearly with the number of variables. Second, we prove that for linearly increasing eigenvalues, the sample component scores will be scaled and rotated versions of the population scores, asymptotically. Thus, the visual information of the sample scores will be unchanged, even though the sample eigenvectors are biased. In the case of pervasive signals, the principal component scores can be used to visualize the population structures, even in extreme high-dimensional situations. [ABSTRACT FROM AUTHOR]

We present a general counting result for the unstable eigenvalues of linear operators of the form J L in which J and L are skew- and self-adjoint operators, respectively. Assuming that there exists a self-adjoint operator K such that the operators J L and J K commute, we prove that the number of unstable eigenvalues of J L is bounded by the number of nonpositive eigenvalues of K. As an application, we discuss the transverse stability of one-dimensional periodic traveling waves in the classical KP-II (Kadomtsev-Petviashvili) equation. We show that these one-dimensional periodic waves are transversely spectrally stable with respect to general two-dimensional bounded perturbations, including periodic and localized perturbations in either the longitudinal or the transverse direction, and that they are transversely linearly stable with respect to doubly periodic perturbations. [ABSTRACT FROM AUTHOR]

Copyright of Journal of College of Education is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

BY MEANS OF THE THEORY OF ELASTICITY, we investigate the structural instability of a parallel array of identical simply-supported plates. One plate interacts with the neighboring plates through surface attractive forces. The proposed method is based on the 2 × 2 transfer matrix for a plate and on the solution of the generalized eigenvalue problem for the plate array. Analytical expressions of the critical interaction coefficients for two, three and four interacting plates are obtained when the end-effect of the plates at the ends of the parallel array and the surface energy of the plates are ignored. The influence of the end-effect and surface energy on the critical interaction coefficient is also numerically studied. Our solution is valid whether the plates are thin or extremely thick. [ABSTRACT FROM AUTHOR]

Copyright of Journal of College of Education is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we establish Z-eigenvalue inclusion theorems for general tensors, which reveal some crucial differences between Z-eigenvalues and H-eigenvalues. As an application, we obtain upper bounds for the largest Z-eigenvalue of a weakly symmetric nonnegative tensor, which are sharper than existing upper bounds. [ABSTRACT FROM AUTHOR]

The quantization of a pair of commuting differential operators is a pair of noncommuting differential operators. Both at the classical and quantum levels, the flows of the Kadomtsev-Petviashvili (KP) hierarchy are defined and further one can consider switching, up to a sign, the ordering of the operators. We discuss the interaction of these operations with the quantization. [ABSTRACT FROM AUTHOR]

Let A and B be almost commuting (i.e., the commutator AB − BA belongs to trace class) self-adjoint operators. We construct a functional calculus φ ↦ φ ( A , B ) for functions φ in the Besov class B ∞ , 1 1 ( R 2 ) . This functional calculus is linear, the operators φ ( A , B ) and ψ ( A , B ) almost commute for φ , ψ ∈ B ∞ , 1 1 ( R 2 ) , and φ ( A , B ) = u ( A ) v ( B ) whenever φ ( s , t ) = u ( s ) v ( t ) . We extend the Helton–Howe trace formula for arbitrary functions in B ∞ , 1 1 ( R 2 ) . The main tool is triple operator integrals with integrands in Haagerup-like tensor products of L ∞ spaces. [ABSTRACT FROM AUTHOR]

The Fokker-Planck equation with a constant diffusion coefficient and a particular polynomial drift coefficient can exhibit a bistable equilibrium distribution. Such model systems have been used to study chemical reactions, nucleation, climate, optical bistability and other phenomena. In this paper, we consider a particular choice for the drift coefficient of the form $$A(x) = x^5 - x^3$$ to exemplify the statistical behaviour of such systems. The transformation of the Fokker-Planck equation to a Schrödinger equation leads to a potential that belongs to the class of potentials in supersymmetric (SUSY) quantum mechanics. A pseudospectral method based on nonclassical polynomials is used to determine the spectrum of the Fokker-Planck operator and of the Schrödinger equation. The converged numerical eigenvalues are compared with WKB and SWKB approximations of the eigenvalues. [ABSTRACT FROM AUTHOR]

We consider commuting operators obtained by quantization of Hamiltonians of the Hopf (aka dispersionless KdV) hierarchy. Such operators naturally arise in the setting of Symplectic Field Theory (SFT). A complete set of common eigenvectors of these operators is given by Schur polynomials. We use this result for computing the SFT potential of a disk. [ABSTRACT FROM AUTHOR]

In this paper, we provide sufficient conditions for the existence of common fixed point for two commuting operators with the technique associated with measure of noncompactness in Banach spaces. Our results generalize Darbo's fixed point theorem and also some fixed point theorems which were recently proved by some authors [2, 13]. [ABSTRACT FROM AUTHOR]

Let A and [ABSTRACT FROM AUTHOR]

A triple of commuting operators for which the closed tetrablock E ‾ is a spectral set is called a tetrablock contraction or an E -contraction. The set E is defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . We show that every E -contraction can be uniquely written as a direct sum of an E -unitary and a completely non-unitary E -contraction. It is analogous to the canonical decomposition of a contraction operator into a unitary and a completely non-unitary contraction. We produce a concrete operator model for such a triple satisfying some conditions. [ABSTRACT FROM AUTHOR]

Commuting differential operators of rank 2 are considered. With each pair of commuting operators a complex curve called the spectral curve is associated. The genus of this curve is called the genus of the commuting pair. The dimension of the space of common eigenfunctions is called the rank of the commuting operators. The case of rank 1 was studied by I. M. Krichever; there exist explicit expressions for the coefficients of commuting operators in terms of Riemann theta-functions. The case of rank 2 and genus 1 was considered and studied by S. P. Novikov and I.M. Krichever. All commuting operators of rank 3 and genus 1 were found by O. I. Mokhov. A. E. Mironov invented an effective method for constructing operators of rank 2 and genus greater than 1; by using this method, many diverse examples were constructed. Of special interest are commuting operators with polynomial coefficients, which are closely related to the Jacobian problem and many other problems. Common eigenfunctions of commuting operators with polynomial coefficients and smooth spectral curve are found explicitly in the present paper. This has not been done so far. [ABSTRACT FROM AUTHOR]

Conditions under which two Toeplitz matrices are permutable have been known since at least 1995. Recently (in 2011) V.I. Gel'fgat stated conditions for permutability of a pair of Hankel matrices. In this communication, we outline a scheme for solving the much more difficult problem of describing all the pairs ( T, H) such that T is a Toeplitz matrix, H is a Hankel matrix, and T commutes with H. [ABSTRACT FROM AUTHOR]

Let L1,L2 be a pair of one-to-one commuting sectorial operators such that each Li for i∈{1,2} satisfies the mi order L² off-diagonal estimates and m1 ≥ m2 > 0. Let HLiP(Rn), i∈{1,2}, and HL1+L2P(Rn) be the Hardy spaces associated, respectively, to the operators Li and L1+L2, where L2:=L2m1/m2 is a fractional power of L2. In this paper, the authors give out some real-variable properties of these Hardy spaces. More precisely, the authors first establish the bounded joint H∞ functional calculus in these Hardy spaces and prove that the abstract Riesz transform Dmi(L1+L2)−1/2 is bounded from HLiP(Rn) to the classical Hardy space Hp(Rn) for all p∈(n/n+mi,1], where i∈{1,2}. Moreover, for all p∈(0,1], the authors show that HL1+L2P (Rn) = HL1P (Rn) + HL2P (Rn) and give a sufficient condition to guarantee HL1P (Rn) ⊂ HL2P (Rn). [ABSTRACT FROM AUTHOR]

Eigenvalue-based methods have been widely investigated for multiantenna blind spectrum sensing in cognitive radio (CR). However, most of them are formulated in the framework of maximum likelihood (ML) estimation, which is optimal only when the number of samples is much larger than the number of antennas. In relatively small-sample scenarios where the number of antennas is comparable in magnitude to the number of samples, their optimality cannot be guaranteed. Based on the random matrix theory (RMT), an eigenvalue moment ratio (EMR) approach is proposed for spectrum sensing. As the distribution of the EMR statistic in the absence of signals can be precisely determined by the RMT, this approach is able to reliably predict the theoretical threshold. Moreover, as the EMR detector is developed from the RMT perspective and utilizes all the signal eigenvalues for detection, it can be superior to state-of-the-art detection algorithms, particularly for relatively small samples. Furthermore, we derive the asymptotic distribution of the EMR statistic in the presence of signals and analyze the theoretical detection probability of the EMR approach. Additionally, the EMR statistic is calculated via the Frobenius inner product and matrix trace operations instead of the eigenvalue decomposition (EVD), which offers computational efficiency. Simulation results are presented to illustrate the superiority of the EMR approach and confirm our theoretical calculation. [ABSTRACT FROM PUBLISHER]

Using the Lax operator formalism, we construct a family of pairwise commuting operators such that the Macdonald symmetric functions of infinitely many variables $${x_{1},x_{2},{\ldots}}$$ and of two parameters q, t are their eigenfunctions. We express our operators in terms of the Hall-Littlewood symmetric functions of the variables $${x_{1},x_{2},{\ldots}}$$ and of the parameter t corresponding to the partitions with one part only. Our expression is based on the notion of Baker-Akhiezer function. [ABSTRACT FROM AUTHOR]

For an action α of Zd by homeomorphisms of a compact metric space, D. Lind introduced a dynamical zeta function and conjectured that this function has a natural boundary when d ≥ 2. In this note, under the assumption that α is a mixing action by continuous automorphisms of a compact connected abelian group of finite topological dimension, it is shown that the upper growth rate of periodic points is zero and that the unit circle is a natural boundary for the dynamical zeta function. [ABSTRACT FROM AUTHOR]

We are interested in classical linearized eigenvalue problems for one dimensional reaction–diffusion equations with small diffusion coefficient. Previously, authors have obtained the precise asymptotic formulas of all eigenvalues and eigenfunctions for f ( u ) = sin ⁡ u , which suggest interesting structure of eigenpairs: existence of two special eigenpairs and the limiting classification of the others by special eigenpairs. In this paper we study the Allen–Cahn case f ( u ) = u − u 3 and obtain the asymptotic formulas of eigenvalues, which leads us to the limiting classification of eigenvalues. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show that we can extend the notion of convergence in the norm‐resolvent sense to the case of several unbounded noncommuting operators (and to quaternionic operators as a particular case) using the notion of S‐resolvent operator. With this notion, we can define bounded functions of unbounded operators using the S‐functional calculus for n‐tuples of noncommuting operators. The same notion can be extended to the case of the F‐resolvent operator, which is the basis of the F‐functional calculus, a monogenic functional calculus for n‐tuples of commuting operators. We also prove some properties of the F‐functional calculus, which are of independent interest. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The estimation of commuting flows at different spatial scales is a fundamental problem for different areas of study. Many current methods rely on parameters requiring calibration from empirical trip volumes. Their values are often not generalizable to cases without calibration data. To solve this problem we develop a statistical expression to calculate commuting trips with a quantitative functional form to estimate the model parameter when empirical trip data is not available. We calculate commuting trip volumes at scales from within a city to an entire country, introducing a scaling parametera to the recently proposed parameter free radiation model. The model requires only widely available population and facility density distributions. The parameter can be interpreted as the influence of the region scale and the degree of heterogeneity in the facility distribution. We explore in detail the scaling limitations of this problem, namely under which conditions the proposed model can be applied without trip data for calibration. On the other hand, when empirical trip data is available, we show that the proposed model's estimation accuracy is as good as other existing models. We validated the model in different regions in the U.S., then successfully applied it in three different countries. [ABSTRACT FROM AUTHOR]

We study the existence and non-existence of positive solutions of a system of nonlinear second-order difference equations with eigenvalues subject to multi-point boundary conditions. [ABSTRACT FROM AUTHOR]

We study examples of formally self-adjoint commuting ordinary differential operators of order 4 or 4g + 2 whose coefficients are analytic on ℂ. We prove that these operators do not commute with the operators of odd order, justifying rigorously that these operators are of rank 2. [ABSTRACT FROM AUTHOR]

In the work by V. A. Zolotarev, Dokl. Akad. Nauk Arm. SSR, 63, No. 3, 136-140 (1976), a triangular model is constructed for a system of twice-commuting linear bounded completely nonself-adjoint operators { A, A} ([ A, A] = 0, [ A, A] = 0) such that rank ( A)( A) = 1 (2 i( A) = A − A, k = 1, 2) and the spectrum of each operator A, k = 1, 2 , is concentrated at zero. The indicated triangular model has the form of a system of operators of integration over the independent variable in L where the domain Ω = [0, a] × [0, b] is a compact set in ℝ bounded by the lines x = a and y = b and a decreasing smooth curve L connecting the points (0 , b) and ( a, 0) . [ABSTRACT FROM AUTHOR]

Abstract: Let and be n-tuples of commuting self-adjoint operators on Hilbert space. For functions f on satisfying certain conditions, we obtain sharp estimates of the operator norms (or norms in operator ideals) of in terms of the corresponding norms of , . We obtain analogs of earlier results on estimates for functions of perturbed self-adjoint and normal operators. It turns out that for , the methods that were used for self-adjoint and normal operators do not work. We propose a new method that works for arbitrary n. We also get sharp estimates for quasicommutators in terms of norms of , , for a bounded linear operator R. [Copyright &y& Elsevier]

Standard canonical quantum mechanics makes much use of operators whose spectra cover the set of real numbers, such as the coordinates of space, or the values of the momenta. Discrete quantum mechanics uses only strictly discrete operators. We show how one can transform systems with pairs of integer-valued, commuting operators $$P_i$$ and $$Q_i$$ , to systems with real-valued canonical coordinates $$q_i$$ and their associated momentum operators $$p_i$$ . The discrete system could be entirely deterministic while the corresponding ( p, q) system could still be typically quantum mechanical. [ABSTRACT FROM AUTHOR]

Einstein, Podolski and Rosen (EPR) have shown that any wavefunction (subject to the Schrödinger equation) can describe the physical reality completely, and any two observables associated with two non-commuting operators can have simultaneous reality. In contrast, quantum theory claims that the wavefunction can capture the physical reality completely, and the physical quantities associated with two non-commuting operators cannot have simultaneous reality. The above contradiction is known as the EPR paradox. Here, we unambiguously expose that there is a hidden assumption made by EPR, which gives rise to this famous paradox. Putting the assumption right this time leads us not to the paradox, but only reinforces the correctness of the quantum theory. However, it is shown here that the entanglement phenomenon between two physically separated particles (they were entangled prior to separation) can only be proven to exist with a 'proper' measurement. [ABSTRACT FROM AUTHOR]

Two operations, e.g. measurements, successively applied to the state of a system are said to be non-commutative of the sequence of their application makes a difference for the final result. Non-commuting operations play a crucial role in quantum theory, where they are intimately related to concepts as central as those of complementarity and entanglement. However their significance is not restricted to the small dimensions of the microworid. For reasons easy to understand, non-commuting operations must be expected to be the rule rather than the exception for operations on mental systems. We demonstrate this with afew examples from our own work, and hope this may contribute to the increasing attention that this exciting new area in conscious- ness studies is currently attracting worldwide. [ABSTRACT FROM AUTHOR]

We construct a family of pairwise commuting operators such that the Jack symmetric functions of infinitely many variables $${x_1,x_2, \ldots}$$ are their eigenfunctions. These operators are defined as limits at N → ∞ of renormalised Sekiguchi-Debiard operators acting on symmetric polynomials in the variables $${x_1 , \ldots , x_N}$$ . They are differential operators in terms of the power sum variables $${p_n=x_1^n+x_2^n+\cdots}$$ and we compute their symbols by using the Jack reproducing kernel. Our result yields a hierarchy of commuting Hamiltonians for the quantum Calogero-Sutherland model with an infinite number of bosonic particles in terms of the collective variables of the model. Our result also yields the elementary step operators for the Jack symmetric functions. [ABSTRACT FROM AUTHOR]

Classifying phases of local quantum systems is a general problem that includes special cases such as free fermions, commuting projectors, and others. An important distinction in this classification should be made between classifying periodic and aperiodic systems. A related distinction is that between homotopy invariants (invariants which remain constant so long as certain general properties such as locality, gap, and others hold) and locally computable invariants (properties of the system that can not change from one region to another without producing a gapless edge between them). We attack this problem using a technique inspired by Kirby's "torus trick" in topology. We use this trick to reproduce results for free fermions (in particular, using the trick to reduce the aperiodic classification to the simpler problem of periodic classification). We also show that a similar trick works for interacting phases which are nontrivial but lack anyons; these results include symmetry-protected phases. A key part of this work is an attempt to classify quantum cellular automata. [ABSTRACT FROM AUTHOR]

For a closed connected manifold N, we establish the existence of geometric structures on various subgroups of the contactomorphism group of the standard contact jet space J1N, as well as on the group of contactomorphisms of the standard contact T*N×S1 generated by compactly supported contact vector fields. The geometric structures are biinvariant partial orders (for J1N and T*N×S1) and biinvariant integer-valued metrics (T*N×S1 only). We prove some forms of contact rigidity in T*N×S1, namely that certain (possibly singular) subsets of the form X×S1 cannot be disjoined from the zero section by a contact isotopy, and in addition that there are restrictions on commuting products of contactomorphisms. Finally, we prove multiplicity results for orbits of certain contact flows in T*N×S1 with Legendrian boundary conditions, which in particular apply to Reeb chords. The method is that of generating functions for Legendrians in jet spaces. [ABSTRACT FROM PUBLISHER]

This work complements the first author's recent asymptotic investigations on a class of boundary-eigenvalue problems for tensile buckling of thin elastic plates. In particular, it is shown here that the approximations for the critical buckling load can be improved by using a modified energy method that relies directly on the asymptotic results derived previously. We also explore a number of additional mathematical features that have an intrinsic interest in the context of multi-parameter eigenvalue problems. [ABSTRACT FROM AUTHOR]

This article concerns the permanence of the single-valued extension property at a point under suitable perturbations. While this property is, in general, not preserved under sums and products of commuting operators, we obtain positive results in the case of commuting perturbations that are quasi-nilpotent, algebraic, or Riesz operators. [ABSTRACT FROM AUTHOR]

We prove that, under sufficient conditions on the spectra, where N is an unbounded normal operator and M is a bounded normal operator in the Hilbert space. [ABSTRACT FROM AUTHOR]

We characterize the commuting Toeplitz operator and Hankel operator with quasihomogeneous symbols. Also, we use it to show the necessary and sufficient conditions for commuting Toeplitz operator and Hankel operator with ordinary functions. [ABSTRACT FROM AUTHOR]