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In this paper, we consider composite quantile regression for partial functional linear regression model with polynomial spline approximation. Under some mild conditions, the convergence rates of the estimators and mean squared prediction error, and asymptotic normality of parameter vector are obtained. Simulation studies demonstrate that the proposed new estimation method is robust and works much better than the least-squares based method when there are outliers in the dataset or the random error follows heavy-tailed distributions. Finally, we apply the proposed methodology to a spectroscopic data sets to illustrate its usefulness in practice. [ABSTRACT FROM AUTHOR]

In this paper, we study a certain partition function a( n) defined by Σ a( n) q:= Π(1 − q)(1 − q). We prove that given a positive integer j ≥ 1 and a prime m ≥ 5, there are infinitely many congruences of the type a( An + B) ≡ 0 (mod m). This work is inspired by Ono's ground breaking result in the study of the distribution of the partition function p( n). [ABSTRACT FROM AUTHOR]

In this paper, the authors establish the L p-mapping properties of certain classes of Marcinkiewicz integral operators along surfaces with rough kernels. The results in this paper essentially extend as well as improve previously known results. [ABSTRACT FROM AUTHOR]

Let x: M n → R n+1 be an n(≥ 2)-dimensional hypersurface immersed in Euclidean space R n+1. Let σ i (0 ≤ i ≤ n) be the ith mean curvature and Q n = Σ(−1) i+1() σ σ i . Recently, the author showed that W n ( x) = ∫ M Q n dM is a conformal invariant under conformal group of R n+1 and called it the nth Willmore functional of x. An extremal hypersurface of conformal invariant functional W n is called an nth order Willmore hypersurface. The purpose of this paper is to construct concrete examples of the 3rd order Willmore hypersurfaces in R 4 which have good geometric behaviors. The ordinary differential equation characterizing the revolutionary 3rd Willmore hypersurfaces is established and some interesting explicit examples are found in this paper. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the spectral gap and the logarithmic Sobolev constant for continuous spin systems. A simple but general result for estimating the spectral gap of finite dimensional systems is given by Theorem 1.1, in terms of the spectral gap for one-dimensional marginals. The study of this topic provides us a chance, and it is indeed another aim of the paper, to justify the power of the results obtained previously. The exact order in dimension one (Proposition 1.4), and then the precise leading order and the explicit positive regions of the spectral gap and the logarithmic Sobolev constant for two typical infinite-dimensional models are presented (Theorems 6.2 and 6.3). Since we are interested in explicit estimates, the computations become quite involved. A long section (Section 4) is devoted to the study of the spectral gap in dimension one. [ABSTRACT FROM AUTHOR]

In this paper, we discuss our most recent results on the optimal L2 extension problem and Siu’s lemma as applications of the strong openness property of multiplier ideal sheaves obtained by Guan and Zhou. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of g-variance and study some properties of this operator. We find the nonlinear variance operator, g-variance, does not preserve some basic properties of traditional mathematic variance. We also consider the relationship [Figure not available: see fulltext.] and [Figure not available: see fulltext.] Var Q[ ξ] ([Figure not available: see fulltext.] and [Figure not available: see fulltext.] Var Q[ ξ]). The result shows that the maximum (minimum) variance is not always equal to [Figure not available: see fulltext.]). If g satisfies some restrictive conditions, we get the uniqueness theorem and the comparison theorem via g-variance. [ABSTRACT FROM AUTHOR]

In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the norm L p (1 ≤ p ≤ ∞) of multiplier function classes and the corresponding m-term Greedy-liked one-sided trigonometric approximation results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Gerber-Shiu discounted penalty function for the surplus process described by a piecewise deterministic Markov process (PDMP).We derive an integral equation for the Gerber-Shiu discounted penalty function, and obtain the exact solution when the initial surplus is zero. Dickson formulae are also generalized to the present surplus process. [ABSTRACT FROM AUTHOR]

In this paper, some theorems of uniform stability and uniform asymptotic stability for impulsive functional differential equations with infinite delay are proved by using Lyapunov functionals and Razumikhin techniques. An example is also proved at the end to illustrate the application of the obtained results. [ABSTRACT FROM AUTHOR]

A ( p, q)-graph G is called super edge-magic if there exists a bijective function f: V ( G) ∪ E( G) → {1, 2, ..., p+ q} such that f( u)+ f( υ)+ f( uυ) is a constant for each uυ ε E( G) and f( V ( G)) = {1, 2, ..., p}. In this paper, we introduce the concept of strong super edge-magic labeling as a particular class of super edge-magic labelings and we use such labelings in order to show that the number of super edge-magic labelings of an odd union of path-like trees ( mT), all of them of the same order, grows at least exponentially with m. [ABSTRACT FROM AUTHOR]

Hecke groups are an important tool in investigating functional equations, and congruence subgroups of Hecke groups play an important rule in research of the solutions of the Dirichlet series. When q, m are two primes, congruence subgroups and the principal congruence subgroups of level m of the Hecke group H(√ q) have been investigated in many papers. In this paper, we generalize these results to the case where q is a positive integer with q ≥ 5, √ q ∉ ℤ and m is a power of an odd prime. [ABSTRACT FROM AUTHOR]

Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the L p metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the stability problem of the generalized sine functional equations as follows: . Namely, we have generalized the Hyers-Ulam stability of the (pexiderized) sine functional equation. [ABSTRACT FROM AUTHOR]

The study of symmetric property in the L 2-sense for the non-positive definite operator is motivated by the theory of probability and analysis. This paper presents some sufficient conditions for the existence of symmetric measure for Lévy type operator. Some new examples are illustrated. The present study is an important step for considering various ergodic properties and functional inequalities of Lévy type operator. [ABSTRACT FROM AUTHOR]

In this paper, we prove that every operator in a class of contraction operators on a Banach space whose spectrum contains the unit circle has a nontrivial hyperinvariant subspace. [ABSTRACT FROM AUTHOR]

In this paper, the non-linear approximation on the class of multivariate functions with bounded mixed derivatives is investigated, and the asymptotic degree of the non-linear width on this class is determined. [ABSTRACT FROM AUTHOR]

In this paper, the Dirac operator on the Klein model for the hyperbolic space is considered. A function space containing L2-functions on the sphere Sm-1 in ĝm, which are boundary values of solutions for this operator, is defined, and it is proved that this gives rise to a Hilbert module with a reproducing kernel. [ABSTRACT FROM AUTHOR]

In this paper, we obtain that a strongly singular integral operator is bounded on Lpw space for 1 < p < ∞. We also obtain that a strongly singular integral operator is a bounded operator from Hpw to Lpw for some weight w and 0 < p ≤ 1. And by an atomic decomposition, we obtain that a strongly singular integral operator is a bounded operator on Hpw for some w and 0 < p ≤ 1. [ABSTRACT FROM AUTHOR]

In this paper we give the suffcient and necessary condition for the existence of any almost isometric operator from C(Ω) into C0(Ω0). As a corollary, we show that there is no ∈–isometry from any abstract M space with a strong unit into C0(Γ) if $$ 0 < \in < \frac{1} {9}. $$ [ABSTRACT FROM AUTHOR]

In this paper, we will study the nonelementary groups of Möbius transformations in $$ \overline{R} ^{n} $$ and some properties are obtained. Also in this paper we will prove several theorems about discreteness criteria and group convergence of nonelementary groups of M( $$ \overline{R} ^{n} $$). [ABSTRACT FROM AUTHOR]

Letbe a unit sphere of thed-dimensional Euclidean space Rd and let(0 < p= 1) denote the real Hardy space onFor 0 < p= 1 andletEj(f,Hp) (j= 0, 1, ...) be the best approximation offby spherical polynomials of degree less than or equal toj, in the spaceGiven a distributionfonits Cesàro mean of order d>-1 is denoted byFor 0p. In this paper, the following result is proved:TheoremLet0N(f)˜BN(f)means that there’s a positive constant C, independent of N and f, such thatIn the cased= 2,this result was proved by Belinskii in 1996. [ABSTRACT FROM AUTHOR]

In this paper, the asymptotic behavior of generalized risk processes without any moment assumptions on the controlling process is described. [ABSTRACT FROM AUTHOR]

In this paper we give a Carleson measure characterization for the compact composition operators between Dirichlet type spaces. We use this characterization to show that every compact composition operator on Dirichlet type spaces is compact on the Bloch space. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the homographic solutions to the rhombus four body problem are the variational minimizers of the Lagrangian action restricted on a holonomically constrained rhombus loop space. [ABSTRACT FROM AUTHOR]

In this paper, we study conharmonic curvature tensor in Kenmotsu manifolds with respect to semi-symmetric metric connection and also characterize conharmonically flat, conharmonically semisymmetric and ϕ-conharmonically flat Kenmotsu manifolds with respect to semi-symmetric metric connection. [ABSTRACT FROM AUTHOR]

In this paper, we study dynamically consistent nonlinear evaluations in L (1 < p < 2). One of our aim is to obtain the following result: under a domination condition, an F-consistent evaluation is an E-evaluation in L. Furthermore, without the assumption that the generating function g ( t, ω, y, z) is continuous with respect to t, we provide some useful characterizations of an E-evaluation by g and give some applications. These results include and extend some existing results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the existence of insensitizing controls for the parabolic equation with equivalued surface boundary conditions. The insensitizing problem consists in finding a control function such that some energy functional of the equation is locally insensitive to a perturbation of the initial data. As usual, this problem can be reduced to a partially null controllability problem for a cascade system of two parabolic equations with equivalued surface boundary conditions. Compared the problems with usual boundary conditions, in the present case we need to derive a new global Carleman estimate, for which, in particular one needs to construct a new weight function to match the equivalued surface boundary conditions. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to derive a new ( p, q)-atomic decomposition on the multi-parameter Hardy space H( X × X) for 0 < p < p ≤ 1 for some p and all 1 < q < ∞, where X × X is the product of two spaces of homogeneous type in the sense of Coifman and Weiss. This decomposition converges in both L( X × X) (for 1 < q < ∞) and Hardy space H( X × X) (for 0 < p ≤ 1). As an application, we prove that an operator T, which is bounded on L( X × X) for some 1 < q < ∞, is bounded from H( X × X) to L( X × X) if and only if T is bounded uniformly on all ( p, q)-product atoms in L( X × X). The similar boundedness criterion from H( X × X) to H( X × X) is also obtained. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the multilinear Hardy operators in higher dimensional cases and establish the CBMO estimates for multilinear Hardy operators on some function spaces, such as the Lebesgue spaces, the Herz spaces and the Morrey-Herz spaces. [ABSTRACT FROM AUTHOR]

Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper is to develop a theory of multi-parameter Triebel-Lizorkin and Besov spaces using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the recent work of Han and Lu in which they established a satisfactory theory of multi-parameter Littlewood-Paley-Stein analysis and Hardy spaces associated with the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. We also prove the boundedness of flag singular integral operators on Triebel-Lizorkin space and Besov space. Our methods here can be applied to develop easily the theory of multi-parameter Triebel-Lizorkin and Besov spaces in the pure product setting. [ABSTRACT FROM AUTHOR]

In the present paper, we establish the stability and the superstability of a functional inequality corresponding to the functional equation f n( xyx) = Σ i+ j+ k= n f i( x) f j( y) f k( x). In addition, we take account of the problem of Jacobson radical ranges for such functional inequality. [ABSTRACT FROM AUTHOR]

In this paper, we study selfinjective Koszul algebras of finite complexity. We prove that the complexity is a nonnegative integer when it is finite; and that the category [Figure not available: see fulltext.] of modules with complexity less or equal to t, is resolving and coresolving. We show that for each 0 ≤ l ≤ m there exist a family of modules of complexity l parameterized by G( l,m), the Grassmannian of l-dimensional subspaces of an m-dimensional vector space V, for the exterior algebra of V. Using complexity, we also give a new approach to the representation theory of a tame symmetric algebra with vanishing radical cube over an algebraically closed field of characteristic 0, via skew group algebra of a finite subgroup of SL(2, C) over the exterior algebra of a 2-dimensional vector space. [ABSTRACT FROM AUTHOR]

In this paper, through an information-theoretic approach, we construct estimations and confidence intervals of Z-functionals involving finite population and with the presence of auxiliary information. In particular, we give a method of estimating the variance of finite population with known mean. The modified estimates and confidence intervals for Z-functionals can adequately use the auxiliary information, at least not worse than what the standard ones do. A simulation study is presented to assess the performance of the modified estimates for the finite sample case. [ABSTRACT FROM AUTHOR]

In this paper we use the T1 theorem to prove a new characterization with minimum regularity and cancellation conditions for inhomogeneous Besov and Triebel-Lizorkin spaces over spaces of homogeneous type. These results are new even for ℝ n. [ABSTRACT FROM AUTHOR]

In this paper, the differential equation involving iterates of the unknown function, with a complex parameter a, is investigated in the complex field ℂ for the existence of analytic solutions. First of all, we discuss the existence and the continuous dependence on the parameter a of analytic solution for the above equation, by making use of Banach fixed point theorem. Then, as well as in many previous works, we reduce the equation with the Schröder transformation x( z) = y( αy−1( z)) to the following another functional differential equation without iteration of the unknown function which is called an auxiliary equation. By constructing local invertible analytic solutions of the auxiliary equation, analytic solutions of the form y( αy−1( z)) for the original iterative differential equation are obtained. We discuss not only these α given in Schröder transformation in the hyperbolic case 0 < | α| < 1 and resonance, i.e., at a root of the unity, but also those α near resonance (i.e., near a root of the unity) under Brjuno condition. Finally, we introduce explicit analytic solutions for the original iterative differential equation by means of a recurrent formula, and give some particular solutions in the form of power functions when a = 0. [ABSTRACT FROM AUTHOR]

In the present paper, we obtain three independent results on the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces. That is, we are going to obtain the characterization of local means, the boundedness of pseudo-differential operators and the characterization of the Hardy-Morrey spaces. By using the maximal estimate and the molecular decomposition, we shall integrate and extend the known results on these spaces. [ABSTRACT FROM AUTHOR]

In this paper the author proves that the commutator of the Marcinkiewicz integral operator with rough variable kernel is bounded from the homogeneous Sobolev space $$ \dot L_\gamma ^2 $$(ℝ n) to the Lebesgue space L2(ℝ n), which is a substantial improvement and extension of some known results. [ABSTRACT FROM AUTHOR]

In this paper we characterize commuting dual Toeplitz operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We also obtain the sufficient and necessary conditions for the product of two dual Toeplitz operators with harmonic symbols to be a finite rank perturbation of a dual Toeplitz operator. [ABSTRACT FROM AUTHOR]

In this paper we characterize the boundedness and compactness of weighted composition operators of H∞ into α-Bloch spaces on the unit ball in ℂ n. [ABSTRACT FROM AUTHOR]

In this paper, a class of anisotropic Herz-type Hardy spaces associated with a non-isotropic dilation on ℝ n are introduced, and the central atomic and molecular decomposition characterizations of those spaces are established. As some applications of the decomposition theory, the authors study the interpolation problem and the boundedness of the central δ-Calderón-Zygmund operators on the anisotropic Herz-type Hardy spaces. [ABSTRACT FROM AUTHOR]

In this paper, general functional equations of rooted essential maps on surfaces (orientable and nonorientable) are deduced and their formal solutions are presented. Further, three explicit formulae for counting essential maps on S 2, $$ \widetilde{N_3 } $$ and $$ \widetilde{N_4 } $$ are given. In the same time, some known results can be derived. [ABSTRACT FROM AUTHOR]

The hyperoperations, called theta-operations ( ∂), are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define ∂-operations. In this paper, we continue our study on the ∂-operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using ∂-operations one obtains, mainly, H V -structures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special H V -rings or H V -fields, so these hyperstructures can be used. Moreover, we study the relation of these ∂-structures with other classes of hyperstructures, especially with the H V -structures. [ABSTRACT FROM AUTHOR]

This paper presents a quadratically approximate algorithm framework (QAAF) for solving general constrained optimization problems, which solves, at each iteration, a subproblem with quadratic objective function and quadratic equality together with inequality constraints. The global convergence of the algorithm framework is presented under the Mangasarian-Fromovitz constraint qualification (MFCQ), and the conditions for superlinear and quadratic convergence of the algorithm framework are given under the MFCQ, the constant rank constraint qualification (CRCQ) as well as the strong second-order sufficiency conditions (SSOSC). As an incidental result, the definition of an approximate KKT point is brought forward, and the global convergence of a sequence of approximate KKT points is analysed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the stability of functional equation given by the pseudo-additive mappings of the mixed quadratic and Pexider type in the spirit of Hyers, Ulam, Rassias and Găvruta. [ABSTRACT FROM AUTHOR]

In this paper, the author considers the boundedness of strongly singular Calderón–Zygmund operator and commutator generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space. Moreover, the boundedness of strongly singular Calderón– Zygmund operator on the predual of Morrey space is discussed. [ABSTRACT FROM AUTHOR]

In this paper, the authors prove that if Ω satisfies a class of the integral Dini condition, then the parametrized area integral $$ \mu ^{\rho }_{{\Omega ,S}} $$ is a bounded operator from the Hardy space H 1(ℝ n ) to L 1(ℝ n ) and from the weak Hardy space H 1,∞(ℝ n ) to L 1,∞(ℝ n ), respectively. As corollaries of the above results, it is shown that $$ \mu ^{\rho }_{{\Omega ,S}} $$ is also an operator of weak type (1, 1) and of type ( p, p) for 1 < p < 2, respectively. These conclusions are substantial improvement and extension of some known results. [ABSTRACT FROM AUTHOR]

In this paper, we show, among other results, that if X is a [separable] locally compact space X [satisfying the first countability axiom] then the space C c ( X) has countable tightness [if and only if it has bounding tightness] if and only if it is Fréchet–Urysohn, if and only if C c ( X) contains a dense ( LM) subspace and if and only if X is σ–compact. [ABSTRACT FROM AUTHOR]

In this paper, the expression of the norm of a self-adjoint integral operator T : L 2(0,∞) → L 2(0,∞) is obtained. As applications, a new bilinear integral inequality with a best constant factor is established and some particular cases are considered. [ABSTRACT FROM AUTHOR]

In this note, we prove a generalization of Hyers’ theorem on the stability of approximately additive mapping and a generalization of Badora’s theorem on an approximate ring homomorphism. We also obtain a more general stability theorem, which gives the stability theorems on Jordan and Lie homomorphisms. The proofs of the theorems given in this paper follow essentially the D. H. Hyers-Th. M. Rassias approach to the stability of functional equations connected with S. M. Ulam’s problem. [ABSTRACT FROM AUTHOR]