Nonsingular subsampling for regression S estimators with categorical predictors

Simple random subsampling is an integral part of S estimation algorithms for linear regression. Subsamples are required to be nonsingular. Usually, discarding a singular subsample and drawing a new one leads to a sufficient number of nonsingular subsamples with a reasonable computational effort. However, this procedure can require so many subsamples that it becomes infeasible, especially if levels of categorical variables have low frequency. A subsampling algorithm called nonsingular subsampling is presented, which generates only nonsingular subsamples. When no singular subsamples occur, nonsingular subsampling is as fast as the simple algorithm, and if singular subsamples do occur, it maintains the same computational order. The algorithm works consistently, unless the full design matrix is singular. The method is based on a modified LU decomposition algorithm that combines sample generation with solving the least squares problem. The algorithm may also be useful for ordinary bootstrapping. Since the method allows for S estimation in designs with factors and interactions between factors and continuous regressors, we study properties of the resulting estimators, both in the sense of their dependence on the randomness of the sampling and of their statistical performance.     

Integral sliding mode control for T–S fuzzy descriptor systems

The present study focuses on designing the integral sliding-mode control (ISMC) for generalized Takagi–Sugeno (T–S) fuzzy singular stochastic systems by involving the Markovian jump type of system parameters. Distinct to the existing works, the present paper concerns about the derivation of sufficient conditions that ensure the global stability of considered T–S fuzzy stochastic singular Markovian jump systems with matched/mismatched uncertainties under fuzzy-based ISMC. In this regard, an improved fuzzy integral sliding manifold function with mode-dependent derivative-term coefficient is proposed where the matched uncertainties become unnecessary and the mismatched uncertainties have been disintegrated during the sliding mode phase. Based on Lyapunov stability theory, a suitable Lyapunov functional candidate by involving the information about the membership functions is constructed with singular and P-type matrices, the stochastic admissibility of corresponding sliding mode dynamics are derived. To proven the effectiveness of the proposed method, a physical experimental problem on cart and pendulum is adapted and simulated via the derived theoretical results and the corresponding results are provided.     

Coincidence degree theory for mappings of class L − (S +)

In this article, we introduce the multi-valued mapping of class L-(S₊) in a Hilbert space and construct a coincidence degree theory for such a mapping.     

A New Characterization of the Analytic Radon-Nikodym Property for Bounded S

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Propertyf −1(S) =g −1(S) for entire and meromorphicP-adic functions

LetW be an algebraically closed filed of characteristic zero, letK be an algebraically closed field of characteristic zero, complete for an ultrametric absolute value, and letA(K) (resp. ℳ(K)) be the set of entire (resp. meromorphic) functions inK. For everyn≥7, we show that the setS _n(b) of zeros of the polynomialx ⁿ−b (b≠0) is such that, iff, g ∈W[x] or iff, g ∈A(K), satisfyf ⁻¹(S _n(b))=g ⁻¹(S _n(b)), thenf ⁿ=g ⁿ. For everyn≥14, we show thatS _n(b) is such that iff, g ∈W({tx}) or iff, g ∈ ℳ(K) satisfyf ⁻¹(S _n(b))=g ⁻¹(S _n(b)), then eitherf ⁿ=g ⁿ, orfg is a constant. Analogous properties are true for complex entire and meromorphic functions withn≥8 andn≥15, respectively. For everyn≥9, we show that the setY _n(c) of zeros of the polynomial , (withc≠0 and 1) is an ursim ofn points forW[x], and forA(K). For everyn≥16, we show thatY _n(c) is an ursim ofn points forW(x), and for ℳ(K). We follow a method based on thep-adic Nevanlinna Theory and use certain improvement of a lemma obtained by Frank and Reinders.     

D sets and a Sárközy theorem for countable fields

We establish that if ? is a countable field of characteristic p, U is a unitary action of ?^? on a Hilbert space ?, and P is an essential idempotent ultrafilter on ?, then for every polynomial r: ? → ?^? with r(0) = 0 one has $$P - {\lim _g}{U_{r(g)}}f = {P_r}f{\rm{ weakly,}}$$ , where P _r is the projection onto the closed subspace $${H_r} = \{ f \in H:{\{ {U_{r(g)}}f\} _{g \in F}}{\text{ is precompact in the strong topology\} }}{\text{.}}$$ . We then derive combinatorial consequences of this result, including results for sufficiently large finite fields.     

Radius of Starlikeness for Class S(a,n)and Its Extension

This paper obtain that the radius of starlikeness for class S(α,n)in [1] is,tespectivety,where α_ is unique solution of equation (αα)~(1/2)=σwith a in (0.1),and α-[1+(1-2α)r~(2n)]/(1-r~(2n)),σ=[1-(1-2α)r~]/(1+r~).Futhermore,we consider an extension of class S(α,n):Let S(α、β、n)denote the class of functions f(z)=z+α_z~(n+1)+…(n≥1)that are analytie in |z|<1 such that f(z)/g(z)∈p(α,n)[1],where g(z)∈S~*(β)[2].This paper prove that the radius of starlikeness of class S(α,β,n) is given by the smallest positive root(less than 1)of the following equations(1-2α)(1-2β)r~(2)-2[1-α-β-n(1-α)]r~+1=0.0≤α≤α_0,(1-α)[1-(1-2β)r~]-n[r~(1+r~)=0.,α_0≤α<1.where α=[1+(1-2α)r~(2)]/(1-r~(2)(0≤r<1),α_0(?(0,1) is some fixed number.This result is also thecxtension of well-known results[T.Th3] and [8,Th3]     

A new impulsive synchronization criterion for T–S fuzzy model and its applications

This paper focuses on the problem of impulsive synchronization of T–S fuzzy systems. A new synchronization criterion is derived for T–S fuzzy systems by utilizing the concept of average impulsive interval. The proposed impulsive control scheme has a simple control structure, and is theoretically and numerically proved to be less conservative than some existing results. The method is also illustrated by applying to Lorenz system, Rössler’s system as well as permanent magnet synchronous motors system.     

Young’s Seminormal Form and Simple Modules for S n in Characteristic p

We realize the integral Specht modules for the symmetric group S _n as induced modules from the subalgebra of the group algebra generated by the Jucys–Murphy elements. We deduce from this that the simple modules for ${{\mathbb F}_p} S_n $ are generated by reductions modulo p of the corresponding Jucys–Murphy idempotents.     

Mixed convexity and optimization results for an (S ? 1, S) inventory model under a time limit on backorders

Das (Oper Res 25(5):835–850, 1977) considered the optimization of a cost function associated with an (S ? 1, S) inventory model assuming the parameters to be the initial number of items in the stock and the service rate. A similar optimization problem associated with an M/E _k /1 queueing system with parameters being the number of servers and the service rate was considered by Kumin (Manag Sci 20:126–129, 1973). Both carried out case-dependent computations and indicated the difficulty of finding general convexity and optimization results for functions with both integer and real variables. In this paper, generalized mixed convexity and computational optimization results for the cost function associated with the (S ? 1, S) inventory system suggested by Das are provided. The generalized convexity results determine the convexity region of the cost function, and therefore the region of possible minimal values of the cost function in the domain. In addition, algorithms to determine the generalized convexity and computational optimization results for the cost function are given.     

Self-Intersection Local Time for Some S′(ℝd)-Ornstein-Uhlenbeck Processes Related to Inhomogeneous Fields

We study existence and path continuity of the self-intersection local time (SILT) for some S′(ℝ^d)-valued Ornstein-Uhlenbeck processes. Examples of such processes arise in particular as fluctuation limits ofparticle systems. We analyze the effect that different types ofmeasures involved in the covariances of the processes have on existence and continuity of SILT. These measures do not necessarily have the regularity and homogeneity properties of those that have been considered before; this precludes some key ingredients of the previous techniques. We develop new technical tools and prove sufficient conditions and some necessary conditions for existence of SILT, and sufficient conditions for path continuity of SILT. The questions of existence and continuity involve problems of existence of integrals and singular integrals. We give examples which illustrate how different types of measures e.g., atomic or with L²-density) may produce different critical dimensions for existence of SILT. One of our motivations is the desire for a better understanding ofwhat SILT represents for S′(ℝ^d)-valued processes.     

T–S fuzzy-model-based robust stabilization for a class of nonlinear discrete-time networked control systems

In this paper, the robust stabilization problem is investigated for a class of nonlinear discrete-time networked control systems (NCSs). To study the system stability and facilitate the design of fuzzy controller, Takagi–Sugeno (T–S) fuzzy models are employed to represent the system dynamics of the nonlinear discrete-time NCSs with effects of the approximation errors taken into account, and a unified model of NCSs in the T–S fuzzy model is proposed by modeling the approximation errors as norm-bounded uncertainties in system metrics, where non-ideal network Quality of Services (QoS), such as data dropout and network-induced delay, are coupled in a unified framework. Then, based on the Lyapunov–Krasovskii functional, sufficient conditions are derived for the existence of a fuzzy controller. By these criteria, two approaches to design a fuzzy controller are developed in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are provided to show the effectiveness of the proposed methods.     

Synchronization analysis for complex networks with coupling delay based on T–S fuzzy theory

In this paper, synchronization problems for a general complex networks are investigated by Takagi–Sugeno (T–S) fuzzy theory. A novel concept named linear approximation method is firstly proposed to solve the synchronization problems for T–S fuzzy complex networks. This novel method can linearize the system into some time-delay subsystems, which can effectively simplify the complicated system and then be easy to acquire the synchronization results. Since the expression based on linear matrix inequality (LMI) is used, the synchronization criteria can be easily checked in practice. Numerical simulation examples are provided to verify the effectiveness and the applicability of the proposed method.     

Majorization properties for certain classes of analytic functions using the Sălăgean operator

In the present paper, we investigate the majorization properties for certain classes of multivalent analytic functions defined by the S?l?gean operator. Moreover, we point out some new and interesting consequences of our main result.     

The Clebsch-Gordan coefficients for the quantum group SμU(2) and q-Hahn polynomials

The tensor product of two unitary irreducible representations of the quantum group S_μU(2) is decomposed in a direct sum of unitary irreducible representations with explicit realizations. The Clebsch-Gordan coefficients yield the orthogonality relations for q-Hahn and dual q-Hahn polynomials.     

A classification theorem for complete minimal surfaces in S6 with constant Kähler angles

In the present paper, we shall determine all complete minimal surfaces in the nearly Kähler sphere S⁶ with constant Kähler angles q ? (0, p)\theta \in (0,\,\pi ) and nonnegative curvatures.     

An analog of bianchi transformations for two-dimensional surfaces in the space S 3 × ℝ1

Bianchi-type transformations are constructed for two-dimensional surfaces with constant negative intrinsic curvature in the space S ³ × ?¹.