Erratum to “Generalized Newton’s method based on graphical derivatives” [Nonlinear Anal. TMA 75 (2012) 1324–1340]

We point out and discuss two erroneous statements in the paper [T. Hoheisel, C. Kanzow, B.S. Mordukhovich, H. Phan, Generalized Newton’s method based on graphical derivatives, Nonlinear Analysis TMA 75 (2012) 1324–1340] that were brought to our attention by Bernd Kummer. Furthermore, the correction of the corresponding global convergence result is given in this note.     

On global asymptotic stability of nonlinear higher-order difference equations

In this paper, we generalize the main theorem of Liz and Ferreiro [E. Liz, J.B. Ferreiro, A note on the global stability of generalized difference equations, Appl. Math. Lett. 15 (2002) 655–659] and some other global stability results for nonautonomous higher-order difference equations to the case when contraction-type steps are incorporated together with the steps when the difference sequence can increase.     

Corrigendum to “Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times” [Stochastic Process. Appl. 111 (2004) 237-258]

The purpose of this note is to correct an error in Baltrunas et al. (2004) [1], and to give a more detailed argument to a formula whose validity has been questioned over the years. These details close a gap in the proof of Theorem 4.1 as originally stated, the validity of which is hereby strengthened.     

No end of the world in 2012 for 4OR

The purpose of this note is to give the readers of 4OR information on the state of the journal and its future, abiding by a triennial tradition which started with Bouyssou et al. (4OR 1(1):1–6, 2003) and continued with Bouyssou et al. (4OR 4(1):1–9, 2006) and Bouyssou et al. (4OR Q J Oper Res 7(1):15, 2009). In the 3 years that have passed since the last editorial note, three volumes of the journal have been published, each containing four issues: vol. 7 (2009), vol. 8 (2010) and vol. 9 (2011).     

On a recent result of Cazenave,Dickstein and Weissler

In this note, we present an estimate from below of the blow-up time of blowing-up solutions of a non-linear non-local in the time evolution equation recently introduced by Cazenave et al. (2008) [1]. Moreover, we give an alternative proof of one of the results of Cazenave et al. (2008) [1] which gives more precise information on the hypotheses than those in the paper Cazenave et al. (2008) [1].     

Rank-one convexity and polyconvexity of Hencky-type energies

We investigate a family of isotropic volumetric-isochorically decoupled strain energies based on the Hencky-logarithmic (true, natural) strain tensor log U. The main result of this note is that for n = 2 the considered energies are rank-one convex for suitable values of two material parameters. We also conjecture that there are values of the material parameters such that the corresponding energies are polyconvex. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comments on: “A family of derivative-free conjugate gradient methods for large-scale nonlinear systems of equations” [J. Comput. Appl. Math. 224 (2009) 11–19]

In this note a simple counter example shows that the proof of Lemma 3.3 in [1, W. Cheng, Y. Xiao and Q. Hu, A family of derivative-free conjugate gradient methods for large-scale nonlinear systems of equations, J. Comput. Appl. Math. 224 (2009) 11–19] is not correct, which implies that Lemma 3.2 in [1] is not enough to ensure Lemma 3.3 in [1]. A new proof is given, which leads to a stronger result than Lemma 3.2 in [1]. And this result not only guarantees that Lemma 3.3 in [1] holds, but also improves the corresponding global convergence Theorem 3.1 in [1].     

On recent developments in the theory of abstract differential equations with fractional derivatives

This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) [1], Belmekki and Benchohra (2010) [2], Darwish et al. (2009) [3], Hu et al. (2009) [4], Mophou and N’Guérékata (2009) [6] and [7], Mophou (2010) [8] and [9], Muslim (2009) [10], Pandey et al. (2009) [11], Rashid and El-Qaderi (2009) [12] and Tai and Wang (2009) [13]] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations.     

A note on strong matrix summability via ideals

Following the line of recent works of Das et al. (2011) [15] and Savas and Das (2011) [19] we apply the notion of ideals to strong matrix summability, and in this note, we introduce the notion of strong A^I-summability with respect to an Orlicz function. We make certain investigations on the classes of sequences arising out of this new summability method.     

Erratum to ``Baire spaces and Vietoris hyperspaces'

The main purpose of this short note is to correct an error in ``Baire spaces and Vietoris hyperspaces', Proc. Amer. Math. Soc. 135 (2007), no. 1, 299-303.

     

On a Zero Duality Gap Result in Extended Monotropic Programming

In this note we correct and improve a zero duality gap result in extended monotropic programming given by Bertsekas (J. Optim. Theory Appl. 139:209–225, 2008).     

On Odd Symplectic Schur Functions

Proctor defined combinatorially a family of Laurent Polynomials, called odd symplectic Schur functions, indexed by pairs (λ, c), where λ is partition andcis a column length of λ. A conjecture of Proctor (Invent. Math.92,1988, 307–332) includes the statement that the odd symplectic Schur functions are actually characters ofSp(2n + 1, C). The purpose of the present note is to prove this.     

Protected points in k-ary trees

Following Cheon and Shapiro (2008) [3], in this note we compute the average number of protected points in all k-ary trees with n internal points.     

Equivalence of Linear Programming and Basis Pursuit

In this note, we show that linear programming and the prominent Basis Pursuit problem (i.e., minimizing the ℓ₁-norm of a vector x subject to an underdetermined linear equation system Ax = b) are theoretically equivalent, and briefly discuss possible ramifications regarding computational complexity and practical applicability. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Convergence of delay differential equations driven by fractional Brownian motion

In this note, we prove an existence and uniqueness result of solution for stochastic differential delay equations with hereditary drift driven by a fractional Brownian motion with Hurst parameter H > 1/2. Then, we show that, when the delay goes to zero, the solutions to these equations converge, almost surely and in L ^p , to the solution for the equation without delay. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann–Stieltjes integral.     

Banach空间三次方程的稳定性问题

给出了三次Hyers—Ulam—Rassias型泛函方程的一种新表示方法af(x+ay)-f(ax+y)=(a(a~2-1))/2[f(x+y)+f(x-y)]+(a~4-1)f(y)-2a(a~2-1)f(x)其中a为整数且a≠0,土1.关于9个三次泛函方程给出等价性证明。对Banach空间三次方程的稳定性问题给予讨论。     

On chaotic set-valued discrete dynamical systems

Let (X, d) be a metric space and let f: (X, d) → (X, d) be a continuous map. In this note we investigate the relationships between the chaoticity of some set-valued discrete dynamical systems associated to f (collective chaos) and the chaoticity of f (individual chaos).     

A note on TI-subgroups of finite groups

A subgroup H of a finite group G is called a TI-subgroup if H ∩ H ^x  = 1 or H for any x ∈ G. In this short note, the finite groups all of whose nonabelian subgroups are TI-subgroups are classified.     

Congruences for Siegel modular forms and their weights

J.-P. Serre proved that the congruences for elliptic modular forms mod p ^m descend to those of weights mod p ^m−1(p−1). Later, this result was generalized by T. Ichikawa to the case of Siegel modular forms. In this note we use elementary methods to reduce Ichikawa’s result to a similar question about elliptic modular forms with level, where results of Katz are available.