Corrigendum to “Gaussian bounds for degenerate parabolic equations” [J. Funct. Anal. 255 (2) (2008) 283–312]

We rectify an error in the proof of the Gaussian estimates for the heat kernel associated to certain weighted elliptic equations.     

Corrigendum to “The envelope theorem for multiobjective convex programming via contingent derivatives” [J. Math. Anal. Appl. 372 (1) (2010) 197–207]

The aim of this note is to formulate an envelope theorem for vector convex programs. This version corrects an earlier work, “The envelope theorem for multiobjective convex programming via contingent derivatives” by Jiménez Guerra et al. (2010) [3]. We first propose a necessary and sufficient condition allowing to restate the main result proved in the alluded paper. Second, we introduce a new Lagrange multiplier in order to obtain an envelope theorem avoiding the aforementioned error.     

Erratum to “Fuzzy rough set model on two different universes and its application” [Appl. Math. Model. 35 (4) (2011) 1798–1809]

The aim of this paper is to correct two mistakes in [Appl. Math. Model. 35 (4) (2011) 1798–1809], which are: one of the properties of fuzzy rough set between two different universes and the definition of the upper approximation with the property for degree fuzzy rough set between two different universes.     

Addendum to “Connesʼ embedding conjecture and sums of hermitian squares” [Adv. Math. 217 (4) (2008) 1816–1837]

We show that Connes? embedding conjecture (CEC) is equivalent to a real version of the same (RCEC). Moreover, we show that RCEC is equivalent to a real, purely algebraic statement concerning trace positive polynomials. This purely algebraic reformulation of CEC had previously been given in both a real and a complex version in a paper of the last two authors. The second author discovered a gap in this earlier proof of the equivalence of CEC to the real algebraic reformulation (the proof of the complex algebraic reformulation being correct). In this note, we show that this gap can be filled with help of the theory of real von Neumann algebras.     

Corrigendum to: “Oscillation criteria for first-order impulsive differential equations with positive and negative coefficients” [J. Comput. Appl. Math. 217 (1) (2008) 28–37]

This communication gives the corrigendum to the paper “Oscillation criteria for first-order impulsive differential equations with positive and negative coefficients” (JCAM (2007), doi:10.1016/j.cam.2007.06.016).     

Rkk (X)-nucléarité (d‘après; G. Skandalis)

We define a notion of nuclearity for C(X)-C^*-algebras yielding the same results of semi-exactness, for Kasparovs bifunctor RKK(X), as those obtained by Skandalis in the case X=. We connect explicitly this new notion of nuclearity with those already known.     

Nd-Fe-B(B≤50at.％)三元系相图的研究

本文用X射线衍射、热学分析、磁性测量等手段研究了Nd-Fe-B(B≤50at.％)三元系相图,主要结果如下:1.重新测定了Nd-Fe二元系相图,确证NdFe₂相是不存在的。2.测定了Nd-Fe-B(B≤50at.％)三元系室温横截面。在该三元系中存在三个化合物:Nd₂Fe₁₄B,Nd₈Fe₂₇B₂₄,Nd₂FeB₃。 指出:在未经退火的Nd-Fe-B三元母合金中,存在有过冷液相(非晶)的可能性。实用Nd-Fe-B新型永磁合金,由三相构成,主相为Nd₂Fe₁₄B,次相为Nd和Nd₈Fe₂₇B₂₄。3.测定了Fe₉₄B₆-Nd₁₂Fe₈₂B₆-Nd_33.5Fe_60.5B₆和Nd₂Fe₁₇-Nd₂Fe₁₄B-Nd₈Fe₂₇B₂₄纵截面。指出:在制备Nd-Fe-B三元永磁合金时,最高烧结温度不得高于1100℃,而后热处理的温度在600℃左右为宜。4.研究了Nd₂Fe₁₄B,Nd₈Fe₂₇B₂₄的结构和Nd₂Fe₁₄B的单相区。Nd₂Fe₁₄B为四方晶系,a=8.800,c=12.190,z=4,空间群为P4₂/mnm,X射线密度D_X=7.60g/cm³,测量密度D_O=7.50g/cm³。在测量精度范围内,观测不到Nd₂Fe₁₄B有单相区存在。Nd₈Fe₂₇B₂₄为四方晶系,a=7.12,c=27.40,z=2,D_X=7.01g/cm³,D_O=7.00g/cm³,可能的空间群为P4₂/n。5.在实验的基础上,讨论了Nd₂Fe₁₄B的热稳定性,并对制备Nd-Fe-B永磁合金的粉末冶金工艺提供了解释。     

General function spaces. III(SpacesB p,q g(x) andF p,q g(x) , 1<p<∞: basic properties)

qNАстОьЩАь РАБОтА (А тАк жЕ ЕЕ пРОДОлжЕНИЕ — РА БОтА «ОБЩИЕ ФУНкцИОНАльН ыЕ пРО-стРАНстВА, IV») пОсВьЩЕНА ИсслЕДОВ АНИУ БАНАхОВых пРОст РАНстВB _{p, q} ^g(x) ИF _p,q ^g(x) РАспРЕДЕлЕНИИ (ОБОБЩЕННых) ВR _n . В спЕц ИАльНых слУЧАьх ЁтИ пРОстРАНстВА РОДстВ ЕННы ИжВЕстНыМ клАсс АМ сОБОлЕВА—лЕБЕгА—БЕ сОВА, ИжОтРОпНыМ И АНИ жОтРОпНыМ. жДЕсь РАссМАтРИВАУт сь слЕДУУ-ЩИЕ сВОИстВА: плОтНОсть г лАДкИх ФУНкцИИ, ЁкВИВ АлЕНтНыЕ НОРМы, ИНтЕРпОльцИь, В клУЧЕНИь И сРАВНЕНИь. ОБЩИЕ ФУНкцИОНАльНы Е пРОстРАНстВА. III (пРОстРАНстВАB _p,q ^g(x) ИF _p,q ^g(x) , 1     

A translation of the T. Levi-Civita paper “Interpretazione Gruppale degli Integrali di un Sistema Canonico” (Rend. Acc. Lincei, 1899, s. 3<Superscript>a</Superscript>, vol. VII,pp. 235–238)

In this paper we provide a translation of a paper by T. Levi-Civita, published in 1899, about the correspondence between symmetries and conservation laws for Hamilton’s equations. We discuss the results of this paper and their relationship with the more general classical results by E. Noether.     

Corrigendum and addendum to “The strong approximation property and the weak bounded approximation property” [J. Funct. Anal. 266 (2014) 5439–5447]

We correct a mistake in the proof of [2, Theorem 1.1] and a proof of the main result in [2] is presented without depending on [2, Theorem 1.1].     

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].     

Corrigendum to “Convergence of invariant measures for singular stochastic diffusion equations” [Stochastic Process. Appl. 122 (2012) 1998–2017]

We correct a few errors that appeared in [Convergence of invariant measures for singular stochastic diffusion equations, Stochastic Process. Appl. 122 (4) (2012) 1998–2017] by I. Ciotir and J.M. Tölle.     

Minimal submanifolds in ℝ<Superscript>4</Superscript> with a G.C.K. structure

In this paper we obtain all invariant, anti-invariant and CR submanifolds in (?⁴, g, J) endowed with a globally conformal Kähler structure which are minimal and tangent or normal to the Lee vector field of the g.c.K. structure.