Scaling impacted structures

Summary The problem of non-scalability of structures under impact loads caused by strain-rate effects is solved in this article by properly correcting the impact velocity. The technique relies on the use of an alternative dimensionless basis, together with a mathematical model which allows the calculation of a correction factor for the impact velocity. This new velocity, when applied to the model, makes it to assure the satisfaction of the scaling laws. The indirect similitude method detailed here is applied to two strain-rate sensitive structures, a double plate under in-plane impact and a beam subjected to a blast load. The results show a very good agreement so that the model and a prototype made from strain rate sensitive materials behave the same.accepted for publication 3 March 2004     

Cyanide-bridged [Fe8M6] clusters displaying single-molecule magnetism (M=Ni) and electron-transfer-coupled spin transitions (M=Co)

Cyanide‐bridged metal complexes of [Fe₈M₆(μ‐CN)₁₄(CN)₁₀ (tp)₈(HL)₁₀(CH₃CN)₂][PF₆]₄?n CH₃CN?m H₂O (HL=3‐(2‐pyridyl)‐5‐[4‐(diphenylamino)phenyl]‐1H‐pyrazole), tp^?=hydrotris(pyrazolylborate), 1 : M=Ni with n=11 and m=7, and 2 : M=Co with n=14 and m=5) were prepared. Complexes 1 and 2 are isomorphous, and crystallized in the monoclinic space group P2₁/n. They have tetradecanuclear cores composed of eight low‐spin (LS) Fe^III and six high‐spin (HS) M^II ions (M=Ni and Co), all of which are bridged by cyanide ions, to form a crown‐like core structure. Magnetic susceptibility measurements revealed that intramolecular ferro‐ and antiferromagnetic interactions are operative in 1 and in a fresh sample of 2 , respectively. Ac magnetic susceptibility measurements of 1 showed frequency‐dependent in‐ and out‐of‐phase signals, characteristic of single‐molecule magnetism (SMM), while desolvated samples of 2 showed thermal‐ and photoinduced intramolecular electron‐transfer‐coupled spin transition (ETCST) between the [(LS‐Fe^II)₃(LS‐Fe^III)₅(HS‐Co^II)₃(LS‐Co^III)₃] and the [(LS‐Fe^III)₈(HS‐Co^II)₆] states.     

Arranging Solid Balls to Represent a Graph

 By solid balls, we mean a set of balls in R ³ no two of which can penetrate each other. Every finite graph G can be represented by arranging solid balls in the following way: Put red balls in R ³, one for each vertex of G, and connect two red balls by a chain when they correspond to a pair of adjacent vertices of G, where a chain means a finite sequence of blue solid balls in which each consecutive balls are tangent. (We may omit the chain if the two red balls are already tangent.) The ball number b(G) of G is the minimum number of balls (red and blue) necessary to represent G. If we put the balls and chains on a table so that all balls sit on the table, then the minimum number of balls for G is denoted by b _T (G). Among other things, we prove that b(K ₆)=8,b(K ₇)=13 and b _T (K ₅)=8,b _T (K ₆)=14. We also prove that c ₁ n ³<b(K _n )<c ₂ n ³ log n, c ₃ n ⁴ log n<b _T (K _n )<c ₄ n ⁴. Received: March 29, 1999 Final version received: January 17, 2000     

Br NQR relaxation and successive phase transitions of CH3NH3HgBr3

The measurement of ⁸¹Br NQR in CH₃NH₃HgBr₃ has been carried out in the temperature range between 80 and 300 K using a pulse NQR method. The temperature dependence of ⁸¹Br NQR frequencies in CH₃NH₃HgBr₃ has revealed that it undergoes three characteristic successive phase transitions at T?=?123, 184 and 239 K. The phase transition temperature at T?=?239 K is the second-order type, whereas those at T?=?184 and 123 K are the first-order nature of the phase transitions. Each phase transition seems to be closely related to the motions of methyl ammonium cation as a partial or whole. The enhancement of 1/T ₁ at T?=?239 K indicates the onset of the molecular motion of the cation as a whole with increasing temperatures.     

Recent development of Faith conjecture

Is a semiprimary right self-injective ring a quasi-Frobenius ring? Almost half century has passed since Faith raised this problem. He first conjectured “No” in his book Algebra II. Ring Theory in 1976, but changing his mind, he conjectured “Yes” in his article “When self-injective rings are QF: a report on a problem” in 1990. In this paper, we describe recent studies of this problem based on authors works and raise related problems.     

NbCl5 a multifunctional reagent for the synthesis of new halogenated aminoquinoline compounds through innovative one-pot reaction and the acidochromism effect

This paper describes an original one-pot way to synthesize nine new halogenated aminoquinoline derivatives using reactions conducted by niobium pentachloride. Subsequently, we describe an efficient and selective reduction reaction of nitroquinolines using niobium pentachloride and zinc, producing important compounds in the organic synthesis.The results showed that it is an important tool to synthesize these compounds, besides being time- and resources-saving and generating good yields. A quick study of acidochromism was performed.     

2-Alkoxy-3-substituted-4-quinolinols from the thermal reactions of N-phenylketenimines bearing ester groups

Several ketenimines bearing ester groups were prepared and their thermal reactions gave 2-alkoxy-3-substituted-4-quinolinols VIa-e via presumed iminoketene intermediates. Subsequent oxidation of 2-alkoxy-3-(3-methylbut-2-enyl)-4-quinolinols VIc and VId provided pyranoquinolines VIIIa and VIIIb.