The concept of energy and its early historical development

The concept of energy, the premier concept of physics and indeed of all science, is here investigated from the standpoint of its early historical origin and the philosophical implications thereof. The fundamental assumption is made that the root of the concept is the notion of invariance or constancy in the midst of change. Salient points in the development of this idea are presented from ancient times up to the publication of Lagrange'sMécanique Analytique (1788).     

Interaction of nonionic dextrans with silver bromide hydrosols

Summary The effects of nonionic dextrans of different molecular weights on the stability of silver bromide solsin statu nascendi in aqueous solutions and watermethanol mixtures have been studied. Regardless of the molecular weight of the polymer no flocculation of the sol is observed. In the presence of indifferent electrolytes sols are destabilized over a given concentration range of the polymer, which depends little on the molecular weight of the latter. The concentration of the electrolytes required to cause destabilization in the presence of dextrans depends on the counterion charge (theSchulze-Hardy rule) but in each case the critical coagulation concentration is lower for the same sol than in the absence of the polymers. At still higher dextran concentrations the sols are protected toward electrolytes. In the presence of methanol more polymer and less electrolyte is needed to destabilize the sol. An explanation of these effects is offered.

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Zusammenfassung Die Effekte der nichtionogenen Dextran-Polymeren von verschiedenen Molekulargewichten auf die Stabilität von Silberbromid Solenin statu nascendi in wässerigen Lösungen und in Wasser-Methylalkohol Gemischen wurden untersucht. Die Makromoleküle allein konnten die Sole nicht koagulieren. Die Sole wurden jedoch destabilisiert in Anwesenheit von bestimmten Mengen von Polymeren wenn Neutralelektrolyte zugesetzt wurden: Die kritischen Koagulationskonzentration der Gegenionen hängt von deren Ladung ab (Schulze-Hardy Regel); jedoch in allen Fällen ist die für die Koagulation notwendige Salzmenge beträchtlich niedriger als in der Abwesenheit von Dextran in denselben Solen. Bei höheren Polymerkonzentrationen werden die Silberhalogenidsole gegen Elektrolytkoagulation geschützt. In Wassser-Alkohol Lösungen ist mehr Polymer und weniger Elektrolyt zur Koagulation der Sole notwendig. Eine Erklärung dieser Beobachtungen wurde angeboten.

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With 14 figures and 2 tables

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1) Supported by the NSF grant GP 42331X.

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2) A part of a Ph.D. thesis byDavid Lindsay.     

Acceleration waves and second sound in a perfect fluid

The evolutionary behaviour of acceleration waves of arbitrary shape in a perfect fluid is investigated. The theory employed allows two coupled mechanical and temperature acceleration waves to propagate with finite wavespeeds. New results are described for waves entering isothermal regions but where the exterior flow velocity is non-zero.     

On the Brauer group and factoriality of normal domains

Let B(R) be the Brauer group of the integrally closed noetherian domain R with quotient field K. We reexamine the proof that B(R) → R(K) is monic for R regular from the point of view of factoriality of R and its extensions. For R local with maximal ideal m, henselization R^h and divisor class group Cl(R) we embed ker $\text{{B(R) → B(K)?B(}\text{R}\text{M}\text{)}}$ into $\text{Cl(R}{}^{\mathrm{h}}\text{)}\text{Cl(R)}$. This is applied to obtain examples of non-regular geometric local domains R for which B(R) → B(K) is monic.     

A problem in second order elasticity

When an incompressible half space of elastic material is twisted by a rigid circular punch bonded to its surface, to first order the azimuthal displacement is zero. In this paper, second order theory is used to investigate the deviation of the surface of the half space from the undeformed configuration.Visiting Simon Fraser University, Burnaby, B.C., V5A 1S6, Canada for the year 1982/83.     

Complexes of Ag(I), Hg(I) and Hg(II) with multidentate pyrazolyl-pyridine ligands: From mononuclear complexes to coordination polymers via helicates, a mesocate, a cage and a catenate

The coordination chemistry of a series of di- and tri-nucleating ligands with Ag(I), Hg(I) and Hg(II) has been investigated. Most of the ligands contain two or three N,N'-bidentate chelating pyrazolyl-pyridine units pendant from a central aromatic spacer; one contains three binding sites (2 + 3 + 2-dentate) in a linear sequence. A series of thirteen complexes has been structurally characterised displaying a wide range of structural types. Bis-bidentate bridging ligands react with Ag(I) to give complexes in which Ag(I) is four-coordinate from two bidentate donors, but the complexes can take the form of one-dimensional coordination polymers, or dinuclear complexes (mesocate or helicate). A tris-bidentate triangular ligand forms a complicated two-dimensional coordination network with Ag(I) in which Ag...Ag contacts, as well as metal-ligand coordination bonds, play a significant role. Three dinuclear Hg(I) complexes were isolated which contain an {Hg2}2+ metal-metal bonded core bound to a single bis-bidentate ligand which can span both metal ions. Also characterised were a series of Hg(II) complexes comprising a simple mononuclear four-coordinate Hg(II) complex, a tetrahedral Hg(II)4 cage which incorporates a counter-ion in its central cavity, a trinuclear double helicate, and a trinuclear catenated structure in which two long ligands have spontaneously formed interlocked metallomacrocyclic rings thanks to cyclometallation of two of the Hg(II) centres.     

Evolution of structure in CH5 + and its deuterated analogues

Diffusion Monte Carlo simulations are used to investigate the effects of deuteration on the fluxionality of CH(5)(+) or CD(5)(+), using an ab initio potential surface, developed by Jin, Braams, and Bowman [J. Phys. Chem. 2006, 110, 1569]. We find that partial deuteration quenches the fluxional behavior. The spectral consequences are also investigated. We find that, while CH(5)(+) and CD(5)(+) are nearly spherical tops, partial deuteration breaks the rotational symmetry and the mixed isotopologues are generally better characterized as symmetric tops. In addition, we investigate the effects of deuteration on the low-resolution vibrational spectrum and anticipate that signatures of this delocalization will be observable in the vibrational spectrum.     

Prospective teachers anticipate challenges fostering the mathematical practice of making sense

Problem solving has long been a priority in mathematics education, and the first Common Core mathematical practice (SMP1) focuses on this priority through the language of “Make sense of problems and persevere in solving them.” We present findings from a survey about how prospective elementary teachers' (PTs) make sense of potential difficulties with fostering SMP1. Findings suggested that PTs' common anticipated difficulties relate to planning a solution pathway and self monitoring whether the solution makes sense. Moreover, a third of PTs disclosed that their anticipated difficulties are linked to their own personal struggles with aspects of SMP1. An alternative interpretation of SMP1 surfaced in which a small number of PTs described SMP1 as necessitating that a teacher teach multiple solution methods to students, instead of engaging students in productive struggle to develop their own strategies. We present a framework illustrating the connections between SMP 1 and Pólya's problem solving phases, and we discuss how these findings connect to and build on previous research of PTs' experiences with problem solving. We offer implications for the targeted support needed in teacher preparation programs to address these struggles, to prevent them from being replicated in their students.