On the Logical Status of the Virtual Work Law

The law of virtual work (VWL) is probably the first law in the history of mechanics; it is previous to the one on the lever, though not completely distinct from it. Here I will discuss the logical status of VWL, that is whether it is an autonomous principle or a theorem of some sort of mechanics. The problem is complicated by the fact that up to now no universally recognised expression has been accepted for it. From this article the problematical nature of VWL demonstrability is quite clear when the mechanics does not characterise completely the constraints. Italian schools in the XVIII century, even if we do not take Lagrange into consideration, had an important role, both in the development of VWL and in the discussion of its role.     

Crystallographic analysis of metal-ion binding to human ubiquitin

The metal-binding ability of human ubiquitin (hUb) towards a selection of biologically relevant metal ions and complexes has been probed. Different techniques have been used to obtain crystals suitable for crystallographic analysis. In the first type of experiments, crystals of hUb have been soaked in solutions containing copper(II) acetate and two metallodrugs, Zeise salt (K[PtCl(3)(η(2)-C(2)H(4))]·H(2)O) and cisplatin (cis-[PtCl(2)(NH(3))(2)]). The Zeise salt is used in a test for hepatitis, whereas cisplatin is one of the most powerful anticancer drugs in clinical use. The Zeise salt readily reacts with hUb crystals to afford an adduct with three platinum residues per protein molecule, Pt(3)-hUb. In contrast, copper(II) acetate and cisplatin were found to be unreactive for contact times up to one hour and to cause degradation of the hUb crystals for longer times. In the second type of experiments, hUb was cocrystallized with a solution of copper(II) or zinc(II) acetate or cisplatin. Zinc(II) acetate gives, at low metal-to-protein molar ratios (8:1), crystals containing one metal ion per three molecules of protein, Zn-hUb(3) (already reported in previous work), whereas at high metal-to-protein ratios (70:1) gives crystals containing three Zn(II) ions per protein molecule, Zn(3)-hUb. In contrast, once again, copper(II) acetate and cisplatin, even at low metal-to-protein ratios, do not give crystalline material. In the soaking experiment, the Zeise anion leads to simultaneous platination of His68, Met1, and Lys6. Present and previous results of cocrystallization experiments performed with Zn(II) and other Group 12 metal ions allow a comprehensive understanding of the metal-ion binding properties of hUb with His68 as the main anchoring site, followed by Met1 and carboxylic groups of Glu16, Glu18, Glu64, Asp21, and Asp32, to be reached. In the case of platinum, Lys6 can also be a binding site. The amount of bound metal ion, with respect to that of the protein, appears to be a relevant parameter influencing crystal packing.     

Non-oxo vanadium(IV) alkoxide chemistry: solid state structures, aggregation equilibria and thermochromic behaviour in solution

The reversible thermochromic behaviour of homoleptic [{V(OR)(4)}(n)] complexes in solution [R = Pr(i) (product I), Bu(s) (B(s)), Nep (N) and Cy (C)] is accounted for the existence of an aggregation equilibrium involving dimeric and monomeric species in which vanadium(iv) is respectively five- and four-coordinate. Bulky R groups such as Bu(t) and Pe(t) (tert-pentoxide) prevent aggregation and therefore give rise to exclusively mononuclear compounds (B(t) and P(t), respectively) that are not thermochromic. The complexes and their temperature-dependent interconversion were characterised by single crystal X-ray diffractometry, magnetic susceptibility measurements and electronic, FTIR and EPR spectroscopies in a wide temperature range. Equilibrium constants and enthalpy and entropy changes for the dimerization reactions have been determined and compared with literature data.     

Hyaluronan: from biomimetic to industrial business strategy

Hyaluronan (hyaluronic acid) is a naturally occurring polysaccharide of a linear repeating disaccharide unit consisting of beta-(1-->4)-linked D-glucopyranuronic acid and beta-(1-->3)-linked 2-acetamido-2-deoxy-D-glucopyranose, which is present in extracellular matrices, the synovial fluid of joints, and scaffolding that comprises cartilage. In its mechanism of synthesis, its size, and its physico-chemical properties, hyaluronan is unique amongst other glycosaminoglycans. The network-forming, viscoelastic and its charge characteristics are important to many biochemical properties of living tissues. It is an important pericellular and cell surface constituent; its interaction with other macromolecules such as proteins, participates in regulating cell behavior during numerous morphogenic, restorative, and pathological processes in the body. The knowledge of HA in diseases such as various forms of cancers, arthritis and osteoporosis has led to new impetus in research and development in the preparation of biomaterials for surgical implants and drug conjugates for targeted delivery. A concise and focused review on hyaluronan is timely. This review will cover the following important aspects of hyaluronan: (i) biological functions and synthesis in nature; (ii) current industrial production and potential biosynthetic processes of hyaluronan; (iii) chemical modifications of hyaluronan leading to products of commercial significance; and (iv) and the global market position and manufacturers of hyaluronan.     

On the divisor function in short intervals

Let d(n) denote the number of positive divisors of the natural number n. The aim of this paper is to investigate the validity of the asymptotic formula

$\begin{array}{lll}\sum \limits_{x < n \leq x+h(x)}d(n)\sim h(x)\log x\end{array}$

for \({x \to + \infty,}\) assuming a hypothetical estimate on the mean

$\begin{array}{lll} \int \limits_X^{X+Y}(\Delta(x+h(x))-\Delta (x))^2\,{d}x, \end{array}$

which is a weakened form of a conjecture of M. Jutila.

     

A convenient synthesis of unsymmetrically substituted terphenyls of biologically active stilbenes via a double Suzuki cross-coupling protocol

A double Suzuki cross-coupling protocol has been devised as a practical route to a variety of terphenyls. Good chemoselectivity was observed. Unsymmetrically substituted triphenylenes were also easily prepared.     

Dynamical Aspects of TEM-1 β-Lactamase Probed by Molecular Dynamics

The dynamical aspects of the fully hydrated TEM-1 β-lactamase have been determined by a 5 ns Molecular Dynamics simulation. Starting from the crystallographic coordinates, the protein shows a relaxation in water with an overall root mean square deviation from the crystal structure increasing up to 0.17 nm, within the first nanosecond. Then a plateau is reached and the molecule fluctuates around an equilibrium conformation. The results obtained in the first nanosecond are in agreement with those of a previous simulation (Diaz et al., J. Am. Chem. Soc., (2003) 125, 672–684). The successive equilibrium conformation in solution shows an increased mobility characterized by the following aspects. A flap-like translational motion anchores the Ω-loop to the body of the enzyme. A relevant part of the backbone dynamics implies a rotational motion of one domain relative to the other. The water molecules in the active site can exchange with different residence times. The H-bonding networks formed by the catalytic residues are frequently interrupted by water molecules that could favour proton transfer reactions. An additional simulation, where the aspartyl dyad D214–D233 was considered fully deprotonated, shows that the active site is destabilized.     

Activation-analysis investigation of the behaviour of biological trace elements during wound healing: The roles of calcium and iron

Summary Instrumental neutron-activation analysis was used for the determination of Ca, Cr, Fe, Co, Ni, Zn, Mo, Ag, Sb, and Hg. Blood and tissue samples of 70 mg each were analysed and, from these, changes in the concentrations of calcium, iron, and zinc in affected tissue were established. In this article the results of the behaviour of calcium and iron are reported. The calcium concentration of the fracture haematoma blood (FHB) is about 20 times higher than that of arterial or venous blood (rabbits). The level and the change with time of the calcium concentration in FHB-deposits (rabbits) can be explained by the participation of calcium in the haemolysis of the erythrocytes of the FHB which has been injected for the formation of the deposits. The behaviour of the iron in the FHB-deposits is in agreement with this explanation. The change in calcium concentration in the crust of punch-hole wounds in the skin (rats) can be attributed to the mobilization of calcium for fibrin formation. As a reason for the level and the change with time of the iron concentration in the tissue in the area of fascia and muscle incision wounds (rabbits) the participation of iron in the formation of collagen is discussed. From comparison of the behavoiur of the iron in the FHB-deposits with that in the area of incision wounds it follows that iron enrichments in the area of a complication-free wound are not predominantly caused by a wound haematoma.

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Zusammenfassung Die Untersuchungen erfolgten mit Hilfe der instrumentellen Neutronenaktivierungsanalyse. Das Verfahren war für die Erfassung der Gehalte an Ca, Cr, Fe, Co, Ni, Zn, Mo, Ag, Sb und Hg ausgelegt. Es wurden Blut bzw. Gewebeproben von jeweils etwa 70 mg analysiert und dabei Änderungen der Calcium-, Eisen- und Zinkgehalte des betroffenen Gewebes festgestellt. In diesem Artikel wird über das Verhalten des Calciums und Eisens berichtet. Der Calciumgehalt des Frakturhämatombluts (FHB) ist etwa 20mal höher als der von arteriellem oder venösem Blut (Kaninchen). Höhe und zeitlicher Verlauf der Calciumgehalte von FHB-Depots (Kaninchen) lassen sich mit der Beteiligung des Calciums an der Hämolyse der Erythrozyten des FHB erklären, das zur Bildung der Depots injiziert wurde. Das Verhalten des Eisens in den FHB-Depots stimmt mit dieser Erklärung überein. Der Verlauf der Calciumgehalte des Schorfes von Hautstanzwunden (Ratten) kann auf die Mobilisierung von Calcium für die Fibrinbildung zurückgeführt werden. Als Ursache für Höhe und zeitlichen Verlauf der Eisengehalte des Gewebes im Bereich von Faszie- und Muskelschnittwunden (Kaninchen) wird die Beteiligung des Eisens an der Kollagenbildung diskutiert. Aus dem Vergleich des Verhaltens des Eisens in FHB-Depots und im Bereich von Schnittwunden folgt, daß die Eisenanreicherungen im Bereich einer komplikationslosen Schnittwunde nicht vorwiegend durch ein Wundhämatom bedingt sind.

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Auszug aus der Dissertation des Herrn Danilo Boani, Technische Universität München. This work was supported by the Bundesministerium für Forschung und Technologie and the Fonds der Chemischen Industrie, and the paper was presented at the International Symposium on Microchemical Techniques, Davos, May 1977.     

Approximation theorems for a family of multivariate neural network operators in Orlicz-type spaces

In this paper, we study the theory of a Kantorovich version of the multivariate neural network operators. Such operators, are activated by suitable kernels generated by sigmoidal functions. In particular, the main result here proved is a modular convergence theorem in Orlicz spaces. As special cases, convergence theorem in \(L^p\)-spaces, interpolation spaces, and exponential-type spaces can be deduced. In general, multivariate approximations by constructive neural network algorithms are useful for applications to neurocomputing processes involving high dimensional data. At the end of the paper, several examples of activation functions of sigmoidal-type for which the above theory holds have been described.     

An Informational Theory of Counterfactuals

Backtracking counterfactuals are problem cases for the standard, similarity based, theories of counterfactuals e.g., Lewis (Noûs13.4, 455–476, 1979). These theories usually need to employ extra-assumptions to deal with those cases (e.g., Lewis’ “standard resolution of vagueness”). Hiddleston (Noûs 39(4), 632–657, 2005) proposes a causal theory of counterfactuals that, supposedly, deals well with backtracking. The main advantage of the causal theory is that it provides a unified account for backtracking and non-backtracking counterfactuals (no extra-assumption is needed). In this paper, I present a backtracking counterfactual that is a problem case for Hiddleston’s account. Then I propose an informational theory of counterfactuals, which deals well with this problem case while maintaining the main advantage of Hiddleston’s account (the unified account for backtracking and non-backtracking counterfactuals). In addition, the informational theory offers a general theory of backtracking that provides clues for the semantics and epistemology of counterfactuals. I propose that backtracking is reasonable when the (possibly non-actual) state of affairs expressed in the antecedent of a counterfactual transmits less information about an event in the past than the actual state of affairs.